An Integrated Approach for Groundwater Potential Prediction Using Multi-Criteria and Heuristic Methods

Abstract

This research focuses on groundwater mapping for the Çumra and Beyşehir Basins in Konya, a semi-arid region in Turkey that plays a crucial role in agriculture and the food industry. Geographic information systems (GIS), the analytical hierarchical process (AHP), and the multi-population-based differential evolution algorithm (MDE) were combined to identify potential groundwater zones. Since direct data on groundwater presence are costly to obtain, thematic maps created from groundwater conditioning factors (such as aquifer, slope, permeability, alluvial soil, soil quality, lithology, precipitation, temperature, salinity, and stone density) can be used to estimate groundwater potential. In this study, these factors were assigned weights using the AHP technique in Model 1 and the MDE technique in Model 2. The TOPSIS (technique for order preference by similarity to ideal solution) method was then employed to simulate groundwater potential, using weights from both techniques. The performance metrics of both models were as follows: Model 1 (RMSE: 114.219, MSE: 13,046.091, and MAE: 99.663) and Model 2 (RMSE: 114.209, MSE: 13,043.785, and MAE: 99.652). The proposed method addresses issues of consistency and bias that might arise from relying on expert opinions through the use of heuristic techniques. Moreover, this approach, which does not require direct data on groundwater availability, enables the creation of accurate predictions while overcoming the challenges of obtaining expensive data in underdeveloped and developing countries. It provides a scientifically sound way to identify and conserve water resources, reducing drilling and other related costs in watershed management and planning.

1. Introduction

Water is considered to be a fundamental resource for sustainable development as well as vital for living things [1,2], where the most utilized water source in the world is groundwater [3].

Groundwater is defined as water in a saturated zone that fills rock and pore spaces [4,5]. Groundwater constitutes approximately 0.6–0.8% of the total water resources worldwide, representing a significant portion of freshwater availability [2,6,7,8]. However, groundwater is more valuable than surface water due to its widespread distribution, low sensitivity, constant chemical composition, constant temperature, and better quality [9,10,11]. Due to these properties, under-groundwater becomes an important asset for environmental sustainability and economic growth in arid and semi-arid regions [12].

Mapping the spatial distribution of groundwater potential is very important for the sustainable, cost-efficient, and systematic management of groundwater resources [3,5,10,13]. Traditional methods, such as drilling, geological, geophysical, and hydrogeological methods are widely used to determine the spatial potential of groundwater [14]. However, these methods are time-consuming, and expensive, especially for large areas, requiring qualified manpower and advanced tools [4,15]. Nowadays, remote sensing, geographic information systems (GIS), statistical methods, multi-criteria decision-making techniques (MCDM), heuristic algorithms, machine learning techniques, and deep learning techniques are used to model groundwater potential and achieve high prediction performances [3,15,16,17,18]. These advanced techniques offer practical and convenient solutions in terms of cost and time.

Mapping groundwater potential is a complex decision-making process that requires consideration of various thematic factors due to the interdisciplinary nature of water-related problems [13]. MCDM and heuristic methods are frequently used to optimize the weights and improve the performance of modeling of these criteria that affect groundwater potential [4,5,19,20,21,22,23,24]. These approaches are important in improving the prediction accuracy by weighing the criteria for groundwater distribution mapping.

In this study, it is aimed to map the groundwater potential of the Beyşehir and Çumra sub-basins in the Konya Closed Basin, which is under the influence of drought in Turkey, by using heuristic methods integrated with MCDM techniques. In mapping, it is aimed to use criteria that are important for the existence of groundwater potential but do not provide information directly on the existence of groundwater. The selection of the criteria will be based on previous studies conducted in this field resulting from a review of the literature. The approach chosen is to use thematic maps built on the weighted criteria integrated with MCDM to accomplish developing two distribution models. In Model 1, the criteria are weighted with the analytical hierarchical process (AHP) technique, and a groundwater availability ranking is created with TOPSIS, thus, the groundwater potential distribution is achieved. In Model 2, the criteria are weighted with the multi-population-based differential evolution algorithm (MDE) technique, and a water availability ranking is created with TOPSIS. The accuracy of the model results will be tested by comparing them with the groundwater distribution map produced from the data for the last five years (2019–2023), containing the groundwater-level measurements obtained from existing wells. By using heuristic techniques, the suggested methodology would enhance the consistency of expert opinion-based methodologies. This will provide a scientific method for groundwater discovery and eliminate the requirement for costly data in developing nations for the identification and management of water assets.

To address two fundamental challenges in groundwater potential mapping, we adopt a hybrid methodology integrating AHP-TOPSIS and MDE-TOPSIS. First, the AHP-TOPSIS framework leverages structured expert judgments to assign criterion weights in contexts where direct hydrological data are limited, thereby ensuring that essential qualitative insights are systematically incorporated. Second, the MDE-TOPSIS approach utilizes observed well data to automatically calibrate these weights through heuristic optimization, which minimizes human bias and enhances objectivity. This dual strategy not only reconciles the need for expert input with data-driven precision but also provides a robust framework for reliable groundwater mapping in data-scarce environments.

Literature Review

The studies on the determination of the potential zones and mapping of the distribution of groundwater are summarized in

Table 1. Studies on mapping of groundwater potential zones.

