Optimization of rain gauge sampling density for river discharge prediction using Bayesian calibration.

River discharges are often predicted based on a calibrated rainfall-runoff model. The major sources of uncertainty, namely input, parameter and model structural uncertainty must all be taken into account to obtain realistic estimates of the accuracy of discharge predictions. Over the past years, Bayesian calibration has emerged as a suitable method for quantifying uncertainty in model parameters and model structure, where the latter is usually modelled by an additive or multiplicative stochastic term. Recently, much work has also been done to include input uncertainty in the Bayesian framework. However, the use of geostatistical methods for characterizing the prior distribution of the catchment rainfall is underexplored, particularly in combination with assessments of the influence of increasing or decreasing rain gauge network density on discharge prediction accuracy. In this article we integrate geostatistics and Bayesian calibration to analyze the effect of rain gauge density on river discharge prediction accuracy. We calibrated the HBV hydrological model while accounting for input, initial state, model parameter and model structural uncertainty, and also taking uncertainties in the discharge measurements into account. Results for the Thur basin in Switzerland showed that model parameter uncertainty was the main contributor to the joint posterior uncertainty. We also showed that a low rain gauge density is enough for the Bayesian calibration, and that increasing the number of rain gauges improved model prediction until reaching a density of one gauge per 340 km. While the optimal rain gauge density is case-study specific, we make recommendations on how to handle input uncertainty in Bayesian calibration for river discharge prediction and present the methodology that may be used to carry out such experiments.