Some chemical and/or isotope indicators are required to interpret radiocarbon data in terms of groundwater residence time. Among the simplest indicators, the Mg:Ca ratio is commonly used in carbonate aquifers. However, this ratio only accounts for the dissolution/precipitation reaction of calcite and dolomite, whereas other dissolution reactions and ion exchanges can greatly influence the chemistry of groundwater. The aim of this study was thus to describe how the Mg:Ca ratio can be modified by the hydrogeochemical setting to define a new indicator based on the major elements in a molasse basin in southeastern France. The new indicator was computed and the results were compared with radiocarbon activity. The study showed the new indicator correlated well with radiocarbon activity. The new indicator is more useful than the Mg:Ca ratio for long residence times and in the sectors where gypsum dissolution occurs.
 Knowledge of groundwater residence time is very useful in understanding groundwater dynamics in aquifers. In carbonate systems, the classical dating method is based on the radiocarbon activity of dissolved inorganic carbon (DIC). However, the interpretation of 14C activity in terms of groundwater age is not simple. Indeed many studies have demonstrated that it is impossible to estimate groundwater age without access to other isotopic or chemical indicators in addition to 14C activity [Glynn and Plummer, 2005; Clark and Fritz, 1997, and references therein]. Studies that use major and minor elements and isotopes provide complete and precise results [e.g., Edmunds and Smedley, 2000; Plummer and Sprinkle, 2001; Petrides et al., 2006] but these are only possible when all the necessary data are available.
 In this study, a simple chemical indicator is proposed to provide a semiquantitative assessment of groundwater residence time. This indicator is based on calcium, magnesium, sodium, potassium, and sulfate concentrations. The accuracy of the indicator is illustrated using data from the molasse aquifer of the Carpentras Basin (Southeastern France). The results suggest this indicator can be used to characterize groundwater dynamics and plan a sampling survey for radiocarbon activity analysis.
2. Hydrogeological Background
 The Carpentras Basin is located northwest of Avignon in the Rhône Valley (Southeastern France). It is a regional molassic foreland basin developed during the Miocene epoch in front of the Alpine block. It is the southern part of a larger basin constituted by twin sub-basins: the Carpentras Basin and the Valreas Basin.
 The substratum of the Carpentras Basin is composed of Cretaceous limestone. Basin material consists essentially of Tertiary deposits, which are typical sediments of tidal and deltaic environments: clays, marls, marly-sands and sandstones [Demarcq, 1970]. These are organized in successive, complex sequences of various facieses depending on regional geomorphologic evolution [Casagrande, 1989] and eustatic level variations [Besson et al., 2005]. In some places, molassic deposits are in contact with Oligocene gypsum. Finally, a Quaternary alluvial plain extends over the top of the Tertiary deposits.
 The sandy molassic layers constitute a complex multilayer aquifer that is 500 m thick in the basin center. The molassic aquifer is unconfined in the recharge area (on the eastern edge) but rapidly becomes semi-confined and then confined under marly and clayey layers toward the center and the west [Lalbat, 2006]. In the northern sector, the aquifer is confined and the Valreas Basin discharges into the Carpentras Basin. The piezometric map established by Faure  indicates three main groundwater flow directions that converge in the Bedarrides discharge zone in the western part of the basin (Figure 1). The first component flows north from the Valreas Basin, the second flows east from the main recharge zone, and the third flows south from a zone with low hydraulic gradients.
3. Main Chemical Reactions and Residence Time
 The most abundant minerals present in the Tertiary deposits of the Carpentras Basin are those commonly found in detritic basins, namely quartz, calcium and magnesium carbonates, evaporites and clay minerals. Since quartz is not very soluble, the hydrochemical evolution of groundwater in the aquifer follows the typical chemical evolution of groundwater in carbonate aquifers containing clay minerals and evaporites. The main chemical processes are the dissolution of carbonate minerals, the dissolution of evaporites, and cation exchange processes with clay (Table 1).
Table 1. Main Hydrochemical Reactions
k = Kdol/Kcc2, s = 10SIdol/102SIcc, SIdol and SIcc are the saturation index of dolomite and calcite respectively.
 Calcite and dolomite, the main carbonate minerals, are contained in bioclasts, are mixed with clay minerals in marly beds, and constitute the cement of the sandstone beds. The evaporite beds are composed primarily of gypsum/anhydrite. Halite has never been mentioned. As the aquifer is confined and no source of CO2 is known, the system is assumed to be closed.
