A mass conserving filter based on diffusion for gravity recovery and climate experiment (GRACE) spherical harmonics solutions

Over the past two decades, the GRACE (Gravity Recovery and Climate Experiment) and GRACE Follow-On mission (GRACE-FO) have provided monthly measurements of the gravity field as sets of Stokes coefficients, referred to as spherical harmonics solutions. The variations of the gravity field can be used to infer mass variations on the surface of the Earth, mostly driven by the redistribution of water. However, unconstrained GRACE and GRACE-FO solutions are affected by strong correlated errors, easily identified as stripes along the north–south direction in the spatial domain. Here, we develop a filter based on the principle of diffusion to remove correlated errors and access the underlying geophysical signals. In contrast to many filters developed for this task, diffusion filters allow a spatially variable level of filtering that can be adapted to match spatially variable signal-to-noise ratios. Most importantly, the formalism of diffusion allows the implementation of boundary conditions, which can be used to prevent any flux through the coastlines during the filtering step. As mass conservation is enforced in the filter, global indicators such as trends in the global mean ocean mass are preserved. Compared with traditional filters, diffusion filters ensure the consistency of the solution at global and regional scales for ocean applications. Because leakage errors occurring during the filtering step are suppressed, better agreement is found when comparing diffusion-filtered spherical harmonic solutions with mascon solutions and independent estimates based on altimetry and in situ data.