IDENTIFICATION OF THE CONTRIBUTING AREA TO RIVER DISCHARGE DURING LOW-FLOW PERIOD

The increasing severity of hydrological droughts in the Mediterranean basin related to climate change raises the need to understand the processes sustaining low-flow. The purpose of this paper is to trial simple mixing model approaches first to identify and then quantify streamflow contribution during low-water periods. An approach based on the coupling of geochemical data with hydrological data allows quantifying flow contributions. In complement, monitoring during the low water period was used to investigate the drying up the trajectory of each geological reservoir individually. Data were collected 5 during the summer of 2018 and 2019 on a Mediterranean river (Gardon de Sainte Croix). The identification of the end-members was performed after the identification of groundwater geochemical signature clustered according to the geological nature of the reservoir. Two complementary methods validate further the characterisation: rock leaching experiments and unsupervised classification (k-means). The use of G-EMMA mixing model coupled with hydrological monitoring of the main river discharge rate shows major disparities in the contribution of the geological units, showing a reservoir with a minor contribution in high 10 flow becoming preponderant during the low-flow period. This finding revealed to be of the utmost importance for managing water resources during the dry period

schists turn into black mica schists (Arnaud, 1999). Rocks are dated between Cambrian and Ordovician for basement rocks and 100 between Bajocian and Hettangian for sedimentary rocks. In terms of land cover, the basin is composed of 90 % of forests and is sparsely populated with low agricultural activity showing less than 2 % of agricultural land. Inhabitants are about 1,200 on average during the year. Anthropic activities that can impact the stream water quality include tourism, with only two campsites and a cheese factory, all located in the downstream section of the basin. Hence the basin can be considered as little affected by human activity and suitable to trial our approach carry out our research. Hydrogeological analyses in the watershed suggest the 105 existence of a water body in the small limestone causse due to its slightly synclinal structure (Faure et al., 2009). The presence of this aquifer corroborates with the presence of a large number of springs at the limit of the sedimentary area. For the schistose part of the basin, no study suggests, to our knowledge, the presence of a water body in these areas. Only the small alluvial plains (very restricted in our basin) are likely to constitute an aquifer with limited capacity, directly connected to the live river channels (Faure et al., 2009). 110 Low-flow values are severe in this watershed, with a discharge rate as low as 100 l/s, namely < 1 l/s/km 2 , at the end of the dry season ( Figure 2). Those low-flow levels occur rather late, with a minimum flow often found during September or October.
The end of the dry season is determined by heavy autumn thunderstorms typical of the region-this study span over, two years 2018 and 2019. A large inter-annual variability can be detected in the period between 2017 and 2019. The year 2018 is notable with a relatively high low-water flow, twice as high as in other years. Therefore, it can be assumed that the analysis of the 115 contributions during these periods may shed some light on the differences in processes leading to this inter-annual variability in the flows. The volumetric discharge rate monitoring reveals that rainfall events have a very low impact on the river flow.
It can be seen that discharge rate variations during the three years of observation are due to rainy episodes, but those present during the summer period lead to low peaks in a very short time. We note that during these events, the flow returns to a level lower than that of the flow measured before the event in 1 to 3 days, which proves that the recharge brought by these rains to 120 the subsurface reservoirs is negligible and makes it possible to disregard it in our future modelling.

