Surface Response to Increased Forcing

Guest Post by Willis Eschenbach [See update at the end]

Thanks to the excellent comments by folks here on my post “A Request for Peer Preview“, I thought I’d go down the rabbit hole of the surface response to increased downwelling surface radiation, AKA “radiative forcing” or just “forcing”.

Surface radiation includes the net solar or “shortwave” forcing plus the downwelling “longwave” infrared thermal radiation from the atmosphere. On a global 24/7 basis, the sum of these two averages about half a kilowatt per square metre.

(Please don’t bother me with claims that downwelling longwave radiation from the atmosphere doesn’t exist. It has been measured, not estimated or modeled but measured, thousands of times by scientists all around the planet for over a century. If you don’t think it’s real, you need to do your homework … and in any case, this is not the place to debate it. I never delete comments on other peoples’ threads, and I almost never delete comments on my own threads, but in this case, I’ll make the exception. Please just take up the debate elsewhere, thanks.)

Now, the most direct way to see how variations in total forcing affect the temperature is to use actual data. So on a gridcell-by-gridcell basis, I took a direct look at how the surface temperature is affected by the variations in forcing. For the surface temperature, I used the Berkeley Earth gridded temperature; and for the radiative forcing, I used the CERES data. I first removed the seasonal variations from both datasets, then used standard linear regression to calculate how much the temperature changed when the forcing changed by one watt per square metre (W/m²) in each gridcell. Then I multiplied that by 3.7, since in theory the forcing increases by 3.7 W/m² when the level of atmospheric CO2 doubles.

Here’s the result of that analysis:

Figure 1. Change over a 20-year period in the temperature due to the change in downwelling longwave (LW) plus shortwave (SW) at the surface.

Note that this gives us 0.15°C per each additional 3.7 W/m². As expected, the ocean changes less than the land, because of its greater thermal mass, and again as expected, the poles change more than the tropics. Note that there are large areas of the tropical ocean where the surface temperatures are negatively correlated with forcing. This means that in those areas, when the temperature rises, the clouds rearrange to cut down incoming radiation.

However, there’s a huge problem with this method—it doesn’t give the surface time to equilibrate and adjust to the changes in forcing, because the changes are occurring on a monthly basis. So this is just a short-term response to changing forcing. But what we want to know is, what is the long-term response to such a change?

In my last post, I pointed to a novel way to calculate this. I took the average of each of the Berkeley Earth and the CERES 20-year 1° latitude by 1° longitude datasets I’d used to calculate Figure 1 above. Then I made a scatterplot where each dot is one gridcell. I calculated a LOWESS smooth of the data to show the average trend. Here’s that graph from my last post.

Figure 2. Scatterplot of surface temperature versus downwelling surface radiation. The slope of the LOWESS curve is the change in temperature resulting from a 1 W/m² change in downwelling radiation.

Upon further consideration, I realized that I could get a more accurate answer by dividing the two datasets up into land and ocean. Here are those results.

Figure 3. As in Figure 2, but for the land only.

Figure 4. As in Figs. 2 and 3, but for the ocean only.

Now, these are interesting in their own right. As we saw in Figure 1, the response of the surface to increased forcing goes negative at high ocean temperatures, but not for high land temperatures. In addition, the data is more tightly clustered around the LOWESS smooth when divided in this manner.

These two graphs lead to the following relationships:

Figure 5. Change in land temperature in °C corresponding to a 3.7 W/m² change in surface forcing at various temperatures/forcing levels.

Figure 6. Change in ocean temperature in °C corresponding to a 3.7 W/m² change in surface forcing at various temperatures/forcing levels.

Note that as expected, the change in ocean temperature is smaller than the change in land temperature at a given level of surface forcing.

Finally, I took the LOWESS smooths for the ocean and the land, and I used them as lookup tables to let me know the average temperature response for any given level of downwelling surface radiation. I used those temperature responses to calculate the expected temperature change for a global 3.7 W/m² increase in downwelling surface forcing for each gridcell on the globe. Figure 5 shows the end result of that calculation.

Figure 7. Expected change in surface temperature in the long term for a change of 3.7 W/m²

Some things of note. First, despite this being the result of an entirely different calculation method from that used in Figure 1, the main features are the same. The ocean still warms less than the land. But since this is long term, the ocean has had plenty of time to equilibrate, so the ratio of the two is not as large (Figure 1, ocean 0.08°C, land 0.31°C per 3.7 Wm2. Figure 7 above, ocean 0.39°C, land 0.71°C per 3.7 W/m² of TOA forcing). We also see that as in Figure 1, the poles warm more than the tropics.

Finally, we see much the same general areas of the ocean cooling while radiation is increasing as we saw in Figure 1.

How well does this represent the long-term response of the surface to changes in radiation? I’d say quite well. Suppose we have two adjacent 1°x1° gridcells of the surface. One is a bit warmer than the other because it has greater downwelling radiation, and the difference between the two temperatures divided by the difference in the two radiation levels is a valid measure of how much the additional radiation heats the planet.

Two key points about this situation. First, the average temperature in those two locations is the result of centuries of them having approximately the same average radiation. We’re talking about variations of a few W/m² over time, and total downwelling radiation averages about half a kilowatt per square metre.

Second, if over that time the global downwelling radiation has slowly increased due to changes in greenhouse gases, the temperature of both locations will have increased, and that will just shift the points a bit up and to the right in the scatterplots above. But it won’t change the underlying relationship of the temperature differences divided by the radiation differences.

So I’d say that this is a very valid way to accurately measure the long-term real-world surface temperature changes from changes in downwelling surface radiation.

And the bottom line of the analysis? An increase of 3.7 W/m² in downwelling surface radiation, which is the theoretical increase from a doubling of CO2, will only increase the surface temperature by something on the order of a half of a degree C.

Hmmm …

[UPDATE] An alert commenter has noted that the nominal 3.7 W/m2 per doubling of CO₂ is measured at the top of the atmosphere (TOA) and not at the surface. It turns out that for each additional W/m2 of forcing at the TOA, the surface forcing increases by about 1.3 W/m2. This increases my estimate of the temperature change from the 3.7 W/m2 from 0.36 °C to 0.47°C, or from about a third of a degree per doubling to about half a degree per doubling. I’ve swapped out the graphics in Figure 7 for the correct values, and fixed the references in the text.

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Here on our dry California forested hillside, the State has officially declared our county a drought area. I went out yesterday to take a look at the two water tanks that together supply both our house and the rental house on our property. Instead of containing 5,000 gallons or so between the two tanks as usual, they had about 1,500 gallons … as you might imagine, I said bad words. Possibilities regarding our two-well water system:

• Float switches in the tanks are bad.
• One or both of the submersible pumps are bad.
• One or both wells silting in.
• One or both wells w/plugged screens on the submersibles.
• The wells need plunging or acid-washing or ??.
• Leakage in the distribution system.
• It’s just the !@#$%^ drought.

Gotta love owning land, you’ll never get bored. For those aware of my checkered past, it’ll be no surprise that I used to drill water wells and install and service pumps for money, but I’m retired, so the guy from the company who drilled our well is coming out on Friday to take a look.

Best to all, stay well, hug your family, glory in the day, because as the song says, “You don’t miss your water ’til your well runs dry” …

w.