Observations on TOA Forcing vs Temperature

I recently wrote three posts (first, second, and third), regarding climate sensitivity. I wanted to compare my results to another dataset. Continued digging has led me to the CERES monthly global albedo dataset from the Terra satellite. It’s an outstanding set, in that it contains downwelling solar (shortwave) radiation (DSR), upwelling solar radiation (USR), and most importantly for my purposes, upwelling longwave radiation (ULR). Upwelling solar radiation (USR) is the solar energy that is reflected by the earth rather than entering the climate system. It is in 1°x1° gridded format, so that each month’s data has almost 200,000 individual measurements, or over 64,000 measurements for each of those three separate phenomena. Unfortunately, it’s only just under five years of data, but there is lots of it and it is internally consistent. As climate datasets go, it is remarkable.

Now, my initial interest in the CERES dataset is in the response of the longwave radiation to the surface heating. I wanted to see what happens to the longwave coming up from the earth when the incoming energy is changing.

To do this, rather than look at the raw data, I need to look at the month-to-month change in the data. This is called the “first difference” of the data. It is the monthly change in the item of interest, with the “change” indicated by the Greek letter delta ( ∆ ).

When I look at a new dataset like this one, I want to see the big picture first. I’m a graphic artist, and I grasp the data graphically. So my first step was to graph the change in upwelling longwave radiation (∆ULR) against the change in net solar radiation (∆NSR). The net solar radiation (NSR) is downwelling solar minus upwelling solar (DSR – USR). It is the amount of solar energy that is actually entering the climate system.

Figure 1 shows the changes in longwave that accompany changes in net solar radiation.

Figure 1. Scatterplot of the change in upwelling longwave radiation (∆ ULR, vertical scale) with regards to the change in net solar radiation entering the system. Dotted line shows the linear trend. Colors indicate latitude, with red being the South Pole, yellow is the Equator, and blue is the North Pole. Data covers 90° N/S.

This illustrates why I use color in my graphs. I first did this scatterplot without the color, in black and white. I could see there was underlying structure, and I guessed it had to do with latitude, but I couldn’t tell if my guess were true. With the added color, it is easy to see that in the tropics the increase in upwelling longwave for a given change in solar energy is greater than at the poles. So my next move was to calculate the trend for each 1° band of latitude. Figure 2 shows that result, with colors indicating latitude to match with Figure 1.

Figure 2. Linear trend by latitude of the change in upwelling longwave with respect to a 1 W/m2 change in net solar radiation. “Net downwelling” is downwelling solar radiation DSR minus upwelling solar radiation USR. Colors are by latitude to match Figure 1. Values are area-adjusted, with the Equatorial values having an adjustment factor of 1.0.

Now, this is a very interesting result. Bear in mind that the sun is what is driving these changes. The way that I read this is that near the Equator, whenever the sun is stronger there is an increase in thunderstorms. The deep upwelling caused by the thunderstorms is moving huge amounts of energy through the core of the thunderstorms, slipping it past the majority of the CO2, to the upper atmosphere where it is much freer to radiate to space. This is one of the mechanisms that I discussed in my post “The Thermostat Hypothesis“. Note in Figure 2 that at the peak, which occurs in the Intertropical Convergence Zone (ITCZ) just north of the Equator, this upwelling radiation counteracts a full 60% of the incoming solar energy, and this is on average. This means that the peak response must be even larger.

Finally, I took a look at what I’d started out to investigate, which was the relationship between incoming energy and the surface temperature. I may be mistaken, but I think that this is the first observational analysis of the relationship between the actual top-of-atmosphere (TOA) imbalance (downwelling minus upwelling radiation, or DLR – USR -ULR) and the corresponding change in temperature.

As before, I have used a lagged calculation, to emulate the slow thermal response of the planet. This model has two variables, the climate sensitivity “lambda” and the time constant “tau”. The climate sensitivity is how much the temperature changes for a given change in TOA forcing. The time constant “tau” is a measure of how long it takes the system to adjust to a certain level.

Figure 3 shows the new results in graphic form:

Figure 3. Upper panel shows the Northern Hemisphere (NH) and Southern Hemisphere (SH) temperatures, and the calculation of those temperatures using the top of atmosphere (TOA) imbalance (downwelling – upwelling). Bottom panel shows the residuals from that calculation for the two hemispheres.

In my previous analysis, I calculated that climate sensitivity and the time constant for the Northern Hemisphere and the Southern Hemisphere were slightly different. Here are my previous results:

                   SH               NH

lambda             0.05             0.10°C per W/m2

tau                2.4              1.9 months

RMS residual error 0.17             0.26 °C

Using this entirely new dataset, and including the upwelling longwave to give the full TOA imbalance, I now get the following results:

                   SH               NH

lambda             0.05             0.13°C per W/m2

tau                2.5              2.2 months

RMS residual error 0.18             0.17 °C

(Due to the short length of the data, there is no statistically significant trend in either the actual or calculated datasets.)

