CONSTRAINED REGRESSION IN SATELLITE METEOROLOGY

Least squares or regression techniques have been used for many problem s in satellite meteorology. Because of the large number of variables a nd the linear dependence among these variables, colinearity causes sig nificant problems in the application of standard regression techniques . In some of the applications there is prior knowledge about the value s of the regression parameters. Since there are errors in the predicto r variables as well as the predictand variables, the standard assumpti ons for ordinary least squares are not valid. In this paper the author s examine several techniques that have been developed to ameliorate th e effects of colinearity or to make use of prior information. These in clude ridge regression, shrinkage estimators, rotated regression, and orthogonal regression. In order to illustrate the techniques and their properties, the authors apply them to two simple examples. These tech niques are then applied to a real problem in satellite meteorology: th at of estimating theoretical computed brightness temperatures from mea sured brightness temperatures. It is found that the-rotated and the sh rinkage estimators make good use of the prior information and help sol ve the colinearity problem. Ordinary least squares, ridge regression, and orthogonal regression give unsatisfactory results. Theoretical res ults for the various techniques are given in an appendix.