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**Bare rock model Assumptions**

Amount of energy coming into the planet from sunlight is equal the amount of energy leaving the earth as IR. Fin = Fout No atmosphere

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**Energy Balance of a Bare Rock**

Tearth = 259 K = -14° C = 6°F

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**How much solar energy reaches the Earth?**

Sun is a nearly constant source of energy Solar 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

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**We know the solar constant S= 1367 W/m2**

But not all solar energy is absorbed by the Earth. Some is reflected. Earth albedo Albedo 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)

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**Some Basic Information:**

Area of a circle = r2 Area of a sphere = 4 r2

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**Let’s do some calculations**

The intensity of incoming sunlight at the average distance from the sun to the Earth = W/m2 Reflected radiation = 30 % of incoming radiation = x W/m2 100 = 400 W/m2 Therefore The energy absorbed by the Earth = 1350 – 400 = 950 W/m2 ~ 1000 W/m2

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**The total absorbed solar radiation**

= 1000 Wm-2 x Area of the circular shadow Fin = 1000 Wm-2 X ( r2) Where r = radius of the Earth

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**Energy radiated from the Earth**

IR radiation emitted by the Earth = σ T4 W/m2 Total energy going out of earth as IR radiation = σ T4 X Area of the sphere Fout = σ T4 x 4r2 Fout = 5.67 x 10-8 x T4 x 4r2 Eout

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**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 m2 1000 = 5.67 x 10-8 K-4 x T4 x 4 T4 = 4 x 5.67 x 10-8 K-4 T = 257 K

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**Simply the temperature of the Earth can be written as**

T4 = S x ( 1- α) 4σ Where s - Solar constant σ – Stephan constant x 10-8 W/m2K4 Α - albedo If 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).

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**A Planet with an Atmosphere**

Tatm = 259 K Tearth = 303 K = 86° F

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Goals for Today 1.PREDICT the consequences of varying the factors that determine the (a) effective radiating temperature and (b) mean surface temperature.

Goals for Today 1.PREDICT the consequences of varying the factors that determine the (a) effective radiating temperature and (b) mean surface temperature.

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