δ -Fit: A fast and accurate treatment of particle scattering phase functions with weighted singular-value decomposition least-squares fitting

Abstract

With a limited number of polynomial terms (so-called "streams"), there are significant differences between a phase function and its Legendre polynomial expansion at large scattering angles, which are important to satellite observations. This study finds that while it takes hundreds of Legendre polynomial expansion terms to simulate the backscattering portion of cloud phase functions accurately, the backscattered radiance pattern can be accurately estimated with only 30 Legendre polynomial expansion terms by replacing the regular Legendre polynomial expansion coefficients by coefficients obtained by a weighted singular-value decomposition least-squares fitting procedure. Thus the computing time can be significantly reduced. For satellite remote-sensing purposes, the weighted least-squares Legendre polynomial fitting is an optimal estimation of the cloud phase function. © 2000 Elsevier Science B.V.