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Understanding mass (re‐)distribution within the Earth system, and addressing global challenges such as the impact of climate change on water resources requires global time‐variable terrestrial water storage (TWS) estimates along with reasonable uncertainty fields. The Gravity Recovery and Climate Experiment (GRACE) and GRACE‐FO satellite missions provide time‐variable gravity fields with full variance‐covariance information. A rigorous uncertainty propagation of these errors to TWS uncertainties is mathematically challenging and computationally inefficient. We propose a Monte Carlo Full Variance‐Covariance (MCFVC) error propagation approach to precisely compute TWS uncertainties. We also establish theoretical criteria to predict the actual convergence and accuracy of MCFVC, showing a convergence after 10,000 realizations with the relative error of 2.8% for variance and 4.7% for covariance at the confidence level of 95%. This can be achieved in few seconds using a single CPU to compute the uncertainties of each 1° resolution globally gridded TWS field. A validation against the rigorous error propagation method indicates relative differences of less than 0.8%. A global uncertainty assessment shows that neglecting the covariance of gravity coefficients can considerably bias the TWS uncertainties, that is, up to 60%, in some basins like Eyre. Flexibility of MCFVC allows the quantification of filtering impacts on the uncertainty of TWS fields, for example, up to 35% in the Tocantins River Basin. An empirical model is provided to reproduce GRACE‐like TWS uncertainty fields for hydrological studies. Finally, experiments of GRACE(‐FO) data assimilation for hydrological applications and sea‐level budget estimation are presented that indicate the importance of accounting for the full covariance information in these studies. Plain Language Summary: Terrestrial water storage (TWS) represents a vertical summation of all available water of the Earth's land surface including groundwater, soil layers, surface water, and snow. Therefore, understanding TWS changes is essential for hydrological assessments. Satellite gravity missions such as the Gravity Recovery and Climate Experiment (GRACE) and its Follow‐On mission (GRACE‐FO) provide a unique opportunity to estimate TWS globally. However, to use GRACE(‐FO)‐like TWS estimates in geophysical and hydrological studies, one needs to quantify their uncertainties reliably at desired spatial resolution. In this study, an efficient statistical Monte Carlo method is presented, which provides high flexibility of processing choices, and satisfies the accuracy needed to compute the uncertainties of GRACE(‐FO)‐like TWS products. The simplicity and generality of this method also allows it to be easily integrated in the operational data post‐processing chains. We demonstrate the importance of the full covariance estimation of TWS products in hydrological data assimilation and sea‐level budget estimation studies. Key Points: A Monte Carlo Full Variance‐Covariance method is proposed to propagate errors of GRACE(‐FO) level‐2 data, where the covariance is hardly reached by traditional methodsConsidering full variance‐covariance information and filtering methods have considerable impacts on the uncertainty of GRACE(‐FO)‐like terrestrial water storage (TWS) fieldsAn empirical model is provided to account for spatial‐temporal variation of GRACE(‐FO)‐like TWS uncertainty fields, and for hydrological studies [ABSTRACT FROM AUTHOR]

Data Assimilation (DA) of time-variable satellite gravity observations, e.g., from the Gravity Recovery and Climate Experiment (GRACE), GRACE-Follow On (GRACE-FO) and future gravity missions, can be applied to constrain the vertical sum of water storage simulations of Global Hydrological Models (GHMs). However, the state-of-the-art DA of these measured Terrestrial Water Storage (TWS) changes into models is often performed regionally, and if globally, at low spatial resolution. This choice is made to handle the considerably high computational demands of DA, and to avoid numerical problems, e.g., instabilities related to the inversion of covariance matrices. To fully exploit the potential of satellite gravity observations and the high spatial resolution of GHMs, we developed a Python-based open-source PyGLDA system that allows performing DA globally at a fine scale with high numerical efficiency. The main novelties of the system include (i) implementing a globe-scale patch-wise DA via domain localization and neighbouring-weighted global aggregation and (2) its great compatibility between basin-scale and grid-scale DAs. This PyGLDA system represents a considerable functional advancement on previous implementations with wide and flexible options offered to allow for various user-specific studies. The modular structure of PyGLDA provides users with various possibilities to interact with (and add/remove) individual water storage compartments, change the representation of observations, and, therefore, the ability to choose different GHMs. In this paper, we present a full description of this system and its application for the Danube River Basin as a regional case study and through a global DA. The DA demonstrations are performed using the monthly TWS fields of GRACE (2002–2010) and the W3RA water balance model at 0.1-degree/daily spatial-temporal resolution. [ABSTRACT FROM AUTHOR]

The global estimation of Thermospheric Neutral Density (TND) and electron density (Ne) on various altitudes are provided by upper atmosphere models, however, the quality of their forecasts needs to be improved. In this study, we present the impact of assimilating space-based TNDs, measured along Low Earth Orbit (LEO) mission, into the NCAR Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIE-GCM). In these experiments, the Ensemble Kalman Filter (EnKF) merger of the Data Assimilation Research Testbed (DART) community software is applied. To cover various space-based TND data and both low and high solar activity periods, we used the measurements of CHAMP (Challenging Minisatellite Payload) and Swarm-C as assimilated observations. The TND forecasts are then validated against independent TNDs of GRACE (Gravity Recovery and Climate Experiment mission) and Swarm-B, respectively. To introduce the impact of the thermosphere on estimating ionospheric parameters, the outputs of Ne are validated against the radio occultation data. The Data Assimilation (DA) results indicate that TIE-GCM overestimates (underestimates) TND and Ne during low (high) solar activity. Considerable improvements are found in forecasting TNDs after DA, that is, the Root Mean Squared Error (RMSE) is reduced by 79% and 51% during low and high solar activity periods, respectively. The reduction values for Ne are found to be 52.3% and 40.4%, respectively. [ABSTRACT FROM AUTHOR]

Water - Global Assessment and Prognosis (WaterGAP) is a modelling approach for quantifying water resources and water use for all land areas of the Earth that has served science and society since 1996. In this paper, the refinements, new algorithms and new data of the most recent model version v2.2e are described, together with a thorough evaluation of simulated water use, streamflow and total water storage anomaly against observation data. WaterGAP v2.2e improves the handling of inland sinks and now excludes not only large but also small man-made reservoirs when simulating naturalized conditions. The reservoir and non-irrigation water use data were updated. In addition, the model was calibrated against an updated and extended dataset of streamflow observations at 1509 gauging stations. The model can now be started using pre-scribed water storages and other conditions, which facilitates data assimilation as well as near real-time monitoring and forecast simulations. For specific applications, the model can consider the output of a glacier model, approximate the effect of rising CO2 concentrations on evapotranspiration or calculate the water temperature in rivers. In the paper, the publicly available standard model output is described and caveats of the model version are provided alongside the description of the model setup in the ISIMIP3 framework. [ABSTRACT FROM AUTHOR]