Sampling and analysis
To identify the hydrogeochemical end-members, a prospecting campaign was carried out before the low-flow period between April and June 2018. Groundwater samples were collected at 17 sites in the watershed (see Figure 1). Boreholes were preferred,   but only a small number of relevant boreholes exist in the area, so most groundwater samples were collected on springs. The 125 prospecting campaign was completed with existing data from the French National Groundwater Data Access Portal (ADES) to increase the number of observation points and consolidate the characterisation of the geochemical end-members. Physical 5 https://doi.org/10.5194/hess-2021-267 Preprint. Discussion started: 31 May 2021 c Author(s) 2021. CC BY 4.0 License. and chemical parameters (temperature, redox potential, hydrogen potential and alkalinity) were measured in situ at sampling sites. These measurements were carried out using a Hach SL 1000 multimeter. Temperature and electrical conductivity were measured with a CDC 401 probe, PH with a PHC 201 probe and redox potential with an MTC 101 probe. Alkalinity was also 130 measured with a Hach multimeter using the reactive chemkey 8 636 200 for schist and granitic groundwater and 8 636 100 for limestone groundwater. Samples for the analysis of major ions were collected in 2 polyethene tubes (one for the cation and one for the anion). Water was filtered through a 0.25 µm cellulose acetate membrane filter. Tubes for the cation analysis were acidified to PH 2 with a drop of nitric acid titrated to 0.5 N and stored until analysis. The analysis was performed by ion chromatography (930 Compact ICFlex, Methrom). Major elements were carried out at the Laboratory of Environmental 135 Isotope Geochemistry, University of Nîmes, EA 7352 CHROME.
For monitoring the low-flow period, the observation site was downsized to two representative sites for each reservoir. These points were selected based on the results of the prospective campaign and the identification of the geochemical end-members (Table 1). The selection of groundwater site was made based on logistical reasons because not all sites could be monitored during 140 the low-water period due to their non-perenity or poor accessibility. Spring with groundwater samples showing the influence of several geologies or boreholes located in the alluvial aquifer were also discarded from the monitoring to avoid bias in the characterisation of the end-members as they draw directly on surface water, and hence do not represent the geochemical signature of the local geological basement. Two monitoring campaigns were carried out during the summer of 2018 and 2019.
Both spanned from June to October; 6 springs and boreholes sites and one surface water point located at the basin outlet were 145 sampled every week. The 2018 campaign focus on the characterisation of the groundwater contribution during the drying up period of the river with weekly monitoring, a greater frequency for surface water and bi-monthly for groundwater. The 2019 monitoring period was completed to include a spatial analysis where the stream was sampled on several sections (4), and was also collected for analysing ( Figure 1). In addition to monitoring, an additional campaign was carried out in 2019 to analyse the spatial contribution of tributaries to the main watercourse throughout its route. Gauging and sampling were performed on five sites distributed along the main river, and six tributaries were targeted (3 per side) using the same sampling and laboratory analysis method presented above. The discharge measure was carried out by diluting gauging on the tributaries and exploring 155 the velocity field using a current meter for the main watercourse. The operation aimed to analyse the contribution of the reservoirs with a spatial approach. However, only one tributary on the northern slope could be analysed as the two others were dry.
2.3 Identification of end-members and selection of representative springs for low-flow surveys 2.3.1 Using groundwater analysis to characterise the end-members 160 The main assumption behind the geochemical approach is that the stream is a discrete mixture of the different groundwater sources in the watershed. The samples analyses were categorised according to the reservoir geological nature and independent statistical analysis based on different graphical representations. Two diagrams for graphical representation are used: the piper diagram, which presents the relative concentration of major elements, and the bivariate solute-solute plots that show absolute value results. end-members were defined by investigating the results from these two graphs, seeking to differentiate ground-165 waters according to the geology of their reservoirs. To validate the identified hydrogeochemical end-members, a principal component analysis (Christophersen, 1992;Long and Valder, 2011) is applied. A definition of end-members by classification was also carried out. This was done by cluster analysis using "k-means", a classification method used in other studies (Fabbrocino et al., 2019;Monjerezi et al., 2011;Moya et al., 2015) to define end-members in a more complex system. Mean analyses were based on major ion concentration normalised to the total dissolved solids to avoid dilution. The number of end-members 170 was defined by the average silhouette method defined by Rousseeuw (1987).

