Guest Post by Willis Eschenbach
After I published my previous post, “An Observational Estimate of Climate Sensitivity“, a number of people objected that I was just looking at the average annual cycle. On a time scale of decades, they said, things are very different, and the climate sensitivity is much larger. So I decided to repeat my analysis without using the annual averages that I used in my last post. Figure 1 shows that result for the Northern Hemisphere (NH) and the Southern Hemisphere (SH):
Figure 1. Temperatures calculated using solely the variations in solar input (net solar energy after albedo reflections). The observations are so well matched by the calculations that you cannot see the lines showing the observations, because they are hidden by the lines showing the calculations. The two hemispheres have different time constants (tau) and climate sensitivities (lambda). For the NH, the time constant is 1.9 months, and the climate sensitivity is 0.30°C for a doubling of CO2. The corresponding figures for the SH are 2.4 months and 0.14°C for a doubling of CO2.
I did this using the same lagged model as in my previous post, but applied to the actual data rather than the averages. Please see that post and the associated spreadsheet for the calculation details. Now, there are a number of interesting things about this graph.
First, despite the nay-sayers, the climate sensitivities I used in my previous post do an excellent job of calculating the temperature changes over a decade and a half. Over the period of record the NH temperature rose by 0.4°C, and the model calculated that quite exactly. In the SH, there was almost no rise at all, and the model calculated that very accurately as well.
Second, the sun plus the albedo were all that were necessary to make these calculations. I did not use aerosols, volcanic forcing, methane, CO2, black carbon, aerosol indirect effect, land use, snow and ice albedo, or any of the other things that the modelers claim to rule the temperature. Sunlight and albedo seem to be necessary and sufficient variables to explain the temperature changes over that time period.
Third, the greenhouse gases are generally considered to be “well-mixed”, so a variety of explanations have been put forward to explain the differences in hemispherical temperature trends … when in fact, the albedo and the sun explain the different trends very well.
Fourth, there is no statistically significant trend in the residuals (calculated minus observations) for either the NH or the SH.
Fifth, I have been saying for many years now that the climate responds to disturbances and changes in the forcing by counteracting them. For example, I have held that the effect of volcanoes on the climate is wildly overestimated in the climate models, because the albedo changes to balance things back out.
We are fortunate in that this dataset encompasses one of the largest volcanic eruptions in modern times, that of Pinatubo … can you pick it out in the record shown in Figure 1? I can’t, and I say that the reason is that the clouds respond immediately to such a disturbance in a thermostatic fashion.
Sixth, if there were actually a longer time constant (tau), or a larger climate sensitivity (lambda) over decade-long periods, then it would show up in the NH residuals but not the SH residuals. This is because there is a trend in the NH and basically no trend in the SH. But the calculations using the given time constants and sensitivities were able to capture both hemispheres very accurately. The RMS error of the residuals is only a couple tenths of a degree.
OK, folks, there it is, tear it apart … but please remember that this is science, and that the game is to attack the science, not the person doing the science.
Also, note that it is meaningless to say my results are a “joke” or are “nonsense”. The results fit the observations extremely well. If you don’t like that, well, you need to find, identify, and point out the errors in my data, my logic, or my mathematics.
All the best,
w.
PS—I’ve been told many times, as though it settled the argument, that nobody has ever produced a model that explains the temperature rise without including anthropogenic contributions from CO2 and the like … well, the model above explains a 0.5°C/decade rise in the ’80s and ’90s, the very rise people are worried about, without any anthropogenic contribution at all.
[UPDATE: My thanks to Stephen Rasey who alertly noted below that my calculation of the trend was being thrown off slightly by end-point effects. I have corrected the graphic and related references to the trend. It makes no difference to the calculations or my conclusions. -w.]
[UPDATE: My thanks to Paul_K, who pointed out that my formula was slightly wrong. I was using
∆T(k) = λ ∆F(k)/τ + ∆T(k-1) * exp(-1 / τ)
∆T(k) = λ ∆F(k)(1 – exp(-1/ τ)) + ∆T(k-1) * exp(-1 / τ)
The result of the error is that I have underestimated the sensitivity slightly, while everything else remains the same. Instead of the sensitivities for the SH and the NH being 0.04°C per W/m2 and 0.08°C per W/m2 respectively, the correct sensitivities should have been 0.05°C per W/m2 and 0.10°C per W/m2.
-w.]
