Integrated Simulation of Groundwater Flow and Nitrate Transport in an Alluvial Aquifer Using MODFLOW and MT3D: Insights into Pollution Dynamics and Management Strategies

Abstract

This study employs an integrated numerical modeling approach using MODFLOW and MT3D to simulate groundwater flow and nitrate transport in the alluvial aquifer of Hennaya plain. The groundwater flow model was calibrated and validated against observed hydraulic heads, showing excellent agreement in both steady-state and transient conditions, with a correlation coefficients (R²) of 0.99 and 0.987, respectively. Meticulous calibration yielded adjusted hydraulic conductivity values between 10⁻¹ and 10⁻¹¹ m/s, with effective porosity ranging from 0.03 to 0.34 and total porosity values varying from 0.29 to 0.38 across the aquifer. Water budget analysis revealed that the aquifer’s primary recharge occurs from the southern side. Nitrate transport modeling indicated that advection is the dominant process, with contaminants migration predominantly occurring from south to north, following the groundwater flow direction. Pollution levels were found to decrease gradually with distance from sources, confirming agricultural activities and sewage disposal as primary contributors to nitrate contamination. Predictive scenarios over a 40-year period explored various management strategies, which suggest that maintaining current nitrogen input rates will lead to continued increases in nitrate pollution, while a 50% reduction in agricultural inputs could significantly improve groundwater quality. However, even with substantial reductions, nitrate concentrations are not expected to reach levels safe for drinking within the simulation timeframe. This study underscores the need for immediate and sustained action to address nitrate pollution in the Hennaya Plain aquifer, emphasizing the importance of stringent nitrogen management practices, particularly in the agricultural sector.

1. Introduction

Groundwater represents a crucial component of the world’s water system and a pivotal resource for both humanity and ecosystems worldwide. Corresponding about one-third of all freshwater on Earth, groundwater supplies nearly 50% of the global’s drinking water [1,2,3] and supports over 40% of irrigated agriculture [4]. Its importance is especially evident in arid and semi-arid regions, where surface water resources are limited or unreliable. However, the status of global groundwater resources is increasingly precarious due to overexploitation, pollution, and the climate change impacts [5,6]. In many regions, groundwater pumping rates surpassed natural recharge capacities, which leads to declining groundwater levels, saltwater intrusion, and land subsidence [7]. Moreover, groundwater quality is deteriorating due to the infiltration of pollutants from diverse sources, which include agricultural runoff, urban wastewater, and industrial discharge [8,9].

Since the late 1950s, water systems contamination has been increased significantly because of the nitrogen diffuse from agricultural activities worldwide [10]. The high nitrate concentrations in groundwater are predominatingly attributed to excessive fertilizer application, which can cause severs public health concerns, such as methemoglobinemia and cancer [11,12,13], when levels exceed the recommended values for drinking water in the World Health Organization guideline (50 mg/L) [14].

The high levels of nitrate risk are not limited to human health, but extend beyond agricultural crops and environmental media [15,16]. The development of the use of nitrogen fertilizers application aimed at enhancing agricultural production, as nitrogen input exceeds demand, plants become unable to absorb it, contributing to the accumulation of undesirable substances in soil, which can adversely affect the quality of the soil and thus the quality of agricultural products [17,18]. Nitrate accumulation in the leaves of crops can lead to nitrate toxicity, which is characterized by symptoms such as leaf chlorosis, reduced photosynthesis, and stunted growth [19,20]. Moreover, crops with high nitrate contents may be unsuitable for human consumption because they can contribute to the health risks associated with dietary nitrate intake [21].

Numerical model techniques, two- and three-dimensional, have been developed to appreciate the processes governing groundwater flow and pollutant transport in aquifers. These models are powerful tools for simulating hydrodynamic and hydrochemical processes and predicting the influence of different management scenarios on groundwater resources. The U.S. Geological Survey (USGS) modular finite-difference three-dimensional groundwater model, MODFLOW, is widely utilized for simulating groundwater flow under various hydrogeological conditions [22,23]. MODFLOW solves the 3D groundwater flow equation applying a finite-difference approach, allowing for the representation of complex aquifer geometries, boundary conditions, and stresses such as recharge and pumping [24,25].

The three-dimensional transport modular (MT3D) code, which is commonly used for the advection, dispersion, and chemical reaction simulation of aquifer systems pollutions, has been developed to address solute transport in large-scale environments [26,27,28]. This code simulates the complex transport advection–dispersion-reaction processes employs a hybrid Eulerian–Lagrangian method [29,30]. The coupling of MODFLOW and MT3D provides a comprehensive framework for modeling groundwater flow and contaminant migration in aquifers, allowing for the evaluation of different management scenarios and the design of effective remediation strategies [31,32].

