1

Geochemical evolution of groundwater in the unsaturated zone of a karstic 1 massif, using the Pco2-SIc relationship 2

PEYRAUBE Na,*, LASTENNET Ra., DENIS Aa. 3 a University of Bordeaux, laboratory I2M-GCE, 4 B18 avenue des facultés 33405 Talence, France 5 * Corresponding author. Tel +33 540002620, fax +33 540003113 6 E-mail addresses: peyraube@hotmail.fr (N.Peyraube), 7 r.lastennet@u-bordeaux1.fr (R.Lastennet), a.denis@u-bordeaux1.fr (A.Denis). 8

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Abstract 10

In karstic environments, groundwater is strongly influenced by CO2 partial pressure 11 variations of air present in the infiltration zone of these aquifers. In order to characterize the 12 geochemical changes in groundwater as it moves through the infiltration zone, we monitored 13 various rising springs in the perched karstic aquifer of Cussac (Dordogne, France), and 14 measured the CO2 partial pressure in air of a nearby cavity (the Cussac Cave) for 24 months. 15 Our method is based on the relationship between the saturation index with respect to calcite 16 (SIc) and the CO2 partial pressure at atmospheric equilibrium with water. We distinguished a 17 value for this last parameter when water is at equilibrium with respect to calcite (SIc=0) 18 called saturation CO2 partial pressure. The use of this parameter can provide information on 19 flow conditions and relationships between water, air, and rock. Cussac aquifer is a suitable 20 area to apply these methods because of its small size, numerous springs, and a cave that 21 provides data for CO2 partial pressure condition inside the massif. Results show that most of 22 the calcium-carbonate mineralization is acquired in the epikarst followed by a precipitation 23 phase in the upper part of the infiltration zone. Groundwater reaches the saturated zone with 24 some degree of saturation depending on CO2 partial pressure variations in air inside the 25 massif. 26 Key words : karst, Saturation index, carbon dioxide, Pco2, unsaturated zone 27

1. Introduction 28

Karst aquifers represent an important resource for fresh water. Their complex 29 behaviour has been studied using various approaches such as geochemical, hydrodynamical, 30 isotopical, and geomorphological approaches. Temporal monitoring of physical and chemical 31 parameters of water in these aquifers, such as temperature and electrical conductivity (Baena 32 et al., 2007), pH, ion concentration and natural tracing (Karimi et al., 2005; Fournier et al., 33 2007; Andreo et al., 2009) have led to an increased awareness of the functioning of carbonate 34 aquifers. Improved models of karst systems were developed through the study of flood events 35 (Lastennet and Mudry, 1997; Vesper and White, 2004), and use of isotopic chemistry, in 36 particular carbon 13 (Emblanch et al., 2003; Spötl et al., 2005). 37

Karst aquifer is commonly divided in two parts, saturated zone and unsaturated zone. 38 The later can in its turn be subdivided in a transmission zone and the upper layer of karst, 39 referred to as the epikarst or subcutaneous zone. The role of the unsaturated zone in the 40 sustainment of water flow in karst system has been exposed by Lastennet (1994) and 41 Emblanch (2003). In particular, the epikarst directs rainwater towards a network of drainage 42 paths (Klimchouk, 2004; Zou et al., 2008). The epikarst also acts as a capacitive zone, i.e. a 43 reservoir with a non-negligible buffer effect (Aquilina et al., 2006; Trček, 2007). 44

The interaction among phases and the activities happening in the karst aquifer are 45 interesting for a hydrogeology study. Actually, the gaseous, liquid, and solid phases in the 46 unsaturated zone are continuously interacting. Water’s capacity to dissolve rock or precipitate 47

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calcite (i.e., the amount of bicarbonate concentration that water transiting through rock 1 accumulates) is strongly influenced by the composition of air within the massif. With this 2 said, CO2 partial pressure (Pco2) of air in the unsaturated zone is difficult to ascertain. 3 Measurements made in karstic cavities are merely estimations due to influences by mixing 4 with external air and dynamic effects of atmospheric pressure and temperature (Troester and 5 White, 1984; Perrin et al., 2003; Denis et al., 2005; Benavente et al., 2010). Baldini et al. 6 (2006) point out that the mixing of cave and outside air influences the representativeness of 7 point measurements. Recent studies have made a combined analysis of Pco2 and radon 8 activity in air (Kowalczk and Froelich, 2009; Fernandez-Cortes et al., 2011) in order to gain 9 an improved understanding of Pco2 variations in caves. 10

Measurement of air Pco2 in unsaturated zones, alternatively in caves, is a significant 11 parameter to consider. This is necessary for understanding calcium-carbonate equilibriums of 12 flows in karstic systems. The combined use of the saturation index with respect to calcite 13 (SIc, defined by Langelier, 1936) and Pco2 with which water is at atmospheric equilibrium 14 (Pco2_eq) allows various characteristics of karstic groundwater to be differentiated (Drake 15 and Harmon, 1973). Bakalowicz (1979), Herman and Lorah (1986), Dreybrodt et al. (1992) 16 and Bono et al. (2001) dealt with medium-term effects of water degassing on bicarbonate and 17 calcium concentration variations, when it emerges into the Pco2 conditions of the terrestrial 18 atmosphere. However in terms of calcite saturation, many authors have used variations as a 19 function of time, very few (Roberge, 1989; White, 1997) have used the linear relationship 20 between SIc and log(Pco2_eq). 21

