Introduction
Foster & Rahmstorf (1) used a multiple regression model based on solar variation, volcanic aerosols, and ENSO to estimate how those factors have influenced surface temperature since 1979; the paper is basically a rehash, with some changes, of earlier published work by others (see for example http://www.agci.org/docs/lean.pdf and references). F&H adjusted measured changes in Earth’s surface temperature based on the results of their regression model, and claimed that the apparent slowdown in warming over the past 10+ years is entirely the result of natural variation, and that there has been absolutely no change in the underlying (secular) rate of warming since 1979. Oh yes, they also concluded that it is critical for people stop burning fossil fuels immediately…. though it is not immediately obvious how a multiple regression model on global temperatures leads to that conclusion.
Many people found the F&R paper to be technically weak, and its conclusions doubtful; my personal evaluation was that the paper was little better than a mindless curve-fit exercise. In spite of the coverage the paper got in some publications, I would normally prefer to ignore such things. But since the F&R paper seems to now have taken on the character of an urban legend, and is pointed to by warming-concerned folks whenever someone notes that warming has been much slower recently, I figured any reasoned critique of F&R is a useful endeavor.
F&R considered the influence of the solar cycle, a change of about 0.1% in solar intensity from peak to trough of the cycle, separately from the effects of stratospheric volcanic aerosols, even though both are expected to change the intensity of solar radiation reaching the Earth’s troposphere and surface. (Why should solar intensity change and volcanic aerosol forcing not be fungible?) Like some earlier publications, F&R also (strangely) limited their analysis to post 1979, even though data on volcanoes, solar cycles, and ENSO over longer periods is available. F&R concluded that variation in solar intensity has much greater influence on surface temperature, on a degree/watt/M^2 basis, than an equivalent change due to stratospheric volcanic aerosols, and further conclude the response of surface temperature to solar intensity variation is essentially instantaneous (no lag!), while stratospheric aerosols influence surface temperature only with considerable lag. Odd, very odd.
Here I offer what I believe is a more robust regression analysis of the same three variables (volcanic aerosols, ENSO, and solar cycle) on temperature evolution since 1950. I will show:
1) An improved index for accounting for ENSO.
2) The best regression fit is found when volcanic aerosols and solar intensity variation are lagged considerably due to thermal inertia of the system. The estimates for the influence of both (on a degrees/watt/M^2 basis) are very similar, not dramatically different.
3) After taking ENSO, volcanic aerosols, and solar cycles into account, the best estimate rate of warming from 1997 to 2012 is less than 1/3 the rate of warming from 1979 to 1996.
I. A Slightly Improved Method for Estimating ENSO Influence on Temperature Trends
The Nino 3.4 index is the monthly average temperature anomaly, in Celsius degrees, for the roughly rectangular area of the Pacific ocean bounded by 120 and 170 degrees west, 5 degrees north and 5 degrees south. This region represents only about 2.5% of the surface area of the Earth’s tropics (~30 north to ~30 south), yet is known to be strongly correlated with the ENSO and with changes in average temperature in the tropics. (For a more complete description see: http://www.ncdc.noaa.gov/teleconnections/enso/indicators/sst.php). Some months ago in a comment at The Blackboard, Carrick showed that Nino 3.4 shows little or no correlation, at any lag period, with temperatures outside of the tropics. That is, ENSO strongly influences tropical temperatures but does not influence temperatures outside the tropics very much. I concluded that if one is going to “account for” the influence of ENSO on global average temperatures using Nino 3.4, then it would be best to estimate the influence based on the variation in temperature anomaly for the tropics only. Eliminating uncorrelated temperature data from higher latitudes ought to improve signal to noise ratio, and yield a more accurate estimate of ENSO driven temperature changes.
The Nino 3.4 index, lagged two or three months, correlates reasonably well with temperature variation in the tropics, and can account for ~65% – 70% of the measured variation in average temperature. But can Nino 3.4 actually provide more information than gleaned from the 2 or 3 month lag correlation?
The answer seems to be that there is a bit more information available. If we consider ENSO to be a cyclical redistribution of heat that accumulates in the tropical Pacific, then it becomes clear the response to a change in ocean surface temperature in the Nino 3.4 region can’t be immediate, nor is the influence going to be accurately described by a specific lagged monthly Nino 3.4 value. During La Nina, stronger trade winds push warm surface water westward toward the Pacific warm pool, and that water is replaced with cooler water which upwells, mainly in the eastern Pacific. When the trade winds drop, an El Nino begins, with warm water flowing eastward from the Pacific warm pool, while the rate of upwelling in the eastern Pacific drops, which leads to warming in the eastern Pacific. The temperature response of the tropics ought to be something other than a simple lag of the Nino 3.4 index, since it takes time for heat to be distributed throughout the tropics.
So how can we use a direct measure of the tropical Pacific temperature anomaly (Nino 3.4) to better estimate the response of global average tropical temperature to ENSO? I reasoned as follows: The temperature rise in the tropics that is associated with an increasing Nino 3.4 temperature takes time to be distributed over all of the tropics, so any response should be gradual. As the tropical temperature rises, heat loss to space increases, and the warming influence for any single month should decay gradually to nothing. The influence of an instantaneous change (eg. a rise in the Nino 3.4 index from 0 C to 2C for only one month, followed by a flat Nino 3.4 index of 0 C for many months) ought to show an exponential-like decay from an initially strong influence. There is not a single monthly Nino 3.4 influence at an optimal lag time, but rather a continuously evolving influence over some extended period. A strong El Nino or La Nina continues to have influence on tropical temperatures even after the Nino 3.4 index has returned to a neutral state.
I modeled the evolution of Nino 3.4 influence by iteratively calculating a new monthly index I call the “Effective Nino Index” (ENI):
ENI(n) = k * ENI(n-1) + (1-k) * Nino34d(n-1)
where ENI(n) is the Effective Nino 3.4 Index
n is the current month
(n-1) is the previous month
Nino34d(n-1) is the detrended Nino 3.4 index for the previous month
k is a constant between zero and one
ENI(n) is essentially a low pass filtered representation of all earlier Nino 3.4 values.  I tested several values of k to see what value generates an ENI which best correlates with temperature evolution in the tropics. Since ~1997, the temperature trend in the tropics has been relatively flat and not influenced by major volcanic eruptions, so I ran a regression of ENI against the detrended tropical temperature anomaly for 1997 to present (I used the Hadley Hadcrut4 tropics history, downloaded from Wood For Trees). The best correlation between ENI and average tropical temperature is at k = 0.703. In other words, in any single month, the running history (2 and more months past, represented by ENI(n-1)) contributes 70.3% of the ENSO influence on average tropical temperature, and the previous month’s Nino 3.4 index contributes 29.7% of the influence on average tropical temperature. Figure 1 shows how the relative influence of any single month of Nino 3.4 declines over time, with zero months lag meaning the current month. (Click on any image to view at the original resolution.)
A comparison of Nino 3.4 with ENI is shown in Figure 2. The lagging effect of the low-pass filter function is clear. Please note that ENI is not a temperature index per se, but an index that represents the weighted contribution of all past Nino 3.4 temperatures, with the relative influence of earlier Nino 3.4 values falling rapidly in importance the further back in time you look.
Figure 3 shows the ENI and the detrended tropical temperature for 1997 to 2012 (Hadcrut4, downloaded from Wood for Trees) on the same graph, and Figure 4 shows the detrended tropical temperatures and ENI for 1950 to 2012.
There is very good correlation in the 1997 to 2013 period, where volcanic influences are minimal. You may note in figure 4 that periods of significant deviation between the detrended tropical temperature anomaly and the ENI correspond to the aftermath of major volcanic eruptions, which is consistent with significant aerosol cooling. The “adjusted” tropical temperature model based on the ENI regression against tropical temperatures is:
Tadj = Torg – (0.1959 +/- 0.016) * ENI
Where Torg is the original Hadley temperature anomaly for the tropics. +/-0.016 is the two sigma uncertainty for the model coefficient.
For the 1997 to 2012 period, the model’s F statistic was 594 (very highly significant), and the R^2 value was 0.756, meaning 75.6% of the total variance in tropical temperatures is predicted by the ENI value. It is important to note that ‘predicted’ is a suitable word, since the ENI influence is due to the combination of all earlier months’ Nino 3.4 values, not the present Nino 3.4 value. Since the ENI is based on the detrended Nino 3.4 index, there is no net contribution to ENI from any general warming of the ocean surface over time.
Figure 5 shows the above ENI adjustment applied to all the Hadcrut4 tropical temperature data since 1950. As we might expect, the influence of volcanic aerosols from Pinatubo shows up much more clearly than in the unadjusted temperature data.
I will use the ENI in the combined regression analysis that includes volcanic and solar effects.
II. About Those Natural Forcings
NASA GISS provides data for their estimate of aerosol influences from 1850 to present (http://data.giss.nasa.gov/modelforce/strataer/). The data is in the form of Aerosol Optical Depth (AOD at 550 nm wavelength), which is converted into a net forcing value (watts/M^2) by multiplying the AOD by a constant of 23 (NASA’s value). The GISS volcanic aerosol forcing since 1950 is shown in Figure 6.
Direct measurements of solar intensity over the solar cycle are only available since 1979 (via satellites), but the correlation between sunspot number (SSN) and measured changes in solar intensity is good, so it is possible to estimate the historical variation in solar intensity based on SSN records. To estimate solar intensity variation, I used the following empirical equation, which comes from regressing measured solar intensity with sunspot number (data from a spreadsheet by Leif Svalgaard):
Solar intensity = 1365.45 + (0.006872 * SSN)Â watts/M^2
Where solar intensity is measured above the Earth’s atmosphere, and SSN is the monthly sunspot number. The R^2 for this regression was 0.984. The variation of solar intensity about an average value is then:
Variation = 0.006872 * (SSN – AvgSSN) watts/M^2
Where AvgSSN is the average number of sunspots over the period being studied (in this case from 1950 to 2012).
If we assume Earth’s albedo is 30%, and average over the entire surface (a factor of 4 compared to the cross-sectional area Earth presents to the Sun), the variation in solar energy reaching the Earth (including the troposphere) is:
Variation = (0.7/4) * 0.006872 * (SSN – AvgSSN) = 0.001203 * (SSN – AvgSSN) watts/M^2
Since the solar cycle is ~11 years long, we expect solar forcing to generate a temperature response with peaks separated by ~11 years. Figure 7 shows the calculated solar forcing since 1950.
III. Regression Model
The regression model has three independent variables: the ENI, with nominal units of temperature (as described above), lagged volcanic forcing, and lagged solar cycle forcing (both with nominal units of watts/M^2). We do not expect an instantaneous temperature response to volcanic and solar forcing, since the thermal mass of the Earth’s atmosphere, land surface and ocean surface are expected to slow the response… that is, to introduce lag between the applied forcing and the response.
A very accurate estimate of the global temperature response to solar and volcanic forcing history would require an accurate model of ocean heat uptake at different latitudes over time, as well as an accurate model of heat transport between high and low latitudes, between land and ocean, and between Earth and space. Since this type of model arguably doesn’t exist, I am forced to use a much simpler lag-type model. The lag model is based on a single constant value with a repetitive monthly calculation that approximates a low pass filter function:
EF(n) = EF(n-1) * (1 – K) + F(n) * K
where:
EF(n) is the effective forcing for month n (solar or volcanic)
F(n) is the actual forcing for month n (solar or volcanic)
K is a decay constant
When K =1, the effective forcing is identical to the actual current forcing. Smaller values of K introduce increasing lag in the response. This type of function is essentially equivalent to the expected response of a “slab” type ocean, or to Lucia’s ‘Lumpy’ model response. Please note that the lag applies to both solar and volcanic aerosol forcings, since these are both radiative forcings.
Since I did not a priori know the best value of K, I tried different values of K and found the value which gave the best fit regression (that is, the highest R^2 value) for the three variables against the detrended monthly Hadley temperature series from 1950 to 2012. The best fit for K was 0.031. Figure 8 shows the “step response” of the lag function with K = 0.031, with F(n) starting at zero and then stepping to constant value of 1 at month 1.
Detrending of the temperature series was used prior to regression because the underlying long-term secular trend, whether due to GHG forcing alone or in combination with other long term influence(s), can’t be accurately modeled by the three variables in the regression, since these three variables are all expected to have relatively short term influence. Using the original temperature data (not detrended) distorts the regression fit by essentially forcing the regression to explain all the temperature change, including any slow secular trend, using the three short-influence variables, and so yields very poor (even physically nonsensical) results.
Figure 9 shows the original and lagged volcanic aerosol forcing, and Figure 10 shows the original and lagged solar forcing.
The best fit regression (with K = 0.031) yields the following constants:
ENI: Â Â Â Â 0.1099 +/-0.0118 (+/- 2-sigma uncertainty)
Volcanic: 0.2545 +/- 0.0277
Solar: Â Â Â 0.233 +/- 0.231
R^2 for the regression was 0.445 (44.5% of the variance was accounted for by the model).
The much greater uncertainty in the solar influence is due to the solar forcing being quite small compared to the other two. Still, it is encouraging that the regression shows the best estimates for response to both radiative forcing variables are very similar… just as one might expect, since radiation is fungible.
Figure 11 shows the temperature influence of the three variables and their combined influence based on the regression constants for each.
Figure 12 shows an overlay of the detrended Hadley temperature series and the sum of the three adjustments (both offset to average zero, which makes visual comparison easier), and Figure 13 shows the adjusted and unadjusted Hadley global temperature series.
I have added the slope lines for the adjusted series from 1979 to 1996 (inclusive) and from 1997 to 2012 (inclusive). The slope since 1997 is less than 1/6 that from 1979 to 1996.
IV. Comments, Conclusions, Caveats, and Uncertainties
Warming has not stopped, but it has slowed considerably. This analysis can’t prove the cause for that change in rate of warming, but any suggestion that solar cycles, volcanic aerosols, and ENSO are completely responsible for the recent slower warming rate is not supported by the data. Some may suggest long term cyclical variation in the secular warming rate has caused the recent slow-down, but this analysis can’t support or refute that suggestion.
It is encouraging that the influence of the ENI on global temperatures (as calculated by the by the global regression analysis) is just slightly more than half the influence found for the tropics alone (30S to 30N): 0.1099+/- 0.0118 global versus 0.1959+/-0.016 tropics. Since Carrick showed almost no correlation of ENSO with temperatures outside the tropics, and since 30S to 30N represents exactly half the Earth’s surface, we could reasonably expect the regression constant for the entire globe to be about half as large as for the tropics… and it is indeed very close to half (and within the calculated uncertainty limits).
The analysis indicates that global temperatures were significantly depressed between ~1964 and ~1999 compared to what they would have been in the absence of major volcanoes.
Here are a few caveats and uncertainties. First, the analysis is only as good as the data that when into it. Historical volcanic forcing from GISS is at best an estimate for all eruptions before Pinatubo; if the GISS volcanic forcing is wrong, then this could distort the regression results. The same is true for all other data, including the Hadley temperature series and the sunspot number model used to calculate solar forcing. While sunspot number is an excellent proxy for solar intensity over the last 3 solar cycles, that does not guarantee sunspot number has always been an equally excellent proxy for solar intensity.
Second, the single constant low-pass filter function used to calculate lagged solar and volcanic forcings is a fairly crude representation of reality. While the true lag function is almost certainly similar in shape, it will not be identical, and this too could distort the regression analysis to some extent. The reality is that there are a multitude of lag constants associated with heat transfer to/from different locations, especially different depths of the ocean.
Third, it is tempting to infer very low climate sensitivity from the regression constants for volcanic aerosols and solar cycle forcing (these constants have units of degrees/watt/M^2, and the values correspond to a climate sensitivity of a little less than 1C per doubling of CO2). This temptation should be resisted, because the model does not consider the influence of (slower) heat transfer between the surface and deeper ocean. In other words, the calculated impact of solar and volcanic forcings would be larger (implying somewhat higher climate sensitivity) if a better model of heat uptake/release to/from the ocean were used.
Request for only constructive comments:Â Skydragon slayers and rabid catastrophic warmers should not feel their comments are required or requested.
(1) Grant Foster and Stefan Rahmstorf 2011 Environ. Res. Lett. 6 044022
So F&R’s adjusted record give a continuous warming since 1979 while your result still shows a slow down around 2000. In the adjustments what’s the main contributor to that difference?
Will you be publishing?
The calculation of solar intensity from SSN using Svalgaard’s empirical correlation still leaves open the possibility that some other aspect of solar variability (e.g., increase in UV, change in solar wind velocity or magnitude) might contribute to the otherwise unexplained leveling off in T after the late 1990s, doesn’t it? Stated otherwise, the conversion of SSN into forcings due to TSI variation need not exhaust the possible influence of solar change on climate.
I wonder if there is a straight-forward way to look for other possible (presumably SSN-associated) effects on T within your regression, even though a way to directly convert such hypothetical effects into forcings is lacking.
Troy Masters has been doing a lot on this, taking in some ideas of KevinC at SkS (and York). One idea that seemed to work well was Kevin’s, using exponential smoothing rather than discrete lag.
Foster said that the reason for restricting to a recent period was that back further would make the underlying linearity of AGW doubtful, and the gas (and aerosol?) forcings would have to be used. It seems to me a good idea to use them anyway.
On further reading, I see your ENI is also an exponential smooth, as is the smoothing for solar and vol.
Nicely done. What is clear is that there is a fair amount of noise in the surface temperature signal, that is, if you consider natural forcings to be noise. Then there’s other not so natural forcings (land use, etc) that still remain and are even more difficult to adjust for. Still, I think you should turn this work into into a paper.
Monckton just published a short essay suggesting that Ben Santer’s 17 year test has been met. http://wattsupwiththat.com/2013/06/13/no-significant-warming-for-17-years-4-months/
[sarc] Your essay still doesn’t prove a colder object can heat a warmer one though. [/sarc]
HR,
F&R make some unjustified assumptions, and give their regression model the freedom to independently set lag constants for all three variable. This leads to some nutty conclusions. The authors should have paid more attention to John von Neuman’s observation about drawing an elephant with 5 adjustable parameters.
.
WheresWallace,
I just did. I won’t try to publish anywhere else, too much else to do.
.
Barry Elledge,
You could do most anything you want, but it would have to have a plausible physical rational. It is hard for me to see any mechanism for solar cycle influence that does not involve a lagged response to applied forcing. The F&R zero-lag solar effect is about as physically unrealistic as I can imagine, and ridiculous on it’s face.
.
Nick Stokes,
I was aware that Troy had looked at F&R to see if their algorithm could reliably detect a known perturbation ( it couldn’t). I was not aware of other peoples efforts. WRT the best approach for selecting a period: Seems to me that restricting the analysis to 1979 and later causes problems because you have too little data to accurately evaluate a weak forcing like the solar cycle. But my primary objection to F&R is the acceptance of physically implausible results; their BS antennas must be very badly oriented, perhaps just disconnected.
.
SteveF —
You wrote “it is tempting to infer very low climate sensitivity from the regression constants for volcanic aerosols and solar cycle forcing.” While I agree that ECS can’t be inferred from analysis which excludes the ocean volume, the elimination of ENSO interference would seem to make for a plausible TCR estimate. I’m not sure what kind of error bar would be appropriate, though.
Anthony,
Thanks.
I have neither the time nor inclination to publish in a peer reviewed journal. I am confident that many of the commenters here will help point out weaknesses/errors.
.
I agree that there is a lot of short term variation which makes evaluating causal relationships more difficult. I think some progress can be made on that front by examining the temporal structure of short term variation for different latitudes and devising appropriate adjustments or those short term variations. For example, there is strong evidence for a persistent temperature oscillation above 30N, with a period of about 21 months. But that is a subject for another day.
HaroldW,
The implied sensitivity from the regression constants has to be lower than even the transient response, though how much lower is unclear. An analysis using a reasonably accurate ocean heat uptake model (say for the top 400 meters or so) would give a much improved estimate of sensitivity, but validating that kind of model (using heat uptake measurements) is not a trivial undertaking.
SteveF, interesting work. Can you provide the data file; for your “adjusted Hadley” series?
Troy Masters found in his studies that “adjusting” the data reduced the trend for last decade or so (the opposite of F&R’s findings). This seems broadly consistent with your work too.
It’d be interesting to see the curve with the ~ 56 year “oscillation” subtracted off. This is the only way I know to “unbend” the post 1998 “kink” in the series.
Carrick,
I can send you the adjusted temperature data by email some time today.
The recent trend is in fact decreased slightly because removing the influence of Pinatubo from the 1997 to ~2000 period raises the adjusted temperature for that period. I was not aware Troy had found something similar, but I can’t say I am surprised. The dominant influence of the volcanic forcing pretty much dictates the outcome… Unless you want to twist the analysis into pretzel like F&R.
SteveF
Heh! To the extent that there is any weakness, it would be fall in the category that F&R has: The potential for ‘overfitting’ from a large ranges of choices one might have made after seeing the data! This is the perpetual problem for explaining the earth’s temperature series. (Even AOGCM’s can’t get away from it because they can chose different aerosols, slightly different solar and so on!)
Having the earth’s response to solar and volcanic be similar in magnitude and time constant is certainly an improvement over F&R. It would be nice to see uncertainty intervals on trends especially for the recent one. ( I’m not sure how to do them. Also: I doubt if F&R’s were correct. You need to account for the uncertainty in all the corrections and adjustments. )
SteveF, that’s an interesting comment about the volcanic forcings. Presumably this indicates that there’s some value in improving the model describing the response of climate to volcanic forcings.
It you are correct (and I don’t see how you wouldn’t be), this would indicate a serious flaw in the F&R methodology.
TroyC’s link is here. (Nick also provided this).
KevinC’s link is here.
KevinC now has this disclaimer at the top of his post:
Getting estimates of uncertainty in the adjusted series would be of real interest of course.
SteveF: As far as I can tell, your model assumes a linear relationship between your ENSO index and global surface temperatures.
Trenberth et al (2002)…
http://www.cgd.ucar.edu/cas/papers/2000JD000298.pdf
…cautioned against this. They wrote, “Although it is possible to use regression to eliminate the linear portion of the global mean temperature signal associated with ENSO, the processes that contribute regionally to the global mean differ considerably, and the linear approach likely leaves an ENSO residual.â€
Compo and Sardeshmukh (2010)…
http://journals.ametsoc.org/doi/abs/10.1175/2009JCLI2735.1?journalCode=clim
…note that it should not be treated as noise that can be removed. Their abstract begins: “An important question in assessing twentieth-century climate change is to what extent have ENSO-related variations contributed to the observed trends. Isolating such contributions is challenging for several reasons, including ambiguities arising from how ENSO itself is defined. In particular, defining ENSO in terms of a single index and ENSO-related variations in terms of regressions on that index, as done in many previous studies, can lead to wrong conclusions. This paper argues that ENSO is best viewed not as a number but as an evolving dynamical process for this purpose…â€
I’ve been illustrating and discussing for a couple of years that the sea surface temperatures of the East Pacific(90S-90N, 180-80W) show that it is the only portion of the global oceans that responds linearly to ENSO, but that the sea surface temperatures there haven’t warmed in 31 years:
http://oi47.tinypic.com/hv8lcx.jpg
On the other hand, the sea surface temperature anomalies of the Atlantic, Indian and West Pacific (90S-90N, 80W-180) warm in El Niño-induced steps (the result of leftover warm water from the El Niños) that cannot be accounted for with your model:
http://oi49.tinypic.com/29le06e.jpg
A more detailed, but introductory level, explanation of the processes that cause those shifts can be found here [42MB .pdf]:
http://bobtisdale.files.wordpress.com/2013/01/the-manmade-global-warming-challenge.pdf
And what fuels the El Ninos? Sunlight. Even Trenberth et al (2002), linked above, acknowledges that fact. They write, “The negative feedback between SST and surface fluxes can be interpreted as showing the importance of the discharge of heat during El Niño events and of the recharge of heat during La Niña events. Relatively clear skies in the central and eastern tropical Pacific allow solar radiation to enter the ocean, apparently offsetting the below normal SSTs, but the heat is carried away by Ekman drift, ocean currents, and adjustments through ocean Rossby and Kelvin waves, and the heat is stored in the western Pacific tropics. This is not simply a rearrangement of the ocean heat, but also a restoration of heat in the ocean.â€
In other words, ENSO acts as a chaotic recharge-discharge oscillator, where the discharge events (El Niños) are occasionally capable of raising global temperatures, where they remain relatively stable for periods of a decade or longer.
In summary, you’re treating ENSO as noise, while data indicate that it is responsible for much of the warming over the past 30 years.
Regards
Lucia, Carrick,
” It would be nice to see uncertainty intervals on trends especially for the recent one. I’m not sure how to do them.”
.
Yes error bars would be nice, but I am not certain how to determine them in a defensible way. A starting point would be to show the individual calculated influences with their associated +/- 2 sigma uncertainties (of course these uncertainties don’t add linearly). How to handle uncertainties in the lag constants for ENI and solar intensity variation is less clear, but these also come from independent regressions, so the respective +/-2 sigma uncertainties could also b e shown. Probably some kind of monte-carlo type analysis could be used, but that looks like more work than I am interested in.
.
With regard to overfitting: I tried to make sure that everything I used in the analysis was physically reasonable. The possibility of over fitting is always going to be present if there are factors/influences which are not included in the model (the regression is torqued toward incorrect results by trying to account for the factors/influences which are not present in the calculation). This is why I pointed out that there were no real surprises: I had expected solar and volcanoes to have similar regression constants (on a watt/M^2 basis), and I expected the global ENI influence to be not far from half the influence in the tropics. That both these expectations were fulfilled gives me some confidence the regression is not terribly over fitted.
It seems clear to me that warming of the atmosphere had indeed slowed down considerably over the past 10-15 years – your post is just another nail……
It is not clear, however, that the rate of change of the TOA energy imbalalance has slowed, even in the slightest. Slow moving decadal cycles could very well bring back a multi-decade period of strong atmospheric warming. It’s all about ocean-atmosphere heat exchanges, only one of which is ENSO.
Bob Tisdale (Comment #115749),
.
WRT linearity of temperature response to ENI: please explain why you think Figures 3 and 4 above do not show reasonable linearity between ENI and tropical temperatures.
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“In other words, ENSO acts as a chaotic recharge-discharge oscillator, where the discharge events (El Niños) are occasionally capable of raising global temperatures, where they remain relatively stable for periods of a decade or longer.
In summary, you’re treating ENSO as noise, while data indicate that it is responsible for much of the warming over the past 30 years. ”
We have been down this road before. I do not want to get into a long exchange with you over the same subject, since that would be a waste of both your time and mine. For the record: I understand very well what you think about the influence of ENSO, and I am utterly unconvinced by your arguments. In fact, I find them to be nonsensical gibberish that betray a complete lack of understanding of science in general. The likelihood of significant warming driven by radiative forcing is something you ought to grips with, if only to stop embarrassing yourself. I am quite certain you won’t ever do that, and that is OK with me. What is not OK is for you to sidetrack a marginally related thread with repetitive (and loony) arguments about global warming being all due to ENSO.
The main problem is that we have a reasonable clue as to what drives temperature cycles up 12 months in length (seasonable variation).
Beyond that the data is so noisy or so short that almost anything COULD be true (depending on sampling methods used).
I believe that there is some merit in being able to identify natural cycles in the 1-15 year range. I think that this will add much to our understanding.
May I pose this http://s1291.photobucket.com/user/RichardLH/story/70051#
as an initial analysys?
SteveF,
Nice analysis. Hear hear for the exponential decay filter. If you don’t have time to publish more formally maybe Troy can incorporate your stuff. Not that I think lack of “traditional” publication detracts from the value of what you’ve done.
Owen (Comment #115754),
I am glad we agree the rate of warming has in fact slowed.
.
“It is not clear, however, that the rate of change of the TOA energy imbalance has slowed, even in the slightest. Slow moving decadal cycles could very well bring back a multi-decade period of strong atmospheric warming. It’s all about ocean-atmosphere heat exchanges, only one of which is ENSO.”
.
Yes, there is clearly a remaining TOA imbalance (http://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/) but there is no evidence of a dramatic recent increase in the rate of heat uptake which could explain the recent drop in the rate of surface warming. There very well could be a future increase in the rate of warming if the recent slow-down is the result of internal cyclical behavior. It is unclear how much any future increase in the rate of warming might be and unclear when the rate of warming might increase.
BillC,
Thanks.
SteveF (Comment #115759)
June 13th, 2013 at 9:33 am
“It is unclear how much any future increase in the rate of warming might be and unclear when the rate of warming might increase.”
I agree, and I am not sure where this leaves us. Atmospheric warming over land will be greater than global atmospheric warming and the impacts of such land warming, even at the levels you are talking about, may be quite problematic in, say, 50 or 100 years.
I am also unsure about what to make of the current oceanic warming as far as its possible deleterious effects are concerned.
In the face of the uncertainty, I am all for an immediate commitment on the part of all developed nations to significantly reduce the rate of use of reduced carbon fuels. The supply is finite, reduced carbon has inherent value in many applications and is far to valuable to just wantonly burn, and the idea of amending our atmosphere so dramatically and quickly is probably not the best course to follow.
SteveF (Comment #115759)
June 13th, 2013 at 9:33 am
“It is unclear how much any future increase in the rate of warming might be and unclear when the rate of warming might increase.â€
How’s about this for a short term prediction 🙂
http://s1291.photobucket.com/user/RichardLH/story/70051
Owen,
“In the face of the uncertainty, I am all for an immediate commitment on the part of all developed nations to significantly reduce the rate of use of reduced carbon fuels. The supply is finite, reduced carbon has inherent value in many applications and is far to valuable to just wantonly burn, and the idea of amending our atmosphere so dramatically and quickly is probably not the best course to follow.”
.
I can’t say I am surprised that you want such a commitment. I think you will be disappointed though, since people who are terribly concerned about warming seem unwilling to embrace anything other than wind and solar, thus making a reduction in fossil fuels impractically expensive….. for everyone, but especially for the poorest. I’d suggest you push for generous funding for development of thorium and fast breeder technology ASAP if you really want to reduce fossil fuel use.
.
In the face of uncertainty, I am more inclined to improve the level of certainty before considering the best course of action on fossil fuel use, but I’d have no problem supporting developmental funding of advanced nuclear and advanced battery technology (which is the only way I see to make renewables economically practical).
Richard LH (Comment #115765),
I can’t tell from that link what you are predicting. Can you just state your prediction(s) and the corresponding date(s)?
SteveF,
If F&R fit the data with several lags as fitted parameters, how did they end up with zero lags?
Also, not that I buy all of Bob T.’s arguments about ENSO, but if the energy ultimately comes from the sun and is amplified by greenhouse gases, and the ocean, with its huge heat capacity, ends up with most of the energy, wouldn’t ocean events like ENSO and PDO, AMO just be reflections of how and with what lag the energy is distributed around the planet? Maybe the lag for how long it takes the heat to be distributed during and after an El nino is different from the lags for how long it takes heat to enter and leave the ocean? Your solar lag I guess could reflect how long it takes heat to enter the coupled ocean/atmosphere but is there another unknown lag (or perhaps several representing all the various ocean events) for how fast it can leave? For example was the large amount of heat coming out of the oceans during 1998 due to a large amount of heat that entered the ocean during a large solar cycle decades or centuries before? Or is it due to a lot of heat that entered the oceans just a few years before?
SteveF (Comment #115755), June 13th, 2013 at 9:12 am:
“For the record: I understand very well what you think about the influence of ENSO, and I am utterly unconvinced by your arguments. In fact, I find them to be nonsensical gibberish that betray a complete lack of understanding of science in general.”
That’s quite a statement. A fair share of pent-up resentment and animosity leaking out there it seems.
No, just some reading of his many posts at WUWT; I do become frustrated when he posts the same things over and over. SteveF
But I do wonder – rationally, not emotionally – exactly what is it about the data that Tisdale presents that so utterly unconvinces you? And in what way exactly is this data nonsensical gibberish? And how specifically does its presentation betray a complete lack of understanding of science in general?
He draws a conclusion (ENSO causes all global warming) which is contrary to radiative physics. I carefully avoid commenting on Bob’s many posts at WUWT, and this is no coincidence, because any comments I made it would be a waste of his time and mine. I do hope he will do the same here. – SteveF
You are aware that Tisdale presents data, are you not? He’s not building a hypothesis. The data from the real world shows us exactly what happens. Specifically when, specifically where and specifically how it happens. We can track the heat through the system, from where it enters to where it ends up.
Of course he presents data… mountains of it. He just interprets it all incorrectly. SteveF
Since 1970, there have only been three (3) instances where global temperatures on a permanent basis have parted with the NINO3.4 SSTa curve. In three abrupt hike-ups: 1978/79, 1988/89 and 1998/99. At all other times, global temperature levels and main ups and downs simply follow NINO3.4 slavishly:
http://i1172.photobucket.com/albums/r565/Keyell/HadCRUT3vsNINO341970-2013b_zpseeb92025.png
The data readily accounts for these sudden global upward shifts above the NINO3.4. They are natural and process-related – ENSO-induced.
The shifts are Trenberth’s ‘ENSO residual’ …
If you keep pretending that ‘NINO3.4’ can be used to represent the entire ENSO phenomenon and all its effects on global climate, including even all the oceanic and atmospheric processes that occur during an ENSO interval outside the relatively minor NINO3.4 region, and hence end up considering ‘ENSO’ to be tropical noise only, then sorry, your analysis will remain moot and without relevance, SteveF. It will explain or reveal nothing.
The oceanically operative ENSO region (~ 40N-40S, 120E-80W) has an eastern and a western half, sectors of ‘the ENSO pendulum’ so to say. The former is the NINO3.4 part, the latter is the West Pacific Warm Pool (WPWP) part. Both of these sectors need to be included to derive the actual ENSO signal. Also, this oceanic (Pacific) ENSO region directly teleconnects atmospherically to the Indian and Atlantic Oceans, forcing them to follow suit. Trenberth writes a lot about this. It is established knowledge. El Niño discharging and La Niña recharging heat is also no mystery.
Again, what is it specifically, SteveF, that so thoroughly unconvinces you about all this …?
Um… all that has absolutely nothing to do with rejecting radiative physics… which is the primary issue I have with all of Bob’s ‘analyses’… for lack of a better word. By the way, you seem to have a bit of hostility yourself. SteveF
SteveF, Very nice. I have been using lower stratosphere data to try and show how the ocean heat recovery from the volcanic events is the main reason for the “pause”, basically the oceans recharged around 1995. That produces about the same change in slope as your adjustments.
https://lh4.googleusercontent.com/-4HJOuEAtcr0/UZ09R25HtPI/AAAAAAAAIPg/Ms7rP0mitrw/s981/NH%2520Oceans%2520and%2520Atmosphere.png
That is in estimated Wm-2 based on SST which I never got around to using to smooth the aerosol forcing. It looks like it might be fun to compare with your adjustment though.
SteveF,
Thanks for replying. No, I have no ‘hostility’ at all. I simply find your dismissal of Tisdale strange, since you give no reason why he’s incorrect, except he ‘contradicts radiative physics’.
Well, whatever floats your boat …
Bill_W,
“If F&R fit the data with several lags as fitted parameters, how did they end up with zero lags?”
They ended up with a near-zero lag for solar only, not anything else… which is one of the problems. The zero lag result is possible because they allowed the calculation to determine the lag for each variable, quite independent of whether the selected lag was physically plausible (near zero lag is NOT plausible).
.
“Also, not that I buy all of Bob T.’s arguments about ENSO, but if the energy ultimately comes from the sun and is amplified by greenhouse gases, and the ocean, with its huge heat capacity, ends up with most of the energy, wouldn’t ocean events like ENSO and PDO, AMO just be reflections of how and with what lag the energy is distributed around the planet?”
Sure, those pseudo cyclical behaviors almost certainly are driven by the distribution of heat. But I am not sure what you are getting at.
.
“Maybe the lag for how long it takes the heat to be distributed during and after an El nino is different from the lags for how long it takes heat to enter and leave the ocean?”
