# Imaging hydrological dynamics in karst unsaturated zones by time-lapse electrical resistivity tomography

Jian Zhang, Colette Sirieix, Dominique Genty, Fabien Salmon, Cecile Verdet, Sylvain Mateo, Shan Xu, Stephane Bujan, Ludovic Devaux, Marie Larcanche

► To cite this version:

Jian Zhang, Colette Sirieix, Dominique Genty, Fabien Salmon, Cecile Verdet, et al. Imaging hydrological dynamics in karst unsaturated zones by time-lapse electrical resistivity tomography. Science of the Total Environment, 2024, 907, pp.168037. 10.1016/j.scitotenv.2023.168037. hal-04650297

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1 **Imaging hydrological dynamics in karst unsaturated zones by time-lapse electrical resistivity tomography**

3 Jian Zhang<sup>a, b, c*</sup>, Colette Sirieix<sup>a, b*</sup>, Dominique Genty<sup>c</sup>, Fabien Salmon<sup>a, b</sup>, Cécile

4 Verdet<sup>a, b</sup>, Sylvain Mateo<sup>a, b</sup>, Shan Xu<sup>d</sup>, Stéphane Bujan<sup>c</sup>, Ludovic Devaux<sup>c</sup>, Marie

5 Larcanché<sup>a, b</sup>

6

7 <sup>a</sup> Université de Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295, F-33400, Talence,
France

9 <sup>b</sup> Arts et Metiers Institute of Technology, CNRS, Bordeaux INP, INRAE Université,
I2M, UMR 5295, F-33400 Talence, France

10

11 <sup>c</sup> Environnements et Paléoenvironnements Océaniques et Continentaux (EPOC),
UMR CNRS, 5805, Université de Bordeaux, 33615 Pessac Cedex, France

12

13 <sup>d</sup> School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, PR
China

14

15

16

17

18

19 * The corresponding authors: Jian Zhang and Colette Sirieix

20 E-mail: jian.zhang@u-bordeaux.fr and colette.sirieix@u-bordeaux.fr

21 Postal Address : Université de Bordeaux - I2M - UMR 5295 - Département GCE

22 Bâtiment A11, 351 Cours de la Libération, 33405 Talence Cedex

23
24 Abstract:

The hydrodynamics of karst terrain are highly complex due to the diverse
fractures and reservoirs within limestone formations. The time delay between rainfall
events and subsequent flow into reservoirs exhibits significant variability. However,
these hydrological processes are not easily visualized in karst topography. Subsurface
geophysics, specifically 2D time-lapse electrical resistivity tomography (ERT),
provides an effective method for studying the relationships between hydrological and
geophysical features. In our research, we adopted ERT in the Karst Critical Zone
(KCZ) to visualize specific karstic zones, including cave galleries, water storage
reservoirs, wetting fronts, soil layers, and potential preferential flow paths down to a
depth of 20 meters. To capture spatial and seasonal variations in resistivity, we
presented a comprehensive approach by combining sixteen inversion models obtained
between February 2020 and September 2022 above the Villars Cave in SW-France—a
well-known prehistoric cave. We used a multi-dimensional statistical technique called
Hierarchical Agglomerative Clustering (HAC) to create a composite model that
divided the synthetic ERT image into eight clusters representing different karst critical
zones. The ERT image clearly visualized the cave gallery with high resistivity values
that remained consistent throughout the seasons. Our analysis revealed a close
seasonal relationship between water excess and resistivity variations in most
infiltration zones, with time delays increasing with depth. The karst reservoirs, located
at significant depths compared to other clusters, displayed sensitivity to changes in
water excess but were primarily affected by fluctuations in water conductivity,
particularly during summer or dry periods. These findings have significant
implications for predicting rainwater infiltration pathways into caves, thereby
assisting in the conservation and preservation of prehistoric caves and their cultural
heritage.

50

51 **Keywords:** Electrical resistivity tomography; Karst reservoirs; Drip rate; Hierarchical
52 agglomerative clustering; Infiltration
The main formation process of karst landscapes is the dissolution of carbonate rocks, resulting in various types of pores, including compact and porous rock, joints, fractures, and fluid conduits (Ford and Williams, 2007). Karst groundwater is one of the most critical water resources worldwide, providing drinking water for approximately a quarter of the world's population (Ford and Williams, 2007). Improving our understanding of the complex hydrogeology of karst aquifers is of considerable importance regarding the protection of drinking water resources (White, 2002). However, karst aquifers, like “black boxes”, are typically characterized by features of fracture-permeable network transport with geometric uncertainty, posing observational challenges for aquifer characterizations (Vacher and Mylroie, 2002; Hartmann and Baker, 2017).

The application of 2D time-lapse electrical resistivity tomography (ERT) has the major advantage of being non-destructive and minimum-invasive when measuring the electrical resistivity targeting the air/soil/rock-filled volumes and water-filled voids in highly heterogeneous aquifers to analyze changes in groundwater characteristics (Samouëlian et al., 2005; Vanderborght et al., 2005; Al Hagrey, 2007; Brunet et al., 2010; Binley et al., 2015; Watlet et al., 2018). Several parameters contribute to variations in ERT measurements, including subsurface composition, moisture content, temperature, porosity, permeability, mineralization, instrumentation, noise, and survey configuration (Telford et al., 1990). ERT monitoring is an extremely efficient method for some hydro-geophysics studies (Kuras et al., 2009; Coscia et al., 2012; Revil et al., 2012; Uhlemann et al., 2016; 2017), including investigations of heterogeneous aquifers (Chen et al., 2018; Torrese et al., 2020; Yan et al., 2023), characterization of water storage zones (Pope et al., 2023; Delgado-Gonzalez et al., 2023; Kadam et al., 2023), and preferential flow studies (De-Carlo et al., 2021; Song et al., 2023).

More specifically, researchers have used ERT on karst landforms to identify
subsurface features, sinkholes, caves, and reservoir dynamics (Gautam et al., 2000;
Zhou et al., 2002; Valois et al., 2010; Chalikakis et al., 2011; Robert et al., 2011;
Carrière et al., 2013; Sirieix et al., 2014; Xu et al., 2017; Verdet et al., 2020; Leopold
et al., 2021). For example, ERT measurements have been utilized to visualize
resistivity variations in karst-unsaturated conduits, in order to assess the mingling of
surface water and matrix water within the upper Floridan karst aquifer in the USA
(Meyerhof et al., 2012). Moreover, ERT and magnetic resonance sounding (MRS)
were employed to investigate the influence of porous matrices in controlling the water
infiltration in apparent karst structures in southern France (Carrière et al., 2016).
Regarding the link between resistivity changes and flow rate variations, Xu et al.
(2017) revealed a close link between some cluster zones and measured underground
flows in the Lascaux Cave, SW-France. More recently, Watlet et al. (2018) used long-
term permanent electrical resistivity tomography (ERT) monitoring to investigate the
complex karst vadose areas in Belgium. This study revealed the recharge processes
with different hydro-dynamics, resulting in the clustering of different areas with a
contrasting evolution during the different hydrological cycles (Watlet et al., 2018).
Taken together, these studies have demonstrated the applicability of the ERT method
to karst hydrological research.