Validation of the end-member geochemical signature with a rock leaching experiments
To confirm the validity of defined hydrogeochemical end-members, a rock leaching approach was implemented. It aims to strengthen the validity of the previously defined end-members by using an inverse approach. Rocks samples representative from these formations are collected, and the rock leaching interaction experiment is carried out in the laboratory the geochemical 175 signature of the formation representing the geology (see Figure 3). This approach defines pristine groundwater and allows us to eliminates end-member showing mixed signature between formations.
The leaching protocol was based on the widely used Afnor X31-210 standard and other articles (Chae et al., 2006;Gong et al., 2011;Grathwohl and Susset, 2009;Yu et al., 2015). For this purpose, three rock samples were collected in each of the identified geological units. Samples were all larger than 10 cm in size, a portion of each sample was set aside for rock sample 180 stable isotopes of water and physicochemical parameters such as electrical conductivity and alkalinity. (Barthold et al., 2011;Bresciani et al., 2018;Burns et al., 2001). In contrast to most research papers, usual conservative tracers are not considered in this study (the stable isotopes of water, bromides and chlorides), as conservative tracers are not affected by interactions with rocks, and hence cannot be used to differentiate the water according to their geological reservoirs (Appelo and Postma, 2005).
One of the study objectives is to test a simple method based on common and cheap tracers. Thus major elements are preferred 200 to other more sophisticated tracers such as the strontium isotope ratio, for instance, used in other studies (Rose and Fullagar, 2005). The methodology to define the number of required tracers and the parameterisation for the use of the mixing model is based on a methodology developed by Barthold et al. (2011). This method first investigates correlations between the different tracers in order to eliminate redundant tracers and retain a number of tracers equal to the number of end-members plus one.
Tracers showing little variability or little correlation with the different end-members are also disregarded for this purpose.

end-member Mixing Model
The End-Member Mixing Analysis (EMMA) was chosen to assess the contribution of the different geochemical end-members identified. Our approach uses EMMA coupled with the Generalised Probability Uncertainty Estimate (GLUE), called G-EMMA (Delsman et al., 2013). This GLUE method, developed by (Beven and Binley, 1992), manages uncertainties by accepting variation in sets of input parameters. A full range of plausible results can be explored with model executions within a In term of the model configuration, the number of iterations chosen was set at 10 8 . To solve mixtures, all defined endmembers and all tracers must systematically be used. The option of "randomsolutes" was activated. It allows to vary randomly the order in which the tracers are used in the modelling calculation randomly. To investigate the impact of the definition of 220 geochemical end-members, four different methods were envisaged and compared. These methods are sorted in descending order according to their expected robustness and accuracy. The objective is to evaluate the loss incurred in the quality of results between these methods, which demand very distinct degrees of treatment: -The first approach so-called hereafter "Time window (1)". Each end-member is defined by its concentration in elements observed at a specific time in the groundwater and used to calculate the part of the mixture in the stream at the closest 225 time measure of observation recorded in the watercourse (preferably before or if suitable just after the measure). The advantage of this method is to consider the seasonal variability of the solute concentration of groundwater.
-The second method, so-called hereafter "Seasonal Mean (2)", consider the mean seasonal value of the groundwaters selected as representative of the reservoir. Therefore, all mixtures are resolved using the annual average of the groundwater sites previously defined as representative of the formation. The variability given to these end-members is defined by the 230 observed seasonal variability of the end-member.
-The third method, so-called hereafter "Geological Mean (3)", is based on an end-member signature defined by the average of the geochemical signature of all groundwater collected in the same geological formation for each reservoir without assessment of their representativeness. To give the same importance to each groundwater site, when some were sampled frequently whilst others were sampled just once, the average of the groundwater geochemical signature is 235 calculated at each site before averaging the full results. The variability defines the variability given to these end-members observed in each of the formations.
-The last method, the so-called "Leaching Method (4)", uses the results of the leachate experiment and considers these results as representative of different end-members. End-members are simply calculated by averaging the three leachates carried out for each formation. Due to the relatively small number of samples, the variability of these end-members is 240 defined by the variability of the results added to the ion chromatography analysis results (5 %).

Results
The results of the end-members' characterisation and validation are presented first, then the results of the mixture models are exposed in the second section. The characterisation of the end-members is based on the analyses of the collected groundwater samples. The K-means classification and leaching approaches presented above are then considered to consolidate the end- On the piper diagram, three end-members are identified (see Figure 4): The first one is marked by a magnesium and calcium signature for cations and bicarbonate for anions. This end-member is composed exclusively of water from sedimentary rock 255 reservoirs, mainly limestones and dolomites, hence consistent with the composition of 3 groundwater found in the literature (Clark and Fritz, 1997). This end-member is also identifiable on the bivariate solute-solute diagram where we can see that these waters have conductivity values much higher than other end-members, ranging between 400 and 450 µs/cm, while most of the others are below 100 µs/cm (see Figure 5). This high conductivity is related to high concentrations of three elements, calcium, magnesium and bicarbonate (3, 2, 5 MEQ/l), while concentrations of other elements remain relatively low.

