Schwartz & Scafetta Estimate Climate Time Scale
One sign of an important paper is to count the number of immediate responses. By that measure, Schwartz 2007 “Heat capacity, time constant and sensitivity of the Earth’s climate system ” appears to have made quite an impact.
The impact is not surprising as this paper represents the relatively rare attempts to estimate climate sensitivity empirically rather than using models. The empirical value turned out to be much lower than generally predicted by climate models.
It appears that three comments on Schwartz’s paper will soon appear in J. Geophys Res. along with Steven Schwartz’s has also published his response. The various papers are a) Schwartz’s response, Scafetta’s comment, Foster, Annan, Schmidt and Mann and Knutti (for which I have no link). I’ve looked at all but Knutti.
Since these things are likely to be discussed, and I have posted my initial thoughts in comments, I thought I’d comment on Scafetta’s very good paper, and Schwartz’s response to Scafetta’s comment. Later I will comment on FASM (though I have already said much of what I think in comments on Friday’s blog post.)
Comments on Scafetta
Scafetta’s approach to Schwartz’s paper was to use the idea in the paper as a springboard for further analysis. In some ways, I see the initial Schwartz paper as “the great idea”, that idea being “Let’s try to estimate the climate time constant based on data. Here’s my first shot!” I see Scafetta’s paper as one that takes the great idea and improves method of applying the idea to get a more accurate answer.
This is the way things work in science. Mistakes may be made along the way, but we need to start out with ideas that permit further analysis.
What’s the great idea?
So, Schwartz’s idea was that we could treat the earth’s climate as a simple “lumped parameter” with one time constant and futher assumed that this “climate lump” was being heated at a rate that, on average, increased linearly with time, but also varied randomly. The random variation in heating was assumed to be “white noise”.
Under this assumption, Schwartz concluded the random component of surface temperature of the planet would be something called “red noise”. Moreover importantly, if one detrend the average temperature, calculated an correlation, ρ of lagged residuals, the correlation, ρ would be a constant. Based on that constant, we could estimate the time constant of the planet.
So, basically, one does some calculations, plots, and read a number off the plot. Schwartz concluded the time constant of the climate was about 5 ±1 years.
But there were problems.. .
Scafetta’s paper noted that Schwartz’s analysis of the time series for Global Mean Surface Temperature is imperfect and might not give the correct result for the time constant for three reasons.
- One is that the autocorrelation (ρ) as a function of lag time in Schwartz 2007 is not a constant function of time, as would have been suggested if the temperature series obeyed the simplified equation for the earth’s climate system described in Schwartz.
- Scafetta also noted that assuming the underlying trend in temperature over time did not suggest a linear increase in temperature over time.
- Finally Scafetta also discussed the known biases that arise when estimating the correlation in lagged residuals from data.
To deal with these issues, Scafetta did three separate things:
- He treated the temperature series as having two time constants: one faster, one slower. This would make sense if, for example, we thought the air or ocean made up two systems. (Alternatively, one could image the air, ocean and deep ocean make up three interconnected systems, or break up the planet in more and more pieces.)
- He de-trended the temperature series two different ways. First, he assumed a linear trends, as did Schwartz. But, recognizing the shortcoming of this method, Scafetta also detrended using the estimate for the mean surface temperature as a function of time as predicted from GISS model results.
- He performed an analysis to estimate the possible bias the estimating the autocorrelation.
Scafetta’s results for the time constant are: a) τ1=0.4 ±0.1 years and τ2=8.7 ±2 years under linear detrending and b)) τ1=0.4 years and τ2=8.1 ±2 years detrending using GISS model data. Scafetta then considers the effect of bias in estimating the autocorrelation from short data samples, and concludes the bias could be 3 years. Therefor, accounting for bias the time scale for the climate may be 12 ± 2 years. (Note: the bias may be smaller than 3 years, as its magnitude depends on the magnitude of the actual time constant.)
