Greenhouse Efficiency Insights – Watts Up With That?

Guest Post by Willis Eschenbach

Abstract: Using the CERES satellite data, it is shown that over the last ~ quarter century, the increase in greenhouse gases has had no detectable effect on the global average surface temperature. On the contrary, the overall increase in available solar energy after albedo reflections is shown to be sufficient to explain the warming. In support of this, variations in available solar energy are shown to agree quite well with the variations in the observed temperature. Go figure.

I got to thinking again about how to measure the efficiency of the very poorly-named “greenhouse effect”, which has absolutely nothing to do with actual greenhouses like the one shown above. Here’s an overview of some of the major energy flows of the climate system.

Figure 1. Monthly surface upwelling longwave (thermal) radiation, along with solar radiation at different altitudes. Equivalent temperatures are calculated using the Stefan-Boltzmann equation. Seasonal variations removed.

The red line shows the 24/7/365 global average solar radiation that strikes the planet, 340 watts per square meter (W/m²) of planetary surface area. However, part of that radiation is reflected back out to space.

The orange line shows the 241 W/m² of solar radiation remaining after clouds, aerosols, and the surface reflect some of the sunlight back to space. Other than a tiny contribution from the geothermal heat, this is the total energy entering the climate system. It’s all we’ve got.

Then aerosols, water vapor, and clouds absorb some of the remaining solar radiation before it hits the ground. The yellow line shows how much of the solar radiation is actually absorbed by the surface itself. At only 164 W/m², it’s less than half of the solar radiation striking the top of the atmosphere.

Before moving on to further questions, please take a moment to look at Figure 1 and contemplate the surprising stability of the overall system. The clouds, ice, plants, and snow that determine the albedo are constantly changing on an hourly, daily, and monthly basis. Despite that, Figure 1 shows that the amount of energy entering the system (orange line) and the amount reaching the surface (yellow line) barely change from year to year.

Coincidence? You be the judge. But I digress …

Here’s the perplexitude. All solids and most gases are constantly absorbing and emitting longwave radiation. The amount of radiation emitted depends on the temperature, so this is sometimes called “thermal radiation”. And on average, because of its temperature, the surface of the earth is emitting almost 400 W/m² of upwelling longwave thermal radiation. See the blue line at the top in Figure 1.

That’s the puzzle. Less than half of the 400 W/m² energy flux that the surface is emitting comes from the sun. Where is the rest coming from?

The answer is that some of the upwelling longwave energy from the surface is absorbed in the atmosphere by clouds, aerosols, water vapor, and what are called “greenhouse gases” or “GHGs”.

At the same time, these clouds, aerosols, water vapor, and greenhouse gases are constantly radiating the energy flux they are absorbing from both the downwelling solar radiation and the upwelling longwave (thermal) radiation. Of course, it’s emitted in the form of longwave (thermal) radiation.

Since the atmospheric thermal radiation is emitted in all directions, about half of it proceeds to space and the other part goes downwards and is absorbed by the surface. And that downwelling thermal radiation is the source of the extra energy that allows the surface to radiate more than just what it gets from the sun. For further information on this question of the so-called “greenhouse effect”, let me recommend my post below.

Looking at Figure 1 reveals that we can measure the overall efficiency of this “greenhouse” system by calculating how much radiation the surface emits for each W/m² it receives from the sun. Overall, the system receives about 240 W/m² of energy flux from the sun, and just under 400 W/m² is emitted by the surface. So the general answer is that the surface emits about 1.65 times the total energy flux that the planetary climate system receives from the sun (solar radiation after albedo reflections).

What I have just calculated, the amount of surface energy flux emitted per 1 W/m2 of incoming solar energy flux, is a measure of the overall efficiency of the greenhouse system. It measures how well the so-called “greenhouse effect” is able to convert solar energy into surface warming. I’ll return to this discussion of greenhouse efficiency in a moment.

Now, the blue line in Figure 1 above shows that over the period of record, the surface upwelling thermal radiation has increased slightly, by about 0.9%. That is because the surface temperature has increased. Here’s a closeup of the change starting in 2000.

Figure 2. A closeup of the surface upwelling longwave radiation shown in Figure 1 above (blue line in Figure 1). As in Figure 1, temperatures are calculated using the Stefan-Boltzmann equation. Seasonal variations removed.

The obvious question is whether this increase in the surface temperature is the result of increasing “greenhouse gases”, which are CO₂, methane, water vapor, nitrous oxide, halogenated gases, and other minor greenhouse gases. According to the IPCC and the canonical theory, the increasing greenhouse gases are indeed what is causing the surface warming shown in Figure 2 above.

Now, if the increase in those GHGs is what has been driving the increase in surface temperature (and surface thermal radiation), that would show up as an increase in the efficiency of the greenhouse system. More greenhouse gases would absorb more upwelling thermal energy flux from the surface, leading to more downwelling energy flux. This would make the surface warmer for the same amount of incoming solar energy flux. That change would be reflected as an increase in the greenhouse efficiency as calculated above.

But as Figure 3 below shows, there’s been no observable change in greenhouse efficiency in the last quarter century.

Figure 3. Greenhouse efficiency, a dimensionless number calculated as the thermal energy flux emitted by the surface (in W/m2) divided by the solar energy flux entering the system (solar radiation minus albedo reflections). This measures how efficient the system is at converting incoming solar energy into increased surface temperature.

I must confess, I was surprised by this graph. I’d expected the efficiency to have risen somewhat due to the increase in greenhouse gases. But there’s no significant trend.

