Terrestrial Water Storage Data Assimilation into large-scale hydrological models: a new sequential filter to mitigate errors of ensemble-based disaggregation schemes

Terrestrial Water Storage (TWS) represents the total amount of water stored on land, which can be measured using satellite gravity missions like the Gravity Recovery and Climate Experiment mission (GRACE) and its Follow-On mission (GRACE-FO), as well as future gravity missions. Integrating TWS data into hydrological models through Data Assimilation (DA) frameworks has been shown to enhance TWS simulations by introducing long-term trends and adjusting seasonal variations. DA is often carried out using sequential ensemble-based methods such as the Ensemble Kalman Filter (EnKF), which is preferred for its straightforward implementation. The EnKF combines model predictions and observations in a Bayesian manner, i.e., weighting them based on their uncertainties. It then uses ensemble statistics to disaggregate the spatially coarse TWS increments into finer model grids and different vertical water storage components. Typically, EnKF-based TWS DA experiments use small ensemble sizes of 20-30 members to minimize computational demands. However, this can lead to spurious correlations that negatively impact the vertical and horizontal increment disaggregation, thus affecting model dynamics.

In this study, we aim to (i) understand how standard ensemble-statistics-driven disaggregation affects DA results, and (ii) propose an alternative filter that avoids using ensemble statistics in the disaggregation process. This new filter follows the design of sequential ensemble-based DA but introduces a new TWS disaggregation scheme, distributing the TWS increment according to the water content of each grid cell and vertical water storage component. We evaluate the performance of both filters by assimilating synthetic and real TWS observations from various regions worldwide. Our results indicate that both filters produce similar monthly TWS estimates that align well with the assimilated observations. However, the EnKF’s increment disaggregation leads to some issues, such as (i) discrepancies between DA results and ground truth for individual water storage component estimates (in the case of synthetic experiments) and (ii) a rapid divergence of model states from the updated state within a few daily timesteps after DA. These issues are particularly noticeable on a sub-monthly timescale but can also extend over several months in some periods and regions. The new filter proposed in this study mitigates these issues, resulting in more accurate estimates for individual components in synthetic experiments and a more natural model response to DA updates overall.