Three Clocks

Guest Post by Willis Eschenbach

I got to wandering through the three main datasets that make up the overall CERES data, and I noticed an odd thing. The three main datasets are the all-sky downwelling solar, upwelling reflected solar, and upwelling longwave radiation, measured in watts per square metre (W/m2). Here are those three datasets:

Figure 1 the three main datasets that make up the CERES all-sky data. Note that as you’d expect, total input (solar ~340 W/m2) equals total output (100 W/m2 reflected plus 240 W/m2 radiation).

What I’d never noticed before is that the three datasets are all running on different clocks. One peaks in December, one peaks in January, and one peaks in July. Not only that, they all have different cycles of rising and falling … go figure.

A word of foreshadowing. I have no particular point to make in this post. Instead, it is a meander, an appreciative inquiry into the components of the shortwave (solar) and longwave (thermal infrared) top-of-atmosphere radiation. And at the end of the day, I suspect you’ll find it contains more questions and wonderment and curiosities than it has answers and insights. So hop on board, the boat’s leaving the dock, there’s a forecast of increasing uncertainty with a chance of scattered befuddlement … what’s not to like?

First, the solar input. Although a lot of folks talk about the “solar constant”, over the course of the year the sun is anything but constant. Because the Earth’s orbit is not circular, annually the Earth moves closer and further from the sun. This gives an annual change of about 22 W/m2, with a high point in early January and a low point exactly six months later in early July. So that’s one clock—peaks in January, bottoms out in July, six months rise, six months fall.

Figure 2. Downwelling solar. Top panel shows actual data. Middle panel shows the regular seasonal variation. The bottom panel shows the residual, calculated as the data minus the seasonal component. Horizontal gold dashed lines show ± one standard deviation of the residual data. This range encompasses about 2/3 of the data. Vertical dashed and dotted lines show January (dashed) and July (dotted).

The sun, of course, is very stable, so the actual variation looks just like the seasonal variation. Note that the standard deviation of the residuals is only about plus or minus a tenth of a watt, which is a variation of about 0.03%, three hundredths of one percent of the size of the signal. In passing, the cyclical variation of about ± 0.03% you see highlighted by the blue line in the bottom panel is the TSI (total solar irradiation) variation associated with the sunspot cycle … but I digress, if one can do that while aimlessly meandering …

The next dataset, reflected solar, is on a slightly different clock. While reflected solar naturally varies with the strength of the sun, it actually peaks in December rather than January.

Figure 3. Reflected (upwelling) solar. Top panel shows actual data. Middle panel shows the regular seasonal variation. The bottom panel shows the residual, calculated as the data minus the seasonal component. Horizontal gold dashed lines show ± one standard deviation of the residual data. This range encompasses about 2/3 of the data.  Vertical dashed and dotted lines show January (dashed) and July (dotted).

To me, this is a very curious signal. To start with, it is at a minimum in August, and a maximum in December. So it rises quickly for four months, then falls for eight months, and repeats. Odd.

In addition, it’s curious because it is so stable. Of the three datasets (downwelling solar, reflected solar, and longwave), the reflected solar is the only one that is unconstrained. The downwelling solar is basically fixed. And the upwelling longwave is physically constrained—in the long run (although not the short run) what goes out is limited by what goes in.

But the variations in reflected solar, both geographical and temporal, are not fixed. Given the varying annual snow, ice, and cloud cover in the polar regions, plus the varying tropical cloud cover, plus the differences in clouds over the extra-tropical areas, there’s nothing obvious that constrains reflected sunlight to be the same, year after year … and yet, as Figure 3 shows, the standard deviation of the residuals is only half a watt per square metre, that’s plus or minus half a percent. And that means that 95% of the months are within one watt of the seasonal average to me. To me, that’s a wonder.

Finally, here is the longwave. Upwelling longwave is basically a function of temperature, so it peaks in the northern hemisphere summer. Of the three datasets, longwave varies the least over the course of the year.

Figure 4. Upwelling longwave radiation. Top panel shows actual data. Middle panel shows the regular seasonal variation. The bottom panel shows the residual, calculated as the data minus the seasonal component. Horizontal gold dashed lines show ± one standard deviation of the residual data. This range encompasses about 2/3 of the data.  Vertical dashed and dotted lines show January (dashed) and July (dotted).

Again, we see only a small variation in the residuals, only ± half a watt per square metre, or about ± 0.2%, two tenths of a percent of the size of the signal. And again the signal is not symmetrical, with the peak in July and the minimum five months later in December. So globally, longwave rises for seven months, then drops for five months.

