Multi-criteria decision making and Dempster-Shafer model–based delineation of groundwater prospect zones from a semi-arid environment

The present study illustrates the delineation of the groundwater potential zones in one of the most critical and drought-affected areas under Bundelkhand region of Uttar Pradesh (India). Hydrological evaluations were carried out using GIS tools and remote sensing data which ultimately yielded several thematic maps, such as lineament density, land use/land cover, drainage density, lithology, slope, geomorphology, topographic wetness index (TWI), DEM, and soil. Thematic layers were assigned relative weightages as per their groundwater potential prospects under multi-criteria decision making (MCDM) method through analytical hierarchy process (AHP). To recognize the groundwater potential zone, weighted overlay analysis was also performed. Additionally, for testing of the Dempster-Shafer model, 16 wells in the study area have been selected. Based on the probability of the groundwater occurrence, the belief factor was equated to delineate groundwater potential zones which illustrate five different potential zones. According to the AHP model, the northwest side of the study area is characterized with very high potential zones whereas the northeast and southeast regions constitute medium and low groundwater potential zones respectively. According to the DS model, very high groundwater potential zones constitute 17% and the remaining area falls under low potential. Overall accuracy of the DS model is higher than AHP model.


Introduction
Rainwater is the only source of freshwater and the occurrence of rainfall is seasonal in nature, resulting into mild to severe droughts (Adimalla et al. 2018). Groundwater has key impacts on human life such as agriculture, industries, and ecological diversity. With the increment in the demand for adequate and better quality water to meet the growing needs, a proper planning of groundwater management is essential (Agrawal et al. 2013). As per the assessment by Central Ground Water Board India (CGWB 2017), total annual groundwater recharge is 432 billion cubic metres (BCM), and the annual exploitable groundwater resources is 393 BCM. The annual groundwater withdrawal for all uses is 249 BCM out of which 221 BCM (89%) is used for irrigation and 25 BCM (10%) is used for domestic purposes. According to a World Bank (2016) report, India will become a water-stress country by 2025 and a water-scarce country by 2050, if not enough measures are taken. Due to rapid urbanization and population growth, excessive and unjustified use of groundwater has caused depletion of groundwater tables which reiterate the need for better understanding of groundwater potential zones (Islam et al. 2021).
In the recent past, many methods have been used by several researchers to delineate the groundwater potential zone. Weights-of-evidence (WOE) technique was used as an effective method for delineation of groundwater potential zones by Ozdemir (2011) and Pourtaghi and Pourghasemi (2014). Some researchers like Oh et al. (2011) and Davoodi Moghaddam et al. (2015) have also used the frequency ratio (FR) technique for identifying groundwater potential zones. The analytical hierarchy process (AHP) analysis by GIS technique was used by Pande et al. (2019); Singh et al. (2010); Shekhar and Pandey (2014); Rahmati et al. (2014); Murmu et al. (2019); and Adiat et al. (2012) to delineate the groundwater potential zone. GIS and analytical hierarchy process (AHP) is the most useful technique for decision making and geospatial data management. This is applicable in various fields of hydrological, geological, and environmental science (Gnanachandrasamy et al. 2018). AHP technique is proven to be a very practical, rapid, and cost effective technique to map the groundwater potential zones and in producing accurate results while traditionally groundwater exploration was costly and time consuming, because it needed ground survey using geophysical, geological, and hydrological tools (Arulbalaji et al. 2019). Nowadays, remotely sensed data is being widely used to provide baseline information such as digital elevation model (DEM), digital terrain model (DTM), and land use/land cover, which are further used for preparation of several geospatial thematic maps required for the delineation of groundwater potential zones. Suja and Krishnan (2009), Nag and Ghosh (2012), Suganthi (2013), and Etishree (2013) weightages were based on Saaty's (1980) scale for distinct thematic maps utilized to identify groundwater potential zones. According to Doke et al. (2018), Das (2019), Adimalla (2020), and Arjun et al. (2021), geological and geomorphological setups are the most influencing factors for groundwater occurrence. As per Debasis et al. (2020), shallow unconfined aquifers, deeper fractures, and joints under semi-confined conditions are the important indicators of groundwater potential in hard rock terrains. Many researchers, such as Adimalla et al. (2018), Arulbalaji et al. (2082), and Gangadharan et al. (2016), have used various thematic layers like drainage density, geology, lineament density, slope, soil, and lithology for the identification of groundwater potential zones.
Another approach to delineate the groundwater potential map is the Dempster-Shafer (DS) model, which has been predominantly used by many researchers (Mogaji et al. 2018;Ali et al. 2017;Nithya et al. 2019;Sahereh et al. 2021) around the world. The main reason to use the DS model is that it provides a set of probabilistic degrees such as Belief, Disbelief, Plausibility, and Uncertainty. The link between obtained thematic layers of probabilistic degree illustrates groundwater potential zones, which is further classified into five categories: Very High, High, Medium, Low, and Very Low.
Groundwater is an extractable asset; due to excessive extraction for agricultural, domestic, and industrial uses, it has been drastically declined; the authorities need to adopt an integrated approach to control excessive extraction of groundwater considering environmental management (Gun 2021). The mapping of groundwater potential zones is essential for best water management practices. The AHP and DS models for the accurate mapping of groundwater potential zones have been used in the present study.

