Surface geostrophic currents derived from the nonlinear diffusion filtering of the GOCE-based satellite-only MDT using the geodesic mean curvature flow

We present nonlinear diffusion filtering of the GOCE-based satellite-only mean dynamic topography (MDT) based on the geodesic mean curvature flow (GMCF). GMCF represents a curvature-driven diffusion filtering, where the processed data are considered as a set of specific contour lines. A properly designed evolution of these contour lines corresponds to smoothing of the processed data. A main advantage is an adaptive smoothing of the contour lines while respecting significant values of gradients. This property can be beneficial for filtering the MDT models since it allows preserving important gradients along main ocean surface currents. We present numerical solution of the GMCF-based diffusion partial differential equations using the finite volume method (FVM) on regular grids. The derived numerical scheme is applied for filtering the satellite-only MDT models obtained as a combination of the DTU21_MSS model and the recent GOCE-based satellite-only global geopotential models. Then the filtered MDT models are used to derive velocities of the surface geostrophic currents over oceans.