Dave, the sensible and latent heat, as you point out, are not lost to the system. They are merely transferred from the surface to the troposphere and stratosphere.

jae, it’s coincidence … isn’t life grand?\

w.

Excellent. I’d noticed also that Dr. Held’s equations were essentially the one-shell case and that sort of is what I was getting at in #16. But I hadn’t thought about trying to do the calculations you did. Still, I need to go look at your spreadsheet as one thing bothers me. Sensible and Latent heat don’t remain total losses to the system. Latent heat is released in the atmosphere and then this is kinetic energy of the gasses in the atmosphere and will result in long-wave IR part of which will escape and part return to the surface.

Admittedly a lot of this additional IR is present prior to a perturbation, but it will itself be perturbed by the surface changes.

If an impossible value is entered, the model will go off the rails, and I know of no way to get it back on except to close it and re-open it.

The easiest approach is to have a single Boolean somewhere, called “BreakCircular”, for example, which is normally set to FALSE.
Ensure that every looped calculation includes, somewhere within the loop, a condition of the form ” if( BreakCircular , 0 , …) “, where the “…” represents whatever you want to calculate in that cell.
In this worksheet, you need them in cells G32, H24, and I16.
Then, when the spreadsheet blows up on you, you just need to set BreakCircular to TRUE, and the spreadsheet will clear. You can then track down the original source of the problem, fix it, and reset BreakCircular to FALSE.

Now, the first thing that you have to understand is that you cannot successfully model the earth with a single atmospheric greenhouse “shell”. This is because a single greenhouse shell would not warm the earth enough to match the known conditions. A single perfect, 100% effective greenhouse shell can do no more than double the incoming radiation. Let us call the incoming radiation from the sun “S” (in watts/m2). At equilibrium, a perfect greenhouse shell must radiate S watts outward, and S watts inward. At equilibrium, then, the planet receives S watts/m2 from the sun, and S watts/m2 from the shell, for a total planetary surface radiation temperature of 2 * S.

The energy from the sun (after albedo) is about 235 W/m2 (all numbers here are somewhat uncertain, I’ll give them as exact figures but please understand that they are approximations). With a single perfect shell, this would mean the equilibrium temperature of the earth would be 470 W/m2. The problem is that the radiation temperature of the earth is 390 W/m2, which means that there are losses amounting to 80 W/m2.

But we know that the losses from sensible heat (24 W/m2) and latent heat (78 W/m2) total 102 W/m2, more than would be available if there were only a single shell. Therefore, the single shell model is energetically impossible. Accordingly, I built a two shell model, as it is the simplest model which provides enough energy to accommodate the known losses. This means that the stratosphere and the troposphere must function as independent absorber/emitters of IR energy.

I have included in the model the very reasonable assumption by Dr. Held that much of the change in energy is taken up by changes in sensible and latent heat losses, rather than in temperature change.

There are some interesting outcomes from the fact that a single-shell model won’t work for the earth. One is that equations such as those given by Dr. Held are not applicable, because they are for a single shell model.

Another is that with two shells, there are some curious interactions and outcomes. One is that it makes a large difference exactly where the energy is absorbed. If the additional 3.2 W/m2 is split between the troposphere and the TOA (as in Collins), I get numbers which are close to those reported by Collins et al. However, there is an important difference. As I had speculated above, the surface does not warm when more energy is absorbed in the troposphere, it cools. However, the changes in temperature are quite small. According to radiative balance, given the absorption of an additional 0.6 W/m2 at the top of the atmosphere and an additional absorption of 2.8 W/m2 in the troposphere, my figures and Collins figures look like this:

SHORTWAVE________Collins___Mine
TOA__________________0.6____0.6
Troposphere__________2.8____2.8
TOTAL________________3.4____3.4
Surface_____________-2.8___-2.8

So far, so good. The surface change is lower than the atmospheric change because of albedo. However, the problem arises because they have increased the sensible and latent heat by too much. The increased absorption in the atmosphere yields increased downwelling long wave, about +0.7 W/m2. This partially offsets the loss of solar radiation. This means that the total change in incoming radiation at the surface (shortwave plus longwave) is about -2.1 W/m2.

But in their results, the change in sensible + latent heat losses is said to be -2.2 W/m2, which is more than the change in total downwelling radiation. This is why they claim that the surface is warming … but it makes no sense physically. Why would the change in losses be greater than ‘ˆ†W, the change in incoming radiation?

Using a physically plausible coupling between the drop in downwelling radiation at the surface and the drop in latent + sensible heat loss, the surface must cool rather than warm. They claim a warming of 0.2°C results from the increased IR absorption in the atmosphere. My radiation balance model shows a cooling of 0.2°C, rather than a warming.

Next, there’s another oddity about a two-shell model. A change of IR absorption in the troposphere alone does not alter the TOA downwelling radiation one bit. TOA radiation only changes when the absorption of the stratospheric layer changes. Thus, the relative change in stratospheric and tropospheric absorption is a major factor in the “climate sensitivity”, which is defined as the ratio of a change in TOA forcing versus a change in surface temperature. This brings up the question of how the effect of a doubling of CO2 (which the IPCC says causes a 3.7 W/m2 change in TOA forcing) is calculated. I have not been able to find accurate information on this question, and would appreciate any pointers.

Finally, according to the model, the climate sensitivity is about 0.2°C per W/m2, in good agreement with the figures from Idso’s “natural experiments” and Lindzen’s estimates, but far lower than the IPCC figures.

I have posted the model for download here, and I invite people to experiment with it and report their findings.

w.

I need a check of my thinking here on the attempts to quantify the surface temperature changes from 3.4 W/m^2 of NIR radiation being completely absorbed by water vapor in the troposphere versus allowing this amount radiation to pass through the troposphere without absorption. The effect of the foregoing is to be compared to that of a CO2 doubling radiative forcing of 3.8 W/m^2.

Can we, at least to a first approximation, compare directly the surface temperature effects of the 3.8 W/m^2 and the 3.4 W/m^2 passing unabsorbed through the troposphere? (I think that the answer to this depends on where in the troposphere most of the extra NIR radiation is absorbed and to that I could not find a direct answer) If we can, than would the simple calculation of surface temperature change be made by assuming a climate sensitivity with net positive feedback of approximately 0.75 degrees K per W/m^2 yield, for the doubling of CO2, a temperature change of 2.85 degrees K and for the unabsorbed NIR radiation a temperature change of 2.45 degrees K. If these calculations are approximately correct, we can then compare them to the case where the 3.4 W/m^2 of NIR is absorbed in the troposphere by water vapor.

Firstly, since the net calculated effect from climate models is that the difference in the 3.4 W/m^2 of NIR radiation being absorbed and being unabsorbed is a surface temperature change of approximately 0.12 degree K, we would have to conclude that the portion of the energy from that absorption that passes through to the surface must be approximately 95% of that of the portion that makes in through from the unabsorbed case.

Secondly, if my thinking is correct to this point, then all the convincing I would need for the accounting of this small difference in temperature change between the absorbed and unabsorbed cases would be to show me how this energy absorbed in the troposphere gets to the surface — in at least semi-quantitative terms.

Isaac Held implies that the transport process is entirely non-radiative (as it would have to be to account for almost all the energy being directed towards the surface), which would imply that the absorbed NIR energy must first heat the troposphere and then be transported away to the surface by convection, conduction or I assume by the hydrological cycle. Held’s equilibrium explanation of this process is not intuitively clear to me and I would be the first to admit that that may be from my lack of correctly understanding it.