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charlie says:
June 1, 2012 at 3:24 am
Thanks, charlie. Yes, the volcanic eruptions are supposed to cool the earth by increasing the albedo.
But the data shows no such spike in the albedo after the eruption. This means that when the eruption happens and drives up the albedo, the albedo elsewhere on the planet must be reducing to compensate. Otherwise, we’d see the spike in the albedo and the corresponding temperature drop. Since we see neither, the climate must be responding to the eruption by a general lowering of the albedo. This makes sense, since in general the albedo decreases when temperature goes down.
w.
willis at 12:53: As you can see, there’s not much difference in the size of the residuals whether you use all, just the first half, or just the second half for the training.
Thanks for that.
RomanM says:
June 1, 2012 at 5:45 am
A most fascinating post, RomanM, many thanks for that.
w.
The solar magnetic flux operates the gate (magnetosphere) which controls the amount of GCR flux which modulates cloud cover. A giant MOSFET.
“since in general the albedo decreases when temperature goes down.”
Does it ?
Cloudiness decreased during the late 20th century warming and is now on the increase again:
http://wattsupwiththat.com/2007/10/17/earths-albedo-tells-a-interesting-story/
“This means that when the eruption happens and drives up the albedo, the albedo elsewhere on the planet must be reducing to compensate.”
Most likely warmed air resulting directly or indirectly from the eruption descends elsewhere and the adiabatic warming in the descending column reduces cloudiness there to offset the increased cloudiness caused by the eruption or its products.
joeldshore says:
June 1, 2012 at 6:38 am
Thanks, Joel. As I showed above, if I increase the time constant to 8 months the fit to the trend becomes very poor. So contrary to your claim, the trend does in fact provide a strong constraint on the model.
If you have temperature and albedo data for e.g. the northern hemisphere on an hourly basis, I’d be glad to use it to test the model. I don’t have the data, and don’t know where to get it, but if you do I’m more than happy to give it a shot. I doubt if it will work at that resolution … but then neither does the time constant of the CCSM3 climate model, which is on the order of 2 years from memory.
Finally, you keep talking about the “ACTUAL KNOWN” sensitivity of the climate models … but I can emulate the climate models with extremely good accuracy, with or without correcting for their illusions about volcanoes, using a much, much lower sensitivity than what you call the “ACTUAL KNOWN” sensitivity of the models.
Why the difference? I haven’t a clue, but it doesn’t give me much faith in the “ACTUAL KNOWN” sensitivity that seems to be neither actual nor known, but only claimed by the modelers. In fact, I don’t have a clue exactly how they are calculating their ACTUAL KNOWN sensitivity … and I would guess that you don’t either. Oh, I know in general, temperature change divided by forcing in some sense, but their results don’t agree with my actual calculations using their actual forcings and actual resulting temperature outputs. Perhaps you believe things simply because some modeler claims that they are true … me, not so much.
Joel, it appears that you don’t believe my results regarding emulating the climate models, but you cannot find any flaw in them. As a result, before making further claims about the ACTUAL KNOWN sensitivity of the models, I would encourage you to use a simple lagged model to calculate the sensitivity for yourself. See if you get the ACTUAL KNOWN sensitivity, or some other number …
w.
Michael J says:
June 1, 2012 at 8:44 am
I have no interest in further discussion with him. He went out of his way to be insulting, snide and dismissive. I said he could apologize or the discussion is over. He refused to apologize. I have not even read any of his successive comments. End of story.
w.
Phil. says:
June 1, 2012 at 8:52 am
The sensitivity for a doubling of CO2 in this analysis is about 0.3°/doubling. The sensitivity found by analyzing the climate models is about 1.1°C/doubling.
w.
Matthew R Marler says:
June 1, 2012 at 9:48 am
Thanks, Matthew. In the earlier thread, you said:
In this formulation, you have:
a = λ/ τ
b = exp(-1/ τ)
I don’t see why you’d want to do that. As it stands, lambda is the sensitivity and tau is the time constant. If you combine them in the form you suggest, what advantage do you gain? When you do that, you just have to unscramble them to extract the time constant and the sensitivity. I don’t get the point. What am I missing?
w.
@Stephen Fisher Wilde
Are you sure global albedo is the right metric?
(…or are you just attempting simplified narrative?)
For example, what is the effect of cloud cover in the summer polar-day (around-the-clock low-angle sunshine) vs. in the winter polar-night (around-the-clock darkness) vs. at the equator — etc.?
Do you assume spatial uniformity of cloud cover impact?
