Water exchange and pressure transfer between conduits and matrix and their influence on...

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Water exchange and pressure transfer between conduits and matrixand their influence on hydrodynamics of two karst aquifers with sinking streams

Vincent Bailly-Comte a,b,*, Jonathan B. Martin b, Hervé Jourde a, Elizabeth J. Screaton b,Séverin Pistre a, Abigail Langston b

a Hydrosciences Laboratory, UMR 5569, University of Montpellier 2, Place E. Bataillon, 34095 Montpellier Cedex 5, Franceb Department of Geological Sciences, University of Florida, 241 Williamson Hall, PO Box 112120, Gainesville, FL 32611, United States

a r t i c l e i n f o

Article history:Received 9 May 2009Received in revised form 15 January 2010Accepted 7 March 2010

This manuscript was handled by P. BaveyeEditor-in-chief, with the assistance ofMichel Bakalowicz, Associate Editor

Keywords:Karst aquifersHydrograph recessionMatrix–conduit exchangeHydrodynamicsCausse d’AumelasSanta Fe River

s u m m a r y

Karst aquifers are heterogeneous media where conduits usually drain water from lower permeability vol-umes (matrix and fractures). For more than a century, various approaches have used flood recessioncurves, which integrate all hydrodynamic processes in a karst aquifer, to infer physical properties ofthe movement and storage of groundwater. These investigations typically only consider flow to the con-duits and thus have lacked quantitative observations of how pressure transfer and water exchangebetween matrix and conduit during flooding could influence recession curves.

We present analyses of simultaneous discharge and water level time series of two distinctly differentkarst systems, one with low porosity and permeability matrix rocks in southern France, and one withhigh porosity and permeability matrix rocks in north-central Florida (USA). We apply simple mathemat-ical models of flood recession using time series representations of recharge, storage, and discharge pro-cesses in the karst aquifer. We show that karst spring hydrographs can be interpreted according topressure transfer between two distinct components of the aquifer, conduit and matrix porosity, whichinduce two distinct responses at the spring. Water exchange between conduits and matrix porosity suc-cessively control the flow regime at the spring. This exchange is governed by hydraulic head differencesbetween conduits and matrix, head gradients within conduits, and the contrast of permeability betweenconduits and matrix. These observations have consequences for physical interpretations of recessioncurves and modeling of karst spring flows, particularly for the relative magnitudes of base flow and quickflow from karst springs. Finally, these results suggest that similar analyses of recession curves can beapplied to karst aquifers with distinct physical characteristics utilizing well and spring hydrograph data,but information must be known about the hydrodynamics and physical properties of the aquifer beforethe results can be correctly interpreted.

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Introduction

Classical hydrogeological surveys, such as well tests for esti-mating hydrodynamic parameters, tracer experiments, and spele-ological and geophysical observations provide only limitedinformation on karst groundwater behavior because of the hetero-geneous distribution of flow and storage within karst aquifers.Many methods using hydrodynamic or hydrochemical analysesof karst springs have been developed to understand both massand pressure transfers within the aquifer. Primary among thesemethods is analysis of hydrograph recession curves, which as-sumes that spring behavior integrates all processes that occur in

the aquifer. Such recession analyses can be based on many charac-teristics of the spring discharge such as flow, water temperature,chemical or isotopic composition as a ‘‘global response” of thekarst aquifer to input events (Kiraly, 2003). For example, the aimof spring hydrograph separation, which is addressed in this paper,is to infer relative contributions from different components of akarst aquifer (Atkinson, 1977; Bonacci, 1993; Padilla et al.,1994). Although critical to wise use of water resource and remedi-ation of introduced contaminants, water provenances (e.g., infiltra-tion, pre-storm water stored in vadose or phreatic zones, etc.)requires measurements of tracers, typically natural or introducedchemicals, and is not included here.

Spring hydrographs have been used to infer geometric andhydrodynamic properties of the aquifer volumes that controlunderground flows, for example, between flow in large channelsor large fissures and flow in thin fissures (Renault, 1959; Schoeller,1965; Forkasiewicz and Paloc, 1967; Drogue, 1969), or conduit

0022-1694/$ - see front matter � 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.jhydrol.2010.03.005

* Corresponding author at: Hydrosciences Laboratory, UMR 5569, University ofMontpellier 2, Place E. Bataillon, 34095 Montpellier Cedex 5, France.

E-mail address: [email protected] (V. Bailly-Comte).

Journal of Hydrology 386 (2010) 55–66

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flow and diffuse (or matrix) flow (Atkinson, 1977; Baedke andKrothe, 2001; Martin and Dean, 2001; Martin and Screaton,2001). Following the model proposed by Maillet (1905), one ormore exponential functions have been used to describehydrograph recessions. For instance, Schoeller (1965) assumes thatsuccessive exponential decreasing limbs on spring hydrographsare due to changes of flow regimes (from turbulent to laminar).Alternatively, Forkasiewicz and Paloc (1967) believe that the de-cline is due to depletion of various components of the aquiferwhich have successively lower hydraulic conductivity. These inter-pretations suggest that karst systems consist of several parallelreservoirs, all contributing independently to the discharge of thespring. Spring hydrographs are thus described by a model of multi-ple reservoirs, each of which empties with a characteristic expo-nential flow rate. As pointed out by Ford and Williams (2007),however, it seems unrealistic to consider different reservoirs tobe hydraulically isolated from each other. Changes in hydrographshave also been explained to result from changes in catchment area,discharge of temporary springs (overflows), or temporary floodingof poljes or caves (Bonacci, 1993). Mangin (1975) considers thatflood flow occurs when the spring hydrograph is still influencedby underground runoff and/or infiltration through the unsaturatedzone, while a unique exponential decrease according to the Maillet(1905) law characterizes the base flow after infiltration stops. Con-sequently, an inflection point on the recession curve represents theend of the infiltration and is used to separate flood flow (alsocalled quick flow), which demonstrates a non exponential de-crease, from base flow, which demonstrates an exponential de-crease (Mangin, 1975). In this conceptual model, groundwatermovement and storage in fractures or intergranular porosity ofthe matrix is neglected, assuming that the strong contrast of sev-eral orders of magnitude in permeability between matrix and con-duits limits exchange and makes the storage in the matrixnegligible (Bakalowicz, 2005). Following this concept, base flowonly originates from water that was previously stored in largekarst voids called Annex to Drains System (ADS, also called ‘‘karstannexes” (Mangin, 1975; BRGM-CNRS, 1992; Mangin, 1994; Pal-mer, 2003; Bakalowicz, 2005)). These voids are supposed to bepoorly connected with the main karst conduits, resulting in highhydraulic head loss and the observed exponential decrease of dis-charge with time (Mangin, 1975).