Hence, in the context of physicochemical processes involved in the evolution of 22 karstic systems, the aim of this paper is to define the evolutionary characteristics of water as it 23 flows through different compartments of the unsaturated zone. The purpose of the article is to 24 provide new tool for hydrogeologist in the karst environment. Generally, this paper provides a 25 better understanding on the water flow characteristics in the so called “black box” which is 26 referred as the karst system. Specifically, this article aims to answer some questions about the 27 flow conditions i.e. is there an exchange between air and water (gas dissolution or 28 degassing)?; is there a slow flow allowing long interaction between water and air in the 29 unsaturated zone or, a quick flow?; and is there a calcite precipitation or a dissolution? 30 Moreover, can we estimate air Pco2 in unsaturated zone? 31 For this particular objective, Cussac cave as a study site seems appropriate. The site 32 provides access to four springs of a karstic aquifer, located at different points between the 33 epikarst and base of the unsaturated zone. Over two hydrologic years, we monitored 34 concentrations of major ions, pH, and temperature of the four springs. Additionally, we 35 monitored Rimstone Pool water and air Pco2 (Pco2_cave) inside the cave. 36 In order to meet the above mentioned concerns, development of methodology was 37 employed. Study of the saturation index with respect to calcite and groundwater Pco2_eq in a 38 time series and in a (-log(Pco2_eq) ; SIc) graph allows comparison and characterization of 39 their interaction with the massif. Interpretation of the measurement distribution on the 40 (-log(Pco2_eq) ; SIc) graph leads to a better understanding of the functional characteristics of 41 the Cussac cave perched aquifer. 42

2. Study site 43

The study site, at the north east edge of the Aquitaine Basin in Belingou Valley, is a 44 small tributary of the Dordogne River (Dordogne department, South West France). 45

The climate is temperate with an average annual temperature of 13°C, an average 46 summer temperature between 22°C and 23°C, and an average winter temperature between 47 2°C and 3°C. The surrounding land cover consists of Oak and Chestnut forest. Although the 48 average annual precipitation varies between 800 and 1000 mm, evapotranspiration from 49

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vegetation leads to a computed effective rainfall ranging from 200 to 350 mm per year. 1 Evapotranspiration reaches a peak in July - November, where rainfall is generally insufficient 2 to produce any significant discharge. Highest discharge rates are reached March - June, except 3 for strong storms. 4

A karstic aquifer developed as a result of contrasting permeability. A map view is 5 presented on Fig.1 while Fig.2 presents a schematic geological section of the site. The walls 6 of the aquifer are composed of marly limestone with very low permeability, from 7 Campanian 3 (30 m thick). Actually, in Cussac site, it can be qualified under a perched 8 aquifer because the wall of the saturated zone is located above the local base level for water 9 which is the Belingou River (flowing south to north). The marly limestone is capped by 10 calcareous sandstone from Campanian 4-5, also known as “Pierre de Dordogne”, the 11 thickness of which can reach 70 m. Finally, a discontinuous, ~ 20 m thick, blanket of clayey 12 sands from Eocen-Oligocen can be seen at the top of the outcrops. Terrain is flat with most 13 fracturing aligned NW to SE. An engraved cave, 1.5 km long with a NW-SE orientation, 14 developed in the calcareous sandstone of the Campanian 4-5 (Fig. 1). Its dimensions are 15 approximately 4 to 5 m high by 6 to 7 m wide, at an almost constant altitude of 118 m. The 16 cave entrance is located slightly above a groundwater discharge known as Farfal Spring. 17 During the year, air in the cave undergoes significant changes in Pco2_cave. Using an 18 eSENSE IP54 infrared probe, we measured variations in temperature and Pco2_cave at four 19 points in the cave: at distances of 350 m and 100 m at the right end, and 350 m and 100 m at 20 the left end, with respect to the cave entrance (Fig. 1 and Fig. 2). Variations of Pco2_cave are 21 similar for the 2005-2009 period (Fig. 3) with a gradual increase from May - July, followed 22 by a slower increase until a maximum of 3.2% (32 000 ppmv) is reached between August - 23 October. Then, a sharp decrease begins in November and lasts until mid-December, bringing 24 the Pco2_cave down to 0.25% (2 500 ppmv), i.e. ten times higher than the Pco2 in terrestrial 25 atmosphere, equal to 0.0388% (388 ppmv in 2010, NOAA Annual Greenhouse Gas Index). A 26 Pco2_cave of 3.2% could be caused by air from CO2 rich zones flowing through the 27 unsaturated zone. The observed decrease in November is due to an inversion of the 28 temperature gradient between cave and outside air, which produces a flow of atmospheric air 29 into the cave. Similar variations occur at all four measurement points. 30

Two time periods were distinguished on the basis of Pco2_cave measurements, mid-31 June - October, with high Pco2_cave values (greater than 2%) and December - April, with 32 lower Pco2_cave values (less than 0.5%). Intermediate levels can be found between these two 33 extremes. Analysis of δ 13C versus PeeDee Belemnite (VPDB) in cave air samples reveals a 34 biogenic origin of the CO2. The annual average value is δ13C = -22.4 ± 1.1‰ VPDB on 25 35 samples. Values associated with winter and springtime are higher (δ13C = -21.2 ± 0.4‰ 36 VPDB on 10 samples) than the values taken during summer and fall (δ13C = -23.4 ± 0.3‰ 37 VPDB on 12 samples). Intermediate values also exist between these two groups. 38

The Cussac site provides access to four springs located in different compartments of 39 the perched karstic aquifer. The epikarst spring (altitude 160 m) has a non-perennial flow 40 caused by overflow from the epikarst aquifer during heavy winter and springtime rains. 41

Two flows emerge from the infiltration zone: Ruijters Spring and Farfal Spring. 42 Ruijters Spring (altitude 110 m) is perennial and discharges through a small channel in a 43 stronger calcareous bank with a flow rate of ~ 1 litre per second. The bank is easily noticed in 44 the surrounding landscape. Farfal Spring (altitude 110 m), also perennial, finds its origins in 45 the same calcareous bank as Ruijters Spring, but drains from a separate supply basin. Farfal 46 Spring surges in an approximately 8 m² and 30 cm deep-water basin. Artificial tracing has 47 revealed that a stream visible over a 5 m deep canyon inside the cave, 700 m south of the 48 entrance, runs into Farfal Spring. Thus, the principal conduit of Farfal Spring has an open 49 surface, which can interact with air inside the massif. Nevertheless, the water surges under 50

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pressure at the discharge point. Farfal Spring has an average flow rate of approximately 5 1 litres per second, and is responsible for a major travertine deposit. Since 2008 we 2 continuously measured the flow rate of Farfal Spring and rainfall at a measurement station 3 close to the cave entrance (Fig. 4). Two significant floods can be distinguished during the 4 recorded period: May 2008 and January 2009. The surface area of the watershed is ~ 1.31 5 km2. 6

