Earth Temperature Model with Albedo Effect · RMPH 2014 #2
Physics · thermodynamics
Problem
Context: The simple modeling of Task 1 assumes Earth is a black body, which is unrealistic since Earth appears luminous from space. Earth's atmosphere (especially clouds) reflects approximately 24% of energy from the Sun, and Earth's surface (especially ice areas) reflects 6% of incident energy. Albedo measures the ratio of reflected to incident radiant flux. Consider terrestrial albedo . 2.a. Determine the expression of average temperature that the Earth's surface should have, in accordance with simple modeling used in this workload. (0.70p) 2.b. Calculate the numerical value of the average temperature that the Earth's surface should have, according to the model in workload 2a. (0.30p)Intuitive explanation
The key insight is that albedo reduces the solar energy Earth actually absorbs—only the fraction of incoming sunlight reaches the surface. Set up an energy balance where this reduced absorbed solar power equals the thermal radiation Earth emits, then solve for the equilibrium temperature. This is the same Stefan-Boltzmann approach as before, but now accounting for reflection losses.
Intuitive explanation
The key insight is that albedo reduces the solar energy Earth actually absorbs—only the fraction of incoming sunlight reaches the surface. Set up an energy balance where this reduced absorbed solar power equals the thermal radiation Earth emits, then solve for the equilibrium temperature. This is the same Stefan-Boltzmann approach as before, but now accounting for reflection losses.