All three extension by Scafetta appear to me to be improvements on Schwartz.
Afterwards, assuming Schwartz’s estimate for the heat capacity is correct, Scafetta estimates the time constant for the climate most consistent with the data is 1.7 C for a doubling of CO2. Accounting for the possibility of bias the sensitivity may be as large as 2.7C for a doubling of CO2.
How does Schwartz respond to Scafetta?
Schwartz seems to more or less endorse Scafetta’s observation.
Schwartz discusses the physical basis for the possibility of time scales of approximately months and accepts the two time scale system as both plausible and an improvement on Schwartz’s first analysis. After accepting this possibility, Schwartz then explain that, owing to the shortness of the 4 month time scale, we could assume the time scale varies as a function of lag as follows:
where ρ(Δt) is the autocorrelation measured as a function of lag time, δt, and ρo is the zero intercept at Δt = 0.
Rearranging this equation, and plotting as a function of lat time on semi-log paper, we would expect to see that at lag time large compared to 0.4 months, ρ should fall on a straight line. This is illustrated in figure 2a from Schwartz, reproduced below:
From Schwartz 2008: In the figure above, Schwartz shows series of data both before and after correcting for bias but uses a different method of bias correction than selected by Scafetta.
To obtain time constants, Schwartz plots the time constant τ calculated using equation (1) above as a function of lat time Δt. and then (I think) he eyeballs the data to obtain estimates of 8.8±2 years and 7.2±1.5 years.
Ultimately, Schwartz revises his estimate of the time constant to 8.5±2.5 years, which is noticeably larger than 5 ±1 year reported in the original paper.
How does this relate to my earlier blog post?
Those familiar with my first blog post discussing Schwartz will recall I observed the even if the earth’s climate obeyed the equation described by Schwartz, the data should obey the relationship discussed above and performed a linear fit on ln(ρ) vs time. I obtained 7.2 ± 2 years based on annual average GISS land ocean data and 8± 2 years based on annual average MetStation data. These magnitude are comparable to the values obtained by Schwartz– and well should be as the two methods are equivalent.
However, I did not account for bias in anyway. (This is because I was entirely unaware of the issue.)
Because I seem compelled to always look at data myself, I will be examining different methods of accounting for bias to see how they might affect my estimates and my uncertainty intervals.
However, as my analysis currently stands my estimates are comparable to those of Scafetta and Schwartz, and were obtained entirely independently. I’m reasonably sure neither read my blog back in December, (when the blog was experiencing 2 visits a day, mostly from me.) I had certainly not read their papers, which were posted on the web quite recently. So, it’s clear that people with different backgrounds are all making similar (though slightly different) arguments and coming forward with similar results.
What does a time scale of 8 years mean?
First, this estimate for the time constant of the earth and the climate sensitivity is much lower than for models. So, there is an inconsistency here.
All other things being equal, the lower time constants means:
- Less “heat in the pipeline” than predicted by models.
- Possibly lower total climate sensitivity– if we also believe Schwartz’ estimate of the climate heat capacity.
Obviously, the method used by Schwartz, and Scafetta involve a great deal of approximation, but approximation is common in science. However, despite the huge amount of simplification, when the very simple model in Schwartz first paper is corrected by recognizing either noise or very short time scale weather noise, the simple model seems to give fairly decent representations of the major features autocorrelation in lagged residuals for measurements of GMST.
Given the reasonable agreement with data, it is difficult to wave away the estimate for 8 years as simply “wrong”.
So, what are we to make of the mismatch between models and this estimate?
Steven Schwartz discussed four possible explanations for the mismatch: a) The 8 year estimate could be in error due to uncertainties in the measured data, b)The time record may be too short to use this method to estimate the time constant, c) The method used to infer the time constant could be inappropriate and, d) Climate models may be inaccurate.