The Hennaya Plain is one of the most important agricultural area in the northwestern Algerian province of Tlemcen, due to its significant groundwater potential. The water resources availability, the soil fertility, the shallow piezometric surface and the high permeability of the aquifer sediments have long been contributed to the development of vast areas for agricultural purposes [33], but in return have exposed the groundwater to contamination with high levels of nitrates. Since the early 1980s, researchers have been paying attention to understand the aquifer’s hydrogeological features and determining the preferential paths for groundwater flow [34,35]. Moreover, in order to analyze seasonal fluctuations in nitrate levels with the aim of finding potential sources of pollutant diffuse [36]. However, comprehensive studies that integrate groundwater flow and nitrate transport modeling to assess the influence of agricultural practices on groundwater quality are lacking. This study aims to develop a coupled MODFLOW-MT3D model for the alluvial aquifer in the Hennaya Plain to simulate groundwater flux and nitrate transport under different scenarios. The specific objectives are (1) to characterize the hydrogeological properties of the aquifer and the sources of nitrate contamination; (2) to develop and calibrate a MODFLOW model for simulating groundwater flow in the aquifer; (3) to develop and calibrate an MT3D model for simulating nitrate transport in the aquifer; and (4) to assess the effects of various management scenarios on nitrate contamination in the aquifer. The results of this paper will provide valuable insights into the processes governing nitrate transport in the Hennaya Plain aquifer and support the development of effective management strategies for protecting groundwater resources in this plain.

2. Materials and Methods

2.1. Study Area

2.1.1. Location, Climate and Land Use

The Hennaya Plain is located in the city of Tlemcen in the northwestern part of Algeria (Figure 1), which covers an area of approximately 2800 ha. The study area extends between 646,000 m and 652,081 m north and between 3,882,190 m and 3,867,160 m west (UTM zone 30N) at altitudes ranging from 210 to 448 m. This region is subject to a semi-arid Mediterranean climate characterized by relatively hot, dry summers and rainy winters, with an average annual precipitation of 395.2 mm per year and temperatures ranging from 16.85 to 18.5 °C (average: 17.8 °C) [37]. The study area is characterized by conditions highly favorable for agriculture, including readily available groundwater, flat topography, fertile soil, and a suitable climate. These factors have led to intensive agricultural practices dominating the landscape. According to available data, approximately 74% of the land is dedicated to agricultural use, encompassing citrus fruit cultivation (primarily oranges and lemons), seasonal crops, and cereal production. Urban and industrial areas occupy about 15% of the total land area. The remaining 11% is composed of various other land use categories, which may include natural areas, recreational spaces, or bare ground (Figure 1). Agriculture has been the primary socio-economic activity in this region for several decades, shaping the local economy and culture. However, this intensive agricultural focus has led to significant environmental challenges, particularly high levels of nitrate contamination in the aquifer. This contamination is primarily attributed to the excessive use of agrochemicals. The largest use is nitrogen-based fertilizers, applied at rates of up to 110 kg/ha/year, in addition to NPK fertilizer with a 22-11-12 formulation applied at rates of up to 84 kg/ha/year. Calculating the total nitrogen input from these fertilizers reveals a substantial application rate of 128.48 kg N/ha/year, with 110 kg from the pure nitrogen fertilizer and 18.48 kg from the NPK fertilizer. These high application rates of fertilizers, while boosting crop yields, have contributed substantially to the nitrate pollution problem in the groundwater.

2.1.2. Geological and Hydrogeological Settings

The Hennaya plain, situated within the Tlemcenien domain [38], features a complex geological and hydrogeological profile dating back to the Mio-Plio-Quaternary age (Figure 2). The plain’s aquifer system is composed of alluvial deposits, primarily consisting of Tortonian sandstones, conglomerates, clayey gravels, and travertines [34,35]. These materials rest unconformably on a marly substratum (Figure 3). The aquifer’s thickness varies significantly across the plain, with thinner sections (less than 5 m) in the northern and northeastern areas, gradually increasing to approximately 40 m in the southern reaches [34]. This variability in thickness has important implications for water availability and management across different parts of the plain. The diverse geological composition of the aquifer, including permeable sandstones and conglomerates alongside less permeable clayey gravels, influences groundwater flow patterns and water retention capabilities. This hydrogeological configuration plays a crucial role in determining water availability, quality, and flow patterns across the Hennaya plain, significantly impacting agricultural practices, irrigation strategies, and overall land use planning in the region [36].

2.2. Groundwater Flow Model

This study employed Visual MODFLOW-v.4.0 software [39] to simulate groundwater flow in this area. MODFLOW solves the three-dimensional equation (Equation (1)) of groundwater flow [40], using a block-centered finite-difference approach.

$${\displaystyle \frac{\mathsf{\partial }}{{\mathsf{\partial }}_x}}\left[K_{xx}{\displaystyle \frac{{\mathsf{\partial }}_h}{{\mathsf{\partial }}_x}}\right]+{\displaystyle \frac{\mathsf{\partial }}{{\mathsf{\partial }}_y}}\left[K_{yy}{\displaystyle \frac{{\mathsf{\partial }}_h}{{\mathsf{\partial }}_y}}\right]+\left[K_{zz}{\displaystyle \frac{{\mathsf{\partial }}_h}{{\mathsf{\partial }}_z}}\right]{\displaystyle \frac{\mathsf{\partial }}{{\mathsf{\partial }}_z}}+W=S_s{\displaystyle \frac{{\mathsf{\partial }}_h}{{\mathsf{\partial }}_t}}$$

(1)

where $K_{XX}$, $K_{yy}$, and $K_{zz}$ represent the values of hydraulic conductivity along the three orthogonal axes coordinates ($x$, $y$ and $z$), h is the hydraulic head, $W$ is the volumetric flow of sources/sinks, $S_s$ is the specific storage, and $t$ is time [22].

The above equation governs the groundwater flow in transient state. In the steady-state, hydraulic heads and gradients remain constant, resulting in no changes in storage over time. Consequently, the time derivative term on the equation right-hand side is equal to zero [40].

