# Dynamics of the Flow Exchanges between Matrix and Conduits in Karstified Watersheds at Multiple Temporal Scales

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}reacts with carbonate rock and (3) hydraulic gradient is sufficiently high to ensure the water renewal and to maintain the karstification potential [1]. This results in complex structures with a heterogeneous permeability field and non-linear hydraulic behavior. Drainage in karstic systems consists of an underground self-organized structure leading to preferential water pathways through a conduit network embedded in either a porous matrix which sometimes is highly permeable (i.e., Floridan Karst aquifer) or a low permeable fissured matrix [2,3]. This drainage organization might be divided between (1) a ‘main drainage system’ (MDS), associated to rapid transit time and (2) an ‘annexe drainage system’ (ADS), associated with a long period of water residence [4,5]. As a result, groundwater water flow in the karstic system could be divided into several compartments with contrasted hydrodynamic behavior.

^{2}.

## 2. Material and Methods

#### 2.1. Study Sites

^{2}and 13.2 km

^{2}[4]. They belong to the carbonated belt bordering the north of the French Pyrenees. The two systems share a common boundary oriented west-east. South of this boundary, the Baget area is affected by the Alas fault: Jurassic to Cretaceous metamorphic limestone dips 45° to 75° under slaty flysch on the southern border. The valley follows the contact between karstified calcareous formations and impervious flysch oriented in a west-east direction. Jurassic and Palaeozoic metamorphic dolomite and flysch constitute the northern border of the watershed. This corresponds to the Sainte-Suzanne marls, playing the role of a tight barrier. North of this barrier, the Aliou watershed is composed of Aptian limestone. The drainage is done in a north-south direction until the outlet located in the Aliou cave.

#### 2.2. Modeling Approach

#### 2.2.1. Conceptual Reservoir Modeling

_{AB}is the recession coefficient associated with the flow from reservoir A (either E, M, or C) to reservoir B (either M, C, or L) or to the outlet S and Q

_{AB}(L/T) is the discharge from A to B. Discharge in (L

^{3}/T) is computed by the product of Q

_{AB}with the total surface of the recharge area (R

_{A}).

_{EM}= a

_{MC}= 1, a

_{EC}= 2 and a

_{CS}= 4. Then we assume turbulent flow with non-linear law in conduit and capillary flow with linear law in the matrix. Both Aliou and Baget karstic watersheds are well karstified and conduit dominated with a short memory effect [31]. The emptying exponent between reservoir M and C is chosen to be equal to the emptying coefficient for E to M as the exchange between the conduit and the surrounding matrix is mainly determined by the hydraulic conductivity of the fissured system [37]. To give better physical realism to the model, it has been chosen to set all output discharge rate through reservoir C (Figure 2) Also, previous studies have shown that the rainfall-runoff relationship for both Aliou and Baget watersheds may be correctly described by making ET equal to zero [14,38,39].

#### 2.2.2. Model Calibration

_{sim}is the discretized time series simulated by the model, and q

_{obs}is the discretized experimental time series measured in the field. The NSE criterion is fluently used to judge the quality of a rainfall-runoff model [28,34,42,43]. Nonetheless, this criterion tends to favor the conformity of the model for the strong discharge values to the detriment of the weakest ones. Introducing a balance error estimation allows us to better describe the quality of the model in the case where overestimation of discharge during low water could introduce important mass errors between observed and simulated data. Also, the effects of bias introduced by some conditions such as large events can be reduced by data transformation [44] or by including the bias as an explicit component, as for the Kling-Gupta efficiency KGE [45]. Here the optimization function W

_{obj}is defined such as:

#### 2.2.3. Scale Effects

## 3. Results and Discussion

#### 3.1. Short-term Varibility of Internal Fluxes

_{MC}shows negative values, which means that the reservoir C feeds the reservoir M. Then, at the end of the rainfall event, the water level in all reservoir drops with different dynamics and after about two days without rainfall, the fluxes between reservoir M and C change direction. Then, the reservoir M feeds the reservoir C during recessional, until the next rainfall event (i.e., new water input in the system). These event scale dynamics are consistent with results obtained with a physically-based approach [58,59]. Nonetheless, these approaches need a correct knowledge of flow geometry to give a reliable discretization of the flow path in so-called “reach” were flow and transport parameters may be considered as homogeneous. The matrix-conduit dynamic had also been highlighted using conceptual modeling [60]. Duran [33] highlighted the dynamic fluxes between the conduit and a surrounding matrix over the Norville chalk aquifer using a KarstMod model coupled with turbidity and electrical conductivity analysis. In the study by Duran [33], the fluxes Q

