Fast, Efficient and Adaptive Interpolation of the Geopotential

Author(s)
Arora, Nitin
Russell, Ryan P.
Advisor(s)
Editor(s)
Associated Organization(s)
Organizational Unit
Daniel Guggenheim School of Aerospace Engineering
The Daniel Guggenheim School of Aeronautics was established in 1931, with a name change in 1962 to the School of Aerospace Engineering
Series
Supplementary to:
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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Text
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Paper
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