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.
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.