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Tuesday, November 6, 2012

Closer Look at Stephens and Gang Budget

Edit to correct the spelling of Stephens

Since I torn into Trenberth and Keilh's Earth Energy Balance, It is only fair that I tear into the Stephens' and gang Earth Energy Balance.  Stephens though does include realistic margins of error, so it will not be as easy.

Here is the biggest test, what does the atmosphere absorb?  Like K&T, Stephens and gang lumps outgoing long wave and down welling long wave together requiring some thought.  398 minus 345 rounded for simplicity is 53 Wm-2, the net outgoing long wave radiation absorbed by the atmosphere.  Solar, Sensible and Latent with this 53 OLR absorbed total 240 Wm-2.  That is approximately the net solar absorbed, notice that 20 Wm-2 all-sky atmospheric window passes through the atmosphere.  The surface absorbs 165 Wm-2 directly from the sun.  If you consider that the atmosphere is a radiant layer, ~ 1/2 of the 240 would be returned to the surface as "active energy" which would equalize at some point in time with the total 240 felt at the surface.  The 240 plus 165 equals 405 less the 20 Wm-2 through the atmospheric window would be 385Wm-2.  This is well within the error range of the Stephens and gang's graphic.

Note that OLR absorbed is 22% of the total absorbed by the atmosphere.  Increased CO2 would increase that value by 3.7 Wm-2 to 56.7 Wm-2.  Then the total absorbed by the atmosphere would be 243.7 and the surface energy would eventually increase from 385 to 388.7 Wm-2 with +/- 17 Wm-2 margin of error for the whole shebang.  That additional 3.7 Wm-2 would increase latent by ~ 3 Wm-2 cooling the surface but adding to the atmospheric absorption.  That could cancel most of the CO2 impact or add up to 3 Wm-2 to the impact producing 391.7 Wm-2 of surface energy( using my 385) at some point in the future.  The high end would be 6.7Wm-2 increase which at an average surface energy of 385Wm-2 would be roughly 1.24 degrees increase in average surface temperature.  That is below the minimum 1.5 Estimated by the IPCC and very close to the range estimated by several "skeptics". More warming that than would require feedbacks that are not evident so far.  That warming would also require warming of the oceans surface which would require warming to some depth in the oceans which requires an undermined time to fully equalize if it in fact could ever equalize.   So the estimated range of warming due to a doubling of CO2 is almost nada to 1.24 C degrees.  Not exactly the alarming number tossed about by climate activists.

Is Stephens and gang's Budget THE Budget?  I have no idea.  It does though more accurately resemble what climate has done of the past 40% of a doubling after considering other factors.

UPDATE 2:  Since I found another misspelling I may as well add this.  When I put in the separation, it is to simplify understanding of what is going where.  Trying to include both the day and night modes will always result in something that looks like it violates the laws of thermodynamics.  The budget cartoon is just that, a cartoon trying to get as much information as possible on one fairly simple drawing.  Someone noticed that the All-sky downwelling longrange is greater than it should be.  That is why I used the net and separated the atmosphere.  At night, the actually altitude of the source of DWLR would be lower than in the day and the amount of surface energy emitted would be less.  I estimated that night Fmin would be about 380Wm-2 and that day Fmax would be about 414Wm-2.  So the 240 Wm-2 I use in the split would be a rough 24 hour average with somewhere in the ballpark of 33Wm-2 variation on an annual daily average.  Like a said before, there Stephens and gang budget is not perfect, but a lot better than all the past budgets I have seen.


  1. The back-radiation of 324 Watt/m^2 and thereby atmospheric absorption of 350 Watt/m^2 is the result of software using the two-stream heat flow formulation.
    That formulation gives the correct temperature distribution, but it gives spurious absorption.
    In the following link the one-stream heat flow formulation is used:

    The outgoing LW surface fluxis 68 Watt/m^2 of which 52 trough the window and 16 Watt/m^2 into the atmosphere.
    The surfaceflux has another contribution of 100 Watt/m^2 due to evaporation and thermals:
    total 168 Watt/m^2.
    From the incoming SW radiation, 72 Watt/m^2 are absorbed by the atmosphere. In total 240 OLR to outerspace.
    No back-radiation and atmospheric absorbtion an order of magnitude lower.

    1. There are quite a few ways of looking at the problem. None provide a great deal of precision. This is just looking at the latest compilation of data and uncertainty which will likely change in the not so distant future.