These are very encouraging results, because they are very close to my prior calculations, despite using an entirely different albedo dataset. This indicates that we are looking at a real phenomenon, rather than the first result being specific to a certain dataset.

Now, is it possible that there is a second much longer time constant at work in the system? In theory, yes, but a couple of things militate against it. First, I have found no way to add a longer time constant to make it a “two-box” model without the sensitivity being only about a tenth of that shown above, and believe me, I’ve tried a host of possible ways. If someone can do it, more power to you, please show me how.

Second, I looked at what is happening when we remove the monthly average values (climatology) from both the TOA variations and the temperatures. Once I remove the monthly average values from both datasets, there is no relationship between the two remaining datasets, lagged or not.

However, absence of evidence is not evidence of absence, meaning that there may well be a second, longer time constant with a larger sensitivity going on in the system. However, before you claim that such a constant exists, please do the work to come up with a way to calculate such a constant (and associated sensitivity), and show us the actual results. It’s easy to say “There must be a longer time delay”, but I haven’t found any way to include one that works mathematically. I can put in a longer time constant, but it ends up with a sensitivity for the second time lag of only about a tenth of what I calculate for a single-box model … which doesn’t help.

All the best, and if you disagree with something I’ve written, please QUOTE MY WORDS that you disagree with. That way we can avoid misunderstandings.

w.

DATA: The Excel worksheet containing the hemispheric monthly averages and my calculations is here. The 1° x 1° gridded data is here as an R “save” file. WARNING: 70 Mbyte file!. The R data is contained in four 180 row x 360 column by 58 layer arrays. They start at 89.5N and -179.5W, with the first month being January 2001. There is an array for the albedo, for the upwelling and downwelling solar, and for the upwelling longwave. In addition, there are four corresponding 180 row x 360 column by 57 layer arrays, which contain the first differences of the actual data.

Advertisements

  Subscribe  
newest oldest most voted
Notify of
Russ in Houston

It was my understanding that NASA doesn’t have direct measure of LW greater than 15.4 micrometers at TOA. How do they calculate the total LW?

Interstellar Bill

“but a couple of things mitigate against it.”
That would be MILITATE, of course,
but ‘argue’ would be less emphatic
because it’s much less metaphoric.
Anyway, great post.
We all know that if your evidence-based calculations
showed any agreement whatsoever with AGW
then we’d have the intellectual honesty to admit it.
When you’ve amassed enough for the paper,
please keep us apprised of your encounters
with the Warmista Pal-Review Barrier.

Hi Willis,
Outstanding work. Your analysis confirms what I’ve suspected but lacked the data/time to work out myself. Albedo increase is overwhelmingly a cooling parameter, as the tropics have a much larger response than the poles, both because of cloud-formation feedback and (I suspect) because of the Jacobean — there’s simply more area at the poles, so even if clouds warm the poles as much as the cool the tropics per square meter, there are a lot more tropical square meters.
Regarding timescales — a five year baseline simply cannot resolve 20 year or longer trends. So rather than saying there are no longer timescales, say that it is impossible to resolve longer timescale behavior than the ones you have observed. Indeed, with timescales that are only half of the length of the data run (for THIS study) the timescales themselves are deeply suspect, although that doesn’t mean I think they are wrong, only that secular variations in random data would be EXPECTED to generate fourier components at the period, half the period, a quarter of the period, etc, as artifacts. You’d have to carefully exclude the possibility of artifacts — not easily done.
It would also be very interesting to turn this into even a crude model of local radiation-equilibrated surface temperature.
rgb

SteveC

Well written and understandable…. at least I “think” so… Thank you for your efforts!

Sorry to put my question on a thread which is not specifically relevant, but here goes. When we look at the way no-feedback climate sensitivity for a doubling of CO2 is estimated, it is assumed that the lapse rate does not change. Are there, in fact, two different types of forcing, one where the lapse rate changes, and one where it does not change? And if so, what is the difference between the two types of forcing?

Robert Clemenzi

In Figure 3, both y-axes are labeled “Residual error”. I think the top one should be “Temperature”.
[You are correct, thanks, fixed. -w.]

Mike Lewis

Just a nit, but in the 4th paragraph you have “upwelling longwave radiation (∆USR) ” but I believe it should be “…(∆ULR)”.
[Thanks, fixed. My theory is, “Perfect is good enough”, so efforts like yours are always appreciated. -w.]

That Willis, doing real science without the expenditure of wads of taxpayer money, he has some nerve. Hey , we can always hope he will start a trend.

