Development of Transient Hydrodynamic and Hydrodispesive Models in Semi-Arid Environments

Abstract

The hydrogeological study of the Rharb coastal basin, located in the semi-arid northwest region of Morocco, focuses on its two aquifers: the Plio-Quaternary aquifer characterized by high-quality water with salt concentrations ranging from 0.4 to 2 g/L, and the Upper Quaternary aquifer, with lower water quality (2 to 6 g/L). The deep aquifer is overexploited for agricultural purposes. This overexploitation has led to declining piezometric levels and the worsening of the oceanic intrusion phenomenon. The study aims to develop a numerical model for a period of 15 years, from 1992/93 to 2006/07 for monitoring groundwater quantity and quality, considering recharge, exploitation, and basin characteristics. A hydrodynamic model based on storage coefficient calibration identifies overexploitation for irrigation, increasing from 93 Mm³ in 1993 to 170 Mm³ in 2007, as the primary driver of declining water levels. A hydrodispersive model highlights higher salt concentrations in the shallow aquifer (up to 6 g/L), high nitrate concentrations due to human activity, and pinpoints areas of seawater intrusion approximately 500 m from the shoreline. Although the deeper aquifer remains relatively preserved, negative hydraulic balances from −15.4 Mm³ in 1993 to −36.6 Mm³ in 2007 indicate an impending critical period.

1. Introduction

Groundwater is a vital resource on a global scale [1]. It constitutes the primary source of drinking water in many countries due to its lower vulnerability to pollution compared to surface water, as well as its availability, accessibility, and relatively low cost [2]. However, excessive exploitation exacerbates the decline in piezometric levels and accelerates the advancement of saline intrusion [3], which is a global issue characterized by the landward displacement of the freshwater–saltwater interface due to density differences [4].

The study of aquifer systems, aimed at understanding the mechanisms that control groundwater flow regimes to preserve the resource, requires extensive information and data. The validity and reproducibility of aquifer analyses strongly depend on the availability of abundant and high-quality data. Organizing them into a coherent and logical structure, supported by appropriate software, ensures their validity and accessibility, thus providing a powerful tool for hydrogeological studies [5].

Hydrogeological modeling is increasingly used to verify data consistency, enhance understanding, and facilitate more effective analysis of complex hydrogeological contexts [6]. Furthermore, groundwater modeling allows for the assessment of aquifer responses to hydrological conditions and promotes sustainable groundwater resource management [7]. Various modeling approaches have been extensively explored in the literature [8,9,10,11]

Hydrogeological models are widely used worldwide for effective groundwater management. In Tunisia, these models help assess the impact of aquifer overexploitation on groundwater salinization [12]. In Australia, they are used to predict the effects of climate change on water availability in arid regions [4]. Similarly, in India, hydrogeological modeling is employed to manage overexploited aquifers by optimizing resource use for agriculture [13]. These tools provide tailored solutions to ensure sustainable water management, enabling informed decision-making and more resilient management strategies in the face of climatic and anthropogenic challenges.

In Morocco, irrigated agriculture is the primary consumer of groundwater [14], playing a crucial role in the national economy by contributing approximately 15% to the Gross domestic product (GDP) and employing nearly 43% of the active population [15]. The Rharb Plain, part of a series of Moroccan coastal plains [16], represents the downstream section of the Sebou hydraulic basin. This region is distinguished by its abundant agricultural production, particularly in cereals, vegetables, and irrigated crops, which are essential for food security and socio-economic development. Located in a semi-arid environment [16] characterized by irregular precipitation, high temperatures, and prolonged droughts, it heavily relies on irrigation to sustain agricultural production and mitigate economic losses associated with water shortages.

The Rharb basin comprises a Plio-Quaternary aquifer with coarse granulometry, facilitating the circulation of deep groundwater, as well as an Upper Quaternary aquifer with fine granulometry, where lower-quality water tends to stagnate. These aquifers are separated by a Quaternary aquitard [17], limiting direct exchanges between them. The expansion of irrigated areas, covering approximately 107,000 hectares [18], disrupts the equilibrium of the deep aquifer in the coastal region, leading to progressive overexploitation.

In this semi-arid context, excessive freshwater extraction from deep aquifers has resulted, since the early 1990s, in significant hydrological deficits and critical qualitative impacts such as contamination by pollutants and seawater intrusion into coastal aquifers. This phenomenon deteriorates water quality, jeopardizing both agriculture and human consumption.

To better understand these complex dynamics, transient hydrodynamic and hydrodispersive models have been developed for the Rharb basin. These models are based on a steady-state hydrodynamic model [18] and are reinforced by a database derived from a Geographic Information System (GIS) [17,19], enhancing analytical and decision-making capabilities. The transient hydrodynamic model, based on the Modular Groundwater Flow Model-Groundwater Modeling System (MODFLOW-GMS), integrates historical pumping [20] and recharge data while refining the storage coefficients of the Plio-Quaternary aquifer to better adapt them to actual conditions. This approach enabled a precise analysis of the piezometric decline of the deep aquifer between 1992–1993 and 2006–2007, identifying key factors influencing groundwater availability, including climate change and evolving agricultural practices.

