Fast Jacobian Mie Library for Terrestrial Hydrometeors

Abstract

This paper presents an approach for the fast accurate computation of several useful Mie-based parameters for homogeneous, spherical, liquid water, and ice hydrometeor distributions over a wide range of frequencies, mean hydrometeor diameters, and physical temperatures as occur in the terrestrial atmosphere. The absorption coefficient, scattering coefficient, backscattering coefficient, and phase asymmetry parameters are cast into functions of three independent variables: frequency, temperature, and mean diameter. An exponential drop size distribution with a constant fractional volume of is used to model polydispersed hydrometeors. The ranges used for frequency, temperature, and mean diameter are [1, 1000] GHz, , and [0.002, 20] mm, respectively. The functions are then sampled on a logarithmic grid. Trivariate cubic spline interpolation using nonuniform basis splines (B-splines) is then used to efficiently represent these 3-D functions in a compact library. By using this method, four important criteria are achieved: 1) fast random computability of any of these parameters given the values of frequency, temperature, and mean diameter; 2) minimal memory usage by storage of only B-spline coefficients; 3) representation of parameters using well-behaved functional forms amenable to analytical differentiation for the evaluation of Jacobians, or alternatively, for higher accuracy, B-spline coefficients calculated using true Jacobian values can be used; and 4) negligibly small and bounded error over the entire domain of the library. These procedures result in considerable acceleration of microwave radiative transfer simulations across a broad frequency spectrum, as demonstrated in calculations for both scattering and nonscattering atmospheres. The methods discussed can also be applied to other geophysical problems requiring rapid calculation of series-based functions of several independent variables, where the function evaluation is a time-consuming process, and maximum error bounds are critical.