Watts Available

By Willis Eschenbach – Re-Blogged From WUWT

I ponder curious things. I got to thinking about available solar energy. That’s the amount of solar energy that remains after reflection losses.

Just under a third (~ 30%) of the incoming sunshine is reflected back into space by a combination of the clouds, the aerosols in the atmosphere, and the surface. What’s left is the solar energy that actually makes it in to warm up and power our entire planet. In this post, for shorthand I’ll call that the “available energy”, because … well, because that’s basically all of the energy we have available to run the entire circus.

Now, I don’t agree with the widely-held idea that the planetary temperature is a linear function of the “radiative forcing” or simply “forcing”, which is the amount of downwelling radiation headed to the surface from both the sun and from atmospheric CO2 and other greenhouse gases. Oh, the radiation itself is real … but it doesn’t set the surface temperature

My theory of how the climate operates is that the globe is kept from overheating by a variety of emergent phenomena. These phenomena emerge when some local temperature threshold is exceeded. Among the most powerful of these emergent phenomena are thunderstorms. In the tropics, thunderstorms emerge when the sea surface temperature (SST) is above about 27°C (80°F) or so. Here’s a movie I made of how the thunderstorms follow the sea surface temperature, month after month.

Figure 1. Tropical thunderstorms are characterized by tall cloud towers. The average altitude of the cloud tops is therefore a measure of the number and strength of the thunderstorms in the area. Colors show average cloud top altitude, with the red areas having the most and largest thunderstorms, and the blue areas almost none. The gray contour lines show sea surface temperatures (SSTs) of 27°, 28°, and 29°C, with the inner ring being the hottest.

Thunderstorms cool the surface in a variety of ways. They waste little energy in the process because they emerge to cool the surface only where it will do the most good—the hottest part of the system.

Among the ways thunderstorms cool the surface is via an increase in the local albedo. Albedo is the percentage of energy reflected back to space. The increase in this reflection (increasing albedo) occurs because the thunderstorm clouds both cover a larger area and are taller than the cumulus clouds that they replace. Their height and area provide more reflective surfaces to reject solar energy back to space.

In addition, the thunderstorm generated winds increase the local sea surface reflectivity by creating reflective white foam, spume, and spray over large areas of the ocean. And finally, a rough ocean with thunderstorm-generated waves reflects about two times what a calm ocean reflects (albedo ~ 8% rough vs ~ 4% smooth). That change in sea surface roughness alone equates to about 15 W/m2 less available energy.

Now generally, we’d expect that additional solar energy would be correlated with warmer temperatures. It’s logical that the relationship should go like this:

More available solar energy –> more energy absorbed by the surface –> higher temperatures. 

We’d expect, therefore, that both the available energy and the temperature should be “positively correlated”, meaning that they increase or decrease together. And in general, that’s true. Here’s the available solar energy, which is the sunshine that makes it past all of the reflective surfaces, the sunlight that is the one true source of all of the energy that heats, agitates, and powers the climate.

Figure 2. Available solar energy after all reflection from clouds, atmosphere, and the planet’s surface. The numbers are 24/7 averages.

As you can see, the poles are cold because they only get fifty watts per square metre (W/m2) or so from the sun. And the tropics get up to 360 watts per square metre (W/m2), so they are hot. The tropics are the main area where energy enters the system, and they’re also the hottest.

So far, what we see agrees with what we’d expect—available energy and temperature are correlated, going up and down together.

Now, my theory is that emergent phenomena act to constrain the maximum temperature. So an indication that my theory is valid would be if the amount of available solar energy were to not only stop increasing at high surface temperatures, but would actually go down with increasing temperature when the SST gets over about 27°C.

To see if this is the case, I turned once again to the CERES data, available here. I’m using the EBAF 4.0 dataset, with data from March 2000 to February 2019. The CERES satellite data has month-by-month information on the size of the incoming and reflected solar energy flows. The information is presented on a 1° latitude by 1° longitude gridcell basis.

According to the CERES data, incoming solar energy at the top of the atmosphere (TOA) is ~ 340 W/m2. The total reflected is ~ 100 W/m2. That leaves 240 W/m2 of available energy to warm the world. (Numbers are 24/7 global averages.)