Groundwater quality has a major impact on human health as well as agricultural and industrial activities. High concentrations of elements such as nitrates and other toxic substances can significantly degrade groundwater resources. In many cases, spatial variations in fluid density play a crucial role in groundwater flow patterns, particularly in coastal areas where density-dependent models are required to accurately simulate saline intrusion and submarine groundwater discharge [21]. Consequently, a hydrodispersive model was developed to monitor water quality changes in both aquifers and analyze the increase in oceanic intrusion into the Plio-Quaternary aquifer. Using the Three-Dimensional Multispecies Transport Model with Modular Solver (MT3DMS), this model simulated the spatio-temporal evolution of water concentrations, accounting for seasonal variations and pumping practices.

Given that the Saltwater Intrusion and Groundwater Flow Model (SEAWAT) is the most commonly used tool for characterizing and projecting the dynamic changes in groundwater flow and salinity [4,14], we employed it to further investigate oceanic intrusion and accurately simulate the advancement of saline water contaminating the deep aquifer in the coastal region.

The model highlights the impact of intensive groundwater exploitation on aquifer salinization. It introduces, for the first time, a multilayer model of the entire Rharb basin, accounting not only for the interactions between the Rharb aquifer system and its external environment but also for the interactions between the deep aquifer, the aquitard, and the shallow aquifer. Thus, developing an effective management model for precise groundwater level control is of paramount importance [22,23].

In light of the growing challenges posed by climate change and overexploitation, particularly in semi-arid regions, rational and effective interventions are necessary to promote sustainable development.

2. Geographical, Geological, and Hydrogeological Framework

The Rharb Basin is located in the northwest of Morocco and covers an area of 4000 km². It is bordered by the Atlantic Ocean to the west, the Drader-Souier plain to the north, the hills of the Rif mountains to the east, and the Maamora plateau to the south. With elevations ranging between 5 and 25 m, this area comprises a coastal zone, continental margins, and a central alluvial plain of the lower Sebou (Figure 1).

From a geological standpoint, the Rharb Basin represents the foreland basin of the Rif mountain range, affected by continuous subsidence since the middle Vindobonian (a period during which the pre-Rif thrust sheets were formed). The Rharb, a subsiding basin since the Tortonian, is primarily structured by two main lineaments: the first, to the north, responsible for the structure of Lalla Zohra [24], and the second, to the south, represented by the Maamora front [24,25].

During the Plio-Villafranchian, the relief of the northern, southern, and eastern borders of the plain was uplifted in response to recent phases of Alpine compression, isostatic adjustments, and eustatic falls, compensated by the abundance of coarse continental inputs deposited by significant fluvio-estuarine systems [26]. In the central part of the basin [21] highlighted, within the Miocene substratum, three satellite basins largely controlled the subsequent formation of the aquifers during the Plio-Quaternary period. To the west of the basin, along the coastal deposits of the NW-SE fault corridors, is the growth of the Lalla Zahra front to the north and a localized folding structure around the city of Kenitra developed.

Furthermore, field data associated with electrofacies resistivity and high-resolution seismic refraction tomography indicate that this region is tectonically active and subjected to significant horizontal movements with a strike-slip component, as evidenced at the Dhar Doum-Lalla Zahra fault, where faults are associated with anticlines and synclines, and the structural setup resembles “fault-propagation folds” or propagation folds at the front of the Rif chain [27].

At the regional scale, new interpretations incorporate the Rharb Basin into a dynamic involving the lineaments of the Rif chain, notably the Jebha and Nekour faults [28,29]. The position of current seismic epicenters confirms the recent activity of some of these lineaments.

This basin is located between two major structural units that serve as sediment sources: the pre-Rif to the north and the Rifian ridges to the south, while to the south are the Maamora Plain and the Hercynian Meseta [30]. The lithostratigraphic succession of the basin ranges from the Miocene to the Upper Quaternary (Figure 2).

During the Lower Quaternary, two distinctive levels are sometimes distinguished within this detrital complex: the Tensiftien, characterized by the reappearance of coarse gravel and more or less clayey sands (up to a maximum thickness of 60 m), and the Amerian, with sediments consisting of clays and loams with limestone nodules (up to a maximum thickness of 50 m).

The Villafranchian (Moulouyan-Regreguian-Saletian) and the Lower Quaternary are difficult to distinguish due to similar depositional conditions. They contain significant spreads of pebbles and gravel found beneath the plain and its northern and eastern peripheries. To the south, the fine sands and gravel of the Maamora are connected to them.

