Work the following problems based on the graphic below depicting the earth\'s bu

Question

Work the following problems based on the graphic below depicting the earth's budget. Calculate the average earth planetary (shortwave) albedo (whole earth including atmosphere and clouds - this is called top of atmosphere albedo). Calculate the average earth surface-only (shortwave) albedo. Explain where the number 390 Wm (in outgoing surface radiation) comes from? Look at the not gain/loss at the earth surface. Rebalance the energy budget for the earth assuming a 0.1 increase in the average surface albedo of the planet. Assume that the contribution to thermals and evaporate-transpiration do not change. Suggestion: recreate the graphic above with new numbers. Discuss your results.

Explanation / Answer

3)

Basically all the energy that the Earth–atmosphere system receives comes from the Sun. This energy is known as the solar constant. On the basis of satellite observations, its value is about 1336 watts per square meter (W/m2). The area of the spherical Earth is four times that of its cross section facing the parallel solar beam and so the top of the Earth's atmosphere obtains an average of about 342 W/m2. About 77 W/m2 is reflected (by clouds, aerosol and atmosphere) back to space and is known as the global albedo. Around 67 W/m2 is absorbed by the atmosphere and so 198 W/m2 is reached at the Earth’s surface. Here about 30 W/m2 is reflected by the Earth’s surface and so only 168 W/m2 absorbed at the surface. Around 67 W/m2 is absorbed by the atmosphere and the greenhouse gases in the atmosphere radiate 324 W/m2. Out of the 168 W/m2 and 324 W/m2 reached the Earth’s atmosphere, 24 W/m2goes to the atmosphere as specific heat and 78 W/m2 moves to the atmosphere as Latent heat. So around 390 W/m2 (324+168-(78+24))radiates as terrestrial radiation (Outgoing radiation).

4)

If there is 0.1 increase in surface albedo, surface albedo changes from 30 to 30.03 (30+(30*0.1/100)).

Albedo= 30.03

So (342-(77+67+30.03))=167.97 W/m2absorbed by the Earth’s surface.

No changes in thermals (24 W/m2) and Evapo-transpiration (78 W/m2).

Back radiation from the atmosphere to the Earth’s surface= 324 W/m2

So surface re-radiation = 324+167.97-(24+78) =389.97 W/m2

Out of this 40 W/m2 goes to space through atmospheric window.

So 389.97-40=349.97 absorbed by the atmosphere.

Total radiation absorbed by the atmosphere =67+349.97+24+78=518.97 W/m2

Out of this 324 W/m2 is reradiated back to the surface.

So Radiation emitted by atmosphere=518.97 W/m2-324 W/m2= 194.97 W/m2

Outgoing Long Wave Radiation = 194.97 W/m2+40 W/m2= 234.97 W/m2

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