Algorithms for Interpolating and Approximating Radiance Profiles
Abstract
Using radiative transfer theory it is Possible to relate the Planck intensity to the upwelling intensity of the atmosphere. The infrared upwelling intensity can be measured by remote sensing from satellites. Using the H- function inversion theory of Chandrasekhar it is possible to represent the radiance function and the Planck function as transform pairs. In this paper we present methods for obtaining a rational function approximation to the radiance profile. The approximation is obtained using rational interpolation and nonlinear least squares techniques. The Planck function can then be determined as an inverse transform. We also consider regularization methods for solving the radiative transfer equation. In this from the problem is transformed into a linear system with quadratic constraints. Two algorithms are given for solving the constrained problem. In practice, however, one cannot obtain meaningful solutions because the matrices involved have low numerical ranks. A singular value analysis is given for matrices derived from data obtained from the NOAA TIROS Operational Vertical Sounder.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 02, 1990
- Accession Number
- ADA262381
Entities
People
- Steven J. Leon
Organizations
- University of Massachusetts Dartmouth