Extracting the time variable gravity field from satellite gravity data using a sawtooth filter

Abstract. The Grace satellite pair has been in operation since March 2002 providing monthly gravity potential solutions. This data set contains the variation of the gravity potential as a function of time however its use is limited by the presence of vertical striping noise which overwhelms the time variable signal. Several sophisticated filters exist to extract the time variable signal from the noise however they are seldom used as these filters are complex and difficult to implement. Consequently a large proportion of users of time variable Grace data use a conventional Spherical Gaussian Filter with a large smoothing radius of 600–1000 km which greatly attenuates the vertical striping noise however it also attenuates the remaining signal significantly. The difficulty in removing the noise is that the vertical striping noise is not band limited. We have studied the nature of the vertical striping noise and have found that it occurs over all harmonic degrees however it is associated only with the high harmonic orders. We also find that it occurs only in the east–west and radial components of the gravity field and that the noise is much greater than the signal in these two components. Further we observe that these two components are very similar at all geographic latitudes and that by performing a phase shift and subtracting one component from the other, one obtains a noise free signal. We use this procedure to define a new filter which we call the Sawtooth Filter and find that this filter offers three interesting properties: (i) it subtracts the vertical striping noise from the time variable signal (ii) it amplifies the higher degree harmonics thus improving the spatial resolution (iii) it is simpler to implement and use than the Spherical Gaussian Filter.