The model domain was discretized into a three-dimensional grid consisting of 40 rows, 20 columns, and 2 layers, with uniform cell dimensions of 300 m by 300 m in the horizontal plane and variable layer thicknesses to represent the aquifer geometry (Figure 4a). The top layer describes the unconfined aquifer, while the bottom layer represents the underlying impermeable bedrock.

Input data for the groundwater flow model represent the most important hydrogeological properties, including hydraulic conductivity and the derived hydrogeological storage parameters. The comprehensive hydrogeological investigation conducted by Hayane on 10 December 1981 involved a series of eleven pumping tests across the study area to determine the aquifer’s transmissivity ($T$). These tests were executed over two continuous days, employing a consistent experimental setup with a constant pumping rate of 3 L.s⁻¹ maintained throughout the entire testing period [34]. The methodology followed standard hydrogeological practices, systematically measuring water level drawdown across 11 test wells to ensure a robust and spatially representative assessment of the aquifer’s hydraulic characteristics. By maintaining a constant flow rate and carefully monitoring drawdown, the research team was able to generate a comprehensive dataset that enabled the precise calculation of hydraulic conductivity using the established relationship (Equation (2)), providing a detailed understanding of the subsurface hydraulic properties essential for groundwater flow modeling.

$$K={\displaystyle \frac{T}{e}}$$

(2)

where $T$ is the transmissivity (m²/s), and $e$ represents the aquifer thickness (m). The calculated $K$ values range from 1 × 10⁻⁵ to 5 × 10⁻¹ m/s for the alluvial aquifer.

The estimation of the key hydrogeological storage parameters—effective porosity ($n_e$), storage coefficient ($S$), and specific yield ($S_y$)—was based on the foundational work of Kozeny and Carman, who established the relationship between porosity and permeability in porous media [40,41,42,43]. The derivation process relies on empirical correlations that relate hydraulic conductivity to storage characteristics, accounting for the specific lithological properties of the aquifer its confined/unconfined conditions. The Kozeny-Carman equation describes the hydraulic conductivity ($K$) as a function of effective porosity ($n_e$) (Equation (3)):

$$K={\displaystyle \frac{{{\mathrm{n}}_e}^3}{C{S}^2}}={\displaystyle \frac{{{\mathrm{n}}_e}^3}{C{S_0}^2{\left(1-{\mathrm{n}}_e\right)}^2}}$$

(3)

where $K$ is the hydraulic conductivity, ne is the effective porosity (dimensionless), $C$ is the Kozeny-Carman constant (typically 5 for alluvial materials), and $S_0$ is the specific surface area of the solid grains (m²/m³).

Building upon this theoretical framework, Domenico and Schwartz [40,41] developed comprehensive empirical relationships through extensive laboratory and field investigations on various sedimentary materials to estimate the other key hydrogeological storage parameters:

• Effective Porosity ($n_e$):

Determined based on the material’s grain size distribution and pore connectivity, typically ranging between 0.1 and 0.25 for alluvial materials.

2.

Storage Coefficient ($S$):

Calculated considering the aquifer’s compressibility and water compressibility, using the following equation (Equation (4)):

$$\mathrm{S}={\mathrm{n}}_e({\mathsf{\rho }}_w·\mathrm{g}·\mathsf{\beta })$$

(4)

where ${\mathsf{\rho }}_w$ is water density, $\mathrm{g}$ is gravitational acceleration, and $\mathsf{\beta }$ is water compressibility.

2.

Specific Yield ($S_y$):

Estimated as the volume of water that can be gravity-drained from an unconfined aquifer (Equation (5)):

$${\mathrm{S}}_y={\mathrm{n}}_e(1-{\mathsf{\theta }}_r)$$

(5)

where ${\mathsf{\theta }}_r$ is the residual water content.

Domenico and Schwartz’s comprehensive table (

Table 1. Typical hydrogeological characteristics of alluvial materials.

Material Type	Hydraulic Conductivity (m/Day)	$\mathbf{Effective}\mathbf{Porosity}\mathbf{(}{\mathbf{n}}_{\mathit{e}}$)	$\mathbf{Storage}\mathbf{Coefficient}\mathbf{(}\mathit{S}$)	$\mathbf{Specific}\mathbf{Yield}\mathbf{(}{\mathit{S}}_{\mathit{y}}$)
Gravel	100–1000	0.13–0.25	0.05–0.10	0.20–0.30
Coarse Gravel	10–100	0.18–0.25	0.10–0.20	0.15–0.25
Fine Sand	1–10	0.30–0.35	0.20–0.30	0.10–0.20
Silty Sand	0.1–1	0.15–0.25	0.30–0.40	0.01–0.10
Sandstone	0.001–0.1	0.10–0.20	0.40–0.50	0.01–0.10
Clay	0.000001–0.001	0.05–0.10	0.50–0.60	0.001–0.05

) summarizes the typical storage coefficients and hydraulic characteristics for various alluvial geological materials, providing a reliable framework for estimating storage parameters when direct measurements are challenging or cost-prohibitive.

While these empirical relationships offer a robust initial characterization, local variations may exist. The derived values should be considered preliminary and may require further calibration during the modeling process to account for spatial heterogeneity in the aquifer system [31].