Having looked at that, I got curious about the strange shape of the seasonal variations in the reflected solar. So I decided to take a look at the latitudinal variations in the solar, reflected solar, longwave, and albedo.

Figure 5. Top of atmosphere (TOA) radiation by latitude. Area weighted. Note the units are terawatts (10^12 watts) per degree of latitude. Area-weighting is done using the official CERES latitude areas, which are for an oblate spheroid rather than a sphere. It makes no visible or numerical difference at this scale, but Gavin Schmidt busted me for not using it, and he’s right, so why not use the recommended data? The radiation in W/m2 is averaged for each degree of latitude. That average value is multiplied by the surface area of the degree of latitude (in square metres / ° latitude). The square metres cancel out, and we are left with watts per degree of latitude. 

You can see the increased reflection from 0-10°N of the Equator. This is the sunlight reflecting from the massed cumulonimbus of the Inter-Tropical Convergence Zone (ITCZ). These tropical thunderstorms of the ITCZ provide the power driving the global equator-to-pole circulation of the atmosphere and the ocean. The increased reflection from 0-10°N is important because of the strength of the incoming sunshine. Half of the incoming TOA solar energy strikes the planet between 25°N and 25°S.

It’s also clear that the albedo in the southern polar regions is much higher than that of the northern polar regions. To investigate the effects of that difference on the radiation datasets, I decided to re-do Figure 5, the radiation by latitude, and look at the differences between June and December. Figure 6 shows June (darker of each pair of lines) and December (lighter lines) for the TOA solar, reflected, and longwave radiation.

Figure 6. As in Figure 5 (without albedo), but for June and December. For each pair of lines, the darker of the pair is the June data, and the lighter is the December data. The dotted blue line is the reverse (north/south) of the light blue line, and is shown in order to highlight the difference in reflected solar near the poles.

OK, so here we finally can see why the shape of the reflected solar data is so wonky. In December, there is much more solar reflection from the Antarctic region, with its very high albedo. December reflections at 70°S are about 500 TW/°. On the other hand, in June at 70°N the reflections are much smaller, only about 350 TW/°. As a result, when these regions swing into and out of view of the sun, we get large differences in reflected sunlight.

But the real surprise for me in Figure 6 was the upwelling longwave. The downwelling and reflected solar profiles are quite different from June to December … but to my shock, the upwelling longwave hardly changes at all. Say what? Heck, in the extra-tropical southern hemisphere there’s almost no difference at all in longwave radiation over the year … why so little change in either hemisphere?

And that, to me is the joy of science—not knowing which bush hides the rabbit … or the tiger.

Finally, Figure 7 shows the TOA net radiation imbalance. This is the downwelling solar energy, less what is reflected, less what is radiated.

Figure 7. Net top-of-atmosphere (TOA) radiation imbalance. Note that this is an anomaly, because there is a known error of about a 5 W/m2 difference in the incoming and outgoing CERES radiation data. So while we can use it for trends and standard deviations, it cannot tell us if there is an overall persistent imbalance in the TOA radiation. Positive values show the system gaining energy, and negative values show it losing energy. Panels as in previous figures, showing the data (top panel) along with the seasonal and residual components of the signal.

I see that this has the reverse of the four-month rise, eight-month fall pattern of the reflected data. The TOA imbalance falls for four months, and then rises for eight months.

Once again, however, the most surprising aspect of this net imbalance data is the amazing stability. There is no trend in the data, and the standard deviation of the residuals is only a bit above about half a watt per square metre.

Remember that this is a system that is moving huge, unimaginable amounts of energy, with average downwelling total surface radiation of half a kilowatt, and peak surface solar insolation of about a kilowatt. More importantly, it is a system with the significant albedo variables being nothing more solid than the ephemeral, seasonal, mutable phenomena of clouds, wind, snow, ice, and vegetation.

In such a system, it is something eminently worthy of study that over the thirteen years of the CERES dataset, for reflected solar and upwelling longwave, 95% of the months are within one watt/m2 of the seasonal average. Within one lousy watt! We assuredly do not know all the reasons why that might be so …

Anyhow, thanks for coming along. Looks like the weather forecast for the voyage was about right. 

All the best to each of you,

w.

Standard Proclaimer: If you disagree with something that I or anyone has said, please QUOTE THE EXACT WORDS that you disagree with. Only then can we understand what it is you object to.

[UPDATE]:

DATA AND CODE: The code is in a zipped folder here. Unzip it and put the individual files into the workspace. You’ll also need the CERES TOA data in the same workspace (WARNNG: 230 Mbytes). The main file is called “Three Clocks.R”, I think it’s all turnkey.