Modeling the Dynamics of the Jebel Zaghouan Karst Aquifer Using Artificial Neural Networks: Toward Improved Management of Vulnerable Water Resources

Abstract

Karst aquifers are critical yet vulnerable water resources in semi-arid Mediterranean regions, where structural complexity, nonlinearity, and delayed hydrological responses pose significant modeling challenges under increasing climatic and anthropogenic pressures. This study examines the Jebel Zaghouan aquifer in northeastern Tunisia, aiming to simulate its natural discharge dynamics prior to intensive exploitation (1915–1944). Given the fragmented nature of historical datasets, meteorological inputs (rainfall, temperature, and pressure) were reconstructed using a data recovery process combining linear interpolation and statistical distribution fitting. The hyperparameters of the artificial neural network (ANN) model were optimized through a Bayesian search. Three deep learning architectures—Multi-Layer Perceptron (MLP), Convolutional Neural Network (CNN), and Long Short-Term Memory (LSTM)—were trained to model spring discharge. Model performance was evaluated using Kling–Gupta Efficiency (KGE′), Nash–Sutcliffe Efficiency (NSE), and R² metrics. Hydrodynamic characterization revealed moderate variability and delayed discharge response, while isotopic analyses (δ¹⁸O, δ²H, ³H, ¹⁴C) confirmed a dual recharge regime from both modern and older waters. LSTM outperformed other models at the weekly scale (KGE′ = 0.62; NSE = 0.48; R² = 0.68), effectively capturing memory effects. This study demonstrates the value of combining historical data rescue, ANN modeling, and hydrogeological insight to support sustainable groundwater management in data-scarce karst systems.

1. Introduction

Karst aquifers are essential components of the global water supply, providing approximately 25% of the world’s drinking water and supporting diverse agricultural needs [1,2,3]. These aquifers, formed mainly through the dissolution of carbonate rocks, exhibit a complex and highly heterogeneous network of flow paths. They are also characterized by significant variations in permeability [4,5,6,7]. The inherent geological and hydrological properties of karst systems are distinguished by their anisotropy, heterogeneity, and nonlinear subsystems [8,9,10]. Due to the considerable variability in hydraulic parameters of karst systems, such as conductivity and storage, a substantial challenge for numerical modeling, also known as the Karst Modeling Challenge or KMC, has emerged [4,5,11]. To address this challenge, hydrogeological modeling is a fundamental tool for the characterization of water resources dynamics within karst systems, facilitating improved management, development, and planning [12]. Karst modeling can broadly be categorized into lumped and physical parameter models [4,13,14,15]. Lumped models are utilized to understand the temporal variability of hydrodynamic behavior, offering insights into water movement patterns within the karst system [4,9,16,17,18]. Physical parameter models provide a detailed examination of the physical properties governing the system’s behavior, which enable a more comprehensive understanding of aquifer functioning [5,15,19,20,21,22]. Table 1 presents the various modeling approaches with their main advantages, disadvantages, and limitations.

Moreover, it is important to underscore that the selection of a modeling approach is contingent on multiple considerations, including but not limited to: the extent and quality of available data [23], geomorphology, and karst features specific to the study area [7], hydrodynamic functioning [24], climatic conditions [25] and the objectives of the investigation [9]. Ref. [4] suggested the integration of diverse methodologies to enhance the modeling of karst formations; nonetheless, this endeavor may introduce added intricacies and constrain its practical applicability.

In addition, the choice of the modeling approach is more complex and challenging when historical data is stored in printed documents, which must be digitized and pre-processed. This problem is emphasized in the challenge and innovation launched by many initiatives, i.e., ReHydrate (“Historical hydrological observations are often stored in printed documents and volumes of archives worldwide. This not only makes them practically inaccessible and unusable for modern hydrological studies but also puts them at risk of permanent loss due to the deterioration of their medium. In addition to the intrinsic value of rescuing past observations, having access to historical data is essential for understanding changes in the hydrological cycle and its extremes, which appear to be increasingly characterizing recent decades in several parts of the world. Several data rescue initiatives exist, but the efforts are highly fragmented in space and time.”) (REtrieve historical HYDRologic dATa & Estimates, https://iahs.info/Initiatives/Scientific-Decades/helping-working-groups/, accessed on 22 September 2025), which aims to preserve and leverage historical data to meet current and future challenges in water resource management [26].

Artificial Neural Networks (ANNs), considered as lumped models, have emerged in the recent decade as a prominent tool in karst hydrodynamic modeling [24,27,28,29,30,31,32]. ANNs are recognized for their capability to forecast hydrological outcomes without a detailed comprehension of the complex karst geometry; thereby simplifying the modeling process while addressing the inherent hydrogeological challenges of karst systems effectively [33,34,35,36,37]. In fact, ANNs can autonomously establish input-output relationships, offer a promising avenue for karst aquifer modeling despite the challenges associated with their “black box” nature and the extensive data requirements for training [24,38,39,40]. Through the efficient application of neural network methodologies, there is a potential for significant advancements in the effectiveness and efficiency of modeling karst aquifers, thereby contributing to the sustainable management and conservation of these vital water resources. Indeed, many karst systems are vulnerable and overexploited, risks which are amplified by climate change. These issues are particularly pronounced in the Jebel Zaghouan karst system in Tunisia, where it has been the main water drinking resource since the Roman era and has been encountering such a concerning situation since 1945 [41,42]. Since 1943, the karst has been subject to increasing anthropogenic pressure due to intensified pumping, highlighting the challenge of sustainable water management amidst growing demand and environmental changes. In consequence, Jebel Zaghouan karst is a crucial system to study. In addition, the study of Jebel Zaghouan karst systems presents further advantages, including the availability of both quantitative and qualitative data, as well as historical raw data series.

Table 1. Karst Modeling Approaches.

Modeling Category	Model	Authors	Advantages	Disadvantages	Limitations
Statistical and Regression Models	Logistic Regression Model (LRM)	[43]	Handle both continuous and discrete variables	Oversimplify karst complex relationships	Clear linear relationship
Conceptual Models	KARSTMODGARDENIARCD Seasonal	[9,14]	Simplify the hydrological process	Inadequate for spatial heterogeneity	Simple systems
Data Driven and Machine Learning Models	Data Mining Models (ANFIS, Fuzzy Logic, ANNs)	[2]	Flexible models Nonlinear Relationships	Data-intensive can be subjective	Data dependency (limited/noisy data)
	ANNs (MLP/CNN/LSTM /NARX)	[24]	Efficient in learning spatial/temporal features	Require substantial computational resources	Need for high-quality and quantity of data
	Support Vector Regression (SVR)	[44]	Effective in high-dimensional spaces	Sensitive to hyperparameter settings	Careful tuning of parameters
Physical-Based/Hydrodynamic Models	MODFLOW	[45,46]	Handle groundwater flow processes	May require simplification of karst features	Porous media flow
	KarstFLOW	[47]	Directly simulate physical processes	Require detailed and hard-to-obtain system data	High computational demand
Empirical and Stochastic Models	Empirical Models	[48]	Simple to implement; requires less data	Limited predictive capability, Restrictive applicability	Reproducibility
	Stochastic Models	[49]	Uncertainty and variability handling, limited data, constraints on time, and few computational resources.	Numerous hypotheses on karst network configuration Complex to set up and interpret	Replicability

Table 1. Karst Modeling Approaches.