_{MC}represent about 10% of the spring discharge. Over the Baget and Aliou watersheds, the contribution of the fluxes Q

_{MC}in the spring discharge is in the same order of magnitude. Zhang et al., [61] proposed a conceptual model coupled with dissolution rates estimations in “slow flow” and “fast flow” systems. They estimated the contribution of exchange from “slow flow” to “fast flow” systems in three catchments to vary between 64.1% and 87.5%.

#### 3.2. Long-Term Variability of Internal Dynamics

## 4. Conclusions

^{2}) in order to assess the dynamics of internal flow and water levels in the different compartments of the watershed (i.e., Epikarst, Matrix, and Conduit). The modeling has been conducted for two different time steps. Based on this modeling approach, hydrodynamics relationships between reservoirs M and C (representative of the matrix with slow flow and the conduit with fast flow and non-linear behavior, respectively) have been more preferentially explored on the short-term scale (i.e., a rainfall event) and on the long-term scale (i.e., inter-annual scale).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Quinif, Y. Karst et évolution des rivières: Le cas de l’Ardenne. Geodin. Acta
**1999**, 12, 267–277. [Google Scholar] [CrossRef] - Ford, D.; Williams, P.D. Karst Hydrogeology and Geomorphology; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2007; ISBN 978-0-470-84996-5. [Google Scholar]
- Kiraly, L. Karstification and groundwater flow. Speleogenesis Evol. Karst Aquifers
**2003**, 1, 26. [Google Scholar] - Mangin, A. Contribution à l’étude Hydrodynamique des Aquifères Karstiques. Ph.D. Thesis, Université de Bourgogne, Dijon, France, 1975. [Google Scholar]
- Marsaud, B. Structure et Fonctionnement de la Zone Noyée des Karsts à Partir des Résultats Expérimentaux. Ph.D. Thesis, Université de Paris XI Orsay, Paris, France, 1997. [Google Scholar]
- Klimchouk, A. Karst morphogenesis in the epikarstic zone. Cave Karst Sci.
**1995**, 21, 45–50. [Google Scholar] - Batiot, C.; Emblanch, C.; Blavoux, B. Total Organic Carbon (TOC) and magnesium (Mg
^{2+}): Two complementary tracers of residence time in karstic systems. Comptes Rendus Geosci.**2003**, 335, 205–214. [Google Scholar] [CrossRef] - Emblanch, C.; Zuppi, G.; Mudry, J.; Blavoux, B.; Batiot, C. Carbon 13 of TDIC to quantify the role of the unsaturated zone: The example of the Vaucluse karst systems (Southeastern France). J. Hydrol.
**2003**, 279, 262–274. [Google Scholar] [CrossRef] - Garry, B. Etude des Processus d’écoulements de la Zone non Saturée Pour la Modélisation des Aquifères Karstiques: Expérimentation Hydrodynamique et Hydrochimique sur les Sites du Laboratoire Souterrain à Bas Bruit (LSBB) de Rustrel et de Fontaine de Vauclusee. Ph.D. Thesis, Université d’Avignon et des pays de Vaucluse, Avignon, France, 2007. [Google Scholar]
- Lastennet, R. Rôle de la Zone non Saturée Dans le Fonctionnement des Aquifères Karstiques. Approche par l’étude Physico-Chimique et Isotopique du Signal D’entrée et des Exutoires du Massif du Ventoux (Vaucluse). Ph.D. Thesis, Université d’Avignon et des pays de Vaucluse, Avignon, France, 1994. [Google Scholar]
- Puig, J.-M. Le système Karstique de la Fontaine de Vaucluse. Ph.D. Thesis, Université d’Avignon et des pays de Vaucluse, Avignon, France, 1987. [Google Scholar]
- Labat, D.; Hoang, C.T.; Masbou, J.; Mangin, A.; Tchiguirinskaia, I.; Lovejoy, S.; Schertzer, D. Multifractal behavior of long-term karstic discharge fluctuations. Hydrol. Process.
