Error covariance calculation for forecast bias estimation in hydrologic data assimilation

To date, an outstanding issue in hydrologic data assimilation is a proper way of dealing with forecast bias. A frequently used method to bypass this problem is to rescale the observations to the model climatology. While this approach improves the variability in the modeled soil wetness and discharge, it is not designed to correct the results for any bias. Alternatively, attempts have been made towards incorporating dynamic bias estimates into the assimilation algorithm. Persistent bias models are most often used to propagate the bias estimate, where the a priori forecast bias error covariance is calculated as a constant fraction of the unbiased a priori state error covariance. The latter approach is a simplification to the explicit propagation of the bias error covariance. The objective of this paper is to examine to which extent the choice for the propagation of the bias estimate and its error covariance influence the filter performance. An Observation System Simulation Experiment (OSSE) has been performed, in which ground water storage observations are assimilated into a biased conceptual hydrologic model. The magnitudes of the forecast bias and state error covariances are calibrated by optimizing the innovation statistics of groundwater storage. The obtained bias propagation models are found to be identical to persistent bias models. After calibration, both approaches for the estimation of the forecast bias error covariance lead to similar results, with a realistic attribution of error variances to the bias and state estimate, and significant reductions of the bias in both the estimates of groundwater storage and discharge. Overall, the results in this paper justify the use of the traditional approach for online bias estimation with a persistent bias model and a simplified forecast bias error covariance estimation.