Numerical simulations have been used to test the interpretationof karst spring hydrographs. These simulations suggest that tran-sient phenomena near a high hydraulic conductivity network aresufficient to yield the observed exponential decrease that occursbetween the flood flow and base flow phases (Kiraly and Morel,1976; Kiraly, 2003; Kovacs et al., 2005; Kovacs and Perrochet,2008). Eisenlohr et al. (1997) have shown that recession limbs ofspring hydrographs cannot be interpreted solely in terms of infil-tration process and discharge from components of the aquifer thatare characterized by distinct hydraulic conductivities. The shape ofthe recession limbs also depends on the geometry and densityof the high permeability channel network as well as on the formof the recharge function (Geyer et al., 2008).

The various conceptualizations of karst spring hydrographslead to interpretations that can differ from each other or evenbe contradictory, largely because they depend strongly oncharacteristics of each study location, such as climate, dynamicsof recharge, geology, regional hydraulic gradient, degree of kars-tification, and respective volumes of unsaturated and saturatedmaterials. These studies often differentiate a flood flow compo-nent related to fast infiltration and groundwater flows withinaquifer volumes of high hydraulic conductivity (conduits), froma slow component often called base flow, related to the slowdepletion of the low hydraulic conductivity volumes or low per-meability volumes (LPV, (Jeannin, 1996)), which represents the

more or less porous matrix of the karst aquifer (intergranularporosity, joints and/or fractures).

Physical interpretation of recession curves, specifically theseparation between flood and base flow, can be complicatedfor any single aquifer, or between aquifers, because the spatialand temporal distribution of recharge is generally unknown. Fur-thermore, karst aquifers often differ in the relative importance ofmatrix porosity within the aquifer, which depends on burialdepths and resulting alteration of the carbonate. Karst aquifersfound in largely unaltered carbonate rocks has been labeled aseogenetic karst systems, while highly altered, dense, and lowporosity karst aquifers have been labeled as telogenetic karstsystems (Vacher and Mylroie, 2002). This distinction of twotypes of karst aquifers is important because the matrix porositygreatly influence the hydrodynamics of the aquifers (Florea andVacher, 2006). Most hydrodynamic studies of karst aquifers usetelogenetic karst systems as examples and consequently may ne-glect the influence of intergranular matrix porosity on springdischarge (White, 2002). However, exchange of water betweenconduits and matrix occurs during floods (Martin and Dean,2001), when hydraulic gradients between the conduit and matrixare reversed (Atkinson, 1977; Drogue, 1980; Jeannin, 1996; Bail-ly-Comte et al., 2009). These conditions result in base flow thatis zero (or negative) (Kiraly, 2003). Indeed, the widely acceptedassumption that base flow contributes to spring flow at thebeginning of the flood event (see for example Atkinson (1977)or Bonacci (1993)) can only be true if the initial water level inthe LPV is high enough to exceed that within the conduitsthroughout the flood.

Some karst aquifers provide the opportunity to simultaneouslymonitor inflows to conduits from allogenic inputs (i.e. sinkingstream) and outflows from conduits at springs. When conduitsare full of water, pressure is transmitted from the sinking streamto the spring, allowing direct measurement of allogenic recharge.This recharge differs from autogenic recharge where both diffuseand local infiltration through soils and epikarst (Mangin, 1975) dis-tributes groundwater flow in the vadose zone into two distinctflow paths. One flow path contributes to flood flow and occurs inhigh permeability zones and the other is slow flow through thematrix porosity and contributes to base flow (Kiraly, 2003; Perrinet al., 2003).

In this study, only flow from the LPV to conduits will be re-ferred to as base flow, which means that a negative flow will beconsidered as a recharge to the LPV from the conduits, and conse-quently as a period without base flow. With these definitions,spring hydrograph separation should thus allow better under-standing of karst aquifer flow, in particular the relative influenceof high and low permeability volumes on karst spring flows, theconsequences of flow inversions between these volumes, and theorigin and evolution of base flow during and following floods,regardless of the porosity or permeability of the LPV. This paperis divided into two parts, the first of which briefly reviews previouswork dealing with hydrodynamic analysis of karst spring hydro-graphs and describes mathematical models for drainage of theconduits and matrix. The second part focuses on two karst sys-tems, one eogenetic and one telogenetic, in which conduit flows(presence of large cave systems), recharge and water level repre-sentative of conduits and LPV are well characterized. The two sys-tems differ greatly in their head gradients and amounts of matrixporosity and permeability. These case studies allow applicationand evaluations of mathematical flow models to discuss the origin,the evolution and the relative importance of flood flow and baseflow during and following recharge in two different karst contexts,and development of conceptual models to show the influence ofexchange between matrix and conduits on flood hydrographs ofkarst springs.

56 V. Bailly-Comte et al. / Journal of Hydrology 386 (2010) 55–66


Methods

Simple mathematical models for karst spring recession

Drainage of low permeability volumes (porous matrix) – MatrixRestrained Flow Regime (MRFR)

Boussinesq (1904) and Maillet (1905) were among the firstauthors to propose simple mathematical models for spring reces-sions. Others have expanded these initial models in attempts toimprove mathematical fits to field measurements (Drogue, 1969,1972; Mangin, 1975). Dewandel et al. (2003) and Ford and Wil-liams (2007) review these different recession models.

In this study, the slow depletion of the LPV is assumed to con-trol the flow regime at the spring during the base flow period onthe spring hydrograph similar to groundwater flow in porous med-ia. An approximate solution of the groundwater flow equation(without recharge) in one (Boussinesq, 1904) or two (Kovacset al., 2005) dimensions for a porous, homogeneous, isotropicand unconfined aquifer gives a single exponential decrease. Kovacset al. (2005) term this flow regime the Matrix Restrained Flow Re-gime period (MRFR):

Q MRFRðtÞ ¼ Q 0 � e�at ð1Þ

where QMRFR(t) [L3 T�1] is the discharge at time t, Q0 [L3 T�1] is thespring discharge when the MRFR period starts and a is the recessioncoefficient [T�1] usually expressed in days. This solution is referredto as model MRFR; Eq. (1) supposes that no delayed rechargeoccurs.