Effluent water, at the base of the unsaturated zone (altitude 95 m), indicates the 7 presence of a small saturated zone, which developed as a consequence of contrasting 8 permeabilities between the calcareous sandstones and the marly limestone. It is not 9 completely correct to refer to this as a saturated zone since it is made up of diffuse slow flows 10 that emerge from a weakly karstified formation. The topography of the study site intersects 11 these flows, leading to a seepage line. A gutter was installed to collect water from this 12 seepage. 13

Finally, the Rimstone Pool, located 50 m inside the cave on the northern side (118 m 14 altitude) is a single 4 m² pool with a water depth of 4 cm. Water droplets from stalactites 15 renew the pool very slowly allowing the pool to be in continuous contact with cave air. 16

3. Methods 17

We implemented bi-monthly monitoring from October 2007 - October 2009, with 18 terrain measurements of conductivity and temperature using a WTW 340 conductivity meter 19 equipped with a Tetracon 325 probe (accuracy 2 µS/cm). We measured pH using a WTW 20 330i pH meter equipped with a Sentix 41 probe (accuracy 0.05 pH units). Bicarbonate 21 concentration was measured at the time of sampling by digital titration using 1.6 N H2SO4 22 with a HACH LANGE alkanity meter (accuracy 2.44 mg/L). 23

Samples were filtered to 0.45 µm and preserved at 4°C in 60 ml HDPE flasks. 24 Contents of the cation flasks were acidified using HNO3 and ion concentrations (Ca2+, Na+, 25 K+, Mg2+, Cl¯ , NO3¯ and SO4

2¯ ) were determined by chromatography, using a Dionex ICS 26 1500 equipped with AS15 columns for the anions and CS12 columns for the cation 27 (measurement accuracy 2%). 28

Mean values of the physicochemical parameters of the groundwater discharges are 29 presented in Table 1. The water has a calcium bicarbonate facies with low concentrations of 30 magnesium (less than 3 mg/l) as a result of the absence of dolomites. Sodium, chloride, 31 sulphate and potassium concentrations are low in all measurements. Water temperature varies 32 between 11 and 13 °C, according to season. The Rimstone Pool water has a stable 33 temperature of 12.8 °C, close to that of the cave. 34

4. Functional relationship between Pco2 and SIc 35

The calcium-carbonate equilibrium in natural waters, especially in carbonated areas, 36 has been well documented. The equilibrium equations can be summarised as follows: 37

38 39 40 41 42 43 44 The expression *

32COH represents the sum of aqueous CO2 and H2CO3. Appelo and 45

Postma (2005) recall that aqueous CO2 is approximately 600 times more common than the 46 H2CO3 form. 47

[ ] [ ]−+ ⋅= 23

2 COCaK c

−+− +→← 233

2 COHHCO K

Gas phase Liquid phase Solid phase

−+ +→←→←+ 3*

2221

3

0 HCOHCOHOHPco KK3

223 CaCOCaCO Kc→←+ +−

[ ] [ ][ ]*

32

3

1COH

HCOHK

−+ ⋅=

[ ] [ ][ ]−

−+ ⋅=

3

23

2HCO

COHK

[ ]( )eqPco

COHK o _2

*32=

5

The calculations for the equilibrium constants K1, K2, Kc and K0, the Henry’s constant 1 for gases, as a function of water sample temperature, are made using the coefficients given by 2 Plummer and Busenberg (1982). The Pco2_eq corresponds to the calculated Pco2 with which 3 water is at atmospheric equilibrium. Calculation of Pco2_eq relies on parameters measured in 4 the field: activity of bicarbonate ion [HCO3¯ ], measured pH (henceforward called pHm), and 5 temperature by assuming that buffering components other than HCO3¯ are negligible. It is 6 defined by: 7

(1) ( ) [ ] ( )1032 _ KKLogpHmHCOLogeqPcoLog ⋅−−= − 8

9 All above equations are based on ionic activity of ions present in the samples. 10

Ionic activity is defined by where the value in square brackets equals ionic 11 activity, the value in brackets equals molar concentration, and γx is the ionic activity 12 coefficient of the ion under consideration. The ionic activity coefficients are calculated using 13 the Truesdell and Jones equation (Truesdell and Jones, 1973). Ionic strength is calculated 14 using molar concentrations of the water ions. 15

The use of these equations to determine water’s saturation with respect to calcite is 16 based on the work of Langelier (1936). In particular, the Saturation Index with respect to 17 calcite, SIc, represents water’s ability to precipitate or dissolve calcite. It is possible to make 18 direct use of the relationship defined by Langelier for the SIc calculation: 19

(2) [ ] [ ]

⋅=−+

cK

COCaLogSIc

23

2

20

If pH is essential due to calcium-carbonate relations (excluding other sources of H+ ion 21 which is common in karstic water) SIc can be calculated with expression (3). This expression 22 introduces the term pHsat representing the pH at which a sample of water would be at 23 equilibrium with respect to calcite. 24

(3) pHsatpHmSIc −= 25

The calcite saturation index can be expressed as a function of the field parameters, 26 pHm, [HCO3¯ ] and temperature. The previously-described mineralization of groundwater is 27 calcium-carbonate based. By considering the groundwater to be electrically neutral and 28 mineralization to be dominated mainly by Ca2+ and HCO3¯ (in the absence of other species 29 such as magnesium or sulphates in significant proportions), one can write: 30

(4) ( ) ( )−+ =⋅ 322 HCOCa 31

or in terms of activities: 32

(5) [ ] [ ]−

+

⋅⋅= −+

3

2

232

HCO

CaHCOCaγ

γ 33

Using the expressions of second ionisation and calcium carbonate dissolution equilibrium 34 constants, expression (2) thus corresponds to: 35

(6) [ ]

⋅⋅++⋅=

−

+−

3

2

22 2

3

HCO

Ca

cK

KLogpHmHCOLogSIc

γγ

36

From expression (1) pHm can be replaced in expression (6), SIc can be written as: 37