The construction of the conceptual model requires the specification of boundary conditions (Figure 4b), which were defined based on geological conditions, contour maps, hydrochemistry, and point data and information [44]. According to a previous study [24], this alluvial aquifer has no-flow boundaries (Neumann condition) at rock outcrops to the north and west, a specified head boundary (Dirichlet condition) to represent inflow from upstream, and the natural groundwater outflows of Ain Boukoura and Ain Ouahab are discharge (outflow) points. Aquifer recharge, considered as a key stress factor in the model, was estimated from precipitation and evapotranspiration data. An average annual recharge of 50 mm/year was applied, with spatial variations based on topography and surface geology. Pumping withdrawals were incorporated into the model, with extraction rates varying from 86.4 m³/day depending on the season.

The model calibration process was conducted in multiple stages to ensure accuracy across different temporal scales and hydrological conditions. The historical piezometric levels, which were exclusively collected and maintained by the National Water Resources Agency (ANRH), provided a comprehensive dataset for this analysis. Initially, the model was calibrated under steady-state conditions using the piezometric campaign data from 1981. During this stage, hydraulic conductivity values were adjusted within plausible limits using a trial-and-error approach to achieve the best fit between simulated and observed hydraulic heads. Following the steady-state calibration, a transient calibration was performed using piezometric campaigns spanning from 1981 to 2020, using available piezometric level and spring discharge data. In this phase, the focus was on adjusting storage coefficient values to accurately capture the temporal variations in hydraulic heads over the long-term period. The performance criteria used were the correlation coefficient (R²) (Equation (6)) and root mean square (RMS) error (Equation (7)), which assess the model’s ability to reproduce both the spatial distribution and temporal evolution of hydraulic heads [45,46]:

$$R^2={\displaystyle \frac{{\sum _i\left[\left(X_{o\mathrm{b}\mathrm{s}}-X_{o\mathrm{b}\mathrm{s}-\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}\right)-\left(X_{sim}-X_{sim-\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}\right)\right]}^2}{\sum _i{\left(X_{o\mathrm{b}\mathrm{s}}-X_{o\mathrm{b}\mathrm{s}-\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}\right)}^2{\sum }_i{\left(X_{sim}-X_{sim-\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}\right)}^2}}$$

(6)

$$RMS=\sqrt{{\displaystyle \frac{\sum _{i=1}^{\mathrm{n}}\left[X_{o\mathrm{b}\mathrm{s}}-X_{sim}\right]}{\mathrm{n}}}}$$

(7)

where $X_{obs}$ is the measured data, $X_{sim}$ is the simulated data, $X_{obs-mean}$ is measured data mean, $X_{sim-mean}$ is the simulated data mean, $i$ is the observed or simulated data, and $n$ is the measuration data number.

Model validation was conducted using an intermediate piezometric campaign from 2012, providing an independent dataset to assess the model’s predictive capabilities. Piezometric maps were created using a geostatistical approach (krigage) with the help of two software packages: the open-source geographical information system QGIS and the commonly-used commercial gridding and contouring program SURFER. These tools allowed for accurate interpolation and visualization of the groundwater levels across the study area. Piezometric campaigns conducted between 1981 and 2020 revealed a general flow direction from south to north, consistent with the regional topography. Hydraulic gradients range from 0.2% to 1.5%, with the highest values observed in the southern part of the aquifer.

2.3. Nitrate Transport Model

The MT3D code [26] was developed to simulate nitrate movement in the aquifer system. The MT3D model utilized the flow fields created by the calibrated MODFLOW models to simulate the advective-dispersive transport of nitrate. The migration of a solute in a porous medium, characterized by its concentration in time and space without considering chemical reactions, is governed by Equation ((8)):

$${\displaystyle \frac{\mathsf{\partial }\mathsf{\theta }\mathrm{C}}{\mathsf{\partial }\mathrm{t}}}={\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }xi}}\left(\mathsf{\theta }\mathrm{D}i\mathrm{j}{\displaystyle \frac{\mathsf{\partial }\mathrm{C}}{\mathsf{\partial }xj}}\right)-{\displaystyle \frac{\mathsf{\partial }qi\mathrm{C}}{\mathsf{\partial }xi}}+qs\mathrm{C}s$$

(8)

where $\mathsf{\theta }$ is the porosity, $C$ is the species dissolved concentration, $t$ is time, $D$ is the coefficient of hydrodynamic dispersion, $v$ is the seepage or linear pore water velocity, qs is the volumetric flus rate per unit volume of aquifer representing fluid sources (positive) and sinks (negative), and $Cs$ is the source/sink flux concentration for species.

Initial nitrate concentrations were interpolated based on historical groundwater quality data from monitoring wells throughout the aquifer (Figure 5). All sample collection, preservation, and transportation were executed by certified hydrogeologists from the National Water Resources Agency, adhering to strict quality assurance and quality control (QA/QC) procedures. Chemical analyses were exclusively conducted in the fully accredited laboratories of this Agency, which is the sole authorized and licensed entity for conducting groundwater quality assessments in agricultural regions, as mandated by state regulatory policies. The no-flow boundaries for MODFLOW were treated as no mass flux boundaries in MT3D, preventing any solute movement across these boundaries [47,48]. Nitrate sources, including agricultural runoff and point-source/sink contamination, were simulated as time-varying specified mass flux boundaries [49]. The model was run in transient mode for a simulation period of 40 years, with stress periods of 10-year time step defined to capture seasonal variations in recharge and nitrate loading and to evaluate long-term nitrate plume evolution and migration in the study area. The model was calibrated against observed nitrate concentration data, with model performance evaluated using statistical measures such as correlation coefficients and root mean square errors [50].

