Guest Post by Willis Eschenbach
This is an extension of the ideas I laid out as the Thunderstorm Thermostat Hypothesis on WUWT. For those who have not read it, I’ll wait here while you go there and read it … (dum de dum de dum) … (makes himself a cup of coffee) … OK, welcome back. Onwards.
The hypothesis in that paper is that clouds and thunderstorms, particularly in the tropics, control the earth’s temperature. In that paper, I showed that a falsifiable prediction of greater increase in clouds in the Eastern Pacific was supported by the satellite data. I got to thinking a couple of days ago about what other kinds of falsifiable predictions would flow from that hypothesis. I realized that one thing that should be true if my hypothesis were correct is that the climate sensitivity should be very low in the tropics.
I also figured out how I could calculate that sensitivity, by using the change in incoming solar energy (insolation) between summer and winter. The daily average top of atmosphere (TOA) insolation is shown in Figure 1.
Figure 1. Daily TOA insolation by latitude and day of the year. Phi (Ī¦) is the Latitude, and theta (Ī) is the day of the year expressed as an angle from zero to 360. Insolation is expressed in watts per square metre. SOURCE.
(As a side note, one thing that isĀ notĀ generally recognized is that the poles during summer get the highest daily average insolation of anywhere on earth. This is because, although they don’t get a lot of insolation even during the summer, they are getting it for 24 hours a day. This makes their daily average insolation much higher than other areas. But I digress …)
Now, the “climate sensitivity” is the relationship between an increase in what is called the “forcing” (the energy that heats the earth, in watts per square metre of earth surface) and the temperature of the earth in degrees Celsius. This is generally expressed as the amount of heating that would result from the forcing increase due to a doubling of CO2. A doubling of CO2 is estimated by the IPCC to increase the TOA forcing by 3.7 watts per metre squared (W/m2). The IPCC claims that the climate sensitivity is on the order of 3Ā°C per doubling of CO2, with an error band from 2Ā°C to 4.5Ā°C.
My insight was that I could compare the winter insolation with the summer insolation. From that I could calculate how much the solar forcing increased from winter to summer. Then I could compare that with the change in temperature from winter to summer, and that would give me the climate sensitivity for each latitude band.
My new falsifiable predictions from my Thunderstorm Thermostat Hypothesis were as follows:
1 The climate sensitivity would be less near the equator than near the poles. This is because the almost-daily afternoon emergence of cumulus and thunderstorms is primarily a tropical phenomenon (although it also occurs in some temperate regions).
2 The sensitivity would be less in latitude bands which are mostly ocean. This is for three reasons. The first is because the ocean warms more slowly than the land, so a change in forcing will heat the land more. The second reason is that the presence of water reduces the effect of increasing forcing, due to energy going into evaporation rather than temperature change. Finally, where there is surface water more clouds and thunderstorms can form more easily.
3 Due to the temperature damping effect of the thunderstorms as explained in my Thunderstorm Thermostat Hypothesis, as well as the increase in cloud albedo from increasing temperatures, the climate sensitivity would be much, much lower than the canonical IPCC climate sensitivity of 3Ā°C from a doubling of CO2.
4 Given the stability of the earth’s climate, the sensitivity would be quite small, with a global average not far from zero.
So those were my predictions. Figure 2 shows my results:
Figure 2. Climate sensitivity by latitude, in 20Ā° bands. Blue bars show the sensitivity in each band. Yellow lines show the standard error in the measurement.
Note that all of my predictions based on my hypothesis have been confirmed. The sensitivity is greatest at the poles. The areas with the most ocean have lower sensitivity than the areas with lots of land. The sensitivity is much smaller than the IPCC value. And finally, the global average is not far from zero.
DISCUSSION
While my results are far below the canonical IPCC values, they are not without precedent in the scientific literature. In CO2-induced global warming: a skepticās view of potential climate change, Ā Sherwood Idso gives the results of eight “natural experiments”. These are measurements of changes in temperature and corresponding forcing in various areas of the earth’s surface. The results of his experiments was a sensitivity of 0.3Ā°C per doubling. This is still larger than my result of 0.05Ā°C per doubling, but is much smaller than the IPCC results.
Kerr et al. argued that Idso’s results were incorrect because they failed to allow for the time that it takes the ocean to warm, viz:
A major failing, they say, is the omission of the ocean from Idso’s natural experiments,Ā as he calls them. Those experiments extend over only a few months, while the surface layer of the ocean requires 6 to 8 years to respond significantly to a change in radiation.
I have always found this argument to be specious, for several reasons:
1 The only part of the ocean that is interacting with the atmosphere is the surface skin layer. The temperature of the lower layers is immaterial, as the evaporation, conduction and radiation from the ocean to the atmosphere are solely dependent on the skin layer.
2 The skin layer of the ocean, as well as the top ten metres or so of the ocean, responds quite quickly to increased forcing. It is much warmer in the summer than in the winter. More significantly, it is much warmer in the day than in the night, and in the afternoon than in the morning. It can heat and cool quite rapidly.
3 Heat does not mix downwards in the ocean very well. Warmer water rises to the surface, and cooler water sinks into the depths until it reaches a layer of equal temperature. As a result, waiting a while will not increase the warmth in the lower levels by much.
As a result, I would say that the difference between a year-long experiment such as the one I have done, and a six-year experiment, would be small. Perhaps it might as much as double my climate sensitivity values for the areas that are mostly ocean, or even triple them … but that makes no difference. Even tripled, the average global climate sensitivity would still be only on the order of 0.15Ā°C per CO2 doubling, which is very, very small.
So, those are my results. I hold that they are derivable from my hypothesis that clouds and thunderstorms keep the earth’s temperature within a very narrow level. And I say that these results strongly support my hypothesis. Clouds, thunderstorms, and likely other as-yet unrecognized mechanisms hold the climate sensitivity to a value very near zero. And a corollary of that is that a doubling of CO2 would make a change in global temperature that is so small as to be unmeasurable.
In the Northern Hemisphere, for example, the hemispheric average temperature change winter to summer is about 5Ā°C. This five degree change in temperature results from a winter to summer forcing change of no less than 155 watts/metre squared … and we’re supposed to worry about a forcing change of 3.7 W/m2 from aĀ doubling of CO2???
The Southern Hemisphere shows the IPCC claim to be even more ridiculous. There, a winter to summer change in forcing of 182 W/m2 leads to a 2Ā°C change in temperature … and we’re supposed to believe that a 3.7 W/m2 change in forcing will cause a 3Ā° change in temperature? Even if my results were off by a factor of three, that’s still a cruel joke.
We can see the effects of water vapour rising but could CO2 also rise in the same way?
Very interesting. You should even be able to make quantifiable predictions for rising CO2 levels with your theory, Willis.
For those who might be interested in seeing Willis’s tropical thunderstorms in action, I recommend a visit to the Typhoon Watch site http://agora.ex.nii.ac.jp/digital-typhoon/index.html.en.
This site, maintained in Japan, compiles daily images into mpeg and wmv files for each month as far back as 1979. Recent observations are available in 120 hr and 240 hr packages. The view is of the western Pacific and east Asia, from pole to pole, centred on the equator just north of Papua New Guinea and provides particularly good impressions of the growth and development of storms in the tropical zone.
Eschenbach: Figure 2 shows my results
Willis, what are you showing?
The chart states: climate sensitivity
Nowhere here or in your other post do you provide a formula for that.
If we take the standard definition
climate sensitivity = change in Radiative Forcing / change in Temperature
I guessing (?) from your wiki insolation chart, you are calculating dRF as the change in daily incoming solar insolation and dividing by dT to calculate a climate sensitivity? Aggregated monthly? Seasonly? If this is roughly correct, what temperature series are you using?
I would really like to understand what you did, but you have included no discussion of the methods or equations used. If the description is too hard, could you provide the code instead?
Thanks
What Willis has not addressed is the fact in some captive environments there are no thunderstorms or atmospheric electrical phenomena at all. None. These are artificial environments never-the-less in which some people exist. Giving rise to the need for a wholly new set of analytical criterion.
Bah: Inverted the formula!
climate sensitivity = change in Temperature / change in Radiative Forcing
It’s a very interesting hypothesis. I must admit, I am not convinced at present, but I am open to persuasion on it.
The area where I would need more evidence is the claim that change from one season to the next is the same (for purposes of measuring sensitivity) as the change from one decade to the next. It does seem to me that some accumulation of heat is possible, or there could be other long-term factors which are not included in seasonal comparisons. However, you could of course be correct.
Willis,
You clearly have the wrong answer. You have not employed a multi-gazillion dollar super-computer, and you have not needed representatives of nearly 200 countries to fly all the way across the world to talk about it.
So you see, there is no way anyone can give your work any credence at all.
Good article. I must read it again to digest. But I can hear the responses now, “not peer-reviewed”
AAAYYYUP!!
Interesting approach Willis. Would the sensitivity be lower yet if the source information was over estimated. The reason I ask is that your source for the thermal/latitude/time graph has a PV map of the US. I have a PV system, and get an average of 4.2 KW/day (exactly what the system is spec’ed to) where the map says I should get 5.5-6KW. In other words, the color of upper Michigan should be in western Colorado. I don’t know what to think of the source data. I always thought PVs would be a great way to look at insolation changes.
Map here: http://en.wikipedia.org/wiki/File:Us_pv_annual_may2004.jpg
Good work Willis, nothing like a simple direct analysis to understand a physical problem. I guess we won’t die after all.
This reminds me of an analysis a friend of mine and his postdoc did of a problem in plasma physics. They came up with an analytic solution by hand that they could solve on a pocket calculator. They absolutely crushed a team of ten physicists at Livermore that used a supercomputer to model the problem. It just goes to show that supercomputers make you stupid, or is it vice versa?
On the ‘SOURCE’ page, under the US map it says “US annual average solar energy received by a latitude tilt photovoltaic cell (modeled).”
Isn’t what you are saying similar to LC09’s estimation of climate sensitivity from the 20-20 tropics, also derives?
Hmmm- a very interesting hypothesis- the planet has its own way of dealing with extra heat. Now, how much is due to man, or nature. This appears to be nature taking care of itself…
The main problem with climate models is that they don’t model cloud cover accurately. All IPCC models use parameters which show clouds as a positive feedback. This is the result of some extraordinary group think.
If you make a 5% change in cloud cover using a radiative transfer model like RRTMG, you see a large change in temperature. GCMs mishandle clouds, which is why most of them produce nonsensically large climate sensitivities.
Hmm.. what do you define as North and Southern hemisphere? Some sort of average latitude from 45 to 90 degrees? Also, how do you compute the winter to summer change? I like your concept, but need some maths, as I suspect it is not trivial to sum an “average” over latitudes and seasons.
RIGHT ON! Several years ago, I did a similar, though much more crude, exercise, looking at winter to summer temperatures for various individual locations. For example, for Phoenix, the radiation goes from 483 Wm-2 in summer to 275 in winter, for a change of 208. Annual temperature change is 22.5. “Sensitivity” is, therefore, 0.1 For Guam, there’s only 62 watts difference and only a 1.5 C change in temperature, so the “sensitivity” is 0.024 (all 30-year averages from: http://rredc.nrel.gov/solar/old_data/nsrdb/redbook/sum2/state.html )
Chaco Canyon.
What they knew, when they knew it and how they used the knowing.
Who are the late ones to a way of knowing?
http://www.exploration.edu/chaco/
Willis,
I really do not think you can derive anything much from this at all.
For example over the oceans the thermal admittance for seasonal changes is far greater than the thermal admittance into space (the part you are trying to characterise).
You need to subtract the oceanic admittance from the total value that you obatin in order to find the admittance into space.
I do not know what you have taken into consideration. Things like that in the equatorial band, you have a pronounced six month cylcle. This faster cycle makes the oceanic admittance even higher.
In general there are good reasons why the amplitude of the seasonal cycle varies from as little a 1C to as much as 30C, between open equatorial ocean and deeply landlocked areas and it is due in the major part to the the thermal admittance of the surface.
Alex
Willis, I think this is common knowledge to alot of people gifted with skills of observation and common sense. Areas of the earth where summer / winter and day / night change are largests are the most sensitive and vise versa, statistics are not needed to support such a claim, its the elephant in the room! A single day would also be a good example of this, it also has the highest change in temperature and greatest change in incoming radiation.
The equator enjoys moderate temperatures with little variation annually and daily due to the high humidity (evapotranspiration) and action of storms / clouds / rainfall. The monsoon belt for example sits over the area of the earth that recives the most energy and here the negative feedback is strongest. In theory, this belt should increase in size to any warming to counter act it. I also have also observed that increased humidity leads to reduced distance of observation (distance objects are whiter), could this change the surface albedo? It seems effects how fast I sunburn and the colour of the sky looking up!
Deserts experiance large diurnal temperature change, some deserts I have experianced can go from -5 at night to 30 or greater in the day – this is apparently due to the lack of water and very low humidity (also long distances of observation and quikcer sun burn as a result). Water vapour helps moderate the temperature as does the sea, hence less diurnal range in coastal zones.
It is a shame that climate scientists miss the elephant in the room and ignore empirical observation and data and opt for some kind of pseudo science based on models and unjustified assumptions over real data. I think you should progress this train of thought as it is something that needs to be brought to the attention of those that think 3.8w/m2 causes large warming in the scale of natural climate variation!
However, they will argue its about extra energy acumulating in the sea causing increased humidity etc… and feedbacks etc… and you need to do your test over 30 years or its just weather!
ouch
http://www.exploratorium.edu/chaco/
Simple, elegant–two hallmarks of an excellent proof.
It’s an interesting theory and I think it deserves more research, but unless I’ve got it wrong, there appears to be one significant issue that it doesn’t explain:
What caused the MWP and LIA?
The theory shows a short term governor. The feedback and control is in days, if not hours. What is the long term system that caused the MWP and LIA? This theory would indicate that they shouldn’t have happened, because the mechanism would mitigate any variation due to TSI fluctuations. What caused this mechanism to be less effective during the MWP and more effective during the LIA?
You can tell by the way that I’ve asked the questions that I’m half-convinced already, but there are definitely things it doesn’t explain.
Ron Broberg (16:38:25) :
Eschenbach: Figure 2 shows my results
Willis, what are you showing?
The chart states: climate sensitivity
Nowhere here or in your other post do you provide a formula for that.
I may have misinterpreted the post but you seem to have answered your own question with your formula
climate sensitivity = change in Temperature / change in Radiative Forcing
plugging in T (summer – winter for a particular band) and R (summer – winter for that band)
Where R is in the range Willis suggests (150/180) there is a lot of latitude in the value of T. So much so that I would doubt that it matters much how T is sourced so long as it is legitimate.
(still digesting the post but he will no doubt be along later to clarify things)
Steve Goddard (17:12:27) :
The main problem with climate models is that they donāt model cloud cover accurately.
Or convection generally in my view.
“Alexander Harvey (17:38:31) :
Willis
…….”
And this is the big difference that makes me trust the skeptic sites so much more then The Team sites. We actually have OPEN discussions of peoples theories, not everyone singing in the same choir! I think the old timers used to call this science……
What does the OLR data series look like when compared to your analysis? Might that be a way to verify? Also, you can “calculate” downward LW radiation as another way to check your data.
Memphis Commercial Appeal: Al Gore, Dolly Parton to receive honorary degrees from Tennessee
Meeting at UT Martin Friday, the UT Board of Trustees voted to award Gore an Honorary Doctor of Laws and Humane Letters in Ecology and Evolutionary Biology. The honorary degree will be presented to Gore, also a former U.S. senator from Tennessee, at the spring commencement of the UTK College of Arts and Sciences on May 14.
He will be the featured speaker at the ceremony, addressing graduates and their families.
The board’s vote comes eight months after Republicans in the state Senate voted down a resolution urging the state to raise money from private donors to erect statues on the State Capitol grounds in honor of Gore and Tennessee’s only other Nobel Peace Prize winner, Cordell Hull, President Roosevelt’s secretary of State during World War II.
“Vice President Gore’s career has been marked by visionary leadership, and his work has quite literally changed our planet for the better,” UTK Chancellor Jimmy G. Cheek said. ..
http://www.commercialappeal.com/news/2010/feb/26/al-gore-dolly-parton-receive-honorary-degrees-tenn/
what a cheek!
Chattanooga Times Free Press: Tennessee: Gore degree debated
Trustee Crawford Gallimore sparked the debate when he asked if the board should be recognizing a public figure aligned with controversial research..
āShould we be giving honorary degrees to people with controversial advocacies,ā asked Mr. Gallimore. āWe have given people (honorary degrees) with a professional life in politics, but those were retired or at the state of senior statesmen. Let us not forget our responsibility of proceeding with exceeding care.ā
Other trustees were quick to defend the recognition and Mr. Goreās record.
āI think we need to be realistic about this,ā said Doug Horne, a UT trustee. āAl has been a leader. Al Gore won the popular vote. He gave up the presidency. I canāt think of any better statesmanship than that.
āEvery leader has to learn to live with opposition. That certainly applies to the presidentā¦ I meanā¦ sorryā¦ vice president Gore,ā said Mr. Horne, the room erupting in laughter.
UT board vice chair Jim Murphy said UT should be awarding more honorary degrees and stirring debate on politically hot button issues, especially in an area like climate change where UT and Oak Ridge National Lab has pumped millions of dollars into research.
āWe need to promote our image and our expertise in that area, and nothing will do that more than having someone like Mr. Gore come and do a commencement speech,ā Mr. Murphy said. āI donāt view this an endorsement of a particular position. One of the things universities are for is encouraging disagreement and dialog. If there are, in fact, people out there that are doing scientific research that disagree with the vice president, I welcome them to come to Oak Ridge and research with us. We need to be careful of pulling us to far under the shell.ā..
http://www.timesfreepress.com/news/2010/feb/26/gore-degree-debated/?breakingnews
Here’s a look using the same idea of seasonal temperature changes to estimate sensitivities, with standard climate models:
http://www.cgd.ucar.edu/ccr/knutti/papers/knutti06jc.pdf
Can you be more specific?
No charge separation mechanism – no visible display/exhibition – what?
.
.
Holey moley! You just found the missing link!
You might remember Beenstock’s paper (http://wattsupwiththat.com/2010/02/14/new-paper-on/), or perhaps my writeup (http://www.2bc3.com/warming.html) where we see that the temperature rise seems to be related to the rate of increase of CO2, not the absolute amount of CO2. Neither of us were aware of your earlier paper showing the earth’s temperature governor, and so we could come up with no explanation for the results we found.
It appears that you have provided us with an explanation! The CO2 is produced in the mid latitudes, and takes a while to get to the tropics where it is better tied to the governor. Uniformly distributed CO2 will have no effect, but it can have an effect if it isn’t distributed uniformly, which it sure as heck isn’t (for example http://www.youtube.com/watch?v=6-bhzGvB8Lo. The time-constant is the equilibration time, which appears to be less than a year.