Reference	Criteria	Method	Study Area
[13]	Groundwater productivity and hydrogeological factors, such as land cover, topology, geology, groundwater table distribution, and groundwater recharge	GIS	Pohang, Korea
[25]	Hydrogeological data	It compares the interpolation performance of kriging, universal kriging, and Delaunay triangulation with IDW and minimum curvature (MC) deterministic methods	Mires Basin of Mesara Valley in Crete (Greece)
[26]	Lithology, lineament density, geomorphology, slope, drainage density, rainfall, and land use/cover	GIS, remote sensing, and multi-criteria decision-making techniques	Raya Valley in northern Ethiopia
[4]	Slope degree, slope aspect, altitude plan curvature, topographic wetness index (TWI), terrain roughness index (TRI), distance from fault, distance from river, land use/land cover, rainfall soil order, geology (unit)	Neuro-fuzzy inference system (ANFIS), invasive weed optimization (IWO), differential evolution, (DE), firefly algorithm (FA), particle swarm optimization (PSO), and bee algorithm (BA)	Koohdasht-Nourabad plain, Lorestan province, Iran
[5]	Slope direction, altitude, slope angle, plan curvature, profile curvature, curvature, sediment transport index, stream power index, topographic wetness index, distance to roads, distance to rivers, rainfall, lithology, soil as input variables, Landsat normalized difference vegetation index (NDVI), and land use/land cover	Teaching, learning-based optimization, and two new hybrid data-mining techniques, including adaptive biogeography fused with biogeography (ANFIS)	Zhangjiamao in China
[10]	Catchment area, convergence index, convexity, diurnal anisotropic heating, flow path, slope angle, slope height, topographic position index, terrain ruggedness index, slope length factor, mass balance index, texture, valley depth, land cover, and geology	Comparison of the predictive capabilities of support vector regression (SVR) and convolutional neural networks (CNNs) in groundwater potential mapping	South Korea, Damyang area
[15]	Elevation, slope, curvature, aspect, drainage density, fault density, distance from the stream, distance from fault, terrain surface texture (TST), (TRI), height above nearest drainage (HAND), rainfall, lithology, and land use	An approach that combines the implementation of four scenarios, each involving ANFIS with six machine learning models	Lake Urmia Basin in northwestern Iran
[16]	Elevation, TWI, slope, aspect, soil clay, soil electrical conductivity (SEC), groundwater EC (GEC)	GIS-based statistical mapping	Iran
[27]	Water table elevation measurements and soil moisture at different depths (ERA5 reanalysis dataset)	Proposed method for simulating water table elevation in shallow unconfined aquifers using soil moisture time series and piezometer measurements	Umbria region of Italy
[28]	Rainfall, land use/land cover, drainage density, lineament density, slope, geology, soil, geomorphology	Artificial neural networks, analytical hierarchy process, GIS	Abay, Ethiopia, Fincha Basin
[29]	Aquifer	A simulation–optimization hybrid model was developed. The model uses SVM to predict groundwater levels and the particle swarm optimization algorithm and Bayesian network to optimize its parameters.	Zanjan aquifer in Iran
[11]	Slope, elevation, curvature, landforms, geology, distance to faults, land type, soils, precipitation, evaporation, TWI, stream power index (SPI), distance to rivers, NDVI, and distance to residential area.	Machine learning, ensemble learning, deep learning, and automated machine learning	Hubei Province of China
[3]	Elevation, aspect, slope, plan curvature, profile curvature, distance from the fault, distance from the road, distance from the river, drainage density, land use, lithology, soil, SPI, TWI, annual precipitation, precipitation of coldest month, precipitation of coldest season, precipitation of wettest month.	Multivariate adaptive regression splines algorithm and support vector regression machine learning models were used. Comparison of prediction capabilities using random search and Bayesian optimization hyperparameter algorithm to optimize the parameters of the SVM model	Markazi Province of Iran
This Study	Aquifer, slope, permeability alluvial soils, soil quality lithology, temperature and precipitation salinity, stone density	GIS, AHP, TOPSIS, and heuristic methods	Beyşehir and Çumra sub-basins of Konya Province, Turkey

with the methods and criteria used.

In many previous groundwater mapping studies, the selection of criteria typically includes parameters that directly express water presence (e.g., stream power index, plan curvature, distance to rivers, lineament, groundwater electrical conductivity, etc.). In contrast, our study pioneers an approach in which the distribution of groundwater potential is modeled without using any direct water-related data. Instead, we exclusively employ indirect criteria, such as aquifer characteristics, slope, permeability, alluvial soils, soil quality, lithology, precipitation, temperature, salinity, and stone density, to infer groundwater potential. This innovative strategy is particularly valuable for regions where direct water data are scarce or prohibitively expensive to obtain, making it a cost-effective solution for data-limited environments.

Moreover, our study contributes a comparative analysis of two different methodological frameworks for groundwater mapping. Model 1 uses the AHP with TOPSIS, while Model 2 integrates a heuristic optimization technique MDE with TOPSIS to automatically derive criterion weights. By contrasting these two approaches, we not only validate the effectiveness of our indirect data strategy but also demonstrate that an objective, algorithmic method can achieve predictive accuracy comparable to that of expert-based evaluations. This dual-method comparison provides new insights into how automated heuristic techniques can supplement or even improve traditional expert judgments in multi-criteria decision-making for groundwater exploration.

Thus, the innovation in our study lies in both the unconventional use of solely indirect indicators for groundwater potential mapping and the systematic evaluation of expert-based versus heuristic methods. This integrated approach offers a novel, reproducible, and economically viable alternative for groundwater assessment, especially in underdeveloped regions where direct water-related data are limited.

The AHP technique used with Model 1 is realized by assigning the weights calculated based on expert opinions to the criteria. However, weights may vary depending on the knowledge and experience of the experts, and different experts may assign different weights to the same parameters. Furthermore, experts’ biases or conflicts of interest may influence weight assignments. This may have an impact on the objectivity, consistency, impartiality, and reliability of the method. The weights derived from the literature review may also vary depending on the studies included and the methodologies used. Different studies may affect the generalizability and validity of the method by assigning different weights to the same parameters. The heuristic optimization methods used with Model 2 apply an objective function to automatically calculate the weights and, therefore, can eliminate the consistency and objectivity issues of weight values based on expert opinion or literature research. These methods can be used in the TOPSIS method to calculate weights in a more objective, consistent, and efficient way, making it a more accurate and useful tool for groundwater potential estimation. In this context, this study will diverge from previous research in the field by utilizing heuristic approaches to enhance expert opinion-based MCDM procedures.

2. Study Area

Beyşehir and Çumra sub-basins, which are sub-basins of Konya Basin, were determined as the application area (Figure 1). One of the few closed basins in the world, Konya Basin does not discharge its waters into the sea. The feature of being a closed basin is that it is surrounded by volcanic mountainous areas up to 3534 m and the limestone feature that forms the water retention basin. The climate in the area is typically continental, with hot, dry summers and cold winters, which greatly influences the water balance in the region. Hydrologically, the basin is primarily fed by rivers and groundwater sourced from the Taurus Mountains to the south [1]. These water resources play a crucial role in sustaining the ecosystem and meeting the agricultural demands of the region. The hydrogeological characteristics of the area are defined by the presence of significant groundwater reserves that are essential for irrigation, especially during dry periods. The groundwater is replenished through rainfall and surface water infiltration, contributing to the overall water supply in the basin.

The geological map and digital elevation model of the sub-basins are shown in Figure 2. The alluvium, clay, sand, gravel, volcanic, and limestone layers that affect both the water retention and groundwater flow of the sub-basins are shown. At the same time, a digital elevation model has been added, which is effective in understanding the hydrogeological dynamics in the field and effectively managing the water resources in the region. In general, it can be stated that the slope for the region is low, and the alluvial structure suitable for water retention for groundwater is predominant.

In the Beyşehir sub-basin, it is very important to take special measures for the groundwater, which has decreased in recent years due to the effect of agricultural irrigation in the basin, and to protect the existence and quality of water resources for this region with high agricultural quality. In the Çumra sub-basin, it is important to protect against the increasing loss of groundwater increasing sinkholes, and the threat of desertification that has started intensively in certain regions. Precise mapping of the groundwater distribution of the intensively farmed basin under these two threats will be provided.

3. Materials and Methods

Within the scope of the study, our objective was to model the distribution of groundwater, defined as the spatial pattern, variability, and capacity of groundwater storage across the study area, using expert opinion and heuristic methods, even in the absence of direct groundwater data. The methodological approach of the study is presented in Figure 3.

