Analytical expressions for past and present recharge interpretation of radiocarbon data in unconfined aquifers: application to Saharan 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 extending a previous model based on a constant recharge represent a convenient alternative approach to the more complex numerical resolution of a particle tracking problem considering climate variability. An application of the developed expressions was carried out to assess past (40ky) and present recharge rates for the North Western Saharan Aquifers System (NWSAS) and the Djeffara plain (Tunisia-Libya). Using the available ¹⁴C data at different outcrops, we obtained local recharge values ranging from 1.27 to 6.86 mm yr^-1. 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 1.32 ± 1.47 mm yr^-1 for the NWSAS and 3.97 ± 1.46 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.