Journal cover Journal topic
Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
Hydrol. Earth Syst. Sci., 17, 3499-3521, 2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
13 Sep 2013
Simultaneous estimation of model state variables and observation and forecast biases using a two-stage hybrid Kalman filter
V. R. N. Pauwels1, G. J. M. De Lannoy2, H.-J. Hendricks Franssen3, and H. Vereecken3 1Department of Civil Engineering, Monash University, Clayton, Victoria, Australia
2NASA Goddard Space Flight Center, Greenbelt, MD, USA
3Forschungszentrum Jülich GmbH, Agrosphere (IBG-3), Jülich, Germany
Abstract. In this paper, we present a two-stage hybrid Kalman filter to estimate both observation and forecast bias in hydrologic models, in addition to state variables. The biases are estimated using the discrete Kalman filter, and the state variables using the ensemble Kalman filter. A key issue in this multi-component assimilation scheme is the exact partitioning of the difference between observation and forecasts into state, forecast bias and observation bias updates. Here, the error covariances of the forecast bias and the unbiased states are calculated as constant fractions of the biased state error covariance, and the observation bias error covariance is a function of the observation prediction error covariance. In a series of synthetic experiments, focusing on the assimilation of discharge into a rainfall-runoff model, it is shown that both static and dynamic observation and forecast biases can be successfully estimated. The results indicate a strong improvement in the estimation of the state variables and resulting discharge as opposed to the use of a bias-unaware ensemble Kalman filter. Furthermore, minimal code modification in existing data assimilation software is needed to implement the method. The results suggest that a better performance of data assimilation methods should be possible if both forecast and observation biases are taken into account.

Citation: Pauwels, V. R. N., De Lannoy, G. J. M., Hendricks Franssen, H.-J., and Vereecken, H.: Simultaneous estimation of model state variables and observation and forecast biases using a two-stage hybrid Kalman filter, Hydrol. Earth Syst. Sci., 17, 3499-3521,, 2013.
Publications Copernicus