A Bayesian analysis of nonstationary generalized extreme value distribution of annual spring discharge minima

Abstract

In many areas throughout the world, extensive groundwater pumping has facilitated significant social development and economic growth, but has typically resulted in a decrease in groundwater level and a decline and change in spring discharge. The declining trend and changing seasonality of spring discharge lead to nonstationarity in hydrological processes. When we apply the generalized extreme value distribution to karst spring discharge, several assumptions including independence, identical distribution, and stationarity must be met. To investigate the response of spring discharge to extensive groundwater development and extreme climate change, a nonstationary generalized extreme value (NSGEV) model is proposed by assuming the location parameter to be the sum of a linear and a periodic temporal function to describe the declining trend and seasonality of spring discharge. Bayes’ theorem treats parameters as random variables and provides ways to convert the prior distribution of parameters into a posterior distribution. Statistical inferences based on posterior distribution can provide a more comprehensive representation of the parameters. In this paper we use Markov Chain Monte Carlo method, which can solve high-dimensional integral computation in the Bayes equation, to estimate the parameters of NSGEV model. Then the NSGEV model was used to calculate the distribution of minimum discharge values of Niangziguan Springs in North China. The results show that NSGEV model is able to represent the distribution of minimum values and to predict the cessation time of Niangziguan Springs discharge with two controllable variables: time and return period. With a 100-year return level, flow cessation of Niangziguan Springs would occur in April 2022. Moreover, the probability of Niangziguan Springs discharge cessation is 1/27 in 2025, and 1/19 in 2030. This implies that the probability of Niangziguan Springs cessation will increase dramatically with time.