Experimental Analysis of EM and MU Algorithms for Optimizing Full-rank Spatial Covariance Model

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&#8217;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.

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Uncertainties of TWS Time Series for Arbitrary Regions - Modelled vs. Formal Covariances

10.5194/egusphere-egu21-1259 ◽

2021 ◽

Author(s):

Eva Boergens ◽

Andreas Kvas ◽

Henryk Dobslaw ◽

Annette Eicker ◽

Christoph Dahle ◽

...

Keyword(s):

Time Series ◽

Covariance Matrices ◽

Gobi Desert ◽

Covariance Model ◽

Spatial Covariance ◽

Formal Approach ◽

Data Set ◽

Terrestrial Water ◽

Spherical Harmonic Synthesis ◽

Processing Steps

Knowledge of the variances and covariances of gridded terrestrial water storage anomalies (TWS) as observed with GRACE and GRACE-FO is crucial for many applications thereof. For example, data assimilation into different models, trend estimations, or combinations with other data set require reliable estimations of the variances and covariances. Today, the Level-2 Stokes coefficients are provided with formal variance-covariance matrices which can yield variance-covariance matrices of the gridded data after a labourious variance propagation through all post-processing steps, including filtering and spherical harmonic synthesis. Unfortunately, this is beyond the capabilities of many, if not most, users. This is why, we developed a spatial covariance model for gridded TWS data. The covariance model results in non-homogeneous, non-stationary, and anisotropic covariances. This model also accommodates a wave-like behaviour in latitudinal-directed correlations caused by residual striping errors. The model is applied to both VDK3 filtered GFZ RL06 and ITSG-Grace2018 TWS data.&#160; With thus derived covariances it is possible to estimate the uncertainties of mean TWS time series for any arbitrary region such as river basins. On the other hand, such time series uncertainties can also be derived from the afore mentioned formal covariance matrices. Here, only the formal covariance matrices of ITSG-Grace2018 are used which are also filtered with the VDK3 filter. All together, we are able to compare globally the time series uncertainties of both the modelled and formal approach. Further, the modelled uncertainties are compared to empirical standard deviations in arid regions in the Arabian, Sahara, and Gobi desert where residual hydrological signal can be neglected. Both in the temporal and spatial domain they show a very satisfying agreement proving the usefulness of the covariance model for the users.&#160;

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