Analytical Expressions of Radiocarbon Distribution in Transient State Unconfined Aquifers and Their Application to Determination of Past and Present Recharges of North Africa Aquifers

In this study, we developed two-dimensional hydrodynamic age expressions for the free-surface aquifer problem required for radiocarbon data interpretation in terms of recharge. Time-varying recharge is accounted for in fully transient or pseudo-steady state alternative analytical expressions applying to weakly or highly hydraulically reactive unconfined aquifers, respectively. These expressions extend the well-known model proposed by Vogel in 1967 and represent a convenient alternative approach to the more complex numerical solution of a particle tracking problem considering climate variability. An application of the developed expressions was carried out to assess past (40 Kyr) and present recharge rates for the North Western Sahara Aquifer System (NWSAS) and the Djeffara plain (Tunisia-Libya). Using the available C-14 data at different outcrops, we obtained local recharge values ranging from 0.2 +/- 1.7 to 4.5 +/- 3.2 mm yr(-1). Here, it is shown that using the standard purely steady-state model for radiocarbon interpretation leads to a present recharge overestimation of up to 360%. A linear relation between the present recharge and the average annual rainfall was obtained and used to identify the regional distribution of the recharge and domain-averaged values. Global values of 1.6 +/- 2.3 mm yr(-1) for the NWSAS and 3.5 +/- 2.3 mm yr(-1) for the Djeffara are in excellent agreement with the values obtained by hydrogeological models and derived using Satellite gravity data. The relation between recharge and rainfall obtained here can be used as a first-order estimate for hydrogeological modeling or water management analysis for aquifers in the Saharan area.