Development of a groundwater recharge model

[摘要] English: Existing groundwater recharge estimation methods appear to mainly generate site specificgroundwater recharge estimates. These methods fail to yield reliable recharge estimates on aregional 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 togroundwater recharge estimation by means of taking these concepts into account. Literature provesthat these concepts have been well accounted for in the field of fractional differentiation. Thisstudy's methodological approach entailed obtaining an exact solution to a selected groundwaterrecharge equation by applying the Laplace and inverse Laplace transform. Upon doing anuncertainty analysis and statistical analysis of the parameters within the solution, it was found thatstorativity and drainage resistance both require accurate estimation when estimating recharge fromthe selected equation. Following this, the Caputo derivative, Caputo-Fabrizio derivative, and theAtangana-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 behaviourof a particular real world problem. It was concluded that groundwater recharge within aheterogeneous and viscoelastic geological formation is well described with the concept of fractionaldifferentiation with the generalised Mittag-Leffler law or the Atangana-Baleanu fractionalderivative. To add, recharge via elastic geological formations can be model via the Caputo andCaputo-Fabrizio derivatives. Furthermore, hydraulic head is assumed to be influenced by uncertainfactors which are not accounted for in the general recharge equations. The Eton approach was thusapplied, 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 improvedunderstanding to groundwater recharge investigations.

[发布机构] University of the Free State