Boussinesq (1904) and Kovacs et al. (2005) expressed a accord-ing to physical parameters using an analytical approach. Theyshow that the recession coefficient (a) is proportional to the ratioT�L

S , where L is the length of the aquifer domain [L], T is the hydrau-lic transmissivity [L2 T�1] and S is the storativity [–] of the equiva-lent porous, homogeneous, isotropic and unconfined media.

Drainage of high permeability volumes (conduits) – Conduit FlowRegime (CFR)

The first part of a recession curve can be strongly influenced byrecharge through the vadose zone modulated by its transferthrough the phreatic zone (Mangin, 1975), which explains whyflood flow is not easily described by mathematical functions.Therefore, we initially assume that springs respond only to an im-pulse in hydraulic head elevation in conduits, there is no diffuse re-charge through the vadose zone, and there is no exchange betweenconduits and matrix. These strong assumptions and their applica-bility to real karst systems will be discussed subsequently.

Under these conditions, the whole conduit network is consid-ered as a single reservoir (R) with infinite hydraulic conductivity,and the Bernoulli incompressible flow equation of fluid dynamicsgives (Eq. (2a)):

VRðtÞ ¼ffiffiffiffiffiffiffiffi2gh

pð2aÞ

where VR is the flow velocity at the exit of R [L T�1], g is the gravi-tational constant [L T�2], and h is the hydraulic head in R [L]. Con-sidering that the horizontal area of R is constant, the massconservation in R during dt gives (Eq. (2b)):

AR � dh ¼ �aR � VR � dt ð2bÞ

where AR is the area of R [L2] and aR is the flow section at the exit ofR [L2].

Combining and rearranging Eqs. (2a) and (2b) gives Eq. (2c)

dQCFR ¼ �2ga2

R

AR� dt ð2cÞ

where QCFR(t) [L3 T�1] is the discharge at time t at the exit of R. Theintegration of Eq. (2c) between the flood peak time tmax [T] and t [T]indicates there is a linear decrease of the discharge according totime:

b ¼ 2ga2

RAR

QCFRðtÞ ¼ Q max � b� t

(ð3Þ

where Qmax [L3 T�1] is the maximum discharge and b [L3 T�2] is theslope of the linear decrease of the spring discharge according totime expressed in m3 s�1 d�1.

We refer to this simple model (Eq. (3)) as Conduit Flow Regime(CFR). It has been shown that b will take high values for a largeflow section at the exit of R, which can be related to a high degreeof karstification (or a high conduit frequency) (Bailly-Comte, 2008).Inversely, b will be low for a high horizontal section in R, meaningthat a small amount of water is stored in the conduit system. It canalso be demonstrated that quadratic head loss in R, which concep-tually represents conduit constrictions, does not modify the linearrelationship in Eq. (3). In this case, b is found to be inversely pro-portional to the quadratic head loss coefficient (Bailly-Comte,2008).

Base flow evolution

The difference between inflow at the swallet and outflow (DQ)at the spring of a sink/rise karst system yields the groundwater dis-charge draining from (or injected to) the LPV to (or from) the con-duit (Eq. (4)):

DQ ¼ Q S � Q A ð4Þ

where QS is the spring discharge and QA is the allogenic recharge.This method allows computing base flow as the positive value

of DQ during and following floods and the amount of loss fromnegative values of DQ.

A comparison of case studies

Study areas

The Vène Spring in the Aumelas-Thau karst systemNear Montpellier, Southern France, the Vène Spring (Fig. 1A),

Station Number 10162X0033) is a temporary spring partly fed bythe sinking of the ephemeral Coulazou River (Bonnet and Paloc,1969). The Coulazou River crosses the Aumelas Causse where thekarst aquifer is formed in Jurassic limestones that are exposed atthe surface (Fig. 1A).

This karst system, known as the Aumelas-Thau karst system, isan example of a telogenetic karst system, and feeds the ephemeralVène Spring in high water conditions. A gauging station is used toestimate discharge a few meters downstream from the Vène Spring(QS, Fig. 1A). In low flow, karst groundwater discharges farther tothe southwest by other permanent karst springs below a Tertiarybasin capped by impervious siliciclastic rocks. A monitoring net-work has been constructed in the region to assess the karst/riverhydrodynamic interactions (Jourde et al., 2007; Bailly-Comteet al., 2008a,b). As part of this network, allogenic recharge is mon-itored using a gauging station upstream from the karst aquifer (QA,Fig. 1A). Water level is recorded in a cave called Puits de l’aven(Fig. 1A) and in a monitoring well PZ2 (Fig. 1). Well PZ2 is a120 m deep, uncased well which has been drilled into the Jurassiclimestone; no large karst voids were identified during the drilling,though fractures and small karst drains were encountered. Previ-ous studies show that this well represents hydrodynamics of theLPV influenced by the Coulazou River (Bailly-Comte et al., 2008b,2009). Puits de l’aven is a cave that is at least 1300 m long with

V. Bailly-Comte et al. / Journal of Hydrology 386 (2010) 55–66 57


perennial water in its base (Douchet, 2007). During floods it acts asa spring and/or a sinkhole along the riverbed and thus is formallyan estavelle.

The Santa Fe River sink/rise system within the upper Floridan aquiferIn north-central Florida, the River Rise Spring is the main outlet

of a sink/rise system sourced by the Santa Fe River (Fig. 1B). Similarto the Aumelas-Thau system, a monitoring network has been con-structed to assess the exchange of water between matrix and con-duit (Martin and Dean, 2001; Martin and Screaton, 2001; Screatonet al., 2004; Martin et al., 2006).

River Sink stage is recorded each day by the staff of the O’LenoState Park and converted to runoff based on a rating curve devel-oped by the Suwannee River Water Management District (QA,Fig. 1B, Rating No. 3 for Station Number 02321898, Santa Fe Riverat O’Leno State Park). Water levels are recorded at a 10 min intervalat the River Rise and converted to discharge using the rating curveproduced by Screaton et al. (2004) (Fig. 1B). Eight wells have beenscreened close to the depth of the main conduit and four additionalwells have been drilled and screened across the water table withina few meters of four of the deep wells. The deep wells are desig-nated by a single digit (1–8) and the shallow wells are designatedby the letter A (4A, 5A, 6A, 7A). Most of these wells are instru-mented so that water level, conductivity, and temperature aremonitored within the LVP at a 10 min time interval. These moni-toring data provide information about pressure (water level) andmass (temperature and electrical conductivity) transfer in the ma-trix during floods.

