7. Let’s calculate the radiative equilibrium temperatures of the Earth’s surface

Question

7. Let’s calculate the radiative equilibrium temperatures of the Earth’s surface and atmosphere

(i.e. you need to calculate Tearth AND Tatmos) assuming that the atmosphere can be regarded as a

thin layer so it emits equally upwards and downwards. The atmosphere has an absorptivity of 0.1

for solar radiation and 0.8 for terrestrial radiation. Assume that the Earth’s surface radiates as a

blackbody at all wavelengths. A balance diagram for this situation is shown on the next page.

a) Write expressions for the total radiation (i.e. in W rather than Wm-2) at each of the 10

locations in the diagram.

b) Write two radiative equilibrium balance equations: one for the atmosphere and one for the

surface.

c) Make assumptions for the Earth’s albedo and solar constant and calculate the radiative

equilibrium temperatures for the atmosphere and the surface.

incoming energy from sun that is not reflected LW transmitted- through atmo Emitted by atmo LW absorbed by atmo Atmosphere SW absorbed by atmo Emitted by atmo Transmitted through atmo SW absorbed by Earth Emitted by Earth LW absorbed by Earth Earth

Explanation / Answer

We know that, the Earth is in the radiative equilibrium since it is having a constant temperature over period of time.

Due to this Stefan-Boltzman Law, we can estimate the following by using the formulae:

E = Te4

Followed by Te = (E/)1/4 and also the earth emission is about 240 Watts m-2

At that point the temperature of the earth with expecting no environment will be around 255 K, which is significantly cooler that of really existing temperature.

Thus, by using the above parameters we can find the following

Te = (E/)1/4

is emissivity = 0.8

So, the temperature is about 287 K or 13.850 C

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.