Greenhouse Efficiency

Guest Post by Willis Eschenbach

Buoyed by equal parts of derision and praise for my last post, “Surface Radiation: Absorption And Emission“, I once again venture into the arena. I had an odd thought. The temperature has been generally rising over the period 2000-2021. I wondered if there was a way I could measure the efficiency of the greenhouse effect to see if the warming was due to increasing greenhouse gases (GHGs). If the GHGs were the cause, then the greenhouse effect would need to be more efficient in terms of warming the surface.

A Prologue: The earth is much warmer than the moon, which receives the same amount of solar energy. It’s generally accepted, including by me, that the warmth is from the very poorly named “greenhouse effect”, which has nothing to do with greenhouses.

Now, if you don’t think the “greenhouse effect” exists, this is NOT the thread for you. There are lots of places to make that argument. This isn’t one of them. We know the earth is warmer than expected. Nobody has ever come up with an explanation for that except the greenhouse effect.

If you are unclear about how the greenhouse effect works, the physical basis of it has nothing to do with CO2 or with the atmosphere at all. I explain this in my posts “People Living In Glass Planets“, and “The Steel Greenhouse“.

To reiterate: PLEASE do not post your opinions here on why the greenhouse effect isn’t real, or why there’s no such thing as downwelling radiation, or that scientists don’t understand the instruments that measure IR. The web is a very big universe. Somewhere out there is the perfect place to make those arguments.

This is not that place.

To return to the question at hand, which is the efficiency of the greenhouse effect, here’s the temperature change during the period of the CERES satellite data.

Figure 1. Surface temperature changes, CERES data. It is a conversion of the CERES surface upwelling longwave data to units of degrees Celsius using the Stefan-Boltzmann equation. It agrees well with e.g. the MSU lower tropical temperature, with a residual standard error of about a tenth of a degree C.

So the question, of course, is why did it warm over that period?

I thought, well, what the greenhouse effect does is to increase the surface temperature. The greenhouse effect starts with a certain amount of energy entering the climate system, and it ends with the surface being warmer and thus emitting more thermal radiation than would be expected if one were to look at say the moon, which gets the same energy from the sun as does the earth.

So … I figured that I could express the efficiency of the greenhouse effect by comparing the upwelling longwave radiation from the surface with the amount of solar energy entering the system. This measures the “end-to-end” efficiency of the entire system, including all feedbacks and interactions. I’ve chosen to express it as a “multiplier”—for every W/m2 of solar input, how many W/m2 of upwelling surface radiation do we get?

The amount of solar energy at the top of the atmosphere is about 340 watts per square meter (W/m2). However, about 100 W/m2 is reflected by the clouds and the surface. This means that the solar energy entering the system is on the order of 240 W/m2.

Upwelling longwave from the surface, on the other hand, is on the order of 400 W/m2. This means that the average greenhouse multiplier is approximately:

400 W/m2 / 240 W/m2 ≈ 1.66

In other words, for every watt per square meter of solar input, we get ~ 1.7 watts per square meter of upwelling surface radiation.

Now, we can run this calculation for each month, looking at the amount of thermal radiation emitted by the surface divided by the solar energy entering the system. Figure 2 shows that result. Remember that for increased greenhouse gases to be responsible for the warming, the greenhouse multiplier needs to increase.

Figure 2. Greenhouse multiplier. The multiplier is calculated as upwelling longwave surface radiation divided by incoming solar radiation (after albedo reflections). A multiplier of 2 would mean that the surface would be radiating two W/m2 of energy for each one W/m2 of solar energy actually entering the system. This shows that the greenhouse has increased the incoming solar radiation by about two-thirds, as measured at the surface.

Now, this is a most interesting finding. The efficiency of the planetary greenhouse has decreased slightly over the period—not significantly, but not increasing either.

In fact, the stability over the period is of interest in itself. Note that the standard deviation of the multiplier is 0.004 W/m2. Over the period, the end-to-end efficiency of the entire greenhouse system hardly varied at all. I’ve written before about the amazing stability of the system. This is another example.

So given the evidence above that the increase in upwelling surface radiation cannot be due to a change in greenhouse efficiency from increased CO2 or any other reason, what is the cause of the temperature increase? Here are the graphs of the two datasets that make up the greenhouse multiplier—the upwelling surface radiation, and the incoming solar radiation.

Figure 3. Upwelling surface thermal radiation (yellow, left panel), and incoming solar radiation after albedo reflections (red, right panel). Blue/black lines are LOWESS smooths of the data.

In Figure 3, we can see why the efficiency of the system hardly varied—the upwelling surface longwave was increasing pretty much in lockstep with the incoming solar energy actually entering the system.

Conclusions: We have observational evidence that the temperature increase from 2000-2021 was not due to an increase in greenhouse gases, or any increase in the efficiency of the greenhouse effect from any cause. The efficiency has been very stable over the period, with a standard deviation of 0.2% and no significant trend.

On the other hand, the change in incoming solar energy is both adequate to explain the increase in warming, and has the same shape as the change in surface radiation (blue LOWESS smooths in both panels in Figure 3). While there are undoubtedly other factors in play, the main cause of the warming is clearly the increase in the amount of solar energy after reflections from the clouds and the surface.

And once again, the clouds rule … go figure …


Math Note: I tend to use “upwelling longwave surface radiation” and “temperature” interchangeably. Yes, I know that radiation varies as the fourth power of temperature, T4. However, the difference is trivial in the narrow range shown in e.g. Figure 3.

Figure 4 shows a comparison of the upwelling longwave shown in Figure 3 and the Stefan-Boltzmann derived temperature. Basically identical in form.

Figure 4. Temperature (yellow, left scale) and surface upwelling radiation (red, right scale)

Policy Note: I was 100% serious about asking people to refrain from commenting about things like how downwelling radiation doesn’t exist and the greenhouse effect isn’t real. Don’t make me tap the sign.

My Usual Request: Misunderstandings abound in communication. When commenting, PLEASE quote the exact words you are discussing, so we can all understand exactly who and what you are responding to.

via Watts Up With That?

September 2, 2022 at 12:51PM

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