Constrained Regional Recovery of Continental Water Mass Time-variations from GRACE-based Geopotential Anomalies over South America

We propose a constrained least-squares approach to estimate regional maps of equivalent-water heights by inverting GRACE-based potential anomalies at satellite altitude. According to the energy integral method, the anomalies of difference of geopotential between the two GRACE vehicles are derived from along-track K-Band Range-Rate (KBRR) residuals that correspond mainly to the continental water storage changes, once a priori known accelerations (i.e. static field, polar movements, atmosphere and ocean masses including tides) are removed during the orbit adjustment process. Newton's first law merely enables the Difference of Potential Anomalies from accurate KBRR data and the equivalent-water heights to be recovered. Spatial constraints versus spherical distance between elementary surface tiles are introduced to stabilize the linear system to cancel the effects of the north-south striping. Unlike the mascons approach, no basis of orthogonal functions (e.g., spherical harmonics) is used, so that the proposed regional method does not suffer from drawbacks related to any spectrum truncation. Time series of 10-day regional maps over South America for 2006-2009 also prove to be consistent with independent data sets, namely the outputs of hydrological models, mascons and global GRACE solutions.