Modeling Category	Model	Authors	Advantages	Disadvantages	Limitations
Statistical and Regression Models	Logistic Regression Model (LRM)	[43]	Handle both continuous and discrete variables	Oversimplify karst complex relationships	Clear linear relationship
Conceptual Models	KARSTMODGARDENIARCD Seasonal	[9,14]	Simplify the hydrological process	Inadequate for spatial heterogeneity	Simple systems
Data Driven and Machine Learning Models	Data Mining Models (ANFIS, Fuzzy Logic, ANNs)	[2]	Flexible models Nonlinear Relationships	Data-intensive can be subjective	Data dependency (limited/noisy data)
	ANNs (MLP/CNN/LSTM /NARX)	[24]	Efficient in learning spatial/temporal features	Require substantial computational resources	Need for high-quality and quantity of data
	Support Vector Regression (SVR)	[44]	Effective in high-dimensional spaces	Sensitive to hyperparameter settings	Careful tuning of parameters
Physical-Based/Hydrodynamic Models	MODFLOW	[45,46]	Handle groundwater flow processes	May require simplification of karst features	Porous media flow
	KarstFLOW	[47]	Directly simulate physical processes	Require detailed and hard-to-obtain system data	High computational demand
Empirical and Stochastic Models	Empirical Models	[48]	Simple to implement; requires less data	Limited predictive capability, Restrictive applicability	Reproducibility
	Stochastic Models	[49]	Uncertainty and variability handling, limited data, constraints on time, and few computational resources.	Numerous hypotheses on karst network configuration Complex to set up and interpret	Replicability

Jebel Zaghouan karst system has already been modeled twice by reservoir models (lumped models) [41] and in [50] with KarstMod [14].

The model of [41] is characterized by four reservoirs: balance, transfer, aquifer, and karst conduits. The main inputs of the model are rainfall and evapotranspiration. The output of the model is the total discharge. It was developed using historical data from 1915 to 1962, with a calibration period from 1915 to 1927 prior to aquifer exploitation and validated from 1958 to 1962. Ref. [41] concluded that the model effectively simulates and monitors karst hydrodynamics, offering valuable capabilities to forecast water reserves and discharge responses in real-time, thus serving as a significant tool for managing and studying karst water resources.

Ref. [51] employed KarstMod to model the rainfall-discharge relationships of karst springs at daily and hourly time steps, as well as to analyze the hydrodynamics of the compartments represented in the model. The simulations successfully reproduced the model’s structure, with acceptable amplitude estimates across the entire time series. However, some flood events were underestimated, and while the simulated recession dynamics closely matched the observed data, the model consistently struggled to replicate rapid recession rates. This limitation was identified as a key factor affecting the overall performance of the simulations.

The main objective of this study is to deepen our understanding of the hydrological processes within the Jebel Zaghouan karst system, a critical resource that has been overexploited but lacks recent and updated studies. This research aims to address the challenges of assessing the hydrodynamic behavior of the karst system by utilizing historical raw data. For this purpose, we compare different data-driven modeling approaches using ANNs, and we evaluate the relevance of these approaches. This paper focuses on the natural karst behavior whose knowledge depends on the reconstruction and preservation of data prior to its exploitation. This foundational understanding is essential for informing future restoration efforts and establishing a sustainable management framework for the system.

2. Materials and Methods

This study aims to characterize the natural hydrodynamic behavior of the Jebel Zaghouan karst aquifer prior to anthropogenic exploitation. Before the development of water abstraction infrastructure, such as galleries and boreholes, the aquifer exhibited a natural functioning that was intrinsically linked to hydroclimatic variables, including precipitation, air temperature, and atmospheric pressure [41].

The methodological framework (Figure 1) comprises five main steps: (i) compilation and digitization of historical data (1915–1944) on precipitation, temperature, atmospheric pressure, and spring discharge; (ii) data gap-filling and reconstruction using both statistical interpolation techniques and autoregressive models based on artificial neural networks; (iii) analysis of the aquifer’s hydrodynamics through the examination of spring discharge time series, including flow duration analysis, autocorrelation (to assess memory effects), and cross-correlation (to evaluate response times); (iv) modeling of karst spring discharge using three deep learning architectures—Multilayer Perceptron (MLP), Convolutional Neural Network (CNN), and Long Short-Term Memory (LSTM). This stage involves model calibration, hyperparameter optimization via Bayesian techniques, and performance evaluation at daily and weekly time scales; (v) analysis and comparison of the model outputs to assess predictive performance and underlying hydrological processes.

2.1. Study Area

The Jebel Zaghouan karst aquifer is located approximately 50 km south of Tunis in Tunisia. It is distinguished by its significant Jurassic formation within the Zaghouan massif, encompassing roughly 19.6 km² (Figure 2).

2.1.1. Geological Context, Aquifer Geometry

The Zaghouan anticline is primarily composed of Jurassic limestones, bordered by rock-fall deposits and Cretaceous outcrops. As illustrated in Figure 3 and Figure A1, the geology of Jebel Zaghouan is shaped by southern and transverse fault systems, which have segmented the structure into distinct blocks. These faults—namely, Kef El Orma, the Great Peak, and Achilles—facilitate the infiltration of meteoric waters [3]. The eastern part of the Zaghouan karst aquifer provides favorable conditions for groundwater storage [3], whereas the western sector, dominated by marl deposits, exhibits reduced storage capacity [41].

The Jurassic limestone body forms a trapezoidal block, cavernous and highly fractured, extending roughly 8 km along a N–40° E direction and averaging 2.4 km in width along a N–45° W axis. Its surface area covers around 19 km² at an elevation of 300 m NGT. Surrounded by marl acting as an impermeable barrier, the massif can be divided into three main compartments arranged from north to south:

• Small Zaghouan, the source of Ain Haroun;
• The transmission station massifs (Kef El Orma, Kef El Blidah, and Jebel Stâa), the largest compartment, feeding major springs such as the Water Temple (Nymphée), Aïn Ayed, and Aïn Oued El Guelb;
• The Great Peak massif, which gives rise to the Sidi Medien spring.

The general dip of the limestone strata combined with the northwestern topography accounts for the presence and abundance of springs along the eastern massif and slopes.

2.1.2. Water Resources

This region experiences an upper semi-arid to sub-humid climate, with variable annual precipitation averaging 467 mm and ranging from 245 to 625 mm over the period 1915–1944. Spatial distribution of rainfall is heterogeneous, and temporal fluctuations are notable (Figure 4). The average annual temperature is around 17.7 °C (https://www.meteo.tn/fr/donnees-climatiques, accessed on 9 October 2020). Historically, the Jebel Zaghouan karst aquifer has been a critical source of drinking water for local cities and the capital, Tunis, previously Carthage during the Roman era [52]. Drinking water was supplied by 132 km of Roman aqueducts, the remains of which can still be seen today along the Tunis Zaghouan Road. The aquifer sustains approximately 14 springs (Ain Essid, Ain Wad el Galb, Ain Ayed, Ain Haroun, Ain Lansarine, Ain Oued Guelb, Galerie 44, Galerie 47, Nila 1, Nymphée, Okka, Sidi Medien, Yahya, and Zkir) (Figure 4) which played a vital role in the local water supply. Additionally, three galleries were constructed to supplement these springs and meet water demand during drought conditions. The first galleries were constructed in 1928 at Ain Ayed. The second one in 1944, followed by the third gallery in 1947. The exploitable reserve of this karst system was quantified at 2.7 million m³ before 1943 (the beginning of the exploitation). During natural functioning, the flow rates exhibited significant variability (Figure 5), ranging from 0.8 to 7 million m³/year.

At present, the Jebel Zaghouan karst aquifer is primarily exploited through a system of nine boreholes and galleries, ensuring the provision of drinking water to the city of Zaghouan and its surrounding rural areas. Among these, three boreholes are dedicated to the abstraction of mineral water for commercial bottling under the brands Cristaline, Aqualine, and Prestine (Figure 4). Since 2015, however, the natural discharge from the galleries has nearly ceased, accompanied by a sustained decline in groundwater levels [53]. In response to the acute water deficit—particularly following the desiccation of Galerie 44 and Galerie 47—two supplementary boreholes, namely Temple and Ain Haroun 3bis, were commissioned in 2017 and 2018 [53].

2.2. Historical Data Collection and Rescue

The input data considered are historical rainfall, temperature, and pressure time series at the daily and weekly scales (

Table 2. Data availability.

Data	Observation Period	Gaps Periods	Gap Filling Method	Comments
Rainfall	1915 to 1944	1929 to January 1930	Linear Interpolation	Historical data (Data from National Archive: http://www.bnt.nat.tn:81/numerisation/khaldounia/periodiques/fr/E-Per-2850/E-Per-2850.htm, accessed on 19 January 2020)
Temperature Pressure	1915 to 1944	1915; 1920 1931 to 1943	Statistical Interpolation	Historical data
Discharge	1915 to 1944	-	-	Historical data in paper format

). They were used to model the Zaghouan karst discharge in its natural hydrodynamic functioning.