**2013**, 27, 3708–3717. [Google Scholar] [CrossRef] - Labat, D.; Ababou, R.; Mangin, A. Analyse multirésolution croisée de pluies et débits de sources karstiques. Comptes Rendus Géosc.
**2002**, 334, 551–556. [Google Scholar] [CrossRef] - Labat, D.; Mangin, A.; Ababou, R. Rainfall–runoff relations for karstic springs: Multifractal analyses. J. Hydrol.
**2002**, 256, 176–195. [Google Scholar] [CrossRef] - Labat, D.; Ababou, R.; Mangin, A. Introduction of wavelet analyses to rainfall/runoffs relationship for karstic basin: The case of Licq-Atherey karstic system (France). Ground Water
**2001**, 39, 605–615. [Google Scholar] [CrossRef] - Ficchi, A. An adaptative Hydrological Model for Multiple Time-Steps: Diagnostics and Improvements Based on Fluxes Consistency. Ph.D. Thesis, Université Pierre et Marie Curie, Paris, France, 2017. [Google Scholar]
- Harbaugh, A.W. MODFLOW-2005, the U.S. Geological Survay Modular Ground-Water Model-the Ground-Water Flow Process; U.S. Geological Survey Techniques and Methods 6-A16; U.S. Geological Survey: Reston, VA, USA, 2005.
- Hartmann, A.; Goldscheider, N.; Wagener, T.; Lange, J.; Weiler, M. Karst water resources in a changing world: Review of hydrological modeling approaches. Rev. Geophys.
**2014**, 52, 218–242. [Google Scholar] [CrossRef] - Chen, Z.; Goldscheider, N. Modeling spatially and temporally varied hydraulic behavior of a folded karst system with dominant conduit drainage at catchment scale, Hochifen–Gottesacker, Alps. J. Hydrol.
**2014**, 514, 41–52. [Google Scholar] [CrossRef] - Denić-Jukić, V.; Jukić, D. Composite transfer functions for karst aquifers. J. Hydrol.
**2003**, 274, 80–94. [Google Scholar] [CrossRef] - Weiler, M.; McGlynn, B.L.; McGuire, K.J.; McDonnell, J.J. How does rainfall become runoff? A combined tracer and runoff transfer function approach. Water Resour. Res.
**2003**, 39, 1315. [Google Scholar] [CrossRef] - Cormary, Y.; Guilbot, A. Ajustement et réglage des modèles déterministes méthode de calage des paramètres. La Houille Blanche
**1971**, 2, 131–140. [Google Scholar] [CrossRef] - Bezes, C. Contribution à la Modélisation des Systèmes Aquifères Karstiques: Établissement du Modèle Bemer, Son Application à Quatre Systèmes Karstiques du Midi de la France; CERGA: Montpellier, France, 1976. [Google Scholar]
- Thiéry, D. Logiciel GARDIENA Version 8.2: Guide d’utilisation; BRGM: Orléans, France, 2016; p. 126, 65 fig., 2ann; Available online: https://www.brgm.fr/sites/default/brgm/logiciels/gardenia/GARDENIA_v8_2_RP-62797-FR_Notice.pdf (accessed on 18 March 2019).
- Fleury, P.; Plagnes, V.; Bakalowicz, M. Modelling of the functioning of karst aquifers with a reservoir model: Application to Fontaine de Vaucluse (South of France). J. Hydrol.
**2007**, 345, 38–49. [Google Scholar] [CrossRef] - Tritz, S.; Guinot, V.; Jourde, H. Modelling the behavior of a karst system catchment using non-linear hysteretic conceptual model. J. Hydrol.
**2011**, 397, 250–262. [Google Scholar] [CrossRef] - Jourde, H.; Mazzilli, N.; Lecoq, N.; Arfib, B.; Bertin, D. KarstMod: A Generic Modular Reservoir Model Dedicated to Spring Discharge Modeling and Hydrodynamic Analysis in Karst. In Hydrogeological and Environmental Investigations in Karst Systems; Environmental Earth Sciences; Springer: Berlin/Heidelberg, Germany, 2015; pp. 339–344. ISBN 978-3-642-17434-6. [Google Scholar]
- Mazzilli, N.; Guinot, V.; Jourde, H.; Lecoq, N.; Labat, D.; Arfib, B.; Baudement, C.; Danquigny, C.; Dal Soglio, L.; Bertin, D. KarstMod: A modelling platform for rainfall—Discharge analysis and modelling dedicated to karst systems. Environ. Model. Softw.
**2017**. [Google Scholar] [CrossRef] - Bittner, D.; Narany, T.S.; Kohl, B.; Disse, M.; Chiogna, G. Modeling the hydrological impact of land use change in a dolomite-dominated karst system. J. Hydrol.
**2018**, 567, 267–279. [Google Scholar] [CrossRef] - Labat, D.; Masbou, J.; Beaulieu, E.; Mangin, A. Scaling behavior of the fluctuations in stream flow at the outlet of karstic watersheds, France. J. Hydrol.
**2011**, 410, 162–168. [Google Scholar] [CrossRef] - Mangin, A. Pour une meilleure connaissance des systèmes hydrologiques à partir des analyses corrélatoire et spectrale. J. Hydrol.
**1984**, 67, 25–43. [Google Scholar] [CrossRef] - Jourde, H.; Massei, N.; Mazzilli, N.; Binet, S.; Batiot-Guilhe, C.; Labat, D.; Steinmann, M.; Bailly-Comte, V.; Seidel, J.L.; Arfib, B.; et al. SNO KARST: A French Network of Observatories for the Multidisciplinary Study of Critical Zone Processes in Karst Watersheds and Aquifers. Vadose Zone J.
**2018**, 17. [Google Scholar] [CrossRef] - Duran, L. Approche Physique, Conceptuelle et Statistique du Fonctionnement Hydrologique d’un Karst sous Couverture. Ph.D. Thesis, Université de Rouen, Rouen, France, 2015. [Google Scholar]
- Baudement, C.; Mazzilli, N.; Jouves, J.; Guglielmi, Y. Groundwater Management of a Highly Dynamic Karst by Assessing Baseflow and Quickflow with a Rainfall-Discharge Model (Dardennes Springs, SE France). Bull. Soc. Géol. Fr.