Sure, some of the heat is distributed in the ocean, some is lost to space, some warms land areas; each process would probably take place at a different rate. But once again, I am not sure what you are getting at.
.
” Your solar lag I guess could reflect how long it takes heat to enter the coupled ocean/atmosphere but is there another unknown lag (or perhaps several representing all the various ocean events) for how fast it can leave? For example was the large amount of heat coming out of the oceans during 1998 due to a large amount of heat that entered the ocean during a large solar cycle decades or centuries before? Or is it due to a lot of heat that entered the oceans just a few years before?”
.
I think you may have some misconceptions of the processes involved. There is of course heat gain (solar) and loss from the ocean surface, with more gain than loss at low latitudes and more loss than gain at high latitudes. Surface currents (and cycles like the ENSO, PDO, etc) are involved in transport of ocean heat from low to high latitudes (as is atmospheric circulation). There is also a pretty much continuous loss of heat from the warm surface at low latitudes to deeper (and colder) water, at an average rate in the range of ~8 watts/M^2. There is also continuous upwelling of deep cold water at low latitudes, which combines with downward heat transport from the warm surface to form the thermocline (a more-or-less stable exponential-shaped drop in water temperature with increasing depth). The cold upwelling water at low latitudes is replaced by sinking cold water at high latitudes in areas of deep convection. Surface currents carry water from low latitudes to high, closing the mass balance. (This is the thermohaline cirulation.) When the ocean surface warms in the tropics, the near-surface water does gain heat, but once you go much below the surface layer, that is, below the well mixed layer, what is really happening is more heat is being carried downward than is compensated for by cold upwelling, so that deeper water warms relative to what it was before, but it remains much cooler than the surface water. When the surface water cools (say due to a volcanic eruption), heat really does “come out of” the surface layer, but the water below the surface water already is a lot cooler… so it is not like heat previously accumulated actually “comes out of” the deeper water, instead cooler surface water just means the rate of loss of heat downward from the warm surface layer is reduced somewhat whenever the surface layer cools. From a practical POV, it is easier to describe the process as “heat entering and leaving the deeper ocean”, but in fact the process is a good deal more complicated than that description indicates. When we consider very long ago periods (hundreds of years in the past) the surface temperatures long ago could indeed lead to “heating” or “cooling” of deeper water relative to what the temperature might be today at equilibrium, but the impact of that long ago period has to be fairly small, because it takes a long time (hundreds of years) for the “heat” at great depth to “escape”… just as it took hundreds of years for that heat to accumulate at great depth.
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I don’t know if that addresses your questions, but I hope it helps.
Kristian (Comment #115815),
” you give no reason why he’s incorrect, except he ‘contradicts radiative physics’”
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That’s quite enough to know that he is mistaken. It is impossible for greater radiative forcing to not cause warming (except in the case of an actively controlled system.. like a mammal’s body temperature). If I told you that the surface of mars has negative gravity, or Mars was composed mainly of hotdogs and mustard, you could save yourself a lot of time by not addressing the specific arguments I offered in support of my claims. You would just say I was nuts. Bob’s conclusions (GHG increases could not have caused any warming, and ENSO proves it) are in the same general group.. OK maybe not as bad as Mars is made of hotdogs and mustard.. but close. His arguments are not worth addressing because his conclusion is utterly wrong on its face.
.
I am sure Bob is a fine fellow and maybe not a bad guy to play a round of golf with, but I’m not going to waste time arguing with him about nonsense.
Re: Kristian (Jun 13 13:37),
The problem of Bob Tisdale is that he fails to recognize that ENSO cannot increase the energy content of the planet. It should only cause oscillations around a mean value, not a trend.
That statement is incorrect. ENSO only modulates the accumulation of energy in the system, it doesn’t cause it. IOW, it is, in fact, noise. If it did cause it, then one should expect substantial cooling sometime in the near future when the cycle reverses.
SteveF,
In other words, you choose theory over observations. Vast amounts of real-world observational data show clearly and consistently that CO2 has had no influence whatsoever (zero) on the three-step modern global warming we’ve seen since 1975, and that ENSO has had a world of the same. But that’s pure nonsense of course, because your ‘theory’ says that CO2 must have had a significant influence. Even though it’s nowhere to be found. Well, sorry about that. It’s all natural. Sun + ocean cycles. Done.
Please look at the data presented, SteveF, before you dismiss them offhand. ENSO is written in capital letters all over them. The alleged CO2 ‘background’ signal is … nowhere to be found. CO2 warming is still an assumption and a claim with no data from the real world to back it up in revealing a causal link CO2 -> temp. Claiming without showing is not science. It is speculation.
DeWitt Payne,
Your post ‘betray[s] a complete lack of understanding of’ the ENSO phenomenon, what it is and how it works.
Of course ENSO can increase (or reduce) the energy content of the planet. It does so during each positive or negative event (El Niño/La Niña). Why shouldn’t it be able to do so also in a multidecadal perspective? Do you really believe there is always perfect symmetry between absorption and release of heat going from La Niña to El Niño to neutral conditions and back? Do you for example think that a half-year medium El Niño or a stretch of neutral states automatically will be able to release all of the ocean heat stored up during a preceding three-year La Niña? We know it’s not so. All we need to do is look at the OHC data.
“ENSO only modulates the accumulation of energy in the system, it doesn’t cause it.”
It most certainly does. And the mechanisms by which it does so are all well-known to science. ENSO is a coupled ocean/atmosphere phenomenon and it surely controls cloud cover, pressure gradients and winds, upwellings and stratification, convection, evaporation and current flows (transfer/transport of heat), recharge and discharge of heat, not just in the tropical/subtropical Pacific, but also (by atmospheric teleconnections) in the Indian and Atlantic Oceans.
The energy itself of course comes from the Sun. But ENSO to a large degree determines how much of the solar heat will be absorbed and subsequently released by the ocean. That is what the process does. It controls and distributes the heat flow into and out of the Earth system.
Kristian,
If all the nonsensical stuff Bob spouts ‘floats your boat’ then good for you. Of course, you will find a lot more kindred spirits on some other blogs than you will here. A deus.
Volcanic eruptions, large enough to affect the global temperature, happen about once every 30 years of so.
Why not start a fashion and write a volcanic aerosol prediction vs. effect on temperature?
You should be able to use the aerosol data from previous eruptions as a guide and derive a testable algorithm.
A big eruption will test all the present models, which use quite different aerosol ‘forcings’.
Kristian (Comment #115835)
June 13th, 2013 at 4:50 pm
“Of course ENSO can increase (or reduce) the energy content of the planet. It does so during each positive or negative event (El Niño/La Niña).”
It most certainly cannot increase or reduce the energy content of the planet. It can only redistribute energy.
“It most certainly cannot increase or reduce the energy content of the planet. It can only redistribute energy.”
And if the redistribution of energy changes the rate of heat loss or gain, then it has an impact on the energy content of the planet. Same old sematics. ENSO though is a bit of a red herring. The shift in energy across the equator that leads to the NH oceans being 3 C warmer than the SH oceans, that is a 17 Wm-2 meridional imbalance, does change the energy capacity of the planet, if the hemispheres where at equal temperatures, the planet would be nearly 1.5 C cooler if you use the surface temperature as a reference. Toggweiler has a simple paper on the Changing Westerlies or the shift in the thermal equator
Brierley et al have a paper where they estimate meridional heat transfer with the isthmus closing and Drake Passage opening to be about 3.2 C global impact and zonal heat distribution has about a 0.6 C impact.
So while, “ENSO done it” may be improper, changes in OHT at common frequencies of 2, 7 15 30, 62, 90 150, 400, 1020, 1400 and 1700 years do appear to have an impact on Earth’s energy capacity unless you happen to know the time frame that the pseudo-oscillation in charge plans on averaging out to zero.
@SteveF (Comment #115755)
I am curious to know what you believe caused the GLOBAL temperature to rise in 1998? Was it an unreported outbreak of cow farts? It appears you believe it was unrelated to the El Nino of that year. Is that the case? If so, to what do you attribute the huge spike in global temperature that hasn’t been seen since in UAH or RSS?
I don’t understand why anybody would think that dynamical changes, such as ENSO, couldn’t change the GMT on a variety of timescales. Accepting that seems easy, quantifying the impact is much more difficult and while that isn’t done it’s going to be easily (and maybe justifiably) ignored by the IPCC.
Tisdale goes too far in concluding that a few interesting regional SST observations explain global warming. But then he wouldn’t be the first person in climate science to get carried away with conclusions that aren’t justified by the evidence. He was far better when he was just presenting the wads of data.
SteveF,
If I take HADCRUT and put a 35 month smoothing on it I get essentially the same thing that you get with your adjusted series. In effect all you are doing in the assumptions you make is ironing out the lumps. Why bother trying to be more ‘physical’?
SteveF:
I am predicting that the 12 month moving average of the UAH global data will fall at or around 0.13C on Dec 2103. (Of course the actual figure will not be available until end 2014.)
Until then I am using the link provided as a quide for likely future behaviour.
It is effectively a cascaded low pass filter and zero crossing detection of the data source.
Ok. So 2103 is a little too far in the future. Dec 2013 is what I asked my fingers to type!
SteveF,
Congratulations on an interesting post.
Just one question: How did you “detrend” the 1950 to 2012 data before fitting parameters and avoid circularity in the process?
SteveF,
On your little debate with Bob Tisdale, I would caution you against throwing out the baby with the bathwater.
There is evidence that the various ocean cycles have a direct effect on incoming radiation via cloud modulation. I have yet to see a convincing explanation of why there was a large observed decrease in albedo and a corresponding increase in incoming SW between 1980 and 1998. This may mean that these cycles do a lot more than just redistribute internal heat.
SteveF says: “What is not OK is for you to sidetrack a marginally related thread with repetitive (and loony) arguments about global warming being all due to ENSO.â€
Sidetrack? My comment was not marginally related. I started off with quote from Trenberth et al (2002) that cautioned against using regression analysis to remove the effects of ENSO. I also included a quote from Compo and Sardeshmukh (2010) that stated that you can’t remove the effects of ENSO through regression analysis. You’ve chosen to ignore them both in your replies to me.
SteveF says: “…please explain why you think Figures 3 and 4 above do not show reasonable linearity between ENI and tropical temperatures.â€
If we look at the tropical sea surface temperature data for the East Pacific (24S-24N, 180-80E) and the Indian-West Pacific (24S-24N, 30E-180) Oceans we can see two things:
http://i39.tinypic.com/2nl7nf6.jpg
(1) that you can remove the ENSO signal from the tropical East Pacific data.
(2) that you cannot remove the ENSO signal from the tropical Indian-West Pacific data, because the sea surface temperatures there do not cool proportionally during the La Niña events of 1988/89, 1998-01 and 2010/11.
And why don’t they cool proportionally during those La Niña events? Because there’s leftover warm water from the El Niños. It’s blatantly obvious in the following JPL animation of sea level residuals after the 1997/98 El Niño, which captures a Rossby wave returning the leftover warm water from the eastern tropical Pacific to the west:
http://bobtisdale.files.wordpress.com/2012/06/animation-3-1.gif
And for example, where did the warm water come from for the 1997/98 El Niño? It came from the 1995/96 La Niña. It’s blatantly obvious in the ocean heat content data for the tropical Pacific, which should be relatively realistic from the early 1990s on with the TAO project:
http://oi46.tinypic.com/sqtslz.jpg
Note: The other sharp rises in that graph are responses to the 1954-57, 1973-76 and 1998-01 La Ninas.
Did downward longwave radiation supply the energy for the 1995/96 La Niña? No. Downward shortwave radiation did:
http://oi45.tinypic.com/2r5chi1.jpg
If you had bothered to read Trenberth et al (2002) that I linked earlier, you would have understood that it’s sunlight, not infrared radiation, that fuels ENSO. They wrote:
“The negative feedback between SST and surface fluxes can be interpreted as showing the importance of the discharge of heat during El Niño events and of the recharge of heat during La Niña events. Relatively clear skies in the central and eastern tropical Pacific allow solar radiation to enter the ocean, apparently offsetting the below normal SSTs, but the heat is carried away by Ekman drift, ocean currents, and adjustments through ocean Rossby and Kelvin waves, and the heat is stored in the western Pacific tropics. This is not simply a rearrangement of the ocean heat, but also a restoration of heat in the ocean.â€
SteveF says: “For the record: I understand very well what you think about the influence of ENSO, and I am utterly unconvinced by your arguments. In fact, I find them to be nonsensical gibberish that betray a complete lack of understanding of science in general. The likelihood of significant warming driven by radiative forcing is something you ought to grips with, if only to stop embarrassing yourself. I am quite certain you won’t ever do that, and that is OK with me.â€
Since we’re taken off the kid gloves… Actually, I don’t believe you understand what I present. Your beliefs in the assumed effects of radiative forcings on the ocean are so fixed that you can’t comprehend what the data shows. Downward longwave radiation data, downward shortwave radiation data, sea surface temperature data, ocean heat content data, cloud amount data, trade wind direction and strength data, sea level data, ocean current data, depth-averaged temperature data, warm water volume data, sea level pressure data, thermocline depth data, etc., all agree with my understandings of ENSO. In other words, my understandings of the “science in general†of ENSO and what causes the oceans to warm are supported by data.
SteveF, it appears you’ve replied to Kristian (Comment #115804) in boldface within his comment without identifying yourself. You may want to clarify that.
SteveF says: “I carefully avoid commenting on Bob’s many posts at WUWT, and this is no coincidence, because any comments I made it would be a waste of his time and mine. I do hope he will do the same here.â€
Actually, I’d welcome your comments a WUWT. There are a good number of persons there like Kristian who understand what I present. Maybe their replies to you would help, since my presentation and discussion of data is apparently not getting through.
SteveF says: “No, just some reading of his many posts at WUWT; I do become frustrated when he posts the same things over and overâ€
SteveF, I’m not writing my posts with you in mind. Any repetition is provided for the persons who are new to WUWT and there are newcomers there daily. If my posts frustrate you, there’s a simple solution. Stop reading them.
Regards.
Paul_K,
Thanks.
The detrend was just subtracting the product of the 1950 to 2012 slope and the time since 1950 from each data point. This of course introduces the potential for overfitting (and “circularity”) since the implicit assumption is that the overall secular trend is linear with time, and it obviously is not perfectly linear; the final adjusted trend is by no means linear. You could assume another secular trend, or better, add one or more variables (like an estimated net GHG forcing history) and then not detrend the temperature data. I was thinking of using the GISS forcing history (less volcanoes) as the fourth variable and see how the regression results turn out. The difficulty is that the low pass type lag function becomes increasingly inaccurate for forcing of longer duration.
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WRT the baby vs the bathwater: I have no doubt that there is the potential for a significant contribution to the temperature history from cyclical (or pseudo cyclical) behaviors. What I object to is the bizarre insistence that ENSO is responsible for ALL warming, and the sad reality that no amount of discussion is going to make any difference.
SteveF: I was wondering if anyone did every managed to cross calibrate the sattelite to the thermometer temperature data in their overlap period and then back applied that correction to the longer therometer series then a different view of history would not appear?
All,
http://redneckphysics.blogspot.com/2013/06/on-ocean-heat-transport-stumbling-block.html
That Oppo Ido-Pacific Warm Pool reconstruction should provide a little insight on ESNO impacts on “global” average temperatures.
Bob Tisdale,
WRT my figures 3 and 4: you did not even answer the very simple question that I asked, so I will ask again: where in figures three and four do you see any indication of nonlinearity between ENI and tropical temperatures? I showed in the post that the ENI appears to predict a large part of the variation in tropical temperatures. Your (many) comments and links about where and how heat is distributed during ENSO is utterly irrelevant to the content of my post.
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WRT identifying myself on Kristian’s post: I thought it was very clear, but I will try to edit the comment again to explicitly identify myself. I can’t do that from the computer I am presently using.
.
WRT the rest of your comments: Please do not waste your time and mine with more of the same. I will not be leaving comments on any of your post so long as you maintain your ENSO monomania.
Jim2,
I don’t think you understood my post. Of course the temperature spike in 1998 was due to a very strong El Nino. Figures 2, 3, and 4 in my post show the tropical temperature increase associated with that El Nino. The influence on global temperatures is shown in figure 11 (the light blue line is the global influence of ENSO). Yes, the spike from that El Nino was stronger than any since then because that was a stronger El Nino than any since then. The analysis I did was based on the Hadley temperature history, not the satellite based lower troposphere (which is only available since 1979). The lower troposphere does appear to react a little more strongly to ENSO than does the surface temperature, which I don’t find surprising.
Richard LH,
I don’t know if anyone has done what you suggest ( generate a ‘synthetic’ satellite history), but you could certainly try.
SteveF: I not trying to generate anything. All I am suggesting is that if you add low pass filter stages and zero crossing detection to the end of the processing required to get to the UAH Global data series (the same as you would do to any other noisy data source to reveal potential underlying structure) then short term, repetative patterns emerge that are worthy of further investigation.
With cycle counts of only 10, 4, 3 and a potential half I cannot think of any statistics that will prove it right or wrong.
Time alone will tell.
SteveF: If I am right then we are in cycle 10 of ‘Climate Summer’ with Dec 2013 being ‘Climate Autumn’ in the sattelite record.
HR 115862 and 115867),
I have no problem with cyclical (and pseudocyclical) influence on temperatures… on a range of time scales. I agree that Tisdale was better when he just posted data… some of it was actually interesting/useful.
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WRT smoothing and why bother: Sure, a 36 month centered average or something similar will remove most of the short term influences like ENSO. The longer term volcanic influence will be reduced but not removed by that filtration. Here is a direct comparison: http://i44.tinypic.com/2vxinw6.jpg (sorry, I used 37 months instead of 35 by mistake, but that shouldn’t make much difference).
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The volcanoes stand out pretty clearly in the blue trace, even while the short term variability is mostly gone. As to whether those two curves are “essentially the same”: I can’t say that I agree they are; they look pretty different to me. As to why use a more physical rational: The objective was to show that a regression analysis to remove known influences as best possible, if done in a more reasonable way, yields much slower recent warming than in the 1979 to 1997 period, contrary to the result from F&R. Which, by the way was done in a remarkably non-physical way, IMO.
@SteveF (Comment #115892)
When the Discovery AMSU web site was working, i.e. when the lower trop sensor was working, if you looked at the temp at various altitudes, the largest temp changes were in lower trop. At higher altitudes, the change was muted until at a certain height, the changes over a year were flat. Then the annual temp curve inverted. Unfortunately, the surface channel isn’t reliable, but I have to wonder why since solar energy heats the land directly, that the surface changes wouldn’t be greater than lower trop.
SteveF (Comment #115913)
June 14th, 2013 at 8:58 am
Here is a direct comparison: http://i44.tinypic.com/2vxinw6.jpg
And if you add 12, 16, 21, and 28 month averages to the same graph in addition to the 37 month one?
http://s1291.photobucket.com/user/RichardLH/story/70051
1. Why are you using sunspot numbers to estimate solar forcing when solid TSI estimates (on a much sounder scientific basis) are available? See, e.g., Wang et. al. (ApJ 2005), or anything by Krivova in the last 15 years. http://rhinohide.org/gw/publications/models/Hateren/skydrive-2012-05-16/data_complete_21Nov2011/TSI_WLS_mon_1882_2008.txt
2. Regardless of Carrick’s comment, there is some residual correlation between ENSO and extra-tropical temperatures at a lag of about 8 months. Thus by fitting your correlation to tropical temps only, you’re underestimating the effect of ENSO on global temps. I.e, there is still ENSO in the global signal that you haven’t removed.
SteveF kindly sent me the time series that he obtained in his fitting. I was able to use this along with the HADCRUT4 data series over the same interval to compute spectral periodograms:
Figure
I always find it useful to see what frequency components a filter is actually removing.
Note the 11 & 22 year spikes that are reduced by the filtering are probably associated with solar forcing (the period of solar forcing is actually 22-years, the period for sun-spots is 1/2 of this).
I should also add that the whole volcanic aerosol thing is a very tricky business, much more so that is usually modeled, and not only by you. The unmodeled issues are the latitude of the erupting volcano and the time of year. A volcano that erupts in the Arctic winter may put out a lot of aerosol, but if the Sun doesn’t shine on it, it won’t have any effect on global temperatures. A volcano that erupts in the tropics can have a much greater effect, even if its aerosol load is less.
jim2,
Sunlight heats both the troposphere and the surface (clouds and water vapor both absorb solar infrared, and atmospheric aerosols (dust, soot, etc.) strong absorb both visible and infrared. Nothing close to 100% (on average) reaches the surface. Of course you need to be a little careful in comparing the lower tropospheric temperatures and surface temperatures, because while they show similar relative trends, the lower troposphere is on average MUCH colder than the surface, with the temperature dropping with altitude according to the atmospheric lapse rate (averages about 6.5C per kilometer, IIRC). So if the lower troposphere has an average altitude of ~5 Km, then the absolute temperature will be in the range of 30C colder than the surface. There are larger swings in the lower troposphere than at the surface, if only because the surface has much more heat capacity than the lower troposphere.
.
The change from greater warming to flat temperatures and then inverted temperatures at increasing altitude has to do how heat flows through different parts of the atmosphere. In the troposphere a great deal of heat is transported upward via convection (both dry and moist convection), while above the troposphere, there is very little thermal convection, and heat is mainly transported by radiation. GHG’s influence the flow of heat via radiation.
KAP (Comment #115929),
1. I was not aware that data was available; I will compare it to the calculated values from SSN. I note that there does appear to be some disagreement between solar researchers on how much intensity varies, especially before 1950.
.
2. The index I used was fitted independently to both the tropics and the global temperature (the analysis including volcanic, solar, and ENSO was global). I set the low pass filtration constant (‘k’ in the post, used to calculate the ENI) using only tropics because I figured that using the global temperature history would introduce a lot of uncorrelated noise and make the determination a lot less certain. The correlation coefficient value for the global average was in fact a little larger than the expected value of half the value for the tropics, which indicates some (modest) influence outside the tropics. If I get a chance I will try determining the lag constant for calculating the ENI based on the global data and see how it compares.
KAP:
As long as you leave it as “some ENSO in the global signal that you haven’t removed, you’ll always be right. 😉
Anyway here’s the figure Steve was referring too.
What this actually says is there isn’t a significant linear response at latitudes outside of the tropics. So if there is significant ENSO signal with an 8-month lag, it most likely is associated with a nonlinear response.
Obvious Steve if using a linear model here, so adding an 8-month lag would “do nothing”.
Carrick,
Thanks for that graphic. I can understand the 11 and 22 year reductions, but I am a bit puzzled by the drop at 8 years. Any ideas?
.
By the way, the variation in solar intensity that I used most certainly does have an 11 year intensity cycle, even if the true solar cycle (in a mechanistic sense) is 22. 😉
KAP (Comment #115931),
I think (but am not sure) that the GISS volcanic forcing history takes that into account.
KAP,
Here is a comparison of the SSN based model I used and the data from the link you provided:
http://i41.tinypic.com/2qn1un5.png
There are some smallish differences, but nothing that will have a huge impact on the regression.
This is an argument that pits one foolishness–that ENSO has practically no effect upon surface temperatures outside the tropics–against another–that ENSO drives climate change.
Should those in the debate ever come to grips with entirely noncontroversial oceanographic facts they will discover that the transport of tropical heat by the wind-driven anticyclonic gyres in the Pacific has a profound effect on SOME areas not only far from the tropics, but (via little-undersood couplings) far from the Pacific , e.g. SE Africa. Nevertheless, ENSO-related processes represent nothing more than the REDISTRIBUTION of heat around the globe–not its alteration.
Sky,
You apparently did not look at Carrick’s graph showing correlation and lag time…. Or did not understand its implications. It is pretty clear from comparing any commonly used ENSO index with temperatures outside the tropics that any influence of ENSO outside the tropics is quite small. If you think there is a clear case to be made for strong influence outside the tropics, then I suggest you make it, rather than referring to ‘foolishness’.
SteveF, ” It is pretty clear from comparing any commonly used ENSO index with temperatures outside the tropics that any influence of ENSO outside the tropics is quite small.”
Right, ENSO represents a small area with the highest heat capacity of the globe. Changing the majority of the heat capacity of the globe has a small impact outside of the tropics. Either the index is less than ideal or your model sucks.
https://lh6.googleusercontent.com/-iOhbCX_6tjo/UbxoLm4bU9I/AAAAAAAAImc/55why0mp6Lc/s803/giss%2520and%2520ersst.png
The tropical SST is in orange, 1915ish was a common perturbation, watch how the regions respond. Notice how the northern extratropics “hunts” producing “noise”.
Oops, I got the GISS baseline wrong. This climate stuff is so baseline dependent it is hard to get any “robustness”.
https://lh5.googleusercontent.com/-Zt1oH-PdG38/Ubx-Yc4PFjI/AAAAAAAAIng/B7BvlEPm0kY/s809/giss%2520and%2520ersst%2520with%2520ipwp%2520baseline.png
There is the correct 1915 to 2010 baseline plus the Indo Pacific warm pool reconstruction.
https://lh4.googleusercontent.com/-WJiDVg2R0KM/Ubx8SnnJOxI/AAAAAAAAIm4/ejLd98zWmpM/s800/giss%2520and%2520ersst%2520with%2520ipwp.png
According to the Oppo recon 1700 was close to the bottom of the LIA
https://lh6.googleusercontent.com/-0Ljwh9NTkS0/Ubx9dAfZtAI/AAAAAAAAInM/UROadZys8_k/s800/giss%2520and%2520ersst%2520with%2520ipwp%2520from%25200%2520ad.png
The actual decent into the LIA probably started around 1600 AD. The MWP wasn’t particularly hot “global” using the IPWP as a “proxy”, but it was pretty “normal” for the Holocene. I believe that is consistent with most analysis. The recovery from the depths of the LIA though might be a tad more significant than some might think. That would make today’s climate pretty normal for the Holocene and the majority of the instrumental record abbynormal, probably the reason that climate is so baseline dependent.
With a “normal” ” climate” range of +/- 0.4 C or there abouts and a margin of error of +/- 0.25 C or there abouts, some of this exotic noise analysis is like pissing yourself in a dark suit if you are concerned about “climate”. For “weather” that is another story.
Hmmm? Long term persistence anyone?
dallas,
I have read over your two most recent comments twice and looked at the graphs. I honestly have not a clue what you are trying to say. Can you repeat, as clearly as possible, what your basic message is?
SteveF “That’s quite enough to know that he is mistaken. It is impossible for greater radiative forcing to not cause warming (except in the case of an actively controlled system.. like a mammal’s body temperature).”
Steve, with that comment you have hit the nail on the head. Your impression that Tisdale is talking “nonsense” is based on _your assumption_ that the system can by treated as governed by simple linear feedbacks.
An assumption that is shared by F&R and the rest of the IPCC AGW crowd and one that is long over due for a serious revision in view of the fundamental failure of models based on that assumption.
Now I’d rather avoid getting into the pro’s and con’s of BT’s hypothesis here, but the question of non linearity is very relevant to your post too. So let’s focus on that.
The whole assumption of a linear response to major volcanic events (or other radiative changes) seems to be a grossly simplistic and unwarranted assumption.
Following up on an idea by Willis Eschenbach, I overlaid tropical SST data for the six biggest events represented in the volcanic record you used above. Dates are aligned using year only, so like months are averaged irrespective of the precise date of the eruptions, since the interaction with annual seasons is more important that the exact delay since eruption.
The result was quite a surprise:
http://climategrog.wordpress.com/?attachment_id=278
I was expecting all the climate ups and downs to roughly average out leaving some detectable volcanic signal plus ‘noise’. What I got was a clear, repetitive pattern with the eruptions falling about half way between two stronger peaks separated by about 11 years.
Now that has huge implications of its own but for the moment I’d like to focus on the implications for linearity and detection thereof.
The first problem is that there is regularly aligned trough about two years after the “average” eruption. This pattern is clearly established both before and after the events so cannot be caused by volcanic debris.
This leads to strong possibility of false attribution and I would suggest this is what most of climate science has been doing for at least the last 30 years, and you have essentially reproduces above.
It is quite difficult to asses how much volcanic effect is present in that graph though there are grounds to see some deepening of the post eruption trough. One thing is sure, it’s a lot less than is usually ascribed.
>>
Volcanic: 0.2545 +/- 0.0277
Solar: 0.233 +/- 0.231
R^2 for the regression was 0.445 (44.5% of the variance was accounted for by the model).
The much greater uncertainty in the solar influence is due to the solar forcing being quite small compared to the other two.
>>
Solar: 0.233 +/- 99% !!?
There are a number of other reasons for that result. Your conclusion that it is due to it being small seems very speculative.
In view of the volcano stack plot I will offer you another one:
Due to the previously undocumented synchronicity between natural climate variations and major volcanic events there is a false attribution of much of the change to volcanism. This equally leads to false estimation of the optimal fitted value and decay time. Imposing the same model (of combined solar and volcanic) on solar leads to a very poor fit to the solar signal.
I’m not stating that as a certainly, just another equally speculative reason which I hope makes the point about false attribution.
I’ll show a bit more about non linear climate response to radiative forcing shortly.
Here is the cumulative integral based on the volcano stack. This makes it a lot easier to see whether the linear response assumption is reasonable.
http://climategrog.wordpress.com/?attachment_id=310
some explanation is required to know what we’re looking at so please read the notes. A quick resume here:
The cumulative integral is level for a constant temperature, downward slope shows cooling , upwards warming. A constant lower but flat integral indicates return to the previous temperature but with loss of degree.days (this can be related to farmers’ use of this as an indication of growth days).
Warmer, cooler relative to what? …
The green lines represent the average temperature for the four years preceding the “average” eruption of the stack plot. This period was chosen to avoid the notably larger peak at -5 years.
For similar reasons I would tend to discount the apparent warming after 6 years which may not be sustained.
So what does this tell us about climatic reaction to a major change in radiative forcing?
NH extra tropics: initial cooling from 6m to about 3.5 years. Fairly flat around 4 years out meaning SST has _recovered_ to it’s previous temperature (but losing some growth days for crops. Ave. temp was down ) 5 to 8 years shows a smaller downward slope of 0.5K.year ie an average drop of under 0.2 K.
Well for tropical NH there is cooler SST from about 18m to 2.5 years after eruption. Then warming to 4 years. by which time there is a flat (same SST as pre-eruption period) but more importantly a total recovery of the number of degree.days. ie. not only has temperature recovered but the _average_ temperature of the whole eruption period is the same as if nothing had happened.
Now that, my friends, is not a “linear” system. In fact it is much closer to being “.. like a mammal’s body temperature”.
It also demonstrates what happens in the tropics reflects an increase in the existing rhythm of ups and downs that manage not only to recover the surface temperature but also maintain a constant average SST despite the massive disruption to incoming radiation.
Now I have not identified those ups and downs with El Nino/Nina events but is seems to clearly demonstrate the principal that larger swings can inject energy into SST.
SteveF,
The discussion should be either “climate” or “weather”. When you say that, ” What I object to is the bizarre insistence that ENSO is responsible for ALL warming, and the sad reality that no amount of discussion is going to make any difference.” you seem to be forgetting what ENSO is an index for changing conditions in the tropics which control the vast majority of the heat in the system.
ENSO is not responsible for “all” the warming or anything, but it is an index for “most” of the energy available for warming. If you look at the charts again, the ENSO region has been warming for a long time.
To complete the volcano evidence here is the same thing for SH.
http://climategrog.wordpress.com/?attachment_id=312
Essentially the same except extra tropical southern hemisphere ends up with a full recovery of SST (and similar loss of growth days).
Since land does not have self regulating capacity of oceans the larger land area of NH seems to be responsible for the net cooling effect of volcanoes noted above.
In conclusion: tropics are totally self regulating “like a mammal’s body” , extra-tropics benefit from this stabilising influence but do lose growth days and average temperature drops during the period of reduced radiation.
Net cooling is limited to temperate regions of NH.
This highly non linear, self-regulation reaction to variations in radiative forcing will lead to serious miscalculation and false attribution if not accounted for.
The presumed and strong negative response to volcanism will lead to an equally incorrect assessment of the effect of AGW since the two counter each other.
In view of the non linear nature of the climate response, the very concept of “climate sensitivity” which is essentially a result of the erroneously assumed linear model.
Oops, last sentence should have finished: In view of the non linear nature of the climate response, the very concept of “climate sensitivityâ€, which is essentially a result of the erroneously assumed linear model, becomes irrelevant.
Greg,
SteveF hasn’t assumed the entire climate system is governed by a simple linear feedback.
I’m confused. Are you suggesting that the eruptions themselves just happen to fall bewteen two natural peaks in weather oscillations? So, it’s just a big coincidence that a whole bunch of eruptions happened to go off in the middle of whatever other oscillations you think happened? (Because I’m not understanding what you think you have shown.)
Lucia: SteveF hasn’t assumed the entire climate system is governed by a simple linear feedback.
Thanks Lucia , but I think you’ll find he has.
>>
The best fit regression (with K = 0.031) yields the following constants:
ENI: 0.1099 +/-0.0118 (+/- 2-sigma uncertainty)
Volcanic: 0.2545 +/- 0.0277
Solar: 0.233 +/- 0.231
>>
It may not be explicitly stated like that. I think this is now so ingrained in climate thinking that it no longer gets stated explicitly, it’s “obvious”. Unless I’ve misread what he’s presenting, those “constants” are from linear regression of his three variables onto the climate record. They are degrees/W/m2 “sensitivities”.
He dismisses Tisdales ideas saying they could not work unless the system was non linear. So I think it was clearly his interpretation that climate is linear.
I think I’ve clearly shown it is not.
“So, it’s just a big coincidence that a whole bunch of eruptions happened to go off in the middle of whatever other oscillations you think happened? ”
Rather than dismissing this as what I “think” happens perhaps you could comment on the data. Tell me what you Think explains what is shown in the graphs .
I’m very interested in any reasoned criticism or if someone can point out another interpretation. Whether this “just happens” or happens for some as yet unexplained reason, or can be shown to be an artefact of the data processing is a very significant question.
If you are confused, have you understood how the plots were generated and what it shows?
Lucia: Because I’m not understanding what you think you have shown.
There’s a lot to be drawn from this analysis , so I’ve tried to cover the main points, even that got a bit long. That’s why I suggested reading comments attached to the graphs.
What I have shown is that if you average out the roughly 2.75 year oscillation in the stacked data by integrating (a kind of low pass filter if you like), the actual dip that is attributable to eruptions is small and short lived.
I see three clear and important results.
1. That there is a residual pattern, not just noise plus a cooling dip.
2. That the dips are linked in time with the eruptions meaning unless this is accounted for there will be false attribution.
3. Once the data is averaged on a regional basis, the tropics are fully self regulating. Even recovering to the point where the average temperature across an eruption does not drop. That implies a strongly non linear response.
The latter is probably the most important result and the most far reaching.
I don’t consider asking you to further explain what you think the data are saying is diminishing “what you think” by asking you what you think.
I have no idea what your graph explains. For all I know what you are showing is an artifact of processing.
I read the post. You describe what you did as
So: No I’m not entirely sure what you did. But it sounds you kinda sort of overlaid stuff by years with eruptions but aligned months. So: Jan 1883, Jan 1902, Jan1912 and so on are all on top of each other. Or not. After that brief description you explain what you think the graph shows.
Greg–
No. As an approximation used in a statistical fit, he is fitting the response to volcanoes to a linear response function. This is not the same as believing the climate system as a whole has a linear response function to everything.
http://rankexploits.com/musings/wp-content/uploads/2013/06/Figure7.png
http://www.woodfortrees.org/plot/rss/derivative/mean:24/mean:18/mean:13/plot/gistemp/derivative/mean:24/mean:18/mean:13/from:1979
The largest +ve rate of change in WTF.org plot are centred on 1986.5 and 1997.5 , those match the up swing of the SSN plot. Equally the biggest -ve rate of change matches the sudden drop in SSN.
