We propose a technique to regularize a GRACE-based mass-anomaly time-series in order to (i) quantify the Standard Deviation (SD) of random noise in the data, and (ii) reduce the level of that noise. The proposed regularization functional minimizes the Month-to-month Year-to-year Double Differences (MYDD) of mass anomalies. As such, it does not introduce any bias in the linear trend and the annual component, two of the most common features in GRACE-based mass anomaly time-series. In the context of hydrological and ice sheet studies, the proposed regularization functional can be interpreted as an assumption about the stationarity of climatological conditions. The optimal regularization parameter and noise SD are obtained using Variance Component Estimation. To demonstrate the performance of the proposed technique, we apply it to both synthetic and real data. In the latter case, two geographic areas are considered: the Tonlé Sap basin in Cambodia and Greenland. We show that random noise in the data can be efficiently (1.5–2 times) mitigated in this way, whereas no noticeable bias is introduced. We also discuss various findings that can be made on the basis of the estimated noise SD. We show, among others, that knowledge of noise SD facilitates the analysis of differences between GRACE-based and alternative estimates of mass variations. Moreover, inaccuracies in the latter can also be quantified in this way. For instance, we find that noise in the surface mass anomalies in Greenland estimated using the Regional Climate Model RACMO2.3 is at the level of 2–6 cm equivalent water heights. Furthermore, we find that this noise shows a clear correlation with the amplitude of annual mass variations: it is lowest in the north-west of Greenland and largest in the south. We attribute this noise to limitations in the modelling of the meltwater accumulation and run-off.

An accurate estimation of water resources dynamics is crucial for proper management of both agriculture and the local ecology, particularly in semi-arid regions. Imperfections in model physics, uncertainties in model land parameters and meteorological data, as well as the human impact on land changes often limit the accuracy of hydrological models in estimating water storages. To mitigate this problem, this study investigated the assimilation of terrestrial water storage variation (TWSV) estimates derived from the Gravity Recovery And Climate Experiment (GRACE) data using an ensemble Kalman filter (EnKF) approach. The region considered was the Hexi Corridor in northern China. The hydrological model used for the analysis was PCR-GLOBWB, driven by satellite-based forcing data from April 2002 to December 2010. The impact of the GRACE data assimilation (DA) scheme was evaluated in terms of the TWSV, as well as the variation of individual hydrological storage estimates. The capability of GRACE DA to adjust the storage level was apparent not only for the entire TWSV but also for the groundwater component. In this study, spatially correlated errors in GRACE data were taken into account, utilizing the full error variance-covariance matrices provided as a part of the GRACE data product. The benefits of this approach were demonstrated by comparing the EnKF results obtained with and without taking into account error correlations. The results were validated against in situ groundwater data from five well sites. On average, the experiments showed that GRACE DA improved the accuracy of groundwater storage estimates by as much as 25 %. The inclusion of error correlations provided an equal or greater improvement in the estimates. In contrast, a validation against in situ streamflow data from two river gauges showed no significant benefits of GRACE DA. This is likely due to the limited spatial and temporal resolution of GRACE observations. Finally, results of the GRACE DA study were used to assess the status of water resources over the Hexi Corridor over the considered 9-year time interval. Areally averaged values revealed that TWS, soil moisture, and groundwater storages over the region decreased with an average rate of approximately 0.2, 0.1, and 0.1 cm yr^-1 in terms of equivalent water heights, respectively. A particularly rapid decline in TWS (approximately -0.4 cm yr^-1) was seen over the Shiyang River basin located in the southeastern part of Hexi Corridor. The reduction mostly occurred in the groundwater layer. An investigation of the relationship between water resources and agricultural activities suggested that groundwater consumption required to maintain crop yield in the growing season for this specific basin was likely the cause of the groundwater depletion.

Geodetic measurements of vertical land motion and gravity change are incorporated into an a priori model of present-day glacial isostatic adjustment (GIA) in North America via least-squares adjustment. The result is an updated GIA model wherein the final predicted signal is informed by both observational data, and prior knowledge (or intuition) of GIA inferred from models. The data-driven method allows calculation of the uncertainties of predicted GIA fields, and thus offers a significant advantage over predictions from purely forward GIA models. In order to assess the influence each dataset has on the final GIA prediction, the vertical land motion and GRACE-measured gravity data are incorporated into the model first independently (i.e., one dataset only), then simultaneously. The relative weighting of the datasets and the prior input is iteratively determined by variance component estimation in order to achieve the most statistically appropriate fit to the data. The best-fit model is obtained when both datasets are inverted and gives respective RMS misfits to the GPS and GRACE data of 1.3 mm/yr and 0.8 mm/yr equivalent water layer change. Non-GIA signals (e.g., hydrology) are removed from the datasets prior to inversion. The post-fit residuals between the model predictions and the vertical motion and gravity datasets, however, suggest particular regions where significant non-GIA signals may still be present in the data, including unmodeled hydrological changes in the central Prairies west of Lake Winnipeg. Outside of these regions of misfit, the posterior uncertainty of the predicted model provides a measure of the formal uncertainty associated with the GIA process; results indicate that this quantity is sensitive to the uncertainty and spatial distribution of the input data as well as that of the prior model information. In the study area, the predicted uncertainty of the present-day GIA signal ranges from ∼0.2-1.2 mm/yr for rates of vertical land motion, and from ∼3-4 mm/yr of equivalent water layer change for gravity variations.

In this study, satellite observations including gravity (GRACE), terrestrial reflectance (MODIS), and global precipitation (TRMM) data, along with the output from the PCR-GLOBWB hydrological model, are used to generate monthly and sub-monthly terrestrial water storage (TWS) estimates and quantify flood events over the Tonlé Sap basin between 2002 and 2014. This study is the first time GRACE data have been used to investigate the hydrological processes over the Tonlé Sap basin. To improve the accuracy of the TWS estimates from GRACE, a signal restoration method was applied in an effort to recover the signal loss (i.e., signal leakage) inherent in the standard GRACE post-processing scheme. The method applies the correction based on the GRACE observations only, requiring no external data or hydrological models. The effectiveness of the technique over the Tonlé Sap basin was validated against several independent data sets. Based on the GRACE observations since 2002, the 2011 and 2013 flood events were clearly identified, and measured to have basin-averaged TWS values of 42 cm (40% higher than the long-term mean peak value) and 36 cm (34% higher) equivalent water height, respectively. Those same years also coincide with the largest observed flood extents, estimated from the MODIS data as 6561 km² (91% above the long-term mean peak value) and 5710 km² (66% above), respectively. Those flood events are also linked to the observed inter-annual variations of water storage between 2010 and 2014. It was shown that those inter-annual variations mainly reflect the variations in the surface water and groundwater storage components, influenced by the change of the precipitation intensity. In addition, this study presents a new approach for deriving monthly and sub-monthly TWS variations over a regularly inundated area by using MODIS reflectance data in addition to GRACE solutions. The results of this study show that GRACE data can be considered as an effective tool for monitoring certain small-scale (82,000 km²) hydrological basins.