In high flow conditions, flood pulses from the Santa Fe River aretransmitted to the River Rise through large karst conduits (Screatonet al., 2004). Increases in the hydraulic head of the conduits lead toflow from the conduits to the porous matrix (Martin and Dean,2001; Martin and Screaton, 2001). At this site, the matrix perme-ability is greater than at the Aumelas-Thau site, but is still signifi-

cantly lower than the conduit permeability. Thus, even thoughSanta Fe River is an eogenetic karst system, the matrix representsan LPV relative to the conduit. Moore et al. (2009) have shown thatthe water chemistry in the Well 4 is relatively constant, thoughthis well is within a few hundred meters of the main karst conduits(Fig. 1B), which suggests little exchange of mass between the con-duit and Well 4. Consequently, we consider water level fluctuationin Well 4 as representative of hydrodynamics of the LPV. The com-plementary shallow Well 4A is compared to Well 4 to assess verti-cal hydraulic gradient within LPV. Finally, conduit head ischaracterized by measurements of water level at the River Rise.

ComparisonsTable 1 summarizes the main characteristics of the groundwa-

ter/surface water interactions and conduits/matrix hydrodynamicproperties for these two karst systems, focusing on their genesis,their hydrologic regime, their hydrodynamics and especially theboundary condition that applies in the conduit system duringflood.

The fundamental characteristics of the karst aquifers as well asthe recharge condition in their conduits (see boundary conditionsin Table 1) differ greatly in these two areas (Table 1), providingideal settings for comparative studies of fundamental processes.Indeed, differences in topography between the two regions createdifferences in water table gradients, resulting in differences in flowrates through the aquifers, as well as responses to extreme precip-itation events. In addition to topographic dissimilarities, physicalproperties of the aquifers differ because of their geologic histories(telogenetic vs. eogenetic). As a result of the age and deformation,the French karst aquifers in Languedoc contain little primaryporosity and most water is stored within fractures and conduits.The lack of deformation of the Florida karst is reflected in the highprimary porosity of the matrix rocks, up to 20% (Table 1, (Martinet al., 2006)). This high primary porosity allows for extensive water

A B

Fig. 1. Location and monitoring network of the A. Aumelas-Thau karst system in South of France (left) and B. the Santa Fe River sink/rise system within the upper Floridanaquifer (right).



storage and influences flow paths through the Floridan aquifer.These fundamental differences allow assigning typical flow behav-ior to each component of the karst spring hydrograph by differentapproaches:

– In the Aumelas-Thau system, flood flow and base flow at VèneSpring can be described according to time-series measurementsof water level in Puits de l’aven and Well PZ2 when concentratedrecharge along the riverbed ceases.– In the Santa Fe sink/rise system, variations of base flowduring the entire recession period can be computed using the dif-ference between outflow and inflow, assuming that autogenicrecharge can be neglected compared to inflows from the sinkingstream.

Flood flow and base flow at the Vène Spring

Spring hydrographs analysis according to water level evolution inmatrix and conduits

In Aumelas-Thau, 19 flood events have been recorded at VèneSpring since October 2002; 10 have been described using simulta-neous water level measurements in Well PZ2 and Puits de l’avensince April 2004. Three distinct types of recession curves have beenidentified at Vène Spring according to the initial (pre-storm) waterlevel in Well PZ2 (Fig. 2):

During low water table conditions, i.e. after the summerdrought, floods recorded at Vène Spring are relatively short, lastingonly a few days. At these times, spring hydrographs shows a lineardecrease with time (Fig. 2A) as long as the water level in conduits(Puits de l‘aven) is higher than the water level in the matrix (WellPZ2). Water level in Well PZ2 slightly decreases at the beginningof the recession, indicating a recharge probably due to a low pres-sure transfer from conduit to LPV and eventually the influence oflocal fast infiltration, but this water level always stays lower thanthe water level in conduits. Moreover, it quickly reaches a constantvalue, which means that the water level evolution in LPV cannotexplain the discharge evolution at the spring. Discharge at thespring during the whole recession is thus primarily influenced bythe water level change in conduits. As a result, flood hydrographsonly show the flood flow component influenced by conduit flow;it is an ideal example of the CFR condition. Bailly-Comte et al.

(2009) showed that the low water table condition is characterizedby hPZ2 < 3500 cmasl prior to the flood.

During medium to high water table conditions, floods recordedat Vène Spring are longer than during low water conditions. Springhydrographs (Fig. 2B) initially show a similar evolution consistingof a linear decrease through time, while the water level in Well PZ2increases slightly. This increase cannot explain the flood recession;it shows that conduits simultaneously feed the spring and rechargethe LPV. An inflection point appears in the hydrograph as soon asthe water level in conduits equals the water level in matrix (WellPZ2). This inflection point is thus interpreted as a flow regimemodification within the karst drainage network, which abruptlychanges from the CFR condition to the MRFR condition.

Under very high water table conditions, the LPV is alreadydrained by an upper karst drainage system (which occurs whenhPZ2 > 4700 cmasl, see (Bailly-Comte, 2008) for details). The springhydrograph in Fig. 2C perfectly represents the MRFR conditionsince only the hydrodynamic properties of the matrix control theflow at the spring, assuming that the discharge capacity of thekarst conduit system is not exceeded (which occur on this sitewhen QS > 5.5 m3/s (Bailly-Comte et al., 2009)).

As a result, these three types of recession curves show thatwater level comparisons between Puits de l’aven and Well PZ2 al-low an understanding of the conditions in the conduits or matrixthat control the flow at the spring. These results also show thatwater level measurements in a well representing the LPV (PZ2)prior to the flood allow forecasting of the spring behavior (seethe initial water level in PZ2 shown in Fig. 2). The CFR and MRFRmathematical models (Eqs. (1) and (3)) should only be used to fitrecession curves of spring discharge when delayed recharge is neg-ligible. This assumption is reasonable when allogenic rechargefrom an ephemeral stream constitutes the primary recharge, pro-ducing the quick response at the spring. In the three types of reces-sion curves exemplified by Fig. 2 allogenic recharge ceased quicklyafter the river flooded, and most surface flow was captured bynumerous sinkholes in less than 1 h. Consequently, QA was negligi-ble when the recession started at the spring (Fig. 2). The recessioncan thus be interpreted as the spring response to an impulse re-charge in conduits. Moreover, as a first approximation, water ex-change between conduit and matrix can be neglected during theconduit flow period since the contrast of permeability betweenconduits and matrix is high and water movements through

Table 1Comparisons of the two case studies showing the main characteristics of the groundwater/surface water interactions and conduits/matrix hydrodynamic properties.

