Revisiting Cent-Fonts Fluviokarst Hydrological Properties with Conservative Temperature Approximation

We assess the errors produced by considering temperature as a conservative tracer in fluviokarst studies. Heat transfer that occurs between karstic Conduit System (CS) and Porous Fractured Matrix (PFM) is the reason why one should be careful in making this assumption without caution. We consider the karstic aquifer as an Open Thermodynamic System (OTS), which boundaries are permeable to thermal energy and water. The first principle of thermodynamics allows considering the enthalpy balance between the input and output flows. Combined with a continuity equation this leads to a two-equation system involving flows and temperatures. Steady conditions are approached during the recession period or during particular phases of pumping test experiments. After a theoretical study of the error induced by the conservative assumption in karst, we have applied the method to revisit the data collected during a complete campaign of pumping test. The method, restricted to selected data allowed retrieving values of base flow, mixing of flow, intrusions of streams, and aquifer answer to drawdown. The applicability of the method has been assessed in terms of propagation of the temporal fluctuations trough the solving but also in terms of conservative assumption itself. Our results allow retrieving the main hydrological properties of the karst as observed on field (timed volumetric samplings, geochemical analyses, step pumping test and allogenic intrusion of streams). This consistency argues in favor of the applicability of the conservative temperature method to investigating fluviokarst systems under controlled conditions.


Introduction and Presentation of Cent-Fonts Fluviokarst
This paper addresses the issue of using the water temperature as a conservative tracer for karstic functioning studies. Whereas costly investments are often necessary to evaluate the potential of karstic aquifers, temperature records may bring cheap complementary method for obtaining information. However underground flows undergo heat transfers with the embedding rocks by advection and by conduction. Despite of this difficulty several studies used temperature as a mixing tracer. Several works [1,2] study the water exchanges between underground flows and surface stream. Others [3] retrieved aquifer recharges solving heat transport equation constrained by measurements of vertical temperature. Slow and rapid equilibrations between ground water and aquifer rocks have been analyzed [4] to study the dynamics of exchanges in fractured carbonate systems. Genthon et al. [5] determined the deep preferential path of rainfall water in caves from annual temperature variations of spring. This author also used temperature to determine limestone drainage in lagoon by removing the  [16]. Note the location of the P7 borehole where far field temperature (T∞) has been recorded.   [16]. Note the location of the P7 borehole where far field temperature (T ∞ ) has been recorded.
Hydrology 2017, 4, 6 3 of 23 Figure 1. Simplified geological map of the Cent-Fonts karst, redrawn after Petelet et al. [16]. Note the location of the P7 borehole where far field temperature (T∞) has been recorded.  The Cent-Fonts karst matches precisely the fluviokarst idea depicted by Smart [29]. Following his definition, fluviokarst consist: in "karst landscapes where the dominant landforms are valleys cut by surface rivers. Such original surface flow may relate either to low initial permeability before caves (and hence underground drains) had developed, or to reduced permeability due to ground freezing in a periglacial environment. In both cases the valleys become dry as karstification improves underground drainage" [30]. White [31,32] proposed a model where the hydrological behaviors are forced by the external boundary conditions. The various recharges in the CS are Allogenic Intrusions, internal Run-off and Porous Fractured Matrix flows. Intrusions of neighbor streams cause the first category of flows. The second results from sporadically floods that occur after heavy rainfalls. The third category gathers percolation flows through soils and epikarstic layer that reach the CS as a Diffuse Infiltration through the fractured and porous rocks of the aquitard (Figure 3a). In the local context of the Cent-Font watershed, the permanent course of Buèges stream matches the Upper Allogenic Stream. Later, at the swallow zone, the Buèges splits into a Surface Stream and an Upper Allogenic Intrusion. The Surface stream forms a non-perennial flow that joins the Hérault River north of Lamalou confluence. The Upper Allogenic Intrusion, Q UAI , joins the CS after an underground journey. Table 1 recalls the notations and acronyms of this article. This model also considers the Diffuse Infiltration that percolates through the CS wall. The only output flow of the fluviokarst is the spring, Q S , that falls into the Hérault River at the karstic base level. The Cent-Fonts karst matches precisely the fluviokarst idea depicted by Smart [29]. Following his definition, fluviokarst consist: in "karst landscapes where the dominant landforms are valleys cut by surface rivers. Such original surface flow may relate either to low initial permeability before caves (and hence underground drains) had developed, or to reduced permeability due to ground freezing in a periglacial environment. In both cases the valleys become dry as karstification improves underground drainage" [30]. White [31,32] proposed a model where the hydrological behaviors are forced by the external boundary conditions. The various recharges in the CS are Allogenic Intrusions, internal Run-off and Porous Fractured Matrix flows. Intrusions of neighbor streams cause the first category of flows. The second results from sporadically floods that occur after heavy rainfalls. The third category gathers percolation flows through soils and epikarstic layer that reach the CS as a Diffuse Infiltration through the fractured and porous rocks of the aquitard (Figure 3a). In the local context of the Cent-Font watershed, the permanent course of Buèges stream matches the Upper Allogenic Stream. Later, at the swallow zone, the Buèges splits into a Surface Stream and an Upper Allogenic Intrusion. The Surface stream forms a non-perennial flow that joins the Hérault River north of Lamalou confluence. The Upper Allogenic Intrusion, QUAI, joins the CS after an underground journey. Table 1 recalls the notations and acronyms of this article. This model also considers the Diffuse Infiltration that percolates through the CS wall. The only output flow of the fluviokarst is the spring, QS, that falls into the Hérault River at the karstic base level.  [31,32] but restricted to recession period (neither runoff nor surface flow). The karstic aquifer is embedded in a saturated PFM drained by a CS that gathers inflows. Outflow discharges at the base level of the neighbor stream through a spring (or pump). The hydrological system includes an upper allogenic stream, which flow joins the CS through a swallow zone. The CS also receives PFM, diffuse flow through an epikarstic layer; (b) An OTS is surrounded by pervious boundaries bounding the CV. Water and thermal energy inputs come from the allogenic streams and PFM. Outputs leave the CS through a spring (or pump). During recession no reverse flow occurs from CS to PFM.  [31,32] but restricted to recession period (neither runoff nor surface flow). The karstic aquifer is embedded in a saturated PFM drained by a CS that gathers inflows. Outflow discharges at the base level of the neighbor stream through a spring (or pump). The hydrological system includes an upper allogenic stream, which flow joins the CS through a swallow zone. The CS also receives PFM, diffuse flow through an epikarstic layer; (b) An OTS is surrounded by pervious boundaries bounding the CV. Water and thermal energy inputs come from the allogenic streams and PFM. Outputs leave the CS through a spring (or pump). During recession no reverse flow occurs from CS to PFM. As mentioned above, the Cent-Fonts resurgence has received much attention since decades (see Ladouche et al. [23] for a review). In September 1992, Cge and the city of Montpellier organized a series of pumping tests but heavy rainfalls and resulting runoff force to stop the experiments after only 16 days. This short time prevents reaching significant aquifer drawdowns despite the high rate of pumping (0.5 m 3 /s). Thus, this experimentation failed to assess the hydrological properties of the karst and let believe in a high water production potential [33].
Many field observations, such as gauging data of the spring, of the Hérault River and of the Buèges stream have been recorded for several years before the summer 2005 pumping test experiments. New boreholes were drilled. New records of temperatures and discharges were collected in Buèges and Hérault. Temperatures and hydraulic heads were also recorded in the "P7" (Figure 1), "Reco", "Cge" and "F3" boreholes ( Figure 2). The 2005 pumping test campaign started with a sequence of step-drawdown tests. Heavy pumping sequences followed with a high constant rate pumping and a drawdown constant pumping (see Table 1 for accurate chronology). The drawdown induced during these heavy pumping allowed speleological explorations of the Cent-Fonts chimney. It also opened the possibility of in situ timed volumetric gauging and geochemical sampling of Hérault River intrusions in the CS. This rich set of data has been extensively analyzed already [26,34]. The present work aims to revisit part of these data to assess the accuracy of conservative tracer assumption for water temperature. In the following, we will consider that two error sources mainly affect the applicability of the method: (1) The natural temporal instabilities that affect the data series; (2) the effect of conservative temperature assumption itself according to our previous work [35,36].
The next section of the paper recalls the theoretical context of Open Thermodynamic System for fluviokarst. Section 3 describes the data chosen from the 2005 pumping test campaign, Section 4 presents their analysis and accuracy assessments. The results are summarized and discussed in Section 5.