**2017**, 188, 40. [Google Scholar] [CrossRef] - Kazakis, N.; Chalikakis, K.; Mazzilli, N.; Ollivier, C.; Manakos, A.; Voudouris, K. Management and research strategies of karst aquifers in Greece: Literature overview and exemplification based on hydrodynamic modelling and vulnerability assessment of a strategic karst aquifer. Sci. Total Environ.
**2018**, 643, 592–609. [Google Scholar] [CrossRef] [PubMed] - Poulain, A.; Watlet, A.; Kaufmann, O.; Camp, M.V.; Jourde, H.; Mazzilli, N.; Rochez, G.; Deleu, R.; Quinif, Y.; Hallet, V. Assessment of groundwater recharge processes through karst vadose zone by cave percolation monitoring. Hydrol. Process.
**2018**, 32, 2069–2083. [Google Scholar] [CrossRef] - Bauer, S.; Liedl, R.; Sauter, M. Modeling of karst aquifer genesis: Influence of exchange flow. Water Resour. Res.
**2003**, 39. [Google Scholar] [CrossRef] [Green Version] - Labat, D.; Ababou, R.; Mangin, A. Rainfall–runoff relations for karstic springs. Part I: Convolution and spectral analyses. J. Hydrol.
**2000**, 238, 123–148. [Google Scholar] [CrossRef] - Labat, D.; Ababou, R.; Mangin, A. Rainfall–runoff relations for karstic springs. Part II: Continuous wavelet and discrete orthogonal multiresolution analyses. J. Hydrol.
**2000**, 238, 149–178. [Google Scholar] [CrossRef] - Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models part I—A discussion of principles. J. Hydrol.
**1970**, 10, 282–290. [Google Scholar] [CrossRef] - Perrin, C.; Michel, C.; Andréassian, V. Does a large number of parameters enhance model performance? Comparative assessment of common catchment model structures on 429 catchments. J. Hydrol.
**2001**, 242, 275–301. [Google Scholar] [CrossRef] - Charlier, J.-B.; Bertrand, C.; Mudry, J. Conceptual hydrogeological model of flow and transport of dissolved organic carbon in a small Jura karst system. J. Hydrol.
**2012**, 460–461, 52–64. [Google Scholar] [CrossRef] - Hartmann, A.; Barberá, J.A.; Lange, J.; Andreo, B.; Weiler, M. Progress in the hydrologic simulation of time variant recharge areas of karst systems—Exemplified at a karst spring in Southern Spain. Adv. Water Resour.
**2013**, 54, 149–160. [Google Scholar] [CrossRef] - Bennett, N.D.; Croke, B.F.W.; Guariso, G.; Guillaume, J.H.A.; Hamilton, S.H.; Jakeman, A.J.; Marsili-Libelli, S.; Newham, L.T.H.; Norton, J.P.; Perrin, C.; et al. Characterising performance of environmental models. Environ. Model. Softw.
**2013**, 40, 1–20. [Google Scholar] [CrossRef] - Gupta, H.V.; Kling, H.; Yilmaz, K.K.; Martinez, G.F. Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. J. Hydrol.
**2009**, 377, 80–91. [Google Scholar] [CrossRef] [Green Version] - Blöschl, G.; Sivapalan, M. Scale issues in hydrological modelling: A review. Hydrol. Process.
**1995**, 9, 251–290. [Google Scholar] [CrossRef] - Ficchì, A.; Perrin, C.; Andréassian, V. Impact of temporal resolution of inputs on hydrological model performance: An analysis based on 2400 flood events. J. Hydrol.
**2016**, 538, 454–470. [Google Scholar] [CrossRef] - Wang, Y.; He, B.; Takase, K. Effects of temporal resolution on hydrological model parameters and its impact on prediction of river discharge/Effets de la résolution temporelle sur les paramètres d’un modèle hydrologique et impact sur la prévision de l’écoulement en rivière. Hydrol. Sci. J.
**2009**, 54, 886–898. [Google Scholar] [CrossRef] - Jothityangkoon, C.; Sivapalan, M. Temporal scales of rainfall-runoff processes and spatial scaling of flood peaks: Space-time connection through catchment water balance. Adv. Water Resour.