Nothing short of beautiful…
Ron Broberg (16:38:25)
No code, it was done in Excel. What I did was calculate the change in temperature from winter to summer in each latitude band, and divide it by the change in forcing winter to summer in that latitude band.
This gives the climate sensitivity for that band.
‘Paul Linsay (16:59:26) :
It just goes to show that supercomputers make you stupid, or is it vice versa?’
It just goes to show you, a computer is a tool, only as good as it’s operator.
Hence, Reid Bryson’s famous quote
Willis,
Why is the error bar of the Artic (90N to 70N) so much smaller than the Antartic (70S to 90S) error bar?
Is this related to amount of data or quality of data?
John
Steve Keohane (16:56:04)
If I understand you correctly, you’ve misunderstood the insolation chart. It is not insolation shown as latitude versus longitude. It is shown as latitude versus the day of the year. If I have misunderstood you, let me know.
This is precisely the kind of material that should be prepared for peer review. Arguments like this need to be brought to the attention of experts, and subjected to their critiques.
This analysis seems to reasonably explain the overall limited level range part of climate variation. If the Solar magnetic field interaction on cloud formation, tilt of the Earth axis , and the location and variation in elevation of land masses (and their effect on large ocean circulation, and wind patterns) are included, I think you are getting closer to the full main causes of variation. There is a likely tipping effect when some of the above interact in the correct way to produce the glacial/interglacial cycles, and the smaller sub-cycles. The main question I would have is how we got into and out of icebox Earth. I do suspect volcanic CO2 accumulation may have had a part in the exit event. However, when large extents of liquid oceans became open, the argument seems to be reasonable that water vapor/clouds took over.
EdB (17:12:50)
To get the results, both the Northern and Southern hemispheres need to be “area averaged”. This is because there is a much smaller area in a latitude band near the poles than in the same width band near the equator. This is done by using a weighted average, where the weighting is the cosine of the latitude of the mid-point of the band.
I have used March – August (spring and summer of the meteorological year) as summer and September – February (fall and winter of the meteorological year) as winter. You can use April – September and November – March instead, the results are very similar.
Alexander Harvey (17:38:31)
What I am interested in is the sensitivity, which is defined as change in temperature divided by change in forcing. Thermal admittance affects that, which is why the ocean is less sensitive than the land. But the formula for sensitivity doesn’t contain a thermal admittance term. In fact there are many things that affect the sensitivity, with the main one (in my opinion) being the thunderstorms and clouds. But those don’t change the calculation, which is āT/āF, the change in temperature divided by the change in forcing. In other words, the difference in thermal admittance can explain the sensitivity, but it doesn’t change the sensitivity.
I don’t understand what “pronounced six month cycle” you are talking about in the tropics. But again, those are things that might explain why the sensitivity is so low … but they don’t mean that the sensitivity is incorrect.
“R E Daw (16:13:28) :
We can see the effects of water vapour rising but could CO2 also rise in the same way?”
Oxygen, argon and nitrogen are all more abundant in the atmosphere than CO2 and all, including CO2, are heavier than water vapor.
CO2 — 12+(2*16) = 44
O2 — 2*16 = 32
Ar — = 40
N2 — 2*14 = 28
H2O — (2*1)+16 = 18
Thus water vapour is lighter than air and triggers convection currents that lead to clouds. http://en.wikipedia.org/wiki/Water_vapor
Graeme W (17:55:14)
I raised several possible explanations for that in the section entitled “Gradual Equilibrium Variation and Drift”.
One additional prediction from the thermostat paper, which I suspect should be verifiable, is that there should be distinctly more radiation from the right-hand side of the thunderstorm band if it does in fact pull hot air from the surface and dump it into the upper atmosphere.
As for pulling CO2 up too – so what? Its hot CO2 which can now radiate all the heat it has captured into space. In fact, it it really is such an efficient hoarder of heat as we have been told, it should increase the efficiency of this “heat pump”.
Willis- you say “This is still larger than my result of 0.05Ā°C per doubling, …”
Are you sure this is per doubling, i.e. an additional 3.7 W/m^2, or is it per W/m^2? Inspired by JAE and Idso’s paper a few years ago, and having an ongoing interest in solar PV, I did this same calculation for various spots in the contiguous US, both coastal and inland, and came up with 0.05 C/W/m^2 for coastal, and about 0.1 C/W/m^2 for inland locations. The average of 0.075 C/W/m^2 would give about 0.3 C for a CO2 doubling.
Excellent discussion.
I seemed to recall similar methods being presented by the late John Daly on his “Still Waiting for Greenhouse” website way back in the 1990’s. A quick search revealed that my memory is not totally shot. Here is the link:
http://www.john-daly.com/miniwarm.htm
There just doesn’t seem to be a way of calculating a high climate sensitivity to increasing CO2 using the actual Earth as a starting point. It appears to be only possible if you ignore the Earth and any ‘real’ data in favor of computer models with built in, massive positive feedbacks.
All of these methods may be over simplified. There may be some factors not accounted for in the calculations, but there is no physical way for these methods to be off by an order of magnitude or more, which would be required for the IPCC to be correct.
Pamela Gray (18:04:14)
Don’t know … another thing to check. I’ll have to see what I can find in the way of ULR and DLR data. I suspect, however, that the answer is in the clouds and thunderstorms, and because of the localized nature of both those phenomena, average values don’t help much.
http://www-ramanathan.ucsd.edu/FCMTheRadiativeForcingDuetoCloudsandWaterVapor.pdf
The above paper calculates the net effect of cloud cover as a -18 Watts per square meter of cloud cover.
That is a LOSS to outer space, making clouds a NET COOLING effect.
Willis, figure you can put that into your work!
Good luck.
Max
This all seems very unscientific to me. Somebody puts out a hypothesis complete with the data and methods used and asks others to comment and critique the conclusion without even the hint of a government grant.
This is dangerous stuff.
“The climate sensitivity would be less near the equator than near the poles. This is because the almost-daily afternoon emergence of cumulus and thunderstorms is primarily a tropical phenomenon (although it also occurs in some temperate regions).”
It’s well known that changes in climate tend to be much smaller near the equator than the poles.
If we consider, say, the Eocene, mean global temperatures were about 8 degrees warmer than the present, but polar temperatures were something like 30 degrees warmer and equatorial temperatures were similar to modern (some old analyses actually claimed they were actually five degrees colder than present equatorial temperatures, and of course this had to be adjusted-now the high estimates are slightly warmer than the present and the low two degrees colder.).
Mesa (18:14:02)
That study appears to do what I have done (except with models instead of observations), but is actually doing something quite different.
They take the net of all of the various changes, changes in solar and changes in clouds and changes in clouds and changes in water vapour and in ice coverage and all the rest, and they call that the forcing. Then they compare that to the temperature change, and get the IPCC canonical number of about 3Ā°C for a doubling of CO2.
But the truth is that the change in the insolation is the only true change in forcing. The rest are all responses to the change in insolation. Thus, the changes in say the clouds tend to reduce the effect of the insolation change. But they are not an independent change, they are a negative feedback to the independent change in the insolation. Thus, they should not be counted as part of the forcing.
Because when we go from winter to summer, the driver of the change is the change in the sun. The rest are feedbacks, either negative or positive, in response to the change in insolation. Winter turns to summer because of changes in the sun, not because of changes in the clouds.
As a result, their models are not measuring what they claim to be measuring.
Graeme W (17:55:14)
“Itās an interesting theory and I think it deserves more research, but unless Iāve got it wrong, there appears to be one significant issue that it doesnāt explain:
What caused the MWP and LIA?”
Heck, what causes the ice ages? I don’t see how this question has any bearing on the concept. You can still have cosmic rays, Milankovich cycles, etc.
I’m sorry, but I didn’t find any of them convincing.
You suggested geography, which may be used to explain the ice ages, but geological time frames (required for geography changes) are too long for the MWP and LIA.
Ocean current and wind pattern changes are definitely a possibility, but then we have to explain why they’re changing. If we can show that they did change and at appropriate times, then that’s another step towards supporting your theory. But we’d need to find such evidence first. If you like, that’s another possible falsifiable aspect of that part of the theory.
Albedo changes would need to be justified by some evidence that it actually occurred. You’ve suggested aerosols like dust, etc. (presumably from volcanoes, etc.) but wouldn’t the system autocorrect to a large degree after those have disappeared from the atmosphere? We’re talking about decades, if not a century or more of time, after all. Whatever causes the change has to persist for that period if it’s to be a reasonable hypothesis.
I didn’t like your suggestion of solar variation, because the entire basis of your theory appears to be around less dependency on variation from the Sun.
Please keep thinking about this, because it sounds like a very promising theory. It’ll just be a matter of seeing how well it stands up to the stones (or thunderstorms) thrown at it.
Hello Willis,
Interesting post. I note only that much, if not most, of the heat lost from the hemisphere that is in winter is transported from the tropics. So the local temperature change is not an isolated response to lower solar heating in winer. Were it possible to actually isolate a region (say everything above the arctic circle, or everything between 40 and 50 degrees) to see its independent seasonal response, then your analysis would be better able to identify the sensitivity. But since such regional isolation is not possible, I think it is difficult to draw solid conclusions about overall sensitivity from seasonal temperature changes.
I agree that moist convection (including thunder storms of course) in the tropics does a lot of cooling, but I do not known how to relate that to climate sensitivity. The discrepancy between the GCM predicted temperature profiles and the measured temperature profiles of the troposphere seems to indicate that the CGM’s underestimate heat transport due to moist convection. Another (perhaps less well known) discrepancy between measurements and the models is the quantity of tropical rainfall: the GCM’s consistently underestimate tropical evaporation and tropical rainfall (which are both good proxies for moist convective heat transport/surface cooling), and so seem to underestimate heat transport via moist convection.
Max Hugoson (19:02:30)
Again, all of the changes in clouds are not drivers of the change from winter to summer. They are responses, also known as feedbacks. As such, they don’t enter into the calculation of sensitivity.
chris y (18:51:48) : edit
Per doubling. It’s āT/āF * 3.7 W/m2 per doubling.
Phil M. (18:36:10)
You misunderstand the purpose of peer review. It is a recent invention, and is only designed to keep real junk from getting printed in a magazine that is designed to make money.
As such, it is only the most surface examination of the issues. I’ve gotten much more stringent reviews here on WUWT than I have gotten from peer reviewers (and less politicised attacks masquerading as reviews as well).
Graeme W (19:19:40) : edit
OK, then you’ll have to propose your own. As I said, I don’t know the answer to the question, and have only posted possibilities. Another one might be increasing aerosols darkening the color of the clouds. Your turn.
But if that’s the only problem with my thunderstorm thermostat hypothesis, I’m a happy man …
Steve Fitzpatrick (19:23:54)
As you point out, all of these are net changes. Part of the reason that the tropics don’t warm much is that they export excess heat. Part of the reason the poles do warm is that they receive the exported heat. However, that does not stop us from noting that for the Southern Hemisphere as a whole, a 188 W/m2 increase in forcing leads to a 2Ā°C temperature increase …
The models are definitely known to underestimate the tropics-to-pole energy transport, although I don’t have the citation to hand. However, again I say that none of that negates my conclusion. When the forcing goes up in the Southern Hemisphere by 188 W/m2, the surface and atmospheric conditions rearrange themselves such that the surface air temperature only increases by 2Ā°C. That is a very low sensitivity.
[quote Willis Eschenbach (18:25:33) : ]
No code, it was done in Excel.
[/quote]
I don’t suppose this is available online? I’d really like to see it.
BTW, nice post and very much in line with how view things.
A few questions about this:
(1.) it is my understanding that the outgoing heat flux, watts per square meter is proportional to the fourth power of the absolute temperature of the radiating surface — is this detail embedded in your calculations? The same is true of the incoming flux except that I believe it is attenuated by a relative distance (from the sun) squared.
(2.) Are you basing your calculations on what might be called the static radiative R-factor of the atmosphere at the surface or at the top of the convection column or some mean effective combination of the two? I believe, on average, the tropopause is above 75 percent of the atmosphere in general and perhaps 90 percent at the tropics so there would be less absorption to outer space from these levels
Interesting proposition Willis.
I also have a strong suspicion thermal convection and cloud development is a very strong thermostat effect.
Sometimes this sort of back of the envelope analysis is more powerful than sophisticated modeling because it is based on the real physics even if we do not understand all the physics we know the results are real.
It would be interesting to see if the current models can in any way replicate this seasonal, latitude band behavior. If not — the model is wrong period.
Larry
I very much like the thermostat hypothesis and the extension here. I’ve been reading WattsUpWithThat and about six books on the weather over the last two years and I have finally put together a conceptual frame on how the climate could respond to greenhouse gasses.
From the weather books I found the well known but somewhat surprising information that the coldest part of the atmosphere is at the tropopause over the equator. The tropopause is at 55,000 feet and -80Ā°C over the tropics, and is at 25,000 feet and -55Ā°C over the poles. This is because the warm moist air over the tropics rises to much higher altitudes before the latent heat of water condensation is used up. The lapse rate of -6.5Ā°C/km continues to a higher altitude. Adding heat and moisture to the tropics should therefore cause the tropopause to rise. Thunderstorms should increase per the Thermostat Hypothesis.
I find some of the descriptions on how CO2 should cause warming naive. In the troposphere CO2 does not simply absorb upward traveling IR from the ground and re-emit it in all directions and return some of the energy to the surface. Long before an excited CO2 molecule will decay, it will collide with other molecules in the atmosphere. CO2 will only emit IR in compliance with the temperature at that altitude. The IR that the CO2 absorbs heats that entire level of the atmosphere. Because the atmosphere at that level is a little warmer, not quite as much water vapor will condense until it gets to a higher altitude so the tropopause should rise.
From Miskolcki’s paper we have the claim that the atmosphere will maintain a constant optical density even as CO2 rises. He claims that water vapor in the atmosphere will decrease as CO2 rises to maintain this constant optical density. This has been remarkably confirmed by a drop in the humidity at the 300 mb level and above over the last 50 years.
Now consider the stratosphere. In the stratosphere the temperature rises with altitude so there is little convection and heat transport is dominated by radiation. The stratosphere must be quite dry as it is in contact with the very cold tropopause so the dew point should equal the temperature at the tropopause. If the tropopause rises, it becomes colder and the stratosphere should become dryer. This could be the mechanism by which Miskolcki’s constant optical density works. The rise in IR absorption in the CO2 bands is made up for by a drop in the IR water bands in the stratosphere. If this is right, the optical density in the troposphere should increase with greenhouse gasses and the optical density only remains constant through the whole depth of the atmosphere.
Finally we have the recent paper by Michael Beenstock1 and Yaniv Reingewertz1
http://wattsupwiththat.com/2010/02/14/new-paper-on/
They analyzed the temperature and CO2 records and found that the rates of change did not match and CO2 did not cause warming in the historical record. However they did find that a change in the CO2 could have caused a short term change in the temperature although once the CO2 stabilized the temperature returned to the stating point. This would be consistent with increased CO2 causing the tropopause to rise as it would take some time for the dew point of the stratosphere to drop as there is no convection to drive a rapid change as the tropopause cools.
The climate changes we have seen seem to be well explained by the changes in the sun and amplification of these changes by cosmic rays per Svensmark and “The Chilling Stars”
LOL! Yes, from my very limited viewpoint, that’s my only problem with your theory. It is, as I understand it, widely accepted that clouds affect climate, and your theory provides a mechanism that explains how this regulates global temperatures (driven from the tropics).
As for my own theories, I know I don’t know enough to suggest anything sensible. Of your suggestions, the ocean current one seems worth investigating further. Is there any proxies that could be used to get a feel for major ocean currents over the last 1000 years? I’m not asking for much….
If I was pushed to suggest other possibilities, I’d look at the effectiveness of your theoretical process in non-tropical regions. If it’s less effective, then that may explain why a long term variation such as the MWP and LIA could exist (the ‘correction’ takes longer or isn’t as efficient). That would also counter any arguments about the MWP/LIA not being global in nature — it would suggest that they may more attributes of mid-range latitudes, and not the tropics. I don’t know enough to know if that’s a reasonable hypothesis or is already contradicted by historical evidence.
Willis,
Nice going.
Seems to me you’ve nailed the order of magnitude at least. Anybody quibbling with your numbers is going to make not a lot of difference to your conclusion
I think this was summed up at JunkScience by the short statement “summer ends”.
That alone rules out runaway effects.
You would think that the people doing the GCMs would do some simple calculations like this to see if the hugely complex models make any physical sense at all. I think think you’ve shown that they don’t and it will be hard to overturn your hypothesis as there doesn’t seem to be any hidden reservoir for the heat from doubling CO2.
magicjava (20:03:39)
Well, saying it’s not “user friendly” would not cover the situation, even “user unfriendly” doesn’t touch it … is there such a thing as “user aggressive”?
However, I’ll post the temperature and the insolation data. The insolation data was digitized from the chart in the head post, so it isn’t totally accurate. If anyone has access to the actual data shown in the head post let me know. Hang on … OK, thanks for waiting, it’s here.
(To digitize the graphic in the head post, I first traced over each section in Vectorworks, my architectural graphics application. I added a database that held the mid-value of the insolation for each section. Then I wrote a program to sample it every degree in both directions, and average it in 5×5Ā° gridcells. Of course, in some areas all of the gridcell was in a single region, so subtle variations were not caught … but it doesn’t affect the results much.)
Willis,
Great, thought provoking work as always. Especially the comments regarding forcing, I always thought it was somewhat insane to consider anything other than the sun as a forcing. Glad to see I’m not alone.
If you’re ever in my neck of the woods I owe you a beer – that goes for Anthony and the mod squad too.
Spector (20:11:14) : edit
My calculations do not include any of the changes that come from increased insolation (changes in evaporation, thunderstorm numbers, outgoing long-wave radiation, changes in dust, etc.). These are the details of how the earth responds to hold the temperature down, but do not figure into the sensitivity.
I am basing it on two things. 1) Top of atmosphere (TOA) changes in insolation, and 2) surface air temperature (HadCRUT3 absolute temperatures, available here, under Data for Downloading, Absolute in the middle of the page. As above, the height of the tropopause is one of the variables in how the earth responds to the increase in insolation, so I do not base my calculations on that.
NickB. (20:38:04)
Where’s your neck of the woods?
O/T – apologies:
1 March: UK Times: Ben Webster: Green fuels cause more harm than fossil fuels, according to report
Using fossil fuel in vehicles is better for the environment than so-called green fuels made from crops, according to a government study seen by The Times…
http://www.timesonline.co.uk/tol/news/environment/article7044708.ece
26 Feb: WaPo: Sunil Sharan: The green jobs myth
For the purpose of creating jobs, then, a “clean-energy economy” will not offer a panacea. This does not necessarily mean that America should not become green to alleviate climate change, to kick its addiction to foreign oil or to use energy sources more efficiently. But those who take great pains to tout the “job-creation potential” of the green space might just end up inducing labor pains all around.
