A two-update ensemble Kalman filter for land hydrological data assimilation with an uncertain constraint

Abstract

Assimilating Gravity Recovery And Climate Experiment (GRACE) data into land hydrological models provides a valuable opportunity to improve the models' forecasts and increases our knowledge of terrestrial water storages (TWS). The assimilation, however, may harm the consistency between hydrological water fluxes, namely precipitation, evaporation, discharge, and water storage changes. To address this issue, we propose a weak constrained ensemble Kalman filter (WCEnKF) that maintains estimated water budgets in balance with other water fluxes. Therefore, in this study, GRACE terrestrial water storages data are assimilated into the WorldWide Water Resources Assessment (W3RA) hydrological model over the Earth's land areas covering 2002-2012. Multi-mission remotely sensed precipitation measurements from the Tropical Rainfall Measuring Mission (TRMM) and evaporation products from the Moderate Resolution Imaging Spectroradiometer (MODIS), as well as ground-based water discharge measurements are applied to close the water balance equation. The proposed WCEnKF contains two update steps; first, it incorporates observations from GRACE to improve model simulations of water storages, and second, uses the additional observations of precipitation, evaporation, and water discharge to establish the water budget closure. These steps are designed to account for error information associated with the included observation sets during the assimilation process. In order to evaluate the assimilation results, in addition to monitoring the water budget closure errors, in-situ groundwater measurements over the Mississippi River Basin in the US and the Murray-Darling Basin in Australia are used. Our results indicate approximately 24% improvement in the WCEnKF groundwater estimates over both basins compared to the use of (constraint-free) EnKF. WCEnKF also further reduces imbalance errors by approximately 82.53% (on average) and at the same time increases the correlations between the assimilation solutions and the water fluxes.

On the Use of Adaptive Ensemble Kalman Filtering to Mitigate Error Misspecifications in GRACE Data Assimilation

“…Due to the narrow range of storage dynamics in surface soil moisture, the improvement was less significant in this layer with the groundwater level, as the most significant contributor, receiving the greatest improvement. This corroborates the results from previous studies (e.g., Girotto et al, ; Khaki, Hoteit, et al, ; Khaki, Ait‐El‐Fquih, et al, ; Schumacher et al, ; Shokri, Walker, van Dijk & Pauwels ; Tian et al, ; Zaitchik et al, ). Conversely, the accuracy of the EnKF with initial α Q =2 (twice the reference error magnitude) slightly degraded in both soil layers and groundwater, comparing to OL.…”

“…It has been proven that the ensemble Kalman filter (EnKF) can improve the accuracy of hydrologic models by merging observations with model predictions. Such observations include soil moisture (e.g., Aubert et al, ; Crow & Ryu, ; Houser et al, ; Pauwels et al, ; Reichle et al, , ; Walker & Houser, ), snow water equivalent (e.g., Barrett, ; Slater & Clark, ; Sun et al, ), streamflow (e.g., Lee et al, ; Clark et al, ), groundwater levels (e.g., Hendricks Franssen et al, ), turbulent heat fluxes (e.g., Bateni & Entekhabi, ; Pipunic et al, ; Xu et al, ) , microwave radiances (e.g., Dechant & Moradkhani, ), and terrestrial water storage (TWS; e.g., Ellett et al, ; Forman & Reichle, ; Forman et al, ; Girotto et al, ; ; Houborg et al, ; Khaki, Ait‐El‐Fquih, et al, ; Khaki, Hoteit, et al,; Khaki, Schumacher, et al, ; Kumar et al, ; Li et al, ; Li & Rodell, ; Smith, ; Tian et al, ; van Dijk et al, ; Zaitchik et al, ). The idea behind the EnKF is to combine observations and model estimates of state variables considering their relative error covariances.…”

Performance of Different Ensemble Kalman Filter Structures to Assimilate GRACE Terrestrial Water Storage Estimates Into a High‐Resolution Hydrological Model: A Synthetic Study

“…The ensemble Kalman filter (EnKF) is a very useful data assimilation (DA) tool to reduce the model errors at each time step by updating the model state variables (Evensen, 2003). DA methods have been successfully applied in hydrologic modeling to assimilate observations from various sources into the model, including soil moisture (e.g., Aubert et al, 2003;Crow & Ryu, 2009;Houser et al, 1998;Pauwels et al, 2001;Reichle et al, 2008Reichle et al, , 2004, snow water equivalent (e.g., Barrett, 2003;Slater & Clark, 2006;Sun et al, 2004), streamflow (e.g., Clark et al, 2008;Lee et al, 2011), groundwater levels (e.g., Hendricks Franssen et al, 2017, microwave radiances (e.g., Dechant & Moradkhani, 2011), and TWS (e.g., van Dijk et al, 2014;Ellett et al, 2006;Forman & Reichle, 2013;Forman et al, 2012;Girotto et al, 2016Girotto et al, , 2017Houborg et al, 2012;Khaki, Ait-El-Fquih, et al, 2017;Khaki, Schumacher, et al, 2017;Kumar et al, 2016;Li & Rodell, 2015;Li et al, 2012;Smith, 2013;Tian et al, 2017;Zaitchik et al, 2008). Therefore, assimilating the GRACE TWS retrievals into a hydrological model yields more reliable water storage estimates in which the drawbacks of both approaches are mitigated.…”

Retrospective analysis of published hydrological researches: models, trends and geographical aspects over the last two decades of hydrological modelling

“…On the other hand, hydrological models can be applied to much larger spatial scales, as on a continental or even a global level. This permits the study of the global consequences of the hydrological cycle (Brakenridge et al 2012, Sperna Weiland et al 2012, Decharme et al 2014and Khaki et al 2017. In accordance with the increasing proportion of research at a continental or world level, the percentage of international cooperation in research activities has been increasing.…”