Solar Symmetry and Balance

By Willis Eschenbach – Re-Blogged From

The CERES satellite dataset is a never-ending source of amazement and interest. I got to thinking about how much energy is actually stoking the immense climate engine. Of course, virtually all the energy comes from the sun. (There is a bit of geothermal, but it’s much less than a watt per square metre on average so we can ignore it for this type of analysis).

So let’s start from the start, at the top of the atmosphere. Here’s the downwelling top of atmosphere (TOA) solar energy for the northern and the southern hemisphere:

CERES NH and SH TOA solar radiation.png

Figure 1. Top of atmosphere (TOA) downwelling solar energy. This is averaged on a 24/7 basis over the entire surface of the earth.

However, we don’t get all of that energy. Much of it is reflected back into space. So I took the CERES solar data and I subtracted the reflected solar. The reflected solar is the total upwelling sunshine at the top of the atmosphere (TOA) that has been reflected from the clouds, the aerosols, the soil, the plants, the ice, and the ocean. The TOA solar minus the TOA upwelling solar reflections is the amount of energy available to heat the planet. Here’s the amount of available solar energy around the world.

Average Available Solar Energy.png

Figure 2. Map of the global distribution of average available solar energy. This is the solar energy remaining after albedo reflection of part of the incoming sunshine back into space.

Once I had the available energy, I subtracted out the seasonal variations. These are the changes that repeat year after year. Removing these repeating signals leaves only the small variations due to irregular changes in the amount of the reflections. (There is also a very small sunspot-related variation in the incoming solar of about a quarter of a W/m2 on a global 24/7 basis. It is included in these calculations, but makes no practical difference).

So here is the first look at how much energy is available to drive the great planet-wide heat engine that we call the climate, divided by hemispheres:

CERES NH and SH TOA solar & available.png

Figure 3. TOA solar and available solar after albedo reflections. Solar is about 340 W/m2, and about a hundred W/m2 of that are reflected back out to space.

Bear in mind that the amount of energy that enters the climate system after albedo reflections is a function of highly variable ice, snow, and clouds … and despite that, there is only very little variation over either time or space. Year after year, somehow the clouds and the ice and the snow all basically balance out, northern and southern hemispheres … why?

As you can see above, the available solar energy in two hemispheres are so near to each other that I’ve had to make the line representing the southern hemisphere narrower than that for the northern hemisphere so that you can see both. To see the two separately we need to zoom in close, as shown in Figure 4 below.

available energy nh sh.png

Figure 4. Available TOA solar energy after albedo reflections, northern and southern hemispheres.

Now, I noticed a few curiosities about this graph. One is that despite the great difference between the northern hemisphere (more land, lots of mid-and-high-latitude ice and snow) and the southern hemisphere (more ocean, little midlatitude land or ice or snow), the amount of average incoming energy is within a half a watt (NH = 240.6 W/m2, SH = 241.1 W/m2, black and red dashed horizontal lines)

Second, the two hemispheres generally move in parallel. They increased to 2003 – 2004, stayed about level to 2013 – 2014, and then increased again.

Third, there’s about an apparent lag between the northern and southern hemispheres. Now, I thought well, that makes sense … but then I realized that there is no annual signal left in the data. And I checked, there’s no six-month signal left in the data either. Not only that, but up until about 2011 the south moves before the north, but after that, the north is moving first. Again … why?

Gotta love the joys of settled science …

In any case, I then wanted to compare the variations in available energy with the variations in surface temperature. Now the CERES dataset doesn’t contain surface temperature. However, it contains a dataset of surface upwelling radiation, sometimes called “radiation temperature” because it varies as the fourth power of temperature. Figure 5 shows the monthly changes in TOA downwelling available solar radiation, compared to surface upwelling radiation.

CERES scatter surface lw vs available solar.png

Figure 5. Scatterplot, surface radiation temperatures (upwelling longwave radiation) versus TOA average available solar energy. Each dot represents the situation in a 1° latitude x 1° longitude gridcell, covering the entire planet. So there are 64,800 dots in the graph above.

So … what is happening in this scatterplot? Obviously, what’s happening depends on the temperature … and maybe more. To understand it, let me give you the same data, divided by hemisphere and by land versus ocean. To start with, here’s what might be the most revealing graph, that of the land in the southern hemisphere.

CERES land SH scatter surface lw vs available solar.png

Figure 6. Scatterplot, southern hemisphere land-only surface radiation temperatures (upwelling longwave radiation) versus TOA average available solar energy.

On the right we have we have the southern parts of Africa and South America … and on the left, we have Antarctica. You can clearly see the different responses between what happens below and above freezing.

Next, here’s the land in the northern hemisphere.

CERES land NH scatter surface lw vs available solar.png

Figure 7. Scatterplot, northern hemisphere land-only surface radiation temperatures (upwelling longwave radiation) versus TOA average available solar energy.

There isn’t anywhere in the northern hemisphere that the land gets as cold as Antarctica. In part, this is because the South Pole is land and the North Pole is water, and in part because much of Antarctica is a high elevation perpetually frozen plateau.

What all of this shows is that the response of the planetary surface to increasing solar radiation is in part a function of temperature. The colder the average temperature, the more the system responds to increasing solar radiation.

With that in mind, I took Figure 5 and calculated the slope of just the part of the world that on average is not frozen. Figure 8 shows that result.

