An Interim Look At Intermediate Sensitivity

Guest Post by Willis Eschenbach

Whenever I find myself growing grim about the mouth; whenever it is a damp, drizzly November in my soul; whenever I find myself involuntarily pausing before coffin warehouses, and bringing up the rear of every funeral I meet; and especially whenever my hypos get such an upper hand of me, that it requires a strong moral principle to prevent me from deliberately stepping into the street, and methodically knocking people’s hats off—then, I account it high time to get to sea as soon as I can.

Ishmael, in Moby Dick.

Yeah, that pretty well describes it. I’d been spending too much time writing about the weather and the climate, and not enough time outdoors experiencing the weather and the climate. So following Ishmael’s excellent advice, I have been kayaking and walking the coast and generally spending time on and around the ocean. During this time I have been considering what I want to write about next. Being on the water again, after the last few years of being boatless, has been most invigorating.

I have chosen to write about my on-and-off investigation of the relationship between changes in surface temperature and corresponding changes in top-of-atmosphere (TOA) radiative balance. I wrote about this previously in a post entitled A Demonstration of Negative Climate Sensitivity. This is an interim report, no code, little analysis, just some thoughts and some graphics, as I am in the (infinitely) slow process of assembling code, data, and results for publication in a journal. Unlike my previous post which used 5°x5° data, in this post I am using 1°x1° data.

Let me start with an interesting question. Under the current paradigm, the assumption is made that surface temperature is a linear function of the TOA imbalance (forcing). But is it true? In particular, is it true all over the world? To answer this, I looked at the monthly TOA radiation imbalance (all downwelling radiation minus all upwelling radiation) versus the change in temperature.

max value r2 temp vs toa imbalFigure 1. Maximum of the R^2 value, temperature vs TOA imbalance. This is the maximum of the individual R^2 for each 1°x1°gridcell, calculated at lags of 0, 1, 2, and 3 months. An R^2 of 0 means there is no relation between the two datasets, and an R^2 of 1 means that they move in lockstep with each other. In the red areas, when the TOA radiation balance changes, the temperature changes in a similar fashion. In the blue areas, changes in temperature and TOA imbalance are not related to each other.

Figure 1 has some interesting aspects.

Figure 1 was created by displaying, for each gridcell, the largest of the four R^2’s, one from each of the four lag periods (0, 1, 2, and 3 months). One interesting result to me was that while the temperature of a large part of the earth slavishly follows the variations in the local TOA balance (red areas), this is not true at all, at any lag, for the area of the  inter-tropical convergence zone (ITCZ, blue, green, and yellow areas). This is evidence in support of my tropical thunderstorm thermostat hypothesis, which I discuss in The Thermostat Hypothesis and It’s Not About Feedback. For that hypothesis to be correct, the surface temperature in the ITCZ must be decoupled from the TOA forcing … and it is obvious from Figure 1 that the ITCZ temperature has little to do with forcing.

Next, I wanted to look at the climate sensitivity. In a general sense, this is the amount of change in the surface temperature for a 1-unit change in the TOA radiation imbalance. There are a variety of sensitivities, from instantaneous to equilibrium. Because I have monthly data, I’m looking at an intermediate sensitivity.

Figure 2 shows the temperature change due to a 3.7 watt per metre squared (W/m2) at various time lags. When the TOA radiation changes, the surface (land or ocean) does not respond immediately. By examining the response at different time lags, we can see the characteristic lag times of the land and the ocean.

temp change from TOA imbalance 0 to 1 mo

temp change from TOA imbalance 2 to 3 mo

Figure 2. Climate sensitivity (temperature change from a 3.7 W/m2 TOA imbalance) for the earth. Sensitivity is determined as the slope of the linear regression line regarding TOA variations and surface temperature for each gridcell, over the period of record. Click on upper or lower image for larger version.

Consider first the land. For most of the land, the strongest response (orange and red) occurs after a 1-month lag. The maximum sensitivity is in the areas of Siberia and the Sahara Desert, at around 0.8° per doubling of CO2. Extratropical land areas are more sensitive to TOA variations than are tropical land areas. The highest sensitivity in the Southern Hemisphere is about 0.3°C per doubling of CO2

Curiously, tropical Africa shows a lagged negative sensitivity. This becomes evident at a 2-month lag, and increases with the 3-month lag.

The ocean, as we would expect, is nowhere near as sensitive to TOA variations as is the land, with a maximum sensitivity of about 0.4°C per doubling, The sensitivity over most of the ocean is on the order of 0.1°Ç per doubling.