In the absence of tracer test data, the longitudinal dispersivity (${\mathsf{\alpha }}_L$) is estimated using Neuman’s (1990) empirical relationship (Equation (9)) [51]:

$${\mathsf{\alpha }}_L=0.0175L^{1.46}$$

(9)

where $\mathrm{L}$ represents the maximum length of the pollutant plume. For our study area, with a maximum plume length of 2000 m, this equation yielded a longitudinal dispersivity value of 1155 m. This approach was selected because it is based on a comprehensive statistical analysis of field observations in alluvial settings and has been validated for plume distances up to 3500 m along the flow axis, making it particularly suitable as an initial parameter for transport modeling. Following standard practice, the transverse (${\mathsf{\alpha }}_T$) and vertical (${\mathsf{\alpha }}_V$) dispersivities were set to 10% and 1% of the longitudinal dispersivity, respectively [52,53]. These dispersivity values were applied uniformly across all model nodes.

2.4. Long-Term Nitrate Pollution Simulation

Solute transport models are generally used to appreciate the dynamics of contaminant migration in aquifer system and predict the future state under varying conditions [54,55]. In this study, the nitrate contamination level was predicted using a calibrated numerical model for solute transport in groundwater. This approach allowed for the simulation of nitrate movement and concentration variations over time within the aquifer system. The model incorporated key hydrogeological parameters, including hydraulic conductivity, porosity, and dispersivity, as well as nitrate-specific factors such as leaching rates from various land uses. Historical nitrate concentration data and land use patterns were used to validate the model’s performance. To forecast future contamination, multiple scenarios were developed based on projected changes in land use, agricultural practices, and sewage discharges. These scenarios were simulated over a 40-year period to provide long-term predictions of nitrate distribution and concentration throughout the study area. The model outputs generated spatially and temporally resolved nitrate concentration maps, enabling the identification of potential future contamination hotspots and the assessment of long-term trends in groundwater quality under various management scenarios.

3. Results and Discussion

3.1. Numerical Flow Dynamics and Model Insights

3.1.1. Steady-State

A steady-state groundwater flow model generally satisfactorily simulates the behavior of an aquifer system. The calibration in this regime was carried out by adjusting the hydraulic conductivity values until the best possible agreement was obtained between the measured and simulated hydraulic heads (Figure 6a). The steady-state run of the model was able to accurately reproduce the measured head in 30 wells (Figure 6b), showing a high degree of agreement between the measured and simulated reference hydraulic heads, with a high correlation coefficient (R² = 0.99) and a very acceptable root mean square (RMS = 2.38 m). This indicates that the model faithfully reproduces water table fluctuations in the aquifer in response to conductivity variations. The model showed that hydraulic conductivity values were spatially unevenly distributed, ranging from 10⁻¹ to 10⁻¹¹ m/s, which can be explained by the heterogeneity of this aquifer system. Figure 7 shows the spatial distribution of hydraulic conductivity, clearly demonstrating that the maximum conductivity values are located in the central part (10⁻¹ m/s) and at the eastern boundary, reflecting the high permeability of the coarse alluvial deposits. In contrast, the low conductivity values are localized in the northern and southern parts, which coincides with higher degrees of clay content and lower aquifer thickness (see Figure 2). The spatial distribution of hydraulic conductivity is a key result, as it highlights the significant heterogeneity within the aquifer system. This information is crucial for understanding groundwater flow patterns and the potential impact of contaminant transport. The hydraulic conductivity map provides a visual representation of the aquifer’s permeability characteristics, which is essential for developing an accurate hydrogeological model and identifying areas of high and low groundwater flow.

3.1.2. Transient State

The transient groundwater flow model was calibrated against observed heads from a 41-year period (1981–2022) with annual readings from 95 monitoring wells. The calibration result shows very good superposition between the measured and calculated potentials (Figure 8a,b), confirming the model’s ability to reproduce temporary variations in water level according to the storage coefficient variations. Total porosity values ranging from 0.29 to 0.38 were estimated for the alluvial and bedrock aquifers (Figure 9). The calibrated transient model achieved an excellent correlation coefficient (R² = 0.987), indicating very good agreement between the simulated and observed heads over the transient simulation period. However, deviations increase upstream of the aquifer in the recharge zones by the southern boundary.

The hydrogeological budget analysis reveals a balanced system, with total inflow and outflow rates approximately equal at 62,700 m³/day (

Table 2. Transient state water budget for medium groundwater conditions.

Inflows	Rates (m3/Day)	Outflows	Rates (m3/Day)
Southern part	35,400.62	Northern part	10,922.14
Storage	23,052.68	Discharge	41,321.25
Recharge	4322.27	Pumping	10,540.80
Total	62,775.57	Total	62,784.19

). Notably, the Groundwater Head Boundary (GHB) from the southern part of the aquifer contributes significantly to the overall recharge, accounting for 56.39% of the total inflow. This result confirms the hypothesis that groundwater recharge primarily occurs from the southern side, which is in line with the hydrogeological characteristics of the region.