Figuring out which of the four applies will require thought and work. Obviously, researchers will continue to strive to resolve the mis-match between models estimate for the time constant and Schwartz estimate. In the meantime, it appears a time constant of 8 years falls in the range of “plausible” based on 125 years of measurements of the Earth’s mean surface temperature.
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54 Responses to “Schwartz & Scafetta Estimate Climate Time Scale”
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Arthur Smith May 6th, 2008 at 3:51 pm
Hi Lucia - reasonable analysis. But realize this kind of analysis only provides a lower bound on climate sensitivity, not an upper bound, because there certainly are slow processes that are not accounted for. The variations of temperature within the 100+ year record up to now do not include any substantial amplitude (aside from the long-term trend, which is subtracted out!) of low-frequency variation. Think of what you’re doing with the correlation calculation in the frequency domain: if you do a Fourier transform of the temperature data then the amplitude of the fast variations is large, and the amplitude of the slow variations is small. When you look at the correlations, any relaxation processes on a particular timescale are weighted by the associated frequency-domain amplitude, so with the data series we have, you’re going to strongly favor time-scales similar to the largest amplitude components. In particular, there’s certainly seasonal variation which would weight relaxations around the 1-year timescale, and there’s known variation with the 11-year solar cycle with would weight relaxations around that length. But I doubt there’s enough data of sufficient quality at this point to detect any relaxation time longer than about 10 years…
lucia May 6th, 2008 at 4:11 pm
Arthur–
Yes. There are difficulties, though I’m not entirely sure this gives a lower bound, particularly not after correcting for bias in the autocorrelation and figuring out what it is.
I’m not entirely sure what you are suggesting with the spectral discussion. I think I might know though.
Ordinarly, in a lab we use an instrument with a very small response time. We often even know that response time. Then, if we wish to know the amount of energy at long wavelengths, we need to sample a long long time. Preferably many cycles of the longest wavelength. But in this case, we know the instrument time constant, but want to know the features of some other system we are studying. (Possibly turbulent flow in a wake of a bluff body? Whatever.)
But here, we are doing the opposite problem. We are trying to detect the time constant of the instrument.
In this case, what we need is many multiples of the time constant of the instrument. Then, we need to have some clue what the forcing function applied to the instrument might be.
Believe it or not, sticking an instrument in a known controlled ‘forcing’ field and watching the response is something we actually do. Depending on the “forcing”, you don’t always need to take data for very long.
That said, I think there is a “time” problem– but it’s one that is discussed by Scafetta and by Schwartz.
I’m going to be testing with manufactured data to test the question if the response of the system is very long, what do we get as an answer. (And the question is, how much do we underestimate this?) I’ll tell you what I find after I do it. I’ve set my spreadsheet up to do this.
It’s sort of repeating what Scafetta did, but in my own “lucia” way, because I guess I like doing this sort of thing.
Bob Tisdale May 6th, 2008 at 4:43 pm
Lucia: I believe Nicola Scafetta is a she. If you discover I’m right and make the pronoun corrections, feel free to delete this.
Regards
lucia May 6th, 2008 at 5:02 pm
Bob– I emailed to ask Nicola. I’d done a google search, and can’t find photographs or any use of he or she in articles! So, I don’t know if “Nicola” is the equivalent of Nicolas or Nicole. It’s very embarrassing to be wrong on this.
Nicola Scafetta May 6th, 2008 at 6:34 pm
Lucia,
thank you for a very good summary of my paper. I could not have done a better job!
BTW, I am “he”. “Nicola” is the Italian male name for English “Nicholas”
Bob Tisdale May 6th, 2008 at 6:37 pm
My mistake.
Steve McIntyre wrote in http://www.climateaudit.org/?p=2451: “I’ve not spent as much time on Nicola Scafetta’s work as I would like to have. I spent about an hour with him at last year’s AGU and he gave an impressive explanation of his ideas.”
I should’ve checked beforehand. Sorry to waste your time.
dover_beach May 6th, 2008 at 7:01 pm
Lucia could you please delete the above. The conumdrum above was solved in writing and my attempt to try and delete rather than edit my comment obviously failed. Remove this comment as well would you. Thanks.
