Assume that the atmospheric absorption coefficient γ varies with height h as

and use the simple model of limb-sounding geometry derived in Section 6.7.4 to show that the reduction in intensity I is given by

where h₀ is the height at which the radiation path passes closest to the Earth€™s surface. For atmospheric aerosols under clear-sky conditions, 1/β ‰ˆ 3 km and 1/γ₀ ‰ˆ 14 km for visible radiation. Estimate the value of h₀ that will reduce the intensity of a transmitted ray by a factor of 10.

y = Yo exp(-h), Aln I = -Yo exp(-Bho) TR 28'