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.
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timetochooseagain says:
June 12, 2012 at 1:24 pm
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.
Mark from Los Alamos says:
June 12, 2012 at 1:40 pm
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.
Stephen Rasey says:
June 12, 2012 at 2:09 pm
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.
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
Myrrh says:
June 12, 2012 at 2:06 pm
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.
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!
“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?
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… 🙂
p.s. are they really measuring upwelling thermal infrared only?
[That’s the only significant upwelling longwave there is, by orders of magnitude. -w]
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.
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.
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.
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.
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
Willis Eschenbach says:
June 12, 2012 at 3:09 pm
Where’s the 5 to 50 µm Solar Willis?
DaveE
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!
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.
“””””…..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.
“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.
“””””…..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.
“””””…..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. ?
Kasuha says:
June 12, 2012 at 3:49 pm
I think your maths is askew.
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.”