The Gravity Recovery and Climate Experiment (GRACE) mission ended its operation in October 2017, and the GRACE Follow-On mission was launched only in May 2018, leading to approximately 1 year of data gap. Given that GRACE-type observations are exclusively providing direct estimates of total water storage change (TWSC), it would be very important to bridge the gap between these two missions. Furthermore, for many climate-related applications, it is also desirable to reconstruct TWSC prior to the GRACE period. In this study, we aim at comparing different data-driven methods and identifying the more robust alternatives for predicting GRACE-like gridded TWSC during the gap and reconstructing them to 1992 using climate inputs. To this end, we first develop a methodological framework to compare different methods such as the multiple linear regression (MLR), artificial neural network (ANN), and autoregressive exogenous (ARX) approaches. Second, metrics are developed to measure the robustness of the predictions. Finally, gridded TWSC within 26 regions are predicted and reconstructed using the identified methods. Test computations suggest that the correlation of predicted TWSC maps with observed ones is more than 0.3 higher than TWSC simulated by hydrological models, at the grid scale of 1°r esolution. Furthermore, the reconstructed TWSC correctly reproduce the El Nino-Southern Oscillation (ENSO) signals. In general, while MLR does not perform best in the training process, it is more robust and could thus be a viable approach both for filling the GRACE gap and for reconstructing long-period TWSC fields globally when combined with statistical decomposition techniques.

Abstract. Measuring the spatiotemporal variation of ocean mass allows for partitioning of volumetric sea level change, sampled by radar altimeters, into mass-driven and steric parts. The latter is related to ocean heat change and the current Earth's energy imbalance. Since 2002, the Gravity Recovery and Climate Experiment (GRACE) mission has provided monthly snapshots of the Earth's time-variable gravity field, from which one can derive ocean mass variability. However, GRACE has reached the end of its lifetime with data degradation and several gaps occurred during the last years, and there will be a prolonged gap until the launch of the follow-on mission GRACE-FO. Therefore, efforts focus on generating a long and consistent ocean mass time series by analyzing kinematic orbits from other low-flying satellites, i.e. extending the GRACE time series. Here we utilize data from the European Space Agency's (ESA) Swarm Earth Explorer satellites to derive and investigate ocean mass variations. For this aim, we use the integral equation approach with short arcs (Mayer-Gürr, 2006) to compute more than 500 time-variable gravity fields with different parameterizations from kinematic orbits. We investigate the potential to bridge the gap between the GRACE and the GRACE-FO mission and to substitute missing monthly solutions with Swarm results of significantly lower resolution. Our monthly Swarm solutions have a root mean square error (RMSE) of 4.0 mm with respect to GRACE, whereas directly estimating constant, trend, annual, and semiannual (CTAS) signal terms leads to an RMSE of only 1.7 mm. Concerning monthly gaps, our CTAS Swarm solution appears better than interpolating existing GRACE data in 13.5 % of all cases, when artificially removing one solution. In the case of an 18-month artificial gap, 80.0 % of all CTAS Swarm solutions were found closer to the observed GRACE data compared to interpolated GRACE data. Furthermore, we show that precise modeling of non-gravitational forces acting on the Swarm satellites is the key for reaching these accuracies. Our results have implications for sea level budget studies, but they may also guide further research in gravity field analysis schemes, including satellites not dedicated to gravity field studies.