(7) ( ) [ ] ( )CLogHCOLogeqPcoLogSIc +⋅+⋅−= −32 3_1 38

[ ] ( )XX X ⋅= γ

6

with −

+

⋅⋅

⋅⋅=

3

2

210

2

HCO

Ca

cKKK

KC

γγ

1

Expression (7) defines a linear relationship between the logarithm of Pco2_eq and the 2 saturation index, for a constant level of bicarbonate ion activity. This linear relationship can 3 be represented by a straight line, a gassing-degassing line or G&D line. The relationship 4 depends on bicarbonate concentration and temperature. As a result of a small range of 5 temperature variations, the influence of parameter C is negligible. Some authors (White, 6 1997) propose an equivalent expression based on activity of calcium ions. However, we find 7 the use of bicarbonate ions more appropriate, as it is a central component in the relationship 8 between air, water and rock, whereas calcium ions only play a role in the interactions of water 9 and rock. 10

As with pHsat, it would be of great interest to know Pco2_eq when water is at 11 equilibrium with calcite (SIc=0). This particular value of Pco2_eq will be named Pco2_sat. For 12 a saturation index with respect to calcite equal to zero, expression (7) leads to expression (8) 13 which defines the Pco2_sat as: 14

(8) ( ) [ ] ( )CLogHCOLogsatPcoLog +⋅= −32 3_ 15

There is a direct relation between SIc, pHm, pHsat, Pco2_eq and Pco2_sat as: 16

(9) ( ) ( )eqPcoLogsatPcoLogSIcpHsatpHm __ 22 −==− 17

In the absence of mixing or precipitation, Pco2_sat corresponds to air Pco2 in the 18 massif with which the water interacts. Water acquires its bicarbonate concentration through 19 dissolution until it is saturated with respect to calcite. 20

From expression (7) we derive expressions (10) and (11), which characterize 21 variations in the saturation index as a function of variations in Pco2_eq and bicarbonate ion 22 activity: 23

(10) [ ] ( ) 1_

constant2

3 −=∂

∂=−

eqPcoLog

SIcHCOLog 24

(11) ( ) [ ] 3constant_3

2 =∂

∂= −HCOLog

SIceqPcoLog 25

The use of these relationships are displayed on the (-log(Pco2_eq) ; SIc) graph in 26 Fig. 5. The theoretical example of water containing 200 mg/L of bicarbonate in equilibrium 27 with respect to calcite for pHm=pHsat=7.35 and Pco2_eq=Pco2_sat=0.48% (values computed 28 using equation (1) and (8) for a temperature of 12°C) is represented on Fig. 5 by point E. 29 Fig. 5 also shows the bicarbonate concentration scale and saturation index tolerance 30 thresholds, from +0.1 to -0.1, between which a sample is considered to be saturated. If water 31 is in a new atmosphere with Pco2=0.1%, Pco2_eq decreases from 0.48% and calcite 32 precipitation occurs. Two trends can be distinguished among the possible variations of water 33 chemistry: 34

- from E to A is a trend along the G&D line, characterised by expression (7) and (10). 35 It corresponds to a change in Pco2 with which the water interacts. According to expression 36 (6), and taking into account the modification of dissolved carbonate species proportions that 37 depend on pH, the decrease of HCO3¯ concentration caused by water degassing is in the 38 magnitude of the decrease of H+ concentration. This variation is negligible compared to the 39 HCO3¯ concentration which can be considered as constant. The water SIc increases at the 40 same rate as the logarithm of Pco2_eq decreases. 41

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- from A to B is a trend along a straight line for constant Pco2_eq. It is characterized by 1 expression (11), corresponding to a decrease in SIc and bicarbonate concentration in an open 2 medium, until SIc equals zero. In the case of under-saturated water, a trend following the 3 constant Pco2_eq line results, through dissolution, in an increase in bicarbonate concentration, 4 for an increasing value of SIc. 5

Such variation, where precipitation occurs after a quick degassing, may occur in a 6 collected diphasic karstic conduit stream that reaches different parts of the karst. Another case 7 would be a slow diphasic diffuse flow, where precipitation occurs simultaneously with 8 degassing. It may lead to a mix of the two previous trends, such as the EC trend in Fig. 5. 9

The kinetic aspect of calcium-carbonate equilibriums was studied by many authors 10 (Plummer et al., 1978; Buhmann and Dreybrodt, 1985). The role of influent factors on both 11 calcite dissolution/precipitation and carbon dioxide gassing/degassing was discussed. Water 12 agitation is a major factor as it modifies mass transportation condition. Water film thickness 13 and surface of contact are other major factors (Dreybrodt et al., 1996, 1997). Temperature, 14 phosphate concentration, and organic matter must also be considered. Most authors agree that 15 longer periods of time are needed for calcite dissolution or precipitation in a non-turbulent 16 flow while a shorter time is needed for gas dissolution, or degassing. Roques (1969) and Ford 17 and Williams (2007) give estimates of a few minutes for gas dissolution and degassing. 18 Generally, reactions in liquid phases are considered instantaneous. 19

However, in real practice on field site, it is barely possible to quantify the time needed 20 for these exchanges because many parameters of the water flow in the unsaturated zone are 21 unknown (water film thickness, agitation of the flow, dimensions of the cracks, roughness of 22 the rock face, etc.). Yet, using a (-log(Pco2_eq) ; SIc) graph makes it possible to asses if the 23 flow is approximately quick or slow. So the conditions goes: 24

- a quick flow will limit the duration of exchange between liquid and solid phases as it 25 is a approximately slow process. But liquid and gas phase’s exchanges may not be as limited 26 as it is a more or less quick process. Therefore, a variation of air Pco2 in the unsaturated zone 27 will not modify water’s Pco2_sat which is an indicator of liquid-solid exchanges. This is 28 because it is in relation with bicarbonate concentration in equation (8). Simultaneously, it will 29 modify water’s Pco2_eq which is an indicator of the air-liquid exchanges. It is notable that a 30 sample taken at a spring during the variation of air Pco2 in the unsaturated zone will move 31 along G&D straight line as Pco2_eq vary, whereas Pco2_sat does not vary significantly. 32

- a slow flow allows a long time of exchange between liquid and solid phases as well 33 as between liquid and gas phases. As a result, a variation of air Pco2 in the unsaturated zone 34 will modify water’s Pco2_eq and water’s Pco2_sat. in this case a sample taken at a spring 35 during the variation of air Pco2 in the unsaturated zone will show a shift from the G&D 36 straight line because Pco2_eq and Pco2_sat vary. 37

