Hydrogeological controls of the Residence Time Distribution: insights from analytical solutions and numerical modelling

Abstract:

The residence time distribution (RTD) is a singular feature in hydrology that has been receiving constant attention for more than half a century. It is not a property of a hydrologic system neither an observable quantity. It is rather a lumped characteristic which makes it a pertinent and useful tool for many problems related to water quality, risk assessment, tracer data interpretation. While climate, geology and topography are recognized as the main drivers of recharge and flow patterns, quantifying their impact on transport and RTDs and their degree of interaction remains challenging.

Recent advances exploring the effect of structure (geometry), boundary conditions and heterogeneity on the RTD are presented. The analysis is based on the development of closed-form expressions in parallel to numerical modelling in steady-state and fully-mixed conditions. Numerical models allow to validate analytical developments in addition to explore more complex heterogeneous configurations (e.g. dipping semi-confined aquifers).

Through a large parametric study and a mechanistic interpretation of residence time acquisition, we show that the RTD can take a great variety of shapes with different metrics (quartiles, moments). In particular, the first quartile can be significantly affected confirming the interest of including structure and recharge complexity when possible. Finally, depending on boundary conditions and external forcings, aquifers can play a role as important as aquitards in the increment of residence times which seems counter-intuitive.

The opportunity of closed-form expressions is finally discussed through a comparison with existing frameworks (e.g. shape free RTDs, SAS functions, physically-distributed models) in light of common data acquisition and inverse problem.