Correcting unintended perturbation biases in hydrologic data assimilation using Ensemble Kalman filter

Authors: Ryu, Dongryeol; Crow, Wade; ZHAN, X - NOAA NESIDS STAR; Jackson, Thomas

Submitted to: Journal of Hydrometeorology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 12/20/2008
Publication Date: 6/1/2009
Citation: Ryu, D., Crow, W.T., Zhan, X., Jackson, T.J. 2009. Correcting unintended perturbation biases in hydrologic data assimilation using Ensemble Kalman filter. Journal of Hydrometeorology. 10(3):734-750.

Interpretive Summary: Data assimilation is a mathematic process by which information gleaned from independent sources is optimally merged to yield the best single estimate of an unknown variable. In the hydrologic sciences such techniques are commonly applied to minimize errors in soil moisture, streamflow and land surface evaporation estimates which are, in turn, used for agricultural applications including: crop yield forecasting, the optimization of fertilizer application, water quality monitoring and irrigation scheduling. This manuscript addresses a specific technical problem encountered when applying a common data assimilation technique to assimilate remotely sensed information into a nonlinear land surface model. The problem manifests itself in systematic errors within key model predictions (e.g. root-zone soil moisture) of great importance for many agricultural applications. A simple procedure for correcting this error is introduced and evaluated using synthetic data. Positive results for this evaluation demonstrate that following the procedure outlined in the manuscript will enhance the utility of remote sensing and data assimilation techniques for important agricultural and hydrologic applications.

Technical Abstract: Hydrologic data assimilation has become an important tool for improving hydrologic model predictions by utilizing observations from ground, aircraft, and satellite sensors. Among existing data assimilation methods, the ensemble Kalman filter (EnKF) provides a robust framework for optimally updating non-linear model predictions using observations. In the EnKF, background prediction uncertainty is obtained using a Monte Carlo approach where state variables, parameters, and forcing data for the model are synthetically perturbed to explicitly simulate the error-prone representation of hydrologic processes in the model. However, it is shown here that, due to the non-linear nature of these processes, an ensemble of model forecasts perturbed by mean-zero Gaussian noise can produce biased background predictions. This ensemble perturbation bias in soil moisture states can lead to significant mass-balance errors and degrade the performance of the EnKF analysis in deeper soil layers. Here, a simple method of bias correction is introduced where such perturbation bias is corrected using an unperturbed model simulation run in parallel with the EnKF analysis. The proposed bias-correction scheme effectively removes biases in soil moisture and reduces soil water mass-balance errors. The performance of the EnKF is improved in deeper layers when the filter is applied with the bias-correction scheme. The interplay of non-linear hydrologic processes is discussed in the context of perturbation biases, and implications of the bias correction for real data assimilation cases are presented.