And yet, it is the basis for the global climate models, and the AGW hypothesis...perhaps that is why both have failed so miserably.
You have to go to the top of the atmosphere to find the beginning of the problem...trenberth's cartoon claims 341.3 wm2 incoming from the sun...the actual incoming radiation from the sun is more like 1370 wm2.... trenberth divides that number by 4 and pretends that by doing so, he has an average incoming solar radiation to the surface of the earth.....he does not take into account that the earth is curved and that during daylight hours, the solar energy reaching the surface gradually increases till just after noon and then decreases till dark....he does not take into account that the earth is a curved surface and that more energy reaches the equator and decreasing amounts reach the surface as you move towards the poles...he does not take clouds into account nor the difference between land, water, ice, prairie, forest, desert....etc.
His cartoon which bears almost no resemblance to the actual world is the basis for both the AGW hypothesis...and the global climate models...again, maybe that is why both have failed so miserably.
Actually he does take that into account. Think global average. You would reduce the sun's energy by exactly half simply because half the earth is in the dark. I have looked at the calculus which shows that if you use Lambert's cosine law of the diminishing energy toward the periphery of a sphere, the actual energy hitting the bright side of the earth is diminished by exactly a half again. The total global average is 1/4 of the energy at noon on the equator.
When you are calculating the total energy hitting the earth you don't need to take into account the difference between land, water, ice, etc. The landscape plays a role on how much short wave energy is reflected back to space. The cartoon has energy flow arrows illustrating that. Take a look at it again with those ideas in mind.
The 165W is certainly a guesstamate. But it could not be in error by more than 20%.