Question

10 points! Consider radiation with wavelength λ passing through a planetary atmosphere comprised entirely of co2 with a molecular absorption coefficient of ka of 10-2"m2/molecule. The atmosphere is isothermal with a surface pressure of 600 Pa, a scale height of 10 km, and gravitational acceleration of 3.71ms 2. Calculate the height and pressure of unit optical depth assuming a zenith angle of a) 0° and b) 45 6

Answer 1

Optical depth gives us the measurement of extinction of radiation through layer. It is defined by tau. if K_abs = Absorption co-efficient. M_a an product = is density of absorption with constant mas mining ration therefore cos theta (dF/dZ) = k_abs product p_a F therefore tau = integral^infinity_z = k_abs p_a product d_Z from above integral we can write, d tau = - k_abs p_a product d z cos theta d F/d z = - F therefore F_out = F_in e^- tau/cos theta \r\n p_a = p_ab product e^(- z/4) H is scale height p_as = density of absorption at surface. Substitute in equation for optical depth. Tau = integral^infinity_z product p_as e^(- z/H) d z Again, d p/d z = -p g therefore tau = - integral^infinity_z k_abs product z^- z/H ds/g as tau = p_s/g product k_abs e^- z/H equation (1) Absorption rate, dF/dz