Finally, Figure 3 shows the relationship between the climate sensitivity and the temperature. Because of the large difference between the land and the ocean, I have shown them separately.

scatterplots climate sensitivity vs temperature

Figure 3. The relationship between climate sensitivity and temperature. Each point represents one gridcell on the surface of the earth. For each gridcell, I have used the time lag which gives the greatest response. Colors show the latitude of the gridcells.

Here, let me point out that I have long maintained that climate sensitivity is inversely related to temperature. This is clearly true for the land.

As I said, not much analysis, just some thoughts and graphics.

Best to all,

w.

DATA

Sea Temps: NOAA ERSST

Surface Temps: CRU 3.1 1°x1° KNMI

TOA Radiation: CERES data

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John Doe

The two best days in a boat owner’s life are the day he buys his boat and the day he sells it.
The days come in pairs but there may be more than one pair.

wsbriggs

Welcome back Willis! I, for one, have seriously missed your contributions here.
as usual, your analysis has excellent graphics supporting your exploration. I’m looking forward to the full paper.

Bill Illis

Wow,
Real data about how the real climate operates. I think you got it here.
This all fits with what we have seen and know about – some polar amplification, flat equatorial Ocean temps going back 140 years, temperature not rising anywhere near the rate predicted in the theory, Land warming in certain places (mainly high latitudes) with very little in the Oceans, very limited feedbacks operating, much more consistent with paleoclimate data, 1000 times higher spatial resolution than anything that has been done with CERES before.
You might have rewritten the book here.

B. McCune

Your analysis is always so visual and that’s a good thing for me. The gray of Antarctica leaped out at me when I went to compare the north pole with the south (or the south with all the rest of the world). Looking at the data for the southern region indicates sparse and short term data. I am guessing that is the reason for the the gray southern region. What a pity that we lack data for such an important part of the world if this is the case.
Bernie

michael hart

Consistent with phase changes of water that can produce large heat fluxes while simultaneously registering minimal temperature changes.

Hans H

Great to have you back, Willis! I really hope you take care of yourself as you are a hero of mine.
Greatings from a snowy and unsually cold Copenhagen.

The observation that there is a significant difference between ocean and land is further evidence that atmospheric CO2 is not a major controlling factor (concentrations are the same over land and sea at the same latitude). The water cycle is the big controlling factor(evaporation/condensation – freeze/thaw).

tty

The lagged negative response in the Sahel (and to a smaller extent in India and northern South America) is presumably a monsoonal effect, warmer temperatures causes the air over land to rise more, which pulls the ITCZ further north with more rains that cools the climate. During previous warmer interglacials this effect caused the Sahara to more or less disappear.

Venter

Welcome back Willis, missed your posts.
Good, succint post as usual.

Figure 1, showing blue at the north pole and equator is interesting. It would be interesting to see what is happening at the south pole. The green at the antarctic peninsula hints that the south pole may also be blue.
The blue region at the north pole indicates that the melting of sea ice at the north pole is not an indication of atmospheric forcings. This has significant implications for climate science on its own, as it has long been publicized that the melting of arctic sea ice was an indication.
A paper showing that there is little of no correlation between arctic temperatures and climate forcings would perhaps be very significant.

Gary

Always good to have you thinking about a new perspective on the climate data, Willis.
If you hadn’t noticed, Bejan and colleagues have done some more work on applying Constructal Theory to climate with this paper” http://www.constructal.org/en/art/Climate_change_%20in_the_framework_of_the_Constructal_Law.pdf. Any comments on that?

The scatter plots are interesting. They show that one of the most basic of climate assumptions is wrong. The climate models that temperature is a linear function of forcings – that sensitivity is a constant.
However, what the scatter plot shows is that sensitivity is not a constant. Sensitivity is a function of temperature as well as forcings. That as temperature increases, sensitivity decreases, until it becomes negative at about 30C.
This suggests that runaway temperature increase is impossible. That the earth has a mechanism in place that operates around 30C to prevent any further temperature increase.
These scatter plots are very significant because the show that the underlying assumption of constant climate sensitivity is wrong. This would help explain why temperatures have not increased significantly in 16 years. Runaway warming is impossible because as temperatures increase sensitivity turns negative, preventing further increase.
This has huge implications in climate science and would explain why we have not seen runaway warming in the paleo records, even when CO2 levels were much higher.

Reblogged this on gottadobetterthanthis and commented:
Thanks Willis.

