A copula-supported Bayesian framework for spatial downscaling of GRACE-derived terrestrial water storage flux

The GRACE and GRACE-FO satellite missions have established mass variations as a fundamentally new observation type for a broad spectrum of applications in Earth science disciplines, including oceanography, geophysics, hydrology and hydrometeorology. Despite its innovation and success in hydrology, the utility of GRACE-derived Terrestrial Water Storage Anomaly (TWSA) and its time derivative Terrestrial Water Storage Flux (TWSF) have mainly been limited to large catchments due to their coarse spatial resolution. 

Here, we propose a method to downscale TWSF and determine its uncertainty within a Bayesian framework by incorporating fine-scale (non-GRACE) data of TWSF and of Soil Moisture Change (SMC) from different available sources. For the Bayesian ingredients, we take GRACE data as the prior and make use of copula models to obtain non-parametric likelihood functions based on the statistical relationship between GRACE TWSF with fine-scale TWSF data and SMC. We apply our method to the Amazon Basin and assess the performances of our products from various fine-scale input datasets of TWSF and SMC. 

Given the lack of ground truth for TWSF, we validate our results against 2 external information sources: (1) space-based observations of Surface Water Storage Change (SWSC) in the Amazon river system and (2) Vertical Crustal Displacements (VCD) observed by the Global Positioning System (GPS). Overall, the results show that the proposed method is able to estimate a downscaled TWSF, which is informed by GRACE and fine-scale data. Validation shows that our downscaled products are better anticorrelated with VCD (-0.81) than fine-scale TWSF (-0.73) and show a mean relative RMSE of 26% with SWSC versus 70% for fine-scale TWSF. 

The proposed methodology, although developed in a context of hydrology and of GRACE data, is generic to a high degree. Within hydrology it can be used for other datasets, which are crucial for hydrological application at regional and local scales. Moreover, the methodology can easily be extended to other disciplines in which downscaling of coarse scale datasets is relevant.