Estimating intermediate water residence times (a few years to a century) in shallow aquifers is critical to quantifying groundwater vulnerability to nutrient loading and estimating realistic recovery timelines. While intermediate groundwater residence times are currently determined with atmospheric tracers such as chlorofluorocarbons (CFCs), these analyses are costly and would benefit from other tracer approaches to compensate for the decreasing resolution of CFC methods in the 5-20 years range. In this context, we developed a framework to assess the capacity of dissolved silica (DSi) to inform residence times in shallow aquifers. We calibrated silicate weathering rates with CFCs from multiple wells in five crystalline aquifers in Brittany and in the Vosges Mountains (France). DSi and CFCs were complementary in determining apparent weathering reactions and residence time distributions (RTDs) in shallow aquifers. Silicate weathering rates were surprisingly similar among Brittany aquifers, varying from 0.20 to 0.23 mg L yr with a coefficient of variation of 7%, except for the aquifer where significant groundwater abstraction occurred, where we observed a weathering rate of 0.31 mg L yr. The silicate weathering rate was lower for the aquifer in the Vosges Mountains (0.12 mg L yr), potentially due to differences in climate and anthropogenic solute loading. Overall, these optimized silicate weathering rates are consistent with previously published studies with similar apparent ages range. The consistency in silicate weathering rates suggests that DSi could be a robust and cheap proxy of mean residence times for recent groundwater (5-100 years) at the regional scale. This methodology could allow quantification of seasonal groundwater contributions to streams, estimation of residence times in the unsaturated zone and improve assessment of aquifer vulnerability to anthropogenic pollution.

Residence Times in aquifers result from their internal structure, from the hydrodynamic transport processes and from the recharge conditions to which they are exposed. Beyond the already known residence time distributions (RTD) for either constant aquifer thickness and/or uniform recharge, we investigate the effect of both distributed aquifer thickness and distributed recharge. We develop a semi-analytical approximation of the RTD for generic trapezoidal aquifers exposed to linearly-variable recharges. The solution is derived for a homogeneous 2D cross-sectional aquifer in steady-state conditions following the Dupuit-Forchheimer assumption according to which the vertical head gradients are much smaller than the horizontal head gradients. Close agreement with 2D numerical simulations demonstrates the relevance of the Dupuit-Forchheimer assumption to estimate RTDs as long as the aquifer thickness remains an order of magnitude smaller than the aquifer length. At equivalent aquifer volume, geometrical structure and recharge conditions result in non-trivial and complex RTD shapes that may be uniform, Gamma-like, power-law-like shapes as well as any Residence Time Distributions in non-uniform aquifer recharge and thickness conditions 2/43 intermediary shapes. The variety of RTD shapes encountered show the need to systematically include the aquifer structure and recharge conditions in the assessment of RTDs and for their subsequent use for problematics related to water quality. The semi-analytical approximation can be further used in a variety of aquifer systems in complement with other existing solutions as a Lumped Parameter Model for RTDs. Letters 43,

Water transit times vary over several orders of magnitude in between and within each of the main compartments of the hydrological cycle (Sprenger et al., 2019). This distribution has fundamental consequences for the water availability, renewal (Gleeson et al., 2016;Jasechko et al., 2017) and quality (Appelo & Postma, 1994;Wachniew et al., 2016). This is especially the case for shallow aquifers in direct connection to anthropogenic activities. Water ages broadly range from some weeks to several decades. This has immediate consequences on the transmission or buffering of recharge deficits and contamination loads (Cuthbert et al., 2019). Being intermediary between the surface and the deeper subsurface, shallow subsurface flows are potentially controlled by both geology and geomorphology (