Changepoint Detection in Hydrologic Series of the Mahanadi River Basin Using a Fuzzy Bayesian Approach

Changepoint (CP) detection methods can be applied to a broad range of real-world problems and are recently gaining popularity in hydrologic studies. The hydrology of river basins is impacted by several factors such as changes in land use, operation of water storage and distribution systems, and climate change; and as a result, a hydrologic series may exhibit distributional shifts and nonstationarity. In this paper, a fuzzy Bayesian model is studied for CP detection in hydrologic time series of annual rainfall and streamflow in the Mahanadi River Basin in India. The model is based on a two-step, fuzzy Bayesian formulation, which gives a probability distribution for the location of the CP. The methodology has broad applicability since it does not require making any distributional assumptions for the data. The first step consists of a fuzzy clustering of raw time series which transforms the initial data with arbitrary distribution into data that can be approximated with a beta distribution. The second step uses the Bayesian approach with the Markov Chain Monte Carlo (MCMC) method for CP detection in the transformed time series. The method is applied to annual maximum and annual average streamflow and subbasin rainfall for Basantpur and Hirakud stations on the Mahanadi river in India. The results obtained are compared with those obtained using standard CP detection procedures, such as a modified standard normal homogeneity (SNH) test and Wilcoxon's nonparametric rank sum test. Both classical and Bayesian CP detection methods used show that the annual streamflow and the annual rainfall have decreased significantly in the Mahanadi Basin, with a possible CP for the Basantpur station between 1975 and 1980 and for the Hirakud station around 1964. The abrupt decrease was most marked in the annual maximum streamflow series for the Basantpur and Hirakud stations and was attributed to the effects of climate change in the upstream regions of the Mahanadi River.