5. Results 38

5.1. Construction of the G&D lines from data 39

For each sample at a given groundwater discharge, we can draw a Gassing & 40 Degassing line (G&D line) with a slope of 1, in the (-log(Pco2_eq) ; SIc) graph. Fig. 6 41 illustrates this for measurements taken at Farfal Spring. Fig. 6 also shows an uncertainty 42 cross. Uncertainty in the pH values (± 0.05 pH units) and bicarbonate concentration 43 (± 2.44 mg/l) leads to a SIc uncertainty of ± 0.056, and a log(Pco2_eq) uncertainty of ± 0.053. 44

Pco2_eq varies from 1.3% in winter to 3.5% in summer. Farfal Spring water is under-45 saturated from June - September, super-saturated from December - April (SIc = [-0.1; +0.2]), 46 and is saturated between those two periods. Bicarbonate concentration did not vary 47 significantly during the two years of measurements, remaining close to 337 mg/l. For each 48 measurement, we used expression (8) to compute Pco2_sat as a function of HCO3¯ . We can 49

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also use the intersection of this line with the abscissa (SIc = 0) to calculate Pco2_sat. Pco2 _sat 1 varies between 2.2% and 2.8%. 2

The full set of degassing lines associated with each measurement generates a band 3 which can be reduced to a single degassing line, taking into account the uncertainty in the 4 values of log(Pco2_eq) and SIc. This straight line, with a constrained slope of 1, is a model 5 governed by expression (7) for the variation of the saturation index with respect to calcite as a 6 function of Pco2_eq and shows a correlation coefficient of 98% with experimental data. The 7 modelled G&D line enables the calculation of a Pco2_sat called “spring model Pco2_sat” 8 which equals 2.5 ± 0.1%. This leads to a modelled bicarbonate concentration (spring model 9 HCO3¯ ) equal to 342 mg/l. The values of these two parameters are intrinsic to this spring, and 10 allow it to be characterized and compared with other springs in the system. 11

Thus, we can display the measurements for each spring on the same 12 (-log(Pco2_eq) ; SIc) graph (Fig. 7) and create a G&D line, characterized according to the 13 method described above. 14

Epikarst Spring is always super-saturated (SIc = (0.8; 1.3]). This is due to drainage 15 over stress-released and aerated limestone upstream from the groundwater discharge that 16 favours degassing. Since the spring becomes active after long rainy periods, we were only 17 able to collect a small number of measurements. Moreover, these bicarbonate concentrations 18 are less homogeneous than those of other groundwater discharges. The Pco2_eq varies 19 between 0.2% and 0.8%, whereas the Pco2_sat varies between 3.0% and 5.2%. Despite this 20 fact, and as a result of the conditions under which the samples were collected, a G&D line 21 describing their average behaviour was defined; the correlation coefficient is 90%. The spring 22 model Pco2_sat is about 4.0%, i.e. in the upper range of all of the groundwater discharges at 23 the site. This is the most mineralized water, with a spring model HCO3¯ equal to 400 mg/l. 24

The bicarbonate concentration obtained from the G&D line of Ruijters Spring is 25 354 mg/l, which is very similar to the value for Farfal Spring (Fig. 7). However, in the case 26 of Ruijters Spring, the water is almost always super-saturated (SIc = [0.0; 0.9]) due to 27 degassing that occurs upstream from the sampling point. The Pco2_eq values vary between 28 0.2% and 2.6%, and equilibrium with respect to calcite is reached for only a few points at 29 which Pco2_eq is equal to Pco2_sat. The latter varies from 2.0% to 3.5%, with the spring 30 model Pco2_sat approximately equal to 2.6%. Although, measurements for Ruijters Spring 31 appear to be less well-aligned along the G&D line, the correlation coefficient between 32 measured SIc values and those obtained from the model (expression (7) is 97%. 33

Degassing from water in the gutter, before it is collected and sampled, causes the 34 water to be super-saturated (SIc = [0.1; 0.6]), with a Pco2_eq lying between 0.4% and 1.1%. 35 Spring model HCO3¯ concentration of the water is 300 mg/l. The value of Pco2_sat varies 36 between 1.4% and 2.0%, i.e. with a smaller variation range than that of the aforementioned 37 springs. The correlation coefficient is 93% and spring model Pco2_sat is approximately 1.8%. 38

5.2. The specific case of Rimstone Pool 39

Rimstone Pool samples are divided into two groups (Fig. 7) that correspond to periods 40 of strong or weak Pco2_cave (air Pco2 in the Cussac Cave), as shown in Fig. 3. Fig. 8 41 specifically shows the variations in Rimstone Pool water during the 2007-2008 and 2008-42 2009 cycles, in a (-log(Pco2_eq) ; SIc) graph. 43

During periods of high Pco2_cave, mid-June - October, water is close to saturation 44 (SIc = [-0.02; +0.1]). Pco2_sat varies between 2.2% and 2.8%, spring model Pco2_sat is about 45 2.6%, and Pco2_eq varies between 1.7% and 2.9%. Measurements taken during this period are 46 aligned with a linear G&D regression (85% correlation coefficient) characterized by a spring 47 model HCO3¯ concentration equal to 342 mg/l. These values are close to those encountered at 48 the Farfal Spring, characterized by a Pco2_sat ranging between 2.2% and 2.8%, and a spring 49 model HCO3¯ concentration equal to 342 mg/l. 50

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Towards the end of fall the water has the highest level of super-saturation along this 1 specific G&D line. These values are then shifted laterally in November, until the beginning of 2 winter, reaching a new G&D line, specific to the period of low Pco2_cave. During December - 3 April, the spring model HCO3¯ concentration is equal to 220 mg/l, the lowest value 4 encountered at any of the springs. The water is always super-saturated (SIc = [0.3; 0.5]), with 5 low Pco2_eq values ranging between 0.2% and 0.4%. The Pco2_sat varies between 0.5% and 6 0.8% and spring model Pco2_sat is about 0.65%. Measurements made during this period 7 reveal significant differences with respect to the degassing regression line, and the correlation 8 coefficient of the model is smaller, with a value of 68%. This value can be explained by the 9 bicarbonate concentration of three samples that are moving toward a new equilibrium and, 10 thus, vary from the average winter bicarbonate concentration. 11