Aumelas-Thau system Santa Fe sink/rise system

Type of karst aquiferTelogenetic Eogenetic

DimensionsDistance (straight line) between

the monitored sinkhole and the spring5.3 km between the cave Puits de l’aven and theVène Spring

4.7 km from River Sink to River Rise

Hydrologic conditions before a floodNo surface flows in the River and no flows at thespring

Base flow at the spring due to sinking surfacestreams and release of groundwater storage

Flood propagation betweenQA and QS (Fig. 1)

Flood transfer through open channel and karstconduits in both vadose and phreatic zone

Flood transfer through karst conduits in thephreatic zone

Allogenic rechargeTime scale Discontinuous recharge (intermittent river).

Sinkholes are filled by surface water in few hoursduring flash floods, coming from non-karst terrains

Continuous recharge, large flood events fromupstream confined terrains that source the aquiferover few days to months

Number of sinkholes between QA and QS More than 15 Only River Sink drains the sinking streamHydrodynamic propertiesMatrix porosity Low (few %) High (around 20%, Martin et al., 2006)Boundary conditions in conduits During flood: Riverbed elevation = head boundary

condition in karst conduits; then, water level insinkholes decreases with no or few influence ofallogenic recharge

Sinking surface flows = flow boundary condition inkarst conduits



conduits towards the spring is enhanced by a strong hydraulic gra-dient through the conduits. These two factors explain why the CFRmodel (Eq. (3)) agrees with measurements.

Evolution of groundwater flows between LPV and conduits at theSanta Fe sink/rise system

Influence of the type of recharge on the flood propagationA direct estimate of flow between conduits and LPV using Eq.

(4) only applies when autogenic recharge is negligible so that re-charge dynamics of the Santa Fe sink/rise system are known.Fig. 3C shows how the discharge at the River Sink (Fig. 1B) andthe River Rise (Fig. 1B) varies during three large floods, two in2005 and one in 2006. At this site, recharge to the aquifer was esti-mated at a daily time step by Ritorto et al. (2009) who used a mass-balance method similar to Dripps and Bradbury (2007).

In 2005, the River Sink discharge (QA) is always less than theRiver Rise discharge (QS), reflecting additional flow at the springand continuous drainage of autogenic water even during floodperiods. Initial water level in Well 4 was relatively high(1050 cmasl), but this level remains much lower than water levelat the spring during the flood peak (Fig. 3B). Thus, autogenic re-charge through the LPV cannot explain a higher discharge in QS

(Fig. 3C). The positives values of DQ also show great variations dur-

A

B

C

Fig. 2. Recession curve analysis at Vène Spring according to water level measure-ments in the aquifer during low (A), medium to high (B) and very high (C) watertable conditions prior to the flood. The horizontal dashed line shows the mean levelof the upper karst drainage network which controls the karst flows from Puits del’aven to the Vène Spring during floods. The vertical dashed line shows the transitionbetween conduit flow and base flow periods. (�) Water level in Well PZ2 prior to theflood is shown on the right axes.

A

B

C

Fig. 3. Evolution of discharge and water level at the Santa Fe River sink/rise systemaccording to recharge estimated by Ritorto et al. (2009).



ing the flood peak (Fig. 3B, see t1). These fluctuations and the pos-itives values of DQ reflect fast infiltration through the thin and highpermeability unsaturated zone, sinkholes and vertical shafts (i.e.fast autogenic recharge) which amplifies the flood peak transferfrom River Sink to River Rise.

In 2006, a high flow event occurred with a lower initial waterlevel in Well 4 prior to the flood (995 cmasl). The estimated auto-genic recharge is higher than for the summer rainfall event(Fig. 3A), but fast autogenic infiltration appears to be relativelylow since DQ exhibits negative peaks during the transfer of theflood peak (Fig. 3B, see t2). During the flood recession, water levelin Well 4 becomes higher than at the River Rise (Fig. 3B, see t3),indicating that conduits drain the LPV following its recharge by dif-fuse infiltration. Consequently, t3 characterizes a flood recessioninfluenced by delayed infiltration which could result from dis-charge from wetlands and perched water table lakes. This delayedinfiltration explains the positive and smoothed values of DQ(Fig. 3B, compare t3 to t1). From June 2006 to December 2006(Fig. 3B, see t4), no recharge occurs (no flows in River Sink and noor little recharge from rainfall on Fig. 3A). Delayed rechargethrough a few meter thick vadose zone (Ritorto, 2007) may thusbe neglected. LPV and conduits reach pressure equilibrium duringthe t4 period during which time a single exponential decreasinglimb perfectly describes the base flow recession curve, as proposedby the MRFR model (Eq. (1)) without recharge. However, quickflows between matrix and conduit cannot be described using DQsince autogenic recharge is found to influence the flood transfer.

Case of simple allogenic rechargeFig. 4 shows a flood that occurred at the end of summer 2008 for

which the rainfall recorded from 08/16/2008 to 09/02/2008 in theconfined catchment area (236 mm),1 upstream of the karst aquifer,is much higher than the rainfall recorded on the karst aquifer(156 mm).2 No recharge estimates are available, but because flood-ing occurred in the summer, medium to high evapotranspiration(ET) would be expected, reducing the relative influence of the auto-genic recharge as compared to the allogenic recharge.

Cumulative flows are the same in River Sink and River Rise(�120 106 m3 from 08/15/08 to 12/05/08), which could be misin-terpreted as low matrix/conduit exchange during the flood trans-fer. Indeed, hydrographs are greatly modified from River Sink toRiver Rise (Fig. 4), which can be explained using water level timeseries at River Rise, and Well 4 and Well 4A (Fig. 1B). Synchronousmeasurements of water level are used to describe vertical ground-water flows by computing vertical hydraulic gradients betweenWell 4 and Well 4A (Fig. 4, see the gray line), while evolution ofhydraulic gradient between Well 4 and River Rise (Fig. 4, see theblack line) characterizes flow from LPV to conduits. Positive valuesof hydraulic gradients indicate downward flow from Well 4A toWell 4 and from matrix to conduit respectively.

