3 Energy Balance of a Bare Rock Tearth = 259 K = -14° C = 6°F
4 How much solar energy reaches the Earth? Sun is a nearly constant source of energySolar constant is the energy flux density of the solar emission at a distance (d)As energy moves away from the sun, it is spread over a greater and greater area.solar constant for Earth,So = 1367 W/m2
5 We know the solar constant S= 1367 W/m2 But not all solar energy is absorbed by the Earth. Some is reflected.Earth albedoAlbedo is the fraction of sunlight which is reflected off a planet. The average albedo of the Earth is about 0.33.For the Earth, α = 0.33 (33%)(1)
6 Some Basic Information: Area of a circle = r2Area of a sphere = 4 r2
7 Let’s do some calculations The intensity of incoming sunlight at the average distance from the sun to the Earth = W/m2Reflected radiation = 30 % of incoming radiation= x W/m2100= 400 W/m2ThereforeThe energy absorbed by the Earth = 1350 – 400= 950 W/m2~ 1000 W/m2
8 The total absorbed solar radiation = 1000 Wm-2 x Area of the circular shadowFin = 1000 Wm-2 X ( r2)Where r = radius of the Earth
9 Energy radiated from the Earth IR radiation emitted by the Earth = σ T4 W/m2Total energy going out of earth as IR radiation= σ T4 X Area of the sphereFout = σ T4 x 4r2Fout = 5.67 x 10-8 x T4 x 4r2Eout
10 Fin= 350 Wm-2 X ( r2) Fout = 5.67 x 10-8 x T4 x 4r2 Fin = Fout 1000 Wm-2 X ( r2)m2 = 5.67 x 10-8 Wm-2K-4 x T4 x 4r2 m21000 = 5.67 x 10-8 K-4 x T4 x 4T4 =4 x 5.67 x 10-8 K-4T = 257 K
11 Simply the temperature of the Earth can be written as T4 = S x ( 1- α)4σWhere s - Solar constantσ – Stephan constant x 10-8 W/m2K4Α - albedoIf we know S and α we can calculate the temperature of the Earth. It is the temperature we would expect if Earth behaves like a blackbody.NOTE : This calculation can be done for any planet, provided we know its solar (S )constant and albedo (α).
12 A Planet with an Atmosphere Tatm = 259 KTearth = 303 K = 86° F
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