The Villars Cave is a typical shallow cave that developed in Jurassic limestone,
characterized by the presence of thin sandy clay Quaternary sediments at the surface,
together with weathered limestone areas that likely alter the drip flow rate and
geophysical signals, providing a specific geological site for geophysical research.
Previous work in the Villars Cave has provided isotopic insight into the seasonality of
infiltration (Genty et al., 2014; Zhang et al., 2020). However, important questions
remain regarding karst reservoir dynamics and geometry, such as the size, number,
and shape of karst unsaturated reservoirs and their dynamics (Genty et al., 2014). In
this study, the 2D TL-ERT method was utilized to investigate and continuously
monitor the subsurface geological features above the shallow Villars Cave over a
monitoring period of 2.5 years. To gain a comprehensive understanding, the 2D ERT
measurements were combined with soil borehole observations and hydrology
monitoring at three cave dripping sites. The purpose of the study is summarized as follows: firstly, we visualize and precisely located various water reservoirs, wetting fronts, soil layers, and cave galleries within the subsurface. This also include documenting their seasonal variations in resistivity to shed light on the dynamic behavior of these features. Secondly, the study seeks to explore the relationship between resistivity measurements and hydrological changes in the seepage zone above the cave galleries. By analyzing resistivity variations, we attempt to gain insights into the intricate interplay between subsurface water flow and resistivity distribution. Lastly, the study aims to identify preferential paths of water flow within the unsaturated zone above the Villars Cave. By visualizing the flow pathway patterns, we hope to reveal the complex hydrological dynamics occurring within the cave's surroundings. By addressing these objectives, the visualization for water infiltration pathways could be helpful in making strategies for the effective conservation and management of cave paintings. In fact, water infiltration could dissolve the paintings or, on the contrary, encourage the deposit of calcite veil that covers the rock paintings. On the other hand, modeling the vadose zone in karst hydrology presents challenges. This research has the potential to enhance our understanding of its behavior and improve modeling accuracy for karst hydrology. Understanding the reservoir and flux circulation is vital for potentially safeguarding the site spatially, such as from pollution or water-related issues, thereby contributing to cave protection. Ultimately, the research aims to improve water management practices, ensure the sustainable utilization and conservation of essential water resources, and evaluate and mitigate natural hazards linked to karst formations.

## 2. Studied area and cave monitoring sites

The Villars Cave (45°26′18″N, 0°47′2″E; Figure 1A; 1B) is located in the north of the Dordogne department, SW-France. The cave developed in a Middle Jurassic (Bajocian and Bathonian) limestone formation (Figure 1D). A complex geological network, over 10 km long, with orientation governed by tectonics (SE-NW), such as
the St. Pardoux fault, formed in the boundary between limestone and schist a few
kilometers north of Villars (Supplementary Figure 1A). The hills, covered with oak
and hornbeam, are about 50 m high (about 200 m NGF, Figure 1D), and are much less
steep than in the surrounding Vézère valley, creating a smoother landscape (Genty,
2008; Zhang et al., 2020). The Villars Cave site, monitored since 1996, has led to the
production of many paleo-climatological records from the study of its speleothems
above the cave itself (Genty et al., 2003, 2006, 2010; Wainer et al., 2009; 2011; 2013).
In addition to analyzing the stalagmites, several other factors have also been
monitored, including cave temperature, pCO2, hydrologic changes, and isotopic
changes in order to better interpret the stable isotope signal within the cave. The
overarching goals of this comprehensive monitoring effort were to provide a deeper
understanding of the stable isotope signal within the cave environment and its
implications for paleoclimate and hydrological processes (Genty et al., 2008; 2014;
Zhang et al., 2020).

The Villars Cave is located in a maritime climate region with mild winters and warm summers (Figure 1A). During part of the monitoring period (2007-2022), the total annual precipitation (P) over the Villars Cave was 1052 mm (standard deviation: SD=124 mm) (Genty, 2008; Genty et al., 2014; Zhang et al., 2020). In contrast to local precipitation, which is more or less distributed throughout the year, there is a considerable seasonal variation in local air temperature, which leads to a significant seasonal variation in water-excess, and consequently to cave stalactite dripping (Genty et al., 2014). The surface layer above the Villars Cave consists of brown soil, which is unevenly distributed and of varying thickness. Some areas have thin layers of soil that are only 0-20 cm thick, while other areas have soil layers that are over 50 cm thick. In addition, in certain areas, tree roots can be seen penetrating through limestone fractures to reach the ceiling of the Villars Cave, which is about 10 meters below the surface (Genty, 2008).
166 **3. Measurement and data processing**

167 **3.1 Meteorological data and drip discharge rate monitoring**

168 From 2020 to 2022, outside meteorological air temperature and precipitation
169 were collected from a weather station above the Villars Cave. The ETP (potential
evapotranspiration) and excess water (also known as effective rainfall) data come
170 from the nearby Meteo-France weather station (Saint-Martin de Freissengeas, 4.8 km
171 East). The ETP of each grid point is calculated by the Penman-Monteith method.
172

173 Drip water monitoring sites were set at different levels in the Villars Cave to
174 detect potential differences in the recharge of the karst aquifer (Figure 1D; Genty,
175 2008; Genty et al., 2014). Vil-#10A is located at the upper level of the cave, and the
176 drip points Vil-#1B and Vil-#3 (100 m away from Vil-#10A) are about 5 m apart,
177 located on the lower level of the cave (Supplementary Table 1; Figure 1D). The drip
178 rate sensor (acoustic STALAGMATE sensor) recorded the drip rate frequency at 15-
179 minute intervals from 10/2019 to 09/2022 from the surface of the sealed box equipped
180 with the acoustic sensor.

181 **3.2 Determination of depth and location of dripping stations by magnetic field**
182 **angle method**

183 The Magnetic Field Angle (MFA) method was used to determine the depth of
184 the dripping stations in the Villars Cave (Supplementary Figure 2; Supplementary
185 method). This method involves moving away from a reference point called Ground
186 Zero (GZ) along a predetermined line with the help of a receiver loop. When the
187 magnetic field is parallel with the ground surface, a null signal is obtained, and this
188 point is used to measure the depth.
189

189 In the study, the depth of the Vil-#10A station in the upper cave gallery was
190 calculated to be 14 meters below the surface. The depth of the Vil-#1B and Vil-#3
191 stations in the lower cave gallery was determined to be 36 meters below the surface
192 (Figures 1C & 1D, Supplementary Table 1). Specifically, the Vil-#10A station is
located 4.3 meters away from the profile of ERT profile (Figures 1C & 1D). On the other hand, the positions of Vil-#1B and Vil-#3 are stated to be approximately 100 meters away from the ERT profile shown in Figure 1C.

## 3.3 ERT measurements

ERT monitoring (Figure 1C) was established to characterize the temporal and spatial variation of the unsaturated area above and near the Villars Cave. From February 2020 to September 2022, we acquired 16 ERT profiles at a frequency of 1 to 2 months (Supplementary Table 2). After several field tests in February 2020, we decided to use three different electrical arrays, including the pole-dipole array with both forward and reverse measurements and an injection pulse duration of 500 ms, and the gradient array with an injection pulse duration of 250 ms. The three electrical arrays were concatenated before inversion. During the initial test survey, we verified the repeatability of the measurements using the method proposed by Peter-Borie et al. (2011). Measurements were made using a SYSCAL Pro resistivity meter with 72 stainless steel electrodes spaced 1 m apart making a 71 m long profile line (Figure 1C). The use of various permanent markers facilitated the precise relocation of the survey lines. Each electrode's position was determined using a Leica® laser theodolite. It is worth noting that from one survey to the next, the previous electrode holes can still be identified. Therefore, the accuracy of these locations is within a margin of less than 1 cm. In parallel, we also tested a 1.5 m electrode spacing to obtain a greater investigation depth (106.5 m long). An inversion resistivity model was calculated using the Res2Dinv® software, applying the L1 norm to the data and a model associated with the refinement of the mesh model (Loke, 2004) to account for large contrasts in resistivity. We performed seven iterations on each survey data set, after which the absolute error stabilized. After seven iterations, the inversion model misfit ranged from 0.83% to 1.7% for all 16 inversion models.
219 **3.3.1 Temperature correction**

220 The electrical resistivity measurement depends on the rock temperature, which 221 varies with time. We thus have corrected the ERT measurements for temperature 222 (Hayley et al., 2007; Genelle et al., 2012; Hermans et al., 2014). This correction 223 requires the knowledge of the temperature in the rock mass at any given time (Salmon 224 et al., 2023). The heat equation governing thermal diffusion therefore must be 225 reconsidered in terms of temperature. However, this equation requires the rock’s 226 thermal diffusivity, which is unknown. We, therefore, adjusted the thermal diffusivity 227 for the calculated temperature to match in situ measurements (Salmon et al., 2023). To 228 do this, we placed three thermocouple sensors at 0.1 m, 0.5 m, and 1 m below the 229 surface above the cave, close to the ERT profile location (about 3 m), and measured 230 the air temperature both inside and outside the caves.