If the effect you claim exists, it will be:
a) imprinted on Earth rotation data via the Law of Conservation of Angular Momentum.
b) detectable via careful hierarchical application of Central Limit Theorem.
The signature I’ve seen in Earth rotation & global wind data relates to poleward tropical sea surface temperature gradients. (Bill Illis has volunteered related illustrations in past WUWT discussions. Also see the work of Jean Dickey at NASA JPL.)
Regards.
Those discussing “time constant” may wish to read:
Scafetta N., 2008. Comment on `Heat capacity, time constant, and sensitivity of Earth’s climate system’ by Schwartz. Journal of Geophysical Research 113, D15104. DOI: 10.1029/2007JD009586.
Willis:
Please do not be upset by Telford. All his posts demonstrate he is not acting in good faith, and there is no purpose in trying to guess why he is acting as he is.
Others are criticising your model in a variety of ways in genuine attempt to falsify it. Be assured that your work really is sufficiently interesting to warrant such attention. And be flattered that it attracts so much constructive criticism.
Richard
Willis: I don’t get the point.
Since any strictly monotonic function can replace exp(-1/ τ), there is no reason to think of τ as a time constant; it’s merely a fitted parameter to make b = exp(-1/ τ), and a = λ/ τ where a and b are the coefficient in a standard vector linear autoregressive model. You could have b=3^τ and a=sqrt(τ),
Why would you want to do this? there is no principled reason to prefer one pair of invertible equations to another, subject to the constraint that if you search hard enough you can find some reparameterizations where the estimation procedure is unstable, and those you would prefer to avoid.
The estimate for τ has no meaning other than it is the estimate that gives the best fit with this model. It’s not “months” or “years” or anything like that.
This is a really great topic. It may have even prompted me to dust off my old Quantum text book from an Upper Division Physics course back in the day. 😉
Paul Vaughan asked:
“Are you sure global albedo is the right metric?
(…or are you just attempting simplified narrative?)”
Since albedo either increases or decreases (never remaining the same for long) the right metric is the netted out result of all factors influencing albedo globally.
If the right observations are recorded accurately enough over a long enough time I am sure that the relationships I describe will become apparent and widely accepted.
Since I first promulgated such ideas there have been numeroius papers which appear supportive and many contributors here and elsewhere have been setting out similar if less complete formulations.
A few years ago my propositions were ‘way out there’. Now, not so much.
Matthew R Marler says:
June 1, 2012 at 2:05 pm
Matthew, the standard form for exponential decay over time is exp(-t/tau), where “t” is the elapsed time. Tau in this case is the time constant, which in fact is the “e-folding time”, or the time it takes for the amount to decay to 1/e. In other words, when t = tau, it resolves to exp(-1), which is 1/e.
In this particular instance, I’m only using it at time t=1, because this is a simple model. However, the amount “tau” actually is a time constant, the e-folding time, in whatever units of time you are working in. In my case, that’s months.
w.
richardscourtney says on June 1, 2012 at 8:36 am
“There is no “ACTUAL KNOWN sensitivity”.
Each climate model uses a different value of climate sensitivity.
Willis has assessed reality so a climate model can be tested against Willis result.”
Some simple questions: If there is no actual known sensitivity then why is Mr. Eschenbach projecting his ‘real world’ assessment into the future? That doesn’t make any sense. Besides CO2 is still increasing and if Mr. Eschenbach is already claiming a 3°C/century trend for the Northern Hemisphere I would not want to know what the trend will be when CO2 has doubled. That’s gonna be catastrophic for the Northern Hemisphere.
How would you establish sensitivity when CO2 is still increasing? Even if CO2 will stabilize in the atmosphere next year (for example) can we be sure that the warming stops immediately or is there still some more warming in the pipeline (what some well respected climate scientists claim) when climatic conditions turn to warming again?
What Mr. Eschenbach has done is making a climatic sensitivity assessment of some real world data in the early phases of CO2 increase in a “Cold” Earth.
Robbie:
At June 1, 2012 at 3:38 pm you say to me:
I answer each of your questions as best I can because they are addressed to me.
You ask
He is NOT “projecting his ‘real world’ assessment into the future“ and he said he is not at June 1, 2012 at 1:31 am where he wrote:
You ask
Clearly, you have not read what he wrote. His model implies that atmospheric CO2 concentration is irrelevant. He wrote;
You ask
Willis’ model is a determination of climate “sensitivity when CO2 is still increasing”.