Lucia says: I deleted it.
Graeme Bird May 6th, 2008 at 11:16 pm
Do we have a dataset where we are sure all the heat island effect has been excised? If we had such a dataset and we went through the same processes it would be interesting to see what the supposed effect of a doubling was then. We wouldn’t want to have this 1.7 getting out there and being quoted as gospel if its just a function of the way they rig up their data at Goddard.
pliny May 7th, 2008 at 12:20 am
A puzzle to me with Schwartz’ original paper was the lack of attention given to his query on p 14
It seems to me that the answer is clearly yes, it is a high-pass filter, and takes out longer term processes. Before detrending, SS got a relaxation time τ of 15-17 years, which would have returned a sensitivity right in the usual range. Afterwards, the time reduced to 5 years, leading to a low sensitivity.
lucia May 7th, 2008 at 5:57 am
Pliny–
Scaffetta adddressed the detrending issue by detrending two ways. First, he did a linear detrend as in Schwartz’s first paper. Second, he detrended using GISS model hindcasts for the trend. The time constant was shorter using the non-linear detrend, but only slightly so. So, the linear detrend seemed to lengthen the time scale. (That is, the opposite of what you suggest.)
Actually, it makes sense that the linear detrend lengthens the time scale because the slowly varying deviations from the trend associated with the slow variations in GHG’s etc look like low period noise. A climate with a short time scale tracks those. So, if you assume the climate is red, but it tracks a “slow” period, the time scale of the temperature signal looks slow.
The Schwartz method, as in paper 1, really needed external noise to be white, not white with a huge slow cycle added to it, not white with measurement noise, but white!
The reason the newer estimates for the time scale are higher is because Scafetta, Schwartz (and me in my blog) correct for the high frequency noise in the data.
Graeme: I could be wrong, but I don’t think the urban heat island effect is a big issue to this method, except in so far as it affects detrending. The urban heat island is important to estimating the precise underlying trend from the data.
Reference May 7th, 2008 at 6:07 am
The discussion of Nicola’s gender was a neat example of the scientific method in action. First there was the assumption of male, this was questioned by a skeptic, evidence was sought but only via proxies, finally the matter was settled when the subject spoke for himself. Empiricism rules! Cheers everyone.
pliny May 7th, 2008 at 7:01 am
Well, Lucia, the first thing to say about Scafetta’s using two detrending methods is that, as he says, the difference in results is insignificant. I think the reason is that they really do the same thing. Whenever you subtract out a smooth function which has been fitted to the signal, you will tend to reduce any low-frequency signal present. That is because that signal will be identified (in part) with the smooth function. That is why detrending acts as a high-pass filter. If you did a linear detrending of a half-sinusoid, from its minimum to its max, you would greatly reduce the amplitude of the signal.
So I’m not reassured that Scafetta tried two methods of detrending; I think any method is likely to suppress the longer time constant processes. Redness or autocorrelation is not the issue here; it is just frequency.
I have to say that the second thing that bothered me about Scafetta’s approach is that he introduces two time constants, and then after fitting, arbitrarily takes the larger one to be the one that determines sensitivity. I’m still trying to work that one out.
lucia May 7th, 2008 at 7:29 am
Pliny–
On the issue of the two time constants in Scafetta, I agree there are “issues”. The reason I didn’t go for a two time constant process in my Dec. comment on Schwartz is that I strongly suspect the system has quite a bit of measurement noise. (In fact, if we subtract GISS from HadCrut on a year by year basis and remove, then we get back an amount of “noise” of the order of magnitude I find in my analysis.)
It’s possible the “measurement noise” has color for a variety of physical reasons related to how the instruments are deployed. But I don’t think it’s possible to resolve the difference between my guess that the extra process is measurement noise or climate physics.
