Over the past several months there have been a number of exchanges at The Blackboard about natural cyclical or pseudo-cyclical contribution to Earth’s temperature history. With the primary point of contention being whether or not natural cyclical variation has misled us about how much of the post 1975 warming has been due to man made GHG forcing. Most of these exchanges have been good natured, but the underlying disagreement is real enough: was the relatively rapid warming from the late 1970’s to the early 2000’s simply the result of GHG forcing combined with man made aerosol effects, or was some (or even all) of the warming over that period due to natural cyclical processes? In other words, is the recent warming representative of Earth’s true response to forcing, or has the warming been significantly ‘overstated’ by the contribution of a naturally occurring positive cyclical component to the measured warming? There is some evidence for both POV’s; my personal position has always been that a significant cyclical contribution seems likely, if based only on the evolution of temperatures since the instrumental record began.
Some have pointed to the de-trended AMO as a reasonable proxy for natural cyclical variation, while others have noted (fairly, I think) that the AMO may in fact be only a proxy for the actual global average temperature; implying that regressions of the AMO against global temperatures is nothing more than regression of something against a proxy of itself, so always yields an uninformative correlation.
Is there a natural cyclical contribution? Certainly we need to look beyond a simple temperature proxy like the AMO to decide.
A clever analysis of Milankovitch forcing is perhaps an illustrative example of the sort of thing that is needed. It is obvious that Earth’s orbital variations cause substantial changes in solar forcing at high latitudes, and in the 1940’s Milankovitch already claimed these were responsible for ice age cycles. But even though it has been widely accepted there have been great changes in Earth’s total ice volume over time, and it has been widely believed that these changes were related to orbital forcing, it was only recently recognized that the rate of change in total ice volume is what best correlates with orbital forcing at high latitudes, not total ice volume. (http://earthweb.ess.washington.edu/roe/GerardWeb/Publications_files/Roe_Milankovitch_GRL06.pdf) The Milankovitch forcing correlation with total ice volume is not good, but there is excellent correlation against the rate of change in ice volume. (I note that the paper’s author Gerard Roe was one of Richard Lindzen’s doctoral students… but that is a different discussion.)
So in the spirit of Gerard Roe’s paper, I suggest the following hypothesis: The Pacific Decadal Oscillation (PDO) does not directly correlate with cyclical variation in Earth’s average surface temperature, but the cumulative influence of the PDO over fairly long periods does correlate strongly with Earth’s historical temperature variation, and perhaps is in large part responsible for the observed cycle-like variation in the historical temperature record.
A bit of information about the PDO
The name “PDO” was coined by Mantua et al (Mantua, Nathan J. et al. (1997), “A Pacific interdecadal climate oscillation with impacts on salmon production”, Bulletin of the American Meteorological Society 78 (6): 1069–1079).
Wikipedia (http://en.wikipedia.org/wiki/Pacific_decadal_oscillation) notes:
“The prevailing hypothesis is that the PDO is caused by a ‘reddening’ of the ENSO combined with stochastic atmospheric forcing. A PDO signal has been reconstructed to 1661 through tree-ring chronologies in the Baja California area.”
and goes on to list several proposed physical mechanisms for the PDO, none of them related to human activities. So it seems unlikely that human GHG forcing is a causal influence on the state of the PDO. The PDO is described by JISAO (http://jisao.washington.edu/pdo/) as:
“a long-lived El Niño-like pattern of Pacific climate variability. While the two climate oscillations have similar spatial climate fingerprints, they have very different behavior in time.”
JISAO has produced a PDO monthly index, from 1900 to the present, with the PDO index defined as the leading principal component of North Pacific monthly sea surface temperature variability pole-ward of 20N for the 1900-93 period. JISAO presents this graphic to depict the difference between “warm phase” (left) and “cool phase” (right) PDO states: (click on any graphic to view at original resolution)
Wood For Trees includes the JISAO PDO index among their sea surface temperature indexes. (http://www.woodfortrees.org/plot/jisao-pdo)
It is pretty clear from inspection of the above graphic that here is rather poor correlation between the PDO index and Earth’s recent temperature history. But let’s suppose that the PDO index influences Earth’s average surface temperature by a cumulative, rather than an immediate effect. That is, let’s suppose that an integral of the PDO index over time can influence Earth’s average surface temperature. What could we look at to evaluate the cumulative effect of the PDO over time? I can think of two reasonable choices: 1) the continuous time integral of the PDO from 1900 forward, and 2) the trailing average (over a specified time, say 25 – 30 years) of the PDO. The figure below shows the cumulative total (the integral) of the monthly PDO index starting in 1900, along with the Hadley HADCRUT4 temperature history.
The mid 1940’s peak in temperature correlates well with the peak in the cumulative PDO index, and the slight decline in temperature from the mid-1940’s to the mid 1970’s tracks the cumulative PDO index almost perfectly, while the rapid warming post 1976 corresponds perfectly to a rapid increase in the cumulative PDO index. Finally, the recent “plateau” in temperature corresponds to the leveling off and decline in the cumulative PDO index.
The graph below shows an adjustment of the HADCRUT4 data based on the cumulative PDO index.
The adjusted HADCRUT4 data no longer has a significant mid-1940’s peak in temperature, no decline in temperature from the mid 1940’s to the mid 1970’s, and slower warming since the mid 1970’s. All of which seems more consistent with estimates of the historical man made GHG forcing. (The constant of 0.00125 was chosen to maximize consistency with that forcing.)
One doubt about the cumulative PDO index is that it implicitly assumes the state of the PDO index in 1900 (and all times since then) continues to influence temperatures today. To avoid this assumption (and limit the period of influence), a trailing average of the PDO index can be used instead. The graph below shows the 25 year trailing average along with the HADCRUT4 historical record.
The graph begins in 1925 because the PDO index data starts in 1900, and 25 years is needed to generate the first data point for the 25 year trailing average. Once again, the variation in the HADCRUT4 trend seems to track the trailing average of the PDO index quite well. The graph below shows an adjustment of the HADCRUT4 data using the 25 year trailing average of the PDO.
Once again, the adjusted temperature trend appears to reasonably follow the historical man made GHG forcing. Finally, the graph below shows the slope of the adjusted temperature trend since 1975.
Observations and Comments
Unlike like the AMO index, which tracks the Earths average temperature closely, the PDO index itself is much more variable, and does not correlate well with average temperature. However, it is clear that a long term cumulative measure of the PDO index correlates quite well with changes in the slope of the temperature trend over the recent past. It is of course possible that this is just coincidence, but the correlation is awfully good, so a causal relationship seems plausible (and IMO likely). Nobody appears to suggest that the PDO is driven by man-made GHG forcing or man made aerosol effects; it is by all accounts a natural process.
Assuming there is a causal relationship, what mechanism is responsible? The honest answer is that I do not know, but it must be related to gradual changes in ocean heat content in the first few hundred meters of the ocean, since this is the part of the ocean which is substantial enough in thermal mass to account for relatively long cumulative effects, and which also has immediate influence on Earth’s average surface temperature. Changes in heat content at great ocean depth would not be expected to have direct influence on the Earth’s surface temperature except on multi-century time scales. So I would expect variations from any secular trend in ocean heat content for the top ~300 meters to be a reasonable measure of the cumulative influence of the PDO over 2 – 3 decades, with much less (and much slower) influence of the cumulative PDO on heat content at greater depth.
Since the state of the PDO tends to persist over multi-decade periods, and since 1998 the index has been mostly negative, it seems likely that the influence on the trend in global temperatures will continue to be negative, at least for the next 15-20 years. Based on past behavior, if the 25 year trailing average index reaches -0.6, then the trend in temperatures could be reduced by about 0.12C over that period, compared to what that trend would otherwise have been. Unless the PDO changes unexpectedly to consistently positive, we can reasonably expect the recent slow rate of global temperature increase to continue for some time. My personal SWAG is a rate of warming over the next 15-20 years of about 0.06-0.07 C per decade, with a true (underlying) secular trend of about 0.12C per decade. If this happens, then the IPCC’s climate model projections are going to look even worse in the coming years than they do today.
What am I missing? The JISAO PDO graph above , from my eyeballing, looks like a somewhat good correlation. As for forcings, I think climate scientists of all persuasions need to adopt a little more humility. With several forcings, solar, GHG, and PDO (perhaps the big three) of unknown power, how might we infer the relative power of each? AR4 stated that it was very likely (<90%) that recent warming was a GHG forcing, so others were essentially noise. With accelerating GHG and no warming for 15+ years, we're back to studying PDO and solar forcing (and black carbon and many other things), but is there any way to make a testable hypothesis? It's just as likely as ever (no, I don't think it was ever likely) that climate sensitivity is high, 4 degrees or higher and the negative PDO and probable ongoing solar grand minimum are offsetting all the GHG forcing. It's also just as likely as ever that climate sensitivity is quite low with recent temperature flat-lining possible evidence. We humans sure have a strong desire to know the future (and how useful that would be!), but as far as I can tell, even testable hypothesis making is beyond our current understanding. Climate scientists of the past, like H.H. Lamb, were modest in their claims of understanding attribution. After pretty much wasting 20 plus years with selective funding of studies to demonstrate AGW, the hard work begins- trying to understand climate so that some day we might create skillful models. SteveF is doing some of that hard work above (thank you!), but it is barely a beginning.
In short the issue is, that the ENSO index is not linear to the temperature response of the ENSO process.
This assumption would, of course, be required for a linear regression and several papers have applied this non-existing requirement regardless.
The ENSO index discribes properties of a certain region in the tropical pacific. However, particularly El Nino events have multiyear after effects which are not included in the ENSO index.
After an El Nino, warm water pools remain on the sea surface and drift polewards. This can be seen on sea surface temperature maps such as
http://www.youtube.com/watch?v=MF5vZErQ6HM
or is supported by other evidence, such as the occurence of tropical fish off the coast of Alaska after an El Nino.
Once those warm water pools drift out of the ENSO index region, they are no longer included in the ENSO index but continue to warm.
In another piece of evidence, Bob Tisdale divided the recent temperature increase into several sections, each starting with a step up due to an El Nino and constant temperature afterwards.
http://bobtisdale.files.wordpress.com/2012/05/4-rest-o-world.png
I would suggest that the constant temperature after an El Nino is a superposition of a slowly declining temperature due to the heat loss of the warm pools and an increasing temperature due to other factors.
It should be noted, that there are no equivalent cool water pools remaining after a La Nina event. Cool water sinks down after the upwelling stops due to gravitiy.
A longer term effect of ENSO is therefore mainly due to El Ninos. A sequence of frequent and/or strong El Ninos (such as 1976-2005) will therefore produce a warming trend, rare and/or weak El Ninos a cooling trend.
So in sum I think, your cumulative or trailing averages are seriously better than just using the ENSO index, as the former will include long term effects of El Ninos. There may be some remaining error due to the symmetric treatment of El Ninos/La Ninas though.
I can kind of understand why the land temp wouldn’t correlate with an ocean cycle. The Sun, atmospheric IR, clouds, rain, and regional weather complicate land temperature.
But it might be expected to correlate with global temps given the fact the ocean is 70% of the surface area. However, the PDO does not correlate well with UAH global channel 5.
http://www.woodfortrees.org/plot/uah/from:1980/normalise/plot/jisao-pdo/from:1980/normalise
But the AMO seems to, to a greater extent:
http://www.woodfortrees.org/plot/uah/from:1980/normalise/plot/esrl-amo/from:1980/normalise
Bob Tisdale shows leftover warm water of the 1997/98 El Nino
(Animation at 42:40)
http://www.youtube.com/watch?v=lmjaNO5DD_Q
Hi Steve,
This reminds me of the old result you had for the cumulative ENSO index…
Mathematically, for a purely sinusoidal function both the running average and the cumulative sum are again sinusoidal functions with the same frequency, but with phase and amplitude shifts. Here the trailing average looks rather different from the cumulative one, showing they correspond to different mixes of low frequency components.
Nonetheless, a lagged response may be easier to “explain” than a cumulative effect, and it may qualitatively be just as good…
Julio, there are some lags and some cumulative responses that vary with hemisphere and heat capacity. If it was easy, it wouldn’t be fun.
What is really tough though is a lot of the cumulative impacts have funky thresholds that trigger the weird stuff like the QBO and shift Sudden Stratospheric Warming events. That is the gravity wave stuff Lindzen cut his teeth on. I don’t see how anyone can “explain” all that much.
http://curriculum.pmartineau.webfactional.com/ssw-animations/
That has quite a few good animations of SSW and SVW events. You can compare the rough intensity of the NH events with UAH NoPol Stratosphere and barely see yet another pseudo-cycle. The large events release on the order of 10^22 Joules in a few weeks. That is part of the meridianal transfer that the models only miss by about 20%.
Trying to figure out that kind of stuff with anomalies is like taking a knife to a gunfight.
Well done SteveF.
This is a detailed analysis of the “back of a napkin” hypotheses I have been pondering for some time now. We know through radiative transfer that increased atmospheric CO2 must cause warming at some level but I suspect that the rapid observed warming from 1980-1998 was a compounding of solar, oceanic and anthropogenic influences that were all at a high level or rising together. I agree that over the next 20 years global temps will likely be pretty flat based on these influences.
If indeed the sun drives the oceans and the oceans drive climate, we still have much to learn.
SteveF,
That’s somewhat beside the point, which is that there appears to be a cyclic component to the climate with a period of ~65 years. That component also appears to antedate the Industrial Revolution and the subsequent massive increase in the human population of the planet. Now people like Ruddiman will tell you that human interference with the climate started with the invention of agriculture thousands of years ago, but somehow I doubt that this was the cause of a quasi- or pseudo-cyclical climate cycle. Until the mechanism behind this cycle is identified, every measure will be a proxy pretty much by definition.
julio (Comment #110224),
I understand that a phase shifted sinusoidal function is what you get from integrating a sinusoidal function, of course. I was not suggesting that the PDO was anything like a sinusoidal function (heck, look at the index data from JISAO!). The cumulative since 1900 function only makes sense if you think the influence of a past PDO state lasts for a very long time; a trailing average for a specified time makes more sense if you think the past PDO state has influence of limited (though fairly long) time.
DeWitt,
“Until the mechanism behind this cycle is identified, every measure will be a proxy pretty much by definition.”
Sure. My point was not to show the fundamental cause of the pseudo-cyclical behavior, but rather to demonstrate that a well known pseudo-cyclical behavior, other than the AMO, seems strongly correlated with ~60 year ‘cycle’. One argument which has been consistently advanced to explain the the 1940′ to mid 1970’s cooling, the rapid warming from the mid 1970’s to the early 2000’s, followed by much slower warming, is that aerosol effects did it all. Certainly nobody has suggested the PDO has been modified by man made aerosols… and unlike aerosols, the PDO is actually based on measurements. My hope is that demonstrating a strong correlation between the long-term PDO influence and temperature fluctuations might help point toward a demonstrable underlying physical explanation.
Manfred (Comment #110218),
I am not sure I see any connection in your comment to what I wrote in the post.
jim2 (Comment #110220),
I think you are missing the message in the post: the PDO index most certainly does not correlate with satellite measurements of the lower troposphere (or any of the average surface temperature series). What correlates strongly with average surface temperature is a cumulative long-term effect (eg. a 25-year lagging average), not the instantaneous PDO index value.
DeWitt,
I found the following article: http://www.ldeo.columbia.edu/~agordon/publications/JES_SSH.pdf from 2004, which shows that the PDO is strongly correlated with changes in the flow of the warm Kuroshio current in the western Pacific. The authors show a graph with low Kuroshio current leading to the “warm phase” of the PDO, which means the western part of the north Pacific is cooler than average, and high Kuroshio current leading the the “cold phase”of the PDO, with a warmer western north pacific. Which makes perfect sense if the flow of the current (carrying tropical heat northward) is varying significantly. The estimated flow changes over decadal periods are quite large. Which means big variations in heat carried out of the western tropical pacific.
.
Is this the physical cause for connection of the PDO to global surface temperature variation? Sure seems to fit… lower heat transport to high northern latitudes where it is more easily lost to space suggests more heat accumulating in the rest of the ocean.
Re: SteveF (Feb 17 21:39),
I’d be willing to bet many quatloos that there is a similar correlation of the AMO to the Gulf Stream. It’s pretty clear that the warming of Svalbard in the early twentieth century (and likely the increased melting of the Arctic sea ice and the more rapid increase of the UAH NoPol anomaly starting around 1995) was related to either an increased flow or a shift in the flow to higher latitudes. You can see in the pattern of ice melting in the vicinity of Svalbard that ocean currents are involved. Ice on the eastern side of the island always melts last. There was an animation somewhere that showed vortices being spun off from the Gulf Stream and heading for the Arctic.
SteveF,
Interesting. Bob Tisdale shows the relationship between PDO and Pacific SST here:-
http://bobtisdale.wordpress.com/2009/04/27/misunderstandings-about-the-pdo-%E2%80%93-revised/
I don’t know what the lag is between Pacific SST and global land-and-ocean temperatures, but I suspect your integration of the PDO might just be bringing the two more closely into phase?
How did you choose your zero for the PDO series?
As far as I can see, you’ve got a completely free choice, which means you’re not integrating (PDO), you’re integrating (PDO + c). If the PDO itself nets out, the integrated result will have a gradient of c.t, meaning you can match any darn trend you like by monkeying with your parameters.
Here the atlantic (esrl, already detrended) and the global sea surface (hadsst2) multidecadal oscillations:
http://www.woodfortrees.org/plot/esrl-amo/plot/esrl-amo/trend/plot/hadsst2gl/detrend:0.664/plot/hadsst2gl/trend/detrend:0.664
Where’s the (anthropogenic) beef? How would you extrapolate the multidecadal oscillations into the next few decades?
Peter Ellis,
I didn’t choose any zero, I used the JISAO index without adjustment. As far as I can tell, JISAO used the average of 1900 to 1997(?) as the zero point, but I am not 100% certain of that. With regard to getting “any darned trend you like”, the only choices I made were to integrate the entire record or to calculate a trailing average. For the trailing average; 25 years and 30 years gave very similar results, 20 years gave a bit too much short term variation, and 15 years way too much short term influence. The shorter averages also tended to lead the ovserved pseudo-cyclical temperature variation.
DeWitt,
The AMO moves in lockstep with the detrended global temperature series. The PDO does not. Slowing of the Kuroshio current corresponds to immediately cooler northwest Pacific surface temperatures, but leads to only very gradually warming global average temperatures. There may be similar variations in Gulf Stream flow, but I don’t think there are so many published estimates.
You’re in good company, Steve.
DeWitt Payne (Comment #110236)
February 17th, 2013 at 10:15 pm
I’d be willing to bet many quatloos that there is a similar correlation of the AMO to the Gulf Stream.
——————
You win the quatloos.
Please note that the Gulf Stream SSTs below are NOT detrended. I hadn’t noticed this before.
AMO back to 1854 and the northern part of the Gulf Stream (not really a stream anymore but more like the northern part of the north Atlantic Gyre).
http://s7.postimage.org/l1fi4uyrf/AMO_NGulf_Stream_Jan2013.png
Weekly back to 1981. I like the higher resolution data.
http://s3.postimage.org/6iluzqt0z/Weekly_AMO_NGulf_Stream_Feb132013.png
Edim (Comment #110240),
Detrending the global average sea surface temperature just shows what we already know: there have been significant cycle-like changes in rate of warming of the ocean surface over the last 100+ years. The real question is what process(es) drive(s) this pseudo-cyclical variation? Some contend that the variation is mainly driven by variation in man-made aerosol effects (which tend to reduce sunlight reaching the Earth’s surface, and so cool). The point of my post was to show that there is a strong correlation between the cumulative PDO (a natural oscillation) and the observed variation in globally averaged ocean surface temperature. Nobody suggests (AFAIK) that the PDO is driven by variation in man-made aerosols.
Bill Illis (Comment #110244),
I think it is pretty clear that if the temperature of the gulf stream off the Eastern USA is higher, then that will lead to a warmer north Atlantic. The question is if that difference in warming is due to a higher velocity Gulf Stream, or warmer water and the same velocity.
.
In the case of the Kuroshio current, the flow changes quite dramatically between positive PDO index (low flow) and negative PDO index (high flow), with the difference estimated in the range of 5-6 Sv (5 or 6 X 10^6 cubic meters per second) out of a total flow of ~26 Sv. The flow of the Gulf Stream seems much less certain but estimates are in the range of 30 Sv.
SteveF,
I understand. I think the correlation between solar cycle frequency (or inverse correlation with the solar cycle length) and global temperature indices (including AMO) is remarkable. I think there is an instantaneous solar cycle frequency (or angular/rotational speed) and it is driving those multidecadal oscillations. Estimating solar cycle length is difficult – the exact timing of the minimums is somewhat arbitrary. Nevertheless, the plots of the unsmoothed SCL looks very similar to global temperature indices (including AMO).
http://ars.els-cdn.com/content/image/1-s2.0-S1364682612000417-gr1.jpg
SteveF, ” The real question is what process(es) drive(s) this pseudo-cyclical variation?” Energy
The mean altitude of NH land masses is 2000 meters or roughly 770 millibar pressure. So comparing ocean cycles to “global” or NH “surface” temperature would produce a 17 to 20% error, period. If you want to do something fun, determine the global “mean” temperature to absolute energy without correcting for altitude. Then compare apples to apples.
I like this animation because it shows what the Kuroshio and the Gulf Stream are about. They are really the same phenomenon.
http://www7320.nrlssc.navy.mil/global_nlom32/navo/WHOSP1_nlomw12930doper.gif
Very nice argument, SteveF.
Figure 2 of the linked 2006 paper by Roe on Milankovitch cycles’ effects on ice is worth viewing for its aesthetic value alone… that is what highly correlated time series look like!
Related, a follow-up remark to the exchange between Peter Ellis (Comment #110239 ) and SteveF (#110241).
We (those of us who aren’t statisticians, that is) first evaluate the meaningfulness of a correlation by applying the Mark I Eyeball test. When something’s interesting, we want to improve on that by applying a mathematically rigorous statistical test, then thinking about its report of significance (P value, etc.).