Gary says:
December 10, 2012 at 5:56 am
If you hadn’t noticed, Bejan and colleagues have done some more work on applying Constructal Theory to climate with this paper”
======
Constructal theory is an interesting idea. Boat owners (mono-hulls) curse it every time they anchor and the wind drops. The boats immediately turn broadside to the swell to minimize the energy used to move with the swell, and in the process roll the guts out of everyone aboard.
Sailboats hang a “flopper stopper” out over the side on a spinnaker pole to prevent this. This changes the energy needed to roll the boat and the hull will quickly turn to face the waves as it now takes less energy to pitch than roll.
What this means is the physical objects seek the minimum energy level required to accomplish the work. Water seeks the easiest path as it were. Not only water, but boat hulls and now it seems climate as well.

Great paper. If I read the charts right it means that the tropics has found its temperature, and any amount of CO2 is totally swamped by the effect of water vapor in the tropics. This seems to validate the thermostat hypothesis, and all climate models will have to take into account the effect of clouds and thunderstorms and their strong negative feedback

cd_uk

Willis
It seems from your plots that the relationship between surface temperature and TOA, that you’re using as a proxy for sensitivity (right?), is a dependent on latitude over land and not over ocean. Therefore, it seems likely that you’re measuring the dampening effects of atmospheric water vapour? In short, you get the greatest response over drier and colder parts of the planet. Was this not a prediction of the original GCMs?
If so how do your results compare to their predicted (projections) for high latitude warming?

RockyRoad

Yes, Welcome back, Willis! Always a thought-provoking exercise–I think you’re onto something big here.
So as the hydrologic cycle is the vast heat radiator and temperature knob for the earth, can we expect current encroachment of the Sahel upon the Sahara to continue until the sand is overtaken with vegetation? Do we know if this has happened with any/each of the past three temperature maxima that have appeared at regular 1,000-yr intervals, as this current one would suggest? When grapes were grown in England and Vikings farmed Greenland, did goat herds thrive across the Sahara?

commieBob

Good news! It looks like the IPCC is going to back away from global warming hysteria. Slashdot has the following story:

“More precise modeling has changed some long term climate predictions: sea levels to rise almost a meter more than present over the next century, but past dire warnings of stronger storms or more frequent droughts won’t pan out. Instead there will be less strong storms, but peak winds in the tropics might be slightly higher. Temperature rise of global average will be about 3 degree C total, including the 1 degree C rise over the 20th century. In places where precipitation is frequent, it will become even more frequent; in arid areas, the tendency will be to become even drier. Some new arid areas are expected to appear in the south of N. America, South Africa and Mediterranean countries. Overall, hardly a doomsday scenario.http://news.slashdot.org/story/12/12/10/0320239/draft-of-ipcc-2013-report-already-circulating

That story links to an ABC News story: http://abcnews.go.com/International/science-hone-climate-change-warnings/story?id=17906408#.UMVJntHQQSk

RockyRoad

I wasn’t surprised to see oceans max out at ~30 degrees; however, I was surprised to see land max out at about 30 degrees also. The oceans benefit from rapid evaporation at that high temperature–is that also the mechanism that operates on land? Or is it merely a function of the granularity of the sample size, with space for relatively few outliers?

Espen

Wow, this is really, really interesting stuff. Like Fred Berple, I was especially intrigued by the scatter plots. I’ve long suspected that sensitivity isn’t linear at all – your scatter plots shows it. So much for “runaway warming” – for all we know, we may be close to the upper limit to how warm the earth can become in the current phase of the Milankovitch cycles and with the current continent configuration!

chris y

Figure 3 is absolutely stunning. The most amazing effect is the swing into negative climate sensitivity at around 30 C. This occurs over oceans even though higher temperatures should cause higher absolute water vapor concentrations and *increase* the climate sensitivity immediately.

ferd bergle:

climate models that temperature is a linear function of forcings – that sensitivity is a constant

Actually they don’t assume sensitivity is a constant. That’s a common assumption by people try to arrive at estimates of climate sensitivity, but it is neither an assumption, nor does it even hold true in the models. see e.g. this

Re: CO2 sensitivity
So it is not necessary to go to an over-elaborate analysis to
plot a graph to show that the CO2 saved N. Hemisphere
or even the world from onset of the new LIA in 1960s.
or to calculate theCO2 feedback sensitivity at 3 degrees C
for doubling of the CO2 concentration.
http://www.vukcevic.talktalk.net/00f.htm
(acrostichis web page)

pochas

Once again, nice work Willis. I also wonder about those areas of negative sensitivity. Is it related to the fact that those are areas of intense precipitation?