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A predominance of sulphate for anions marks the second end-member. The signature for cations is relatively undifferentiated but tends towards a slightly more magnesian facies. This leads to groundwater marked by a predominance of sulfates ions located in water hosted in the black mica schist formation. However, all springs sampled in this formation do not systematically show an excess in sulphate. Indeed, sulphate contents vary from 0.3 to 1 MEQ/l and remain relatively low for all other elements.
According to previous studies, this sulphated signature could result from schists alteration (Mayer et al., 2010).

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Groundwaters from the third pole come from quartz mica schists reservoir. The end-member shows a large dispersion with an undifferentiated signature. These waters are characterised by a very low conductivity (less than 60 µS/cm) and very low concentration in all elements, which strongly differentiates them from other analysed end-members ( Figure 5). Therefore, this end-member can be considered as undifferentiated, i.e. no element is present in greater proportion than the others. The observed dispersion of the signature on the piper diagram can be explained by the very low concentrations of elements, leading to a large 270 variation of the geochemical facies due to only small variations of individual element concentrations.
Also presented in Figure 4 and 5, a unique groundwater sample collected in the granite show surprisingly high bicarbonate, calcium and magnesium content (2, 1 and 1 MEQ/l) and also, to a lesser extent, the presence of sulphates. These concentrations place this sample on the mixing line between two previously defined end-members, the limestone and the black mica schist endmembers. The influence of the limestone end-members seems coherent because of the topography and stratigraphic position of 275 the granitic layer crossing the limestone plateau. Moreover, drillings in the area show that the black mica schist layer is present just below the limestone plateau. It is, therefore, possible that springs collected in the granite sections are, in fact, water that percolated through the limestones and then the black mica schists.
A seasonal evolution in ion concentrations is clear in both the waters of the black mica schists and the limestones (see Figure   5). During the drought period, ions concentrations increase, particularly visible for Ca, Mg, HCO 3 and SO 4 . This increase in 280 concentration is 12 % for the limestone waters and 20 % for the black mica schists waters.
Finally sodium facies marks the water from wastewater treatment plants for cations and high concentrations of sulphates and chlorides for anions with a relatively high electric conductivity (350 µS/cm).

Rock leaching experiment
The results of the rock leaching experiments lead to leachate geochemical signatures quite close to theses observed for ground-285 water samples analyses. The differences observed between groundwater and leachate water are of the order of 20 % in conductivity with lower concentrations on average for leachate water. Four end-members of lixiviation are visible on the bivariate solute-solute diagrams of groundwater and leachate samples ( Figure 6). These results can be summarised as follow: -Black mica schist leachates show a high proportion of sulphates and higher magnesium than calcium contents.  -Quartz mica schists leachates are defined by a neutral signature with conductivity lower than 30 µS/cm. Larges amount of potassium is observed in the leachates of the crystalline rock samples typical of the weathering of potassium feldspars (Appelo and Postma, 2005;Clark and Fritz, 1997). Since no collected water shows this signature 300 marked in sodium and considering that this layer has a very small spatial footprint, this granitic reservoir is disregarded in estimating the contributions to streamflow. Leachate results raise questions regarding the relatively large amount of potassium in the metamorphic rock samples. These quantities are three times higher than those observed in the groundwaters. These differences can be explained by the leaching method (crushing of the rocks to a very fine granulometry), which favours the potassium solution via the alteration of potassium 305 feldspars (Appelo and Postma, 2005;Clark and Fritz, 1997) while K in situe may already have been lixiviated.