Study area
The district Mahoba is located in Uttar Pradesh state of India, and lies between 25° 01′30″ and 25° 39′40″ north latitude and 79° 15′00″ and 80° 10′30″ east longitude (Fig. 1a). The total geographical area of the district is 2,884 km 2 which has four administrative blocks and five towns. According to the Census of India (2011), the total population of the district is 875958. The district experiences a typical subtropical climate punctuated by long and intense summers, and mild winter and moderately heavy rainfall during the rainy season. The maximum mean monthly atmospheric temperature has been recorded as 47.5 °C during the month of May and minimum 8.3 °C in January. Temperature generally starts rising from March and reaches highest in May. June onward temperature starts decreasing and almost establishes around 36 °C during August and September. During the monsoon period (July to September), the relative humidity attains at its highest level which varies between 80 and 85% while it is lowest at 30% during peak summer months of April and May. Major soil type is sandy deep loamy while average rainfall for the last 10 years is estimated to be 770 mm. There is no meteorological observatory located in Mahoba district; however, five rain gauge stations have been established by the UP irrigation department (Pandey, 2002).
The rock formations of the Bundelkhand massif are characterized by compact and partially granite which do not allow rain to percolate and store under subsurface. Secondary porosity in the form of joints and cracks allows some water to pass through weather zones into phreatic aquifers (T. K Pant, 2009). The hilly and hard rock terrain cause heavy overland flow and water during the rainy season. As a result, base flow occurs in the river as a part of groundwater.
Agriculture being the main source of livelihood for the people of Mahoba district requires excessive extraction of groundwater; both groundwater and surface water are used for irrigation purposes. Most of the agricultural land depends upon precipitation. Swami Brahmanand Dam with storage capacity of 89.8 billion litres and Arjun Sagar Reservoir with storage capacity of 16.6 billion litres are the two major basins which collect most of the rainwater through run-off. Total length of the irrigation canals is approximately 455 km. Dhasan, Urmil, Birna, and Arjun rivers follow through the district; these rivers and streams form the natural drainage lines of the district and separate many administrative boundaries.

Hydrogeology
Since, the area is characterized by the hard rock (Massive Granite) in majority and overburden consisting of clay, silt, and sand, the phreatic aquifer is formed in overburden while unconfined to confined conditions have been observed in fractured granite (Fig. 1b). The hydrogeological map reflects that the groundwater movements are sluggish in hard rock area while it is faster in overburden (Fig. 1c). The overburden mostly behaves as aquitard and aquifer (CGWB 2009).

