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Published byDorian Willison Modified about 1 year ago

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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. F in = F out No atmosphere

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T earth = 259 K = -14° C = 6°F Energy Balance of a Bare Rock

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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, S o = 1367 W/m 2

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We know the solar constant S= 1367 W/m 2 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 For the Earth, α = 0.33 (33%) (1)

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Some Basic Information: Area of a circle = r 2 Area of a sphere = 4 r 2

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Let’s do some calculations The intensity of incoming sunlight at the average distance from the sun to the Earth = 1350 W/m 2 Reflected radiation = 30 % of incoming radiation = 1350 x 30 W/m = 400 W/m 2 Therefore The energy absorbed by the Earth = 1350 – 400 = 950 W/m 2 ~ 1000 W/m 2

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The total absorbed solar radiation = 1000 Wm -2 x Area of the circular shadow F in = 1000 Wm -2 X ( r 2 ) Where r = radius of the Earth

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IR radiation emitted by the Earth = σ T 4 W/m 2 Total energy going out of earth as IR radiation = σ T 4 X Area of the sphere F out = σ T 4 x 4 r 2 F out = 5.67 x x T 4 x 4 r 2 Energy radiated from the Earth E out

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F in = 350 Wm -2 X ( r 2 ) F out = 5.67 x x T 4 x 4 r 2 F in = F out 1000 Wm -2 X ( r 2 )m 2 = 5.67 x Wm -2 K -4 x T 4 x 4 r 2 m = 5.67 x K -4 x T 4 x 4 T 4 = x 5.67 x K -4 T = 257 K

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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). Simply the temperature of the Earth can be written as T 4 = S x ( 1- α) 4σ Where s - Solar constant σ – Stephan constant x W/m 2 K 4 Α - albedo

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T atm = 259 K T earth = 303 K = 86° F A Planet with an Atmosphere

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