Statistical Applications to Downscale GRACE-Derived Terrestrial Water Storage Data and to Fill Temporal Gaps

The Gravity Recovery and Climate Experiment (GRACE) has been successfully used to monitor variations in terrestrial water storage (GRACETWS) and groundwater storage (GRACEGWS) across the globe, yet such applications are hindered on local scales by the limited spatial resolution of GRACE data. Using the Lower Peninsula of Michigan as a test site, we developed optimum procedures to downscale GRACE Release-06 monthly mascon solutions. A four-fold exercise was conducted. Cluster analysis was performed to identify the optimum number and distribution of clusters (areas) of contiguous pixels of similar geophysical signals (GRACETWS time series); three clusters were identified (cluster 1: 13,700 km2; cluster 2: 59,200 km2; cluster 3: 33,100 km2; Step I). Variables (total precipitation, normalized difference vegetation index (NDVI), snow cover, streamflow, Lake Michigan level, Lake Huron level, land surface temperature, soil moisture, air temperature, and evapotranspiration (ET)), which could potentially contribute to, or correlate with, GRACETWS over the test site were identified, and the dataset was randomly partitioned into training (80%) and testing (20%) datasets (Step II). Multivariate regression, artificial neural network, and extreme gradient boosting techniques were applied on the training dataset for each of the identified clusters to extract relationships between the identified hydro-climatic variables and GRACETWS solutions on a coarser scale (13,700–33,100 km2), and were used to estimate GRACETWS at a spatial resolution matching that of the fine-scale (0.125◦ × 0.125◦ or 120 km2) inputs. The statistical models were evaluated by comparing the observed and modeled GRACETWS values using the R-squared, the Nash–Sutcliffe model efficiency coefficient (NSE), and the normalized root-mean-square error (NRMSE; Step III). Lastly, temporal variations in GRACEGWS were extracted using outputs of land surface models and those of the optimum downscaling methodology (downscaled GRACETWS) (Step IV). Findings demonstrate that (1) consideration should be given to the cluster-based extreme gradient boosting technique in downscaling GRACETWS for local applications given their apparent enhanced performance (average value: R-squared: 0.86; NRMSE 0.37; NSE 0.86) over the multivariate regression Remote Sens. 2020, 12, 533; doi:10.3390/rs12030533 www.mdpi.com/journal/remotesensing Remote Sens. 2020, 12, 533 2 of 29 (R-squared: 0.74; NRMSE 0.56; NSE 0.64) and artificial neural network (R-squared: 0.76; NRMSE 0.5; NSE 0.37) methods; and (2) identifying local hydrologic variables and the optimum downscaling approach for individual clusters is critical to implementing this method. The adopted method could potentially be used for groundwater management purposes on local scales in the study area and in similar settings elsewhere.

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