Willis Eschenbach

Jim Cripwell says:
June 12, 2012 at 12:32 pm

Sorry to put my question on a thread which is not specifically relevant, but here goes. When we look at the way no-feedback climate sensitivity for a doubling of CO2 is estimated, it is assumed that the lapse rate does not change. Are there, in fact, two different types of forcing, one where the lapse rate changes, and one where it does not change? And if so, what is the difference between the two types of forcing?

Jim, I’m not clear about what your question is. The lapse rate changes constantly, both spatially and temporally. So … I don’t even know how to start answering.
w.

pochas

The quarter-wave lag for the annual cycle would be 3 months, not greatly different from what you are seeing. Could it be that you are actually looking at local forcing from the annual cycle? Or else, where does the forcing that is producing your observations come from?
If the forcing is from the annual cycle, your sensitivity calculation would still be appropriate as it doesn’t seem to depend on the nature of the forcing.
Willis, keep up the good work. You have the field all to yourself.

Mike Lewis

Your efforts are appreciated in ferreting out this information. This really makes one sit up and take notice.

Willis Eschenbach

Robert Brown says:
June 12, 2012 at 12:28 pm

Hi Willis,
Outstanding work. Your analysis confirms what I’ve suspected but lacked the data/time to work out myself. Albedo increase is overwhelmingly a cooling parameter, as the tropics have a much larger response than the poles, both because of cloud-formation feedback and (I suspect) because of the Jacobean — there’s simply more area at the poles, so even if clouds warm the poles as much as they cool the tropics per square meter, there are a lot more tropical square meters.

Indeed. That’s why I have area-adjusted the data in Figure 2. It clearly shows that the strong cooling response in the tropics is much larger than the corresponding response at the poles.

Regarding timescales — a five year baseline simply cannot resolve 20 year or longer trends. So rather than saying there are no longer timescales, say that it is impossible to resolve longer timescale behavior than the ones you have observed. Indeed, with timescales that are only half of the length of the data run (for THIS study) the timescales themselves are deeply suspect, although that doesn’t mean I think they are wrong, only that secular variations in random data would be EXPECTED to generate fourier components at the period, half the period, a quarter of the period, etc, as artifacts. You’d have to carefully exclude the possibility of artifacts — not easily done.
It would also be very interesting to turn this into even a crude model of local radiation-equilibrated surface temperature.

rgb
Robert, thanks as always for your comments. Regarding longer trends, you are correct that at this timescale you can’t resolve e.g. 20 year trends. The difficulty I see is that if there are longer trends, then they need to be much smaller than the trend that I find. This is because if there is a longer timescale involved, and if the sensitivity is of the same order of magnitude as what I find above, the longer trend distorts the shorter results introducing large errors.
At least that’s what I’ve found, but perhaps I’m not looking at it correctly.
All the best,
w.

Thanks for the R file.
Re: Figure 2 Values are area-adjusted, with the Equatorial values having an adjustment factor of 1.0.
I’ve got to ask a dumb question about that adjustment. Y-axis is labeled W/m^2. Is it really?
If there is an area adjustment then are you multiplying the calculated slope by cos(latitude)? Then the Y value is not W/m^2 but proportional to W/sq-degree. W/sq-degree doesn’t add clarity.
The X-axis is linear. True, there are fewer sq-meters at Latitude 80 than at Latitude 8, but the graph Y-axis is labled as alrealy normalized by area.
Better would be to keep Y axis in W/m^2 (unadjusted) since it is a gold standard unit. And plot the X-axis as linear cos(latitude) and re-lable with a variable latitude width.

I may be mistaken, but I think that this is the first observational analysis of the relationship between the actual top-of-atmosphere (TOA) imbalance (downwelling minus upwelling radiation, or DLR – USR -ULR) and the corresponding change in temperature.

Interesting observation if you are correct… Willis, you do ask the most intriguing questions that one might have expected to have already been asked by those who are paid to do these things.

timetochooseagain

Willis-I think there is a serious problem with looking at the seasonal cycle to judge the sensitivity and response time. I am surprised nobody in earlier threads raised this objection (rather, they made arm waving arguments about needing “extra response times”) The problem is:
The system in question (or rather, pair of systems, Northern Hemisphere, Southern Hemisphere) is reacting to a change in TOA radiation, yes, but the change is not uniform over the globe, and moreover the systems in question are capable of transfering heat horizontally from one to the other, thus it is inappropriate to guage their reaction to just the change in heat flux with space, since-especially considering one Hemisphere will be cool when the other is warm-there is heat exchange not just at the TOA boundary, but across the equatorial boundary.

timetochooseagain

Jim Cripwell says: “it is assumed that the lapse rate does not change. Are there, in fact, two different types of forcing, one where the lapse rate changes, and one where it does not change? And if so, what is the difference between the two types of forcing?”
Typically in models, the lapse rate is consider to have a “feedback” effect. Typically in models this feedback is negative, albeit incredibly weak, and tied closely with how they handle the water vapor feedback (which, in models, is uniformly positive).
Current atmospheric temperature data indicate that either the model’s lapse rate effect is wrong, or the temperature records are wrong (or some combination of the two). This is the infamous “hot spot” issue.

