A gray system model for studying the response to climatic change: The Liulin karst springs, China

Gray system theory uses a black-gray-white color spectrum to describe a complex system whose characteristics are only partially known or known with uncertainty. In this study, we use gray system theory to investigate the relation between precipitation and spring flows in a karst region in China. The gray incidence analysis was applied to the Liulin Springs, Shanxi Province, China to analyze the time-lag between spring flow and precipitation. The results showed that the average groundwater residence time at Liulin Spings is about 4 years. The gray system GM(1,2) model was subsequently used as a predictive tool for spring discharge. It was found that model predictions are in agreement with observed data. This study also shows that the discharge of the Liulin Springs primarily responds to climate change; anthropogenic impacts are secondary. The continuous decline of water level in the karst aquifer and waning of spring discharges in semi-arid regions of China might be largely a response of the groundwater system to the decline in regional precipitation over the past two decades.