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OPEN Groundwater contamination

modelling in Ayad River Basin,
Udaipur
Kuldeep Pareta

Groundwater, a vital freshwater resource catering to agricultural, domestic, and industrial needs,
faces a pressing challenge of contamination due to escalating human activities. This study focuses
on the Ayad River Basin in the Udaipur district of Rajasthan, employing the FEFLOW simulation
code for the first time. A steady-state numerical model and a groundwater contaminant prediction
model for total dissolved solids (TDS), nitrate, and fluoride were developed, simulating trends over
the next five years with an accuracy exceeding 95%. The results reveal an eastward increase in TDS,
nitrate, and fluoride concentrations, attributed to contamination from two waste disposal sites-
Titadi and Baleecha. Titadi, operational for four decades until closure in 2010, retains residual waste
over 32 thousand ­m2. The initiation of a new dumping ground at Baleecha by the Udaipur Municipal
Corporation post-2010 exacerbates regional contamination. Nitrate contamination is particularly
high in agricultural zones with excessive chemical fertilizer usage. Of the 27 scenarios tested, 23
support using the water for irrigation but would require treatment before using it for drinking.
Recommendations include deploying a chemical sensor network for real-time data input into the
web enabled FEFLOW model, real-time monitoring and alerts, and a mobile application providing
personalized guidance on water usage and health risks in case of contamination. This study can be
beneficial to decision-makers, who work on the policy and groundwater management strategies.

Keywords Groundwater, Contamination, FEFLOW model, Ayad river, Udaipur

Water, essential for life, faces increasing risks due to significant changes in hydrology caused by climate ­change1,2.
In this situation, groundwater plays a crucial role in maintaining regional water resource ­stability3,4. Ensuring
reliable water supply requires a comprehensive approach that integrates surface and groundwater as a single
hydrological ­resource5,6. Surface water and groundwater are closely linked and depend on each o­ ther7–10. Climatic
and geographic factors create complex interactions between surface water and groundwater, so contamination in
one often affects the ­other11,12. Human activities significantly contribute to groundwater ­pollution13–18. Practices
like pesticide use in agriculture, industrial waste discharge, pipeline leaks, coal mining, and landfills significantly
pollute groundwater, risking this essential ­resource19–21. Groundwater, like other water sources, is vulnerable
to contamination, making rigorous monitoring and protection e­ ssential22–25. Groundwater and surface water
interact in large landscapes due to many different f­ actors26,27. Groundwater moves into and out of streams across
the landscape, showing complex water flow p ­ atterns28–30. Understanding and managing how water systems are
connected is crucial for using water resources s­ ustainably31–33.
Researchers use various methods to measure contaminants in groundwater. Groundwater modeling is a
key approach to understand and predict how the system will behave in the ­future34,35. Groundwater models
can be divided into physical, analogue, and mathematical ­types36,37. Physical models, like the Sand tank, show
how groundwater works in a lab setting, but they can have scaling ­issues38–40. Analogue models use electron-
ics to mimic water flow, while mathematical models use equations to represent groundwater systems, which
can be solved with numbers or ­formulas41–43. Analytical models give exact answers for simple situations, while
numerical models estimate solutions for more complex c­ ases44. Prominent tools for measuring groundwater
pollution include MODFLOW and FEFLOW, which provide good r­ esults45–48. Analytical models usually assume
steady-state, one-dimensional conditions, but some, like analytical element models, can handle two-dimensional
groundwater ­flow49,50. Contaminant transport models can use one-dimensional groundwater flow and one-, two-,
or three-dimensional transport c­ onditions51–54. Numerical models are widely used in practical applications for
several reasons, primarily due to their versatility and ability to handle complex s­ cenarios55–57. Numerical mod-
els are preferred in most practical applications due to their ability to manage complexity, flexibility, scalability,

DHI (India) Water & Environment Pvt Ltd., New Delhi, India. email: kupa@dhigroup.com

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predictive capabilities, data integration, cost-effectiveness, and suitability for scenario testing. These advantages
make them powerful tools for understanding and managing groundwater systems effectively. Modelers face a
tough challenge in simplifying real-world problems ­accurately58. The accuracy of numerical models depends on
precise data input, the size of steps used in space and time (larger steps can lead to more errors), and the method
chosen to solve the model ­equations59–62. Paying attention to these details is crucial to make sure groundwater
models are reliable for assessing and managing contamination effectively using scientific m ­ ethods63,64.
A detailed groundwater flow and contamination transport model has been carefully created for the Ayad
River Basin, using the advanced features of the FEFLOW model. The primary objective is to conduct a compre-
hensive assessment of the probable concentrations of Total Dissolved Solids (TDS), nitrate, and fluoride within
the affected area. Contaminant transport models play a crucial role by accurately simulating how contaminants
move and change chemically underground alongside groundwater ­flow36,65,66. The model is advanced because it
can accurately calculate how contamination levels of TDS, nitrate, and fluoride change month by month. Fur-
thermore, it carefully shows how substances move and mix in the area where different water sources meet, giving
detailed insights into how contaminants interact underground. The model results clearly show the vertical and
horizontal spread of each contaminant. A notable contribution of this study is the pioneering generation of an
empirical equation that correlates migration distance with time, presenting a quantifiable m ­ etric67. This innova-
tive approach is a special addition to what we already know, making this study different from previous efforts in
the field. The empirical equation offers a valuable tool for quantitative measurements, previously unexplored in
the region. This novel methodology significantly advances our comprehension of contaminant dynamics in the
Ayad River Basin, providing a robust foundation for informed decision-making in the realms of management
and remediation strategies.
Rathore et al.68 conducted a study on the Ayad River post its passage through Udaipur’s urban and industrial
areas. Sampling at points of domestic and industrial effluent discharge identified significant contamination,
focusing on key parameters such as pH, temperature, conductivity, total dissolved solids (TDS), dissolved oxygen
(DO), biochemical oxygen demand (BOD), chemical oxygen demand (COD), total organic carbon (TOC), acid-
ity, alkalinity, total hardness, chloride, nitrate, phosphate, microbial population count (MPN), and heavy metals.
Their findings highlighted severe pollution downstream of industrial discharge points. Kalal et al.69 investigated
surface water quality of the Ayad River, focusing on pollutants during June to August 2020. Parameters assessed
included total hardness, TDS, chloride, sulphate, fluoride, iron, pH, BOD, COD, and DO. Elevated pollution
levels were observed at industrial discharge points, with COD and BOD concentrations reaching 480.0 mg/l and
162.0 mg/l respectively, indicating severe organic pollution. Dhayachandhran et al.70 conducted a GIS-based
assessment of groundwater quality along the banks of the Adyar River. Their study identified issues such as high
electrical conductivity, ion concentrations, and chloride dominance stemming from industrial and residential
effluent discharge. Seawater intrusion exacerbated groundwater quality near coastal areas, necessitating robust
management strategies for water quality improvement. In a groundwater quality study of the Banas River Basin,
Pareta et al.71 analyzed data spanning 2000–2018, emphasizing physico-chemical parameters. Significant con-
taminants identified included fluoride, nitrate, chloride, calcium carbonate (­ CaCO3), and salts. Utilizing the
Water Quality Index (WQI), the research revealed a declining groundwater quality index (GWQI) from west to
east, with elevated salinity and hardness particularly noted in the eastern micro-watershed (MWS).
Groundwater flow and contaminant transport modeling present significant challenges, as noted by Diersch
et al.72, due to the complexity of managing spatially and temporally variable parameter fields. Integration of
FEFLOW with GIS ARC/INFO addresses these challenges by providing a robust platform for managing para-
metric and geometric data, advanced computational tools, graphical visualization capabilities, and interactive
data exchange functionalities. Sarma et al.73 emphasize the increasing importance of simulating contaminant
transport in both unsaturated and saturated groundwater zones, driven by rising water demands. Integrated
models that consider interactions between these zones offer more accurate predictions compared to standalone
models, crucial for effective regional groundwater management by better forecasting solute movements within
groundwater systems. Kumar et al.74 underscores the utility of groundwater contaminant transport models
such as MODFLOW, MT3DMS, RT3D, FEFLOW, and MODPATH in predicting contamination behavior and
facilitating management strategies. They stress the necessity for precise modeling objectives and appropriate tool
selection to ensure accuracy and avoid errors in groundwater management practices.
This study focuses on assessing groundwater quality in the Ayad River Basin, located in Udaipur district,
Rajasthan, using the FEFLOW simulation software. The primary objective is to develop a numerical model
capable of predicting the spatial distribution and temporal trends of total dissolved solids (TDS), nitrate, and
fluoride contamination over the next five years with a high accuracy exceeding 95%. The investigation addresses
significant contamination challenges arising from human activities, particularly from historical and current waste
disposal sites such as Titadi and Baleecha. The study aims to provide insights crucial for developing effective
groundwater management strategies, emphasizing the importance of real-time monitoring and intervention to
mitigate contamination impacts on agricultural and domestic water supplies in the region.