Mark from Los Alamos

If you were to heat an infinitesimally thin surface that was over a perfect insulator, the blackbody radiation would be emitted in a cosine distribution with respect to the normal to the surface. However, when you heat a layer that has a finite thickness, the long wave radiation emitted from below the surface can’t escape as readily in directions away from the normal, it has to go through a thicker and thicker layer of material as the angle from the normal gets larger and larger. This results in a cosine-squared distribution of emission – it’s highly peaked toward the normal and falls off rapidly.
It may be that your satellite data wasn’t properly adjusted for the surface radiation angular distribution.

Willis, you write “Jim, I’m not clear about what your question is” Thank you for reading my comment. I am not quite sure either. When the proponents of CAGW estimate the no-feedback climate sensitivity for a doubling of CO2, there is an assumption that the lapse rate does not change as a result of the change in forcing caused by a doubling of CO2. This assumption does not seem to have ever been justified. I suspect that if it were to be assumed that the lapse rate does change, then the estimated no-feedback climate sensitivity for a doubling of CO2 would be considerably less that 1.2 C.
You are looking at total climate sensitivity; no-feedback plus feedbacks. I have seen people claim that all forcings have the same climate sensitivity. Thus if there were a change of solar forcing of 3.7 Wm-2, this would also have a climate sensitivity of 1.2 C. But if a change of solar forcing does, in fact, change the lapse rate, then the climate sensitivity would be less than 1.2 C; as your figures clearly indicate.
So, to repeat my question, are there two types of forcing; those that cause the lapse rate to change, and those that do not?

Myrrh

What happened to the longwave direct from the Sun to Earth? Thermal Infrared, Heat, that which we actually feel as heat direct from the Sun because it is the heat from the Sun which actually heats up land and oceans and us?
Shortwave, mainly visible, and the two shortwaves either side of uv and near infrared, are not thermal energies (they work on electronic transition scale and not on molecular/atomic vibrational which is what it takes to heat stuff up); at best as heat producers will be the light’s part in photosynthesis, which the plants use to convert to chemical energy in the creation of sugars, not until the plant burns the sugars will heat be given off and this is released in transpiration.

I have to correct a detail about my 1:17pm post, without changing the essence.
The Y-axis in Figure 2 is labeled W/m2 ∆ULR per W/m2 ∆DSR.
But you have stated there is an adjustment that I guess is
Y-axis as plotted = (calculated slope by 1 deg Latitude bin) * cos(mid point of latitude in bin)
The cos only affects the numerator (W/m2 ∆ULR) without affecting the denominator. The Y value at Latitude 45 degrees is only 71% of what it should be. The better way of showing the data is not to adjuste the Y value, but to plot the X-axis latitude in proporation to the area of the earth at that latitude X = (cos(latitude of bin)). Then the integral of Y over X will still give an unbiased estimator of the overal W/m2 ∆ULR per W/m2 ∆DSR across all latitudes. Each Y will remain the true slope of the latitude binned data without adjustment.

Jim,
It doesn’t really matter. You can define your “no-feedback” reference climate sensitivity however you like, as long as you are internally consistent in what you then call a “feedback.”
The “1 C per doubling of CO2” is a reference system that warms uniformly in the troposphere, and then holds everything fixed except for the increased emission to space that results from the warming.
You could, of course, create an alternative reference system in which the lapse rate changes in addition to the enhanced blackbody radiation to space. Define this as your “no feedback” value. This would diminish the no-feedback sensitivity, but then enhance the strength of “feedbacks,” since you are no longer including a negative feedback as being a feedback. The net result is of course independent of how one formulates the problem, but in fact there are arguments in the literature for choosing different reference systems (as it is can lead to different ways of conceptualizing the problem).

DocMartyn

Willis, this is a plot of the Ocean fraction by latitude
http://www.bridge-9.org.uk/temp/Ocean%20Fraction%20(Web).png
It is available as a xlsx file
http://www.bridge-9.org.uk/temp/Ocean%20Fraction.xlsx
The O/L ratio is almost certainly the thing causing you asymmetry in Figure 2.

Willis Eschenbach

Jim Cripwell says:
June 12, 2012 at 1:42 pm

So, to repeat my question, are there two types of forcing; those that cause the lapse rate to change, and those that do not?