Validation of the end-member by statistical classification
In order to confirm the end-members' characterisation and clustering independence, a statistical approach has been carried out on collected groundwaters. Focussing on the groundwater end-member analyses, the WWTP's water was not included in the statistical analysis. The first step in this method is to define the number of clusters. The inertia curvature of groundwaters shows 310 in both cases that the optimum number of classes is three (Figure 7). This number of three classes corresponds to the number of identifiable end-members found in the catchment. This number is to be used for upcoming k-means analyses. Inertia curves define the k-means method based on the 3 classes, gives equivalent results to previous analyses on groundwater samples to characterise the end-members. Moreover, the three clusters defined by this method correspond to the three identified end-members and hence to the three main geological reservoirs, namely limestone, quartz mica schists and black mica schists.

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Indeed, the first cluster is defined by a low conductivity and high proportion of bicarbonates in the water, which is coherent with the quartz mica schists reservoir ( Table 2).
The second cluster is defined by high sulphates and magnesium proportion and corresponds to the black mica schists reservoir. The third shows a high proportion of calcium, magnesium and bicarbonates in the water, and high electrical conductivity, which is coherent with the limestone reservoir.

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The location of the groundwater samples, identified by clusters, are plotted on the geological map showing the good correspondence between the 3 clusters and the three geological reservoirs (see Figure 8). Only one outlier is visible and corresponds to the point presents in the granite formation and previously identified as a mixture of limestone and black mica schist.

Choice of tracers
Regarding the choice of tracers used in the mixing model, previous studies as ( Barthold et al., 2011;Christophersen, 1992) recommend disregarding those with too strong inter-correlation or too weak variances. Principal component analysis (Figure 9) shows the strong correlation between the limestone end-members (in green) with the Ca 2+ , Mg 2+ , HCO 3 − and Sr 2+ tracers.

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Black mica schist (in navy blue) is significantly connected to SO 2− 4 and to a lesser extent to Cl − and F − . The pole of quartz mica schist (in cyan) shows a very low variance with both axes. However, it shows a slight inverse correlation with the axis 2 which variance is explained by SO 2− 4 . Based on those observations selected tracers are HCO 2− 3 , SO 2− 4 , Mg 2+ and Na + . HCO 2− 3 was selected for its correlation with the limestone end-members and SO 2− 4 for its correlation with the black mica schist end-member. Sodium was also se-335 lected due to its connection to the wastewater pole. Minor ions have been disregarded due to their low frequency of detecting concentrated water, particularly for fluorides on Ca−HCO 3 water. Due to its low concentration in the totality of the measured elements, no tracers are specifically designed for quartz mica schists since it acts as a dilution pole for all tracers. Low mineralisation in all tracers is the marker of this end-member. To improve the efficiency of the model in the contribution calculation, the choice was made to add tracer to the tracers chosen by the end-members. Because of their strong explanation of variance, 340 calcium and magnesium were selected, but with the high correlation between these elements (Table 3), only magnesium is Figure 9. Principal component analysis .
selected to limit the weight of the calcareous water contribution to the mixtures. Magnesium is preferred at calcium because it is slightly correlated to the pole of black mica schists making it more relevant and different to Bicarbonates (Figure 9). These selected tracers have the particularity of being reactive in groundwater reservoirs, allowing them to be marked by the passage in this reservoir but can be considered as conservative in the watercourse. Indeed, in the stream, water-rock interactions are 345 reduced, and equilibrium is rapidly obtained with the atmosphere. The measurement of dissolved oxygen in the springs and surface water confirms this by revealing identical oxygen concentrations to those found in the streams and springs. In this analysis, it is evident that it is impossible to differentiate waters of quartz mica schists and rainwater. Indeed, rainwater collected in the area with an electrical conductivity of 14 µS/cm is only slightly lower than that of the mica-schist water, has 350 an average electrical conductivity of 44 µS/cm 2 . Moreover, rainwater shows an undifferentiated signature, similar to the water from the quartz mica schists reservoir. Hence, this model must be used exclusively in low-flow conditions so that the proportions of water identified as issued from quartz mica schists are not confused with the portion issued from rainwater.