(The writer, a director of the Smart Grid Initiative at GE from 2008 to 2009, has worked in the clean-energy industry for a decade)
http://www.washingtonpost.com/wp-dyn/content/article/2010/02/25/AR2010022503945.html
Willis Eschenbach (18:32:21) Willis, what I am getting at is the data from the ‘SOURCE’, has the chart I linked to above. It is apparently modeled solar radiation shown as expected photovoltaic (PV) output, and models the output here in western Colorado to be 5.5-6.0 KW average daily output annually. I happen to know from my system the reality is 4.2 KW, and that matches expectations of the installer. The model is 36.9Ī% over reality. Therefore, I have to wonder on what assumptions all of the materials shown that wiki page are based. Secondly, if they do over estimate the solar energy in their models, does that lower your estimate of climate sensitivity?
I realize your chart is latitude vs. time-of-year, and I’m looking at the average for my latitude for any given day, ie. the average daily value of a horizontal line drawn across your chart for a given latitude. I wondered if their values are from the same modeling as the PV chart and are also too high.
have you considered that the particulates or aerosols might be introduced, not into the Earth’s atmosphere, but between the sun and the Earth’s orbit, as a feature of the solar system ingesting massive clouds of interstellar dust and fine ices, that decrease the total solar energy reaching the Earth for a longer time. Given that it takes the solar wind more time to flush out the intruding interstellar clouds, thus giving the fairly rapid onset and gradual release from the glacial epochs?
Why does it always have to be a local problem?
Mr. Eschenbach:
From: Thermostat Hypothesis
Good paper. I admire the smooth flow of your words and initially concur with the points you made, to say absolutely may take some time for it all to sink in.
Would you like to know of a one percent or so āas-yet unrecognized mechanismā that makes your conjecture of high-altitude radiation between the tropics and poles even more concrete? My guess is few would ever know of it and I have never heard it mentioned in climate science to date. You may accept it or reject it as you see fit, just want to make sure you read it.
TA (16:47:03)
Yes, accumulation of heat and other long term changes are indeed possible. But in the Southern Hemisphere, a change of 188 W/m2 in insolation (forcing) leads to a change of 2Ā°C in temperature.
The IPCC, on the other hand, says that a change of 2.5 W/m2 of forcing leads to a change of 2Ā°C in temperature …
So even if my numbers are out by an order of magnitude, which seems quite unlikely, the IPCC numbers are still way off. Even assuming that my numbers are wrong by an order of magnitude, you’d still need CO2 to rise to 3,900 ppmv (from their current 385 ppmv) to result in a 2Ā°C temperature change …
Willis Eschenbach — OK, then youāll have to propose your own. As I said, I donāt know the answer to the question, and have only posted possibilities.
Comet or asteroid strike in a more remote part of the world. Happens all the time; almost impossible to detect 300-800 years hence. A recent strike I read about was near Java or Borneo or something; had it hit a city, it would have wiped it out. Anyway, hit the right spot with enough force, and changes in ocean currents, slight increase in volcanism due to hitting a fault etc. could have a great deal of effect not necessarily localised for quite some time. There were how many years of cooling due to Krakatoa alone?
I’m not sure you need to postulate *anything* to explain the LIA.
Willis, you might like to check out some work by Stephen Schwartz related to this topic. I think some of his wokrs supports your model.
Schwartz et al. Influence of anthropogenic aerosol on cloud optical depth and albedo PNAS, 2002 v. 99: 4, 1789
Schwartz S. E. Heat capacity, time constant, and sensitivity of Earth’s climate system. J. Geophys. Res.,5 112, D24S05 (2007).
Stephen E. Schwartz, Response to Comments on āHeat capacity, time constant, and sensitivity of Earth’s climate systemā, Atmospheric Science Division, Brookhaven National Laboratory. URL: http://www.ecd.bnl.gov/steve/pubs.html#top
Seen this from Gore (scare tactics again)
http://www.nytimes.com/2010/02/28/opinion/28gore.html?pagewanted=1
We Canāt Wish Away Climate Change
February 27, 2010
Willis thank you for a post that even makes an untrained high school graduate (barely) understand what you are trying to say. This is why I read this blog because for the most part people here are patient with us (the unwashed masses) and that makes me feel that maybe there is hope that those in the ivory towers will get locked in and never be able to come out again.
paulID (21:25:36) :
And it’s people like you that make it clear to me that the time spent here is not a waste. Thanks for just commenting, yeah Willis’s paper stimulates the mind doesn’t it.
Sorry Willis,
That is not an appropriate formula for sensitivity . You need to calculate the amount of radiation out due to the change in temperature, so you must subtract the amount abosrbed, or you get nonsense.
You have chosen to investigate a cyclic forcing so you must pay attention to admittances. You simply must or you get bizarre results. The admittance into the ocean is in parallel to and much larger than the admittance into space. Unless you subtract it from the total admittance you are off by between one and two orders of magnitude over the oceans, and smaller but significant amount over the land masses due to thermal inertia alone.
Also the motion of the atmosphere drags low seasonal amplitudes from the ocean to the land. Only in a few remote landlocked spots is this minimised. Try your calculations for the areas with the highest seasonal range, like parts of Mongolia and Estern Siberia where the amplitudes are around and greater than +/- 30C. Even there you must take account of admittance. For even in such places there is a seasonal lag between peak insolation and peak temperature.
Regarding the tropics, if you are on the equator there are two peaks in insolation, spring and autumn, summer and winter have lower insolation, look at your graphic. This effect diminishes as one approaches mid latitudes and then reverses towards the poles.
There is a sizable six month component, and higher components, at the poles, think about it. The pattern of insolation is not exactly sinusoidal is it. This second and these higher order components are associated with higher admittances.
You have come up with some numbers but you do not seem to have allowed for surface admittance at any point and it is a dominating factor, along with the transference of thermal mass, and associated heat, by atmospheric motion and ocean currents.
These motions tend to reduce the seasonal range over the continental land masses as they pick up low thermal amplitudes, in the case of the atmosphere as it passes over the oceans, and in the case of the oceans as the gyres pass through their low amplitude legs, and they transfer these low amplitudes to the land and the higher latitude oceans respectively. On the way they pick up the higher continental amplitude which they dump back into the oceans in the case of the atmosphere, or transfer towards the equator in the case of the gyres. Plus of course there are the meridonal fluxes.
I see that you note three reasons why you think the ocean is not a major player in this and I am afraid that you are misled. The seasonal cyclic flux component into the oceans is far greater than the seasonal flux component into space. You can see that the temperature amplitude is low over the oceans, but why think that this is due to an ultra high thermal admittance into space when you have a huge thermal admittance all around you in the ocean itself.
Alex
I don’t think it is reasonable to do these calculations per hemisphere. In the tropics, solar insolation varies very little and neither does temperature. At higher latitudes, solar insolation varies a lot and so does temperature.
Some parts of Siberia vary by 70-80C between winter and summer. The oceans don’t vary very much because of their large heat capacity. Three months of summer isn’t long enough to make significant variations in deep ocean temperature.
There are a lot of different factors being munged to together in the sensitivity calculation. We know that changes in solar output of one percent have a significant impact on temperature, so it is not unreasonable to expect that climate is much more sensitive than what is being represented in these calculations.
need CO2 to rise to 3,900 ppmv (from their current 385 ppmv) to result in a 2Ā°C temperature change
This may indeed be accurate!
TX for the post.
Tim L
Willis. You say “But the truth is that the change in the insolation is the only true change in forcing. The rest are all responses to the change in insolation. Thus, the changes in say the clouds tend to reduce the effect of the insolation change. But they are not an independent change, they are a negative feedback to the independent change in the insolation. Thus, they should not be counted as part of the forcing.”
This allows you to ascribe all of the observed temperature change to the change in TOA insolation.
There is a danger here, and it is one that the IPCC fell prey to (rather willingly!). When looking at possible causes of temperature change other than CO2, the IPCC either eliminated them (eg. Svensmark’s theory was dismissed because it didn’t match data after ?1995), or included them at an unjustifiably low level (eg. solar variation, where they ignored empirical data that the solar cycle had a larger effect than could be explained by insolation changes), or counted them as a CO2 feedback (eg. water vapour and clouds), Consequently, they felt able to claim that virtually all of the observed temperature change was caused by CO2, and coded their computer models accordingly (look for “constrained by observation” in the IPCC Report).
Thus the IPCC have no provision for there being any significant influence on temperature that is independent of CO2.
Coming back to your paper : By assuming that all factors such as clouds, water vapour and ice coverage are insolation feedbacks, you have allowed yourself to ascribe all observed temperature changes to insolation changes. If some of these factors are in fact independent of insolation to any significant extent, then you have an invalid assumption.
For example, if some changes in cloud cover are not a response to insolation changes, but are a response to something else (Galactic Cosmic Rays for example), then you cannot assume that all observed temperature changes are caused by insolation changes, In this particular example, there is a strong relationship between GCRs and solar activity, so you may just be OK, but is the GCR relationship specifically to insolation or is it to a different solar activity?
Incidentally, you could I think eliminate this as a possible problem by conducting your study over a period of many years, rather than just one (“a year-long experiment such as the one I have done”).
—–
There is another question which I haven’t thought through : Your calculations of sensitivity appear to be based on short timescales (less than 1 year). The IPCC works on “equilibrium climate sensitivity”, and if I understand them correctly it may take several decades for equilibrium to be reached. Are you comparing like with like?
In other words, when you use the temperature change over a season, is it representative of the temperature change that would result if that season’s insolation forcing were to continue for several decades?
Graeme W (17:55:14) – you said:
“Itās an interesting theory and I think it deserves more research, but unless Iāve got it wrong, there appears to be one significant issue that it doesnāt explain:
What caused the MWP and LIA?”
There is a theory, currently under study at CERN (“Cloud” experiment) that changing magnetic flux between sun and earth, changes the rate of cosmic rays entering the atmosphere, which in turn changes the rate of cloud cover development.
If correct, that explains why the climate changes over time.
Physicists such as Ken McKracken, are making great strides in understanding these mechanisms.
Ken believes current trends suggest that it is quite likely that the earth is entering a significantly cooler period.
I should have added that Willis’ theory meshes very well with the above.
The IPCC do not claim 3 C from 3.7 W/m2. The 3C is after feedbacks. 3.7 from CO2 + 3.7 from increased water vapor + 3.7 from slow feedbacks, roughly.
Anyway, all you have shown is that it takes a lot of energy to increase the temperature of water (and even more to melt ice and snow).
Willis, I suspect you might be interested in this analysis which also suggests a much lower climate sensitivity:
http://www.palisad.com/co2/eb/eb.html
Hi Willis,
I have two objections:
1) A hemisphere is an open system with two interfaces, one to the sky which is of interest for calculating sensitivity but the other interface is to the opposite hemisphere and is neglected in your discussion. A lot of heat flows across the equator each six months.
2) The “summer thermal solstice” (here at 35 degrees south in Sydney Aust) is 21 Jan, which is quite some time after the insolation maximum. This and the winter “thermal solstice” are the only times that insolation and heat loss are at equilibrium. (neglecting heat flow to other hemisphere in point 1) So you can’t use the whole summer temperature average in your calculation but should restrict it to the temp and insolation on the single date.
Willis, I just luuuuuurve your posts.
But I have a question. The geometry of insolation. Have you included a formula that calculates the integral of insolation throughout each day for each latitude, starting from a horizontal sun at dawn, rising to a higher sun at midday? Clearly, insolation is not just a multiple of length-of-day, and varies from low polar light to high tropical light; the loss due to low sun is most apparent at polar latitudes.
Thanks.
John Ritson (23:30:32) :
“So you canāt use the whole summer temperature average in your calculation but should restrict it to the temp and insolation on the single date.”
That wouldn’t help much.
“The Gulf Stream transports about 1.4 petawatts of heat, equivalent to 100 times the world energy demand”, to name one.
Willis, I think you’ve only calculated the climate sensitivity under the atmospheric conditions of that year. Changing conditions, for instance due to the heat accumulating in the ocean might give different results. It might be interesting to look at an El Nino year and a La Nina year and see what difference might occur with different conditions.
Hi Willis,
I have been looking at the frequency response of climate sensitivity, and the observations show evidence for a low pas filter response: i.e. low climate sensitivity for annual cycles and increasing climate sensitivity for longer cycles. IMHO the IPCC modeled estimates have a warm bias.
Below is a graph where observed and modeled climate sensitivities are plotted relative to logarithmic cycle period on the x-axis. The blue line was a first crude estimate.
http://members.casema.nl/errenwijlens/co2/Climate_sensitivity_period.gif
http://members.casema.nl/errenwijlens/co2/howmuch.htm
Willis
When the forcing goes up in the Southern Hemisphere by 188 W/m2, the surface and atmospheric conditions rearrange themselves such that the surface air temperature only increases by 2Ā°C.
Thanks for that one sentence summary of “(3×2’s) problem with CO2 as a primary driver of climate”. Wish I could have put it better myself.
Those bringing soot or whatever to the party really need to step back for a moment and look at the numbers. 1.4 billion cubic km of water wins every time.
is climate electric?
nice one willis
I have calculated 0.2 deg C for surface, mid-northern altitude bellow 50N. We have difference of ~20C between January and July and from the insolation chart, summer-winter difference in insolation is 350W/m2.
My objection is, the CO2 “forcing” is present all the time, while Sun insolation changes during the year. Had the polar summer last 10 years in a row, temperature would surely rise there, until some kind of balance would be restored? Also our mid-latitudes receive more sun energy in summer than tropics, but since it is just for a limited time (two months), we will not reach the tropic climate which would otherwise happen. The equilibrium can not establish itself.
Mike Jonas (22:53:47) :
There is another question which I havenāt thought through : Your calculations of sensitivity appear to be based on short timescales (less than 1 year). The IPCC works on āequilibrium climate sensitivityā, and if I understand them correctly it may take several decades for equilibrium to be reached. Are you comparing like with like?
In other words, when you use the temperature change over a season, is it representative of the temperature change that would result if that seasonās insolation forcing were to continue for several decades?
We are back to “heat in the pipeline”, something that nobody seems able to pinpoint convincingly.
“Lon Hocker (18:21:30) :
Holey moley! You just found the missing link!
You might remember Beenstockās paper (http://wattsupwiththat.com/2010/02/14/new-paper-on/), or perhaps my writeup (http://www.2bc3.com/warming.html) where we see that the temperature rise seems to be related to the rate of increase of CO2, not the absolute amount of CO2. Neither of us were aware of your earlier paper showing the earthās temperature governor, and so we could come up with no explanation for the results we found.”
I was aware of it all the time, that’s why i had no problems swallowing the solution by Beenstock and Reingewertz. Had i known you didn’t know i would have told you… i had read Willis’ hypothesis before.
Re: John Ritson (Feb 28 23:30), says
“A hemisphere is an open system with two interfaces, one to the sky which is of interest for calculating sensitivity but the other interface is to the opposite hemisphere and is neglected in your discussion. A lot of heat flows across the equator each six months.”
I’d like to know your source for this assertion. George White, in his post I linked to earlier (http://www.palisad.com/co2/eb/eb.html), says
“A common explanation for why hemispheric asymmetry doesn’t matter is that an energy flux flows between hemispheres to equalize the system. This is contradicted by examining ocean circulation currents and weather circulation patterns. The hemispheric specific flows in the oceans and atmosphere run parallel to each other at the equator. The satellite data show very little seasonal temperature variability across a 30Ā° slice of latitude centered on the equator. This is important because an energy flux must be accompanied by a proportional temperature differential. Thermodynamics tells us that energy flows from warm bodies to cold bodies. The warmest part of the Earth is the equator, which means that energy flows from the equator to the poles, but not across the equator, except due to some tropical weather systems and some minor coupling where Northern and Southern ocean currents run parallel to equatorial currents. This weak coupling is often considered part of the Thermohaline circulation. The result is that the 2 hemispheres are only weakly thermodynamically coupled and respond to change mostly independent of each other.”
Gary Palmgren (20:18:42) :
Your view equals mine.
It’s funny how much the AGW hypothesis blinds people in the warmistocracy; if we can see it they should be able to as well.
Long term insolation variations got a brief mention above.
Useful references on this are as follows:
Berger, A.; Loutre, M.F. 1991. Insolation values for the climate of the last 10 million years. Quaternary Science Reviews 10: 297-317.
Berger, A. 1992. Orbital Variations and Insolation Database. IGBP PAGES/World Data Centre-A for Paleoclimatology Data Contribution Series #92-007. NOAA/NGDC Paleoclimatology Program, Boulder, Co, USA.
These refs show the change in insolation at various latitudes each 1000 years going back 100’s of thousands of years.
I think Willis’ analysis is incorrect (or maybe I understood it wrong). I’m not sure if it is considering differences between average winter and summer temperatures and average irradiances, or if it is considering top temperature diferences vs top irradiance differences, but in any case it would be wrong because it doesn’t account for the fact that the maximum and minimum temperatures do not occur at the same time that the maximum and minimum irradiances, there is a lag.
In the NH, maximum irradiance happens by mid June but maximum temperatures happen in late July or early August, when irradiance is already quite lower than the maximum. It would be incorrect to claim that the maximum irradiance in June can only warm the NH to as much as it is in early August. No, the potential is greater. Had the irradiance stayed as it was in mid June, temperatures in August would have been certainly higher. But irradiance had been declining for a while.
The interesting point for the irradiance is the point when temperatures stop going up and start going down. At that point, you can claim that the solar irradiance’s potential for warming the climate has been fully achieved. If there was more warming in the pipeline for the existing solar forcing at that point, temperatures would keep going up, and if the temperature was too high, it would have started to go down earlier.
So I think the procedure should be: substract the temperature of the hotest minus the coldest average day of the year for each latitude band, and the average solar forcings that exist IN THOSE PRECISE DAYS. Then you divide them and you get the true sensitivity. It should give a higher value than calculated by Willis, although I think that it will remain extremely low compared to the IPCC calculations.
So Willis can show minimal sensitivity. I can do better – negative sensitivity to solar forcing. In Paris, insolation declines after mid-summer, but the temperature does not peak till August. Declining insolation gives higher temperature = negative sensitivity. QED
Alternatively, this may just indicate that the Willis’ analysis is flawed and that Kerr et al. are correct
This analysis assumes that only the ocean skin is warmed over the annual cycle. This is correct, but Willis makes the further assumption that this layer is always thin, perhaps ten metres or so. In reality, the “ocean skin”, the mixed layer, can be much thicker, often over a hundred metres thick – see the climatology published by de Boyer Montegut.
Thanks Willis and Anthony.
