The spherical Slepian basis as a means to obtain spectral consistency between mean sea level and the geoid

The mean dynamic topography (MDT) can be computed as the difference between the mean sea level (MSL) and a gravimetric geoid. This requires that both data sets are spectrally consistent. In practice, it is quite common that the resolution of the geoid data is less than the resolution of the MSL data, hence, the latter need to be low-pass filtered before the MDT is computed. For this purpose conventional low-pass filters are inadequate, failing in coastal regions where they run into the undefined MSL signal on the continents. In this paper, we consider the use of a bandlimited, spatially concentrated Slepian basis to obtain a low-resolution approximation of the MSL signal. We compute Slepian functions for the oceans and parts of the oceans and compare the performance of calculating the MDT via this approach with other methods, in particular the iterative spherical harmonic approach in combination with Gaussian low-pass filtering, and various modifications. Based on the numerical experiments, we conclude that none of these methods provide a low-resolution MSL approximation at the sub-decimetre level. In particular, we show that Slepian functions are not appropriate basis functions for this problem, and a Slepian representation of the low-resolution MSL signal suffers from broadband leakage. We also show that a meaningful definition of a low-resolution MSL over incomplete spherical domains involves orthogonal basis functions with additional properties that Slepian functions do not possess. A low-resolution MSL signal, spectrally consistent with a given geoid model, is obtained by a suitable truncation of the expansions of the MSL signal in terms of these orthogonal basis functions. We compute one of these sets of orthogonal basis functions using the Gram–Schmidt orthogonalization for spherical harmonics. For the oceans, we could construct an orthogonal basis only for resolutions equivalent to a spherical harmonic degree 36. The computation of a basis with a higher resolution fails due to inherent instabilities. Regularization reduces the instabilities but destroys the orthogonality and, therefore, provides unrealistic low-resolution MSL approximations. More research is needed to solve the instability problem, perhaps by finding a different orthogonal basis that avoids it altogetherGeoscience and Remote SensingCivil Engineering and Geoscience

Satellite altimetry for geodetic, oceanographic, and climate studies in the Australian region

This chapter provides an overview of recent research applications utilizing satellite altimetry around Australia. Topics covered include improving the quality of altimeter sea surface height (SSH) data in coastal regions, observing and understanding the structure and variability of the major boundary current systems, estimating regional sea-level changes, and determining and verifying the marine gravity field using altimetry. The approaches highlighted in this chapter use altimetry synergistically with all available oceanic data including other remote sensing techniques, drifting buoys, and in situ data such as coastal tide-gauges. The results presented are an integration of altimetric and in situ data with a high-resolution computer model in order to simulate the sea-level changes in Australian coastal and offshore regions. Through such synthesizing research approaches, satellite altimetry continues to make an important contribution to a number of key strategic research areas in the Australasian region