Groundwater quality
The groundwater is contaminated with fluoride in pockets under granite and alkali granite, particularly in the extreme southern region of the study area. Weathering is responsible for leaching of fluoride into the groundwater. It has deteriorated because of geogenic activities. In the northern part of the study area, negligible thickness of overburden (weathered rock and loose soil) is present. Therefore, the concentration of TDS, fluoride, and bicarbonate in groundwater increases due to poor fluxing of groundwater. In the central and northern part of the study area, concentration of the nitrate in the groundwater has increased due to anthropogenic activities such as unlined septic tanks and unplanned sewerage systems. Additionally, terrain under granite-gneiss contains fixed atmospheric nitrogen which gets added to the soil through bacteria present in plants and soil, natural lighting. Nitrification also occurs due to ammonification of animal waste and plants. Hydro-chemical facies reveal that the nature of groundwater is Na + -Cl − , mixed Ca 2 + -Mg 2 + -Cl − and Ca 2 + -HCO − 3 type the study area (Arjun Ram et al. 2021).

Data and methodology
Pre-processing of remotely sensed data, i.e. Sentinel 2, was done using ArcGIS software, which is used for preparing thematic layer of land use/land cover; the data have a spatial resolution of 10 m for blue, green, red, and infrared bands which gives more accurate details about features of the earth surface (Cavur et al. 2019). Analysis of thematic Fig. 1 a Location map of the study area. b Cross-section of the study area. c Hydrogeological map of the study area layers such as geomorphology, lithology, soil, land use/land cover, slope, drainage density, lineament density, altitude, and topographic wetness index (TWI) was considered. The data pertaining to the study area were downloaded from the European Space Agency website (https:// scihub. coper nicus. eu/). CartoDEM data were used for generating digital elevation model (DEM), altitude, lineament density, and topographic wetness index, which have 30 m of resolution and downloaded from National Remote Sensing Center's website called Bhuvan (https:// bhuvan-app3. nrsc. gov. in/ data/ downl oad/). It is processed in ArcMap platform to generate flow accumulation with direction. Flow direction of streams represents the drainage network of the study area, and resulted into a thematic layer of drainage density. The DEM data is also used for the preparation of slope which is an important factor for delineation of groundwater potential zone. It mainly represents movement of water on the surface which is known as surface run-off. The steps involved to delineate the groundwater potential zone have been depicted in Fig. 2.
Ancillary data pertaining to thematic layers as geomorphology (scale 1:250 K) and lithology (scale 1:50 K) were collected from Bhukosh portal (https:// bhuko sh. gsi. gov. in/ Bhuko sh/ Public) of Geological Survey of India, whereas soil map was downloaded from (http:// www. nicra-icar. in/ nicra revis ed/ images/ state wisep lans/ Uttar% 20Pra desh/ UP50-Mahoba-26. 07. 14. pdf) National Bureau of Soil Survey and Land Use Planning (NBSS&LUP) Regional Center Delhi. According to the report of NBSS & LUP, the soil type for the selected region of Mahoba district is deep loamy soil with very low slope (< 3-5%). Selected thematic layers were further processed using multi-criteria decision making (MCDM) technique of AHP and DS model. Finally weighted overlay analysis has been carried out to calculate overall weightages for each thematic layer. The maps were further classified into five categories under groundwater potential zones. Wells data have been used for the validation of the groundwater potential zones. The receiver operating characteristics (ROC) curve method was also employed to compare the groundwater potential zone maps obtained from both the models.
The following section compiles the findings of a literature review of several research articles, leading to the main conclusion that the topic groundwater potential mapping has drawn attention of researchers (hydro-geologists) in the recent decades. AHP and DS models have been widely used by researchers all over the world due to their convenient nature. These methods are very practical and rapid and  (Gnanachandrasamy et al., 2018). Both AHP and DS models have been discussed below:

