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.
Figure 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.
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.
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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Ed_B: Bob Tisdale has data showing what happens. He does not assert any “theory”, rather he just shows what the data shows.
Bob Tisdale performs good and thorough data analyses. However, he does more than that. He asserts that El Ninos erupt as something more than the underlying dynamical processes that generate ENSO, AND that they have generated the excess heat others attribute to CO2. Booth of those are theoretical hypotheses beyond “showing what happens”.
John Shade says:
December 11, 2012 at 9:20 am
Thanks, John. By “TOA forcing” I mean the imbalance of upwelling and downwelling radiation at the top of the atmosphere.
w.
Moritz.B says:
December 11, 2012 at 10:14 am
An interesting question. I make no attempt to even touch the issue of heat exchange. I am examining the claim of the modelers that the change in surface temperature is a linear function of the change in TOA forcing. Their fundamental equation is:
∆T = λ ∆F
where delta T (∆T) is the change in temperature, delta F is the change in TOA forcing, and lambda (λ) is the climate sensitivity. I wanted to see where and how much that relationship held true on the earth’s surface.
The inverse relationship between temperature and sensitivity is indeed related to the export of heat from the ITCZ to the poles. However, that does not imply that there is any miscalculation. I am just looking at their fundamental equation. In the case of the ITCZ, the temperature in that region is NOT a linear function of the forcing. In fact, temperature in that region has little to do with the forcing at all. As you point out, this is because of the export of heat from that region.
It does raise an interesting question, however, which is the relationship between surface temperature and outgoing radiation … I need to take a look at that one, to see where and how it deviates from the T^4 curve. That should show interesting peculiarities in the ITCZ region …
But of course, the usual problem … so many musicians … so little time …
w.
Willis –
Trying again after my earlier response: you are regressing temperature change on TOA imbalance, which (I surmise) is essentially regressing temperature change on net power in, which is highly seasonal. I think what you get is the (inverse) specific heat capacity per unit area of the cell, modified for albedo. The ocean has high specific heat, so has low ‘sensitivity’, and arid regions have low specific heat, and high sensitivity.
I still have slight concerns about the granulariy of monthly analysis versus the annual periodicity, but mostly I’m struggling to relate the above, very interesting, data, with what I might need to know to understand better or critque models of CO2 induced AGW.
Surely no model of AGW concerns itself with the massive swings in TOA inbalance which are seen seasonally? Isn’t the starting point for modelling that TOA must on average stay in equilibrium as a boundary condition, and that changes happen at the bottom of the atmosphere?
Doubtless I’m missing something, or possibly lots. Any help much appreciated.
Slowly but surely Willis converges on a basic truth: downwelling longwave infrared does not warm the ocean but rather raises the evaporation rate. He also does a nice job of discovering that ocean doesn’t have a lag of many years but rather just several months.
Nice job Willis. It’s not going to be pleasant admitting to Springer he was right about DWLIR not able to warm the ocean nearly as much as it warms dry land.
John Doe says:
December 11, 2012 at 2:32 pm
John, come back without the snark if you want an real answer. The short answer is, the slower response of the ocean has to do with heat capacity, not infrared absorption, and you are acting like a jerk.
w.
PS—For those interested in a complete fisking of the foolish claims that John Doe is making (but doesn’t have the balls to sign his real name to), see my post “Radiating the Ocean“. John, when you can answer the four objections to your cockamamie theory that I listed in that post, come back and discuss your answers, you might have a point. Until then, please take your bad attitude elsewhere.
RERT says:
December 11, 2012 at 2:15 pm
As the map shows, it’s far from that simple. Some parts of the land have higher sensitivity than others, some parts of the ocean have no sensitivity at all. So I can’t just be measuring inverse specific heat.
Good question, RERT. Climate models are just weather models with more variables and run for a longer time. A typical time-step for them is about half an hour, so they assuredly have to be concerned with the “massive swings in TOA imbalance” which occur on daily, monthly, and seasonal scales.
w.
aaaWillis-
While this post is getting far down the list at WUWT, I still can’t stop thinking about it. To me this is a really elegant analysis. I hope we can regard this as progress report with more to follow.
I hope you will follow up on the suggestions about seasonality.
If I understand your Figure 1, you used all monthly data for the grid cells, with each data point for the regression being one month of paired data, (with the temperature data lagged as described) and the total data points being five years of monthly data (60 data pairs). What if you ran the regression for only 3 months of TOA corresponding to a season (say March, April, and May) with the correspondingly lagged temperature data. Admittedly that would give only 15 data pairs for 5 years, with a smaller temperature range for most latitudes, but it might show if there were significant differences season to season, in both the r^2 and the coefficients.
For Figure 2, then, use the equation for the season, and use just 3 month temperature averages for all five years so that the average temperature would be calculated from 15 months of data..
I hate it when someone suggests that I do lots more work. I think “Why don’t you do it yourself” I think I might try to. I could probably handle the spreadsheet development, but I am no so sure about downloading the data and my computer handling- what-64,800 grid cells? Maybe just try a subset.
Anyway, thanks for an enjoyable several days of expanding my understanding.
Thanks for your reply, Willis (December 11, 2012 at 12:36 pm). But my puzzle is why that imbalance, which as far as I can see is better regarded as an effect, a consequence of the planet’s shape and some fluid dynamics, is called a ‘forcing’. That is the terminology used by computer modellers to introduce what they see as causes, as drivers of temperature changes.in particular.