Historical rainfall, temperature, and pressure data are essential for analyzing long-term trends and variability in our karst system responses. These records, sourced from early 20th-century meteorological service reports and archives of the National Library of Tunisia (Figure A2), address critical gaps in existing datasets. Rescuing and digitizing these data enhances our ability to reconstruct past conditions, refine karst system models, and evaluate changes over time.

2.3. Data Preprocessing

2.3.1. Rainfall

Two historical meteorological stations are located near the Zaghouan karst zone: Zaghouan Contrôle and Zaghouan SM (Figure 4 and

Table 3. Station coordinates.

Station	Latitude	Longitude	Altitude (m NGT)
Zaghouan Contrôle	36°23′45″	10°08′57″	218
Zaghouan SM	36°24′11″	10°08′41″	176

). The primary rainfall dataset analyzed in this study was obtained from the Zaghouan Contrôle station, covering the period from 1915 to 1944.

A data gap was identified from 1 January 1929 to 31 January 1930. To address this, linear interpolation was performed using rainfall records from the nearby Zaghouan SM station, situated only a few hundred meters away. This preprocessing step enabled the reconstruction of a continuous daily and weekly rainfall series for the Zaghouan Contrôle station.

To implement this approach, a correlation analysis was carried out between the annual cumulative rainfall totals of both stations, thereby assessing the reliability of data transposition between the sites. Additionally, the correlation analysis was extended to a trimester basis, according to the hydrological year in Tunisia (starting in September). Rainfall data were divided into four trimesters: September to November (first trimester), December to February (second trimester), March to May (third trimester), and June to August (fourth trimester).

For each trimester, linear regression models were developed using available data. The resulting trimester-specific regression equations were then applied to reconstruct the missing daily rainfall data for the Zaghouan Contrôle station, under the assumption that the quarterly correlations remained valid at the daily scale.

2.3.2. Temperature and Pressure

In addition to rainfall, we use two additional input data types: temperature and pressure, measured on a daily scale. In the karst water balance, temperature and pressure are exogenous variables that influence the quantity of water transitioning from the epikarst to the karst aquifer. Consequently, these variables impact the temporal evolution of discharge at the karst outlet.

Temperature and pressure data were unavailable at the two study stations during the study period. To address this limitation, we used observations from the Tunis meteorological station, located ~50 km away. Using Tunis as a proxy for Zaghouan is justified because near-surface air temperature and atmospheric pressure exhibit much longer spatial decorrelation scales than precipitation. The climate literature shows that air temperature decorrelates over ~10³ km and that pressure/geopotential-height anomalies organize into basin-scale teleconnection patterns, implying high coherence at scales of tens of kilometers [54,55]. This approach is justified by the strong correlation observed between the two locations over a common period from 2000 to 2005 (Figure 6).

However, Zaghouan station data do not cover the entire study period from 1915 to 1944. Instead, data are available at Tunis station for the period from 1921 to 1930. Unfortunately, this dataset is insufficient to fill the gaps between 1915 and 1921, and between 1931 and 1944 (Figure 7).

To develop a continuous time series, temperature and pressure data from the Tunis meteorological station were compiled for the period 1944–2021, despite the presence of missing values. As data gaps were largely synchronous across both variables, cross-variable imputation was deemed unsuitable. Instead, a reconstruction method was applied to fill the gaps. Following this, temperature and pressure at Tunis were further estimated using linear correlation equations derived from data recorded between 2000 and 2005 at both the Tunis and Zaghouan stations.

Various methods are available for filling gaps in time series data, ranging from simple approaches such as forward/backward filling, mean or median substitution, and linear or spline interpolation, to more advanced techniques including moving averages, regression-based imputation, Kalman filtering, K-Nearest Neighbors (KNN) imputation, Seasonal ARIMA (SARIMA) models, and machine learning methods such as random forests or recurrent neural networks. Ref. [56] suggests that simpler, local methods like interpolation and KNN perform well for short, isolated gaps, but their accuracy declines for long, continuous gaps, where local information is insufficient to capture the underlying dynamics or seasonal patterns. In such cases, Probability Distributions Reconstruction (PDR) offers an effective alternative by reconstructing missing values based on the statistical properties of the observed data, preserving both the probability distribution and seasonal characteristics. PDR models the variable’s distribution rather than relying on neighboring points, generates synthetic values that maintain statistical consistency, and can adapt to temporal and seasonal variations. For extensive gaps, seasonally aware models or the incorporation of external data can also provide more reliable reconstructions. In our study, we used the Probability Distributions Reconstruction (PDR) approach.

Daily values of these variables vary randomly from year to year and across different years for the same calendar day.

Let i represent the number of years (i = 1⋯30) and j the number of calendar days (j = 1⋯365). We define T_ij and P_ij; as the daily temperature and pressure, respectively, for year i and day j. For each day j, a time series T._j; and P._j; are constructed, yielding 365 series for each variable (730 series). Each series is then fitted with its own probability distribution function, denoted DT_j; and DP_j;, respectively, resulting in 365 distributions for each variable.

To reconstruct the missing values, a random sample is drawn from a uniform distribution, followed by the calculation of the quantile using, respectively, the inverse of the normal and log normal distribution corresponding to day j.

2.3.3. Discharge at Nymphée Spring

The discharge at the karstic outlet of the Nymphée is a crucial parameter in our modeling efforts. It serves as the output data characterizing the hydrodynamic functioning of the Zaghouan karst system.

Historical discharge data for the study period from 1915 to 1944 were collected in paper format by SONEDE (DGRE). These discharge records were cataloged using a non-uniform temporal scale, ranging from weekly and biweekly to monthly intervals. The printed records (Figure A3) were scanned and digitized using Optical Character Recognition (OCR) technologies. This digitization process was followed by manual verification and correction to address errors introduced during the conversion. Subsequently, a filtering process was applied to clean the dataset, removing inconsistencies, duplicates, and errors. After the conversion, linear interpolation was performed to obtain a uniform discharge series with a weekly and daily time step (Figure 8).

Table 4. Statistical parameters of daily discharges at Nymphée Spring.

Statistical Parameter	Values (m3/s)
Average discharge	0.080
Median discharge (Q2)	0.062
Minimum discharge	0.002
Maximum discharge	1.140
25th percentile (Q1)	0.042
75th percentile (Q3)	0.088
Standard deviation	0.083

shows the main statistical parameters of daily discharges. The highest recorded discharge, approximately 1.140 m³/s (99.99th percentile), occurred on 6 June 1932, following a period of intense rainfall as shown by the concurrent spike in daily precipitation at the Zaghouan station. Similarly, the significant discharge peaks observed on 17 April 1921 (0.65 m³/s; 99.66th percentile) and 23 April 1929 (0.57 m³/s; 99.35th percentile) are closely associated with substantial rainfall events. These findings highlight the piston flow functioning of the karst through its reactivity to extreme rainfall, as illustrated in Figure 8.

2.4. Hydrodynamic Characterization of Karst Through the Discharge at Nymphée

2.4.1. Characterizing Flow Regime Using the Ranked Method

The ranked flow method is used to characterize the flow regime and specific events at the karst outlet through the analysis of its discharge. Proposed by [48], it involves classifying discharge into amplitude classes. Subsequently, a statistical adjustment is applied to the discharge. This adjustment highlights the frequency of exceeding or not exceeding the discharge classes. The representative curve of ranked flows is obtained by plotting the discharge classes on the x-axis and the non-exceedance frequencies on the y-axis [17]. The ranked flow curve facilitates the identification of abnormally high and low flows [34]. Regarding the outlet of the Nymphée of the Zaghouan karst, we determined the ranked discharge curves on a daily scale. This was performed to provide an analysis, visualize, and compare the discharge distribution at different scales. Furthermore, we adopted class amplitudes proportional to the sample size of each time scale (N), with the amplitude A calculated as follows: A = √N.

