Uncertainties of Terrestrial Water Storage Anomalies for Global Basins – A Comparison Between Modelled and Formal Covariances

The application of GRACE and GRACE-FO observed gridded terrestrial water storage data (TWS) often requires realistic assumptions of the data variances and covariances. Such covariances are, e.g., needed for data assimilation in various models or combinations with other data sets. The formal variance-covariance matrices now provided with the Stokes coefficients can yield such spatial variances and covariances after variance propagating them through the various post-processing steps, including the filtering, and spherical harmonic synthesis. However, a rigorous variance propagation to the TWS grids is beyond the capabilities of most non-geodetic users.

That is why we developed a new spatial covariance model for global TWS grids. This covariance model is non-stationary (time-depending), non-homogeneous (location-depending), and anisotropic (direction-depending). Additionally, it allows latitudinal wave-like correlations caused by residual striping errors. The model is tested for both GFZ RL06 Level-3 TWS data as provided via the GravIS portal (gravis.gfz-potsdam.de) and ITSG-Grace2018 GravIS-like processed Level-3 TWS data. The model parameters are fitted to empirical correlations derived from both TWS fields. Both data sets yield the same model parameters within the uncertainty of the parameter estimation.

Now, the covariance model derived thereof can be used to estimate uncertainties of mean TWS time series of arbitrary regions such as river basins. Here, we use a global basin segmentation covering all continents. At the same time, such regional uncertainties can be derived from formal variance-covariance matrices as well. To this end, the formal ITSG-Grace2018 variance-covariance matrices of the spherical harmonic coefficients are used. Thus, the modelled and formal basin uncertainties can be compared against each other globally, both spatially and temporally. Further, external validation investigates the usefulness of the basin uncertainties for applications such as data assimilation into hydrological models. Our results show a high agreement between the modelled and the formal basin uncertainties proving our approach of modelled covariance to be a suitable surrogate for the formal variance-covariance matrices.