Abstract

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.

Highlights

  • During the last decade, data assimilation has been frequently applied for the correction of errors in hydrologic model results

  • Other studies have focused on the estimation of the forecast bias in addition to the model state variables, using the discrete (Kalman, 1960) and the ensemble Kalman filter for both linear and nonlinear systems, in a Published by Copernicus Publications on behalf of the European Geosciences Union

  • = bok−+1 fk,k−1(.) is a nonlinear operator representing the model in state-space, including the model parameters and the meteorological forcings. i is the ensemble member number, and wik−1 is a realization of the model error, which can be obtained by a perturbation of the model parameters, state variables, and/or meteorological forcings

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Summary

Introduction

Data assimilation has been frequently applied for the correction of errors in hydrologic model results. A number of methods are available for this purpose, of which the most commonly used are Newtonian nudging (Stauffer and Seaman, 1990), the extended Kalman filter (Welch and Bishop, 1995), the ensemble Kalman filter (Evensen, 1994), variational assimilation (Rabier et al, 2000), and the particle filter (Gordon et al, 1993). These methods have been applied for the assimilation of various variables. Other studies have focused on the estimation of the forecast bias in addition to the model state variables, using the discrete (Kalman, 1960) and the ensemble Kalman filter for both linear and nonlinear systems, in a Published by Copernicus Publications on behalf of the European Geosciences Union

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