**2001**, 24, 1015–1036. [Google Scholar] [CrossRef] - Robinson, J.S.; Sivapalan, M. An investigation into the physical causes of scaling and heterogeneity of regional flood frequency. Water Resour. Res.
**1997**, 33, 1045–1059. [Google Scholar] [CrossRef] [Green Version] - Cholet, C. Fonctionnement Hydrogéologique et Processus de Transport dans les Aquifères Karstiques du Massif du Jura. Ph.D. Thesis, Université de Bourgogne Franche-Comté, Besançon, France, 2017. [Google Scholar]
- Goldscheider, N. A new quantitative interpretation of the long-tail and plateau-like breakthrough curves from tracer tests in the artesian karst aquifer of Stuttgart, Germany. Hydrogeol. J.
**2008**, 16, 1311–1317. [Google Scholar] [CrossRef] [Green Version] - Li, G.; Loper, D.E.; Kung, R. Contaminant sequestration in karstic aquifers: Experiments and quantification. Water Resour. Res.
**2008**, 44. [Google Scholar] [CrossRef] [Green Version] - Mohammadi, Z.; Gharaat, M.J.; Field, M. The Effect of Hydraulic Gradient and Pattern of Conduit Systems on Tracing Tests: Bench-Scale Modeling. Groundwater
**2018**. [Google Scholar] [CrossRef] - Worthington, S.R.H.; Soley, R.W.N. Identifying turbulent flow in carbonate aquifers. J. Hydrol.
**2017**, 552, 70–80. [Google Scholar] [CrossRef] - Ender, A.; Goeppert, N.; Goldscheider, N. Spatial resolution of transport parameters in a subtropical karst conduit system during dry and wet seasons. Hydrogeol. J.
**2018**. [Google Scholar] [CrossRef] - Dewaide, L.; Bonniver, I.; Rochez, G.; Hallet, V. Solute transport in heterogeneous karst systems: Dimensioning and estimation of the transport parameters via multi-sampling tracer-tests modelling using the OTIS (One-dimensional Transport with Inflow and Storage) program. J. Hydrol.
**2016**, 534, 567–578. [Google Scholar] [CrossRef] - Cholet, C.; Charlier, J.-B.; Moussa, R.; Steinmann, M.; Denimal, S. Assessing lateral flows and solute transport during floods in a conduit-flow-dominated karst system using the inverse problem for the advection–diffusion equation. Hydrol. Earth Syst. Sci.
**2017**, 21, 3635–3653. [Google Scholar] [CrossRef] - Charlier, J.-B.; Moussa, R.; Bailly-Comte, V.; Danneville, L.; Desprats, J.-F.; Ladouche, B.; Marchandise, A. Use of a flood-routing model to assess lateral flows in a karstic stream: Implications to the hydrogeological functioning of the Grands Causses area (Tarn River, Southern France). Environ. Earth Sci.
**2015**, 74, 7605–7616. [Google Scholar] [CrossRef] - Bailly-Comte, V.; Martin, J.B.; Jourde, H.; Screaton, E.J.; Pistre, S.; Langston, A. Water exchange and pressure transfer between conduits and matrix and their influence on hydrodynamics of two karst aquifers with sinking streams. J. Hydrol.
**2010**, 386, 55–66. [Google Scholar] [CrossRef] - Zhang, Z.; Chen, X.; Soulsby, C. Catchment-scale conceptual modelling of water and solute transport in the dual flow system of the karst critical zone. Hydrol. Process.
**2017**, 31, 3421–3436. [Google Scholar] [CrossRef] - Anghileri, D.; Pianosi, F.; Soncini-Sessa, R. Trend detection in seasonal data: From hydrology to water resources. J. Hydrol.
**2014**, 511, 171–179. [Google Scholar] [CrossRef] - De Stefano, L.; Duncan, J.; Dinar, S.; Stahl, K.; Strzepek, K.M.; Wolf, A.T. Climate change and the institutional resilience of international river basins. J. Peace Res.
**2012**, 49, 193–209. [Google Scholar] [CrossRef] [Green Version] - Wagener, T.; Sivapalan, M.; Troch, P.A.; McGlynn, B.L.; Harman, C.J.; Gupta, H.V.; Kumar, P.; Rao, P.S.C.; Basu, N.B.; Wilson, J.S. The future of hydrology: An evolving science for a changing world. Water Resour. Res.
**2010**, 46. [Google Scholar] [CrossRef] [Green Version] - Sarrazin, F.; Hartmann, A.; Pianosi, F.; Wagener, T. V2Karst V1.0: A parsimonious large-scale integrated vegetation-recharge model to simulate the impact of climate and land cover change in karst regions. Geosci. Model Dev. Discuss.
**2018**, 11, 4933–4964. [Google Scholar] [CrossRef]