Study area
The Ayad River Basin, spanning 1207 k­ m2, is geographically positioned between 24°50′16" to 24°27′46" northern
latitude and 73°31′44" to 73°59′44" eastern longitude. Administratively, it encompasses four tehsils (Girwa, Mavli,
Vallabh Nagar, and Gogunda) in Udaipur district and one tehsil (Nathdwara) in Rajsamand ­district75. Originating
from the Gogunda hills in north-west Udaipur, the Ayad River flows over a 68 km stretch before entering the
Vallabh Nagar reservoir to the east of Udaipur (Fig. 1). As a seasonal river, it serves as a tributary to the Berach
River, which, in turn, is a tributary to the Chambal River in the Yamuna basin. The Ayad River Basin experiences
a tropical, semi-arid climate, characterized by summer temperatures ranging from 28.8 °C to 42.3 °C and winter

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Figure 1.  Location map of Ayad River Basin, Udaipur, and extents of the flow and transport model.

temperatures from 3.5 °C to 18.8 °C. The average annual rainfall is 640 mm, predominantly influenced by the
southwest monsoon, delivering about 90% of the annual precipitation from July to mid-October. Groundwater,
sourced from wells and hand pumps, constitutes 69% of the total irrigated area, with surface water contributing
the remaining 31%.

Materials and methods

Data collection
This investigation leverages a comprehensive dataset, encompassing precipitation records from three raingauge
stations, pumping rate data derived from 17 monitoring wells, hydraulic-head data collected from 45 groundwater
monitoring wells, subsurface lithological information (lithologs) obtained from 11 borelogs, and groundwater
quality data originating from 8 monitoring wells. These datasets were meticulously gathered from diverse sources,
including the Water Resource Department (WRD), Govt. of Rajasthan; the College of Technology and Engi-
neering (CTAE), Udaipur; the Ground Water Department (GWD), Govt. of Rajasthan; and the Central Ground
Water Board (CGWB), Govt. of India.

Precipitation data
Precipitation data spanning from 2000 to 2022 was gathered from the Water Resource Department (WRD), Govt.
of Rajasthan for three distinct rain gauge stations-namely, Udaipur (Girwa), Badgaon, and Biliya (Fig. 1). This
comprehensive time series dataset was meticulously curated to serve as input for the FEFLOW model.
In 3D modeling, the flux boundary condition is characterized by the unit (L/T), denoting an influx of water
across a defined area over a specific time. Given the presence of three distinct rain gauge stations, the basin
boundary underwent segmentation into three delineated sections through the application of the Thiessen poly-
gon method. Subsequently, all nodes within the top slice of the resultant Thiessen polygons were designated to
represent rainfall-induced flow, thus establishing a comprehensive representation of the inflow dynamics across
the basin boundary.

Monitoring wells data with pumping rate

The pumping rate data pertaining to the year 2016 was acquired from 17 monitoring wells locations, sourced
from the College of Technology and Engineering (CTAE), Udaipur. The geographical distribution of these bore-
holes is visually represented in Fig. 1, with detailed information provided in the accompanying Table 1. These
data points served as a foundational dataset for the estimation of critical hydraulic properties of the aquifer,
including hydraulic conductivity and storage coefficient. This dataset was utilized to construct a robust model
of the aquifer, enabling the estimation of its hydraulic properties. These hydraulic properties play a pivotal role
in comprehending the dynamics of water flow within the aquifer, offering valuable insights for predicting future
water availability and quality.

Hydraulic‑head data
The hydraulic-head data encompassing both pre-and post-monsoon periods spanning from 2011 to 2022 were
meticulously gathered from 45 groundwater monitoring wells, sourced from the Ground Water Department
(GWD). Govt. of Rajasthan (Fig. 1). The application of a hydraulic-head boundary condition involves assigning a
predetermined hydraulic head value to a specific node within the model. In contrast to calculating the hydraulic
head as an outcome of the simulation, these nodes are characterized by having their head values predetermined

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Total depth Wells,

of the wells pumping
Pumping well below land Rate (flow) Type of from model
S. no name X (m) Y (m) surface (m) Z (top) m Z (bottom) m Well Type ­m3/d Radius (m) aquifer layer
Baleecha,
1 Goverdhan 365,749.17 2,713,589.79 05.03 613.24 608.21 MLW 276.0 2.66 Unconfined Layer-1
Vilas
Barhmnon Ka
2 360,762.84 2,729,316.22 05.20 626.24 621.04 MLW 560.0 1.68 Unconfined Layer-1
Guda
3 Bedwas 369,621.72 2,719,609.36 28.40 567.32 538.92 MLW 192.0 1.86 Unconfined Layer-2
Bhilon Ka
4 370,660.78 2,729,564.44 05.60 806.62 801.02 MLW 639.0 2.94 Unconfined Layer-1
Bedla
5 Chikalwas 363,967.44 2,726,375.30 29.18 608.20 579.02 MLW 551.7 2.47 Unconfined Layer-2
6 Dheenkli 373,863.14 2,721,035.09 28.20 585.05 556.85 MLW 579.0 4.61 Unconfined Layer-2
7 Eklingpura 372,419.31 2,715,999.09 24.30 570.43 546.13 MLW 631.0 2.36 Unconfined Layer-2
Eklingpura,
8 372,367.82 2,717,684.23 29.20 557.31 528.11 MLW 406.0 1.95 Unconfined Layer-2
Manwakhera
Farm Pond,
9 371,730.80 2,720,885.02 29.50 578.67 549.17 MLW 360.0 2.33 Unconfined Layer-2
CTAE
10 Gorela 362,928.29 2,719,386.51 21.97 617.60 595.63 MLW 588.0 2.50 Unconfined Layer-2
11 Kaladwas 374,259.44 2,716,844.67 05.10 554.96 549.86 MLW 174.0 1.72 Unconfined Layer-1
12 Kushal Bagh 369,431.44 2,714,329.75 29.00 594.78 565.78 MLW 503.0 2.57 Unconfined Layer-2
13 Liyon Ka Guda 362,828.37 2,724,960.67 29.50 621.78 592.28 MLW 536.0 3.40 Unconfined Layer-2
Manpura
14 367,958.65 2,730,192.22 22.04 625.06 603.02 MLW 654.0 2.36 Unconfined Layer-2
Lakhawali
Pheniyon Ka
15 362,998.28 2,726,325.80 27.95 615.81 587.86 MLW 499.0 3.84 Unconfined Layer-2
Guda
16 Rehta, Debari 380,024.96 2,721,982.43 24.20 551.59 527.39 MLW 516.0 3.11 Unconfined Layer-2
17 Seesarma 364,608.30 2,720,673.43 04.25 608.45 604.20 MLW 475.0 3.65 Unconfined Layer-1

Table 1.  Pumping wells considered in the numerical model. Source: College of Technology and Engineering
(CTAE), ­Udaipur76.

by the boundary condition. This condition can result in either an inflow into the model when neighboring nodes
exhibit lower potential or an outflow from the model in the presence of a gradient from neighboring nodes
toward the boundary condition. Head boundary conditions find application in scenarios where the hydraulic
potential is known in advance, such as in surface water bodies with a direct connection to groundwater, pump
sumps maintaining a constant level for dewatering, or seepage faces in conjunction with a constraint condition.