Result of mixing analysis
The results obtained using the G-EMMA with the "time window" method are shown in Figure  The drying curve of these two reservoirs is consequently very different, reflecting two very different behaviours with a much steeper slope and therefore demonstrating a much lower low water production capacity for the quartz mica schists during the low-flow period. The specific flow rates calculated with respect to the outcropping surfaces of each geology are less than 1 l/s/km 2 for quartz mica schists and more than 2 l/s/km 2 for black mica schists. All this underlines the importance of the black 390 mica schists reservoir supporting low-flow levels worsening in the extremely low-flows period.

Uncertainly of mixing analysis
To compare the results obtained with the different approaches considered for end-members signature characterisation, the outputs of the four models (Time window, seasonal mean, geological mean and leaching experiment) were plotted together in Figure 11. All four approaches give similar results and trends than that observed with the "Time window" method. Dispersion in 395 the contributions remains high, reaching a variation of 25 % between the two quantiles and nearly 50 % between the limit of the models: time window and seasonal mean present low dispersion in the range of possible contributions. However, general trends seen on contribution graphs remain identifiable and consistent from one model to another, with an increase in the contribution of black mica schists and a decrease in the contribution of quartz mica schists during summers. The first autumn rains can explain the steep increase in the contribution of quartz mica schists and the decrease in black mica schists' contribution at the 400 end of the season. The autumn rains reverses the contribution of these two reservoirs as they recharge the quartz mica schists' reservoirs, which are much larger in surface area than those of the black mica schists and directly diluting the river water, acting, as a contributing of the quartz mica schists reservoir diluting the surface water.
Differences are nevertheless visible between the four outputs: The selection graph by geology, which uses average values of all water collected in the same formation, shows the greater variability for the contribution of the quartz mica schists reservoir.

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This variability can be explained by a larger dispersion in waters signature encompassing all groundwater analyses over the observed period, thus integrating seasonal variations and leading to the definition of less constrained end-members. This gives the model greater freedom to solve mixtures.
The "leaching method" also shows less constrained outputs. These are mainly visible on the contribution of the limestone pole, of which the contribution is more important than for the other three models outputs. This relates to the fact that limestone 410 leachate end-member is artificially less concentrated than for other approaches, leading to an overestimation of its contribution. There is also a difference between the "Time window" method and the "Seasonal mean" method while the signal appears smoothed. This difference can be explained by the account being taken or not of the seasonal drift (see Figure 11). Regarding the "seasonal average" output, the results show a lower contribution of the waters with the highest low-flow electrical conductivity and a higher contribution of the waters with the lowest loading.

