Inverse atmospheric radiative transfer problems: A nonlinear minimization search method of solution

Abstract

The mathematical inversion of the equations of radiative transfer is an important tool for the remote sensing and probing of the atmosphere. These equations take the form of first-kind Fredholm integral equations (extinction and primary scattering of solar radiation, thermal emission from the atmosphere-surface system), ratios of such equations, and nonlinear integrodifferential equations (multiple scattering). A nonlinear minimization search method for solving these various equations is presented and discussed relatively to uniqueness, stability and accuracy of the solution it yields. The method is a direct search in parameter space aimed at minimizing the objective function of the problem considered without resorting to a gradient approach. The proposed algorithm is basically a nonlinear least-squares minimization which relies on a random number generator to find an improved iterate at each step. It makes constant use of the measurements in order to arrive at the solution. It does not depend on the initial guess for well-behaved problems, and does not require any a priori information on the solution. It is quite general and can be applied to any inverse problem which can be reduced to the determination of a certain number, however large, of unknown parameters. The computation times involved tend to increase in proportion to the first power of the number of variables in opposition to most classical optimization methods where the proportion is to the cube of the number of variables. Illustrations are provided in the field of environmental particulate pollution where aerosol physical parameters are sought from measurements of solar extinction ratios.