As regular readers of this blog know all too well, when it comes to climate-relevant time series, that is rarely straightforward!
In another context (Mann08’s abusive employment of the Tiljander series), I’ve discussed the Bonferroni correction. This is an effort to take rigorous account of “the number of hypotheses under consideration” when estimating the significance of a correlation. It seems to me that this is the concern that underlies Peter Ellis’ point.
In particular, in seeking a relationship between the PDO and HADCRUT4, SteveF took a series of looks, starting with the simplest, then moving stepwise towards more complex — but still physically plausible — relationships. It was a couple of those more complex relationships that returned the most interesting results (see figures in the OP).
It seems to me that each decision-of-what-to-look-at represents a hypothesis. Peter Ellis notes that the zero-point for the PDO given by Wood For Trees is rather arbitrary, and that using a different zero will give a different integration, and thus a different correlation with HADCRUT4. Likewise for a different choice of lag period.
I don’t mean to belittle the possible significance of the PDO/global temperature correlation that SteveF has discovered. Rather, to note at an early point in the discussion that statistical evaluation of the relationship of the two time series will have some inherent difficulties.
Unfortunately, we have relatively limited access to the ideal solution — data from an alternate-universe Earth with which to test the strongest hypothesis.
dallas (Comment #110248) ,
I really have no idea what you are trying to say.
SteveF: I’ve argued against this for years. Sea surface temperature data contradict your post. See here:
http://bobtisdale.wordpress.com/2009/04/27/misunderstandings-about-the-pdo-%e2%80%93-revised/
And here:
http://bobtisdale.wordpress.com/2009/05/25/revisiting-%e2%80%9cmisunderstandings-about-the-pdo-%e2%80%93-revised%e2%80%9d/
And here:
http://bobtisdale.wordpress.com/2010/04/16/is-the-difference-between-nino3-4-sst-anomalies-and-the-pdo-a-function-of-sea-level-pressure/
And here:
http://bobtisdale.wordpress.com/2010/09/03/an-introduction-to-enso-amo-and-pdo-part-3/
And here:
http://bobtisdale.wordpress.com/2010/09/14/an-inverse-relationship-between-the-pdo-and-north-pacific-sst-anomaly-residuals/
And once again here:
http://bobtisdale.wordpress.com/2011/06/30/yet-even-more-discussions-about-the-pacific-decadal-oscillation-pdo/
You wrote, “Assuming there is a causal relationship, what mechanism is responsible?â€
There is no mechanism through which the PDO can vary global surface temperatures. The PDO does not represent the sea surface temperatures of the North Pacific (north of 20N). In fact, the PDO is inversely related to the sea surface temperature anomalies of the North Pacific. The PDO is basically an aftereffect of ENSO and the sea level pressure of the North Pacific.
ENSO is the mechanism through which global surface temperatures vary over the long-term, not the PDO.
http://oi46.tinypic.com/2qidagy.jpg
In the discharge mode (El Niño), ENSO releases heat to the atmosphere primarily through evaporation and redistributes warm water from the tropical Pacific:
http://oi47.tinypic.com/24zgfgk.jpg
And in the recharge mode (La Niña), ENSO replenishes the heat released by the El Niño and creates the warm water for the El Niño(s) that follow:
http://oi47.tinypic.com/2coogo7.jpg
You wrote, “Unlike like the AMO index, which tracks the Earths average temperature closely, the PDO index itself is much more variable, and does not correlate well with average temperature.â€
That’s because the AMO is detrended North Atlantic sea surface temperature anomalies. The PDO, on the other hand, is NOT detrended sea surface temperature anomalies of the North Pacific, north of 20N. The PDO is the leading principal component of the sea surface temperature anomalies of the North Pacific with the global sea surface temperature anomalies removed from each 5degX5deg grid. The PDO is also standardized which exaggerates its importance—by about 5.5 times…
http://i53.tinypic.com/2yjxydk.jpg
…where the AMO data are typically not standardized.
Regards
AMac,
Well, what actually got me thinking about this was the difference between the smoothed PDO and the smoothed HADCRUT4 series: http://www.woodfortrees.org/plot/hadcrut4gl/mean:61/from:1900/plot/jisao-pdo/mean:61
.
When the PDO switches from a positive to a negative persistent state, that seems to correlate with a change in the slope of the the temperature series, but not correlate with the actual temperature. I found that odd, and completely different from the AMO: http://www.woodfortrees.org/plot/hadcrut4gl/mean:61/from:1900/plot/esrl-amo/mean:61/from:1900
SteveF, it is just choosing a surface for making a direct comparison.
If you have a cold phase PDO with the typical wind direction, it would change that average cloud ceiling over land. If you pick 6000 feet for the mean ceiling, the pressure would be about 600 millibar with a temperature of ~ 255 K degrees (236 Wm-2). You would have a land amplification of the changes in coastal SST which would change the average atmospheric boundary layer or cloud ceiling.
So you could use potential temperature or simpler in my opinion, stick to energy. When you compare to anomalies in the NH you would get a larger temperature change than the energy change would indicate. Using different smoothing without considering energy you are just trying to “fit” one index to another index.
Bob Tisdale (Comment #110252),
I understand that you think the ENSO controls the Earth’s climate, but I must respectfully disagree with that conclusion. The ENSO is of course an important pseudo-cyclical factor (as any inspection of the correlation between ENSO and temperature in the tropics shows). Still, there is more going on than just the ENSO…. like man made GHG forcing. Your oft-repeated conclusion that man-made GHG forcing is irrelevant or insignificant is, IMO, nothing short of bizarre, since it is contrary to the known radiative properties of GHG’s. The extent of amplification of direct GHG effects is a legitimate subject for discussion, but that man made GHG’s warm the Earth is not.
.
The PDO is the deviation of the north pacific temperature (north of 20 degrees) from its long term average, with the ‘positive’ PDO index representing cooler western north Pacific temperatures. If that deviation is related to changes in the volume of the Kuroshio current (which seems to be the case) then there may be some tie-in to the state of the ENSO, since the height and temperature of the west Pacific warm pool ought to be (in part) regulated by warm water flow out of the pool to the Kuroshio current. Estimated changes in the flow of the Kuroshio current (about 5 * 10^6 M^3/second out of ~26 * 10^6 M^3/second) between PDO states represents a change in heat flux on the order of 0.315 petawatt if we assume the water cools by ~15 C.
.
The significance of this change in heat transport can be judged by comparing with the total solar flux of about 120 petawatts (240 watts per square meter on average, assuming Earths albedo of ~30%). So the change in the heat transported northward by the Kuroshio current between PDO states is on the order of (0.315/120)* 240 = 0.63 watt/per square meter if averaged over the entire Earth. That is not an insignificant change.
SteveF, In case this doesn’t come out, it is just BEST versus PDO,
http://www.moyhu.blogspot.com/p/climate-plotter.html
The lack of fit between 1940 and 1980 I am pretty sure has to do with land use changes associated with the war and post war expansion.
Dallas,
I click on that link as see a blank graph. Please capture and post an image of what you are trying to demonstrate.
BTW, the ‘PDO’ data on that site looks nothing like the JISAO data I used.
Re: SteveF (Feb 18 10:43),
> Estimated changes in the flow of the Kuroshio current between PDO states represents a change in heat flux on the order of 0.315 petawatt if we assume the water cools by ~15 C.
I just wanted to check the 15 C cooling figure — that’s an awfully big differential; seems like there might be a missing decimal point. Or not; a quick Web search only yielded Wikipeda noting that “The Kuroshio is a warm current (24 °C annual average sea surface temperature), about 100 km wide…”
AMac (Comment #110250)
What I think AMac is inferring here is what struck me on reading this thread introduction: Mining for a fit in attributing a source for a cyclical global temperature is a statistically perilous proposition given the required Bonferroni accounting (or something like it) and how difficult that would be to track when you sit down to draw up different graphs and attempt to track the graphs you might have already viewed and discounted.
I would think that proper spectral analysis of the longer term instrumental records (CET) and perhaps temperature reconstructions, if a reliable ones could be found, would be a better approach to looking for cycles in the global temperatures. Obviously presenting a physically sound bases for cycles would be the best approach.
I think in the back of the minds of some skeptics on these matters is the thought that many climate scientists, and particularly scientists/advocates, are not readily motivated to find cycles and that the effort needs a push from outside that science community.
AMac (Comment #110258),
By 15 degrees, I mean the temperature difference between where the water begins (tropics) and ends (north pacific sub polar).
Hmm?
https://lh6.googleusercontent.com/-stvnrbh6bEM/USJhrdhixoI/AAAAAAAAHMQ/_8mvThd_KwI/s912/pdo%2520best.png
I am not sure what PDO Nick uses, but it looks like it includes the same trend as his AMO series.
I have been looking at the reference surface thing for a while. The best I can tell, the real “global” mean temperature referenced to sea level surface temperature would be about 17 C, the 14 to 15 C would be roughly 200 to 300 meters above sea level. During the LGM with sea levels roughly 100 meters lower, there would need to be about a 1 C correction. Makes things kinda fun have frames of reference floating around 🙂
dallas,
I do not know what Nick uses, but it sure isn’t the PDO index.
WRT changes in sea level during ice ages: the tops of ice sheets would be high (and very cold) and the sea level slightly lower, and maybe 0.5C warmer as a result. Ice sheets displace some atmosphere and so increase its depth elsewhere. But I am not sure what the point of noting that is.
SteveF, Dallas,
The plotter gives the source info if you Ctrl-Click on the label of the curve (bottom left panel, where you select it).
This one is from Michael Mann, which I guess won’t redound to its credit here. The info page is here (scroll down, there are several sets).The data was here, but seems to have moved.
@SteveF (Comment #110234) . You are right, I did mis-interpret your article. Probably, the link between oceans and other variables like the neutron count, muon count, TSI, solar ultraviolet, solar cycles, or others should be input into an ocean cycles model in a search for how energy enters the oceans and is later released. It is hard to believe oceans don’t have a dominate influence on global temps. Man produced GHG would have some extra input into the ocean heat content also.
Nick,
Thanks. PDO index data from Mike Mann? Maybe the JISAO data would be better.
Kenneth Fritsch (Comment #110259),
Humm… I looked at a total of five trends: the cumulative since 1900, and trailing averages of 30, 25, 20, and 15 years, in that order, because I figured that something near 30 years would best capture a hypothetical ~60 year cycle if driven by a cumulative effect. I guess I should never have looked beyond 30 years, or maybe never looked beyond the cumulative trend. I’m not really sure how my confirming my suspicions that shorter trailing averages would not correlate well with changes in temperature trends reduces the validity of the correlation for longer trailing averages, or for the simple cumulative trend, since both of those showed pretty much the same thing, but I’ll take your word for it.
.
The close relationship between variations in the volume of the Kuroshio current and the state of the PDO strikes me as worth evaluating as a cause for changes in the rate of heat accumulation by Earth oceans over time. You make a guess (educated we hope) about causation, make some predictions based on that guessed causation, and see if those predictions turn out to be right. I don’t know any other way to do it.
SteveF (Comment #110267)
“You make a guess (educated we hope) about causation, make some predictions based on that guessed causation, and see if those predictions turn out to be right. I don’t know any other way to do it.”
My point is not the methodology you applied. A scientist will often do preliminary testing like you describe. If the discovery is something that will show causation or make a good case for it, no one will be concerned about the Bonferroni accounting because it would then be a moot point. On the other hand, if one wanted to start hypothesizing about a relationship without making the causation connection, you have to start accounting for all your trials.
Steve, since you have not attempted a hypothesis here I am going to forgive you. I do, however, think that a number of good scientists and usually those from the hard sciences get confused about the preliminary testing they do that can lead to confirmation or a good approximation of causation with what a statistician has to deal with when there is a relationship without a good and independent case for causation.
SteveF,
Yes, I probably will switch – I used JISAO for most other ocean cycles. The (minor) reason I used Mann’s PDO data was that he quoted annual numbers, which I can use directly, while JISAO is monthly. Easy to average, but it means that users can’t immediately see that the numbers plotted correspond to the source. However, if the source has wandered, that advantage is lost.
Steve, Dallas,
I agree that JISAO is the right data to use, not Mann. I’ve changed it, and I’ll change the AMO too.
SteveF, “But I am not sure what the point of noting that is.”
Just that reference temperature can make a huge difference. Since there is a longer term 52 year trend in the North Pacific, supposedly, I don’t think that massaging the PDO with anomalies will produce much.
“Hidden in the original PDO is a trend that is identical to the trend in the North Pacific High, and is captured as our fourth common trend. It is important in two areas, including near the coast of North America, that are strongly influenced by the NPH. This result also clarifies what has happened in the calculations of the PDO. As higher frequency dynamics usually contain higher variance than lower frequency dynamics, the PDO has captured the area that has the highest variance in the stochastic cycles, but this region mostly coincides with the region whose trend is related to the trend NPH. The fourth common trend has a spectrum with significant peaks at 52.26 and 13 years, which coincide with the so-called â€Seuss wigglesâ€, suggesting a solar influence to this component.”
http://arxiv.org/pdf/1204.2486.pdf
BTW, that paper also notes the 1982-1984 “shift” which is the reason I ran across it while looking for hints on the longer term cycles.
Nick,
Wow! That is fast service. 🙂
SteveF
Did you think about doing a ‘Tamino’ to the data and removing the ENSO and volcanic signal from the adjusted temperature record? A less lumpy line might be more convincing to some.
(P.S. I approve of the scepticism you show to your own work and enjoyed the post)
HR (Comment #110278)
I thought about trying to remove the ENSO signal, but figured it would add complexity and maybe charges of ‘matherbation’ in some quarters. 😉
SteveF (Comment #110233)
February 17th, 2013 at 8:57 pm
Manfred (Comment #110218),
I am not sure I see any connection in your comment to what I wrote in the post
—————————————–
Yes, I did not read your post thoroughly and implied that you used the ENSO index (like Foster&Rahmstorf), though you were using PDO all along.
SteveF says: “The PDO is the deviation of the north pacific temperature (north of 20 degrees) from its long term average…â€
Wrong. The PDO does not represent the deviations of sea surface temperatures of the North Pacific. You’ve just called the PDO the sea surface temperature anomalies of the North Pacific and the PDO does not represent the sea surface temperature anomalies of the North Pacific:
http://i51.tinypic.com/rr39d5.jpg
The PDO only represents the spatial pattern of the temperature anomalies of the North Pacific, north of 20N. That is, with respect to one another, it’s warmer in the Kuroshio-Oyashio Extension (KOE) than it is along the west coast of North America during negative PDO and vice versa during a positive PDO. The strength of the spatial pattern determines how far the PDO deviates from zero.
SteveF says: “Your oft-repeated conclusion that man-made GHG forcing is irrelevant or insignificant is, IMO, nothing short of bizarre, since it is contrary to the known radiative properties of GHG’s.â€
IF my “oft-repeated conclusion that man-made GHG forcing is irrelevant or insignificant is…bizarre†to you, please provide links to the multitude of climate model-based peer-reviewed papers that use “the known radiative properties of GHG’s†and that explain how and why:
1, The sea surface temperatures of the East Pacific Ocean (90S-90N, 180-80W))—that represent 33% of the surface area of the global oceans—have not warmed in 31 years:
http://i47.tinypic.com/hv8lcx.jpg
2, The sea surface temperatures of the Atlantic, Indian and West Pacific Oceans (90S-90N, 80W-180, called the Rest of the World in the following graph) only warmed during the strong El Nino events of 1986/87/88, 1997/98 and 2009/10. That is, please provide links to papers that explain why the sea surface temperatures show no warming without those El Nino events:
http://oi45.tinypic.com/2qspjkz.jpg
And if you’re wondering why we’d divide the oceans into those two subsets, all you have to do is examine a map of the warming (or not warming) trends of the global oceans for the Reynolds OI.v2 sea surface temperature dataset:
http://oi48.tinypic.com/2vccorr.jpg
3, (Because the North Atlantic is also impacted by another mode of natural variability called the AMO, it’s logical to examine the sea surface temperatures of the South Atlantic, Indian and West Pacific Oceans as a separate subset.) The sea surface temperatures of the South Atlantic, Indian and West Pacific Oceans would have cooled if not for those strong El Nino events of 1986/87/88, 1997/98 and 2009/10:
http://oi47.tinypic.com/24zgfgk.jpg
4, The warming of the ocean heat content of the tropical Pacific (0-700 meters) is dependent on La Nina events of 1973/74/75/76 and 1995/96:
http://oi47.tinypic.com/2coogo7.jpg
5, The warming of the ocean heat content of the extratropical North Pacific (0-700 meters) is dependent on a 2-year climate shift:
http://oi47.tinypic.com/53mk3d.jpg
That’s how and why those portions of the oceans have warmed (or not warmed, in the case of the East Pacific sea surface temperatures). I’ve looked for the climate model-based peer-reviewed papers for 4 years that explain how and why the oceans warm in those fashions. As far as I know, they do not exist.
Further, based on the “the known radiative properties of GHG’sâ€, please provide links to the climate model-based peer-reviewed papers that explain why the sea surface temperatures of the Pacific Ocean as a whole have not warmed in almost 20 years:
http://oi48.tinypic.com/246qcu0.jpg
To paraphrase what you’d written, IMO, it’s truly bizarre to believe the assumed radiative properties of GHG’s have had any impact on the warming of the oceans.
SteveF says: “If that deviation is related to changes in the volume of the Kuroshio current (which seems to be the case) then there may be some tie-in to the state of the ENSO…â€
There’s a tie-in to the processes, not only state, of ENSO. Let me provide you with an overview:
An El Nino event releases a monumental volume of naturally created warm water from beneath the surface of the west Pacific Warm Pool. Some of that warm water spreads across the surface of the central and eastern tropical Pacific—what some people refer to as the El Nino since it warms the sea surface temperatures of central and eastern equatorial Pacific. Coastally trapped Kelvin waves cause the sea surface temperatures to warm along the west coast of North America (and the PDO is positive). Much of the warm water released by the El Nino remains below the surface of the central and eastern equatorial Pacific. After the peak of the El Nino, the leftover warm surface waters are returned to the west (blown there by the renewed trade winds), and after the peak of the El Nino, the leftover subsurface waters are returned to the western tropical Pacific by Rossby waves. After the 1997/98 El Nino, there apparently was only one Rossby wave and it can be seen at about 10N in the following animation of sea level anomalies:
http://bobtisdale.files.wordpress.com/2012/06/animation-3-1.gif
Part of the leftover warm water is picked up by the Indonesian Throughflow and carried into the eastern tropical Indian Ocean. Part of the leftover warm water is picked up by Kuroshio Current and carried poleward to the Kuroshio-Oyashio Current, east of Japan, where it warms the sea surface temperatures there:
http://i52.tinypic.com/wjvow.jpg
(and the PDO is negative).
And if you’d like to watch it happen refer to the animations included in the following post:
http://bobtisdale.wordpress.com/2010/12/08/the-enso-related-variations-in-kuroshio-oyashio-extension-koe-sst-anomalies-and-their-impact-on-northern-hemisphere-temperatures/
Let me repeat two statements from my earlier comment:
1, The PDO is basically an aftereffect of ENSO and the sea level pressure of the North Pacific.
2, The PDO is also standardized which exaggerates its importance—by about 5.5 times…
http://i53.tinypic.com/2yjxydk.jpg
Regards
Bob Tisdale,
One of my business partners, when confronted with someone who has managed to convince themself that something which is inconsistent with reality is true, simply describes that person as “lost in the weeds”. Which I think is a fair description of where you currently are located.
.
The fundamental issue is a simple one: do you or do you not believe adding GHG’s to the Earth’s atmosphere must warm the Earth’s surface to some extent?
.
If your answer is no, then it is unlikely any amount diacussion about patterns of ocean warming and cooling will be productive. You see, I have found that any rational technical analysis, no matter how complicated the subject, must remain consistent with our understanding of basic physical processes like radiative heat transfer. When someone has drawn conclusions which are obviously contrary to those basic understandings, I must conclude that they are lost in the weeds.
.
So if you agree that adding GHG’s to the atmosphere must, to some extent, warm the Earth’s surface, then I will be happy to discuss ocean warming and cooling patterns. If not, then any discussion would be only a waste of time for both of us. There has to be some agreed upon common understanding for a technical discussion to be productive….. or even meaningful.
SteveF, Your buddy is in the restaurant business? Restaurant staff spend a good bit of the time “in the weeds” 🙂
Getting everyone on the same page as to how much impact CO2 will have looks like mission impossible. I find it easy to forget CO2 and just consider adding 4Wm-2 to the system resistance to heat loss due to whatever combination of causes.
If you add 4 Wm-2 uniformly to the system and then look at the lack of uniform distribution of outgoing long wave radiation, you wouldn’t expect that 4 Wm-2 added to magically create an new uniform distribution of energy loss would you?
From Bob’s perspective or frame of reference, adding 4 Wm-2 to a surface layer that has an average surface temperature of 21 C, 294K S-B equivalent 425 Wm-2 is close to negligible, especially when regional SST cange make excursion of +/- 2 C which at 425 Wm-2 would be over 10 Wm-2. CO2 “forcing” would have less impact on Bob’s layer.
“You see, I have found that any rational technical analysis, no matter how complicated the subject, must remain consistent with our understanding of basic physical processes like radiative heat transfer.”
‘Our’ understanding might be wrong, actually IMO it is wrong. The problem is not radiative heat transfer, but overall heat transfer at the Earth’s surface. You cannot solve that by radiative heat transfer only (i know orthodoxy claims it’s all taken into acount).
The surface is cooled primarily by non-radiative heat exchange with the atmosphere and secondarily by direct IR to space plus net IR exchange surface->atmosphere. The atmosphere on the other hand can be cooled only by IR to space. On the face of it, increasing the emissivity of the atmosphere should cool the surface. However, this could easily be negligible or insignificant compared to the other factors influencing global climate change.
Edim, “‘Our’ understanding might be wrong, actually IMO it is wrong. The problem is not radiative heat transfer, but overall heat transfer at the Earth’s surface. You cannot solve that by radiative heat transfer only (i know orthodoxy claims it’s all taken into acount).”
