Regional Geoid Undulations from CHAMP, Represented by Locally Supported Basis Functions

Regional geoid undulations are determined from CHAMP data using various locally supported basis functions to assess their respective efficiency, accuracy and multi-resolution representation properties. These functions include (biharmonic) B-spline tensor wavelets (with or without compression), multiquadrics (with or without flexible centering and predetermined smoothing) and radially symmetric truncated polynomials.

It is concluded that the B-spline wavelet model is the computationally most efficient approach. The non-periodic variation of the B-spline wavelets allows one to handle data on a bounded domain with small edge effects, and the piecewise linear version allows one to model the geoid using a patch-wise approach. The use of multiquadrics without centering in the data points and predetermined smoothing constant allows handling of heterogeneously distributed data using global optimization. The linear multiquadrics model fits the data best when comparing the residuals of different models with a fixed number of unknowns. For an efficient data synthesis the nonlinear models are best suited due to their far smaller number of basis functions. The smoothest surface was obtained using the nonlinear polynomial approach, whereas the multiquadrics show peaks and the wavelet models show horizontal and vertical edges in their representations. The linear B-spline wavelets are biharmonic, and the approach is capable of an efficient multi-resolution representation of regional gravity field models combining satellite (CHAMP, GRACE, GOCE) and in-situ data.