Effective Radiation Level (ERL) Temperature

Guest Post by Willis Eschenbach

Lord Monckton has initiated an interesting discussion of the effective radiation level. Such discussions are of value to me because they strike off ideas of things to investigate … so again I go wandering through the data.

Let me define a couple terms I’ll use. “Radiation temperature” is the temperature of a blackbody radiating a given flux of energy. The “effective radiation level” (ERL) of a given area of the earth’s surface is the level in the overlying atmosphere which has the physical temperature corresponding to the radiation temperature of the outgoing longwave radiation of that area.

Now, because the earth is in approximate thermal steady-state, on average the earth radiates the amount of energy that it receives. As an annual average this is about 240 W/m2. This 240 W/m2 corresponds to an effective radiation level (ERL) blackbody temperature of -18.7°C. So on average, the effective radiation level is the altitude where the air temperature is about nineteen below zero Celsius.

However, as with most thing regarding the climate, this average conceals a very complex reality, as shown in Figure 1.

Figure 1. ERL temperature as calculated by the Stefan-Boltzmann equation.

Note that this effective radiation level (ERL) is not a real physical level in the atmosphere. At any given location, the emitted radiation is a mix of some radiation from the surface plus some more radiation from a variety of levels in the atmosphere. The ERL reflects the average of all of that different radiation. As an average, the ERL is a calculated theoretical construct, rather than being an actual level from which the radiation is physically emitted. It is an “effective” layer, not a real layer.

Now, the Planck parameter is how much the earth’s outgoing radiation increases for a 1°C change in temperature. Previously, I had calculated the Planck parameter using the surface temperature, because that is what is actually of interest. However, this was not correct. What I calculated was a value after feedbacks. But the Planck parameter is a pre-feedback phenomenon.

If I understand him, Lord Monckton says that the proper temperature to use in calculating the Planck parameter is the ERL temperature. And since we’re looking for pre-feedback values, I agree. Now, this is directly calculable from the CERES data. Remember that the ERL is defined as an imaginary layer which calculated using the Stefan-Boltzmann equation. So by definition, the Planck parameter is the derivative of that Stefan-Boltzmann equation with respect to temperature.

This derivative works out to be equal to four times the Stefan-Boltzmann constant time the temperature cubed. Figure 2 shows that value using the temperature of the ERL as the input:

Figure 2. Planck parameter, calculated as the derivative of the Stefan-Boltzmann equation. 

Let me note here that up to this point I am agreeing with Lord Monckton, as this is a part of his calculation of what he calls the “reference sensitivity parameter λ0” (which is minus one divided by the Planck parameter). He finds a value of 0.267 °C / W m-2 up to this point. as discussed in Lord Monckton’s earlier post, which is the same as the Planck parameter of -3.75 W/m2 per °C shown in Figure 3.

Now again if I understand both Lord Monckton and the IPCC, for different reasons they both say that the value derived above is NOT the proper value. In both cases they say the raw value is modified by some kind of atmospheric or other process, and that the resulting value is on the order of -3.2 W m-2 / °C . (In passing, let me state I’m not sure exactly what number Lord Monckton endorses as the correct number or why, as he is not finished with his exposition.)

The problem I have with that physically-based explanation is that the ERL is not a real layer. It is a theoretical altitude that is calculated from a single value, the amount of outgoing longwave radiation. So how could that be altered by physical processes? It’s not like a layer of clouds, that can be moved up or down by atmospheric processes. It is a theoretical calculated value derived  from observations of outgoing longwave radiation … I can’t see how that would be affected by physical processes.

It seems to me that the derivative of a theoretically calculated value like the ERL temperature can only be the actual mathematical derivative itself, unaffected by any other real-world considerations.

What am I missing here?

w.

My Request: In the unlikely circumstance that you disagree with me or someone else, please quote the exact words you disagree with. Only in that way can we all be clear as to exactly what you object to.

A Bonus Graphic: The CERES data is an amazing dataset. It lets us do things like calculate the nominal altitude of the effective radiation layer all over the planet. I did this by assuming that the lapse rate is a uniform 6.5°C of cooling for every additional kilometre of altitude. This assumption of global uniformity is not true, because the lapse rate varies both by season and by location. Calculated by 10° latitude bands, the lapse rate varies from about three to nine °C cooling per kilometre from pole to pole. However, using 6.5°C / km is good for visualization. To establish the altitude of the ERL, I divided the difference between the surface temperature and the ERL temperature by 6.5 degrees C per km. To that I added the elevation of the underlying surface, which is available as a 1°x1° gridcell digital dataset in the “marelac” package in the R computer language. Figure 3 shows the resulting nominal ERL altitude:

Figure 3. Nominal altitude of the effective radiation level.

The ERL is at its lowest nominal altitude around the South Pole, and is nearly as low at the North Pole, because that’s where the world is coldest. The ERL altitude is highest in the tropics and in temperate mountains.

Please keep in mind that that Figure 3 is a map of the average NOMINAL height of the ERL …

A PERSONAL PS—The gorgeous ex-fiancee and I are back home from salmon fishing, and subsequent salmon feasts with friends along the way, and finally, our daughter’s nuptials. The wedding was a great success. Just family from both sides in the groom’s parents’ lovely backyard, under the pines by Lake Tahoe. The groom was dashingly handsome, our daughter looked radiant in her dress and veil, my beloved older brother officiated, and I wore a tux for the first time in my life.

The wedding feast was lovingly cooked by the bride and groom assisted by various family members, to the accompaniment of much laughter. The bride cooked her famous “Death By Chocolate” cake. She learned to cook it at 13 when we lived in Fiji, and soon she was selling it by the slice at the local coffee shop. So she baked it as the wedding cake, and she and her sister-in-law-to-be decorated it …

Made with so much love it made my eyes water, now that’s a true wedding cake for a joyous wedding. My thanks to all involved.

Funny story. As the parents of the bride, my gorgeous ex-fiancee and I were expected by custom to pay for the wedding, and I had no problem with that. But I didn’t want to be discussing costs and signing checks and trying to rein in a plunging runaway  financial chariot. So I called her and told her the plan I’d schemed up one late night. We would give her and her true love a check for X dollars to spend on the wedding … and whatever they didn’t spend, they could spend on the honeymoon. The number of dollars was not outrageous, but it was enough for a lovely wedding.

“No, dad, we couldn’t do that” was the immediate reply. “Give us half of that, it would be plenty!”

“Damn, girl …”, I said, “… you sure do drive a hard bargain!” So we wrote the check for half the amount, and we gave it to her.

Then I created and printed up and gave the graphic below to my gorgeous ex-fiancee …

… she laughed a warm laugh, the one full of summer sunshine and love for our daughter, stuck it on the refrigerator, and after that we didn’t have a single care in the world. Both the bride and groom have college degrees in Project Management, and they took over and put on a moving and wonderful event. And you can be sure, it was on time and under budget. Dear heavens, I have had immense and arguably undeserved good fortune in my life …

I’m happy to be back home now from our travels. I do love leaving out on another expedition … I do love traveling with my boon companion … and I do love coming back to my beloved forest in the hills where the silence goes on forever, and where some nights when the wind is right I can hear the Pacific ocean waves breaking on the coast six miles away.

Regards to all, and for each of you I wish friends, relations, inlaws and outlaws of only the most interesting  kind …

w.