ature measured at the top-of-atmosphere based on the upwards flux Ft there). Assume radiative equilibrium. (a) Show that the infrared optical depth of the planet's surface r is related to the surface temperature T, and the measured temperature Tm by Calculate the infrared optical depth at the surfaces of () Earth, where T. 300 Kand T 250 K

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4. The surface temperature of a planet is T, and the measured temperature is Tm (i.e. the temper-
ature measured at the top-of-atmosphere based on the upwards flux Ft there). Assume radiative
equilibrium.
(a) Show that the infrared optical depth of the planet's surface 7 is related to the surface
temperature T, and the measured temperature Tm by
Calculate the infrared optical depth at the surfaces of
(a) Earth, where T, = 300 K and Tm = 250 K.
(b) Venus, where T, = 750 K and Tm = 230 K.
(c) Mars, where T, = 240 K and T, = 220 K.
Transcribed Image Text:4. The surface temperature of a planet is T, and the measured temperature is Tm (i.e. the temper- ature measured at the top-of-atmosphere based on the upwards flux Ft there). Assume radiative equilibrium. (a) Show that the infrared optical depth of the planet's surface 7 is related to the surface temperature T, and the measured temperature Tm by Calculate the infrared optical depth at the surfaces of (a) Earth, where T, = 300 K and Tm = 250 K. (b) Venus, where T, = 750 K and Tm = 230 K. (c) Mars, where T, = 240 K and T, = 220 K.
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