Nonparametric Data Assimilation Scheme for Land Hydrological Applications

M. Khaki*, F. Hamilton, E. Forootan, I. Hoteit, J. Awange, M. Kuhn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Data assimilation, which relies on explicit knowledge of dynamical models, is a well-known approach that addresses models' limitations due to various reasons, such as errors in input and forcing data sets. This approach, however, requires intensive computational efforts, especially for high-dimensional systems such as distributed hydrological models. Alternatively, data-driven methods offer comparable solutions when the physics underlying the models are unknown. For the first time in a hydrological context, a nonparametric framework is implemented here to improve model estimates using available observations. This method uses Takens delay coordinate method to reconstruct the dynamics of the system within a Kalman filtering framework, called the Kalman-Takens filter. A synthetic experiment is undertaken to fully investigate the capability of the proposed method by comparing its performance with that of a standard assimilation framework based on an adaptive unscented Kalman filter (AUKF). Furthermore, using terrestrial water storage (TWS) estimates obtained from the Gravity Recovery And Climate Experiment mission, both filters are applied to a real case scenario to update different water storages over Australia. In situ groundwater and soil moisture measurements within Australia are used to further evaluate the results. The Kalman-Takens filter successfully improves the estimated water storages at levels comparable to the AUKF results, with an average root-mean-square error reduction of 37.30% for groundwater and 12.11% for soil moisture estimates. Additionally, the Kalman-Takens filter, while reducing estimation complexities, requires a fraction of the computational time, that is, ∼8 times faster compared to the AUKF approach.

Original languageEnglish (US)
Pages (from-to)4946-4964
Number of pages19
JournalWater Resources Research
Issue number7
StatePublished - Jul 2018

Bibliographical note

Funding Information:
We would like to thank Tyrus Berry and Timothy Sauer for their valuable help in this study. M. Khaki is grateful for the research grant of Curtin International Postgraduate Research Scholarships (CIPRS)/ORD Scholarship provided by Curtin University (Australia). F. Hamilton is supported by National Science Foundation grant RTG/DMS-1246991. This work is a TIGeR publication. The GRACE data are acquired from the ITSG-Grace2014 gravity field model (Mayer-Gürr et al., 2014). In situ groundwater and soil moisture measurements are obtained from the New South Wales Government (NSW; gw.shtml) and the OzNet network (, respectively. Meteorological forcing data are provided by Princeton University (http://hydrology. Other data used in this study can be found at DOI: 10.6084/m9.figshare.5942548. A more detailed discussion of the results can be found in the supporting information (Huffman et al., 2007; Mu et al., 2011).

Publisher Copyright:
©2018. American Geophysical Union. All Rights Reserved.


  • Kalman-Takens
  • adaptive unscented Kalman filtering (AUKF)
  • data assimilation
  • hydrological modeling
  • nonparametric filtering

ASJC Scopus subject areas

  • Water Science and Technology


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