Theoretical Context
An Open Thermodynamic System (OTS) does not require a precise knowledge of the locations and shapes of its boundaries to study the balance of the fluxes that enter or quit its Control Volume (CV). In that sense, CS of fluviokarsts are similar to CV of OTS (Figure 3b). We will benefit of this analogy to study the balance of fluxes and energy in the Cent-Fonts fluviokarst CV despite the inaccurate knowledge of its boundaries [35].
In our previous work [36] we assessed the error resulting, in OTS, of conservative temperature assumption within the theoretical context of White's fluviokarst model. This analysis relied on two successive numerical solving of thermal behavior. The first considered the temperature as a conservative tracer, while the second, following works by Covington et al. [37,38] solved the complete set of energy equations including convective, diffusive and dispersive terms. The amplitude of differences between both results shows the first order of the error due to the conservative assumption. We drew abacus curves of this error versus thermal diffusivity ratio and the Peclet numbers, Prandtl numbers and Reynolds numbers of the CS. The error remains less than 1 percent in the dimensionless space and converges to zero for the most extremes values of karst features. This dimensionless error needs to be rescaled for each singular fluviokarst to calculate its physical amplitude.
In our study, we consider water as a Boussinesq fluid with constant thermal capacity, thermal expansion and density. As a result, water motion forms a zero divergence velocity field in the PFM and in the CS (Equation (1)). div( It is possible to convert the volume integrals over fluviokarst CS in flux integrals over the PFM boundaries and hydraulic sections of conduits entering or leaving the CS. Then, the terms of Equation (2) are equal to the input flows into the CS (positive algebraic values, q i ) and to the flows escaping from the CS (negative algebraic values, q o ). Therefore, the continuity equation leads to the mass conservation equation that links the various flows.
The first law of thermodynamics stipulates that the internal energy change of the CV (Equation (3)) corresponds to the balance of the energy differences between all the incoming and outgoing flows (index j) and considering the work done. Thus, the internal energy change (δE) is equal to the summation of: the enthalpy by unit of mass (h j ), the potential energy (e pot j ), the kinetic energy (e cin j ), the external heat transfer (δΦ j ) and the work exchanges (δW j ) with the surrounding [39,40].
In the following, we will consider no chemical contribution to enthalpy and flow transfers with negligible exchange between heat and work. We also will consider steady flux conditions in the CV (we discuss this point later). These hypotheses cancel the internal energy change but also the potential energy and kinetic energy changes. Then, Equation (3) becomes a balance between the specific enthalpies by unit of time of the flows entering (h i ) and escaping (h o ) the CS (Equation (4)).
Now, specific enthalpy depends only on thermal capacity (Cp) and temperature (referred to an arbitrary value T a ) (Equation (5)).
Finally, with constant density and thermal capacity Equation (6) reduces to a classical mixing equation (Equation (7)) that links temperatures ( • K or • C) and mass transfers in the CS.
Equations (2) and (7) form the basis of a linear system able to discover two unknown flows in the CS (so-called Q k and Q l in Equation (8)). Thus, these the two unknown flows are (Equation (9)).
As mentioned above, we will use the theoretical results of Machetel and Yuen [36] to quantify the sensitivity of the model to the conservative enthalpy assumption. However since we assumed that no other sources of heat are present (neither chemical heat, nor work conversion to heat), enthalpy conservation comes down on to temperature conservation. We will also use the differential form (Equation (10)) of Equation (9) to assess the effects of temperature and discharge uncertainties solving Equation (9).
The applicability of the method developed above depends on a "reasonably" steady CS. This is never the case in nature where temperature and flow variations due to human activities or diurnal or meteorological cycles disrupt steadiness. This is a recurring problem for hydrological studies. It can be significantly with careful choice of working periods and a 24-h moving averaging of data impacted by diurnal effects [10][11][12]. The thermal inertia of soil also damps the meteorological or seasonal effects with deepening [14,15].
However, we also have to trust on the common sense of operators and analysts to "instinctively" avoid the most unstable periods for data collection. Thus, the conservative temperature assumption is unsuitable for runoff flow studies or all other kinds of events that imply transient and unstable thermal or water fluxes in the CS. This is why, the present work use a restriction of the White's model to the recession period, with no run-off flow, and with a complete loss of the Upper Allogenic Stream (no surface stream). The 2005 Cent-Fonts pumping tests take place during the summer season when rainfalls are scarce on the watershed. However, even during that time, we focused the method on "steadiest" periods for water temperatures and flows. This is also why, despite available data until November, we stopped our analyses on 6 September (16:55) when a runoff due to a heavy thunderstorm flooded the boreholes (Figure 4).

