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

With a limited number of polynomial terms (so-called "streams"), there are significant differences between a phase function and its Legendre polynomia l expansion at large scattering angles, which are important to satellite ob servations. This study finds that while it takes hundreds of Legendre polyn omial 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 th e regular Legendre polynomial expansion coefficients by coefficients obtain ed by a weighted singular-value decomposition least-squares fitting procedu re. Thus the computing time can be significantly reduced. For satellite rem ote-sensing purposes, the weighted least-squares Legendre polynomial fittin g is an optimal estimation of the cloud phase function. (C) 2000 Elsevier S cience Ltd. All rights reserved.