Actually you can solve it by radiant physics only. All you have to do solve a few minor details with relativist heat conduction where energy flux is limited by the speed of second sound instead of light. That is about as easy as solving all the Navier-Stokes equations.
opps, I am likely to get banded to my on thread again 🙂
Edim,
“‘Our’ understanding might be wrong, actually IMO it is wrong.”
You mean radiative physics? Or some specific projected extent of warming due to added GHG’s? The issue is not if there are factors which modify the expected radiative influence (there certainly are: water vapor changes, cloud changes, atmospheric and ocean heat transport, etc.) it is if you accept that adding GHG’s must warm the surface relative to not adding GHG’s. If someone accepts the basic premise of GHG radiative forcing causing warming, then discussion about the details may be a productive use of time. If not, any attempt at discussion is silly.
SteveF (Comment #110267)
“…I figured that something near 30 years would best capture a hypothetical ~60 year cycle if driven by a cumulative effect.”
The integral of the sin(x) function is -cos(x) +c which is phase shifted by 1/4 of the period. If you thought there was a ~60 year cycle then there should be a ~15 lag. 25 years implies a 100 year cycle.
Dealing with cumulative sums can be tricky. The code below demonstrates some of the steps that I performed to discreetly calculate sin(x)’s integral given full cycles of data.
x=(0:200) # 200 year time series
y=sin(2*pi*x/100) # sin wave with period 100 years
plot(x,y,type=’l’) # plot sin wave
cy0 = cumsum(y) # cumulative sum
cy1 = cy0 – mean(cy0) # calculate anomoly
cy2 = cy1/(sqrt(2)*sd(cy1)) # convert to 1 amplitude
lines(x,cy2,col=2) # shows phase shift of 1/4 period (i.e. 25yrs)
grid()
Also note that if a one-box model is applied, then the amplitude of the response approaches zero as the shift approaches 1/4 of the period.
Dallas, SteveF,
I disagree and we can leave it at that. I don’t want to hijack this thread and I also think that discussion with someone who think adding GHG MUST warm the Earth’s surface (other factors constant) is hardly possible.
AJ,
Sure, all true if you are talking about a sine wave. But the PDO index is nothing like a sine wave…. more like a very noisy squarish – triangle wave. Look at the 121 month trend of the PDO index: http://www.woodfortrees.org/plot/jisao-pdo/mean:121
Edim, A disagreement while discussing climate change I am shocked. What I said though is right. The transistion from pure radiant transfer to a higher density thermodynamic environment is a Byatch.
When SteveF attempts a cumulative impact without considering energy capacity, he is going to come up with less than desired results. When Hansen considers the cumulative impact of CO2 without considering the heat capacity limits, he is going to come up with less than desirable results.
As AJ points out, integrating a sine function would produce a lag and a constant. Think of that constant as the charge in a battery or the reactive energy in a RC circuit. As the charge increases the cumulative impact changes.
Then to boot, the PDO is about the noisiest index to select. You can force it to fit just about anything by adjusting your filtering. Not that it may not be useful if you hit a filtering with some meaning behind its use, but that is unlikely if you are attempting to fit to another noisy, less than ideal metric, GMT anomaly. You will end up pulling out all the stops using “novel” methods that will produce what you think should be produced.
It is a complex problem so brain farts are more likely than epiphanies. Luckily, brain farts are allowed in polite company.
SteveF
Fixed. There is absolutely no reason why climate response to that forcing MUST result in a warmer surface.
Your statement, as originally written, has failed validation by observation, one third of all CO2 ever produced by man has been added to the atmosphere since 1998 but HadCrut4 and HadSST2 show no significant warming in that period.
Either CO2 forcing is much less significant than thought or climate response to that forcing is negative or natural variations (euphemism for what science doesn’t understand about climate) overwhelm that forcing
Personally, I favour the latter
*download CDIAC’s data
Edim,
” I also think that discussion with someone who think adding GHG MUST warm the Earth’s surface (other factors constant) is hardly possible.”
.
Which suggests that for you discussion with most everyone who comments at The Blackboard is hardly possible. This is a conclusion on which we completely agree.
Gras,
You and Edim should work together to further scientific understanding. Ciao.
dallas,
“When SteveF attempts a cumulative impact without considering energy capacity, he is going to come up with less than desired results. ”
I have not a clue what you mean by this. Can you explain clearly what you are suggesting?
SteveF, The impact changes with total heat capacity. With a higher heat capacity, the cumulative impact decreases more energy would be lost, i.e. Sudden Stratospheric Warming events. As an analogy, the initial current draw when charging a discharged battery is greater than a charged battery.
You would have the same problem trying to integrate solar. You know there is some impact, but that impact would have to change depending on the “charge” level of the oceans. Not only would the impact change, the lag would also change.
So let’s look at Hansen. CO2 allows the atmosphere to accumulate more energy but it doesn’t add sufficient mass to the atmosphere to increase the energy storage capacity so it can contain that energy. The lid on the pot rattles releasing energy. That is the SSW events, stratospheric not cooling like it is supposed to situation, diurnal temperature range not playing by the rules, and all the other lovely divergences.
Maybe it would be more correct to ask if extra CO2 will add EXTRA ENERGY to the surface of the Earth. This allows for the possibility that after the energy is added, feedback mechanisms come into play to dissipate that energy and there is no increase in temperature.
I think most could admit to extra energy being added to the surface by extra CO2 while arguing the global temp wouldn’t rise as a result.
OK, not MOST, but some.
jim2,
“extra energy being added to the surface by extra CO2 while arguing the global temp wouldn’t rise as a result”
.
I wonder if you can understand how much of a stretch of reality that statement is? Probably not. A system with a set-point and active compensation to reach that set-point (like a well adjusted PID controller, or the internal temperature control in a mammal) can result in no change for an applied disturbance, but that’s about it.
Re: jim2 (Feb 19 11:51),
Dissipate that energy to where exactly? Unless it goes directly to space, any dissipation just increases the temperature. Also, that would be equivalent to 100% negative feedback. Outside a voltage follower circuit, that seems unlikely. The Planck response is probably the strongest negative feedback that has been identified and it still allows the temperature to increase when the forcing increases.
SteveF, here is a better example.
https://lh3.googleusercontent.com/-N-UooPvi6c8/USPqWXI6I5I/AAAAAAAAHPY/rd3-urE5B3s/s901/SteveF%2520amo%2520pdo%2520index.png
The Sudden Stratospheric Warming events release a great deal of energy to space. Since you have a northern Pacific higher versus a north Atlantic low, the PDO and AMO combined would give you some indication of the over the pole differential that would impact the polar vortex. A Pacific high sliding under an Atlantic low would basically force energy higher in the atmosphere where the tropopause is lower near the pole. Stratospheric warming with a couple of 10^22 Joules worth of energy lost to space from time to time. That might have a climate impact.
Taking the AMO minus the PDO would give you an indication of the relative strength of the SSW events. Something that seems to be missing from most of the climate papers I have seen. The PDO by itself though, lacks a mechanism to do much of anything.
BTW, that ~11 year saw starting in 1985 might also make an interesting post.
@110300, 110301
No stretch of reality here. The clue:
“I think most could admit to extra energy being added to the surface by extra CO2 while arguing the global temp wouldn’t rise as a result.”
Note the word “global.”
While the extra energy of the ground will make its way into the air shortterm, the potential feedbacks like clouds could mitigate most of the warming from the extra energy.
I don’t see some metaphysical path from the ground to space, just the atmosphere.
DeWitt Payne, why would dissipation necessarily increase temperature? We’re interested in the temperature of certain things, like the atmosphere or oceans. There are plenty of places energy could dissipate to without increasing the temperature of those. The only way what you say would be true is if we’re interested in some total temperature of the entire planet.
In electronics, this would be akin to looking at the temperature of a CPU in a system with unsaturated heat sinks.
jim2,
“While the extra energy of the ground will make its way into the air short term, the potential feedbacks like clouds could mitigate most of the warming from the extra energy.”
.
Humm…. There are some well known negative feed-backs (like reduced solar intensity due to high albedo clouds), but there are also well known positive feedbacks (like an increase in water vapor… a GHG… with rising temperature). The real issue is not projecting that GHG forcing must raise average surface temperatures (it must), it is projecting how much warming GHG’s will produce when all feedbacks are accurately considered. And more immediately, what information, if any, can we glean about variations in those feed-backs over time.
.
The point of my post was that the well known periods of greater and lesser rates of warming and cooling must have been caused by something. Climate modelers (shamelessly, and with little or no supporting data) assume varying levels of man-made aerosols to explain the historical variations. IMO, this is just a kludge, because there is a wealth of evidence of pseudo-cylical variation in proxy records, extending to long before humans were emitting GHG’s.
.
But when someone insists that GHG’s must have little or no influence on temperature, they adopt a terribly weak argument… much weaker even than the comical arguments of modelers about aerosol effects. Do yourself a favor and accept that GHG’s can potentially cause significant warming. The important argument is about how much.
Re: Brandon Shollenberger (Comment #110305)
It doesn’t “necessarily,” but heating of some sort is usually the end of the road for energy “dissipation.”
DeWitt:
Given the unexplained early 20th century temperature increase, other significant human forcings, and the biased high GCM results it’s not unreasonable to look for potential IR sinks or pathways that may store or transmit the extra energy. Who knows, maybe Bob Tisdale is on to something. I think it’s a mistake to dismiss his ideas out of hand just because we all know CO2 will increase IR.
For instance, it has been recently discovered that some bacterium can use IR for photosynthesis. Also, there is that crazy professor Pollack at the U of Wash who claims that water surface tension is a 0.5-mm thick liquid crystal layer that forms best in the presence of IR. These specific pathways are likely bollocks, but I think investigators should look harder than just turning the aerosol knob up beyond 11 to explain why CO2 is not making the expected changes to climate.
Obviously, where climate fits into the crests and troughs of ocean cycles is a very important piece of the puzzle.
Oliver:
The only way it doesn’t is if it is lost to the system (in this case via radiative loses). Even if the initial mechanism for dissipation is acoustical, rather than thermal, the acoustic wave gets attenuated by atmospheric absorption, converting that into thermal energy.
Of course increased thermal energy isn’t the same thing as increased temperature of one component (e.g. atmosphere) in a multi-phase system…
Howard (Comment #110309),
” Who knows, maybe Bob Tisdale is on to something.”
.
Not if that something leads to the conclusion adding GHG’s does not warm the Earth’s surface. Sure, there are obvious oceanic cycles which influence surface temperatures, and known significant variations in Earth’s surface temperature, independent of GHG forcing (heck, that is what my post is about!). But there is no way that adding GHG causes NO warming. So long as Bob (or anyone else) subscribes to that kind of nonsense, few will take his analyses seriously.
@110307
Where is your proof of …
“increase in water vapor?”
Carrick, isn’t another way changing the mass of the system?
Regardless, my point is as you said, increasing total energy is not the same as increasing one component’s temperature. DeWitt Payne’s point could only be true if we conflate the two.
Or I guess we could start talking about the former instead of the latter. After all, now that atmospheric temperatures aren’t showing signs of warming, global warming proponents are saying we have to look at total energy content of the planet to discuss “global” warming.
jim2,
Clausius–Clapeyron is a reasonable starting point for discussion. OTOH, you probably reject that as well…. OK, neva mind.
Brandon Shollenberger (Comment #110314)
Specifically, what kind of energy did you have in mind?
Brandon,
“After all, now that atmospheric temperatures aren’t showing signs of warming”
.
Say what?
http://www.woodfortrees.org/plot/uah/from:1996/plot/uah/from:1996/trend
http://www.woodfortrees.org/plot/uah/from:1998/plot/uah/from:1998/trend
http://www.woodfortrees.org/plot/uah/from:2000/plot/uah/from:2000/trend
http://www.woodfortrees.org/plot/uah/from:2002/plot/uah/from:2002/trend
http://www.woodfortrees.org/plot/uah/from:2004/plot/uah/from:2004/trend
In fact, the trend is positive for every starting year to the present, from before 1996 to 2007.
The nice things about all these oscillations (AMO or phase-shifted-and-smoothed-PDO) is that they are all currently entering their downward phase. I guess this is necessary if these oscillations are to match the recent slowdown in warming.
.
This is a good thing because the hypothesis will be self-testing within the next 15 years. Actually, even the next large El Nino event should bring some clue about their actual impact.
Clausius-Clapeyron is a good starting point and it predicts that water vapor should increase by 7.0% per 1.0C. All of the climate models have this feedback built into them roughly at 7.0% or 2.0 W/m2 feedback per 1.0C.
The data to date, however, indicates that it might be more like 4.5% per 1.0C.
http://s7.postimage.org/i0fl6h07v/Water_Vapour_RSS_UAH_Temps_Jan13.png
I’ve looked at this in many different datasets and this seems to be the number.
What is always overlooked, as well, is that the ENSO really controls this value. It has more influence than anything else (or at least it impacts the value by such a large amount that it seems to be the main control mechanism). [And the ENSO has no up or down trend over the long-term so might we expect water vapour to have no trend as well?].
The IPCC and climate science relies on cherrypicking a starting point (La Nina) and an ending point (El Nino) to exaggerate their numbers.
If we had realistic temperature numbers to rely on going back, we might find the C-C relation falls apart and we might find the ENSO runs it completely and/or that the planet fully compensates – ENSO and water vapor back to 1948.
http://s7.postimage.org/jrced6lwb/ENSO_TCMV_Jan13.png
SteveF (Comment #110317)
Are those short period trends statistically different than 0?
SteveF (Comment #110317)
And your point is? Not one of those trends you cite is significant.
SteveF:
“So long as Bob (or anyone else) subscribes to that kind of nonsense, few will take his analyses seriously.”
I could say the same thing about your “positive trend analysis”. The signal has gone flat, it’s quite obvious.
Then there is this nugget:
“jim2,
Clausius–Clapeyron is a reasonable starting point for discussion. OTOH, you probably reject that as well…. OK, neva mind.”
You sound like a Hollywood stereotype of a Junior High School “Mean Girl”. Jim2 comes back half-way and you double the smackdown.
Why are you polluting your own guest post with unnecessary petty rudeness?
SteveF (Comment #110315)
It appears you might as well not mind … you have no data.
Hmm, Willett et al 2007 looks at expected and observed levels of water vapour. Is there some problem with this analysis?
Bob, Kenneth Fritsch,
No. Of course, most of those trends are not statistically different from zero… the period is too short, except maybe starting in the pre-1997 period. But that is not the point. Every calculated slope from each of those starting years to present is positive. Or, if you prefer, our best estimate of the true trend is positive in each case. That is not really consistent with no indication of recent warming in the atmosphere.
Phil Scadden (Comment #110324),
I don’t think that data like that matters much to some.
Howard,
“Why are you polluting your own guest post with unnecessary petty rudeness?”
.
Because I grow tired of people who spout nonsense that pollutes my (and others) posts. From the dragon slayers who claim photons do not exist, to those who insist on someone providing data to ‘prove’ radiative transfer is correct, to people who insist increases in GHG’s couldn’t possibly cause warming: they all waste their own time and the time of people who try (inevitably, in vain) to help them understand some basic science. Please spare everyone this rubbish.
Steve F, ” Bob, Kenneth Fritsch,
No. Of course, most of those trends are not statistically different from zero… the period is too short, except maybe starting in the pre-1997 period. But that is not the point. Every calculated slope from each of those starting years to present is positive. Or, if you prefer, our best estimate of the true trend is positive in each case. That is not really consistent with no indication of recent warming in the atmosphere.”
Your point about an “eyeballed” trend is trivially true but still incorrect. The slope is barely positive but you really have no idea whether it is truly positive, flat, or negative. You are correct that more time is needed, but until that time arrives you cannot not state the slope is positive, unless your point is that you only wish to guess. A small, but important point.
toto,
“Actually, even the next large El Nino event should bring some clue about their actual impact.”
.
Well, a single el Nino does not a trend make. But I agree that the next 15 years will be informative. You perhaps noted my SWAG: about 0.06 or 0.07C per decade for the next 15 or20 years. Do you have a SWAG?
Re: Howard (Feb 19 16:39),
Umm, did you read the post that started these comments? The early 20th century temperature increase is explained well by some sort of pseudo-cyclical process that isn’t anthropogenic in origin. But that doesn’t explain the continued increase in the late 20th century. Ron Broberg, for one, uses a combination of a sine wave and an exponential function for an empirical fit to three different temperature records from 1880 to the present. All the fits predict a slowdown in the rate of increase of temperature from 2000 to 2020, some more than others. So the underlying trend after the removal of the cyclic component is not just positive by increasingly positive, just like the increase in anthropogenic forcing.
Bob,
This is the comment I was responding to: “After all, now that atmospheric temperatures aren’t showing signs of warming”.
.
The trend to present for every single starting year between 1996 and 2004 is positive in the UAH satellite data. No, they are not statistically significant at 95% confidence after about 1996 (too noisy and too short), but that does not mean the best estimate for the slope is not in each case positive. Can you “prove” warming at 95% based on those recent trends? Heck no, but those trends do represent some “signs of warming” in the atmosphere. They say the chance is better than 50% that there has been warming.
Woah, boys and girls.
Edim
If it wasn’t for the bracketed stipulation, this would be reasonable. With the “other factors constant†included, it is equivalent to stating that adding rubble to a bucket (other factors constant) doesn’t make it heavier.
Jim2
I like this. Yes, it most certainly will.
“This allows for the possibility that after the energy is added, feedback mechanisms come into play to dissipate that energy and there is no increase in temperature.†Feedback mechanisms can act to amplify or damp the effect, but feedback as it’s normally understood doesn’t completely counteract perturbations to a system.
“I think most could admit to extra energy being added to the surface by extra CO2 while arguing the global temp wouldn’t rise as a result.†That is actually an uncommon claim, but not a unique one, see below. It’s not impossible, but seeing as how we observe definite dips in temperature when volcanos inject a load of sulphate into the upper atmosphere, those feedback mechanisms seem oddly selective.
SteveF
Willis Eschenbach has made this very claim about the climate, likening the response to a speed governor. Don’t think he’s got very far with it though.
Jim2
This has been measured and documented in several papers. IIRC, the increase is smaller than predicted by the fixed relative humidity assumption but it is real nevertheless.
Howard
SteveF isn’t denying that; it’s right there in his guest post! “ we can reasonably expect the recent slow rate of global temperature increase to continue for some time. My personal SWAG is a rate of warming over the next 15-20 years of about 0.06-0.07 C per decade.†His point is that there is mounting evidence for cyclic natural variability and it may be possible to use the PDO index to account for it and determine the underlying trend with greater accuracy. That’s it. People jumping in on the discussion to claim that GHG don’t do anything even with everything else held constant are apt to make one tetchy, although I do agree that Jim2 probably got a rougher response than he deserved.
Oliver, I meant to type thermal so my phrasing was the same as Carrick.
SteveF, you’ve offered a specific set of evidence and said it shows a greater than 50% chance there has been warming. I don’t believe your evidence supports your claim. Would you like to explain how you justify it, statistically speaking?
SteveF
Thanks for a good article.
Here is my interpretation of the global mean surface temperature:
http://orssengo.com/GlobalWarming/GmstModel.png
Oh and further note on humidity. There are good reasons to expect that relative humidity will be constant but models do not assume that it will be so.
Brandon,
“you’ve offered a specific set of evidence and said it shows a greater than 50% chance there has been warming…. Would you like to explain how you justify it, statistically speaking?”
.
Well, if all you have is limited data and you find the OLS trend for that that data, then the OLS trend represents the most probable trend. That is, there is a 50% chance the true slope is higher than the OLS trend slope and 50% chance it is lower than the OLS trend slope.
.
If the OLS trend is non-zero, then there is a greater than 50% probability that the true slope is positive if the OLS trend slope is positive, and a greater than 50% probability the true slope is negative if the OLS trend slope is negative. The fact that you can’t draw any conclusion at 95% confidence does not mean you can’t draw conclusions at lower than 95% confidence.
“I don’t think that data like that matters much to some.”
Well jim2 asked for data…
Brandon, ”
Oliver, I meant to type thermal so my phrasing was the same as Carrick.
SteveF, you’ve offered a specific set of evidence and said it shows a greater than 50% chance there has been warming. I don’t believe your evidence supports your claim. Would you like to explain how you justify it, statistically speaking?”
I hope we all know that it can’t be justified statistically. I to await an explanation.
Phil – thanks. Is there a compendium of humidity observations somewhere available to the public. The article you cited has a nice summary, but it is a little light on detail.
Again, basic question being is there humidity data on the web as there is data for various temperatures, etc.?
Phil said, “Oh and further note on humidity. There are good reasons to expect that relative humidity will be constant but models do not assume that it will be so.”
Near surface oceans yeah, probably constant. Over land there is a question mark and there is another with distribution with altitude. Deep convection is getting lots of looks right now because of that. With a higher surface temperature and specific humidity, the condensation temperature would increase, so there would likely be a lower cloud ceiling where water is abundant. Then starting at a lower base, there should more deep convection.
There is a radiosonde study that indicates a trend in lower marine cloud base and “stretching” i.e. higher build with more deep convection, but it is radiosondes, so who knows. Once you throw in aerosol indirect effects, clouds will drive you nuts. Anyway, C-C doesn’t seem to handle supersaturation all that well from what I have seen.
“the face-value 35-year trend in zonal-average annual-average specific humidity q is significantly negative at all altitudes above 850 hPa (roughly the top of the convective boundary layer) in the tropics and southern midlatitudes and at altitudes above 600 hPa in the northern midlatitudes. ”
http://link.springer.com/article/10.1007%2Fs00704-009-0117-x?LI=true
Bob 110338,
“I hope we all know that it can’t be justified statistically.
.
Sure it can. See my reply to Brandon #110336. For any OLS estimate, half the probability of the true trend lies above and half below the OLS trend line.