The gradients between the conduit (measured at the River Rise)and Well 4 and between Well 4 and Well 4A become negativesimultaneously with the DQ becoming negative at the start ofthe flood. This timing indicates that allogenic water flows to theLPV in all directions around the conduit and that recharge fromthe surface through the LPV is negligible at that time. Subsequentlyin the recession curve, DQ and the hydraulic gradient betweenWell 4 and River Rise become positive at the same moment. Thus,hydraulic gradients within the LPV both between Well 4 and Well4A and between the LPV and conduits (W4 and River Rise) reflectsDQ, suggesting that DQ can be considered as a measure of ex-

change between LPV and conduits. A positive value for DQ canbe considered the onset of baseflow to the spring, even thoughthere is no inflection point on the spring hydrograph at this time.

This flood event shows how allogenic water is initially stored inthe LPV (DQ < 0) and subsequently is released and drained by con-duits (DQ > 0). In other words, DQ shows how exchange of waterbetween matrix and conduit modifies the quick flow transfer,although cumulative flow at the sink and rise over the time ofthe flood does not reflect this exchange of water. Based on theDQ evolution shown in Fig. 4 between 08/25/08 and 09/04/08,there was clear exchange during this flood of around 30% of allo-genic recharge. This amount of water was stored in the porous ma-trix during the flood before being slowly drained by conduits to thespring during the recession. Although the flow inversion betweenmatrix and conduits is clearly shown by the discharge volumes,it does not generate a clear change in the spring hydrograph.

Comparisons of Aumelas-Thau and Santa Fe River sink/rise systems

Fig. 2A and B shows that the hydrograph recession of Vène Springperfectly fits Eq. (3) when water level is higher in the cave (conduit)than in the well (LPV), which characterizes the CFR condition. Floodflows at Vène Spring thus reflects discharge from a conduit networkpreviously recharged by a pulse of allogenic recharge. Linear de-creases of flood flows are usually not observed on hydrographs ofkarst springs, even in karst systems where matrix porosity is verylow, because of the influence of fast and delayed infiltrationthrough the epikarst and the vadose zone. Indeed, the dynamicsof recharge has such a strong influence on the flood flow transferthat it often becomes impossible to physically interpret the floodflow period, i.e. to assign a flow behavior to each flow period. Atthe Vène Spring, short and focused allogenic recharge easily allowsseparating the CFR component of the spring hydrograph.

Using numerical methods based on two-dimensional analyticalsolutions describing the hydraulic response of a theoretical karstaquifer with simple geometries, Kovacs et al. (2005) have shown

0

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Fig. 4. Flood event at the River Rise mostly influenced by allogenic recharge.Rainfall data are provided by the O’Leno State Park station.

1 Average value of cumulated values of stations 234 (Louis Hill Tower), 235 (NewRiver Tower) and 263 (Union Tower).

2 Average of cumulated values of stations 240 (O’Leno State Park) and 02321975(Santa-Fe River at US441 near High Springs)



that both flood and base flow recessions should be characterizedwith exponential decreases, but with two different recession coef-ficients. If the recession coefficient is low, however, an exponentialdecrease is close to a linear decrease, but the hydrograph is conse-quently nearly flat, which is not consistent with the field observa-tions in Fig. 2B and C. Another explanation of the linear decrease offlood flows observed at the Vène Spring (Fig. 2A and B) could befound by considering both the contrast of permeability betweenconduits and matrix, and the hydraulic gradient in conduits: Inthe Aumelas-Thau system, this contrast is high and hydraulic gradi-ents between sinkholes in the riverbed and Vène Spring can exceed1%, suggesting that water exchange between conduits and matrixis low compared to flow in the conduits. Limited exchange meansthat the conduit/matrix boundary can be approximated by a no-flow boundary, as proposed by the CFR mathematical model (Eq.(3)). In case of higher matrix permeability (fractures or intergran-ular porosity) and lower hydraulic gradients in conduits, exchangeof water between the conduit and matrix could explain an expo-nential evolution of spring discharge as proposed by theoreticalmodels with simple geometry (Kovacs et al., 2005).

When water level in Well PZ2 is high prior to the flood, it re-mains higher than the water level in conduits during the flood(Fig. 2C). Thus, karst conduits only drain the matrix and never re-strain groundwater flow as long as the discharge capacity of karstconduits is not exceeded. This process explains why spring hydro-graphs perfectly follow a single exponential decrease related to therelatively slow depletion of the LPV volume (Eq. (1)), which char-acterizes the MRFR condition (Fig. 2B after 5/7/07, and Fig. 2C).

Influence of two aquifer volumes of different hydrodynamicproperties is also identified at the Santa Fe sink/rise system, high-lighting the concept of double porosity of karst aquifers. Both con-tinuous recharge at the sink (QA) and water exchange between ahighly permeable matrix and conduits drive the flood flow transfer,which prevents the use of Eq. (3) to describe the hydrodynamicbehavior of the River Rise. Exchange of water between matrix andconduit can be compared to stream/aquifer interactions (or bankstorage) which control the surface flow routing in open channels(Cooper and Rorabaugh, 1963; Pinder and Sauer, 1971; Hunt,1990; Moench and Barlow, 2000; Chen et al., 2006). There are how-ever some non negligible differences since surface flow routing inopen channels and water flow routing in a conduit system underpressure are governed by different processes, and thus representedby different equations. Moreover, pressure in conduit flow can en-hance the loss of water from conduits to matrix porosity.

Maillet’s law (1905) can also explain an exponential decrease ofdischarge from the spring as due to the emptying of large karstvoids poorly connected to the main karst conduit (karst annexes(Mangin, 1975)). Such karst voids or cavities were not encounteredwhen drilling Well PZ2 (Aumelas-Thau) or Well 4 (Santa Fe Riversink/rise), suggesting that groundwater is actually released frommatrix porosity (intergranular porosity and/or from dissolved frac-tures and joints) during base flow according to Eq. (1) for both theeogenetic and telogenetic studied karst systems.