Old Engineer, thanks very much for your kind thoughts. I don’t think that this work could be done in an Excel spreadsheet, at least in something less than geological time. It’s not only 68,400 gridcells, it’s that many for each of the datasets (ULR, USR, DSR, sea temperature, land temperature, and a couple of land masks). Then you have the derived datasets like the net TOA imbalance, that’s another 64,800 gridcells … the list is long.
I used the computer language “R” to do the work. I taught myself “R” a few years ago at the urging of Steve McIntyre, and I have never regretted it (many thanks, Steve!). It handles good-sized datasets without breaking a sweat (although you need lots of memory, my machine has 8 GBytes and I wish it could take more). It is designed to do just this kind of heavyweight number crunching on good-sized datasets.
Anyhow, keep up the good work, I’ll continue my investigations.
All the best,
w.
Willis
May I suggest that you look into the GPGPU acceleration of R. Some of the accelerations are up to 80x faster. Please email me, I have a proposition for you regarding your machine memory bounds.
http://wp.me/p1uHC3-6o
gymnosperm:
That blog post that you linked to gets confused here:
Actually, no. This is the old confusion about the fact that some infinite series have finite sums.
So, for example, let’s imagine that some extra water vapor gets into the air and this water vapor causes the temperature to rise by 1 C. What happens next? Well, that temperature rise will cause more water vapor to evaporate, which will then cause a further temperature rise…which will then cause more water vapor to evaporate and more temperature rise…and, pretty soon, you have boiled away all the water, right? Well, no, not necessarily. It depends how large the positive feedback is. Let’s say it is such that for each degree rise in temperature, the additional water vapor that evaporates then causes another 0.5 C rise.
So, the amount temperature rise of 1 C causes the amount of water vapor to rise so that temperature rises by 0.5 C. Then that additional temperature rise of 0.5 C cause the amount of water vapor to rise so that temperature rises by 0.25 C…and so on. In the end, what you have is the infinite geometric series 1 + (1/2) + (1/4) + (1/8) + … and that series does not diverge. Instead, it converges to 2. So, the effect of the water vapor feedback in this case is to double any perturbation (including a perturbation originally produced by water vapor itself).
There does not need to be a negative feedback to prevent the water vapor feedback from “blowing up” and boiling all of the water on the planet.
Hi Willis –
Having thought a little more about it after my last reply, I’m happy that it is indeed more complicated than specific heat. Calling this ‘sensitivity’ is also OK, with the one important caveat that it overloads the term with the more common ‘climate sensitivity’, which relates long term global temperature change to CO2 forcing. I don’t see why the rise in temperature in the spring, and its decline in the fall, divided by the increase/decrease in TSI, gives you a number with any bearing on the more usual usage of climate sensitivity other than a similarity of units.
Again, please help me understand: I can’t believe I’m the only one who is confused, unless I’m misinterpreting enough to be off in LaLaLand….
RERT says:
December 12, 2012 at 1:11 pm
Mmm … well, we can start by noting that “climate sensitivity” is the sensitivity of the climate to any forcing, not just to CO2 forcing.
Next, we note that global climate sensitivity relates long term global temperature change to long term global forcing.
Finally, we note that global climate sensitivity is nothing but the global average of local climate sensitivity, which is the local temperature change in response to local forcing.
In other words, what I am looking at is medium term (one month), local climate sensitivity, which can be averaged to give medium term global climate sensitivity. This relates medium term local temperature changes to local changes in forcing. As my charts show, for most of the earth there is a clear and strong local temperature change in response to local forcing changes, just as the current paradigm says … but not for all of the earth.
It is in these critical areas around the equator that the heavy lifting of the giant climate engine goes on, and it is in these areas that the temperature is adjusted and regulated by the thermostatic action of clouds and thunderstorms and El Ninos/La Ninas.
w.
This is my current understanding. Climate sensitivity is something that exists in models If they are sufficiently stable) and is the surface temperature change induced in due course over time to an instantaneous change in the radiation budget at the top of the atmosphere. Often it is shorthand for the change due to a step change in the radiation budget deemed appropriate to a step change in ambient CO2. So in the model, the driving force is the change in the radiation budget and the outcome, the result, is the change in surface temperature. In the real atmosphere the change in the surface temperature would be the driving force, and the change in the radiation budget would be the outcome, the result. In other words, the models do things backwards in unobservable ways, but there is faith that the final results are good enough to justify a colossal, unprecedented disruption to the world’s economic system (esp. production and use of energy) and much else besides, not least the empowerment assumed by some to scare children to raise recruits for this disruption.
Sorry Wilis – my tendency to use sloppy language approximates my tendency to be dogged. Your response above seems completely in line with my understanding of what you’ve done, so I think I’m at least on the right page. But long term climate change is, if you believe it, about changes of the order of a few watts lasting forever. The data you have is for changes of the order of two hundred watts over six months. Somewhere floating arond is the invitation to challenge the 2-6 Kelvin per 3.7 watts with the much lower numbers you present. But the circumstances are so radically different that the comparision is highly tendentious.
Just as an example of why, consider if summer lasted forever: it would get very very hot. Ditto winter very very cold. The winter-summer temperature spread will be far higher at equilibrium than over a season. So the equilibrium (long term) sensitivity will be higher than the real-world data you measure.
The data you have extracted is really interesting, but if people misuse it as an argument against the IPCC sensitivity it will be adding to the fog of misinformation which bedevils both sides of this debate.
Once again, thanks for crunching a great deal of data to produce some real world information.