SteveF (Comment #110327)
Steve, you invited “this rubbish” into the comments with this line in your guest post…
Some people do think that ALL of the warming was due to natural cyclical processes. It’s hardly fair for you to chew them out for the comments they make when it was you who left the door open for people to make these kind of comments.
Skeptikal (Comment #110344),
What I object to is people insisting on things contrary to a basic understanding of science. Like adding GHG’s to the atmosphere has no possibility of warming the Earth’s surface. It just wastes everyone’s time, including their own.
Finally! I found a convenient humidity chart.
http://www.ncdc.noaa.gov/bams-state-of-the-climate/2009-time-series/humidity
Hmmmm … specific humidity has been falling since 1948???
http://jennifermarohasy.com/2009/05/relative-humidity-has-been-falling/
Does that specific humidity chart mean the Laws of Science have been broken?
SteveF, perhaps I was unclear, but I do not need an explanation of basics of OLS regressions. The question I have is about how we interpret them. Namely, how you interpret a handful of linear regressions done on a single data set as sufficient to establish a greater than 50% probability there has been warming. That is, of the atmosphere, not just that series.
Discussions of mechanics of OLS don’t address that. But if we’re going to have one, we shouldn’t say untrue things about them. Linear regressions are not some inherently ideal approach to testing for an increase/decrease in temperature. It is possible to have a series with a greater than 50% chance of decreasing while an OLS regressions comes back positive.
jim2,
“Does that specific humidity chart mean the Laws of Science have been broken?”
No, it means that relative and specific humidity are different measures. Relative humidity is specific humidity divided by the humidity at saturation (the weight of water vapor in air at saturation increases with rising temperature). The saturation level increases by about 7% per degree C increase in temperature. So warming can cause falling relative humidity even while specific humidity rises.
.
It is the specific humidity in the air which controls the contribution of water vapor to GHG warming. It is the relative humidity which controls how much air must cool (how much it must rise above the surface) before water vapor begins to condense as cloud droplets. In air that is not saturated, the rate of cooling (due to gas expansion) is ~10C per Km altitude, but that drops to ~5C per Km rise once water vapor begins to condense, because the condensation of water liberates heat.
Brandon,
If the data is not normally distributed (autocorrelated, skewed, etc.), then sure, the OLS trend could deceive. But I did not think that was what you were suggesting. In any case, the question is: what is the best evidence we have of the recent trend? I think a fair answer is that the recent trend is much lower in slope than prior to 1998, and its true value is uncertain, but it is more likely positive than negative. (in the satellite data set)
DeWitt:
You are being sarcastic, right? You can’t possibly believe that we just happened out of the Little Ice Age right when the Industrial Revolution started kicking in due to some long hidden blob of warm water that just decided to burp out at the right time?
SteveF, you say you think “a fair answer” is one particular thing. Earlier, you gave the same answer and said it could be drawn from one particular set of evidence. I’ve asked how we could reach that conclusion from the evidence you referred to, and you’ve given me no useful answer.
I know you’ve complained about wastes of time on this thread. Should I assume asking you further questions on this point would qualify as such?
SteveF, I note you edited your comment to add a qualifier, “in the satellite data set.” That wasn’t present when I originally responded. As such, let me now emphasize this exchange began with you saying certain evidence showed a greater than 50% chance there has been warming in the atmosphere. Your conclusion was not limited to a single series. It was stated for the planet’s atmosphere.
Edit: For clarity, I said there were no signs of atmospheric warming. You said I was wrong, that certain linear regressions for UAH show warming in atmospheric temperatures.
Steve F
Brandon explained what I meant when I said you could not do it statistically. But when you say, ” and its true value is uncertain, but it is more likely positive than negative. (in the satellite data set)”, I maintain that is still invalid.
Re: Brandon Shollenberger (Comment #110333)
*Confused* So can you summarize what you meant?
Oliver, it’s as Carrick said in #110310. Increasing the thermal energy of a system (such as the planet) is nit the same as increasing the temperature of a component (such as the atmosphere). To understand the distinction, consider what “global warming” refers to. Quite often, people use it to refer to atmospheric temperatures. Is this “right”? Our planet is made up of more than just the atmosphere. For example, what about the ocean?
DeWitt Payne said dissipation of energy would necessarily increase “the temperature.” The temperature of what?
Bob, there are a variety of issues with SteveF’s claim, even if we limit the focus to the UAH series (instead of what matters and was being discussed, actual temperatures).
First, UAH has notable autocorrelation. Without accounting for that, any conclusion is suspect. Second, SteveF changed the starting point by 12 months for each of his regressions. This could matter for autocorrelation (depending on its structure), but it could also matter for seasonal purposes. After all, his regressions do not use full annual cycles, but rather, include an extra month at the end. That is made more problematic by the fact that endpoint is fixed. Which brings us to a third issue. Fixing one endpoint while varying another increases the weight of the data at one end. If that data happens to be at a high point, that’ll artificially increase OLS trends.
And that ignores the fact OLS is not some end-all test. There are other regressions one could use that may show different results (such as by giving a different weight to outliers). There are even tests one could use other than regressions (like changepoint algorithms). None of these are guaranteed to give the same results.
I suspect SteveF would get similar results if he analyzed UAH in a more meaningful way. I just think if there are that many issues in just examining UAH, it is absurd to suggest his tests show there is a greater than 50% chance atmospheric temperatures have increased. I think it would take more than a couple minutes with WFT to justify a conclusion like that.
Brandon
Hmmm. My statistical ability is around high-school level (if that) so this may be a completely wrong-headed question, but… say you are given two nominally identical coins. On flipping, one returns heads 51% of the time and the other 50% of the time, as determined statistically after a google of flips. You are then tasked with determining which is which.
Now, obviously with sufficient flips, the difference between the coins will become manifest. After a particular number of flips, you can have 95% confidence that you know which is which. But, if after just ONE flip of each, one comes up heads and the other comes up tails, is it not fractionally more likely that the “heads” coin is the 51% returner? Your confidence in the result would be pathetic of course, hence “not statistically significant”, but nevertheless that data would give you a minuscule nudge in one direction. Would you not be justified in claiming that the “heads” coin has a greater than 50% chance of being the 51% returner?
matt, sure. That’s why what SteveF said may sound reasonable. He over-simplified things to the point where it sounds like your example. In reality, it isn’t. To see an example, picture a sin wave. Note how it has constant cycles. Imagine what would happen if you did a linear regression over one cycle. Now imagine if you did it over three. Or ten. In each case, you should come back with no trend.
Now imagine you did your regression not over a whole cycle, but only part of one. Would it still be zero? No. You could get a positive or negative trend depending on which part of the cycle you used. If you only used the part of the cycle that was positive, you’d have a positive trend. Would you take that to mean the data is increasing? Of course not.
That shows you can have a positive trend for non-meaningful reasons. You can even extend the effect over any number of cycles as long as an uneven length is used (as SteveF did by using a single month in 2013). I don’t think that effect matters (much) in this case, but it shows things aren’t as simple as a coin flip. There are many issues which need to be considered.
And that’s just for the one series. What if UAH did show warming, but the same test done for RSS showed cooling? How could you draw a conclusion about atmospheric temperatures by only looking at one series? That’d be like flipping your coins twice but ignoring the results from the second time.
“Edim
â€I also think that discussion with someone who think adding GHG MUST warm the Earth’s surface (other factors constant) is hardly possible.â€
If it wasn’t for the bracketed stipulation, this would be reasonable. With the “other factors constant†included, it is equivalent to stating that adding rubble to a bucket (other factors constant) doesn’t make it heavier.”
matt, I mean the factors independent of the postulated CO2 forcing, like solar for example. Regarding your bucket analogy, I claim that we don’t add any rubble and consequently it doesn’t make it heavier. There’s no rubble added. Nature will demonstrate this in the next few decades. I have been predicting ~flat linear 30-year trend by ~2020. It already started decreasing in ~2005. Let’s see how it plays out.
Re: Howard (Feb 19 22:35),
There are quasi-periodic climate cycles longer than 60 years. The Roman warm period, followed by cool period then the Medieval warm period and the little ice age are likely the result of a ~1500 year cycle. That’s considered to be related to oceanic circulation. According to the best estimates, anthropogenic climate forcing didn’t become significant until the middle of the twentieth century. So yes, the warming in the 18th century at the beginning of the industrial revolution is not directly attributable to human activity.
SteveF: I have three responses to your Comment #110284 on February 19th, 2013 at 7:20 am. I’ll present them in separate replies.
First, in general, your reply seems to be a redirection from the topic at hand. Your post is about your claim of an impact of the PDO on global temperatures. It was based on your misunderstandings of the PDO. That is, you failed to understand that the PDO does not represent the sea surface temperature anomalies of the North Pacific. Can we therefore take your need to redirect the topic of discussion as an acceptance that you were wrong about the role of the PDO?
Second, SteveF says: “The fundamental issue is a simple one: do you or do you not believe adding GHG’s to the Earth’s atmosphere must warm the Earth’s surface to some extent?â€
Of course, I believe that adding “GHG’s to the Earth’s atmosphere must warm the Earth’s surface to some extentâ€. And for the oceans, that additional infrared radiation likely adds to evaporation at the ocean surface but not to the warming of sea surface temperature or ocean heat content. The reasons I say that is that there is no evidence that greenhouse gases have had any impact on the warming of global sea surface temperatures during the satellite era and there’s no evidence that it had any role in the warming of ocean heat content.
In fact, I’ve admitted that the additional downward longwave radiation likely has a limited impact on surface temperatures in numerous posts. I discussed it in the closing of my book, which is included in the free preview here:
http://bobtisdale.files.wordpress.com/2012/09/preview-of-who-turned-on-the-heat-v2.pdf
There, I wrote:
Proponents of anthropogenic global warming, after reading the book from cover to cover, might conclude that I did not disprove the hypothesis of manmade carbon dioxide-driven global warming, and they’re correct. I even admitted that within these pages. It’s likely anthropogenic greenhouse gases have had an impact on the additional warming of land surface air temperatures that’s above and beyond the warming attributable to the natural warming of the global oceans. That additional land surface air temperature warming, however, has also been caused by land-use change, the urban heat island effect, poor surface station siting, overly aggressive corrections to the land surface temperature records, black carbon, aerosols, etc.
However, this book clearly illustrated and described the following:
1. The sea surface temperature and ocean heat content data for the past 30 years show the global oceans have warmed. There is no evidence, however, that the warming was caused by anthropogenic greenhouse gases in part or in whole; that is, the warming can be explained by natural ocean-atmosphere processes, primarily ENSO;
2. The global oceans have not warmed as hindcast and projected by the climate models stored in the CMIP3 and CMIP5 archives, which were used, and are being used, by the IPCC for their 4th and upcoming 5th Assessment Reports; in other words, the models cannot simulate the warming rates or spatial patterns of the warming of the global oceans; and,
3. Based on the preceding two points, the climate models in the CMIP3 and CMIP5 archives, which are used by the IPCC, show no skill; that is, the climate models provide little to no value as tools for projecting future climate change on global and regional levels.
SteveF, you later wrote: “So long as Bob (or anyone else) subscribes to that kind of nonsense, few will take his analyses seriously.â€
Your opinion—that is, the opinion of someone who obviously cannot read, interpret and note the importance of the time-series graphs I’ve presented to him—really doesn’t matter to me or have any bearing on a discussion of global warming.
And that’s a good lead-in to my third reply, which follows.
Third, SteveF, everyone reading this thread can see that you’ve failed to respond to the very basic requests I made of you in my second comment to you on this thread. That is, your reply to that comment provided no links to climate model-based peer-reviewed papers that explain how and why the oceans have warmed. Here are my requests once again:
HHHHH
IF my “oft-repeated conclusion that man-made GHG forcing is irrelevant or insignificant is…bizarre†to you, please provide links to the multitude of climate model-based peer-reviewed papers that use “the known radiative properties of GHG’s†and that explain how and why:
1, The sea surface temperatures of the East Pacific Ocean (90S-90N, 180-80W))—that represent 33% of the surface area of the global oceans—have not warmed in 31 years:
http://i47.tinypic.com/hv8lcx.jpg
2, The sea surface temperatures of the Atlantic, Indian and West Pacific Oceans (90S-90N, 80W-180, called the Rest of the World in the following graph) only warmed during the strong El Nino events of 1986/87/88, 1997/98 and 2009/10. That is, please provide links to papers that explain why the sea surface temperatures show no warming without those El Nino events:
http://oi45.tinypic.com/2qspjkz.jpg
And if you’re wondering why we’d divide the oceans into those two subsets, all you have to do is examine a map of the warming (or not warming) trends of the global oceans for the Reynolds OI.v2 sea surface temperature dataset:
http://oi48.tinypic.com/2vccorr.jpg
3, (Because the North Atlantic is also impacted by another mode of natural variability called the AMO, it’s logical to examine the sea surface temperatures of the South Atlantic, Indian and West Pacific Oceans as a separate subset.) The sea surface temperatures of the South Atlantic, Indian and West Pacific Oceans would have cooled if not for those strong El Nino events of 1986/87/88, 1997/98 and 2009/10:
http://oi47.tinypic.com/24zgfgk.jpg
4, The warming of the ocean heat content of the tropical Pacific (0-700 meters) is dependent on La Nina events of 1973/74/75/76 and 1995/96:
http://oi47.tinypic.com/2coogo7.jpg
5, The warming of the ocean heat content of the extratropical North Pacific (0-700 meters) is dependent on a 2-year climate shift:
http://oi47.tinypic.com/53mk3d.jpg
That’s how and why those portions of the oceans have warmed (or not warmed, in the case of the East Pacific sea surface temperatures). I’ve looked for the climate model-based peer-reviewed papers for 4 years that explain how and why the oceans warm in those fashions. As far as I know, they do not exist.
Further, based on the “the known radiative properties of GHG’sâ€, please provide links to the climate model-based peer-reviewed papers that explain why the sea surface temperatures of the Pacific Ocean as a whole have not warmed in almost 20 years:
http://oi48.tinypic.com/246qcu0.jpg
To paraphrase what you’d written, IMO, it’s truly bizarre to believe the assumed radiative properties of GHG’s have had any impact on the warming of the oceans.
HHHH
And to paraphrase what you’d later written: When someone has drawn conclusions about climate chnage based on an hypothetical, imperfect climate model-based representation of how and why the oceans warm, which does not agree with data, I must conclude that they are lost in the weeds.
Regards
“First, UAH has notable autocorrelation. Without accounting for that, any conclusion is suspect. Second, SteveF changed the starting point by 12 months for each of his regressions.”
Here is the complete picture of UAH trends over time intervals in the last 23 years. There are very few regions of negative trends, and most of those over short periods, including the last up to two years.
If you want to argue statistical significance, this version shows which areas pass. This calc takes account of autocorrelation with a Quenouille correction.
But Steve is right to point out that it is the estimated value of trend that counts, not the significance. His statement is that the physics of GHG’s can be expected to cause warming of something less than 0.1°C/decade (I expect more). That kind of warming is observed. You can’t ask for more than that. To achieve significance over a short period, the trend would have to be very much higher. That isn’t what is expected, based on the physics.
Phil Scadden (Comment #110324)
February 19th, 2013 at 7:34 pm
Hmm, Willett et al 2007 looks at expected and observed levels of water vapour. Is there some problem with this analysis?
—————-
For one thing, it is just surface specific humidity, and its time period is 1973 to 2003 (which just happens to start in a cold period – well just as a large El Nino was ending and a sustained La Nina was starting – with a sharp drop in the AMO also starting and it ends in a relatively warm period).
You can go over the data in more detail here.
http://www.metoffice.gov.uk/hadobs/hadcruh/
And this is what it looks like compared to the earlier precipitable total column water vapor data I charted earlier back to 1948.
Its the same – and it is even more the same when you use NCEP’s surface specific humidity numbers – but total column is better.
http://s4.postimage.org/92b92qo25/Hadcruh_vs_NCEP_TCWVJan13.png
DeWitt:
Yeah, it’s possible. However, the ocean and solar mechanisms are still at the arm-waving stage to explain the 1Kyr, 1.6Kyr and 2.5Kyr quasi-periodic warming bumps that take place on an overall declining Holocene temperature record.
So many mechanisms, so little data!
Howard, it is all in the mixing. For the oceans to fully mix, it takes about 1700 years on average. Since the oceans have different layers, they mix at different rates. Since the Earth is asymmetrical thermally, it should be pretty obvious that there will be odd cyclic frequencies.
Since SteveF is trying a cumulative impact, how much can accumulate depends on the size of the bag and how fast you can dump stuff into it. Now how much would longer term cycles effect bag filling? That is not rhetorical, it depends on the condition of the bag.
If you want an estimate of how full the bag is, you could weigh it or get real fancy, or you could just look at the top.
That would be the stratosphere and mesosphere with that funky turbopause that is supposed to be the limit of convection. Guess what impacts that turbopause? SST, internal oscillation, GHGs and fluctuations in orbital forcings including the moon.
http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000038159
I have no idea if Christian’s dissertation is ground breaking or not, but 70 to 85 % natural variation in the stratosphere is kind of interesting.
Nick Stokes,
Thanks for the links to your trend analysis. The first is OK. The second one seems to be dead.
Edim:
Just to be clear, it’s your position then that GHGs don’t trap heat energy?
SteveF, it works for me.
Some of Nick’s pages require a bit of intervention to get them to work (like enabling WebGL for his newer stuff, which BTW is cool as hell, you can see some of the movies you can generate here).
I know you need to have javascript enabled in order to use that page. Nick might be able to say what other things are required.
dallas (Comment #110370)
“Using the statistical methods, variability in temperature and ozone is successfully forecasted up to the year 2100.”
I find this comment in that link a curious one and particularly the “successfully” part.
I would be interested in seeing the author’s cross validation results.
SteveF,
Sorry about that – the paste inserted a newline, which probably confused the javascript. This might work, but anyway, it’s just the other plot with “Trend-significance” pressed.
Bob Tisdale,
.
I am pleased that you agree rising GHG must warm Earth’s surface to some extent. You then say additional infrared radiation causes more evaporation from the ocean surface, but no warming. Evaporation of water increases due to an increase in surface temperature (and corresponding increase in vapor pressure). If you increase the radiant energy received, then the surface temperature must rise as a result; how much it rises due to an increase in radiant energy depends on the local conditions (wind speed, wave action, humidity in the air, etc). Infrared near 15 microns wavelength (emission for CO2) is of course absorbed only by the first mm or less of the ocean’s surface, but outside of a dead calm, there’s plenty of wave action/turbulence near the surface which continuously mixes the 1 mm surface into the well mixed layer (which on average is ~50-60 meters depth).
.
So it is hard for me to see how an increase in radiant energy from GHG’s received at the ocean surface can’t cause some increase in temperature of the well mixed layer. Much of the solar energy received by the ocean surface is in the infrared range (http://en.wikipedia.org/wiki/File:Solar_Spectrum.png) where water is very opaque (http://en.wikipedia.org/wiki/File:Absorption_spectrum_of_liquid_water.png), so nearly all that infrared solar energy is also absorbed in the top 1 mm to 1 cm. Are you suggesting that an increase in solar infrared would also have no influence on ocean surface temperature? Does that solar infrared also only cause an increase in evaporation but no temperature increase?
.
I will address some of the other issues you raise in other comments.
Carrick,
Thanks – yes, you need Javascript, and I think you had to explicitly enable WebGL on your Mac (though that’s not used in this link). IE doesn’t support WebGL. But apart from JS, this link doesn’t use anything exotic – I think the problem was the incorrect newline.
Bob Tisdale:
I’m glad to hear you accept that radiative physics is actually an understood branch of the physical sciences, however, it’s a flawed approach to argue over what complex phenomena tell us about physics models without actually extending your results to a model itself.
Anything is possible if you leave it to vigorous hand waving. For you to make a convincing argument, you’d need to develop at least a “cartoon” mathematical model, where you get the type of warming you are describing without the need to invoke additional warming from GHGs.
As it is, I think you are seeing the equivalence of patterns in random clouds.
To give an example, I’ve argued off and on that stratospheric cooling appears to exhibit a “stair stepped” response to volcanic events. For example RSS temperature, lower stratosphere. In a discussion over on James Annan’s blog, I managed to convince myself this was an example of seeing a pattern where no existed.
If you just went a bit back further in time than is afforded by satellite data (in this case I looked at HADAT2), you see this instead:
figure,
namely a continued cooling trend with complex volcanic responses overlaid on it. Without invoking a mathematical model, the plausible model seemed to be “stair-stepping”, by invoking a linear trend model, we see it’s a much less plausible explanation of these data.
I sometimes refer to the science of looking at wiggles in figures, without employing even a simple model, “wiggleology”. We all engage in it, humans are prone to spot patterns, even when none really exist.
As I said on James’ blog, “[Tisdale] may have described an aspect of the dynamics associated with temperature change, that haven’t been widely accepted yet, that might pertain to how climate responds to a change in net forcing. So even if right, I don’t see how this upsets any apple carts.”
Or, as I said, you may just have engaged in wiggleology. More work needs to be done to make a plausible case.
And even then, you should avoid attribution of cause without a plausible mathematical model that produce this behavior.
Nick Stokes,
That link worked. Thanks. You obviously put a lot of effort into that page; I am impressed.
SteveF (Comment #110325)
I think the point should be that trends in short temperature series are not good indicators of the longer term trends to which those short excursion might belong. We have a longer term warming trend that can be attributed to GHGs and natural causes and a current pause in warming due probably to natural causes and perhaps the cyclical nature of global temperatures.
SteveF, I think it is best to ignore the less informed opinions that do not add to the discussion of the points of your post. The moment you reply the discussion becomes personalized and tends to go further off topic.
I personally judge that spectral analyses of long term temperature records and temperature proxies (if it can be shown that the proxies might exist that respond reasonably well to temperature) is the preliminary step in better understanding any cyclical component in long term temperature series.
Without good confidence in model results finding temperature series cycles or having a method validating climate model results, I think the importance of finding reliable temperature proxies to look further back in time becomes a very important issue. The discovery of those proxies would take an entirely different and more basic approach than that used by climate scientists such as Mann have used in doing temperature reconstructions. I am not at all sure that in the current crop of climate scientists there are individuals willing to do the non heroic and hard work that would required to get the basic work done.