The Pliocene is characterized by marine deposits of calcareous sandstones, sandstones, and sands located in the coastal zone. Regressive deposits [26] and conglomerates identified by their outcrops in the north of the basin, yellow sands in the east, and continental sediments, pebbles, and silts located upstream of the confluence zone of the Sebou and Ouergha rivers. The thickness of this level is low, and its hydrogeological interest is limited.

The Mio-Pliocene is associated with the subsidence and sedimentary infill of the syn-tectonic foreland basin. It is characterized by a thick series, with a thickness that can reach 2000 m of gray or blue marls. Laterally, these marls transition to discordant molasses of the foreland, displaying chaotic facies where extensive submarine landslides can be observed. This forms the general substrate of the overlying terrains.

From a hydrogeological standpoint, this sedimentary succession includes two aquifers: one aquifer ranging in age from the Pliocene to the Lower Quaternary, composed of coarse sediments through which the waters of the deep aquifer flow, and another aquifer from the Upper Quaternary through which the waters of the shallow groundwater flow. The two aquifers are separated by an aquitard, consisting of compact Lower Quaternary clays, which pressurize the deep waters in the center of the basin. At the outcrops in the north, east, south, and west of the basin, the aquifer becomes unconfined (Figure 3).

3. Methods and Tools

3.1. Transient Hydrodynamic Model

For the transient hydrodynamic model, the working method involves using the numerical MODFLOW model, derived from the calibration of permeabilities in the steady-state system [17]. This model consists of a workspace containing the 3D block diagram of the basin (Figure 4a), built from mechanical boreholes and enhanced by data from geoelectrical profiles, as well as the layers of the conceptual model (Figure 4b). These data are stored in a geographic database created using ArcGIS (Figure 4c). New data, including storage coefficients to be calibrated (Appendix A), piezometric histories, and recharge and pumping histories [23], are input into the transient-state model.

The computational code MODFLOW, developed in Fortran by the USGS [31], is based on solving the general partial differential equation of diffusivity for flow, through a combination of the continuity equation and Darcy’s law (Equation (1)).

$${\displaystyle \frac{\delta }{\delta x}}\left(K_x{\displaystyle \frac{\delta H}{\delta x}}\right)+{\displaystyle \frac{\delta }{\delta y}}\left(K_y{\displaystyle \frac{\delta H}{\delta y}}\right)+{\displaystyle \frac{\delta }{\delta z}}\left(K_z{\displaystyle \frac{\delta H}{\delta z}}\right)-Q=S_S{\displaystyle \frac{\delta H}{\delta t}}$$

(1)

With H: hydraulic head [L], K: hydraulic conductivity [LT⁻¹], S_s: specific storage coefficient [L⁻¹], Q: injected or pumped water volume [L³T⁻¹], t: time [T].

Subsequently, the MODFLOW calculation parameters are updated in transient mode to account for the temporal evolution of the groundwater system in response to external disturbances, primarily precipitation, and abstractions. Similar to the steady-state hydrodynamic model, the development of the transient model follows the model construction process [32] (Figure 5).

The main adjustments made to the MODFLOW tool include reconfiguring the model for transient state and defining initial conditions to consider during simulations. The objective of transient modeling is to calibrate the storage coefficients of the Plio-Quaternary aquifer by comparing the calculated piezometric levels, for each time interval, to measurements from the five pilot piezometers. The available measurements of this coefficient before calibration range from 0.01 to 0.2 for the unconfined aquifer and from 0.0001 to 0.001 for confined aquifers. A series of simulations is initiated with the aim of reducing the gap between calculations and measurements until the stage where the results are deemed satisfactory while adhering to the modeling cycle [33] (Figure 6).

The resolution of the first-order linear differential system to calculate the piezometric height (H) is done according to the following equation:

$$TH=Q+a^{2}S\left({\displaystyle \frac{\delta H}{\delta t}}\right)$$

(2)

With T: transmissivity (L²T⁻¹), a: surface area of the cell (L²), S: storage coefficient.

Thus, the storage volume ΔV at each cell i, j, k level is expressed as follows:

$${\displaystyle \frac{∆V}{∆t}}=S_{i,j,k}\left(∆R_j\ast ∆C_i\ast ∆V_k\right)\ast {\displaystyle \frac{\left(H_{i,j,k}^m-H_{i,j,k}^{m-1}\right)}{\left(t^m-t^{m-1}\right)}}$$

(3)

With ΔV/Δt: variation of storage per unit time during the time step Δt, S_i,j,k: storage coefficient of cell i, j, k, ΔR_j: distance between neighboring nodes, ΔC_i*ΔV_k: surface area of the exchange facet, H^m_i,j,k H^m−1_i,j,k: heads at nodes (i, j, k) and (i−1, j, k) at time step m, t^m − t^m−1: time interval separating time steps m and m − 1.