2.4.2. Estimating Memory Effect Using Autocorrelation of Discharge

The autocorrelation of the discharge variable (Equations (1) and (2)), also referred to as serial correlation, measures the linear correlation of the discharge with itself at different time lags k:

$${\mathrm{r}}_{\mathrm{k}}={\displaystyle \frac{{\mathrm{C}}_{\mathrm{k}}}{{\mathsf{\sigma }}_{\mathrm{x}}^2}}$$

(1)

$${\mathrm{C}}_{\mathrm{k}}={\displaystyle \frac{1}{\mathrm{n}}}{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}-\mathrm{k}}\left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)\left({\mathrm{x}}_{\mathrm{i}+\mathrm{k}}-\overline{\mathrm{x}}\right)$$

(2)

where ${\mathrm{r}}_{\mathrm{k}}$ the autocorrelation coefficient at lag k. It measures the linear relationship between the time series and its lagged version, ${\mathrm{C}}_{\mathrm{k}}$ the covariance between the time series x_i and its lagged version ${\mathrm{x}}_{\mathrm{i}+\mathrm{k}}$. Here, n is the sample size, corresponding to the temporal lag (in days, weeks, or months); x represents the discharge at time t, $\overline{\mathrm{x}}$ is the mean discharge of the series, and σ_x denotes the standard deviation [11].

The autocorrelation structure of Nymphée spring is analyzed through the autocorrelation function (ACF), which plots autocorrelation coefficients against the corresponding lag times. It enables the characterization of the system’s memory effect, defined as the lag necessary for the autocorrelation coefficient to reach a minimal threshold, commonly set at 0.2 [57]. This memory effect represents the maximum duration during which the discharge significantly correlates with itself, indicating the inertia of the karst system [17,34]. For the Nymphée spring at Zaghouan, we computed and analyzed autocorrelograms based on daily (Figure 9a), weekly (Figure 9b), and monthly (Figure 9c) discharge data. Then, the memory can be summarized depending on the temporal scale in

Table 5. Memory effect characterization in function of discharge temporal scale.

Temporal Scale	Memory Effect Value (Days)
Daily	109
Weekly	105
Monthly	108

.

The ACFs of the three discharge time scales at Nymphée Spring exhibit a rapid decline over the first lags, followed by oscillations around zero after approximately 105 days, 15 weeks, and 3.6 months, respectively. This pattern reflects a finite memory effect of the aquifer system rather than a persistent long-term trend. If a deterministic trend were present, the ACF would decay more gradually and remain positive over long lags; since this behavior is not observed, detrending was not applied. Although an exponential model with a sill equal to 1 can be appropriate for correlation structures characterized by monotonic decay, the observed ACF displays oscillatory dynamics associated with recharge and release processes. Consequently, interpreting the characteristic memory time provides a more meaningful representation of aquifer behavior, as it captures the underlying hydrogeological processes.

2.4.3. Estimating Lag Time Using Cross Correlation and Significance Test Between Rainfall and Discharge

• Cross correlation

In addition to the autocorrelation analysis discussed previously, the cross-correlation (Equations (3) and (4)) between precipitation and discharge time series offers valuable insight into the transfer dynamics of the karst system. The cross-correlation coefficient (r_k) is used to quantify the relationship between the two series as a function of the temporal lag k (in days, weeks, or months), and is defined as follows:

$${\mathrm{r}}_{\mathrm{k}}={\displaystyle \frac{{\mathrm{C}}_{\mathrm{k}}}{{\mathsf{\sigma }}_{\mathrm{x}}{\mathsf{\sigma }}_{\mathrm{y}}}}$$

(3)

$${\mathrm{C}}_{\mathrm{k}}={\displaystyle \frac{1}{\mathrm{n}}}{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}-\mathrm{k}}\left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)\left({\mathrm{y}}_{\mathrm{i}+\mathrm{k}}-\overline{\mathrm{y}}\right)$$

(4)

where n is the sample size; k is the time lag (in days, weeks, or months); ${\mathrm{x}}_{\mathrm{i}}$ represents rainfall; $\overline{\mathrm{x}}$ is the mean of the rainfall series; ${\sigma }_{\mathrm{x}}$ is the standard deviation of the rainfall sample; ${\mathrm{y}}_{\mathrm{i}+\mathrm{k}}$ represents discharge; $\overline{\mathrm{y}}$ is the mean of the discharge series; and ${\sigma }_{\mathrm{y}}$ is the standard deviation of the discharge sample. The cross-correlogram produced from this analysis characterizes the temporal relationship between rainfall and discharge, identifying the lag period that reflects the response time of the aquifer to precipitation events. In a causally linked system, a positive lag indicates the period during which rainfall exerts a direct influence on discharge. This lag is governed by the internal functioning of the aquifer, and its extent—the so-called memory effect—represents the maximum duration over which rainfall continues to affect discharge [58]. In this study, cross-correlograms were generated for daily, weekly, and monthly discharge series (Figure 10a–c), allowing for the determination of characteristic response times and a comprehensive assessment of the persistence of rainfall’s influence on the karst system’s hydrodynamics. The correlograms show a high degree of variability around zero. This “noisy” character is mainly due to the irregularity of rainfall events and the reduction in the number of effective observations in the semi-arid context. Nevertheless, interpretation is not based on point-to-point fluctuations, but on the location of the significant maximum. Here, the maximum correlation reflects the characteristic response time of the karst system.

Table 6. Time lags corresponding to maximum cross-correlation coefficients at different temporal scales.

Temporal Scale	Lag with High Cross-Correlation Coefficient r (Days)
Daily	55
Weekly	56
Monthly	30

presents the lag times at which precipitation (P) and discharge (Q) series show their strongest linear correlation at daily, weekly, and monthly temporal scales. These values emphasize the linear temporal link between P and Q, while acknowledging that other factors also influence the hydrodynamics of the karst system.

• Significance testing

To deepen the characterization of the dependence between the rainfall and discharge time series, we applied a significance test using Kendall’s rank correlation coefficient τ in different temporal scales (Equation (5)):

$$\left|\tau \right|>{\mathrm{u}}_{\mathsf{\alpha }/2}·\sqrt{{\displaystyle \frac{2\left(2\mathrm{n}+5\right)}{9\mathrm{n}\left(\mathrm{n}-1\right)}}}$$

(5)

where n is the sample size, α is the significance level, and u_α/2 is the α/2 percentile of the Normal distribution (u_α/2 = 1.96).

No significant instantaneous dependence was found between rainfall and discharge at daily, weekly, or monthly scales, which is consistent with the delayed hydrodynamic response typical of karst systems. To further assess the karst’s response time, we conducted additional significance tests using lagged discharge series relative to rainfall. This approach enabled us to identify the lag at which Kendall’s τ reaches its maximum value (

Table 7. Lag time analysis across temporal scales using Kendall’s rank correlation.

Temporal Scale	Lag (Days)	Kendall’s Coefficient (τ)	Significance Threshold
Daily	114	0.0940	0.013
Weekly	126	0.150	0.034
Monthly	120	0.230	0.072

). The results reveal a substantial increase in correlation when the appropriate lag is applied: at the daily scale, a lag of 114 days produced a significant τ; optimal lags of 18 weeks and 3–4 months were found for the weekly and monthly scales, respectively. On average, the optimal lag across all temporal scales is about 115 days, which corresponds to the characteristic response time of the system. Kendall’s τ and cross-correlation address complementary aspects of the rainfall–discharge relationship. Kendall’s τ, being a non-parametric rank-based test, evaluates the statistical significance of monotonic dependence and helps identify the characteristic lag. Cross-correlation, in contrast, quantifies the linear dependence as a function of lag, providing insight into the dynamic transfer of signals. By combining both approaches, we capture both the statistical significance of monotonic dependence (Kendall’s τ) and the temporal dynamics of linear dependence (cross-correlation), which together offer a more robust characterization of the karst aquifer response. The results show that cross-correlation analysis highlights shorter response times (55–56 days at daily and weekly scales, and 30 days at the monthly scale), reflecting the influence of rapid flow components. In contrast, Kendall’s τ identifies longer lags of about 115–126 days, which represent the dominant delayed response of the aquifer. This duality is consistent with the hydrodynamic behavior of karst systems, where both quick conduit drainage and slow diffuse flow coexist, the latter controlling the overall system inertia. The pronounced lag, therefore, further supports the conclusion that the Zaghouan karst is characterized by low hydraulic inertia and a slow response to rainfall inputs. Consequently, the hydrodynamic characterization is identified as a C6-type aquifer under the typology of [27,50,53] with moderate variability and delayed discharge response.