No clue. James Hansen, in “Efficacy of Climate Forcings“, claims that a W/m2 of CO2 has more effect than a W/m2 of solar, but it’s models all the way down, and I can’t see the logic. However, the two types of forcing (longwave and shortwave) do have one very large difference. Shortwave (solar) radiation penetrates a couple hundred metres into the ocean, while longwave (“greenhouse”) radiation only penetrates the very skin.
What effect that has on the lapse rate, however, I wouldn’t begin to guess.
w.

F. Ross

Nothing to do with the science involved here but, as with many graphical representations of mathematical functions, I’d just like to say that figure 1 is visually stunning.
[Thanks. In addition to it being my first light so to speak on CERES, my first graph, its lovely quality is why it is Figure 1. I assure you it is ugly in black and white. In addition to my other foibles, I’m a graphic artist and a cartoonist, I liked the look. -w.]

DocMartyn

“Mark from Los Alamos says:
If you were to heat an infinitesimally thin surface that was over a perfect insulator, the blackbody radiation would be emitted in a cosine distribution with respect to the normal to the surface. However, when you heat a layer that has a finite thickness, the long wave radiation emitted from below the surface can’t escape as readily in directions away from the normal, it has to go through a thicker and thicker layer of material as the angle from the normal gets larger and larger. ”
Just how does a molecule know when the photon it is going to emit is going to pass through vacuum or into other molecules?
You think that before there is an electron transition the electron gets out a rule and measures the matter density all around it?
The radiation emitted from a layer of water molecules five molecules below the surface of the ocean and 5×10^10000 is identical if they are at the same temperature.
Now what happens is they play swopsie, energy is emitted and absorbed
W W W W W W W W W W W W W W W
Now if there is a temperature differential then there will be an overall directional flux, as the warm water has a slightly different Stefan-Boltzman distribution; there is slightly more blueish and slightly less redish photons coming from the warmer end of the chain.
Molecules don’t know anything, they don’t know the direction of an energy step, when in tumbling motion they are equally likely to radiate in any dimension.

Willis Eschenbach

timetochooseagain says:
June 12, 2012 at 1:24 pm

Willis-I think there is a serious problem with looking at the seasonal cycle to judge the sensitivity and response time. I am surprised nobody in earlier threads raised this objection (rather, they made arm waving arguments about needing “extra response times”) The problem is:
The system in question (or rather, pair of systems, Northern Hemisphere, Southern Hemisphere) is reacting to a change in TOA radiation, yes, but the change is not uniform over the globe, and moreover the systems in question are capable of transfering heat horizontally from one to the other, thus it is inappropriate to guage their reaction to just the change in heat flux with space, since-especially considering one Hemisphere will be cool when the other is warm-there is heat exchange not just at the TOA boundary, but across the equatorial boundary.

As far as I know, although there is an exchange of atmosphere from one hemisphere to the other, it is both slow and not all that large. I’m happy to be corrected, but when you look at say the lag between the CO2 concentration in the NH and SH, it has a time scale of years. I find it difficult to believe that the effect would make much difference to what I am considering here.
In particular, it seems that the TOA imbalance for each hemisphere is sufficient to explain almost all of the variation in hemispheric temperatures … which leaves very little for a purported transfer to explain.
All the best,
w.

Willis Eschenbach

Mark from Los Alamos says:
June 12, 2012 at 1:40 pm

If you were to heat an infinitesimally thin surface that was over a perfect insulator, the blackbody radiation would be emitted in a cosine distribution with respect to the normal to the surface. However, when you heat a layer that has a finite thickness, the long wave radiation emitted from below the surface can’t escape as readily in directions away from the normal, it has to go through a thicker and thicker layer of material as the angle from the normal gets larger and larger. This results in a cosine-squared distribution of emission – it’s highly peaked toward the normal and falls off rapidly.
It may be that your satellite data wasn’t properly adjusted for the surface radiation angular distribution.

Mark, you raise an interesting question. The longwave radiation doesn’t come from deep in the ocean, or even shallow in the ocean. It is absorbed in the first tens of microns in the ocean, and thus emitted from the same ultra-thin layer. I doubt that makes any significant difference to the distribution.
w.

