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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 behaviour 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 modelled basin uncertainties for GFZ RL06 and ITSG-Grace2018 TWS data with the formal basin uncertainties from the ITSG-Grace2018 solution. The modelled and formal uncertainties fit both in the spatial and temporal domain. We further evaluate the modelled uncertainties by comparison to empirical uncertainties over arid regions. Here, again the appropriateness of the modelled 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.