Saturday, October 1, 2011

That Damn Cartoon and the Third Viscount of Puzzles

This is silly, but that cartoon, the K&T energy budget, is still generating confusion and it is the old version. The reason is still the big ass arrows showing 390 upwelling radiation and 324 downwelling radiation. So here's the deal as I see it.

If the Earth was a rock in space, a blackbody object, at 288 degree K, it would radiate heat to space at a rate of 390 Wm-2. At the Top of the Atmosphere TOA, the Earth only radiates 235 Wm-2. 235 Wm-2 is what a blackbody would radiate if it were at 255 degrees K. So because of the atmosphere the Earth is 33 degrees K or C warmer than it would be otherwise, that is the greenhouse effect.

But the Earth is not a rock floating in space, the Earth is a planet covered with water that has an atmosphere and it happens to have a big hotter blackbody, the Sun, shining 342 Wm-2 on the TOA. So the K&T guys drew this cartoon to show basically what is going on, but for a cartoon, this one is pretty confusing. It is confusing mainly because every thing is averaged. For its intended purpose, that is just fine, but it is being used for not its intended purpose.

So how to make sense of the cartoon for some other purpose? Well, you have to change things around. If we did a day cartoon, then numbers for the Sun would be doubled, latent and thermals would be doubled. All the IR numbers would be the same, they happen day and night so their average is just fine, it is just the Sun that gets turned off and on. All the ratios would stay the same for the day side (left) and the night side(right).

So on this copy I have the day values with one, the IR absorbed by the clouds as 54 with a question mark. The 40 straight from the surface to space, I could double if I just wanted to do a day balance, but the 54? may not be 54 Wm-2. Why? Because that number would depend upon the daytime average temperature, which I don't have.

Other than the question mark, we have 336 plus 134 or 470Wm-2 of absorbed sunlight and 204Wm-2 transferred from the surface to the atmosphere. 407-204=203Wm-2 may be locked into the oceans for some time or radiated to the clouds or space. Whatever happens, you can't tell from this cartoon.

If you go into night mode, then we have 390Wm-2 leaving the surface, 324 coming back which means a net of 66Wm-2 of which 40 passes through the atmosphere and 66-40=26Wm-2 absorbed by the atmosphere. The only thing is, the atmosphere was warmed during the day, so that 26 is likely less at night since the sun is turned off. So, since we don't know the what the actual number is, only that it changes, we can't really do a night energy balance. It should be clear, that since at night the surface temperature decreases locally, that the sky is not warming the surface, just slowing down the rate of cooling. During the day, the sky absorbs sunlight and reflect some, so it is slowing down the rate of warming. So what is actually happening in the sky, other than averages is not known, looking at this cartoon.

What the cartoon does show is the average of everything that is happening, not that the sky is warming the Earth or cooling the Earth, just that the energy flows balance at this particular temperature and solar radiation. After changing the IR absorbed by the sky to a net, you can see the rough balance of what is warming the sky and the rate of heat loss at night from the surface depends on that energy, or effective temperature of the sky. The same thing happens during the day, the effective temperature of the sky effects the heat flows from the surface. All of the heat flow, not just the outgoing radiation.

Energy is fungible, meaning it can change from conductive, convective, which has latent and sensible components and radiant. So at night, that 390 up can be split between any of the heat transfer modes, but on average, the total outgoing flux will be 390 on average. The same would be true for the 324 shown coming down.

The 324 coming down, doesn't warm at night very often. It can. There can be times when a warm air front moves in at night, but heat flows from warm to cold and typically the air temperature near the surface is cooler than the surface.

If you compare all the numbers at the TOA, the energy coming in equals the energy going out. This may not be in balance at any given moment in time, but on average it is and at the TOA it adjusts quickly to try and stay in balance. At the surface, the energy in on average will equal the energy out, but the time of imbalance can be much longer. In the middle of the atmosphere, if the surface and the TOA are in balance, it will try to become in balance. Everything wants to be in balance, but it will never happen.

So what else can the cartoon tell us? Well, the average numbers for the types and quantities of heat flow gives us a rough idea what the impact of a change to one of the flows might have, or how sensitive the temperature may be to a change in heat flux. At the surface we can use the averages of solar absorbed, 168 plus thermals, 24 plus latent 78 plus radiant, 26 calculated as the net, and 40 lost to space for a total of 168 in and 24+78+26+40=168 out. If the 26 changes by 3.7, then the total radiative impact would be (26+3.7)/(168+3.7)=0.173 or 17.3% if everything else remained the same, versus 26/168=0.154 or 15.4%. The 3.7Wm-2 change would produce a 17.3-15.4=1.9% change in the energy balance or a 0.019*33K=0.63K change in surface temperature. If the 26 increased as in this calculation, that would result in a decrease in surface temperature, a decrease would be an increase in surface temperature. The other fluxes and/or temperature would change some, trying to regain balance. Looking at the atmosphere, 67 solar plus 24 thermal plus 78 latent plus 26 radiant equals 195Wm-2 total. If we change the radiant flux by 3.7, then (26+3.7)/(195+3.7)= 0.15 or 15% versus 26/195=0.133 or 13.3 percent. The difference, 15%-13.3%=1.7% or 0.017*33=0.56K change in temperature, if every thing else remained the same, which probably won't happen.

Since I used 3.7, which happens to be the expected change in radiative forcing due to a doubling of CO2, the the surface sensitivity is about 0.63 and the atmosphere sensitivity is about 0.56 degrees K per doubling or the no feedback climate sensitivity based on the K&T energy balance cartoon. Since some of the other things are likely to change besides temperature, this should be a minimum climate sensitivity, no guarantees though.

Anyway, I think this is what Christopher Monckton of Brenchley was attempting to use as a proof of lower climate sensitivity.

If this happens to be a reasonable estimate of minimum sensitivity, then it may be possible to get an estimate of something close to a reasonable maximum sensitivity by doubling or tripling the no feedback to approximate radiative water vapor feedback. Water vapor can produce negative feedbacks with cloud cover change, so a doubling would be a reasonable estimate for the surface, implying a 1.26 sensitivity. For the atmosphere, it would be more likely that a tripling would be possible as the negative potential feedback clouds would have on the surface would have some positive feedback on the atmosphere which would receive the increased latent heat and absorbed solar radiation of the clouds, yielding a 1.62 approximate sensitivity. Since one impacts the other, the transient climate sensitivity may lie in the range 1.26 to 1.62 K. This happens to be close to estimates, so there may be some validity, I wouldn't count on the accuracy too much though.

Since a no feedback climate sensitivity does not exist, there will be feedbacks, this nearly a pointless exercise, but if the Third Viscount of Brenchley is posing a puzzle, this may be part of the answer.

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