Data assimilation for distributed hydrological catchment modeling via ensemble Kalman filter

Catchment scale hydrological models are critical decision support tools for water resources management and environment remediation. However, the reliability of hydrological models is inevitably affected by limited measurements and imperfect models. Data assimilation techniques combine complementary information from measurements and models to enhance the model reliability and reduce predictive uncertainties. As a sequential data assimilation technique, the ensemble Kalman filter (EnKF) has been extensively studied in the earth sciences for assimilating in-situ measurements and remote sensing data. Although the EnKF has been demonstrated in land surface data assimilations, there are no systematic studies to investigate its performance in distributed modeling with high dimensional states and parameters. In this paper, we present an assessment on the EnKF with state augmentation for combined state-parameter estimation on the basis of a physical-based hydrological model, Soil and Water Assessment Tool (SWAT). Through synthetic simulation experiments, the capability of the EnKF is demonstrated by assimilating the runoff and other measurements, and its sensitivities are analyzed with respect to the error specification, the initial realization and the ensemble size. It is found that the EnKF provides an efficient approach for obtaining a set of acceptable model parameters and satisfactory runoff, soil water content and evapotranspiration estimations. The EnKF performance could be improved after augmenting with other complementary data, such as soil water content and evapotranspiration from remote sensing retrieval. Sensitivity studies demonstrate the importance of consistent error specification and the potential with small ensemble size in the data assimilation system.

[1]  P. Kitanidis,et al.  Real‐time forecasting with a conceptual hydrologic model: 2. Applications and results , 1980 .

[2]  Jeffrey G. Arnold,et al.  The Soil and Water Assessment Tool: Historical Development, Applications, and Future Research Directions , 2007 .

[3]  D. Aubert,et al.  Sequential assimilation of soil moisture and streamflow data in a conceptual rainfall-runoff model , 2003 .

[4]  Henrik Madsen,et al.  Parameter estimation in distributed hydrological catchment modelling using automatic calibration with multiple objectives , 2003 .

[5]  Wade T. Crow,et al.  Comparison of adaptive filtering techniques for land surface data assimilation , 2008 .

[6]  Yan Chen,et al.  Data assimilation for transient flow in geologic formations via ensemble Kalman filter , 2006 .

[7]  C. Willmott,et al.  Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance , 2005 .

[8]  Patrick Willems,et al.  Parameter estimation in semi‐distributed hydrological catchment modelling using a multi‐criteria objective function , 2007 .

[9]  Peter Droogers,et al.  Calibration of a distributed hydrological model based on satellite evapotranspiration , 2008 .

[10]  Gabrielle De Lannoy,et al.  Improvement of modeled soil wetness conditions and turbulent fluxes through the assimilation of observed discharge , 2006 .

[11]  Peter A. Troch,et al.  Catchment-scale hydrological modeling and data assimilation , 2003 .

[12]  Alexander Y. Sun,et al.  Comparison of deterministic ensemble Kalman filters for assimilating hydrogeological data , 2009 .

[13]  D. McLaughlin,et al.  Hydrologic Data Assimilation with the Ensemble Kalman Filter , 2002 .

[14]  D. McLaughlin,et al.  Assessing the Performance of the Ensemble Kalman Filter for Land Surface Data Assimilation , 2006 .

[15]  Misgana K. Muleta,et al.  Sensitivity and uncertainty analysis coupled with automatic calibration for a distributed watershed model , 2005 .

[16]  G. Evensen Data Assimilation: The Ensemble Kalman Filter , 2006 .

[17]  Edzer J. Pebesma,et al.  Latin Hypercube Sampling of Gaussian Random Fields , 1999, Technometrics.

[18]  Qian Hong,et al.  Parameter uncertainty analysis of the non-point source pollution in the Daning River watershed of the Three Gorges Reservoir Region, China. , 2008, The Science of the total environment.

[19]  Dong-Jun Seo,et al.  The distributed model intercomparison project (DMIP): Motivation and experiment design , 2004 .

[20]  R. Reichle Data assimilation methods in the Earth sciences , 2008 .

[21]  Wade T. Crow,et al.  An adaptive ensemble Kalman filter for soil moisture data assimilation , 2007 .

[22]  G. Blöschl,et al.  Soil moisture updating by Ensemble Kalman Filtering in real-time flood forecasting , 2008 .

[23]  P. Houtekamer,et al.  Ensemble size, balance, and model-error representation in an ensemble Kalman filter , 2002 .

[24]  R. Ibbitt,et al.  Hydrological data assimilation with the ensemble Kalman filter: Use of streamflow observations to update states in a distributed hydrological model , 2007 .

[25]  I. Rodríguez‐Iturbe,et al.  Random Functions and Hydrology , 1984 .

[26]  D. Seo,et al.  Overall distributed model intercomparison project results , 2004 .

[27]  Wade T. Crow,et al.  A land surface data assimilation framework using the land information system : Description and applications , 2008 .

[28]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

[29]  Peter K. Kitanidis,et al.  Real‐time forecasting with a conceptual hydrologic model: 1. Analysis of uncertainty , 1980 .

[30]  Thomas J. Jackson,et al.  Modeling and assimilation of root zone soil moisture using remote sensing observations in Walnut Gulch Watershed during SMEX04 , 2008 .

[31]  Dongxiao Zhang,et al.  Investigation of flow and transport processes at the MADE site using ensemble Kalman filter , 2008 .

[32]  D. Hollinger,et al.  An improved state-parameter analysis of ecosystem models using data assimilation , 2008 .

[33]  M. Bierkens,et al.  Assimilation of remotely sensed latent heat flux in a distributed hydrological model , 2003 .

[34]  Jon C. Helton,et al.  Latin Hypercube Sampling and the Propagation of Uncertainty in Analyses of Complex Systems , 2002 .

[35]  Soroosh Sorooshian,et al.  Dual state-parameter estimation of hydrological models using ensemble Kalman filter , 2005 .

[36]  Dennis McLaughlin,et al.  An integrated approach to hydrologic data assimilation: interpolation, smoothing, and filtering , 2002 .

[37]  Jeffrey G. Arnold,et al.  Soil and Water Assessment Tool Theoretical Documentation Version 2009 , 2011 .

[38]  Wade T. Crow,et al.  Impact of Incorrect Model Error Assumptions on the Sequential Assimilation of Remotely Sensed Surface Soil Moisture , 2006 .

[39]  Dara Entekhabi,et al.  An Ensemble Multiscale Filter for Large Nonlinear Data Assimilation Problems , 2008 .