Analytical hierarchical process (AHP)
Analytical hierarchical process (AHP) is a practical and the most common method based on GIS to delineate the groundwater potential zones. This method is useful to integrate several hydrological thematic layers (Arulbalaji et al., 2082). Out of nine thematic layers, only seven were selected to delineate the potential zones in the study area. The weightage for the selected thematic layers was computed using Saaty's scale (1980). According to Gangadharan et al. (2016), weight assignment, pairwise comparison matrix, weight normalization, and consistency assessment are all part of the AHP model. This strategy is capable of decreasing the problem complexity and assisting in the adoption of simplified decisions based on comparisons (Kannan 2010;Celik 2019). Lineament is considered the main influencing factor for groundwater potential zones in hard rock terrain; therefore, it is given the highest importance value (Indrani and Umesh 2020). Researchers (Biju et al. 2018;Ahmadi et al. 2021;Melese et al. 2022) have considered lineament density as the most important factor and given high importance value for the same. Researchers (Muzzafar Ahmad Sheikh and Kumari Rina 2017, Indrani and Umesh 2020, Narender and Ramesh 2021) have considered geomorphology as an important influencing factor in the AHP model. Muzzafar Ahmad Sheikh and Kumari Rina (2017) have used slope and LULC with low importance value in Quaternary Sediments and rock terrain under AHP technique. According to Jasrotia et al. 2016) and Narender and Ramesh (2021), lithology, soil, and drainage density are given relatively low importance values for the delineation of groundwater potential zones.
All the thematic layers are given importance value which is used for weightage calculation. The proposed ranking of the thematic features defines weightage values. Further, to compare all of the factors, a pair-wise comparison matrix (W) is created (Eq. 1). Using the eigen-vector technique described by Saaty, the process of normalizing weights (Wij) is derived (Eq. 2) from the matrix table (Neissi et al. 2020;Nithya and Jeeva 2018).
Normalization of the eigenvector of the largest eigenvalue of the pairwise comparison matrix computes relative importance of each element. Factors of the class that are expected to have high groundwater potential are given higher comparative weightage (Suganthi 2013).
The consistency ratio (CR) is used to validate the consistency of a judgement. It is calculated by dividing the CI by the random consistency index (RCI) and is represented algebraically in the equation below (Debasis 2020).
If the CR value is less than 0.1, the judgement value must be accepted; otherwise, a new comparison matrix must be constructed with fresh judgement value for all parameters until the CR value is less than 0.1. The following expression is used to calculate the CI: where λmax is the maximum eigenvalue of "W," and the sequence of the square matrix is known as n. If W is entirely constant, then λmax equals n, resulting in a zero CI. As the level of inconsistency rises, so does the value of λmax (Saaty 1980). An overlay analysis is performed to determine overall weightages for all thematic layers. The potential zone for groundwater has been computed as follows: or: GWPZ = ∑ (Geomorphology rank X weight + Lithology rank X weight + Soil rank X weight + Lineament density rank X weight + Slope rank X weight + Drainage density rank X weight + Land use/land cover rank X weight).
where Fi denotes the relative weighting of several geoenvironmental parameters used to estimate groundwater potential, and Wi denotes the ranking of those elements (Achu et al. 2020). The groundwater potential zone was created by dividing the study region into five classes: (1) Very good, (2) Good, (3) Medium, (4) Low, and (5) Very low. (1)

Dempster-Shafer model
The theory was first introduced by Dempster (Dempster 1967) which was further developed by Shafer (1976); the DS model represents spatial integration of mathematical calculations (Sahereh et al. 2021). To use the DS model, weighting of the factors of the thematic layers is calculated, which offers the following probability layers: Belief, Disbelief, Uncertainty, and Plausibility. All factors in the same course are united, to create a predicted underground water zone (Ali et al. 2017). If we divide each data layer into numerous classes, then the weight values of each class Belief (B) and Disbelief (D) are calculated as follows: The following equations are used to calculate Plausibility (P) and Uncertainty (U): The groundwater potential map can be obtained using the following equation ( the percent of groundwater out of the domain the percent of pixels out of the domain After preparing the thematic layers, class and weight values are calculated for each of these layers based on the actual groundwater well data (training data). The impressive factors which received greater belief (Bel) values have more efficiency on groundwater potential (Ali et al. 2017).

Results and discussion
After preparing 9 data layers and classification of each layer into its factors, the weight values of each factor were calculated using the DS model based on actual groundwater well training data. In AHP model, TWI and altitude were not considered as they have very less importance value; therefore, only 7 data layers were considered for the analysis; characteristics of considered thematic layers according to its importance value have been depicted. Each layer has played an important role for determining the groundwater potential zones in the study area. The results obtained during the entire study have been discussed below: In AHP model, all the thematic layers were given importance value (Table 1) which were used for weightage calculation; the proposed ranking of the thematic features defines weightage values. Further, to compare all of the factors, a pair-wise comparison matrix (  are derived using the eigen-vector technique described by Saaty. The normalized weightages are given in Table 2.

