The physics behind groundwater recession and hydrologically passive mixing volumes
Authors: Bhaduri Baibaswata , Fovet Ophelie , Muddu Sekhar , Ruiz Laurent 
Published: May 2023

Abstract. Transit time and water age characteristics are fundamental descriptors of catchment response, and their determination is vital for the implementation of sustainable strategies for managing nutrients and other contaminants in water environments – especially for groundwater where the deeper stores take decades to flush the dissolved solutes. The deterministic transit time models can be broadly categorized into 2 sorts – lumped models based on conceptual parameters and distributed models based on physical and quantifiable hydrodynamic parameters. Due to their simplicity, applicability and flexibility, lumped conceptual models are thus far widely and successfully used in modelling the groundwater flow, transport, and transit time of solutes. Usually, a bunch of parallel hydrological response units work in harmony to model the desired hydrological and solute concentration time-series. But sole reliance on calibration, non-scalability, leveraging on hydrologically passive mixing volumes, lack of forward modelling potential and ineffective scrutiny of the physical basis of the parameters of these conceptual models often generate skepticism in the research community. To address this issue, we devised a technique to determine the physical basis of these conceptual reservoirs, and to establish a mathematical connection between physical hydrodynamic parameters and lumped conceptual parameters. A lumped groundwater nitrate transit time model composed of two parallel stores (slow and fast) was previously calibrated (using GLUE) to generate the time series of baseflow and nitrate concentration time series in a groundwater dominated agricultural catchment in France. In this study, we generated synthetic 2D Dupuit-Forchheimer unconfined aquifers using a standard finite element code (FEFLOW 7.5) to replicate outputs of the lumped model. Furthermore, sensitivity tests were performed on these synthetic catchments and overall, a clear mathematical connection between physical and conceptual parameters was demonstrated. It was further observed that the difference between fast and slow stores can be explained using dual porosity – with drainable porosity affecting recession, and immobile porosity affecting the size of hydrologically passive mixing volumes. The spatial mean of the age distributions, the mean transit time and the half nitrate recovery time agreed with each other for both stores. Further sensitivity tests showed that lumped conceptual stores individually cannot acknowledge dispersivity – the difference in attenuation of different stores, in unison, produce a pseudo-dispersive behavior. Also, being purely depth-based, there is a scale issue in lumped models – an erroneous input of catchment dimension can yield the identical results for a completely different set of hydrodynamic parameters leading to equifinality. Therefore, transit times should always be normalized by catchment scale while cross-comparing catchments using lumped models. These finding can help reduce calibration reliance of lumped models, providing options to investigate parameter effectiveness, and offers these models a forward modelling potential which can be used to calculate the flow and transport behavior of catchments that lack long term observed time series but have proper measurements of hydrodynamic properties.