Period (a): Data Collected Prior the Beginning of the Pumping Test
Several years of flows and water temperatures have been recorded at the karst spring and in Buèges since 1997 to study the recession of the base flows during dry periods. This knowledge is essential to understand the answers of the aquifer during the pumping tests. The base flow (Q S ) gathers the upper allogenic intrusion of Buèges stream (Q UAI ) and the diffuse infiltration (Q PFMB ). The study of the karst recession conducted from 1997 to 2001 used a modified Mangin method to distinguish the parts played by Q PFMB and Q UAI to the base flow [23]. Q S is described thank to three terms calculated from a Maillet homographic function [41]. Hence, two recession coefficients appear that characterizes the respective recession evolutions of Q PFMB or Q UAI . Ladouche et al. [23] calculated recession coefficients of 0.0080 (1998); 0.0088 (2000) and 0.0088 (day −1 ) (2001) for the Q PFMB contribution to the base flow [23] (p. 64).
Complementary flows and water temperatures have been recorded in the weeks preceding the step-drawdown sequence on 27 July (see Table 1 for an accurate chronology of the pumping tests). Figure 4 presents the far field (T ∞ ), the Upper Allogenic Intrusion (T UAI , Buèges), the Neighbor Allogenic Intrusion (T NAI , Hérault) and the CS (T CS , in Cge borehole) temperatures recorded from 1 July to 6 September. During the pumping tests, Cge's devices provided CS hydraulic heads and temperatures until their disconnection by drawdown. T CS temperature was also recorded in the F3 borehole at the output of the pump (see Figures 2 and 4). Complementary flows and water temperatures have been recorded in the weeks preceding the step-drawdown sequence on 27 July (see Table 1 for an accurate chronology of the pumping tests).

Period (b): Data Collected during the Step-Drawdown Sequence (27 to 30 July)
Step-drawdown sequences are one of the most often performed pumping test to find out the behavior of wells and aquifer features. For the Cent-Fonts pumping test campaign, the pump has been placed directly inside a large CS conduit. The hydraulic heads recorded in F3, Reco and Cge will display such close curves they will be undistinguishable at the Figure 5 scale despite the bottleneck between Cge and F3 boreholes (Figures 2 and 5). This superposition of curves reveals the hydraulic connectivity in this final part of the CS. Thus, the step-drawdown sequence will efficiently find out the resurgence yield by overestimating or underestimating the rate of pumping drying the spring.  Table 1. Note the four "coma-shaped" events (due to sudden deepening followed by recovering) that occurred on the hydraulic head for each of the pumping of the step-drawdown sequence (period b); the almost constant rate of hydraulic head increase during the constant high rate pumping (periods c and e) and the rapid stabilization of the hydraulic head during the equilibrium pumping (period g).

Period (b): Data Collected during the Step-Drawdown Sequence (27 to 30 July)
Step-drawdown sequences are one of the most often performed pumping test to find out the behavior of wells and aquifer features. For the Cent-Fonts pumping test campaign, the pump has been placed directly inside a large CS conduit. The hydraulic heads recorded in F3, Reco and Cge will display such close curves they will be undistinguishable at the Figure 5 scale despite the bottleneck between Cge and F3 boreholes (Figures 2 and 5). This superposition of curves reveals the hydraulic connectivity in this final part of the CS. Thus, the step-drawdown sequence will efficiently find out the resurgence yield by overestimating or underestimating the rate of pumping drying the spring. Table 2 recalls the step-drawdown chronology, the pumping rates and the drying effects on griffons. Q P of 0.2 and 0.3 m 3 /s did not achieve the completed drying of griffons while it was reached for 0.4 and 0.5 m 3 /s [26] (pp. 55-59). These results allow inferring that between 27 July and 30 July the base flow of the resurgence spring (that is Q PFMB + Q UAI ) was ranging between 0.3 and 0.4 m 3 /s. Four "coma-shaped" events (due to sudden deepening followed by recovering) occurred on the hydraulic head for each pumping of the step-drawdown sequence ( Figure 5, Period (b)). During that time, the CS temperature remains constant to a few tens of degree while, on the opposite, T UAI (Buèges) and T NAI (Hérault) display diurnal temperature oscillations that reach 1 to 3 degrees ( Figure 4). These diurnal temperature variations oscillate over 4 degrees, of meteorological trend that affect both T UAI and T NAI between 11 July and 30 July. The meteorological trend has the same amplitude on T UAI and T NAI . The amplitude of T UAI diurnal oscillations remains lower than those of T NAI because of shortness Buèges course and its low emergence temperature (12.5 • C). The stability of T CS despite these oscillations results from the damping effects of soils and 10 days underground transfer from the losses area to the Cent-Font resurgence [20].
(Hérault), TCS (recorded in CGE borehole until disconnection on 13 August 12h15 and at pump output), and T∞ (recorded in the P7 borehole).