2.5. ANN Modeling Approaches

In this study, we simulate Zaghouan karst Nymphée spring discharge with deep learning models: MLP, CNN, and LSTM. The approach used meteorological (rainfall, temperature, and pressure) data as input and the discharge as output. The details of each modeling approach can be found in Appendix B.

2.5.1. Models Architectures

• MLP

Our MLP models for daily and weekly forecasting have been structured to capture complex, nonlinear relationships between inputs and karst aquifer discharge. Both architectures include dense layers interspersed with dropout layers to prevent overfitting and enhance generalization (Figure 11):

▪

MLP model for daily forecasting consists of an input layer with 348 neurons, connected to a first dense layer of 115 neurons activated by ReLU. A second dense layer expands this representation to 182 neurons, again activated by ReLU. After this, a dropout layer (rate determined by Bayesian optimization) is included to mitigate overfitting. Finally, the output is generated through a dense layer with a single neuron, providing the predicted discharge value.

▪

MLP model for weekly forecasting starts with an input layer of 54 neurons feeding into a dense layer of 206 neurons with ReLU activation. A subsequent dense layer reduces dimensionality to 81 neurons. Similarly to the daily model, a dropout layer is applied here for regularization. The output layer is again a dense layer with one neuron, yielding the weekly discharge forecast.

• CNN

Our CNN architectures are structured to capture local patterns and temporal features effectively:

▪

CNN model for daily forecasting consists of an initial 1D convolutional layer (Conv1D) with 119 filters and a kernel size of 3, followed by a MaxPooling1D layer to reduce temporal dimensionality. Subsequently, a dropout layer is introduced to mitigate overfitting. The output from dropout is flattened and passed through a dense layer comprising 73 neurons (activated with ReLU), followed by a final dense layer with a single neuron outputting the forecast discharge.

▪

CNN model for weekly forecasting follows a similar but adjusted structure, starting with a Conv1D layer featuring 152 filters (kernel size of 3). A subsequent MaxPooling1D layer reduces feature size, followed by dropout. The flattened output is then processed through a dense layer containing 154 neurons with ReLU activation. Lastly, a dense output layer with a single neuron provides the predicted weekly discharge (Figure 12).

• LSTM

Our LSTM architectures are specifically designed to model long-term temporal dependencies within the discharge time series (Figure 13):

▪

Daily forecasting model begins with an LSTM layer that accepts input sequences of shape (115, 3), producing an output sequence of 58 time steps, each with 128 features. A Dropout layer is subsequently applied to reduce the risk of overfitting. The resulting sequence is then flattened and processed by a dense layer comprising 73 units with ReLU activation. Finally, a single-unit dense layer provides the predicted daily discharge.

▪

weekly forecasting model employs a similar structure, initiating with an LSTM layer that processes input sequences of shape (17, 3) and outputs a sequence of 9-time steps with 128 features each. Following dropout regularization, the output is flattened and passed through a dense layer containing 154 ReLU-activated units, culminating in a single-unit dense layer that generates the weekly discharge prediction.

2.5.2. Hyperparameter Tuning and Evaluation

For all three architectures, we applied Bayesian Optimization to tune hyperparameters (

Table 8. Grid of search for Bayesian optimization.

Model	Temporal Scale	Sequence Length (in Days)	Batch Size	Dropout	Learning Rate
MLP	Daily	(100 to 130)	(16, 256)	(0, 0.5)	(1 × 105, 1 × 101)
	Weekly	(13 to 19)	(8, 256)
CNN	Daily	(100 to 130)	(8, 256)
	Weekly	(13 to 19)	(4, 256)
LSTM	Daily	(100 to 130)	(8, 256)
	Weekly	(13, 19)	(4, 256)

). We were inspired by the Python 3.13.5 implementation performed by [59]. We used 50 optimization steps with 10 repetitions per step. We also adopt stops if no improvement after 10 consecutive steps.

Also, in all three models, the acquisition function used is expected improvement, while the optimization target function is defined as the mean of the Nash–Sutcliffe efficiency (NSE, Equation (6)), the squared Pearson’s correlation coefficient (R², Equation (7)) and the Kling Gupta coefficient (KGE, Equation (8)). These three criteria are widely recognized and well established for evaluating forecast accuracy, particularly in water related studies [60]. Their combined use ensures a comprehensive assessment of model performance, capturing both the predictive accuracy and the strength of linear relationships in the forecast outputs.

$$\mathrm{NSE}=1-{\displaystyle \frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{x}}_{\mathrm{i}}^{\mathrm{obs}}-{\mathrm{x}}_{\mathrm{i}}^{\mathrm{pred}}\right)}^2}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{x}}_{\mathrm{i}}^{\mathrm{obs}}-{\overline{x}}^{\mathrm{obs}}\right)}^2}}$$

(6)

$${\mathrm{R}}^2=1-{\displaystyle \frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{x}}_{\mathrm{i}}^{\mathrm{obs}}-{\mathrm{x}}_{\mathrm{i}}^{\mathrm{pred}}\right)}^2}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{x}}_{\mathrm{i}}^{\mathrm{obs}}-{\overline{\mathrm{x}}}^{\mathrm{obs}}\right)}^2}}$$

(7)

$$\mathrm{KGE}=1-\sqrt{{\left(\mathrm{r}-1\right)}^2+{\left(\mathsf{\alpha }-1\right)}^2+{\left(\mathsf{\beta }-1\right)}^2}$$

(8)

where

• ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{obs}}$ observed value at time step i;
• ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{pred}}$ simulated value at time step i;
• ${\overline{\mathrm{x}}}^{\mathrm{obs}}$: Mean of observed values
• r: Pearson correlation coefficient between observed and simulated values
• α: Variability ratio (standard deviation ratio)
• β: Bias ratio (mean ratio)

All three model types in this study were trained with a maximum of 150 epochs. To mitigate overfitting, early stopping with a patience of 10 epochs was implemented. The testing period for model evaluation spanned from 1915 to 1921, during which the data were exclusively used for testing purposes. So, the full dataset going from 1915 to 1944 were divided into three subsets: 80% for training, 10% for early stopping, and 10% for validation during hyperparameter optimization.

To ensure consistency, all data were normalized between −1 and 1, and models were initialized randomly based on the random seed. To account for this dependency, each optimization step was repeated ten times, with the mean target function value recorded. We adopt a sequence-to-value (seq2val) set up: given a fixed-length window of past inputs, the model predicts the next time-step discharge. We chose seq2val because our objective is one-step-ahead forecasting at daily and weekly scales; unlike seq2seq, it avoids compounding multi-step errors, simplifies training and tuning, and maximizes data use via sliding windows. In fact, for modeling the discharge at date t, we used input data: rainfall, temperature and pressure at time t − X_i where X_i is the modeling shift time (Equation (9)).

$$\hat{\mathrm{Q}}\left(\mathrm{t}\right)=\mathrm{f}\left({\mathrm{X}}_{\mathrm{t}-{\mathrm{X}}_{\mathrm{i}}}\right)=\mathrm{f}\left({\mathrm{R}}_{\mathrm{t}-{\mathrm{X}}_{\mathrm{i}}},{ \mathrm{T}}_{\mathrm{t}-{\mathrm{X}}_{\mathrm{i}}},{\mathrm{P}}_{\mathrm{t}-{\mathrm{X}}_{\mathrm{i}}}\right)$$

