Development of a groundwater recharge model

Existing groundwater recharge estimation methods appear to mainly generate site specific groundwater recharge estimates. These methods fail to yield reliable recharge estimates on a regional scale. This is due to failure in accounting for the concepts of heterogeneity, viscoelasticity, and the memory effect. Accordingly, this study was aimed at developing a new approach to groundwater recharge estimation by means of taking these concepts into account. Literature proves that these concepts have been well accounted for in the field of fractional differentiation. This study’s methodological approach entailed obtaining an exact solution to a selected groundwater recharge equation by applying the Laplace and inverse Laplace transform. Upon doing an uncertainty analysis and statistical analysis of the parameters within the solution, it was found that storativity and drainage resistance both require accurate estimation when estimating recharge from the selected equation. Following this, the Caputo derivative, Caputo-Fabrizio derivative, and the Atangana-Baleanu derivative were applied and an exact solution was obtained for each derivative; and upon doing a numerical simulation for each of these solutions, the results depict the behaviour of a particular real world problem. It was concluded that groundwater recharge within a heterogeneous and viscoelastic geological formation is well described with the concept of fractional differentiation with the generalised Mittag-Leffler law or the Atangana-Baleanu fractional derivative. To add, recharge via elastic geological formations can be model via the Caputo and Caputo-Fabrizio derivatives. Furthermore, hydraulic head is assumed to be influenced by uncertain factors which are not accounted for in the general recharge equations. The Eton approach was thus applied, and reveals the uncertain function has a significant effect on hydraulic head distribution. Ultimately, this study concludes that a groundwater recharge model incorporating heterogeneity, viscoelasticity, the memory effect, and uncertainties, will generate a new and improved understanding to groundwater recharge investigations.