Review of Box Model of the Earth Calculations (Lecture 3: Friday Aug 1st)

1) Box: Earth

2) Burden: Amount of Energy measured in J

3) Input Flux: (J/s =Watts) 343 W/m2 easier to think about

i) This is an average for the year over 1 square meter of earth

4) Output Flux: (J/s = Watts)

5) So if the earth is at steady state:

i) The total output flux must be? 343 W/m2

ii) Input doesn’t change for our purposes since it depends on the sun

6) What are the output fluxes then?

i) Reflected sunlight = Input * Albedo = 343 W/m2 * 0.3 = 103 W/m2

ii) Radiation emitted by the Earth

a) IR Radiation emitted by the Earth

b) IR = Total – Reflected where Total output = 343 W/m2

IR = 343 W/m2 – 103 W/m2 = 240 W/m2

7) What is the Temp of the earth if it gives off 240 W/m2

i) Use the S-B equation: P = AσT4

8) The earth HAS to be at least this warm!!!

i) This is not the average surface temperature of the earth. This is the Temp of the Green House Gas (GHG) Layer. The surface temperature of the earth is warmer.

Recapping the above:

30% Reflected (Out), 70% Reflected (IR) To be at steady state: In = Out

In = 343 W

Out1 = 343*0.3 = 103 W

100% in (343W) Out2 = IR = 343-103 = 240W

(emission of radiation)

Radiation of energy is dealt with in the Stefan-Boltzman Equation

P = AσT4 Where P is in Watts

A is in m2

σ is in W/m2K4

T is in K

T = 255K = -18°C or 0°F

This is the temperature of the earth as seen from space. We are actually seeing the temperature of one square meter of something from up above the surface not the surface of the earth itself.

1) For the earth to be at steady state we HAVE to be emitting at 255K, but that doesn’t mean that’s what our surface temperature has to be

2) The surface of the earth is some other temperature

3) Temperature of the earth without green house gases (GHG) would be 255K

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4) GHG layer is more or less transparent to visible light

5) GHG layer absorbs IR radiation

6) Additional energy from GHG layer (down=240W) is the reason why the surface is warmer than 255K.

Ex.: Real temperature of the earth’s surface:

1) Input fluxes = Output fluxes for steady state

2) (Sunlight 343 W) + (IRghg 240W) = Albedo 103W + AσT4 surface

343 + 240 = 103 W + AσT4 surface

480 W = AσT4 surface

T = 303 K, 30°C, 85°F

Avg Tearth = 288J why? The GHG layer isn’t a perfect absorber. So you don’t have as much energy to warm the earth’s surface. So not as much admitted by the GHG layer is not a perfect blankets.