(9)

where

• $\hat{\mathrm{Q}}\left(\mathrm{t}\right)$: Predicted discharge at time t
• f: Model function trained to map inputs to discharge
• ${\mathrm{X}}_{\mathrm{t}-{\mathrm{X}}_{\mathrm{i}}}$: Input feature vector at time t − X_i
• ${\mathrm{R}}_{\mathrm{t}-{\mathrm{X}}_{\mathrm{i}}}$: Rainfall at time t − X_i
• ${\mathrm{T}}_{\mathrm{t}-{\mathrm{X}}_{\mathrm{i}}}$: Temperature at time t − X_i
• ${\mathrm{P}}_{\mathrm{t}-{\mathrm{X}}_{\mathrm{i}}}$: Pressure at time t − X_i
• X_i: Time shift (lag) used in the sequence

2.5.3. Data Splitting Strategy

To ensure robust and unbiased evaluation of the ANN models, our historical dataset (1915–1944) was chronologically divided into three subsets (Figure A4), reflecting specific hydrological contexts and historical developments within the Jebel Zaghouan karst system:

• Test set (1915–1920, ~10%): This initial period, untouched by model training, was exclusively used to evaluate model predictive capabilities on completely unseen data.
• Validation set (1921–1927, ~10%): Immediately following the test period, this set was utilized for early stopping and hyperparameter tuning to prevent overfitting.
• Training set (1928–1944, ~80%): The most recent period, encompassing significant events including drought episodes and the construction of galleries in 1928 and 1944, was reserved for training the neural networks. This period was selected deliberately to capture the aquifer’s hydrodynamic responses under specific varying stresses.

This chronological data-splitting approach preserves temporal dependencies inherent in hydrological systems and reflects real-world forecasting conditions, thus enhancing the models’ operational applicability.

3. Results

3.1. Data Pre-Processing

3.1.1. Rainfall

The main statistical characteristics of the Zaghouan Contrôle and Zaghouan SM stations are summarized in

Table A1. Rainfall characteristics.

Rainfall (mm/year)	Zaghouan Contrôle	Zaghouan SM
Minimum	252	230
Maximum	994	927
Average	520	503
Median	507	506
Standard deviation	170	168

. In the data collected, there are some gaps reported. In order to fill them, a linear correlation analysis on an annual scale was performed and showed a strong correlation (R² = 0.97) between the two stations (Figure 14).

To capture potential seasonal variability in the correlation, linear regression was also performed for each hydrological trimester. The resulting models showed strong consistency, justifying their use in filling daily gaps (Figure 15):

The trimester-wise correction method enabled the reconstruction of a complete daily rainfall dataset for the period 1915–1944, allowing to fill gaps and obtain continuous daily data for the entire study period (Figure 16).

3.1.2. Temperature and Pressure

Daily mean temperature and pressure values for the Tunis station were reconstructed using the PDR approach. The agreement between reconstructed and observed data was evaluated over the full overlapping period (2000–2005). The results show an RMSE of 3.7 °C with R² = 0.97 for temperature, and an RMSE of 8.4 hPa with R² = 0.99 for pressure. Based on the established correlations, these parameters were then estimated at the Zaghouan karst site for the period 1915 to 1944 (Figure 17).

3.1.3. Discharge

A class interval of 0.011 m³/s (950 m³/day) was defined for flow ranking, resulting in 102 hb. The ranked flow series was then fitted with a log-normal distribution to construct the flow duration curve (Figure 18). Slope breaks, marked by red lines, correspond to operational discontinuities in the karst system and are interpreted in

Table A2. Interpretation of slope breaks in the ranked flow curves according [61].

Classification	Slope of the Lines	Position of the Break	Interpretation
A	α2 > α1	High percentages	Operation of overflow Leaks to another system Temporary storage Leaks or overflow of the gauging station during high water
B	α2 < α1	High percentages	Inflows from another system The gauging station accounts during floods for flows not belonging to the system
C	α2 > α1	Low percentages	Formation of a reserve
D	α2 < α1	Low percentages	Contribution of a reserve from a previous cycle
E	α2 > α3 and α1 < α2	Double break	Trapping of a reserve during recession and restitution during the drying up

. The presence of a double inflection indicates reservoir effects—specifically, water storage during recession and delayed release during low-flow conditions. These features are characteristic of poorly drained karst systems, either due to limited karstification and fracturing of carbonate aquifers or boundary-controlled drainage, which reduces the system’s responsiveness to rainfall. In such contexts, the karst acts as a filter, attenuating rainfall signals.

The obtained flow regime was classified as type E, in line with [61], who notes that in poorly drained or boundary-controlled karst systems, the transmission of rainfall variability is significantly dampened.

3.2. Hyperparameters

The Bayesian optimization, conducted for each ANN architecture with 50 steps with 10 repetitions per step can be evaluated with the best iteration and its best corresponding target (

Table 9. Convergence results of Bayesian Optimization hyperparameter tuning.

Model	Best Iteration Number	Best Target
MLP Daily	11	0.783
MLP Weekly	26	0.855
CNN Daily	1	0.858
CNN Weekly	40	0.831
LSTM Daily	16	0.701
LSTM Weekly	25	0.678

).

The best combination of optimized hyperparameters for each ANN architecture across daily and weekly temporal scales is summarized in

Table 10. Best hyperparameters from Bayesian optimization.

Model	Temporal Scale	Sequence Length (in Days)	Batch Size	Dropout	Learning Rate
MLP	Daily	116	40	0.207	5 × 10−3
	Weekly	126	39	0.013	5 × 10−2
CNN	Daily	115	69	0.37	5 × 10−3
	Weekly	119	127	7 × 10−3	4 × 10−2
LSTM	Daily	115	8	0.3	2 × 10−4
	Weekly	119	6	0.01	2 × 10−2

. The optimized hyperparameters include input sequence length, batch size, dropout rate, and learning rate.

The optimal hyperparameters obtained from Bayesian optimization show distinctions among models and temporal scales, highlighting their different sensitivities to the karst system’s hydrodynamic complexity. Sequence lengths (115–126 days) emphasize the significant temporal dependencies inherent to karst hydrology. CNN models require larger batch sizes and higher dropout rates, indicating greater complexity and stronger regularization needs, whereas LSTM models prefer smaller batches and lower learning rates, reflecting their capacity to precisely capture sequential dependencies. MLP maintains moderate values, balancing computational efficiency and stability. These differences underscore the necessity of tailored hyperparameter tuning to optimize each model’s predictive performance for karst aquifer modeling.

3.3. Performance by Model and Temporal Scale

The methodology was focused on 3 ANN architectures: MLP, CNN, and LSTM. All of them were analyzed on a daily and weekly temporal scale to model discharge based on climatic input variables: rainfall, temperature, and pressure.

3.3.1. MLP

The MLP model at the daily scale (Figure 19a) performs well, with KGE’ = 0.81, NSE = 0.62, and R² = 0.68, indicating strong predictive capability. The confidence interval is narrow, reflecting stable predictions. However, the model overestimates discharge by 55.41% on average, while underestimation is minimal at 0.27%. At the weekly scale (Figure 19b), the model’s performance drops significantly (KGE’ = 0.21, NSE = −0.15, R² = 0.66). The widening confidence interval suggests greater uncertainty, and overestimation remains high, further emphasizing the model’s inability to generalize effectively over longer periods.

3.3.2. CNN

The CNN model at the daily scale struggles (Figure 20a), showing weak correlation (KGE’ = 0.23, NSE = −0.27, R² = 0.61). The predicted discharge deviates substantially from observations, with overestimation exceeding 55%, and wide confidence intervals reflecting high uncertainty. Underestimation is negligible. At the weekly scale (Figure 20b), the model further deteriorates (KGE’ = 0.14, NSE = −0.28, R² = 0.65). It fails to capture peak discharge events accurately, and the confidence interval remains wide, confirming its lack of reliability. Overestimation continues to dominate, reinforcing that CNN is not well-suited for this forecasting task.

3.3.3. LSTM

The LSTM model at the daily scale (Figure 21a) performs moderately well (KGE’ = 0.53, NSE = 0.35, R² = 0.65), with reasonable trend following capabilities but some deviation in peak discharge predictions. Overestimation is present but generally lower than that of CNN and MLP. Underestimation remains minimal. At the weekly scale (Figure 21b), the model significantly improves (KGE’ = 0.62, NSE = 0.48, R² = 0.68), making it the most reliable option for long-term forecasting. The confidence interval is narrower compared to the other models, indicating higher prediction stability. Overestimation is still present but less pronounced than in MLP and CNN, making LSTM the best-suited model for long-term predictions.