Subsurface lithological information

Subsurface lithological information (lithologs) of 11 borelogs (Fig. 1) for year 2016 have been collected from
Ground Water Department (GWD). Govt. of Rajasthan in hard copy format. The lithological log data has includ-
ing of hydrological abstract, thickness, discharge, type of aquifer, yield test (V-NOTCH). By using this infor-
mation, entire aquifer has been divided into 4 slices. These slices are slice-1 (0–6 m), slice-2 (6–30 m), slice-3
(30–70 m), and slice-4 (70–100 m) present the aquifer of the basin (Fig. 4). These 3D layer configuration has
been used for switching the model type from 2 to 3D and vice versa, for setting up the basic 3D structure, or for
changing the model layering later on. It has also used for creating layer pinch-outs using tetrahedral elements
and for assigning elevations to the nodes.

Groundwater quality data

Groundwater quality data encompassing 16 key water quality parameters were gathered from the Ground Water
Department (GWD), Govt. of Rajasthan, and the Central Ground Water Board (CGWB), Govt. of India for 8
locations, spanning the period between 2011 and 2022, as illustrated in Fig. 1. The GWD and CGWB diligently
monitors groundwater quality during the months of May and June annually. The comprehensive set of water
quality parameters includes pH (power of hydrogen, − ­log[H3O+]), electrical conductivity (EC), total hardness
in terms of calcium carbonate (TH, C ­ aCO3), calcium (­ Ca2+), magnesium (­ Mg2+),
­ aCO3), total alkalinity (TA, C
sodium ­(Na+), potassium ­(K+), iron ­(Fe2+), carbonate hardness ­(CO32−), bicarbonate ­(HCO3−), chloride ­(Cl−),
sulfate ­(SO42−), nitrate ­(NO3−), fluoride ­(F−), and total dissolved solids (TDS). These parameters collectively
contribute to a comprehensive analysis providing a general overview of groundwater contamination within the
Ayad River Basin. Notably, among the 16 parameters, nitrate (­ NO3−), fluoride (­ F−), and total dissolved solids
(TDS) exhibit the most pronounced contamination levels in the study area. Consequently, these three critical
groundwater quality parameters will serve as pivotal inputs for the forthcoming groundwater contamination
modeling efforts within the Ayad River Basin.

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Development of the numerical model

The finite difference method and finite element method stand out as predominant numerical approaches for
solving groundwater flow or solute transport ­equations77. The selection between these methods hinges on the
specific modeling objectives and the complexity of the issues under consideration. When dealing with intricate
concerns, the finite difference method may yield divergent results compared to the finite element ­method78. It is
crucial to note that the modeling approach alone does not singularly determine model outcomes; other factors,
including initial conditions, boundary conditions, space discretization, and data quality, exert significant influ-
ence. In numerical modeling, hydrogeologists employ these methods to approximate solutions for intricate system
differential equations by transforming them into discrete equations and partitioning the domain into grids or
meshes. The dissection of a region and discretization of differential equations are typically accomplished using
approximation techniques such as finite difference, finite element, and finite volume method. These methods
can be employed individually or in combination to mitigate the computational complexity of numerical models.
Each approach comes with its unique advantages and limitations, with considerations for applicability, ease of
use, performance, and computational speed.

Modelling approach
The initial stage in any modeling endeavor involves delineating the model objectives. In the modeling process,
meticulous attention is directed toward the acquisition and processing of data. Nonetheless, the pivotal step in
modeling is the conceptualization of the model. Following the construction of the model and its preliminary
execution, subsequent steps encompass calibration, verification, and sensitivity analysis. A graphical representa-
tion of the sequential stages in groundwater modeling is depicted in Fig. 2.
A numerical model for groundwater flow and contamination transport was constructed using the FEFLOW
groundwater modeling software. FEFLOW was chosen for its distinctive advantages over alternative modeling
systems, including the ability to employ flexible meshes essential for accommodating the 3D geometry of the
model area. Additionally, FEFLOW’s capability to conduct density-dependent flow modeling was crucial for
capturing buoyancy effects associated with contamination layers.
The developed FEFLOW model was employed to analyze the dynamic behavior of nitrate, fluoride, and total
dissolved solids contamination. Predictions were made regarding the expected duration of contamination over
a specified period, 5 years. The outcomes of the model were instrumental in formulating strategies aimed at
mitigating the average contamination levels of nitrate, fluoride, and total dissolved solids in abstracted water.

Formulating modelling objectives. The main objective of this study is to investigate groundwater contami-
nation in the Ayad River Basin. Specifically, the study aims to discern the current state of contamination and
project future trends, focusing on key parameters such as nitrate (­ NO3−), fluoride (­ F−), and total dissolved solids
(TDS). The overarching goal is to employ the FEFLOW model to comprehensively analyze and quantify the
extent of groundwater contamination. By doing so, it seeks to provide valuable insights into future trends, pre-
dicting whether the level of nitrate, fluoride, and TDS will rise of fall.

Model conceptualization. Model conceptualization involves qualitatively describing a groundwater system by

detailing the water balance, hydrological conditions, and aquifer ­characteristics61. It is a crucial stage in ground-
water modeling, following the identification of model objectives, and requires data on aquifer properties, hydrol-
ogy, boundary conditions, and hydraulic ­parameters79–82. A robust conceptual model should simplify real-world
complexities while aligning with modeling goals and management needs, particularly in understanding con-
taminant transport and water flow dynamics.
For this study, the conceptual model included key factors such as flow and transport processes, model extent,
spatial discretization, 3D mesh setup, structural geology, initial conditions, boundary conditions, recharge, mate-
rial parameters, calibration, validation, water balance, and groundwater quality prediction. Once the conceptual
model was developed, a mathematical model was created to represent the assumptions and equations of the

Figure 2.  Modelling process flow chart.

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conceptual model, which were solved through numerical methods. This approach ensured accurate predictions
and effective management of groundwater quality in the Ayad River Basin.

Governing processes
Flow process. The groundwater flow process is simulated, incorporating unsaturated flow effects through the
utilization of the Richards’ e­ quation83. This equation, a simplified dual-phase model, efficiently captures water
movement and desaturation effects, derived from the principles of mass and momentum ­conservation84. The
Richards is expressed as:
  
∂θ ∇υ/
= ∇ · K(θ) − ez
∂t γ
where θ is the volumetric water content, t is time, K(θ) is the unsaturated hydraulic conductivity, ψ is the pressure
head, γ is the unit weight of water, e­ z is the unit vector in the vertical direction.
The equation describes how water content (θ) changes over time due to fluxes driven by gradients in pressure
head (ψ) and the unsaturated hydraulic conductivity (K(θ)). Richards’ equation is crucial in modeling processes
such as infiltration, groundwater recharge, and plant water uptake in agricultural and environmental studies. Its
solutions provide insights into the movement and distribution of water in soils and other porous media under
varying moisture conditions.