 Calcite dissolution (1) is quite rapid relative to groundwater residence time in the aquifer (several tens of thousands of years). In fact, the process begins as soon as water infiltrates into the soil and takes place primarily in the unsaturated zones and the shallow alluvium aquifer. Consequently, groundwater in the molassic aquifer is at or close to saturation with calcite even near the recharge zone. Actually, 95% of samples have a calcite saturation index greater than −0.3 (the mean being −0.04) and the field pH ranges from 6.87 to 7.88 [Lalbat, 2006] indicating that DIC is made up of more than 79% bicarbonate ions [Appelo and Postma, 2005].
 Dolomite, however, takes much longer to dissolve. The congruent dissolution of dolomite (2) in Table 1 can only occur near the recharge zone while groundwater is still undersaturated with calcite. This reaction would therefore be limited to areas where water enters the molassic aquifer without flowing through an alluvial cover. Accordingly, it is not considered to be a key process at the basin level and is disregarded in this study.
 Incongruent dissolution of dolomite (3), on the other hand, occurs in a large part of the basin, where groundwater is saturated with calcite but not yet with dolomite. As the reaction (3) proceeds, the Mg:Ca equivalent ratio increases. The ratio is therefore time-dependent and theoretically tends toward k = Kdol/Kcc2 [Appelo and Postma, 2005].
 Clay beds contain Na+ and K+ but the affinities of both these elements are lesser than the affinities of Ca2+ and Mg2+. It follows that clay exchanges Na+ and K+ ions against Ca2+ and Mg2+ ions from groundwater (4). With the removal of Ca2+ and Mg2+ ions, the solution becomes undersaturated with respect to calcite and dolomite and these minerals consequently dissolve. However, the Ca2+ and Mg2+ ions in solution are immediately subject to further exchange processes with clay until equilibrium is established between the clay, the solution, and the carbonate minerals. As a result, the (Na + K):(Ca + Mg) equivalent ratio should increase as the ion exchange processes evolve, i.e. as groundwater residence time increases.
 Anhydrite/gypsum dissolution is much more rapid than that of dolomite. Hence, the main time-dependent chemical reactions in the molasse aquifer are the incongruent dissolution of dolomite and the ionic exchange processes. This suggests the following chemical indicator:
where Mg, Ca, Na, and K are concentrations in meq.1−1.
 However, because the dissolution of anhydrite/gypsum induces dedolomitization (6) when groundwater is at or near saturation with calcite, the Mg:Ca ratio may change abruptly and significantly with no relation to residence time. An SO42− fraction must therefore be included in the indicator i to correct Ca2+ and Mg2+:
where b = (1 + k · s)−1; a = k · s · b; k = Kdol · Kcc−2; s = 10SIdol · 102SIcc; and SIdol and SIcc are the saturation index of dolomite and calcite respectively. SO4(0) is an assessment of the background concentration of SO42−, i.e., the mean concentration without anhydrite/gypsum dissolution.
4. Application for the Carpentras Basin
4.1. Data and Method
 A total of 397 samples from the molassic aquifer were available in the Carpentras basin. The data came from four chemical surveys conducted between 1985 and 2005: 145 samples taken in 1985 [Roudier, 1987], 152 in 1996 [Musset, 1999], 40 in 2004 and 60 in 2005 [Lalbat, 2006]. The surveys covered the entire basin (Figure 2).
 In addition, 18 measurements of 14C activity with δ13C and 3H were available (Table 2). Sampling points were distributed across the basin along the ENE-WSW groundwater flow path. Unfortunately, pH, temperature, alkalinity, and major ion concentrations were not recorded with the radiocarbon activity measurements. Such complementary information is required for most adjustment models used to interpret radiocarbon activity in terms of residence time. Consequently, some simple models were used to compute radiocarbon ages [Ingerson and Pearson, 1964; Evans et al., 1979; Gonfiantini and Zuppi, 2003]. These adjusted ages are not accurate but they do provide a rough estimate of residence time.
Table 2. Radiocarbon Activity of DIC, δ13C, 3H, Mg:Ca Equivalent Ratio, and ic of Groundwater From the Molassic Aquifer With Estimations of Residence Time Provided by Adjustment Models
 The statistical study of the hydrochemical data showed that one can not distinguish the results of one survey from others [Lalbat, 2006]. Besides the 20-year observation period (1985–2005) was short in comparison with residence time. Consequently, it was assumed that the hydrochemical composition of the groundwater remained constant, i.e. steady-state conditions, over the observation period. The data from the four surveys are therefore treated as a unique dataset.
 The indicators Mg:Ca and ic were computed. The coefficient k was determined from the values of the reaction constants computed according to the temperature of sample. The coefficient s was determined for each point according to the estimation of the saturation index provided by Phreeqc software [Parkhurst and Appelo, 1999]. The value of SO4(0) was assumed to be equal to the mode of the distribution of the SO42− concentrations (about 0.65 meq.1−1). The Mg:Ca and ic values were kriged over the basin (Figure 2). The kriged ic values were then plotted as a function of the adjusted radiocarbon ages at the 18 locations where radiocarbon activities were measured previously (Figure 3).
