The Mysterious Case of the Missing Heat

In the discussion or diatribe on the Kiehl and Trenberth missing heat it appears a good portion of the heat was found. Not all the heat though, that's bugging me.

Nature is pretty simple in a complex way. Yes, that sounds like a contradiction, but it is our understanding that is insufficient, we over think simple and under think complex.

Which is where I am now. The inverse square law is pretty common in nature. That's why the triangles on the drawing are shaped the way they are, that's why it is a part of so many equations. The Stefan-Boltzmann equation is an example of the inverse square law, F=simga(T)^4 is F=simga(T^2)^2 The full derivative of F=simga(T)^4 would be dF/dT= 4*A*sigma(T)^3 + C(T)^2 +CT + D. The full equation for determining Specific Enthalpy is the exact form with different coefficients. They are related or relative in nature. That is Relativistic Heat Conduction, simple, but complex.

In normal day to day calculations, the dominate order of the equation can be used and the remainder assigned a constant and coefficients to adjust the numbers.

In a lot of ways the full equation describes four dimensions, zeroth, 1st, 2nd and 3rd.

Nature can throw a curve ball where the second order terms are in sync or 180 out and make the simplified assumption invalid. That appears to be the case with lots of missing things now that we have better ways of measuring our world and our universe. What was once adequate may no longer be. Finding classical solutions and comparing them to observed data is science, not assuming anything is ever 100% correct.

That is where I am. The coefficients I resolved for one condition are not the same in all others. Time to find the second order effects, not throw away the first order results, refine them.

How you look at the problem makes all the difference. Would 2(F/?)^2=(2*(simga)^1/2(T^2))^2, unlikely, but always something that should be kept in mind. Things can be over simplified. For that form to work, F would need a new coefficient.

These are idle ramblings of course, the full equation is the proper place to start.