Disentangling uncertainties in distributed hydrological modeling using multiplicative error models and sequential data assimilation

The quantification of uncertainty in hydrologic modeling is a difficult task, as it arises from a combination of physical measurement errors, errors due to different temporal or spatial scales, and errors in the mathematical description of hydrologic processes. This paper presents an approach to infer during a calibration process the statistical properties of the principal error sources, namely, parameter, precipitation, potential evapotranspiration, and structural model uncertainty, by means of sequential data assimilation (SDA). We perform SDA using a particle filter that combines stochastic universal resampling and kernel smoothing with local shrinkage to improve its performance in comparison to traditional filters. Precipitation, potential evapotranspiration, and structural model uncertainty are incorporated into the calibration process using multiplicative error models. The particle filter is applied to a large-scale distributed model of the Rhine River to demonstrate its usefulness when characterizing error sources. Diagnostic checks and a synthetic case study show that the posterior distributions can be considered as reliable. The posterior multiplier distributions are used to identify whether a systematic bias exists and to illustrate that uncertainty from those sources can be reduced significantly in comparison to the prior assumptions adopted. Evaluating the predictive uncertainty shows that the overall error in hydrologic models is sufficiently characterized by the different error sources used here. Results indicate, however, that the assumptions taken in the output error model and the simplifications of the multiplicative models do not always hold in practice. Therefore, more sophisticated error models and a better quantification of the discharge measurement error are required to further improve characterization of error sources.