Bayesian methods for estimating multi-segment discharge rating curves

Abstract

This study explores Bayesian methods for handling compound stage-discharge relationships, a problem which arises in many natural rivers. It is assumed:(1) the stage-discharge relationship in each rating curve segment is a power-law with a location parameter, or zeroplane displacement; (2) the segment transitions are abrupt and continuous; and (3) multiplicative measurement errors are of equal variance. The rating curve fitting procedure is then formulated as a piecewise regression problem where the number of segments and the associated changepoints are assumed unknown. Procedures are developed for describing both global and site-specific prior distributions for all rating curve parameters, including the changepoints. Estimation and uncertainty analysis is evaluated using Markov chain Monte Carlo simulation (MCMC) techniques. The first model explored accounts for parameter and model uncertainties in the interpolated area, i.e. within the range of available stage-discharge measurements. A second model is constructed in an attempt to include the uncertainty in extrapolation, which is necessary when the rating curve is used to estimate discharges beyond the highest or lowest measurement. This is done by assuming that the rate of changepoints both inside and outside the measured area follows a Poisson process. The theory is applied to actual data from Norwegian gauging stations. The MCMC solutions give results that appear sensible and useful for inferential purposes, though the latter model needs further efforts in order to obtain a more efficient simulation scheme.

Derivation of a new continuous adjustment function for correcting wind-induced loss of solid precipitation: results of a Norwegian field study

“…Therefore numerical methods have to be used. This study applies an importance-sampling technique described in Reitan and Petersen-Øverleir (2009) where it was used to select segmentation models in hydraulic rating curve analysis.…”

Generalized extreme value shape parameter and its nature for extreme precipitation using long time series and the Bayesian approach

“…It can, however, be estimated using the Monte Carlo technique known as importance sampling. We used a particular importance sampler, developed by Reitan and Petersen-Øverleir (2009) and also explored by Aas (2010/2011), to calculate the BML, which is briefly described here. (It was later used in other applications.)…”

Flood modelling: parameterisation and inflow uncertainty

“…Functions that are more complex have been developed to better capture transitions to overbank flow. For instance, Reitan and Petersen-Øverleir (2009) proposed the use of multiple powerlaw segments. However, the use of these complex functions is often complicated by a limited number of direct measurements of water levels and discharge during floods, which are needed to parameterise the power-law segments related to high flow conditions.…”