You ask
If you accept the implication of Willis model then atmospheric CO2 concentration is not relevant so your questions are misplaced.
You ask
No. What Mr. Eschenbach has done is to assess climatic sensitivity of the Earth which exists.
Now, let me ask you some questions.
Why did you not read the words of Willis Eschenbach which answer your questions?
And
Why have you asked me these questions and not asked them of Willis Eschenbach when it is his work and not mine?
Richard
Please re-read his post. Willis isn’t talking about 0.3°/C per decade, but 0.3°/C per doubling of CO2. If he is correct, I can live with that.
richardscourtney says on June 1, 2012 at 4:14 pm
“Why did you not read the words of Willis Eschenbach which answer your questions?
And
Why have you asked me these questions and not asked them of Willis Eschenbach when it is his work and not mine?”
First question: Just read under Figure 1: “For the NH, the time constant is 1.9 months, and the climate sensitivity is 0.30°C for a doubling of CO2. The corresponding figures for the SH are 2.4 months and 0.14°C for a doubling of CO2.”
A doubling of CO2! That hasn’t happened yet. So yes he is projecting his assessment into the future. Mr. Eschenbach is clearly claiming something about CO2 sensitivity. Besides he hasn’t responded to me yet.
Your second question: I was responding to your statement about no actual known sensitivity.
D. J. Hawkins says:
June 1, 2012 at 4:59 pm
“Please re-read his post. Willis isn’t talking about 0.3°/C per decade, but 0.3°/C per doubling of CO2. If he is correct, I can live with that.”
Have you seen Figure 1 closely and what it reads underneath? It is claiming a 0.3°C/decade trend for the NH.
Mr. Eschenbach is wrong if he means a 0.3°C per doubling of CO2. It means a negative feedback (probably due to water vapor – what else?) of more than 75%. And that is 100% wrong. It isn’t happening now and it won’t happen in the future.
I’ve explained that here: http://wattsupwiththat.com/2012/05/29/an-observational-estimate-of-climate-sensitivity/
Robbie says:
June 1, 2012 at 3:38 pm
Robbie, I’m not following you. I’ve shown results from 1984-1997 inclusive … where am I projecting anything into the future? I see that you also say:
The measurement “for a doubling of CO2” is not projecting into the future. It is merely a way of measuring climate sensitivity. It can be measured in °C for each additional W/m2 of forcing. More generally, it is measured in °C for each doubling of CO2, which is said to result in 3.7 W/m2 of addition forcing. So “per doubling of CO2” means nothing about the future, it is just a way to measure climate sensitivity that merely means “per 3.7 W/m2 of additional forcing.”
Thanks,
w.
oops, I wrote: A change in forcing has about 90% of its total effect during the month of the change in forcing (the 90% approximation is from your spreadsheet, showing the decay of the effect in subsequent months.)
Rereading the spreadsheet, I see that was wrong.
Willis wrote: Matthew, the standard form for exponential decay over time is exp(-t/tau),
I appreciate that. but since t is held constant, the functional form of the function of tau is irrelevant, and as I wrote any pair of invertible transforms is equivalent to the linear vector autoregressive model.
Robbie says:
June 1, 2012 at 5:24 pm
First, I’m just reporting my results. I see that you don’t like them, and I see that you think if you say that very loudly and with great vehemence, it will make you right … unfortunately, your passion is not relevant.
In the other thread you refer to, you gave the standard explanation, which is that water vapor will be the dominant feedback, and it is strongly positive. Me, I think that the dominant feedback is clouds and thunderstorms, and they are strongly negative.
Now, what I’ve done above is provide this funny thing called “evidence supporting my claim”. You have provided merely an explanation and a strong re-statement of your claim.
If you don’t like my evidence, restating your claims over and over won’t change anything. You need to either find holes in my logic, math, data, or procedures, or find evidence that supports your claims. Please be clear than results from global climate models are not evidence …
My best to you in your search for evidence to bolster your claims,
w.
Matthew R Marler says:
June 1, 2012 at 5:51 pm
Yes, but your claim is that tau is NOT a time constant. You said:
… so are you now agreeing with me that in fact it is a time constant?
I use lambda and tau, Matthew, because in fact they are the sensitivity and the time constant. You can replace them with “a” and “b”, as you point out, where a = lambda/tau and b=e-1/tau … but then you just have to reverse the replacement to extract the sensitivity and the time constant. I don’t get why you’d want to do that. What’s the advantage?
w.