3.2. Hydrodispersive Model

For the hydrodispersive model, and to replicate the history of the saltwater wedge advancement in the Plio-Quaternary aquifer, the MT3DMS module is utilized to study the dispersion of chemical solutes in both aquifer layers of the aquifer system, according to the finite-difference method [21] (Equation (4)).

$${\displaystyle \frac{\delta \left(\theta C_k\right)}{\delta t}}={\displaystyle \frac{\delta \left(\frac{\theta D_{ij}\ast \delta C_k}{\delta x_j}\right)}{{\delta x}_i}}-{\displaystyle \frac{\delta \left({\theta \vartheta }_i\ast C_k\right)}{{\delta x}_i}}+qsCsk+\Sigma Rn$$

(4)

With C_k: dissolved concentration of species k [ML⁻³], θ: porosity of the subsurface medium [−], t: time [T], x_i: distance along the respective Cartesian coordinate axis [L], D_ij: hydrodynamic dispersion coefficient tensor [L²T⁻¹]; v_i: seepage or linear pore water velocity [LT⁻¹], qs: volumetric flow rate per unit volume of aquifer representing fluid, Cs_k: concentration of the source or sink flux for species k [ML⁻³], ΣRn: chemical reaction term [ML⁻³T⁻¹].

The SAEWAT module is employed to investigate the inland advancement of the freshwater–saltwater interface. It is a 3D groundwater flow modeling application for variable-density flow coupled with multi-species solute transport. SEAWAT builds upon the MODFLOW and MT3DMS interfaces and utilizes them for boundary condition setting and post-processing. At the boundary conditions, it integrates flow equations, mass conservation, and solute transport equation.

3.3. Simulation Period, Spatio-Temporal Discretization, and Boundary Conditions

The Rharb aquifer system did not show significant declining trends until the early 1990s. Simulations are conducted from the beginning of this decade, where pumping activities experienced a notable increase, causing disturbance to the aquifer system equilibrium. We have considered a period of 15 intervals from 22 September 1992 to 22 September 2007, based on the availability of historical data on withdrawals for agricultural irrigation purposes. The discretization [28] of the study area respects the following two conditions: Horizontally, and to better target the most sensitive areas (aquifer–river interfaces, boundary conditions…), we opted for a refined mesh by assigning cell sizes ranging from 6.25 × 10⁻² m² to 1 km² after utilizing the MODFLOW USG Quadtree Grid. This results in 46,748 cells to represent the entire system, with 14,252 for the upper aquifer, 12,259 for the aquitard, and 20,237 for the lower aquifer. Vertically, the model is three-layered, and the cells adhere to the actual thickness of the aquifer formations.

The boundary conditions of the transient model are as follows (Figure 7).

The southern boundary is a constant head condition represented by the discharge of groundwater from the Maamora aquifer to the Rharb aquifer. The northern boundary is a no-flow condition represented by the divide between surface waters of the Drader-Souier plain and the Rharb plain. The western boundary is an imposed potential condition representing the discharge of groundwater from the Rharb aquifer to the Atlantic Ocean. The eastern, southeast, and southwest boundaries are no-flow conditions defined by the extension limits of the hydrogeological basin. Rivers are represented as boundaries with imposed potential or Dirichlet conditions [34]. The main infiltration zones include coastal strips, eastern and southern areas where permeable outcrops allow the system to receive an average of 113.4 million cubic meters per year (0.4 mm/day).

3.4. Inputs and Outputs

For the transient hydrodynamic model, sampling points are represented as an imposed flux condition and are incorporated into the model with the indication of the pumping rate. These withdrawals are internal numerical data consisting of a 2368 daily historical value from three surveys conducted by COMBE [20], ENGEAMA (Inquiry 1992), and the Sebou Hydraulic Basin Agency [18] following the surveys of 2005 and 2008 (

Table 1. Inventory of input and output data for the transient model of Rharb basin.

Data	Infiltration (Input)	Pumping Well (Output)	Storage Coefficients
Time series	22 September 1992–22 September 2007		-
Entity	156 polygons	2368 points	7 points (Appendix A)
Time (interval)	seasonal	annual	-

).

To simplify the task and since irrigation withdrawals constitute more than 90% of the total withdrawals, we only consider irrigation data. Data on drinking water reserved for consumption and industrial water are not precise, and some information such as coordinates is missing. The return flow from irrigation is also subtracted from the inputs to compensate for the portion of water supply for drinking and industrial purposes as outputs since their volumes are analogous. Recharge data are inserted based on the division of the Rharb plain into 156 parcels derived from the calibration of the steady-state model. Each group of parcels (cells with equal infiltration values) is assigned a series of 60 values corresponding to the seasonal distribution of recharge for the entire study period. This distribution depends on the recharge, which in turn is a function of rainfall and soil type (Figure 8).

