Its weird that someone would say that earth is 33° “warmer than it should be”, especially when they already reduced the amount of heat by 30% before the calculation started. My approach is that everything is exactly what it should be, and if someone says that there is heat coming from an ice-cold atmosphere, my first thought is that someone miscalculated. And that someone is less than normally talented.
Gravity stumbled in at the end where it seems like it acts like a loop of thermal energy radiated balanced by gravity pulling mass to the surface. Its a reasonable claim I think, heat expands mass and lift the atmosphere. Displacing mass is work, and work needs input of energy. Earth only radiate 240W/m^2 to space but surface emission is 390W, a heat-gravity loop at the surface could be an explanation. Since the atmosphere is limited to mostly longer waves of radiation it gets it´s energy from the surface, the heat source. The surface intensity is entering the equation as a potential of approximately-385W/m^2 equal to 288K. Since the surface subtract 385W in the equation which is transferred to the atmosphere, gravity is a conservative force keeping mass and heat balanced.
All points of interest above the surface now have a clear independent relationship which needs only one number, in line with theory. I view gravity as a balanced force acting with a power equal to surface emission of thermal energy.
The blackbody hemispheric intensity gives another relationship between the effective temperature and the temperature at the tropopause, than the spherical shell where absorbed and emitted intensity at the surface is TSI/(4/3)^2 and 1/2*TSI(4/3)^2. Both methods give close results. The fraction 4/3 is from the volume of a sphere. Used as non-participating matter, it is an ideal case like the surface of a blackbody. It is a good fit.
The earth core is said to have a temperature of about 6000 kelvin, I assume that it has the same temperature as the surface of the sun.
If we use the same approach as for the surface and atmosphere, the internal layers decrease by 3/4 for each surface and another 3/4 for the volume above that surface. If the core is 5780 Kelvin and there is 4 pairs of surfaces and volumes, the surface receives 0.0000000567*5780⁴/4^8 W/m² from the core, and 0,0000000567*255⁴*4W/m² from the sun. I doubt cold air is the heat source if the balance is so accurate between the core and the sun.
Temperature is the signal, it is the only force/energy we observe in the universe, and it is independent of space and mass. My conclusion is that the temperature is the first dimension. The one dimensional signal then expands in space through three dimensions, which is called space. The only difference between the signal and space three dimensions is time passed to define the expansion. This turns the common definition of reality on its head, we instead have one dimension of energy that expands in three dimensions of time. Suddenly the expansion of the universe makes sense and its nature becomes logical in relation to observation and energy.
If we use the units for stress/pressure/thermal resistance and treat gravity as a radiated force acting to balance thermal radiation, gravity have the function of balancing the inflation of heat into a steady state conserving mass. With units for stress/pressure/thermal resistance in N/m^2 and inverse square law, we can see that the power is equal for emission of thermal radiation and emission of gravity.
There is no greenhouse effect, there is only temperature.
If we use the relationship:
There is another solution:
For emitted radiation from the surface, we need to balance it to the square, which is the source intensity: . The incoming energy from the sun is balanced to the internal energy , and from the known mean addition of only 90mW from internal generation we can assume near perfect equilibrium of the solid sphere earth. That means that a nonparticipating spherical shell must contain a minimum of twice that amount, to balance incoming and outgoing radiation, and a body in equilibrium will behave in a similar way.
Now go and light a fire, combust fuel, use electricity from nuclear power and coal, anything that make energy flow outside our metabolism. That is what we are here for and that´s what we are good at. That is why earth looks like a bursting star-egg on the dark side, where it would be impossible to have light without humans putting it there.