Spatial analysis to modelling results
The investigation of the spatial distribution of the different reservoir contributions was carried out. This spatial approach consisted in collecting samples and measuring the flow rate along the river length along with the main tributaries on the same day. This campaign was carried out during the 2019 low-water period (October 10th). At that time, the measured flow rate was 142 l/s, while this year's lowest flow rate was 135 l/s. The measurement was performed on the three biggest tributaries in the 420 right and left banks. Only one of the targeted tributary was surveyed on the left bank, as all other streams had dried out.
The results underline the black mica schists' predominant contribution to low-flow throughout the watershed (see Figure   12). The results also show an uneven spatial distribution of the specific flow rate. The mainstream specific discharge varies widely from the headwater to the outlet, with more than 2 l/s/km 2 at the most upstream section (station 1, 6 or 8) decreasing to approximately 1 l/s/km 2 at the outlet (station 5). Regarding the tributaries, the differences are even greater with specific flows 425 of less than 0.1 L/km 2 on the Northern slope (left bank, station 7),and reaching nearly 2 l/s/km 2 on the Southern slope (right bank,6,7,9). The contribution of the upper limestone reservoir remains nevertheless a minor contribution (< 20 %, at station 1 or 6) and cannot explain the observed upstream high flow rates. It is noticeable that the upstream flow already relies heavily on the black mica-schists and quartz mica-schists reservoirs. The high upstream and southern slope specific flow rates may be explained by the presence of a black mica schist stratum, identified as the main source of water during low water levels, Mixture models are powerful tools that can deal with many scenarios and thus provide a wide range of possible solutions (Soulsby et al., 2003;Uhlenbrook and Hoeg, 2003). They deliver valuable information if the decisive parameters, such as uncertainties and end-members, are properly considered. The main challenge in studies using this tool concerns the avalibility  (Ali et al., 2010;Christophersen, 1992;Correa et al., 2019;Genereux, 1998;Iwasaki et al., 2015). heterogeneity in the geological formation or the weathering conditions and the need to consider a more appropriate value for defining end-members rather than a maximum or minimum.
In response to this issue, we test four different methods to define the end-members' signature and assess their relevance. As a reminder, the first two are based on the analysis of collected groundwater defined as representative of a specific reservoir, one considering the "seasonal mean" of the groundwater geochemical signature as an end-member, and the other takes into account 465 the geochemical signature of the groundwater samples, collected at roughly the same time as the modelled surface water.
The third method considers an average signature on all groundwater samples from the geological formation over the entire watershed, the "Geological Mean" approach, and the last one is based on the results of the rock leaching experiments, the "Leaching" approach. It appears that the methods based on rock leachate analyses and the "geological mean" present structural limitations. Regarding the "Leaching" approach, the shortcomings are linked to the limestone leachate experiments, with 470 leachates showing significantly lower mineralisation than that observed for the groundwater, for the limestone rock formation due to a close system concerning the gas CO 2 during the leaching experiment, imposed by the experimental conditions.
Regarding the "geological mean" method, the over-representation of the data on water collected during the pre-campaign period, between March and May 2018, i.e. in a hydrological situation of low average flow, induces an underestimation of the mineralisation of the end-member and an increase of the standard deviation. This leads to high variability in the obtained results 475 and their uncertainties.
The other two approaches, the "Time Window" and the "Seasonal Mean" approach, give very concordant results. However, slight discrepancies appear in the modelled parts of mixing (see Figure 11). This is especially visible in the second part of summer 2018 when the "Time Window" method differs from the "Seasonal Mean" method showing a minor decrease in the black mica schist reservoir contribution and a minor increase in the quartz mica-schists reservoir contribution. This discrepancy a visible dynamic after this event. This result suggests that the average seasonal method would not consider certain variations during the low-water period due to its excessive smoothing of the poles. Therefore, the 'Time Window' method would allow for results with greater temporal precision. Moreover, the absence of considering the seasonal variations of the end-members leads to an overestimation in low-flow of the mixing proportions of the reservoirs with a greater seasonal increase than the others.

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Despite the greater fluctuations for the "time window" method, it gives visibly finer results and allows a fine understanding of temporal dynamics.
Based on those observations, it can be recommend using the "Time Window" approach to identify the signature of endmembers in a context of significant seasonal variability. The other approaches allow for assessing the trends but are not precise enough to compute the precise part of mixing.

Discussion about results
The study of the contribution at the level of the watershed's outlet or, more generally, over the whole watershed shows the importance of black mica schists during low water periods. In marge of the low water periods, it can be seen that the majority of the water flow comes from the quartz mica schists. Nevertheless, the contribution of the black mica schist reservoir remains very important considering its small surface area of only 20 % of the catchment area. The drying curves of these two reservoirs 495 are very different, reflecting two very different behaviours with a much steeper slope and demonstrating a much lower water production capacity in low water levels for the quartz mica schists during the low-flow period. The specific flows calculated with the outcropping surfaces of each geology are less than 1 l/s/km 2 for the quartz mica schists and more than 2 l/s/km 2 for the black mica schists. All this underlines the importance of the black mica schist reservoir supporting the low water levels, which is even more marked when the flows are lower.