In the study, two models were created for the potential distribution of groundwater:

• In Model 1, the groundwater conditioning factors were weighted with the AHP technique, which is one of the expert opinion-based MCDM techniques, and priority ranking was created using the TOPSIS technique.
• In Model 2, the groundwater conditioning factors were weighted with the MDE technique, which is one of the heuristic techniques, and priority ranking was created using the TOPSIS technique.
• The accuracy of Model 1 and Model 2 results was tested by comparing them with the groundwater distribution map produced from data obtained by measuring groundwater levels in drilled wells for the last five years (2019–2023).

3.1. Dataset Description

Within the scope of the study, our objective was to model the distribution of groundwater potential using a minimum dataset that comprises a carefully selected set of key parameters indirectly indicating groundwater availability. This minimum dataset included factors such as aquifer properties, slope, permeability, alluvial soils, soil quality, lithology, precipitation, temperature, salinity, and stone density. These variables were chosen because they capture the critical hydrogeological and climatic influences on groundwater potential while avoiding the need for direct groundwater measurements, which are often costly and difficult to obtain.

All factors were derived using data provided by the relevant government institutions, ensuring a standardized and reliable dataset. Official reports from agencies, such as the State Water Affairs and the Meteorological Service, were utilized to generate parameters, such as aquifer, slope, permeability, precipitation, and temperature.

Aquifer (Aq): Aquifers are critical for evaluating groundwater levels and managing water resources since their intrinsic properties directly influence water storage and flow [27,29]. In our study, the aquifer parameter was quantified by considering three key characteristics: aquifer thickness, which indicates the vertical extent of the aquifer and directly correlates with its storage capacity, hydraulic conductivity, which measures the ability of the aquifer material to transmit water and reflects the ease with which groundwater can flow, and storage capacity (or specific yield), which represents the volume of groundwater that the aquifer can store and subsequently release, serving as a crucial indicator of groundwater availability during recharge and discharge cycles. Derived from comprehensive geological surveys and reports provided by the State Water Affairs, these parameters collectively offer a robust measure of an aquifer’s capacity to function as an effective reservoir for groundwater storage and recharge.

Slope (Slp): The optimal slope should be less than 2% so that the groundwater flow rate does not prevent the collection of water [30,31]. The slope is an important indicator in determining where groundwater will be located.

Permeability (Per): The capacity of a rock or soil to transmit liquid and gas. It affects the availability and productivity of groundwater in a geological formation [4].

Alluvial soils (AS): Fine-textured, moist, water-saturated, low permeability, and rich in organic matter. Water retention is high in these soils, and they form an important soil for water retention [30,31].

Soil quality (SQ): It was carried out by analyses taken from surveys and samples for the determination and evaluation of land classes, taking into account erosion damage, wetness, humidity, suitability for plant growth, and climatic factors. As a result of these analyses, soils were classified according to their quality from one to eight. This classification provides an important criterion for the presence of groundwater in the soil.

Lithology (Lit): It acts as a conduit and reservoir for groundwater [4]. Rock properties are important in determining the potential distribution of groundwater in terms of water retention and permeability.

Temperature (Tmp) and precipitation (Pr): These parameters are of great importance among the factors affecting agricultural production [32]. Variability in precipitation amount and precipitation distribution with the climate change, especially in crop production, causes vital deviations in agricultural yield and a decrease in the average annual per capita water amount [33,34]. The spatial distribution of precipitation and temperature is important in determining and monitoring groundwater distribution.

Salinity (Sal): Groundwater salinity raises serious global environmental and health issues, such as deterioration of soil structure and quality, reduction of agricultural production and biodiversity, water pollution, and human health problems [35,36]. A value of 0 indicates areas where significant salt deposits are absent, while a value of 1 denotes regions where salt domes or salt-bearing sediments are present, which could potentially impact groundwater quality. Regions with high salinity are eliminated and not included in the mapping due to the negative effects they will have on groundwater in terms of drinking water or agricultural use.

Stone density (SD): Stone effect and stone density (SD). While directing the flow of groundwater at the surface, it also creates a suitable area for its collection [37].

3.2. Dataset Collection

The existence of data inventory for the criteria was obtained from institutions within the basin.

Table 2. Resources for the criteria and sub-criteria.

Study Area	Criteria and Sub-Criteria	Production of Maps	Resources
Beysehir and Cumra sub-basins	Aquifer	The map is produced by interpolation according to the aquifer-specific productivity values obtained from the reports provided by State Water Affairs.	State Water Affairs
	Slope	Slope analysis is performed and a map is produced by classifying it according to a 2% slope change.	Minister of Environment, Urbanisation, and Climate Change
	Permeability	Permeability is scored by experts according to the structure of the ground and the suitability of water availability. The map is produced according to this scoring.	State Water Affairs
	Alluvial soils	The availability of groundwater increases depending on the thickness of the alluvium. The map is produced by interpolating the alluvial thicknesses from the reports provided by the Minister of Environment, Urbanisation, and Climate Change	Minister of Environment, Urbanisation, and Climate Change
	Soil Quality	Soil classes are scored by experts according to their suitability for groundwater presence. The map is produced according to this scoring.	State Water Affairs
	Lithology	There are 16 lithology layers in the studied basin area. Each lithology layer is scored by experts according to its suitability for groundwater presence. The map is produced according to this scoring.	Mineral Research and Exploration General Directorate
	Precipitation	A rainfall map is produced by interpolating the cumulative sum of rainfall in the last five years (2019–2023).	Meteorological Service
	Temperature	A temperature map is produced by interpolating the cumulative sum of the temperature in the last five years (2019–2023).	Meteorological Service
	Salinity	The map is produced by eliminating salt domes and sediment areas.	Minister of Environment, Urbanisation, and Climate Change
	Stone Density	Stone impact and stone density are scored by experts according to their suitability for groundwater presence. The map is produced according to this scoring.	State Water Affairs

shows the criteria for which data inventory was needed, map production techniques, and the sources provided.

In the literature, interpolation methods are frequently used in QGIS 3.42 software for groundwater-level mapping [25,38]. Common geo-reference system spatial analysis of the thematic layers for the 10 criteria determined for the study area was carried out using GIS software. All maps were evaluated in grayscale format and the datum used is WGS84 and the coordinate system is geographic (Figure 4).

3.3. AHP Method

The AHP technique was used to estimate the weights of the mapping criteria for groundwater potential distribution based on expert opinion and the literature. The distribution of groundwater potential using the AHP approach has been the subject of several studies published in the literature [20,21,39,40].

Developed by Saaty [41], the AHP method is used to systematically identify the importance of multi-parameters by examining pairwise relationships and their influence on the focused problem [42]. Despite its reliance on expert opinion, the AHP process maintains objectivity by employing a step-by-step methodology. The methodology starts with the problem definition step, which includes the selection of criteria that affect the decision-making process for a specific case. After the criteria and the alternatives to be selected based on those criteria are determined, a decision-making hierarchy is created, as shown in Figure 5.