Kenneth, “Successful forecasting” is pretty gray. The range he has for weak and major is pretty large and since there is a SSW event of some type just about every two years in the NH, being right more than half the time would be successful. When I found his paper I was looking for a more energy based SSW rating system, but his is still too broad for what I wanted. He did assign some percentages to QDO AO’s and solar forcing that I was looking for. The AO or annular oscillations relate to SteveF’s post. PDO by itself isn’t much, but AMO-PDO is a decent proxy for the northern annular oscillation. A strong AMO-PDO can release much more energy to space than a weak AMO-PDO. How much impact that would have on surface temperature would depend on how much energy is in the system in the northern hemisphere. That would also have an impact on the QBO.
Like I said, I am not sure how ground breaking the paper may be, but I like the mixed approach he uses.
Bob Tisdale,
With respect to climate models: I have said nothing good about climate models, so I am not sure why you focus on them in several of your comments, including the above. Climate models are clearly unable to accurately (or even reasonably accurately) simulate lots of things, including regional warming patterns, ocean heat uptake, average surface warming, changes in atmospheric temperature profiles, and lots more. I am have never defended the accuracy of climate models, and I have said many times that basing public policy on the projections of climate models is extremely unwise, and doing so may lead to foolish, wasteful, and perhaps damaging public policy. I find your conclusions about ENSO being responsible for virtually all observed warming bizarre for reasons which have nothing to do with climate models or their failings.
Nonsense. The graphic in my post shows the temperature pattern associated with each phase. I later posted a reference showing variation in the flow volume of Kuroshio current which appear to explain that pattern, and which are strongly correlated with the PDO index. I even made a quick estimate of how much the changes in the Kuroshio would impact northward heat transport. By the way, as far as I have been able find, variations in the volume of western boundary currents like the Kuroshio appear mainly related to the strength of westerly wind shear on the ocean surface from ~30 to ~50 degree latitudes.
.
No evidence? Assuming for a moment that it is possible to “explain” through a long series of cure-fitting exercises all that ocean warming to ENSO rather than GHG forcing, that by no means proves the explanation is correct, especially if that explanation simultaneously requires one accept that increased infrared radiation on the surface of the ocean causes an increase in evaporation but does not increase temperature… which is pure pseudo-scientific nonsense… in fact, bizarre.
Carrick, DeWitt, Dallas
In field geology, we use the technique of multiple working hypothesis. In this way, many ideas are entertained and none too precious to throw away. It helps to allow jumping to easy conclusions, false correlations and wiggleologizing random stuff… then throwing the nonsense out and going with what survives the data accumulated during the mapping exercise. The climate seems to me like 10,000 Rube Goldberg contraptions that interact. Many do nothing and a few carry most of the workload. It’s an exciting field because no one really has a big picture idea on what all is actually going on. First, attack the known unknowns.
From the chart in Comment #110347, we see the increase of specific humidity that correlates with the 1998 El Nino. Can someone explain why, if H2O is the primary amplifier of atmospheric temperature, the temperature and S.H. didn’t keep going up? It went down again, so it does not look like a strong amplification.
While CO2 does add some warming, it appears to be a rather small signal riding on top of a much larger one driven by oceans.
jim2 #110385,
Because the system (including all fee-back effects) in inherently stable, not unstable. Which is to say: if you increase the radiant energy arriving at the surface, then the loss of heat increases faster due to a temperature rise than the influence of any positive feed-backs.
.
Say you increase the energy arriving at the surface by 1 watt/M^2. You could expect the temperature to rise by a certain amount if there are no net feedbacks… let say for sake of discussion the temperature would rise (absent any feed-backs) by 0.3C. This is a the fundamental feed-back for the system, and defines the “sensitivity” of the system to a change in “forcing”: 0.3C/watt/M^2. Once that temperature increases by 0.3C, the next question is: would that increase of 0.3C change the ease with which heat is lost by the surface? A positive feedback means that the loss of heat becomes somewhat more difficult as the temperature increases (the sensitivity value increases above 0.3C/watt/M^2), while a negative feedback means the loss of heat becomes somewhat easier as the temperature increases (the sensitivity value decreases). Any system where positive feedbacks overwhelm the ability of the system to lose heat would “run away” (indicating infinite climate sensitivity). Since we exist, we know for sure that Earth does not ever “run away”, and at no time in the last multiple billions of years has Earth had infinite climate sensitivity.
“Just to be clear, it’s your position then that GHGs don’t trap heat energy?”
Carrick, yes that’s the Null Hypothesis, which hasn’t been rejected IMO. The so-called GHGs (and clouds) radiate more than 90% of the Earth’s cooling power to space (in average). That’s the consensus estimate.
http://asd-www.larc.nasa.gov/erbe/components2.gif
Edim,
Carrick is a physicist and a practicing scientist (focuses on sound related studies, I believe), with lot of years experience. You make yourself an excellent foil.
SteveF, so what? I know enough of physics (thermodynamics, fluid dynamics, heat transfer…) to have an opinion and if I’m wrong, so be it. Saying GHGs must warm is not science.
Gang, the “trap heat” is a bit debatable. Interact is a term I like. Oddly, we know more about the interactions of CO2 with radiant energy than just about anything else. So CO2 forcing makes a great baseline. We are not all that sure how well GHGs play with others, but they play with themselves nicely.
Now if someone would like to explain why 184K 65Wm-2 seems to be a solar system standard for CO2, I am all ears.
Edim, you’re allowed your opinions, but it would be useful for you, if you were to delve a bit more into the philosophical underpinning of science, how scientific knowledge is established and how it advances. Having some knowledge of the mechanics of thermodynamics, fluid dynamics, etc isn’t the same thing as understanding this other.
The gap between where you are and others on this blog relates to our real world experience in going from hypothesis testing to (for many of us) development of practice techniques or even sensors (SteveF and myself at least).
It would help in your discussions if you separated the concept of radiative physics (which is well established), atomic physics as it relates to the interactions of molecules with photons, and the much more complex problem of how a climate system reacts to a change in the concentration of atmospheric CO2.
dallas, “trapping of heat” is an accepted rubric to describe a much more complex physical process, sort of like the inaptly named “greenhouse gas effect”.
Carrick (Comment #110379)
February 20th, 2013 at 9:03 am
If you just went a bit back further in time than is afforded by satellite data (in this case I looked at HADAT2), you see this instead:
figure, namely a continued cooling trend with complex volcanic responses overlaid on it.
————–
HadAT2 at 50 hPa has a positive trend from 1995-2012 (once the impact of Pinatubo fully wore off). 18 years now.
http://www.metoffice.gov.uk/hadobs/hadat/hadat2/hadat2_monthly_global_mean.txt
Carrick, and both tend to raise hackles. Personally, I like “Greenhouse Effect” because if you consider everything in the greenhouse, you have a system. Since the main point of a greenhouse is to prevent freezing, some extra thermal inertia is a good thing 🙂
Edim,
“Saying GHGs must warm is not science.”
.
No, but measuring how GHG’s absorb and radiate in all directions at certain infrared frequencies is. And that does mean that they inhibit the radiant flow of heat from Earth to space at those frequencies (and yes, that inhibition takes the form of ‘back-radiation’). When you say that GHG’s don’t cause warming, you are either refuting a wealth of data on the radiative properties of GHG’s, and/or refuting the validity of radiative physics as a whole. Either position is simply mistaken.
dallas (Comment #110382)
I thought the paper was a dissertation and not a peer reviewed publication. I like dissertations because the authors’ feel obliged to explain what they are doing in great and sometimes very easy to understand detail.
My point was the author talks about a successful prediction in the future or least that is how I read it. It also sounds like the author did a lot of fitting of a statistical model to past data and that is why I had an interest in how cross validation was performed.
Kenneth, I did too, but he references a previous publication where he was the lead author.
The statistics is over my head, but he used several data sets and “training” periods then hindcasts on the other sets and/or sections. It looks like he also predicted the 2011/12 winter previously and included the results in the paper. His prediction missed on intensity a bit, no vortex breakdown that winter, but was fairly close it seems. I wonder how he did for this winter since it had a major?
jim2 – the Paltridge paper used the NCEP reanalysis data which wasnt “fit for purpose” in terms of analyzing trends. The paper essentially exposes artifacts in the reanalysis not present in better products. See Dessler and Davie 2010 for more detail.
Edim -your diagram doesnt contradict GHG theory. If you have science background, http://scienceofdoom.com steps through the textbook description of the theory. You cant realistically have a discussion about the correctness of the theory without understanding it first. By all means show evidence that contradicts the textbook, but read it first so you know whether or not what have really is a contradiction.
Edim et al.,
The infrared spectrum of outgoing longwave ratiation at TOA clearly shows a net effective attenuation of the OLR from the surface in the wavelength regions affected by CO2, H2O, CH4, O3, and N2O (http://www.giss.nasa.gov/research/briefs/schmidt_05/curve_s.gif). The CO2 “ditch” is quite large, and that ditch, while saturated at the center, broadens on the wings as atmospheric CO2 levels increase.
A little time with the MODTRAN calculator (http://geoflop.uchicago.edu/forecast/docs/Projects/modtran.orig.html) will demonstrate that increasing CO2 levels, with other factors held constant, results in a further attenuation in the total calculated W/m^2 due to OLR.
@Comment #110398
Thanks. Too bad so many papers are paywalled.
@Comment #110398
Thanks. Too bad so many papers are paywalled.
Owen, yes the ditch is wide. While Edim my doubt CO2 has any impact, there are other that think the impact is over estimated.
I am in the over estimated by a factor of two group.
https://lh3.googleusercontent.com/-Cvi3eAiAy9s/UQK2Z6ZB2AI/AAAAAAAAG4Y/fDcj_U6Oy4g/s705/1500%2520versus%2520375%2520tropics%2520and%2520subarctic.png
I did that a while back, that compares the tropics to sub-arctic winter as I take a little journey up through the atmosphere. OMG, there is a tropical troposphere hot spot at about 6000 meters, just above the average cloud base. The sub-arctic has a warm spot but a little lower. It is almost like there is non-linear relationship.
Now I have heard that the CO2 ditch will spread and block some of the atmospheric window radiation. Most of that “window” would be in the H2O spectrum and I do believe that cloud bases are mainly H2O.
Not being a card carrying physicist, I would believe that atmospheric water vapor in close proximity to an increase in radiant forcing could behave somewhat like an antennae ground plane redirecting isotropic energy causing it to behave more anistoprically. I don’t think that bodes well for getting the maximum efficiency out to the CO2 radiant impact.
Then what do I know, I would never use average energy for a sinusoidal input to a system with energy storage capacity. That would be more an RMS kinda thing. (Note: not standard deviation unless you consider the energy offset or floating neutral .)
http://geotest.tamu.edu/userfiles/216/Dessler10.pdf for non-paywalled version. Here is tip for getting paper.
Go to scholar.google.com and search with the paper title. If there is an alternative source, it shows up on the right. Scholar is also very handy for finding follow-up papers – check the Cites.
Phil Scadden (Comment #110404)
February 20th, 2013 at 4:00 pm
http://geotest.tamu.edu/userfiles/216/Dessler10.pdf
for non-paywalled version. Here is tip for getting paper.
——————
And then Dessler reverses himself in this new paper and says the reanalysis datasets were right after all.
http://geotest.tamu.edu/userfiles/216/dessler2013.pdf
BIll Illis:
You can see that in the residual that I plotted. But here’s what James had to say on this:
So, while it’s interesting, it’s not a novel result.
I think I can explain why this is asymmetric (it has to do with stable versus unstable vertical temperature profiles). A topic I didn’t raise on James’ blog is whether climate models “get this asymmetric response to +/- forcings right” or not.
Of course any system that has an asymmetric response in this sense will exhibit hysteresis. That’s a bit OT here.
SteveF,
Be of good cheer. Your major points come across well. I’m poorly equipped to evaluate many of the mathematicalogically complexificacious refutations — like many other lurking readers, I suspect. Alas.
Notwithstanding that: when an argument suggests that RTEs are in error, or that the Earth’s climate sensitivity is subject to positive feedback upon incremental rises in temperature [# 110386] — I (we) know enough to recognize such arguments and discount them.
The remaining informed commenters are raising some good points, and providing grist for some interesting exchanges.
Sorry Bill, I am not seeing that all. The earlier paper rejected old NCEP reanalysis used by Paltridge (as had other before him but with less analysis) in favour of the new reanalysis products which are also used in the new paper. I cant see any mention of the NCEP/NCAR reanalysis in the new paper from a very quick pass over it. Can you point me more specifically to what you are reading?
SteveF writes “it is if you accept that adding GHG’s must warm the surface relative to not adding GHG’s.”
The question of “how much” is paramount and IMO hinges on energy uptake of the oceans. Without it CO2’s influence has no real teeth.
So over land, yes the fundamental physics behind AGW is straightforward but over water it is not. The competing basic fundamental physical realities of increased DLR causing the ocean to cool slower (ie warm) vs increased DLR causing increased evaporation making the ocean cool faster is not a fundamental “warming” result.
TTTM,
“The competing basic fundamental physical realities of increased DLR causing the ocean to cool slower (ie warm) vs increased DLR causing increased evaporation making the ocean cool faster is not a fundamental “warming†result.”
.
Hummm… what causes increased evaporation is a warmer surface. The ocean is different from land in that the ocean has unlimited water available for evaporation and high heat capacity, while the land has relatively low heat capacity and (usually) limited water. But increases in ocean surface temperature will cause increased evaporation… if there is no increase in temperature (all else being equal) evaporation will not increase. The is nothing special about downwelling long wave radiation from GHG’s that leads to increased evaporation, except to the extent it increases ocean surface temperature.
SteveF writes “But increases in ocean surface temperature will cause increased evaporation… if there is no increase in temperature (all else being equal) evaporation will not increase.”
DLR is absorbed into the to 10um of the ocean’s cool skinned surface. Energy supplied by the DLR cannot move down into the ocean due to that cool skin and so it has two choices.
It can either radiate back upwards at the same rate it arrives (this is the heart of the reduced cooling effect) or it can be used in the evaporation process. This is a direct use of the energy in that top 10um and doesn’t involve warming of the ocean (all else being equal)
TimTheToolMan (Comment #110412)
Sure it can, if the water in the cool skin gets mixed around. And even without physical mixing, the water is touching the water right underneath it; a warmer skin layer will receive less (net) heat by diffusion from the water below than a cooler layer.
Tim has discussed this in excruciating detail of at http://scienceofdoom.com/2010/12/05/does-back-radiation-heat-the-ocean-part-three/
Unless there is something new to say, I’d say not worth repeating here.
Oliver writes “Sure it can, if the water in the cool skin gets mixed around. And even without physical mixing”
Te very top of the ocean is the coolest place. Mix it down into the water immediately below it and it is cooling that water.
He then writes “the water is touching the water right underneath it; a warmer skin layer will receive less (net) heat by diffusion from the water below than a cooler layer.”
Net energy movement is upwards. You are describing the “less cooling” effect I mentioned.
Re: TimTheToolMan (Comment #110415)
If I understand correctly, you said that energy supplied by DLR cannot make it down into the ocean, and also that none of the processes described involve warming of the ocean.
In fact, if you exchange heat between the skin layer and the ocean below, there is no separation between the part of the energy supplied by DLR and any other part, so some of that heat does make it into the ocean. Furthermore, the net result of a warmer skin layer can indeed be heating of the ocean below the skin layer (obviously, the part of the ocean which is the skin layer is already warmer).
You may of course claim that all this still means “less cooling, not warming,” but what is the point of making this distinction?
P.S.: The assertion that net heat transport in the ocean is upward is also not correct.
Oliver writes “It is also incorrect that net energy movement in the ocean is upwards.”
Net energy from the processes we’re describing.
Obviously the visible sunlight that does penetrate the ocean warms it at depth and one could say that was “downwards” but I personally wouldn’t. Considering net energy flow is IMO important. You say that the ocean warms by the DLR moving into the ocean against the net flow of energy in the skin that is leaving. I say it results in less cooling.
The important point that I think we both agree on is that net flow is upwards for that energy as the ocean cools.
Anyway all that is beside the point that DLR energy is absorbed where the evaporation is happening and must (all things being equal) enhance the evaporation without an increase in overall temperature.
Brandon Shollenberger (Comment #110361): “Imagine what would happen if you did a linear regression over one cycle [of a sine wave]. Now imagine if you did it over three. Or ten. In each case, you should come back with no trend.”
A small correction — even taking a linear regression over a full cycle will *not* (necessarily) produce a zero trend. It depends on the phase at which you start. See, for example, this. The OLS trend can be as high as about 30% of the peak slope of the sinusoid (for a one-cycle calculation). Less, of course, as one includes more and more full cycles.
Phil writes “Unless there is something new to say, I’d say not worth repeating here.”
Yes. Except of course that the actual physical property of DLR being absorbed where evaporation is occurring will (all things being equal) directly increase evaporation all by itself without increase in ocean temperature and that is an important effect to be considering when looking at the net effect of increasing DLR over the ocean.
HaroldW, good point. I don’t know why I didn’t think about that. I’ve even talked about that exact effect before.
Oh well. At least it means OLS is worse at doing what SteveF used it for, not better. If you have to make an error, it’s better for the error to strengthen your point, not weaken it.
HaroldW:
Even that result depends on whether you fit to just a linear trend, or linear trend + a sine wave. 😉
Carrick, yes, but we were discussing what SteveF did, not what Tamino did 😉
Tim – covered in Part 2.
Which Part 2 Phil? SoD has many categories…
Nevermind I guess you mean part two in the series you posted earlier. I agree that increased DLR slows the rate of cooling. I dont necessarily agree that SoD has the exact process right but that is another conversation and not overly important for this conversation.
The thing is that in addition to that, increased DLR must increase evaporation. It is a fundamental result.
Take away the fact that its DLR supplying the energy and consider whether adding energy into the top 10um of the ocean will increase evaporation and the answer is most certainly yes irrespective of any consideration of where the energy came from.
Bringing DLR back into the equation means that there are two competing effects. One of slowed cooling (warming) and one of increased cooling from evaporation and so it is absolutely not a given from simple arguments of basic physics that DLR overall warms the ocean.
SteveF says: “With respect to climate models: I have said nothing good about climate models, so I am not sure why you focus on them in several of your comments, including the above.â€
This may be the first post of yours that I’ve read, and I did not understand your opinion of climate models. But you’re still avoiding my comment, so I’ll rephrase my requests later.
SteveF says: “Nonsense. The graphic in my post shows the temperature pattern associated with each phase.â€
You still can’t grasp reality, SteveF. The spatial pattern does not represent the temperature. The following is a graph of the sea surface temperature anomalies of the North Pacific, north of 20N, versus the PDO. They are not the same. And if you look closely enough, you can see they’re inversely related.
http://i51.tinypic.com/rr39d5.jpg
Again, SteveF, there’s no mechanism through which the PDO can vary global surface temperatures. You need to look at the sea surface temperature anomalies there, not the PDO.
SteveF says: “I later posted a reference showing variation in the flow volume of Kuroshio current which appear to explain that pattern, and which are strongly correlated with the PDO index…â€
Yes, you did. But you still fail to comprehend that the PDO is inversely related to the sea surface temperature anomalies of the North Pacific. Here’s a link to the KNMI Climate Explorer.
http://climexp.knmi.nl/selectfield_obs.cgi?someone@somewhere
Plot the sea surface temperature anomalies there. You’ll discover I’m right. The region that dominates the variations in the sea surface temperatures of the North Pacific is the Kuroshio-Oyashio Extension (the area east of Japan in the maps you provided). You’ll discover that the sea surface temperature anomalies there are also inversely related to the PDO.
SteveF says: “No evidence? Assuming for a moment that it is possible to “explain†through a long series of cure-fitting exercises all that ocean warming to ENSO rather than GHG forcing, that by no means proves the explanation is correct, especially if that explanation simultaneously requires one accept that increased infrared radiation on the surface of the ocean causes an increase in evaporation but does not increase temperature… which is pure pseudo-scientific nonsense… in fact, bizarre.â€
That’s right, SteveF. No evidence. You’ve avoided this so far, so I’ll repeat it once again, but I’ll eliminate the reference to climate models. If you believe that the increase in manmade greenhouse gases emissions have somehow, magically, contributed to the warming of the global oceans, please then explain why:
1, The sea surface temperatures of the East Pacific Ocean (90S-90N, 180-80W))—that represent 33% of the surface area of the global oceans—have not warmed in 31 years:
http://i47.tinypic.com/hv8lcx.jpg
2, Please explain why the sea surface temperatures of the Atlantic, Indian and West Pacific Oceans (90S-90N, 80W-180, called the Rest of the World in the following graph) only warmed during the strong El Nino events of 1986/87/88, 1997/98 and 2009/10. That is, please provide links to papers that explain why the sea surface temperatures show no warming without those El Nino events:
http://oi45.tinypic.com/2qspjkz.jpg
And if you’re wondering why we’d divide the oceans into those two subsets, all you have to do is examine a map of the warming (or not warming) trends of the global oceans for the Reynolds OI.v2 sea surface temperature dataset:
http://oi48.tinypic.com/2vccorr.jpg
3, (Because the North Atlantic is also impacted by another mode of natural variability called the AMO, it’s logical to examine the sea surface temperatures of the South Atlantic, Indian and West Pacific Oceans as a separate subset.) Please explain why the sea surface temperatures of the South Atlantic, Indian and West Pacific Oceans would have cooled if not for those strong El Nino events of 1986/87/88, 1997/98 and 2009/10:
http://oi47.tinypic.com/24zgfgk.jpg
4, Please explain why the warming of the ocean heat content of the tropical Pacific (0-700 meters) is dependent on La Nina events of 1973/74/75/76 and 1995/96:
http://oi47.tinypic.com/2coogo7.jpg
5, Please explain why the warming of the ocean heat content of the extratropical North Pacific (0-700 meters) is dependent on a 2-year climate shift:
http://oi47.tinypic.com/53mk3d.jpg
6, Further, based on the “the known radiative properties of GHG’sâ€, please explain why the sea surface temperatures of the Pacific Ocean as a whole have not warmed in almost 20 years:
http://oi48.tinypic.com/246qcu0.jpg
Consider this last part of my comment as a reply to your comment #110377.