As others have remarked before, these cooling events that are usually attributed to volcanism are already happening before the eruptions. As can be confirmed by doing a shorter 12/9/7 month filter on the same data, the down turn started after the peak SSN just before 1990. You can even see a shoulder due to the secondary peak in SSN in 1990 before it really drops hard.
Note here I’m plotting dT/dt , since that is a power term and SSN is being taken a proxy of solar radiative power.
Perhaps F&R were not correct in finding a very short delay if they were looking at temperature but in fact all these comparisons should be done on dT/dt, otherwise there will be all sorts of different phase delays to account for.
There’s a lot more to this than meets the eye but let’s get on the same page before I comment further.
lucia (Comment #116098)
June 15th, 2013 at 2:24 pm
Greg–
Thanks Lucia , but I think you’ll find he has.
No. As an approximation used in a statistical fit, he is fitting the response to volcanoes to a linear response function. This is not the same as believing the climate system as a whole has a linear response function to everything.
>>>
OK, I was commenting on what was posted here. To that extent he is treating things as linear.
I was obviously not suggesting that he though every aspect of climate was linear, Stephan-Boltzmann is not, wind energy is not. I though it was obvious I was referring to what he presented here. Steve is pretty smart on the maths , I’m not assuming he’s a total idiot.
So perhaps we can accept that we are talking within the context of what was posted here.
My key point is that the climate response to volcanism is strongly non linear. That is what I was showing.
I am also commenting on what he posted here.
I don’t yet see your graph shows this. But maybe you can explain your graphs further.
Lucia, I’ve posted three rather long comments, there are full explanations of how the graphs are derived where they are shown, or linked directly. I can’t repeat all that. What bit don’t you follow?
this is not trivial so take the time to read what I’ve presented.
In terms of non linearity try to understand hadSST NH tropics cumulative integral (red line) :
http://climategrog.wordpress.com/?attachment_id=310
Now if that integral does not remain negative it means that the average temperature of that region saw no impact from the eruptions.
A linear response would show a permanent drop in temperature. A linear response, compensated by an increasing AGW forcing would eventually recover to the same temperature but would still have a lower mean because of the years it was down.
The only way it can recover to the same average temp is if there is an active control mechanism. The kind of thing SteveF used to ridicule Tisdales ideas.
What these plots show is that there is such an active (non linear) mechanism controlling tropical SST, very much like the body temp of a mammal that he referred to.
The implications of that for current climatology are huge, so if anyone can blow a hole in that interpretation by showing how it is wrong, that would be useful.
Greg Goodman,
I was away from my computer today.
.
I must admit that like Luxia, I am not really following what you are saying. But just to be perfectly clear, I do not think much of anything in the physical world has a perfectly linear dependence on one or more variables. For example, we know that blackbody radiation goes at the fourth power of temperature… Not very linear at all. Yet over a few degrees a linear function can be a very good approximation.
Linear regression analyses are routinely used, even when the processes being considered are known or suspected to be nonlinear, because over a limited range of values even very nonlinear processes are approximated pretty well by a linear response. Is the approximation perfect? Heck no! But in a broad range of fields, a linear approximation is found to be useful.
Like I said, I am not sure what exactly about the post you object to. Can you describe, in as simple terms as you can, what specific errors are in my post? There is no need to tell me all the details, I need first to understand what you object to.
Greg Goodman,
I fogot one other point I wanted to clarify: I do not reject Bob Tisdale’s analyses based on anything having to do with linear vs nonlinear responses to anything. I reject them because his conclusions are ridiculous. They are ridiculous because he concludes that radiative forcing can increase without causing some warming. Pure and utter rubbish.
SteveF (Comment #115759)
June 13th, 2013 at 9:33 am
“Yes, there is clearly a remaining TOA imbalance (http://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/) but there is no evidence of a dramatic recent increase in the rate of heat uptake which could explain the recent drop in the rate of surface warming.”
Sorry to be so late in responding to the point above, but I had to think about it a bit. Since the heat capacity of the ocean is so much greater than that of the atmosphere (~1000X), we simply could not measure the tiny increase in ocean heat uptake needed to stall the warming of the atmosphere.
Greg
I’ve read what you presented. I asked you a question. Instead of answering it, you got huffy. Then you asked me if I knew what the graph showed, I quoted what you said, said what I thought that meant and you ignored that disucussion.
Why? Can’t other forcings be acting? What happens if the volcanic eruptions is embedded in long period with net positive forcing? (Real questions– not rhetorical. I’m trying to tease out what you are claiming here.)
What if there are sustained external forcings? Or oscillatory ones? Or white noise? Or any other sorts?
How do they show that?
I’m not trying to “blow a hole”. I’m just
(a) asking you to clarify some details about what you are claiming the graphs who and
(b) asking you to clarify more fully in general and explain why you think these graphs show what you claim.
Maybe they do. Maybe they don’t. But explanations would be useful.
Solar forcing looks wrong. See Kopp and Lean (link here. Peak to valley should be about 1 W/m2
Leif’s formula, and just about everything else has to be corrected according to Leif for Kopp and Lean. Worse, SSN is turning out to be a not very good proxy.
Barry Elledge (Comment #115729)
June 13th, 2013 at 12:12 am
“The calculation of solar intensity from SSN using Svalgaard’s empirical correlation still leaves open the possibility that some other aspect of solar variability (e.g., increase in UV, change in solar wind velocity or magnitude) might contribute to the otherwise unexplained leveling off in T after the late 1990s, doesn’t it?”
These ‘other’ aspects tend to be correlated themselves with the SSN so would in a natural way just be folded into the regression.
On using the SSN instead of other [more ‘physical’] reconstructions of TSI I will point out that these reconstructions are themselves based on the sunspot number. In fact, on the Group Sunspot Number which is very likely not correct, see papers 1770, 1740, 1710, 1700, 1700, 1660 on my website.
Eli Rabett (Comment #116122)
June 15th, 2013 at 8:46 pm
“Solar forcing looks wrong. See Kopp and Lean (link here. Peak to valley should be about 1 W/m2”
But should be multiplied by 0.7/4 [albedo, sphere], so it not wrong.
Steve, I think you are misinterpreting what BT is putting forward but I’ll leave it at that for now to focus on your post.
” Is the approximation perfect? Heck no! But in a broad range of fields, a linear approximation is found to be useful.
Like I said, I am not sure what exactly about the post you object to. Can you describe, in as simple terms as you can, what specific errors are in my post? There is no need to tell me all the details, I need first to understand what you object to.”
Yes I realise that even T^4 can be approximated as linear for small dT around 300K and all the rest seems a fairly reasonable first approximation at least. All this leads to models (even highly complex GSMs which do not make simplistic approximations) that are, in effect, showing linear responses to radiative forcing.
The problem is the tropics does not actually comply. Thunderstorms, which are not reproduced in any model because of granularity are highly non-linear. Once threshold conditions are reached, strong positive feedback occurs within the the storm making it self maintaining. Since the TS itself is a neg. f/b, this makes it a strongly non-linear neg. f/b.
Willis Eschenbach pointed this out quite a long time ago calling it a “governor”. I think the volcano plots show it is even stronger than a thermostatic governor, it even manages to maintain the long term average or cumulative integral. That makes it more like an industrial PID controller. That is _probably_ the actual mechanism but let’s avoid delving into that before agreeing on what is shown in the data.
I’m not objecting to any particular step in your post, it is all pretty standard treatments using std methods. But that is whole problem and it affects the whole of current modelling attempts on the larger scale. It just does not fit the data. It is now blatantly obvious that the current modelling paradigm has failed post 2000 once we are in a period with no significant volcanism and steadily rising CO2.
I think this goes beyond the need to retune a few coeffs, I think the whole process which leads to “roughly linear” response is fundamentally wrong. Lucia has asked some specific questions so I’ll develop this further in replying to here next. I will just point out that until quite recently I was what would be called luke-warmist. I even suggested to Willis that while tropical storms are highly non-linear locally this did not preclude them acting as a linear negative feedback on the global scale. The volcano stack plots lead me to a very different position and so need thorough examination.
Lucia: I’m not trying to “blow a holeâ€. I’m just…
Oh please, do try, that is what is needed. I’m not getting huffy but I was a little irritated by your initial comments about what I “think” I’m seeing but maybe I miss read your intent. Your probing questions are most valuable.
===
“Why? Can’t other forcings be acting? What happens if the volcanic eruptions is embedded in long period with net positive forcing? (Real questions– not rhetorical. I’m trying to tease out what you are claiming here.)
===
Already covered that.
===
What if there are sustained external forcings? Or oscillatory ones? Or white noise? Or any other sorts?
===
Sustained: already covered. White noise, any random effects should be at least roughly cancelled out by overlaying and summing the six events, spanning a hundred years. Like I said, I expected this leave a clear volcanic signal and some messy noise. What came out was a big surprise. Oscillatory? Well I think this is exactly what is shown. The significant point is that these oscillations do not have random phase with respect to the eruptions otherwise they too would roughly average out. In fact that was my original motivation. We know there are periodic variations and I wanted to use the averaging effect to remove or at least diminish then to prevent false attribution that I could see was happening, particularly around Mt Pinatubo.
There remains the question of whether this pattern is just fortuitous. An accidental overlapping of various wiggles that just happens to produce that pattern. I think is unlikely but way to assess that is needed.
To recap the processing : the average temperature anomaly data from hadSST3 is taken for each of the four regions : tropical and extra-tropical for both NH,SH for a span of about 6 years either side of the six major events. The calendar year of the eruption is subtracted from each series of anomaly data and the resulting monthly anomalies are added. This is, in effect, like averaging the climate response to all the events except that I don’t divide by six. It’s just the sum. That gives the first graph:
http://climategrog.wordpress.com/?attachment_id=278
Since it is hard to determine just how much volcanic effect is added to the periodic form I used the cumulative integral to average out any repetitive signal. That gives the following:
http://climategrog.wordpress.com/?attachment_id=312
http://climategrog.wordpress.com/?attachment_id=310
Similar results are obtained from hadCRUT4 land and sea, UHA LTL, icoads SST etc. eg
http://climategrog.wordpress.com/?attachment_id=286
The clearest and most significant result here is for NH, SH tropics. They show that the even the average temperature has maintained six years after the event, despite as much as a 20% reduction in incoming radiation. The most obvious explanation is that there is a non-linear climatic response that compensates but before going any deeper into that could you both say whether you follow me so far and can understand the processing I have done to get this far?
If we can agree about what the graphs show (rather than why), then we can discuss whether is it fortuitous, what mechanisms may or may not be causing it and what it means for linearity of global climate.
Thanks.
BTW how can I get quoted text to be indented on this forum? Is it possible to get a blank line for a new paragraph?
To give some feeling for what the data looks like, here are the individual, eruption centred time series before summation. In this case ICOADS SST, tropical NH
http://climategrog.wordpress.com/?attachment_id=313
Massive volcanoes, tropical storms, perfectly stable climate regulation. Out of the strong came forth sweetness. 😉
A fine article and analysis, food for thought. Fig 12 is the killer graph – impressive fit. It would be interesting – at the risk of making the post Bob Tisdale-like in terms of hundreds of figures – to make versions of fig. 12 aligned to the separate forcings individually, i.e. ENSO only, Volcanic only, solar only. My guess is that ENSO by itself would align quite well to HadCrut.
Greg,
Use [blockqoute]…[/blockqoute]
change square brackets to angle brackets
Leave a blank line with ‘new line’ ‘space’ ‘new line’
Many thanks. 😉
Â
Still not getting a clean line break unless I add ampersand nbsp; , rather laborious.
Greg Goodman,
Well, I agree that what you are presenting seems quite extraordinary and demands explanation, but I am still not quite understanding the processing you have done nor the implications. Are you mean-centering the temperature data in some way, or are you retaining the unadjusted anomaly information before summation? If you take 6 samples of years at random, and repeat what you have done (as though they were volcano years) do you see the same apparent oscillatory behaviour? If (instead) you take 6 samples of years deliberately selected to be two years prior to a major downspike in tropical temperatures, and do the same thing do you reproduce the oscillatory behaviour? Do your 6 volcanoes by coincidence or other all happen to have occurred at the same relative time during the solar cycle?
If you are not aware of the fact, you might note that the power spectrum of tropical air temperatures at the lowest elevations does apparently exhibit an oscillation at 2.75 years. See here for example:
http://users.cms.caltech.edu/~hou/papers/CLIDY-2013.pdf
It may be that because of your temporal shift and averaging process that you are losing the volcano signal in the noise.
I have a couple of comments to add regarding linearity because I think there is a misunderstanding of the canonical form of volcano response under the assumption of a linear response, but I will defer that until I understand what you are showing here.
Using same processing on SSN is also revealing , I’ll get back and explain the processing again.
http://climategrog.wordpress.com/wp-admin/post.php?post=317&action=edit&message=1
SteveF” Are you mean-centering the temperature data in some way, or are you retaining the unadjusted anomaly information before summation? ”
No, just taking the regional mean anomaly for each eruption period as a time series, subtracting the integer year of eruption from dates of each time series to overlay them, then averaging each month for the six data sets.
“If you are not aware of the fact, you might note that the power spectrum of tropical air temperatures at the lowest elevations does apparently exhibit an oscillation at 2.75 years. See here for example:”
Looks interesting and thorough but I’ll need time to digest that paper.
SteveF “It may be that because of your temporal shift and averaging process that you are losing the volcano signal in the noise.”
I don’t understand that. I am specifically aligning the temperature records on eruption years. That should average out any other non-synchronous variations and “noise” and emphasise the volcanic effect, not lose it. That was the aim of applying this method.
There could be some dephasing of a few months relative to the precise eruption data (March , June or whatever) but that will be small in relation to the duration of the atmospheric effect which lasts several years.
The important seasonal effect (warmer winter , cooler summers) was the reason I chose to retain calendar month alignment. Again, that should strengthen the visibility of any volcanic effects.
Eli Rabett (Comment #116122):
“Solar forcing looks wrong. See Kopp and Lean (link here. Peak to valley should be about 1 W/m2”
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No, Eli, the Earth is not flat and black. As SteveF writes:
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“If we assume Earth’s albedo is 30%, and average over the entire surface (a factor of 4 compared to the cross-sectional area Earth presents to the Sun)”
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Peak to valley should be about 0.15 W/m2 as in Steve F’s figure 7.
Greg Goodman, “The problem is the tropics does not actually comply. Thunderstorms, which are not reproduced in any model because of granularity are highly non-linear. Once threshold conditions are reached, strong positive feedback occurs within the the storm making it self maintaining.”
It is more than just the tropics, the NH oceans are 3 C warmer than the SH on average. If you use 26.5 C as a convective triggering potential, the hemispheres are at different positions relative to the control point. So you have different hemispheric “sensitivities” to different forcings. With a larger hemispherical difference , the QBO, that pesky 29 to 30 month pseudo-oscillation, impact varies. That changes the SSW event intensity and regularity which is a NH primary “relief” valve.
Dallas” If you use 26.5 C as a convective triggering potential, the hemispheres are at different positions relative to the control point. So you have different hemispheric “sensitivities†to different forcings.”
I did not mention a fixed trigger temperature. I would imagine there are other relevant parameters such as SLP and wind patterns since wind is a major part of the +ve feedback. Without digging too deep into exactly modelling what and why my graphs don’t show much difference between tropical NH and SH, more so in extra-tropics which I suspect is to do with land ratios.
My key aim at the moment is to confirm or refute the apparent self-regulation of the tropics. That, if it is confirmed is a game changer for current climatology thinking.
Greg Goodman
Uhmmm… I asked a question. This does not supply me the answer to the question. Where do you think you already covered it?
If you think this answers it it doesn’t:
Why wouldn’t an increase in AGW forcing result in an increase in the cummulative degree days? (Assuming we are still discussing that graph? Or some other graphs?) Maybe you need to do a post where you clearly discuss what you are doing quite specifically– with all the details in one place– and what this metric you are using does under some hypothetical circumstances. That is: Use synthetic data and show us what your analysis picks out and why.
As I said: No. You haven’t covered it.
You may think this is the only question that remains. But I don’t think you’ve even show what happens to which graphs under sustained forcing. (Also: It would be better to collect all your arguments in one post rather than presenting it by writing a series of comments all linking to different graphs in different posts, none of which itself contains a full argument. I don’t know what your full argument is. Naturally, if I don’t know what it is, I can’t ‘take it apart’. This doesn’t mean your argument is right: it means I don’t entirely know what it is.)
But you aren’t aligning the eruptions themselves. At least one happened in March. Another in November. If your volcanoes are spread out over a year, then the response is going to be smeared out over a year. It might not matter if the dip and recovery was something that takes 10 years, but you are looking for a dip in the viscinity of 2-3 years later. Averaging that dip over a year and showing monthly data that is misaligned is going to smear things considerabily. (If you do some monte carlo with hypotheticals you’ll see that.)
Lucia:
Now you indicate you’ve read it and disagree, we can discuss it.
A steadily increasing forcing would lead to a parabolic increase in CDF. If it was strong enough to compensate a 20% drop in solar input over a short scale like six years, it would be clearly visible in the preceding 6 years too. It is not.
The averaged initial drop does not even go negative until about 18 months and it’s back up to zero at 4 years. Any AGW effect would have to be massive to account for that and would then continue in parabolic fashion beyond 4 years. This is most decidedly not happening.
The reaction in the tropics is an active non-linear one and cannot be explained by linear volcanism vs linear AGW.
SteveF,
I’ve been meaning to follow up on earlier comments, but other things intruded. I’m impressed by what you’ve done – I think it’s a good thing to be doing and you’re doing it carefully.
I’d press the point though about the period, and Foster’s restriction to post-1979. I take your point about less data giving a less reliable regression, but Foster’s case has merit too. It’s seen in your Fig 12, where you are fitting detrended Had to the forcings. Detrending is meant to take out secular variation which the zero mean (approx) short term forcings would have trouble reproducing. But it doesn’t do it very well here – there is a dip in the middle. It’s too long term for ENSO; volcanoes don’t match and solar is too small. Something’s gotta give.
What gives are the end regions. The fit struggles to get away from the mean line, so it underlies near each end, and overlies in the middle. But it seems to come back to a good fit at the now end, and I think this contributes to the “pause”.
I’d suggest trying different intervals, and in particular starting 1979.
Is it? Have you tested that assertion?
You avoid quoting the bit where I explained why I’d chosen keep seasons aligned and then make an assertion without having looked at the data. Not very helpful.
There is a notable warming of January or February in NH following an eruption. A similar cooling of the hottest summer months. If I align as you suggested that would tend to blur the volcanic signal. I’ve looked at the data, described that effect and explained the alignment I used on that basis.
Owen,
“Sorry to be so late in responding to the point above, but I had to think about it a bit. Since the heat capacity of the ocean is so much greater than that of the atmosphere (~1000X), we simply could not measure the tiny increase in ocean heat uptake needed to stall the warming of the atmosphere.”
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The problem is that the only measure of imbalance that we have is the measured heat accumulation in the oceans. If you accept that measured rate of uptake is good enough to say there is no evidence of a drop in imbalance (and I agree, there is no indication in a reduced imbalance) you can’t at the same time say the data is so poor that we can’t see an increase in that imbalance. The counter argument is that the data are not good enough to detect a fall in the imbalance. It is very clear there has been a large decrease in the rate of warming, and the discrepancy between GCM projections of warming and observed warming has reached the point where a reasoned explanation is required. The climate science community is aware of this.
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The whole point of my post was to show that the explanation offered by F&R simply does not stand up to even the mildest of critical analysis; it is flawed in several ways and inconsistent with the best available data. The simplest explanation, and one which I think most likely correct (because it is the simplest), is that the GCM’s have greatly overestimated positive feedbacks.
“…but you are looking for a dip in the viscinity of 2-3 years later. ”
A smooth exponential forcing variation as SteveF uses here of that sort of duration would be slightly broadened by introducing an “error” of +/- 3months. It would not be any less in the integral and would be no less visible.
Nick Stokes,
Thank you for your constructive comments. I appreciate the issues associated with using a linear detrend, and there are no simple solutions save for adding a plausible radiative forcing history as a fourth variable, and that introduces other issues. ( see my reply to Paul_K above). I had considered doing the analysis over a shorter period (and I may still) but did not try that because at any credible lag, the influence of volcanoes starting in 1964 would leak over into an analysis starting in 1979, distorting the results.
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But I hope you don’t lose sight of the main issues with F&R: by allowing ANY lag for each variable and disconnecting the solar cycle from radiative forcing, they are allowing the regression to almost perfectly match the linear secular trend that they assume at the outset. I was (and remain) astounded that an analysis and results which are so obviously physically implausible would not have been noticed by the authors, editor, and reviewers. Had I been the editor, I would not even have bothered to send the paper out for review…… it is IMO that bad.
SteveF: ” The simplest explanation, and one which I think most likely correct (because it is the simplest), is that the GCM’s have greatly overestimated positive feedbacks.”
I fully agree. The main reason to use hypothetical positive feedbacks that have no basis in observation, stems from the need to balance the volcanic forcing. Unless there is a flaw in my analysis, that too has apparently been greatly overplayed.
During a period where both exaggerated forcing are applied together this can work to within rough degree that models kind of reproduce something like recent climate (ie very approximatively).
Once there is a period with only one, the illusion that the estimates are about right falls apart. It has taken the time since Mt P. effects subsided for this to become irrefutably obvious.
It is just this imbalance that prompted me to examine the volcano reaction more closely. If it stands up to scrutiny it will explain a lot.
SteveF (Comment #116150)
June 16th, 2013 at 6:33 am | Reply w/ Link
The simplest explanation, and one which I think most likely correct (because it is the simplest), is that the GCM’s have greatly overestimated positive feedbacks.
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why are there not any models that test negative feedback? why do they all assume positive feedback? surely it would be a reasonable exercise to include negative feedback in some of the models, lower the estimates for aerosols and train them on the data before 2000 then see how well they forecast after 2000.
I expect they (negative feedback models) will do a much better job going forward from 2000 than the positive feedback models.
5 of the 6 major eruptions you looked at coincided (coincidentally!) with El Ninos – which peak around New Year and it takes the best part of a year for their heat to reach the poles. Just bad luck I think.
Makes me wonder about blaming Ice Ages on Milankovic cycles come to think of it.
fred burple,
There are well known positive and negative feedbacks, and GCM’s already have both. The issue is that some of those feedback are very uncertain in magnitude, especially the influence of clouds on both albedo and infrared loss to space. The parameters for feedbacks the modelers have used vary enough between modeling groups that making the models fit historical warming requires each group to adopt different assumed (really assumed, not measured) historical aerosol offsets, with more sensitive models having proportionally larger offsets.
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Th models also struggle with long term cyclical (or pseudocyclical) behavior in the temperature history, so aerosols are also used to ‘fix’ this. In all, the GCM’s are ‘circular’ in the sense that parameter choices dictate diagnosed climate sensitivity, and the aerosol kludge makes it all fit. I understand the difficulties, but object to the apparent reluctance of the climate science community to address the obvious problems the models have. My perception is that political considerations are inhibiting progress.
It has already been reported in the literature that there is a significantly higher chance of a La Nina event two years after a major eruption and equally an El Nino about 6 years later.
That could be taken to suggest that volcanic cooling somewhat contributed to the onset of La Nina, maybe even a rebound El Nino (though the paper stopped short of any such speculation).
Now since we do not know what causes either Nino/Nina cycles nor eruptions any comment on whether this is “coincidentally” coincidence or “bad luck” is pretty silly and decidedly unscientific.
However, your comment that most of those eruptions coincide with El Nino emphasises the possibility of confounding natural cycles with temporally coincident volcanic events.
The number of events we have to work with is unfortunately very small, but the apparent pattern is intriguing.
This pattern is surprising but again, because we don’t know the cause of either there is no reason to _assume_ that there is no linkage or to be surprised when we see some pattern emerge.
I was also surprised to see this result. That led me to question my earlier assumption that I would see a clear volcanic signal plus climate noise rather than to question what the data shows.
Greg
If the volcanic eruptions cause temperature drops, the trajectory will be relative to the date when the volcano erupted– not relative to January of the year in which the volcano erupted. I don’t need to “test” this.
But more importantly: You are the one making a claim based on your figure. You figure is based on a method you created. You should be the one testing whether your method which spread the eruptions over a year smears the dip.
That’s because that is irrelevant to the smearing. I’m not sure why you would keep seasons aligned, but even if that’s a “good” reason to keep seasons aligned, it still would not prevent smearing.
How do we know what happens in Jan and February is due to the eruption? How do we know it’s not an artifact of you method? What do you get in non-volcanic eruptions years?
Which graph shows it’s decidedly not happening? Do you have a graph that shows what happens after 20 years? How do you know the “back up to zero” is not due to the AGW effect? Is it because you think it’ would have to be “massive”? Who says it can’t be whatever you would call massive?
Sorry for all the series of questions– but you really do need to make your case. It would be wiser if you did so in a more complete blog post at your blog so your full argument can be put together rather than spreading out all over comments.
Lucia: Which graph shows it’s decidedly not happening? Do you have a graph that shows what happens after 20 years?
Any of the cumulative integral plots, this one for example:
http://climategrog.wordpress.com/?attachment_id=310
That shows not only temperature of tropics but the longer term average temp is recovering within four years and this cannot be explained by AGW because it does not rise in a way compatible with AGW, so there is no need to look to 20 years out.
There may be an AGW signal on that scale but whether there is or not is irrelevant to the recovery shown in four years that can not be explained as AGW vs volcanics.
I certainly will be writing this up as an article at some stage but I’m interested to see whether anyone who has enough understanding of the subject can point out any careless error or obvious misinterpretation of what this analysis seems to show.
” You should be the one testing whether your method which spread the eruptions over a year smears the dip.”
I find that more reasonable than making assertions. It would probably be a good idea to plot both to satisfy the question.
Are you able to see that whatever limited extent it does spread the peak, the area under the peak (ie the integral which I’m plotting) will not change?
The ‘smeared’ peak will be lesser in magnitude of longer duration but still of equal area.
Addition is a linear process. The integral will be _exactly_ the same.
Greg
How does this graph show me what is happening after 20 years?
What would a rise “compatible” with (AGW + volcano) look?
Why can’t a dip due to a volcanoe followed by a recovery due to AGW be what you compatible with (AGW+ volcanics)
Yes. You are just making assertions without showing anything to support them. It would be better to support your assertions.
Able? Your assuming the extent is limited even though– evidently– you haven’t looked.
A thousand apologies Paul_K , I some how managed to parse “Paul_K” as Steve_F !
In fact part of that confusion was inherent in the fact that when I saw a post here by Steve_F, I made a false mental link to your excellent and highly technical posts that you did here recently similarly dealing with linear model equations. Similar subject matter and similar format pseudo lead me to one of the damned false attribution problems that so often happens in climate science 😉
Odd no one picked me up on it.
I already explained all that in a direct reply to one of you comments.
http://rankexploits.com/musings/2013/estimating-the-underlying-trend-in-recent-warming/#comment-116147
If you could at least read what I post, and if you disagree with some part of it say so rather than just posting regardless, it would be more productive.
I see no point in repeating myself, so I would invite you read my reply and if there is some part of that that you do not agree with or do not understand, come back with a specific enquiry.
Your last comment suggest you either missed my reply, did not understand or just chose to ignore it.
My guess is that you have not yet grasped what these plots signify.
If that is the case, please state where the problem is and I will try to explain.
Are you able to see that whatever limited extent it does spread the peak, the area under the peak (ie the integral which I’m plotting) will not change?
Able? Your assuming the extent is limited even though– evidently– you haven’t looked.
==
Are you now trying to suggest that +/- 3 months ‘error’ in start date will smear the effect to 20 years? Steve’s plot shows it is gone after about 6.
http://rankexploits.com/musings/wp-content/uploads/2013/06/Figure-6-500×363.png
The forcing is gone after 6 years, tropical climate has recovered by four years certainly by 6 , why would I need to look out to 20 years to look for other effects compensating something that is already over in the most thorough and total way?
I really don’t see where are going.
Where do you get ±3 months error in start date for your method? You overlapped all “Jan with Jan” right? So your method has a ±6 error in start date which meas as much as a 12 month mis-alignment in volcanic eruptions. And you are diagnosing an effect with a time scale (according to you ) of somewhere between 2 and 3 years. So your “smear” is substantial.
Moreover, Steve showed a graph of monthly forcing estimates. If he averaged those forcings over a year, the forcings would be smeared with shallower peaks and spread out over a longer time.
How do you know it recovered? I don’t even know your definition of “recovered”, but it doesn’t seem to be your cummulants reach an assymptotic value. Your cummulants accumulate negative values reach a minimum and then rise— as we would expect if we have “volcano + AGW” with volcanoes causing temporary cooling and AGW causing secular warming.
GregGoodman #116165,
I did see that you had mixed up ownership of Paul’s comments, but figured either you or he would figure it out.
Greg:
Technically a nearly impulsive signal like volcanic forcings contains a large band of frequencies. They just have a particular phase relationship so that you end up in the time-domain with a single spike. Unless the system response preserves this (it generally won’t), you’d expect to see a low-frequency response or “ringing” that far exceeds the width of the initial impulse.
Beyond that, the oceans response to forcing isn’t linear as James Annan explained on his blog:
[Asymmetric response to positive & negative forcings is a form of nonlinearity.]
Here’s a mean profile for ocean temperature versus depth:
Figure.
The negative gradient in temperature with depth means that the ocean is stable against a positive temperature change on its surfce (basically you can only get local heat energy exchange via conduction), but that you will generally get convection if the ocean surface suddenly cools (and heat energy convection occurs much more rapidly than than conduction).
SteveF (Comment #116150)
June 16th, 2013 at 6:33 am
“If you accept that measured rate of uptake is good enough to say there is no evidence of a drop in imbalance (and I agree, there is no indication in a reduced imbalance) you can’t at the same time say the data is so poor that we can’t see an increase in that imbalance.”
The point I was trying to make is that only a very small increase in the rate of ocean heat uptake is needed to greatly slow down the rate of atmospheric warming (due to the difference in heat capacities). Such a small increase may well be hidden within the uncertainty in the slope.
“It is very clear there has been a large decrease in the rate of warming, and the discrepancy between GCM projections of warming and observed warming has reached the point where a reasoned explanation is required.”
I agree completely.
Lucia: “How do you know it recovered? I don’t even know your definition of “recoveredâ€, but it doesn’t seem to be your cummulants reach an assymptotic value. ”
I don’t mind someone playing devil’s advocate, that can be useful, but your persistently ignoring what I’ve already explained means your input is of little use.
Thanks for taking the time to comment.
Greg Goodman
You haven’t provided any explanation for how you know. Do your cummulants reach an assymptotic value and stick at one value? No they don’t. Do they start to increase? Yes. They do. Is that exactly what we would expect if the series was (AGW+Volcanoes)? Yes it is.
I’m not going to apologize that my input “is of little use” to you. But as far as I can see your argument to “how we know” amounts to “if we ignore the fact that the cummulants start to increase and I cut off the increase by only looking at a few years, we can pretend the increase we see wouldn’t continue more than 6 years and then we can pretend we’ve “shown” there is no AGW and there is little volcano effect even though the cummulants look pretty much exactly the way one would expect volcanoes went off when AGW was occurring and we smeared the volcanoes.
If you are saying something else: Say it. But right now you need to:
1) Show there is no smearing effect.
2) Show how cummulants would look if there is an AGW trend of the magnitude we think existed at the time of each volcanic eruption & volcanoes you smeared the volcanoes and you cut off your plots after 6 years.
Otherwise, unless you can show that your graphs don’t look as we expect them to look under that hypothesis, you can’t say your graphs have shown anything other than precisely what we would expect if there was AGW and volcanoes.
3) S
Carrick: “Technically a nearly impulsive signal like volcanic forcings contains a large band of frequencies.”
The explosion may be impulsive, the all the crap in the atmosphere certainly isn”t.
Annan : ”
on the other hand (or even include a shallow mixed-layer ocean) then hysteresis really isn’t an issue (at least in models under moderate perturbations).”
Models are joke in the tropics. The do not model anything of the key behaviour (tropical storms) that determine tropical climate. All they have is hand-rolled fudge factors that balance the global energy budget.
This is precisely the problem I’m trying to highlight.
If Dr Annan thinks it takes 20y then he ought to look at what happens in the tropics and not what happens in the models. I don’t doubt that what he describes is a fair reflection of what the models do.
Recognition of the asymmetry is what Tisdale has been trying to say for years. Unfortunately he lacks the training to present it in a fashion that acceptable to a lot of scientists/engineers. That does not mean he is wrong. ENSO is not a symmetrical process with long term mean zero impact. This is the fundamental assumption of modellers so far; a bit of random wobble would be nice for the pics but does not really matter long term. Wrong!
Cooler ocean has less losses, less TS and less cloud cover. This enables the OHC to increase even under reduced surface insolation after a volcano. El Nino dumps OHC to the atmosphere but only part of this is lost to the system. These two could hardly be more different yet they are treated as unimportant “internal variability”. They are substituted by _random_ noise in models. Wrong again.
As my graphs show , the actual climate reaction to volcanic masking is fast and total recovery.
http://climategrog.wordpress.com/?attachment_id=310
Certain commentators seem to have trouble grasping that when the cumulative mean gets back to the same level as before an eruption, this means that SST has got _warmer_ than average and compensated for the cooler period by an equally long warmer period. The _average_ temp does not even drop. A plant in the tropics would not lose net growth days (degree.days) if it lives at least 5 or 6 years.
Now, however much you rework the fudge factors you are not going to reproduce that kind of behaviour with the current model paradigm.
Greater than average swings in El Nino/Nina cycle provides a mechanism to capture more of whatever solar is available into OHC and also to to dump it to the atmosphere. There is at least a mechanism there for more radiation _capture_ even during lower total energy availability. What BT is still unwilling to accept is that this is just the mechanism and begs the question of what is driving ENSO.
I’m going to follow up SteveF’s suggestion of aligning some non-volcanic La Nina years to see what it looks like and Lucia’s preferred alignment on eruption date. Since she is unable to see that this makes no difference to the integral she will surely not be the last and showing both will be quicker that trying to explain to those intent on not understanding.
Thanks for all the comments.
When you do this also be sure to do some tests using psueudo data add in a secular trend due to AGW+ volcanoes. That’s the situation where the smearing will matter most because the depression due to the volcanic activity happens in different spots on your plot while the positive contribution due to AGW happens through all months.
Now you indicate you’ve read it and disagree, we can discuss it.
Lucia, I explained it once. I then linked again to my comment and asked you to read and say if there was something you did not get or that you found to be wrong. Lets’ try again:
” A steadily increasing forcing would lead to a parabolic increase in CDF. If it was strong enough to compensate a 20% drop in solar input over a short scale like six years, it would be clearly visible in the preceding 6 years too. It is not.
The averaged initial drop does not even go negative until about 18 months and it’s back up to zero at 4 years. Any AGW effect would have to be massive to account for that and would then continue in parabolic fashion beyond 4 years. This is most decidedly not happening. ”
1. There is no parabolic rise before the eruption
2. If AGW is responsible for the recovery of temp and average temp within 4 years it would be strong and rocket off the top off the graph, clearly visible both before and after. I would not need to scan out to 20 years to find it. Do you know what a parabola looks like ? Maybe I’m assuming too much and you’re not saying.
3. If there is a weak AGW forcing that takes 20 y to recover Mt P then SST would not recover within 4 years.
4. Even if it did recover to the pre-eruption SST there is no way it could recover to degree.day sum in that time without the forcing being massively greater than the already unrealistic large CO” + fictitious feedbacks.
I have described what it would look like, apparently I need to draw a picture too.
This is not obvious stuff to grasp so that may be a necessary step. Part of the problem is explaining the graphs to others. So I may have to make a false plot to spell all this out.
SteveF,
Just a suggestion – why not try quadratic detrending. It should fix the dip-in-the-middle problem in Fig 12, and it would be a useful check – as would varying the interval.
Nick Stokes (Comment #116186)
June 16th, 2013 at 1:29 pm
A 60 cosine would be more realistic than a linear detrend.