The weights of the criteria are first determined using the steps involved in the AHP approach, as shown in Figure 5, and the priority of the alternatives is then determined using the same steps. In this study, each map pixel was treated as an alternative. Finally, the overall ranking is determined by multiplying the weights of the criteria by the scores of the alternatives. The alternative regarded as the closest to the right decision is the one with the most value. However, when there are plenty of alternatives, making pairwise comparisons becomes very cumbersome. To overcome this difficulty, the AHP technique is integrated with other multi-criteria decision-making techniques. In this study, as each pixel in the map was regarded as an alternative, the decision-making problem consisted of millions of alternatives, which made it impossible for AHP application. Nevertheless, AHP was still a good option for prioritization of criteria. Therefore, the weights of the criteria were determined using the AHP method, and the alternatives were ranked using the TOPSIS technique. The AHP diagram design for this study is given in Figure 6.

Based on the proposed hierarchy, an evaluation form was developed, providing the decision-maker with a framework for comparing the criteria in pairs, as shown in Figure 7.

Within the scope of the form created in Figure 7, it was ensured that people who have an idea about the subject and are experts in their fields were determined as participants. The number of accessible experts who would provide a 10% consistency rate in multi-criteria decision-making techniques was taken as the basis. As the number of experts increased, the level of reaching the 10% rate for each participant decreased, and 15 people were determined as the appropriate sample size in order to provide this rate. The participants selected as a sample were academicians with academic knowledge on geographic information systems, rural area and regional planning, land management and administration, water and water management, basin planning and agriculture and rural area development on the subject of groundwater, and qualified publications, as well as geological engineers, environmental engineers, urban and regional planning, hydrogeological engineers, and survey engineers who are experts in these sectors. The volunteers selected due to the content of the survey were those who had mastery over the subject or had taken part in the feasibility and survey stages of the underground dam site research process, knew the difficulty of the process, and were qualified to make effective decisions in obtaining results that will provide concrete benefits for the public and society.

A scale of significance values designed in [43] was employed to ascertain which criterion was more important than the others (1: equally important, 3: moderately important, 5: strongly important, 7: very strongly important, and 9: absolutely important).

The answers obtained from the evaluation form were transferred to the comparison matrix, an example of which is given in Figure 6. For example, if the “stone density” and “salinity” criteria were decided to be of equal importance, the column with the value 1 was marked. If the “stone density” criterion was decided to be more important than the “salinity” criterion, the relevant column on the left side of the evaluation form needed to be marked, considering the degree of importance. On the contrary, if the “salinity” criterion was decided to be more important than the “stone density” criterion, the relevant column was marked on the right side of the evaluation form, considering the degree of importance.

After the designed AHP evaluation form was filled out by the participants, the geometric mean of each of the answers given by the participants was calculated using Equation (1), and a group decision evaluation form was obtained:

$$a_{11}=\sqrt[n]{P_1{P}_2{P}_3\dots P_m}$$

(1)

Here, $a_{11}$ is the average value obtained for the first question in the group decision evaluation form, and P₁, P₂, …, and P_m are values given by each participant for the first question, where m is the number of participants. The geometric mean was determined for each question in the same manner, and all geometric means ($a_{ij}$) were transferred to the 10 × 10 decision matrix, as shown in Equation (2):

$$\mathrm{AHP} \mathrm{Decision} \mathrm{matrix}=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1j}\\ {{\displaystyle \frac{1}{a}}}_{12}& a_{22}& \dots & a_{2j}\\ ⋮& ⋮& \ddots & ⋮\\ {{\displaystyle \frac{1}{a}}}_{1j}& {{\displaystyle \frac{1}{a}}}_{2j}& \cdots & a_{ij}\end{array}\right]$$

(2)

The values $a_{ij}$ allocated in the decision matrix were normalized as ($a_{ij}^{\prime }$) using Equation (3), and the mean value for each row in the normalized matrix was calculated using Equation (4) to determine the weight ($w_i$) of each parameter, where n is the number of criteria:

$$a_{ij}^{\prime }={\displaystyle \frac{a_{ij}}{{\sum }_{i=1}^n{a}_{ij}}} , i,j=\mathrm{1,2},\dots ,n$$

(3)

$$w_i=\left({\displaystyle \frac{1}{n}}\right){\displaystyle \sum _{i=1}^n}{a}_{ij }^{\prime }, i,j=\mathrm{1,2}, \dots , n$$

(4)

After obtaining weight, the consistency ratio (CR) given in Equation (5) needed to be calculated to ensure that judgments were consistent:

$$CR={\displaystyle \frac{CI}{RI}}$$

(5)

Here, RI refers to the average random consistency index, which is derived from a random consistency table and represents the average consistency index of randomly generated pairwise comparison matrices. Its value depends on the size (n) of the matrix [44]. RI is essential in the AHP method, as it is used in calculating the consistency ratio (CR), which helps determine whether the pairwise comparisons provided by the decision-maker are consistent. RI was obtained from the average random consistency table given in Table 3 [45]. CI is the consistency index, which was calculated using Equations (6) and (7). Lambda (λ) in the equations is the eigenvalue.

Table 3. Average random consistency.

N	1	2	3	4	5	6	7	8	9	10
RI	0	0	0.58	0.9	1.12	1.24	1.32	1.41	1.45	1.49

Table 3. Average random consistency.

N	1	2	3	4	5	6	7	8	9	10
RI	0	0	0.58	0.9	1.12	1.24	1.32	1.41	1.45	1.49

$$CI= \frac{{\lambda }_{max}-n}{n-1}$$

(6)

$${\lambda }_{max}=\frac{1}{n}\sum _{i=1}^n\frac{{\sum }_{i=1}^n{a}_{ij }{w}_{i }}{w_i}$$

(7)

If CR was less than 0.10, the comparison matrix was decided to be consistent. If the consistency value found was greater than 0.10 for each participant, the pairwise comparison matrix was reviewed, and the above steps were repeated after adjustments were made.

3.4. TOPSIS Method

Once weights were calculated with AHP, potential areas with groundwater were prioritized using the TOPSIS technique, which is an abbreviation for “the technique for order of preference by similarity to ideal solution”. TOPSIS is one of the multi-criteria decision-making techniques that consider both the distance to the positive ideal solution and the distance to the negative ideal solution when ranking alternatives [46]. AHP provides a structured way to determine the weights of criteria, while TOPSIS helps in ranking alternatives based on these weighted criteria [47]. This integrated approach enhances the decision-making process for groundwater management.

