Umbral, Penumbral and Ante-umbral Warming of the the Upper Atmosphere

I constantly get sidetracked with minutia and forget to explain some of the simpler but interesting parts of atmospheric physics I am picking up along the way.  Umbra, Penumbra and Ante-umbra are parts of a shadow.  Umbra is the darkest part, because of the total height of our atmosphere, there are few hours were it is absolutely dark at any point in our upper atmosphere.  That is because sunlight is passing on its way through and because of the density gradient in the atmosphere, lens effect tends to bend the light.  At dawn and sunset, the path length through the atmosphere is the longest, meaning more solar photons can be absorbed by atmospheric gases. 

If you are not a fan of umbra, call it the sunset to dusk lag of dawn to sunrise lag.  In either case until the sun is 18 degrees below the horizon, you don't have dark dark.  The higher you are above sea level the less dark dark you experience.

If you consider that the top of the atmosphere is the Turbopause at an altitude of ~100 kilometers, 100 kilometers versus a radius of 6371 kilometers is quite small.  The area difference is only 3.1 percent.  Due to the path length though, the absorption efficiency would be some what greater for the shorter wavelengths of Sun light.

With an average solar irradiance or 1361 Wm-2, 3.1 percent absorption would be 42 Wm-2 likely not included in the energy budgets with some more possible.

So the upper atmosphere may absorb more energy than included in the basic Earth Energy Budget, no big deal right because Eout has to equal Ein and doing the normal math, it still is 341Wm-2 average, right?  Not really.  The timing is different.  During penumbral absorption the upper atmosphere would basically be preheating which would reduce surface heat loss and during ante-umbral absorption, upper atmosphere heating would be reducing the rate of heat loss.  I use reducing because this energy likely never directly impacts the surface, instead it helps maintain the upper atmosphere temperature inversions. 

In the Antarctic which doesn't have liquid sea water all the way to the pole, in winter the only energy it gets is transferred by atmospheric circulation which the polar vortex can block and the mesosphere/stratosphere temperature inversions which gain most of their energy from O2 and Ozone solar absorption.  This absorption appears to set the atmospheric sink temperature on Earth at 184 K degrees.  Since Vensus also has that magic temperature,  upper atmosphere absorption should also be there.

So far, with this ~42 Wm-2 and the ~20 Wm-2 K&T missed in the Earth Energy Budgets, we are looking a a large portion of the Greenhouse Effect that is simple math and model errors.  Kind of funny huh?