From May to mid-June, the measurements on the graph shift back to the degassing line 12 specific to measurements from the period with high Pco2_cave values. 13

5.3. Temporal evolution of Pco2_cave, Pco2_eq, and Pco2_sat 14

Pco2_eq expresses the final state of water after it has undergone various degassing, 15 gassing, precipitation, and dissolution phases during its drainage through the massif. 16 Degassing at the outlet is related to the prevailing conditions at the site. 17

Are displayed on Fig. 9 temporal variations of Pco2_cave (air Pco2 in Cussac Cave), 18 Pco2 at atmospheric equilibrium (Pco2_eq), and Pco2 at atmospheric equilibrium for ISc equal 19 to zero (Pco2_sat) for Farfal Spring and Rimstone Pool. 20

Pco2_eq of Farfal Spring varies according to the same cycle as Pco2_cave, although it 21 corresponds to a slightly higher range of values: from 1.3% to 3.5% instead of 0.2% to 3.2%, 22 for the case of Pco2_cave. Pco2_sat of Farfal Spring is, on the contrary, stable and has no 23 seasonal periodicity. Pco2_eq of Rimstone Pool water is close to Pco2_cave, and follows the 24 same seasonal variations. Pco2_sat of Rimstone Pool also varies throughout the year, 25 according to the same cycles as Pco2_eq. The value of Pco2_sat is similar to Pco2_eq from 26 June - October. It is at its lowest from December - April, and remains higher, by a few tenths 27 of a percent, than Pco2_eq. 28

6. Discussion 29

In this method of studying karstic systems our measurements are plotted on a 30 (-log(Pco2_eq) ; SIc) graph and for each groundwater discharge we determine: a straight 31 G&D regression line of slope equal to 1, spring model Pco2_sat from the Gassing&Degassing 32 model, and, lastly, spring model HCO3¯ concentration. Plotting the points on a 33 (-log(Pco2_eq) ; SIc) graph allows different groundwater discharges to be characterised. At 34 the same time, variations of Pco2_eq and Pco2_sat on a temporal diagram illustrate the 35 conditions encountered by water flowing in the massif and depicts exchanges between 36 gaseous, liquid, and solid phases. 37

This discussion deals with the combined use of Pco2_sat, spring model bicarbonate 38 concentration, and Pco2_eq in spatial and temporal characterization of flows draining through 39 karstic systems. In the case of the Cussac system, it is then possible to propose a functional 40 representation of flow and to determine the intrinsic values of these parameters. This 41 approach is possible on our site because of the small system, the numerous springs, and the 42 presence of a cave providing partial information on conditions inside the massif. 43

6.1. The epikarst zone 44

Water of Epikarst Spring in the Cussac system is produced by infiltration of rainwater, 45 which has absorbed CO2 from the ground (in situ measurements between 0.6% and 1.5%), 46 and then from air in the epikarst, Pco2 of which is unknown. Epikarst water is strongly 47 mineralized (spring model HCO3¯ equal to 400 mg/l), and is systematically super-saturated. It 48

10

degases as a consequence of the open nature of the epikarst aquifer’s groundwater discharge 1 area. The water’s Pco2_eq is influenced by these conditions. However, Pco2_eq does not 2 represent the air Pco2 encountered by the water in the epikarst compartment further upstream 3 from the epikarst Spring. 4

On the other hand, Pco2_sat, the minimum air Pco2 encountered by water in the 5 process of attaining its calcium-carbonate mineralization, comes close to Pco2 of the epikarst 6 atmosphere. In the upper part of the Cussac karstic system, Pco2_sat ranges from 3.0% to 7 5.2%, the minimum CO2 partial pressure in the air of the epikarst. These high values are 8 similar to air Pco2 measured in another epikarst in the region, Lascaux cave where air Pco2 of 9 8% have been measured (Lopez, 2009). This value is higher than soil air Pco2 and may be due 10 to an accumulation of CO2 in the epikarst. The process leading to this accumulation is still 11 under study. 12

6.2. Upstream of the infiltration zone 13

Water originating in the epikarst drains towards preferential flow areas situated 14 upstream from the infiltration zone. There is no discharge originating directly in this upper 15 zone. However, we can obtain characteristics of this zone indirectly through water present in 16 Rimstone Pool and in Farfal Spring, the system’s main outlet. 17

In Fig. 7 we see that there is an agreement between Pco2_sat calculated for water of 18 Farfal Spring and water feeding into Rimstone Pool from June - October (i.e., Pco2_sat 19 between 2.2% and 2.8%). Similarly, values of spring model HCO3¯ concentration are 20 identical during this period and equal to 342 mg/l for both springs. These measurements 21 indicate similar flow conditions upstream from both groundwater discharge points. The water 22 observed at both discharges comes from the zone upstream of the infiltration zone. The 23 prevailing conditions in this area are observed by way of the mineralization and characteristic 24 parameters (spring model Pco2_sat and spring model HCO3¯ concentrations). On the other 25 hand, Pco2_eq is influenced by the site’s downstream conditions, and cannot provide 26 information related to the system’s upper compartment. 27

On the basis of this data, we can deduce that water originating in the epikarst 28 encounters an area of lower air Pco2, causing precipitation, and, thus, leading to a 29 considerably lower calcium-carbonate mineralization than that of the epikarst water. The 30 water residence time in this subsystem is sufficient, with this lower air Pco2, for it to reach a 31 new state of calcite equilibrium. Pco2_sat has small temporal variations, from 2.2% to 2.8%, 32 during these two cycles (Fig. 9), which indicates that flow conditions and water-rock 33 interaction times are relatively constant. This is an intrinsic characteristic of the Cussac 34 perched karstic system. 35 In this configuration (water precipitation), Pco2_sat equals the maximum air Pco2 of 36 the atmosphere in which water has flowed in the upper part of the infiltration zone. However, 37 contrary to our observations in the downstream area of the system (see hereafter), we do not 38 have direct access to Pco2_eq, which would be related to atmospheric air Pco2 in the upstream 39 area of the massif. 40