The TOPSIS technique starts with a matrix where alternatives are listed in rows and criteria are in columns. Each pixel in the map is an alternative location where groundwater may be present. Equation (8) illustrates the matrix that will be formulated if the decision problem includes m alternatives and n criteria:

$$\mathrm{T}\mathrm{O}\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{S} \mathrm{D}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{m}\mathrm{a}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{x}=\left[\begin{array}{ccccc}{a}_{11}& \cdots & a_{1j}& \dots & a_{1n}\\ ⋮& \ddots & \dots & \ddots & ⋮\\ a_{i1}& \ddots & a_{ij}& \ddots & a_{in}\\ ⋮& \ddots & \dots & \ddots & ⋮\\ a_{m1}& \cdots & a_{mj}& \dots & a_{mn}\end{array}\right]$$

(8)

Values in the decision matrix were normalized through the utilization of Equation (9), and a normalized weighted decision matrix given in Equation (10) was produced by multiplying each row with the weight obtained from the utilization of the AHP approach:

$$a_{ij}^{\prime }={\displaystyle \frac{a_{ij}}{ \sqrt{{\sum }_{i=1}^n{a_{ij}}^2}}} , i=\mathrm{1,2},\dots ,m and j=\mathrm{1,2}, \dots , n$$

(9)

$$v_{mn}=\left[\begin{array}{ccccc}{a}_{11}^{\prime }*w_1& \cdots & a_{1j}^{\prime }*w_j& \dots & a_{1n}^{\prime }*w_n\\ ⋮& \ddots & \dots & \ddots & ⋮\\ {a_{i1}^{\prime }*w}_1& \ddots & a_{ij}^{\prime }*w_j& \ddots & a_{in}^{\prime }*w_n\\ ⋮& \ddots & \dots & \ddots & ⋮\\ a_{m1}^{\prime }*w_1& \cdots & a_{mj}^{\prime }*w_j& \dots & a_{mn}^{\prime }*w_n\end{array}\right]$$

(10)

The best alternative and the worst alternative were determined by finding the ideal solution $A^{+}$ and the solution $A^{-}$ that was furthest from the ideal solution. $A^{+}$ and $A^{-}$ were calculated using Equations (11) and (12):

$$A^{+}=\left\{v_1^{+},\dots ,v_n^{+}\right\}=\left\{\left(\underset{i}{\max }{v}_{ij}\left|i∊I\right.\right),\left(\underset{i}{\min }{v}_{ij}\left|i∊I^{\mathrm{\prime }}\right.\right)\right\}$$

(11)

$$A^{-}=\left\{v_1^{-},\dots ,v_n^{-}\right\}=\left\{\left(\underset{i}{\min }{v}_{ij}\left|i∊I\right.\mathrm{\prime }\right),\left(\underset{i}{\max }{v}_{ij}\left|i∊I\mathrm{\prime }\right.\right)\right\}$$

(12)

To prioritize alternatives, the distance of each alternative to the best solution and the worst solution must be calculated. Each alternative distance ($S_i^{+}$) from the ideal solution was calculated using Equation (13), and the distance ($S_i^{-}$) from the worst solution was calculated using Equation (14):

$$S_i^{+}=\sqrt{\left(\sum _{j=1}^n{\left(v_{ij}-v_j^{+}\right)}^2\right)}$$

(13)

$$S_i^{-}=\sqrt{\left(\sum _{j=1}^n{\left(v_{ij}-v_j^{-}\right)}^2\right)}$$

(14)

Finally, the ranking of alternatives was obtained according to the relative closeness values ($C_i^{+}$), which were calculated using Equation (15):

$$C_i^{+}=S_i^{-}/(S_i^{+}+S_i^{-}) , 0<C_i^{+}<1$$

(15)

3.5. Heuristic Algorithms

Heuristic algorithms apply swarm intelligence to optimization problems by mathematically modeling the behavior of individuals interacting with each other and moving toward a common goal, or evolutionary processes, such as natural selection, genetic evolution, and social learning [48]. These methods try to achieve the best result by performing random or directed searches over a given solution space. Commonly used heuristic optimization methods include techniques such as the genetic algorithm (GA) [49], differential evolution algorithm (DE) [50], ant colony optimization (ACO) [51], particle swarm optimization (PSO) [52], and artificial bee colony optimization (ABC) [53].

In this study, the criteria were weighted by the multi-population-based differential evolution algorithm (MDE), and the TOPSIS hybrid technique was used to prioritize and model the groundwater potential distribution. The MDE algorithm was preferred because it does not require any parametric presetting and outperforms many prominent algorithms in the literature [54,55].

Multi-Population-Based Differential Evolution Algorithm (MDE)

The MDE, introduced in [54], is an iterative stochastic global optimization algorithm with a population-based, non-recursive structure. Adaptable to real-valued unimodal and multimodal problems, the MDE operates without an internal parameterization phase with limited or unlimited search capacity. The fact that solution vectors can be developed separately and in parallel is due to the non-recursive nature of the MDE. The characteristic mutation operator of the MDE has elitist, random, and noise components. Of these components, the elitist component increases the unimodal and the random component increases the multimodal problem-solving capability of the MDE. The noise component prevents the end of numerical diversity in the population [54].

Within the framework of discrete mathematics, the workings of the MDE algorithm are detailed using analytical concepts. The elements of the MDE population matrix $\mathcal{A}$ were defined by Equation (16), and the objective (fitness) values of the vectors $\mathcal{A}$_i*, denoted by fit$\mathcal{A}$_i*, were computed using Equation (17):

$${\mathcal{A}}_{i*;j}~U\left(low\left(j\right),up\left(j\right)\right)∍\left[i^{*},j\right]\leftarrow \left[ \left\{\mathrm{1,2},3,...,k,...,3\cdot N\right\} , \left\{1:D\right\} \right]$$

(16)

$$fit{\mathcal{A}}_{i*}=\mathcal{F}\left({\mathcal{A}}_{i*}\right)$$

(17)

Here, N denotes the number of vectors in the population $\mathcal{A}$_i=1:3N, while D indicates the dimensionality of the problem. The low(j) and up(j) denote the lower and upper boundaries of the search space for the j-th variable of the problem F. The MDE randomly selected N vectors from $\mathcal{A}$ to form a subpopulation matrix $\mathcal{B}$. Following the MDE’s iterative evolutionary procedure, the vectors in $\mathcal{B}$ were updated and then placed back into $\mathcal{A}$.

By applying Equation (18), one derives the best vector that secures the global solution along with its associated objective function value:

$$\left[BestVal,Best\right]\leftarrow \left(\mathit{min}(fit{\mathcal{A}}_k),{\mathcal{A}}_k\right)∍\left(k\in i *\right)$$

(18)

The general system equation of the MDE is given in Equation (19):

$$T=\mathcal{B}+map\odot \left(temp+noise-\mathcal{B}\right)$$

(19)

In Equation (19), T stands for trial vectors, map for the crossover control matrix, temp for the transient vectors, and noise for the noise values. The noise in the equation prevents distortion of the numerical entropy in the trial vectors.

