A Bayesian Approach to Incorporate Imprecise Information on Hydraulic Knowledge in a River Reach and Assess Prediction Uncertainties in Streamflow Data

Abstract

Daily streamflow records are the basis for many water resources related studies and are almost always taken as free of error. However, streamflow data are not actually measured in the field, but estimated based on daily measurements of water level in conjunction with the rating curve. As the rating curve is only an approximation of the real relationship between water levels and discharge values, daily streamflow data contain uncertainties. The quantitative assessment of these uncertainties is important to obtain a more realistic description of the uncertainties in many water resources related studies. Bayesian inference is very attractive in this case because it can easily incorporate the often imprecise knowledge available on the hydraulic behavior of the river into the analysis, providing a natural way to not only evaluate the uncertainties in the streamflow sample, but also to consider these uncertainties in the estimated hydrologic variable of interest, such as flood quantiles, reservoir yield, water quality parameters, etc. This paper presents a fully Bayesian model capable of incorporating imprecise knowledge on the hydraulic behavior of the river, when available, to estimate the uncertainties in the daily streamflow data. The method was applied to a gauge station in the Madeira River with an abundance of hydrologic knowledge and gauging data, providing an opportunity to understand how prior knowledge on the hydraulics of the river reach, and the amount of measurement data affects uncertainties in the predicted streamflow data.