For the hydrodispersive model, the first stage in building the Mass Transport model (MT3DMS) involves using input data from the hydrodynamic model, as well as data related to water chemistry [35] (

Table 2. Inventory of hydrodispersive model data of the Rharb basin.

Data	Description
Geometry	Stratigraphic trilayer model.
Hydrogeological parameters	Hydraulic conductivities, Porosity, Dispersivity, etc.
External stresses and initial conditions	Initial water concentrations: rain, groundwater, etc.
Boundary conditions	Imposed volumic concentration of the nappe-ocean boundary.

).

The initial average porosities assigned to the three layers of the model are 0.4 to 0.45 for the upper aquifer, 0.35 to 0.45 for the aquitard, and 0.2 for the lower aquifer. The longitudinal dispersivity is approximately 20 m for all cells of the model. The groundwater concentration map of the Rharb basin established for the low-water period of 1964/1965 serves as the reference state (Figure 9). The dry residue at 180 °C is approximately 0.7 g/L for the Plio-Quaternary aquifer and ranges from 1 to over 6 g/L for the phreatic aquifer.

The concentrations of rainwater range from 0.1 to 0.2 g/L and are assigned to recharge zones based on the conceptual model, except where cell-by-cell correction is necessary. The Advection, Dispersion, Sources/Sink Mixing, and Transport Observation packages are used when selecting MT3DMS packages. They facilitate the handling of solute propagation in the aquifer system, thereby adhering to the principles of hydrodispersive modeling and studying solute propagation.

Continuing with the hydrodispersive model, the second stage is building the Variable Density Flow Model (SEAWAT). The inputs of the VDF package enable control over density calculations (

Table 3. Commonly used values for the Variable Density Flow package [36].

Variable	Reference Value	Slope
Density	1000 kg/m3	n/a
Salt Concentration	0 mg/L	0.714
Temperature	25 °C	−0.375 kg/m3/°C
Pressure Head	0 m	4.46 × 10−3 kg/m4

).

Given that the concentration of seawater is 35.7 g/L compared to a reference concentration of 0 g/L, and its density is 1025 kg/m³ compared to a reference density of 1000 kg/m³, the DRHODC ratio (Density/concentration slope) is expressed as:

$$DRHODC={\displaystyle \frac{1025\left({\mathrm{k}\mathrm{g}.\mathrm{m}}^{-3}\right)-1000\left({\mathrm{k}\mathrm{g}.\mathrm{m}}^{-3}\right)}{35\left({\mathrm{k}\mathrm{g}.\mathrm{m}}^{-3}\right)-0\left({\mathrm{k}\mathrm{g}.\mathrm{m}}^{-3}\right)}}=0.7$$

(5)

The coastline serves as a boundary condition of the imposed potential type. In the context above, this boundary condition sets a constant hydraulic head at 0 m, representing the natural condition of the groundwater base level. This boundary is considered during hydrodynamic calculations as a quantitative condition. At this stage, a value of 35.7 g/L is assigned to this boundary for qualitative characterization.

3.5. Water Quality and Géochimical Facies

To determine the hydrogeochemical facies of the shallow waters exploited in the basin, we analyzed a sampling network composed of 39 sampling points (the 2013 survey on the Rharb Basin, conducted by the Hydraulic Agency of the Sebou Basin). These water samples, taken from the groundwater, are considered representative of the entire aquifer (Figure 10).

The analyses conducted are primarily mineralogical. Depending on the amount of solution sampled, the analyses are more or less complete, with priority given to the analysis of the nitrate ion, the most representative element of aquifer pollution. Other elements analyzed include major ions: Ca²⁺, Mg²⁺, Na⁺, K⁺, Cl⁻, NO₃⁻, and SO₄²⁻; minor elements: SiO₂, and trace metals: Mn and Fe. Electrical conductivity, pH, total dissolved solids, and alkalimetric titration are also determined (Appendix C).

4. Results

The main objective in hydrodynamic modeling is the adjustment of the storage coefficient, which governs the hydraulic system’s behavior under transient conditions. The calibration of the hydrodynamic characteristics is carried out as follows:

-

Introduction of permeabilities obtained from calibration in steady-state conditions,

-

Introduction of storage coefficients measured in the field,

-

Refinement of the distribution of the storage coefficient to better match the piezometric history,

-

Possible reassessment of the permeabilities (new steady-state calibration) if required.

The model calibration is considered successful after a series of simulations that result in a good match between the measured piezometric levels and the potentials calculated by the model. Furthermore, the quality of the model calibration can be assessed using the following criteria:

-

Reconstruction of the historical data from monitoring piezometers,

-

Distribution of the storage coefficient,

-

Analysis of the balance from the calibration (inflows and outflows) for the different time intervals.