Bob
“You still can’t grasp reality, SteveF. The spatial pattern does not represent the temperature. The following is a graph of the sea surface temperature anomalies of the North Pacific, north of 20N, versus the PDO. They are not the same.”
This is getting silly. Steve has given a perfectly correct definition of the PDO as the leading principal component of N Pacific SST. As such it is an SST pattern, as shown in the graphic, which comes from the JISAO site. Yes, it is not the observed N Pacific SST. No-one said it was. It is a principal component, derived from the observed SST.
Hi Carrick: Model? The climate science community is required to create models that explain how and why this planet has warmed, not me. To date, the climate science community has not done so. ENSO portrays itself as a recharge-discharge oscillator in the instrument temperature record.
Recharge:
http://oi47.tinypic.com/2coogo7.jpg
Discharge:
http://oi47.tinypic.com/24zgfgk.jpg
Yet the climate science community cannot create climate models that simulate ENSO, which is they [Foster and Rahmstorf (2011), etc.] portray ENSO as noise. With respect to hand waving, isn’t that all the climate science community has been doing all along with their fatally flawed climate models?
Also, thanks for the note that my work was being discussed over at Annan’s blog. I’ll have to leave a comment there.
Regards
Nick Stokes, “This is getting silly. Steve has given a perfectly correct definition of the PDO as the leading principal component of N Pacific SST. As such it is an SST pattern, as shown in the graphic, which comes from the JISAO site. Yes, it is not the observed N Pacific SST. No-one said it was. It is a principal component, derived from the observed SST.”
The PDO is a “noisy” principal component which can mean that the “noise” or variance is the “signal” not the magnitude. There are two main cycles in the system, slower oceans and faster atmosphere. Ocean warming is much more dependent on the rate of mixing than the skin effect. So Bob and SteveF are talking past each other by considering different cycles in the combined system.
If you detrend and normalize the PDO and AMO you would see they have the same basic underlying trends, just a huge difference in variance.
Nick Stokes says: “This is getting silly. Steve has given a perfectly correct definition of the PDO as the leading principal component of N Pacific SST. As such it is an SST pattern, as shown in the graphic, which comes from the JISAO site. Yes, it is not the observed N Pacific SST. No-one said it was. It is a principal component, derived from the observed SST.â€
Yes it is getting silly and your comment doesn’t help. As I noted a number of times to SteveF, the PDO is inversely related to the sea surface temperature of the North Pacific. Through what mechanism, Nick, would the PDO cause global surface temperatures to warm if, while the PDO is rising, the difference between the North Pacific sea surface temperature anomalies and global sea surface temperatures is declining, meaning the North Pacific is contributing less to global sea surface temperatures?
http://i52.tinypic.com/15oz3eo.jpg
That graph is from the following post, which I linked here in a comment to SteveF a couple of day ago:
http://bobtisdale.wordpress.com/2010/09/14/an-inverse-relationship-between-the-pdo-and-north-pacific-sst-anomaly-residuals/
“You mean radiative physics?”
“…it is if you accept that adding GHG’s must warm the surface relative to not adding GHG’s.”
SteveF, no I mean physics of heat transfer at the Earth’s surface and it seems that evaporation rules (latent heat in water vapor). Heat transfer physics includes radiative heat exchange, of course. Adding GHGs increases emissivity of the atmosphere, do you accept that?
“Edim, you’re allowed your opinions, but it would be useful for you, if you were to delve a bit more into the philosophical underpinning of science, how scientific knowledge is established and how it advances. Having some knowledge of the mechanics of thermodynamics, fluid dynamics, etc isn’t the same thing as understanding this other.”
Carrick, I said enough knowledge and I would add understanding too. Actually, more than enough. Furthermore, you emphasize radiative physics and that’s all I hear from the convinced (red herring?). I accept radiative physics. Adding CO2 should increase emissivity of the atmosphere, am I wrong?
“When you say that GHG’s don’t cause warming, you are either refuting a wealth of data on the radiative properties of GHG’s, and/or refuting the validity of radiative physics as a whole. Either position is simply mistaken.”
SteveF, again I accept radiative properties of GHGs. I claim heat transfer problem at the Earth’s surface needs to be solved properly to calculate the surface temperature. Handwaving radiative physics is not enough.
Owen, what is your graph evidence of, regarding Earth’s surface temperature? Spectral flux at the TOA in the new steady state, after an increase in CO2 will be the same, quantitatively.
Edim,
“Spectral flux at the TOA in the new steady state, after an increase in CO2 will be the same, quantitatively.”
—————————————
Exactly. And to achieve the re-adjusted flux, the surface temperature must increase to increase the intensity of OLR in the “window” regions where greenhouse gases do not absorb.
Edim,
“Adding CO2 should increase emissivity of the atmosphere, am I wrong?”
—————————
It does increase the IR emissivity. CO2 is responsible for a sizeable portion of the OLR emission, but the CO2 emission occurs at the tropopause at ~255 K and is considerably reduced in intensity from the blackbody emission (in the region of the CO2 transitions) from the earth’s surface at ~288K. The net effect of increasing CO2 is, therefore, increasing attenuation of OLR and concomitant warming of the earth’s surface.
Bob:
Actually it’s your responsibility to demonstrate that any argument you make is physically plausible. That means you do need an analytic model, otherwise you are just hand waving. Analytic model≠climate model. A two box model is an example of an analytic model.
AFAICT “wiggleology” is an impossible word – as wiggle is germanic in origin, and -ology is greek.
In fact, there are no known -ologies that start with a ‘w’
http://users.tinyonline.co.uk/gswithenbank/ologies.htm
I beleive that a valid term from the greek might be more like strifoyÏrismology.
Much more understandable, I’m sure you’ll agree.
Edim, the fact radiative physics is well established is not a red herring.
If you accept that CO2 increases the ability of the atmosphere to trap heat energy, then you know, all other things being equal, that increasing CO2 will increase atmospheric temperature.
Think again about your comment:
Did you misstate?
steveta_uk, the US didn’t spend more of its GDP than most countries produce becoming the dominant warlord on this planet to quibble over which words we can combine and which we can’t.
That said, I do like strifoyÏrismology. It’s much clearer, as well as being nearly unpronounceable, both of which are attractive qualities for scientific lingo.
Anyway, you know what they say, “You get an ology, you’re a scientist.”
Owen, again overemphasis on the radiative part of the Earth’s surface heat transfer. I don’t see the graph as evidence of “adding GHGs must warm”. By the way, what do you think of this paper?
http://onlinelibrary.wiley.com/doi/10.1029/2012JD018551/pdf
30 ppm increase in atmospheric CO2 (1996 – 2011) and the net-LW (up of course) increased 2.3 W/m2! Where’s the beef?
Carrick says: “As it is, I think you are seeing the equivalence of patterns in random clouds.â€
In addition to presenting cloud amount data, the response of which to ENSO has been studied and documented, I’ve also presented the only paper that discusses where the warm water for the 1997/98 El Niño came from. It’s McPhaden 1999:
http://lightning.sbs.ohio-state.edu/geo622/paper_enso_McPhaden1999.pdf
McPhaden writes:
“For at least a year before the onset of the 1997–98 El Niño, there was a buildup of heat content in the western equatorial Pacific due to stronger than normal trade winds associated with a weak La Niña in 1995–96.â€
The trade winds reduced cloud cover over the western equatorial Pacific, which decreased downward longwave (infrared) radiation and increased downward shortwave radiation (sunlight)…
http://i45.tinypic.com/35jjeic.jpg
…which created in turn, as McPhaden wrote, “a buildup of heat content in the western equatorial Pacific.â€
Now if you’d like to factor in the impact of manmade greenhouse gases, according to the NOAA Annual Greenhouse Gas Index…
http://www.esrl.noaa.gov/gmd/aggi/
…the downward longwave radiation from manmade greenhouse gases increased from 1.064 to 1.089 watts/m^2 from 1995 to 1997, or a whopping total of 0.025 watts/m^2. Compare that to the increase of 22watts/m^2 in DSR—but don’t forget DLR only impacts the top few mm, while DSR is also called penetrating radiation. We’re talking many orders of magnitude difference. Or as I’ve written numerous times, there’s no evidence that manmade greenhouse gases had any effect on the warming of the oceans.
Thanks for the reminder, Carrick. I’ve never gotten around to posting that comparison of western equatorial Pacific DSR and DLR flux.
Regards
Carrick, I think CO2 (if anything) decreases the ability of the atmosphere to trap energy, by radiating the gained atmospheric energy to space. The bulk of the atmosphere increases the ability – it receives the energy easily from the surface (non-radiatively), but cannot radiate efficiently to space.
Edim:
Then you are completely wrong-headed on this. Perhaps your grasp of the basic theory isn’t quite as good as you had thought.
Seriously you really think this has been missed?
Bob, thanks for the comments, but I’m going to have to bow out of this. Sometimes the languages we speak are enough different that communication is difficult. I would try, but I’m never sure whether you actually understand anything I say, and in any case, I’m slammed right now at work.
For steveta_uk, slammed. Now you know. â„¢
Carrick, yes I’m serious. What is your opinion of the paper?
http://onlinelibrary.wiley.com/doi/10.1029/2012JD018551/pdf
Nick Stokes (Comment #110367)
Nick, I’m not sold on the legitimacy of the Quenouille correction
[N = n * (1-r)/(1+r), where N is effective sample size, n is observed size and r is the lag-1 ac coefficient]. It seems biased far high to me, when I compare it’s results to simple frequencies from repeated, simulated red noise series with known AR(1) coefficients. It leaves far too many spuriously significant results.
Re: Edim (Feb 21 08:55),
You have a perfect right to hold and defend an incorrect opinion, but it is just an opinion based on a very limited understanding of the physics involved and is incorrect. It is possible to calculate to high precision the outgoing atmospheric emission spectrum at the TOA. Increasing CO2 decreases emission because the increased emissivity of CO2 replaces the emission from water vapor at lower altitude where it’s warmer. That’s because the ‘ditch’ gets wider. Here’s the MODTRAN calculated clear sky difference spectrum for 750 ppmv -375 ppmv CO2 using the sub-arctic winter atmosphere model (it’s what I had lying around). Note that the majority of the difference is negative. There is a small increase in emission from the stratosphere where increasing CO2 does increase emission because the stratosphere temperature increases with altitude. But the net is a reduction in total emission of 1.6 W/m². CO2 forcing is lowest at high latitude in the winter because the temperature difference between the surface and the tropopause is the smallest for the different seasons and latitudes. That increase in emission in the center of the CO2 band would go away rapidly because the stratosphere would cool rapidly.
Bob Tisdale,
” there’s no mechanism through which the PDO can vary global surface temperatures.”
.
Sure there is. The state of the PDO index is closely associated with substantial (3-5 Sv) variation in the flow of the Pacific western boundary current (Kuroshio). Which means the amount of heat transported northward varies quite a lot with the state of the PDO (by up to ~0.63 watt per square meter, averaged over the entire Earth). Changes of that size in northward heat transport seem to me sufficient to make globally significant changes in things like overall rate of loss of heat to space and rate of ocean heat accumulation.
.
“If you believe that the increase in manmade greenhouse gases emissions have somehow, magically, contributed to the warming of the global oceans..”
‘magically’ is a very strange word choice. There is nothing magical about an increase in GHG’s causing warming, since adding GHG’s restricts the escape of heat from Earths surfaces, including the oceans. The fact that certain areas of the ocean have warmed more than others tells us little except that ocean warming, and rates of heat accumulation, are complicated in geographical distribution by ocean surface currents and pseudo cyclical atmosphere-ocean patterns like the ENSO, PDO, and others. There are, no doubt, very reasonable explanations for the observed warming patterns (or regional lack of warming) that you note. Those reasonable explanations do not include the conclusion that GHG driven warming is ‘magical’. It is this mistaken mindset which leads to the weeds my friend.
Folks
There is a strong correlation between global mean surface temperature and CO2 concentration in the atmosphere:
http://www.woodfortrees.org/plot/hadcrut3vgl/mean:732/from:1958/normalise:12/plot/esrl-co2/compress:12/to:1983/normalise
i.e: It is the warming that is increasing the CO2 concentration!
Re: Edim (Feb 21 09:27),
It’s inconclusive because, as the authors point out, the surface energy balance isn’t closed. The contribution from vertical and horizontal air movement, convection and advection, is unknown. In short, the variability is mostly weather, not climate.
Edim,
Thanks; best laugh I had in some time…. although I did nearly snarf my coffee.
SteveF
And Foster and Rahmstorf will have to do more rebaselining. 🙂
I guess my swag is a bit higher, but then… there is the “WAG” in SWAG.
Jim Bouldin
“..far too many”? How much is “far”? 6% false positives when you intend to get 5%? Or 25%?
In Nick’s comment he’s just noting that he made the correction. Some people forget to consider the issue at all and report results using white noise.
The Quenouille correction does result in too many false positives However, the error appears to depend on ‘n’ and ‘AR(1)’– the exact same variables that matter in the first place. The problem is fixable by devising an iterative scheme. Certainly, if you are going to criticize Quenouilli, it’s worth running the cases at the value of (n,r) for Nick’s data and say whether in his case, the false positives are 5.000001% vs. say 50.0%. The former would be “too many” if the target rejections rate was 5% but few would call it “far too many”. The latter would certainly be “far too many”. In either case, you could just super-correct the Quenouilli correction to see if you still reject.
The larger difficulty is if you don’t have enough data (n) for the Quenouilli correction to give close to the correct false positive rate (say <10% when you intend to get 5%), you won't have enough data to truly say put to rest any arguments the residuals might be something other than 'red'. In reality, the assumption that the residuals are 'red' rather than something else could result in either over or under estimating the uncertainty intervals. The fact that the assumption of "red" itself can overwhelm the possible error means that -- at least for quick communications in blog comments-- Nick using Quenouilli and saying that's what he used is going to be pretty standard and mostly fine.
If Nick wanted to do so, he could add the "Lee and Lund" correction Tamino advocated way back when before he decided to go for ARIMA and then start doing multiple regressions and so on..... (Lee and Lund also doesn't quite work for AR1. It can result in either too few false positives depending on the values of n and AR(1).)
Jim #110447,
I’ve mentioned a study I did of AR(n) model regression, where I iteratively get the coefficients right. Near the bottom I checked the Quenouille approx for a specific case (Jones temp since 1995), and it did pretty well. Ar(1) itself is usually a model that fits only approximately, so one can overdo the search for a best CI assuming Ar(1).
In that particular app, I needed something that could be calculated with cumulative sums, because each diagram can have half a million regressions. It would take a very long time if I had to do full summations for each point.
Jim Bouldin (#110447), Nick Stokes (#110454) –
Is there any particular reason why you wouldn’t use the known minimal-error solution rather than tweaking the OLS result? See, e.g. Matlab’s lscov function; I’m sure that R has an equivalent.
(1) For the AMO to be a proxy for global temperatures would presuppose there is an efficient mechanism for transferring heat from the atmosphere to the sea surface. There is no such mechanism.
(2) The cumulative PDO vs HADCRUT4 Global charts above are wiggle-matching, pure and simple. Any correlation is illusory.
Bob Tisdale has this right, as usual.
lucia (Comment #110453)
Lucia, my Monte Carlo estimates of CIs and comparing those results with the Lee and Lund method and that due to Quenouille are in line with your observations here.
The link to the Lee and Lund paper is here:
http://biomet.oxfordjournals.org/content/91/1/240.full.pdf+html
Jaechoul Lee’s dissertation is linked here and includes nearly all that was in the Lee Lund paper:
http://athenaeum.libs.uga.edu/bitstream/handle/10724/6927/lee_jaechoul_200308_phd.pdf?sequence=1
I have since seen a number of papers authored by Lee and Lund that deal with statistical methods as applied to climate science.
Lucia,
I get the following results from 5000 runs of AR1 processes, each of length n = 133, with the following lag-1 coefficients, *after* making the Quenouille correction. I used pf(f, model df, residual df) in R, with all three params obtained from the standard lm function and the residual df being corrected for by Quenouille’s method. n = 133 was chosen because it represents the common instrumental record period for the major instrumental temp records:
AR1 coeff. False pos. %
0.25 16.8
0.50 26.6
0.75 47.0
0.90 62.6
0.99 71.5
1.00 67.8
This is what I mean by “far too many”.
Re: jorgekafkazar (Comment #110456)
I believe you have this backward. SST has a huge influence on atmospheric temperatures. There are a set of well-known mechanisms for transferring heat from the sea surface to the atmosphere, and they are the main ways the atmosphere gets heated in the first place.
HaroldW (Comment #110455)
“Is there any particular reason why you wouldn’t use the known minimal-error solution rather than tweaking the OLS result?”
In my case, yes. I had to do several million of them. You can do this efficiently by using accumulated sums. I also had to have something that I could program in Javascript.
Jim
Thanks for the specifics.
Seeing your numbers: I don’t know how meaningful that is when applied to figuring out whether Quenouille uncertainty intervals computed over that period will be too large or too small. If 133 is supposed to be years, I doubt the true lag1 correlation coefficient for the *random* component of temperature is anything as high as 0.25. It’s certainly not 0.99. To diagnose the true false positive rate you need to use a realistic magnitude for the lag1 autocorrelation for the fluctuations. I would be surprised if it’s higher than… oh… 0.15. (I might be surprised to learn it’s larger than 0.10. But there is no way to say for sure– as will become apparent below.)
That said:
1) If you believe AGW, you simply can’t estimate the lag-1 autocorrelation by examining the residuals to a linear fit because you wouldn’t believe the deterministic trend is linear over 133 years. You would believe the *deterministic* trend was more or less trendless pre-1920 and then began to have some non-linear shapeliness. (Some rise due to GHG’s, drops due to aerosols, rise due to GHG’s and so on). The existence of a deterministic deviation from the linear fit means the residuals to a linear trend will have higher lag-1 autocorrelations and higher power than what you would compute if you could do the analysis properly. Doing it properly which requires subtracting the true deterministic signal (which you don’t know) to get the actual “noise” part. Since you don’t know the true form of the deterministic signal, arguments would ensue. ( You might propose to subtract a multi-model mean from models as a consensus estimate of the deterministic trend. Note it’s not linear.)
2) If you don’t believe in AGW but wish to test for the significance of a linear trend, you should look at the correlogram for the residuals from the linear trend. You will see that under the assumption that the residuals from linear are ‘noise’, you will find the noise isn’t “red”.
Both these problems are bigger issues than the false positive rate using Quenouille with a lag-1 correlation coefficient that realistically describes the magnitude of the autocorrelation in the “noise” (i.e. random or ‘not deterministic’) part of the temperature variations. I think this especially because I don’t think the autocorrelation coefficient for surface temperature from year to year for *actual weather noise* is as high as 0.25.
Problem (1) will have the opposite effect of the error in the Quenouille method; it will result in computed uncertainty intervals at are “too large” in the practical sense that you would wish to detect that the rise in temperature is real and you will tend to get too few false positive findings. The reason for this is your estimate of “r” will be too large relative to the real value. (You can test this out by doing the same synthetic experiments with the temperature following T=0 + a* t_i^2 + v_i where v_i is your red noise. Do t_i = 1 through 133. But make a mistake and fit to T= mt_i. Then look at what happens to your estimate of the AR1 coefficient. It will increase above the ‘correct’ value you used to generate the noise. If you examine the rms of the residuals, you’ll see those also increase above the value that corresponds to “noise” you used to drive the random component.
Problem(2) means you would need to try to find the best possible fit for the noise. It’s not going to be AR(1).
For what it’s worth: If you fit to ARIMA with a small number of data points, and test the false positive rate, it’s still going to be too high!
Jorge kafkazar,
Illusory. Right. Check in a decade and see if the correlation continues to hold.
Re: jorgekafkazar (Feb 21 13:40),
Umm, those statements are mutually exclusive. Bob Tisdale says ENSO drivcs the climate. ENSO is all about sea surface temperature creating changes in air temperature.
Harold,
The reason for me is sort of the standard reason for everything one does in R: if what you want to do is not implemented straightforwardly in some basic function you are familar with, you are faced with slogging through the (often many) packages/functions to try to find something that does AND which you can understand exactly how it functions. Typically, *very* time consuming and frustrating. I’m doing it right now for ac correction. There are some, but they are scattered hither and yon in various packages.
Lucia,
Thanks for the thoughts., will reply later. Mainly, I was just making a general observation on Quenouille’s method.
Jim Bouldin–
As a general observation, it’s correct. The false positive rate under the assumption the residuals are red is too high. I’m just putting it in context. If you are curious, repeat the same analysis but find the false positive fitting synthetic red noise using AR(1) in R. You’ll still get a high false positive rate. So the problem isn’t “Quenouille” specific.
Some algebraic corrections for the Quenouille method exist, but if you test them, they don’t “really” work in the sense that no simple method gets you the exactly right false positive rate– or at least not if applied to a linear fit. Either the false positive rate is too high or too low depending on the fix. I find that you can rig up an iterative method that “works”, but these aren’t “quick and dirty” like the Quenouille’s method.
Lucia (#110468) –
I understood from Hu McCullough’s post on CA that there was an exact expression for the standard error of the trend estimate in the presence of AR(1) noise. Is it just that you don’t consider this a “simple method” that you find there’s no accurate method of getting the correct false positive rate? Or is it due to the inaccuracy of the estimate of rho?
Edim (Comment #110441)
February 21st, 2013 at 8:49 am
“By the way, what do you think of this paper?
http://onlinelibrary.wiley.com…..018551/pdf
30 ppm increase in atmospheric CO2 (1996 – 2011) and the net-LW (up of course) increased 2.3 W/m2! Where’s the beef?”
————————-
Thanks for the reference – a very interesting paper even though it is localized to US only. Especially interesting are the SW-down findings.