Period (b): Data Collected during the Step-Drawdown Sequence (27 to 30 July)
Step-drawdown sequences are one of the most often performed pumping test to find out the behavior of wells and aquifer features. For the Cent-Fonts pumping test campaign, the pump has been placed directly inside a large CS conduit. The hydraulic heads recorded in F3, Reco and Cge will display such close curves they will be undistinguishable at the Figure 5 scale despite the bottleneck between Cge and F3 boreholes (Figures 2 and 5). This superposition of curves reveals the hydraulic connectivity in this final part of the CS. Thus, the step-drawdown sequence will efficiently find out the resurgence yield by overestimating or underestimating the rate of pumping drying the spring.  Table 1. Note the four "coma-shaped" events (due to sudden deepening followed by recovering) that occurred on the hydraulic head for each of the pumping of the step-drawdown sequence (period b); the almost constant rate of hydraulic head increase during the constant high rate pumping (periods c and e) and the rapid stabilization of the hydraulic head during the equilibrium pumping (period g).  Table 1. Note the four "coma-shaped" events (due to sudden deepening followed by recovering) that occurred on the hydraulic head for each of the pumping of the step-drawdown sequence (period b); the almost constant rate of hydraulic head increase during the constant high rate pumping (periods c and e) and the rapid stabilization of the hydraulic head during the equilibrium pumping (period g). Table 2.
Step-Drawdown Phase Long high rate pumping is used to assess the answer of the aquifer to drawdown. From 1 August to 9 August, the hydraulic head in the CS increases linearly with time (note that to avoid concave curves in Figure 5, the data are not plotted versus the log of time as usual). However, the drawdown induces a reversal of the hydraulic head that triggers the intrusion of Hérault in the CS and a new contribution that adds to the base flow Q PFMB coming from the PFM. Two new flows, Q NAI and Q PFMD are added to Q PFMB and Q UAI while spring drying let Q P be the only discharge of the CS. During that time, T UAI and T NAI display diurnal and meteorological variations while T ∞ , recorded 25 m below the surface in the P7 borehole, remains remarkably constant (Figure 4, Period (c)).
T CS is recorded both in the Cge and F3 boreholes. The first is measured close to the arrival of the neighbor allogenic intrusion of Hérault ( Figure 2). The second T CS is recorded deeper, close to the arrivals of Q UAI and Q PFMB . These two flows carry temperatures T UAI and T ∞ lower than this of T NAI . Thus, the values of the two T CS series diverge rapidly as soon as the drawdown triggers arriving of hot intrusive Hérault water in the CS branch near the Cge borehole. T CS (Cge recorded) increases rapidly a few hours after the starting of the high rate constant pumping from its 13.7 • C constant value since 2 August, 12h05. After a few days of transient evolutions, the temperatures in Cge and F3 boreholes stabilize respectively around 20 and 15 • C. Their temporal variations are correlated with the meteorological and diurnal trends observed for T NAI and T UAI (Figure 4, Period (c)).
The second series of T CS records (F3) stabilizes rapidly around 15 • C. It displays diurnal oscillating changes that are clearly due to the mixing of hot Q NAI with the cold Q PFMB , Q PFMD and Q UAI in the vicinity of the pump. This stabilization of the T CS increase indicates that Q NAI acts like an almost constant vadose flow despite the increase of the hydraulic head between the water table and Hérault [26] (p. 191).
According to Maréchal et al. [34] we will considerer in the following the dewatering of the conduit network as a supplementary outgoing flow from the CS, Q CS .

Period (d): Recovering Test (9 August)
The 6 h pump stop of 9 August allowed a recovering of 3.43 m ( Figure 5, Period (d), and [26] (p. 65). During the interruption, Q NAI brought warm water of Hérault that accumulated in the chimney above the pump. After pump re-starting, the temperature, T P displayed a short peak 9 August, 13h05 consecutive to the rapid extraction of this warm water. Similar phenomena occurred at the restarting 22 August, 13h30 and 3 September, 07h45 (Figure 4, Periods e and g).

Period (e): Constant High Rate Pumping (9 August to 2 September)
After 6 h of recovering, high rate pumping has been restarted from 9 August until 2 September. During Period (e), the hydraulic head decreased almost linearly with a slope similar to the one of Period (c). On 13 August at 12h15, the drawdown reached the level of the temperature probe in Cge borehole (51.6 m NGF), causing its disconnection and the loss of the T CS signal recorded there. At the end of Period (e), the drawdown approached the level of the pump in F3 that caused its stopping ( Table 1).
As mentioned above for Period (c), two diurnal and meteorological trends are noticeable in the T NAI and T UAI temperature records. These variations are also present in the last part of T CS (Cge recorded) and in T CS (F3 recorded) (Figure 4, Period (e)).
From the beginning of August, the drawdown allowed speleological explorations of the resurgence branches ( Figure 6). Surprisingly, while significant Q PFMD infiltrations were expected in CS, no water was apparently percolating through the chimney wall (Figure 6a-c). However, several cascading vadose flows were observed between marks 657-658 of the lifeline (Figure 6d

Period (e): Constant High Rate Pumping (9 August to 2 September)
After 6 h of recovering, high rate pumping has been restarted from 9 August until 2 September. During Period (e), the hydraulic head decreased almost linearly with a slope similar to the one of Period (c). On 13 August at 12h15, the drawdown reached the level of the temperature probe in Cge borehole (51.6 m NGF), causing its disconnection and the loss of the TCS signal recorded there. At the end of Period (e), the drawdown approached the level of the pump in F3 that caused its stopping ( Table 1).
As mentioned above for Period (c), two diurnal and meteorological trends are noticeable in the TNAI and TUAI temperature records. These variations are also present in the last part of TCS (Cge recorded) and in TCS (F3 recorded) (Figure 4, Period (e)).
From the beginning of August, the drawdown allowed speleological explorations of the resurgence branches ( Figure 6). Surprisingly, while significant QPFMD infiltrations were expected in CS, no water was apparently percolating through the chimney wall (Figure 6a-c). However, several cascading vadose flows were observed between marks 657-658 of the lifeline (Figure 6d Table 3); (e) Second Hérault intrusion at lifeline mark 670 (1 September) (CS2 in Table 3).
Water samples were collected 1 September at the above intrusion points. We used PP ® bottles previously washed with chlorydric acid, then bromydric acids, to prevent contamination [42]. Bottles and corks have been rinsed four times on site. The solutions have been filtered, acidified and  Table 3); (e) Second Hérault intrusion at lifeline mark 670 (1 September) (CS2 in Table 3).
Water samples were collected 1 September at the above intrusion points. We used PP ® bottles previously washed with chlorydric acid, then bromydric acids, to prevent contamination [42]. Bottles and corks have been rinsed four times on site. The solutions have been filtered, acidified and prepared in two dilutions for analysis. Complementary samples were collected the same day at the Buèges spring, in Hérault and at the pump. The samples were analyzed for the Rb, Sr, and Ba on the VG Plasmaquad II turbo ICPMS of Montpellier 2 University (Table 3 and Figure 7). Sr, Rb, and Ba have been chosen as field tracers for water circulation and mixing [4] Petelet et al. 2003). Figure 7 shows the alignment of the samples in a (Ba/Sr) vs. (Rb/Sr) graph. The alignment of point denotes a mixing between two poles [43]. According to the regression curves and the rate of pumping Q P = 0.4 m 3 /s, Q NAI ranges from 0.039 to 0.048 m 3 /s for Ba, from 0.060 to 0.083 m 3 /s for Sr, and from 0.077 to 0.087 m 3 /s for Rb. However, the lower values of the Ba/Sr ratio may reflect a sorption effect onto mineral-water interfaces [44]. The averaged value of these six measures gives Q NAI = 0.066 m 3 /s.  The samples were analyzed for the Rb, Sr, and Ba on the VG Plasmaquad II turbo ICPMS of Montpellier 2 University (Table 3 and Figure 7). Sr, Rb, and Ba have been chosen as field tracers for water circulation and mixing [4] Petelet et al. 2003). Figure 7 shows the alignment of the samples in a (Ba/Sr) vs. (Rb/Sr) graph. The alignment of point denotes a mixing between two poles [45]. According to the regression curves and the rate of pumping QP = 0.4 m 3 /s, QNAI ranges from 0.039 to 0.048 m 3 /s for Ba, from 0.060 to 0.083 m 3 /s for Sr, and from 0.077 to 0.087 m 3 /s for Rb. However, the lower values of the Ba/Sr ratio may reflect a sorption effect onto mineral-water interfaces [46]. The averaged value of these six measures gives QNAI = 0.066 m 3 /s.  Table 3). The alignments of points are characteristic of a two-pole mixing between Buèges and water Hérault. Two dilutions have been applied on the samples before ICPMS analyses (open squares: dilution by a factor two, open circles: no dilution). Assuming that Buèges water composition is characteristic of the far field water composition, we can write, after Vidal [45]: QNAI = QP (cP − cUAI)/(cNAI − cUAI), where cP, cUAI and cNAI respectively stand for mass concentrations of Rb, Ba and Sr in QP, QUAI and QNAI (Table 3).

