A spatial-varying non-isotropic Gaussian-based convolution filter for smoothing GRACE-like temporal gravity fields

Abstract

The strong noise of satellite-based Time-Variable Gravity (TVG) field is often suppressed by applying the averaging filters. However, how to appropriately compromise the data blurring and de-noising remains as a challenge. In our hypothesis, the optimum spatial averaging filter expects to contain averaging kernels that capture the same amount of orbital samples everywhere, to avoid introducing excessive data blurring. To achieve the goal, we take advantages of the spherical convolution and introduce extra spatial constraints into a Gaussian kernel: (1) its half-width radius adapts to the global inhomogeneity of satellite orbit, and (2) the kernel is reshaped as an ellipsoid to adapt to the regional anisotropy. In this way, we designed optimal filters that contain a spatially-Varying non-isotropic Gaussian-based Convolution (VGC) kernel. The VGC-based filter is compared against three most popular filters through real TVG fields and another closed-loop simulation. In both scenarios, VGC-based filters retain more realistic secular trend and seasonal characteristics, in particular at high latitudes. The spatial correlation between the VGC estimates and the simulated ground truth is found to be 0.95 and 0.86 over Greenland and Antarctica, which is found to be 10% better than other tested filters. Temporal correlations with the ground truth are also found to be considerably better than the other filters over 90% of the globally distributed river basin. Besides, the VGC-based filters provide tolerable efficiency (3.5 s per month) and sufficient accuracy (integral error less than 3%). The method can be extended to the next generation gravity mission as well.

Plain Language Summary

Time-Variable Gravity (TVG) fields of the Gravity Recovery and Climate Experiment (GRACE) and its Follow-On mission (GRACE-FO) need proper filtering to suppress the noise before being applied for intended geophysical studies. Existing filters are generally designed in the spectral domain. Though they are numerically efficient, they can hardly treat the noise in fairness, globally. As a result, the TVG fields may get over-smoothed after applying those filters, particularly in regions with high-latitudes. However, it would be mathematically simple to design a filter by applying a spherical convolution, whose kernels can be easily constrained and tuned in the spatial domain. This study introduces filters with spatially-Varying non-isotropic Gaussian-based Convolution kernel (VGC) that is enforced to comply with the spatial distribution of the TVG noise. The proposed filter is found to preserve a finer spatial resolution of TVG fields, and at the same time, to be able to de-noise them at a comparable level as the existing techniques. Geophysical applications that use GRACE-like TVG fields might have benefits from this practical filtering technique.