View from the Solent

ferd berple says:
December 10, 2012 at 6:20 am
….
What this means is the physical objects seek the minimum energy level required to accomplish the work. Water seeks the easiest path as it were. Not only water, but boat hulls and now it seems climate as well.
====================================
Not just physical objects. That’s the principal of least action http://www.principlesofnature.net/principle_of_least_action.htm

Gary Pearse

Willis, the elegance blows me away! With heavyweights in climate science tuning multicomponent models, the most principal component being CO2, to take simply net TOA downwelling radiation and 3.7W/m^2 (nothing controversial there!) and show the variability in sensitivity between land, ocean and latitude is an E=mc^2 moment. That the sensitivity turns negative in both cases at about 28 C – the thermostat setting- is the most beautiful demonstration in climate science or maybe even science since the golden age. I knew I was reading something very special when you came out with the thermostat hypothesis – and now you have essentially enclosed this sweet nut into a universal climate theory. How can the linear thinkers who make up the famous 97% wiggle out of this? It will be instructive to see how many of the well known CliSci folk will cling to the scuttled ship.

Ian W

chris y says:
December 10, 2012 at 6:48 am
Figure 3 is absolutely stunning. The most amazing effect is the swing into negative climate sensitivity at around 30 C. This occurs over oceans even though higher temperatures should cause higher absolute water vapor concentrations and *increase* the climate sensitivity immediately.

Chris, higher absolute atmospheric water vapor concentrations would only act as a positive feedback (increasing sensitivity) if you only consider radiative forcing. But water vapor carries latent heat up past the denser atmosphere and releases that latent heat as it condenses into clouds and more latent heat when/if those clouds freeze at height. At the same time the clouds increase the atmospheric albedo cooling the surface and perhaps drop rain further cooling the atmosphere and surface below.
The other effect of heightened humidity which everyone ignores is that as you raise atmospheric humidity you raise atmospheric enthalpy. So although the energy content of the air may increase its temperature will not increase at the same rate if at all.

It is always wise to both challenge and critically examine assumptions, we all know that but many fail to do so. Your reminder is both cogent and timely. Alas for all to many it will be ignored as it requires far to many to actually think about something instead of accepting the “pablum” being fed to them.

Keith AB

Good one Willis. Always thought provoking and well presented with it.
It looks to me, and I am just a Tyro in this game, that the real regulator is the ocean. 1.3 Billion cubic Kilometers and that has to change in temperature if the Earth does. To get some perspective I calculated that each of the 7 billion humans on Earth would have to burn the equivalent of 100 times the amount of fossil fuel we do today over a lifetime of 70 years to raise the ocean temperature by 1 deg Celsius.
There is no way that atmospheric CO2 can warm anything up more, or faster, than the direct heat of combustion as that would be a perpetual motion machine. I haven’t begun to consider the cooling effect of evaporation, nor have I considered the effect of people currently burning biomass taking up the much more efficient energy from power stations so my 100 times is very conservative. However it is obvious from your short paper that evaporation in the tropics has a huge effect for climate stability.
So to get back to my point, which is made by Willis’ Fig.2. It really is all about the liquid ocean which acts as the global regulator. It is good that Willis gets to float on it. I walk down to it at least once a week and also contemplate its vastness. It makes me realise just how silly we are to think that we can over power its awsome being.

beng

Thanks, Willis. Excellent analysis of the major factors.
I wonder which warmers can really appreciate this…

Willis Eschenbach

John Doe says:
December 10, 2012 at 4:20 am

The two best days in a boat owner’s life are the day he buys his boat and the day he sells it.
The days come in pairs but there may be more than one pair.

Thanks, John. In my experience, that’s true for every kind of boat except a kayak. They are just too much fun and too little upkeep to ever be a problem.
w.

Willis Eschenbach

Gary says:
December 10, 2012 at 5:56 am

Always good to have you thinking about a new perspective on the climate data, Willis.
If you hadn’t noticed, Bejan and colleagues have done some more work on applying Constructal Theory to climate with this paper” http://www.constructal.org/en/art/Climate_change_%20in_the_framework_of_the_Constructal_Law.pdf. Any comments on that?

