A spatial covariance model for GRACE and GRACE-FO terrestrial water storage data

Gridded terrestrial water storage (TWS) observed by GRACE or GRACE-FO typically show a spatial error structure that is anisotropic (direction depending), non-homogeneous (latitude depending), and non-stationary (time depending).

We will introduce a new covariance model characterizing this error behavior analytically with a direction depending Bessel function of the first kind. The anisotropy of this function is governed by a shape parameter allowing for longer correlation lengths in longitudinal than in latitudinal direction. The wave-effect of the Bessel function allows us to account for the residuals of the GRACE striping errors. Both size as well as shape parameters of the Bessel function vary smoothly with latitude. These variations are implemented via even Legendre polynomials. The non-stationarity of the covariance is modeled with time-varying point variances. The validity of this covariance model on the sphere was thoroughly tested with a Monte-Carlo approach.

First, we apply this covariance model to 5 years of simulated GRACE data (Flechtner et al., 2016) where true errors are readily available from the differences of the synthetic input and the finally recovered gravity fields. For the 50 largest discharge basins, we obtain more realistic time series uncertainties than from propagating the formal errors associated with the Stokes coefficients. For smaller basins, however, the covariance model tends to provide overly pessimistic uncertainty estimates.

Second, the model is adapted to real GRACE and GRACE-FO data to obtain realistic error covariance information for arbitrarily shaped basins from globally gridded error information. We will show the current plans to update GFZ’s GravIS portal (http://gravis.gfz-potsdam.de/home) so that area- and time-dependent error information which is critically important for the assimilation of GRACE-based TWS data into numerical models will become readily available to the user community.