Transport process. Contaminant migration is assessed through the advective–dispersive transport model
within FEFLOW, integrating advective transport (associated with water movement) and dispersive/diffusive
transport processes. During the steady-state calibration phase, no contamination transport is calculated. Nev-
ertheless, a transport model for contaminants is introduced, incorporating a static (immobile) contaminant
distribution to account for density effects during the steady-state calibration.

Density dependency. Variations in contamination within the aquifers surrounding the Ayad river, and major
lake, reservoir are recognized for their impact on the hydraulic system, primarily attributed to buoyancy forces.
The model incorporates these buoyancy forces by employing a linear correlation between fluid density and dis-
parities in nitrate, fluoride, and TDS concentrations.

Hydraulic and transport model extent

The hydraulic model shares the same spatial extent as the transport model, as depicted in Fig. 1. Utilizing this
expanded model extent facilitates the utilization of natural features as boundary conditions, including (i) the
surface catchment water divides to the west; (ii) the assumed boundary streamlines near the edge of the Ayad
River Basin; and (iii) the Ayad River within the basin, along with major lakes and reservoirs in the central part
of the basin. The total dimensions of the hydraulic flow model and transport model span 46.8 km in an east–west
direction and 42.3 km in the north–south direction, covering an area of 1206.7 ­km2. The vertical extent of the
hydraulic model and transport model coincides with that of the ArcGIS 3D model, ranging from the highest
point at 1011.45 m to the lowest point at 457.67 m.

Spatial discretization
The FEFLOW modelling software employs a flexible 3D meshing technology grounded in a 2.5D mesh geometry,
wherein a completely unstructured 2D mesh is extruded over a designated number of layers with variable thick-
ness, extending into a 3D domain. The layers can be made discontinuous by deactivating specific elements of the
mesh, allowing for pinch-outs of geological layers. This process unfolds in two distinct steps, namely Horizontal
2D meshing and vertical 3D layer setup, elucidated in the subsequent sub-sections.

Horizontal discretization. The primary aim of the horizontal mesh is to establish an optimal triangular mesh
geometry that effectively approximates both human-made and natural features pertinent to the modelling pro-
cess. Specifically, the relevant features for this modelling work include the flow model’s domain extent, the trans-
port model’s domain extent, and the abstraction ­wells85. A secondary objective in this context is to ensure an
average element size conducive to both the flow and transport models. The average element size in the outer
basin and the inner area around the wells is approximately 1000 m and 10 m, respectively, with a smooth transi-
tion zone between them. Figure 3 illustrates the geometry of the finite element mesh. An effective measure of the
2D triangular mesh’s quality is the distribution of triangle angles, ideally nearing 60° (equivalent to an equilateral
triangle). A standard benchmark involves assessing the number of elements with angles larger than 90° or 120°.
The present model exhibits excellent mesh quality, with only 0.1% of the mesh angles exceeding 90° and none
surpassing 120°.

Layer configuration (3D mesh setup). Density-dependent flow models, exemplified by the model discussed
here, demand meticulous vertical discretization, particularly in regions with density gradients. FEFLOW, a
finite-element model utilizing layered unstructured grids, provides significant flexibility to tailor model layers
­ bjectives86. Model layers, also known as numerical layers, may deviate from the geometric arrange-
to diverse o
ment of hydrogeological layers (formations/units). In this context, three objectives guide the approach: main-
taining model layer thickness within an acceptable range for accuracy and stability, ensuring element geometry

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Figure 3.  Finite-element mesh and compact supermesh in Ayad River Basin, Udaipur.

Figure 4.  3D finite-element mesh.

approximates geological contacts from the structural geological model, and minimizing the total number of
elements for reasonable run-times.
These objectives are achieved through a combination of a stratigraphic layering approach, where geological
and model layers consistently coincide, and a block model, wherein all layers are horizontal with a specified
thickness. The extents of geological units are assigned based on their intersection with the model elements. The
model incorporates a three-layer configuration to represent the subsurface geological conditions accurately. The
first layer has an average thickness of 6 m, ranging from 735.94 m to 729.94 m above mean sea level (amsl). The
second layer is 24 m thick, extending from 729.94 m to 705.94 m amsl. The third layer ranges from 705.94 m to
635.94 m amsl. The specific types of aquifers (confined or unconfined) within these layers have been detailed in
Table 1. This layered structure is crucial for accurately simulating groundwater flow and contaminant transport
dynamics across different depths. Figure 4 depicts the geometry of the resulting mesh, comprising 59.56 thousand
active finite elements and containing 10.91 thousand active nodes.

Structural geology
The Ayad River Basin in Udaipur underwent an extensive geological examination, integrating diverse data
sources, including the Geological Survey of India’s 1:50,000 scale map, Landsat-9 OLI-2 + PAN satellite imagery
(15 m resolution), and SRTM DEM data (30 m resolution)75. The resultant geological map, presented in Fig. 5,
offers insights into rock types, lithology, and lineaments. The analysis reveals a spectrum of rock types span-
ning the Archaean to Upper Proterozoic eras, categorized into the Bhilwara, Aravalli, and Delhi s­ upergroups87.
Notably, the Archaean-era Mangalwar Complex, representing the Bhilwara supergroup, is situated approximately
55 km southwest of ­Chittorgarh88. The Gurali formation of the Debari group serves as a geological boundary,
delineating the Bhilwara supergroup from the Aravalli ­supergroup89. The Aravalli Mountain range primarily
comprises rocks from the Proterozoic-era Delhi Supergroup, with crystalline rocks from the Archaean age posi-
tioned between various geological formations, including the BGC/Bhilwara group, Aravalli supergroup, Palaeo-
Proterozoic cover sequences, and Delhi fold belt rocks, equivalent to those in the BGC ­group90. This collaborative
use of geological maps, satellite imagery, and elevation data has yielded a comprehensive understanding of the
Ayad River Basin’s geological composition, providing insights into its intricate and dynamic geological history.

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Figure 5.  Geological ­map91, and lithologs cross-section92 of Ayad River Basin, Udaipur.

Following the successful generation of the 3D mesh, the model layers offer an effective approximation of the
structural geological model. To facilitate the subsequent assignment of parameter values in FEFLOW, various
sets or selections of finite elements are established in the FEFLOW model. These selections within FEFLOW are
formulated by utilizing elevation data from each aquifer layer (slice), specifying the upper and lower extents of
the slice, and incorporating 3D triangulated data for intrusion-type model objects.

Initial conditions
Hydraulic head/water levels. The initial hydraulic head conditions for the transient modeling forecast are
derived from a steady-state model run utilizing the parameter set specific to each scenario (Fig. 6).

Nitrate, fluoride, and TDS contamination. The water quality parameters are examined to assess their conform-
ity with the standards outlined by the World Health Organization (WHO), as delineated in Table 2. This rigorous
evaluation is conducted to ascertain that the groundwater quality parameters align with the prescribed guide-
lines, ensuring their compliance with recommended standards for safe drinking water.
The spatial distribution maps of nitrate, fluoride, and Total Dissolved Solids (TDS) contamination in the Ayad
River Basin were generated using the Inverse Distance Weighting (IDW) interpolation method in ArcGIS. IDW
interpolation estimates values at unsampled locations based on the weighted average of nearby sampled values,
where closer samples have higher influence. For this study, the average values of each contamination parameter
from 2011 to 2022 were utilized. This method was chosen for its ability to effectively represent gradual changes

Figure 6.  Elevation and hydraulic head in Ayad River Basin, Udaipur.

