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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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?
“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
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?
In Figure 3, both y-axes are labeled “Residual error”. I think the top one should be “Temperature”.
[You are correct, thanks, fixed. -w.]
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.
Jim Cripwell says:
June 12, 2012 at 12:32 pm
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.
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.
Your efforts are appreciated in ferreting out this information. This really makes one sit up and take notice.
Robert Brown says:
June 12, 2012 at 12:28 pm
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.
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.
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.
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.
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.
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?
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).
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.
Jim Cripwell says:
June 12, 2012 at 1:42 pm
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.
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.]
“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.