Analyses and applications of three spatial discretization methods

As detailed in recent reports [2 §1; 3; & op. cit. therein], a need has long been well established and many investigations undertaken at NCAR and elsewhere, to create high-resolution numerical simulation methods for atmospheric dynamics, that are accurate similarly to spectral methods and computationally efficient similarly to finite-element type methods. Two research codes that demonstrate the strengths of the spectralelement method (SEM) with static-conforming or dynamic-nonconforming adaptive mesh refinement (AMR) are the spectral-element atmosphere model (SEAM) [9, & op. cit. therein] and the geophysical-astrophysical spectral-element adaptive refinement (GASpAR) code [7, 8], respectively. Especially for long-time, potentially parameter-sensitive simulations such as climate, spatial discretizations should accurately validate physical conservation laws such as mass and energy; this motivates another part of our research (§§2.2, 2.3). Finally, for high-resolution data assimilation, ordinary spatial discretizations yield impractically large systems, so to remedy this we have developed special 2D wavelet analyses in a limited-area atmosphere model (§2.4).