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WHO93 Average data (2011–2022)

S. no Water quality parameters Desirable limit Permissible limit Min Max Ave
1 Nitrate ­(NO3−) mg/L – 50 0.01 650.03 57.14
2 Fluoride ­(F−) mg/L 0.6 4 0.01 4.13 0.58
3 Total dissolved solids (TDS) mg/L 500 1000 331.50 4270.50 1082.06

Table 2.  Standards according to WHO protocols and observed ranges and averages.

in contamination levels across the basin, ensuring a continuous and spatially representative visualization of
groundwater quality parameters. The spatial distribution of nitrate, fluoride, and TDS contamination in Ayad
River Basin is sown in Fig. 7.
The lower thresholds for nitrate, fluoride, and total dissolved solids (TDS) contamination have been estab-
lished in accordance with the permissible limits defined by the World Health Organization (WHO). This meticu-
lous adherence to WHO standards ensures that the specified levels for these contaminants align with globally
recognized guidelines, emphasizing a comprehensive approach to groundwater quality assessment.

Boundary conditions and recharge

Pumping wells. A total of 17 wells have been included in the model. Relevant well properties are listed in
Table 1 and their locations are shown in Fig. 1. For each well, an additional one-dimensional finite element
known as Discrete Feature Element (DFE) has been incorporated into the finite-element mesh. This element
aligns with the actual dimensions of the well screen, defined by its top and bottom elevations, and emulates the
conduit formed by the well screen. This inclusion facilitates water abstraction from all formations intersecting
with the screen. The transmissivity of this element has been selected to match the anticipated screen diameter
under the assumption of laminar flow, with intra-screen flow calculated using the Hagen-Poiseuille flow law.
Furthermore, each well is associated with a minimum water level, below which abstraction is not feasible. This
minimum water level represents the depth at which the pump is positioned, and water abstraction is hindered if
the water level falls below this threshold. Insufficient water abstraction may occur due to two main reasons: (i)
the aquifers cannot yield an adequate amount of water, leading to a reduction in pumping rate to align with the
aquifer yield; (ii) if the water level descends below the minimum hydraulic head, the well becomes deactivated,
typically due to nearby pit dewatering activities.

Recharge. The model incorporates two distinct recharge systems: (i) diffusive (aerial) recharge applied at the
surface. This recharge is implemented as an aerial source at the upper boundary of the model, representing
net recharge. Rainfall data, obtained from three rain gauge stations in the Ayad River Basin, is utilized for this
purpose, with model inputs derived through the thiessen polygons method based on these stations; (ii) recharge
along drainage lines is depicted as a line source. Utilizing Shuttle Radar Topography Mission (SRTM) DEM data
with 30 m spatial resolution (source: NASA Earth science data) and employing ArcGIS software, drainage lines
are generated. All drainage lines are assumed to possess a uniform infiltration rate per unit length. The total net

Figure 7.  Spatial distribution of nitrate, fluoride, and TDS contamination in Ayad River Basin, Udaipur.

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recharge is determined by the superposition of both effects. Each effect can be selected independently and has
undergone calibration.

Material parameters
Material parameters are allocated as constant values to the main formations outlined by the structural geological
model. This structure has been incorporated into the numerical model during the establishment of the hydrogeo-
logical structure. No additional zonation within the principal formation was introduced. This section elucidates
the assumptions and data sources utilized to derive the parameter values.

Hydraulic conductivity. FEFLOW facilitates the implementation of hydraulic conductivities in three distinct
axes to accommodate anisotropy. In the present model, the orientation of these primary axes aligns with the
main coordinate axes ­(Kxx, ­Kyy, and ­Kzz). The calibration process determines all hydraulic conductivity values
(Table 3; Fig. 8). The hydraulic conductivity in horizontal directions (­ Kxx and K
­ yy) is presumed to be isotropic
­(Kxx and ­Kyy are identical) to streamline the degrees of freedom.

Specific yield and porosity. The principal parameters influencing porosity in the FEFLOW model include the
absolute porosity utilized in the flow model, referred to as "unsaturated porosity," and the porosity relevant to
mass transport, termed "mass-transport porosity." Within the context of the unsaturated flow model, FEFLOW
establishes saturation limits, defining both a residual saturation (lower limit) and a maximum saturation (upper
limit). These parameters collectively implicitly define specific yield. To streamline complexity, default values for
residual and maximum saturation (0.25% and 100%, respectively) are adopted, resulting in the negligible differ-
ence between absolute porosity and specific yield. The mass-transport porosity is assumed to be equal to specific
yield, with a lower limit imposed to ensure model stability. Parameter values are selected based on relevant
literature, with adherence to the LOM model principles whenever applicable. A detailed listing of these values
is provided in Table 4.

Unsaturated parametric model. The selection of the unsaturated model type necessitates the specification of
parameters governing the water retention curve and the relative reduction of hydraulic conductivity concerning
reduced saturation, encapsulated in the relative permeability relationship. At a regional scale, the significance
of these parameters is generally mitigated, provided that the chosen values facilitate the infiltration of applied
recharge. Consequently, a simplified van Genuchten m ­ odel95 has been employed for its pragmatic applicability.
This model entails three distinct fitting parameters: alpha is determined on an element-wise basis as the recipro-
cal of the layer thickness. The van Genuchten parameters are set to default values in FEFLOW, namely n = 1.964
and m = 0.4908. This selection aims to ensure numerical stability while closely approximating actual capillary
behavior. The relative permeability is configured to scale linearly with saturation, with the fitting parameter delta
set to unity. This approach has demonstrated efficacy in optimizing both model stability and computational
run times at the spatial scale under consideration. Typical parameters for a van Genuchten model are given in
Table 5.

Calibration
The model parameters pertinent to flow, namely hydraulic conductivity, and recharge, encompassing the assumed
head values at the reservoir and lakes, underwent calibration against mean water levels derived from a steady-
state model. The primary goal of the calibration process was to ascertain a parameter set that concurrently
meets the following criteria: (i) achieves a satisfactory fit between the model-derived water levels and observed

Component Parameters Unit Prior range Initial value Range of model evaluations Calibrated value
Kxx m/s 1 × ­10−9–1 × ­10−2 1 × ­10−4 2.4 × ­10−6–5.1 × ­10−3 4.2 × ­10−5
Kvy m/s 1 × ­10−9–1 × ­10−2 1 × ­10−7 1.0 × ­10−5–9.9 × ­10−3 6.1 × ­10−4
Geological layer-1 (sand/clay/silt/gravel) 0–6 m
Sy – 0.00–0.35 0.15 0.01–0.33 0.26
Ss 1/m 1 × ­10−9–1 × ­10−2 9.94 × ­10−5 5.6 × ­10−5–7 × ­10−4 8.6 × ­10−5
−9 −2 −4 −5 −8
Kxx m/s 1 × ­10 –1 × ­10 1 × ­10 9.9 × ­10 –1.5 × ­10 9.3 × ­10−6
−9 −2 −7 −8 −6
Geological layer-2 (weather and fractured: dolomitic limestone-sand- Kvy m/s 1 × ­10 –1 × ­10 1 × ­10 1.7 × ­10 –9.9 × ­10 4.9 × ­10−7
stone/granite-phyllite) 6–30 m Sy – 0.00–0.35 0.1 0.0–0.32 0.16
Ss 1/m 1 × ­10−9–1 × ­10−2 6.89 × ­10−4 7.0 × ­10−5–5.3 × ­10−4 2.2 × ­10−4
Kxx m/s 1 × ­10−9–1 × ­10−2 1 × ­10−4 1.2 × ­10−8–3.3 × ­10−3 6.1 × ­10−6
Kvy m/s 1 × ­10−9–1 × ­10−2 1 × ­10−7 1.1 × ­10−8–9.4 × ­10−4 3.6 × ­10−7
Geological layer-3 (compact: phyllite, granite, schist, gneiss) 30–100 m
Sy – 0.00–0.35 0.02 0.01–0.31 0.04
Ss 1/m 1 × ­10−9–1 × ­10−2 3.68 × ­10−6 5.9 × ­10−7–4.9 × ­10−6 4.1 × ­10−6
Kxx = Horizontal hydraulic conductivity in X, ­Kvy = Horizontal hydraulic conductivity in Y, ­Sy = Specific yield,
Where:
­Ss = Specific storage

Table 3.  Hydraulic conductivity and specific yield.