4.1. Storage Coefficients of the Plio-Quaternary Aquifer

Following the comparison of piezometric levels between the model and recordings from pilot piezometers (

Table 4. Lambert coordinates of pilot piezometers used to calibrate storage coefficients of Rharb basin.

Reference Piezometer	X (m)	Y (m)
540/8	421,070	420,144
698/8	397,061	425,246
1552/8	394,915	421,195
1562/8	416,958	448,815
1564/8	416,468	454,357
1765/8	407,665	447,225
1807/14	412,817	411,091

), adjusting storage coefficients enables a spatial distribution generalized at the basin scale.

The reliability of the result is assessed through the measurement of the calibration uncertainty of the calculated and measured loads at the monitoring well levels (Figure 11a,b), and by establishing a measurement/calculation relationship (Figure 11c).

The pilot piezometers are selected based on their positions, which enable them to record piezometric fluctuations in rapid response to changes in recharge/pumping volumes (zones of outcrop in the West and South of the Plio-Quaternary aquifer). The storativity coefficients range from 0.01 to 0.3 along the coastal zone, which is influenced by the marine environment, where Quaternary formations are predominantly sandy. They range from 0.01 to 0.2 along the southern zone near the contact with the Maamora aquifer, an area influenced by continental factors, where formations are predominantly gravelly-sandy. In the outcrop areas of the Southeast and Northeast Plio-Villafranchian basin, where formations consist of coarse materials (pebbles, gravel, etc.), the coefficients range from 0.1 to 0.35.

Sometimes, lithological sequences of the Plio-Quaternary aquifer contain, in certain localities, compact clayey and marly layers ranging in thickness from 1 to 2 m, which act as impermeable screens (Appendix B). These clayey strata put pressure on the waters of the so-called free part of the deep aquifer and reduce the proportion of gravitational waters, resulting in storage coefficients ranging between 0.001 and 0.002, values relatively lower than the standards known for free aquifers.

The storage coefficients range from 5 × 10⁻⁶ to 1 × 10⁻⁵ in the central zone of the basin, where the deep aquifer is confined due to the impermeable formations of the Amerian and the Soltanian (Figure 12).

4.2. Water Balances

The calibration of the transient model allows for the development of 15 balances relative to the selected intervals. According to the analysis of the balances, the system becomes increasingly deficient, transitioning from −15.4 million m³/year in September 1993 to −36.6 million m³/year in September 2007 (

Table 5. Hydrological balances for the periods 1992/93 and 2006/07 in the Rharb basin.

September 1993	In (m3/d)	Out (m3/d)	September 2007	In (m3/d)	Out (m3/d)
Recharge	346.217	0	Recharge	344.919	0
Maamora	182.220	0	Maamora	176.652	0
Ocean	0	−110.654	Ocean	0	−84.826
Rivers	126.829	−140.910	Rivers	157.537	−148.621
Drains	0	−80.831	Drains	0	−66.891
Well	0	−255.249	Well	0	−466.723
Storage	45	−109.767	Storage	6.611	−18.827
Total	655.311	−697.411	Total	685.719	−785.888
Deficit	−15.4 Mm3/year		Deficit	−36.6 Mm3/year

).

The volumes discharged to the ocean decrease over time, and the volumes drained by the hydrological network decrease in favor of infiltration (Figure 13). This is due to the decline in piezometric levels, caused by withdrawals which increased from 93 million cubic meters per year in September 1993 to 170 million cubic meters per year in September 2007. It is noted in this regard that the probable decrease in future precipitation may amplify the effect of exploitation on groundwater reserves, to discuss a combined effect of climate change and overexploitation.

The representation of the evolution of recharge/discharge shows that the fluctuation changes pace from one curve to another (Figure 13). During the study period, the two curves related to withdrawals and discharge exhibit significant variations compared to the rainfall curve. It is observed that despite rainfall remaining more or less constant over time, overexploitation of deep waters leads to a decrease in volumes discharged to the ocean.

This indicates that, despite the volumes of rainfall received by the basin during the study period, it is primarily the pumping of freshwater from the deep aquifer that plays the most impactful role in the Rharb aquifer system.

4.3. Spatiotemporal Evolution of Salt Concentrations

For the hydrodispersive model, the concentrations of the phreatic waters did not show remarkable changes between 1992/93 and 2006/07 because the geography of the iso-zones remained practically the same. However, the concentrations of waters evolved in certain areas at the level of the aquitard and the Plio-Quaternary aquifer.

