Saturday, April 9, 2011

The Energy Budget Puzzle

The Nasa Earth's Energy Budget just lists percentages. Solar incoming varies a little and many of the listed elements vary a bit. Below I have listed the values of the arrows with the Watts per meter squared values. There is a little bit of a rounding error, no big deal. If you like, take a guess at the values of each in the year 2100 if the average temperature of the Earth warms by 3 degrees C.
Now 2011
Incoming Solar Watt/M^ 342
Reflected by Atm. 6.00% 20.52
Reflected by Clouds 20.00% 68.4
Reflected by surface 4.00% 13.68

absorbed by atm 16.00% 54.72
absorbed by clouds 3.00% 10.26
Radiation Absorbed by atm 15.00% 51.3
Absorbed via conduction 7.00% 23.94
absorbed via latent heat 23.00% 78.66

Radiated to space Clouds&atm 64.00% 218.88
Radiated Direct to space 6.00% 20.52
Radiated from Surface 21.00% 71.82
Absorbed by land/ocean 51.00% 174.42

As a note remember, if the Earth's temperature warms by 3 C, by the Stefan-Boltzmann law, the energy leaving Earth would increase by the fourth power of the temperature increase So, E(2100) would be 5.67e-8*[(291)^4-(288)^4] equals 16.5 Watt/M^2 more, or will it?

I had to correct E(2100) above. That should be the only correction.

This links to what is hopefully my final answer to the puzzle

To witness a remarkable face plant, use this link to my error filled first answer.

Update: 10:37 10 Apr, Should you comment, try to play nice and not insult anyone other than me. I don't care, but some people are sensitive.


Fred Moolten said...

Dallas - I calculate the increase in emitted energy to be about 16 W/m^2, based on the SB constant of 5.67 x 10^-8.


Fred Moolten said...

Regarding my previous comment, the projected 3 C increase was for the surface, and so the calculated 16 W/m^2 increase in emissions is from the surface. The change in the amount of radiation escaping to space would be a bit less, because the surface would be warming from about 288 K to 291 K, while the average escape temperature would be changing from about 252 K to 255 K, and so the SB calculations would reflect that difference.


Dallas said...

Interesting Fred. I will give my answer probably in the morning.

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