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Figure 8.  Hydraulic conductivity in the Ayad River Basin, Udaipur.

S. no Unit Porosity, pt S. no Unit Porosity, pt

Unconsolidated deposits Rocks
1 Gravel 0.25–0.40 1 Fractured basalt 0.05–0.50
2 Sand 0.25–0.50 2 Limestone 0.05–0.50
3 Silt 0.35–0.50 3 Sandstone 0.05–0.30
4 Dolomite 0.00–0.20
5 Shale 0.00–0.10
4 Clay 0.40–0.70
6 Fractured crystalline rock 0.00–0.10
7 Dense crystalline rock 0.00–0.05

Table 4.  Porosity values (applied in base case scenarios). Source: Freeze et al.,94.

regional long-term water levels; (ii) maintains consistency with the prevailing understanding of local and regional
hydrogeological conditions.

Steady‑state model setup. The model underwent an initial steady-state run, initially excluding the abstraction
effects from pumps. For the subsequent transport model, an essential prerequisite was a reasonable approxima-
tion of the initial conditions for nitrate, fluoride, and total dissolved solids (TDS) contaminations, which were
incorporated into the model at the commencement of the run. A static concentration distribution for nitrate,
fluoride, and TDS was employed, with a caveat that the mass transport model could not be entirely deacti-
vated, as calibration necessitated consistency with the hydraulic head in the transient forecasting model. It was
observed that variations in nitrate, fluoride, and TDS distributions yielded significant differences in steady-state
water levels. Calibration procedures were executed employing a dual approach, combining automated inverse
modeling facilitated by an algorithm for parameter estimation within the PEST uncertainty estimation software,
alongside manual adjustments.

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S. no Textural class N θr ­(cm3/cm3) θs ­(cm3/cm3) ά (1/cm) n

1 Sand 126 0.058 0.37 0.035 3.19
2 Loamy sand 51 0.074 0.39 0.035 2.39
3 Sandy loam 78 0.067 0.37 0.021 1.61
4 Loam 61 0.083 0.46 0.025 1.31
5 Silt 2 0.123 0.48 0.006 1.53
6 Silt loam 101 0.061 0.43 0.012 1.39
7 Sandy clay loam 37 0.086 0.40 0.033 1.49
8 Clay loam 23 0.129 0.47 0.030 1.37
9 Silty clay loam 20 0.098 0.55 0.027 1.41
10 Silty clay 12 0.163 0.47 0.023 1.39
11 Clay 25 0.102 0.51 0.021 1.20

Table 5.  Typical van Genuchten model parameters (ά, n) including residual (θr), and saturated (θs) water
contents compiles from the UNSODA ­database96. n indicates the number of soils or samples of a given textural
class from which the mean values are compiled.

Calibration parameters. Hydraulic conductivity

The calibration of hydraulic conductivity involves distinct adjustments for horizontal components (­ Kxx and
­Kyy) and the vertical component (­ Kzz), as detailed in Table 3. Zonation for hydraulic conductivity is delineated
based on the primary geological units stipulated in the conceptual model (Section "Structural geology", struc-
tural geology).

Recharge. Diffuse recharge: Recharge is administered as a function of specified fractions relative to the assumed
mean annual precipitation rates, which are 819 mm/year for Udaipur (Girwa), 575 mm/year for Badgaon, and
1032 mm/year for Biliya. Distinct recharge factors are applied, delineating variations in the surface geological
characteristics for the respective regions.
Drainage lines: Additional recharge is introduced along the drainage lines prevalent in the model area.

Consent to participate
By participating in this research on "Groundwater Contamination Modeling in Ayad River Basin, Udaipur" I
consent to the utilization of my data for academic purposes.

Results and discussion

Calibration of hydraulic head
The calibration has been conducted using a combination of automated calibration through inverse modelling and
manual calibration (using the parameter estimation capability of the ­PEST97,98 calibration and uncertainty model-
ling software). Utilizing the Parameter ESTimation (PEST) tool embedded in the FEFLOW module, hydraulic
head (groundwater level) simulations were conducted, as illustrated in Fig. 9. The fidelity of the simulation results
reached an accuracy level of approximately 98%.

Figure 9.  Calibration results of hydraulic head (simulated vs. observed).

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Calibration of contaminant transport model

Calibration is the process of refining the model representation of the hydraulic properties to achieve a desired
degree of correspondence between the model simulations and observations of the solute concentrations. In
this study, calibration of contaminant transport model is achieved by adjusting the dispersivity values until the
observed solute concentration matches with the calculated solute concentration. The TDS, nitrate, and fluoride
concentrations in each groundwater monitoring well (observation well) are collected from SGWD, and CGWB.
The calibration is stopped when a reasonable match between the observed and calculated concentration is
achieved. After the calibration of contaminant transport model, the ­R2 for TDS, nitrate, and fluoride contaminant
transport model are obtained as 0.991, 0.994, and 0.958, respectively, and shown in Fig. 10. Longitudinal and
transverse dispersivity values were modified by trial and error in order to match the observed and simulated
values. Calibration shows that mass transport model is sensitive to dispersivity values. Table 6 gives the calibrated
parameters of the contaminant transport model, and these are within the range reported by Gelhar et al.99.
The overall mean error (ME), mean absolute error (MAE), root mean square error (RMSE), and R-squared
value for groundwater level, and TDS, nitrate, and fluoride contamination are given in Table 7.

Groundwater quality prediction

Contaminant transport modeling has been conducted for three primary constituents: Total Dissolved Sol-
ids (TDS), nitrate (­ NO3−), and fluoride (­ F−), which exhibit elevated concentrations in the Ayad River Basin.
Concurrently, other parameters such as pH (measured as the negative logarithm of hydronium ion concen-
tration, − ­log[H3O+]), electrical conductivity (EC), total hardness as calcium carbonate (TH, ­CaCO3), total
alkalinity as calcium carbonate (TA, C ­ aCO3), calcium ­(Ca2+), magnesium ­(Mg2+), sodium (­ Na+), potassium
­(K+), iron ­(Fe2+), carbonate hardness ­(CO3−), bicarbonate ­(HCO3−), chloride ­(Cl−), and sulfate ­(SO42−) exhibit
relatively normal distribution. The presence of high TDS, nitrate, and fluoride concentrations in groundwater
within the Ayad River Basin raises concerns due to their potential long-term adverse effects on human health if
not adequately addressed. The developed model is employed to predict the travel distance of each of these three
contaminants over a 5-year period. Alarming zones are identified in areas where contaminant concentrations

Figure 10.  Calibration results of contaminant transport model (simulated vs. observed).

Calibrated parameters reported by Gelhar et al.99 Calibrated parameters of this study

Contamination Hydraulic Horizontal Vertical Diffusion
Aquifer material type conductivity (m/s) Effective porosity Dispersivity Dispersion (m) dispersivity dispersivity coefficient ­(m2/d)
TDS 6.97 × ­10−5 0.33 30.5/9.11100 0.53 29.31 10.12 0.057
Unconfined −5
Nitrate 9.55 × ­10 0.42 01.6/0.76101 0.52 01.42 00.74 0.048
aquifer
Fluoride 5.10 × ­10−5 0.26 10.0/2.02102 0.49 09.95 01.06 0.049

Table 6.  Calibrated parameters of contaminant transport model.