The quality of phreatic waters deteriorates from the peripheries toward the center of the upper Quaternary aquifer (Figure 14a), with concentrations ranging from 2 to over 6 g/L. This is attributed to the poor lateral movement of solutes in the sediments of the upper Quaternary. The concentrations of water in the aquitard show an increase during the study period (Figure 14b). The impermeable aquitard acts as an obstacle that blocks the propagation of solutes toward the deep aquifer. The concentration of deep waters is less than 0.4 g/L in the peripheries of the basin, especially in the Mnasra area, thanks to the natural replenishment of waters during rainy events. This concentration increases from 0.7 g/L (reference value) to 2 g/L in some localities at the center of the basin due to exchanges with mediocre phreatic waters where the aquitard is locally absent (Figure 14c).

The curve showing the evolution of salt concentration in the deep aquifer at the outcrops of the Plio-Quaternary aquifer (cell n° 273,532) records a decrease, from 0.7 g/L (the initial value assigned to the waters of this aquifer) to 0.2 g/L (Figure 15). This implies that over the years, groundwater tends to reach chemical equilibrium with values close to those of rainwater; hence, the softest waters of the deep aquifer are found near recharge zones. Confined waters may register concentration values of up to 2 g/L in some areas (cell n° 295,951) due to exchange by drainage with underlying wet environments.

4.4. Oceanic Intrusion

For the Variable Density Model (SEAWAT), the iso-concentration curves of the water are parallel to the coastline, responding to the advance of oceanic waters due to the lowering of the piezometric level of the Plio-Quaternary aquifer and the resulting loss of head. The level of contamination of the aquifer by oceanic waters is not the same along the coastal boundary of the basin. In the south at latitude 416,000 m, oceanic waters penetrate more than 500 m into the aquifer, with a transition zone of 250 m (total of 750 m) (Figure 16). However, in the north, this interface is close to the shore with an average transition zone of 200 m.

The cross-sectional tomographic profile, perpendicular to the coastline at the location ‘Ouled Berjal Oued 1′, southwest of the basin (West X: 386.428, Y: 414.343, Z: 3 m; East X: 387.678, Y: 414.187, Z: 34 m), is one of the measurements taken during a 2008 survey conducted by the Sebou Hydraulic Basin Agency (ABHS). In accordance with the norms predefined by the ABHS, the electrical tomography profiles were carried out using a SYSCAL PRO system with 5 cables, each 500 m long, and an inter-electrode spacing of 10 m. The maximum electrode separation for the current electrodes is 560 m.

Oulad Berjal-1 profile serves as a reference for comparison to confirm SEAWAT results. It reveals the presence of saline waters extending 350 m from the shoreline, with electrical resistivities below 10 Ω.m. Between 350 and 500 m, freshwater from the Plio-Quaternary aquifer appears on the profile, giving way to the mediocre waters of the phreatic aquifer beyond 500 m from the shoreline (Figure 17).

4.5. Water Quality and Géochimical Facies

The presence of nitrates in the aquifer indicates an exogenous influence on the natural conditions of the environment. These high nitrate concentrations, their random spatial distribution, and significant local variation signal the existence of localized and important anthropogenic activity.

Stiff diagrams are selected to graphically represent the concentrations of major elements, excluding nitrates, expressed in meq/L. These concentrations are plotted on either side of a vertical axis. This type of representation has two main advantages: different water types produce distinct diagram shapes that can be recognized at a glance, and the total concentrations are easily perceived by the elongation of the diagram. An improvement was made by adding lines connecting the Na⁺ + K⁺ poles to Mg²⁺ and Cl⁻ to SO₄²⁻ [37]. (Figure 18).

In general, the chemical facies of the groundwater in the Rharb aquifer varies between two extreme types: calcium bicarbonate on one hand, and sodium and/or calcium chloride on the other. The calcium bicarbonate type characterizes the water in the dune cordon areas (F8/911), while the sodium and/or calcium chloride type is found between the cities of Sidi Slimane and Sidi Kacem (F14/648, GP5, and F14/R2964). These variations are not uniform across the entire aquifer but depend on the water table level and, especially, the geological context of the sampling point. Typically, the water transitions through an intermediate type, such as calcium chloride or sodium bicarbonate, indicating the presence of chemical reactions between the water and its environment (dissolution-precipitation reactions, cation exchange reactions).

5. Discussion

The first limitation of the hydrodispersive model is the representation of the displacement of the sea wedge. The geometry of the freshwater–saltwater interface along the coastal zone is not vertical as theoretically indicated in the model, but rather inclined from top to bottom toward the onshore direction (Figure 19).

The model calculates the movement of the saltwater wedge toward the continent, cell by cell (Figure 16). Each cell maintains the same concentration throughout its entirety (35.7 g/L) just a few meters from the oceanic boundary where saltwater reaches the water table surface. Once the water at the water-table surface becomes fresh, the application of the Ghyben–Herzberg principle (Equation (6)) becomes the sole means to locate the depth of the freshwater–saltwater interface. SEAWAT provides the location perpendicular to the ocean coastline of this interface, and it’s up to the user to calculate the depth.

$$Z=40\ast h$$

(6)

With Z: depth of the freshwater–saltwater interface relative to sea level (m), h: piezometric height (m).