Nick Stokes,
The problem is that any arbitrary detrend impacts the results in predictable ways. Using a quadratic would for sure ‘fix’ the dip in the middle, but could also remove a big part of the real volcanic influence and so substantially underestimate the volcanic effects. Like I said before, I don’t think there are any perfect ways to detrend. I will think about this issue some more.
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Of course, each trial detrend takes some time to do and to report as well, and since Big Oil stopped my monthly payoff checks some time ago, I have to make a living some other way, which takes time. 😉
SteveF,
Related to my earlier post, I offer the following calculation. In this post you show a drop in slope in increasing global atmospheric temperature from 0.0188 K/yr (in the period 1979-96) to 0.0027 K/yr (in the period 1997-2012), giving a net reduction of 0.0161 K/yr. Using the heat capacity of the atmosphere (5E+21 J/K) from Wikipedia, 0.0161 K/yr yields a rate of heat reduction of 8E+19 J/yr in the heating of the atmosphere. If all of that reduction is due to increased ocean heat uptake (a reasonable scenario), we would expect an equivalent increase in OHC slope of 8E+19 J/yr.
The current (2005-2013) OHC slope using the 3-month heat content from NOAA is 8E+21 J/yr. Thus, the slowdown of atmospheric temperatures from your analysis would produce only a 1% increase in the OHC slope (too small to be measured accurately, given the noise in the OHC data).
Thus the current slowdown could easily be due to a very small cyclic increase in ocean heat uptake that we simply cannot measure accurately. If the heat transfer is part of a multi-decadal cycle (AMO, PDO, or other), we would expect the rate to eventually increase again.
Owen,
” Such a small increase may well be hidden within the uncertainty in the slope.”
Just as might a small decrease. You can’t have it both ways. Fortunately, Argo will continue to collect data. Our ability to determine TOA imbalance will improve a lot over the next decade.
Owen,
We cross posted, or I would have replied to both your comments at once. WRT your second comment: I think you are a bit confused about the processes involved. The atmospheric heat capacity is minuscule, only equal to about 4 meters of ocean. The TOA imbalance is pretty much independent of change in atmospheric temperature, and the surface temperature doesn’t tell you about the temperature of the whole atmosphere anyway. The only way that you can evaluate imbalance is with ocean heat content. As far as I am aware, nobody suggests that an imbalance would ever only show up in atmospheric temperature. Remember what is supposed to be happening: GHG’s inhibit the loss to space. So, the heat has to go someplace. That place is mostly the ocean, not the atmosphere. That is the imbalance. If the atmosphere warms or cools slightly, then we expect that to change the rate of loss of heat to space, and so change the imbalance.
Greg:
Well, I was discussing volcanic forcings, as were you, which isn’t “all of the crap in the atmosphere”, and does look rather impulsive.
Remember your comment that elicited my response was:
My point is even though the width of the “spike” from volcanic forcing is six years in width, there will be frequency content that is much lower in frequency than this from the volcanic forcing.
Here’s a simple numerical experiment:
download the volcanic forcings, then low pass them with a causal filter.
What do you see? Is the response still six years in width?
Greg:
This has nothing to do with anything.
Vertical stability of a fluid is just 1-d hydrodynamics and is extremely well understood:
The physics that James is describing is associated with the stability of a vertical layer of fluid, and does not rely in any way on global circulation models.
Regarding the response of climate to volcanic forcing, here’s HadAT2 data for 50hPa:
Figure.
It certainly looks like there is a slow response (“rebound”) in the temperature record after Pinatubo in this temperature series.
Carrick,
Your link to the temperature profile seems to be broken.
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I completely agree that ocean warming and cooling are not symmetrical; as you note the ocean is stable to warming but (potentially) unstable to cooling due to the onset of convection. However, over much of the oceans the well mixed layer is much warmer than the water below the well mixed layer, so there has to be quite a lot of cooling of the well mixed layer before convection goes much deeper. Even a very strong volcano would cool the well mixed by only a degree or so, and deepening of the well mixed layer would be relatively modest. At higher latitude there is a shallow summer seasonal thermocline which merges in winter via convection with the water below until reaching the permanent (much deeper) thermocline.
SteveF—the file had a “.html” extension which could be problematic for some browsers since it’s a JPG.
I saved it on my dropbox account.
It isn’t a huge effect I agree, and the models agree with you too—Isaac Held’s student presented some results a bit over a year ago at AGU looking at the hysteresis associated with this “one-way heat valve”. Basically you compute the transient climate response (TCR) to a positive going change in radiative forcing and compare it to a negative going one.
If I remember right the effect amounted to about a ~10% difference in TCR.
Regarding the mixed layer, remember we start by assuming radiative equilibrium, then “diddle” with the radiative forcing and see what happens. If you have a strictly linear response, that change in forcing will get efficiently transmitted through the mixed layer.
Do you know what the deep ocean temperature data say regarding the response to Pinatubo? I think we should be looking at the tropical belt, rather than full ocean BTW.
There are various problems with this analysis of temperature. First, volcanic aerosols have negligible influence on global temperature. All so-called “volcanic cooling” occurrences are nothing more then misidentified La Nina coolings. The entire global temperature curve is a concatenation of El Nino peaks and adjacent La Nina valleys, sometimes quite distorted but recognizable. They are not in phase with volcanic eruptions which can coincide with any part of an ENSO oscillations. When the timing is just right and the eruption coincides with an El Nino that has just peaked, a La Nina valley will follow and immediately get recruited for that volcano’s cooling. This is what happened with Pinatubo. But when the eruption coincides with a La Nina valley and the next El Nino is just beginning to build up there is only an El Nino mountain after that eruption: heat, not cooling. Volcanologists are still scratching their heads about it. This was the case with El Chichon in Mexico. But the belief that it somehow must have had a hidden volcanic cooling is so strong that model makers keep showing it as your figure 9 testifies. The same thing happened with Katmai, the greatest eruption in the twentieth century. That one likewise is not followed by cooling because an El Nino happens to be in the place where volcanologists are looking for its cooling. And of course there are also intermediate situations which randomly vary the amount of cooling that different eruptions produce. I estimate that the true cooling from a typical eruption does not amount to any more than that from good stretch of cloudiness does and is indistinguishable from it. Secondly, the discussion of the ENSO influence shows lack of understanding what an El Nino is. First, ENSO does influence global temperature but its influence is periodic and normally has no long term influence. The super El Nino of 1998 is an exception and I will come to that. An El Nino starts out as an El Nino wave crossing the ocean along the Pacific equatorial counter-current. It runs ashore in South America, spreads out north and south along the coast, and warms the air above it. Warm air rises, interferes with trade winds, mixes with the westerlies and we notice that an El Nino has started. The Nino3.4 feature sits right in the middle of that counter-current and watches all the El Nino waves go by. The lag time is the time it takes for an El Nino wave in the middle of the Pacific to reach South American shore. They don’t all make it to South America because various things like storm surges stirred up by a typhoon can stop it right in its tracks. When this happens its warm water spreads out in the middle of the Pacific and creates an El Nino on the spot instead of on the coast. That is called an El Nino Modoki or Central Pacific El Nino and it will introduce irregularities into the ENSO rhythm. This does not stop the ENSO oscillation because its power source is the trade winds. ENSO has existed as long as the current equatorial current system has existed which is to say since the Panamanian Seaway closed. But any wave that runs ashore must also retreat. When the El Nino retreats from the coast sea level drops by half a meter behind it, cold water from below fills the vacancy, and a La Nina has started. As much as the El Nino warmed the air, La Nina will now cool it. Walker circulation will gather the return flow into two equatorial currents that are dead-ended in the west Pacific. That is because New Guinea and the Philippines block their entrance into the Indian Ocean. As a result, water piles up in the triangle between them and forms the Indo-Pacific Warm Pool, the warmest water on earth. When that pile is high enough, gravity flow back east begins. It takes the form of a new El Nino wave that follows its predecessor to the South America coast. This cycling is a harmonic oscillation. If you blow across the end of a glass tube you get its resonant tone, determined by the dimensions of the tube. Trade winds are the equivalent of blowing across a tube and the ocean answers with its own resonant tone, about one El Nino wave every five years or so. All of this is repetitive and does not change the long term mean temperature of the world. The one exception is the super El Nino of 1998. It is the highest El Nino peak of the century and it carried more warm water across the ocean than any other El Nino before it. This caused a step warming that raised global temperature by a third of a degree Celsius and then stopped. There has been no warming since then and there was none before it either, back to 1979. But the temperature has stayed at that level with the result that all years in the twenty-first century are now warmer than those in the nineties. Hansen noticed that and pointed out that of the ten warmest years, nine occurred after 2000. He is right of course but he is wrong to attribute this warming to the greenhouse effect. As is well known by now, there has not been any kind of warming for the last 15 years. It is not a slowdown but a full stop. What we are seeing is a failure of atmospheric carbon dioxide to produce any kind of warming. Hence, its climate sensitivity is exactly zero. This happened also in the eighties and nineties but was covered up by the fake “late twentieth century warming” used by all ground-based temperature curves before 1998. GISTEMP, HadCRUT and NCDC withrew it last fall and are now going with satellite values for the eighties and nineties. This lack of greenhouse warming follows from and is explained by the Miskolczi theory of greenhouse warming. In the satellite era there was no warming in the eighties and the nineties. And there was also no warming in the twenty-first century. This leaves a narrow window between them, just enough for the super El Nino and its associated step warming. Between and among them they use up all the time of the satellite era, leaving no time for any greenhouse warming. This means 34 years without any greenhouse warming. In view of this fact, can you believe that any warming before the satellite era could have been greenhouse warming? I think not.
Arno Arrak,
I wonder (based on your comment): Did you actually read and understand the post? In particular, did you look at figure 5, where the influence of ENSO on average tropical temperature was subtracted from the Hadley temperature series for the tropics? Please note that the adjustment was estimated based on the 1997 to 2012 period correlation between tropical temperatures and the ENSO index I described. Please also note that once the influence of ENSO was subtracted, the response to Pinatubo and the other large volcanoes become more visible (as we would expect).
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Based upon your other comments, it seems you share many of the misconceptions that Bob Tisdale labors under. I suggest that you consider the possibility that most of what he says about ENSO is nonsense.
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Finally, rather that write very long comments which cover many (apparently unrelated) subjects, could you please focus comments on one or at most a couple related subjects? Trying to lay out your theory of climate in a single comment will make it difficult for people to respond without refuting each of the subjects you cover. If you focus on one or two subjects people can reply without investing too much time.
Carrick,
Thanks for posting the second link to the graphic. The only comment I have about it is that while it conveys the general idea of the thermal profile, it may mislead a little about the depth of the well mixed layer. The graphic suggests about 250 meters for the well mixed layer, while it is really more like ~60 meters on average. The cooler water is really not very far down, even in the tropics.
I see Tamino has a new post, also talking about the dip in the middle.
SteveF: “Like I said before, I don’t think there are any perfect ways to detrend. I will think about this issue some more.”
One way to remove a trend is that the derivative. Since you are dealing with temperature and trying to work out rates of change this would seem a more sensible option.
The other thing is that dT/dt has the units of power, which seems a good choice if you are wondering about the effects of radiative forcings.
I never cease to be amazed by the amount of effort that goes into guessing the rate of change from a temperature time series rather than working with the rate of change directly.
Niels A Nielsen (Comment #116141)
June 16th, 2013 at 3:54 am
Thanks to you and Leif for correcting Eli. In his typical drive-by fashion, the Wabbit substitutes his preconceptions and prejudices for actually taking the time to understand what I wrote; nothing new there, but I do tire of pointing out his silly errors.
Nick,
I just visited Tamino’s site – doubling his hit rate in the process. Do you really want me to comment on this level of hypocrisy?
Or maybe he really isn’t one of the coauthors of the original piece of crap?
Greg Goodman,
“I did not mention a fixed trigger temperature. I would imagine there are other relevant parameters such as SLP and wind patterns since wind is a major part of the +ve feedback. Without digging too deep into exactly modelling what and why my graphs don’t show much difference between tropical NH and SH, more so in extra-tropics which I suspect is to do with land ratios.
My key aim at the moment is to confirm or refute the apparent self-regulation of the tropics. That, if it is confirmed is a game changer for current climatology thinking.”
Your charts should show considerable difference between the tropical NH and SH, but only if you consider the actual energy.
https://lh5.googleusercontent.com/-ttXy7g-0jBE/Ub4y5nQUYnI/AAAAAAAAIoM/-S26Jr-P_nk/s609/tropics%2520in%252020%2520degree%2520bands.png
There is a small anomaly difference and difference in the lag times following the volcanic perturbations. Doesn’t look like much but there is ~20Wm-2 difference between the equator and southern band and 10 Wm-2 difference between the equator and northern band. Meaning there is about a 10Wm-2 difference between the northern band 10N-30N and southern 30S-10N. If you look at the anomalies, heck there is only couple tenths of degree difference. 1.5 C or ~10Wm-2 is a large enough imbalance to redistribute energy pretty effectively though, so NH “sensitivity” to volcanic forcing is different that SH “sensitivity”.
Since that imbalance changes with time, “Sensitivity” should also change with the degree of meridional imbalance.
https://lh3.googleusercontent.com/-rluwWFP_b1Y/Ub4-dcefh1I/AAAAAAAAIoo/zIucJJpa8N4/s912/Equitorial%2520imbalance.png
That shows the equatorial imbalance in T anomaly and I removed the “Great Pacific Climate Shift”, 1974-1976 so you can see the rough sawtooth pattern it can create in paleo reconstructions like this,
https://lh4.googleusercontent.com/-WJiDVg2R0KM/Ubx8SnnJOxI/AAAAAAAAIm4/ejLd98zWmpM/s800/giss%2520and%2520ersst%2520with%2520ipwp.png
Nick,
Thanks for the heads-up on the Tamino post. Yes he is quick to jump on the same subjects we have discussed here but strangely does not note that exactly the same problems apply to ANY selected detrending, including the linear detrend in F&R.
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Funny how Tamino gets all worked up when people point out the obvious prejudices in the analytical choices of F&R, yet heaps ridicule on everyone who disagrees with him…. about anything.
.
Strange he would not just comment here on my post as you have Nick. Will I be allowed to defend myself against the attacks that are sure to follow at ‘Open Mind’? I am not counting on it.
Greg Goodman,
“A thousand apologies Paul_K”. None necessary. I have been called much worse things than SteveF.
Payl_K,
“Do you really want me to comment on this level of hypocrisy?”
.
I can’t speak for Nick, but I really do.
A similar stack of La Nina events as suggested by SteveF.
http://climategrog.wordpress.com/?attachment_id=318
SteveF: Strange he would not just comment here on my post as you have Nick. Will I be allowed to defend myself against the attacks that are sure to follow at ‘Open Mind’? I am not counting on it.
Â
You will certainly not be allowed to defend youself. Don’t even go there. If he wanted to comment openly and fairly he would do so here.
Grant behaves like a coward and a bigot, that is why he will not step outside his own blog where he can ensure no one contradicts him or pulls him up on his BS, however wrong he is. From there he can safely insult people and then ban them to prevent them defending themselves. Open mind, not.
http://climategrog.wordpress.com/2013/03/11/open-mind-or-cowardly-bigot/
Steve,
“strangely does not note that exactly the same problems apply to ANY selected detrending, including the linear detrend in F&R”
Well, what he says in his paper is that it’s OK if you stick to post 1979 because then it’s approximately linear. A natural objection is that we don’t actually know that, the S/N is too low to tell. But I think it is OK in F&R; what it really means is that the regressors have enough flexibility on that time scale that there is no (or not much) systematic discrepancy.
It’s a solvable problem. You are basically trying to take out some fairly high frequency effects (subdecadal) and in detrending you can subtract anything that does not intrude majorly in that frequency range. Quadratic would be OK, even 60 year cycle as Greg suggests, though there’s no reason for the added complication.
The objective of detrending is to ensure that the signal that you can associate with regressors are the lowest frequency in the regressand. Then the regression can separate the HF as noise.
Nick Stokes:
And he seems to be in a bit of a snit about it. lol
SteveF:
Nor should you, but if you do, it’s a very comfortable environment for Tamino, since he has plenty of lap dogs to defend him there. And if you get too close to the truth he can always pull the plug (like they did with Brandon and SkS).
And he’s concentrating on a non sequitur—the dip in the middle—when the real issue is the over-fitting he & Rahmstorf were engaging in.
Regarding the ocean temperature profile—I was trying to convey to Greg G the structure that produces this “thermal heat valve” effect. I thought it looked a bit “thick” too.
It isn’t that hard to pull up vertical temperature profiles with ARGO if we really wanted to look at what is “typical.”
Greg Goodman,
Your analysis apparently reproduces an already known 2.75 year cycle in tropical temperatures. I don’t know whether to be surprised at this or not. The fact that you are aligning calendar months – and reproducing the cycle – strongly suggests that it is orbital. (If the peaks could occur anytime in the year then your methodology should suppress the cycles.) I don’t know if the fact that these cycles are orbitally controlled is known wisdom or not. However, let’s accept that you can reproduce these cycles by taking 6 time samples which happen to correspond to periods of volcanic eruptions.
Your postulate is that the volcanic effect is negligible, if I understand you correctly. The challenge is to demonstrate that if volcanic forcings are negligible then your processing of the data would expose the fact. At the moment, this is not clear to me (nor to Lucia if I understand her correctly). One of the problems is that your processing of the data introduces a large variance in location (i.e. average temperature) of the time series just from sampling. You take 6 samples which have a large spread of average temperatures over the time interval relative to each other. The volcanic signal may well be smaller than the range of temperatures you are sampling. Consequently , the smearing in time of the low temperature spike (which you are doing by aligning calendar months) may be sufficient to ensure that the volcanic signal is lost in the noise.
Nick:
Curious argument, but I don’t think it’s actually true (the slow-down post 2000 comes to mind).
I do agree with your previous suggestion of repeating the calculation starting from 1979, since this is the only way to directly compare the effect of differences in assumptions between the two statistical models.
I’d also try quadratic detrending: As you will recall I went through four order on your blog as part of a sensitivity test on the effect of order of the detrending polynomial.
link to comment.
PaulK, are you talking about ENSO seasonal-cycle phase locking?
There’s a nice write-up located here entitled “ENSO’s irregularity and phase locking”. See Section 3.2.
Carrick,
“Curious argument, but I don’t think it’s actually true (the slow-down post 2000 comes to mind).”
I think it is. The objective of the analysis is to express that slowdown in terms of the regressors, and it seems that is possible. It wouldn’t be possible to express the overall linear rise since 1979, and it seems not possible to represent the dip in the middle either.
You can think of multiple regression as providing basis functions to span the low frequency part of the signal, and then low pass filtering. Either linear and quadratic need to be included, or subtracted out by detrending. But you don’t want to subtract out the “pause”; that’s what we’re trying to resolve.
Nick,
There is absolutely no reason to believe that the apparent large change in the rate of warming circa 2000 represents any less of a problem for the F&R linear detrend than the 1970’s dip we have been discussing. Either way, you use a best fit line through all the data and accept that non-linearity in the data contaminates the regression. The exact same problems apply to F&R as to my analysis, the only difference is that the F&R analysis probably understates the volcanic effect somewhat, while my analysis probably overstates the volcanic effect somewhat. Whatever critique applies to one applies equally to the other. Further, the F&R analysis discounts the potential for contamination of the early part of the data with influence of earlier volcanic eruptions.
For the record, I posted the following at Tamino’s blog:
.
“Humm… That guy Steve F may actually understand quite a lot more than you give him credit for. I am puzzled that you would not comment on the post where it appeared, rather than here. Is there something wrong with commenting at Lucia’s blog? We who have participated there have already discussed in some detail your objections to the linear detrending (before you objected). I invite you participate.”
.
I don’t expect it to appear, but figured I would make sure selective editing was not used to distort what I actually wrote.
Steve,
” Either way, you use a best fit line through all the data and accept that non-linearity in the data contaminates the regression.”
I don’t think you’re using a best fit line for regression. You’re detrending, which means that you’re working out a best fit line, subtracting it before regression, and adding it later. It could be something else – I suggest best fit quadratic.
The actual regression you perform is against sol, vol and ENI. And you want to represent the slowdown in terms of those variables as best possible. The slowdown kink isn’t contaminating the data, it’s the signal. Neither you nor F&R should be aiming to include it in detrending, and I don’t think you do.
Nick:
Well I agree…that’s why I generally do a sensitivity analysis.
But what I also suggested doing (on another thread) is to detrend using a polynomial fit the series that doesn’t include the part we want to test.
Anyway, here’s what I get for first order versus fourth order detrended HadCrut4.
1950-2012 effect of detrending.
It appears that Tamino has to resort to a crude graphic to argue his point.
I also note with amusement Tamino’s word choice about “the sound and the fury”, which more fully quoted is:
Perhaps this is a bit self-referential.
Nick,
Of course it is detrending, I was on the phone while writing, and miss-wrote.
.
Still, whatever you choose (say quadratic) for a detrend, you need to defend it in terms of a physical justification. (To do otherwise is to fall into the Von-Neuman-elehant trap.) The quadratic detrend implicitly assumes that temperature changed (for whatever reason) according to a quadratic function. How would you propose to justify that with a physical explanation any better than you can justify my linear de-trend (or Tamino’s for that matter)?
Paul_K-
I did some quick fiddling with synthetic data of a “fake AGW+ fake volcano” and have concluded that the appearance of the cumulants in the 6 year period is strongly affected by choice of baseline. So… I’m now wondering about the baseline. Greg really needs to show a lot of stuff with synthetic data to clarify the specific details of his processing and to explain what happens with different choices of baselines.
SteveF:
I believe Steve is correct here. When you stretch the fit from 1950-2012, you move the basis functions associated with polynomial detrending farther away from the basis functions associated with the regression against the physical variables being studied. So the problem gets “better” not worse.
The graphic I showed in my previous comment shows as bit of very low frequency (~60 year period) variability getting “eaten” by the fourth order fit. However a 60-year period doesn’t have significant overlap with the frequency components associated with the physical variables that are being regressed against.
I’d expect little to no difference comparing first order to forth order for what Steve is doing. I honestly don’t think it would matter for 1979-current either, but I’m willing to be surprised.
Carrick,
I think what all Tamino’s sound a fury will boil down to is that he doesn’t like people pointing out even obvious weaknesses in his analyses.
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Can you send me that 4th order detrend via email?
Paul, thanks for you comments about where I need to go with this.
Firstly “spreading”:
“Tambora” at 1815.33
“Krakatau ” at 1883.5
“Santa Maria ” at 1902.75
“Mt Agung ” at 1963.21
“El Chichon” at 1982.25
“Mt Pinatubo” at 1991.55
so if we take June as a rough median month for the events we are like 0.5+/-0.25 as the “error” compared to exact eruption date. If most of the effect is gone in four years that is a potential error of about +/- 6.7% ,not a massive smoothing.
This will affect the time series stack, but the signal is pretty confused there anyway, 6% is not going to help or hinder that jumble. The cumulative integrals attempt clarify the signal from the fairly regular natural signal and the h.f. noise. Whether or not there is a 6% spreading due to alignment, the integral will be identical after 4 years and nearly identical before that. I think this is a pointless concern in looking at the integral. Do you see a problem with that?
Now I think it is fairly accepted that volcanic masking stops heat getting out in winter (or at night) as well as cutting down incoming and causing cooler days/summers. This is more the case over land and does not seem to apply in the tropics, which appear self-regulating and don’t have winter and summer anyway.
If I ignore this and use exact dates the spring eruptions will show a cooling 3 m later and the autumn events will show warming three months later. The June events six months later (for NH). Thus a lot of the volcanic effects will cancel. That was my concern and the logic for using integer years and keeping seasons aligned. I now think the two need plotting separately to verify this, to avoid repeating the argument.
Comparing the stacked time-series to the CDF concentrating on the tropics plot line:
http://climategrog.wordpress.com/?attachment_id=278
http://climategrog.wordpress.com/?attachment_id=310
we see that climate response in the tropics is to amplify the magnitude of the usual 2.75 year cycle. The rising segments of CDF correspond to above average SST and match the timing of the usual positive part of the time series. Similarly the drops match usually low SST.
We further note that this rapidly restores the integral, degree.day product of SST to the pre-eruption value. The increased amplitude oscillations continue for at least another cycle.
Steve:
Or, put my parlance, people who are concerned about truth don’t get all bent when other people criticize their work.
SteveF writes “I think what all Tamino’s sound a fury will boil down to is that he doesn’t like people pointing out even obvious weaknesses in his analyses.”
Tamino’s sensitivity has a long tail indeed.
Hi Carrick,
You mean, was I referring to this…
No, I wasn’t. Or at least I don’t think I was. (smiley)
Steve
“The quadratic detrend implicitly assumes that temperature changed (for whatever reason) according to a quadratic function.”
I don’t agree. All you’re doing is exempting that portion from the regression, because you don’t, for whatever reason, think a fit would be meaningful. Because of the frequency issue, there is little interaction between the exempted variables and the regressors anyway. But if you included them in the regression, it would try to fit and produce artefacts.
On Carrick’s point about Tamino’s shorter interval, that would apply to higher order, but not, I think, to linear, which even over 30 years is not very close to the regressors (in a scalar product way).
Carrick,
Slightly more seriously, I was just completely ignorant of the fact that the tropical temperature record does have a dominant peak in the frequency domain corresponding to a periodicity of 2.75 years. But the literature has quite a bit on the subject.
Paul_K, 😉
nah.. I meant something closer to this:
figure.
Nick:
I agree.
Paul_K:
Yes, it turns out to be one of those “well-known facts” that is actually well-known.
Paul K, Carrick,
It looks to me like there is a strong ~21 month persistent oscillation in the average temperature above 30 N and a ~48 month persistent oscillation below 30 S. The influence of ocean gyre rotational periods perhaps?
Nick #116247
Steve, I got that a bit wrong. It’s true that the detrend function is subtracted and added again, but you do need that when you’ve subtracted it, there’s nothing (as best you can) left in that freq range, so to that extent it does need to be a kind of fit.
I see this process as a two stage regression. You have LF (polynomial, mid-range (ENI etc) and HF noise. You could either regress LF and MF together, or do it in blocks (detrending) as you do.
Carrick:
Interestingly, Tamino did the same thing to me a while back, and it led me to make my first post on this blog. There’s a decent chance I’d have never made my series of posts here on Cook et al’s recent paper if not for that.
SteveF,
I think that quite legally you can get rid of the circularity argument by recognising that your model fit is of the form:-
T = f(t) + α1*solar+α2*volcanic+α3*ENSO
Instead of making f(t) a linear function, you can make it a polynomial and simultaneously fit the parameter values for the α’s and the coefficients of f(t). You minimise the residuals of T. You can then test for best fit on the basis of AICc. This would perhaps then avoid hypocritical comments from people who have made more elementary mistakes in statistical model structure.
Re:Carrick (Comment #116249)
June 16th, 2013 at 7:19 pm
Thanks, Carrick. At least I understand this. It is pretty extraordinary. It is not obvious to me at all why El Nino events should be orbitally controlled. Or am I missing a simpler explanation?
Paul_K,
Thanks, but exactly how would you choose a polynomial?
Nick,
The problem is defining ‘that frequency range’. I looked at my regression and tried lag constants which generate much shorter volcanic responses. The result (no surprise) is that as the fit worsens, the volcanic and solar responses both fall, while the ENSO response stays almost the same. So of course, the calculated trend post 1997 was increased…. due to zero residual influence of Pinatubo. That is, with a very short volcanic influence, there is effectively nothing but ENSO impacting the post 1997 period. But even with this, the warming rate post 1997 remains at half or less the rate between 1979 ant 1996.
SteveF (Comment #116264)
Nick,
The problem is defining ‘that frequency range’.
If you did a regression with all six variables, 1,t,t^2,ENI,Vol,Sol,
you’d be inverting a 6×6 matrix of scalar products, formally equivalent to a scaled covariance matrix. The frequency range separation effect should mean that the 3×3 block of products between the first three and the rest is small. That’s why you can partition it into effectively a two-stage regression via detrending. But it’s not essential.
Paul_K:
I share with you the opinion that this behavior is extraordinary.
I haven’t looked at the literature in depth in several years, but last I looked the actual origins of the phase-locking weren’t well understood.
Given I have some research experience involving coupled nonlinear oscillators, you can probably see why this system would be of particular interest to me…
SteveF:
I’m not sure… what’s the relationship between the 21-month oscillation and the ocean gyre rotation periods? That’s something I’m not familiar with.
Paul_K (Comment #116260)
Paul, I was drawn into looking a frequency spectra of W. Pacific trade winds by a recent paper discussed on WUWT. I think Stuecker et al looked in the right place but missed most of what was there.
http://wattsupwiththat.com/2013/05/26/new-el-nino-causal-pattern-discovered/#comment-1323791
The blog discussion is disjointed, as ever, so I’m in the process of writing this up. In short I think it can be shown that variable ENSO “period of between 3 and 5 years” is in fact two harmonic periods that result from amplitude modulation of 4.43 years. Stuecker et al concentrate on one frequency which IMO they use the wrong formula on. I manage to account for nearly all the major peaks in their EOFs
as amplitude modulation and beats arising from luni-solar periods.
http://climategrog.wordpress.com/2013/06/04/on-reinterpretation-of-stuecker-et-al-2013/
Climate science has spent so long regarding anything to do with celestial influence, other than the obvious monthly tides, as some sort of pagan heresy that none of this gets investigated.
Keeling published something on this in 1993 but even then almost apologises for mentioning it.
http://www.pnas.org/content/94/16/8321.long
My impression is that ENSO is luni-solar driven and much of the claimed tele-connections are common cause.
The peaks extracted in Stuecker 2013 seem to point to a fundamental role of the lunar perigee that accounts for the main “3 and 5 year” periodicity in ENSO and the QBO as beats of the longer period with the annual cycle.
That is essentially what s2013 was reporting but IMHO they failed to realise what they were looking at.
Re: SteveF (Comment #116261)
June 16th, 2013 at 8:09 pm
Hi SteveF,
I wasn’t exactly suggesting that YOU should choose the polynomial. I was suggesting that you should allow an algorithm to choose it.
You test fit a second order, third order, 4th order polynomial. In each case you fit not just the coefficients of the polynomial, but also the parameters controlling contributions from ENSO, Solar and volcanic. In other words, you minimise the residuals across the full parameter space. For each fit you calculate the AICc. You will run out of information gain from the model fit when you reach some polynomial order n. You will find that n is probably 3 or 4.
When you get to the final fit, you have a good look at the residuals to ensure that there is no evidence of low frequency mis-specification.
Unless you do this, I think the methodology is always exposed to the challenge of circularity. There is a high likelihood that (a) some of the low frequency change is aliased in your high frequency elements and (b) that the residuals will show apparent mis-specification over the full interval examined.
The F&R paper is of course exposed to the same challenges. Curious that Tamino didn’t mention this.
Paul_K,
Thanks. After thinking about it, I understood what you suggested. It is a good approach and relatively easy to implement, though I will have to teach myself a bit about AICc to judge if the increase in parameters is really improving the total quantity of information or just “drawing an elephant” with multiple arbitrary parameters.
The whole exercise is elephant drawing and as you initially commented should not have got into the peer reviewed literature.
You can chose whether you want and african elephant, an indian elephant or a AGW elephant by restricting the period of the data you chose to fit and how you detrend.
Grant “Tamino” Foster is bright and competent and well able to manipulate the tools he uses to get a desired result. Apparently he adheres to “the ends justifies the mean” skool of climatology and sees no harm in attempting to mislead everyone if it is for “the cause”.
It is rather revealing that he chooses to include pre-1975 to ‘rubbish’ what you do but finds a good reason not include this in his paper.
Blatant hypocrisy is also justified if it is for “the cause”.
Re:Greg Goodman (Comment #116281)
June 17th, 2013 at 3:23 am
Thanks for this, Greg. I am learning a lot, including the fact that ENSO events carry filofaxes and howl at the moon. I was completely unaware of a lot of the stuff you referenced. I need to go through it with a lot more care to understand the implications.
On a minor pedantic note – because I cannot see that it affects your main conclusions – you comment in your article that the transferred energy corresponds to the integral of the forcing which therefore moves temperature 90 degrees out of phase with the forcing frequency. This seems self-evident. However, it is actually quite fundamentally incorrect, or at least it is only true if you assume that there is zero radiative response to the temperature change.
Given your background, I am hoping that you can follow this summary argument without any difficulty.
Basic flux balance equation:-
Net flux change = Cumulative forcing – T/S
where T = temp anomaly (change) and S is the climate sensitivity per unit of forcing. I am going to use the simplest linear relationship between energy and temperature for a single capacity system, but what I am going to show can be extended to other ocean models where the LHS is replaced by a linear system of equations.
CdT/dt = F(t) – T/S
Set Ï„ = C*S and re-arrange
dT/dt + T/ Ï„ = F(t) * S/Ï„
This can be solved analytically using an integrating factor, Factor = exp(t/τ). If we now set the forcing term F(t) = sin(ωt) (with boundary condition F = 0 at t=0) and solve the integral equation, we find the solution is:-
T = Asin(ωt) – Aωτcos(ωt) + Aωτexp(-t/Ï„)
where A = S/(1+(ωt)^2)
The third term on the right disappears for large values of t. You can see that the first term puts temperature in phase with the forcing. The second term moves it out of phase, but in accordance with the response time of the system. In other words, if Ï„ is small, then the temperature response is approximately in phase with the forcing. As Ï„ becomes larger, the response moves more and more out of phase. The important thing to note is that there is no phase shift arising from the integration of the forcing term, because this is offset by the integration of the T/S term in the original equation.
My apologies for the pedantry. It is just that this particular meme has cropped up several times in recent posts and I have been meaning to post a clarification.
Carrick, “I’m not sure… what’s the relationship between the 21-month oscillation and the ocean gyre rotation periods? That’s something I’m not familiar with.”
They both have a non-radiant component, tides. The natural or unforced variations are just changes in the mixing efficiency of the entire system, oceans to turbopause.
The fun part is picking some time period where the “unforced variations” are not influencing the forced surface temperature estimates. SteveF’s “dip” happens to be timed with the Great Pacific Climate Shift, which appears to be part of a 100 to 150 year pseudo-cycle. There is even an ~1800 year lunar cycle which would impact tides and “fixed” sea ice. Since the solar sun spot cycle happens to correlate with temperature, the radiant forcing mania keeps people from remembering that sea ice floats and tides change how high.
You could try and figure all that out, or add +/- 1 C error bars and forget about it.
T = Asin(ωt) – Aωτcos(ωt) + Aωτexp(-t/τ)
where A = S/(1+(ωt)^2)
Thanks PaulK that’s very helpful. It coincidentally seems similar to what Murray Sably was presenting about CO2 in Hamburg recently, but I digress.
what is crucial it seems to note the strong and different frequency dependence of the coefficients A and Aωτ
The in phase term is 1/ω^2 the quadrature term is 1/ω. So unless I’m mistaken this means that high frequencies will be dominated by the quadrature term and longer periods will be in phase.
ie the instant reaction will be out of phase as I suggested but much longer scales will be in-phase. The phase will progress from one extreme to the other in between those two limits.
There is an added complication that is not accounted for in this simple solution and that is that increased surface temp will produce a radiative negative feedback (in quadrature as just stated).
So the forcing term becomes:
F(t) = sin(ωt)+ k* cos(ωt)
now any modulation of the sine by its cosine derivative gives birth to the second harmonic:
sin(x)*cos(x)= 0.5 * sin(2*x)
then the beast begins to sing.
such harmonics abound once you start digging into the spectra of climate variables. I was very suspicious of this sort of thing when I first came across it. But I think it is a natural result of the instantaneous response being in quadrature to forcing change. Similar arguments apply to evaporative feedbacks.
Such enlightening pedantry is most welcome 😉
Carrick (Comment #116270),
“what’s the relationship between the 21-month oscillation and the ocean gyre rotation periods? That’s something I’m not familiar with.”
