Scatterplot Sensitivity

Guest Post by Willis Eschenbach

This is the third post looking at the use of 1° latitude by 1° longitude gridcell-based scatterplots. The first post, Global Scatterplots, looked at a gridcell-based scatterplot of surface cloud radiative effect (CRE) versus temperature. The CRE measures how much clouds either warm or cool the surface through the combination of their effects on shortwave (solar) and longwave (thermal) radiation.

Figure 1. Original caption: Scatterplot, surface temperature (horizontal “x” axis) versus net surface cloud radiative effect (vertical “y” axis). Gives new meaning to the word “nonlinear”.

The slope of the yellow/black line shows the change in CRE for each 1°C change in temperature. Note the rapid amplification of the cloud cooling above about 25°C.

The second post, Solar Sensitivity, used the same method to investigate the relationship between available solar power (top-of-atmosphere [TOA] solar minus albedo reflections) and temperature. Here’s the graphic from that post.

Figure 2. Original caption: Scatterplot, gridcell-by-gridcell surface temperature versus available solar power. Number of gridcells = 64,800. The cyan/black line shows the LOWESS smooth of the data. The slope of the cyan/black line shows the change in temperature for each 1 W/m2 change in available solar. The data in all of this post is averages of the full 21 years of CERES data.

As before, the slope of the cyan/black line shows the change in surface temperature per one W/m2 change in available solar power.

In this one, the points of interest were the three roughly straight sections, particularly the right one. In that section, additional solar power isn’t raising the temperature.

Figure 3 below shows the slope of the cyan/black line versus available solar power.

Figure 3. Original Caption: Slope of the trend line in Figure 2. This shows the amount of change in the temperature for a 1 W/m2 change in available solar.

This method of looking at the data is of great interest because it reveals long-term relationships between the variables. Each gridcell has had thousands of years to equilibrate to its general current temperature and available solar power. So looking at the temperatures of both nearby and distant gridcells with slightly different available solar power shows long-term relationships between solar and temperature, not what happens with a quick change.

Next, it’s of value because the slope is relatively insensitive to changes in average temperature or average available solar. Changes in average temperature merely move the cyan/black line up or down, but this causes very little change in the slope on the cyan/black line.

Similarly, changes in average solar move the cyan/black line left or right. And changes in both average temperature and average solar displace the data diagonally … but none of these change the variable of interest, the slope of the cyan/black line, in any significant manner.

Now, for this post I wanted to look at the relationship between the very poorly named “greenhouse” radiation and surface temperature.

And what is greenhouse radiation when it’s at home?

All solid objects, including the earth, emit thermal radiation. It’s how night-vision goggles work. They allow us to “see” that radiation.

Some of the radiation from the earth goes directly to outer space. But some is absorbed by the atmosphere. This is eventually re-radiated in all directions, with about half going up and half going back towards the earth. This downwelling (earth-directed) longwave thermal radiation is called “greenhouse radiation”.

Now, a smart guy named Ramanathan pointed out that we can actually measure the amount of this greenhouse radiation from space. For every gridcell, we take the amount of radiation emitted at the surface. From that, we subtract the radiation escaping to space. The remainder is what was absorbed by the atmosphere and re-directed downwards—the greenhouse radiation.

So I wanted to see what happens to surface temperatures when greenhouse radiation changes. But there’s an immediate problem. The amount of greenhouse radiation goes up and down whenever the surface temperature changes. If the surface is warmer and radiating more, more is absorbed by the atmosphere, and as a result of the increase in surface temperature, greenhouse radiation is larger.

To remove that difficulty, we can express the greenhouse effect as a percentage of upwelling (directed to space) longwave surface radiation. This takes the direct effect of surface temperature on greenhouse radiation out of the equation. Figure 4 shows the resulting relationship between surface temperature and the greenhouse effect as a percentage of upwelling radiation.

Figure 4. Scatterplot, gridcell-by-gridcell surface temperature versus greenhouse radiation percentage. Number of gridcells = 64,800. The red/black line shows the LOWESS smooth of the data. The cyan/black line’s slope shows the change in temperature for each 1 W/m2 change in available solar. The few negative gridcells are at the poles, and they show the effect of the importation of heat from the tropics.

And here is the corresponding graph of the slope, once the percentages are translated back into W/m2.

Figure 5. Slope of the trend line in Figure 4. This shows the amount of change in the temperature for a 1 W/m2 change in greenhouse radiation.

This has both similarities and differences from the warming due to changes in available solar shown in Figure 3 above. Both start out high on the left, and both end up with a low unchanging slope on the right. However, the greenhouse warming is much larger in the middle. This leads to a global area-weighted average climate sensitivity of 0.58°C per 1 W/m2 additional greenhouse radiation.

This in turn equates to about 2°C per doubling of CO2. This is about the same equilibrium climate sensitivity found by Nic Lewis in his recent study Objectively combining climate sensitivity evidence, viz:

The resulting estimates of long-term climate sensitivity are much lower and better constrained (median 2.16 °C, 17–83% range 1.75–2.7 °C, 5–95% range 1.55–3.2 °C) than in Sherwood et al. and in AR6 (central value 3 °C, very likely range 2.0–5.0 °C).

Finally, this method gives a climate sensitivity estimate for each gridcell. Here is that map, showing how much the surface temperature is estimated to change for each additional W/m2 of greenhouse radiation.

Figure 6. Expected temperature change resulting from a 1 W/m2 increase in greenhouse radiation.

This makes some sense. The blue areas are the location of the intertropical convergence zone and the Western Pacific Warm Pool. They are generally covered with cumulus and thunderstorm clouds. These act as a 100% absorber of upwelling radiation … so any additional CO2 will make little difference. In addition, temperatures in these areas are up near the maximum, so they won’t warm much from increased greenhouse or solar radiation.

Well, there are probably more insights to be drawn from all of this. But this post is long enough, so I’m going to leave it there. I’m sure, for example, that I can get better results by subdividing the data, both by north/south hemisphere and by land vs ocean. That will do a better job of only comparing like with like. But sadly, there are never enough hours, in either a day or a lifetime

And as usual, what I’ve found brings up more questions than answers. I view my writings in some sense as my ongoing lab notebook, where I get to have a permanent record of what I’m finding, and you get to learn about things when and as I learn about them.

My very best to you all, and thanks for your continued interest, participation, and critiquing of my ongoing investigations into the mysteries of this amazing universe,

w.

My Perennial Request: When you comment please quote the exact words you are discussing. It avoids all kinds of misunderstandings.

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October 21, 2022 at 12:25PM

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