231 Using the estimated diffusivity, the heat equation was calculated in the rock mass 232 to determine the temperature at each point within the massif over time. This 233 temperature calculation is performed in conjunction with the time series data. 234 Furthermore, a temperature correction was applied to the inversion resistivity data 235 using a ratio model (equation (1)), which is commonly used to correct resistivity data 236 with the corresponding reference temperature (Ma et al., 2011; Xu et al., 2015; 2017; 237 Supplementary Figure 3):

238
239
$$ \rho_c = \rho_i \times [1 + \delta \times (T_c - T_{\text{ref}})] \quad \mathbf{Eq. (1)} $$

240 Where ρ_c stands for resistivity after temperature correction, ρ_i is interpreted as 241 resistivity after inversion, and T_c represents temperature during the ERT survey. δ is 242 the temperature slope compensation value, which is set at 0.025 by most geophysicists 243 (Keller and Frischknecht, 1966; Besson et al., 2008). Consequently, we selected T_ref 244 as the reference temperature of 12.55°C, which is the average annual temperature 245 recorded in the cave during the entire monitoring year (Supplementary Figure 3).
246 **3.3.2 Hierarchical Agglomerative Clustering (HAC)**

In addition, in order to characterize the differences in resistivity between seasons, we need to interpret the variability observed in the different zones of ERT images. The researchers utilized a classical unsupervised classification method called Hierarchical Agglomerative Clustering (HAC) to analyze the data. HAC follows a bottom-up algorithm, as described by Saporta, 1990. This algorithm helps to create an ordering of blocks, resulting in a single image where distinct zones can be differentiated based on their seasonality. In the present study, the HAC method enables whose electrical resistivity changes in a similar manner over the years to be grouped together.

HAC is a commonly used technique in various contexts to identify heterogeneity, particularly in geotechnical studies. For example, Genelle et al. (2012) used HAC to identify geotechnical heterogeneity in a landfill cover. The method was also applied to a cave study, the prehistoric Lascaux Cave in SW-France, which allowed us to recognize the reliability of the method (Xu et al., 2015; 2017). Later, Lharti et al. (2023) compared the HAC and K-means methods in the Lascaux Cave, noting that the HAC method was particularly effective in identifying areas already known to be waterlogged or clayey.

The HAC classification was finalized using 16 ERT images captured between February 2020 and September 2022. These resistivity values after temperature corrected are logarithmized and standardized according to the following equation (Xu et al., 2015; 2017; Equation 2):

$$[\log10(\rho_i)]_{DCR} = \frac{\log10(\rho_i) - \mu[\log10(\rho_i)]}{\sigma[\log10(\rho_i)]} \quad \text{Eq. (2)}$$

$[\log10(\rho_i)]_{DCR}$ is the standardized center resistivity (DCR); $\rho_i$ is the resistivity after corrected temperature; $\mu[\log10(\rho_i)]$ is the average of the $\log10(\rho_i)$ resistivity; $\sigma[\log10(\rho_i)]$ is the standard deviation of the $\log10(\rho_i)$ resistivity.

To perform HAC, the resistivity data assigned to the blocks are arranged in a matrix with the number of rows equal to the number of blocks and the number of
columns equal to the number of surveys. The results are generally summarized in a dendrogram, where the number of clusters needed to retain the $[log10(ρ_i)]_{DCR}$ resistivity measurements can be selected. We choose the Euclidean distance and the Ward linkage criterion for the HAC analysis methods, which allow clusters to be formed such that the sum of squares of pooling within clusters is minimized. Users then choose the number of clusters according to knowledge of the research sites and objectives.

## 4. Results

### 4.1. ERT measurements

The main measurement results were gathered in 16 ERT images made from February 2020 to September 2022 (Supplementary Figure 4). The ERT profile, from northeast (NE) to southwest (SW) on a 71 m-long profile, covers the Bajocian and Bathonian limestone formations (Supplementary Figure 1). Here, strong resistivity contrasts were observed, giving a broad picture of the cave galleries and karst reservoirs, which are more or less saturated.

The distribution of relative frequency based on 16 ERT measurements suggests that the resistivity data are mainly concentrated between 245 Ω·m and 9772 Ω·m. The highest values (165–178 m NGF) correspond to the caves, while the lower values (<245 Ω·m) correspond to the top soil. According to the frequency analysis of resistivity, the median resistivity of the limestone in the Villars Cave is 1521 Ω·m, which is higher than the resistivity of the nearby well-investigated geophysical site (Lascaux Cave) with a median of 556 Ω·m (Coniacian limestone) (Xu et al., 2016; Verdet et al., 2020). This difference suggests that the limestone in the Villars Cave has undergone less weathering compared to the limestone in the Lascaux Cave.
298 **4.2 HAC method applied to ERT image classifications**

299 We applied the HAC method using Minitab® version 19. This method relies on a
correlation matrix derived from the normalized and standardized resistivity data. The
300 resistivity similarity of blocks between different clusters decreases with time as the
301 distance at which they merge increases. Conversely, blocks belonging to clusters are
302 merged at very low distances, exhibiting similar resistivity behaviors (also see
303 Method section). The statistical parameters for each cluster are summarized in Figure 2A.
304 Here, the classification line corresponding to the greatest distance is selected to
305 highlight the main characteristic research zones of stratigraphic structures. The
306 dendrogram shows three distinct primary clusters (clusters A, B, and C) (Figure 2A).
307 Clusters A, B, and C display median resistivity in all the ERT measurements ranging
308 from 2321 Ω·m to 100054 Ω·m, 80 Ω·m to 1277 Ω·m, and 493 Ω·m to 2635 Ω·m,
309 respectively. They may be composed of karst structural systems with completely
310 different geological characteristics (Figure 2A).
311

312 To get as much detail as possible to highlight potential sub-regions, we decided
313 to make more cutoffs (classification lines), grouped into eight clusters (see dashed
314 lines in Figure 2A) as follows:

315 Cluster A, consisting of clusters 1, 7, and 8, shows the highest median value for
316 electrical resistivity (Figure 2B). Block areas with the largest resistivity values were
317 grouped together in cluster A (clusters 7 and 8, altitude: 165-178 m) (Figure 2B), with
318 the high median values, ranging from 5001 to 8245 Ω·m and from 3471 Ω·m to
319 100054 Ω·m, respectively (Table 1). However, compared to clusters 7 and 8, cluster 1
320 with a slightly lower median value, ranging from 2321 Ω·m to 4957 Ω·m (Table 1), is
321 distributed around clusters 7 and 8 (Figure 2B).