Another limitation of the model developed in this study is the choice of the period 1992/93–2006/07. This choice is based on the availability of agricultural withdrawal data collected during the 2005 and 2008 campaigns by the Sebou Hydraulic Basin Agency. We are considering improving the work by extending the simulation beyond 2007, within the framework of a new collaboration with the relevant authorities. Once this is done, we will be able to propose forecasting scenarios to assess the effects of climate change and demographic growth.

To now discuss future scenarios for water resource management at the Rharb Basin, we first wish to mention that the Rharb plain plays a key role in Moroccan agriculture, with significant contributions to national cereal production (73.6% of the cultivated area), as well as substantial areas dedicated to beetroot (17,300 ha) and citrus (129,288 ha) cultivation. However, this intensive agricultural activity, coupled with decreasing rainfall and climate change, places considerable pressure on local groundwater resources. The overexploitation of the Rharb coastal aquifer exacerbates the situation, necessitating urgent management measures to preserve water quality and availability.

To mitigate these impacts and safeguard the environment, a range of strategies must be adopted. These include the development of new dams to reduce withdrawals from groundwater, facilitate aquifer replenishment through controlled water releases, and accelerate artificial recharge techniques, such as treated water injection. Additionally, rationalizing fertilizer use and implementing wastewater treatment plants in rural centers are crucial steps to prevent pollution from agricultural and industrial activities [38,39].

Furthermore, the implementation of monitoring systems is essential to track real-time water quality and levels, providing early warning alerts in case of degradation. An integrated water resources management (IWRM) approach, involving all stakeholders, will help ensure the sustainable management of water resources, balancing demand with the need to protect the Rharb aquifer. The prudent use of these resources should be a top priority to address both qualitative and quantitative groundwater challenges in arid and semi-arid regions [40].

6. Conclusions

This study, focusing on the Rharb basin, a region situated within a semi-arid environment, enables the development of a transient hydrodynamic model and a hydrodispersive model using the MODFLOW, MT3DMS, and SEAWAT computational codes.

The development of a hydrodynamic model in a transient regime, by adjusting the storage coefficients for the period September 1992/September 2007, reveals a declining water situation marked by increasing deficit balances, due to irrigation pumpings. The justification of the results through calibration and correlation with the monitoring wells allows for the attribution of zoning of storage coefficients on the basin scale, ranging from 5.10⁻⁶ to 1.10⁻⁴ in the deep confined zone and from 1.10⁻³ to 3.5.10⁻¹ in the free zones.

The development of the hydrodispersive model allows for tracking the spatial distribution of salt concentrations during the same period, taking into account various hydrogeological parameters and the initial concentrations assigned to different layers of the model.

The quality of groundwater is poor over the 15 study intervals, with concentrations ranging from 2 to 6 g/L, and the distribution of iso-concentrations has not evolved over time due to poor water circulation in the upper Quaternary aquifer. Limited water circulation, long residence time, and significant evaporation in the surface aquifer restrict the spread of ionic species, leading to notable local enrichment in major elements. In the Plio-Quaternary aquifer, the water quality is generally good (ranging from 0.4 to 2 g/L). In recharge zones, the concentrations of deep groundwater do not exceed 0.4 g/L, due to water renewal during rainy episodes, while locally in the center of the basin, these values can reach 2 g/L due to exchanges with overlying environments. The aquiclude acts as a barrier to the chemical contamination of the deep aquifer waters, thanks to the properties of the lower Quaternary clays that slow down the propagation of dissolved elements.

The development of the hydrodispersive model also allows for locating the freshwater–saltwater interface in September 2007 at 500 m from the oceanic shoreline, with a transition zone of 250 m thickness to the southwest of the basin. This interface gradually approaches the shoreline in a northward direction.

Modeling work over a geographical extent of 4000 km² represents a significant challenge, aimed at providing for the first time a multilayer model of the entire Rharb basin. This model takes into account not only the interaction between the aquifer system of the Rharb and the external environment but also the interaction between the deep aquifer, the aquitard, and the shallow aquifer. Nevertheless, it is recommended to use this work as preliminary guidance for pumping tests to ensure greater accuracy and provide new data, which in turn can enrich such modeling efforts.

In summary, this research highlights the crucial importance of understanding the hydrogeological mechanisms at work in the coastal basin of Rharb, especially as groundwater aquifers in Morocco’s coastal regions are under serious threat due to climate change [41]. It underscores the need to develop tools and numerical models for sustainable management of groundwater resources, preventing the harmful consequences of overexploitation, and ensuring a balanced and responsible use of these precious resources for future generations, thus contributing to environmental sustainability.