.
I am not certain there is any connection, but the gyre rotational periods are at least in the temporal range that could have a cyclical influence in the appropriate time range. The northern cyclical pattern is really quite surprising in consistency and persistence.
So the forcing term becomes:
F(t) = sin(ωt)+ k* cos(ωt)
Is it equally possible to solve that?
Way back in time
“SteveF (Comment #115895)
June 14th, 2013 at 7:16 am
Richard LH,
I don’t know if anyone has done what you suggest ( generate a ‘synthetic’ satellite history), but you could certainly try.”
OK. First attempt.
Force Calibration of Global temperature data series
Force the various data sources into alignment by adjusting their offsets and scales to provide a best fit over their whole overlap period, 1979 to today.
Methodology
Align OLS trends in the sources by using offset and scale factors by trial and error.
http://www.woodfortrees.org/plot/hadcrut4gl/offset:-0.16/scale:0.86/trend/from:1979/plot/rss/trend/plot/uah/offset:0.1/trend/plot/best/from:1979/offset:-0.4/scale:0.5/trend
Using the parameters derived from the above, back project the thermometer data to create a satellite referenced data series.
HADCrut4 Global mean
Offset: -0.16
Scale: 0.86
RSS – No adjustment
UAH
Offset: 0.1
BEST
Offset: -0.4
Scale: 0.5
Output
http://www.woodfortrees.org/plot/hadcrut4gl/offset:-0.16/scale:0.86/plot/rss/plot/uah/offset:0.1/plot/best/offset:-0.4/scale:0.5
Or better ordering of output
http://www.woodfortrees.org/plot/best/offset:-0.4/scale:0.5/plot/hadcrut4gl/offset:-0.16/scale:0.86/plot/rss/plot/uah/offset:0.1
Comparison
http://www.woodfortrees.org/plot/best/plot/best/offset:-0.4/scale:0.5/plot/hadcrut4gl/offset:-0.16/scale:0.86/plot/rss/plot/uah/offset:0.1
RichardLH,
The Best (land-only) history is not measuring the same thing as the others (which are global). If you really want to generate a model of tropospheric temperatures based on correlation between surface and satellite trends, you could just download the data from Wood for Trees as a text file, then work in Excel.
Re:Greg Goodman (Comment #116300)
June 17th, 2013 at 7:16 am
“So the forcing term becomes:
F(t) = sin(ωt)+ k* cos(ωt)
Is it equally possible to solve that?”
Yes, Greg, it’s quite trivial. We put cos(ωt) = sin(ωt+Ï€/2), and we have already solved the problem for the sine input. The solutions are additive, so we can just write down the full solution after modifying the initial boundary condition.
T = A[sin(ωt)+k*cos(ωt)] – Aωτ[cos(ωt)-k*sin(ωt)] + A[ωτ-k]exp(-t/τ)
where A = S/(1+(ωt)^2)
You wrote:
We may be talking a slightly different language, but the radiative feedback term is built into the equation I solved. The expression (1/S) is often written as lambda, the (linear) feedback. The value of lambda (in theory at least) is the aggregate of all the positive and negative temperature-dependent feedbacks – Planck, Water Vapour, Clouds, Lapse Rate and albedo.
2.75 years is exactly 1/8 of 22. That might imply it’s phase locked to the solar cycle somehow.
“SteveF (Comment #116314)
June 17th, 2013 at 9:55 am
RichardLH,
The Best (land-only) history is not measuring the same thing as the others (which are global). If you really want to generate a model of tropospheric temperatures based on correlation between surface and satellite trends, you could just download the data from Wood for Trees as a text file, then work in Excel.”
I do realise that the two are not directly comparable. However they will be related. I deliberately included HadCrut4 as an intermediate step.
This is all addressing what is probably the elephant in the room. As far as I can tell it is still the case that no one is trying to do this sort of cross calibration. Satellite to thermometer over the whole 34 years of overlap. The IPCC duck the question.
The Satellite and thermometer are supposed to be providing the same output after all, estimations of average global temperature. They differ in their interpretation and probably definition of the value. More seriously, they differ in their rate of change of the value.
I think that this needs addressing.
This is just a first pass at attempting to answer that question.
“SteveF (Comment #116314)The Best (land-only) history is not measuring the same thing as the others (which are global).
That is a sensible comment. However, it is surprisingly similar if you take account of the change in magnitude.
http://climategrog.wordpress.com/?attachment_id=219
It seems land changes about twice as fast as ocean temps and this is pretty much in line with the estimated heat capacity of land. (Est. because you need to calculate how moist the ‘average’ soil is).
Greg Goodman (Comment #116329)
June 17th, 2013 at 12:40 pm
“It seems land changes about twice as fast as ocean temps and this is pretty much in line with the estimated heat capacity of land.”
Possibly surprisingly the scaling factor for BEST is exactly 0.5 in the above treatment!
Well it’s not that surprising since it was BEST that I used for that plot.
but you could regard it as confirmation of your scaling.
The way that both the short and long term variations seem to match in my rate of change plot gives the sort of cross validation you referred to.
Apart from the war-time whoops in ICOADS, which is a well known problem, this does point out a deviation in BEST in the 70’s. That temporary increase in dT/dt will leave BEST with an notable spurious warming by the end of that decade.
It seems unlikely land could have gone its own way for ten years so I think it’s more likely an indication of an undetected error in BEST.
Other than that, its encouraging to see different records in fairly good agreement.
“It seems land changes about twice as fast as ocean temps and this is pretty much in line with the estimated heat capacity of land. (Est. because you need to calculate how moist the ‘average’ soil is).”
more like 1.8.
you’ll find that this is somewhat higher than all the GCMs.
SteveF (Comment #116066)
June 15th, 2013 at 5:53 am
Sky,
You apparently did not look at Carrick’s graph showing correlation and lag time…. Or did not understand its implications. It is pretty clear from comparing any commonly used ENSO index with temperatures outside the tropics that any influence of ENSO outside the tropics is quite small.
============================================================
What is it about blog-based “climate scientists” that makes them think that everyone else is even more in the dark than they are? FYI, there is a vast evidence-based oceanographic [sic!] literature on the REMOTE effects of ENSO on both temperature and rainfall outside the tropics. Some of it can be found by googling “ENSO teleconnections.” Carrick’s “correlation and lag time” analysis would not get him into Oceanography 401, let alone past it. (BTW, the connection is not in the 2.75yr cycle.) And there are far more effective ways (proper filtering) to make your case about recent temperature “trends” than your simple model.
Sky,
What is it that you are trying to say? That Carrick’s graphic is in error? Or are you saying that the pretty obvious lack of correlation between ENSO and average temperatures outside the tropics is due to someone looking at the wrong data? Please. ENSO does change rainfall patterns, and no doubt has specific influences via ‘teleconnections’. That doesn’t mean ENSO has a large influence on average temperatures outside the tropics.
.
If you think there are papers which prove otherwise, then by all means provide those references. Telling people “Go search with Google to find the references which prove I am correct.” is a pretty feeble argument. You don’t get to assign ‘homework’, especially when you won’t (or can’t) even point to a single reference to support your argument. People are not going to do that. I rather suspect you wouldn’t do it either.
This is in reference to
Some of the analysis is so obvious, it’s not a great mystery why climate scientists don’t dwell on it.
Take the HadCrut datasets which separate the land and ocean, and reconstruct the global temperature out of the combination:
http://theoilconundrum.blogspot.com/2013/05/proportional-landsea-global-warming.html
The observation that land temperature rises at twice the rate of SST is quite striking. And the fact that the missing half is entering the deeper ocean waters is not at all surprising. This heat is getting buried as a lagged transient value and so the ocean value should not be included in any ECS calculation (perhaps a TCR but not ECS).
The land is likely the true measure of ECS and it has a value of 3 C per doubling of atmospheric CO2. This is in agreement with the value established by the BEST team:
http://berkeleyearth.org/xls/forcing-comparison.xlsx
WebHubTelescope writes “And the fact that the missing half is entering the deeper ocean waters is not at all surprising.”
Your assumption rests on the fact that GHGs affect the sea surface in the same way they affect the land surface and that is fundamentally wrong. The land doesn’t evaporate.
Ocean warming has not been measured to account for “the other half” and a good portion of that heat is still missing.
Re:WebHubTelescope (Comment #116371)
June 17th, 2013 at 10:18 pm
…who managed to apply a piece of non-physics to a spurious correlation.
I thought you were doing quite well up to that point.
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“the fact that “?? Stating with such certainty something for which there is no evidence is foolish.
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The oceans warm at half the rate because they (in particular the tropics) are self regulating systems, not passive absorbers, re-radiating.
http://climategrog.wordpress.com/?attachment_id=310
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Until modellers get beyond trivial “parametrisations” and model the way the tropics _really_ respond to a change in incoming radiation they will continue to search for missing heat which is not there.
Â
Mosh’
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So you are saying the scaling should be 0.55556 rather than 0.5 it seems, and that GSMs are even closer to unity than either of those.
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Yet another “parametrisation” they have to fudge to get a fundamentally flawed model to hind-cast about right.
PaulK
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thanks, you are of course correct.
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The exponential term is a kind of “spin up” reaction from the zero initial conditions and can effectively be ignored.
Of the other two, do you agree with my reading of the solution you showed that the instantaneous response is in quadrature, as I initially stated and slides in phase to be in phase at long periods?
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Do you have an indication of the order of magnitude of tau for this relationship?
Â
thx
Just spotted this intersting photo from NASA GEOS13 (14th May 2010)
http://www.flickr.com/photos/24662369@N07/4607059166
Fascinating oscillatory pattern of cloud around equator somewhat north of actual equator. Also note a similar pattern of patches of almost no cloud reflected on the southern side.
Mid May is getting towards max northern extent of annual solar cycle. I think this demonstrates the auto-regulation of tropics in action. More solar input in N , more cloud cover. Opposite in SH. Nearly clear skies.
The oscillatory pattern is reminiscent of similar patterns that can be found at regular intervals in the clouds of Jupiter.
This analysis has a canonical formulation. The following is a derivation of Ocean Heat Content based on Hansen’s 1981 paper:
http://theoilconundrum.blogspot.com/2013/03/ocean-heat-content-model.html
Note how well we can track the data from Levitus and Balmaseda/Trenberth.
This is about the heat entering the ocean, and I suppose it is too pedentic to remind you that water cannot evaporate when it is under the water!
Paul_K said
It appears that you are saying that the log sensitivity of temperature to atmospheric concentration of CO2 (long ago predicted) is a spurious correlation.
Could you please tell me at which point this agreement will cease to become a non-spurious correlation. Will that occur when the temperature anomaly reaches 1.5C, 2C, or perhaps 3C?
It would be nice to know what you think the criteria is for eliminating non-spurious correlations.
GG said:
Look at what you wrote. You claim that what I said (the mainstream scientific explanation, Hansen 1981, Manabe before that, BTW) is foolish certainty, yet you claim with certainty that oceans are self-regulating systems.
It sounds like you believe that the ocean has a thermocouple, sensor, algorithm, and mechanism which it applies to control around a set point. That would imply that there is an intelligent controller. Some have postulated that the global biota performs this kind of function, but there is no certainty behind this either.
Step back and evaluate the system as if it was similar to a dumb heat sink attached to your PC’s CPU. That’s the way I do it. Could be wrong but it is surprising how close we can get to the empirical observations:
http://theoilconundrum.blogspot.com/2013/03/ocean-heat-content-model.html
WebHubTelescope writes “I suppose it is too pedentic to remind you that water cannot evaporate when it is under the water!”
Well that would be true if that’s where the GHGs deposited their energy but in fact they deposit it at the very surface within the top 10um of the cold ocean skin. DLR doesn’t penetrate the ocean.
I’ve posted here my version in which I have tried using linear and quadratic, and also starting 1979. I used my 6-variable regression rather than detrending, and I used the R function nlm() to optimise the exponential smoothing delays. I did HADCRUT, GISS and NOAA.
The results aren’t very consistent, at least for the post-1997 trends. They are mostly more positive than Steve’s, but not always, and may even be negative.. I’ve going to work further on it, and produce confidence intervals.
Webster said, “It sounds like you believe that the ocean has a thermocouple, sensor, algorithm, and mechanism which it applies to control around a set point. That would imply that there is an intelligent controller. Some have postulated that the global biota performs this kind of function, but there is no certainty behind this either.”
The system has quite a few “setpoints”. There is a meridional imbalance of ~17 Wm-2 that would have stable limits. There is ~18 Wm-2 of latent energy transfer to land as precipitation which would have stable limits. There are zonal imbalances, Pacific versus Atlantic that would have stable limits. They are are coupled which you could call an “intelligent control” system, but you might want to ask the designer.
Try 20-70N separately, more chance of a correlation to volcanism. You really need to look at tropics separately, the response is very different to higher latitudes.
Greg Goodman,
No, not really, Greg. The first term is always a scaled version of the forcing function F(t). The second term is always a slippage associated with the response time of the system. If the forcing functino is a polynomial of order n, then the temperature response will always asymptote to a polynomial of order n. If F(t) is an oscillatory function, then the slippage might re-align the temperature phasing with the forcing, but this would be entirely coincidental.
Tau typically has a value of between 3 and 4.5 years to emulate the forced response of AOGCMs over the instrumental period, but this needs some severe health warnings. There are many instances where it is not appropriate to assume a constant heat capacity model. There are other instances – for example when there is a high frequency forcing spike – where a smaller value of tau would be appropriate or a more sophisticated ocean model would be a lot better.
WHT: …. That would imply that there is an intelligent controller.
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No. It does not need a microprocessor nor an “algorithm”. It simply indicates a non-linear feedback.
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When the tropical climate is dominated by phenomena like tropical storms that are self-maintaining once triggered, such non-linear behaviour is a likely result.
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The “mainstream” as you call it failed totally. Hansen’s career as an activist masquerading as a scientist has just come to a long over due end.
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Rather than going into denial about the problem we need to look at other models.
Â
When a model can reproduce something like the following we may be back in business:
http://climategrog.wordpress.com/?attachment_id=310
Nick,
You clearly have been very busy over the past few days. 😉
.
I am a little uncertain about a couple of the things you have done, but I need to think a bit about your graphics to ask appropriate questions. One thing that would help that process is clarification of what the red traces in the graphics for “Variation Components”. The label is ‘Sol’, suggesting solar, but the traces appear to have both a cyclical (expected for solar) and secular (unexpected for solar) component. Can you clarify?
I have tried incorporating linear, quadratic, cubic, and quartic secular functions in my regression model, so that there is no ‘detrend’ done at all, only a calculated secular contribution, with the individual coefficients for the secular contribution determined by the regression (as suggested by Paul_K), and also looked at using the linear only secular trend but changing starting year. I also calculated (correctly I hope) the AICc values for the different secular functions. As Paul_K expected (smart guy that Paul_K) the AICc minimum appears to be for the quartic secular function, although the differences between quadratic and above are not large. As you found, the quadratic and higher order secular functions consistently lead to a larger modeled temperature increase in the 1997 to present trend than the linear function (no surprise there), though all still lower than the 1979 to 1996 period, but in spite of the lower AICc scores, I have strong reservations about the resulting coefficients: the volcanic coefficient becomes quite small compared to the solar coefficient, and the ‘optimized’ lag coefficient becomes very short, both of which I think may not be plausible on physical grounds.
.
I plan to put a new post up as a follow up in a few days. I will cross post this comment at Lucia’s so that people are more aware of what you have done. After that, any comments related to your work I will post at your blog.
Greg Goodman, “Try 20-70N separately, more chance of a correlation to volcanism. You really need to look at tropics separately, the response is very different to higher latitudes.”
There ya go! That is the point I made in the beginning, the hemispheres do not have the same “sensitivity” to volcanic forcing. Since the NH is more sensitive and the THC transports energy to the NH from the SH you can have inconsistent lags with awfully long time scales. Trying to remove, Volcanic, ENSO and Solar is a waste of time without knowing the “mean” and the time required to recover to that mean. Starting at 1915ish, 1950ish, 1976ish all produce different results which to me indicates there is longer term persistence or recovery not considered.
It is easier just to remove CO2 in a range from 0.8 to 1.6 C per doubling since we at least have a start time and reasonable estimate of “global” forcing for that one part of the puzzle.
Re: TimTheToolMan (Jun 18 06:50),
Ghg’s do not deposit energy. Increased DLR reduces the rate that energy leaves the surface by radiation at a given temperature. The net energy flow is still upward to the atmosphere and space. It’s not at all like turning on a heat lamp. The rate of evaporation will still be determined by the usual suspects, the wind velocity, relative humidity and temperature difference between the air and the water.
PaulK “No, not really, Greg. The first term is always a scaled version of the forcing function F(t). The second term is always a slippage associated with the response time of the system. If the forcing functino is a polynomial of order n, then the temperature response will always asymptote to a polynomial of order n. ”
T = Asin(ωt) – Aωτcos(ωt) + Aωτexp(-t/τ)
where A = S/(1+(ωt)^2)
Thanks Paul. Shouldn’t that coeff be tau not t ? Otherwise the system will stop oscillating despite the forcing still being present?
where A = S/(1+(ωτ)^2)
Assuming I’m correct for the moment, that means that the HF response is dominated by the quadrature term and the LF is dominated by the in phase term. So when we look at the overall response on a timescale that is sufficiently long that we average out the HF we find a response that is in phase.
This is precisely what Murray Salby uses to explain current CO2 levels being orthogonal to temp yet geological records show it to be in-phase.
This is basically a question of frequency filtering and “which side of” tau we are on.
Re:Greg Goodman (Comment #116414)
June 18th, 2013 at 9:17 am
“…where A = S/(1+(ωt)^2)
Thanks Paul. Shouldn’t that coeff be tau not t ? ”
Hell, you’re perfectly correct. Excuse the typo.
It should be:-
A = S/(1+(ω τ)^2)
Slight correction. Salby shows how d/dt(CO2) correlated to T in recent detailed data, yet CO2 correlates (with ~800 lag) in ice core record (ie course sampling and physical low pass filtering).
“Hell, you’re perfectly correct.”
Thanks, at least it proves I’m still awake. 😉
So that brings me back to my original statement: that radiative forcing will induce a dT/dt response and the result (which in view of your correction I should have stated : short term response) will be orthogonal.
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The long term (many tau intervals) will be a lagged signal that correlates with time series of the forcing (ie not orthogonal like dT/dt) which is, I think, what you were putting forward as “asymptote”.
This all clears up something that has been bugging me for a while. I was only seeing the first part and was meeting resistance from others. It seems the reality is “a bit of both”. This now gives me sound theoretical basis for what is what and why.
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Thanks again for the pedantry. Pedantry is an important part of science that too often gets skipped.
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Do you think that reconciles both points of view correctly with the maths?
SteveF #116407,
Thanks for your comments. The red trace is meant to be solar, but as you say, it shouldn’t have a secular part. I think that can only have entered during the exponential smoothing, but I can’t see any defect there. It’s likely that this is related to my inconsistent late trends. Checking.
Re: WebHub Telescope (Comment #116389)
June 18th, 2013 at 6:32 am
You are confusing the non-physics with the spurious correlation. I am happy to accept the approximation that forcing from CO2 varies logarithmically with atmospheric concentration.
Let’s stay for the moment with the non-physics. The GCMs typically recognise around 9 forcing series with quite different frequency content. Suppose however that there was only one series – that of CO2 – and that it shows a non-linear timeseries over the full time period. Let us further suppose that you could fit a linear regression between this series and temperature that did actually pass criteria for non-spurious regression. (You can’t, but I’ll get to that in a moment.) The first question is: how do you relate the coefficients of this regression fit to climate sensitivity? I could suggest some models to do it, but my first point is that it is not straightforward. The magnitude of temperature change in the first year of an incremental forcing is a function of the response time of the system and the first derivative of the CO2 forcing series. Even with the simplest of physics models the relationship between the forcing and the temperature at each point in time should not be a simple linear relationship, other than for some very specific shapes of forcing series.
Now let’s further suppose that hypothetically the remaining 8 series all add up to an aggregate forcing series which is exactly equal at each point in time to the CO2 forcing series. You regress against just the CO2 forcing series once again. You get the same answer as above in terms of the coefficients – obviously since nothing has changed – so now how do you relate the coefficients of the regression fit to climate sensitivity? Same answer or different? This is known as “omitted variables biasâ€.
The above two problems relate to the non-physics issue. The second problem also leads to spurious correlation .
But now let’s talk about “spurious regression†which is a slightly different animal. A bivariate regression between ln(CO2) and temperature fails Granger-Newbold criteria – the residuals are non-stationary, autocorrelated and I(1). The temperature series tests positive for I(1) because of multidecadal excursions. These excursions are not present in the ln(CO2) series. A bivariate regression is therefore spurious; moreover, more sophisticated methods to find a co-integration model lead to very strange results which do not suggest a causal relationship – or even a sensible relationship based on expectations from the physics.
DeWitt writes “Ghg’s do not deposit energy.”
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Theory has it that CO2 radiates about 1.1W with a doubling. You cant just ignore this because down that path, thar be sky dragons 😉
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DeWitt goes on with “Increased DLR reduces the rate that energy leaves the surface by radiation at a given temperature.”
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I agree that is one of the effects of increased DLR but its not the only one. The rhetorical question is …what happens to evaporation if you increase the amount of energy in the top 10um of the ocean surface with everything else being equal?
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DeWitt finishes with “The net energy flow is still upward to the atmosphere and space. It’s not at all like turning on a heat lamp. The rate of evaporation will still be determined by the usual suspects, the wind velocity, relative humidity and temperature difference between the air and the water.”
.
And I agree that the net energy flow is upward. The atmosphere is on average cooler than the ocean. I agree that DLR isn’t at alll like a heat lamp because the DLR is less than the ULR from the ocean (a heat lamp would be more) and I agree that the total evaporation is determined by all those things but we’re not talking about total evaporation here. We’re talking about additional evaporation due to additional GHGs.
Tim, I believe the issue at hand relates to terminology rather to substantive issues:
To “deposit heat energy” requires an active process (an internal power source is required). Think heat pump–active.
To “cause the deposition of heat energy” does not require an active process (no internal power source is required). Think insulation–passive.
Since the mechanisms by which CO2 cause heat energy to be redistributed in the atmosphere are entirely passive , you probably shouldn’t say “GHGs deposit heat energy”, at least not in a technical forum.
Carrick writes “Since the mechanisms by which CO2 cause heat energy to be redistributed in the atmosphere are entirely passive ”
Just so we’re clear, do you think a doubling of CO2 radiates about 1.1W/m2 energy towards he ocean or not?
.
Or perhaps more specifically do you think a doubling of CO2 means there are 1.1W/m2 energy worth of photons now striking the surface of the ocean than before that doubling?
The global land warms up twice as fast as the global ocean surface temperatures. This means that 1/2 of the heat is diffusing downward into the ocean. This is also very consistent with the OHC data which shows that the total heat content rate of increase throughout the layers is about half the current excess radiative forcing of 1.6 w/m^2 .
Another interesting invariant is that the global temperature can be estimated very accurately from
TG=1/2(f*0.71+0.29)Tl+ 1/2(0.71+0.29/f)To
Where the fractions are proportion of land and ocean and f=1/2, which is the fraction of heat diffusing downward.
Try it on Tg=HadCrut, T0=HadSST, and Tl=crutem4vgl and you will see what I mean.
The complete derivation is described here:
http://theoilconundrum.blogspot.com/2013/05/proportional-landsea-global-warming.html
That’s an obscure one. Explain how it can fail with a sharp knee in the curve.
Re:WebHubTelescope (Comment #116477)
June 18th, 2013 at 10:48 pm
Obscure? I suspect that means that you have never tested a time series for spurious regression. However, there are a number of perfectly respectable variants around. Why don’t you pick one, ANY ONE, and show me that this regression can pass for anything other than spurious?
“The global land warms up twice as fast as the global ocean surface temperatures. This means that 1/2 of the heat is diffusing downward into the ocean. ”
Why do you keep making this spurious assertion? If we assume (as you are doing) that both are being subject to the same radiative forcing, you still need to account for specific heat capacity. Rock has about 1/4 the SHC of water. To get to 0.5 you need to consider land as ‘moist’ rock and guess how moist it is as a global average, as I already explained.
Paul, are you able to comment on my earlier question?
http://rankexploits.com/musings/2013/estimating-the-underlying-trend-in-recent-warming/#comment-116447
I have been critical for a long time that climate science spends most of it effort trying to understand climate change by avoiding looking at change ( ie dT/dt ), instead trying to divine it by looking at the time series.
It has been pointed out by Allen MacRae, Murray Salby and others that it is d/dt(CO2) that correlates with temperature on the decadal scale.
This reflects Henry’s Law. In the short term, it is temp driving CO2 not the opposite.
http://climategrog.wordpress.com/?attachment_id=223
My argument has been that if we want to see the effects of radiation as a driver (or “forcing”) of surface temperature we should be comparing it to dT/dt.
The differential equations governing this seems essentially the same as for the case of CO2. The conclusion will be analogous.
We need to be looking for correlations between dT/dt and radiation time series NOT comparing rad(t) to T(t).
Now that fast response will not fade away with time once it is in the record but if we look at much longer time scales and and filter out the short term variation we will be left with the in-phase term. I think this is what you getting at.
Again, like the CO2, the LF response of the system will be in phase the short term response orthogonal.
The added benefit is that taking the diff, helps to render the temp time series stationary which is an essential step in doing frequency analysis.
I’m pretty sure I’m right about this but you clearly have a good understanding of all this and it would be helpful if you could say whether you think there’s any pedantic errors in what I’m stating.
thx.
Sure, Granger-Newbold is definitely obscure as it sounds like it came out of the econometrics literature. Climate science is a combination of applying math and physics, not just seeing if will pass some statistical test.
There is that word “spurious” again.
Specific heat and the coefficient of diffusivity work together to define the volume that will be able to sink heat. A low diffusivity generates a very shallow depth for sinking heat and therefore a small volume. I would avoid knocking solutions that apply some real physics, even if the approaches are first order.
I assume that many climate scientists don’t have the patience to continually debunk what Salby has been saying. Salby doesn’t mention Henry’s law and the activation energy of CO2 would have to be a few electron volts, which is completely unrealistic. The obvious check is to look at the partial pressure of Argon, which I bet hasn’t changed much at all. Perhaps its better to keep mum, and let Salby dig himself a deeper hole.
What is weird is that Salby’s textbook on atmospheric and climate science appears fairly comprehensive.
It occurs to me that Paul_K’s solution equation also contains the exponential impulse response that Steve is trying simulate by spreading the input forcings like volcanic and ENSO.
We can also see that this is not too good because it will be equivalent to exponentially extended forcing to the first two terms as well.
Since all the detrending jive is an attempt to remove the long term frequencies trying to fit dT/dt may be better. The derivative does the equivalent of removing the linear trend (it becomes a constant) and also diminishes the longer term in proportion to their period: the 60y cycle will be severely attenuated.
Since we are explicitly trying to remove the longer frequencies we can effectively remove the first term from the solution eqn. The solution (the temp time series) becomes orthogonal to the forcing and since its derivative is orthogonal this should better match the forcing time series than T(t) which is what all current attempts are aiming at – and having problems.
What I would suggest is to stop all the arbitrary detrending and try fitting the dT/dt (simple first difference of the time series) to the unmodified forcings.
I’m a little dubious about using ENSO as an input forcing since it is also part of the resultant temp response. However, it may help compensate for the lack of any accounting of the _active_ tropical response to radiative forcing that is not accounted for in a linear response model.
I did note that ENSO tends to be strong after a major eruption so the may be helpful.
It will also get rid of the need to artificially spread or “lag” the inputs since affecting dT/dt has a persistent effect on T(t).
Again the CO2 analogy is helpful. If you look at Temp vs CO2 there is a 9month lag and a not too great correlation. If you compare to d/dt(CO2) you get much better correlation and not lag. It’s a case of working with the right variables.
So far on rad(t) vs T(t) I don’t think we are !
The other argument is physical dimensions. dT/dt is power and so is the forcing. Trying to fit energy to power is like trying to fit apples to oranges.
Webster, ” The obvious check is to look at the partial pressure of Argon, which I bet hasn’t changed much at all. Perhaps its better to keep mum, and let Salby dig himself a deeper hole”
It has been pointed out before that Argon has differing degrees of super-saturation in isotherms/density layers which depend on the mixing efficiency and temperature of the down welling water. The situation is not “cut and dried” to the point you can ignore the various thermoclines and deep ocean mixing layers.
WebHubTelescope says “I would avoid knocking solutions that apply some real physics”
The real physics is that infrared doesn’t penetrate the ocean surface so the whole argument “We assume that excess heat (mostly infrared) is injected through the ocean’s surface and works its way down through the depths by an effective diffusion coefficient.” …is spurious.
WHT ” Salby doesn’t mention Henry’s law and the activation energy of CO2 would have to be a few electron volts, which is completely unrealistic. ”
Salby’s presentation was only supposed to be explaining the apparent paradox of d/dt(CO2) correlating in modern records yet CO2(t) correlating in the geological record. It was not supposed to be a complete treatment of the atmosphere. I did not agree with all he presented but I think he made a good job of explaining that using enough maths to make it clear where he got his relationships from without losing everyone.
What’s you point about activation energy?
WHT:
And again you are unable to show you are not being spurious. Paul_K issued you a specific challenge that you use ANY test and you come back whining again about whether his test is “obscure” or not. Clear evasion.
I said you had not accounted for SHC in making an unjustified claim assuming there must be as much energy hitting land a sea and assertingthat therefore there was a ‘missing half’ that was being sequestered in deep oceans. You come back with some hand-waving about diffusion which ignores diffusion in rock and does not argue one way or the other.
So your argument is not even “first order”. To make ‘solutions that apply some real physics’ you need to do a little better than wave a word like ‘diffusion’ around and hope it will scare everyone off.
So far you’ve failed to account for SHC. If can do that , then add in some extra work about how diffusion in land differs from diffusion in the oceans you may have a further refinement to add. So far you have not even got off the ground with the first part.
How about you start by replying to Paul_K in a meaningful way. I think that may save us all some time typing.
Re: Greg Goodman (Jun 19 03:36),
Henry’s Law doesn’t have much to do with the trends in atmospheric CO2 over scales of less than thousands of years. Salby and the others apparently don’t realize that different mechanisms are in play than simply solubility of CO2 in sea water, not to mention that the temperature changes are too small to have caused anywhere close to the recent observed change in atmospheric CO2.
On the annual scale, the fluxes of CO2 into and out of the atmosphere are dominated by fluxes into and out of the biosphere, i.e. growth and decay. Those fluxes are an order of magnitude greater than human emissions from fossil fuel combustion, cement manufacture and land use/land cover changes. These fluxes don’t have to be exactly the same from year to year. That’s what causes differences in the year over year change in atmospheric CO2. But on a decadal scale or longer, the annual variations average out and we see an increase that correlates extremely well with the rate of human emissions.
For glacial/interglacial transitions, the CO2 level is likely driven by solubility. Since it takes thousands of years for the ocean to equilibrate to a temperature change, it’s only logical that CO2 lags temperature. That doesn’t mean that CO2 can’t contribute to additional warming. It just means that the initial warming is not driven by CO2, but by changes in albedo in the Northern Hemisphere probably caused by the Milankovitch cycles.
Nick Stokes has posted his latest results (http://www.moyhu.blogspot.com.au/2013/06/better-adjusted-global-temperatures-for.html), with both linear and quadratic detrending, both starting from 1950 and from 1979, and with the three major surface indicees. With quadratic detrending he gets +1.078 K/century for Hadcrut 4 for 1997 to present, +1.315 K/century for GISS, and +0.913 K/century for NOAA. These values compare with F&R values of 1.70, 1.71, and 1.75 respectively, but F&R values are from 1979 to present. A recent slowdown, but less than a factor of 2.
DeWitt, ” Salby and the others apparently don’t realize that different mechanisms are in play than simply solubility of CO2 in sea water, not to mention that the temperature changes are too small to have caused anywhere close to the recent observed change in atmospheric CO2.”
Firstly mention of Henry’s Law was my bad, it’s a pressure relationship, I had my CO2 vs AO plot in mind.
http://climategrog.wordpress.com/?attachment_id=259
Salby does not mention it IIRC. What he does show is how the same relationship (in fact the same maths this I was discussing with Paul_K here in relation to temp change) can produce a short term change that is orthogonal and a long term averaged response that is in phase. If you have not watched his presentation , I suggest you do. Then see whether you can fault his maths.
One thing is sure, the rate of change correlates much better with T(t) than the straight concentration. You can argue about whether that shows causality if you wish , I’ve just scaled to fit. But at least it’s the right shape, the time series of CO2 does not fit.
http://climategrog.wordpress.com/?attachment_id=223
http://climategrog.wordpress.com/?attachment_id=233
Of course the annual cycle of about 5ppm is dominant, that’s why it gets filtered out before considering any of this.
You justapose the two statement like that make an assertino into a proof. I agree with the first. That in no way justifies, proves or even suggests the second is true.
Actually, it correlates very well with temperature if you use d/dt(CO2) as I have shown for a second time above. If you wish to argue against that how about coming up with facts and data rather than assertions, that for some odd reason you expect me to believe despite my having looked at the data and plotted the relationship.
is likely to… could be… may be as much as….
Facts my friend, not chat.
Besides CO2 is a bit a diversion except for the fact that is follows the same maths. What interests me here if that we should be doing all this fitting game against dT/dt , not the time series.
No one able to comment of that ??
DeWitt/Steve_F,
1/8 of 22 is 1/4 of 11, correct? What am I missing?
More broadly, it wouldn’t surprise me if ENSO and other tropical climate phenomena, as well as the 60-ish year cycle, are all solar harmonics/subharmonics. Why not? And why couldn’t we hypothesize a quasi-oscillatory pattern at the 60-ish year level that happened to experience a higher peak nicely timed with a rise due to CO2? Then Bob Tisdale could be half right 🙂
BillC : More broadly, it wouldn’t surprise me if ENSO and other tropical climate phenomena, as well as the 60-ish year cycle, are all solar harmonics/subharmonics. Why not?
Â
Well I can do better then why not, there is certainly some circumstantial evidence :
Â
http://climategrog.wordpress.com/?attachment_id=283
http://climategrog.wordpress.com/category/periodic-analysis-of-climate/
BillC (Comment #116538)
“1/8 of 22 is 1/4 of 11, correct? What am I missing?
More broadly, it wouldn’t surprise me if ENSO and other tropical climate phenomena, as well as the 60-ish year cycle, are all solar harmonics/subharmonics. Why not? “
Because the sunspot cycle isn’t properly periodic. If it’s going to transfer energy to a 2.75 year process, then at some point in the 22 year cycle the faster cycle has to be in the right relative phase. But the phase variability of the 22 year cycle is of the order of the whole period.
It’s hard enough to excite an 8th harmonic of something that is really periodic. Q
Here’s the graph that came from for a reminder:
http://climategrog.wordpress.com/?attachment_id=278
If anyone is interested in how the individual eruptions are timed w.r.t SSN, look at this. Comment below graph so I won’t repeat them here.
http://climategrog.wordpress.com/?attachment_id=315
Basically two groups that are roughly aligned. What is most significant for the question of regression fitting of the period Nick, Steve , F&R etc are fitting to, is that the two eruptions in that period happen about a year before the solar cycles hit their steepest decent. That is just when the ash is reaching it max effect.
Now if we start using exponential spreading functions on the volcanic signal we are removing the only feature that distinguishes it from the solar signal : the width of the trough.
Also if we are fitting the time series T(t) when the maths and physics shows that at least the fast response will be related to dT/dt we are further blurring the lines that would give some hope of the regression differentiating between the two.
SteveF (Comment #116358)
June 17th, 2013 at 6:05 pm
Sky,
What is it that you are trying to say? That Carrick’s graphic is in error? Or are you saying that the pretty obvious lack of correlation between ENSO and average temperatures outside the tropics is due to someone looking at the wrong data? Please. ENSO does change rainfall patterns, and no doubt has specific influences via ‘teleconnections’. That doesn’t mean ENSO has a large influence on average temperatures outside the tropics.