If the shorter time constant is climate physics, the physical mechanism does need further exploration. Neither Schwartz nor Scafetta did that fully. This leaves that issue “open”. But that’s no real criticism of either the comment nor the response. Comments and responses to published papers are necessarily short, and more incomplete than full papers. Editors want these things to be short.
So, we may see more from both Schwartz and Scafetta in that regard.
On the detrending: Your comment brings up an issue similar to that discussed by Arthur. I could be wrong, but I’m pretty sure this issue doesn’t much affect the accuracy of measuring the time constant of the climate. It is a well known issue when measuring energy spectrum of the system using an instrument with a known problem. One is sort of the “inverse” problem compared to the other. (I don’t mean inverse in the pure mathematical sense; hence the scare quotes “”.)
However, I admit I could be wrong on my opinion about this, and you and Arthur could be right. So I’m going to be doing some informal “blog quality” testing. (Using EXCEL!) It will take me a little while, but afterwards, I’ll be able to state an opinion based on actually looking into the issue specifically.
My blog philosophy is: I post back of the envelop stuff people often do and shove in drawers. Many of these things don’t merit writing up formally, but they are worth making available. (Soon, I need to organize my categories so people can find them!)
Francois O May 7th, 2008 at 7:34 am
It seems to me that using the GISS model to detrend really amounts to assuming what the forcings are. The linear detrend assumed a linear forcing (say exponential CO2 with logarithmic response).
That said, there are two things that one should keep in mind. First, nothing says that the forcings are only GHG. It’s the combination of all forcings, including solar. The sensitivity one gets is K/(W/m2), and is really quite agnostic in terms of what forcing gives the W/m2 part.
Secondly, the GISS model itself makes a lot of assumptions regarding forcings. In particular, it assumes aerosol forcings that litteraly mimmick the temperature evolution of the 20th century, to the point that it’s ridiculous, given that the uncertainty of our knowledge on aerosols pre-1990 is about 1000%. But that’s the only way that Hansen can get a good agreement with observations. In the end, therefore, it is really a high-pass filter, disguised as the “actual” forcing.
The choice of two time constants seems a bit arbitrary. Why two and not three or four? Actually, I’ve had to deal before with effects in disordered media (like glass or polymers) that involve a distribution of time constants. For example, when one looks at the relaxation curve, it’s no more an exponential, but rather a “stretched” exponential, of the form exp(-a*t^b), with exponent “b” being smaller than one. I wonder if that could be applied here.
A final comment. It would be interesting to use either ocean temperatures, or ocean heat content, as the basis for the analysis. Since oceans are where the heat is actually stored, maybe the result would have more physical significance.
lucia May 7th, 2008 at 7:55 am
Francois O
Yes. Detrending this way is basically following the assumptions that
a) the mean forcings are well understood and correctly applied to the AOGCM code, and
b) the climate model results in the correct result for the ensemble average for the temperature variation over time when driven by the mean forcings.
On the one hand, there are those who don’t believe either (a) or (b). But those people also don’t believe the climate models estimate of the time constants near 20-30 years. So, that leaves no estimate whatsoever. In which case, 8 years would at least represent some sort of empirical estimate. It might be wrong, but we are left with no estimate at all. (Which is ok. Sometimes we just don’t know.)
On the other hand, there are those who believe both (a) and (b). In that case, detrending using the model estimate seems plausible. So, what Scafetta did is precisely correct under the assumptions that both (a) and (b) are correct.
This observation will be very important when discussing the FASM response to Schwartz. Applying the initial Schwartz method to GCM data would only be plausible if the AOGCM runs included “noise” in their forcings. The TSI has loads of noise. It’s not exactly white but there are “shitwads” of energy at high frequencies. There are other external factors making the external forcing term noisy. These include farmers in Nebraska plowing their field in spring, people in various countries spewing more or less aerosols depending on the state of the economy, the occasional minor volcanic eruption that washes out quickly. All of these things are smoothed in the input file for GCM’s. So, the assumption that extrenal forces are white is not replicated in GCM’s.
