Radiative Transfer

Planetary Equilibrium Temperature:

For the earth, the atmospheric albedo, which is entirely produced by reflections from cloud tops, is approximately 0.3.

What we wish to do is to derive a simple expression for how the atmosphere modifies the tempearature of a planetary surface

Before doing this, we need to make some assumptions about our atmosphere.

These assumptions allow us to treat the atmosphere is a thin, uniform slab of material at constant density and temperature.


First some constants:

Going back to the planetary equilibruim temperature we see that

4σT4 =Fo(1-A)

or

T4 = ((1/4*1370)/σ)(1-A)

T = 278*(1-A)1/4

For A = 0.3 one gets T = 254K


One Layer Model (e.g. our atmosphere)

We assume the following:

Energy Balance in the One Zone Atmosphere

Fo = incident flux
Ts = transmission percentage of short wavelength incoming radiation
Tt = transmission percentage of outgiong long wavelength radiation
Fg = Flux from ground
Fa = Flux from the atmosphere.