This latest offering from you, Willis, is, once again, a model of rationality and brilliant communication skills. Your ability to explain complex concepts simply, clearly and in an entertaining way set a benchmark for clarity. Your postings and the ideas they spin off are real food for thought.
Anthony, I feel enormously fortunate and grateful that I have access to all that you include in WUWT. The Blogosphere enriches itself and becomes more powerful exponentially with the passing of each day with the exchange of ideas such as these.
Willis,
A nice extension of your hypothesis which I agree with in general terms.
However I think you are in much the same position as Bob Tisdale with his ENSO work in that although I find all that both of you say to be highly persuasive and in accordance with observations it does leave the longer term term climate change scenario unaccounted for.
I have tried to work backwards from the energy in/energy out balance whereas you and Bob are working forwards from specific observed phenomena. In fact Svensmark’s work has the same characteristic as does that of many others.
I don’t see any essential inconsistency between the three of us since your work could mesh with Bob’s and mine with both of you.
Nevertheless we do have to get the two approaches from different directions to meet in the middle somehow and I think that the best way to do that is to
note the undoubted effect on rates of energy flow from sea to air to space that results from latitudinal shifts in the global air circulation systems.
Such a shift can be linked both to Bob’s ENSO phenomena and your tropical thermostat and to my emphasis on the changing speed of the global hydrological cycle which I contend is the true climate governor globally.
My favoured source of the variations in the rate of energy flow through the Earth system is the oceans rather than the sun, atmosphere or cosmic rays. More specifically I suspect variability in temperatures along the horizontal line of the thermohaline circulation. Such irregularities need not be large in order to produce large effects on the air above because water holds so much more energy than air.
However I have been unable to find adequate data on such matters so far. The thermohaline circulation is generally assumed to be very stable and thermally constant but since everything in nature varies I have my doubts. The MWP to LIA to modern warm period could well be reflected by subtle temperature variations along that circulation taking 1000 to 1500 years to complete a circuit. Can anyone rebut that for me ?
Willis, as ever your posts are illuminating. WRT the argument that the oceans and circulation currents are acting as short-term sinks dampening the observed sensitivity, surely this can be estimated or at least bounded by examining the lags between longest day and hottest day?
The sink reversal after the longest day should be symmetric to a first approximation to the flow leading up to the longest day. I’m no physicist but the magnitude should then be calculable?
Alexander Harvey (22:31:20)
I understand what you are saying. When energy hits the earths surface, it does not all go directly to warming of the surface. Depending on the admittance, it is partitioned. Some of it warms the surface, and some of it passes through the surface and goes to warm the substrate. Thus, if we have cyclical forcing, the change in the surface temperature of the solid is not proportional to the incoming forcing. This would seem to indicate that admissivity is an issue.
But if the system is at equilibrium, that excess heat in the substrate has to come out of the substrate. And when it does so, it has to warm the surrounding air, either by conduction or radiation. So overall, regardless of the emissivity, by the end of the cycle all of the incoming energy has to warm the surrounding air. And that is what we are measuring, surface air temperature.
Some of the warming of the air occurs directly, as a result of the direct warming of the skin surface. And the rest of the air warming occurs when the rest of the energy (the partitioned amount which warmed the substrate rather than the surface) comes back to the surface and then warms the air.
At least that’s how I see it, although I could well be wrong, wouldn’t be the first time. Fight my ignorance here, and explain why admittance makes a difference when we are only talking about surface air temperature. Regardless of the admittance, all of the incoming solar energy ends up warming the air, albeit with a slight delay for part of the energy. Although this will slightly decrease the peak temperatures, it won’t affect the average temperatures as long as the averaging period encompasses the peak. I don’t see how this will make the huge difference that you claim.
Many thanks for your participation,
w.
Fig. 1 in Mr. Eschenbach’s article is the theoretical daily-average solar insolation at the top of the atmosphere. Due to to the low solar elevation angle at a given polar area during the short time span around the summer solstice, insolation reaching sea level is much less than shown in Figure 1, due to the extra thickness of atmosphere existing in the path of the solar radiation, even though the polar region receives 24 hours of sunlight. This extra atmospheric thickness produces greater amounts of atmospheric absorption and scattering, resulting in substantially greater attenuation of the solar insolation at the poles during the corresponding summer solstice. I also note that Fig. 1 appears to have a couple of technical problems regarding the 500 and 550 watts per sq. meter shaded areas for positive values of Phi (Ī¦).
This 2-tiered figure, by William M. Connolley using HadCM3 data, depicts the annual mean solar insolation, and allows comparison between top of the atmosphere and at the earth’s surface. The observer will notice the substantial differences due to the atmosphere, especially at the polar regions.
http://en.wikipedia.org/wiki/File:Insolation.png.
This figure, by Robert A. Rohde, depicts the direct solar radiation spectrum (for a 90 degree solar elevation, at the zenith), for both at the top of the atmosphere (yellow), and at sea level (red). Notice the large and frequent H2O absorption bands in the infrared spectrum (750nm and greater wavelengths), dwarfing the CO2 absorption bands. The absorption bands shown are too short for earth long wave radiation (outgoing), thus mainly attenuate incoming solar radiation. Many persons viewing this graph for the first time will be surprised to learn that greenhouse gases (mainly H2O) also play a significant role in absorbing incoming sunlight in the shorter IR region (750 nm thru 2500 nm).
http://www.globalwarmingart.com/wiki/File:Solar_Spectrum_png
Hi Alex,
I don’t have a source, I just made it up to provoke discussion.
I can hit the paragraph you quoted over the boundary (out of the ballpark if you insist)
1) Willis is making a quantitative argument and that para has no numbers in it. If the author can put an upper bound in Joules per annum crossing the equator then you win the point, until then please try harder.
2) In summer ( I mean January) the hottest place is not the equator (how could it be, it’s not directly under the sun at that time), The hot spot is further south. So heat does flow north.
I bet is a “lot” too.
The point is how weakly coupled does “weakly coupled” really mean.
stevengoddard (22:34:35)
So do you also object to the IPCC calculating the climate sensitivity for the entire planet?
Interesting, so clouds and thunderstorms control the Earths temperature. The question is, what controls the clouds and thunderstorms??
Corbyn would say solar particles control thunderstorms.
Svensmark would say cosmic rays control the clouds.
Richard Telford (00:58:02)
Isn’t the ocean skin the top Imm which is 0.3C cooler than the ocean bulk below ?
Sunlight gets into the ocean bulk below to a depth of 100 metres or more depending on wavelength and water turbidity.
At the very top few microns of the ocean skin is the Knudsen layer where all the evaporative action takes place so that all downwelling IR (and more, thus the cooling of that 1mm) is converted to latent heat of evaporation.
Hi Willis,
I think this is a promising approach, but needs some further consideration on the absorption of energy by the ocean.
You said:
3 Heat does not mix downwards in the ocean very well. Warmer water rises to the surface, and cooler water sinks into the depths until it reaches a layer of equal temperature. As a result, waiting a while will not increase the warmth in the lower levels by much.
I did some calcs last year, verified by Leif Svalgaard, which show that the sea level rise attributable to temperature increase (thermal expansion of the ocean, the steric component) between 1993 and 2003 of around 5400Km^3 equates to a net increase in ocean heat content of @14×10^23J. This is equivalent to @4W/m^2 additional forcing, far greater than anything co2 can do and probably due to reduced cloud cover during active solar cycles 22 & 23.
This increase in temperature spread proportionally right down to the thermocline in a fairly linear manner from the bottom of the mixed surface layer. The thermocline in the tropics can be as little as 30m, but as much as 1200m in the temperate latitudes. Therefore, although it is counterintuitive to the warm water rises commonsense, energy must have been mixed downwards on at least a decadal scale. This is infact confirmed by the 0.15C rise in the average temperature of the top 700m of global ocean over the same time period.
People on the skeptical side are very resistant to this logical truth. I think it’s because they have an aversion to any conception which could admit of some ‘heat in the pipeline’. However, the point is that it is Solar derived heat, nothing to do with co2. The way to get past it is to simply consider where else the extra energy could go. It can only escape from the ocean at a rate the atmosphere permits: more energy out, more evaporation, more water vapour, more humidity, hotter atmosphere, less temperature differential between atmosphere and ocean – slower heat loss from ocean. If the excess energy from a hyperactive sun can’t escape upwards, it must get mixed downwards by tidal action and subducting currents near the poles.
My simple solar-ocean energy model which works using a TSI proxy (sunspot number) and a simple ocean heat content estimation tehnique (cumulative count of sunspot numbers above and below the ocean neutral value emirically determined from the change in TSI over the solar cycle compared to SST’s) shows that the heat content changes on multidecadal scales at least, possibly centennial.
This opens the way for a solar explanation for temperature variation on the longer timescale. In my view your brilliantly described thunderstorm mechanism is more about the redistribution of heat within the Earth-Ocean climate system than a planet wide thermostat. Your ideas, coupled with Stephen Wildes ideas about the equatorial-polar shifts of the jet streams (and thus Hadley Cell bondaries) could account for much of the intra terrestrial variation we see in the temperature records of individual countries relative to each other. Ferenc Mickolczi’s theory on the dynamic equilibrium of the atmosphere as a whole, and my ideas on amplified centennial solar variation modulaed by OHC might account for longer term variation of the global temperature.
Mike Jonas (22:53:47) : edit
… snip more on cosmic rays …
I am looking at changes in average temperature based on changes in average forcing. Thus, it is not really a “year-long experiment”, that’s a bit of a misnomer. It is not studying the evolution of the system over time.
āā
Well, for the system to come to total equilibrium, the temperature of the entire planet down to the core would have to change … so we’re not talking about total equilibration.
By looking at the lag between peak insolation and peak temperature (about a month), it appears that if the season’s insolation forcing were to continue at a constant value the majority of the equilibration would occur on the same timescale.
Willis Eschenbach
ā1 The only part of the ocean that is interacting with the atmosphere is the surface skin layer. The temperature of the lower layers is immaterial, as the evaporation, conduction and radiation from the ocean to the atmosphere are solely dependent on the skin layer.ā
This is an assumption leading to incorrect conclusion.
Temperature of the lower layers are the most crucial in the regions of heath release to the atmosphere.
http://www.windows.ucar.edu/earth/Water/images/thermohaline_circulation_conveyor_belt_big.gif
Warm waters of Arctic are at some depth due to higher salinity (specific gravity)
http://www.divediscover.whoi.edu/arctic/images/ArcticCurrents-labels.jpg
Arctic currents are the engine of the heat transport across the North Atlantic Ocean.
Just an addendum to my post at (02:14:54)
Willis’ thermostat may well operate at a planet wide level if the mechanism he descibes affects the rate of heat lost to space, which given the transport of energy up through the centre of the thunderstorm systems seems possible if the variation in storm intensity varies sufficiently on longer timescales. Could there be a hookup with Anthony’s posts on hurricane energy over the last 30 years here?
Relevant to the simple v complex thread, there is a story that Thomas Edison, towards the end of his career was given several bright young men to “help” him, which he did not really want. One day, the young men came to Edison and asked for something to do. Exasperated, he gave them a light bulb and asked them to determine it’s internal volume. The young men went away and laboured long with calipers, rulers, slide rules etc and eventually came back with an answer. Edison took one look and said, “Your at least 10% out”. He drilled a small hole in the bulb, poured in water until full and then poured it into a measuring cylinder. The young men were 10% out.
This is the difference between an “expert” and an “inpert”!
Oops. Grammatical error. Smacks head. “Your at least 10% out” should read “You’re at least 10% out”. Edison was American so may be he did misspell it!
Re: John Ritson (Mar 1 02:00),
“If the author can put an upper bound in Joules per annum crossing the equator then you win the point, until then please try harder.”
You are mixing your metaphors. Is this cricket, baseball or tennis?
If it’s cricket or baseball, I am batting and you are bowling/pitching. And you haven’t bowled the ball yet. You need to justify your assertion first.
El Ninjo, blocking high’s and the most negative AO since the 50’s show how irrelevant the Global temperature measurements really are and how insignificant the role of CO2 is.
http://icecap.us/images/uploads/AO.JPG From icecap.us
An analysis like this would be more persuasive and more thorough if it included a heat balance. Energy is conserved, temperature is not. This allows setting up a nice balance sheet. Most energy is in the form of heat. Some of it is in phase change.
Figuring the temperature response of the earth to an a change in energy inputs is like computing the heat capacity. And all the heat capacities of water and air are known. The capacity of land is probably available as well. The concept of “Sensitivity” sounds to me exactly like the physics concept of heat capacity. Is it not?
Willis,
. . . and to the memory of Jane Austen, who will probably forgive you : )
John
Willis,
Great theory but I think there is an additional factor which augments your hypothesis. In brief your suggestion is that increased heat trapped at the equatorial regions must result in increased storms/clouds/convection and so on that move heat upward in the atmosphere and outward toward the poles.
With that thought in mind, consider the absorption spectrum of all the āgreenhouseā gases combined which has a window of almost zero in the 10 to 12 micron range. Thereās a pretty good graphic from Wikipedia that shows this at
http://upload.wikimedia.org/wikipedia/commons/7/7c/Atmospheric_Transmission.png
This essentially defines the āsweet spotā for longwave to escape into space no matter what the concentration of CO2, water vapour, ozone and so on, as if it was an “open window”. Rough guesstimate (ie mine) is the sweet spot ranges from -35 to about +15 C. So, consider the implications of that to your original hypothesis which is that the earth regulator maintains a temperature of about plus or minus 3 degrees.
Since the tropics are already above the +15 C mark, they are in the āgreenhouse zoneā and trap heat. They then move heat toward the temperate zone and poles which are in the temperature range where longwave is not absorbed by GHG, ie below +15 C. Combine that with radiance rising proportional to T^4, and the efficiency with which excess heat would be radiated into space by the temperate and arctic zones would overwhelm even very large increases in forcing with only 2 or 3 degrees of temperature rise NO MATTER HOW MUCH CO2 AND WATER VAPOUR. The only way for forcing to break through that upper limit would be to inject so much heat so fast that it would drive most of the planet surface above the 15 C mark and “close the window”.
Going the other way, this same mechanism would define the low end as well. In a cooling cycle the amount of energy being pushed from tropics to poles would drop, causing the poles to cool down. As they drop in temperature, the coldest parts of the year start to hit into -35. As they do, the GHG āopen windowā starts to close, sending heat that used to be zipping out to space back to earth. The cooler the earth gets, the larger the area at the poles where the GHG window now is closing and retaining heat. Those ice sheats could only get so far before the additional heat being retained by the coldest parts of the planet would balance off the cooling mechanisms.
I think it no coincidence that I live in Winnipeg, a city known for cold winters, which features a -35 to -40 cold snap once or twice every winter, yet cities far to the north of Winnipeg get very little colder. Winnipeg is close to the border, so just above the 49th parallel. Hereās the COI graph of temps from the 80th parallel:
http://ocean.dmi.dk/arctic/meant80n.uk.php
As you can see, when temps start hitting downward to -35, the āopen windowā starts to close making it almost impossible to go more than another few degrees down because GHG’s start retaining heat. Winnipeg’s low temp extremes are very little different from low temp extremes 30 degrees latitude farther north. Just as you would need a stupendous amount of energy to jump the whole planet surface temp ABOVE the āopen windowā to get serious warming, you would need a stupendous amount of cooling to get the whole planet BELOW the āopen windowā.
It seems to me that the thermostat proposed by Willis is the mechanism by which heat is moved around the planet, more the ventilation system than the thermostat. That āopen windowā from 10 to 12 microns sets an upper limit that small amounts of forcing canāt get past, and a lower limit that starts retaining heat as soon as it cools down, keeping the range within very tight boundaries.
…a 3.7 W/m2 change in forcing will cause a 3Ā° change in temperature
.. and the missing words are “over the long term” (probably 30 – 50 years).
The point about the theory of AGW is that the summer/winter oscillation in forcing is entirely predictable and stable. Other than the solar and Milankovitch cycles there is no significant change in total insolation from year to year. Therefore the temperature of the atmosphere has had thousands of years to adjust to a totally regular and predictable rise and fall in energy inputs over the calendar year. Effectively the “burner” under the saucepan has been set.
The problem with increased CO2 in the atmosphere is that it changes this long-established balance of insolation (energy in) and radiation from the stratosphere (energy out) by not letting quite as much energy out of the atmosphere as previously. More energy is therefore “trapped” in the atmosphere. Somebody has put a lid on the saucepan!
What the climate models try and do is to determine what the effect of this extra trapped energy will be.
To be honest I have not a clue (although I have some suspicions), and I don’t reckon the modellers have the answer (yet) either – because of their poor understanding of the water vapour and cloud feedbacks both at low level and in the stratosphere.
However I think it is completely spurious to try and use the relationship of the normal seasonal changes in insolation with the air temperature as somehow analogous to a long term change in the radiative balance of the atmosphere. This whole paper is basically a red herring.
I am more and more coming round to the view that the only skeptic worth reading in the blogosphere is Roy Spencer. He seems to be the only one who is actually doing real science and is targeting his efforts on the big gaps in knowledge with one of the few tools that may actually be able to quantify these complex feedbacks on a global scale – the satellites.
Your theory is quite interesting but as far as i can tell it rests on the asumption that winter is a static situation and that summer is a static situation. If the summer heatflux was kept hypotheticaly constant for 10 years and the winter heaqtflux was kept hypotheticaly constant for 10 years you would get a much higher delta T and thus your sensitivity would go up.
In other words when you reach the maximum heatflux in the summer the temperature would continue to rise if the heatflux stayed that high and something similar would happen in the winter.
You have compensate for this somehow.
Another problem is thast the sensitivity is probably not linear as a function of forcing.
What is the third measure – the daily average insolation – is it Wm^-2?
Willis,
“When the forcing goes up in the Southern Hemisphere by 188 W/m2, the surface and atmospheric conditions rearrange themselves such that the surface air temperature only increases by 2Ā°C. That is a very low sensitivity.”
Sure, taken on its face, that suggests very low sensitivity. But there is nothing that says heat is not transported between hemispheres. There is a lot of heat accumulation/loss for the ocean with seasonal changes as well. Some heat in the southern hemisphere is certainly transported to the northern hemisphere in the northern winter and vice-versa in the southern winter, and a lot of heat is absorbed by the ocean in the summer that is released in the winter, which tends to minimize temperature shifts.
Don’t get me wrong Willis, I’m all for trying to use seasonal variation to make estimates of climate sensitivity, independent of climate models, but I think examination the regional temperature changes versus seasonal changes in solar flux will not generate a very accurate value. A more robust estimate could be done (I think) by examining as a heat balance the whole-earth seasonal budget: short wavelength in, short and long wavelength out, seasonal change in ocean heat (Argo) and surface temperatures.
First a clue, I went to the UT that isn’t about to hand multiple honorary diplomas to a failed divinity student.
I currently reside in the DFW area, and said free beer will come with a 100% Not Funded by Big Oil Guarantee (unless my checks for participaring on this blog ever show)
Cheers!