3.3.4. Overall Performance

This analysis evaluates the predictive performance of the three ANN architectures (MLP, CNN, and LSTM) at daily and weekly temporal scales using KGE’, NSE, and R² metrics (

Table 11. Evaluating MLP, CNN, and LSTM Performance at Daily and Weekly Scales.

Model	Temporal Scale	KGE′	NSE	R2	Score
MLP	Daily	0.81	0.62	0.68	0.7
	Weekly	0.21	−0.15	0.66	0.2
CNN	Daily	0.23	−0.27	0.61	0.2
	Weekly	0.14	−0.28	0.65	0.2
LSTM	Daily	0.53	0.34	0.65	0.5
	Weekly	0.62	0.48	0.68	0.6

). The MLP model provides the highest accuracy at the daily scale (KGE’ = 0.81, NSE = 0.62, R² = 0.68) but significantly deteriorates for weekly forecasts. CNN consistently underperforms at both scales, with low KGE’ (≤0.23) and negative NSE values, reflecting substantial deviations from observed discharges. Conversely, the LSTM model exhibits moderate daily performance and demonstrates superior reliability at the weekly scale (KGE’ = 0.62, NSE = 0.48, R² = 0.68). Additionally, MLP and CNN show significant prediction bias (maximal global overestimation > 55%), whereas LSTM maintains more stable predictions, emphasizing its ability to capture the hydrological response effectively over longer periods.

These numerical findings are further illustrated in Figure 22, which provides a Taylor diagram summarizing the performance of MLP, CNN, and LSTM models at daily and weekly time steps (see Table 11 for detailed performance metrics). The black dot and dashed circle indicate the reference standard deviation from observed discharge. Blue arcs represent the standard deviation of model predictions, black dashed rays correspond to correlation coefficients, and magenta dotted arcs denote centered root mean square differences (cRMSD). The diagram is consistent with the numerical results in Table 11: LSTM models (both daily and weekly) are located closest to the reference, demonstrating their ability to reproduce observed variability while maintaining relatively high correlations, thereby offering the best compromise between accuracy and robustness. MLP models show moderate performance, with daily simulations performing better and approaching LSTM performance, while weekly simulations deviate more from the reference. CNN models exhibit the weakest performance overall, particularly at the daily scale, where correlations are markedly lower, although the weekly configuration provides slight improvements in variability representation. Overall, these results emphasize the superiority of recurrent architectures (LSTM) in capturing hydrological dynamics characterized by temporal dependencies and memory effects, whereas feed-forward (MLP) and convolutional (CNN) approaches remain more limited in this regard.

These results align with previous studies highlighting LSTM’s strength in modeling complex temporal dependencies in hydrological systems, especially karst aquifers characterized by significant delayed responses to rainfall [8,24]. Similar trends were reported by [24], who found LSTM networks superior in groundwater level forecasting due to their capability to manage long-term memory effects. Ref. [2] previously demonstrated MLP’s effectiveness for daily scale hydrological predictions, consistent with our findings, while also emphasizing its performance reduction over longer temporal horizons. Conversely, the observed underperformance of CNN in this study contrasts somewhat with findings by [24] who showed moderate CNN efficiency; however, such differences could arise from distinct data characteristics and hydrodynamic complexities of the studied karst systems.

4. Discussion

Our results align with recent literature and offer new insights into the hydrological functioning of semi-arid karst aquifers, particularly their pronounced memory effects and lagged responses. Notably, we observed significant temporal dependencies between climatic variables and the discharge of Jebel Zaghouan, with optimal sequence lengths of 115 to 126 days (approximately four months). Such lags confirm the strong hydrological memory characteristic of semi-arid karst systems, where rainfall infiltrates rapidly through conduits but is released more slowly from the matrix over extended periods [62,63]. Similar memory effects are documented in Mediterranean regions, such as the Fontaine de Vaucluse and Lez springs in southern France [20,64] and Croatian coastal karst springs [22]. Comparable phenomena have also been observed in semi-arid regions like the Zagros Mountains in Iran, where spring discharge lags range from weeks to years, depending on the extent of karstification and aquifer storage capacity [63]. Furthermore, Ref. [65] highlighted multi-scale memory effects in mountainous karst regions, underscoring the necessity of integrating long historical data sequences into predictive models.

Building on these hydrodynamic observations, isotopic and groundwater dating investigations in the Zaghouan karst system in 2021–2022 provided complementary evidence for the coexistence of rapid and delayed flow components [46]. This duality closely reflects the TORCAL model of [61], which characterizes karst systems where temporary storage during recession is followed by gradual release during baseflow, particularly in structurally immature or poorly drained systems. Stable isotope analyses in 2 boreholes (Temple and Ain Ayed 3, 141.5 m and 156 m deep, respectively) of the outflow sampled at weekly step during the rainfall season between September 2021 and April 2022, revealed two different behaviors [53]: a low temporal variability in Temple (Oxygen-18 between −4.96‰ and −5.55‰), indicating a well-mixed system, and in Ain Ayed 3 a larger local temporal variability (δ¹⁸O between −5.08‰ and −6.34‰) which could show a direct influence of rainfall at short time step in this borehole (rainfall showing a stronger isotopic variability, and depending on altitude recharge or/and air mass origin). We can hypothesize an efficient blending of the recharge at annual to interannual scales, dampening the isotopic signal. The strong correlation between δ¹⁸O and d-excess (R² = 0.989) in the groundwater suggests a mixing from different karst compartments. While recharge is generally dominant at lower elevations, more depleted isotopic values observed during certain events point to episodic high-altitude contributions. Collectively, these patterns indicate diffuse recharge filtered through structurally complex, weakly connected storage zones, rather than exclusively discrete, event-driven infiltration.

Groundwater dating sampled in September 2022 at 2 sites (EcoMusée and Temple, 256m and 141.5m deep, respectively) reinforces these findings [53]: Tritium concentrations (1.6–1.7 TU) indicated relatively recent recharge (from the last few decades), while radiocarbon data (~63.4% ¹⁴C) pointed to much older water (approximately 3000 years BP), evidencing the coexistence of both young and fossil groundwater within a dual-porosity system. The renewal rate inferred from tritium (~1.2–1.3%) and an average residence time of ~80 years further highlighted the slow exchange between mobile and immobile water domains [46].

This hydrodynamic and isotopic framework has direct implications for modeling and prediction using artificial neural networks (ANNs). Given the system’s complex internal storage and memory effects, models capable of representing long-range temporal dependencies are essential. In this context, ANN models implicitly integrate dual recharge regimes and physico-chemical influences on aquifer dynamics, thereby providing a coherent link between short- and long-term memory processes in karst systems. In our modeling experiments, LSTM architectures provided the best overall compromise between short- and long-term forecast reliability [8,59]. For weekly predictions, the LSTM model excelled (KGE’ = 0.64, NSE = 0.50), likely due to its capacity to capture extended temporal dependencies inherent to karst hydrology. This finding aligns with the results of [24] who also found that LSTM models substantially outperformed CNN and MLP architectures in predicting karst spring discharge, especially at weekly to monthly timescales. In contrast, for daily predictions, the MLP performed better (KGE’ = 0.81, NSE = 0.62), consistent with earlier results by [2] who noted high accuracy for short-term forecasts but limitations in capturing longer-term memory effects.

