Unsupervised ensemble Kalman filtering with an uncertain constraint for land hydrological data assimilation

M. Khaki*, B. Ait-El-Fquih, I. Hoteit, E. Forootan, J. Awange, M. Kuhn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


The standard ensemble data assimilation schemes often violate the dynamical balances of hydrological models, in particular, the fundamental water balance equation, which relates water storage and water flux changes. The present study aims at extending the recently introduced Weak Constrained Ensemble Kalman Filter (WCEnKF) to a more general framework, namely unsupervised WCEnKF (UWCEnKF), in which the covariance of the water balance model is no longer known, thus requiring its estimation along with the model state variables. This extension is introduced because WCEnKF was found to be strongly sensitive to the (manual) choice of this covariance. The proposed UWCEnKF, on the other hand, provides a more general unsupervised framework that does not impose any (manual, thus heuristic) value of this covariance, but suggests an estimation of it, from the observations, along with the state. The new approach is tested based on numerical experiments of assimilating Terrestrial Water Storage (TWS) from Gravity Recovery and Climate Experiment (GRACE) and remotely sensed soil moisture data into a hydrological model. The experiments are conducted over different river basins, comparing WCEnKF, UWCEnKF, and the standard EnKF. In this setup, the UWCEnKF constrains the system state variables with TWS changes, precipitation, evaporation, and discharge data to balance the summation of water storage simulations. In-situ groundwater and soil moisture measurements are used to validate the results of the UWCEnKF and to evaluate its performances against the EnKF. Our numerical results clearly suggest that the proposed framework provides more accurate estimates of groundwater storage changes and soil moisture than WCEnKF and EnKF over the different studied basins.

Original languageEnglish (US)
Pages (from-to)175-190
Number of pages16
JournalJournal of Hydrology
StatePublished - Sep 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.


  • Constrained data assimilation
  • Ensemble Kalman Filter (EnKF)
  • Hydrological modeling
  • Unsupervised Weak Constrained Ensemble Kalman Filter (UWCEnKF)
  • Water budget closure

ASJC Scopus subject areas

  • Water Science and Technology


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