An improved energy balance model

Goals: understand the effects of atmosphere and Greenhouse gases

on the earth temperature.

Summary: Earth Energy Balance Equation

Pin = Pout

Pin = (1-A) S π REarth2, Pout = 4π REarth

2 σ TEarth4

Tearth= 255K

Q1Planet-X is at a distance R=2R_earth from the

sun. its temperature should be

A) 2 T_earth;

B) T_earth / 2;

C) T_earth /\sqrt{2};

D) depends on the radius of X-planet.

Earth Energy Budget Sheet

Green house effect

1) Model one: Glass layer effects on the earth temperature;

2) An atmospheric model with Green house effect (with Green house gases).

Q1 (facts)

Atmosphere mainly

A) reflects visible lights;

B) absorbs infrared radiations from the earth;

C) emits infrared radiation towards the earth;

D) Both A), B) and C)

One-layer atmosphere model

Assumptions:

a) Atmosphere absorbs all infrared radiation from the earth; So that earth radiation not seen from outside.

b) Atmosphere emits blackbody radiation.

Now the energy balance for the surface of the Earth is:

• Pin = (1-A) S π REarth2 + σ Te

4 4π REarth2

• Pout = σ Ts4 4π REarth

2

σ Te4

Now the energy balance for the surface of the Earth is:

(1-A) S π REarth2 + σ Te

4 4 π REarth2 =

σ Ts4 4π REarth

2

• Ts4 = (1-A) S / 4σ + Te

4 = 2 Te4

(Assuming Te = 255 K )

You should get Ts = 303 K = 30 ºC

• Not really – too hot!

Issues:

• Is atmosphere a thin layer?

• Is it totally absorbing in infrared?

Earth Energy Balance

• The more complex models involving multilayer atmosphere partially transparent in infrared come up with better estimates of temperatures of the surface of the Earth – about 15 ºC

Different layers of the atmosphere

Major green house gases