Period (f): Recovering Test (2 September to 3 September)
A second stop of the pump lasts 24 hours and 25 minutes, from 2 September to 3 September, that induced a 13.49 m recovering in the chimney ( Figure 5).

Period (g): Drawdown Constant Pumping (3 September to 6 September)
The equilibrium-pumping (Period (g)) followed one month of constant pumping at constant rate that resulted in an important drawdown. After the recovering of Period (f), the equilibrium-pumping aimed to assess the dynamics of aquifer answer to hydraulic head. It started on 3 September at 7h45 with QP = 0.324 m 3 /s. The pumping rate has been dropped to QP = 0.304-0.305 m 3 /s a few hours later to stabilize the hydraulic head at 35.0 ± 0.1 m NGF ( Figure 5).
Since, this value is around 40 m deeper than the karst base level the Hérault intrusion remained active (the first intrusion of Hérault occurred for 76.7 m NGF on 1 August at 07h10).  Table 3). The alignments of points are characteristic of a two-pole mixing between Buèges and water Hérault. Two dilutions have been applied on the samples before ICPMS analyses (open squares: dilution by a factor two, open circles: no dilution). Assuming that Buèges water composition is characteristic of the far field water composition, we can write, after Vidal [43]: Q NAI = Q P (c P − c UAI )/(c NAI − c UAI ), where c P , c UAI and c NAI respectively stand for mass concentrations of Rb, Ba and Sr in Q P , Q UAI and Q NAI (Table 3).

Period (f): Recovering Test (2 September to 3 September)
A second stop of the pump lasts 24 hours and 25 minutes, from 2 September to 3 September, that induced a 13.49 m recovering in the chimney ( Figure 5).

Period (g): Drawdown Constant Pumping (3 September to 6 September)
The equilibrium-pumping (Period (g)) followed one month of constant pumping at constant rate that resulted in an important drawdown. After the recovering of Period (f), the equilibrium-pumping aimed to assess the dynamics of aquifer answer to hydraulic head. It started on 3 September at 7h45 with Q P = 0.324 m 3 /s. The pumping rate has been dropped to Q P = 0.304-0.305 m 3 /s a few hours later to stabilize the hydraulic head at 35.0 ± 0.1 m NGF ( Figure 5).
Since, this value is around 40 m deeper than the karst base level the Hérault intrusion remained active (the first intrusion of Hérault occurred for 76.7 m NGF on 1 August at 07h10).

Revisiting the 2005 Pumping Test Data
The challenge of studying temperature as a conservative tracer also faces the natural complexity of karsts, which CS mixes water coming from low resistance conduits and low permeability PFM. A few decades ago, studies were often considering medium where CS was not disrupting the aquifer but continuous models were unsatisfactorily. Since a few years, improved analytical models take better into account for the different behavior of the two types of reservoirs [34] or even three reservoirs [45]. However, despite the importance of calibration for the models, temperature has not been used probably because of the non-conservative character of this signal [26,34]. In the following we will take benefit of particular periods of the pumping test to get new constraints for the models.
Our process consists, firstly, to revisit the data of Period (a) to recalculate the base flow Q PFMB that forms the background over which the assessment of Q PFMD is possible. Secondly, we benefit of the base flow knowledge to reevaluate the intrusion of Hérault, Q NAI , on Period (g). Thirdly, relying on Q PFMB and Q NAI , we re-assess Q PFMD , the answer of the aquifer to drawdown, during the constant pumping (Periods (c) and (e)).

Revisiting the Data
Unlike Maréchal et al. [34], but following the results of [26] (p. 64), we consider that the recession of the Cent-Fonts base flow is better described separating the Buèges contribution Q UAI . Then, the recession of Q PFMB is calculated using Equation (11) in which we need to set the amplitude coefficient Without pumping, the only flow leaving the CS is the one of the spring. In July 2005, as the surface course of Buèges fully disappears, and since no pumping affects the resurgence, no drawdown occurs in the CS. Under these natural conditions Q S gathers Q UAI and Q PFMB and the water table in CS sits on top of the base level by a few centimeters. This weak hydraulic head is enough to prevent Hérault to intrude.
Then, replacing q k = Q PFMB , T k = T ∞ , q l = −Q S , T l = T CS , q i = Q UAI and T i = T UAI in Equation (8) leads to the Equation (12) below where the spring discharge Q S and the base flow Q PFMB are unknowns.
It is, therefore, possible to fix Q PFMB (t o ) in the recession curve with the values Q UAI , T UAI , T CS and T ∞ recorded for several weeks. Figure 8 displays an enlargement of these records from 14 July (00:00) to 19 July (23:55). T UAI displays diurnal oscillations of 0.2 to 0.4 • C around its 24-h moving averaging and a small meteorological increasing trend of a few degrees (Figure 8, top). In bottom panel of Figure 8, Q UAI also displays diurnal oscillations due to the water catchments upstream of the swallow zone. Concurrently, T ∞ and T CS remain remarkably stable (Figure 8, top). The Q PFMB curve in the bottom panel of Figure 8 displays the results of Equation (12) solving. We calculated its mean values (0.336 m 3 /s) and affected it at the median time to = 16 July (12:00) to extrapolate the PFM base flow for the remainder of our study (Equation (13)).