6.3. Downstream of the infiltration zone 41

Water originating in the upstream zone continues across the massif, forms a drainage 42 basin discharge (visible at one point in the cave referred to as the canyon) and continues to the 43 outlet at Farfal Spring, situated 700 m downstream. 44

The data provided by monitoring the water in Rimstone Pool (4 m² with a 4 cm water 45 depth) located in the cavity close to the system outlet, is of interest in that it allows the kinetic 46 factor of the equilibrium reactions to be approximated. In Fig. 9 it can be seen that water has a 47 large range of Pco2_eq variations. Pco2_eq in the water of Rimstone Pool follows Pco2_cave 48 as a function of time and has the same seasonal periodicity. This observation indicates that 49

11

liquid-gas equilibrium is reached very rapidly and that Pco2_eq is a good indicator of the area 1 near the outlet over which the water is drained. 2

In Fig. 9, water’s Pco2_eq in Farfal Spring, as with Rimstone Pool, shows a clearly 3 cyclic behaviour. The Pco2_eq (water) ranges between 1.3% and 3.5%, whereas that of the air 4 in the cave oscillates between 0.3% and 3%. These low measured values indicate that the cave 5 has greater exchanges with the outside air during the winter. The Pco2_eq of water gives a 6 more accurate indication of air Pco2 inside the massif. Water in this part of the infiltration 7 zone has a two-phase flow whereby CO2 is exchanged with air from the massif, the Pco2 of 8 which is highly variable as a function of time. 9

Influence of air on water equilibrium results in gassing and degassing phenomena 10 during water drainage through the transmission zone of the massif. This water can even 11 under-saturate in summer, through a renewed increase in Pco2_eq (Pco2_eq > Pco2_sat), 12 thereby regaining in aggressiveness (Fig. 9). But the water does not precipitate nor dissolve 13 calcite. This indicates a quick flow through the area downstream of the infiltration zone and a 14 low interaction time between gas, liquid, and solid phases. It can also indicate the absence of 15 conditions leading to an agitation of water such as a waterfall. Water cannot equilibrate its 16 bicarbonate concentration with new air Pco2 and appears super-saturated (Pco2_eq < Pco2_sat) 17 or under-saturated (Pco2_eq > Pco2_sat) depending on the air Pco2 encountered in this part of 18 the karstic system. A good alignment of the data along the G&D line in Fig. 7 depicts this 19 behaviour in Farfal Spring water. 20

Contrary to the stability of Farfal Spring, explained above, Pco2_sat of Rimstone Pool 21 water has cyclic variations, reflecting the fact that Rimstone Pool water is influenced by 22 calcite precipitation from December - May (low Pco2_cave). In Fig. 8, it can be seen that data 23 points shift between two G&D lines, which are representative of the state of equilibrium and 24 the season. In winter, the water is more strongly super-saturated, and has a much lower spring 25 model HCO3¯ concentration (210 mg/l), as a consequence of calcite precipitation. However, 26 the latter exhibits a threshold: when SIc decreases to approximately 0.25, precipitation no 27 longer occurs out of the weakly saturated water, or does so too slowly to be observed by the 28 temporal monitoring. Fig. 9 illustrates that in winter Pco2_sat of water does not reach the 29 value of Pco2_eq, thus indicating a small degree of super-saturation. 30

6.4. Towards the saturated zone 31

As a perched system, the site will not have a true saturated zone. However, because of 32 the excavation of Belingou Valley, there is a diffuse network of flows above the aquifer wall. 33 This network emerges along an effluent water line and is sampled by a positioned water-34 collection gutter. The spring model HCO3¯ concentration, and spring model Pco2_sat, of this 35 flow are 300 mg/l and 1.8%, respectively (Fig. 7). These values are lower than those of the 36 system’s other discharges, including the principal outlet. This would indicate that the water 37 from this diffuse network has precipitated in an environment poor in CO2. 38

Water from groundwater discharges similar to Ruijters and Farfal Springs could have 39 circulated above the “saturated” zone in low air Pco2 areas. The slow drainage through this 40 weakly karstified medium of the saturated zone gives the water time to degas, precipitate, and 41 infiltrate the region. The Pco2_sat of the gutter water reaches a maximum value of 1.8% for 42 the air Pco2 in the area above the “saturated” zone. 43

6.5. Functional model of the karst unsaturated zone 44

The combined use of the parameters proposed in our method has allowed us to 45 interpret the operational mode of the perched karstic system under study (Fig. 10). Our 46 observations indicate that dissolution occurs mainly in the epikarst zone where the air Pco2 is 47 higher than 3.0% to 5.2%. While, precipitation in the upper part of the infiltration zone 48

12

dominates due to degassing in an atmosphere containing Pco2 levels lower than 2.2% to 2.8%, 1 resulting in clogging of cracks and a reduction in infiltration flow. 2

This upper zone has the role of a calcium-carbonate equilibrium buffer and discharge 3 regulator. These characteristics have led to a surprisingly stable mineralization of the water 4 observed at the system outlet during both observed hydrologic cycles. In the area downstream 5 from the unsaturated zone, where the drainage is organised, the flows make use of an old 6 network of conduits (paleokarst), and are continuously readjusting their equilibrium with air 7 Pco2 of the ambient massif ranging from 1.3% to 3.5%, without dissolving or depositing 8 calcite. This phenomenon occurs further downstream, in the open air (travertine) or the 9 underlying saturated medium. 10

This method is promising for characterization of the drainage conditions in 11 hydrogeological systems, of atmospheric environment of underground flows, and for 12 differentiation between the different origins of such flows. 13

Finally, it should be pointed out that the CO2 dynamics of air in the massif are 14 different from those of air in the cave present in our study site. If exchanges do occur with 15 outside air, they are less pronounced in the network of cracks inside the massif than in the 16 large openings corresponding to the explorable cavities. 17

