A discussion of empirical orthogonal functions and their application to vertical temperature profiles

It has been found that empirical orthogonal functions have a special application in the deduction of temperature soundings from radiometric measurements made by artificial satellites. The methods of Lorenz, Obukhov, and Holmström for the generation of empirical orthogonal functions are discussed and compared. These methods all reduce to that of solving eigenvalue problems. It is shown that Holmström’s approach is identical to that of E. Schmidt and that his results are identical to those of Obukhov. Furthermore, the computational procedure of Holmström is found to be equivalent to O. D. Kellogg’s method for finding eigenfunctions, which in the discrete case reduces to the well-known power method with deflation for matrices. A measure of variance is given to select the number of empirical functions to be used relative to the errors in physical measurements.