Items Total number of wells Overall mean error (ME) Mean absolute error (MAE) Root mean square error (RMSE) R-squared value
Groundwater monitoring wells (m) 45 9.32 9.53 12.40 0.989
TDS contamination (mg/l) 8 0.83% 1.30% 1.62% 0.991
Nitrate contamination (mg/l) 8 0.60% 1.89% 2.28% 0.993
Fluoride contamination (mg/l) 8 0.71% 1.38% 1.46& 0.957

Table 7.  Overall mean error (ME), mean absolute error (MAE), root mean square error (RMSE), and
R-squared value for groundwater level, and TDS, nitrate, and fluoride contamination.

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surpass established standard limits. The permissible limits are defined in accordance with the guidelines set
forth by the ­WHO93.
The execution of the prediction model was carried out without accounting for water abstraction through
pumping activities. This baseline run serves the purpose of validating the quasi-steady state assumption con-
cerning the initial distribution of Total Dissolved Solids (TDS), nitrate, and fluoride. The rationale behind this
validation lies in assessing whether the TDS, nitrate, and fluoride distribution, established under quasi-steady
state conditions, would remain relatively unchanged over an extended simulation period in the absence of
pumping-induced disturbances. The baseline run provides insights into the displacement of TDS, nitrate, and
fluoride resulting from natural water movement, allowing an evaluation of the assumption that the background
water movement is insignificantly small compared to the TDS, nitrate, and fluoride movement induced by water
production activities. This assumption neglects the effect of background movement, considering it to be negligible
in comparison to the impact of TDS, nitrate, and fluoride movement attributed to water extraction. To ascertain
the validity of this assumption, the prediction model was executed under natural, undisturbed conditions, ena-
bling the observation and analysis of the background movement of TDS, nitrate, and fluoride within the system.

Total dissolved solids (TDS)

The contaminant transport model specifically targeting total dissolved solids (TDS) underwent a phased develop-
ment, initially being executed for multiple time periods. Subsequently, a decision was made to limit the model’s
simulation to a duration of 5 years. The refined model was then executed for the designated 5-year period. Post-
simulation, the cross-sectional data for each groundwater monitoring well (observation well) was meticulously
extracted, which is presented in Fig. 11. This process ensures a focused examination of the temporal and spatial
distribution of TDS within the groundwater system, providing valuable insights into the contaminant’s behavior
and impact over the specified time frame.
Upon comprehensive analysis of well locations within the Ayad River Basin, notable variations in the 500 mg/l
total dissolved solids (TDS) feature emerge. Specifically, at Bhoyana and Kanpur, the feature extends up to 320 m
from the observation well. This substantial extension could be attributed to diverse sub-surface lithological
characteristics, hydraulic conductivity variations, and porosity dynamics. In contrast, other locations such as
Srimali ki Karia, Undri, Sisama, Ramgiri, and Savina exhibit a comparatively shorter reach of the 500 mg/l TDS
feature, extending up to 200 m from the observation well. Notably, at Hariyab, the same feature reaches only
140 m from the observation well.
Considering the permissible limit set at 1000 mg/l, it is observed that TDS levels increase significantly in the
eastward direction at all locations. The distinct patterns in TDS distribution underscore the influence of local
hydrogeological factors and emphasize the need for targeted interventions to curb the rapid increase in TDS
levels, particularly in the eastern region of the study area. This detailed assessment provides valuable insights for
implementing strategic measures to mitigate and manage TDS contamination effectively.

Nitrate
The nitrate contaminant transport model has been executed, mirroring the approach applied to the total dis-
solved solids (TDS) contaminant transport model, spanning a 5-year period. Analysis of the forecasted data
reveals compelling patterns when considering the permissible limit of 50 mg/l for nitrate. Noteworthy obser-
vations include the 50 mg/l features extending approximately 340 m from the observation well in Srimali Ka
Karia, Ramgiri, Savina, and Hariyab. In Bhoyana, the same feature reaches 240 m from the observation well,
while in Undri, Sisarma, and Kanpur, the feature extends up to 500 m (Fig. 12). Although no explicit correlation
with subsurface lithology is evident in the features pattern in all observation wells, a discernible influence of
weathered/fractured rocks, characterized by varying hydraulic conductivity and porosity, is noted. The nitrate
contaminants in all groundwater monitoring wells (observation wells) exhibit an eastward movement, aligning
with the direction of groundwater flow.
Upon analyzing the land use, temperature, and rainfall dynamics within the Ayad River Basin, a discernible
positive correlation emerges between the percentage of cropland in a specific area and the concentration of nitrate
in groundwater. Notably, environmental factors, including temperature and precipitation, play pivotal roles as
co-factors in this relationship. Higher average temperatures exhibit an inversely proportional relationship with
nitrate contamination in groundwater, a phenomenon potentially attributed to increased evapotranspiration
processes. Concurrently, increased average precipitation serves to dilute nitrates within the soil, consequently
leading to a reduction in groundwater nitrate concentration. These findings underscore the multifaceted inter-
play between land use, climatic elements, and groundwater quality, offering valuable insights into the complex
dynamics of nitrate contamination in the study area. The primary driver of nitrate contamination in the region
is identified as the excessive use of chemical fertilizers. A crucial recommendation emerges to curtail this source
of contamination, advocating for the adoption of natural (organic) fertilizers as a more sustainable alternative.
This strategic shift aligns with the broader objective of mitigating nitrate contamination in the study area.

Fluoride
The fluoride contaminant transport model underwent a simulation analogous to the TDS and nitrate contami-
nant transport models, spanning a 5-year period. Despite the permissible limit for fluoride contaminants in
all groundwater monitoring wells (observation wells) being within the acceptable range of 4 mg/l93, there has
been limited spatial movement observed. Over the 5-year modeling period, fluoride contaminant (4 mg/l) has
extended up to 20 m from the observation wells, with a discernible eastward trend mirroring the groundwater
flow (Fig. 13). The presence of fluoride in groundwater stems from the weathering and leaching of fluoride-
bearing minerals within rocks and sediments.

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Figure 11.  Contaminant transport model result for TDS (travel distance 5 years).

Ingesting fluoride in modest amounts (< 0.5 mg/L) offers dental health benefits by reducing dental caries.
However, higher concentrations (> 4 mg/L) may lead to fluorosis. While fluoride levels are currently low in Ayad
River Basin, practical strategies should be developed to ensure the provision of fluoride-safe drinking water to
rural communities in the region. This emphasizes the need for ongoing monitoring and mitigation efforts to
safeguard public health in the face of potential fluctuations in fluoride concentrations.