Assessment of Error Due to Data Variability
Two kinds of inaccuracy may affect the measures and, therefore, the use of QUAI, TUAI, TCS and T∞ for the method described in this article. The first are the precisions of the measures while the second relate to the difference between the steady state and the physical conditions in the CV. In the following, we will consider that modern thermometers result in negligible errors (less than 0.1 °C) in front of those resulting of unsteady behaviors. For Buèges gauging, the level error δQUAI at the swallow zone is not explicitly mentioned [26]. However, it is reduced by the total swallowing that limits it to the one of the zone entry. It is also reduced by the low flow context that allows more accurate gauging [44]. Therefore, without better assessment of this error, it seems reasonable to consider that it remains lower than a few liters by second. This level matches the one of standard errors induced by the diurnal variations (Table 4).
Equation (10) provides a powerful tool to assess how errors spread through the solving. According our preceding comments, and considering the stability of TCS and T∞, we have reported δT∞ = 0 and δTCS = 0 in Equation (10). The differential form of Equation (9) becomes Equation (14), for which the numerical coefficients have been calculated by using the mean values and the Standard Errors of temperatures and flows. The conduit system temperature T CS recorded in the CGS borehole and the matrix-conduit flow temperature T ∞ are almost constant over this period while the upstream allogenic intrusion temperature T UAI displays both diurnal and meteorological trends that are smoothed by the 24-h averaging. The upstream allogenic intrusion, Q UAI , also displays a diurnal behavior due to water catchments upstream of the swallow zone. Q PFM , is solved with Equation (14).

Assessment of Error Due to Data Variability
Two kinds of inaccuracy may affect the measures and, therefore, the use of Q UAI , T UAI , T CS and T ∞ for the method described in this article. The first are the precisions of the measures while the second relate to the difference between the steady state and the physical conditions in the CV. In the following, we will consider that modern thermometers result in negligible errors (less than 0.1 • C) in front of those resulting of unsteady behaviors. For Buèges gauging, the level error δQ UAI at the swallow zone is not explicitly mentioned [26]. However, it is reduced by the total swallowing that limits it to the one of the zone entry. It is also reduced by the low flow context that allows more accurate gauging [46]. Therefore, without better assessment of this error, it seems reasonable to consider that it remains lower than a few liters by second. This level matches the one of standard errors induced by the diurnal variations (Table 4).
Equation (10) provides a powerful tool to assess how errors spread through the solving. According our preceding comments, and considering the stability of T CS and T ∞ , we have reported δT ∞ = 0 and δT CS = 0 in Equation (10). The differential form of Equation (9) becomes Equation (14), for which the numerical coefficients have been calculated by using the mean values and the Standard Errors of temperatures and flows.
More realistic physical conditions have been searched for in the CS by operating 24-h moving averaging on the diurnal variations of raw data (Table 4, columns 6 and 8). Such numerical process accounts for the natural thermal and kinetic inertia acting along underground water flows and allows damping the error that could arise from their neglecting. Thus, over a few days, a meteorological trend increases the temperature recorded at the Buèges swallow zone by one to two • C (Figure 8). However, the final standard error remain limited to 0.64 • C on raw data ( Table 4, column 6) and to 0.55 • C after 24-h averaging of the data ( Table 4, column 8). The natural damping of temperature fluctuations that affects Q UAI during its underground travel to the CS prompts to consider the standard error as an upper bound.
Equation (14) shows that 1 • C of error on T UAI induces 38 L/s (liters by second) of error on Q PFMB ; and that one L/s of error on Q UAI induces 7 L/s on the final result. We can therefore expect that Q PFMB is obtained to a few tens of L/s (around 20%) ( Table 4, columns 7 and 9). This is consistent with the step drawdown tests that revealed a spring flow Q PFMB + Q UAI comprised between 0.3 and 0.4 m 3 /s.

Assessment of Error due the Conservative Temperature Assumption
Another way to explore the effects of non-stationarity on the solutions consists in confronting karst numerical models that consider (or not) temperature as a conservative tracer. This has been done in a previous study where several numerical models have been calculated over very broad ranges of karst morphological and hydrological parameters. According to Equation (15) of [36] a first order of the error induced by the conservative temperature assumption is reached by the following Equation (15): The error, ε', is calculated versus the hydrological and morphological properties as thermal diffusivity ratio (9.93), Conduit Peclet number (1.5 × 10 8 ), Prandtl number (6.99) and Conduit Reynolds number (4.29 × 10 4 ). Tables 1 and 5 (Table 4, Period (a)) the first order of the error δT = 1.93 • C. Coming back to Equation (14), we can see that it may induce 0.073 m 3 /s of error for Q PFMB . This result is higher but remains consistent with the previous estimate and the results of the step drawdown tests.

Revisiting the Data
As recalled above, the equilibrium-pumping that started on 3 September (7h45) and ended on 6 September (6h00) followed one month of constant pumping and a one day recovering. After a few hours, the initial rate Q P = 0.324 m 3 /s has been lowered to Q P = 0.304-0.305 m 3 /s that stabilized the hydraulic head at 35.0 ± 0.1 m NGF ( Figure 5). This hydraulic head is around 40 m deeper than the base level Hérault. Consequently, the Hérault intrusion Q NAI remained fully active during all the equilibrium-pumping.
During Period (g), the incoming flows in the CS are Q UAI , Q NAI and both basic and drawdown induced PFM contribution Q PFM = Q PFMB + Q PFMD . These input flows equilibrate the output flow Q P while the stabilization of the hydraulic implies that the dewatering of the CS stops (Q CS = 0). Hence, Equation (9) can be rewritten as Equation (16) to calculate Q NAI , and Q PFM .
We focus on a remarkably stable 24-h data range from 4 September (12:00) to 5 September (12:00) ( Figure 9). Indeed, the sinusoidal shapes of T UAI and T NAI are fully damped by the 24-h moving averaging, while T ∞ , T P , and Q UAI remain rather constant.
The bottom panel of Figure 9 displays the results obtained for Q NAI and Q PFM . They lead to mean values of Q NAI = 0.070 m 3 /s and Q PFM = 0.219 m 3 /s. The first agrees well with the geochemical results presented in Section 3 while the second is only a few L/s higher than the base flow Q PFMB = 0.216 m 3 /s obtained from Equation (11) for t = 5 September (00:00). This seems indicate that, a few hours after stabilization of the hydraulic head, the PFM contribution due to drawdown, Q PFMD , is very low.  Table 1). The conduit system temperature (TCS) and the matrix-conduit flow temperature (TP) are stable over this period while the Upstream Allogenic Intrusion temperature (TUAI) and the Neighbor Allogenic Intrusion temperature (TNAI) display sinusoidal diurnal trends that are smoothed by the 24-h moving averaging. Bottom: The Upstream Allogenic Intrusion recharge (QUAI) and the pump discharge (QP) remain almost constant during Period (g). Solving of Equation (16)