3.1.3. Model Validation

To further evaluate the performance and reliability of the calibrated groundwater flow model, an intermediate piezometric field campaign was used to collect an additional set of hydraulic head measurements across the model domain. These validation data points were intentionally excluded from the initial calibration process to provide an independent dataset for model testing. The measured heads from the intermediate campaign were compared against the model’s simulated heads at the corresponding locations and times (Figure 10a). Statistical metrics were calculated to quantify the fit between the simulated and observed validation data, showing excellent correlation coefficient (R² = 0.978) (Figure 10b). Plots of simulated versus observed heads, along with residual distributions, were visually inspected to identify any potential spatial bias or heteroscedasticity in the model’s ability to match the validation points. Overall, the strong agreement between the intermediate validation data and model simulations increases the confidence that the calibrated model parameters and boundary conditions appropriately represent the groundwater flow conditions within the study area. Any systematic deviations may motivate further model refinements prior to simulating future predictive scenarios.

3.2. Nitrate Migration Mechanism Analysis

The calibration process was performed using the key parameters (hydraulic conductivity, storage parameters) obtained in the groundwater flow model, in addition to adjusting the dispersion coefficient values to achieve the best fit between observed and simulated nitrate concentrations. The nitrate transport model was successfully calibrated using historical data from 1983 to 2023, which showed a good agreement with observed data (Figure 11a), yielding a correlation coefficient (R²) of 0.965 and a root mean square error (RMSE) of 8.99 mg/L (Figure 11b). The results of modeling nitrate migration in this aquifer have demonstrated a significant correlation between the nitrate spatial distribution and the hydrogeological characteristics of the aquifer. Stress periods clearly illustrate that nitrate plume deployment follows the same direction as groundwater flow, extending from south to north. This observation indicates that the advection process primarily governs nitrate migration [49]. Furthermore, these findings revealed that nitrate concentrations remain high at approximately all pollution sources, particularly in intensive agricultural areas, and gradually decrease along the plume path, which is consistent with the natural processes of dispersion, dilution and attenuation that occur in groundwater. These observations confirm the significant impact of human activities on nitrate contamination of groundwater. However, the extent of this reduction depends on several factors, such as aquifer permeability, groundwater flow velocity and the geometry of the aquifer system. Notably, spatial analysis revealed a significant correlation between nitrate concentrations and hydraulic conductivity, with the highest nitrate levels consistently observed in zones characterized by higher conductivity. This correlation suggests that areas with increased hydraulic conductivity facilitate more rapid and extensive contaminant transport, potentially creating preferential pathways for nitrate migration through the aquifer. The observed relationship underscores the critical role of aquifer heterogeneity in pollutant distribution and transport mechanisms, highlighting the importance of detailed hydrogeological characterization in understanding nitrate contamination dynamics.

Trial-and-error calibrations of nitrate migration parameters within predefined ranges resulted in values of 1155 m for longitudinal dispersion (${\mathsf{\alpha }}_L$) and 115.5 m for transverse dispersion (${\mathsf{\alpha }}_T$), suggesting significant nitrate propagation along the main flow direction. During this calibration process, variations in effective porosity have a more significant effect on nitrate movement than changes in longitudinal dispersion, which confirms that the advection process is dominant for nitrate transport.

The analysis of nitrate concentrations in the Ain Boukoura and Ain Wahab springs revealed alarming trends of persistent and increasing groundwater contamination throughout the study period (Figure 12). These two springs were selected as representative observation points to compare simulated and observed nitrate concentrations in the local aquifer system. In Ain Bougura, the average measured nitrate concentrations showed a dramatic increase from 69 mg/L to 106 mg/L over the course of the study (Figure 12a). Similarly, Ain Wahab exhibited an even more severe increase, with average nitrate concentrations rising from 68 mg/L to 115 mg/L (Figure 12b). These observed concentrations consistently and significantly exceeded the maximum contaminant level (MCL) of 50 mg/L set for nitrates in drinking water. The simulated values of nitrate concentrations closely mirrored these measured patterns, validating the model’s capability to accurately represent the nitrate dynamics in the aquifer. The persistent exceedance of the MCL in both springs indicates a chronic and widespread nitrate pollution problem in the plain. This level of contamination not only poses significant risks to human health but also raises concerns about broader environmental impacts. The extreme levels observed, particularly in Ain Wahab where concentrations reached more than two times the MCL, suggest that the consequences of this pollution may extend beyond immediate health risks to potentially cause other environmental problems. The close agreement between simulated and measured nitrate concentrations validates the effectiveness of the model in predicting nitrate dynamics in this hydrogeological setting. This agreement provides confidence in using the model for future scenarios and management strategy evaluations.

3.3. Future Nitrate Contamination Prediction

The calibrated nitrate migration model was employed to generate predictive models for the period from 2023 to 2063, considering three distinct scenarios: (1) continuation of current nitrogen input rates; (2) elimination of wastewater nitrogen inputs, and (3) 50% reduction in agricultural nitrogen inputs. The nitrogen input utilized in the migration model calibration for each scenario (

Table 3. Estimated annual nitrogen input to the groundwater for each scenario.

