Fast, Efficient and Adaptive Interpolation of the Geopotential
Author(s)
Arora, Nitin
Russell, Ryan P.
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Abstract
Conventional high-fidelity geopotential computations rely on expensive spherical harmonics
(SH) series. In this study an interpolation scheme is proposed that classically improves compute
speed at the expense of memory. The approach is exact in the sense that accelerations
are calculated naturally as the gradient of the fitted potential, and continuity and smoothness
to arbitrary order are ensured across local cells using the Junkins weight functions. Millions
of local interpolating functions are chosen with a new adaptive method that minimizes coefficient
storage subject to a maximum error threshold. Analytic inversions of the normal
equations associated with each candidate interpolant allow for rapid solutions to the least
squares process without resorting to the conventional numerical linear system solvers. Accordingly,
time is afforded to cycle through hundreds of candidate interpolants for each of
the millions of nodes, resulting in a global model with a highly optimized memory requirement
and uniform error distribution. Speed is ensured by choosing simple polynomials as
candidate interpolants. For example, the interpolation approach (deemed FETCH) fitting
the full GRACE02C 200 200 spherical harmonics (SH) field requires 1.8 Gigabytes of
memory and achieves over 300x speedups compared to a Pines SH implementation. The
error profile of the interpolation model is adaptively selected throughout the global domain
to conservatively mirror the published expected errors of the SH fitting function.
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Date
2011-08
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