Fast Spherical Harmonic Transform Routine FLTSS Applied to the Shallow Water Test Set

Abstract

The fast spherical harmonic transform algorithm proposed by Suda and Takami is evaluated in the solutions of the shallow water equation test set defined by Williamson et al. through replacing the Legendre transforms of the NCAR spectral transform shallow water model (STSWM) with routines of the fast Legendre transform with stable sampling (FLTSS), which is the first implementation of the Suda?Takami algorithm. The Suda?Takami algorithm is an approximate algorithm with the computational complexity O(T?2 log T log ε?1), with T being the maximum wavenumber and ε the accuracy parameter of the FLTSS. The influence of the approximation errors of the FLTSS upon the numerical solutions is investigated. For all test cases of the Williamson et al. test set, the FLTSS stably solved the equations with the results that can be explained well with the accuracy ε. The stability in longer time integrations is also assessed, where test case 7 of an analyzed atmospheric initial condition was stably integrated for 1 yr. The FLTSS was faster than the STSWM at T170 and had higher resolutions on an Intel Mobile Pentium 4, where the lower space complexity (memory requirements) of the FLTSS was advantageous in addition to the lower computational complexity.