Assessment of Error Due to Data Variability
A procedure similar to the one described in Period (a) has been applied to Period (g) assessing the error due to data variability. The mean values of the parameters obtained on this interval have been introduced in the reduced form of Equation (10) to calculate the propagation of these errors through the resolution process (Equation (17) In this analysis, we will consider that pump gauging error δQP is negligible in front of δQUAI. Equation (17) shows that 1 °C of error on TNAI induces 5.6 l/s of error on QNAI or QPFM; that of 1 l/s on QUAI results in 0.760 l/s; and that 1 °C on TUAI induces 1.2 l/s. When the standard error of Table 4 are introduced in Equation (17), the error falls to a few l/s (a few %) ( Table 4, Period (g)).  Table 1). The conduit system temperature (T CS ) and the matrix-conduit flow temperature (T P ) are stable over this period while the Upstream Allogenic Intrusion temperature (T UAI ) and the Neighbor Allogenic Intrusion temperature (T NAI ) display sinusoidal diurnal trends that are smoothed by the 24-h moving averaging. Bottom: The Upstream Allogenic Intrusion recharge (Q UAI ) and the pump discharge (Q P ) remain almost constant during Period (g). Solving of Equation (16)

Assessment of Error Due to Data Variability
A procedure similar to the one described in Period (a) has been applied to Period (g) assessing the error due to data variability. The mean values of the parameters obtained on this interval have been introduced in the reduced form of Equation (10) to calculate the propagation of these errors through the resolution process (Equation (17)).
In this analysis, we will consider that pump gauging error δQ P is negligible in front of δQ UAI . Equation (17) shows that 1 • C of error on T NAI induces 5.6 L/s of error on Q NAI or Q PFM ; that of 1 L/s on Q UAI results in 0.760 L/s; and that 1 • C on T UAI induces 1.2 L/s. When the standard error of Table 4 are introduced in Equation (17), the error falls to a few L/s (a few %) ( Table 4, Period (g)).

Assessment of Error Due the Conservative Temperature Assumption
During the equilibrium pumping, but also during constant pumping, most of the CS mixing occurs near the pump, in the top part of the chimney just beside Hérault (Figure 2). This proximity causes the diurnal oscillation of TP that occur with a delay of 20 h (Figure 4). The drawdown changes significantly the configuration of the CV with a mixing zone close to Hérault. The distance between the river and the chimney that contains the pump is less than 200 m. We have to take these consequences of the drawdown to assess the error due to the conservative temperature approximation during heavy pumping. Therefore, using these delay and distance to estimate the properties of the CV, the CS Peclet number and the Conduit Reynolds number fall respectively to Pe = 3.9 × 10 6 and Re = 2.78 × 10 4 ( Table 5). The ratio of (PFM to Water) thermal diffusivities and the Prandtl number remain unchanged. We will use this new dimensionless configuration revisiting the data on Periods (e) and (g). (With these new values the abacus curves of Figure 4 of [36] tell that ε' reaches around 0.002 at the exit of the CS. With ε' = 0.002, T P = 288.88 K, T NAI = 298.25 K and T ∞ = 285.35 K (Table 4, Period (g)) δT reaches 0.62 • C. Through Equation (17), it induces a 0.003 m 3 /s error for Q PFM . Similarly to the comparison of error on Period (a), both methods of error assessment lead to consistent results.

Revisiting the Data
The knowledge of Q PFMB and Q NAI makes possible a backward analysis of the data recorded during Periods (c) and (e). Indeed, Q PFMB forms the background over which it is possible to assess Q PFMD . On the other hand, the vadose character of the Hérault intrusion results in a constant amplitude despite an increasing drawdown [26] (p. 191). These two previous results bring two "corner stones" situations separated by the constant pumping sequence. This allows us calculating two unknown flows: Q PFM that includes the drawdown induced contribution Q PFMD and the dewatering of the CS (Q CS ). The linear increase of the hydraulic head with time over Periods (c) and (e) ( Figure 5) suggests a constant dewatering rate, bolstering us to assume a near steady CV situation. The input flows are Q UAI , Q NAI , Q PFMB , Q PFMD and the output flows are Q CS and Q P .
In order to maintain these "constant" conditions at best, our data processing skipped the data 24 h before and after the stopping. This allowed avoiding the transient phenomena observed at the restarting of the pump for temperature ( Figure 4) and discharges. Consequently, we focused our analysis from 10 August (00:00) to 1 September (19:10). Within the context, Equation (9) can be rewritten as Equation (17).
The brutal increase of the temperature records in the Cge borehole shows that, as soon as Hérault intrudes through the horizontal shallow branch of the CS, T CS (Cge) is less representative of the dewatering temperature T CS . Therefore, we will alternatively consider that the temperature recorded at the pump may represents another assessment T CS (f3). This assumption seems reasonable since T CS (f3) is only a few degrees higher than the T CS temperature obtained on Period (a) before the mixing with the hot Hérault water.
The results of calculations for Q PFM and Q CS are presented on the lower diagram of Figure 10. From Q PFM and Q PFMB (Equation (13)), it is easy to calculate Q PFMD . For both T CS (Cge) and T CS (f3) assumptions, Q PFMD (Cge) and Q PFMD (f3) curves display diurnal oscillations but do not display clear increasing trends despite of drawdown deepening. Figure 10 shows that Q PFMD (Cge), Q PFMD (f3), Q CS (Cge) and Q CS (f3) are clearly affected by the diurnal and meteorological oscillations on Q NAI and Q UAI . Considering the most advantageous situation T CS (Cge), Q PFMD ranges between 0.030 and 0.050 m 3 /s. However, this drawdown induced contribution is probably overestimated because of a too hot dewatering temperature assumption T CS . Indeed, the calculation forces the system to equilibrate on the pump temperature. This will increase the low temperature contribution Q PFM at the expense of the hot dewatering Q PFM . On the other hand Q PFMD (f3), computed taking the pump temperature as T CS seems really too low since it would induces a zero or even negative contribution of Q PFM to drawdown. In any case, these results seem consistent with short transient flows coming with the increase of the hydraulic head. These conclusions are consistent with the ones of Maréchal et al. [34], and consistent with the shortness of the flows observed at the beginning of the equilibrium-pumping phase.
Hydrology 2017, 4, 6 18 of 23 increasing trends despite of drawdown deepening. Figure 10 shows that QPFMD(Cge), QPFMD(f3), QCS(Cge) and QCS(f3) are clearly affected by the diurnal and meteorological oscillations on QNAI and QUAI. Considering the most advantageous situation TCS(Cge), QPFMD ranges between 0.030 and 0.050 m 3 /s. However, this drawdown induced contribution is probably overestimated because of a too hot dewatering temperature assumption TCS. Indeed, the calculation forces the system to equilibrate on the pump temperature. This will increase the low temperature contribution QPFM at the expense of the hot dewatering QPFM. On the other hand QPFMD(f3), computed taking the pump temperature as TCS seems really too low since it would induces a zero or even negative contribution of QPFM to drawdown. In any case, these results seem consistent with short transient flows coming with the increase of the hydraulic head. These conclusions are consistent with the ones of Maréchal et al. [34], and consistent with the shortness of the flows observed at the beginning of the equilibrium-pumping phase.  Table 1). Top: The records of the conduit system temperature (TCS) in CGE borehole have been interrupted after its drawdown disconnection 13 August ( Table 1). Top: The records of the conduit system temperature (T CS ) in CGE borehole have been interrupted after its drawdown disconnection 13 August (12:15). Two extreme hypotheses have been considered. The first extrapolating the last value measured T CS (CGE) = 19.67 • C; the second assuming T CS (F3) = T P . The temperature recorded at the pump output displays a low amplitude sinusoidal oscillation due to the direct intrusion of the Hérault intrusion. Concurrently, the matrix-conduit flow temperature remains constant. Bottom: Assessment of the matrix-conduit flow Q PFM and of Q CS corresponding to the dewatering of the CS. Q NAI is considered as constant. The matrix-conduit flow Q PFM gathers the base flow of the resurgence (Q PFMB ) and the supplementary contribution of matrix-conduit flow induced by drawdown Q PFMD .

