Using Legendre Functions for Spatial Covariance Approximation and Investigation of Radial Nonisotrophy for NOGAPS Data
Abstract
This report gives the results of an investigation into the approximation of a two-month history of pressure height innovation data from NOGAPS. Two ideas were investigated. The first investigation was prompted by the fact that all positive definite functions on the sphere have an expansion in terms of Legendre functions with positive coefficients. It was found that for all levels the approximation of the covariance data for pressure height innovations by Legendre functions led to positive coefficients for up to 25 terms except at the some low and high levels. The approximation was constrained to be near zero at distances greater than about 0.6 radians. The interlevel data was approximated indirectly using thickness approximations and these approximations also predominantly led to positive coefficients except when some of the high and low levels were involved. Positive aspects of the scheme are that the least squares approximation is linear and that the interlevel approximations are obtained by a transformation on the coefficients of the single level and thickness approximations without regard to parameters related to correlation distance used by some other methods.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2001
- Accession Number
- ADA388378
Entities
People
- Richard Franke
Organizations
- United States Naval Research Laboratory