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The analysis of the spatial distribution is in agreement with the location of the reservoirs and provides relevant results on the distribution of the productive reservoirs. We can see that the black mica schists are the biggest contributors, and the main resource area of this formation comes from the upstream part of the catchment. This result may appear contradictory due to the absence of outcrops of this formation in this part but can be justified by the presence of this formation under the limestone plateau (Arnaud, 1999). Other factors support this assertion: on the slopes where the black mica schists are inexistent, the 505 flow rates are much lower than on the rest of the basin, and almost all the tributaries dry up during severe low water. These results allow the clear identification of the main reservoir in the low water support and could be used to guide stream water management in this catchment area to preserve the resource of this essential reservoir.
These robust results in the contribution consolidate the conclusions made by other authors who highlight the importance of groundwater in the hydrology of mountain areas (Gabrielli et al., 2012;Hale et al., 2016;Uchida et al., 2006). Nevertheless, 510 the significant contribution of groundwater from metamorphic rocks in the basin is in contrast to traditional hydrological assumptions that consider such basement rocks in mountainous regions as having limited aquifer potential (Younger, 2007).
However, there are significant differences between both schist reservoirs, with overall higher contributions from the black mica and lower contributions from the quartz mica schists. The analysis of the tributary contributions highlight an ever great variability linked to the upstream-downstream and south side north side oppositions. These show that the flow is mainly 515 produced during low-flow on the southern slope and, more precisely, on its upstream part. The contribution is mainly from the black mica schists in this upstream zone. One another tributary (the Valat des Oules) has a very high specific flow (1.7 l/s/km 2 ), with a contribution comming mainly from the quartz mica schists. This singularity lends credence to another hypothesis in which this difference in low-water productivity comes from a difference in weathering in the mica schists. This difference in alteration would give the more weathered rocks a greater storage capacity and higher productivity at low water.

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This higher productivity of the weathered zone has been shown in other studies (Floriancic et al., 2018;Mwakalila et al., 2002;Smith and Patton, 1981;Witty et al., 2003). It is shown that these weathered zones (e.g. saprolite or other regoliths) can serve as a larger baseflow maintenance reservoir than the underlying bedrock (Smith and Patton, 1981;Witty et al., 2003). This possible predominance of the weathered zone causes complications in interpreting the influence of bedrock type on baseflow due to the difficulty of separating it from the contribution of the unweathered zone (Mwakalila et al., 2002). It would be relevant 525 to test methods to differentiate these contributions such as the investigation based on the lithium isotopes ( (Millot et al., 2010)).
Others may be considered, indeed, a more important fracturing of a rock may cause great differences in contributions (Uchida et al., 2006), or the orientation of the schistosity plane of the layers oriented mainly towards the north (Arnaud, 1999) which can lead to more important storage of the reservoirs on the southern slope and more rapid draining of the groundwater from the northern slope.

Conclusions
The results presented in this article are convinsing. They show that the use of tracers, as basic as major elements, revealed to be relevant to identify the contribution of the different geological reservoir to streamflow during a low-flow period in small catchment areas. The method using groundwater major element analysis of each geological reservoir to characterise the endmembers leads to sound results and validation by statistical analysis, and rock leaching analysis provides robustness to the 535 end-members characterisation. Hence, the paper's first objective is validated: to identify and characterise the contributors to the stream flows based on simple major element analysis.
The second objective relates to the quantification of the contributions of each identified end-member. The different approaches used to characterise the geochemical signature of the end-member, i.e., "time window", "seasonal mean", "geological mean", and "leaching", lead to comparable results. The distinction of a specific geochemical end-member associated with each 540 geological reservoir and the measure of discharge rates allows us to quantify their contributions to the river flow. The results outline the discrepancy between the outcropping surface area of each geological reservoir and its contribution in terms of flow to the river.
It can be seen for this catchment area that the black mica schists reservoir become predominant during the e low-flow , although it shows only a relatively small spatial coverage. Moreover, the spatial analysis of flow contributions shows that the 545 main contribution of this formation comes from the upstream part of the catchment where this formation hardly outcrops.
Therefore, we can foresee a relatively large cover reservoir of this formation on this part of the catchment. These results highlight the key role of this reservoir and alert the stakeholders on the need to efficiently manage and preserve these specific water resources, especially in increasing pressure and climate change.
These encouraging results were probably facilitated because the basin is relatively simple from a geological perspective and 550 shows very little anthropic activity that could significantly impact the river's chemistry and complexify the analysis. It would appear relevant to trial this method on more complex catchments and/or those with a higher anthropic impact. The results of this study underline the predominance of a reservoir, with a small spatial extent in the support to low-water periods of the basin as a whole. They highlight the importance of a greater understanding of the functioning of watersheds at low-flows to develop a better strategy for the management and preservation of the resource because of future climate trends. Competing interests. The authors declare no conflict of interest.