Conceptual model and discussion

These observations can be used to develop a conceptual modelof groundwater flow through conduits embedded in matrices withvariable amounts of porosity and hydraulic conductivity in re-sponse to a sudden increase of hydraulic head in the conduit sys-tem due to focused recharge. The evolution of springhydrographs is exemplified by the Aumelas-Thau system for sys-tems with high hydraulic gradients within conduits and contrast-ing permeability between conduits and matrix (Fig. 2). In thiscase conduits and LPV behave as two parallel reservoirs with two

different hydraulic heads during quick flow recession. This condi-tion continues for as long as the hydraulic head in conduits is high-er than the hydraulic head in the LPV (from t0 to ti on Fig. 5). Oncepressure equilibrium between the conduit and LPV is reached, con-duit flow regime (CFR) ends and Matrix Restrained Flow Regime(MRFR) begins. This modification to the flow regime occurs whenthe recession curve changes from a linear decrease to an exponen-tial decrease at the Vène Spring (ti on Fig. 5 – Site A) in the case ofmedium to high initial water level in the LPV. After matrix restrainflow regime (MRFR) begins, karst conduits drain groundwaterstored in the LPV and the spring behavior only depends on the ma-trix hydrodynamic properties (e.g. after ti on Fig. 5 – Site A). Thiscondition induces an exponential decrease of the spring discharge,as described by Eq. (1).

This conceptual model can also be used to understand hydrody-namics at the Santa Fe sink/rise system (Fig. 5 – Site B). Duringflood flows, water exchange between conduits and the LPV implythat conduits and matrix are two dependent subsystems. The linksbetween these subsystems means that the CFR condition will bemore complex than in the previous case of low matrix porosity,and that groundwater flow will slowly change from the CFR tothe MRFR condition without a visible inflection point on the springhydrograph (Fig. 5 – Site B). Moreover, a low contrast of permeabil-ity between conduits and matrix and a high effective porosity arenot consistent with the low initial water level in the LPV shownin Fig. 5. Thus, no schematic spring hydrograph is given for Site Bin the case of low antecedent condition in the matrix.

Both systems studied show MRFR conditions which can be char-acterized by a single exponential decrease on the spring hydro-graph, but values of the recession coefficient are much lower inthe Santa Fe sink/rise system (a < 0.01 d�1, Fig. 5) than in the Aum-elas-Thau system (a > 0.1, Fig. 2B and C). This difference can beinterpreted by considering a lower T

S�L ratio in the Santa Fe sink/risesystem, i.e. a lower hydraulic diffusivity T

S since both karst aquiferlengths (L) are of the same order of magnitude (Fig. 1). A lowerhydraulic diffusivity in the Floridan aquifer is consistent with thestrong inertial behavior of eogenetic karst aquifers (Florea andVacher, 2006). This characteristic is mainly due to the high porosityof the limestone (thus a high storativity and a low hydraulic diffu-sivityT

S), which explains why this aquifer is one of the most produc-tive aquifers in the world. In contrast, the matrix porosity ofJurassic limestones of the Aumelas-Thau system is low (thus alow storativity and a high hydraulic diffusivity T

S because of thelow fracture porosity).

Base flow at River Rise, as defined as the positive value of DQ, isrelatively low and constant as long as the discharge simultaneouslydecreases at River Sink and River Rise. Consequently, discharge vari-ations at River Rise (QS) are strongly influenced by the recharge inRiver Sink (QA). Similar to this behavior in karst aquifers, low flowsin surface streams are also controlled by base flow due to bankstorage effects, which are also characterized by an exponential de-crease (Cooper and Rorabaugh, 1963). As a result, identifying anexponential decrease on karst spring hydrographs does not neces-sarily mean that groundwater is released from the LPV to conduits.In a general way, dynamics of recharge has to be well identified be-fore analyzing recession curves.

Consequences for karst spring modeling

Although the examples shown are systems dominated by allo-genic recharge, we suggest that the conceptual model has applica-bility to many karst systems. Most karst aquifers are connected tosurface streams, which can be perennial, intermittent or ephem-eral. These streams are drained by sinkholes (Zhou, 2007) or by fo-cused recharge at particular points (sinkhole, swallow hole, ponor)



of endorheic area as a consequence of flooding of karst depressionslike dolina and polje (Salvayre, 1964; Mijatovic, 1988; Currenset al., 1993; Bruxelles and Caubel, 1996; Lopez-Chicano et al.,2002; Bradley and Hileman, 2006). Recharge through the epikarst(Mangin, 1975) also occurs as temporary storage and fast infiltra-tion through vertical shafts or paleo-conduits. This fast infiltrationdrains towards the conduit system in the vadose zone therebyincreasing hydraulic head in conduits as compared to the LPV. Fastinfiltration is also shown in cases of highly permeable matrix inFig. 3B where DQ exhibits strong positive variations during the2005 flood transfer, as discussed previously. Furthermore, empiri-cal (Drogue, 1969, 1980; Tripet, 1972; Jeannin, 1996) and theoret-ical (Jeannin, 1996 and references herein) approaches showed thatflow reversals from conduits to LPV occur for various types of karstaquifers during flood, whatever the recharge processes.

We show that groundwater flows from conduits to LPV even fol-lowing the main recharge event. This flow decreases as the con-trast of permeability between conduits and LPV increases. Incases of low matrix permeability, loss of water from conduit to ma-trix is negligible as compared to conduit flows. In these settings,spring discharge represents conduit flow that can be describedby the emptying of a reservoir with infinite hydraulic conductivity(Fig. 2A before 5/7/07 and Fig. 2B). In case of high matrix perme-ability, loss of water from conduit to matrix is part of the aquiferrecharge. It thus strongly modifies the flood wave propagation tothe spring by storing water during flood that is slowly releasedduring base flow.

Since most aquifers have fast recharge, results of our studyshould represent many types of karst aquifers. Similar behaviorsshould occur in karst aquifers with a combination of allogenic

and autogenic recharge, although the processes should be lessprominent. Allogenic recharge in the two systems used as casestudies here provide sufficient constraints to assess the influenceof each aquifer volume, thereby allowing a physical explanationof the two different components on a karst spring hydrographthrough the CFR and MRFR models.

Considering conduits and matrix as two linked aquifer volumesthat are interdependent in terms of hydraulic head may have greatconsequences on karst spring conceptual modeling. Indeed, simpleconceptual models commonly state that karst spring behavior canbe simulated using a model with two reservoirs connected in series(see for instance (Kiraly, 2003; Geyer et al., 2008)). Recharge is splitinto low permeability and a high permeability reservoirs; the lowpermeability reservoir is slowly drained by the high permeabilityreservoir connected to the spring (Fig. 6A).