To investigate the relationship between the surface temperature and the available energy, I looked at just the liquid ocean (not including sea ice). I do this for several reasons. The ocean is 70% of the planet. It is all at the same elevation, with no mountains to complicate matters. There’s no vegetation sticking up to impede the winds. It is a ways from human cities. All of this reduces the noise in the data, and makes it possible to compare different locations.

What I’ve done is to make a “scatterplot” of available energy versus sea surface temperature (SST). Each blue dot in the scatterplot below shows the available solar energy versus the sea surface temperature (SST) of a single 1°x1° gridcell.

Then I’ve used a Gaussian average (yellow & red with black outline) to see what the data is doing overall. (In this dataset, it turns out that the Gaussian average is basically indistinguishable from averaging the data in bins of a tenth of a degree (not shown). This lends support to the validity of the line.) The yellow/red line outlined in black shows the 160-point full-width-half-maximum (FWHM) Gaussian average of the data. The red area simply highlights the part above 27°C.

Figure 3. Scatterplot of available solar energy versus liquid sea surface temperature. Blue dots show the results for each 1° latitude by 1° longitude gridcell. Yellow/red line is 160-point full-width-half-maximum (FWHM) Gaussian average. The part of the data where the average SST above 27°C is highlighted in red

In Figure 3 we see that above ~ 27°C, the thunderstorm initiation temperature, the available solar energy stops rising, takes a ninety-degree turn, and starts dropping. You’ve heard of things being “non-linear”? This graph could serve as the poster child of non-linearity …

It’s worth noting that at temperatures from about 3°C to 27°C, the temperature is indeed a linear function of the available solar energy. So the common misunderstanding is … well … understandable. In that temperature range the sea surface is going up about 0.1°C per additional W/m2, which is the same as ~0.4° C per doubling of CO2 … but of course, that ignores the area in red, where the relationship is totally reversed and energy goes down as temperature goes up.

This is strong support for my theory that emergent phenomena actively regulate the global temperature and constrains the maximum temperature. It is also evidence against the current theory of how climate works, which is that the temperature slavishly follows the available energy in a linear fashion … as I noted, this is as non-linear as you can get..

In the areas where the sea surface temperature is over ~ 27°C there is less and less energy available with each additional degree C of surface warming. The size of the decrease is large—6.6 W/m2 less energy is available when the surface temperature has risen by each additional 1°C.

Figure 4 shows the location of these areas (shown in blue/green with white borders) where available solar energy goes down when the temperature goes up (negative correlation).

Figure 4. Gridcell by gridcell correlation of available solar energy and surface temperature. Blue box show the tropical area discussed below (130°E – 90°W longitude, 10°N/S latitude).

Investigating the energy flows further, loss of incoming energy via increased albedo is only one way thunderstorms cool the surface. It is an important method of thermoregulation because it acts just like the gas pedal in your car—the thunderstorms are controlling the amount of energy entering the planetary-scale heat engine we call the climate. And above a sea surface temperature of ~ 27°C, they are cutting the incoming energy down.

The thunderstorms which are cutting down the total available solar energy are also cooling the surface in a host of other ways. First among these is evaporation. Thunderstorms make rain, and it takes solar energy to evaporate the rain. That energy is then not available to heat the surface.

Figure 5 Scatterplot of the sea surface temperature versus the rainfall in the equatorial Pacific area shown by the blue box above (130°E – 90°W, 10°N/S). The blue dots show results from the TAO moored buoys in the blue box. The red dots show gridcell results from the Tropical Rainfall Measuring Mission (TRMM) satellite rainfall data and Reynolds OI sea surface temperatures. Graphic from my post Drying The Sky

Figure 5 above has SST data from two separate datasets, Tao buoys and the Reynolds OISST dataset. It also has rainfall data from two separate datasets, the TRMM data and TAO buoys. They agree very well, giving support to the relationships displayed.

And once again, it is highly non-linear …

Because the tropical oceanic thunderstorms are temperature related, so is the rain. Above 27°C, every single 1°x1° gridcell (red dot) and every TAO buoy (blue dot) in the equatorial Pacific area outlined in blue in Figure 4 above has rain.