This is an important finding. Despite increasing GHGs, there has been no corresponding increase in greenhouse efficiency since the turn of the century. This means that whatever is driving the temperature increase shown in Fig. 2, it’s not increasing GHGs.

Note that I’m not saying that the GHGs don’t increase the downwelling longwave radiation. They do. They absorb more upwelling radiation and thus perforce, they increase the downwelling radiation. I’m saying that the increase in downwelling radiation is NOT showing up as an increase in surface temperature. If it were, we’d see it in the efficiency calculations shown above.

My next question was, is it possible that this greenhouse efficiency measurement is too crude to detect the expected change in efficiency from increased GHGs? To determine if this is the case, I looked at the change in efficiency that we’d expect to see from the increase in CO₂ and other greenhouse gases over the period. Figure 4 below shows the trend of the expected change in efficiency from increased GHGs (orange line).

Figure 4. As in Figure 3, but with the addition of the trend of the increased efficiency expected from the increase in the well-mixed greenhouse gases (orange line). Per the IPCC, the total effect of all greenhouse gases (GHGs) combined is about twice the effect of the CO₂ alone. So in Fig. 4, the increase in total GHG radiation is calculated as twice the increase in CO₂ radiation. See the end notes for the full calculations.

If the increase in surface radiation were the result of increased greenhouse efficiency from the increased well-mixed GHGs, it would show up in Figure 4 above as the efficiency increasing with a trend as shown by the orange trend line. So the greenhouse efficiency measurement is quite sensitive enough to detect the theoretical increase due to increased GHGs.

But in the event, since the year 2000 there’s been no such increase in greenhouse efficiency. There’s no such trend.

So … what’s going on here? That’s really two related questions.

The first question is, where is the extra energy for the known surface warming coming from? Clearly, it’s not coming from the increased GHGs, or we’d have seen an increase in greenhouse efficiency.

The second question is, what has happened to the increased downwelling thermal radiation from the atmosphere? We know that the increased GHGs are causing increased downwelling radiative flux because we can measure it from satellites … but it’s not causing increased surface temperature. We know that energy can’t be created or destroyed … so what’s happening to it?

Regarding the first question, the extra energy must be coming from the sun. Aside from the GHGs, it’s the only other game in town. To demonstrate that the sun is totally sufficient to explain the rise in the planet’s surface temperature/thermal radiation, Figure 5 below is a graph comparing the surface upwelling thermal radiation to the solar input radiation times the average greenhouse efficiency (~1.652).

Figure 5. Surface upwelling longwave (thermal) radiation in red. Black and black/white lines show the solar input radiation (TOA solar minus albedo reflection) times the average greenhouse efficiency (1.652).

Note how closely the variations in the output (surface radiation) correspond to the variations in the input (the amount of solar energy flux entering the system). Both show the same rise-level-rise-level-rise pattern, in the same amounts and at the same times. This shows that the changes in surface temperature are exactly what we’d expect from the change in solar input, given the average efficiency of the system as a whole.

In other words, a greenhouse gas explanation is not needed and is indeed superfluous over this period—given the known greenhouse efficiency, the surface temperature is responding to the change in solar input exactly as expected … while in the background, Occam quietly hones his razor …

Regarding the second question, which was … hang on, what was it? … oh, ok, it was, what has happened to the increased downwelling thermal radiation from the atmosphere, since we know it’s not warming the surface?

Let me refer folks to my post below entitled “The Details Are In The Devil”. It discusses the problem of relating changes in downwelling radiation to changes in temperature in an actively governed system, which is a large part of the answer to the second question.

Another part of the answer to the second question is in the following post:

There are more answers to the second question. There’s advection. There’s sensible heat loss from the surface. There’s Nino/Nina-driven transport of warm water to the poles to speed up energy loss to space. Then there are the giant natural refrigerators we call “thunderstorms” cooling the surface in a myriad of ways …

… but that’s enough for now. Further affiant sayeth naught.

Here, after a foggy week, it’s a bluebird day. I can see the sunlight on the ocean six miles (ten km) from my house, my grandkids are laughing in the next room, what’s not to like?

Best of life to all,

w.

The Usual: When you comment please quote the exact words you are discussing. I can defend my words. I can’t defend your interpretation of my words.

The Math: First, the required trigger warning.

Then, the data. It’s a small (20 kb) .csv file in my public dropbox here.

Next, the math.

The variables are:

coshort—the monthly atmospheric CO₂ levels for the period analyzed

surf_lw_up_all_mon—monthly surface longwave up, all-sky conditions (not just clear skies)

toa_avail_all_mon—monthly available solar radiation after albedo reflections

themult—monthly efficiency factor as calculated in Fig. 3, surface thermal radiation divided by available solar radiation

coforce—monthly total GHG forcing in W/m²

theco—GHG forcing expressed as a change in greenhouse efficiency

The functions are:

log2—logarithm base 2

first—first value of a series

mean—average value

getfitted—returns the linear fit (regression line or trend line) of a variable as a series of values

Comments are whatever follows the hashmark “#” on a line.

The calculations in R computer language are:

> coforce = log2(coshort / first(coshort)) * 3.7 * 2 # monthly total GHG forcing over the period

> theco = (coforce + mean(surf_lw_up_all_mon)) / mean(toa_avail_all_mon) # monthly GHG forcing expressed as a change in greenhouse efficiency

> theco = theco - first(theco) + first(getfitted(themult)) # adjust it to start at the start of the red fitted linear regression line in Fig. 4.

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