The map crossover control matrix was constructed using Equation (20):

$$map=\left|\alpha -{\beta }^{\odot \delta }\right|<0.50∍\left\{\begin{array}{l}{\alpha }_{1:N}~U\{0,1\}\\ {\beta }_{(i=1:N,j=1:D)}~U(0,1)\\ {\delta }_{1:N,1:c}~U\{0,5\}\end{array}\right.$$

(20)

Here, $U\left(0,1\right)$ denotes a uniform distribution in the interval [0, 1], $U\{0,1\}$ refers to a discrete uniform distribution between 0 and 1, and the constant c required to form δ was determined using Equation (21):

$$If\left({\kappa }^{\omega }<0.50\right) then c=1 else c=D |\kappa ~U(0,1);\omega ~U\{0,5\}$$

(21)

Further, $tem{p}_i\left(j\right)$ was calculated using Equation (22) to denote the j-th variable of transient vector i. Here, the r vectors were obtained using Equation (23) and the scale scaling variable was obtained using Equation (24). At the start of the MDE’s iterative computation process, the vectors b_i, where ${ b}_i={\mathcal{A}}_{j_0\left(i\right)}$, were randomly selected from the set $\mathcal{A}$:

$$tem{p}_i\left(j\right)=b_{r\left(1\right)}\left(j\right)+scale\cdot \left(dx-dy\right) ∍ i=\left\{1:N\right\},j=\left\{1:D\right\}$$

(22)

$$r=permute(N,2) ∍ r\ne i,r\left(1\right)\ne r\left(2\right)$$

(23)

$$scale=\left|\kappa -a^b\right|\cdot c^d\leftarrow \kappa , a ~ U\{0,1\} ; b~U\{0,10\} ; c~N(0,1) ; d~U\{0,5\}$$

(24)

$noise$ vectors were calculated as shown in Equation (25):

$$noise=\mathcal{B}\odot {10}^{\mathsf{\varphi }}\odot \left(\left(\left(\kappa \left(N,1\right)-0.50\right)\diamond D\right)\odot Q\right)$$

(25)

Here, the random variables and matrix appearing in Equation (25) are defined as $\varphi ~U\left\{-12,-9\right\} ; \kappa ~U(0,1) ; Q_{1:N,1:D}=1$. The dx and dy values used in Equation (22) were generated using Equations (26) and (27):

$$If \left(\kappa <0.50 \right) then \left(dx=b_{r\left(1\right)}\left(j\right)\right) else \left(dx=Best\left(j\right)\right)$$

(26)

$$If \left(\kappa <0.50 \right) then \left(dy=b_i\left(j\right)\right) else \left(dy=b_{r\left(1\right)}\left(j\right)\right)$$

(27)

The MDE used the vectors $\mathcal{B}=⟨b_{i=1:N}⟩$ to evolve the trial vectors T. Equation (28) was used to keep the parameters T within the search bounds, and the quality of the vectors T, fitT, was calculated using Equation (29):

$$If \left(T_i\left(j\right)<lo{w}_j\right) \left|\right| \left(T_i\left(j\right)>u{p}_j\right) then T_i\left(j\right)~U(lo{w}_j,u{p}_j)$$

(28)

$${fitT}_i=\mathcal{F}\left(T_i\right)$$

(29)

Equation (30) specified the use of fitTrial values for updating $\mathcal{B}$ and fit$\mathcal{B}$ values:

$$If \left({fitT}_i<fi{t}_i\right) then \left[fit{\mathcal{B}}_i,b_i\right]\leftarrow \left[{fitT}_i,T_i\right]$$

(30)

The end of the computational process of an iteration in the MDE involved updating the population and the global solution. This is illustrated in Equations (31) and (32):

$$\left[\mathcal{A}\left(j_0\right),fit\mathcal{A}\left(j_0\right)\right]\leftarrow [\mathcal{B},fit\mathcal{B}]$$

(31)

$$\left[BestVal,Best\right]\leftarrow \left(\mathit{min}(fit{\mathcal{A}}_k),{\mathcal{A}}_k\right)∍\left(k\in i\right)$$

(32)

The working principle of the MDE can be expressed as individuals randomly leaving or being separated from an imaginary herd as a sub-herd for feeding purposes. Individuals, $\mathcal{B}$, who left the herd to feed returned to $\mathcal{A}$ to share their knowledge of more efficient food sources. The best was recalculated at each iteration. Differences in feeding behavior between individuals $\mathcal{B}$ were simulated using a crossover control matrix (map) and a scaling value (scale).

4. Results

4.1. Finding the Weights of the Criteria with AHP

Based on the studies in the literature, 10 criteria were determined for groundwater potential determination: aquifer (Aq), slope (Slp), permeability (Per), alluvial soils (AS), soil quality (SQ), lithology (Lit), precipitation (Pr), temperature (Tmp), salinity (Sal), and stone density (SD).

Participants filled out ten AHP evaluation forms consisting of the selected criteria, and the decision matrix including geometric means for the criteria is given in

Table 4. A decision matrix with geometric means.

	Aq	Slp	Per	AS	SQ	Lit	Pr	Tmp	Sal	SD
Aq	1.00	2.85	1.95	1.38	5.84	3.77	2.62	5.33	6.56	5.84
Slp	0.35	1.00	2.13	1.05	4.68	2.80	2.36	4.44	6.03	5.76
Per	0.51	0.47	1.00	1.05	4.33	2.04	2.04	3.60	4.74	4.16
AS	0.73	0.96	0.96	1.00	4.47	2.47	1.95	4.50	5.16	3.56
SQ	0.17	0.21	0.23	0.22	1.00	1.43	2.16	1.80	3.49	1.94
Lit	0.27	0.36	0.49	0.40	0.70	1.00	1.73	2.81	4.47	2.27
Pr	0.38	0.42	0.49	0.51	0.46	0.58	1.00	3.65	4.35	2.96
Tmp	0.19	0.23	0.28	0.22	0.56	0.36	0.27	1.00	1.65	1.29
Sal	0.15	0.17	0.21	0.19	0.29	0.22	0.23	0.61	1.00	1.04
SD	0.17	0.17	0.24	0.28	0.51	0.44	0.34	0.78	0.96	1.00

and normalized values are given in

Table 5. Normalizer matrix.

	Aq	Slp	Per	AS	SQ	Lit	Pr	Tmp	Sal	SD
Aq	0.26	0.42	0.25	0.22	0.26	0.25	0.18	0.19	0.17	0.20
Slp	0.09	0.15	0.27	0.17	0.20	0.19	0.16	0.16	0.16	0.19
Per	0.13	0.07	0.13	0.17	0.19	0.14	0.14	0.13	0.12	0.14
AS	0.19	0.14	0.12	0.16	0.20	0.16	0.13	0.16	0.13	0.12
SQ	0.04	0.03	0.03	0.04	0.04	0.09	0.15	0.06	0.09	0.07
Lit	0.07	0.05	0.06	0.06	0.03	0.07	0.12	0.10	0.12	0.08
Pr	0.10	0.06	0.06	0.08	0.02	0.04	0.07	0.13	0.11	0.10
Tmp	0.05	0.03	0.03	0.04	0.02	0.02	0.02	0.04	0.04	0.04
Sal	0.04	0.02	0.03	0.03	0.01	0.01	0.02	0.02	0.03	0.03
SD	0.04	0.03	0.03	0.04	0.02	0.03	0.02	0.03	0.03	0.03

.

Weights calculated with the AHP technique are given in

Table 6. AHP weights of selected criteria.

Criterion	Weights
Aquifer	0.237
Slope	0.172
Alluvial Soils	0.151
Permeability	0.134
Precipitation	0.077
Lithology	0.075
Soil Quality	0.064
Temperature	0.034
Stone Density	0.031
Salinity	0.025

. The consistency rate of the decision matrix created for the criteria was calculated as 0.03.