The relatively poor performance of the CNN model in our study—across both temporal scales—contrasts with the moderate results reported in other karst contexts [24,39,59]. This difference can be largely attributed to variations in dataset characteristics and the specific suitability of the models. CNN architectures are primarily designed to extract spatially coherent features and therefore perform better when spatially distributed inputs, such as gridded precipitation or catchment-scale variables, are available [39]. In our case, the dataset was predominantly temporal and lumped, limiting the effectiveness of convolutional filters in capturing relevant patterns. Moreover, the hydrodynamics of the Zaghouan aquifer are dominated by extended temporal dependencies, which are more effectively captured by recurrent architectures such as LSTM [24]. These considerations indicate that CNNs may be most appropriate in hybrid or spatially enriched modeling frameworks, while LSTMs remain preferable for forecasting in strongly memory-driven, semi-arid karst aquifers [59]. Among the three models, MLP and CNN exhibited substantial positive global biases (with a maximum > 55%). This overestimation primarily arises from target-distribution imbalance under low-flow conditions, where rare high-discharge peaks—shaped by prolonged droughts and episodic heavy precipitation—dominate training. When combined with uncertainties in rainfall data, the limited historical discharge records, difficulties in reconstructing temperature and pressure, and structural model limitations, these factors bias the learning process. Under variance-weighted objectives such as NSE, R², and KGE, errors at moderate to high flows dominate the loss, systematically favoring overestimation at low flows. This is in line with findings by [66], who identified rainfall measurement uncertainty as a major contributor to predictive errors, especially in semi-arid environments with sparse and unevenly distributed data networks. Approaches such as multi-source data integration, bias correction, and advanced gap-filling methods have been shown to enhance model performance under these constraints. For example, Ref. [67] demonstrated that combining gauge, radar, and satellite rainfall data can significantly improve discharge forecasts; in this study, only one rainfall gauge was available. Additionally, recent deep learning-based reconstruction methods, such as EEMD-LSTM, have proved effective in improving historical data recovery and reducing forecast uncertainty [68]. Other strategies can also help mitigate such biases, including stratified sampling or over-sampling of low-flow periods to balance mini-batches, as well as cost-sensitive or quantile-weighted loss functions that assign greater weight to errors under low-flow conditions [69,70].

Overall, ANN-based models generally demonstrated better predictive capability than traditional conceptual models (e.g., KarstMod), especially in data-rich scenarios [39]. Conceptual models offer greater process interpretability and can handle low-flow and recession periods effectively, but often struggle to capture rapid, nonlinear flood events [6]. Indeed, Karstmod reached an NSE of 0.60 over the 1915–1927 period. However, daily discharges were interpolated from infra-weekly data, and evapotranspiration was derived from monthly means distributed uniformly by day. This smoothing procedure limits daily variability, and the model only includes one high peak in the studied period.

The conceptual reservoir model performed slightly lower, with an NSE = 0.54 for the same 1915–1927 period and was subject to the same limitations (interpolated discharge, constant daily ETP, and only one high peak flow event).

Our ANN approach (LSTM) differs in two ways. First, it is trained over a longer period (1915–1944) that includes four distinct high peak events, thus encompassing more hydrological variability. Second, it explicitly integrates daily variability in temperature and pressure, which directly influences evapotranspiration and thus offers a more robust representation of discharge dynamics. The LSTM achieved a KGE′ of 0.62 and an NSE of 0.48 of the same order of magnitude as Karstmod, but with the added benefit of robustness according to KGE′. Since KGE′ is widely recognized as a more balanced diagnostic of hydrological model performance, particularly under variable flow regimes [60], this indicates that the ANN approach provides improved reliability in capturing both low- and high-flow dynamics.

Additionally, ANN models—particularly LSTM—are well suited for representing such rapid and nonlinear events, though they may be less effective during low-flow conditions if such events are underrepresented in the training data [39,59]. Emerging hybrid approaches that combine data-driven and conceptual models have shown promise in bridging these limitations; for example, in the Ljubljanica karst basin, integrating conceptual rainfall-runoff models with machine learning corrections significantly improved flow predictions, particularly during extremes [39]. Furthermore, physics-informed deep learning methods, such as ConvLSTM models that incorporate simulated snow dynamics, further advance predictive accuracy and interpretability by embedding physical processes within ANN architectures [68].

Our findings indicate that the LSTM model offers the most suitable compromise for discharge prediction in karst aquifers, balancing short-term responsiveness and long-term stability. However, the significant biases observed across all ANN models highlight the need for further calibration and the adoption of advanced uncertainty quantification and bias correction methods—such as Monte Carlo dropout or Bayesian approaches—to improve future predictive accuracy [24].

Results show that the karst structure enables temporary water storage in cavities and fissures; however, extraction through boreholes risks prematurely draining these reserves. Intensive pumping accelerates the natural discharge of the system, thereby disrupting the gradual feeding of springs and resurgences. This disruption is even more pronounced in poorly drained systems where limited hydraulic connections slow aquifer replenishment. Under natural conditions, the water stored in the karst aquifer is progressively released, sustaining spring flows during dry periods. Excessive withdrawals reduce this baseflow, increasing the risk of spring desiccation and compromising water availability for both human use and ecosystems.

To ensure sustainable management of the karst system, it is therefore essential to:

• Limit intensive pumping during low-flow periods by adapting abstraction volumes and establishing seasonal withdrawal quotas with stricter regulation during droughts.
• Guide withdrawals and predict long-term impacts through regular piezometric monitoring of water levels in wells and spring discharges, together with karst-specific hydrogeological models.
• Enhance artificial recharge through rainfall infiltration by developing controlled infiltration systems, and by preserving natural recharge to maintain storage.
• Diversify water supply sources to reduce pressure on the karst aquifer.

This need for sustainable management is further underscored by the fact that the aquifer is currently experiencing a severe hydrological drought [53], impairing its natural functioning and recharge capacity, while ongoing studies aim to assess the potential impacts of climate change on its future dynamics

5. Conclusions

This study highlights the effectiveness of Artificial Neural Networks (ANNs), with a particular focus on the Long Short-Term Memory (LSTM) architecture, in modeling the complex hydrodynamic behavior of the Jebel Zaghouan karst aquifer. Through historical data reconstruction, advanced statistical and probabilistic techniques, we were able to characterize the hydrodynamic functioning of this karstic system. Also, comprehensive comparative analyses of ANN architectures addressed critical challenges in modeling karst aquifers under semi-arid, data-limited conditions.

Results revealed the LSTM model’s superior performance for weekly discharge predictions, successfully capturing the karst system’s characteristic memory effects and delayed hydrological responses. The Multi-Layer Perceptron (MLP) architecture demonstrated robust predictive capability on a daily temporal scale but exhibited significant limitations in forecasting longer-term dynamics. Conversely, the Convolutional Neural Network (CNN) consistently underperformed, underscoring its limited suitability for modeling temporal dependencies inherent in karst hydrology.

Furthermore, integrating isotopic analyses and detailed hydrodynamic evaluations provided crucial insights into the aquifer’s dual recharge mechanisms and internal storage dynamics, strengthening the interpretative capacity of the ANN models. Despite promising outcomes, notable predictive biases were identified, indicating the necessity for enhanced calibration procedures, integrated multi-source data methodologies, and advanced uncertainty quantification approaches in future studies. Additionally, employing alternative data reconstruction techniques, such as hybrid or ensemble methods, could potentially enhance modeling precision and reliability.

Despite its strategic importance as a major groundwater resource in northeastern Tunisia, the hydrodynamic behavior of the Zaghouan karst aquifer remains poorly studied. Its complex recharge mechanisms, significant storage capacity, and sensitivity to climatic variability call for more focused research efforts to support sustainable water management in the region. Indeed, it functions as a temporary storage system, but intensive pumping disrupts its natural discharge, reduces baseflow, and increases the risk of spring desiccation. Sustainable management requires regulated withdrawals, monitoring, artificial recharge, protection of recharge zones, and diversification of water sources to safeguard both water availability and ecosystem health. These findings may also have broader applicability across Mediterranean karst aquifers, where similar hydrological complexities and climatic constraints exist, as demonstrated in studies such as [26,40,44].

In conclusion, this research not only advances methodological approaches essential for sustainable karst water resource management but also underscores the critical importance of historical data preservation. The study provides a scientific basis for informed decision-making and the development of resilient strategies aimed at safeguarding vulnerable groundwater resources amid ongoing climatic variability and anthropogenic pressures.

Future research should also address the interpretability of ANN models, for instance, through explainable Artificial Intelligence approaches such as SHAP, and consider the integration of spatially distributed data within hybrid ANN–conceptual modeling frameworks. Such developments would further improve both the robustness and the transparency of predictions, thereby enhancing their utility for water resource management.