===========================================================
What I am saying in plain English is that ENSO has a profound, but non-uniform effect upon temperatures in various different areas well outside the tropics. The transport of heat from the tropics poleward is not a simple “conveyor belt” process, wherein the signature of, say, NINO3.4 would be reproduced elsewhere after some specified time lag. There are too many chaotic processes of various scales that interfere alon the way. Simply looking for a peak in the cross-correlation function doesn’t cut it analytically. What does is the cross-spectral coherence in the power-rich frequencies of the wide-band tropical temperature spectrum. It reveals strong coherence with NINO3.4 at patently extra-tropical stations in many areas (not only in South America, but in central California, Yukon Territory, Victoria province down under, etc.), albeit at different frequencies and phase lags.
Your surmise that I would reject a general pointer to a specific topic from a professional in an area outside my expertise is mistaken. I would much prefer that to a web link providing usually only an academic abstract. Clearly, you have a different mind-set, which I’m not going to go through boxes in storage to satisfy.
You describe this correlation as springing up punctually in different areas without any clear chain of effects linking the two.
That would suggest common cause rather then direct causality via teleconnections that are not connected.
It is very easy to debunk Salby. The slight CO2 fluctuation is clearly a result of seasonal outgassing related to Henry’s Law.
What you want to do is get the CO2 data from a measuring station that shows very little local seasonal variation. Let’s try American Samoa — this is what the CO2 measurement looks like, completely untreated
http://img40.imageshack.us/img40/5634/kcp.gif
Take this curve and try convincing someone that temperature is driving it.
American Samoa is right in the middle of the Indo-Pacific Warm Pool and essentially sees the monotonic advance of CO2. Mauna Loa is enough off the equator to pick up a seasonal asymmetry, and all you are doing is chasing vestiges of Henry’s Law.
And what about the left over noise … If we take the residuals against the power law fit and compare that against the man-made carbon residuals estimated from the CDAC data, we get this chart:
http://img43.imageshack.us/img43/4521/f5y.gif
Notice that the left-over measured CO2 noise lags the estimated yearly carbon emissions by a little over one year. This is powerfully effective evidence and isn’t even close to being a “spurious correlation”.
I always like to think that experienced climate scientists have all sorts of tricks up their sleaves to debunk this kind of wild theorizing by Salby and his ilk, but that is really not part of their job description.
I make no claims of causality, simply because the mechanisms in teleconnections are not clearly understood. Indeed, it may be a matter of concommitant variables, driven by an unknown common cause.
What’s a “man-made carbon residual ” and how do you get it?
This is the carbon emissions data gathered from the Carbon Dioxide Information Analysis Center at Oak Ridge. This data is convolved with the CO2 sequestering Green’s function to generate a CO2 profile:
http://img191.imageshack.us/img191/7375/2quu.gif
The residual is the difference from the polynomial fit. The Mauna Loa, Samoa, and Carbon growth all use the same second-order polynomial fit. So what you see are essentially the detrended noise profiles, where the noise is actually the slight modulation in yearly global carbon emissions. All these pieces have to fit tightly together to reduce the residual errors to zero. At this point, what’s left is truly a fraction of a PPM of systemic noise. All the aleatory noise is accounted for.
I appended all the information to this older blog post
http://theoilconundrum.blogspot.com/2012/03/co2-outgassing-model.html
“What you want to do is get the CO2 data from a measuring station that shows very little local seasonal variation. Let’s try American Samoa —Take this curve and try convincing someone that temperature is driving it. ”
http://climategrog.wordpress.com/?attachment_id=396
I got the data straight from Scripts Institute, since the data source you suggested was not a “raw” as you thought , if you’d read notes at the bottom of the file. It also stopped in 2008.
Just like the MLO dataset its rate of change shows a strong similarity to global mean SST . This is pretty much expected on the basis that CO2 is supposed to be a “well mixed” gas.
This demonstrates exactly what Salby was saying, well done.
Temperature does not explain all the variation, the rest is probalby atmospheric pressure that I showed earlier.
Hey GG, you and Salby will lose big time on this one. The CO2 signal is comprised of (1) a slight seasonal fluctuation caused by outgassing and (2) a strong fossil fuel emission component that has the secular rise along with fluctuations caused by global economic conditions that vary with time.
Are you British or from a commonwealth country per chance? I was wondering based on how you spell “maths”.
Amazing. You suggest I use a certain dataset because you consider it better. I then show you that it displays the same behaviour as MLO (which you said was contaminated by being offset from the equator), once you look at the right variable. It confirms the relationship the Salby, MacRae and others have pointed out.
Instead of commenting on what the data shows you just tell me I will “lose big time” and start a list of assertions that ignore the data.
http://s.ytimg.com/yts/swfbin/watch_as3-vflbQIt9o.swf
I can see the deprogramming process is going to be long 🙁
Greg,
WHT is right. You have shown a plot with a reasonable (but only just) wiggle match suggesting temperature related fluctuations. But differencing disguises the trend, which is there as a constant positive offset. That is the trend from emissions. Your plot does not associate that with temperature, and there is no physics in which that cause would make sense.
So all you have is a set of wiggles which go nowhere that may be temperature related, and a steady addition of CO2 which is not.
Re:WebHubTelescope (Comment #116497)
June 19th, 2013 at 6:31 am
Classic. You think that the statistical underpinning of econometrics is not founded on math? You reject advanced statistics because you don’t like the solidly founded empiricism or you can’t follow the math, but you are quite happy to accept a conclusion founded on no physics at all and bad statistics?
Maybe this simple demonstration is sufficient even for you to follow.
The attached graphic shows a forcing series which consists of a simple sine function of periodicity 60 years superimposed on a straight line growth. Temperature is forward-modeled using the linear feedback equation.
A bivariate fit between the forcing and temperature shows a very high R^2. (This is statistically significant if you ignore the last 40 years of development of statistical theory. More advanced application suggests that the regression is spurious.) The second graph shows the resulting relationship between forcing and temperature, on which the correlation is based.
http://img109.imageshack.us/img109/6703/5kv5.jpg
Can you still not see any problem here with the structural model, even with your rejection of statistical theory? The theoretical stats can’t tell you why a fit is structurally wrong – just that it is likely to be (structurally wrong).
The addition of this dross to what would otherwise have been a good paper on temperature averaging was and remains, in my opinion, quite gratuitously offensive.
Greg Goodman,
Greg,
I have had a few problems retaining links with Lucia, so a couple of replies that I thought I had submitted did not make it through. A short answer to your previous question is that, yes, I think we are on the same page in terms of how a forcing “propagates” into temperature.
At the same time, I have to say that I share the view of WHT, Nick Stokes and DeWitt that the low frequency behaviour of the atmospheric CO2 profile is largely a response to man-made emissions with only a small temperature-driven element. The derivative form sees only the high frequency response, which is largely driven by temperature.
I think that many people underestimate just how large this high frequency temperature response is because of doing solubility calculations based on average global temperature change. The reality is that large volumes of CO2 are released, swirled around, and re-dissolved every year in the mid-latitudes. However, the long-term impact of temperature change on CO2 should be quite small.
GG, The CO2 data we are analyzing is the foundation of the entire AGW concept. I was able to decompose the residual atmospheric [CO2] signal as a combination of a purely thermal seasonal signal (periodic CO2 outgassing and absorption) and a signal that shows the variation in worldwide carbon emissions (due to global economic conditions).
As I stated earlier, I am not sure why climate scientists haven’t demonstrated this decomposition in the past. For all I know, they have. I don’t go to climate science conferences or know of any climate scientists personally, and certainly could have missed the paper that demonstrates the characterization in a similar manner that as I have.
That said, I contend that what you are seeing is a serious “spurious correlation”. I am doing this to show that you and Salby and others (Humlum, “Bart”, lots of skeptics at ClimateEtc) are fooling yourself into believing that those correlations at 1988 and 1998 have anything to do with temperature. As I demonstrated, those are clearly related to shifts in fossil fuel combustion levels.
This is called an impasse and I believe it will take somebody with a good physics and statistics background like Nick Stokes to perform a tie-breaker evaluation.
BTW, whatever link to that flash move you provided, I can’t get it to run. Is that the Salby lecture?
Regarding the Granger-Newbold metric, I was originally asking at what stage would the global land temperature anomaly be attributable to something other than a statistical artifact.
The average land temperature signal is at levels of 1.2C above the historical baseline right now. So if it reaches 2C in the next 50 years, I assume we would have the same problems with trying to distinguish it from a statistical artifact. I could certainly simulate an excursion of that magnitude via a random walk with a weak enough Ornstein-Uhlenbeck reversion-to-the-mean parameter. (But then we would have to be prepared for the random walk back down)
Since you didn’t answer that question when I asked, I have to infer your answer would be along these same lines.
I guess that is part of the reason that climate scientists don’t just rely on this piece of data. They also look at ocean heat content, paleoclimate data, melt rates, etc, to reduce the uncertainty in isolating the root cause of what the measurements are telling us.
Paul_K
Thanks. So the short term is derivate based and orthogonal ; long term is in-phase and proportional to forcing TS.
That is same maths, essentially for both CO2 patterns and rad vs temp. Temp responds to rad forcing in a similar way to how CO2 responds to temp. (Notwithstanding other CO2 inputs, just it temp response).
Then there’s the added complication of atmospheric pressure. In fact the temperature dependency is because of temperature variations of the “constant” in Henry’s Law which is a pressure relationship.
I think difference between d/dt(CO2) and T(t) is probably mainly pressure but have not established this beyond noting that post 2000 seems strongly correlated to AO. Less closely during 1975-1995.
http://climategrog.wordpress.com/?attachment_id=259
I remained of that opinion for a long time until understanding what this IDE solution implies. Now I’m re-evaluating if that still holds.
The time constant, tau, seems such that decadal scale is dominated by dT/dt. At interdecadal we seem to be entering the mixed regime. Centuries is probably dominated by the in-phase response. But note: this is still the response of CO2 conc to temp, not the opposite.
So the long term natural climate variation coming out of LIA will be contributing a signal similar to the net residual of anthop. emm that are not absorbed. This leaves a significant problem for differentiating the two in the data. IIRC annual carbon cycle is about 150 Gt to human 5Gt and we don’t understand the processes or have the data to calculate how much remains.
If we look at the higher derivatives we can get two estimations of the changing “sensitivity” of d/dt(CO2) relationship.
http://climategrog.wordpress.com/?attachment_id=233
From that I’ve estimated the the fast inter-annual dynamic response as 8ppm/year/K and the interdecadal (circa 50y) response in rate of change as 4 ppm/year/kelvin
Maybe we could infer a millennial scale, human free figure, for the direct CO2(t) in phase response from ice cores.
That gives us both extremes of the in phase and orthogonal terms and one value for the intermediate phase which is ‘polluted’ by the residual human emissions. That is one too few points for the number of variables but is a good start.
The intermediate value of 4ppm is determined by tau (in combination with the two extreme sensitivities) and the anthro term.
If we can establish one more point we should be able to have a first stab at differentiating the temp response and residual emissions.
The AO plot may give us another value. 2002-2006, long term trend in Temp is flat. Several indicators suggest this may the turning point so we have a possibly unique point in the record to look at a “stable” dT/dt,
and AO seems to ‘account for’ virtually all the the variability around 2ppm/year. Maybe 1968-74 would give another. Hmm.
sky,
The point of my post was to examine the F&R paper, which considered how lagged ENSO, among other factors, influences global average temperatures. I am not sure how I could proceed without, well, comparing lagged ENSO to global average temperatures. I trust that you (who claim to be a professional in the field) have raised exactly the same objections over the ENSO correlation at Tamino’s blog over ENSO as you have raised here, which began:
That thoughtful and constructive gem seems to me a perfect way to voice your objections to the post, especially for a real climate scientist. So, in the spirit of another of your thoughtful and constructive comments, I ask: what is it about people who describe themselves as climate scientists that makes them so uncivil?
WHT:” I was able to decompose the residual atmospheric [CO2] signal as a combination of a purely thermal seasonal signal (periodic CO2 outgassing and absorption) and a signal that shows the variation in worldwide carbon emissions (due to global economic conditions).”
You did not decompose anything. You simply _assumed_ that temperature has no effect beyond annual and assigned the rest to AGW.
The maths of the IDE and the physics of out-gassing tell us there will be a d/dt(CO2) correlation and we find one operating on the decadal scale. We know there is an in phase response from the geological record . At least that bit seems uncontentious (though error bars may be big and diffusion may be a problem. )
What I’m trying to do is to decompose the two, You still seem “in denial” about the existence of the d/dt(CO2) relationship.
sky:
Whether it does or doesn’t, the linear correlation with ENSO34 vanishes outside of ±30°, so you can’t regress against lagged ENSO34 to predict it. If the relationship is chaotic, you’d need to develop a (nonlinear) statistical model to relate ENSO34 to these supposed temperature changes.
SteveF:
Possible answers (more than one may apply): not very bright, not very knowledgable, poorly socialized.
SteveF” I ask: what is it about people who describe themselves as climate scientists that makes them so uncivil?”
This matter is too important to waste time discussing. We must set up a $100bn PER YEAR fund with no legal accountability or auditing and do it now.
We should end our arrogance and hubris and stop questioning their authority. They are way smarter that we are (they’ve all got PhDs) we should let them run the world.
Of course they get uncivil. Of course they commit wire fraud. It’s not easy getting the right balance between being honest and being effective. The last thing you need is some smart arse at the back of the class asking difficult questions.
Please, Steve, show a bit of compassion. 😉
sky:
You just got through saying “What I am saying in plain English is that ENSO has a profound, but non-uniform effect upon temperatures in various different areas well outside the tropics”, which implies causality. They both can’t be true.
Regardless, if temperature in the extratropics were linearly related to temperature from ENSO34 via some hidden underlying cause, there’s be a non-zero linear correlation. This is directly testable, and due to the lack of observed correlation, the assumption of “concommitant variables” can be rejected.
Re:WebHubTelescope (Comment #116587)
June 20th, 2013 at 6:30 am
Well, with respect, that was not the question you raised. This was your first statement.
I responded that the BEST team had applied a piece of non-physics to a spurious correlation.
The question you then raised was this:-
You are now raising a completely different question about whether we can attribute statistical significance to the recent warming, and, if not, how long do we have to wait. My answer to the first part is that we do not yet know whether the warming is statistically significant. My answer to the second part is that I don’t know:-
http://rankexploits.com/musings/2013/the-occams-razor-oscillatory-model/
http://en.wikipedia.org/wiki/File:Co2-temperature-plot.svg
First approx to ice core (100ka-400ka scale record) in phase sensitivity , from the y axis scaling:
(420-160)/(15-(-11))=10 ppmv / K.
the variations shown to respond on that scale are of order 10ka.
WHT,
I don’t know about real climate scientists, but I drew a distinction between short-term temperature influence and simultaneous absorption of much (about half) of the CO2 released from fossil fuels back in 2009. http://wattsupwiththat.com/2009/05/22/a-look-at-human-co2-emissions-vs-ocean-absorption/
.
Which, by the way, was a response to speculation by Roy Spencer that ocean warming had caused all (or most) recent CO2 increase, not CO2 emissions. WRT ice-age driven CO2 changes, I think the key thing is that the long term equilibration between atmospheric CO2 and the ocean is primarily set by the surface temperature where water upwells and warms (that is, at lower latitudes) since it is the temperature sensitive desorption of CO2 from the warmer surface water which ultimately controls the atmospheric concentration, not ocean temperatures at high latitudes, which can become no colder than the freezing point of seawater.
To eliminate the temperature dependence in the Mauna Loa data, I compensated the data by subtracting off the SST numbers from the IPWP region with a gain of 3ppm/C.
The residuals from the Mauna Loa data then match with Samoa, which is smack dab in the middle of the IndoPacific Warnm Pool. I agree with SteveF that the hottest ocean temperatures control the steady state partial pressure of outgassed CO2.
The leftover residuals after this compensation for seasonal outgassing match well with the CO2 response from fossil fuel emissions.
It is truly an amazing set of cookbook steps which leads to a stunning concordance. And I can use these adjectives because I like the math and science for its own sake.
SteveF
Nice, I had not seen that (with the volume of posts at WUWT hardly surprising!)
a word on units; you state your equation as annual increments so K2 is comparable to ppm/K/year factors. Since you appear to have scaled to the overall change in the whole record, your K2 compares to my 4ppm/year/K inter-decadal figure. Reasonably good agreement.
Where I think you logic is faulty is that you assume the long term rise entirely due to emissions and hence conclude 50% absorption. Now preceding discussion of the IDE shows that there _will be_ a long term in phase reaction to temp as well as the short term one we seem to agree upon numerically.
What should alert you to this is the post 2000 rise. If you scale your green line to 50% you will see a significant divergence post y2k.
The MLO rise still fits your model but it does not fit your assumption of absorption. I would say that treatise comes closer to confirming Spencer’s proposition than to disproving it.
Greg Goodman,
It’s easy to show that the ocean is a net sink for CO2, not a source. Consider the CO2 data from Barrow, AK and the South Pole. The annual average concentration is highest at Barrow, and lowest at the South Pole and the difference is increasing over time The blindingly obvious conclusion is that the Northern Hemisphere, which has a higher ratio of land to ocean, is the source of excess CO2 and the Southern Hemisphere, which has a lower ratio of land to ocean is the sink. If ocean outgassing was the source of CO2, then the opposite should be true.
The seasonal temperature variation is much, much larger than the year to year temperature change. Yet the seasonal signal is dwarfed over time by the long term trend. The seasonal signal does not in any way explain the long term trend.
WHT: “subtracting off the SST numbers ”
If you would actually state clearly and mathematically what you have done it would be a lot easier to see where methods differ. It seems your “gain” may be akin to my 4ppm/year/K but you don’t state clearly what you are doing and I’m not going to reply on the basis of a guess. You love maths, use it to clearly document what you’ve done rather than imprecise chatty phrases that leave us no wiser.
Stating what coords you mean by IPWP would also help.
Also your samsio data set have undergone some severe smoothing and is not “raw” as you suggested. The data I got directly from Scripts has considerably more variability. That may account for your smaller ‘gain’.
” The seasonal signal does not in any way explain the long term trend.”
why does that even enter into a discussion about data where all <12m variation has been removed?
Sure the ocean is a “net sink” our emissions must be going somewhere. But if it is a bit less “net sink” because of the increase in temp, it amounts to the same thing.
Within the limitations of all this simplistic linear modelling we can just regard the two as additive.
Re:DeWitt Payne (Comment #116611)
June 20th, 2013 at 10:17 am
DeWitt,
Interesting but not definitive. The Northern Hemisphere average surface temperature since the mid 70’s has heated up a lot more than the Southern.
Re: Greg Goodman (Jun 20 10:29),
The ‘less of a net sink’ is small compared to emissions. Ice core data says global CO2 dropped by about 5 ppmv, from ~285 to ~280 ppmv during the Little Ice Age. That’s about 3 years worth of emissions at today’s level from a larger temperature change.
No one seems to be ‘getting’ the implications of IDE solution that Paul gave. The short and long term are both there. One is orthogonal and related to the derivative the other is in-phase. HF dominates the short term, LF dominates the long term.
Now if we can see the d/dt(CO2) signal in the data we know that the in-phase signal is there too and it’s the same thing just without the diff. (It is precisely the frequency weighting from the diff that means HF dominates but it is the _same signal_.
Perhaps that’s the answer. We can calibrate the HF response : 8ppm/year/K , all we need to do now is integrate but I’m getting concerned about ignoring the exp term in doing that. (It will be zero for the in-phase part but may affect the coeff we’re reading off the short response).
DeWitt Payne, “The blindingly obvious conclusion is that the Northern Hemisphere, which has a higher ratio of land to ocean, is the source of excess CO2 and the Southern Hemisphere, which has a lower ratio of land to ocean is the sink.”
Right. The issue is what impacts the sink efficiency or should be. One thought is that the temperature and pressure of the thermocline(s) and the rate of deep water mixing is a significant factor. The inconsistent lag of CO2 with temperature in the paleo records indicates something more interesting is going on.
Stott with USC thinks the variation the CO2-Hydrate stability horizon explains a lot of the details. That doesn’t change the fact that FF emission don’t add to atmospheric CO2, but may help explain the why about half.
Nick Stokes,
Showing my ignorance of the sun (which I’ve claimed before) why do you guys talk about a 22 year cycle? It peak to peak etc is 11 years?
Re: Paul_K (Jun 20 10:45),
And how much of that is land? If you plot the UAH NH and SH ocean anomalies, the data mostly overlap. The current anomaly is 0.06 for the NH and 0.01 for the SH. The trend lines are different, but that’s because the NH ocean had a cold spell relative to the SH in the mid 1980’s and a warm spell in the mid 2000’s.
Barrow also has a higher seasonal variation of CO2 than the South Pole or Mauna Loa.
Re: Greg Goodman (Jun 20 10:56),
You still miss the point that the driver for the HF response is the seasonal temperature which is large magnitude. The LF response, if it were temperature related, would be the year over year temperature change, which is tiny. Let’s say it’s 0.8 K in 30 years or 0.027 K/year. That give you 0.2 ppmv/year from temperature change, if you had calculated temperature change correctly. Or about 10% of the current rate of change of atmospheric CO2. But wait. That 0.8 K is the global temperature change. We need the SST change. The UAH global ocean anomaly has a linear trend of 0.0117 K/year. That’s 0.09 ppmv CO2/year.
DeWitt Payne, you’re half way there. Now look at coeffs of the two terms and take omega into account. 😉
for a driver of T=sin(ωt)
CO2 = Asin(ωt) – Aωτcos(ωt) + Aωτexp(-t/τ)
where A = S/(1+(ωτ)^2)
Greg Goodman,
“Now preceding discussion of the IDE shows that there _will be_ a long term in phase reaction to temp as well as the short term one we seem to agree upon numerically.”
.
Sure, but ignoring the mechanistic issues for a moment, the ice age change in CO2, if ascribed to changes in ocean temperature, was about 85 PPM for a swing of perhaps 5C in low latitude temperatures… that implies an equilibrium (not year-on-year) response in CO2 of about 85/5 = 17 PPM/degree. That 17 PPM per degree is reached over several hundred years equilibration time (the famous temperature leads CO2 observation). The relatively long equilibration time is due to the time needed for dissolved CO2 concentration along the thermocline (which increases with depth, just as temperature falls with depth) to equilibrate with the atmospheric concentration, a processes will take at least several hundred years. The temperature rise of the ocean surface since the preindustrial period is under 1C, suggesting something less than 17 PPM of atmospheric increase could be expected to have come from ocean warming. The actual rise in CO2 over the industrial period is about 120 PPM, consistent with CO2 emissions being the overwhelmingly dominant cause.
Yes, it does depend a lot on tau.
http://climategrog.wordpress.com/?attachment_id=233
The swings I evaluated 8ppm/a/K on were of about 3.3a period, or ω=0.52
Just taking the AOGCM figure of 3.5 for an order of magnitude guess I find ten year period 2.pi.omega=10 ( ω=1.6 )gives 1.6/0.52/3.5*8= 7ppm/K
70 ppm/K 100a period etc.
I century long rise would be like a 200y periodicity so 140 ppm/K, that would suggest 0.7K rise over 20th c. would be of the order of 98 ppm, which is about what it was I think.
Now that was rough as guts and I would not put that forward as a serious result but it shows ballpark that it _could_ account for most of the rise. It now needs doing more sensibly and all the usual caveats need noting.
I repeat I do not consider that shows it was all thermal but it shows that it is of the right order to require a proper calculation. My initial worry is tau.
If anyone can see any logical flaw in the calculation please point it out. This was just done off the top of my head.
Paul, do you think I’m applying formula correctly?
BillC:
One full cycle of the solar magnetic field is about 22-years. The sun-spot cycle (and presumably solar luminosity cycle) has a maximum every 11-years.
Curiously, and for reasons I don’t immediately6 understand, the 22-year cycle is clearly resolvable in long-duration temperature spectral periodograms, whereas the 11-year cycle is not.
Figure.
Paul, I’m wondering how this analysis ties in with your post where you derived a cyclic model. You found a 61 year periodicity and a longer one for which I could not see a statement of the fitted period.
Could you post the period and amplitude of the the three periodicities of you fitted model? It would be interesting to see whether they tie up. I suppose they should . so that may be one way to evaluate tau.
All this relies on S being constant and so implies the assumption of a one slab ocean and that all this is contained within the mixed layer. That is probably not too outrageous if we limit it to the century or so.
At least in order to establish whether the answer is 10 or 100 ppm over that period for 0.7K rise.
Re: Greg Goodman (Jun 20 12:17),
The total change for atmospheric CO2 for a temperature change of 5K from glacial to interglacial was ~100 ppmv, 180-280ppmv. By your calculation it should have been 500 ppmv. And again, the ocean is either a sink or a source. If it’s a source, than all human emissions need to be added on top of the amount coming from the ocean. If that were the case, the atmospheric CO2 level would be over 600 ppmv. But of course, it’s not and you’re wrong.
The assumption behind the derivation is flawed. Anthropogenic emissions are a confounding variable that correlates with temperature for reasons other than Henry’s Law. Your correlation is therefore spurious. The statistical tests that fail to reject unit roots in both the temperature and CO2 time series are wrong for similar reasons.
Re: SteveF (Jun 20 11:33),
The equilibration time of the world ocean is more like 2,000 years. I was able to fit the Vostok ice core CO2 data to the deuterium isotope anomaly using an ocean time constant of ~2500 years. The 800 year number is just the offset in the two curves resulting from that time constant.
“The assumption behind the derivation is flawed. Anthropogenic emissions are a confounding variable that correlates with temperature for reasons other than Henry’s Law.”
and if I say that your assumption is “flawed” so you are “wrong”?
You are _assuming_ a priori that increased atmospheric CO2 is of human origin and that it has a significant affect or global SST. You assume my method is wrong in order to say it is wrong. Circular logic.
“By your calculation it should have been 500 ppmv. ”
No, I stated there is an implicit assumption that S is constant , it would not be on that time-scale. So _your_ calculation of 500ppmv is erroneous and has no bearing on what I suggest.
” And again, the ocean is either a sink or a source.”
So repeating yourself whilst ignoring my reply to that issue makes right??
I repeat. Your turn.
You are clearly competent so if you could present credible, objective points rather than trying to summarily dismissive because you don’t agree it would be more useful.
Greg Goodman,
Human CO2 emissions are completely sufficient to explain the atmospheric CO2 concentration. In fact, the problem is explaining why the atmospheric concentration isn’t higher than it is. This is the so-called missing sink problem. I haven’t been paying close attention to this research, so maybe it’s not a problem any more. But I wrote this post a while back to see how the empirical fit to an impulse response of the Bern CO2 model fit using the actual emission data. Note that my understanding of the function given in the IPCC WGI report was naive. I treated it as a four box model. In fact, it’s just an empirical fit that looks like a four box model. The figure links are broken so here they are: Figure 1, Figure 2, Figure 3.
Btw, I’m all the way there. You’ve gone over the edge. The LF response to temperature is bounded by the glacial/interglacial data to about 20 ppmv/K.
SteveF: ” the ice age change in CO2, if ascribed to changes in ocean temperature, was about 85 PPM for a swing of perhaps 5C in low latitude temperatures…”
Between glacial and interglacial there is a flip between two different stable climate states. That change-over shows clear positive feedbacks in operation. There is also a massive volume of water that changes state. What is CO2 content of ice?
I don’t think it is reasonable to suggest a simple linear model will be valid across such a change and I did not assume that it was.
However you are doing so in presenting that calculation as disproving what I put forward.
Re: Greg Goodman (Jun 20 14:22),
I told you why you were wrong. d[CO2]/dt is not just a function of temperature. If you treat it that way, you’ll get the wrong answer. You’re looking at the wiggles and ignoring the underlying trend that has increased with increasing emissions from about 0.8 ppmv/year in 1959 to over 2 ppmv/year in 2005. That was not a function of increasing temperature. Human emissions increased from 3.9 PgC in 1959 to 9.4 PgC in 2005. Not surprisingly, the ratios are nearly identical. Try correlating d[CO2]/dt with both emissions and temperature and see what you get. The data links should be in the article I linked.
Re: Greg Goodman (Jun 20 14:37),
It isn’t a linear model. It’s an upper bound. But the ratio of annual emissions to d[CO2]/dt is pretty close to linear.
See graph
The higher slope line does not include land use CO2 emissions.
Hmm. Looks like the link didn’t work.
See graph
Goodman, It’s documented on my blog. It looks like you are left to doing gotcha tricks.
The Annual Change equation is very close to what I am doing but I use the Green’s function/impulse response approach favored by climate scientists to estimate emitted CO2.
For the Samoa set there is no gain to be had from the seasonal signal, it is all fossil fuel co2 in the residual. Quite amazing.
The missing sink in CO2 sequestration is not an issue. The problem has been not using a diffusional response and instead applying a damped first order response. Exponentially damped responses don’t work for solving these kinds of diffusion problems. That’s why one uses a Green’s function solution to a Fokker-Planck type of diffusion equation and convolve that with the carbon emission forcing function. The missing sink disappears.
It essentially boils down to thin tail vs fat tail dynamics. Diffusion is fat tail and that accounts for all the CO2. It may be that the climate scientists haven’t been the most articulate in explaining what’s happening, but the research papers I have read show that they do apply an impulse response with the correct fat diffusional tail.
Re: WebHubTelescope (Jun 20 15:30),
You would think they would put that in, oh say, the IPCC WGI report. Like I said, it was a somewhat naive approach. I was surprised it worked as well as it did.
I put a comment on your blog. I think you misread the x axis on the δ40Ar, CO2, CH4 and δ18O figure. Going to the right is going back in time. It looks very much to me that CO2 and CH4 still lag temperature not the other way around.
DeWitt Payne (Comment #116663)
I know it’s sufficient and the trivial assumption is that it all stays in the atmosphere. Then when we realise it does not we assume part of it gets absorbed and the rest is what accounts for the increase.
None of which, of course means those assumptions are correct.They are simply the most obvious.
The article on the Bern model is interesting.
Hub:”It’s documented on my blog.”
Well how about linking to it instead of just banging up a graph? I’m not going to go digging. If you have something explaining the graph why are we discussing where you’ve hidden it instead of what if contains. “Amazing”.
“It isn’t a linear model. It’s an upper bound. ”
Saying it is an upper bound assumes the system is the same in both regimes. What is the mean atmospheric pressure during a glaciation? Same as now? I don’t know , so I’m not going assume it is.
Hub’s suggestion that a linear model is not appropriate merits thought, though I don’t see that exclusively using a diffusion model is appropriate for the response of the mixed layer which is well, getting mixed, not diffusing.
Maybe diffusion between slabs, but as he says it’s slow, so we probably come back to linear for <100 y response in the mixed layer.
more info here
http://theoilconundrum.blogspot.com/2012/03/co2-outgassing-model.html
Also thanks DeWitt, I will try to clean the time axis up.
Re: Greg Goodman (Jun 20 16:07),
There always an infinite number of possible mechanisms to explain an observation. That’s why Occam’s Razor was proposed in the first place. The various sites where CO2 is measured show considerable difference in their seasonal behavior. Obviously local temperature is important. But assuming that the LF behavior is caused by CO2 emissions and seasonal fluctuation is caused by local temperature is the simplest mechanism that accounts for all the data. Your mechanism, as far as I can tell, has no means of dealing with emissions. Or at best, it produces the same results, but with more complexity.
I keep repeating that the ocean is a sink and not a source because you still still fail to see that your mechanism violates that assumption. It also doesn’t explain little details like the change in the δ13C anomaly. Your global temperature sensitivity is going to drop drastically if you include emissions in your model.
The Little Ice Age also puts a bound on the sensitivity of the rate of change of atmospheric CO2 to temperature. Plug the ice core CO2 data for the pre-industrial period into your model and see what temperature it predicts. I’m guessing it will say that there was only a tiny change in temperature.
Greg Goodman,
Let’s try this another way. What a change in local temperature is doing, ignoring the biosphere, is modulating the equilibrium between the air and the ocean. In the absence of emission, the concentration wouldn’t change. If you put a slug of fossil fuel derived CO2 into the atmosphere, the rate of absorption will be slightly less at higher temperature and slightly higher at lower temperature. But all of the initial atmospheric concentration increase is because of the added CO2, not temperature. Increase the rate of emission and the concentration increases faster. Increase temperature with no emission and the concentration will go up, but with a sensitivity of only a few ppmv/K. The equilibration time for a temperature increase is on the order of 2,000 years.
Note that for a single slug of fossil fuel CO2, the concentration will decay over time with final equilibration requiring the ocean to equilibrate, which takes ~2,000 years. The equilibrium level in the atmosphere will be somewhat higher than it was before because there’s more total carbon in the system. But we’re adding CO2 to the atmosphere continuously so while very little of the added CO2 in one year is absorbed that year, all the previous years CO2 hasn’t yet reached equilibrium.
Dewitt, This compares the law dome 2000 year CO2 high resolution CO2 with the Neilsen 2004 Southern Ocean SST and the Oppo 2009 Indo-Pacific Warm Pool reconstruction.
https://lh3.googleusercontent.com/-dyw6fPClKlc/UcOuyx5M0PI/AAAAAAAAItY/mbLFk1sAftc/s865/neilsen%2520oppo%2520with%2520co2.png
While I understand making pragmatic assumptions, there are occasionally a little more interesting possibilities that don’t involve “Global” temperature correlations.
As long as the Bern carbon cycle model is mentioned, I can’t help but notice that the multiple exponentials of that model essentially duplicate the shape of a diffusional impulse response profile.
Notice how the fat-tails of the Bern model match the fat-tails of a diffusional response:
http://imageshack.us/a/img18/8127/normalizeddecayofco2.gif
I assume that they keep it in the multi-exponential format because then they can use conventional first-order linear response theory via additive rules. For my own purposes, I don’t care as I just perform a numerical convolution to get the result.
BillC,
Look up “Hale Cycle”. I agree with Carrick’s “curiously”.
Greg Goodman,
The three-sine-cycle fit to temperature (which I don’t defend as a valid null) are as follows:-
Canonical form is amp*Sin(2*pi*t/period – lag) where t is time in calendar years.
amp 0.91509 0.10417 0.04935
period 581.073 60.7799 21.33
lag 2031.25 1803.82 1787.51
Greg,
You asked: “Paul, do you think I’m applying formula correctly?”
I am sure that you are, but I haven’t checked. The more important issue is whether the governing equation (to which this formula is a solution) is a valid representation of the relationship between Δ(CO2) as predicand and T as a pseudo-forcing.
Note that for a single step change in Forcing, the linear feedback equation gives an exponential temperature gain which is bounded (and which at large values of time asymptotes to T = Forcing times Climate Sensitivity per unit forcing). If you want to use the same governing equation as an isomorph for temperature-driven CO2 change, then DeWitt’s argument re the maximum bounding of CO2 change for a temperature rise is therefore valid. If you don’t accept the argument that it is bounded, you need to change the governing equation, which means you need to change the “formula”.
Greg,
Sorry my use of the term “exponential temperature gain” is ambiguous. Specifically for a fixed step forcing, F,
T = F*S*(1 – exp(-t/tau)) where S is the climate sensitivity to a unit change in forcing.
Thanks Paul, that last comment addresses another question I have with the original solution equation. The signs are wrong for the short term response. The initial response to an increasing forcing can’t be negative. Is the following correct?
T = Asin(ωt) + Aωτcos(ωt) – Aωτexp(-t/Ï„)
where A = S/(1+(ωτ)^2)
That reduces to 1-exp() for a step so I think all terms have correct sign.
Well spotted. I thought there was something artificial about that model. It may well be a linear approximation to a diffusion model.