Land Use Group	Agriculture			Wastewater
LU class	Seasonal crops	Arboriculture	Cereals	Urban areas
Area (ha)	828.8	725.2	518	420
Scenario 1
kg N/ha/yr	160	180	30	17.6
kg N/yr	132,608	130,536	15,540	7392
Total t N/yr	278.684			7.392
Scenario 2
kg N/ha/yr	160	180	30	-
kg N/yr	132,608	130,536	15,540	-
Total t N/yr	278.684			-
Scenario 3
kg N/ha/yr	80	90	15	17.6
kg N/yr	66,304	65,268	7770	7392
Total t N/yr	139.342			7.392

) was calculated by estimating the precipitation effective infiltration, assigning nitrate rates to each land use class, and accounting for the corresponding land use surface. Consequently, in all scenarios, the overwhelming plurality of nitrate input to the groundwater stemmed from agricultural sources (95.46%, 100% and 94.96% for the first, second and third scenarios, respectively). These scenarios were designed to evaluate the long-term impacts of various management strategies on groundwater nitrate concentrations in the Hennaya Plain aquifer.

The spatial distribution of nitrate concentrations predicted for 2063 (Figure 13) reveals a complex interplay between groundwater flow dynamics and various nitrate input scenarios, providing crucial insights into the long-term impacts of current practices and potential mitigation strategies on groundwater quality. As the analysis extends to 2063, it becomes evident that the main plume of contamination continued its northward migration, accompanied by fluctuations in nitrate concentrations over time. This long-term perspective underscores the significance of understanding the spatio-temporal aspects of groundwater contamination, highlighting the need for adaptive management strategies that can address evolving patterns of nitrate distribution in aquifers over extended periods.

Scenario 1: Under the current nitrate input conditions, the model projects a significant deterioration of groundwater quality by 2063. The maximum nitrate concentrations are expected to increase from 211.01 mg/L in 2023 to 249.1 mg/L by 2063, representing an 18% increase over four decades (Figure 13a). This alarming trend suggests that without intervention, the groundwater system will continue to accumulate nitrates, potentially posing serious threats to human health and the environment.

Scenario 2: The second scenario, which simulates the complete elimination of nitrate inputs from sewage sources, shows a modest improvement compared to the previous case. Despite this intervention, nitrate concentrations are still projected to reach 238.95 mg/L by 2063 (Figure 13b). While this represents a 4.07% reduction compared to Scenario 1, it indicates that sewage-related inputs are not the primary driver of nitrate pollution in this groundwater system. The continued increase in concentrations, albeit at a slower rate, suggests that other significant sources of nitrates persist.

Scenario 3: The third scenario demonstrates the most promising results, with a projected decrease in maximum nitrate concentrations from 211.01 mg/L to 119.59 mg/L over the 40-year period (Figure 13c). This 43.3% reduction highlights the significant impact of agricultural activities on groundwater nitrate levels. By implementing measures to halve the nitrate inputs from agricultural sources, the model predicts a reversal of the current increasing trend, indicating a path towards groundwater quality improvement.

The time series analysis of forecasted nitrate levels in the monitoring springs, Ain Boukoura and Ain Wahab, reveals significant variations across three scenarios over a 40-year projection period (Figure 14). In the first scenario, both springs exhibit a concerning upward trend in nitrate levels. Ain Wahab is predicted to reach 178 mg/L by 2063, while Ain Boukoura shows an even more dramatic increase to 177 mg/L. This substantial rise in nitrate concentrations suggests that current practices and conditions, if left unchecked, could lead to severe water quality degradation in these springs. The second scenario presents a more nuanced picture. Ain Boukoura still shows a notable increase, with nitrate levels rising from 102 mg/L in 2023 to 156 mg/L in 2063. This represents a 52.94% increase over four decades, indicating persistent challenges in managing nitrate inputs in this area. In contrast, Ain Wahab shows only a marginal increase from 112.6 mg/L to 134 mg/L (19%) over the same period. The disparity between these two springs is attributed to Ain Boukoura’s proximity to areas of intensive agricultural activities, highlighting the significant impact of land use on underground water quality. The third scenario offers the most optimistic outlook. Both springs show a gradual decrease in nitrate concentrations, with Ain Boukoura projected to reach 83 mg/L and Ain Wahab 80 mg/L by 2063. This represents reductions of approximately 18.62% and 28.95% from their respective 2023 levels. These promising results suggest that implementing effective mitigation strategies could significantly improve water quality in both springs over time.

These results underscore the critical role of agricultural practices in shaping long-term groundwater nitrate concentrations. While addressing sewage-related inputs (Scenario 2) shows some benefit, it is clear that agricultural sources dominate the nitrate budget in this system. The marked improvement observed in Scenario 3 suggests that focusing on agricultural best management practices could be the most effective strategy for mitigating nitrate pollution.

The persistent increase in nitrate concentrations under Scenarios 1 and 2 highlights the long-term consequences of current practices and the inertia within groundwater systems. Even with immediate action, the legacy of past nitrate inputs continues to influence water quality for decades. This emphasizes the urgency of implementing protective measures and the need for long-term planning in groundwater management.

It is important to note that while Scenario 3 shows significant improvement, the projected nitrate levels (120 mg/L) still exceed typical drinking water standards (50 mg/L). This suggests that while a 50% reduction in agricultural inputs is a substantial step, further reductions or complementary strategies may be necessary to achieve safe nitrate levels for human consumption. Theoretically, it may be possible to reduce nitrate inputs to the minimum required to meet drinking water standards, but practical agriculture constraints make this a very challenging goal. A 50% reduction in current nitrate inputs represents the maximum possible agricultural intervention based on plant needs.