Much appreciated, Gary. Steven Mosher was kind enough to send me a copy of that paper. It’s a fascinating study, but I haven’t been able to fully wrap my head around it yet.
w.

beng

****
RockyRoad says:
December 10, 2012 at 6:27 am
So as the hydrologic cycle is the vast heat radiator and temperature knob for the earth, can we expect current encroachment of the Sahel upon the Sahara to continue until the sand is overtaken with vegetation? Do we know if this has happened with any/each of the past three temperature maxima that have appeared at regular 1,000-yr intervals, as this current one would suggest? When grapes were grown in England and Vikings farmed Greenland, did goat herds thrive across the Sahara?
****
IIRC, the Sahara greening occurs with the ~20k yr precession cycle — summer insolation max in NH expands the monsoon to partially cover it, and min is solid desert like now. I think the last Sahara greening lasted until about ~6000 yrs ago as the summer insolation was declining from the 10000 yr ago max.
I’m unsure whether this Sahara greening occurs even during the glacial periods (which last ~90 kyrs) in addition to the interglacials, tho.

jorgekafkazar

Note that the average terrestrial TSI is 369 times larger than the estimated direct greenhouse forcing of 3.7 watts/m². I.e., the CO2 forcing is only a very small fraction, about a quarter of a percent, of the TSI. It doesn’t take much variation in the estimation of other climate phenomena to overwhelm any putative effect of CO2. Thus the AGW greenhouse effect, despite its in-laboratory grounding, remains just that: theoretical, and unproven on the larger scale. Small wonder that certain climate scientists resort to mummery in attempting to tease a corresponding temperature signal out of some of the noisiest data on Earth.
[Note, too, that Perihelion to Aphelion TSI varies by far more than 3.7 watts/m², going between 1,413 and 1,321 over the course of a year, a difference of 92 w/m².]

snowrunner

It has always seemed obvious to me that you should see a bigger temperature rise for the same amount of forcing in cold or dry areas (eg the Arctic and Sahara) for the simple reason that water vapour takes more energy to heat up than dry air. This seems to be what you have shown. Now I wonder if you can turn this around so that instead of calculating the mean global temperature (which has always seemed pretty meaningless to me) a sensitivity weighted average was calculated. This would roughly correspond to global atmospheric enthalpy I guess. My guess is that the only thing that is keeping global mean temperature relatively high at the moment is the fact that somewhere has to be warmer than average, and at the moment it happens to be the Arctic.

D Böehm

A seminal work, Willis. Really excellent. Your conclusion is short and sweet:
…climate sensitivity is inversely related to temperature. This is clearly true for the land.
And the oceans have only a 0.1º sensitivity. When averaged with the land, that would mean a ≈0.0º global sensitivity for 2xCO2. Miskolczi got it right.
Climate alarmism is based on the ‘received wisdom’ that climate sensitivity is directly related to temperature. The only argument has been over the magnitude of the forcing for 2xCO2. By showing empirically that sensitivity becomes inversely related as temperature rises, you have really upset the mainstream climate apple cart.

Willis Eschenbach

jorgekafkazar says:
December 10, 2012 at 10:15 am

Note that the average terrestrial TSI is 369 times larger than the estimated direct greenhouse forcing of 3.7 watts/m². I.e., the CO2 forcing is only a very small fraction, about a quarter of a percent, of the TSI.

Jorge, I fear you are comparing apples and oranges here. The greenhouse forcing of 3.7 W/m2 is calculated as a 24/7 global average over the surface area of the earth. TSI, on the other hand, is the solar energy hitting a square metre at the top of the atmosphere (about 1368 W/m2). It is not averaged over the surface of the earth.
As a result, to convert TSI to the same units as the CO2 forcing, we have to divide the TSI by 4, which gives us a 24/7 global average solar radiation of about 342 W/m2. The CO2 forcing is then about one percent of the (globally and temporally averaged) TSI.
Having said that, you are correct, that is still quite small. I classify that as a “third-order” forcing. In my classification, a “first-order” forcing changes the total forcing by more than 10%. Clouds are an example of this strength of forcing.
Second order forcings are those that change the total forcing by between 1% and 10%.
Finally, third order forcings are those that change the total forcing by one percent or less … which, as you point out, includes a doubling of CO2.
w.

ferd berple says:
December 10, 2012 at 6:03 am
“That as temperature increases, sensitivity decreases, until it becomes negative at about 30C.”
This fits one of my hypothesis on the effects of CO2, that it’s mainly effective up to a little past 0C, where water vapor takes over.
The peak co2 wavelength that isn’t swamped by water absorption is ~10um which is ~15C through maybe 14um @~-66C (co2 boiling point is -57C).
So an Ice ball earth with minimal water vapor, and large areas of ocean covered in ice restricting co2 from dissolving into water, will accumulate co2 in the atm, building until the planet starts to warm, and more water vapor accumulates bringing temps up the rest of the way.
Also remember that IR coming in at .5u takes 20 times as long to radiate out at 10u, and yet on clear nights air temps drop like a rock, and is limited to how fast the ground can cool.

