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Calculating Mean Solar Radiation Flux Absorbed Per Unit Area at Earth

-- | March 6, 2016

Question: The mean solar radiation flux absorbed per unit area of Earth’s surface is calculated as FS(1-A)/4, where FS is the solar constant and A is albedo. I can see how this would be valid for a sphere illuminated from all directions, but inasmuch as only half of the globe is illuminated at any given time, I would think that the correct calculation should be FS(1-A)/2. Am I missing something here? — David

Answer: The reason for the factor of 1/4 is due to the “mean” part of your definition. You are calculating the mean solar radiation flux absorbed per unit area on the Earth’s surface. The solar constant refers to the amount of solar energy received over the Earth’s disk facing the Sun. This means that you need to spread-out the solar radiation received on an area facing the Sun, or pi*R^2, over the entire surface area of the Earth, or 4*pi*R^2. The ratio of these two areas is 1/4, which is where the factor of 1/4 comes from in your equation.

Jeff Mangum

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