Adaptive Rating Curve Estimation: AdaptRatin

Water resource management is impossible without accurate information about stream discharge. However measuring  stream discharge is difficult and therefore stream height measurements, which are easier to obtain, are used as proxies. The conversion of stream height to stream discharge relies on a stage-discharge relationship, which is unique to individual gauging stations and is known as a ‘rating curve’. Accurate assessment  of this  rating curve and accompanying predictions, is essential for effective water resources management. However, the stage-discharge relationship  is often non-stationary, due to erosion or sediment deposition at gauging sites which results from natural processes such as flooding.  As a result, the rating curve needs to be re-calibrated regularly. This paper present an approach to estimate the time varying stage-discharge relationships, which we call  ‘AdaptRatin’. ‘AdaptRatin' first partitions the time-ordered data into an unknown yet finite number of segments, which are locally stationary. Within each segment, the stage-discharge relationship is  modelled non-parametrically by placing a Gaussian process prior over the unknown relationship. We take a Bayesian approach and inference regarding the number and location of locally stationary segments and the corresponding rating curve for each segment  is made via the joint posterior distribution of these quantities. We use  Reversible Jump Markov Chain Monte Carlo (RJMCMC) to obtain a sample based estimate of this joint posterior. We demonstrate the ability of ‘AdaptRatin’ to successfully capture the changes in the stage-discharge relationship over time and provide reliable estimates of the underlying stage-discharge relationship for each time period for both stationary and non-stationary processes.