Abstract. Ultra-sensitive space-borne accelerometers on board of low Earth orbit (LEO) satellites are used to measure non-gravitational forces acting on the surface of these satellites. These forces consist of the Earth radiation pressure, the solar radiation pressure and the atmospheric drag, where the first two are caused by the radiation emitted from the Earth and the Sun, respectively, and the latter is related to the thermospheric density. On-board accelerometer measurements contain systematic errors, which need to be mitigated by applying a calibration before their use in gravity recovery or thermospheric neutral density estimations. Therefore, we improve, apply and compare three calibration procedures: (1) a multi-step numerical estimation approach, which is based on the numerical differentiation of the kinematic orbits of LEO satellites; (2) a calibration of accelerometer observations within the dynamic precise orbit determination procedure and (3) a comparison of observed to modeled forces acting on the surface of LEO satellites. Here, accelerometer measurements obtained by the Gravity Recovery And Climate Experiment (GRACE) are used. Time series of bias and scale factor derived from the three calibration procedures are found to be different in timescales of a few days to months. Results are more similar (statistically significant) when considering longer timescales, from which the results of approach (1) and (2) show better agreement to those of approach (3) during medium and high solar activity. Calibrated accelerometer observations are then applied to estimate thermospheric neutral densities. Differences between accelerometer-based density estimations and those from empirical neutral density models, e.g., NRLMSISE-00, are observed to be significant during quiet periods, on average 22 % of the simulated densities (during low solar activity), and up to 28 % during high solar activity. Therefore, daily corrections are estimated for neutral densities derived from NRLMSISE-00. Our results indicate that these corrections improve model-based density simulations in order to provide density estimates at locations outside the vicinity of the GRACE satellites, in particular during the period of high solar/magnetic activity, e.g., during the St. Patrick's Day storm on 17 March 2015.

The Gravity Recovery and Climate Experiment (GRACE) mission has enabled mass changes and transports in the hydrosphere, cryosphere and oceans to be quantified with unprecedented resolution. However, while this legacy is currently being continued with the GRACE Follow-On (GRACE-FO) mission there is a gap of 11 months between the end of GRACE and the start of GRACE-FO which must be addressed. Here we bridge the gap by combining time-variable, low-resolution gravity models derived from European Space Agency’s Swarm satellites with the dominating spatial modes of mass variability obtained from GRACE. We show that the noise inherent in unconstrained Swarm gravity solutions is greatly reduced, that basin averages can have root mean square errors reduced to the order of $$\text {cm}$$ cm of equivalent water height, and that useful information can be retrieved for basins as small as $$1000 \times 1000\,\hbox {km}$$ 1000 × 1000 km . It is found that Swarm data contains sufficient information to inform the leading three global mass modes found in GRACE at the least. By comparing monthly reconstructed maps to GRACE data from December 2013 to June 2017, we suggest the uncertainty of these maps to be $$2{-}3\,\text {cm}$$ 2 - 3 cm of equivalent water height.

Abstract. Measuring the spatiotemporal variation of ocean mass allows one to partition volumetric sea level change, sampled by radar altimeters, into a mass-driven and a steric part, the latter being related to ocean heat change and the current Earth’s energy imbalance. Since 2002, the Gravity Recovery and Climate Experiment (GRACE) mission provides estimates of the Earth’s time-variable gravity field, from which one can derive ocean mass variability. However, GRACE has reached the end of its lifetime with data degradation and several gaps during the last years, and there will be a prolonged gap until the launch of the follow-on mission GRACE-FO. Therefore, efforts focus on generating a long and consistent ocean mass time series by analyzing kinematic orbits from other low-flying satellites; i.e. extending the GRACE time series. Here we utilize data from the European Space Agency’s (ESA) Swarm Earth Explorer satellites to derive and investigate ocean mass variations. We investigate the potential to bridge the gap between the GRACE missions and to substitute missing monthly solutions. Our monthly Swarm solutions have a root mean square error (RMSE) of 4.0 mm with respect to GRACE, whereas directly estimating trend, annual and semiannual signal terms leads to an RMSE of only 1.7 mm. Concerning monthly gaps, our Swarm solution appears better than interpolating existing GRACE data in 13.5 % of all cases, for 80.0 % of all investigated cases of an 18-months-gap, Swarm ocean mass was found closer to the observed GRACE data compared to interpolated GRACE data. Furthermore, we show that precise modelling of non-gravitational forces acting on the Swarm satellites is the key for reaching these accuracies. Our results have implications for sea level budget studies, but they may also guide further research in gravity field analysis schemes, including non-dedicated satellites.