Sensitivity analysis
Conducting a global sensitivity analysis necessitates the exploration of parameters at various levels, typically
involving three distinct levels within the parameter space. Various strategies exist to achieve this objective, rang-
ing from the manipulation of individual parameter values, as seen in the one-at-a-time (OAT) test plan, to the
execution of extensive sets of random parameter values through Monte-Carlo Simulations. These methodologies
differ in terms of numerical complexity, the labour-intensive nature of model establishment, and their effective-
ness in discerning the sensitivity of parameters and their ­combinations103.
The study employs the fractional factorial test design (FFD) ­method104. In this experimental design, all
parameters are tested at three levels: base case, lower level, and upper level. This ensures that any primary effects

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Figure 12.  Contaminant transport model result for nitrate (travel distance 5 years).

of individual parameters remain unconfounded by combination effects of order two. A total of 27 scenarios are
necessary to execute the test plan fully. For each of the 27 parameter sets outlined in the test plan, both a steady-
state model (configured identically to the calibration model) and a contaminant transport model (configured
similarly to the water quality assessment model) are generated.
Initially, the steady-state model is executed, providing a hydraulic head distribution for assessing the model-
to-measurement misfit compared to the calibrated base case. Scenarios with unacceptably large residuals, indicat-
ing inconsistency with observed field data, are excluded from the sensitivity study. For scenarios demonstrating
satisfactory calibration quality, the predictive run is conducted, utilizing the results of their respective steady-state
models as initial hydraulic head conditions. As the test plan favors extreme parameter values, some sets may
potentially strain the model beyond stability limits. Therefore, model scenarios undergo testing for numerical
performance, and transient runs exhibiting unstable behavior are eliminated from the study.
A series of steady-state scenarios were formulated and executed, with resulting water level distributions
exported and compared to the primary calibration target. Each model’s calibration quality was classified based
on the model-to-measurement misfit: (i) very good (residual generally less than 0.5 m), (ii) good (most residual
around 1 m or below), (iii) okay (most residual around 2 m or below), (iv) acceptable (most residual around 3 m

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Figure 13.  Contaminant transport model result for fluoride (travel distance 5 years).

or below), (iv) moderate (most residual around 5 m or below), and (v) unacceptable (most residual exceeding
5 m). Table 8 details the classification for each model run, guiding the rejection or acceptance decision.

Conclusion
A numerical model based on the groundwater modelling software FEFLOW has been developed with the pur-
pose of estimating the expected water quality in the Ayad River Basin, and prediction the affected area over the
next 5 years. This model meticulously evaluates the concentrations of total dissolved solutes (TDS), nitrate, and
fluoride, crucial for irrigation and domestic water supply in the Ayad River Basin. The established threshold
concentrations stand at 2000 mg/l for TDS, 50 mg/l for nitrate, and 4 mg/l for fluoride. Calibration of the model
involved a comprehensive approach, relying on average steady-state water levels and incorporating prior knowl-
edge of expected parameter values derived from aquifer test evaluations. Additionally, a thorough sensitivity
analysis was executed to estimate the anticipated variations in model results due to inherent uncertainties associ-
ated with parameter values. This analytical process aimed to pinpoint the influential parameters contributing to
the observed variations, enhancing the model’s reliability and predictive capabilities.

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Model-to-measurement fit Model-to-measurement fit

Wells in Ayad River Wells in Ayad River
Scenario Basin Raw water supply Decision Scenario Basin Raw water supply Decision
1 Okay (+) Acceptable (+) Accepted 15 Okay (+) Moderate (+) Accepted
2 Okay (+) Acceptable (+) Accepted 16 Moderate (+) Inacceptable (+) Rejected
3 Good (−) Good (+) Accepted 17 Moderate (+) Inacceptable (+) Rejected
4 Acceptable (+) Okay (+) Accepted 18 Very good (0) Good (+) Accepted
5 Inacceptable (+) Inacceptable (+) Rejected 19 Moderate (−) Moderate (−) Accepted
6 Good (+) Okay (+) Accepted 20 Okay (−) Acceptable (−) Accepted
7 Moderate (−) Acceptable (−) Accepted 21 Good (−) Good (+) Accepted
8 Okay (−) Okay (+) Accepted 22 Okay (−) Okay (−) Accepted
9 Good (−) Okay (+) Accepted 23 Moderate (−) Moderate (−) Accepted
10 Good (−) Good (0) Accepted 24 Moderate (−) Moderate (−) Accepted
11 Good (+) Inacceptable (+) Rejected 25 Moderate ( ) Moderate ( −) Accepted
12 Acceptable (−) Good (−) Accepted 26 Good (−) Good (−) Accepted
13 Good (−) Okay (+) Accepted 27 Acceptable (−) Acceptable (−) Accepted
14 Good (−) Okay (+) Accepted Scenario source: ­ESH104

Table 8.  Model-to-measurement fit of sensitivity scenarios. Significant values are in bold.

The calibrated steady-state model and contaminant transport model exhibit an impressive accuracy exceed-
ing 95%. According to the contaminant prediction model, TDS levels demonstrate a substantial increase in the
eastward direction across all locations. These discernible patterns in TDS distribution underscore the localized
hydrogeological influences, emphasizing the necessity for targeted interventions to mitigate the rapid escalation
of TDS levels, particularly in the eastern region of the study area. High levels of total dissolved solids (TDS),
nitrate, and fluoride contamination are prominently observed in the eastern and southeastern region of the
Ayad River Basin. This phenomenon can be attributed to the presence of two waste disposal sites, namely Titadi
and Baleecha. Titadi, a landfill in operation for four decades until its closure in 2010, still exhibits residual
waste covering an area of 32,000 ­m2. Concurrently, the initiation of a new dumping ground at Baleecha by the
Udaipur Municipal Corporation (UMC) post-2010 has contributed to the exacerbation of contamination in the
specified regions. Upon scrutinizing land use, temperature, and rainfall dynamics within the Ayad River Basin,
a notable positive correlation emerges between the percentage of cropland in a specific area and the concentra-
tion of nitrate in groundwater. The primary driver of nitrate contamination is attributed to the excessive use of
chemical fertilizers. A critical recommendation advocates curbing this contamination source by transitioning
to natural (organic) fertilizers as a more sustainable alternative. While fluoride levels are currently low in the
Ayad River Basin, practical strategies need development to ensure the provision of fluoride-safe drinking water
to rural communities in the region. This underscores the imperative for ongoing monitoring and mitigation
efforts to safeguard public health in anticipation of potential fluctuations in fluoride concentrations (Table 8).
The sensitivity analysis, conducted through the fractional factorial test design (FFD) method, encompassed
a total of 27 model-to-measurement fit scenarios. Out of these, 23 scenarios received acceptance, signifying that
water can be used for irrigation purposes. However, treatment is deemed necessary before considering the supply
for drinking purposes. This comprehensive analysis and decision-making framework contribute to informed
water management strategies.

Scope of future work

Some idea for groundwater quality analysis that has not been widely explored is the use of artificial intelligence
(AI) techniques in combination with groundwater quality modelling using FEFLOW model.

• Sensor network deployment: should be set up a network of chemical sensors specifically designed to detect
various contaminants in groundwater, such as heavy metals, nitrates, TDS, fluoride, pesticides, or organic
pollutants. These sensors should be connected to FEFLOW model through MIKE OPERATIONS Web that
can collect and transmit real-time data to web. FEFLOW model should be run automatic every day at a
particular time and should be display the predictive modeling result on the MIKE OPERATIONS Web.
• Real-time monitoring and alerts: should be implemented a real-time monitoring system that continuously
analyzes the incoming data from the sensor network, and model prediction result. If the system detects any
sudden changes or anomalies in groundwater quality beyond specified thresholds, it should generate alerts
to notify relevant stakeholders, such as water resource management authorities or local communities.
• Mobile application: should be developed a user-friendly mobile application that allows individuals, such as
farmers or residents in affected areas, to access groundwater quality information in real-time. The applica-
tion can provide personalized recommendations for water usage, awareness about potential health risks, and
suggestions for alternative water sources if contamination is detected.

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Data availability
The datasets used and analysed during the current study available from the corresponding author on reasonable
request.

Received: 19 February 2024; Accepted: 15 July 2024

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Acknowledgements
Author is grateful to Managing Director, DHI (India) Water & Environment Pvt Ltd, New Delhi. India for pro-
viding the necessary facilities to carry out this work.

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Funding
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Competing interests
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