## Sunday, June 9, 2013

### Entropy Budget for Earth - Discussion of Nick Stokes Stab at it.

Since the typical climate blog fair lately really sucks, I was wandering around Nick Stokes' Moyhu blog when I came upon his stab at an Earth Entropy budget.  My static model approach doesn't try to pick out entropy or work since I think that is a couple of steps ahead of the current game.  The first hurdle is the Ground and Shell that Nick uses versus the black body cavity and shells that I use.  "Ground" or "surface" are too vague and subject to advection aka meridional and zonal heat flux which complicates modeling.

The red 40 in Nick's drawing is the problem.  I first started this blog because I discovered an 18 to 20 Wm-2 error in the K&T Earth Energy Budgets that produced the nearly double estimate of that "window" relative to that "Ground" surface.  If you are off by 18 to 20 Wm-2 because of poor choices of frames of reference, things will not get any better anytime soon.  When some of the top minds in the climate science game make such a mistake, getting them to admit it is rather difficult.

To show the problem instead of "Ground" I use the Black Body Cavity i.e. the global oceans which have a much more stable temperature.  The only problem with that frame of reference is that the oceans only cover ~70% of the "surface".    The big benefit though is that the reference has stayed within a degree or so for a very long time.

I added the Ocean BBC with shell on the side.  If the oceans covered 100% of the surface the shell would be 233K degrees based on half the energy of the source.  Since the oceans only cover 70% of the surface, the shell is appoximately 213.2 K with an approximately 20 Wm-2 "window" energy based on the Stephens et al. budget.  Since ~ 50 Wm-2 of the source energy is advected to produce a uniform shell, the actual "window" would more likely be 25 Wm-2 or half of the advected energy, which would be self absorbed during the advection.

Since the "shell" is simply a frame of reference, using the ocean 334.5 Energy and 70%, 234 Wm-2 could also be used producing the apparent ~236 Wm-2 average OLR value.  This simple approach does not include atmosphere SW absorption, but since the source 334.5 Wm-2 is a product of all radiant forcing over a large time scale, it is fairly easy to include a "surface" and atmospheric boundary layer to extend the budget.

With this modified Stephens et al. Budget cartoon, just adjust the 345.6 +/- 9 DWLR value to 334.5 +/- 9, where the +/- 9 is more likely plus and a good portion due to entropy produced by ocean and atmospheric circulation which has been estimated in the 4 Wm-2 range.

You can visit Nick's blog post here but I need to look at what impact the revision of the "window" his estimates, but this 288K "Ground" legacy error appears to be gumming up the works.  Until the impact of that 20Wm-2 error is recognized with something more than a note saying that a "minor adjustment" was made to the budget, not much is going to happen.