Calibration of a distributed flood forecasting model with input uncertainty using a Bayesian framework

In the process of calibrating distributed hydrological models, accounting for input uncertainty is important, yet challenging. In this study, we develop a Bayesian model to estimate parameters associated with a geomorphology-based hydrological model (GBHM). The GBHM model uses geomorphic characteristics to simplify model structure and physically based methods to represent hydrological processes. We divide the observed discharge into low- and high-flow data, and use the first-order autoregressive model to describe their temporal dependence. We consider relative errors in rainfall as spatially distributed variables and estimate them jointly with the GBHM parameters. The joint posterior probability distribution is explored using Markov chain Monte Carlo methods, which include Metropolis-Hastings, delay rejection adaptive Metropolis, and Gibbs sampling methods. We evaluate the Bayesian model using both synthetic and field data sets. The synthetic case study demonstrates that the developed method generally is effective in calibrating GBHM parameters and in estimating their associated uncertainty. The calibration ignoring input errors has lower accuracy and lower reliability compared to the calibration that includes estimation of the input errors, especially under model structure uncertainty. The field case study shows that calibration of GBHM parameters under complex field conditions remains a challenge. Although jointly estimating input errors and GBHM parameters improves the continuous ranked probability score and the consistency of the predictive distribution with the observed data, the improvement is incremental. To better calibrate parameters in a distributed model, such as GBHM here, we need to develop a more complex model and incorporate much more information.