SPECTRAL TRANSFORM SOLUTIONS TO THE SHALLOW-WATER TEST SET

Solutions to the test case suite proposed by Williamson at al. (J. Com put Phys, 102, 211 (1992)), for the shallow water equations in spheric al geometry, are presented. The solutions have been generated using a conventional spectral transform technique combined with a semi-implici t time differencing scheme, For several of the lest cases, closed-form solutions do not exist. For these cases, high-resolution numerical in tegrations of the spectral transform model are used to provide referen ce solutions against which alternative numerical schemes and lower res olution spectral transform solutions can be evaluated, The sensitivity of the high resolution numerical solutions, associated with temporal truncation, spatial truncation, and internal dissipation, are quantifi ed in order to help bound their uncertainty. In almost all of the test cases, the spectral trans-form method proves to be a highly accurate solution technique. This is particularly the case at resolutions typic ally associated with atmospheric general circulation models used to si mulate the atmosphere's climate, The most serious deficiency of the sp ectral transform method, in the context of the test cases, is the intr oduction of spurious minima and maxima into the solution (caused by Gi bbs phenomenon), when sharp gradients exist. Although this behavior is not necessarily a problem for accurately simulating fluid flow, it ca n become a serious problem for atmospheric general circulation models if the spurious wave structures result in nonphysical states such as n egative water vapor mixing ratio. (C) 1995 Academic Press, Inc.