One thing I did not understand from DeWitt’s article was how it could end up with a 20% residual with an exponential “tank” model.
where does that come from?
re. three-sine-cycle fit to temperature , why give lags of that order? The lag in a sine is best expressed in 0 – 2pi range.
OK, so we are agreed that we can view it as linear superposition.
We are also agreed that (without emissions) if you raise the mean SST by 0.7K , CO2 will rise.
What I’m saying is the rise due to increasing temp and increasing emissions will look similar. There is a danger of confounding the two. I’m not suggesting 100% absorption , I’m trying to use the d/dt(CO2) which we can measure to infer the magnitude of the in-phase term.
I’ll comment on bounding next.
“Note that for a single slug of fossil fuel CO2, the concentration will decay over time with final equilibration requiring the ocean to equilibrate, which takes ~2,000 years.”
I think there are two processes being confounded here. I do not see that the time constant of one can be taken for the other.
The time for the ocean temperature to equilibrate is thousands of years because of heat diffusion and stratification of ocean water. This should not be confused with time it takes the ocean to equilibrate to a change in CO2. That has to happen _as well as_ the thermal equilibrium and adds to the lag, it is not the same delay or the same lag.
The geological record deuterium record you worked with is a primarily a surface proxy related to the ratio at the moment of evaporation or precipitation. So the geological ice core “temperature” is SST. The 800 year lag tells us something about heat diffusion and ocean thermal equilibration as much as CO2 equilibration times. It is a combination of the two.
Diffusion of CO2 in/out of the ocean has it’s own time constant and has nothing to do with heat diffusion time constant. Your insistence on 2000 years to equilibrate CO2 is to confound the two processes. It does not indicate CO2 decay is even of that order. That value we must find elsewhere.
Hub’s diffusion convolution is a nice technique but ignores the presence of a mixed layer as I already pointed out but he ignored.
It seems the Bern model is a simple linear approximation to reproduce that though I have not researched its derivation.
Short term response will be determined by the mixed layer, which is mixed. So diffusion relations are not appropriate. Maybe a two slab model will be needed if deep temp OHC indicates it is needed on multidecadal scales. Paul has indicated the linear model can “easily” be modified to account for that if needed.
I think the linear equation can be used to model the response of the mixed layer.
Paul_K
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I am using the short term response to derive the sensitivity. That is the same sensitivity for the long term with frequency dependency determined by the coeffs you derived.
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I am not saying it is not bounded, what I am questioning is the applicability of the bounds DeWitt is deriving from the geological record covering swings between two different climate regimes.
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Even if we use more a recent core we still have to deal with 2000 year temperature equilibration of deep ocean that is not reflected in the “temp” derived from the ice core. Salby also raises the question of diffusion of CO2 in the ice that means range of CO2 may be seriously under estimated. (I am not totally convinced by his conclusions on that but the issue is legitimate). The core record compares instantaneous SST with the CO2 response to a 2000 integral of temperature. Thus the recent , high resolution cores are not informative about “sensitivity”.
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DeWitt, Occam’s razor does not justify simplifications that confound two variables by ignoring one of them.
Greg #116706
“Diffusion of CO2 in/out of the ocean has it’s own time constant and has nothing to do with heat diffusion time constant.”
Actually they are related; the ratio is the Schmidt Number and for a given species is fairly predictable.
There is a turbulent diffusivity in the mixed layer.
Greg Goodman,
“…equilibrate is thousands of years because of heat diffusion and stratification of ocean water. This should not be confused with time it takes the ocean to equilibrate to a change in CO2.”
.
Hummm…
Actually, diffusion of heat and molecular diffusion are both probably too slow to contribute much. Equilibration of temperature along the thermocline is mainly the result of shear driven eddy mixing (from horizontal motion which changes in speed/direction with depth), not heat transfer. Look at the thermal conductivity of water and use that value to estimate the rate of equilibration in a stratified tank (no shear driven eddy mixing) which is a couple of kilometers deep. My recollection (I did this a long time ago, after Lucia gently pointed out that I was nuts to imagine thermal conduction is important) is it takes orders of magnitude longer than what the shape of the thermocline and rate of upwelling (about 4 meters rise per year) tell us it should take.
.
I haven’t done the molecular diffusion calculation for CO2 dissolved in water (maybe DeWitt has), but I’m pretty sure that will turn out to be orders of magnitude too slow, so shear driven mixing causes most of that equilibration as well.
Greg,
Ouch. Sorry, again. I wrote…
Canonical form is amp*Sin(2*pi*t/period – lag) where t is time in calendar years.
The canonical form for the sine function should have read…
…amp*Sin(2*pi*(t-lag)/period). As correctly stated t is in calendar years.
Greg, “Even if we use more a recent core we still have to deal with 2000 year temperature equilibration of deep ocean that is not reflected in the “temp†derived from the ice core.”
There is a lag of about 2000 years between the SST and deep ocean temperature. There is no 2000 years to “equilibrium”. The Holocene started with a “seesaw” SH temperatures started warming first, then the NH warmed/SH cooled, then the NH cooled while the SH warmed. The first 80 ppm CO2 lagged the “seesaw” mixing/warming then stabilized. About 5000 years ago, according to the Antarctic cores, CO2 reversed its decline and started a slow rise with the SH part of the “seesaw”.
That is why I showed this,
https://lh3.googleusercontent.com/-dyw6fPClKlc/UcOuyx5M0PI/AAAAAAAAItY/mbLFk1sAftc/s865/neilsen%2520oppo%2520with%2520co2.png
The Oppo IDPW reconstruction is a fair proxy for “global” temperature and according to Web “global” CO2 so the Law dome high resolution CO2 reconstruction should follow the IPWP. The Neilsen Southern Ocean reconstruction indicates a kind of Holocene do over with SH SST rising out of phase with NH SST, which looking short term you could blame ACO2 as a cause, but since the CO2 decline shifted positive 5000 years ago, there may another little wrinkle involved, like a shift from the 100ka glacial/interglacial world to a new beat.
https://lh3.googleusercontent.com/-bnfSiuz7AV8/UcRM6tiocGI/AAAAAAAAIug/t8oc_YOjYcc/s841/Stott%2520lea%2520with%2520co2.png
Since ENSO is part of the discussion, That is the Stott Western Pacific with Lea Galapagos versus the ED3 CO2 reconstruction.
The “seesaw” has not stopped, so “Equilibrium” needs to be used with caution. Note that both the Stott and Lea reconstructions vary only about 2 degrees in the past 22 ka. That would be about 40 ppmv per degree if Webster is right with his IPWP aka ENSO regional relationship to CO2.
Interesting enough that Stott and others are pursuing alternate theories.
SteveF, ” Look at the thermal conductivity of water and use that value to estimate the rate of equilibration in a stratified tank (no shear driven eddy mixing) which is a couple of kilometers deep.”
That is one of those paradoxes. Turbulent mixing/diffusion/ventilation is (are) the primary means of heat transfer but at a stratified layer, conduction only has to have a small impact at the boundary layer, to start, not drive, the whole process. It starts getting extremely complex since diapycnal flow into a density/temperature layer doesn’t have to change much. fractions of a degree, to change the efficiency. That is why the fluid dynamics guys make the big bucks.
That is a good point Nick.
When GG lobs up these pronouncements:
” This should not be confused with time it takes the ocean to equilibrate to a change in CO2.
…
Diffusion of CO2 in/out of the ocean has it’s own time constant and has nothing to do with heat diffusion time constant.
“
it confuses the point that these are not time constants in the conventional sense. With diffusion, you can’t describe processes as a 1/e decline, because the damping is not exponential.
Consider that the Bern model for CO2 sequestration is an approximation to a diffusional model of carbon randomly walking in and out of the carbon cycle. When it is permanently out of the carbon cycle the CO2 becomes sequestered. The abstraction that we use is one of CO2 diffusing deeper and deeper into the ocean layers. As the CO2 goes deeper, it gains a higher probability of permanently becoming sequestered.
This is where the Schmidt Number analogy and comparing diffusional process comes in.
Heat as a form of thermal excitation goes through the same process as the CO2 diffusing downward. It randomly walks upward and downward through diffusional eddies and large-scale upwellings/downwellings until it becomes more-or-less “sequestered” in deeper layers. Obviously, the longer it takes for the heat to get down there, the longer it would takes to come back out, and that’s the basis for the fat-tails observed.
So the gist of the Schmidt Number argument is that the medium/carrier of the diffusing particles, whether it is heat or CO2, is very similar. Like the Einstein relation relating mobility to diffusivity, what we are modeling are processes that work across many scales, and where diffusion rules, the general trends look Fickian.
Don’t think of diffusion as it is defined in terms of conduction. It is actually an “effective diffusion”. Eddy diffusion is clearly not diffusion in the classical molecular sense but it is diffusion because it follows a random walk process when the parcels move up and down (vertical eddy diffusion) or laterally (horizontal eddy diffusion). If one applies the same mathematical abstraction to even larger scale effects such as hydrostatically-balanced upwellings/downwellings, you can also model this as a diffusion process with a differing coefficient.
When these ranges of diffusivity are modeled as a continuum, one can then start making sense of the ocean heat content dynamics. That is what I tried to do here:
http://theoilconundrum.blogspot.com/2013/03/ocean-heat-content-model.html
and gosh darn does it work well to capture the general dynamics.
My goal has always been to capture elements of climate science as a first-order model that replaces the mind-boggling detail with stochastic uncertainty in the parameters.
Re: Greg Goodman (Jun 21 00:53),
That’s the fraction of CO2 remaining in the atmosphere tank. For an equilibrium process, if you add something to one reservoir, all reservoirs end up at a higher level than before. But that’s a naive model. The tanks don’t leak. In fact, CO2 keeps going down. But it takes about 500,000 years to get back to the original level once emissions cease. David Archer has more models than just MODTRAN on line. Here, for example, is an impulse response model for CH4 and CO2.
Webster, “If one applies the same mathematical abstraction to even larger scale effects such as hydrostatically-balanced upwellings/downwellings, you can also model this as a diffusion process with a differing coefficient.”
Right, but you have an asymmetrical “slab” with mechanical “pumping”. Sooner or later you are going to have to divide your model into separate volumes where you will find you have a coupled system with all the weird oscillations they can produce.
DeWitt,
If I understand that David Archer model for CO2 uptake, I suspect it is far from correct. Since ~50% of emissions are currently being absorbed, and that rate of uptake is proportional to the “disequilibrium” between the ocean surface and the atmosphere, were all CO2 emissions to suddenly stop, we would expect an initial rate of decline in atmospheric CO2 equal to (about) the current rate of uptake, or about equal to half the current CO2 emissions. Over time the rate of fall in CO2 would gradually slow, of course.
.
Archer’s model suggests the response to a slug of CO2 is an instantaneous step upward followed by an extremely slow decline. Seems to me more likely that a slug causes a step up followed by a rapid exponential-like decline for a brief time, then a slower decline as the CO2 goes into the deeper ocean.
Re: SteveF (Jun 21 07:05),
The diffusion coefficient for CO2 in water is about 2E-05cm²/s. Effective eddy diffusion coefficients are on the order of 1 cm²/s. Just like most of the atmosphere where conduction is ignored except at boundaries, diffusion in the ocean is insignificant compared to turbulent mixing. 14C from atmospheric nuclear weapons tests has been used to study mixing in the ocean as well as other tracers like sulfur hexafluoride.
Note that 0.1-0.2 cm²/s is considered slow mixing.
Re: SteveF (Jun 21 09:00),
You’re not looking at the model correctly. Most of the absorption in any given year is from CO2 emitted in the previous years. After one year, only 13.5% of the CO2 emitted that year is absorbed. And it gets slower after that. Only 6.5% additional is absorbed in the next year and it takes 30 years for 50% absorption and hundreds of years to 75% absorption. Here’s a graph I created assuming all emissions ceased in 2005. From the peak at 379 ppmv, it only dropped to 344 ppmv in 2100.
DeWitt Payne (Comment #116733),
Thanks for the diffusion value.
.
I like the SF6 tracer studies a lot more than the C14 studies, because SF6 is biologically inert. The C14 results can potentially be misled by the continuous rain of organic particles from the sunlit surface towards the deep, where bacteria oxidize almost all of it to CO2 (save for resistant materials like alkenones). The profile of dissolved oxygen in the ocean shows a clear depletion of oxygen-rich deep water to a minimum as it makes it’s way toward the surface, meaning that at least some CO2 is being produced at depth, rather than diffusing downward. Of course that O2 depleted water gains oxygen as it passes the minimum point… due to eddy driven down-mixing. I would like the C14 studies a lot more if some estimate of this effect were included, but I have not seen that.
Re:Greg Goodman (Comment #116700)
June 21st, 2013 at 12:43 am
No Greg, I think I did actually manage to transcribe one thing correctly. (Smiley) The signs in the original solution for F(t) = sin(wt) were correct: T = Asin(ωt) – Aωτcos(ωt) + Aωτexp(-t/Ï„)
The initial gradient is always positive.
Lots of interesting relationships being quoted here let’s try to summarise.
At constant temp, an increase in atm CO2 will result in an increased partial pressure of CO2 and hence a transfer to the ocean. This is dependent upon atm pressure, temp variable Henry’s const and other factors if we want to dig deeper.
Once in the mixed layer it will get.. mixed.
RIK WANNINKHOF JGR 1992
“where 660 is the Schmidt number of CO2 in sea water at 20øC”
2000/660=3.33 years.
There will be transfer by proper diffusion , which is apparently far too small (does that mean we can stop messing with Schmit?) , eddy pseudo diffusion which can look a bit like real diffusion with a fat tail but is quicker. All of that can be simulated to first order approx by three linear model exponential decays, if you want everything to remain nice and easy to model.
After all that I don’t see much grounds for assuming thermal time constant applies equally to CO2.
There is also the question of permanent conversion of CO2 by biotic elements and that will not come back out with warming. Most of that will happen in surface waters and will not need to diffuse / mix.
Bern model 1.18 years can be confounded with the annual cycle and has been filtered out in all that is discussed so far. >600a time constant is too slow to have much to do with last 120 years or so I’m trying to work on. So that model leaves us with 18.6a tau for consideration. IMO it’s excessive but it’s one value. In view of the usual IPCC fashion of using the answer to frame the question, I do not give it much weight.
Paul suggested AOGCMs produce a tau of 3.5a
I looked at decay bomb test C14 and IIRC found 5-7a , I’ve seen other estimations in that range and consider that more likely.
5 +/-2 years may do for a first estimate of uncertainty range on that figure.
DeWitt: “That’s the fraction of CO2 remaining in the atmosphere tank.”
A figure worth retaining for the impulse response. How long it takes to descend somewhere near that will depend upon time constants used.
So it would seem my point about ice-core records not being informative for the sensitivity ratio of temp and CO2 stands and attempts to use such figures to set bounds on the relationship between the two over the last 100-150 years are incorrect and don’t necessitate my abandoning the linear model if it produces figures out side such a range.
OK, for high frequency limit ω>>τ (large omega) A=S ; Aωτ>>A so first time is negligible. Due to HF cos is oscillating fast about the decaying exp. Looks good , beg your pardon.
😉
Re: Greg Goodman (Jun 21 10:14),
Nope. Different processes. Equilibration of a slug of CO2 is not the same as equilibration to a step change in temperature even though both involve diffusion. The ice core record does, in fact, bound the response to a step change in temperature. The modeled equilibration to a slug of CO2 has nothing whatsoever to do with temperature.
Question: Does your model say that the CO2 level would be what it is today even if there had been no fossil fuel burned, cement manufactured or land use/land cover changes assuming the same temperature profile? Conversely, would the CO2 level be at the pre-industrial level assuming the same total emissions but no temperature change?
You do realize that a yes answer must require the instantaneous absorption of 100% of all emissions. Needless to say, that’s unphysical.
Being able to fit a model to the data doesn’t prove that the model is physically realistic. The low frequency sine wave that Paul_K fitted to the temperature data in no way proves the existence of a ~500 year climate oscillation or disproves the influence of greenhouse gases on global temperature. It’s mathturbation as Tamino would put it.
Cappy said:
Just to pin this down, I asserted that the seasonal fluctuations in the Mauna Loa CO2 measurements follow a Henry’s Law linear scaling of the Indo-Pacific Warm Pool sea surface temperatures. This bounds a range of latititudes from 9N to 21S.
Subtract this from the CO2 measurements and what is left is the monotonic rise of aCO2 plus any fluctuations due to economic variability, damped by a convolution with the CO2 sequestration impulse response.
And how was that Bern model calibrated? By assuming T vs CO2 is same as ice core record and MLO can be assumed to be x% of human emissions.
Unfortunately a whole world of different models could be made to fit that gently rising curve. We need to look rate of change not the cumulative integral of CO2 to study the variation and attempt attribution.
If a significant proportion of that rise is due to the rise global SST then those time constants of the Bern model will come down. Plot the same thing with 3.5 or 5 years and you get a different picture entirely.
If I put tau of 18.6 years into my earlier equations instead of 3.5 the results will be about 5 times smaller. ie 14ppm for the century long change. So the Bern model is either based on the ice core assumption or amounts to the same thing.
“This bounds a range of latititudes from 9N to 21S.”
Perhaps it would be useful to specify exactly what region you are refering to by IPWP. Then we can have a look.
Greg Goodman,
What about the fact that the global temperature trend has been negative for the last 11 or 12 years but the CO2 concentration has continued to increase from ~366 ppmv in 1998 to ~392 ppmv in 2011? Oh, wait. I know the answer to this: It’s a lagged response. If that’s the answer, though, it again implies instantaneous total absorption of emissions.
Re: Greg Goodman (Jun 21 11:14),
The long term rate of change tracks emissions. Q.E.D.
Re: Greg Goodman (Jun 21 11:14),
Nope. Tracer measurements among other things.
http://www.climate.unibe.ch/~joos/model_description/model_description.html
Actually that CO2 behavior modeled by Archer is composed of an instantaneous step up followed by an extended climb caused by the CH4 taking hold and leading to further outgassing of CO2 and more predominantly the decomposition reaction of CH4 and O2 into CO2 and H20.
Try turning the CH4 to zero and you can see what happens.
Remember that Archer is the climate scientist interested in catastrophic AGW and so he has all the catastrophic elements in place.
Thanks to DeWitt for pointing this app out because I hadn’t seen it before.
http://climategrog.wordpress.com/?attachment_id=397
Samoa d/dt(CO2) vs SST
I would say that Samoa station CO2 follows _global_ SST better than IPWP SST. In particular Samoa is totally out of phase (inverted) in 1980, 1986 and 1996. It would seem your idea that this area reflects global behaviour is mistaken.You recommended that CO2 record as being free from some kind of variation
Â
I found the same thing using MLO.
Â
Rate of change of atmospheric CO2 is a better indicator of global SST that N.Pac or IPWP SST.
Â
You will not in that plot I have tried to scale things to the long term changes to examine your idea. Clearly a different scaling is required to match better match the short term variations.
Â
This is in line with what I have already presented : 4ppm/a/K inter-decadal ; 8ppm/a/K for inter-annual, which is absolutely in line with frequency dependency of the linear relationship.
It seems much of you idea this CO2 station was “better” was because the version of the data you got had been spline smoothed or something plus your additional convolution smoothing . The version I got here shows similar variability to MLO.
Re: WebHubTelescope (Jun 21 11:50),
Oh, I did. On a 10,000 year time scale you get basically the same plot for the same total amount of carbon. It’s only on scales of 1,000 years or less that you can actually see the conversion of CH4 to CO2. The CH4 is completely converted in less than 40 years.
Re: Greg Goodman (Jun 21 12:04),
Let’s see. 10 years at -0.048 K/decade (2002-2011). That would be 4*10*(-0.048) or -1.9 ppmv CO2? Or have I done something wrong.
DeWitt said:
Right, so the slug for CO2 and CH4 is each halved to keep the same overall stoichiometric results.
I always have to remind myself that Archer and his students work on some narrow aspect full time, and it is up to us individually to keep up with the detailed analysis.
“Remember that Archer is the climate scientist interested in catastrophic AGW and so he has all the catastrophic elements in place.”
That is very interesting !
It was precisely David Archer’s site that alerted me to the limited importance of CO2 late in 2007 IIRC.
At the time he had notes for his students and demonstrated using MODTRANS which could be use interactively to comfirm the results that showed reducing CO2 output would make absolutely no difference to global temps.
I was disappointed some time later when I wanted to go back to it that he no longer provided acces to MODTRANS. I presumed he may have found he was violating his licence or something.
Has he turned his shirt?
GG said:
You keep on doing that same move, expecting everything to be served up to you on a sliver platter. I tried spelling IPWP out as Indo-Pacific Warm Pool and provided the bounded latitudinal coordinates for that region.
But OK, here again is the blog page where I describe the IPWP.
http://theoilconundrum.blogspot.com/2012/03/co2-outgassing-model.html
Scroll to the bottom, where I actually made up a map, with the dotted line for the constraining region:
http://img9.imageshack.us/img9/6527/ipwp.gif
Hope you are now satisfied.
“Let’s see. 10 years at -0.048 K/decade (2002-2011). That would be 4*10*(-0.048) or -1.9 ppmv CO2? Or have I done something wrong.”
Haven’t we been here before?
Same answer as last time you are not taking into account the omega dependency of the coeffs. Just read back, I think I’ve gone though it in enough detail by now and its pretty simple. Well within the capabilities of most here it seems.
“You keep on doing that same move, expecting everything to be served up to you on a sliver platter.”
I don’t want a silver platter , I just want you to say exactly what you are doing to give it due consideration. I do not want to guess what you mean only for you to say I got it wrong, or go on a googling trip or read your whole blog until I find it.
Anyway, I chose one area, may differ a little from yours.
Greg Goodman, are you British or from somewhere where they just like to argue for argument sakes?
You will get nowhere if you keep on posing these strawmen of spurious correlations and not include some basic physical considerations that set the constraints on the problem.
Science is about moving forward and seeing how far you can go by building up a set of self-consistent pieces. When it starts completely falling apart, you will know, but until that time, you try to go with the flow of promising ideas.
Your trial balloon suggestions have been debunked and you should probably consider dropping the d/dt(CO2) vs SST line of reasoning. It is not promising and it not going to go anywhere.
DeWitt:” The long term rate of change tracks emissions. Q.E.D.”
There you go with the trivial dismissive statements again.
The long term rate of change tracks outgassing due to temp increase Q.E.D.
Easy isn’t it?
Your statement is untrue since emisions are far higher. My rate of change plots show a notable correlation show me a similar correlation to human emissions and it may get interesting.
All I can see is a slight dip in emissions after the two eruptions. Obviously California’s air con budget is so large it can be seen in the global emissions record. 😉
WHT: Your trial balloon suggestions have been debunked
Where exactly?
Cappy said:
And sooner or later you will drown in the complexity and the management of the parameter space.
Consider these points:
1. A coupled system the way you describe it is essentially a diffusional model. The volumes consist of compartmental slabs which exist to describe flow in both directions, up and down. In other words, the compartments model the divergence of the mass or heat flow within the slabs. That is the topological basis of the heat equation or the Fokker-Planck equation or any of the diffusion/continuity equations.
2. A random walk IS a weird oscillation. Without a reversion to the mean parameter (such as in Ornstein-Uhlenbeck), it will generate every oscillation wavelength known. That is indeed weird.
My background is in the semiconductor industry and when I was working on diffusional research topics heavily, it was common to be able to work out diffusion problems (such as doping profiles and oxidation growth) completely by analytical means. Certainly, one could set these up as slab computations (and oftentimes you would need to if you were making heterostructures) but in the end you would get the same answer.
The big distinction we have here is the earth is not some homogeneous environment as a substrate is. Yet we can use the same generic mathematical approaches while applying the techniques of uncertainty qualification and temporal and spatial dispersion to describe the variability. Whether that kind of approach will be completely successful, I don’t know, but it is worth considering, and that’s where I am spending my time.
If you want to keep setting complexity snare traps and fish chum along the path, that is your right, but I will keep on ignoring them, as I always have.
DeWitt: The modeled equilibration to a slug of CO2 has nothing whatsoever to do with temperature.
That is _exactly_ my point . You keep insisting on 2000 equilibration and that is temp, you try to apply it CO2. At least we are now agreed they are not the same.
Jeez. do you bother reading anything I say before attempting to reply ?
I’m not going to waste my time repeating myself. In short “no”. Go back and read what I’m suggesting would be helpful for those keen to refute it.
DeWitt Payne (Comment #116747)
In your haste to refute without thinking you missed two key points.
1/ I never said temp explained _all_ change in CO2 I have said from the out set the aim is to assess the proportion attributable to the two factors.
2/ If temp is proportional to d/dt(CO2) const temp means what …?
You are capable of relevant comment, please try to keep up.
Webster, “1. A coupled system the way you describe it is essentially a diffusional model. The volumes consist of compartmental slabs which exist to describe flow in both directions, up and down. In other words, the compartments model the divergence of the mass or heat flow within the slabs. That is the topological basis of the heat equation or the Fokker-Planck equation or any of the diffusion/continuity equations.”
Right, in between perturbations, then it is like hitting restart. You have to know the initial conditions and relevant time frames. ~400 years per 0.8C is a long time frame.
“2. A random walk IS a weird oscillation. Without a reversion to the mean parameter (such as in Ornstein-Uhlenbeck), it will generate every oscillation wavelength known. That is indeed weird.”
Right, and if your base model while on an upswing, you over estimate, a down swing would lead to an under estimation. So instead of actually looking at the longer term data, you pick the noisiest of the noisy to “fit” with the maximum slope and call that a valid estimate.
If you divide the volumes you then have the ability to compare response between volumes, not that complicated. Then you could understand why OHT needs to be considered in an asymmetrical model with relevant time frames of up to 2000 years.
Look at this again.
https://lh5.googleusercontent.com/-Zt1oH-PdG38/Ubx-Yc4PFjI/AAAAAAAAIng/B7BvlEPm0kY/s809/giss%2520and%2520ersst%2520with%2520ipwp%2520baseline.png
Then a little further back in time.
https://lh6.googleusercontent.com/-0Ljwh9NTkS0/Ubx9dAfZtAI/AAAAAAAAInM/UROadZys8_k/s800/giss%2520and%2520ersst%2520with%2520ipwp%2520from%25200%2520ad.png
Then a longer time frame.
https://lh3.googleusercontent.com/-bnfSiuz7AV8/UcRM6tiocGI/AAAAAAAAIug/t8oc_YOjYcc/s841/Stott%2520lea%2520with%2520co2.png
Now did man’s activities save the world from a new glacial period or did the system response change?
Your simple diffusion models are a one way street, coupled systems like going both ways.
Your model of Temperature-driven reality is not as good as the carbon emission model of reality.
http://img69.imageshack.us/img69/7626/hyc.gif
That is all there is to it. My model has essentially one tunable parameter, the adjustment time for aCO2 sequestration, and the rest is based on empirical data.
If you want to do a real shoot-out, the next thing to do is you come up with a model that fits this interval better, and then we can do a log-likelihood or cross-entropy comparison of the models and apply an AIC or BIC metric to evaluate which model is better.
But I am not going to waste my time on that, because much of the time, you get an intuitive feeling about what is right. You then file that away and you move on to the next piece of the puzzle. If it fails down the road in some inconsistent fashion, well, that’s tough.
You apparently just don’t want to move on. DeWitt has pointed out lots of back-of-the envelope calculations where the d/dt(CO2) vs SST argument fails. Why don’t you try your argument on the raw Mauna Loa data where you don’t average over the 12 month yearly signal? That one will blow your mind.
It looks as if Murry Salby has painted himself into the same corner with a similar premise.
“DeWitt has pointed out lots of back-of-the envelope calculations where the d/dt(CO2) vs SST argument fails. ”
Has he posted anything that actually takes into account what I’ve said ? So far I see him ignoring my replies to his question “what am I missing” and making same mistake again.
Apparently for him “what am I missing?” means the same as QED. It’s not really intended as a question.
” raw Mauna Loa data where you don’t average over the 12 month yearly signal? That one will blow your mind.”
Firstly, I never said I took the annual average, I don’t know where you got that. Second I was working with MLO until _you_ told me it was biases and that I should use samsoi. Now you want to flip back.
You are losing coherence.
“…. much of the time, you get an intuitive feeling about what is right. You then file that away and you move on to the next piece of the puzzle.”
So you have a gut feel that you’re right , you have a gut feel that I’m wrong. You’ve “file that away” and I should move on.
I like some of you convolution work but you don’t really expect me to take that kind of reasoning seriously do you?
I still don’t recall a post or a link that explains how you got that graph in a way that allows it be reproduced. If I could , I may find it shows something, I may find an error. For the moment it’s little more than a lot of dots.
You suggested I looked at IPWP, I did and found it bore less resemblance to CO2 than the global mean. You have not even commented on that.
The trace elements calibration of Bern link looks relevant and interesting. I’ll have to study that.
Other than (possibly) that I don’t see any convincing objections. In fact I don’t much indication that anyone other than Paul_K even realises what this means.
http://www.climate.unibe.ch/~joos/model_description/model_description.html
“…the HILDA model. It includes two well-mixed surface boxes, representing low and high-latitude surface water masses, a well-mixed high-latitude deep water box and…”
Interesting that they see high lattitudes as the major deep sink.
I have already noted a surprising importance of Arctic Oscillation in dCO2 as well:
http://climategrog.wordpress.com/?attachment_id=231
It is most strongly correlated around the temperature turning points : early 70’s and post 2000.
Re: Greg Goodman (Jun 21 12:52),
That’s exactly the point. CO2 goes into the atmosphere and then into the ocean and the biosphere. It is unnecessary to invoke anything else like temperature to understand the long term trend. It’s an equilibrium process, but it has a finite rate.
You keep saying that, but I see no evidence that you have actually taken it into consideration in your model. I don’t see a factor for rate of emission anywhere in the formulas you have presented, just temperature. The problem you have is that the rate of change of CO2 emission more or less matches the rate of change of temperature, at least until recently. So if you don’t include emission in your curve fit, you will attribute all the change in CO2 to temperature.
Re: Greg Goodman (Jun 21 12:52),
Speaking of making nonsensical statements: There is no outgassing to speak of. CO2 is being emitted from fossil fuel combustion, cement manufacture and land use/land cover changes and a lot of it is being absorbed by the ocean, not being emitted. The reason I keep harping on this is that you keep making statements that contradict it. You insist that you don’t actually mean it, but your math speaks for itself.
And again, if temperature is the major driver of CO2 concentration, why is CO2 still increasing at about the same rate while the temperature is actually decreasing?
Greg Goodman,
What I want to see is a model from you that includes emissions. Something like this:
d[CO2]a/dt = f(d[CO2]e/dt) + f((dT)/dt)
where [CO2]a is ppmv in the atmosphere and [CO2]e is GtC emitted converted to ppmv using 1 GtC of emissions = 2.13 ppmv. I believe you will find that the emission term will explain the low frequency behavior while the temperature term will be reduced to wiggle matching the year over year behavior.
That was a parody of you own statement that I quoted in the preceding line. You deliberately take it out of that context to make it look like seriously meant it.
Very amusing.
Greg Goodman (Comment #116641)
June 20th, 2013 at 12:17 pm
What part of that are you having trouble understanding?
DeWitt said:
And remember, it is not just Greg Goodman that has this blind spot.
So do Murry Salby, Ole Humlum, the commenter Bart/Bartemis, and then many followers on Climate Etc and WUWT. They all seem very tenacious in believing what they are finding is correct.
We will see if Salby ever gets his research findings published. A few people have noted that Salby hasn’t even acknowledged Henry’s Law or Clausius-Clayperon in his presentations.
Greg Goodman,
There are lots of lines of reasoning, and lots of empirical evidence, which all show CO2 emissions are primarily responsible for increases in atmospheric CO2. Lots of these have been laid out on this thread. IIWY, I would carefully rethink this issue. The weight of the evidence is overwhelming.
Carrick (Comment #116594)
June 20th, 2013 at 7:52 am
sky:
What I am saying in plain English is that ENSO has a profound, but non-uniform effect upon temperatures in various different areas well outside the tropics
—————————————————————————
Whether it does or doesn’t, the linear correlation with ENSO34 vanishes outside of ±30°, so you can’t regress against lagged ENSO34 to predict it.
========================================================
The linear correlation with NINO [sic!] 3.4 varies greatly from region to region outside the tropics, but doesn’t vanish uniformly–even at zero lag. There are many station records in the regions I mentioned (and others that I didn’t) that clearly disprove your sweeping contention. And nowhere would I ever use simple regression against that lagged regional index for any purpose.
The global interconnectivity of temperature variations through little understood mechanisms is evident even in the variously flawed global temperature indices, which all show moderate cross-spectral coherence in the power-rich frequency bands of NINO3.4. Your comment rejecting the idea of cocommitant variables simply reveals lack of comprehension of the implications of such coherence.
==========================================================
SteveF:
So, in the spirit of another of your thoughtful and constructive comments, I ask: what is it about people who describe themselves as climate scientists that makes them so uncivil?
—————————————————————————–
Possible answers (more than one may apply): not very bright, not very knowledgable, poorly socialized.
==========================================================
Nowhere have I described myself as a “climate scientist;” on the contrary I’d be insulted to be called such. Both of you apparently believe that ad hominens are a good substitute for knowlege. For a working research oceanographer, that’s reason enough to disregard the babble of blog stars, which is endemic on both sides of the climate debate
Re: Greg Goodman (Jun 21 15:22),
I don’t understand why you would think that there is some sort of periodic CO2 behavior that has never previously been observed that needs explaining when emissions modulated slightly by local SST at the various observing stations is both obvious and completely adequate.
Sky,
Thanks so much for your constructive and helpful contribution to this thread.
.
Let me rephrase my earlier question: what makes YOU so uncivil?
DeWitt Payne (Comment #116787)
June 21st, 2013 at 5:16 pm
So having persistently ignored what I actually said, when I put it under your nose, again, you completely ignore it rather than apologise.
You clearly have nothing credible to say, no manners and no integrity.
Thanks for trying.
SteveF (Comment #116782)
June 21st, 2013 at 4:09 pm
I see a lot of preconceived ideas, some things like the ice core data setting bounds which I have questioned and not seen any counter argument in reply.
Perhaps you could list the overwhelming evidence for me. I may be biased and over looking key points that were raised. I looked at this a few years back and swallowed the “consensus” view based on ice core arguments. I now have reason to question the validity of applying the ratio of ice core SST and ice core CO2 for reasons I have stated.
If you disagree, I’d be interested if you have a counter argument. Apart from the ice core ratio , what am I overlooking that has been pointed out?
thx.
WebHubTelescope (Comment #116781)
June 21st, 2013 at 3:46 pm
Hey, if you have something to say about me say it to me , not as a third party comment. You may find it useful to quote my reply to DeWitt’s witless questions instead of cropping them out and pretending I did not reply.
The level of intellectual honestly here (lack thereof) is quite amazing.
sky:
Never anywhere did anybody say it “vanishes”, just that it stops having much explanatory value.
The plot I showed above was for maximum linear correlation versus it’s lag. Above 30°N, the maximum correlation drops below 0.15. Even were this statistically significant, it has low explanatory power, which is a justification for not including it.
Um no, this just demonstrates that you could use a statistic course and are a poser.
SteveF,
Just to let you know that I haven’t lost sight of the original thread and I am waiting all agog to see what happened with your latest tests!
Greg,
Calm down a little.
I think there is a way for you to apply some objective tests to your postulate. You need to do an “exact model fit” to your hypothesised model using short term data, where the derivatives are strongly controlled by the high frequency data, and then compare this with values fitted over the longer term. You can do this both with and without a man-made contribution.
I included in this referenced article a numerical solution to the linear feedback equation, which takes less than 10 minutes to set up on a
spreadsheet. (See derivation of Equation A8 in Appendix A.)
http://rankexploits.com/musings/2011/noisy-blue-ocean-blue-suede-shoes-and-agw-attribution/
The advantage here is that it can accommodate all of the input frequencies simultaneously.