7. Summary and conclusions 18

The method described in this paper was designed to study geochemical equilibriums of 19 water in the infiltration zone while it flows through the unsaturated zone of a perched karstic 20 aquifer. When calcite is predominant, this method is based on the index of saturation with 21 respect to calcite (SIc) and water’s Pco2_eq. Each spring can be characterised by a linear 22 G&D fit with a slope of 1 in a (-log(Pco2_eq) ; SIc) graph. This line provides a model for 23 groundwater discharge and determines the spring model Pco2_sat and bicarbonate 24 concentration associated with it. The Pco2_sat also allows various groundwater discharges to 25 be compared in a (-log(Pco2_eq) ; SIc) graph and characterises their intrinsic properties. 26 Contrary to Pco2_eq, it is independent of the conditions under which water is sampled at a 27 site. The combined use of Pco2_eq and Pco2_sat allows CO2 content of air in which water 28 flows to be estimated and permits hypotheses to be made about characteristics of groundwater 29 flows. 30

We have thus shown that, in the case of epikarst water, Pco2_sat represents the 31 minimal Pco2 needed in air through which water flows, for this water to acquire by dissolution 32 its measured calcium-carbonate mineralization. In the case of water that has already 33 precipitated during the course of its flow underground, the Pco2_sat represents maximum air 34 Pco2 encountered in the massif (this is the case for Farfal and Ruijters Springs, and water 35 collected by the gutter). 36

A comparison between temporal variation of Pco2_sat and the Pco2_eq provides 37 insight into flow conditions and, in particular, water-air-rock exchange duration. If the latter is 38 sufficient for near equilibrium to be reached between solid, liquid, and gaseous phases, the 39 observed periodicity of air Pco2 in the massif is reflected in Pco2_sat (i.e., Rimstone Pool). If 40 the exchange duration is too short, the periodicity which may be found in Pco2_eq is absent 41 from Pco2_sat, and water is unbalanced with respect to calcite. In the current functional model 42 of the perched aquifer of Cussac, the calcium-carbonate mineralization is acquired by 43 dissolution in the epikarst. The ensuing transition of water through the infiltration zone, where 44 the air Pco2 is weaker, can cause calcite to precipitate. Water then reaches the saturated zone, 45 in a state of saturation that depends on variations in air Pco2 encountered in the massif. 46

The method proposed in this paper should be applied to systems that contain well 47 developed saturated zones and are characterized by mixing of different types of water. 48

49

13

Acknowledgments 1

The authors wish to thank the DREAL Aquitaine and the DRAC Aquitaine for their 2 funding and support. Financial support was also given by the European project FEDER. Ph 3 MALAURENT and J.B DESBRUNAIS are specially thanked for their field help. 4

5 6 7 8 Nomenclature 9

abbreviation definition [Ca2+] activity of calcium ion (Ca2+) molarity of calcium ion G&D Gassing&Degassing γCa2+ ionic activity coefficient of calcium ion γHCO3¯ ionic activity coefficient of bicarbonate ion [HCO3¯ ] activity of bicarbonate ion (HCO3¯ ) molarity of bicarbonate ion K0 Henry’s gas dissolution equilibrium constant K1 equilibrium constant of first ionisation of aqueous CO2 K2 equilibrium constant of second ionisation of aqueous CO2 Kc equilibrium constant of calcite dissolution Pco2 CO2 partial pressure Pco2_eq CO2 partial pressure with which dissolved CO2 would be at

atmospheric equilibrium Pco2_sat CO2 partial pressure with which dissolved CO2 would be at

atmospheric equilibrium when water is at equilibrium with calcite (Saturation Index with respect to calcite equal to zero)

pH potential Hydroxide, “p” is a mathematical operator meaning -log() pHm measured value of pH pHsat value of pH at which water would be at equilibrium with calcite

(Saturation Index with respect to calcite equal to zero) SIc Saturation Index with respect to calcite spring model HCO3¯ HCO3¯ value obtained by the G&D model of a spring spring model Pco2_sat Pco2_sat value obtained by the G&D model of a spring

10

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Figures 1

2

3 Figure 1 4 Geographic and geological context of Cussac Cave aquifer (Dordogne, France). Location of 5 groundwater discharges and air Pco2 measurements in Cussac Cave [1], Epikarst Spring; [2], 6 Farfal Spring [3], Ruijters Spring [4], Rimstone Pool [5], and gutter. 7 8

9 Figure 2 10 Schematic geological section of Cussac Cave. 11 12

17

1 Figure 3 2 Air Pco2 variations in Cussac Cave since 2005, measured at 100 m. and 350 m. from the 3 entrance, in both left and right directions. 4 5

6 Figure 4 7 Hydrograph of Farfal Spring and rainfall measured close to the spring. 8 9

18

1 Figure 5 2 Possible evolution of water in (-log(Pco2_eq) ; SIc) graph. CO2 partial pressure is also given 3 in percent, above the abscissa axis. This figure shows the bicarbonate concentration scale in 4 mg/l at 12°C. 5 6

7 Figure 6 8 Water samples from Farfal Spring (2007 - 2009) in t (-log(Pco2_eq) ; SIc) graph. The Farfal 9 Spring model is a least squares linear fit to the experimental data, with an imposed slope of 1. 10 It defines spring model Pco2_sat and spring model HCO3¯ . 11 12

19

1 Figure 7 2 Water samples from springs in Cussac Cave, in (-log(Pco2_eq) ; SIc) graph. Spring model 3 HCO3¯ concentration in mg/l is given for each spring: Epikarst Spring; Farfal Spring, Ruijters 4 Spring, Rimstone Pool, and gutter. 5 6 7

8 Figure 8 9 Water samples from Rimstone Pool in (-log(Pco2_eq) ; SIc) graph. Samples are grouped 10 according to their sampling date: summer, autumn, winter, and spring. Trends can be seen for 11 fall 2007 and 2008. Two models describing the evolution of Rimstone Pool water are 12 established from summer and winter sample distributions. 13 14

20

1 Figure 9 2 Evolution of equilibrium and saturation values of Pco2 from water in Farfal Spring and 3 Rimstone Pool (October 2007 - October 2009). Air Pco2 in Cussac Cave is also shown. 4 5

6 Figure 10 7 Model of water mineralization process as a function of Pco2 found in the unsaturated zone: 8 ground, epikarst, and sectors upstream and downstream from infiltration and saturated zones. 9 10

21

1 Table 1 2 Mean values and standard deviations of physicochemical characteristics of springs in Cussac 3 Cave. 4

5