Investigation of the Relationship among Rainfall, Unsaturated Water Pressure and Ground Water Level Using Grey System Theory

Rainfall is infiltrated through the surface into the vadose zone and induces the variation of the ground water level. However, the hydrological system of the rainfall infiltration is complex. How to establish the relationship between the rainfall and variation of the ground water level becomes an important topic. In this study, the grey system theory is utilized to investigate the relationship among rainfall, unsaturated water pressure and ground water level. First, the grey relational analysis among ground water level, rainfall and unsaturated water pressure are performed. Six different depths of unsaturated water pressure are used for the grey relational analysis and the depth with the optimal grey relational grade is obtained. Then the GM(1,3) model is established based on sequences of ground water level, rainfall and unsaturated water pressure in the depth with the optimal grey relational grade. Second, the GM(1,2) model is established only using the sequences of ground water level and rainfall data. The comparison of the GM(1,2) and the GM(1,3) models are performed to assess the accuracy of ground water level forecast. Finally, the concept of the time lag is used to reestablish the grey models GM(1,2) and GM(1,3) and predict the variation of ground water level. The results show that the GM(1,3) model has the higher accuracy than the GM(1,2) model for ground water level forecast. The optimal time lag is equal to 23 hours in the study site. The accuracy of the ground water level forecast is higher in the GM(1,3) model with the time lag than the one without it. Keywords:Grey system theory, Ground water level, Rainfall, Unsaturated water pressure.