Willis Eschenbach

Stephen Rasey says:
June 12, 2012 at 2:09 pm

I have to correct a detail about my 1:17pm post, without changing the essence.
The Y-axis in Figure 2 is labeled W/m2 ∆ULR per W/m2 ∆DSR.
But you have stated there is an adjustment that I guess is
Y-axis as plotted = (calculated slope by 1 deg Latitude bin) * cos(mid point of latitude in bin)
The cos only affects the numerator (W/m2 ∆ULR) without affecting the denominator. The Y value at Latitude 45 degrees is only 71% of what it should be. The better way of showing the data is not to adjuste the Y value, but to plot the X-axis latitude in proporation to the area of the earth at that latitude X = (cos(latitude of bin)). Then the integral of Y over X will still give an unbiased estimator of the overal W/m2 ∆ULR per W/m2 ∆DSR across all latitudes. Each Y will remain the true slope of the latitude binned data without adjustment.

Interesting thought, Stephen. I puzzled long and hard about how to properly adjust it. I’ll take a look at doing it your way and see how that comes out.
w.

Dolphinhead

Anthony these posts from Willis are excellent. Already comments from Robert Brown and Chris Colose. You should keep them as a sticky at the top of the home page for a few days

Willis Eschenbach

Myrrh says:
June 12, 2012 at 2:06 pm

What happened to the longwave direct from the Sun to Earth? Thermal Infrared, Heat, that which we actually feel as heat direct from the Sun because it is the heat from the Sun which actually heats up land and oceans and us?

Good question, Myrrh. The thermal infrared from the sun is classed as “shortwave” along with the visible and UV, and are all included in the downwelling shortwave radiation (DSR). Here’s why:

As you can see, the wavelengths of all of the solar radiation are an order of magnitude or more shorter than those of the upwelling longwave …
w.

Steve C

Willis, we who have too much else to keep up with salute you. Congratulations on, and thanks for, another outstanding piece of work. If there are any senior academics reading these comments, please note that this man is long overdue for an honorary doctorate, at least.
And greetings to SteveC, above!

David A. Evans

“Now, is it possible that there is a second much longer time constant at work in the system? In theory, yes, but a couple of things mitigate against it. First, I have found no way to add a longer time constant to make it a “two-box” model without the sensitivity being only about a tenth of that shown above, and believe me, I’ve tried a host of possible ways. If someone can do it, more power to you, please show me how.”
Of course there is also the possibility that sensitivity is a tenth of that shown.
DaveE.

Chris Colose writes “This would diminish the no-feedback sensitivity, but then enhance the strength of “feedbacks,” since you are no longer including a negative feedback as being a feedback.”
Fair enough. However, I have another difficulty after what you have written. Taking the change in lapse rate to be a feedback, as you suggest, this would be a negative feedback. I have only seen references to positive feedbacks in the literature supporting CAGW. Has anyone estimated the size of the negative feedback that would result from the change in lapse rate which would occur if surface temperatures rose by 1.2C? If so, do you by any chance know of a reference as to what the value is?

Myrrh

But Willis, these are different critters, these are shortwave not longwave, these are not thermal infrared which is longwave which is heat which is the thermal energy of the Sun on the move to us which the invisible thermal infrared we feel as heat, that’s why it’s called thermal. We cannot feel shortwave.
Visible light penetrates that deep in the oceans because water is transparent to visible, it does not absorb visible, it transmits it through. Again there, in the ocean, visible light will be used for what visible light is good for, seeing things and in photosynthesis; I’ve read somewhere that 90% of our oxygen is produced by photosynthesis in the ocean.
NASA used to teach that it was longwave thermal infrared which we feel as heat, but now it says this doesn’t reach the surface and, as the AGW energy budget has it, its properties, of being able to heat stuff up, has been given to shortwave which can’t do this.
NASA used to teach: “NASA: “Far infrared waves are thermal. In other words, we experience this type of infrared radiation every day in the form of heat! The heat that we feel from sunlight, a fire, a radiator or a warm sidewalk is infrared.
Shorter, near infrared waves are not hot at all – in fact you cannot even feel them. These shorter wavelengths are the ones used by your TV’s remote control.”
[This is where I discovered what NASA had changed here: http://wattsupwiththat.com/2011/07/28/spencer-and-braswell-on-slashdot/#comment-711886 It’s now fully pushing this idea that the real direct heat from the Sun doesn’t reach us and shortwaves direct from the Sun heat land and ocean, which is, quite frankly, absurd.]
This is the real missing heat from the KT97 and kin energy budget… 🙂

Myrrh

p.s. are they really measuring upwelling thermal infrared only?
[That’s the only significant upwelling longwave there is, by orders of magnitude. -w]

Kasuha

To explain the fact that tropics have greatest response to change in incoming radiation, you don’t have to speculate about thunderstorms. Just the basic physical knowledge that thermal emission grows with fourth power of temperature is enough. Tropics, the place with highest temperature, has logically greatest response as well.
The thing I don’t understand is, after you identified that tropics are the most sensitive spot, you cut the data right through it and divide them between the two hemispheres. That just makes no sense to me.