Assessment of Error Due to Data Variability
Following the same procedure, the mean values of the parameter over this interval (Table 4-Period (e)) have been introduced into the reduced form of Equation (10) to establish the formal and numerical forms of Equation (20).
δQ PFM = 0.0044 δT ∞ + 0.039 δQ U AI + 0.0024 δT U AI + 0.447 δQ N AI + 0.0092 δT N AI δQ CS = −0.0044 δT ∞ − 1.289 δQ U AI − 0.0024 δT U AI − 1.697 δQ N AI − 0.0092 δT N AI (20) One • C of error on T CS value induces 4.4 L/s of error for Q PFM . Finally, 1 • C of error on T UAI induces 2.4 L/s of error and one • C on T NAI results in 9.2 L/s of error. The introduction of the Standard error (24SE- Table 4) in Equation (20) leads to 14 to 21 L/s of error on Q PFM and on Q CS . Thus, small amplitude of Q PFMD makes the error is of the same order than Q MCD itself.

Assessment of Error due to the Conservative Temperature Assumption
As mentioned above, we consider that the hydrological configuration induced by drawdown is the same the one of Period (g). Then, the CS Peclet number and the Conduit Reynolds number remain the same and, ε' keeps the same value around 0.002 at the exit of the CS.
Therefore, the error on temperature balance due to the conservative approximation δT remains of the order 0.62 • C. Such temperature error would induce several tens liters by second of errors.

Summary and Discussion
The heat and matter exchanges occurring through the karstic boundaries impose a consideration of the Open Thermodynamic System (OTS). Within this framework, the first principle of thermodynamics leads to an enthalpy balance between flows entering and leaving the CV. Combining this property with mass conservation leads to systems of two equations involving the flows and temperatures. If formal physical conditions (steady states) are never achieved in nature, they are approached during particular periods as recession or certain phases of the pumping tests. These periods have been used these to calculate "corner stones" descriptions of the hydraulic regime between which we extend the results. The restriction of our model to the quietest part of the recession period cuts off the risk of disruption an approximate steady state by flooding and the possibility of reverse flow from CS to PFM. That way the periods of data revisiting were chosen outside of the recovering and the analysis has been stopped as soon as the flood event of 6 September occurred.
Revisiting the data recorded during these three periods with our theoretical analyses leads to a recalculation of consistent hydrological behavior of the karstic system. Thus, the speleological, hydrological or geochemical observations validated by previous studies [26,34] are not refuted despite of a less optimistic yield of the resurgence. This is particularly the case for spring drying during the step drawdown sequence, the results of geochemical analyses or the base flow recession of the resurgence.
Even though it is never perfectly reached in nature, the steady state approximation is necessary to use the method. While such state is assumed, temperatures equilibrate at the PFM/Conduit interface. However, this situation does not mean cancelling of embedding rocks/water heat transfer at the interface. Indeed, as shown in Machetel and Yuen 2015, PFM temperature gradient is maintained by the advection of cold, far field, water that counteracts the heat diffusion from CS to PFM through the wall. During the recession period, mixing of intrusive flows hotter than far field temperature, results in CS temperature hotter than in PFM. However, when a steady state is reached (or approached), all these local conductive effects (inside PFM and CS but also between PFM and CS) are taken into account by the final enthalpy balance. This is the most interesting property of the OTS approach that refers to the comparison of integrated incoming and leaving external heat sources and not on the local thermal properties inside of the "black box". It is clear that what we called "conservative temperature assumption" may better be called as "conservative enthalpy approximation". However since we assumed that no other sources of heat are present (neither chemical heat, nor work conversion to heat); enthalpy conservation comes down on to temperature conservation.
Thus, the application of the method to the first period (before pumping) of the Cent-Fonts pumping test experiments allowed assessing the basic recession flow of the resurgence. Then, the equilibrium-pumping allowed assessing the Hérault intrusion and the supplementary contribution induced by drawdown. The analysis shows that errors induced by unsteadiness reach a few tens of liters by second. They are of the same order of magnitude than the errors induced by conservative approximation itself.
In conclusion, we have confirmed the validity for using the thermometric method by the field observations that never contradict the results. It would be advantageous; insofar data exists, to check the method on other sites. It could also be interesting and of relatively low additional costs to develop recording and processing of temperature profiting of next pumping experiments. Indeed, as it does not require sophisticated equipment or procedures, the additional costs should remain low compared to drilling and pumping operations.
Our works may open the opportunity of using the steadiest part of the pumping test sequences to calibrate the global operating mode of complex resurgence system. Combining energy equation and mass conservation equations, temperature measurements in surface waters and boreholes may allow assessing the flow properties in borehole or mixing in karst CS. It seems therefore constitute an efficient tool to separate and calculate the karstic properties and could be a promising tool worthwhile to apply on other sites.