A statistical model for karst spring discharge estimation under extensive groundwater development and extreme climate change

To acquire better understanding of spring discharge under extreme climate change and extensive groundwater pumping, this study proposed an extreme value statistical decomposition model, in which the spring discharge was decomposed into three items: a long-term trend; periodic variation; and random fluctuation. The long-term trend was fitted by an exponential function, and the periodic variation was fitted by an exponential function whose index was the sum of two sine functions. A general extreme value (GEV) model was used to obtain the return level of extreme random fluctuation. Parameters of the non-linear long-term trend and periodic variation were estimated by the Levenberg-Marquardt algorithm, and the GEV model was estimated by the maximum likelihood method. The extreme value statistical decomposition model was applied to Niangziguan Springs, China to forecast spring discharge. We showed that the modelled spring discharge fitted the observed data very well. Niangziguan Springs discharge is likely to continue declining with fluctuation, and the risk of cessation by August 2046 is 1%. The extreme value decomposition model is a robust method for analysing the nonstationary karst spring discharge under conditions of extensive groundwater development/pumping, and extreme climate changes. Editor D. Koutsoyiannis; Associate editor J.