Ian H

Consider the north pole. In summer I would expect the ULR to react quickly to changes in DSR. In winter however I would not expect this for fairly obvious reasons. This factor alone means that averaged over the entire year the ULR at the poles will show up as being far less reactive to changes in DSR than at the equator.
What applies at the poles applies to a lesser extent near the poles. The angle of incidence of incoming radiation varies during the year. This can be conceptualised as changing the size of the window through which DSR must pass to get to various latitudes. You say your calculations are area adjusted. I presume this is an adjustment for the area at each latitude. But the calculations also need to be adjusted with respect to the area of this solar window, an adjustment that changes throughout the year.
Have you contemplated such an adjustment? How much of the difference in reactivity between poles and the equator is accounted for by this mechanism.

P. Solar

Excellent follow on from your earlier articles , Willis. This is building into something more solid.
One word of warning with fitting “linear trends”. Any and all methods of linear regression that you are going to be based totally on an assumption that there is minimal error in the independent variable (x axis to the layman). This is a pre-requisite condition of mathematical derivation of the method and the result is not accurate ( or even mathematically valid ) if that condition is not fulfilled.
This is certainly not the case with this sort of data. In short this will give you invalid results. Read on.
It will not be totally off the wall but it will be wrong, and the slope will always be too small. How much it is wrong depends on the size and relative magnitude of the x and y errors (uncertainties).
Sadly there is no short answer to how to get the “right” answer. It requires detailed knowledge of the nature of the experimental uncertainties that we almost never have access to.
I have looked at this in detail in relation to some of Spencer’s work on TOA and spent a lot of time searching and digging expecting there to be some less used, fancy matrix method, but sadly there’s no magic fix. The fix is to arrange to have control over the independent variable, not to have two independent ones!
What I can suggest is that you do the same thing but invert the axes. This gives you the same problem the other way around. However, this at least gives you two bounding extremes within which the “correct” slope should lie.
Some people then start bisecting the angle or other tricks but none of it is legit without knowledge of the errors. (If both errors are equal you can either bisect or use a method that minimises the mean square error at 45 degrees, instead of the vertical (y) error ). However, if you do the normal method both ways, having a limited range is a good start. How wide it is depends upon the proportion of the errors. With the 1 degree slots it may not be too bad.
This will certainly be better than just knowing one boundary value and believing it is the correct slope.
I would not expect this to change the overall shape of figure two enormously but I think it should affect the heights and hence you bottom line params a bit.
It should be fairly easy to try in Excel , you just need to flip the x and y ranges. I’d suggest you duplicate the chart and just invert the referenced column ranges , that way you can see both at the same time side by side.
BTW I discussed this with Roy Spencer at one stage and he recognised it was an issue but had not found a good solution either (though I got the impression he’d not spent as much time as I had trying to find one).
Hopefully this will enable you to minimise the effects of this problem get an idea of range within which the slope should lie.
Nice work.

otsar

Thank you Willis for the great post.
Once upon a time the experts told us we did not know enough, we could not do it , it would not work.
We were so ignorant we went ahead and did it, and it worked.

Jim- something like Fig. 7 in http://www.gfdl.noaa.gov/bibliography/related_files/bjs0801.pdf may be a good start, though there are many papers on this.

rgbatduke

This is because if there is a longer timescale involved, and if the sensitivity is of the same order of magnitude as what I find above, the longer trend distorts the shorter results introducing large errors.
Unless the short-time scale “trend” you are seeing is short time scale noise on a longer term trend. It is the difficulty of resolving this (without long term data) that I’m commenting on. As always, you should glance at the Koutsoyiannis hydrology paper where he shows the same data at three different timescales to appreciate the point (which he makes far more elegantly in a single figure than I can convey in words).
I agree, however, that since you have two sources of data, one with a longer series, and both give the same numbers it increases the believability of those numbers. But not by much given that both still have a very short timescale overall.
As a single example that could explain the data but confound the assertion “there are no longer time timescales”, consider what might be the case if Svensmark is approximately correct — or oppositely correct, so the albedo response is in opposition to insolation changes (but still of solar origin, somehow). 5 years is basically all in solar cycle 24, which is itself pretty anomalous, and might not reflect at all how solar state, insolation, and albedo were correlated in the “grand solar maximum” decades of the 20th century (allowing for the possibility that Lief’s claim that they weren’t, actually grand maxima to be true).
Our difficulty is twofold. First, our older (pre-satellite) data mostly sucks, on nearly everything. We have maybe 50 years of halfway decent measurements, 30 years of “good” measurements (in varying degree, depending on what is being measured), and I’m not sure we have achieved “great” measurements of climatological parameters and quantities yet. Second, we just don’t have a good, really believable model of global climate that works over as little as a single century, let alone the last hundred thousand, 1 million, 25 million, billion years. So yeah, I’m going to remain skeptical on the question of longer timescales because of the possibility of significant external (non-feedback) drivers or coupling to very long timescale drivers (oceanic heat reservoirs turning over that HAPPEN to have coincided with a pattern).
As you say, lack of evidence isn’t convincing evidence of lack, especially when there isn’t a good reason to think that you COULD resolve certain classes of multivariate dynamics with long time scales with such a short interval of data.
Again, I’m not really arguing. I find your analysis persuasive (brilliant, even:-) but not conclusive regarding the specific question of timescales.
I would recommend that you look at Spencer’s analysis of susceptibilities (he reviewed it in his book on the global warming blunder) designed to address the issue of climate sensitivity. Correlating the fluctuations (as you are doing, if I understand you) is good, but there is information to be extracted not from the lagged correlations but from the slopes themselves.
rgb

