Evaluation of Hantush’s S Function Estimation Methods for Predicting Rise in Water Table

Hantush’s model is widely used for predicting rise in water table in response to groundwater recharge. Several approximate methods of the Hantush mound function, S(α, β) have been developed to overcome the limitations of Hantush’s tabulated values of the S(α, β) function. These approximate methods have their own advantages and disadvantages, and it is difficult to identify the most accurate and computationally efficient S(α, β) estimation method. In this study, performance of four different algebraic approximate S(α, β) estimation methods are compared with the Hantush method using the published data. The four different methods considered are Swamee and Ohja (1997) (SO), Singh (2012) (SI), Vatankhah (2013) (VA) and Gauss-Legendre quadrature (GL) method with various Gaussian points (GP). Seven statistical accuracy and computation efficiency indicators are used to assess the performance of different S(α, β) estimation methods. The GL method with 100 to16 GPs is found to be the most accurate S(α, β) estimation method. This is followed by the SO, GL with 14 to 12 GPs, VA, GL with 10 GP, SI, and GL with 9 to 3 GPs. A good trade off between accuracy and efficiency is found with the SO, VA, and GL method with 14, 12 and 10 GPs. Comprehensive analysis of different S(α, β) estimation methods, and their ranking based on overall performance index will be helpful in modelling water table rise due to groundwater recharge, optimum design of recharge basin, and evaluation of effectiveness of recharge basins in groundwater recharging.