On the choice of two time constants: I am of the opinion the shorter one is measurement uncertainty. So, that makes it non-arbitrary, and I set mine to zero. But I could be wrong. Also, I could easily concoct a physical argument for the short one and the long one. But there will be some arbitrariness.
On the general issue: I agree that it would be interesting to do more analyses and use ocean temperatures or ocean heat content. I bet we’ll see some soon– provided the data are available.
The reason I think Schwartz paper was mostly brilliant is he’s got people trying to get empirical estimates to test models. His first paper was very approximate, but he admitted most of the “flaws” the critics are bringing forward in the paper itself.
Arthur Smith May 7th, 2008 at 8:13 am
Hi Lucia - yes, definitely further analysis is warranted - I’ve been looking at FFT’s of the HADCRU temperature series (since it’s the longest) - 1899 points, so close to 2048 which works for Excel’s “Fourier analysis” procedure. That comes to just over 170 years time-span, so the minimum frequency interval you can look at in the analysis is 1/170 years, and realistically you don’t get a reliable curve until you’re at several multiples of that, at least with this procedure. So it’s hard to tell anything about frequency patterns in the temperature data at longer than 50-year time scale.
Do you know if anybody else has just looked at the spectrum of temperature variations like this in the past? It seems a pretty obvious thing to do.
I’ll need to spend a bit more time before I can show a graph, but the main features seem to be:
(1) there’s a very robust peak at a frequency of 1 year^-1: you see that on the 2048 graph, and on FT’s of 1024 and 512 points corresponding to 43 and 85-year time spans in the CRU data. I haven’t looked at the other data sets yet, but so far the strong annual peak (and subsidiary peaks at multiples of that frequency - i.e. 6 months, 4 months, 3 months…) is clear.
(2) There’s another robust peak at about 0.28 year^-1 (3.6 year period)
(3) Another robust peak is at about 0.12 year^-1 (8.3 year period). However, it’s missing in one older data series I looked at (1922-1965, 512 points), where it seems to shift to about 0.094 year^-1 (10.6 year); the full series seems to show two peaks, one at 0.12 and a second (about half the height) at 0.094.
(4) There appears to be another robust peak around 0.05 year^-1 (20 year period)
(5) The low-frequency pattern is very unstable when analyzing the data different ways.
In particular, the raw and de-trended temperature series differ considerably at low frequencies - of course the 0-frequency component is 0 for the de-trended graph (it’s just the average value across the series) but detrending also removed considerable weight from the next 4 points in the 2048 FFT, i.e. I wouldn’t consider any of the spectrum of temperature variation at lower than 0.025 year^-1 (40 year period) reliable from this data.
Arthur Smith May 7th, 2008 at 8:22 am
Correction to my feature #3 - the two peak frequencies in the 2048 FFT’s are at 0.094 and 0.111 year^-1 (10.6 year and 9 year period, respectively). Of course the resolution is only 0.006 year^-1 so that would be 9 +- 0.5 years, and 10.6 +- 0.7 years - anyway, just wanted to note that the shorter (stronger) period is probably slightly longer than the 8.3 I said originally.
lucia May 7th, 2008 at 8:30 am
Arthur–
I absolutely agree that you need more time to accurately get the correct amount of energy, and identify the correct shape of the spectrum particularly at the large scales. What I’m not sure of is the amount of error that propagates into the estimate of the response time of the system under this particular method.
Post the graphs, and I’ll add known deviations at different frequencies to my blog quality exploratory uncertainty estimates. That hasn’t been done, and it will be interesting to see what happens. (If you don’t have a place to store the graphs, I’ll post.)
I think empirical estimates are important– and I think the most positive contribution of Schwartz is to get the ball rolling and motivate people to get them. Even he doesn’t claim his numbers are beyond reproach– and he says so in his article!