David A. Evans

Willis Eschenbach says:
June 12, 2012 at 3:09 pm
Where’s the 5 to 50 µm Solar Willis?
DaveE

Ian H

Ignore my previous statement. This mechanism is taken account of in the data itself. So at the north pole in winter I presume the data shows DSR fixed at zero. Hence there IS no change in DSR for ULR to react to. Motto to self. read things twice before leaping to keyboard.
As Homer Simpson would say – “doh”.
Also “nuts”. hmmmmm ………… donuts!

Gary Pearse

So it would seem that with this simple model, one can arrive at a close estimate of earth’s temps on a gridded basis, can we not? How would it compare to UAH, CRUTEM, GISS, etc. I think this may be the best way to get average global temps without the politics.

George E. Smith;

“””””…..Mark from Los Alamos says:
June 12, 2012 at 1:40 pm
If you were to heat an infinitesimally thin surface that was over a perfect insulator, the blackbody radiation would be emitted in a cosine distribution with respect to the normal to the surface.
Well there wouldn’t be any black body radiation, since an “infinitesimally thin surface” (your words) wouldn’t absorb any incident radiation so it couldn’t be a black body absorber; and hence in thermal equilibrium, it wouldn’t be a black body radiator either.
Your thick absorber however could be a black body (near) radiator. For example the oceans act as a near black body radiator; earth is actually the black planet; not the blue planet..
And any black body radiator is a Lambertian source. Anyone wh has such a thing can check it for themselves.

P. Solar

“If there are any senior academics reading these comments, please note that this man is long overdue for an honorary doctorate, at least.”
Why honorary? That’s for people who don’t know anything about the subject. I’d say Willis is already ahead of a large number of people with climate related PhDs. ( And I’m not joking or trying to flatter Willis ).
Mind you if someone offered me a PhD in climatology, I’d perforate it into conveniently sized squares.

George E. Smith;

“””””…..David A. Evans says:
June 12, 2012 at 4:04 pm
Willis Eschenbach says:
June 12, 2012 at 3:09 pm
Where’s the 5 to 50 µm Solar Willis?
Dave…..”””””
Well Dave, 98% of the solar spectrum energy lise between 0.25 microns, and 4.0 microns, with only 1% residual at each end, so there is no more than 1% of solar energy beyond 4.0 microns, and most of that comes between 4.0 and 5.0 microns, so basically there isn’t much of your 5 to 50 micron solar energy.

George E. Smith;

“””””…..Gary Pearse says:
June 12, 2012 at 4:08 pm
So it would seem that with this simple model, one can arrive at a close estimate of earth’s temps on a gridded basis, can we not? How would it compare to UAH, CRUTEM, GISS, etc. I think this may be the best way to get average global temps without the politics…..”””””
So why don’t you figure it out and post it here since you seem to know how to do it. ?

David A. Evans

Kasuha says:
June 12, 2012 at 3:49 pm

To explain the fact that tropics have greatest response to change in incoming radiation, you don’t have to speculate about thunderstorms. Just the basic physical knowledge that thermal emission grows with fourth power of temperature is enough. Tropics, the place with highest temperature, has logically greatest response as well.

I think your maths is askew.

Gary Pearse

George E. Smith; says:
June 12, 2012 at 4:21 pm
“””””…..Gary Pearse says:
June 12, 2012 at 4:08 pm
“So why don’t you figure it out and post it here since you seem to know how to do it. ?”
George, Willis’s paragraph below is the centrepiece of this article. Did you miss it?:
“Finally, I took a look at what I’d started out to investigate, which was the relationship between incoming energy and the surface temperature. I may be mistaken, but I think that this is the first observational analysis of the relationship between the actual top-of-atmosphere (TOA) imbalance (downwelling minus upwelling radiation, or DLR – USR -ULR) and the corresponding change in temperature.”