- #1
il27
Homework Statement
:[/B]Use the energy balance equations you wrote down for the ground layer, the atmospheric layer, and the above the atmosphere layer (space) in part (a) to show that the ground temperature Tg can be expressed in terms of the emission temperature TE as follows:$$ T_g = (2f)^.25T_E $$
and provide an algebraic expression for f .
Homework Equations
Ground equation:
$$ (1 - \alpha - a)\frac{f_0}{4} + e \sigma T_a^4 = \sigma T_g^4 $$
Layer:
$$ \frac{af_0}{4} + e \sigma T_g^4 = 2e \sigma T_a^4 $$Top of atmosphere:
$$ \frac{f_0}{4} = \frac{ \alpha f_0}{4} + (1-e) \sigma T_g^4 + e \sigma T_a^4 $$