Vukcevic (02:47:48) :
Willis Eschenbach ……….. Warm waters of Arctic are at some depth due to higher salinity (specific gravity)”
http://www.whoi.edu/cms/images/halocline_18008_56197_56788.jpg
Willis,
Answering your question, I think that measuring climate sensitivity across the whole planet makes more sense than comparing seasonal changes per hemisphere, because seasonal effects average out when looking at the entire globe over longer periods of time.
I do agree with your assessment that clouds are a critical controlling factor, and are probably modeled incorrectly by IPCC models.
Can anyone tell me what falsifiable predictions the AGW crowd has stated that would falsify AGW?
johnnythelowery (15:12:51) :
I miss Manuel already. His Iron sun and all that(what ever that is-still canāt figure out what the hell heās barking on about!). Can I petition for a month long ban instead of life time. Iām sure heāll behave in the future. Itās just to see a fellow realist get a smack down here at WUWT.
REPLY: I dunno. I warned him about it many times. He just kept trying to sneak in stuff and I got tired of his thread bombing. I will say this for him he was courteous. ā Anthony
28 02 2010
Yes you did on several occasions. I’ll bring his name up in the summer to see if I can persuade you to let him back on under probationary terms. Maybe punishment can be metted out, like, having to Watch ‘an inconvenient truth’. in slow motion!
RE: Willis Eschenbach (21:04:24) : “The IPCC, on the other hand, says that a change of 2.5 W/m2 of forcing leads to a change of 2Ā°C in temperature ā¦”
I believe the IPCC may be hiding a simplification in stating a forcing number of this type. According to Stefan-Boltzmann, radiative power forcing is proportional to the fourth power of the absolute temperature. Thus differential power forcing, which is the inverse (1/x) of what they have cited above, must be proportional to four times the cube of the absolute temperature. Thus, I believe, the factor cited above can only valid around some specific reference absolute temperature.
Willis: Was that you at the APPLE CONVENTION who urged the share holders to reject AL GORE on re-election to the board of directors?? I can’t find the article that talked about it. If it was–My heatfelt thank you. The time has long passed when we have to get off our arses and do something! I think there is probably nothing more freightening to AL GORE than the prospect of being challenged in public. Thanks Thanks Thanks.
Would make more sense to use equal area latitudal bands. With nine bands it would be
1: 51Ā° 3’N – 90Ā° 0’N
2: 33Ā° 44’N – 51Ā° 3’N
3: 19Ā° 28’N – 33Ā° 44’N
4: 6Ā° 22’N – 19Ā° 28’N
5: 6Ā° 22’S – 6Ā° 22’N
6: 19Ā° 28’S – 6Ā° 22’S
7: 33Ā° 44’S – 19Ā° 28’S
8: 51Ā° 3’S – 33Ā° 44’S
9: 90Ā° 0’S – 51Ā° 3’S
Shows how small polar regions really are (if A is area south of some latitude, R is Earth radius, then fi=ArcSin(A/(2*Pi*R^2)-1) is latitudal angle – Archimedes, Lambert).
However, it does not address the basic problem of the method. If climate is modelled as a linear time shift invariant system with some definite temperature anomaly response function to a steplike change in radiative forcing, one can look at the corresponding transfer function (Fourier transform of first derivative) in the frequency domain.
It is easy to see that in frequency bands having no excitation, the transfer function can not be determined. Therefore it makes sense to consider spectrum of excitation provided by diurnal & annual cycles.
Frequencies of both cycles are peretty stable, annual one (tropical year) is f1=31.689 nHz, diurnal cycle is f2=11.574 uHz. Excitation at any geographic location is some mixture of the two signals.
Signals like this have discrete spectra with lines at harmonics and sums/differences of them. That is, spectral lines can be located at n*f1+k*f2 (n=…,-2,-1,0,1,2,…; k=…,-2,-1,0,1,2,…) but nowhere else.
Power at harmonics of both f1 & f2 are decreasing sharply as absolute value of harmonic number is increasing, so in practice one does not have too many spectral lines to work with. We can also see that f2>>f1. It means that spectrum of excitation consists of bunches of closely spaced lines with wide gaps among them.
It should be enough to guess value and first (possibly second) derivative of transfer function at several multiples of f2, nothing else. Also, harmonic structure of both annual and diurnal cycles depend on location. Annual cycle is fairly sinusoidal in the Tropics (it does not have much stuff in harmonics) while diurnal cycle has similar problem at the poles. Also, polar annual cycle is close to half sinusoid, so it does not have power at even harmonics. It means that for some locations we have to make with less datapoints or derivatives.
This information is not enough to determine transfer function unconditionally.
One has to make assumptions on the form of transfer function, restricting the choice to a set dependent only on a few parameters. Having done so and given vales and derivatives at some points in the frequency domain the problem might be solvable for parameters. If we are lucky, the solution is unique.
However, as it is well known, assumption is the mother of all f***ups.
Assume for the sake of argument the temperature response to be a first order filter. The response to a steplike change of irradiation of magnitude delta_j is delta_T*(1-exp(t/t0), where delta_T is the final equilibrium temperature anomaly and t0 is relaxation time. We can see that the system gets close to equilibrium only if t>>t0. Initially it only shows a linear rise approximated by delta_T*(t/t0).
If t0 >> 1 year is also assumed (not unreasonable, relaxation time of both large ice sheets and ocean turnover is several millenia), with excitation having no lower frequency component than f1 above, only delta_T/t0 can be estimated, neither delta_T nor t0 alone.
If “climate sensitivity” is defined as delta_T/delta_j, it can NOT be determined by this method (provided relaxation time is much longer than a year). For this end some excitation containing considerably lower frequencies is needed, like Milankovitch cycles, a large volcanic eruption or a Maundner-like solar minimum. With low frequency comes long observation time. We either wait for some more centuries or try to reconstruct historic changes in both forcing and temperature.
On the other hand, if one is only interested in the initial slope of response, delta_T/t0 is more than enough. And as we have seen, it IS measurable by the method described in main article. It tells us how fast temperature would change in the short term, not what its target value vould be, nor how soon it would be approximated. As we have no idea what relaxation time might be, a century may well be considered “short term”.
Also, a first order filter response may be simplicistic. It could be a more complicated filter with several time constants and gains.
We have also assumed linearity. It is either true or not. But the method is suitable to detect at least some nonlinearities. If we see too much energy in a temperature response frequency band where there was no excitation (no frequency component in annual+diurnal insolation anywhere on the globe), it could be interpreted as the indication of some strong nonlinearity in the system. Or some other forcing, independent of cyclic orbital changes.
This analysis has nothing to do with climate as such. Just ordinary signal processing.
TLM (04:28:52), I think you are misunderstanding this article. Willis is not discussing primary CO2 warming. He is discussing the increase in warming (sensitivity) that CO2 warming is supposed to create.
As for the article itself, it certainly opens the door for more research. I think several valid criticisms have been mentioned. But, I’m not sure they would cause a significant change in the numbers. Hopefully, this will give some thoughts for further research (isn’t that what science is all about?).
BTW, I keep seeing more and more support for Miskolczi’s theory. Now we even have a mechanism (tropospheric changes). It will be interesting to see if this progresses.
johnnythelowery (06:42:54) :
I miss Manuel already. His Iron sun and all that(what ever that is-still canāt figure out what the hell heās barking on about!).
I understand Anthony’s action, Oliver is more than tenuous with his thread relevance at times. I’ve taken him in as a refugee on my blog for now. He has his own solar system thread there for those interested in his theory.
Of relevance to Willis’ theory I have a thread there on OHC and solar variation too.
http://tallbloke.wordpress.com/
If the whole thing works as a first order low pass, then the maximum that temperature can lag energy input is 90 degrees, right? Now where I am it’s six weeks or 45 degrees. And for a simple electrician like me that’s an important number. Means your temperature signal has dropped to 70%. If de phase lag is something like 80 degrees, signal drops to 10%. Maybe that helps, maybe I’m completely on a wrong track.
Willis,
I like your climate theory but I don’t like the physics behind the sums you use to support it.
If one took a filament in a vacuum (say a light bulb) and passed a constant current through it it would heat up to an equilibrium temperature that allowed it to radiate the electrical energy away. If one then did the same with an alternating current of the same average power you would get the same heating and roughly the same peak temperature. In the second case the temperature would oscillate a little with the peak to peak variation depending on the frequency of the electrical current and the thermal capacity of the filament. In the case of a light bulb one sees little fluctuation in temperature yet the input energy is varying by 100% over the cycle.
In the first case we could add a small additional constant current and measure the “forcing”.
Your calculation is equivalent to taking the whole of the power variation in the second case and relating it to the small temperature fluctuation seen in the filament. This would clearly be in no way equivalent.
You may argue that the annual variation in solar energy relative to the earth’s thermal mass is slow compared with domestic electricity passing through a filament but I am pretty sure it not slow enough to make your sums work. As others have pointed out a more sophisticated energy balance calculation is needed.
However it is an interesting line of thought and should be followed up.
johnnythelowery:
Here’s the link:
http://news.cnet.com/8301-31021_3-10459872-260.html
Jimbo (06:10:49) :
“Can anyone tell me what falsifiable predictions the AGW crowd has stated that would falsify AGW?”
Yes. They say difference of ASR (Absorbed Shortwave Radiation) and OLR (Outgoing Longwave Radiation) averaged over the globe is about 0.9 W/m^2. Unfortunately accuracy of (satellite) measurement is too poor to decide the question (systematic error is several W/m^2). If it could be made sharper (error around or below 0.1 W/m^2) and no such difference would be found for several years, it would falsify the theory.
Also, if there is a difference of such magnitude, OHC (Ocean Heat Content) should increase steadily (ocean heat capacity being three orders of magnitude higher than that of atmosphere). It is a relative measurement, so only precision should be improved, but it should anyway. Unfortunately Argo floats are still not up to the task.
So the short anwer to your question is yes, it is falsifiable. The long answer is no, not yet.
TLM,
Your “lid on the saucepan” argument is incorrect.
Increased greenhouse gases make it more difficult for heat to escape, so temperature rises to keep equilibrium. Heat is not “trapped.” It finds it’s way out.
There are longer term effects of ocean equilibration, but over the last few years there is no sign that ocean heat content is increasing.
Good stuff Willis.
I think you are using TOA solar insolation. I have the Albedo numbers by 10 degree latitude bands which could be built in as well and improve the results.
The high Arctic has the highest solar insolation in the summer but it also has the highest Albedo at 0.5 – approximately 50% of the summer solar insolation is just reflected off into space, significantly reducing the surface solar insolation input. Whereas in the equatorial regions, the Albedo is only about 0.250
The Albedos vary between the seasons as well. Between 60N to 70N, the summer Albedo is about 0.4 while the winter Albedo is about 0.75 (the low solar incidence angle means the majority of what little solar insolation there is in the winter, is just reflected off into space as well). As you move closer to the equator, the seasonal change is less. The range provided in each latitude band provides a rough gauge of how much Albedo changes between the summer and winter.
This would likely provide different values for the sensitivities by latitude. (I think one would have to run the numbers to say how the amounts and the relative differentials would change).
http://img706.imageshack.us/img706/2697/albedomodel.png
Willis
If it wouldn’t be too difficult, would you also do a ‘figure one’ sometime for what it looked like at the deepest part of the last glacial period? And put these two together on a brief post?
Great stuff!
tallbloke (07:54:45) :
johnnythelowery (06:42:54) :
I miss Manuel already. His Iron sun and all that(what ever that is-still canāt figure out what the hell heās barking on about!).
I understand Anthonyās action, Oliver is more than tenuous with his thread relevance at times. Iāve taken him in as a refugee on my blog for now. He has his own solar system thread there for those interested in his theory.
Of relevance to Willisā theory I have a thread there on OHC and solar variation too.
http://tallbloke.wordpress.com/
Hi Tallbloke: Total fair doos on Anthony’s part. Let me ask a dumb question
(no, don’t know him from Adam) : Does his idea have any relevance to the issues here, AGW, solar forcings, etc? Would the composition of the sun (Iron) have any relevance to the general climate debate here? I don’t understand what his idea is, and why an obviously intelligent guy ignores warnings we all have read to keep harping on about it here. Thanks for taking him in and I’ll definately be visiting.
Willis!
Your a genius!.I took me some time understanding what you really is measuring.By this you leave the proof to the AGWers to explain and calculate why the actual difference in radiance balance are not bigger.
The warming “depot” in the ground doesnt help them,neither does the oceans.Eather way you rationalized them and quantified ther influence as a lump toghether.The probability that the “radiance delay” or boost from oceans and ground could vary to a degree that significantly effects your calculations is highly unbelivieble.
You took the easy but smart way to point this out.Another forgotten factor is the expansion of the atmosphere if it gets hotter another non estimatet cooling factor.The planet is a smart construction with a multiple backup security systems.Not the same sensitive house of cards as the AGW alarmism.
Yoy have great friends in Roy Spencer Lindzen and Choi and also Christy you are all pointing in the same direction.
Willis, Your order-of-magnitude analysis of complex global weather systems is far more informative than manipulating huge quantities of intensive properties like atmosperic and SSL temperatures (much of which has been corrupted). Better to have an understanding of the detail, before it buries you! Well done!
Hi Tallbloke: Total fair doos on Anthony’s part. Let me ask a dumb question (no, don’t know Oliver from Adam) : Does his idea have any relevance to the issues here: AGW, solar forcings, etc? Would the composition of the sun (Neutron star core/Iron) have any relevance to the general climate debate here? I don’t understand what his idea is, and why an obviously intelligent guy ignores warnings we all have read to keep harping on about it here. Thanks for taking him in and I’ll definately be visiting you over there.
This has been well understood for decades. Hansen talked about Polar Amplification a long time ago.
This also is a well understood feature of weather. San Jose is a lot hotter than San Francisco because of proximity to the ocean.
Cirrus clouds are believed to cause more warming than cooling. Other clouds block incoming SW and outgoing LW. There isn’t a simple answer for this and climate models don’t do a good job with them.
Well that is the $64,000 question, but I don’t think this simple analysis answers it. There are many complex factors which go into the equation.
John Whitman (03:51:15)
Glad someone noticed …
w.
Thanks Sean. The APPLE CORP. BOARD OF DIRECTORS AND SHAREHOLDER MEETING ‘Gadfly’ is SHELTON EHRLICH…..
‘………………….At the first opportunity for audience participation just several minutes into the proceeding, a longtime and well-known Apple shareholder–some would say gadfly–who introduced himself as Shelton Ehrlich, stood at the microphone and urged against Gore’s re-election to the board. Gore “has become a laughingstock. The glaciers have not melted,” Ehrlich said, referring to Gore’s views on global warming. “If his advice he gives to Apple is as faulty as his views on the environment then he doesn’t need to be re-elected……….” Thanks SHelton……………..whoever you are.
Thanks for the additional info, Willis.
Especially the info on your dt calculations.
If I have this right, for any particular latitude band, you are calculating
Tave_summer = [Tmar + Tapr + Tmay + Tjun +Tjul + Taug] / 6
Tave_winter = [Tsep + Toct + Tnov + Tdec +Tjan + Tfeb] / 6
dT = Tave_summer – Tave_winter
If you will humor me, I have a couple of additional questions.
How are you calculating T for any particular month in a particular latitude band?
Which data series are you using?
How do you extract the data for a particular latitude band?
Are you using the same method to get a summer and winter RFave with dRF = abs(RFave_summer – RFave_winter)?
And as someone asked above,
Are you using the TOA (Top of Atmosphere) insolation or insolation at ground?
From you comment on clouds as feedback and your wikipic,
I’m guessing TOA.
johnnythelowery (06:42:54) : Said
“I miss Manuel already. His Iron sun and all that(what ever that is-still canāt figure out what the hell heās barking on about!). Can I petition for a month long ban instead of life time. Iām sure heāll behave in the future. Itās just to see a fellow realist get a smack down here at WUWT.”
Can I put in a plea for a months ban as well? As you say Anthony he is always polite so that helps the nature of the general discourse. Even better, in my old school they used to promote the bad boys to positions of responsibility. How about asking Manuel to provide the material for his own thread? We can read, learn, then go wildly off topic š
tonyb
The annual sensitivity is dT/dF for the 6 month extremes… but what of he _daily_ sensitivity? The day-night temperature swings in deserts can show about 40 K change from about 1000 W/m2 forcing… still only 0.045 K.m2/W, but obviously the transient admittances are even more important on this short time scale. I don’t have a conclusion, just a suggestion that you dig a bit deeper.
Willis,
You are dealing with a cyclic system, and not permitting it to equilibrate. Apart from the transfer of energy from the high to low insolation areas, winter temps are warmer than the winter solar flux could sustain because the earth is coming off a summer. Summer temps are cooler than the additional flux would support for the inverse reason. Calculating the sensitivity as the seasonal difference underestimates vs an increase in both over many cycles.
I concur with Goddard that looking at something like mutli year changes in solar flux due to solar cycles would be more productive.
Grizzled,
How hot do you think it would get in the desert, if the sun stayed up high in the sky for 30 hours instead of just 8? Maybe 90C?
You can’t draw any conclusions about sensitivity until the system gets closer to equilibrium. I’ve fried eggs on top of Coleman coolers in the desert.
Tonyb
Regarding Oliver. He’s got his own Headline/Blog and Comments thread regarding his Neutron Star surrounded by an Iron casing theory of the center of the sun. Check it out. it’s very interesting. Don’t know why he wouldn’t listen to Anthony.
http://tallbloke.wordpress.com
Willis
I observe many climatologists to be confused about what is meant by “falsifiable.” As an effect of this confusion has been to base ultra-expensive public policy proposals upon unfalsifiable and thus unscientific climate models, I’d like to dispel their confusion. I hope you won’t be offended if I use a critique of your article as the vehicle for an attempt at doing so.
You’ve stopped short of providing a falsifiable hypothesis. To make your hypothesis falsifiable, you’d need to cast it into the form of a predictive model. Each prediction of such a model would state the outcome of an independent statistical event. The totality of such events would form the statistical population of any study in which your model would be tested. In a falsifiable hypothesis, the set of all possible outcomes would be described in sufficient detail for the actual outcomes to be measured.
tallbloke (02:14:54)
Always good to hear from you, tallbloke.
Yes, heat does mix down in the ocean. But as you point out it is a slow process, because it is opposed by the tendency of warm water to rise.
My point is that the earth is basically in equilibrium. This means that whatever energy enters the ocean is matched by energy leaving the ocean. That means that, albeit with a slight (one month) lag, all of the solar energy striking the ocean heats the air.
Yes, that lag also means a slight reduction in a temperature average that is centered around the peaks in insolation as I have done. But because the lag is short (one month), that reduction is not large, on the order of 10%.
While this is true, it does not affect my analysis. My analysis is based on equilibrium conditions.
