Multiplier – Increases with that?

Guest post by Willis Eschenbach

This is a follow up from my previous post titled Greenhouse balance. If you haven’t read it, you might want to, as it introduces many of the concepts that I will discuss in this post.

I have to think about the repeated claim that CO doubles₂ increase the radiant force from the top of the atmosphere (TOA) to 3.7 watts per square meter (W/m²)… And in turn, add 3.7 W/m² of the forced TOA causes a warming of ~3°. In other words, they say that ~1.2 W/m² of the additional radiant force causes some degree of warming.

What got me thinking was the Stefan-Boltzmann equation. It relates temperature to the amount of thermal radiation emitted. It shows that the radiation changes as the fourth power of temperature, T⁴. This means that the warmer an object is, the more energy it needs to put into the object to increase its temperature by each degree.

So how much extra energy is needed to raise the earth’s temperature (by about 15°C) by one degree Celsius?

According to the SB equation, it requires an additional ~5.2 W/m² absorbed by the surface to raise the earth’s temperature by one degree Celsius. But as discussed in my previous post, only ~80% of the absorbed surface energy is expressed as temperature. This means that to warm the earth by 1°C, 5.2/.8 = 6.5 W/m is required.² energy absorbed at the surface each time it is heated by 1°.

Now, recall that their claim is 1.2 W/m² of the forced TOA causes a degree of warming … thus requiring 6.5 W/m² at the surface.

Presumably, their claim is that the different responses amplify the change in the radiant force. But spin 1.2 W/m² at TOA to 6.5 W/m² at the surface? That’s a little trick. I don’t see that happening at all.

Now, let me back up an image from my previous post, along with a caption.

Figure 1. Greenhouse multiplier. The multiplier is calculated as the rising long-wave surface radiation divided by the incident solar radiation (after albedo reflection). A multiplier of 2 means that the surface will radiate two W/m of energy for every W/m² solar energy actually enters the system. This suggests that greenhouses have increased solar radiation by about two-thirds, as measured at the surface.

Now, over the period of the CERES record, the pressure on greenhouse gases increases by about 0.7 W/m².

This should theoretically be increased by a 6.5/1.2 response to the value at the surface. in this case it converts 0.7 TOA W/m² up to 3.8 W/m² at the surface.

This allows us to see what the change in greenhouse efficiency shown in Figure 1 would be if the absorbed surface irradiance was increased by 3.8 W/m2. Figure 2 is the same as Figure 1, but includes the expected change from the additional absorption of 3.8 W/m2.

Figure 2. As shown in Figure 1, but including the trend in the multiplier expected from the forced increase in TOA greenhouse gases.

Hmmm… a few points.

First, I simply don’t believe their numbers. Their claim is double the amount of CO₂ provides an additional 3.7 W/m² at TOA, and it heats up the surface by 3°C. That’s about 1.2 W/m² each level of warming.

But we know that it needs 6.5 W/m² to raise the earth’s temperature by one degree…

I do not see any physical process whereby 1.2 W/m² can somehow increase to 6.5 W/m².

Second, even if warming is only 1°C for every doubling of CO₂, we can still see it in the image. Figure 3 shows that result.

Figure 3. As shown in Figure 2, but with CO₂ forced to be calculated at one degree of warming per doubling of CO₂is one degree per 3.7 W/m².

But we also don’t see a trend less in the multiplier. Instead, the multiplier has a slight but insignificant decrease, and it is not like what we would see if increasing GHG actually increased the surface temperature.

However, at least that less trend is somewhat reliable since the gain from TOA to the surface is from 3.7 W/m² to 6.5 W/m². Still, a huge reach… it will require strong positive feedback and I haven’t seen that anywhere.

Now, the important thing to remember about this system’s performance measurement is that it should be end-to-end. I mean we start with the energy entering the system (reflection minus the sun) and we end up with the surface temperature.

In between the sun and the surface, we have a series of emerging climate phenomen. In addition, they include variable shortwave and longwave radiation effects of the cloud, change in surface albedo, and TOA albedo, the highly variable energy flow from the tropics to the poles, variability in aerosols, La Nina/El Nino pumps, variations in the duration and strength of thunderstorms, variations in perceived/latent heat loss from the surface… and changes in the gas Greenhouse.

And what seems to be happening is that, as I’ve said for years, changes in greenhouse gases are being counteracted by a combination of some of the other emerging climate variables included above.

What a wonderfully complex world we live in!

w.

Postscript-As with the previous post, stick to the topic. Claims that the greenhouse effect is bogus or that the radiation spills down has no place in the comments on this post, and they will be scrutinized from a great height. You are welcome to discuss those issues… just not on this particular post.

My usual—I can defend my word. I cannot defend your (wrong) interpretation of my words. Please REVIEW the EXACT WORD you are discussing in your comments, so that we can all understand who and what you are answering.