According to the results given in Table 6, “aquifer” (23.7%) was the most important criterion for groundwater potential detection. The priorities of other criteria were as follows: slope (17.2%), alluvial soils (15.1%), permeability (13.4%), precipitation (7.7%), lithology (7.5%), soil quality (6.4%), temperature (3.4%), stone density (3.1%), and salinity (2.5%).

4.2. Finding Weights with Multi-Population-Based Differential Evolution Algorithm (MDE)

Heuristic optimization algorithms are typically used to optimize an objective function (cost function). The objective function represents a quantitative measure of the goal to be optimized. This function evaluates the quality of any particular solution and usually reflects a criterion by which the problem should be improved or optimized. Heuristic optimization algorithms iteratively search for solutions to achieve a given objective by minimizing or maximizing the objective function.

In this study, 10% of the groundwater well levels in the study area, consisting of a total of 2,093,008 pixels, were randomly selected with a uniform distribution for model training. Equation (33) shows the cost function used. The MDE algorithm was run with 20 populations and 250 iterations:

$$\begin{gathered} \mathit{arcmin}{\displaystyle \frac{1}{N}}{\displaystyle {\sum }_{i=1}^N}{{(C}_i^{+}\left(w\right)-D_i)}^2, {\displaystyle {\sum }_{j=1}^n}{w}_j=1 \\ 0\le C_i^{+},D_i\le 1 \end{gathered}$$

(33)

In Equation (33), $C_i^{+}$ represents the relative closeness to the ideal solution calculated according to the heuristically updated weights $w$, and $D_i$ represents the scaled expression of the water level of the groundwater wells in the value range [0, 1].

The final weights calculated with the MDE technique are given in

Table 7. The MDE weights of selected criteria.

Criterion	MDE
Aquifer	0.258
Alluvial Soils	0.164
Slope	0.153
Permeability	0.119
Precipitation	0.084
Soil Quality	0.069
Lithology	0.067
Temperature	0.037
Stone Density	0.027
Salinity	0.022

.

According to the results given in Table 7, “aquifer” (25.7%) was the most important criterion for groundwater potential detection. The priorities of other criteria were as follows: alluvial soils (16.4%), slope (15.3%), permeability (11.9%), precipitation (8.3%), soil quality (6.9%), lithology (6.7%), temperature (3.7%), stone density (2.7%), and salinity (2.2%).

The rankings of the weights obtained with AHP, one of the MCDM methods, based on expert opinion, and the weights obtained with MDE, one of the heuristic algorithms, were compared (Figure 8).

According to Figure 7, when the general ranking was compared, it was determined that the aquifer was the most effective criterion in determining the groundwater potential area in both methods. Permeability, precipitation, and temperature were in the same order in both methods. The weight ranking of slope and alluvium criteria and the weight ranking of lithology and soil class criteria changed in both methods. It can be said that stone density and salinity had the same weight ranking and had the least impact.

As a result of comparison of both methods, it was determined that all the criteria considered formed weights close to each other. The highest difference between the calculated weights was observed in the aquifer layer. Weight differences decreased in permeability, slope, precipitation, and lithology criteria, respectively. Weight differences were equal in soil quality, stone density, and salinity criteria. It can be said that the least weight difference was in the alluvium criterion, and almost the same weights were determined.

The trends of the weights calculated according to both methods are visualized and compared in Figure 9.

According to Figure 9, it can be said that aquifer, slope, alluvium, and permeability criteria were intensely effective in groundwater exploration with the calculated weights. This trend showed that the process can be managed with less data by using certain criteria with high-weighted effects in groundwater exploration. Research on groundwater with less data and low cost is important in discovering groundwater assets to prevent water scarcity in underdeveloped countries.

4.3. Ranking and Validation of Weights with TOPSIS

The TOPSIS technique is a method frequently used in groundwater mapping in recent years [56,57,58,59,60,61]. In this study, the thematic maps related to the criteria determined for groundwater potential were weighted with AHP in Model 1 and MDE in Model 2 and ranked with the TOPSIS technique, and groundwater potential distribution was mapped.

To verify both model results, a groundwater distribution map was produced by measuring the level of water in the well for the last five years (2019–2023). In this case, only data from the wells that have been regularly collected and recorded in the field during the previous five years were used. The cumulative sum of the groundwater, which is the total depth of water measured below the ground surface over a period of time, was calculated using data obtained from 33 wells’ data in the field for the last five years (2019–2023). The calculated values were mapped in a GIS environment. This cumulative sum was used to reflect overall changes in groundwater levels and their potential impact on water resource management. For groundwater-level mapping, the inverse distance weighting (IDW) method, which is among the interpolation methods frequently used in the literature, was used [62,63].

The results of Model 1 and Model 2 were tested for accuracy by comparing them with the groundwater distribution map obtained from well data. Accordingly, the performance metrics of the models are compared in

Table 8. Comparison of model results.

	Model 1	Model 2
	AHP and TOPSIS	MDE and TOPSIS
RMSE	114.219	114.209
MSE	13,046.091	13,043.785
MAE	99.663	99.652

.

The performance metrics in Table 8 were used to evaluate the accuracy of both models. These metrics (such as correlation coefficient, RMSE (root mean squared error), MAE (mean absolute error), or kappa coefficient) show how close the models are to the real data. These metrics were used to evaluate the accuracy of the groundwater distribution predictions of both models.

The RMSE values of both models were very similar, which indicates that the prediction errors of both models were close to each other. The lower the RMSE, the higher the model’s accuracy. Here, the RMSE value of Model 2 was slightly lower, but the difference was quite small.

MSE gives the mean square of the difference between the predicted values and the real values. Again, the difference between Model 1 and Model 2 was very small, and both models had similar levels of error.

MAE gives the mean absolute difference between the predicted values and the real values. We observed that these value were also very similar. A low MAE indicates that the model’s predictions are close to the actual data. As a result, there were very small differences between the performance metrics of both models. Although Model 2 (MDE and TOPSIS) had slightly lower RMSE, MSE, and MAE values, these differences were not very significant. In this case, it can be said that although both models had very similar accuracy levels for groundwater distribution predictions, Model 2 performed slightly better.

Table 8 shows that both Model 1 and Model 2 yielded nearly identical performance. To provide a clearer comparison, percentage differences between the models were calculated. The RMSE values differed by 0.010, corresponding to approximately 0.009%, the MSE values by 2.306 (0.018%), and the MAE values by 0.011 (0.011%). These minimal differences confirmed the high consistency between the predictive performances of both models.

In addition, a Bland–Altman plot was employed to visually assess the level of agreement between the two models (Figure 10). The plot demonstrated that most of the data points fell within the 95% limits of agreement, with a negligible bias. The clustering of the differences around the mean line further supported the conclusion that both models yielded highly similar results.