From your comment above, you may have misread the paper, from which I quote below:
“INCREASING downwelling longwave (LWâ€down) of +1.5 Wm−2 per decade and DECREASING upwelling LW (LWâ€up) of−0.9 Wm−2 per decade produce a +2.3 Wm−2 per decade increase in surface netâ€LW, which dwarfs the expected contribution to LWâ€down from the 30 ppm increase of CO2 during the analysis period.” CAPS are mine.
HaroldW,
Hu gave a standard error which assumed ρ known – ie did not allow for uncertainty in it. He then went on to discuss how estimators for ρ were biased etc, and said he was working on a method that would allow for that. I haven’t seen that yet.
That’s what I was working on here. The uncertainty if you’re estimating both β and ρ. You can’t write down an explicit expression any more, because it requires solving a multivariable quadratic. But that’s easy enough numerically. There’s R code.
HaroldW
There is. And it works perfectly if you know the magnitude of the AR(1) coefficient based on something other than the data itself. But, as a practical matter, you generally don’t know it. Instead you estimate it based on the data. When you do that, biases ensue.
Yes. Specifically the bias in the estimate.
You can rig up methods that iterate and then get the correct false positive rate. Ideally, you concoct the method before looking at the data you are going to analyze. 🙂
@Owen (Comment #110470)
I don’t understand why the downwelling +1.5 Wm-2 per decade does not suffice for the entire number for the surface. The fact that there is less upwelling doesn’t matter for the surface.
SteveF says: “Sure there is. The state of the PDO index is closely associated with substantial (3-5 Sv) variation in the flow of the Pacific western boundary current (Kuroshio).â€
Then you should be able to plot the resulting variations in the sea surface temperature anomalies of the North Pacific. Please show us. And then compare those results to the PDO, which you say causes those variations.
SteveF says: “‘magically’ is a very strange word choice. There is nothing magical about an increase in GHG’s causing warming, since adding GHG’s restricts the escape of heat from Earths surfaces, including the oceans.â€
Once again, you have not provided an explanation for each of items I presented to you. One would have to assume the reason you’re avoiding it is because you cannot. I’ll continue to stand by my earlier statement that there is no evidence that greenhouse gases have had any impact on the warming of global sea surface temperatures during the satellite era and there’s no evidence that it had any role in the warming of ocean heat content.
DeWitt Payne: “Umm, those statements are mutually exclusive. Bob Tisdale says ENSO drivcs the climate. ENSO is all about sea surface temperature creating changes in air temperature.â€
You’re going to have to study ENSO a little more, DeWitt. ENSO presents itself as a recharge-discharge oscillator in the instrument temperature record. As I wrote above, in the recharge mode (La Niña), ENSO replenishes the heat released by El Niños and creates the warm water for the El Niño(s) that follow. The two periods highlighted in red are the 1973/74/75/76 and 1995/96 La Ninas:
http://oi47.tinypic.com/2coogo7.jpg
In the discharge mode (El Niño), ENSO releases heat to the atmosphere primarily through evaporation and redistributes warm water from the tropical Pacific. The 4 periods highlighted in red are the 1982/83 El Nino (and the few months leading to it), and the 1986/87/88, the 1997/98 and the 2009/10 El Nino events:
http://oi47.tinypic.com/24zgfgk.jpg
Regards
Carrick says: “Sometimes the languages we speak are enough different that communication is difficult. I would try, but I’m never sure whether you actually understand anything I say…â€
I understood what you said, but I obviously disagree with you about the role of a skeptic in the global warming debate.
Regards
When water evaporates from the surface of the Earth, it cools the surface. This keeps the surface from getting too hot. But because that water vapor is also the atmosphere’s primary greenhouse gas, water vapor acts to keep the Earth’s surface warmer than it would otherwise be. Which effect is stronger?
Here they say the surface cooling effect of evaporation is stronger – net effect of water vapor is cooling.
http://www.weatherquestions.com/What_is_water_vapor.htm
Edim, “Here they say the surface cooling effect of evaporation is stronger – net effect of water vapor is cooling.”
That is pretty much the argument, but the interaction of all water impacts and all radiant gas impact have to be compared, regional IMO. As long as the water vapor can transport the energy from the surface efficiently, it will likely be a net cooling, but it all depends on the transportation of the energy, vertically and horizontally, where the horizontal was not very well considered.
One thing that is true is that when the PDO is low or negative, it is less likely that there will be strong El Ninos. You only get minor El Ninos or they get cut-off midway through strengthening like last year.
You get more La Ninas and stronger La Ninas and the global temperatures tend to decline.
I would like to see the development of better index than the PDO. The problem is the North Pacific is very big. The north part can be warm while the south part is cold. The eastern side can be cold while the west side is warm. There are dozens of different patterns that can develop.
And there are at least a dozen different major ocean currents moving this warm/cold water around. The Equatorial current, the north Equatorial Counter-current, the Kurushio, the Pacific Gyre, the Alaska, the California, the Equatorial Pacific Under-current, the North Equatorial Under-Counter-current, the Tehuantepec upwelling currents. The list goes on.
I think the ENSO is just more clear and has a big enough impact on its own to cover off the PDO impact.
Lucia (#110472), Nick(#110471) –
OK, I get that Ï [AR(1) correlation coefficient] is unknown in a normal situation. [In Jim Bouldin’s case, he’s working with a synthesized data set, so he actually does know Ï.] So what I think you’re saying is that as one needs to iterate to arrive at unbiased estimates of both Ï and the standard error, then one may as well start with a simpler formula, viz. Quenouille. Is that right?
.
One other question — when you’re running these tests, are you evaluating the spread of the OLS trend estimate, or of the MLE (which depends on Ï)? Or doesn’t it make any difference?
DeWitt Payne (Comment #110448)
February 21st, 2013 at 9:52 am
Modtran
————————
Re-run the numbers with low clouds present. Now it is completely different and clouds dominate the emissions, especially the DLW. And the Arctic is low cloud covered upwards of 65% of the time.
Now how do the clouds change in the Arctic when it gets warmer/colder. Maybe clouds dominate the whole thing.
HaroldW,
The contention in my post was that it’s not hard to iterate to get it right. On the other hand, Quenouille is pretty good too.
One complication with fitting both β and ρ is that you then have a covariance matrix rather than a simple sd for β.
Bob Tisdale:
Actually, the issues I was raising have nothing to do per se with the global warming debate, nor with what role a so-called skeptic is supposed to play in such a debate, but having more to do with the difference between analysis of data and
wiggleologystrifoyÏrismology.If you see yourself as playing a role in a debate, and that exclusively, then what you are doing is very self-limiting.
Cheers, have data to analyze of my own for a report due today.
Nick (#110482) –
Thanks, I reviewed what you wrote and although I’m not fluent in R, managed to get the gist of it. I agree that your function makes it look pretty straightforward to get it right.
What I was trying to say is that using the Quenouille adjustment may give a reasonable approximation to the standard error, but unless one also changes the central estimate from the OLS value (as your function does), the job is only half done.
Bob Tisdale,
The temperature pattern in the North pacific is only one of the potential influences/interactions that I want to look at when I have time to do so, which is unfortunately not right now.
No, except to say I am sure they all have reasonable explanations. Those ‘items’ are even likely in part due to ENSO. But those observations in no way prove that rising GHG forcing does not warm the oceans. You seem to be saying “Look, there are variations in ocean surface temperature, therefore increasing downwelling infrared can’t possibly warm the ocean.” It is a bizarre argument because it is contrary to well known physical behaviors.
Like many who understand little or no science, I am sure you will continue to stand by those statements, independent of whether or not they make any sense. Finally, the ocean can warm or cool, or the ocean’s heat content can increase or decrease, but that heat content can’t be warmed or cooled. (I assumed you understand this, but since you wrote the same odd thing twice, maybe not.)
.
I think Carrick (#110445) had the right idea. This is a waste of both our times. Hasta.
Lacking the chops to appreciate the quantitative (i.e. meaningful) arguments, I offer a short qualitative comment.
In #110483, Carrick remarked on “the difference between analysis of data and
wiggleologystrifoyÏrismology.”This notion is worth keeping in mind regarding the exchanges upthread among Nick Stokes, Jim Bouldin, HaroldW, Lucia, and others, with respect to calculating Quenouille uncertainty intervals and autocorrelation.
In #110462, Lucia notes, “[Properly doing curve-fitting to time-series data] requires subtracting the true deterministic signal (which you don’t know) to get the actual ‘noise’ part.” With a touch of understatement, she continues, “Since you don’t know the true form of the deterministic signal, arguments would ensue.”
Earlier in that paragraph, she offered a specific as to the temperature record, in that “If you believe AGW [sic]”, then “you wouldn’t believe the deterministic trend is linear over 133 years. You would believe the *deterministic* trend was more or less trendless pre-1920 and then began to have some non-linear shapeliness. (Some rise due to GHG’s, drops due to aerosols, rise due to GHG’s and so on.)”
That brings us back around to the topic of the original post — SteveF’s suggestion that there may be a pseudo-cyclical influence of a PDO-correlated phenomenon upon the temperature record, exhibiting a quasi-period of ~25 to ~30 years. See the 2nd graph titled “25 Year Trailing Avg. of PDO Vs. HADCRUT4 Global”.
Assuming this phenomenon is real, its influence will show up as noise when fitting a many-decade temperature record to a linear curve. Or to a curve that is (linear to ~1920), then (linear with added non-linear GHG effects, post-~1920).
Thank goodness for aerosols! 😉
Re: Bill Illis (Feb 22 06:35),
My analysis is at TOA looking down. Cloud cover will lower that emission a few watts but there will still be a CO2 ditch and it will still get wider when CO2 increases. The whole planet has about 60% cloud cover. When CO2 increases, the cloud tops will have to warm too. Warmer cloud tops, warmer cloud bases and warmer surface. That is, to achieve radiative balance, the surface temperature offset still has to be increased.
Re: Bob Tisdale (Feb 22 04:09),
Read Jorge’s comment and see if my reply to him, not to you, is reasonable in that context.
Nick Stokes (Comment #110482)
“The contention in my post was that it’s not hard to iterate to get it right. On the other hand, Quenouille is pretty good too.”
I agree that the old brute force methods are not that difficult or time consuming to perform and thus if we have our doubts about the CIs that derive from the less precise estimates why not do the iterations or Monte Carlo calculations. I think that Grant Foster’s use of the Lee/Lund method gave CIs wider than are obtained by Monte Carlo when estimating CIs for the recent temperature trends, but the method he applied “helped” his conclusion more. Also Foster did not rigorously test the Arima model that he used (1,0,1).
We can discuss endlessly methods of estimating CIs under conditions of auto correlations, but the critical point is how much difference does it make to supporting a published conclusion. It requires sensitivity testing that is sometimes lacking in climate science publications.
Also Lucia brings forth some interesting considerations on handling multiple trends in temperature series and how do you determine or assume that the trends are deterministic and how these considerations can affect the handling of the data. Do you detrend and if so on what basis do you detrend? I would probably favor detrending on a linear segmented basis, but that requires some major assumptions. It is not so much what methods or assumptions are correct but rather to be aware of these conditions and the assumptions that are being made either implicitly or explicitly.
Taking this discussion further into temperature proxies used in reconstructions brings forth an interesting observation that these proxy series are sufficiently long to be fitted with an Arfima model that might show long term persistence and that in some cases this can be done. Does that mean that temperature series have long term persistence and we can use an Arfima model to model those series. I do not think that should be case unless one could independently show that indeed these proxies are responding reasonably and quantitatively well to temperature – and I have not seen this happen.
SteveF I apologize for going this far off topic on your thread, but I get into these esoteric points and cannot help myself.
Kenneth,
So long as you don’t start saying that increasing GHG’s could not possibly cause warming, most any (technical) OT remark is OK with me. 😉
Lucia expressed concern that the numbers on false positives above were not very relevant to real world data. Here are the numbers for values of the AR(1) coefficient <= 0.25. 5000 runs, as before.
Table headings:
1. AR(1) coeff.
2. % exceeding p = .05 without Quenouille correction.
3. % exceeding with the correction.
0.05 .0632 .0630
0.10 .0766 .0764
0.15 .0912 .0902
0.20 .1062 .1052
0.25 .1342 .1314
The third column should all be ~ .05 if the method is accurate. Combined with the first set of numbers presented, there are two possibilities: (1) I am doing something wrong, or (2) the Quenouille correction is essentially worthless.
AMac (Comment #110486),
The correlation is with a trailing average of 25 years, not a cycle with a period of 25 years. In terms of ‘cycles’, if there is in fact a cycle, then it would be more like 60 years.
StreveF (Comment #110490)
StreveF, the physics of GHG warming are well in hand and behind me these days and I think these discussions would do better to deal directly with the analysis details. In this case we are interested in the cyclical nature of global temperature series and a possible source of that phenomena.
I have seen these manipulations of data from temperature series and indexes before that you and Bob Tisdale have shown here and I am concerned about the lack of presenting hypotheses (for matching indexes to temperature series) that could be tested and an understanding of how easy or difficult it is to selectively manipulate the data to obtain the preferred (and untested) match. Whether the index causes, to some extent, the variations in global temperatures or the other way around could be addressed by the time lags – if any exist.
For my purposes and at this time I am not so much interested in what might cause the cyclical nature of long term temperature cycles but rather the amplitude and frequency of those cycles and whether we can show what occurred going back in time. Given the current state of climate models in accomplishing this task, I look to yet-to-be-found long term temperature proxies for informing this relationship. If we can trace the migration of human beings going back tens of thousands of years, I would hope we could find proper historical temperature proxies.
Jim Bouldin (Comment #110491)
A real quick estimate of the Quenouille correction is to multiply the CIs by square root((1+AR1)/1-AR1)). I get something like 1.29 for that factor for AR1=0.25. Your results are in p.values, but I think you are doing something wrong.
It seems that instead of focusing on one regional temperature of the sea or another, the global sea surface average temperature should be considered WRT global atmospheric temperature.
Kenneth, if what you say is correct then some things don’t line up here.
In R, p values from the “lm” linear regression function are based on Fisher’s F statistic. The lm output spits out the f value and the model and residual degrees of freedom. I then correct the residual df value using Quenouille’s method, and re-estimate the p value using function “pf”: pf(f, model df, corrected residual df). The results don’t change much, even with large changes in the residual df. This can easily be seen by running say pf(5,1,133) vs pf(5,1,43). Such a drop in the residual df corresponds to a lag-1 autocorr. coefficient of 0.5, and yet very little change in p results from it (it goes from .027 to .035). The only other place where a change in the actual vs effective sample size can be made is in the denominator of the f statistic itself, and it may well be that that has to be changed also. If that’s the case, you’re now recomputing the test statistic itself, which means R’s standard tools of lm and pf are now worthless and you’re essentially recoding the entire guts of OLS regression to solve this problem!
All of which is a complete nightmare and time sink. Now maybe somebody’s done that and put it in a package somewhere, but my admittedly cursory searches so far haven’t found it. The solution here is simple: just estimate the false positive rate by simulation for different AR(1) coefficients, estimate those same coefficients from whatever data you’re analyzing, and make the necessary corrections. Much more intuitive, much more confidence in the results, and much quicker.
Kenneth, I agree. Relating a regional index to a regional cause/effect then to something more global makes more sense to me.
The only difference between the ENSO index and the PDO index is regional factors and transport delays.
https://lh4.googleusercontent.com/-_AOWFk1GAzA/USfQ0g6WeiI/AAAAAAAAHP0/O7fLsMVOFAE/s912/pdo%2520mei%2520tsi%252011yr%2520sd.png
Roy Spencer has a post regarding sea surface temps and model output.
http://www.drroyspencer.com/2013/02/tropical-ssts-since-1998-latest-climate-models-warm-3x-too-fast/
Lucia (Comment #110462) ,
Here are what I get for the lag-1 autocorrelation coefficients
(rho(1)) for the residuals from an OLS linear regression for each of the four major global mean surface T sets for the periods from 1880 on, and from 1920 on:
1880+ 1920+
NCDC 0.738 0.649
BEST 0.475 0.457
HadCrut 0.651 0.614
GISS 0.721 0.614
The point here is not to argue for the legitimacy or superiority of a linear trend line, but that if such a line is fit, there will be some serious autocorrelation to be accounted for.
For the raw data the values are:
1880+ 1920+
NCDC 0.925 0.888
BEST 0.799 0.723
HadCrut 0.903 0.854
GISS 0.919 0.884
Jim Bouldin (Comment #110496)
To be honest I do not understand your table. I assume you ran 5000 simulations of a series with the AR1 values as you noted in the table. From that you obtain distributions of trends on which you can calculate the probabilities (and CIs). That part I understand if that is what you are doing. You talk about applying the Quenouille correction and that is were I do not follow what you are doing. The Quenouille correction is used to adjust the degrees of freedom for calculating CIs for a trend with AR1. You should end up with different CIs from the Monte Carlo and the Quenouille correction but the Quenouille correction has to make some difference in CIs and in p.values.
I have blamed R for a lot of problems which I later found were mine and mine alone. Sometimes the mistake is a piddling one.
Also the advantage with R is you can readily post the code you used for all to see and look for errors.
Kenneth,
I’m adjusting the p value for each trial, not the confidence interval for all trials. This is done using pf(f, model d.f., residual d.f.), where pf is the probability of observed F, f = Fisher’s F statistic, model d.f. = 1, and the residual d.f. has been adjusted (lowered, from the value returned by the lm function), using the Quenouille method. What I’m not sure about is whether I need to adjust the F statistic itself as well, because it contains a term involving the N (total number of observations) in the denominator. I’m guessing that is the problem here. But doing so involves essentially starting from scratch and building a whole new function that incorporates Quenouille’s method. That ain’t gonna happen; I’ll stick to randomization tests and be quite confident with what they tell me about error rates and any needed corrections.
Jim Bouldin (Comment #110501)
“That ain’t gonna happen; I’ll stick to randomization tests and be quite confident with what they tell me about error rates and any needed corrections.”
I agree that the Monte Carlo is the way to go, but for future reference you should be able to incorporate Quenouille’s method into an R function very easily. I might even do that for my own satisfaction.
Quenouille is a good place to start because it’s well know, somewhat “standard” and give asymptotically correct answers as the number of data in your sample approach infinity. But if someone objects on the grounds that it gives a large false positive rate, I don’t know any simple algebraic tweak that results in a correct false positive rate. However, I do know you can devise an itterative method that
1) starts with Quenouille.
2) iterates to estimate the error in the estimated value of the lag 1 correlation coefficient given the value you observed in your data and
3) creates a method that returns the correct false positive rate.
I don’t know if this is the only possible way– but I don’t know of any non-iterative closed form method that actually works when you fit a linear trend to data.
.
In blog posts when I show red noise, I’ve used Lee and Lund’s correction. I then also test with various arimas and pick a case that gives the widest uncertainty intervals of those tested. This isn’t picked because it’s “best” but to represent an upper bound if people think that the case might be arima. (It is the case that if you run synthetic tests you will find that the ability to correctly detect which “arima(p,0,q)” type function matches the synthetic data you used to generate data is rather imperfect. You can discover that if you generate noise that is ARMA11, and then find the best fit ‘p’ and ‘q’ using the aic coefficient, you will often make mistakes and, the mistakes tend to result in excess false positives. My showing ARIMA(p,0,q) with p or q up to 4 that has the widest uncertainty intervals reduced the false positive rate while making no particular claim that I’ve correctly identified which ARIMA method is “right”. The difficulty is that it is definitely a “weird” method. But I like it for blog posts. )
Jim
I didn’t think you were arguing for a linear trend. What I’m trying to explain is that autocorrelation used in Quenouille is supposed to be the autocorrelation for “the noise”. But your computed values are including deviations from linear that are “the signal”. As such, the autocorrelation you compute will be larger than the true value for “the noise”.
To understand what I’m saying, the appropriate example is to run your synthetic red noise tests but instead of using a linear trend for “the signal” use a quadratic. Then look at what happens to your computed autocorrelations and the the estimated power of “the noise”.
dallas (Comment #110497)
My point here would be that you need to make an hypothesis that can be tested with some metric and then test it. In order to determine how to place CIs on the result we need to know amongst other things how many iterations were made to obtain the relationship being tested.
Even after doing this there is the question of cause and effect which sometimes can be attributed better if there is a lag and then knowing what lags what. After that the you would need to show that the effect applies outside the modern warming period – which gets us back to temperature proxies.
Obviously if we had the basic physics to explain these cyclical effects, or whether there are substantial cyclical effects, we could short cut all of the above – but I would not hold my breath on that pathway.
Jim Bouldin (Comment #110501)
Why would you not run the Monte Carlo on the 5000 simulated series and obtain CIs or p values for the trend on that and then compare those values to what you obtained using the Quenouille adjustment on the series as defined by the trend, AR1 and white noise used in the Monte Carlo?
Jim, (Jim Bouldin (Comment #110491)_)
I really wonder whether you are doing that Quenouille correction right. I’m guessing from the numbers that these are two-tailed results – ie when you say 5%, that’s 2.5% above and 2.5% below.
Then for those Ar coefficients, the Q factors are sqrt((1+Ï)/(1-Ï))
ie for Ï 0.00 0.05 0.10 0.15 0.20 0.25
they are:
1.000 1.051 1.106 1.163 1.225 1.291
Back-calculating the t-values from your no-quenouille p-values:
1.960 1.858 1.771 1.689 1.616 1.498
Applying Q gives t-values:
1.960 1.953 1.959 1.964 1.980 1.934
or one-sided p-values:
0.975 0.975 0.975 0.975 0.976 0.973
or back to compare with your .05:
0.050 0.050 0.050 0.050 0.048 0.054
Quenouille does work.
Actually that last result incorporated intermediate rounding. Without that:
0.0500 0.0508 0.0503 0.0494 0.0479 0.0532
SteveF (Comment #110291) February 19th, 2013 at 9:29 am
As per your graph, one can make the case that the period is ~100yrs, so a 25 yr lag is acceptable. However, I added the HadCRUT4 time series to your graph:
http://www.woodfortrees.org/plot/jisao-pdo/mean:121/plot/hadcrut4gl/mean:121
Your method helps explain the “decline” between ~1940-1975, but after that period the lines have opposing slopes.