Matthew R Marler

Here, let me point out that I have long maintained that climate sensitivity is inversely related to temperature. This is clearly true for the land.
Nice work, and lots of it. At the highest temperature, the mean of the feedbacks is still positive. It looks like a simple extrapolation yields a hypothesis that at at higher maxima than observed now, the mean feedback would be 0. I came up with a similar hypothesis from some simple calculations based on the Graeme Stephan updated energy flow diagram that Dr Curry presented at ClimateEtc a few weeks ago.

old engineer

Willis-
Along with everyone else, I am glad to see you back. Good to hear you took some time “to smell the roses.”
Let me check to make sure I understand your analysis. As I understand your post:
First you used surface temperature data and the corresponding (in time and space) TOA radiation data to do a linear regression for the whole planet in 1 degree boxes. You state you used monthly data. Question: What time periods did you use? Every month of the year for one year? Average over a number of years for each month? Or a single month averaged for several years.
You did this for four different temperature lags.
Then using the best (highest r^2) regression equation for each box ,you calculated the temperature change for a decrease of 3.7 W/m^2 in TOA outgoing radiation. ( I was somewhat confused when you switched to “doubling of CO2,” but assume that a change 3.7 W/m^2 represents a doubling of CO2).
The resulting scatter plots show the climate sensitivity as a function of some temperature. I assume that the temperature is the average monthly temperature in box. Again, my question is about the time period used for the average monthly temperature. Looks like these plots deserve a lot of study. Lots can be inferred from them.
Thanks again for your post. It is always edifying to see what can be done with real data.

pochas

Until the climatologist community gets over its radiative fantasies and begins to examine the actual dominant factors in climate physics we’ll continue to hear about CO2, which is a minor player if any. Talking about sensitivity “to a doubling of CO2” just feeds the crocodile when any such sensitivity is so small as to be negligible, especially against powerful negative feedbacks from convection and the water cycle, which apparently have the Climate Illuminati baffled. We can actually expect climate changes well beyond anything attributable to CO2, and because of the all-pervading CO2 radiative phantasm, scientists and academics cannot make credible predictions.

Willis Eschenbach

Matthew R Marler says:
December 10, 2012 at 11:11 am

Here, let me point out that I have long maintained that climate sensitivity is inversely related to temperature. This is clearly true for the land.
Nice work, and lots of it. At the highest temperature, the mean of the feedbacks is still positive. It looks like a simple extrapolation yields a hypothesis that at at higher maxima than observed now, the mean feedback would be 0. I came up with a similar hypothesis from some simple calculations based on the Graeme Stephan updated energy flow diagram that Dr Curry presented at ClimateEtc a few weeks ago.

Matt, good to hear from you, thanks for the comments.
Rather than looking at it as “feedback”, it is more useful to see the climate as a governed system. “Cruise Control” in a car is perhaps the most common everyday example of a governed system. A governed system is “homeostatic”, meaning it tends to keep a given variable within some range of a target value. In the case of the car, it keeps the speed within some range of a target speed by varying the amount of fuel going to the engine.
Now, suppose you have a car under “cruise control”. The ground is reasonably level overall, but it contains mild ups and downs. When the car goes up a slight incline, the cruise control increases the flow of fuel to the engine to maintain the speed. When it goes down the slight incline, the fuel flow is correspondingly decreased.
If the ground is reasonably level, the amount of fuel increase on the inclines will be about the same as the amount of fuel decrease on the declines. This could be described as a net feedback of zero, as you have done above.
However, in fact what is happening is not zero. It is a series of strong but opposite control inputs which balance out over time, and that is very different from a condition called “no feedback”.
w.

joeldshore

D Boehm says:

And the oceans have only a 0.1º sensitivity. When averaged with the land, that would mean a ≈0.0º global sensitivity for 2xCO2. Miskolczi got it right.

You seem to have misunderstood what Willis has said about the relationship between climate sensitivity and temperature. All that he is saying is that the sensitivity is a (slowly) decreasing function of the temperature. [I’m not saying that I completely agree with Willis’s analysis or even his use of the term “climate sensitivity” in this context, but let’s leave that aside for now and assume what he is saying is correct.]
This is not actually surprising since the no-feedback climate sensitivity derived from the Stefan-Boltzmann equation is also a decreasing function of the temperature: If the intensity I is proportional to T^4 then dT/dI, which is the inverse of dI/dT is proportional to T^3 where T is the absolute temperature (i.e., temperature measured in Kelvin).

