Average and the Sub-Surface

The chart above is just distributions of incident energy on a sphere based on cosines.  The blue curve is the peak incident energy by degree of latitude, the orange is the peak incident energy allowing for meridional curvature and the yellow is considered the average incident energy, which would be roughly the average sub-surface energy.  If the sphere is made of solid material, the average sub-surface energy would be about 20% of the peak energy available.

If the sub-surface is fluid, or the rate of energy transfer in the sub-surface is greater than the loss of energy from the sub-surface, the sub-surface average would tend to spread into a more uniform distribution.  I used the SQRT(COS(pi())) to simulate a near optimum spread.  The actual efficiency of the spread would depend on the fluid properties and the rate of heat loss from the surface above the sub-surface.

The curves above just consider the power cycle.  If the sphere rotates at the perfect rate, the peak curves would be equivalent to a half rectified sine wave with 50% on and 50% off.  Then using the COS^2, the input "signal" RMS value would be COS^2/2.  If we consider the residual "average" we now have a range which depends on the mixing efficiency of the sub-surface layer.

There is some confusion over what is surface and sub-surface.  The layer with the most efficient mixing should define the sub-surface layer which would be the most effective ideal blackbody source.

On Earth, that sub-surface would be the oceans.  If Earth were a pure water world with near ideal sub-surface mixing efficiency, the average energy of the sub-surface would be approximately 23% of the input energy.  1361*0.23=313 Wm-2.  That average is slightly below the freezing point of fresh water and slightly above the freezing point of salt water with a salinity of ~35g/kg.  Since salt is reject when ice is formed, the minimum energy required for liquid brine should be considered which is -32 F, -17.7 C or 255.45 K degrees.  Since that mixing efficiency is less than ideal, the average subsurface energy is slightly higher, since roughly 8% of the polar regions are land mass not ocean.

Earth is blessed to have a fairly well mixed salt water ocean covering about 70% of the planet.  So blessed in fact that the number of coincidental factors that need to be considered are close to miraculous.  Earth hit a universal sweet spot and man caught Earth at just the right time.

The point of this post though is to highlight the importance of considering the sub-surface mixing efficiency.  If the rotation speed changes, the impact on the sub-surface would be huge.  If the location of the land masses reduce the mixing efficiency of the deep ocean currents, the impact can be huge.

Until  warmists begin to consider the real greenhouse, the global oceans, there will not be any progress made trying to understand the miraculous world we inhabit.

Update:  In case anyone would like to play with the sub-surface impact, here are a few numbers:

140.56 mkm^2 is the Northern hemisphere ocean area from the equator to 65N, average solar would be close to 1337Wm-2 for for the NH half year.  196.4 mkm^2 is the Southern hemisphere oceans from the equator to 65S with an average solar insolation of about 1385 Wm-2 for that half year.  There is more "under the ice" area in the NH but the THC mixing is predominately driven by the southern ACC which will require a little thought.  From the looks of it though, the sub-surface average is one of the few solar forcing estimates that actually makes sense.  With the total ocean area of 337 million km^2 of a total global surface of 510 mkm^2, the 66% typically open ocean area at roughly 311 Wm-2 would produce a "shell" ERL energy of 202 Wm-2.  This would seem to make the radiant "blackbody" work, but there is still a pretty large range of uncertainty.