The polar form of the spherical harmonic spectrum: implications for filtering grace data
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Representing the spherical harmonic spectrum of a field on the sphere in terms of its amplitude and phase is termed as its polar form. In this study, we look at how the amplitude and phase are affected by linear low-pass filtering. The impact of filtering on amplitude is well understood, but that on phase has not been studied previously. Here, we demonstrate that a certain class of filters only affect the amplitude of the spherical harmonic spectrum and not the phase, but the others affect both the amplitude and phase. Further, we also demonstrate that the filtered phase helps in ascertaining the efficacy of decorrelation filters used in the grace community.
KeywordsPolar form of spherical harmonics Amplitude and phase of spherical harmonic coefficients Filtering on the sphere Low-pass filtering Gravity Recovery and Climate Experiment (GRACE)
This study was initiated within the German Research Foundation (dfg) funded project “Direct Water Balance” within the special priority programme spp1257 Mass transport and mass distribution in the system Earth. The study was completed within the framework of the dfg Sonderforschungsbereich (sfb) 1128 Relativistic Geodesy and Gravimetry with Quantum Sensors (geo-Q). The authors would like to thank the dfg for the financial support given to the study through the two projects. We thank the editor, associate editor and two anonymous reviewers for their constructive review, which has helped us in improving the manuscript. We thank the grace data centers for making the level-2 data publicly available. All the figures in this document were prepared with the Generic Mapping Tools (gmt) software.
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