Idealized atmosphere and Energy Fluxes

What would an idealized model of the atmosphere resemble?

a simple 1-dimensional, 1-layer radiative equilibrium model of the atmosphere accounting for the greenhouse effects

What would the atmosphere behave like if we only considered SW radiation or only LW?

the atmosphere would behave like a grey body

What is the albedo of the the terrestrial system?

A = 0.3

Absorptivities for SW and LW are:

different

E₀ :

intercepted shortwave (SW) radiation at TOA = S₀/4 (1-A)

E_s :

SW radiation incident at surface

E_LW1 :

LW radiation emitted by surface

E_LW2 :

fraction of E_LW1 radiated to outer space at TOA

E_A:

LW radiation emitted by the atmosphere; equal in upward and downward directions

T_S :

radiative equilibrium temperature of the surface

T_A :

radiative equilibrium temperature of the atmosphere

Where do we want radiative equilibrium? What does this mean?

at every level (TOA and Earth’s surface), meaning that incoming radiant flux = outgoing radiant flux

What dos the atmosphere behave like?

we assume it behaves like a non-black body and that the surface of the Earth is a black body

What of the atmosphere do we assume is a black body?

Assume its long wave emission will be that of a black body (emitting at its temperature) times its emissivity coefficient

Kirchhoff’s Law: (reminder)

emissivity = absorptivity (at the same wavelength)

E_s in greater detail is what:

is left of E₀ after a small part of it has been absorbed by the atmosphere as it travelled from the TOA to the surface

How do you find radiative temperatures TA, Ts, and radiant fluxes E_A?

apply the equation of E_s and E₀ at the Earth’s surface to find the radiative equilibrium temperature.

What is the expected surface temperature of this idealised model with greenhouse atmosphere?

~ 13ºC

what is the observed mean Earth’s surface temperature?

~ 15ºC

What was the estimate for Earth’s surface temperature for an Earth without atmosphere?

T_s = T_e = ~ -18ºC

Since the real energy budget of the terrestrial system is more complex what do we need to add?

clouds, sensible and latent heat transfer, multiple layers in atmosphere, and latitudinal and seasonal differences in surface temperature