In addition, by the time the open ocean temperature reaches its maximum value of 30°C, almost every gridcell has nearly three meters (ten feet, or 120″) of rain. At high sea surface temperatures, rain is not optional. This is clear evidence of the thermal nature of the thresholds involved.

It’s an important point. The thresholds for all of these emergent temperature-regulating climate phenomena (e.g. dust devils, cumulus fields, thunderstorms, squall lines) are temperature-based. They are not based on how much radiation the area is receiving. They are not affected by either CO2 levels or sunshine amounts. When the tropical ocean temperature gets above a certain level, the system kicks into gear, cumulus clouds mutate into thunderstorms, albedo goes straight up, and rain starts falling … no matter what the CO2 levels might be. Temperature-based, not forcing-based. It’s an important point.

And below is the rainfall data from 40° North to 40° South, expressed as the amount of energy needed to evaporate the rain.

Figure 6. Scatterplot of 1° x 1° gridcell annual average ocean-only thunderstorm evaporative cooling on the vertical axis, in watts per square metre (W/m2) versus 1° x 1° gridcell annual average sea surface temperature on the horizontal axis. Evaporative cooling amount is calculated from the rainfall—it takes ~ 80 W/m2 for one year to evaporate a metre of rainfall. Graphic from my post, How Thunderstorms Beat The Heat

As I write this, I think hmm … I could use the relationship shown in red above, between tropical sea surface temperature and evaporative cooling. Then I could add that TRMM data to the solar availability data to see how much is available after albedo and evaporation. Hmm … I’m off to write a another bunch of code in the computer language simply called “R”.

(Best computer language ever, by the way, and R was something like the tenth computer language I’ve learned. It’s free, cross platform, free, killer free user interface “RStudio”, free packages to do almost anything, good help files, and did I mention free? I owe Steve McIntyre an unpayable debt for convincing me to learn to code in R. But I digress, I’m off to write R code …)

OK, here’s the result. The scatterplot as above, scale about the same, but this time showing what’s left after removing both albedo reflections and the energy used for evaporation. This covers the area where rainfall was measured by the TRMM, from 40° N latitude to 40° S latitude.

Figure 7. Scatterplot, available solar energy minus evaporative cooling, versus sea surface temperature from 40°N latitude to 40°S latitude. Because it is only the middle latitudes the ocean doesn’t get much cooler than 15°C.

I note that when we include evaporative cooling, the drop in available energy starts at a slightly lower temperature, 26°C vs 27°. And it is decreasing much faster and further than just the 6.6 W/m2 decrease per degree of degree warming from albedo alone as shown in Fig. 3 above.

Figure 7 shows that there is 44 W/m2 less available energy per additional degree of warming above 26°C. So it is decreasing about seven times as fast as from albedo alone. On average there is less energy left over for warming at 30°C than at 15°C … go figure.

And finally, here’s the distribution of the solar energy once we’ve subtracted the reflected energy and the energy used for evaporation. What remains is the energy available to heat the planet and to fuel plant growth.

Figure 8. Available solar energy after albedo and evaporation losses. TRMM data only covers from 40° N to 40°S latitude.

Note that there are some areas of the oceans where any additional solar forcing goes into increasing clouds, increasing thunderstorms, and increasing evaporation, with little to nothing left over to heat the area …

Now, remember that my hypothesis is that the widely-believed claim that there is a linear relationship between forcing and temperature is not correct.

Instead, I say emergent phenomena come into existence when a temperature threshold is passed, and that they act to oppose further heating.

My main conclusions out of all of this? It supports my hypothesis regarding emergent phenomena regulating the temperature, and this is clear evidence that temperature is NOT a linear function of forcing.

And on a side note, the US passed a sad milestone today—the number of COVID pandemic deaths (a once-off phenomenon) finally equaled two-thirds of the annual number of deaths from obesity. In the face of this hidden gustatory emergency of 300,000 US obesity deaths per year, I recommend mandatory gastric banding of the entire populace and fine-enforced social distancing from donuts …

My best regards to everyone, end all lockdowns, the emergency is over. Let’s get back to work, school, and play,


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