J.‐P. Montillet

Several different basis functions have been used to represent the Earth's gravity field in order to generate estimates of mass variations on Earth from the analysis of data of the Gravity Recovery and Climate Experiment ( grace ) and its successor grace Follow‐On missions, including spherical harmonics, mass concentration elements (mascons) and slepian functions. Each approach depends inherently upon accurate modeling of the orbits of the pair of satellites as they revolve around the Earth, so that the observations of inter‐satellite changes in range (or, more specifically, range rate) can be exploited to identify mass variations. We have developed software using a classical orbit modeling approach, mascons and 24‐hr orbit integration, to estimate simultaneously corrections to orbital parameters and the temporal gravity field from grace data. Rather than using the range rate, we use the range acceleration as the inter‐satellite observable as it aids in localizing the mass variations. Level‐1 B range acceleration observations contain high levels of high‐frequency noise that inhibits their usefulness for this purpose. Instead, we generate range acceleration observations by numerical differentiation of the Level‐1B range rate prefit residuals. Simulations show that the gravity signal is not attenuated in this process. Our monthly estimates of mass anomalies from grace data (2003–2016) agree well with previous studies, both spatially and temporally. When converted to spherical harmonics our time series of C 2,0 , derived from grace data alone, are close to the independent estimates from satellite laser ranging, but the overall solution is improved by substituting the SLR C 2,0 .