A Grey Seasonal Index Model for Forecasting Groundwater Depth of Ningxia Plain

Forecasting the depth of groundwater in arid and semiarid areas is a great challenge because these areas are complex hydrogeological environments and the observational data are limited. To deal with this problem, the grey seasonal index model is proposed. The seasonal characteristics of time series were represented by indicators, and the grey model with fractional-order accumulation was employed to fit and forecast different periodic indicators and long-term trends, respectively. Then, the prediction results of the two were combined together to obtain the prediction results. To verify the model performance, the proposed model is applied to groundwater prediction in Yinchuan Plain. The results show that the fitting error of the proposed model is 2.08%, while for comparison, the fitting error of the grey model of data grouping and Holt–Winters model is 3.94% and 5%, respectively. In the same way, it is concluded that the fitting error of groundwater in Weining Plain by the proposed model is 2.26%. On the whole, the groundwater depth in Ningxia Plain including Yinchuan Plain and Weining Plain will increase further.