The Number of Significant Proper Functions of Two-Dimensional Fields

The proper functions and values of a two-dimensional field (pollution concentration over St. Louis) were found using the discrete matrix method and a continuous integral equation method. For the matrix case, statistical tests were applied to determine the number of significant proper values/functions. In the integral equation case, the number of significant proper functions were determined from the self-consistency of equally valid quadrature methods. It was found that there were only about half as many significant proper functions using the integral equation formulation as were found using statistical methods.