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We investigate the potential of two independent component analysis (ICA) methods, i.e., the temporal and spatiotemporal ICA, for separating geophysical signals in Gravity Recovery and Climate Experiment (GRACE) data. These methods are based on the assumption of the statistical independence of the signals and thus separate the GRACE‐observed mass changes into maximal independent signals. These two ICA methods are compared to the conventional principal component analysis (PCA) method. We test the three methods with respect to their ability to separate a periodic hydrological signal from a trend signal originating in the solid Earth or the cryosphere with simulated and Center for Space Research GRACE mass changes for the time period of January 2003 to December 2010. In addition, we investigate whether the methods are capable of separating hydrological annual and semiannual mass variations. It is shown that both ICA methods are superior to PCA when non‐Gaussian mass variations are analyzed. Furthermore, the spatiotemporal ICA resolves successfully the lack of full temporal and spatial independence of the geophysical signals observed by GRACE both in global and regional simulation scenarios. Although the temporal and spatiotemporal ICA are nearly equivalent, both superior to PCA in the global GRACE analysis, the spatiotemporal ICA proves to be more efficient in regional applications by recover more reliably the postglacial rebound trend in North America and the bimodal total water storage variability in Africa. ICA performs favorably in separating trend and hydrological signals in GRACE dataThe ICA method is mostly superior to PCA for separating different hydrology signals

The application of terrestrial water storage (TWS) data observed with GRACE and GRACE‐FO often requires realistic uncertainties. For gridded TWS data, this requires the knowledge of the covariances, which can be derived from the formal, i.e., formally estimated in the parameter estimation, variance‐covariance matrix provided together with the Stokes coefficients. However, the propagation of monthly variance‐covariance matrices to TWS data is computationally expensive, so we apply a spatial covariance model for TWS data. The covariance model provides non‐homogeneous (location depending), non‐stationary (time depending), and anisotropic (orientation depending) covariances between any two given points. Further, the model accommodates wave‐like behavior of East‐West‐directed covariances, which residuals of GRACE striping errors can cause. The main application of such spatial covariances is the estimation of uncertainties for mean TWS time series for arbitrary regions such as river basins. Alternatively, regional uncertainties can be derived from the above mentioned formal variance‐covariance matrices of the Stokes coefficients. This study compares modeled basin uncertainties for GFZ RL06 and ITSG‐Grace2018 TWS data with the formal basin uncertainties from the ITSG‐Grace 2018 solution. The modeled and formal uncertainties fit both in the spatial and temporal domain. We further evaluate the modeled uncertainties by comparison to empirical uncertainties over arid regions. Here, again the appropriateness of the modeled uncertainties is shown. The results, namely the TWS uncertainties for global river basins, are available via the GravIS portal. Further, we provide a Python toolbox, which allows computing uncertainties and covariance matrices. Gridded terrestrial water storage (TWS) data, as observed with the satellite missions GRACE and GRACE‐FO, are a valuable tool for many scientists studying the water cycle. However, many of those studies require knowledge about the uncertainties of the observed TWS changes. In this work, we provide and test a mathematical model which provides such uncertainties for the TWS time series. Alternatively, such uncertainties can be derived from the original signal via error propagation. However, such a task is often beyond the scope of many data users. We compare basin uncertainties computed with the model to uncertainties directly derived from the original signal to validate the model results. The validation shows a very high agreement between the two sets of TWS uncertainties. We further test the modeled uncertainties by comparison to empirical uncertainties over arid regions. The results of this work are publicly available for 100 global river basins and 92 climatically similar regions via the GravIS portal (gravis.gfz‐potsdam.de). Further, a Python toolbox will enable every user to independently compute TWS time series uncertainties for any region. Spatial covariance model allows efficient calculation of terrestrial water storage uncertainties from Gravity Recovery And Climate Experiment and GRACE‐Follow‐OnEstimates are consistent with formal errors derived from ITSG‐Grace2018 Stokes CoefficientsCovariance model is applied in the data processing of GravIS portal and available as Python tool box Spatial covariance model allows efficient calculation of terrestrial water storage uncertainties from Gravity Recovery And Climate Experiment and GRACE‐Follow‐On Estimates are consistent with formal errors derived from ITSG‐Grace2018 Stokes Coefficients Covariance model is applied in the data processing of GravIS portal and available as Python tool box

Gravitationally consistent solutions of the Sea Level Equation from leakage‐corrected monthly‐mean GFZ RL06 Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On (GRACE‐FO) Stokes coefficients reveal that barystatic sea level averaged over the whole global ocean was rising by 1.72 mm a−1during the period April 2002 until August 2016. This rate refers to a truely global ocean averaging domain that includes all polar and semienclosed seas. The result corresponds to 2.02 mm a−1mean barystatic sea level rise in the open ocean with a 1,000 km coastal buffer zone as obtained from a direct spatial integration of monthly GRACE data. The bias of +0.3 mm a−1is caused by below‐average barystatic sea level rise in close proximity to coastal mass losses induced by the smaller gravitational attraction of the remaining continental ice and water masses. Alternative spherical harmonics solutions from CSR, JPL, and TU Graz reveal open‐ocean rates between 1.94 and 2.08 mm a−1, thereby demonstrating that systematic differences among the processing centers are much reduced in the latest release. We introduce in this paper a new method to approximate spatial leakage from the differences of two differently filtered global gravity fields. A globally constant and time‐invariant scale factor required to obtain full leakage from those filter differences is found to be 3.9 for GFZ RL06 when filtered with DDK3, and lies between 3.9 and 4.4 for other processing centers. Spatial leakage is estimated for every month in terms of global grids, thereby providing also valuable information of intrabasin leakage that is potentially relevant for hydrologic and hydrometeorological applications. Satellite gravimetry as realized with the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On (GRACE‐FO) missions is measuring tiny variations in the Earth's gravity field that are directly caused by divergent horizontal mass transports such as the melting of ice sheets and the corresponding discharge of melt water into the ocean basins. Between April 2002 and August 2016, this mass inflow caused sea level to rise by 1.72 mm each year as quantified from the latest GRACE reprocessing performed at our institute. The indirect observation principle of GRACE limits the spatial resolution so that highly localized mass loss signals are smeared out into the larger surrounding area, and possibly even from land into the ocean. We propose here a new method to quantify this so‐called spatial leakage from the difference of gravity fields smoothed with slightly different spatial filters. A scale factor is obtained from exploiting the availability of two independent methods to estimate the mass component of sea level rise: The first method spatially integrates over the global gravity fields in all regions away from the coasts, and the second method utilizes a (leakage‐corrected) mass distribution over the continents to calculate the gravitationally consistent distribution of water masses in all ocean basins. We estimate this scale factor as 3.9. Mean barystatic sea level rise is biased high by 0.3 mm a−1when estimated with a 1,000 km coastal buffer zoneFractional spatial leakage in monthly GRACE gravity fields is quantified with two differently strong DDK filtersFractional leakage is scaled by a factor of 3.9 to make results from the Sea Level Equation consistent with open‐ocean integrations