Inverse modeling of the hydrological and the hydrochemical behavior of hydrosystems: Characterization of Karst System Functioning

Abstract

Inverse modeling of mass transfer characterizes the dynamic processes affecting the function of karst systems and can be used to identify karst properties. An inverse model is proposed to calculate unit hydrographs as well as impulse response of fluxes from rainfall‐runoff or rainfall‐flux data, the purpose of which is hydrograph separation. Contrary to what hydrologists have been doing for years, hydrograph separation is carried out by using transfer functions in their entirety, which enables accurate separation of fluxes, as was explained in the companion paper [Pinault et al., this issue]. The unit hydrograph as well as impulse response of fluxes is decomposed into a quick and a slow component, and, consequently, the effective rainfall is decomposed into two parts, one contributing to the quick flow (or flux) and the other contributing to the slow flow generation. This approach is applied to seven French karstic aquifers located on the Larzac plateau in the Grands Causses area (in the south of France). Both hydrodynamical and hydrogeochemical data have been recorded from these springs over several hydrological cycles. For modeling purposes, karst properties can be represented by the impulse responses of flow and flux of dissolved species. The heterogeneity of aquifers is translated to time‐modulated flow and transport at the outlet. Monitoring these fluxes enables the evaluation of slow and quick components in the hydrograph. The quick component refers to the “flush flow” effect and results from fast infiltration in the karst conduit network when connection is established between the infiltration and phreatic zones, inducing an increase in water head. This component reflects flood events where flow behavior is nonlinear and is described by a very short transfer function, which increases and decreases according to water head. The slow component consists of slow and fast infiltration, underground runoff, storage in annex‐to‐drain systems, and discharge from the saturated zone. These components can be further subdivided by measuring chemical responses at the karst outlet. Using such natural tracers enables the slow component of the unit hydrograph to be separated into preevent water, i.e., water of the reservoir and event water, i.e., water whose origin can be related to a particular rainfall event. These measurements can be used to determine the rate of water renewal. Since the preevent water hydrograph is produced by stored water when pushed by a rainfall event and the event water hydrograph reflects rainwater transfer, separating the two components can yield insights into the characteristics of karst aquifers, the modes of infiltration, and the mechanisms involved in karstification, as well as the degree of organization of the aquifer.