Bayesian methods for estimating multi-segment discharge rating curves |
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Authors: | Trond Reitan Asgeir Petersen-Øverleir |
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Institution: | (1) Department of Mathematics, University of Oslo, P. O. Box 1053, Blindern, 0316 Oslo, Norway;(2) Norwegian Water Resources and Energy Directorate, P. O. Box 5091, Majorstua, 0301 Oslo, Norway |
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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 zero-plane 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. |
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Keywords: | Power-law rating curve Stage– discharge relationship Segmented regression Changepoint analysis Bayesian analysis MCMC Extrapolation uncertainty Poisson process |
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