322 Cluster B, consisting of clusters 2 and 4, shows the lowest median values,
323 ranging from 261 Ω·m to 1277 Ω·m and 80 Ω·m to 534 Ω·m, respectively, with most
324 conductive areas distributed mainly on the soil surface and probably in weathered
325 limestone zones (from NE to SW direction) at 50-60 m of the ERT profile (Table 1;
Figures 2 and 2B).

Cluster C, including clusters 3, 5, and 6, with median values ranging from 775 Ω·m to 1763 Ω·m, 1432 Ω·m to 2635 Ω·m, and 493 Ω·m to 1133 Ω·m, respectively (Table 1), is located in the middle zone between 177 m and 165 m NGF (clusters 3 and 5) and lower zones deeper than 165 m NGF (cluster 6) of the ERT profile (Figure 2B).

## 4.3 Rainfall amount, evapotranspiration, and drip rate

The daily hydroclimatic parameters of the Villars Cave are presented in Figure 5, including rainfall (R) and rainfall minus evapotranspiration (R-ETP), which is considered effective rainfall or water-excess when it is greater than 0. We observed that the change in water-excess is seasonal, with a maximum in winter and a minimum in summer-autumn. The total annual value of the water-excess was 477 mm in 2020 and 508 mm in 2021, respectively (Figure 3A). During the year 2022, R-ETP remained below 0 from May to October, indicating that potential evapotranspiration was higher than the precipitation during this period. This anomaly is attributed to an unusually dry year, as shown in Figure 3A.

To characterize the variability of cave dripping water, we monitored the drip-rate monitoring between September 2019 and September 2022 (Table 2), by using STALAGMATE drip counters under three drip stations located at different depths, as described in section 3.2. The discharges from the three drip water sites (Vil-#10A: depth 14m, Vil-#1B, and Vil-#3: depth 36 m) ranged from 0.60 to 180.67 (SD: 37.43) drips/min (Vil-#10A), 1.6 to 61.1 (SD: 15.29) drips/min (Vil-#1B), and 0 to 44.4 (SD: 6.96) drips/min (Vil-#3). We also noted that the drip rate of Vil-#10A and Vil-#3 stations' drip rate was more variable than that of Vil-#1B (Figure 3).

During the first cycle of 2019-2020, water-excess rose to be significantly above 0 from mid-September 2019 (Figure 3A). It took about 45 days for infiltration to be filled the reservoirs and reach the percolation threshold, allowing the water to move down into the cave (Figure 3A). As a result, there was an increase in the
354 dripping rate in November 2019 in stations Vil-#10A and Vil-#3, and in December in
355 station Vil-#1B (Figures 3B and 3C). Drip rates remained high until approximately
356 May 2020 with a general decrease until December 2020. During the humid period,
357 there was a systematic link between the water-excess and the drip rate variations in
358 Vil-#10A, with a time delay of several days as we depicted in Figure 3A. During the
359 2020-2021, the hydrological cycle of Vil-#10A and Vil-#3 dripping stations began to
360 increase in December 2020, lasting until approximately August 2021 (Figures 3A and
361 3B). The fact that the beginning of the cycle at the Vil-#1B dripping station occurred
362 later than Vil-#10A and Vil-#3, close to January or February, implies that there are
363 distinct pathways and reservoirs involved in the infiltration process across the
364 different sites (Figures 3A, 3B and 3C).

365 Once the percolation threshold was reached for the reservoirs to fill up with
366 water, we conducted a cross-correlation analysis of the three monitoring sites, Vil-
367 #10A, Vil-#3, and Vil-#1B, in order to quantify the time delay between water excess
368 and drip rates. The mean lag time have been determined in the interval of 5-9 days for
369 Vil-#10A station, 56-94 days for Vil-#1B station, and 4-11 days for Vil-#3 station
370 (Supplementary Figure 5).

371 These results show the following: (1) Vil-#10A and Vil-#3 have a similar
372 water-excess/dripping time delay even though they are located at different levels (14m
373 deep for Vil-#10A and 36 m deep for Vil-#3). (2) According to the time series, the Vil-
374 #3 station has a much more dampened dripping amplitude despite a similar time delay
375 with the Vil-#10A station. (3) At the dripping point of the Vil-#1B station, located in
376 the lower gallery, we observe a much longer time lag and lower mean drip rate
377 compared to Vil-#10A.

4.4 Recognition of soil layers and cave zones from ERT images

379 The superficial part of the ERT images shows low resistivity values
380 corresponding to clusters 2 and 4 (Figure 2B). Cluster 4 has a median value of 106
381 Ω·m, with a range between 80 Ω·m to 534 Ω·m (Table 1) at 5-13 m and 52-71 m on
382 the ERT profile (from NE to SW), characterized by a highly variable resistivity with
383 the HAC method (Figure 2B). The specific resistivity values were observed at these
384 locations on the ERT profile, as evidenced by the results of our soil drillings, which
385 can be identified by the nature of the soil (clay and organic matter) (Supplementary
386 Figure 6, Figure 2B). The soil's upper layer of consists of extremely weathered
387 limestone, with thicknesses exceeding 0.6 m, 0.75 m, and 0.45 m at the respective
388 locations of 9.5 m, 56 m, and 60.5 m (Figure 2B and Supplementary Figures 6 and 7).

389 Cluster 2 has a median resistivity value of 351 Ω·m, ranging from 261 Ω·m to
390 1277 Ω·m (Figure 2B; Table 1). It is situated on the surface, specifically between 15
391 m and 50 m on the profile line (from NE to SW), as well as in a deeper zone (altitude:
392 172 to 177 m, NGF) that can be seen between 50 m and 60 m on the ERT profile
393 (Figure 2B). We further divide cluster 2 into two distinct sub-clusters, namely clusters
394 2.1 and 2.2 (Figure 4A):

395 (1) Cluster 2.2, located in the superficial part of the ERT profile (Figure 4A),
396 shows a median electrical resistivity value of 219 Ω·m, with a range from
397 160 Ω·m to 1047 Ω·m (Figure 4B). The median resistivity value of cluster
398 2.2 is slightly higher but comparable to the median resistivity value of
399 cluster 4 (106 Ω·m, top-soil). Cluster 2.2 displays seasonal variations,
400 which are commonly linked to water excess (Figures 4A and 4B). The
401 surface in cluster 2.2 is confirmed to be the top soil that is about 0.2 m
402 thick, as observed at two locations situated at 24 m and 38 m on the ERT
403 profile (Figure 4B).

404 (2) The median resistivity of cluster 2.1 is 403 Ω·m, ranging from 304 Ω·m to
405 2029 Ω·m, which is higher than cluster 2.2 (Figure 4B). Cluster 2.1 is
406 associated with the soil layer situated below the layer of cluster 2.2, as well
407 as in the deeper section between 50 m to 60 m of the ERT profile (altitude:
408 172 m to 177 m, NGF) (Figure 4A). Cluster 2.1 exhibits the seasonal
409 fluctuations that are associated with the water excess (Figures 4A and 4B).
410 In particular, after digging the soil, the limestone areas were observed to be
411 undergone weathering (small limestone blocks mixed with sandy soil)
between depths of 0.4 m and over 0.75 m (56 m on the ERT profile in Figure 4B). Hence, it is possible that cluster 2.1 could represent a mixture of weathered limestone with sandy soils with high porosity. However, due to the limitations of the manual auger, it was not possible to excavate deeper to determine the exact boundary (>0.75 m) (Supplementary Figure 6 and 7).

