Earth Temperature Model with Atmospheric Absorption · RMPH 2014 #3

Physics · thermodynamics

Problem

Context: The Sun emits energy mostly in the visible spectrum, while Earth's relatively low surface temperature causes emission in the infrared spectrum. Careful climate modeling accounts for the atmosphere. Atmospheric gas has specific absorption properties characterized by transmission coefficients:

\tau_{vis}

for visible light and

\tau_{ir}

for infrared, representing the ratio of energy passing through the atmosphere to energy entering it. If radiation is completely absorbed, the transmission coefficient is zero; if not absorbed at all, it equals one. Task 3 determines Earth's temperature

T''_P

using modeling that accounts for partial reflection (albedo

A

) and atmospheric absorption (transmission coefficients

\tau_{vis}

and

\tau_{ir}

). 3.a. Determine the expression of average temperature

T''_P

that the Earth's surface should have, in accordance with modeling used in this workload. (2.50p) 3.b. Calculate the numerical value

T''_P

when

A = 0.3

\tau_{vis} = 0.8

and

\tau_{ir} = 0.1

. (0.30p) 3.c. Using modeling proposed in this workload, calculate the average temperature on Earth's surface for the values in Table 1: (1.20p)

Case	I	II	III	IV
$\tau_{vis}$	1	1	1	1
$\tau_{ir}$	1	1	0	0
$A$	0.3	0.0	0.0	0.3
$T''_P$ (K)
$t''_P$ (°C)

Related theory

thermodynamics

Browse the problem library