This close alignment prompted a discussion on expert bias—an inherent risk in the AHP approach. Although AHP relies on subjective expert judgments that can introduce variability, our results indicate that the experts’ assessments were consistent and aligned with the underlying physical processes governing groundwater potential in the study area. This consistency may be attributed to the rigorous selection of experts and the use of a group decision-making process (via geometric means) to mitigate individual biases, or it may reflect the robustness of the chosen criteria (e.g., aquifer, slope, and permeability). Nonetheless, while the similar performance does not entirely eliminate the possibility of expert bias, it underscores the need for further investigation—such as sensitivity analyses—to better understand the conditions under which expert-based methods can approximate the objectivity of heuristic approaches, like MDE-TOPSIS.

The errors associated with the models were found to be nearly identical, demonstrating high performance in predicting groundwater distribution based on the evaluated metrics. In addition, the results of Model 1, Model 2, and the groundwater distribution maps produced with well data for the last five years (2019–2023) were compared (Figure 11).

The maps obtained according to the calculation results of Model 1 and Model 2 were visualized in terms of the locations where groundwater was available and where groundwater availability was decreasing. Accordingly, it is seen that the groundwater distribution map based on well data overlapped on the map at a high rate following the performance metrics in Model 1 and Model 2.

To quantitatively assess the predictive performance of groundwater potential models, the receiver operating characteristic (ROC) curve was employed. In the evaluation of groundwater potential, the ROC curve is widely used as a method to analyze model performance [64,65]. The curve graphically illustrates the trade-off between the true positive rate and the false positive rate across various threshold levels, thereby indicating the model’s ability to discriminate between areas of high and low groundwater potential [66]. A curve closer to the upper-left corner indicates superior classification performance, while the area under the curve (AUC) provides a summary measure of the model’s overall performance. AUC values range from 0.5 (no better than random) to 1.0 (perfect discrimination), with ranges of 0.5–0.6 signifying poor, 0.6–0.7 moderate, 0.7–0.8 good, 0.8–0.9 very good, and above 0.9 excellent discrimination [67].

Figure 12 presents the ROC curves obtained for Model 1 (AHP-TOPSIS) and Model 2 (MDE-TOPSIS), with corresponding AUC values of 0.6244 and 0.6546, respectively. According to commonly accepted thresholds, these AUC values place both models in the “moderate” performance category. Despite the modest gap in performance, both models demonstrated sufficient accuracy to guide groundwater exploration efforts, as evidenced by AUC values exceeding 0.60. In addition, the tight clustering of the ROC curves for the two methods confirmed that the criteria selected for groundwater potential mapping were robust and captured essential hydrological and geological factors. Overall, the results reinforced the robustness of the selected criteria for groundwater potential mapping, while underscoring the value of combining expert knowledge with algorithmic objectivity to enhance model reliability.

5. Discussion

The results obtained should be compared with the literature in terms of the criteria, criteria weight, and methodology used in the study. When the literature is examined, numerous studies have been conducted on determining the importance weights of the criteria affecting groundwater potential using the AHP method [19,21,26,68,69,70,71,72]. The ranking of the criteria weights obtained in this study was compared with findings from the literature. Based on this comparison, the importance weights of the aquifer and alluvial layer criteria in determining the potential areas of groundwater were very close to the study conducted in [71]. Specifically, in both studies, the aquifer and alluvial layer criteria were ranked as the first and fourth most important factors in determining groundwater potential, respectively. The findings of our study are consistent with those of [27], who concluded that shallow aquifers with infiltration as the main mechanism of recharge further emphasize the importance of aquifer dynamics.

In this study, the slope criterion was considered as a geomorphological feature. Accordingly, the weight of the slope criterion determined in the study was in the second rank, similar to the studies in [19,70,72]. In addition, since this study was carried out without a direct criterion for groundwater, different results were obtained from the weight levels of the criteria in the studies in [21,68,69], which calculated the weight levels for the criteria related to the level of humidity.

In the studies in the literature on mapping, groundwater and groundwater-related data directly related to groundwater are often considered in determining the criteria for collecting groundwater and keeping it in a structure suitable for use. In [15], the authors performed groundwater potential modeling using K-folding and state-of-the-art metaheuristic machine learning approaches. Hydrological factors were used in this modeling. Patidar conducted groundwater potential zone mapping using the GIS-based AHP-TOPSIS integrated approach in Ujjain District, India, in 2022 and utilized the land use map, where groundwater data are directly available. The authors of [11] conducted groundwater potential mapping in the Hubei Province of China in 2022 using machine learning, ensemble learning, deep learning, and autoML methods and utilized river network data. The authors of [3] used water data from land use maps to perform groundwater potential mapping using support vector machine optimization based on the Bayesian multi-objective hyperparameter algorithm. The authors of [60] conducted geographic modeling and analysis of groundwater stress-prone areas in the Murshidabad district of India using TOPSIS, VIKOR, and EDAS techniques and used groundwater data. Similarly, it is seen that many studies have modeled groundwater and groundwater-related criteria [12,26,57,73,74]. In this study, unlike the literature, the spatial distribution of groundwater was modeled without any direct data on groundwater. Therefore, this study can be characterized as an original study with its methodological approach to discovering groundwater in underdeveloped regions without direct data on groundwater availability.

In determining the weights of the criteria for mapping, MCDM techniques, machine learning techniques, and heuristic methods are frequently used in the literature [4,5,10,26,28,29,75]. This study differed from the literature by presenting an approach that enables the improvement of MCDM techniques with heuristic methods. The study contributes to the literature by using heuristic methods to improve the non-objective errors of expert opinions obtained by MCDM. In this context, the study presents a unique study that integrates both MCDM and heuristic methods with a hybrid technique that uses less data. The study provides a scientific way to discover traces of groundwater in underdeveloped and developing countries with less data and less drilling costs in meeting the needs for water.

6. Conclusions

In this study, an approach that integrates heuristic methods with expert opinion-based MCDM techniques for modeling and mapping groundwater potential with the technologies developed in recent years was put forward. Within the framework of this approach, criteria that have no direct data on groundwater availability that will affect the groundwater potential distribution were used. The weighting of these criteria was carried out with AHP, one of the MCDM techniques, and MDE, one of the heuristic methods. It was determined that the weights for the criteria determined in both methods were close to each other, but there were differences in their rankings. It was determined that the aquifer criterion had a very high level of importance in the discovery of groundwater potential areas, while the stone density and salinity criteria had the least impact in terms of weight ranking. According to the trends formed by the weights, it can be said that aquifer, slope, alluvium, and permeability criteria should be prioritized data sources for groundwater research.

In the study, the weights determined based on expert opinion and heuristic methods were mapped by the TOPSIS technique in Model 1 and Model 2, respectively. The results of Model 1 and Model 2 were compared with the groundwater distribution map produced with well data for the last five years (2019–2023) obtained from the region, and their accuracy was tested with performance metrics. In terms of the performance metrics obtained, both models showed successful results.

As a result, this study showed that by using criteria that do not contain direct data on groundwater and finding the weighted effects of certain criteria, successful results can be obtained with less data at a low cost. At the same time, the study improved the expert-judgment-based MCDM techniques with heuristic methods. This has been effective in improving the consistency and objectivity problems in mapping based on expert opinion.