Clusters 7 and 8 exhibit a consistently high median resistivity (7168 Ω·m) (Figure 2B), without showing seasonal variations over time (Figures 5A and 5H). The comparison of the location of these clusters with the cave plan map allowed us to attribute these zones to the cave galleries (Figures 1C and 2B), showing that: (1) Cluster 7 (Figure 2B) has high resistivity zones located on the ERT profile at 6-22 m (Zone A, Figure 1C) and 40-54 m (Zone B, Figure 1C). (2) Cluster 8 (Figure 2B), located at a vertical altitude of 168 m-178 m NGF, displays a high resistivity signal observed at 60-71 m (Zone C, Figure 1C), indicating the presence of an undiscovered cave gallery or a sinkhole collapse.

## 5. Discussion

### 5.1. Clustering resistivity variabilities with local water excess in the different ERT zones

According to Archie's law (Archie, 1942), if the electrical resistivity of a rock formation varies with time, it implies that the degree of saturation ($S_w$) or the resistivity of water ($\rho_w$) is changing with time, as the porosity ($\phi$) is assumed to be constant. Therefore, changes in the electrical resistivity of the rock over time can reflect changes in the rock's water content, responding to local water-excess (Xu et al., 2017).

As observed in Figure 5, there is a strong correlation between water-excess (blue part in Figure 5A) and resistivity over time. Resistivity decreases sharply following an increase in water excess as there is more water in the limestone. Here roughly, we observe a well-marked seasonality over time, with the resistivity in
clusters 1 to 5 increasing in summer and autumn, and decreasing in winter and spring (Figures 5B-5F). Furthermore, it is worth noting that each cluster displays a distinct range of resistivity values, despite some seasonal similarities exist between them (Figures 5B-5F).

To facilitate a point-to-point comparison of water excess and resistivity variability, we plotted them on the same graph for each cluster (Figures 6 and 7). The superficial part of the ERT images (essentially cluster 4 and cluster 2) displays obvious seasonal changes and represent a relatively quasi-synchronous response to the local water-excess (Figure 6A). We also noted a high variability in resistivity where the highest median value is 534 Ω·m, and the lowest median value is 80 Ω·m (cluster 4, Figure 6A). It is assumed that the resistivity of water (ρ<sub>w</sub>) remained constant within the rock mass and assuming the porosity (φ) remained constant over time (Genty et al., 2001), we can estimate that the top soil water saturation (S) in cluster 4 varied approximately within the range of S<sub>min</sub> to S<sub>max</sub>, where S<sub>max</sub> is approximately 2.6 times for S<sub>min</sub>. In addition, the surface soil layers responded to the local drought periods of July 2020 and July-September 2022 (Rainfall-ETP<0), since high resistivity values were observed (Figure 6A). In more detail, we observed a minimum water-excess of 46.30 mm in June and July 2020 (Table 2 and Figure 6A). As a result, the relative frequency distribution of resistivity observed in the top-soil layer does not show some values less than 245 Ω·m compared to the other months (Supplementary Figure 8B). Similarly, from May 2022 to September 2022, the water-excess fell to 96.2 mm (Table 2 and Figure 6A). As a result, there was a shift in the frequency distribution of relative resistivity towards higher values, reaching peaks as high as 2563 Ω·m for the median value, and resistivity values below 245 Ω·m were no longer present (Supplementary Figure 8H). In detail, the resistivity of cluster 2.1 which is the deeper part of cluster 2 varies with the seasons. This means it could act as the role of a pathway between the superficial top-soil and the deeper part of the limestone.

Cluster 5 is also sensitive to water-excess presenting with a median resistivity of 1649 Ω·m, with a range between 1432 Ω·m to 2635 Ω·m (Figure 6B). The time lag between cluster 5 and water-excess appears slightly higher than for sub-surface
clusters 2 and 4 (Figures 6A and 6B). However, the variability of water saturation in cluster 3 over time is basically the same in cluster 5 (Figure 6B). We suggest that cluster 5 likely corresponds to the Bajocian and Bathonian limestone, where seasonal variation may be due to water filling or draining of the fissure network.

Cluster 3, with a median resistivity value of 941 Ω·m, ranging from 775 Ω·m to 1763 Ω·m, is located at the same altitude (165-178 m, NGF) as cluster 5 (Figures 6B & 2B). Similarly, cluster 3 also experiences only a few days or one month of time delay with water-excess (Figure 6B). One observation worth mentioning is that cluster 3 has a lower median resistivity value than cluster 5, indicating a comparatively higher porosity (Figure 6B). Moreover, the drilling was carried out above the cluster 3 (at 9.5 m on the profile sees Figure 2B), showing a weathered limestone (blocks of limestone). Based on the above observation, we can conclude that cluster 3 acts as a preferred water pathway due to its higher porosity, functioning as a transmission belt (located on the right side of Figure 2B), which supplies water to deeper zones linked to cluster 6.

Cluster 1 has a median resistivity value of 3040 Ω·m, ranging from 2321 Ω·m to 4957 Ω·m (Figure 7A), a higher resistivity value than cluster 5 (1649 Ω·m). Cluster 1 is mainly distributed around the cave gallery and along the 10-50 m section of the ERT profile (at an altitude of 176 m-178 m, NGF) (Figure 2B). Cluster 1 resistivity increases in summer/autumn and decreases in winter/spring, basically in the same pattern or ahead of the cave dripping rate (Vil-#10A) (Figure 3A). We observed a time delay of about 1-2 months for cluster 1 in response to local water-excess (Figure 7A). This delay may be associated with the percolation threshold between water-excess and drip rate as described in section 4.3 (Figure 3; Figure 7A). Bulk resistivity is directly inversely proportional to the conductivity of the water based on Archie's law, called the "water conductivity effect" (Archie, 1942). However, the field monitoring conducted in earlier research between 1996 and 1997 shows that the electrical conductivity of the water varied slightly, and was around 356 μS/cm (summer months) and 372 μS/cm (winter months) at station Vil-#10A (cluster 1) in the upper gallery (Baker et al., 2000; Genty et al., 2001). Consequently, based on the
observations and results obtained in Vil-#10A, it can be concluded that the upper gallery does not exhibit any significant "water conductivity effect", as water conductivity of the water in this zone remains stable and does not change with time.

Cluster 6, located at the lowest altitudes of the ERT profiles, has a median resistivity value of 808 Ω·m, ranging from 493 Ω·m to 1133 Ω·m. Resistivity values in cluster 6 are lower than in cluster 5 (1649 Ω·m) (Figure 7B), suggesting higher water content. In wet periods, cluster 6 median resistivity displayed seasonal variability linked to water excess, but it appeared to be far more time delayed to water-excess than other clusters (Figure 7B). However, there were two long-term inconsistent excursions with water-excess in the dry periods (May-October 2020 and April-October, 2022), especially in summer (Figure 7B). Unlike cluster 1, the resistivity of cluster 6, situated in the deeper sections of the profiles (below 165 m NGF), appeared to be predominantly influenced by the "water conductivity effect" in the dry/summer periods (Archie, 1942). Water conductivity in the lower gallery station Vil-#1B, which is situated close to the altitude of cluster 6, is higher and varied seasonally from 600 µS/cm (summer months) to 460 µS/cm (winter months) (Baker et al., 2000; Genty et al., 2001). The resistivity variability in cluster 6 is interpreted as the outcome of a "piston flow" infiltration system, wherein the infiltration water conductivity increased significantly during summer/dry periods due to its prolonged residence time, resulting in intensified mineralization within fissures and micro-fissures.

