Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation

This paper reviews the methods which may be used to estimate the state of the atmosphere, i.e., the distribution of temperature and composition, from measurements of emitted thermal radiation such as are made by remote sounding instruments on satellites. The principles of estimation theory are applied to a linear version of the problem, and it is shown that many of the apparently different methods to be found in the literature are particular cases of the same general method. As an aid to understanding, the optimum linear solution is described in terms of the geometry of n dimensions, with n = 3 for illustration. In generalizing the approach to the nonlinear problem there are two stages: (1) finding any member of the infinite family of possible solutions, which may be done by any convenient iterative method, and (2) finding the optimum solution by satisfying appropriate constraints.