The validation of hydrodynamic and hydro-dispersive models requires a rigorous methodological approach that critically examines the model’s predictive capabilities and inherent uncertainties. This study proposes a comprehensive validation strategy founded on three complementary technical approaches:

First, additional pumping tests are essential to deepen our understanding of the aquifer’s hydrodynamic characteristics. These tests provide crucial empirical data that can help refine the model’s parameters and reduce uncertainties in hydraulic conductivity and transmissivity estimations.

Secondly, implementing a systematic and regular monitoring of nitrate concentration analyses allows for a temporal and spatial evaluation of contaminant dynamics. This longitudinal tracking enables us to assess the model’s accuracy in predicting solute transport mechanisms and identifying potential discrepancies between theoretical predictions and actual field observations.

Thirdly, a hydrogeological tracing study using chemical tracers is proposed to meticulously track pollutant propagation and underground flow behaviors. By introducing specific chemical tracers, we can obtain high-resolution insights into subsurface transport dynamics, which are critical for validating the model’s predictive performance.

These combined methods serve a crucial purpose: systematically confronting theoretical model predictions with concrete empirical observations. Such a comprehensive validation approach allows for:

• Calibrating model parameters with greater precision;
• Identifying potential sources of uncertainty;
• Quantifying the model’s predictive reliability;
• Establishing confidence intervals for key hydrological parameters.

Limitations inherent in our current model include potential uncertainties arising from:

• Spatial heterogeneity of geological formations;
• Variability in hydraulic conductivity;
• Simplifications in boundary condition representations;
• Potential measurement errors in field data collection.

Future research should focus on further refining these validation techniques, potentially integrating advanced geostatistical methods and high-resolution sensing technologies to reduce predictive uncertainties. By adopting this multi-faceted validation approach, we enhance the scientific rigor of our hydrodynamic model and provide a transparent assessment of its capabilities and limitations.

4. Conclusions

This study represents a significant scientific contribution to territorial policies for water resource management, offering a methodological framework that can be transposed to other similar hydrogeological contexts. The developed modeling methodology, combining MODFLOW and MT3D models, now constitutes a valuable technical reference for water resource decision-makers and managers. Moreover, the modeling methodology could be adapted to other agricultural plains with comparable hydrogeological characteristics, particularly in Mediterranean regions where agricultural pressure and water scarcity are major challenges. The originality of this research lies in its ability to provide accurate predictive tools, enabling decision-makers to anticipate scenarios of nitrate pollution evolution. The detailed mapping of contamination dynamics, with the identification of pollutant propagation trajectories, represents a significant methodological advancement for the integrated management of water resources.

The integrated modeling approach using MODFLOW and MT3D proved to be an effective tool for simulating groundwater flow and nitrate migration in the Hennaya Plain aquifer. The groundwater flow model demonstrated excellent agreement between simulated and observed hydraulic heads in both steady-state and transient conditions, validating its reliability for further predictive simulations. Through meticulous calibration, key parameters were adjusted, with hydraulic conductivity values varying from 10⁻¹ to 10⁻¹¹ m/s and effective porosity estimated at 0.03 to 0.34 across the aquifer. Analysis of the water budget revealed that the primary recharge of the aquifer occurs from the southern side, highlighting the importance of this area for the overall groundwater dynamics of the plain. The pollutant migration modeling results indicated that nitrate transport is predominantly governed by advection process, following the general groundwater flow path from south to north. The gradual decrease in pollution levels with increasing distance from contamination sources strongly supports the hypothesis that agricultural activities and sewage disposal are the primary contributors to nitrate pollution in the aquifer. Predictive scenarios spanning a 40-year period provided crucial insights into the future state of nitrate pollution under various management strategies. Continuation of current nitrogen input rates is projected to result in a persistent increase in nitrate pollution levels. While sewage-related inputs show a modest upward trend, they remain a significant concern. However, a 50% reduction in agricultural inputs emerges as a promising mitigation strategy, potentially leading to substantial improvements in groundwater quality. Nevertheless, it is noteworthy that even with this significant reduction, nitrate concentrations are not expected to decrease to levels deemed safe for drinking water within the simulation timeframe. These findings underscore the urgent need for implementing stringent nitrogen management practices, particularly in the agricultural sector. The study also highlights the long-term nature of groundwater remediation processes, emphasizing the importance of immediate and sustained action to address nitrate pollution. Future research should focus on refining these management strategies, exploring innovative agricultural practices, and investigating potential remediation technologies to accelerate the restoration of groundwater quality in the Hennaya Plain.

In order to preserve the grounwater potential of this region, a strategic approach must be implemented to monitor the evolution of nitrate concentrations in groundwater, and to deepen and extend the knowledge acquired on the aquifer of the Hennaya plain. It will be crucial to develop integrated research that combines multidisciplinary approaches, involving hydrogeology, agronomy, and environmental sciences. Future research should focus on:

• Developing more sophisticated predictive models integrating high-resolution data and artificial intelligence algorithms to refine the understanding of pollution dynamics;
• Studying potential remediation technologies, such as phytoremediation and nitrate treatment methods, to accelerate the restoration of groundwater quality in the Hennaya plain;

Another promising line of research will be the evaluation of new sustainable agricultural practices, including precision farming, rational fertilization techniques, and alternative cultivation methods to minimize nitrogen inputs. The establishment of long-term environmental observatories, using connected sensors and real-time monitoring systems, will also be a fundamental tool for understanding the dynamic evolution of groundwater quality. Finally, interdisciplinary collaborations will be essential to transpose and adapt these research methodologies for better management and preservation of this resource.