By comparing the ERT's seasonal signal changes with rainfall data (input) and drip rate data (output), we estimated the inertia of the reservoir inertia and identified the fast-response zones in clusters 2-4 and the delay times in cluster 1 (1-2 month). We also confirmed that clusters 3 and 2.1 are pathway of water flux pathways. ERT images were used to determine changes in the reservoirs (number, location, depth, size) and their water saturation, which can be linked to cave hydrological signatures (drip rate changes).
527

## 5.2. Schematic diagram of the unsaturated karst zone around Villars Cave

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In view of the geophysical analysis and hydrological knowledge of the studied region, we developed a schematic geo-electrical synthetic model (Figure 8). The boundaries in the geo-electrical structure's boundaries are inferred from the HAC method (Figure 2B). The model delineates the limestone, top-soil, weathered limestone, privileged feeding zone, and storage zones based on their resistivity values and temporal resistivity variations linked to cave water drip rate (Figures 5, 6, and 7).

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From this synthetic image, it is possible to draw a schematic diagram of the groundwater movement pathways in the critical karstic zone (KCZ) above the Villars Cave (Figure 8). We can speculate that the most of the water flow originates from the soil layers and interconnected epikarst reservoirs, and subsequently, it moves deeper into the porous limestone zone (cluster 3). However, precipitation can also infiltrate vertically through fracture networks in the Bajocian and Bathonian limestone (cluster 5, Figure 4). The rapid water circulation observed in cluster 2 is highly sensitive to local rainfall, which is compounded with the superficial top soil and weathered limestone areas mixed with sand at the surface and between 50-60 m (altitude: 172 m to 177 m, NGF) of the ERT profile (Figure 8).

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Regarding storage zones in Villars, cluster 6 is able to act as a water reservoir from a fast fissure network transport of water in cluster 5 and the transport of water from cluster 3 and cluster 2.1 (Figure 8). Similarly, it appears that cluster 1 also acts as a storage zone with a hydrological behavior closely linked to the dripping rate in the upper gallery (Vil-#10A) (Figure 7A). Cluster 1 stores local rainwater and regulates its release over time, with potentially significant implications for feeding upper gallery stalagmites in the Villars Cave.

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To summarize, the cluster characteristics and behaviors are not randomly distributed but they highlight the structures of the infiltration zone which can be interpreted as reservoirs, or preferential rapid or slow infiltration zones. By testing

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and validating ERT and hydrology methods at a specific site (Villars Cave) developed
in a vadose zone, we can deepen our understanding of the site and its hydrological
behavior, which may be similar to other caves in the region. This can give us more
insights into the hydrogeological and hydrological processes in the karst environment
and improve our ability to manage and protect these sensitive karst environments.

## 6. Conclusions

Long-term monitoring of the karst vadose zone above the Villars Cave in SW-France, involving 2.5 years of ERT data combined with drip rate measurements inside the cave, has provided valuable insights into the geometry and dynamics of aquifer recharge processes. By employing the Hierarchical Agglomerative Clustering (HAC) method on ERT images, distinct clusters (clusters 1 to 8) were identified, exhibiting different resistivity zones linked to dripping water sources within the Villars Cave.
Below are the main conclusions drawn from the study:

(1) Clusters 2 and 4, located in the superficial layer of ERT profiles, correspond to the top soil (clusters 4 and 2.2) and slightly deeper weathered limestone (cluster 2.1). Resistivity variations in these clusters directly relate to changes in water-excess and local drought period.

(2) Cluster 5, situated in the middle layers of the ERT images, exhibits pronounced seasonal resistivity changes. The cluster presents short delay with water-excess variations, likely attributed to the filling or draining of fissures and micro-fissures.

(3) Cluster 3, predominantly located on the right side of the ERT images and characterized by slightly lower resistivity, appears to act as a preferential infiltration pathway moving to deeper reservoirs. Like cluster 5, cluster 3 also demonstrates a delay of a few days or one month after water-excess.

(4) Cluster 6, located in the deeper part of the ERT profile, displays seasonal variability in resistivity during wet periods but exhibits low resistivity values during summer or dry periods. This behavior is likely due to the
583 presence of mineralized infiltration waters.

584 (5) Cluster 1, distributed around the cave galleries, consists of high-resistivity
585 limestone and is connected to the cave dripping hydrology. This cluster
586 exhibits a delay of 1-2 months with respect to water excess, suggesting the
587 presence of a percolation threshold that supplies water to the cave
588 stalagmites in Villars.

589 (6) Clusters 7 and 8 exhibit extremely high resistivity values without any
590 seasonal changes. These areas coincide with the cave galleries or sinkhole
591 collapses.

592 By conducting a comprehensive analysis that combines ERT results and drip
593 water measurements, we can effectively characterize the origins of drip rate signals in
594 cave systems. This integrated approach provides valuable insights into the
595 hydrodynamic behavior of water flow and the lithological/geological constraints
596 present in the karst subsurface. Establishing direct links between changes in
597 subsurface resistivity and dynamic water percolation processes within the cave
598 environment, our in-depth understanding of the hydrogeological processes contributes
599 significantly to the management and conservation of water resources in karst regions,
600 helping to develop sustainable water use and environmental protection. The approach
601 not only provides a novel and promising method for studying different flow types and
602 their origins in caves but also enhances our understanding of karst aquifer recharge
603 processes, which is vital for cave and paleoclimate studies.

604 Acknowledgments

605 We thank the Versaveaud family, who are always interested in our research, and
606 their constant help makes the long-term monitoring work in Villars Cave possible. We
607 want to express sincere thanks to Olivier Mestre for the help with meteorological data.
608 We thank Thierry Baritaud for his help in data collecting and field trips. We thank
609 Daniel Chailloux, Laurent Magne, Gilles Souchet for their help in determining the
610 drip sites. This work was supported by I2M programs on decorated caves for
611 geophysical surveys and thermal monitoring. This research was also supported by the
China Scholarship Council (CSC) to Jian. Zhang (201906990014). This long
monitoring work (DG) has been funded, since 1996, by several programs from the
CNRS (INSU), and three laboratories (GEOPS, Orsay, Paris-Saclay University;
Laboratoire des Sciences du Climat et de l'Environnement, LSCE,
CEA/CNRS/UVSQ and Environnements et Paléoenvironnements Océaniques et
Continentaux, EPOC, University of Bordeaux, France). Villars Cave is part of the
sites that are studied by the CNRS GIS group called GEMS "Groupe d'Etude des
Milieux Souterrains", dir. B. Lartiges GET Toulouse". Department of Environmental
Sciences, University of Bordeaux, financially supports this project.

621 CRediT authorship contribution statement

622 **Jian Zhang**: Conceptualization, Methodology, Formal analysis, Writing - review & editing. **Colette Sirieix**: Supervision, Revising and editing, Reviewing, 623 Funding acquisition. **Dominique Genty**: Review & editing, Supervision, Funding 624 acquisition, Dripping monitoring data. **Cecile Verdet, Marie Larcanche and Shan 625 Xu**: Software and data analysis, **Fabien Salmon**: Thermal model, **Sylvain Mateo**: 626 Geophysical Field works, **Stéphane Bujan** and **Ludovic Devaux**: Field works. 627

628 Declaration of Competing Interest

629 The authors declare that they have no known competing financial interests or
630 personal relationships that could have appeared to influence the work reported in this
631 paper.

