### Abstract

The traditional hydrological time series methods tend to focus on the mean of whichever variable is analysed but neglect its time-varying variance (i.e. assuming the variance remains constant). The variances of hydrological time series vary with time under anthropogenic influence. There is evidence that extensive well drilling and groundwater pumping can intercept groundwater run-off and consequently induce spring discharge volatility or variance varying with time (i.e. heteroskedasticity). To investigate the time-varying variance or heteroskedasticity of spring discharge, this paper presents a seasonal autoregressive integrated moving average with general autoregressive conditional heteroskedasticity (SARIMA-GARCH) model, whose the SARIMA model is used to estimate the mean of hydrological time series, and the GARCH model estimates its time-varying variance. The SARIMA-GARCH model was then applied to the Xin'an Springs Basin, China, where extensive groundwater development has occurred since 1978 (e.g. the average annual groundwater pumping rates were less than 0.20m<sup>3</sup>/s in the 1970s, reached 1.20m<sup>3</sup>/s at the end of the 1980s, surpassed 2.0m<sup>3</sup>/s in the 1990s and exceeded 3.0m<sup>3</sup>/s by 2007). To identify whether human activities or natural stressors caused the heteroskedasticity of Xin'an Springs discharge, we segmented the spring discharge sequence into two periods: a predevelopment stage (i.e. 1956-1977) and a developed stage (i.e. 1978-2012), and set up the SARIMA-GARCH model for the two stages, respectively. By comparing the models, we detected the role of human activities in spring discharge volatility. The results showed that human activities caused the heteroskedasticity of the Xin'an Spring discharge. The predicted Xin'an Springs discharge by the SARIMA-GARCH model showed that the mean monthly spring discharge is predicted to continue to decline to 0.93m<sup>3</sup>/s in 2013, 0.67m<sup>3</sup>/s in 2014 and 0.73m<sup>3</sup>/s in 2015.

Original language | English (US) |
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Pages (from-to) | 2855-2866 |

Number of pages | 12 |

Journal | Hydrological Processes |

Volume | 29 |

Issue number | 13 |

DOIs | |

Publication status | Published - Jun 30 2015 |

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### Keywords

- Anthropogenic activities
- Heteroskedasticity
- Karst spring
- Piecewise analysis
- SARIMA-GARCH model
- The Xin'an Springs

### ASJC Scopus subject areas

- Water Science and Technology

### Cite this

*Hydrological Processes*,

*29*(13), 2855-2866. https://doi.org/10.1002/hyp.10407