Agreed. This is inevitable when the earth warms or cools. But my analysis is not looking at long term warming or cooling of a degree or less. I’m looking at the annual changes.
There are a couple parts that you are overlooking. First, a main temperature control mechanisms is the emergence of reflective clouds and thunderstorms with increasing temperature. This does not “redistribute heat within the Earth-Ocean climate system” as you say above. It prevents heat from entering the system. The same is true about the wind-driven increase in ocean albedo. This also does not redistribute heat, it reflects heat out of the system.
The second is that when warm wet air is taken aloft in the core of a thunderstorm, it bypasses the majority of the greenhouse gases. This means that much more of the heat that it contains is free to radiate to space. Again, this is not a “redistribution”, it is an increased loss to space.
Again, this is a misconception. The cloud/thunderstorm does much more than redistribute heat. It actively increases heat loss from the system as a whole.
My best to you,
w.
Wiilis,
If I have understood you correctly you are looking at the ratio of the principal 12 month components of the seasonal variation of the flux (F’) to the seasonal variation of the temperature (T’).
F’ = T’*Y {where Y is the admittance}.
Or T’=F’/Y
Now for this sinusoidal component we have:
F’ = F*e^(iwt) {where F is the amplitude of that component, i is root -1, w the angular frequency and t the time.
and T’ = T*e^(iwt+p) {where T is the amplititude, and p the phase angle}
so T*e^(iwt+p) = F*e^(iwt)/Y
or T*e^(ip) = F/Y where Y is a complex number {the vector e^ip is just a rotation, it has unit length}
Now for admittances in parallel (as in this case) Y is additive
Let us say:
Y = Ys + Ye {where Ys is the admittance into space and Ye the sum of the admittances into the environment}.
I think you are looking for Ys = Y-Ye {where Y is your measured F/T}
The climate sensitivity (CS) when given as degrees K per doubling equates to
Ys = 3.7W/CS so CS = 3.7W/Ys
Now for your value of 0.15K, your recovered value for Ys is:
Ys = 3.7/.15 =~ 25W/K
Now the admittance of 1 m^3 of well mixed water is approximately
4200000*2*pi/(365.25*24*3600)) for a cycle with a period of one year
=~ 0.84W/K
and guestimates for the total Admittance for the ocean could range from 42 to 84 W/K
similarly the Admittance of the atmosphere is around 3W/K and the earth’s is very varied and not all that big.
So Ye is ~ 3W/K over land and (45-87)W/K over the oceans.
So over the oceans T = 2K could imply an oceanic flux amplitude of 90-176 W {I have left out all the per metre squared bits too save mess}
Now it is likely that you will find that on the western margins of the temperate oceans the ocenic flux amplitude will well exceed the solar amplitude. This is to be expected due to flux from the atmosphere which has passed over a region of high temperature amplitudes. The reverse effect is likely to be found over the eastern seaboards of the contintents.
I think that well isolated parts of the temperate oceans have T=~2.5K, so it is quite possible that almost the entire flux is oceanic or , Y =~ Yo {the oceanic admittance}.
Now the figures for the oceanic admittance are guestimates but figures much lower than 40W/K seem unlikely to me.
Now you are looking for Ys = Y – Ye, but Ye = Yo + Ya {Ya = atmospheric admittance} is likely to be bigger than Y over parts of the ocean and almost equal to it in isolated parts of the ocean. The reason it can be bigger is that the local Y = F/T {where F is the local solar flux amplitude} ignores the additional flux from the atmosphere as it passes from land to ocean.
Over the land Y will be greater than Ye {Ye =~ Ya} where prevailing winds come from the ocean and will decline in value towards Ye in isolated continental regions {actually really only in Mongolia/Eastern Siberia do they get close}.
The atmospheric Ya is a common factor in Ye across the globe and simple calculation implies that if over land Ys was zero then Y=Ye and a 150W value for F would imply a maximum for T ~ 150/3 = 50K (which is only around 1.5 times the Siberian amplitude, so the slack there is just 1.5W/K . The IPPC’s CS of 3K equates to 0.8W/K which is perhaps a little low. I am not going to argue about precise values for F as they differ from TOA insolation value anyway.
Unfortunately the problem is ill-conditioned in that over the oceans Y and Ye are similar in magnitude and Ye can be greater than Y=Fsolar/T locally, and the uncertainties in Ye are large and you need to determine the reciprocal of Y-Ye to find CS = 3.7W/(Y-Ye).
Now in all the above I have only dealt with the amplitudes of the variations, This is justified becuase we are treating Y = F’/T’ {variations in amplitude} as a stand in for Y = dF/dT {i.e linearity has been assumed over the ranges of the amplitudes}, the mean values of total Flux and absolute surface tmperature are of no interest, we only need the amplitudes of the local variations.
So readers be warned, arguments based on the total values of solar flux and surfaces temperatures are not necessarily relevant here, we are looking only for the slope dF/dT. So for instance the average flux from say the equator to the pole is of no interest only the amplitudes of any seasonal component of such fluxes would be relevant.
Alex
Willis Eschenbach (02:22:25) : “I am looking at changes in average temperature based on changes in average forcing.”
What I was getting at wrt clouds is this : if a change in GCRs, say, caused a change in cloud cover at a point in time during your experiment, then it would alter the temperature without altering TOA insolation. In the context of your experiment, that’s a forcing that isn’t an insolation feedback. That would invalidate your basic assumptions.
Assuming that such [non-feedback] forcings are not an annual phenomenon, doing your experiment over multiple years could eliminate them as a possible factor.
Willis “By looking at the lag between peak insolation and peak temperature (about a month), it appears that if the seasonās insolation forcing were to continue at a constant value the majority of the equilibration would occur on the same timescale.”
Sounds reasonable, but I’m not sure that’s a valid assumption. Analogy : Water on a stove takes a long time to boil, but stops warming almost immediately when removed. [“almost” = heat in transit in the pot].
toyotawhizguy (02:00:19)
Well, if William Connolley says it’s raining, the first thing I do is look out the window. I see you are following in his footsteps. There is no such thing as “HadCM3” data.
HadCM3 is a climate model. Climate models do not output “data”, they output the results of the theories of whoever programmed the model. I know that Connelly thinks that the outputs of models are “data” … but that’s just a measure of the depth of his delusionary belief system.
In any case, the atmospheric absorption is meaningless for my analysis. I am looking at the relationship between TOA forcing and temperature. As such, the absorption by the atmosphere is only one of a host of things that go into determining the final temperature. These include albedo changes, airborne dust, tropical-polar heat fluxes, annual changes in the jet stream, and a host of other phenomena. But although they can explain the relationship between the forcing and the temperature, they don’t change the relationship.
The hockey team could label their their AGW theory as Pride and Prejudice
John of Kent (02:12:07)
I agree that both of those may certainly have some effect over the long term, although there’s more to learn. I suspect that that those are among the reasons for the long term drifts in the cloud/thunderstorm controlled equilibrium temperature.
However, on a day to day basis, both clouds and thunderstorms are controlled by temperature. That’s why you see them in the tropics mainly in the afternoons, while the mornings are clear. It’s not because there’s more cosmic rays in the afternoons …
Vukcevic (02:47:48)
Temperatures of the lower layers are immaterial until they get to the skin surface. When they are in the lower layers, they are totally insulated from the atmosphere.
When they reach the skin surface, they can then exchange energy with the atmosphere.
But again, this doesn’t affect my analysis. I am looking at annual changes, not the long term changes that you reference.
Eschenbach: I am looking at the relationship between TOA forcing and temperature.
I guess that brings up another question. Are you modeling the RF based on an assumed or averaged Solar Constant (‘So’ in the wiki article on insolation) or are you using a measured value? If you are using measurements, which data series?
davidmhoffer (04:08:08)
Willis,
I agree entirely, with one caveat – the “sweet spot” (usually called the “atmospheric window”) only exists when the sky is clear. This is because clouds are essentially black bodies for all longwave frequencies. Since cloud cover on the earth is on the order of 60%, this is far from a trivial factor.
I have not thought through all of the implications of this for my theory, however. Many thanks for the new idea.
w.
TLM (04:28:52)
I understand that you think that. However, your heartfelt opinion on the matter is not that useful. I have pointed out that all of the sunlight hitting the ocean heats the atmosphere (albeit with a slight lag of about a month). This indicates that a change of e.g. 3.7 W/m2 should not take long to warm up the planet either. I know that you claim it will take decades. But since the sun striking the planet warms it immediately, and the stored heat from such a change comes back out with only a one month lag, you’ll need more than your opinion to claim it will take a decade for the earth to react to a change in forcing.
Thank you for sharing, but you misunderstand the purpose of my posting here. It is not to claim that they are 100% correct and accurte. It is to expose my ideas to the critical glare of public scientific criticism. This is called the “scientific process”.
However, it is not forwarded by claims about who you might or might not find “worth reading”. If you have something scientific to add, please bring it on. Your un-cited claim that the earth is extremely slow to respond to a change in forcing is both unscientific and contradicted by our experience. The surface air warms and cools very quickly, we see it every day. And the stored heat comes back out with only about a month’s lag. Neither fact supports your argument.
Peter SĆørensen (04:32:46)
I’m not taking about the maximum heatflux. I’m talking about the average heatflux, which is a very different beast.
I agree, it’s one of my main complaints about the climate models. However, in the narrow temperature ranges we’re talking about, I don’t think that is a major issue.
Robert of Ottawa (04:54:48)
Yes, it is Watts per square metre.
Steve Fitzpatrick (05:09:44)
I’ve never read anything that suggests that a significant amount of heat is transported from one hemisphere to another. Do you have a cite for that?
Also, while heat is stored in the ocean and then released, it is not accurate to say it is “released in the winter”. The lag between the peak insolation shows that as soon as the insolation starts to drop, the ocean begins releasing its heat. This only makes a small difference in the winter/summer averages.
johnnythelowery (07:06:08)
Wasn’t me, but like you, I certainly thank whoever it was.
Rienk (08:02:36)
Not sure how you are measuring this, but a lag of a month in a cycle with a period of a year seems like only 30Ā° to me, and six weeks is 41.5Ā°.
However, I also think your number (70% drop in signal from a 45Ā° phase lag) refers to the peak signal, not the average signal. Please recompute the change in the average signal from such a lag when the average is centered around the peak in the un-lagged signal, and contains a half cycle.
cal (08:03:47)
The problem with your example is that unlike with the climate, energy is added during both the positive and negative swings of the current. In addition, because of the very high frequency of the cycles, there is almost no temperature change in the filament with time. Neither of these are true in the current situation.
Because of this, it doesn’t parallel the situation we are investigating, so we can’t use it to help understand the situation.
Pascvaks (09:10:11)
Unfortunately, data from that period is extremely scarce. We don’t know how much the globe changed winter to summer back then. So, good idea, but no data.
Ron Broberg (11:34:14)
As mentioned above, I used the HadCRUT3 absolute temperature set available here.
I used area-weighted averaging to extract the various values.
Yes.
TOA
Steve Goddard (12:12:38)
I repeat that I am dealing with average temperatures, not peak temperatures. If the desert sun stayed at the average intensity of the whole dawn to dusk period for 30 hours, the average dawn to dusk temperature would get slightly warmer, but not much.
Ron Broberg (13:39:20)
I don’t understand. What are you calling “RF”? Radiative forcing? If so, I don’t understand the question. The solar constant is ~ 1,366 W/m2 at TOA. The difference if I were to assume 1,360 or 1,370 W/m2 is trivial in this analysis. What’s the point here?
Willis Eschenbach;
I agree entirely, with one caveat ā the āsweet spotā (usually called the āatmospheric windowā) only exists when the sky is clear. This is because clouds are essentially black bodies for all longwave frequencies. Since cloud cover on the earth is on the order of 60%, this is far from a trivial factor.>>
So everything I know about clouds is in your last sentence… but might I hazard some guesses?
1. I expect that clouds predominate in warmer climes, less so in cool ones (ie below +15)?
2. At only 40% clear sky, the atmospheric window would still be capable of limiting temperature increases.
3. Clouds donāt stand still. Any warming they cause at surface would be like compressing a coiled spring… provided the surface temp doesnāt go over that +15 top end (not likely in the arctic regions) and would uncoil (P=CT^4) when the cloud cover moves off. So the 40% window would move around over time. Lag yes, but the heat still escapes?
4. What temperature is the cloud at? I assume that if LW from earth surface at (for sake of argument) 25 degrees C hits a cloud on the way up and gets absorbed, then what temperature does the cloud re- emit at? Is it in the atmospheric window? If yes, then some gets emitted down and some up (photons have a remarkable lack of sense of direction) and the cloud is now leveraging the atmospheric window?
5. Anecdotal thought here… Iāve seen way too many 40 below mornings for my liking, or 30 below for that matter. I donāt remember any clouds those days. Clear blue sky in January in Winnipeg = did anyone plug the block heater in last night? No? Back to bed the car wonāt start anyway.
6. On the cooling side of the cycle… clouds would be less of a factor. As surface temperatures drop below the atmospheric window, water vapour would start absorbing again and re-emitting before clouds could get to it. Presuming the clouds have a net warming effect, this would augment the thermostat limiting temperature decreases. If they have a net cooling effect, the GHG would still be able to limit the temperature decrease, it would just take longer because they have to fight off the clouds 60% of the time. (Unless 1. Above is correct and then there wouldnāt be much cloud in the areas acting as the thermostat)?
7. This ought to be fairly easy to test. If one had a long term surface temperature set broken down by latitude (that you could trust), and an outgoing LW dataset at TOA broken down by latitude (that you could trust), I would think that you could correlate efficiency of LW emission to space by temperature band, clouds or no clouds.
Eschenbach: I donāt understand. What are you calling āRFā? Radiative forcing? If so, I donāt understand the question. The solar constant is ~ 1,366 W/m2 at TOA. The difference if I were to assume 1,360 or 1,370 W/m2 is trivial in this analysis.
Thanks. Yes, RF = radiative forcing
Parameterized solar constant at 1,366 W/m^2
What’s the point?
Just trying to understand your methodology. Of course, modeling the solar constant with a fixed parameter is justified here. Using measured data would only adjust it by one part in several hundred – and then only if you were measuring over a span of years.
Willis, you wrote:
The problem with your example is that unlike with the climate, energy is added during both the positive and negative swings of the current. In addition, because of the very high frequency of the cycles, there is almost no temperature change in the filament with time. Neither of these are true in the current situation.
If you look at power rather than current you will see that there is a sinusoidal input just like the insolation in your example. I should have been more careful in my description but I thought it would be obvious that I would comparing watts in with watts out.
The frequency in my example is high but the load is very much smaller. I am not saying that this makes it an exact analogy but I am trying to allert you to a potential flaw in your logic. This is the nub of the problem. I believe that the relatively small variation in average global temperatures is due to the thermal inertia of the earths climate system and not to low sensitivity. Others have made the same point in different ways. I could be wrong but it needs a more detailed analysis to prove it one way or another.
cal (08:03:47) :
>In the case of a light bulb one sees little fluctuation in temperature yet the input energy is varying by 100% over the cycle.
This is of course true but the fluctuation in heat and therefore the light output will lag the 100Hz/120Hz input cycle by close to 90 degrees. What that means is you’re far into the stopband of a first order lowpass filter.
If temperatures were lagging by three months then I wouldn’t believe the results were accurate. Two months, I’m fine. one month and I’m happy. Four months is nightmare time. Because now you’re past 90 degrees and therefore into a second order system.
Alexander Harvey (13:20:29) : edit
Alex, thanks much for your detailed analysis. I didn’t understand the bottom line, however. Are you saying that we can’t estimate the answer? Or are you saying that we can estimate the answer, but you haven’t done so? If the latter, could you give us an estimate of the answer?
Many thanks for your work in fighting my ignorance, and I mean that seriously, not as a snark of any kind, this is science at its best,
w.
Rienk (15:40:52)
The lag is 4-6 weeks.
w.
cal says:
How does the much larger heat capacity of the oceans vs the atmosphere affect any claims that increasing CO2 is going fry us all?
Masive amounts of GCM software exists to solve these problems. You can’t make a back of the envelope qualitative calculation of climate sensitivity.
Willis Eschenbach would you please tell me what is the physical quantity “forcing” and how is it measured. I have some idea about the others but “forcing” really puzles me. And if you have time would you tell me what is “down welling” or “up welling” radiation.
Bill Illis (08:47:27)
Bill, what is the source of that information?
w.
Steve Goddard (16:12:49) : edit
If you believe that the GCMs are anything more than tinkertoy models, you haven’t looked at the problems. These include a near-total lack of discussion by the modelers of the following issues:
1. Propagation of errors in the models. In any iterative model, this is a very important issue.
2. A listing of all of the āparametersā of each model, with justification for their values and an estimate of what an error in that parameter would lead to in the final result.
3. The effect of the simulation of viscosity dissipation in the models.
4. The approximations of the Navier-Stokes equations, and any discussion of whether they converge.
5. Verification and Validation, which is a part of software engineering that is routinely done on all mission-critical software.
6. Software Quality Assurance, which again is a crucial part of software engineering for any important software. These last two are routinely used on software for everything important from elevators to jet airplanes to space missions. In WG1 they donāt even rate a mention.
All of these issues have been raised, time after time, by people concerned about the models. Yet they are totally untouched in the IPCC WG1. Shows how serious the modelers are about actually seeing if their models are worth more than a bucket of warm spit …
George Steiner (17:48:01) : edit
George, good questions. Climate science, like any other specialized field, has its jargon.
A “forcing” is anything that changes the amount of energy absorbed or emitted by a part of the climate system. Solar insolation is a forcing, for example, as is greenhouse radiation. People also speak of e.g. “cloud forcing”, meaning the change in radiation due to clouds.
Downwelling and upwelling refer to the direction of radiation with respect to the surface. Sunshine on the surface is downwelling, longwave (infrared) radiation from the earth to space is upwelling. Longwave radiation is often referred to as DLR or ULR for down (up) welling longwave radiation. The atmosphere and clouds produce both DLR and ULR.
The only stupid question is the one you don’t ask …
Thanks, Willis, for an elegant back-of-the-envelope analysis.
Willis,
I’m sure you know that I share the same criticisms of climate models as what you listed. I’ve made most of those complaints here myself.
Nevertheless, the mathematical approach they take is more or less the correct one for the difficult problem they are attempting to solve. Will they ever be any value? I doubt it. But I don’t think any other approach will do much better.
Climate is inherently unpredictable for the same reasons as weather more than about three days out.
Gary Hladik (18:58:48) : edit
Thanks for the vote, Gary. However, in my mind the jury is still out as to whether my analysis is valid or not. I think that the admittance issue does not change my results significantly, but I’ve been wrong before, and Alex makes a good case. I’m still waiting for a numeric result from his analysis.