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792

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824

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Caption

**Figure 1.** (A) Location of the Villars Cave. (B) A 3D structural cave diagram and the distribution of monitoring sites (red circles): Vil-#3, Vil-#1B, Vil-#10A. The reader is referred to (Genty, 2008 and Genty et al., 2014) for detailed site descriptions and maps. (C) Localization of ERT profiles above the Villars Cave map. The red line indicates the ERT profile we monitored for 2.5 years. The dotted circles Zone A-C correspond to the ERT image identified three cave galleries in Figure 3B. (D) A structural diagram and the distribution of surveillance sites of the Villars Cave (Vil-#1B, Vil-#10A, and Vil-3#). The red square shows the profile of ERT. The drip points Vil-#1B and Vil-#3 are about 5 m apart, located on the lower level of the cave while the drip points Vil-#10A are located on the upper level of the cave. This section clearly shows that Stations Vil-#1B and Vil-#3 are at the same altitude as the Trincou stream.
862

863 **Figure 2.** Results of the Hierarchical Agglomerative Classing (HAC) for all
864 monitoring periods for the profile (71m) above the Villars Cave. (A) Dendrogram to
865 create three and eight clusters. (B) Distribution of blocks considering their clusters.
866 Clusters 7 and 8 correspond to the high-resistivity zones identified on the Zone A-C in
867 cave plan map in Figure 1C.

868

869 **Figure 3.** Comparison of the variability of daily R-ETP (rainfall minus
870 evapotranspiration) and drip-water rates (Vil-#3, Vil-#1B, Vil-#10A) during
871 September/2019- September/2022. Water-excess (rainfall-evapotranspiration > 0).
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873

**Figure 4. (A)** Cluster 2 is divided into clusters 2.1 and 2.2 blocks, **(B)** Comparisons between median resistivity variations for clusters 2.1 and 2.2 and water excess.

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**Figure 5.** Evolutions of the median resistivity of clusters 1-8 with local water-excess. The individual blocks from the synthetic model were associated with a similar seasonal resistivity variability gathered into 6 clusters (1-6). However, clusters 7 and 8 only exhibit a high resistivity without an obvious seasonal variability. The arrows indicated the decrease in resistivity in cluster 6 in the dry/summer periods.

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**Figure 6. (A)** Evolutions of the median resistivity of clusters 2 and 4 with local water-excess. **(B)** Evolutions of the median resistivity of clusters 3 and 5 with local water-excess. A similar seasonally variable resistivity was found in 4 clusters (2-5) with no or few days of delay with local water excess.

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**Figure 7. (A)** Evolutions of the median resistivity of cluster 1. **(B)** Evolutions of the median resistivity of cluster 6. Dashed lines indicate the point at which resistivity and water excess and drip rate begin to increase in response to a delay in the percolation threshold. The red dotted area is affected by water conductivity.

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**Figure 8.** Schematic geo-electrical model of the ERT survey line. The wiggle arrows represent preferential flow, and the straight arrows represent vertical flow in the pipe and fissure.

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<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>
<figure><img src="image_14.png" /></figure>
<figure><img src="image_15.png" /></figure>
<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>
Limestone

Cluster=5, Median=1649 Ω*m

Cave galleries

Cluster 7.6.8, Median=7168 Ω*m

High resistivity limestones
with heritage zones

Cluster=1, Median=3040 Ω*m

Top-soil

Cluster 4, Median=106 Ω*m

Parent limestones
favorable water path

Cluster=3, Median=941 Ω*m

Top-soil and
weathered limestones

Cluster 2, Median=351 Ω*m

Reservoirs

Cluster=6, Median=808 Ω*m

<figure><img src="image_19.png" /></figure>
<table><caption>1 Table 1 Statistical parameters: for the resistivity of each cluster (Median and Standard Deviation (SD), Average value)</caption><thead><tr><th rowspan="2"></th><th colspan="3">Cluster 1</th><th colspan="3">Cluster 2</th><th colspan="3">Cluster 3</th><th colspan="3">Cluster 4</th><th colspan="3">Cluster 5</th><th colspan="3">Cluster 6</th><th colspan="3">Cluster 7&8</th></tr><tr><th>median</th><th>SD</th><th>average</th><th>median</th><th>SD</th><th>average</th><th>median</th><th>SD</th><th>average</th><th>median</th><th>SD</th><th>average</th><th>median</th><th>SD</th><th>average</th><th>median</th><th>SD</th><th>average</th><th>median</th><th>SD</th><th>average</th></tr></thead><tbody><tr><td>2020/2/18</td><td>2592</td><td>1199</td><td>2871</td><td>289</td><td>119</td><td>299</td><td>803</td><td>262</td><td>788</td><td>94</td><td>30</td><td>90</td><td>1442</td><td>455</td><td>1565</td><td>781</td><td>194</td><td>831</td><td>8521</td><td>38310</td><td>28029</td></tr><tr><td>2020/7/2</td><td>2821</td><td>1481</td><td>3217</td><td>626</td><td>292</td><td>722</td><td>1277</td><td>684</td><td>1434</td><td>297</td><td>110</td><td>310</td><td>2079</td><td>666</td><td>2059</td><td>493</td><td>175</td><td>526</td><td>4610</td><td>2012</td><td>4922</td></tr><tr><td>2020/10/9</td><td>4249</td><td>2582</td><td>5007</td><td>342</td><td>219</td><td>390</td><td>1051</td><td>967</td><td>1405</td><td>94</td><td>35</td><td>98</td><td>1801</td><td>1087</td><td>2126</td><td>1133</td><td>343</td><td>1198</td><td>7762</td><td>36587</td><td>26594</td></tr><tr><td>2020/11/18</td><td>3557</td><td>1472</td><td>3596</td><td>274</td><td>195</td><td>337</td><td>979</td><td>572</td><td>1066</td><td>89</td><td>34</td><td>90</td><td>1571</td><td>767</td><td>1841</td><td>1028</td><td>682</td><td>1145</td><td>6505</td><td>29441</td><td>20534</td></tr><tr><td>2021/1/7</td><td>2321</td><td>988</td><td>2502</td><td>296</td><td>121</td><td>304</td><td>841</td><td>242</td><td>802</td><td>88</td><td>31</td><td>92</td><td>1440</td><td>522</td><td>1579</td><td>815</td><td>188</td><td>808</td><td>7331</td><td>13138</td><td>13553</td></tr><tr><td>2021/4/15</td><td>2763</td><td>1053</td><td>2874</td><td>306</td><td>115</td><td>313</td><td>840</td><td>254</td><td>841</td><td>97</td><td>34</td><td>99</td><td>1539</td><td>435</td><td>1619</td><td>848</td><td>209</td><td>860</td><td>7137</td><td>35945</td><td>25528</td></tr><tr><td>2021/5/20</td><td>2713</td><td>1388</td><td>2928</td><td>270</td><td>124</td><td>287</td><td>775</td><td>196</td><td>749</td><td>82</td><td>27</td><td>84</td><td>1447</td><td>481</td><td>1540</td><td>792</td><td>255</td><td>835</td><td>7797</td><td>36811</td><td>26502</td></tr><tr><td>2021/7/5</td><td>3212</td><td>1811</td><td>3483</td><td>331</td><td>158</td><td>354</td><td>955</td><td>597</td><td>1069</td><td>113</td><td>45</td><td>114</td><td>1571</td><td>556</td><td>1691</td><td>877</td><td>181</td><td>902</td><td>8706</td><td>27297</td><td>22180</td></tr><tr><td>2021/9/24</td><td>3461</td><td>1816</td><td>3839</td><td>399</td><td>271</td><td>456</td><td>998</td><td>834</td><td>1275</td><td>119</td><td>49</td><td>119</td><td>1841</td><td>641</td><td>1892</td><td>989</td><td>387</td><td>1073</td><td>7397</td><td>40900</td><td>29570</td></tr><tr><td>2021/11/10</td><td>3395</td><td>1355</td><td>3629</td><td>339</td><td>154</td><td>351</td><td>975</td><td>368</td><td>1057</td><td>106</td><td>32</td><td>97</td><td>1758</td><td>460</td><td>1807</td><td>1018</td><td>315</td><td>1056</td><td>7723</td><td>23464</td><td>19976</td></tr><tr><td>2021/12/9</td><td>2765</td><td>1022</td><td>2773</td><td>261</td><td>113</td><td>279</td><td>796</td><td>266</td><td>813</td><td>80</td><td>25</td><td>79</td><td>1501</td><td>502</td><td>1580</td><td>851</td><td>221</td><td>871</td><td>7252</td><td>23548</td><td>18736</td></tr><tr><td>2022/1/27</td><td>2527</td><td>1596</td><td>2863</td><td>295</td><td>143</td><td>320</td><td>802</td><td>241</td><td>768</td><td>90</td><td>30</td><td>90</td><td>1524</td><td>524</td><td>1597</td><td>750</td><td>255</td><td>801</td><td>8357</td><td>24816</td><td>20659</td></tr><tr><td>2022/3/16</td><td>2753</td><td>1093</td><td>2906</td><td>263</td><td>114</td><td>277</td><td>779</td><td>224</td><td>778</td><td>83</td><td>26</td><td>82</td><td>1432</td><td>387</td><td>1543</td><td>860</td><td>231</td><td>868</td><td>7047</td><td>25115</td><td>19151</td></tr><tr><td>2022/5/11</td><td>2454</td><td>1223</td><td>2877</td><td>408</td><td>160</td><td>444</td><td>876</td><td>307</td><td>883</td><td>144</td><td>61</td><td>160</td><td>1605</td><td>578</td><td>1663</td><td>633</td><td>169</td><td>666</td><td>9420</td><td>3960</td><td>9914</td></tr><tr><td>2022/6/23</td><td>3394</td><td>2112</td><td>3867</td><td>703</td><td>445</td><td>828</td><td>1318</td><td>683</td><td>1448</td><td>300</td><td>88</td><td>277</td><td>2110</td><td>633</td><td>2174</td><td>541</td><td>362</td><td>610</td><td>5620</td><td>3460</td><td>6981</td></tr><tr><td>2022/9/16</td><td>4957</td><td>3813</td><td>6208</td><td>1277</td><td>1168</td><td>1764</td><td>1763</td><td>2744</td><td>2707</td><td>534</td><td>181</td><td>551</td><td>2635</td><td>973</td><td>2621</td><td>531</td><td>230</td><td>583</td><td>5055</td><td>3118</td><td>5981</td></tr><tr><td>Median</td><td>3040</td><td>1997</td><td>3465</td><td>351</td><td>507</td><td>483</td><td>941</td><td>969</td><td>1118</td><td>106</td><td>139</td><td>152</td><td>1649</td><td>697</td><td>1806</td><td>808</td><td>356</td><td>852</td><td>7168</td><td>27673</td><td>18676</td></tr><tr><td>Maximum</td><td>4957</td><td>3813</td><td>6208</td><td>1277</td><td>1168</td><td>1764</td><td>1763</td><td>2744</td><td>2707</td><td>534</td><td>181</td><td>551</td><td>2635</td><td>1087</td><td>2621</td><td>1133</td><td>682</td><td>1198</td><td>9420</td><td>40900</td><td>29570</td></tr></tbody></table>
<table><tr><td>Minimum</td><td>2321</td><td>988</td><td>2502</td><td>261</td><td>113</td><td>277</td><td>775</td><td>196</td><td>749</td><td>80</td><td>25</td><td>79</td><td>1432</td><td>387</td><td>1540</td><td>493</td><td>169</td><td>526</td><td>4610</td><td>2012</td><td>4922</td></tr></table>