**Figure 1.**Localization of the Aliou (

**a**) and Baget (

**b**) karstic watersheds in the south of France with physiographic maps, modified from [30]. The circle indicates the position of the hydrometric station located at the outlet of the basin.

**Figure 2.**

**Top**: synthetic time series of rainfall, spring discharge (Q

_{spring}) and matrix-conduit flow dynamics (Q

_{MC});

**Bottom**: Structure of the reservoir model: epikarst (E), matrix (M) and conduit (C) are inter-connected from the top to the bottom of the structure. Q

_{MC}corresponds to the flow from reservoir M to reservoir C and depends on the difference between water levels in M and C. The model is considered on several time steps: (

**a**) the water level is higher in reservoir C, so Q

_{MC}< 0; (

**b**) the water level in reservoirs C and M are equal, so Q

_{MC}= 0 and (

**c**) the water level is higher in M so Q

_{MC}> 0.

**Figure 3.**Example of event base time series for KarstMod model on Aliou watershed on the hourly sampling rate: (

**a**) Rainfall time series with observed and simulated discharge; (

**b**) water level in KarstMod reservoirs E, M and C and (

**c**) fluxes between reservoir M and C. When Q

_{MC}> 0, the flow goes from reservoir M to C, otherwise the flow goes from reservoir C to M.

