Data assimilation in integrated hydrological modelling in the presence of observation bias

Abstract. The use of bias-aware Kalman filters for estimating and correcting observation bias in groundwater head observations is evaluated using both synthetic and real observations. In the synthetic test, groundwater head observations with a constant bias and unbiased stream discharge observations are assimilated in a catchment-scale integrated hydrological model with the aim of updating stream discharge and groundwater head, as well as several model parameters relating to both streamflow and groundwater modelling. The coloured noise Kalman filter (ColKF) and the separate-bias Kalman filter (SepKF) are tested and evaluated for correcting the observation biases. The study found that both methods were able to estimate most of the biases and that using any of the two bias estimation methods resulted in significant improvements over using a bias-unaware Kalman filter. While the convergence of the ColKF was significantly faster than the convergence of the SepKF, a much larger ensemble size was required as the estimation of biases would otherwise fail. Real observations of groundwater head and stream discharge were also assimilated, resulting in improved streamflow modelling in terms of an increased Nash–Sutcliffe coefficient while no clear improvement in groundwater head modelling was observed. Both the ColKF and the SepKF tended to underestimate the biases, which resulted in drifting model behaviour and sub-optimal parameter estimation, but both methods provided better state updating and parameter estimation than using a bias-unaware filter.