Which is what I love about WUWT. Rather that posing as a site like RC that claims that the science is settled and they’re going to spoon feed it to us, this site is the epitome of real science. I make claims, and people see if they can shoot them down.
Onwards …
Willis Eschenbach (14:04:40) :
With regard to the transport of heat between hemispheres, the primary north/south transport mechanism in the tropic is the Hadley circulation, which is on average centered near the equator(http://en.wikipedia.org/wiki/Atmospheric_circulation). Note however that the equatorial convergence zone of the Hadley circulation is not really centered on the equator, but instead tracks the solar angle:
“Though the Hadley cell is described as lying on the equator, it is more accurate to describe it as following the sunās zenith point, or what is termed the “thermal equator,” which undergoes a semiannual north-south migration.”
Which is essentially saying that the center of flux of heat poleward changes with season form ~23 degrees north in the northern summer to ~23 degrees south in the northern winter. This means that heat from one geographical hemisphere (the hemisphere in summer) is indeed transported in large quantity to the other geographical hemisphere (the hemisphere in winter) by the Hadley circulation, because the Hadley cell does not lie on the geographical equator, but rather follows the north-south season change in the position of the sun (or the point of highest solar input).
With regard to ocean heat accumulation/release with seasonal progression (especially outside the tropics), as you said, the ocean heat does indeed lag the solar thermal input through all seasons, making the average temperature warmer that it would otherwise have been through fall and winter, and cooler than it would otherwise have been through spring and summer. However, the seasonal change in ocean surface temperature is much smaller at each latitude over ocean than over land, which (I think) can only be explained as a strong influence of the uptake and release of heat by the ocean. Finally, major ocean currents (http://upload.wikimedia.org/wikipedia/commons/0/06/Corrientes-oceanicas.gif) carry a huge quantity of heat poleward year round, further warming high latitudes in the winter, especially in the northern hemisphere. Without the influence of the oceans, seasonal temperature swings at higher latitudes would be much higher than they are.
As I said earlier, I just don’t think you can generate an accurate estimate of overall global climate sensitivity if you ignore the contributions of atmospheric heat transfer from the tropics poleward, and ignore the substantial tempering effect of the ocean. The temperature in polar regions in winter (with essentially zero solar heat input) would fall to extremely low temperatures due to radiative heat loss (the blackbody temperature of space is ~3K) if they were thermally isolated from the rest of the globe. But they are not isolated; they receive substantial heat from lower latitudes throughout the winter, and also receive heat from gradual cooling of the ocean in winter.
Every graduate student should be required to present their research, stage by stage, on the internet. The feedback and learning value would be tremendous.
Willis: If I correctly understood your argument, you have calculated “climate sensitivity” by divided the mean summer/winter temperature differences (dTsw) by the mean difference in daily summer and winter insolation (dWsw) in watts/m2 and then multiplied by (3.6 W/m2)/2XC02. This derivation assumes that seasonal temperatures respond quickly to changes in solar insolation. This assumption is not true. The coldest winter temperatures (in the US) come at the end of January, not on the shortest day of the year on December 21 and the warmest temperatures often come in late July, not on the longest day of the year. Where I grew up in coastal California, the average temperature on June 21 is 1 degC colder than on September 23 because the nearby ocean takes so long to warm up.
If temperature were determined solely by solar insolation, the summer/winter temperature difference would be the same in the center and at the coasts of continents at a given latitude. If temperature were solely determined by insolation, the temperature of the spring and fall equinoxes would be identical. There is a 6 degC difference where I live, about half of the spread between the daily low (with no insolation) and daily low (with 2X average daily insolation.)
So one can easily see that it takes at least one month for surface air temperature dominated by land to respond to changes in insolation and longer for surface air temperatures dominated by water to respond. However, persistent circulation of air (both vertically and horizontally) takes place on time scales faster than monthly, so the same air is not actually responding to the changes in insolation that reach the earth.
You can find information about how the location of the thermocline varies with season at: http://www.villasmunta.it/oceanografia/the_three.htm See Figure 1-2-3. Seasonal temperature changes in the thermocline reach 100 meters.
Finally, we know that warm air holds more water-vapor, so the greenhouse effect is stronger in the winter. If one takes the IPCC’s estimate for water-vapor feedback of about 2 W/m2/degC, you’ve got a substantial summer vs. winter forcing. Then there is cloud feedback to worry about. If winter skies are dominated by low clouds and summer skies by higher clouds, radiative cooling from cloud tops will be much less efficient in the summer. Is albedo the same in summer and winter?
Willis Eschenbach (13:15:19) :
tallbloke (02:14:54)
Hi Willis,
I think this is a promising approach, but needs some further consideration on the absorption of energy by the ocean.
Always good to hear from you, tallbloke.
Willis, many thanks for your considered and detailed reply to my post. I hope you saw the answer to some of the issues you raised in the short addendum I added a couple of comments later.
I can see you have your hands full here with the many excellent and more immediately relevant replies you have recieved on this thread, so I will take my time over considering your full response. Perhaps one thing we might agree on is that your error bars might be tightened down by a decadal length study which removes some of the signal introduced by the changing solar-oceanic energy balance over the solar cycle length.
Thanks again.
0.05C/3.7W is 370 W for the 5 C increase since last glacial. Wonder where those 370 watts came from.
lgl (00:17:00) :
You say:
ā0.05C/3.7W is 370 W for the 5 C increase since last glacial. Wonder where those 370 watts came from.ā
The paleoclimate record strongly suggests that the climate system is bistable (i.e. stable in each of two states; viz. glacial and interglacial). If this apparent bistability is real then the energy accumulation you assert is an indication of a change from one state to the other.
The fine analysis conducted by Willis Eschenbach only concerns the climate sensitivity of the present interglacial state.
Therefore, your comment is not relevant to the present discussion unless you can provide an explanation for the apparent bistability of the climate.
Richard
Willis,
The Albedo data comes from “Thermal Environments” by James F. Clawson of the Jet Propulsion Laboratory. It is used to control spacecraft and satellites and I believe it uses ERBE data. I haven’t found an on-line copy of it but the data is provided as an extract in a few places. Here’s one.
http://www.tak2000.com/data/planets/earth.htm
When I run all the numbers using these figures, I get a global Albedo value of 0.2983 which is exactly the amount in Trenberth’s latest Earth Radiation Budget paper.
You can also download the climatologies from ERBE here (as usual, they do not make it easy). Use Total Albedo which incorporates the effects of clouds versus Clear-Sky or Surface Albedo which doesn’t.
http://iridl.ldeo.columbia.edu/SOURCES/.NASA/.ERBE/.Climatology/.total/albedo/?help+datatables
Steve Goddard,
Increased greenhouse gases make it more difficult for heat to escape, so temperature rises to keep equilibrium. Heat is not ātrapped.ā It finds itās way out.
Exactly! That is global warming caused by greenhouse gases. The temperature rises in order restore the radiative balance.
My “saucepan” analogy was not meant to show that heat is permanently trapped, but that the temperature of the contents in the saucepan rise higher if there is a lid on it than if there is not (I am assuming the contents are not boiling of course!)
Willis,
If you have something scientific to add, please bring it on.
Okey dokey, how about Karl et al 2006?
Old stuff I know but as you will be aware the Greenhouse effect predicts that as more heat is trapped in the troposphere less reaches the stratosphere. The effect will be to cause a rise in temperature in the troposphere and fall in the stratosphere. This is exactly what the satellites and radiosondes are reporting. Look at the graphs on page 8 of the executive summary here:
http://www.climatescience.gov/Library/sap/sap1-1/finalreport/sap1-1-final-execsum.pdf
Also go to
http://discover.itsc.uah.edu/amsutemps/
and look at how the troposphere (ch5) temps are rising year on year while those in the stratosphere (ch12) at 31km up are cooling.
The observations from the satellites are showing exactly what the theory predicts. How that increase in troposheric temperatures will affect the weather and clouds is uncertain. We may see some negative feedbacks but apparently no major ones yet. Overall the satellite data is showing a slightly smaller trend rise in temperatures than the surface stations – but there is barely 20 years of data to work with. It takes a long time for a 0.2c – 0.3c a decade increase in temperatures to become apparent when the weather “noise” is tens of degrees and the year-to-year “noise” in average temperatures is 0.5c or so. Add in 30 and 60 year variations in NAO / PDO to add longer term “noise” and it becomes difficult to tease out a mere 3c in 100 years.
My argument with your piece was primarily the last two paragraphs – which make the common falacial comparison between short term variations in insolation and temperature between summer and winter (that I would call “weather”) and longer term trends in average temperatures (that I would call “climate”).
Willis, I didn’t receive an answer to my question, perhaps it was too convoluted. Looking at your “SOURCE”, the map of the Insolation Top of Atmosphere, is described as: “Theoretical insolation at the top of the atmosphere” I have no easy way of verifying the numbers. However, on the same page is a “modeled” Photovoltaic (PV) Solar Radiation map:
http://en.wikipedia.org/wiki/File:Us_pv_annual_may2004.jpg
On this map, since I have a PV system, I can compare this model to reality, and the model overestimates actual output by 36.9%. My question is two-fold:(1) Is all of the ‘data’ on your “SOURCE” page from the same model(s), (2) and if true, how would an error of that magnitude affect the calculations? I assume much less energy into the system, about 27% less.
Willis, great job. You do analyzes I wish I could do. Some of the criticisms above stem from their own misunderstandings, not problems w/yours.
One improvement would be to analyze seasonal energy (enthalpy) changes instead of simple temp changes — you’d need relative humidity or dew-points to do this. There prb’ly isn’t sufficient data for this, tho.
I wonder what legitimate scientists like Pielke Sr, Spencer, Cristy or our resident Leif S. think about this.
Thank you Willis for a nice piece of work, which has got me thinking! Below are my first thoughts (usually the best). Sorry if they are presented in a disjointed way.
Your logic looks correct to me and your low calculated sensitivity is what I would expect to see, bearing in mind how remarkable stable the climate has been over long periods of time.
By focusing on the average seasonal changes this evens out short-term variation. Also if there is energy being held in the oceans over long time periods, then unless the rate of emission is much greater than rate of storage, by using just one year of data the effect will be minimal.
The amount/type of cloud cover is a key element in preventing run-away cooling or warming and perhaps it is the propensity for water vapour to form clouds that causes longer-term climate change?
Water has many strange and unique properties (see link below), not least it’s very unusual phase-change behaviour. Cloud formation depends on many factors, such as amount/type/altitude of aerosol, microscopic ice crystals, ions, high energy particles e.t.c. We need to have a better understanding of how these factors contribute at all spacial scales if we are to understand what’s happening.
Anomalous properties of water
http://www1.lsbu.ac.uk/water/anmlies.html
Observation suggests that systems displaying deterministic chaos seek to maximise entropy. The positive cooling effects of turbulent processes like thunderstorms are an important part of the Earth’s governor – hurricanes too have an important role in this. Again, we need a better understanding of how these systems operate and the amounts of energy expended so that their effects can be properly incorporated into the GCMs.
Thanks again for exposing your ideas to the WUWT ARP (Audience Review Process) – closed science leads to closed minds š
Steve Keohane (07:12:11) : edit
Steve, sorry I missed it. The photovoltaic map is how much energy is striking the ground, or more accurately, a flat plate facing southward perpendicular to the noon sun.
The data I used, on the other hand, is the top-of-atmosphere (TOA) insolation. As such, it will be larger than the sunlight that hits the ground, mostly because of reflection by clouds (which is why there is more sunlight in the southwest in your map.)
w.
Willis Eschenbach (14:12:34) :
Plus this bit from your post:
Ermmm…I’m not really measuring anything at all, or even doing much in the way of calculations. I simply assumed a more or less sinusoidal shape for both insolation and temperature. The min. and max. values are whatever you have and whatever they are. That doesn’t make any difference to the point I was trying to get accross. And not making a good job of, sadly.
I know that where I’m sitting (54 degrees north) our max. and min. temps are lagging the longest and shortest day of the year by about 6 weeks. Call it a month and a half, or 45 degrees. And if the system can be modelled as a first order lowpass, which I think is what you’re doing, then phase and magnitude of the output are inextricably linked. And thus I can calculate what the temperature signal would have been if it had been able to follow the input instantaniously. Simply divide by the cosine of the lag.
Willis Eschenbach (16:05:11) :
Which is all we need. for 4 weeks >cos(360*4/52)=0.885 and for 6 weeks >cos(360*6/52)=0.749. Simply divide whatever your sensitivity is by that number and you’ve corrected for lag. So I think your way of doing this is valid because the lag is fairly small and ignoring it doesn’t lead to a big change in outcome. No order of magnitude change anyway. And all that because the time constants of the exitation frequency and the system are fortuitiously similar.
Richard S Courtney (05:34:21) :
“The fine analysis conducted by Willis Eschenbach only concerns the climate sensitivity of the present interglacial state.”
It concerns the thermal inertia of this planet but tells absolutely nothing about its climate sensitivity.
You need 155 W for 150 days to heat a 100 meter water column (a common mixed layer depth) 5 C, and that’s what is reflected in this article.
Tropical clouds and thunderstorms are an important regulatory heat
engine stabilising the earth’s climate, as has been well argued in both this article and the previous one.
However the hasty dismissal of the role of the ocean below 10m depth
needs to be challenged. The criticism by Kerr et al. is I believe valid.
Ocean heat capacity is a huge confounding factor in looking at temperature stability and summer-winter range. Dr Eschenbach acknowledges this in allowing for the importance of the continental mass at each latitude band. If you draw a global map of summer-winter temperature range it looks like a smoothed land map. The range correlates very strongly with distance from the sea.
First the ocean has the vast majority of the climate’s heat. And of this nearly all is below 10 m depth. While the ocean does have a variable temperature profile sometimes showing a spike at the thermocline, one does not have to argue (against heat principles) for warm water to descend to the cold depths, in order for there to be a role for ocean deep circulation in climate modulation over the short, medium and long term.
For instance, the global deep circulation – quite different from the surface circulation – is driven by cold water downwelling in places such as the Norwegian sea. Climate changes such as in solar-atmosphere-cloud heat balance cause variation in downwelling which in turn, via changes in ocean circulation over various timescales, affect climate form the tropics to the poles. There is evidence that what is called the Atlantic Multidecadal Oscillation involves linkage between Norwegian Sea downwelling, the resultant South Stream deep current and its surface reaction North Atlantic
Drift. The latter – some data suggests – strengthens and weakens during positive and negative AMO phases respectively.
The variation in Arctic ice cover is probably dominated by this oceanic circulation variation – not directly by atmospheric factors.
(e.g. GEOPHYSICAL RESEARCH LETTERS, VOL. 32, L04602, doi:10.1029/2004GL022112, 2005; http://mgg.coas.oregonstate.edu/~andreas/pdf/K/koesters05grl.pdf.)
In general the major oceanic oscillations have a fundamental effect on climate, in profound way as argued by Tsonis:
http://www.agu.org/pubs/crossref/2009/2008GL036874.shtml
and also
http://www.springerlink.com/content/n7111278w0866276/
Clouds and thunderstorms are clearly an important climate component acting for stabilisation and damping – but to argue that the deep ocean is irrelevant to climate is to risk finding yourself in deep .. er .. water.
Bill Illis (06:31:19)
You da man, many thanks.
w.
lgl (12:54:18)
If we were measuring the temperature of the mixed layer, you’d be right. But we’re measuring air temperature, which is related to ocean skin temperature, and has nothing to do with what’s happening 150 metres down.
As someone who has dived extensively, I am very familiar with the diurnal changes and the vertical temperature profile of the ocean. We’re interested in about the top ten metres or so, that’s where the action of the sunlight is greatest. When diving there is often a pronounced thermocline around that depth. Per your figures, for 155 W/m2 to change that by 5Ā°C it takes about 15 days. This is in reasonable agreement with the seasonal lag in peak temperatures.
Willis Eschenbach (13:55:34):
” I agree, itās one of my main complaints about the climate models. However, in the narrow temperature ranges weāre talking about, I donāt think that is a major issue.”
This is the only real question I have had about this article. I agree with the basic premise and I like the way you have segmented the earth in climate forcing zones.
Willis,
I second Bill Illis on correcting for albedo before you calculate sensitivity. The albedo in the Antarctic is even higher than the Arctic according to the figures I’ve seen (Grant Petty, A First Course in Atmospheric Radiation). Also, when looking at changes in albedo over time, it’s a mistake to calculate an average albedo for the planet as a whole and then use that to calculate a planetary average energy flux. You should use the albedo and insolation by latitude to calculate the total flux.
Other points: the forcing from doubling CO2 is not uniform with latitude. It’s highest in the tropics, ~6 W/m2, and lowest at the poles, ~2W/m2. There’s high meridional heat transfer from the tropics to higher latitudes in both hemispheres. We know this because there is observed excess LW radiation to space from high latitudes compared to absorbed solar radiation. The total flux peaks at about latitude 45 N and S at a magnitude of ~5 PW. That’s about 9% of the total energy absorbed by the planet in each hemisphere. Heat transfer by eddy diffusion in the ocean is at least an order of magnitude faster than static diffusion, possibly several orders of magnitude faster. Heat transfer from the surface down is approximately matched by upwelling from the so-called thermo-haline circulation. We know this because the average depth of the thermocline is constant over time.
DeWitt Payne (17:44:10)
The albedo is a response to the forcing, not a forcing. That is why I have not included it.
Cite? Please don’t cite climate models, I’m looking for evidence.
Basically true, but … I don’t see what this has to do with my analysis.
DeWitt Payne (17:44:10) :
Other points: the forcing from doubling CO2 is not uniform with latitude. Itās highest in the tropics, ~6 W/m2, and lowest at the poles, ~2W/m2.
You might want to consider this paper which I stumbled upon a while back
http://ams.confex.com/ams/Annual2006/techprogram/paper_100737.htm
The link is to the abstract, but you can access the full paper by clicking the extended abstract link. The experiment utilized spectral analysis to differentiate the contributions of the various greenhouse gases to downwelling longwave radiation. I would refer you particularly to Tables 3a and 3b which are respectively the seasonal figures for winter and summer. In the cold, air of winter dry CO2 does show a significant contribution to DLW, 34.7 W/m2 of a total of about 150 W/m2, almost 25%. What I found interesting is what happens in the summer when the H2O contribution increases above 200 W/m2. The CO2 contribution decreases not only in relative terms, but also in absolute terms so that it amounts to 10.5 W/m2 out of a total of approx. 270 W/m2. Since this experiment was done in Canada, even the elevated DLW of summer is significantly below the figures I’ve seen quoted for Tropical and subTropical latitudes, which are generally well in excess of 300W/m2. If the suppressive effect of H2O is present at those latitudes, it would seem to suggest that total effect of CO2 would only constitute about 2% the greenhouse effect there and any marginal increases would be even less significant. Admittedly there could possibly be a greater effect from CO2 over large desert areas and the latitude bands in Willis’ graph do seem to suggest that,although that may be mostly a coincidence from what I understand of his analysis.
oops, “cold, dry air of winter”
Richard S Courtney (05:34:21) :
“The paleoclimate record strongly suggests that the climate system is bistable (i.e. stable in each of two states; viz. glacial and interglacial). If this apparent bistability is real then the energy accumulation you assert is an indication of a change from one state to the other.