 The computed Mg:Ca values are between 0.05 and 2.97 for the whole dataset. The kriged map of this ratio (Figure 2a) shows a complex, irregular pattern. In general, high value areas and low value areas are scattered throughout the basin and appear to be randomly distributed. Because of the spatial distribution of the ratio, it is not possible to draw a conclusion regarding the spatial evolution of the chemical age of water.
 Computed ic values vary from 0.02 to 9.4, i.e. a range three times greater than that of the Mg:Ca values. Unlike the Mg:Ca pattern, the ic indicator shows a more regular pattern (Figure 2b). The low ic values (less than 0.8) occur in the east and the northwest, in two homogeneous zones with smooth gradients. The intermediate and high values (greater than 1.6) are grouped together in three parts of the basin: the south, the north, and the southwest. The main difference between the maps shown in Figures 2a and 2b is related to the presence of gypsum around the Gigondas Massif. This highlights the importance of the SO4 correction.
 The radiocarbon activities of groundwater are between 0.18 and 86.55 pmc (percent modern carbon), i.e. between tens thousand of years and the present in radiocarbon age (Table 2). Tritium activities (measured in 1982 and 1985) are low in most cases (below the detection threshold), confirming these waters infiltrated before 1950. In fact, tritium activity is detectable in only three samples (91, 101 and 121), which also have the highest radiocarbon activities. These three waters are therefore more recent (waters sampled in 1985) and infiltrated after 1950. Radiocarbon and tritium data are thus consistent in distinguishing old water from young water. Moreover, measured radiocarbon activities cover the whole range of radiocarbon ages and decrease gradually along the groundwater path from ENE to WSW.
 The kriged ic values increase globally with adjusted radiocarbon ages (Figure 3). The squared correlation coefficient (R2) is 0.56.
5. Discussion and Conclusion
 The pattern of the Mg:Ca ratio in the Carpentras Basin cannot be explained by the residence time of groundwater alone. The Mg:Ca ratio does not distinguish truly old waters from waters that appear to be old because of dedolomitization, nor is it useful when groundwater is saturated with calcite and dolomite. When the Mg:Ca ratio is modified to account for dedolomitization and ion exchanges on clay, the new computed ratio, ic, is relatively well correlated (R2 = 0.56) with adjusted radiocarbon ages accounting for uncertainties on adjustment models and appears to be a good indicator of groundwater residence time in the context of the Carpentras Basin.
 The pattern of ic (Figure 2b), i.e. the pattern of residence time, shows that the hydraulic gradient does not fit the increase in residence time. First, the high ic values in the north can be interpreted as the entry of old groundwater from the Valreas Basin. The value of ic decreases toward the south due to mixing with younger groundwater in the Carpentras Basin. Second, molassic sediments in the south are very clayey and the hydraulic gradient is very low. As a result, groundwater in this area could be almost stagnant with a high residence time and, accordingly, a high ic value.
 The available radiocarbon data do not show the high residence times in the north and south because the 14C survey was designed mainly from piezometric data to fit on a flow line from the eastern recharge zone to the western discharge zone. As expected, 14C activity decreases from east to west while residence time increases, but it does not provide much information on the flow pattern at the basin level because the data are not distributed throughout the whole basin. The ic indicator would clearly be useful for designing an optimal and efficient survey. It could be particularly effective when groundwater paths are complex like in multilayered aquifers, aquifers with multiscaled flows [Tòth, 1995], or aquifers with hydraulic barriers.
 Only 18 activities of 14C were available in the basin. This is not a sample-size large enough to statistically test the correlation, and more data from different systems would have to be used to confirm this result and better define the limits of the method. However, in Figure 3, the 29-sample scatterplot computed from the Valreas molassic basin data [Huneau, 2000] following the same method is very close to the regression line (except for young waters).
 The ic indicator could be calibrated against adjusted radiocarbon ages by regression if enough 14C data were available. It could then be used for quantitative estimations of residence time. Moreover, concentrations of major ions are almost always available and the analysis of these ions is 20 to 30 times less costly than radiocarbon analysis. So ic could be a powerful tool for enhancing the knowledge of flow patterns, particularly in large basins since it can provide denser information at less cost. It is theoretically less accurate than radiocarbon ages but radiocarbon activity is influenced by many unknown components of the system (organic matter, fossil organic carbon, mantel degassing, etc) and residence time is the result of a model. The ic indicator would thus be a good compromise between accuracy and cost.
 In conclusion, ic could be used in three steps of a hydrogeological study: first to plan the radiocarbon survey; second to calibrate against the adjusted radiocarbon residence times; and third to improve the spatial density of information.