Estimating nonlinear hydrological rating curves and discharge using the Bayesian approach

Abstract

Here an objective methodology for establishing hydrological rating curves based on Bayesian statistics is presented. The Bayesian approach naturally combines the statistical model for the data which incorporates the hdyrological model, the data themselves and a priori information which is based on previously collected data and scientific knowledge. Data collected by the Hydrological Service in Iceland at the National energy Authority are analyzed, using scientific and heuristic methods, establishing a priori knowledge about the required parameters. The combination of data and a priori knowledge results in a posterior distribution which is used to estimate parameters of the rating curve and to predict discharge for a given water level. The Bayesian approach provides a more accurate prediction error for discharge than the current approach based on least squares.