The use of orthogonal polynomials in the analysis of meteorological data

This thesis comprises 5 chapters. The first chapter is concerned with the general problem of setting up approximations to arbitrary functions by linear combinations of sets of functions of known structure. The second chapter discusses the mathematical basis of the various approximation criteria namely L1, L2 (Least squares) Minimax. Chapter III outlines the method of orthogonal least squares
approximation and discusses its advantages over
the conventional methods discussed in Chapter II.
The fourth chapter describe a project undertaken by the author as a practical application of orthogonal least squares approximation. The results of fitting the 850 hpa height fields over Southern Africa by bivariate Legendre Functions of order 1 to 4 are shown in figures 1 to 10. Chapter V summarises the work in this dissertation and contains some observation on the applicability of the method to actual analysis of meteorological data.