The fine analysis conducted by Willis Eschenbach only concerns the climate sensitivity of the present interglacial state.
Therefore, your comment is not relevant to the present discussion unless you can provide an explanation for the apparent bistability of the climate.”
Your comment makes no sense. Something had to move the climate from one state to the other, and according to Willis E’s estimate it would take ~300 W per square meter. That’s essentially a second sun in the sky.
Just for general reference, here is a table of the associated black-body (100% emissivity) forcing temperatures associated with the TOA effective solar power radiation (insolation) levels of figure 1 in the main article here. I have calculated these values using 5.670E-8 for sigma, the Stefan-Boltzmann constant. I have also added an estimated background radiation from space, about 4.6E-6 W/m2, to each table value. I believe these temperatures would only be realized on a naked rotating black-body planet with a filtering process sufficient to average the daily energy received. Note that temperatures on the moon reportedly range from -153 to +107 degrees Celsius.
I do not propose to indicate these calculations might be directly applicable to conditions on Earth.
TOA Percent Kelvin Forcing
Insolation Solar Forcing Temperature
W/m2 Constant Temperature (Celsius)
0 0.0% 3.0 -270.2
50 3.6% 172.3 -100.8
100 7.3% 204.9 -68.2
150 10.9% 226.8 -46.4
200 14.6% 243.7 -29.5
250 18.2% 257.7 -15.5
300 21.9% 269.7 -3.5
350 25.5% 280.3 7.1
400 29.2% 289.8 16.6
450 32.8% 298.5 25.3
500 36.5% 306.4 33.3
550 40.1% 313.8 40.7
1370 100.0% 394.3 121.1
Boris (05:16:11) :
You quote me and say as follows:
Richard S Courtney (05:34:21) :
āThe paleoclimate record strongly suggests that the climate system is bistable (i.e. stable in each of two states; viz. glacial and interglacial). If this apparent bistability is real then the energy accumulation you assert is an indication of a change from one state to the other.
The fine analysis conducted by Willis Eschenbach only concerns the climate sensitivity of the present interglacial state.
Therefore, your comment is not relevant to the present discussion unless you can provide an explanation for the apparent bistability of the climate.ā
Your comment makes no sense. Something had to move the climate from one state to the other, and according to Willis Eās estimate it would take ~300 W per square meter. Thatās essentially a second sun in the sky.
***************
My “comment makes no sense”? Please reconsider.
If there are two states then each state has a climate sensitivity. In the absence of other knowledge, there is no reason to suppose that these sensitivities are the same (and it is unlikely that they would be).
Also, something has to induce a transition between the states. And there is no reason to suppose that the sensitivity during a transition would be the same as the sensitivity in either state (and it is unlikely that it would be).
But you are using “Willis Eās estimate” for one state and applying it to both states and the conditions during transitions. Thus, you estimate “it would take ~300 W per square meter” to achieve the transition”.
In other words, you are assuming that “Willis Eās estimate” is applicable to all the conditions of both climate states and their transitional conditions when Willis E does not make such an assumption (he only considers the present state).
The assumption is an adoption of your own: n.b. it is not part of Willis E’s analysis.
Your assumption is very unlikely to be correct.
You say your assumption indicates a need for “~300 W per square meter” to change the system from one state to the other, and this is confirmatory that your assumption is not correct.
So, as I said, “your comment is not relevant to the present discussion unless you can provide an explanation for the apparent bistability of the climate.ā
And that explanation must include a justification of your assumption that “Willis Eās estimate” is applicable to all the conditions of both climate states and their transitional conditions.
Richard
One point that needs to be stressed is that Willis’ analysis uses empirical, real-world observations (and so do the Idso’s “simple” analyzes). This bypasses all the “theories” — theories must agree w/real-world observations, not the other way around. There may be issues with what data Willis used and how, etc, but for the “theories” to come up w/sensitivity values so much greater than empirically-derived ones strongly suggests there is something basically wrong and/or grossly incomplete w/the “theories”.
I hope I’m not stating the obvious.
Re: Willis Eschenbach (Mar 2 19:15),
This an assumption on your part for which you provide insufficient justification.
Measured IR spectra looking down from altitude show a much larger dip in emitted flux in the CO2 band at low latitude than at high latitude (Petty, A First Course in Atmospheric Radiation, 2nd edition, figures 8.2 and 8.3, pp223, 225,6). The cause is that the difference in temperature between the effective emission altitude at 667 cm-1 for CO2 and the surface temperature is much higher in the tropics than at high latitudes. If you plug the numbers into MODTRAN, not only is the forcing from doubling CO2 lower, but it takes a smaller change in surface temperature to restore total LW Iout to the original value. MODTRAN is not a climate model. It’s a radiation transfer model that has been validated against observation many times.
Boris (05:16:11):
(reply to Richard S Courtney (05:34:21) )
“Your comment makes no sense. Something had to move the climate from one state to the other, and according to Willis Eās estimate it would take ~300 W per square meter. Thatās essentially a second sun in the sky.”
Help me out here. Your reading of Willis E’s climate heat interpretation is one of the following:
(a) for the earth’s climate to drop to glacial again, the sun will have to temporarily leave the solar system, or
(b) you dont believe in ice ages.
To say “something” has to move the climate suggests one has been beguiled by the spurious concept of “forcings”. A system with chaotic-nonlinear / nonequilibrium pattern dynamics, produces system changes between attractors intrinsically or internally. External factors do of course exert an entraining effect. (Although whether you call a factor external or internal depends on what you include in your system.)
Notwithstanding the heat inertia, the nonlinear climate system obeys the log-log power law that states that global climate temperature fluctuations include frequent small ones (e.g. ENSO oscillations), fewer bigger ones (LIA, MWP) and even fewer really big ones _glacial – interglacial. These are indeed as Richard Courtney says, attractors (“strange attractors). It can be a red herring to be fixated on forcings since such systems produce switches / flips intrinsically.
How – where does all the heat go? Thats the challenge to find out. When all is said and done, the future understanding of climate (so far unreached) will be one based on understanding the chaotic nonlinear nature of the system. Not just paying lip service to it, but built on it. The recent work of Tsonis is a good start.
http://www.agu.org/pubs/crossref/2009/2008GL036874.shtml
The “constructal law” proposed by Willis E and Bejan is also pointing in the right direction.
Willis,
Hope you are still following this thread still. I re-read both your articles, the paper by Bejan, and then thought about it in the context of our discussion re the atmospheric window. I concluded that:
1. There is clear evidence to support the atmospheric window (at the lower end at least) and this is easily available.
2. The behaviour of the atmospheric window, in WINTER, is the primary driver of Earth’s thermostat.
Too long to post here and you need all the pictures along with the explanation so please take a look:
http://knowledgedrift.wordpress.com/2010/03/03/theory-of-earths-thermostat-it-is-the-poles-in-winter/
Phlogiston:
I completely agree your comments at (13:26:33).
To ensure that my view is not misunderstood, I again summarise it here as follows.
The basic assumption used in the numerical climate models is that change to climate is driven by change to radiative forcing. And it is very important to recognise that this assumption has not been demonstrated to be correct. Indeed, it is quite possible that there is no force or process causing climate to vary. I explain this possibility as follows.
The climate system is seeking an equilibrium that it never achieves. The Earth obtains radiant energy from the Sun and radiates that energy back to space. The energy input to the system (from the Sun) may be constant (although some doubt that), but the rotation of the Earth and its orbit around the Sun ensure that the energy input/output is never in perfect equilbrium.
The climate system is an intermediary in the process of returning (most of) the energy to space (some energy is radiated from the Earth’s surface back to space). The Northern and Southern hemispheres have different coverage by oceans and, therefore, as the year progresses the modulation of the energy input/output of the system varies. Such a varying system could be expected to exhibit oscillatory behaviour and it does: the mean global temperature increases by 3.8K from July to January and falls by the same amount from January to July each year.
Hence, the system is always seeking equilibrium but never achieves it.
Iimportantly, the oscillations could induce harmonic effects which have periodicity of several years. Of course, such harmonic oscillation would be a process that – at least in principle – is capable of evaluation.
However, there may be no process because the climate is a chaotic system. Therefore, the observed oscillations (ENSO, NAO, etc.) could be observation of the system seeking its chaotic attractor(s) in response to its seeking equilibrium in a changing situation.
Very, importantly, there is an apparent ~900 year oscillation that caused the Roman Warm Period (RWP), then the Dark Age Cool Period (DACP), then the Medieval Warm Period (MWP), then the Little Ice Age (LIA), and the present warm period (PWP). All the observed rise of global temperature in the twentieth century could be recovery from the LIA that is similar to the recovery from the DACP to the MWP. And the ~900 year oscillation could be the chaotic climate system seeking its attractor(s). If so, then all global climate models and āattribution studiesā utilized by IPCC and CCSP are based on the false premise that there is a force or process causing climate to change when no such force or process exists. Indeed, glacial and interglacial states may be the result of there being two chaotic attractors.
It seems likely that the climate system exhibits both harmonic oscillation and chaotic attractor seeking.
But the assumption that climate change is driven by radiative forcing may be correct. If so, then it is still extremely improbable that – within the foreseeable future – the climate models could be developed to a state whereby they could provide reliable predictions. This is because the climate system is extremely complex. Indeed, the climate system is more complex than the human brain (the climate system has more interacting components ā e.g. biological organisms ā than the human brain has interacting components ā e.g. neurones), and nobody claims to be able to construct a reliable predictive model of the human brain. It is pure hubris to assume that the climate models are sufficient emulations for them to be used as reliable predictors of future climate when they have no demonstrated forecasting skill.
Hence, empirical assessments such as those of Idso and that of Eschenbach (above) are essential if we are to evaluate the validity of the assumptions which form the basis of existing numerical climate models.
Richard
Willis,
Very elegant idea but I have a couple questions.
1. Why focus on temperature rather than energy?
2. Why focus on atmospheric temps rather than ocean heat content?
3. Isn’t it stealing a base to assume that the northern hemisphere is completely separated thermally from the southern hemisphere?
It seems obvious that you are on the right track, or at least one of the right tracks, but wouldn’t it be better to correlate global cloud cover to ohc? Is that intractable?
Steve Koch (21:44:02) : edit
I would prefer to, but we don’t have the data for that.
I would prefer to, but we don’t have the data for that.
As far as I know, the amount of energy exchanged between the hemispheres is trivially small compared to the amount of energy contained in the hemispheres. If there is data that says otherwise, I’d love to see it.
Even with the current argo floats, we still have only limited coverage for ocean heat content. More to the point, correlating cloud cover with ohc doesn’t give us sensitivity. Likely worth doing, just not what I was doing.
Thanks for the interesting questions,
w.
DeWitt Payne (12:04:21)
Here’s a map of the albedo in February and August.
Note that the albedo is highest in the Southern Hemisphere in February, which is when the sun is warmest in the Southern Hemisphere. Brazil and Southern Africa are white, high albedo.
In the Northern Hemisphere summer, on the other hand, the albedo is high. In August, the upper parts of Africa and South America have high albedo.
Now, unless you want to claim that the changing albedo north and south is making the sun move north and south, I think I’ve made my point.
Willis Eschenbach (01:57:20) :
Here’s a paper on energy transport: http://www.cgd.ucar.edu/cas/Trenberth/trenberth.papers/i1520-0442-21-10-2313.pdf
I think fig.1 a) contradicts your claim “that the albedo is highest in the Southern Hemisphere in February”. True for the tropics, but the opposite at higher latitudes.
And why are you trying to convince people that 10 meters is a representative mixed layer depth?
“Weāre interested in about the top ten metres or so, thatās where the action of the sunlight is greatest. When diving there is often a pronounced thermocline around that depth”
This isn’t science. It doesn’t matter where the action of the sunlight is greatest when the heat is mixed tens or hundreds of meters down (or what your close to shore diving is telling you).
I think what you are doing here is setting up the proverbial “straw man”, that is countering an argument that hasn’t been made. Nobody is saying that positive feedbacks work within a single year!
Many of the positive feedbacks hypothesised gradually build up over a number of years, not from season to season.
The main ones are:
1. warming releases CO2 from the oceans which reinforces the anthropogenic release of CO2. The warming of the oceans in response to increased back-radiation from CO2 in the atmosphere would likely take decades, not a single season.
2. a decline in Arctic summer sea ice reduces the albedo of the oceans at high latitudes during the period of greatest insolation at that time of year leading to greater absorption of the back-radiation. Again, warming of the oceans is a long-term phenomenon – not a Winter/Summer one.
3. warming increases the anaerobic breakdown of vegetation currently locked up in permafrost which releases methane. Again a multi-year effect.
4. warming of the oceans may prompt the release of methane clathrates. This would definitely take several decades.
All of these have counter arguments but your paper sets out to address why positive feedback does not occur when it gets warmer in Summer. What is the point?
TLM,
In 2005, Hansen predicted that ocean heat content (ohc) would rise significantly in the next few years. He was very specific in his prediction (IIRC it was something like 10^22 joules increase in ohc/year).
That did not happen, as ohc instead levelled off and recently is declining. The question is why was Hansen’s model falsified? Maybe increased cloud cover has something to do with it.
To take the dynamic effects out of the model, perhaps you can compare the insolation anomalies to the temperature anomalies _at the extremes of temperature_ (which lag the sun by about six weeks). The off-peak sun at peak (average daily) temp should give a reasonable approximation to dT/dF for the earth as a whole.
Willis,
You need to determine the admittance into space, whereas you seem to have determined the total admittance of the system Y = F/T and viewed the two as equivalent
You need to subtract out the other admittances to obtain the admittance into space but you have not. Nor do you seem to have quantifiied them in any detail. You do express an opinion about only the top ten metres being significant but do not seem to have quantified the effect of that.
The Surface Mixed Layer, also know as the Well Mixed Layer, is on average substantial and varies by season and latitude, you may find various figures quoted, but the greater range seems to be from 10-500 metres. It tends to be low at the equator and greatest in midlatitudes. I gave admittance values for 50m and 100m well mixed layers. But it does not end there. Once you have settled on a depth estimate for a well mixed layer, you have to connect it to the ocean below. This is another susceptance which on average may be equivalent in effect to a another 20m well mixed layer for a 12 month cycle ~ 15W/K plus a conductance of ~15W/K due to diffusion down into the lower levels.
Based on those figures the total oceanic admittance for a 50m well mixed layer would be ~45W/K and for a 100m layer ~85W/K. These are significant values that I simply do not think can be ignored.
I equated your CS value for midlatitudes ~25W/K (for land and ocean) in my last above. I do not know what figures you get for land and ocean seperately. But if you get figures in or below the range 45-85W/K over the ocean then they could be due to oceanic admittance alone.
Finally, if the admittance into space over the oceans were say 25W/K and that only the top ten metres of the ocean is significant (8W/K of susceptance).
You have 25W/K of conductance and only about 8W/K of susceptance which leads to a phase angle of about 18 degrees of arc which is much the same as 18 days which is considerably less than the couple of months plus that typically occurs.
(If the figure you get for the conductive admittance into space over the oceans is greater than 25W/K, the phase angle would be even smaller.)
On the other hand a system with just an ocean comprising of a well mixed 50m and a diffusive lower ocean would have a phase angle of around 70 degrees (or days), which is more in the ballpark.
Over the land, 25W/K of conductance would imply only about one week of phase lag in landlocked areas (assuming an admittance due to the atmosphere of around 3W/K) not the ~3 weeks that actually occurs.
Now I do not know what figures you have for land and ocean seperately. But I expect that you get a smaller admitance than 25W/K over the land, making the resultant phase angle more reasonable, but an admittance greater than 25W/K over the ocean implying an even smaller phase angle for the case where only the top 10 metres of the ocean were worth considering.
I do not know what figures you would get for these phase angles so I can not comment further.
I think my views are quite clearly that: the problem is ill-conditioned (see my previous), that the oceanic admittances are poorly quantified and vary with latitude, that you have taken a view that the effects of the admittances of the land, atmosphere, and oceans are insignificant and have hence failed to make any allowances for them.
I doubt that I can be of more assistance other than advise you to produce a range of results based on a plausible range of oceanic, atmospheric, and land admittances, and see where that leads you. I rest on that final thought.
Alex
Richard,
Your post is once again nonsense. I see a lot of hand waving about climate states. But the state that we are in, if correctly described by Willis, suggests an enormous amount of energy is necessary to move us to a glaciation. If you disagree, then what positive feedback amplifies the cooling? And why would this positive feedback not amplify the warming?
Alexander Harvey (16:22:36)
Actually, you can be of more assistance. This is because I’m not sure I even understand the mathematical details of your argument about admittances, although it seems probable that your points are valid.
So if you truly would like to be of assistance, can I once again ask you to take reasonable assumptions of oceanic, atmospheric, and land admittances and use your detailed understanding of admittance to produce a range of what you would call sensitivity values?
As I have said before, even if my numbers are out by an order of magnitude, my results are still way, way lower than the canonical IPCC values. So because of my lack of understanding of your argument, I have to ask your assistance in trying to get to the true value of the sensitivity. Could you do the calculations and report back to us? Because I don’t know if I can do them correctly, and I am very reluctant to do them wrong and get into an endless argument about my errors.
Many thanks for your help in this,
w.
Willis – this is a quick observation on the fly having just seen the dialogue above with DeWitt Payne re: albedo.
How is the graphic you show in comment Willis Eschenbach (01:57:20) generated? One obvious thing that strikes me is the image seems to show stronger reflection off land which is more perpendicular to the suns rays with the Sahara and the Andes appearing “seasonally constant”. Is that what you mean by albedo being a response to the forcing?
Re: the graphic – Has this image been generated by a timelapse composite? Does it have any calibration? How is cloud cover treated?
From a very rough counting squares approach I get the land area between the tropics to be about 1/5 of the Earth’s surface. Hence land’s seasonal impact on the albedo is going to be factored accordingly as one would expect sea water to have an albedo which is constact with angle of incident light. My understanding is that the tropics account for the vast majority of received insolation and that the oceans are the major recipients and distributors of solar energy in this zone.
I had a quick look at the graphic 1a) that Igl references and it shows the monthly albedo anomaly from the annual average. The -20deg to +20deg latitude bands seem consistent with your graphic.
Apologies if all this is either covered above, irrelevant or plain wrong; it’s an “on the fly” observation in case any of it is relevant/helpful – I haven’t read all the comments or your “Thermostat” article but I like your use of daily and seasonal insolation variation to get another view on sensitivity values.