The nth order time-dependent reflection function for a finite homogeneous atmosphere

摘要

An equation satisfied by the time-dependent nth order reflection function is derived from the equation of radiative transfer for a finite homogeneous atmosphere, which scatters radiation isotropically, whose upper surface is illuminated by time-dependent uniform parallel rays of radiation. The exact solution of this equation for an extreme case is briefly discussed. With the aid of the Laplace transform, the first and the second order reflection functions are expressed analytically, which are expected to play important roles in the numerical inversion of the Laplace transform. The time dependence of incidence is described by Dirac's δ function. Two time parameters, a mean time t1 spent by a photon in an absorbed state and a mean free time between two successive collisions t2, are thereby taken into account.