2

3

4

<table><caption>Table 2 Calculate the monthly average drip rate.</caption><thead><tr><td>Date</td><td>VIL-1B (Average Monthly drips/min)</td><td>VIL-10A (Average Monthly drips/min)</td><td>VIL-#3 (Average Monthly drips/min)</td></tr></thead><tbody><tr><td>October-2019</td><td>8.71</td><td>2.41</td><td>0.09</td></tr><tr><td>November-2019</td><td>8.11</td><td>80.65</td><td>13.16</td></tr><tr><td>December-2019</td><td>28.52</td><td>120.85</td><td>18.41</td></tr><tr><td>January-2020</td><td>46.87</td><td>40.12</td><td>3.51</td></tr><tr><td>February-2020</td><td>51.69</td><td>62.73</td><td>9.28</td></tr><tr><td>March-2020</td><td>51.70</td><td>89.83</td><td>15.52</td></tr><tr><td>April-2020</td><td>39.66</td><td>12.44</td><td>3.59</td></tr><tr><td>May-2020</td><td>34.94</td><td>34.94</td><td>8.39</td></tr><tr><td>June-2020</td><td>25.37</td><td>9.31</td><td>2.81</td></tr><tr><td>July-2020</td><td>19.57</td><td>6.97</td><td>1.31</td></tr><tr><td>August-2020</td><td>14.58</td><td>5.02</td><td>0.56</td></tr><tr><td>September-2020</td><td>10.01</td><td>2.81</td><td>0.37</td></tr><tr><td>October-2020</td><td>7.61</td><td>2.90</td><td>0.50</td></tr><tr><td>November-2020</td><td>5.14</td><td>5.78</td><td>0.33</td></tr><tr><td>December-2020</td><td>4.61</td><td>57.31</td><td>9.05</td></tr><tr><td>January-2021</td><td>8.17</td><td>71.19</td><td>7.14</td></tr><tr><td>February-2021</td><td>49.19</td><td>108.15</td><td>19.78</td></tr><tr><td>March-2021</td><td>35.45</td><td>18.28</td><td>1.73</td></tr></tbody></table>
<table><tr><td>April-2021</td><td>28.22</td><td>10.58</td><td>1.42</td></tr><tr><td>May-2021</td><td>21.54</td><td>32.87</td><td>1.77</td></tr><tr><td>June-2021</td><td>28.23</td><td>17.67</td><td>0.70</td></tr><tr><td>July-2021</td><td>21.80</td><td>13.09</td><td>0.31</td></tr><tr><td>August-2021</td><td>17.91</td><td>9.13</td><td>0.82</td></tr><tr><td>September-2021</td><td>14.26</td><td>6.90</td><td>0.47</td></tr><tr><td>October-2021</td><td>10.31</td><td>4.94</td><td></td></tr><tr><td>November-2021</td><td>8.77</td><td>3.63</td><td>Instrument stopped</td></tr><tr><td>December-2021</td><td>7.61</td><td>47.68</td><td></td></tr><tr><td>January-2022</td><td>17.96</td><td>56.49</td><td>3.38</td></tr><tr><td>February-2022</td><td>28.37</td><td>41.11</td><td>5.32</td></tr><tr><td>March-2022</td><td>43.30</td><td>52.76</td><td>4.22</td></tr><tr><td>April-2022</td><td>44.05</td><td>51.24</td><td>5.03</td></tr><tr><td>May-2022</td><td>34.16</td><td>21.45</td><td>2.76</td></tr><tr><td>June-2022</td><td>23.17</td><td>7.81</td><td>1.77</td></tr><tr><td>July-2022</td><td>14.96</td><td>5.88</td><td>1.49</td></tr><tr><td>August-2022</td><td>11.71</td><td>5.21</td><td>1.04</td></tr><tr><td>September-2022</td><td>8.26</td><td></td><td>0.72</td></tr><tr><td>October-2022</td><td>4.02</td><td></td><td>0.46</td></tr></table>

5

6

7
Local meteorological
rainfall and and
temperature

<figure><img src="image_20.png" /></figure>

Electrical
resistivity
tomography

Karst reservoirs, infiltration pathways, seasonal
changes

Infiltration flows: transfer
processes time delay
Water budget

Cave drip water
hydrology
(drip rate measurements
under stalactites)