(I’m also going to have to dig out “Lumpy” again!)
lucia May 7th, 2008 at 8:38 am
Oh– Arthur, If we can think of a better approach to the estimate, it could be worth writing paper describing the method and providing the results. As the short comings of the current approach are identified and method to correct them implemented, we may actually eventually find the correct value.
pliny May 7th, 2008 at 8:38 am
Lucia,
Great to hear that you’re thinking of experiments. I’d like to do some too, but won’t be able to for a day or so. But what I would suggest is this. Make up some synthetic data with an IPCC-type time constant (just one) of about 15 years and some noise. Put it through the detrender, and try to recover the time constant.
lucia May 7th, 2008 at 8:53 am
Arthur (again, heh!)
Oddly enough, peak near 1 year has been noted in the difference in anomalies between measurement groups. Atmos first noticed it here:
http://atmoz.org/blog/2008/04/...../#more-506
And because I was intrigued I toss out my theory explaining it here:
http://rankexploits.com/musing.....at-1-year/
I don’t know if my explanation is correct. But I think it will be worth comparing the amount of energy at different frequencies by doing the test Atmoz did. This will give us insight into whether that energy is more likely “climate physics” or “measurement uncertainty”. (Go tell Atmoz he was brilliant for looking at this in the first place. )
But as you can see, my first inclination when I see odd things is to ask, “Could it be measurement uncertainty?” And when testing theories I always ask myself: “How would measurement uncertainty affect my confidence in the answer?”
Depending on the analysis method, even small amounts of measurement uncertainty can really screw things up in ways people who always use models and synthetic data sometimes don’t anticipate. These things are important to know when you are designing an experiment because you want to make sure you could conceivably answer the question you asked before you build your test rig and purchase your equipment.
pliny– Your thoughts are more forward looking than my first steps. First, I’m going to see what happens with no trend at all. I’ll report that. If we find lots of error this way, we’ll know that detrending only makes things worse. But, if we get ok answers with no detrending, then well move on to your suggestion.
steven mosher May 7th, 2008 at 9:52 am
Lucia, I agree with some of the things Francois, has said, in particulat looking only at SST as opposed to
Land and Sea. Just a thought
lucia May 7th, 2008 at 10:02 am
Steve– I’ll look at SST only. But, it will be deferred until I get a handle on the uncertainties in the method using “pseudo-data”. The reason is that I think most of us will find any furture results more convincing if we figure out the plausible method to estimate uncertainties before we get an answer!
One of the reason I like more standard method of hypothesis testing to idiosyncratic ones is that the standard method gives us a systematic way of estimating biases and uncertainties. Even in the event that we know the standard method is not perfect, this is still better than everyone just giving their opinion without doing numbers.
Of course, this is a blog, so I’ll be doing it all at “blog quality”. (OTOH. Every rational person does things “blog quality” first to at least figure out which things couldn’t possibly work if you throw all the analytical bells and whistles at the data hoping to get a “peer reviewed” quality result.)
So… you’ll probably all laugh when you see my “excel montecarlo” estimates of biaes based on 10 sets of “pseudo-data” generated results. But it will at least let me know which things deserve more detailed investigations. Ten is often enough to see if a hypothetical problem is so small we don’t need to look at it, or so large one could never ever figure out the correct result using the data at hand.
With regard to things Arthur is asking about the limitations of 125 years per se, this is a real open issue.
Arthur Smith May 7th, 2008 at 12:01 pm
Hi Lucia - actually, I just started doing the same fourier analysis process with the RSS data (first pass was HADCRU) and there’s *NO* 1-year peak in that, but there are clear 3.6 and 9-year peaks at exactly the same positions as in the HADCRU data. So I suspect there’s something in the Hadley data that’s skewing things in a seasonal fashion (improper weighting of the land stations?) that’s not there in reality… or maybe it should be there and RSS is missing it? Anyway, I want to look through the other datasets first to see how stable these patterns are.