Kenneth, “Obviously if we had the basic physics to explain these cyclical effects, or whether there are substantial cyclical effects, we could short cut all of the above – but I would not hold my breath on that pathway.”
We do have the basic physics. We have an ocean with unbalanced input power distributing that power to an unbalanced load with unbalanced mixing ratios and we only need to determine approximately a 1% impact on the system performance 🙂 There is a fairly challenging non-radiant fluid dynamics part of the puzzle that simple averages of anomalies are not really going to provide the degree of accuracy required, especially with a fictitious less than ideal radiant “shell” with zero thermal mass as the reference.
Kenneth, BTW, I reference Toggweiler et al quite a bit about the long term ocean psuedo-oscillations and mixing. The Antarctic Circumpolar Current which began with the opening of the Drake Passage has an estimated flow of 100 to 150 Sv. A small change in surface winds at the ACC can produce a 10 to 20 Sv variation in the Thermal Haline Circulation. According to Toggweiler, the opening of the Drake Passage could have produced a 4-5 C abrupt change in climate causing the NH to warm by 3 C at the expense of SH cooling of about the same amount. It takes about 150 years for a 90% mixing of a SH impact on the ACC. Total mixing of the oceans takes on the order of 1700 years and thanks to ocean land distribution, the precessional cycle has an associated “harmonic” of 4300 years which the obliquity cycle having harmonics of 5000 and 5700 years.
20 Sv is a fairly substantial variation which appears to be natural.
AJ (Comment #110508),
I think the discrepancy is trailing versus center averages. The trailing average contains information about the trailing period. The center average contains information about both the pasts (relative to the specified date) and the future (relative to the specified date). It is only the past that can be causal.
Jim Bouldin (#110501) –
Yes, that’s right – you must adjust the f value as well, as Nick has shown.
SteveF (Comment #110511)
Perhaps. I noticed that I wasn’t considering the integral of the PDO (i.e. the main point of your post). So I didn’t really make an argument against the hypothesis.
Lucia (Comments 110468 & 110503):
Yes, I understand your points there. It seems that I’m thinking in more general terms and first approximations of trend direction/magnitude, and you’re thinking in terms of application to a particular series whose drivers you understand something about. I agree that one should always try to get the deterministic part of an observed process as right as possible before doing CI and value corrections, because they’re designed to correct for non-independence in the noise component. But for first approximations of trend direction and magnitude, especially when you don’t have a good understanding of the mechanics of the system in question, and also want to minimize the possibility of over-fitting the data (important!), then all deviations from the linear trend line are legitimately considered as the noise component, even if, in physical reality, they are not. From the standpoint of their effect on the accuracy and precision of the linear trend estimate, they are noise. That doesn’t mean of course that you should just always fit a linear trend as your first approximation when the data clearly show some kind of long term acceleration or periodicity or other deterministic pattern. Which in turn leads to the issue of noise and signal as functions of time scale and resolution of observations.
SteveF, “only the past can be causal.” Yes, and using some cumulative method should be required which would produce lags. I have this same issue with Vaughan Pratt picking a 15 year lag out of the air for his curve fitting exercise. This were averages become a PITA.
http://redneckphysics.blogspot.com/2013/02/battle-of-thermal-equators.html
There is a reason for the lags and to find them you would have to follow the energy through the system. PDO is closer to the output of the system than the input. So by smoothing the PDO and comparing it to the “global” average, you will find a significant correlation because you are comparing a delayed effect to the cause.
Kenneth, (Comment #110505)
That’s exactly what I did, with a trend of zero in all cases. The problem (apparently) is that I didn’t apply the Q correction correctly. It has to be applied to both the the residual degrees of freedom and to the F statistic itself. I only applied it to the former.
Nick, 110506
Thanks for that. But I don’t understand why you are computing and correcting a t statistic there. The F statistic is the test statistic used in ANOVA of linear regression estimates. Also, my understanding of the correction isthat it’s (1-r)/(1+r), so not sure why you’ve inverted and squared rooted it. Assuming it must have to do with your applicaton of it to the t statistic.
Jim, #110517
” But I don’t understand why you are computing and correcting a t statistic there.”
To be specific, let’s think about your Ï=0.25 number. The trend scaling is arbitrary; suppose β=±1 is your xritical range where you are measuring the fractions that fall outside. With Ï=0, that fraction is 0.05, which corresponds (in R, qnorm(0.975)) to a t-value of 1.96, the standard error must be 1/1.96=0.51.
Now Quenouille says that as Ï increases, the variance increases as (1+Ï)/(1-Ï). The se increases with the square root. At Ï=0.25, that increased value is 0.51*1.291=.658. That would mean a new t-value of t=1/.658= 1.520. You can look up the corresponding p-value (in R, pnorm(1.520)), which is 0.9357. That means you expect in your Monte Carlo that 0.0643 of trends will lie above 1, and in all 0.1286 will lie outside the range (both sides). You found 0.134 in a sample of 5000.
Using Quenouille as a correction just reverses this arithmetic. An apparent p of .9357 (=(1-.1286)/1) corresponds to a t of 1.52, which should be inflated by 1.291 (sqrt(1+Ï)/(1-Ï)), giving 1.96, which then gives p=.975, or 95% two-sided.
Jim, #110517
” But I don’t understand why you are computing and correcting a t statistic there.”
To be specific, let’s think about your Ï=0.25 number. The trend scaling is arbitrary; suppose β=±1 is your critical range where you are measuring the fractions that fall outside. With Ï=0, that fraction is 0.05, which corresponds (in R, qnorm(0.975)) to a t-value of 1.96, the standard error must be 1/1.96=0.51.
Now Quenouille says that as Ï increases, the variance increases as (1+Ï)/(1-Ï). The se increases with the square root. At Ï=0.25, that increased value is 0.51*1.291=.658. That would mean a new t-value of t=1/.658= 1.520. You can look up the corresponding p-value (in R, pnorm(1.520)), which is 0.9357. That means you expect in your Monte Carlo that 0.0643 of trends will lie above 1, and in all 0.1286 will lie outside the range (both sides). You found 0.134 in a sample of 5000.
Using Quenouille as a correction just reverses this arithmetic. An apparent p of .9357 (=(1-.1286/2) corresponds to a t of 1.52, which should be inflated by 1.291 (sqrt(1+Ï)/(1-Ï)), giving 1.96, which then gives p=.975, or 95% two-sided.
SteveF
Thought provoking.
Re: “the cumulative influence of the PDO over fairly long periods does correlate strongly with Earth’s historical temperature variation, and perhaps is in large part responsible for the observed cycle-like variation in the historical temperature record.”
That reminds me of David Stockwell’s Solar Accumulation (Integration) Theory. That suggests support for your model e.g., PDO may be solar accumulation modified by ocean fluctuations.
Stockwell’s predicted 90 deg phase lag distinguishes from AGW. What is the PDO-temperature lag?
Does PDO “cointegrate” with temperature?
See Beenstock et al.
Stockwell suggests different mechanisms: Solar Supersensitivity
SteveF,
Rather than an equally weighted moving average, why not try an exponentially weighted average? That puts more weight on the most recent point and exponentially less weight on preceding points.
Nick, thanks for the nice explanation.
So, you are correcting the confidence intervals bounding the 95% CI, by adjusting the standard error of the slope estimate using a t statistic, rather than the F statistic p value itself via adjustments to the sample size. That’s interesting, I would not have thought to do it that way (nor would I have known that se = 1/t), but I can definitely see it as you’ve described it. I now wonder if Quenouille’s method is applicable to F statistic corrections at all, and if so, how exactly (the paper describing it is old (late 1940s) and I can’t get it right now). If not, I wonder if there’s a similar type correction out there.
David L Hagen, “The difference between AGW theory and solar supersensitivity (SS) might lie more in the mechanisms. SS treats the ocean as a conventional greenhouse — shortwave solar isolation is easily absorbed, but the release of heat by convection at the ocean/atmosphere boundary is suppressed, so gradually warming the interior.”
That is pretty much the way to approach the problem, as two greenhouses. It doesn’t require “super sensitivity” though, just separate accounting of inputs, i.e. more boxes in the models. Then the impact of solar is 0.707*deltaTSI for a system with real capacity (oceans) instead of deltaTSI/4 for a “shell” with zero thermal capacity.
RE: dallas (Comment #110523)
February 23rd, 2013 at 1:51 pm
That is pretty much the way to approach the problem, as two greenhouses. It doesn’t require “super sensitivity†though, just separate accounting of inputs, i.e. more boxes in the models. Then the impact of solar is 0.707*deltaTSI for a system with real capacity (oceans) instead of deltaTSI/4 for a “shell†with zero thermal capacity.
*****************************************************************************
This has been my difficulty with GCMs expressing solar variability only in terms of TSI. Solar absorption by the oceans is highly wavelength dependent and TSI does not account for this. Besides the cyclical variation in the solar spectrum that vary absorption rates, a cloudy day has a modest effect on TSI but solar absorption by the oceans effectively drops to zero. TSI is an oversimplification of our principle heat source and the way earth absorbs this heat over time. This is a major flaw in most GCMs and one of the reasons we don’t have a better understanding of natural variation.
ivp 0″This is a major flaw in most GCMs and one of the reasons we don’t have a better understanding of natural variation.”
It is only a major flaw if the assumption doesn’t have enough accuracy for the task. If “sensitivity” to CO2 equ was 3 C plus, it would be a valid assumption. With equilibrium “sensitivity” to CO2 eq 1.6 C or less, now it is no longer a valid assumption. You are supposed to learn from your models, that is the real problem, trying to fix and fudge instead of learn.
Since the “global” approach seems to be seriously limited, now would be the time to consider “modular” approaches. There is more than one way to skin a catfish and sometimes it is nice to know several ways.
Nick Stokes (Comment #110506)
Nick, I believe that the Quenouille correction diverges from the Monte Carlo estimates for p values when you go beyond AR1= 0.25. I simulated Arima AR1 series with a standard deviation of 2 a mean of 0 and a trend of 1.2 per century for a time series 1320 months long. Below UC is the uncorrected p value, Q is the Quenouille corrected p value and MC is the Monte Carlo estimated p value. The Monte Carlo runs used 5000 simulations.
AR1= 0.25 UC=1.83e-11 Q=1.77e-7 MC=1.63e-7
AR1= 0.45 UC=3.07e-10 Q=1.32e-4 MC=5.29e-4
AR1= 0.75 UC=3.07e-10 Q=1.66e-2 MC=8.60e-2
One should determine the fitted series for auto correlation in using any correction and at that point half work in doing a Monte Carlo is finished. The Quenouille correction is applicable for an AR1 auto correlation only and many temperature series are not AR1.
DeWitt Payne (Comment #110521),
.
I actually thought about that, since the diffusion of heat into the ocean ought to be an exponential function. But I figured it would make the post more complicated than I wanted, would add more “tuned parameters”, and would be difficult to implement in Excel. I was not thrilled with investing the time to code it in Basic or Fortran. (If I were not so busy I would probably learn R.)
Jim,
With or without correlation, these trends are (in your Monte) normally distributed with zero mean. So there is only one parameter, σ, which acts as a scale. The t-values are just the scaled values. You’ve chosen a fixed point to mark the tail, so it’s simplest to estimate σ from the p-values. Quenouille predicts (well) how σ depends on Ï.
In R, if r=c(0,0.05,0.1..) and Q=sqrt((1+r)/(1-r)), then the numbers in your #110491 are predicted by
p=2-2*pnorm(1.96/Q)
The same scaling will affect any other testing you try to do; F tests etc.
Re: SteveF (Feb 23 16:40),
Exponentially weighted sounds more complicated than it actually is. It’s barely more difficult to implement in Excel than a simple moving average. You select a weighting factor α, for your time series y(t). The EWMA is then S(t) = α*y(t) + (1-α)* S(t-1). The smaller the alpha, the greater the smoothing. Some people refer to 1-α as λ. Obviously, α or λ must be in the range 0-1. IIRC, you can make it acausal by filtering once in each direction. I think that removes some complicated phase shifts as well.
SteveF,
A bit off topic. Roe’s paper showed the relation between insolation and ice-melt rate. Ohmura’s paper “Physical Basis for the Temperature-Based Melt-Index Method” states:
”
The accuracy of the temperature-based melt-index method is reexamined based on ï¬eld data
and literature. This simple method indeed makes it possible to estimate the rate of the melt with sufï¬cient accuracy for most purposes. The author questioned how this seemingly simplistic method yields such a high accuracy. A physical explanation is presented below that has a more profound foundation than mere computational simplicity or the easy availability of input data.
”
http://journals.ametsoc.org/doi/pdf/10.1175/1520-0450(2001)040%3C0753%3APBFTTB%3E2.0.CO%3B2
In my mind this makes the ice-melt rate a good proxy for surface air temperature. When I hear of the proxies used for paleo temperature, however, it seems to me that they are using ice volume. When I hear statements like “CO2 follows temperature by 800 years”, I’m wondering if co2 actually follows temperature by ~25,000 years (i.e. 1/4 of the 100K year glacial cycle) and that it would actually be a proxy for the amount of energy in the climate system.
Do you know if this “issue” has been explored in the scientific literature?
Thanks Nick (#110528). I can now definitely see your original point on this topic, that Quenouille’s method is good as a first approximation, and therefore something you would use when performing tens of thousands of analyses exploratorily. It’s sure as heck far better than using uncorrected values!
Given Kenneth’s results (#110526) however, I would still use a randomization test (with say 10^5 or more trials) for any particular series of definite importance (global T for example), especially when the lag-1 rho was high.
Somebody above mentioned that esimating the AR(1) coefficient from real data was a potential problem. But to apply any correction you have to estimate the autocorrelation in the data (rho(1) when using Quenouille and the AR(1) coefficient when randomizing) and I don’t see that the potential for mis-estimation of either is particularly more problematic than the other, nor immune to corrections themselves using the same type of simulations.
Diffusion into the ocean is not exponential. It is the typical transient solution to the continuity equation, with a 1/sqrt(time) response.
DeWitt and SteveF, I have been playing around with integrating data over alternative ‘memories’ at this point just using a declining straight line rather than an exponential.
–
with r this could be coded like this:
#step 1: create the ‘moving integral’ filter to simulate a memory of (example) 75 time periods
coef.75<-rev(cumsum(rep(1/75,times=75)))
–
#step 2: implement using the "filter" function in r
integrated.memory75.data<-filter(data,coef.75,method=c("convolution"),sides=1))
–
The result is the implementation of a filter over a window of 75 time periods with coefficients declining linearly from 1 to 1/75. The window length can just be changed to whatever filter width you want to experiment with.
The correction from Lee/Lund via Grant Foster for an Arima (1,0,1) series is:
SE corrected=SEraw*sqrt(1+2*p1/(1-p2/p1)), where p1 and p2 are the first and second auto correlation coefficients of the regression residuals, respectively.
Using the Arima series with ar=0.37, ma=-0.22, sd= sqrt(3.84) , a trend of 1.25 per century and a series length of 1320 months, I compared the p values obtained using the Lee/Lund correction, from the 5000 run Monte Carlo simulations and the uncorrected p value.
p value using the uncorrected SE is 2.18e-13.
p value using the Lee/Lund corrected SE is 1.43e-09.
p value using Monte Carlo is 2.07e-08.
This exercise shows again that while a parameterized correction increases the CIs (and the p values) the results differ from a Monte Carlo. Another problem can occur when the series is not properly characterized or at least characterized differently. An example of this difference was discussed a few months back at the Black Board with the Grant Foster use of the Lee/Lund correction on temperature series, that I judged to be better characterized by Arima(0,0,2) and were given as Arima(1,0,1) by Foster. That difference changed the CIs significantly.
Kenneth, #110526
Yes, that looks right. For a sort of “Ar(1.5)” there’s the adaption Tamino used – I think it’s Lee and Lund. And the higher ρ is, the less likely that simple Ar(1) will work.
That’s why I was advocating the “solve the polynomial” approach here. In principle it works for Ar(n), just slightly messier to code. And it simultaneously estimates the Ar() coefficients and the trend. It’s just polynomial algebra on the same sums (Σ y_i y_(i-1) etc) that any other method would use.
Carrick and SteveF: Sorry for the delay in replying. I was busy with other matters.
Carrick: You’ve suggested that I need create a model of ENSO and its aftereffects. Are you aware that the climate science community still can’t model ENSO? They’ve been trying for multiple decades and still have no idea how to do it. I see no reason for me to even ponder it. In place of that, I have presented numerous datasets to confirm my understanding of the coupled ocean-atmosphere processes of ENSO and their aftereffects, including sea surface temperature, sea level, ocean currents, ocean heat content, depth-averaged temperature, warm water volume, sea level pressure, cloud amount, downward shortwave radiation, downward longwave radiation, precipitation, the strength and direction of the trade winds, lower troposphere temperature, combined land+sea surface temperature, etc. And I’ve animated maps of many of those variables to allow the visualization of the impacts of ENSO. In other words, I’ve done more than hand-waving and wiggle matching.
SteveF: Looking back at the my approach on this thread, I should have used a different tack. I should have made a suggestion. Hopefully now it won’t land on deaf ears.
Instead of using abstract forms of data, like the PDO, try using absolute and anomaly forms of the data. It’s much easier to deal with and you won’t confuse your readers.
Regards
Nick Stokes (Comment #110535)
I’ll have a look at your link and method. What is the advantage of that method over a Monte Carlo?
My point with Lee/Lund as applied by Tamino is that it has it limitations also.
Tamino estimated an Arima(1,0,1) by observing the acf of the regression residuals and did not show that an attempt was made to fit the series of interest to an Arima model more directly.
Kenneth Fritsch:
I understand Nick needs his code to run on Javascript, but for “beefier” applications, I’ve been wondering whether there are benefits myself.
As you probably know, my preference is to use a spectral-based method for Monte Carlo’ing—my prejudice is this has fewer assumptions built in to it… for example, you can model non-stationary & non-Gaussian processes with this approach.
To illustrate how I would use it, is I would develop a spectra based model for the noise in the measurement. If I wanted to test the affect of this “real-world” noise on my trend estimation for example, as a function of the fitting (“integration”) period, I would generate a series of instances of the noise, fit to each of them separately, then look at the statistical properties of the ensemble of OLS trends.
For example what I did here, to estimate the uncertainty.
I’ll note that often you get a power-law like relationship between your uncertainty and the integration period, here I found
$latex \sigma_T = 15.6^\circ\hbox{C} \times T^{-1.1.4}$.
Presumably any “wobble” you see in a less robust estimate is just going to be related to noise… it’s not going to tell you anything new or meaningful about the real uncertainty in the trend estimation.
(Which is the problem with F&R’s curve fitting exercise, a smoother curve doesn’t imply a more accurate result.)
Kenneth Fritsch:
“What is the advantage of that method over a Monte Carlo?”
Computation time. A MC with 5000 replications takes nearly 5000 times longer, and still doesn’t get the exact answer. Not that “exact” means much given the approximate assumptions.
My main claim is that it’s the logical extension of OLS – it uses the analogous scalar products, and gets the best answer you can get from them, given the assumptions.
Nick:
I’m not sure in what sense it gives the “best answer”, given that the original paper was titled “Approximate tests of correlation in time-series,” but there are better analytic expressions than Quenouille’s correction based on the assumptions he made.
If you want a reference to a study examining the efficacy of Quenouille’s correction, see Ledolter Communications in Statistics—Simulation and Computation 38: 771–787, 2009.
It is pay-walled, so here’s figure 1.
If I understand right, Quenouille’s approximation fails as $latex N$ becomes too small (though still large by physical experimental standards), and/or when the autocorrelation in the data becomes to high.
Anyway, I’m pretty sure it’s justified for Nick’s simulation work (very large $latex N$). Of course there are many results that don’t work well on “real” data, that work fantastically well on (otherwise nearly noiseless) simulation results….
Carrick,
Sorry I wasn’t clear there – I was referring to my solve polynomial method, not Q.
Thanks Nick, that does clear it up!
Nick Stokes (Comment #110543)
Nick, I applied your method to a simulated Arima(1,0,0) with ar=0.706, sd=sqrt(4.11), trend = approximately 1.2 century and a series length of 1320 months. I compared the results for your method with the uncorrected results and a 5000 run Monte Carlo.
The results for a p value were: uncorrected = 5.2e-05, NS= 5.2e-02, MC= 4.2e-02.
Your method nailed the ar at 0.703.
I’m impressed with your method, but posters here will tell you that that is not a difficult task. You mentioned your method can handle AR2 by merely adding the AR2 lag column. Can you do Arima series with ma (moving average) coefficients? The MC take my computer something over a minute and your method was a few seconds.
Looking at the results above, if I ever have a close call with claiming statistical significance, I now have a choice between NS and MC – depending on my predisposition for a result.
Kenneth,
Thanks for trying it. Yes, I think adding MA terms should be no problem.
I developed (back then) a new code which mechanizes the algebra, and works for Ar(n). I’m checking it now – not quite getting the right answers, but I’ll post a link when I do. It should be fairly easily generalized to include MA.
Kenneth,
I had forgotten that I had drafted a post last June on the generalized method. It’s here. I haven’t finished the examples, which gave some difficulty, which I rediscovered just now. If I try to reinterpret your example output as Ar(2), it gives a reasonable trend sd and ar(1) coeff, but a small but decidedly non-zero ar(2) coef. I’m checking.
Still, it’s a clearer way of looking at the math, and coding.
SteveF
Here is what you are trying to say in a graph:
http://bit.ly/13Wi8d9
SteveF,
Here’s an interesting bit from 1922 about Arctic ice melting:
http://www.snopes.com/politics/science/globalwarming1922.asp
The melting then was apparently caused by a northward shift in the Gulf Stream. It’s likely that some of the melting now is a result of a similar shift. A centered 21 year moving average of the AMO index bottomed out in 1913 and the 67 year period sine wave fit was at a minimum in 1911. It bottomed out again in 1978 and reached a maximum in 2011.