The depletion of the reservoir representing the low permeabil-ity volume in Fig. 6A also gives the antecedent recession, which isadded to the fast infiltration during quick flow and is used to showthe volume of water that is stored and released within the aquifer(see for instance (Atkinson, 1977)). Following this assumption,Fig. 6A shows that: (i) the LPV and conduits always contribute tospring flows, (ii) quick flows at the spring are considered as thesum of conduit flows and matrix flows and (iii) pressure equilib-rium between the LPV and conduits are not considered. This hydro-dynamic behavior is not consistent with our observations at boththe Aumelas-Thau and Santa Fe systems, two systems with dis-tinctly different aquifer properties. Our observations have impor-tant consequences for interpretations of recession curves andmodeling of karst spring flows, particularly for interpretations ofrelative importance of base flow and quick flow from karst spring

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Fig. 5. Schematic representation of high (C = conduit) and low (M = matrix) permeability volumes during flood and its consequences on flood hydrographs of the studiedkarst springs in response to a sudden hydraulic head elevation in conduits. Low, medium to high and very high initial water levels are depicted by the initial water level inmatrix (hM) when conduits are filled with water (t0, see the left part of the figure); ti is the transition time from CFR to MRFR. Aumelas Cause represents Site A hydrographsand Santa Fe River Rise represents Site B hydrographs.



hydrographs (e.g. (Bonacci, 1993; Padilla et al., 1994)). Our resultsindicate that karst spring hydrographs should be interpretedaccording to both aquifer subsystems which control the flow re-gime at the spring, and to water exchange caused by hydraulichead difference between the LPV and conduits (Fig. 6B). Theseobservations reflect karst systems as ensembles of conduits of rel-atively low storage capacity embedded in a low-permeability ma-trix where groundwater is stored and slowly drained by conduits,but that the low-permeability matrix can buffer flood pulses tovarying degrees depending on its physical characteristics, primar-ily its porosity and permeability.

Conclusion

We have shown that for karst aquifers with low matrix porosity,quick flows at the spring correspond to a flow regime influenced bythe hydrodynamic properties of the conduit network. In contrast,for karst aquifer with high matrix porosity, quick flow dependsultimately on the magnitude of water exchange between matrixand conduits. When conduits are filled with water without delayedinfiltration and conduit/matrix exchange is low, a linear decrease isobserved in the spring discharge, which can be interpreted as theemptying of the conduit network. These hydrograph characteris-tics are specific to karst aquifer with both low matrix permeabilityand focused recharge, exemplified by a sinking stream, inducing aninstantaneous recharge of the conduit system. In this case, a un-ique inflection point on the decreasing limb shows a change of flowregime from CFR to MRFR. In most other cases, no simple mathe-matical fit can be used to analyze quick flows at the spring sinceinfiltration dynamics and/or matrix/conduits exchanges stronglyinfluence conduits flow.

We also demonstrate that a single exponential decrease charac-terizes the base flow when recharge ceases or become negligible,

which can be explained by the drainage of the LPV by conduits.The recession coefficient can thus be used to estimate some hydro-dynamic properties of the matrix component itself. These observa-tions allow consideration of a different conceptual model for karstspring hydrograph analysis where discharge evolution at thespring results from pressure equilibrium between two aquifer sub-systems of different hydrodynamic properties. This model requiresrecharge and water level time series in different subsystems of akarst aquifer to interpret the spring hydrograph. Each of these vari-ables is easily obtained through monitoring pressure head at wells,springs and conduits when a sinking stream constitutes the mainrecharge of the karst system.

As a consequence of the strong spatial heterogeneity of karstaquifers, water level time series in wells are often considered asuseless or hard to interpret at the karst system scale, particularlywhen compared to karst springs hydrographs. However, our obser-vations show that ‘‘well-chosen” water level time series allowunderstanding hydrodynamics of low (matrix with intergranular,joints and/or fracture porosity) and high (conduits) permeabilityvolumes, which together with simultaneous discharge time seriesat the spring are essential to understand the whole karst aquiferbehavior.

As a result, considering porosity of the LPV and hydraulic gradi-ents within conduit systems should improve the environmentalimpact assessment of pollutants in surface waters drained by karstsinkholes. Indeed, when matrix/conduit exchange is low, drainageof pollutants towards the spring should be fast and limited to thequick flow response at the spring, but also with little dilution. In-versely, high matrix/conduit exchanges should induce a delayedbut diluted discharge of the pollutants, with potential sorption/desorption phenomena within the porous carbonate rocks. Differ-ences in contaminant behavior in these two systems will be criticalfor remediation strategies. This idea could be reinforced by the useof natural tracers of the infiltration. For example high resolution

Recharge Recharge

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volume

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Q

Fig. 6. Conceptual models of karst springs hydrodynamics with two reservoirs connected in series (1) or in parallel (2) showing relative influence of low and highpermeability volumes on a karst spring hydrograph. CFR: Conduit Flow Regime – MRFR: Matrix Restrained Flow Regime. The solid black line represents the spring hydrographand the dashed line represents flow between the conduit and matrix (DQ).



time series of temperature (Martin and Dean, 1999; Screaton et al.,2004) or specific electrical conductivity and regular sampling ofmajors ions and total organic carbon (e.g. Batiot et al., 2003).Chemical tracers require knowledge of the variations of the se-lected tracer in the surface water and the unsaturated zone, as wellas the characterization of pre-event waters in conduits.

Finally, we show how two karst systems that have distinct char-acteristics and are observed with similar field methods can be de-scribed by the same conceptual model. The unifying aspect of thesekarst aquifers is their double porosity behavior, regardless of theorigin, extent and dynamics of the karstification process.

Acknowledgments

The authors would like to thank Schlumberger Water Servicesfor this productive collaboration and for the use of numerous dataloggers, the ‘‘Conseil Général de l’Hérault” for its financial supportand the ‘‘Syndicat intercommunal d’adduction d’eau du BasLanguedoc’’ for the use of wells, M.-G. Tournoud of the Hydro-Sciences Montpellier Laboratory for the use of discharge time ser-ies at the Vène Spring, the Florida Department of EnvironmentalProtection and the staff of O’Leno State Park for their cooperation.Santa Fe Sink/rise research was funded by the National ScienceFoundation grants EAR-003360 and EAR-0510054 and by the Flor-ida Department of Environmental Protection Grants S00060,S0141, and S0181. Valuable suggestions made by three anonymousreviewers are greatly appreciated.

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