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.

RRAWFLOW: Rainfall-Response Aquifer and Watershed Flow Model (v1.15)

“…RRAWFLOW allows the use of as many as two superposed gamma functions, herein referred to as double-gamma IRFs, to produce additional IRF shapes such as a doublepeaked curve; several examples of these are shown in Long and Mahler (2013), except with different combinations of lognormal and exponential functions. Approaches similar to this have been used to represent the components of quick flow and slow flow in watershed modeling (Jakeman and Hornberger, 1993) and for conduit and diffuse flow in karst systems (Pinault et al, 2001;Long, 2009;Long and Mahler, 2013). In these examples, each parametric function represents one of two flow components.…”

“…In many hydrologic systems, however, the IRF changes with changing climatic conditions, resulting in a change in response characteristics (Larocque et al, 1998;Long and Mahler, 2013). Additional details and examples of time-variant IRFs for hydrologic applications include Pinault et al (2001), Jukić and Denić-Jukić (2006), and Long and Mahler (2013).…”

“…Deconvolution methods include Fourier harmonic time-series analysis (Blank et al, 1971;Delleur and Rao, 1971), linear programming (Neuman and de Marsily, 1976), and time-moment analysis (Dreiss, 1989). Estimations of nonparametric IRFs by model calibration include those described by Pinault et al (2001) and Jukić and Denić-Jukić (2006). A potential problem with nonparametric IRFs is that hundreds or even thousands of IRF ordinates may be needed to define the IRF, depending on the IRF length and time step.…”

“…Further, an over-fitted model results in a poor model fit when tested on a conditional validation period that was sequestered from the fitting process. Pinault et al (2001), Jukić and Denić-Jukić (2006), and Ladouche et al (2014) described different methods to constrain the nonparametric IRF and reduce the number of fitting parameters.…”

Flood modelling with a distributed event-based parsimonious rainfall-runoff model: case of the karstic Lez river catchment

“…Black-box or reservoir models are therefore preferred to physical-based models and have thus been widely used for karstic catchments. Some authors use inverse modeling to determine rapid and slow flow impulse response of the karstic system and either identify some properties of karstic systems (Pinault et al, 2001) or propose groundwater level warning thresholds for flash floods (Maréchal et al, 2008). Parsimonious reservoir rainfall-runoff models with interconnected reservoirs are also used as management tools to predict spring discharges (Fleury et al, 2007(Fleury et al, , 2009 or regional water levels (Barrett and Charbeneau, 1997).…”