Climate alarmism is based on the ‘received wisdom’ that climate sensitivity is directly related to temperature.

No…It is not. Where have you seen it claimed that the climate sensitivity is proportional to the temperature?
You seem to understand neither what the conventional scientific understanding is nor what Willis has shown here. Not surprisingly, your misunderstandings are in the direction of causing you to believe what you want to believe.

Matt G

I posted something like this the other week and fits well with the graphics shown on this article.
The 3.7W/m2 is claimed for a doubling of CO2, yet 324 W/m2 is claimed for all greenhouse back radiation. A doubling of CO2 therefore is just 1.1% of the total. If 33c represents the total for greenhouse gases this just represents 0.36c rise per doubling of CO2. This is being generous because most of the warming from greenhouse gases occurs in the first parts with it being logarithmic. Forgot to put before that this also doesn’t take a water body into account either on the surface. This value fits around the middle between 0.1c and 0.8c mentioned in figure 2.
There is obviously some disagreement here compared with the theoretical 1c per doubling CO2. The reason is obviously because this is partly derived from ideas over land not the ocean. The 324 W/m2 claimed for all greenhouse gases doesn’t warm a bucket of water in the shade during one day, so 1.1 percent of this even if atmospheric levels in future were reached are so miniscule. No wonder we can’t measure the difference from zero now with many decades until the possibility for a doubling of CO2 is reached.
Since the 1960’s CO2 levels have raised 90ppm until now so a doubling of CO2 won’t occur until it hits 630ppm. That means we are 28.57% of the target for a doubling of CO2. Therefore CO2 should have since the 1960’s only warmed the planet by 0.1c. This 0.1c being on the high side and other AGW issues bringing this value to around 0.1c (~0.05+0.05). The planet since then has risen 0.4c so only 25 percent at the most has come from AGW; natural makes up at least 75 percent. With 75 percent mainly making up the declining global low cloud albedo and reduced negative swings in the ENSO. NO wonder we are going through a long non-warming period because the natural climate is driving the planet.

Willis:
I think you’d better leave this to the PROFESSIONALS! You know, like the PROFESSIONALS who invented the airplane (whoops, sorry…amatuers), OK, then the telephone (whoops, sorry, teacher of the deaf, no science training…), alright, the Light Bulb, Phonograph, Motion Picture Camera…(whoops, sorry, 1 1/2 grades of education then home schooled…), OK…the RADIO!!!!, darn, an ENGINEER yes, but for telegraphy…no physics background, no University position.
WELL, darn it then, how about the INTEGRATED CIRCUIT? Whoops, once again, B.S. Electrical Eng., left at Texas Instrument labs, ALONE during the “holidays”…with all the equipment, newly hired, no specific assignment. Used the lithography/epitaxial transitor process to make a two transistor amplifier, with resistors and capacitors made using diffusion processes in the Silicon substrate. (When he was called in to the “head offices” to explain what he had done, putting a two transistor amplifier in a TQ-5 transitor (top hat)mounting…HE THOUGHT they were going to fire him for “misuse” of equipment…not hardly. )
But again, no “credentials”, no PEER REVIEWED PAPERS…
Obviously Willis, the ONLY thing you can do is produce things that WORK or are COMPLETELY correct, based on NATIVE GENIUS.
You need to be CONTROLLED and held down. (Or start a “stock” company, Willis Inc., so we can INVEST NOW!)
Max

Willis Eschenbach

old engineer says:
December 10, 2012 at 11:16 am

Willis-
Along with everyone else, I am glad to see you back. Good to hear you took some time “to smell the roses.”

Yes, although this time of year rather than smelling the roses I’m sniffing the sea breeze for rain coming in off of the ocean … my thanks to you and everyone for the good wishes. I generally write only when I can’t stand not writing, and as with many things in my life, the intensity of that comes and goes.

Let me check to make sure I understand your analysis. As I understand your post:
First you used surface temperature data and the corresponding (in time and space) TOA radiation data to do a linear regression for the whole planet in 1 degree boxes. You state you used monthly data. Question: What time periods did you use? Every month of the year for one year? Average over a number of years for each month? Or a single month averaged for several years.

I did a linear regression on a gridcell-by-gridcell basis. Dataset size was limited by the length of the shortest dataset, which is the CERES dataset, about five years of monthly data. For each gridcell, I regressed five years of TOA imbalance data against five years of surface temperature data.

