Knowing that you said that it depicts a flat Earth, despite the explanation of how the energy budget was arrived at, confirms my original conclusion. Now, as for back radiation, is it your contention that it is impossible for the upper atmosphere to reflect radiation back to the Earth?
Till you can acknowledge that it depicts a flat earth, there is no point in continuing. The men who made the budget both acknowledged that /4 was a mathematical way to have the incoming solar flux reach the entire surface of the earth simultaneously. The only way to illuminate the entire surface of a sphere is to either have two sources of illumination or you skin it and lay its surface out flat. I don't know why you refuse to acknowledge that fact when the men responsible for the budget confirmed my statment.
Just a question, requiring a yes or no answer, no condescension or lengthy explanation of unrelated issues necessary, and yes, I do understand the laws of thermodynamics on which you've based this assumption.
The second law of thermodynamics states:
Second Law of Thermodynamics: It is not possible for heat to flow from a colder body to a warmer body without any work having been done to accomplish this flow. Energy will not flow spontaneously from a low temperature object to a higher temperature object.
It expicitly states that energy will not flow from a cooler object (atmosphere) to a warmer object (surface of the earth) unless some work is done to accomplish the movement. Absorption and emission do not constitute work.
Here is the equation from the k-t energy budget that I provided.
Look to the right side of the equals sign. It is a corrupted derivative of the Stefan - Boltzman law which they used in an attempt to balance the incoming energy with the outgoing energy. As a side note, the reason that they used P/4 and laid the entire surface of the earth flat so that the entire surface of the earth could be irradiated simultaneously by the solar flux is that they used the Stefan -Boltzman (S-B) to balance the outgoing radiation with the incoming solar flux. The S-B law only deals with instantaneous solar fluxes so it became necessary to irradiate the entire surface of the earth at once in order to apply the S-B law.
This is the S-B law in its simplest form:
If the warmer object is radiating energy to a cooler background, the S-B law takes the form:
Now look back at the right side of the equation from the k-t energy budget. You can disregard the (1-f) because that is dealing with lost energy that isn't really part of the budget. Note that they apply the S-B law twice. The correct form of the equation that immediately preceeds this paragraph represents the S-B law which depicts energy flows in accordance with the second law of thermodynamics. That is, it represents energy flowing from a warm radiator to a cooler background.
P = the net radiated power.
e = the emissivity of the radiator (surface of the earth)
A= the radiating area
T = the temperature of the radiator
= the temperature of the background
= the Stefan - Boltzman constant (
)
The equation is describing the net radiated power as the difference between the temperature of the radiator (T) and the background (
).
Now note the equation from the k - t energy budget. The S-B law is used twice and in effect shows energy radiating from the warmer radiator to the cooler background and then changes the cooler background to a radiator and has it radiating to the warmer radiator which it has changed to the cooler background.
What they have done is taken the S-B law
and changed it to
. If you have ever taken algebra, you may recognize that they simply applied the distributive law to the equation. If you have ever taken phisics at the 2000 level or higher, you may know that you can't simply go about applying algaebraic properties to equations dealing with physics problems unless you first explicitly define the reason for applying the property.
In a math class, you simply need an answer so you may apply algaebraic properties as you like because there is no risk. In physics, however, you are not only seeking an answer, you are defining a physical process. For example, you can apply the distributive property to the SB equation and you will get the same answer for P as you would if you did not apply the property; BUT, you have altered a physical process and in doing so have violated the second law of thermodynamics and corrupted the S-B law in order to achieve that violation. No such definition for the reason the distributve property was ever, nor has ever been given. The reason is obvious to anyone who understands the objective of the energy budget. They needed backradiation and corrupting the S-B law would allow them to do it. The problem is that they violated the second law of thermodynamics.
Now, if you can show an equation that allows backradiation without corrupting the S-B law, I would be very interested in seeing it.
I just don't think they apply the way you think that they do, but then, there is no point in going into that until you give your clear and unequivocal answer.
Perhaps you hope they don't apply the way they actually do, or you wish that they don't apply the way you wish they did, but there is no wiggle room in the second law for backradiation. It says that it is NOT POSSIBLE for heat to flow from a cooler body to a warmer body and that heat WILL NOT flow spontaneously from a cooler object to a warmer object. In order to have backradiation, you must alter the statement of the second law of thermodynamics.
Is that unequivocal enough for you?