CERES scatter surface lw vs available solar trended.png

Figure 8. As in Figure 5, and including the trend of the unfrozen parts of the globe.

Now, I found this to be a most curious graph. Here’s the curiosity. The greenhouse effect is the reason that the surface of the planet is warmer than we’d expect from simple calculations of the amount of sunlight hitting the Earth. This is because the greenhouse gases absorb the upwelling surface radiation, and when they radiate, about half of the radiation goes up, and half goes back towards the earth. As a result, the earth ends up warmer than it would be otherwise.

If the poorly-named “greenhouse effect” were 100% perfect, for every additional watt per square metre (W/m2) of sunlight entering the system, the surface would radiate two W/m2—one W/m2 from the sunlight, and one W/m2 from the downwelling radiation from the atmosphere. Based on the ratio of the incoming radiation and the radiation from the surface, we can say that the overall greenhouse multiplier factor of the perfect greenhouse is 2.0. (See my post The Steel Greenhouse for a discussion of this.)

Of course, in a real world, the multiplier factor will be less. We know what the long-term overall average multiplier factor for the planet is. We can calculate it by dividing the overall average upwelling longwave radiation from the surface by the overall average available solar energy. The average upwelling surface longwave radiation is 398 W/m2, and the average available solar energy is 240 W/m2. This gives a greenhouse multiplier factor of 398 / 240 = 1.66.

And that’s the curiosity because in Figure 8 the average multiplier factor is 0.72, well below 1.0. Because this multiplier is less than one, it would imply that the world should be much colder than it is …

How can we resolve this apparent contradiction? To me, it is evidence of something that I have said for many years. This is that the sensitivity of the surface temperature to the amount of downwelling radiation is not a constant as is assumed by mainstream climate scientists. Instead, it is a function of temperature. At temperatures above freezing, the surface upwelling radiation increases by about three-quarters of a W/m2 for each additional W/m2 of incoming solar radiation.

But when the earth is quite cold, such as is the case in Antarctica, the surface temperature is much more responsive to changes in incoming radiation. Here’s the situation in Antarctica:

CERES antarctic scatter surface lw vs available solar trended.png

Figure 9. As in Figure 8, but showing the situation in Antarctica

Note that this sensitivity is not a result of the land ice on Antarctica melting and changing the albedo. Almost all of Antarctica is frozen year-round.

Now, there is one other way we can look at this situation. We’ve looked above in Figures 5 to 9 at the long-term, basically steady-state situation shown by the average state of the  68,400 one-degree by one-degree gridcells that make up the surface of the planet. However, instead of the steady-state long-term average shown above, we can also look at how things change over time. Figure 10 shows the change in time of the anomaly in temperature over the period of the CERES satellite observations, as compared to the anomaly in average TOA solar energy.

CERES surface lw and available solar.png

Figure 10. Monthly surface longwave and TOA solar radiation.

You can see that other than the jumps in surface radiation due to the warm El Nino events of 2009/10 and 2016/17, there is a close relationship between available sunshine. A cross-correlation analysis (not shown) verifies that there is no lag between the changes in the solar input and the surface response.

We can also determine the nature of the short-term relationship between these two variables by using a scatterplot, as shown in Figure 11 below:

CERES scatter surf lw avail solar monthly.png

Figure 11. Scatterplot, monthly averages of available top-of-atmosphere available solar energy and surface upwelling longwave radiation.

As we would expect, the trend is smaller in the short-term data monthly changes shown in Figure 11 than the trend in the longer-term gridcell average data shown in Figure 8 (0.58 versus 0.72 W/m2 surface change per W/m2 solar input change).


Overall, the response of the non-frozen surface to increasing solar radiation is an average increase of about 0.7 W/m2 of upwelling surface radiation for each 1 W/m2 increase in available solar energy.

 Below freezing, this response increases with decreasing temperature, until at typical Antarctic temperatures of -20°C to -60°C the response is about 5 W/m2 for each 1 W/m2 increase in available solar energy.

Per the Stefan-Boltzmann equation, the change in surface temperature corresponding to a 1 W/m2 change in surface longwave radiation ranges from 0.2°C per W/m2 at 0°C, to 0.16°C per W/m2 at about 30°C.

Given a change of 0.7 W/m2 for a 1 W/m2 change in incoming solar energy, this would indicate a temperature change in the unfrozen part of the planet of from 0.11°C per additional W/m2 at 30°C, to 0.16°C per additional W/m2 at 0°C.

The increased downwelling radiation estimated for a doubling of CO2 is 3.7 W/m2. Ceteris paribus, this would indicate that if solar radiation increased by 3.7 W/m2, we would see a temperature increase of 0.4°C to 0.6°C depending on the surface temperature.

Finally, as a side note, the average change in TOA downwelling total solar irradiance (TSI) due to the change in sunspot activity is on the order of 0.26 W/m2 peak to peak (global 24/7 average). However, only 240/340 = 70% of this is available, the rest is reflected back to space. Given the relationship of 0.72 W/m2 surface change per each additional W/m2 of TOA available solar energy, and a maximum temperature change per watt of 0.16 °C per W/m2, this would indicate a maximum effect of 0.26 * 240/340 * 0.72 * 0.16 = 0.02 °C from that change in TOA solar radiation …

It’s a lovely evening here on our hill above the sea, a few clouds, cool air … I wish all of you the joy of this marvelous life.


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