You should note from the derivation that this form as presented only works for one-year timesteps, assuming that t (and the coefficients) are defined in years. However, you can redefine t and the coefficients to be in months and it works equally well then for one month timesteps. Alternatively, If you want variable timesteps then you need to redefine the “alpha” parameter.
Set up the forward model. Input temperatures and predict CO2 concentration. (Test it against the analytic solutions first.)
Minimise the residual sum of squares against observed CO2 values by selecting your two parameter values. Do this for short-term. This is your “exact model fit”. Then see how it looks in the long term for two cases: 1) assuming that the Temperature is the same as the short term 2) allowing both parameters to vary.
I suspect that you will find that you have a missing piece – the man-made emmission contribution. Tell us how big it is from the longer-term case. If you really don’t have a missing piece then definitely tell us and write the definitive paper on the subject. (smiley)
Greg
“If you disagree, I’d be interested if you have a counter argument.”
We’ve put about 400 Gton carbon into the atmosphere. Where has it gone?
Thanks for the suggestion Paul. I was hoping to get some agreement on the principal of the method before knowing the outcome. However, it seems that anything with even to possibility to challenge the entrenched _assumptions_ gets rejected before it is even tested.
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There will be a “missing piece” term. Despite having stated that from the outset everyone seems intent on missing that I actually said I expect both to be present and my aim is to find the proportion of each that is indicated by this method.
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My approach is to try to estimate the linear model contribution caused by the temperature changes. The difference between that and actual measured (eg MLO) atm CO2 will be the unabsorbed human contribution.
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One possible result would be that it predicts about 10ppm and is in agreement current assumptions. Rough calculations suggest that will correspond to a tau of about 20 years. So I think it will come down to an argument about what value of to use for tau. Even if that is the ‘best fit’ value, at least it will provide a model that follows d/dt(CO2) and reconciles both the emissions and the so far ignored temperature response in one equation. I would have thought that was worthwhile perusing.
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Apparently, even the possibility that it may challenge preconceived ideas is too much for some. Since the result has been rejected even before we know whether is agrees or not is not very encouraging. It seems hard to find even the darkest corner of the internet where anyone is still interested in objective scientific investigation. Thank you for the ray of hope presented by your replies.
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There is an important corollary for Steve’s article too since some attempt should be made to do the same thing with the rad vs T relationship. The primary response to volcanism will be a dT/dt one everyone seems intent of fudging it to fit T(t). I was hoping to be able to modify Nick’s R code to fit dT/dt instead but I find R as readable as Mandarin Chinese and don’t have time to do all I’d like.
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Since neither temp nor CO2 fit the data at all well post 2000 I’m surprised no one is willing to recognise that the HF response to even to the most trivial linear model is totally missing from current attempts fit both responses
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My starting point is 8 ppm/a/K for 3.3 year variations, which I think can determined quite accurately from good quality data. That calibrates all the messy constants like the pertinent heat capacity etc included in the A coefficients. The food fight will really start in choosing what tau value to apply.
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If that one value can slide the result between mostly anthrop and mostly thermal at least it will provide an exit strategy for the next ten years.
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I will look at what you suggested. I was particularly impressed with the maths in ‘blue suede shoes” and the other article. That is what set me on this train of thought.
Nick,
I think that the argument is that the human emissions are tiny next to the huge natural annual flux, thus still leaving the possibility that the year on year change is predominantly temp controlled. I don,t think that the argument works but the mass balance argument dorsn’t work to defeat it. I think greg needs to work through the numbers for short term and long term to convince himself.
Nick “We’ve put about 400 Gton carbon into the atmosphere. Where has it gone?”
I don’t quite get the point of that comment. It’s already recognised that about half of it gets reabsorbed by the biosphere and the oceans. Whether it is 50%, 80% or 90% is just a question of parameter fitting and our abisimal lack of data and knowledge of the carbon cycle. I don’t think it is an argument or counter argument to anything to say “where has it gone?”
We know where it’s gone, the question is what proportion ends up absorbed.
Someone said the ocean has to be either a sink or a source, like you have to choose. In fact it’s both, on all time scales. Unless something hits saturation and goes all non linear we can treat things linear and hence additive.
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WHT says it’s diffusive which makes a lot of sense but apparently that can be approximated by three linear responses, so we can remain in the linear game. Thus we have some percentage of re-absorption PLUS some out-gassing due to temperature increase. That much seems uncontroversial.
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It is a superposition of two effects. If out-gassing is more significant than current guesses, then the implication is that the percentage of emissions that the system absorbs must be greater.
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This is not proposing throwing everything out and starting again. It is just a question of proportions, parameter values.
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Currently the thermal contribution is regarded as being small and is ignored. My model includes it into the model instead of ignoring it. It _could_ still end up being of the order of 10 ppm but at least it would included in the model. The method also allows it be greater (or even less) than the current small value for long term but includes it in a way that fits the significant 8ppm/a/K level that matches MLO.
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This _is_ the proper solution to the linear equations everyone seems so keen to simplify everything into (for understandable reasons, that I’m not against as a first approximation).
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So far everyone seems to ignore the HF response term and tries to fit HF perturbations (like volcanism in the case of the radiative response) to the LF term of the solution.
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It is hardly surprising that fitting exercise is not going too well.
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For those who want an explicit formula of how my approach combines the two, this can be summarised by:
observed = thermal (T,tau) + k * emmitted
It becomes a play-off between tau and k in the way I have described above. My rough guess is that the current “consensus” is something like 20 years and 50%.
If the dominant tau for the period of the data we have available is nearer to 5 years, then the percentage absorbed will be higher.
Even if 20 years turns out to be the best fit, we still get a model that follows dT/dt quite closely which would be nice.
Not ignoring half of the solution to the linear model everyone is so keen to use also appeals to me but then maybe I’m just pedantic or argumentative or something. 😉
Paul_K,
I will write a post this weekend, which will include some additional (more defensible/reasonable) correlations, along with a more complete explanation for why F&R got the (wrong) results that they did. It turns out there is more to it than just non-physical parameter choices.
Steve_F: “Some months ago in a comment at The Blackboard, Carrick showed that Nino 3.4 shows little or no correlation, at any lag period, with temperatures outside of the tropics.”
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I think the reason that Nino3.4 “works” as a global linear variable is that tropics are actually highly non-linear and are virtually immune to variations radiative forcing beyond a slight dip which not only recovers but recovers the longer term integral of degree.days. ie really _zero_ net effect.
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http://climategrog.wordpress.com/?attachment_id=312
If you follow the link below the graph you get the full picture NH, SH plus an explanation of how it was derived. Tropics are immune to variations in radiative forcing, extra-tropics recover temp but lose degree.days
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Adding and ENSO term is similar to diffusion behaviour being modelled as three linear transients. Nino_3.4 is “internal”, not exogenous, but is an expression of the non-linearity of the tropical ocean response. In that respect it can work as exogenous if you still want to model tropic as having a linear response. It’s all a bit of a kludge but there is a lot of computational advantages in pretending everything is linear. It’s just important to realise what is being done and why it works.
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So far I don’t see any recognition of either, at any level. In fact no one beside Eschenbach seems to have noted that the tropics have zero long term impact from volcanoes.
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One thing that was visible in Nick’s plots on his moyhu site is that his “ENI” forcing ends up roughly in anti-phase with the volcanic signal, which tends to reinforce my point.
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I have posted a comment on Nick’s site explaining how I think the correct HF and LF response to Paul_K’s equation can be included in a multivariate regression analysis. You may like to see whether that could be applied to your method.
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http://moyhu.blogspot.com/2013/06/better-adjusted-global-temperatures-for.html?showComment=1371895073817#c4873431491953120105
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I apologise for inserting a lot on CO2 discussion here but as I have noted in several places this is because the same kind of linear equation is applied to both and the exactly the same issues arise. What applies to one applies to the other, but with different coeffs and time constants.
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dT/dt is power, radiation forcing is power , why are you trying to fit this forcing to energy ( the cumulative integral ) whilst completely ignoring the short term response?
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Maybe there is a good reason that I’m over looking. If so perhaps you can explain.
Greg, “I think the reason that Nino3.4 “works†as a global linear variable is that tropics are actually highly non-linear and are virtually immune to variations radiative forcing beyond a slight dip which not only recovers but recovers the longer term integral of degree.days. ie really _zero_ net effect.”
Nino 3.4 worked, past tense, because it was created as an index. The next version might be Nino 3.3 N.1. The warmest part of the tropical Eastern Pacific is north of the equator at ~latitude 10N. In 60 years it may be 10S. PDO is another index that may need to be adjusted for “climate” use as “global” patterns shift. Climate just needs better indexes that can be more easily used over much longer time scales. The AMO is a good climate index with about 55% correlation with “global” temperatures. The tropics as a whole divided at the equator is also a good climate index because of changes in meridional imbalance i.e. the ITCZ or “Thermal Equator” as Toggweiler like to say.
I am not too impressed with over using linear approximations.
I tend to agree but like I said, there is a huge computational and theoretical advantage if everything can be _approximated_ as linear. The key is to firstly recognise/admit this is what you’re doing.
I don’t see it explicitly said that this is what the Bern model is doing. Has the close equivalence do a diffusion model that WHT pointed out even been realised?
I certainly don’t see anyone recognising the stability of the tropics to changes in radiation and viewing ENSO type “forcing” as a correction factor to account for tropical non-linear response.
Interesting. Do you have a link or a more precise indication of how to build such an index?
Greg, Depends on the purpose. I am looking at the impact of meridional imbalances so I use the ERSST3 ocean data in 30 degree bands differences across the equator.
https://lh5.googleusercontent.com/-l_ML6EeOkZo/UcWnUhatdvI/AAAAAAAAIvM/sccomFl3vCU/s896/equatorial%2520imbalance.png
One 0-30 gives the longer term trend and the other 30-60 shows the “noise”since 30-60 south is so stable.
A zonal Eastern Pacific minus Atlantic is useful but that is mainly for checking paleo. An IPWP minus E. Pac. would probably be best for just long term surface temperature.
Just found one of Paul’s other posts while search an answer.
http://rankexploits.com/musings/2013/observation-vs-model-bringing-heavy-armour-into-the-war/
Isn’t this another indicator of what I’m saying : frequency dependence of temperature response. Since all work so far seems to totally ignore the HF orthogonal response and hence hopes it averages out (or more likely hasn’t even thought about it), what is left is the increasing amplitude of the LF response.
If modellers and those analysing model output are determining CS from the relationship between between the in-phase response you will get a strong response over longer periods. Look at the coeff of Paul’s solution equation.
It will eventually flatten out but if they are comparing periods where omega.tau is significant w.r.t unity to periods where the denominator has settle closer to unity, yes we will see an increase in “apparent” sensitivity even with a totally constant linear model.
Now the models are complex but the concept of CS implies measuring the overall behaviour by analogy with precisely this simple linear model.
Perhaps the ‘curvilinear’ bit is a manifestation of what I’m trying to draw attention to.
Or maybe ‘hundreds of papers” have not looked at the solution to the linear equation they are imagine they are using?
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It is a linear _feedback_ model. It seems that most are stopping at the word linear.
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Even the in-phase response is not _linear_ , it has frequency dependence.
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Hopefully Paul can confirm that I’m not misreading this.
Any model of atmospheric CO2 has to be consistent with long term as well as short term data, for example: the Law Dome ice core data for the last 1000 years. Note that, unless you believe in Mann’s hockey stick, there were significant temperature changes during this time including the Medieval Warm Period and the Little Ice Age. Anyone who thinks the modern temperature rise is a continuation of the recovery from the LIA, should note that CO2 flattens out for a short period near the 1010-1570 baseline value of 282 ppmv from about 1800-1850 after the dip to 275.3 ppmv in 1620.
Dewitt, “Anyone who thinks the modern temperature rise is a continuation of the recovery from the LIA, should note that CO2 flattens out for a short period near the 1010-1570 baseline value of 282 ppmv from about 1800-1850 after the dip to 275.3 ppmv in 1620.”
Right, but compared with the IPWP and Southern Oceans,it looks more interesting.
https://lh3.googleusercontent.com/-dyw6fPClKlc/UcOuyx5M0PI/AAAAAAAAItY/mbLFk1sAftc/s865/neilsen%2520oppo%2520with%2520co2.png
I wouldn’t put it past a 4.5 billion year old planet to have a few tricks up its sleeves.
Indeed Law Dome has an interesting temperature record obscured by more hide and seek games from the usual suspects.
http://climateaudit.org/2010/04/05/ipcc-and-the-law-dome-graphic/
Greg, and Antarctic temperatures can be anti-phase to SH temperatures depending on the cause of the temperature change. CO2 forcing should cause an initial Antarctic cooling analogous to stratospheric cooling, which stabilizes once the oceans start to approach the new heat capacity.
It is an amazingly complex system.
Check this out.
https://lh3.googleusercontent.com/-iS0fQarNeAU/UcXH3jzHHDI/AAAAAAAAIvo/dV2diJCpaOQ/s708/sopol%2520surf%2520ls.png
The Southern Extratropic Lower Stratosphere and Admundsen Scott are in phase with each other and out of phase with global surface temperature from ~1980 to 2000. then you have some atmospheric chemistry kick in, ozone and/or stratospheric water vapor with a dash of colder than normal and rapid solar melting of stratospheric ice crystals. All the standard radiant and atmospheric chemistry stuff that should be included in the models.
When GISS adds the Antarctic surface stations with their long range interpolation, they add variance to the SH LOTI data the should not exist.
It is hilarious.
Just a quick look at rate of change at Law Dome vs the high res temp proxy from Gomez
http://climategrog.wordpress.com/?attachment_id=398
Re: Greg Goodman (Jun 22 10:35),
You do know that the Antarctic Peninsula where Gomez is located has been warming much faster than the rest of the Antarctic, at least since 1957, don’t you? See O’Donnell et. al., 2010. You can read about it at Climate Audit.
I have just plotted the frequency response of the two coeffs since it helps to see it laid out. I suggest Steve and anyone else trying a F&R style regression to the temperature time series have a look.
IMO the whole process is invalid until you are averaging out everything faster than at least 5x the dominant time constant.
This seems to being TOTALLY ignored so far.
http://climategrog.wordpress.com/?attachment_id=399
I would like to know if anyone sees a fundamental error in what I’ve shown because I suspect this destroys F&R in one clean hit.
Greg, when you are comparing the orthogonal with the in phase, is that because it is something you noticed or is your goal to explain why is exists? With a spherical aqua world we have our own thermal wave pool so you can have standing waves build that will mask any correlation.
https://lh4.googleusercontent.com/-uEdwPFb9kVk/UcYRVG8RSzI/AAAAAAAAIwE/qbUuVIn3mMg/s997/seasonal%2520cycle%2520shift.png
Like that. The 0-15N and 50-70N SST bands are fairly well correlated. The 25-45N band pops into a stable “standing wave” after the 98 El Nino creating the “plateau”. That is mainly due to a shift in the regional seasonal cycle timing.
Best for example has a large seasonal cycle retained and any data set will generally have the seasonal cycle removed making them baseline dependent to some degree. F&R should never have been published because it is meaningless to remove signals that you have no clue what time frames they can have impacts over.
Dallas: “Greg, when you are comparing the orthogonal with the in phase, is that because it is something you noticed or is your goal to explain why is exists? ”
My approach for a long time was that dT/dt was most directly connected to a radiative forcing because it is dimensionally equivalent.
this means that the first place I would search for a correlation would be between the derivative and the forcing. Not cumulative integral of the energy. I have never understood why most of climate science spends most of its effort staring at the time series to understand change instead of studying the change.
A few left field players have noted that d/dt(CO2) correlates much better than CO2(t) and does not have the 9m lag seen in the latter. This did not surprise me since it was the same point I’d been making about temperature.
I saw Salby’s Hamburg lecture last week and the maths looked credible. The efficiency of explaining a long, in-phase response and a rapid, orthogonal response as both being the result of the same trivial feedback equation appealed to me. It just rang true. I saw the parallel to the dT/dt issue that had been bugging me for a long time.
Now when Paul_K posted that equation to explain something to me, it all fell into place. BOTH the derivative and the direct signal are there in the solution to the linear feedback model. We should be look for the derivative in all the recent data, the direct correlation will only dominate on very long scale (in relation to whatever time constants dominate whatever it is we are looking at).
If we want over-simplify a simplistic model dT/dt probably dominates the decadal scale response and T(t) the centennial scale. (Don’t hold be to that I’m just sketching out the principal)
Now this does seem to be born out by the data in both temp response to rad forcing and CO2 response to temp. as I have illustrated a number of times above. And that is all good and as it should be if the linear feedback models are anywhere near being useful.
When I noted the long term amplitude would keep increasing in amplitude up to quite long periods and started putting some numbers on it made more and more sense.
That how I got into this but is really just anecdotal. The key issue is the implications of the maths. And no one so far has come up and said I’m wrong about how I’m interpreting Paul’s solution to the basic linear feedback.
Not that there seems much grounds for argument unless I’ve made a silly slip up. And if I’m right, a lot of published work has been (probably unintentionally) ignoring half that solution and missing the frequency dependent amplitude of the bit it’s kept.
The implications of this are profound for the way we analyse time series and how we estimate climate sensitivity from data and from model output.
For a start I think it may explain the ‘curvilinear’ paradox of the longer model runs.
DeWitt, good point but Gomez is not on the peninsula it is on the part of the continent leading up to it , so the difference is less dramatic.
http://climateaudit.files.wordpress.com/2010/12/olmc_comparison.png
Like I said,it’s just a quick look that illustrates the d/dt relationship is there too. I was not attempting to use the post 1960 slopes to apportion thermal vs anthro.
Greg,
Paul, all the plots and comments I’ve made about CO2 have had the 12m cycle filtered out for precisely that reason.
What I’d really value a second opinion on is how I’m interpreting the response equation.
http://climategrog.wordpress.com/?attachment_id=399
It seems that both the direct forcing and its derivative are present in the response. Which, unless I’m missing something means any attempt to fit just one (usually the in-phase term) is spurious.
That will have far reaching consequences for estimations of CS.
Greg,
I should have added that you cannot get the linear feedback equation to phase shift by more than pi/2, irrespective of how large a value of tau that you choose.
Paul_K,
Yes, the seasonal fluctuation is mainly driven by northern hemisphere plant growth, confirmed by both the timing and the observation that the seasonal fluctuation is stronger in the northern hemisphere than in the southern due to the large forest areas of the northern hemisphere. IIRC, there has even been confirmation of the seasonal cycle in atmospheric O2 (a much more difficult analytical task).
Paul_K,
Keeling et al, Nature 1992 is what I was remembering. A very clear seasonal O2 signal is described, and models for the causes of seasonal variations in O2 and CO2 are shown.
Re:Greg Goodman (Comment #116892)
June 23rd, 2013 at 4:02 am
Greg,
I think that your interpretation may be missing the obvious. The phase shift in temperature relative to the input forcing is controlled by the magnitude of tau. For any value of ω, if tau is made very small, the solution approaches an in-phase solution. For any value of ω, if tau is made sufficiently large, then the solution eventually gets to be pi/2 out of phase. And quite independently the derivative term dT/dt is always exactly pi/2 out of phase with T for any values of ω and tau.
{Write sin(theta) = -cos (theta+pi/2) and cos(theta) = sin(theta+pi/2) to test.}
However, I don’t think that this will introduce any large shocks into the empirical calculation of CS. I could be wrong, but I think that it is fairly well known that the GCM results can be emulated very well with a linear feedback equation. Typically, fitted values of tau are low (3 to 4.5 years), and the equilibrium climate sensitivity works out to be around 1.5 deg or thereabouts for a doubling of CO2. This type of calculation takes into account the variable frequency of the inputs.
Equally, various authors have recognised one of the problems which you highlight – that you can’t simply plot output against input – and have sought to get round the problem by regressing (net flux minus forcing) against temperature. these methods again lead to an estimate of equilibrium climate sensitivity of around 1.5 deg C. You can do the same with ocean heat content instead of net flux and recently the Otto et al paper, using the most pessimistic view of ocean heat gain, arrived at a value of 2 deg C.
The above methods don’t have a problem with the variable frequencies in input and output.
If there are problems in the above methods, they arise from two sources. The first is that we do not know what causes the 60-year cycle in temperature, and consequently it is often treated as a response to known forcing (which it isn’t). The second problem arises because of the assumption that the feedback term is a simple linear function of temperature. In contrast, the GCMs show a curvature in the net flux-temperature relationship for a fixed forcing, which has the effect of doubling the estimates of equilibrium climate sensitivity. The Armour paper was trying to explain this relationship in terms of the different rates of temperature change at different latitudes. His explanation works reasonably well for the CCSM4 model on which it was tested, but looks dodgy for a lot of other models because of quite different profiles of feedback with latitude. We still don’t know whether this curvilinear behaviour is “realworld” or just a function of the models. I believe that it is a much bigger contributor to uncertainty in climate sensitivity that the challenge of dealing with multiple frequencies in the inputs.
Greg,
Paul, all the plots and comments I’ve made about CO2 have had the 12m cycle filtered out for precisely that reason.
Do you mean filtered out or de-seasonalised?
“Do you mean filtered out or de-seasonalised?”
Filtered out as I said. Deseasonalising another flakey method seems ubiquitous in climate science. The only interest I can see in using it is that you don’t lose a few years data at the end of the record as you would with a convolution filter. Since seasonal variations vary in magnitude you end up with a seasonal variation in the deseasonalised “anomalies”. Best avoided.
For the record I used a triple running mean with 12, 9 and 7m widths. This is a well behaved filter with a zero at 12m
Sure. Not aware I was suggesting otherwise.
That’s exactly what I was saying, thanks for the confirmation.
Equally, various authors have recognised one of the problems which you highlight – that you can’t simply plot output against input – and have sought to get round the problem by regressing (net flux minus forcing) against temperature. these methods again lead to an estimate of equilibrium climate sensitivity of around 1.5 deg C.
Isn’t the obvious answer to add the derivative of the forcing to the response side of the regression?
In fact the full solution response. is the forcing + tau * derivative of forcing + exp term
So that is what should be regressed against the resulting temperature record.
I think the exp term could be generated by a convolution of the input or it’s derivative. WHT seems to understand that sort of trick so perhaps he could provide an exact expression.
Agreed. And it is hard not to see confounding the two as being deliberate at this stage.
Hand on, the phase shift is controlled by ωt , not tau. Now until ωt<<1 is true the amplitude of the coeffs of both F(t) and d/dt( F(t) ) will be rising.
If we take your "typically, fitted values of tau are low (3 to 4.5 years)" as a starting point that means we need to filter out an change faster than say 5 tau: 15 to 22.5 years to get a stable result that reflects the asymptotic value that is the true 'sensitivity'.
That is not what is being done here by Steve, by Nick or by F&R.
An none of that gets around the need to include the derivative of the forcing.
Does that much make sense?
“That’s exactly what I was saying, thanks for the confirmation.”
Actually that’s not “exactly” what I was saying but close. Again it’s ωt. Since tau generally comes from things like the “effective” heat capacity and we are approximating the linear response of a single slab ocean mixed layer, it is tau that should be fixed in your discussion. Since there are many frequency components your discussion should be based on fixed tau and varying ω , then it becomes : “exactly what I was saying”.
typo: “Hand on, the phase shift is controlled by ωt , not tau. ”
That should read omega.tau , obviously.
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That comment is trying to say two things and may be confusing.
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“And none of that gets around the need to include the derivative of the forcing.” To do what Steve and everyone is doing, I see no way to avoid including the derivative of the forcing.
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Second point:
To get close to the asymptote in the magnitude of the response we need to look at 1/(1+(ωτ)^2)
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If we take “3 to 4.5 years” for tau, that gives the cross-over point ωτ=1 at 19 and 28 years respectively, and we need to satisfy the condition ωτ<<1 and take 1/5 as satisfying that limit, that means low-pass filtering the data at 95 or 141 year respectively.
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Since no one seems to be doing this, nor recognising the need or the reason, shorter model runs will show a sensitivity from fitting an _under-estimation_ of the response to the driver. Thus it seems to me would under-estimate the true response of the model. Longer runs would get closer to estimating the true asymptotic value for the model.
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Since the derivative will have little left once suitably long filtering is applied, it may be satisfactory to not include dF/dt in this kind of regression. Equally it should be safe to ignore the transient term.
I think I can see a way to test whether d/dt(CO2) signal is out-gassing or not and that may end up refuting what Salby is putting forward, but it needs acceptance of the idea of the derivative being present in the response:
response = A * forcing – A * tau * d/dt(forcing) + A * omega * tau * transient
No one seems to have much to say about that.
Re:Greg Goodman (Comment #116938)
June 23rd, 2013 at 4:45 pm
Greg,
That’s not a general solution – it only works for a sinusoidal oscillation in the driver.
Steve_F
I think I have a much better explanation as to why this “works better” as in index.
Following a comment by Nick Stokes on his regression thread, about ‘lags’, I dug out the Laplace transform solution of the linear negative feedback model. It’s the convolution of forcing with an exponential.
So Steve, what you’ve actually done here with the exponential “smoothing” using a convolution filter, is to derive the negative feedback response to that input signal. (Assuming that you do this with the correct exponential delay.) Now if one tries to regress the input on the output it won’t work. Using a convolution you are in with a chance but that does not get around the problem of unattributed variations like the 60 year cycle that F&R are trying to melt away with all this jiving around.
Since this is the system response, the response must be the same irrespective of where the radiative forcing comes from so: fungible, yes, it should be and everything gets the same “tau”.
In fact, since this is the system response to any forcing that can be considered to have a linear response, it ought to apply to all the “forcings”.
“Greg, That’s not a general solution – it only works for a sinusoidal oscillation in the driver.”
Thanks Paul, but since this is linear and any input can be broken down by fourier analysis and the outputs stacked up , doesn’t that amount to the same thing?
That is to say, if I did FA of any input time series, applied this soltution to each fourier term and added the results, I would get the sine terms giving a frequency dependant version of the input; the cosine terms giving the same frequency depenancy applied to the derivative of the input and a stack of exponential terms that are also dependant on frequency.
No?
Greg,
In general, I don’t think you can invoke Fourier to argue that the properties of any arbitrary function will be the same as a sine function!
The general (exact) solution for arbitrary F(t) is given by:-
T = exp(-t/ Ï„)*(S/ Ï„) * (INT+Const)
where INT = Integral of{ exp(t/ Ï„)*F(t) } and “Const” is a constant of integration.
We can integrate INT by parts to obtain
Int = F(t)*Ï„*exp(t/Ï„) – integral of{Ï„*exp(t/Ï„)*F'(t)}
= F(t)*Ï„*exp(t/Ï„) – F'(t)*Ï„^2*exp(t/Ï„) + integral of {F”(t)*Ï„^2*exp(t/Ï„)}
Can you see the series which is developing here? For an arbitrary function, this series will continue forever with alternating sign and increasing powers of Ï„. For a sine series of the form F(t) = sin(ωt) we note that F”(t) = -ω^2*F(t), and so the third term above becomes -(ωτ)^2 * INT. This allows an easy solution.
INT(1+(ωτ)^2) = F(t)*Ï„*exp(t/Ï„) – F'(t)*Ï„^2*exp(t/Ï„)
If you follow this through, you should obtain the solution we have discussed for the sinusoidal input. But if F(t) is, say, an nth order polynomial where n=6, the higher derivative terms don’t disappear from this solution.
Alternatively, you might just try plugging your solution into the original equation to see if it works.
Paul: “In general, I don’t think you can invoke Fourier to argue that the properties of any arbitrary function will be the same as a sine function!”
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In fact I’m invoking linearity to say what I’m saying, not Fourier. I’m using Fourier to decompose the original which I assume you don’t object to, then linearity to build the response.
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Having looked at this a bit more, the key is in the last term. There are as many transient terms as there are individual sines and cosines. We know the sum of the periodic terms since it’s just the original forcing and its derivative*tau. That’s nice and easy.
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Now the transient terms will have the same Fourier coeffs as the first two terms so are in principal accessible. There is the additional omega (frequency proportional) dependency.
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We can see from the graph at the top of my post that the overall coeff for the sum of all transients peaks at omega*tau=1 and falls off at both extremes of the frequency variable. That may allow some simplifications in some consideration, but let’s put that to one side for the moment.
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So the full solution can also be expressed as follows:
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A * forcing – AÏ„ * d/dt(forcing) + Aωτ*exp(-t/Ï„) * FFT( forcing )
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and that last term is starting to look like the convolution I suggested it was earlier.
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Now that seems to be a totally general and full solution. Do you see any objection so far?
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Thanks for your continued attention. Critical comment from someone well versed in this is helping make this more coherent.
BTW your polynomial case can be rejected by the requirement to be bounded by finite energy as you pointed out yourself in ‘Blue Suede Shoes” or it companion article.
A * forcing – Aτ * d/dt(forcing) + Aωτ*exp(-t/τ) * FFT( forcing )
Laplace solution is like the last term without the omega. Why the difference? 😕
Greg Goodman (Comment #116943),
The ENI function is based on exponential lag “response” to the “forcing” specified by the Nino 3.4 index, but with the response limited to the tropics. Since the ENI uses a detrended Nino 3.4 index, it averages to zero, and so has no net “forcing” over long periods, only balancing positive and negative “forcing”. The idea is that the Hadley circulation tends to create a more-or-less thermally isolated tropical region which has natural internal pseudo-oscillation, and the ENI index captures the temporal response to that internal behavior in terms of average temperature. The ENI has only a relatively short lag, consistent with the behavior being modeled, and that short lag constant would not be suitable for modeling the global response to external forcing, or even the tropical response to an external forcing.
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The overall response of the Earth to an external forcing for sure involves lags on a wide range of time scales. Modeling the temporal response to any specified change in forcing over time would seem to me to be a significant challenge.
Re: Paul_K (Jun 23 03:38),
Barrow, AK CO2 peaks in April/May and reaches a minimum in August/September. That’s neither peak insolation, or temperature. In fact, it probably correlates best with ice cover of the Chuckchi Sea. In other words, it’s not temperature.
Greg,
Probably because this isn’t a general solution. You can’t get an omega term into the solution if you don’t define and expand the forcing term. It only appears as a differential of the (specific) sinusoidal term. As I said, try plugging your general solution into the original equation to see if it works. I don’t think that it does.
On a minor point, if you have a general solution then it really does have to cover an arbitrary polynomial. I disbarred all polynomials as a null hypothesis for natural variation. But a general solution needs to be able to accommodate, say, a test of what happens if we create an (unbounded) exponential or cubic increase in forcing. Otherwise it is not a general solution.
Fourier’s theorem allows that all oscillatory functions can be represented as the sum of sinusoidal elements – not that all functions can be so represented. The difference is quite important here.
Steve F:
My “uncivility” is reserved for those who gratuitously personalize a
critique of foolish ideas and display arrogant presumption in their defense.
Carrick:
The rhetorical posture of a well-rehearsed “Umm” may impress the benighted, but let’s see where such a stance leaves you from a scientific perspective.
From the outset, you show no sign of any integrated comprehension of the following realities:
1. Heat transport poleward from the tropics by winds and wind-driven ocean currents is what maintains higher-latitude temperatures at levels well above those produced by local insolation. Many zonal heat-budget studies have established this unmistakably.
2. That transport is turbulent on many scales, resulting in fairly rapid vanishing of simple temperature correlation downstream from the source. Because a whole spectrum of wavenumbers is involved, the temporal cross-correlation of variations likewise effectively vanishes–but not uniformly across the power density spectrum. Both diffusive and coherent transports of heat continue nevertheless.
3. The physical process called ENSO has been long recognized as holding the key to the global re-organization of circulation patterns–both air and sea–that occurrs during El Nino episodes. It is intimately involved in heat transport not only in the Pacific basin, where the “pineapple express” brings moist tropical air to usually dry California, but (through sometimes far-less-understood mechanisms) with air temperature variations in many remote regions around the globe. Such teleconnections show up clearly under cross-spectrum analysis of vetted century-long station records, which often enough reveals squared coherence >0.7 and stable relative phase (greatly varying from region to region) in the power-rich ENSO frequency bands. This typically accounts for a good fraction (~1/3) of total variance of yearly temperature averages in teleconnected regions.
4. Although ENSO is well-known on an empirical basis, nobody has yet come up with a comvincing dynamical explanation of what ultimately drives it. Inasmuch as solar-connected factors cannot be ruled out inter alia as the ultimate cause, the ENSO-coherent global variations can only be considered logically as concommitant variables.
5. Simplistic lagged cross-correlation examinations are incapable of revealing any such relationships, because there is no uniform arrival-time lag of heat contributions from any source. Such methods lack explanatory power in a real-world setting–except in the minds of those who know little beyond linear regression. The chaotic unpredictability of the Stokes derivative en route virtually ensures confounding results at extra-tropical latitudes, even when dealing with strictly Eulerian data in a purely temporal framework.
On the contrary, you make sweeping judgements of putative lack of any significant extra-tropical temperature effects precisely on such flimsy basis, all the while conflating ENSO with the local NINO3.4 index.
And then you have the temerity to twist the context and meaning of my words in order to depict me as a “poser” in need of a basic statistics course. The rich irony of your transparent CYA ploy had even the most humorless of my collegues laughing.
I’ll leave it–and this thread–at that.
A nice resumé of the way climate works, sky.
It underlines how futile the whole attempt to reduce climate change to one globally averaged linear coefficient “climate sensitivity” is.
I think ENSO confounds two phyical effects. One is the decidedly non-linear negative feedback of the tropics. The mechanisms that stabilise the tropics appear as an extra ‘forcing’ around changes in energy input like that due to volcansim and solar variations (which are significant in UV).
http://climategrog.wordpress.com/?attachment_id=310
The second, the pseudo oscillatory element, which is a long term lunar tide linked to the apsides cycle. This is split by modulation with a longer periodicity into two peaks around 3.8 and 5.2 years which has obscured its origin.
All these frequencies can be found by spectral analysis of trade wind data.
http://climategrog.wordpress.com/?attachment_id=283
Paul_K
You are right , this is not a fully general solution. I had already wondered about it depending on whether FFT was definable and even a linearly increase would pose a problem there.
However in principal, if such a term exists (eg log response to exponentially rising CO2 conc.), it can be dealt with separately and added in again using the linearity argument.
The transient term is not quite right as I have written it but I don’t see anything wrong with this method for any input for which FT is defined. That implies a condition of stationarity: variations with components longer than the dataset would need to be removed by filtering or detrending.
Since that is what everyone is doing anyway that does not impose an additional condition on the processing.
I’m still curious as to why this method produces a result which is forcing + derivate + transient, whereas the Laplace solution is just a convolution of the forcing, since I don’t see either as being incorrect.
This probably means that the two are equivalent for the restricted case of a stationary input function, but that it is not obvious.
OK, I took Paul’s suggestion and ran some test data. It shows the two approaches are identical for an input that can be represented as a Fourier series.
http://climategrog.wordpress.com/?attachment_id=402
I’ve written an explanation and some commentary:
http://climategrog.wordpress.com/?attachment_id=399
In effect we can see that the solution is the weighted sum of forcing and its derivative , both passed through a low-pass filter whose frequency response is given by Paul’s A=1/(1+(wt)^2)
I’m not sure I can see a reason to prefer this method computationally or for fitting but having shown they are equivalent it gives a lot more insight into the relationship between input and output.
That should provide some insights into both temperature and CO2. More on that later.
Thanks to Paul for being pedantic and poking me in the right direction. 😉
My lashed up test data of three equally weighted cosines, turns out to be quite a good ‘forcing’ to reproduce AMO (itself a detrended SST index).
http://climategrog.wordpress.com/?attachment_id=403
This points out the futility of trying to “explain” the post-2000 plateau without any representation of the 60 year variability in the model being used.
It also points out the futility of trying to ignore the 9y cycle that Curry/BEST published on recently. This will necessarily result in false attribution of the two dips in that short post-79 record being attributed to (spuriously) to volcanism.
This was the _real_ reason for Grant “Tamino” Foster restricting his analysis to the satellite period.
Since Tamino is technically competent, it’s hard not to see this as deliberate obfuscation.