You did this for four different temperature lags.
Then using the best (highest r^2) regression equation for each box ,you calculated the temperature change for a decrease of 3.7 W/m^2 in TOA outgoing radiation. ( I was somewhat confused when you switched to “doubling of CO2,” but assume that a change 3.7 W/m^2 represents a doubling of CO2).

Correct, including the fact that the IPCC says that a doubling of CO2 will increase the TOA downwelling radiation by 3.7 W/m2. I have used their value for simplicity and comparison with other estimates.

The resulting scatter plots show the climate sensitivity as a function of some temperature. I assume that the temperature is the average monthly temperature in box. Again, my question is about the time period used for the average monthly temperature.

Good question. Actually, it is the average annual temperature for a given gridcell over the ~ 5-year period of record.

Looks like these plots deserve a lot of study. Lots can be inferred from them.
Thanks again for your post. It is always edifying to see what can be done with real data.

Indeed, it is a most fascinating line of inquiry.
w.

Matt G

Damn, in my previous post should be raised 80ppm. so this changes the values through it a little, although the conclusion is still the same.
These now change to 25.4% of the target for a doubling of CO2 and 0.09c contribution from CO2 since the 1960’s.

@Willis:
I presume that “forcing” in this posting is defined as “Watts/ M^2” (with no particular time dimension?).
Overall, nicely done. Very nicely done.
Be aware that as you are using monthly AVERAGE data, that averaging process can induce a time lag in the apparent response. (Don’t know if it does in this case, as I don’t know how your average is computed, but it is a common problem with ‘moving averages’ in financial indicators, for example, where the ‘lag’ is critical as you find out about market reversals some time after they happened…)
Oh, and I just ran into another statistical “issue” with temperature data averages. We all, typically, assume they are Standard Normal Distributions. But if they are not (say they are a Cauchy Lorentz distribution instead), you can have the case where the “mean” is not defined.
http://chiefio.wordpress.com/2012/12/10/do-temperatures-have-a-mean/
Some kinds of data distributions are what is called “pathological” and have no valid mean…
Don’t know if it applies to what you are doing, or not, but it needs thinking about.
The other thing that would be an interesting extension of this work is to look at the two polar regions on a summer vs winter comparison. I think that matters, and would likely give more clarity to the reasons for the behaviour. During winter, the poles are in one regime that is highly different from the summer regime. I’d expect that they well might have opposite responses to ‘imbalances’. During the winter there is nearly NO “downwelling” anything. (Heck, the height of the stratosphere becomes ‘indistinct’ then and there; as the ‘troposphere’ essentially goes way). During the summer, you have a long persistent solar flux, that ought to show up an ‘imbalance’ even more strongly.
In short, I think you will find that the Equator response is on the order of “same day” (with the formation of the Thunderstorms you love so much 😉
http://chiefio.wordpress.com/2010/12/02/does-convection-dominate/
http://chiefio.wordpress.com/2010/12/28/ignore-the-day-at-your-peril/
while the polar regions have quarterly regimes. Doing a time analysis on both with the same monthly time step will work, but will not be as strong a signal as time scales tailored to the local process speeds.
This paper measures heat flow in Africa and finds it happens from ground level up to the high troposphere in hours, same day:
http://hal.archives-ouvertes.fr/docs/00/31/68/93/PDF/angeo-19-1001-2001.pdf
(Oddly, it loaded just yesterday. Today I’m not getting a download. I’ll presume it’s a local issue (not getting a DNS resolution for the server). If need be, I have it archived and can dig out a copy.)
My read of one of the graphs (in case the server is just gone):

The upshot of it all to me is pretty simple. Those graphs at lower elevations are darned near constant. There is about a 275 K to 285 K variation in temperature at 4 km altitude over the course of a clear tropical day. It’s the troposphere that has the largest wiggles. At 22.5 km about 200K to 250K as I eyeball the graphs. AND, IFF I’ve read the paper correctly, it says they are due to convections from the surface heating.

So to capture that will take less than monthly data… Especially the ‘negative response’ of a thunderstorm that comes and goes in hours. (Using a smaller time step ought to show your expected response even more strongly.)

Here’s an alternate link that’s working right now:
http://www.ann-geophys.net/19/1001/2001/angeo-19-1001-2001.pdf

David

“Under the current paradigm, the assumption is made that surface temperature is a linear function of the TOA imbalance (forcing)”
No, it isn’t.