**Figure 4.**MASH of the daily rainfall (w = 30 days, Y = 15 years). The dates correspond to the starting year, noted Ys, for shifting horizon average, so the corresponding shifting horizon period is from the starting year Ys to Ys + 15 years. Due to the 15 years moving average window, the abscissa finished in 2003.

**Figure 6.**Contribution of the exchange between reservoir M and reservoir C to the total discharge on the annual scale (

**left**) and the monthly scale (

**right**).

[24 h] | [1 h] | |||||
---|---|---|---|---|---|---|

Period | Warm-Up | Calibration | Validation | Warm-Up | Calibration | Validation |

from | 1 January 1968 | 1 October1970 | 1 October 1980 | 1 October 2009 | 1 October 2010 | 1 October 2012 |

to | 30 September 1970 | 30 September 1980 | 31 December 2016 | 30 September 2010 | 30 September 2012 | 31 May 2017 |

Parameter | Calibration [24 h] | Calibration [1 h] | ||
---|---|---|---|---|

Aliou | R_{A} | Recharge area | 14.8 km^{2} | 14.2 km^{2} |

k_{EM} | Recession coefficient from E to M | 6.10 × 10^{−3} mm/day | 1.11 × 10^{−4} mm/h | |

k_{EC} | Recession coefficient from E to C | 9.83 × 10^{−3} mm/day | 2.69 × 10^{−3} mm/h | |

k_{CS} | Recession coefficient from C to S | 2.36 × 10^{−3} mm/day | 1.80 × 10^{−4} mm/h | |

k_{MC} | Recession coefficient from M to C | 3.17 × 10^{−1} mm/day | 2.41 × 10^{−2} mm/h | |

Baget | R_{A} | Recharge area | 15.8 km^{2} | 13.1 km^{2} |

k_{EM} | Recession coefficient from E to M | 3.36 × 10^{−3} mm/day | 2.09 × 10^{−4} mm/h | |

k_{EC} | Recession coefficient from E to C | 2.71 × 10^{−3} mm/day | 4.35 × 10^{−4} mm/h | |

k_{CS} | Recession coefficient from C to S | 1.21 × 10^{−3} mm/day | 7.21 × 10^{−4} mm/h | |

k_{MC} | Recession coefficient from M to C | 7.03 × 10^{−2} mm/day | 1.25 × 10^{−1} mm/h |

**Table 3.**Model performances for calibration and validation periods for daily and hourly KarstMod models (NSE: Nash Sutcliff Efficiency, BE: Balance Error and KGE: Kling Gupta Efficiency).

[24 h] | [1 h] | ||||
---|---|---|---|---|---|

Periods | Calibration | Validation | Calibration | Validation | |

(1970–1980) | (1980–2016) | (2010–2012) | (2012–2017) | ||

Aliou | NSE | 0.53 | 0.51 | 0.63 | 0.5 |

BE | 0.88 | 0.97 | 0.99 | 0.91 | |

KGE | 0.58 | 0.51 | 0.67 | 0.54 | |

Baget | NSE | 0.59 | 0.52 | 0.56 | 0.47 |

BE | 0.94 | 0.89 | 0.98 | 0.77 | |

KGE | 0.61 | 0.52 | 0.64 | 0.44 |

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**MDPI and ACS Style**

Sivelle, V.; Labat, D.; Mazzilli, N.; Massei, N.; Jourde, H.
Dynamics of the Flow Exchanges between Matrix and Conduits in Karstified Watersheds at Multiple Temporal Scales. *Water* **2019**, *11*, 569.
https://doi.org/10.3390/w11030569

**AMA Style**

Sivelle V, Labat D, Mazzilli N, Massei N, Jourde H.
Dynamics of the Flow Exchanges between Matrix and Conduits in Karstified Watersheds at Multiple Temporal Scales. *Water*. 2019; 11(3):569.
https://doi.org/10.3390/w11030569

**Chicago/Turabian Style**

Sivelle, Vianney, David Labat, Naomi Mazzilli, Nicolas Massei, and Hervé Jourde.
2019. "Dynamics of the Flow Exchanges between Matrix and Conduits in Karstified Watersheds at Multiple Temporal Scales" *Water* 11, no. 3: 569.
https://doi.org/10.3390/w11030569