Geomorphology
It is one of the important parameters widely considered for the delineation of the groundwater distribution in various landforms. Higher water retention capability is denoted by river/water bodies and active floodplain which is considered the best landform for groundwater potential. Alluvial plains deposited along with the river channel and flood plains are given highest rank while moderately dissected hills and valleys are given least ranking (1-5). The accumulated weightages for different geomorphological factors vary from 16 to 80 which indicates that factors with higher weightages influence groundwater potential. Northwest side of the study area (Fig. 3a) is covered by alluvial plains which indicate higher possibility of groundwater. In the DS model, belief factor varies from 0 to 0.53 and disbelief 0.16 to 0.50. Uncertainty rate varies from 0.12 to 0.51. It reflects higher groundwater occurrence in low uncertainty zones which are classified as dams and reservoirs.

Lineament density
As a result of faulting and jointing, lineaments relate to zones of enhanced porosity and permeability in hard rock area; hence, they are very much important in groundwater investigations (Sreedevi et al. 2001;Koch & Mather 1997). Higher groundwater potential is expected where the geological linear features are more intensive. The lineament trends northeast and southwest direction (Fig. 3b). In the AHP model, the accumulated weightages vary from 24 to 120; since the layer received the highest weightages, it is the most influencing factor for the groundwater potential delineation. Lineament density was classified into following intervals: < 0.03, 0.03-0.10, 0.10-0.18, 0.18-0.28, 0.28-0.48 km/km 2 as very low, low, medium, high, and very high respectively. The highest lineament density interval received the top ranking. In the DS model, the belief factors vary from 0.20 to 0.54, which is considered one of the most influencing thematic layers; higher beliefs are present along with low lineament density.

Lithology
Lithology controls soil porosity and water permeability and affects the specific storage of groundwater. Obtained normalized weightage from the AHP comparison matrix is 0.12 and the overall weightages vary from 12 to 60. Several lithological features of the study area are marked in the map (Fig. 3c). Coarse-grained porphyritic granite is dominant lithounits. Alluvium is characterized by silt, clay admixed with calcareous nodules. Sand and silt and clay are given the highest rank which constitute low geographical coverage. Hydraulic conductivity varies from 3.3 × 10 −6 to 5.2 × 10 −5 m/s in massive granite and fractured granite respectively. It varies from 2 × 10 −7 to 2 × 10 −5 m/s for silt and fine sand respectively. In the DS model, the belief factor varies from 0 to 0.64; higher in belief reflects high groundwater zone; thus, it is an important factor for groundwater

Slope
Slope expresses the steepness of the ground surface or terrain. The nature of geological and geodynamic processes, surface runoff, and infiltration rate are affected by slope. Here steep slopes imply low recharge because of the rapid flow of water while gentle slopes indicate higher groundwater recharge. The map (Fig. 3d) reflects that the majority of the region in the study area constitutes slope ranging from 0 to 4 degree. The calculated normalized weight for the slope from the AHP comparison matrix is 0.16 and overall weightages vary from 16 to 80. The slope is classified into the following intervals: 0-1.26, 1.26-2.40, 2.40-4.17, 4.17-10.74 and more than 10.74 degree. The northwest side of the study area has a gentle slope varying from 0 to 2 degrees while the northeast side is characterized by 2 to 4 degrees. Steeper slopes are observed in the southwest region of the study area which varies from 4 to 32 degrees (Fig. 3d). The run-off is also coherent to the direction of steeper slope (NE-SW). In the DS model, belief rates vary from 0 to 0.64, and area under zero belief rate indicates unavailability of groundwater while higher belief associated with gentle slope indicates availability of groundwater.

Soil
Soil surface condition influences the infiltration as well as transmission rate. Soil varies in its composition and has different slopes and textures. Loamy soil as observed in the study area is formed with the mixture of silt, clay, and sand. These soils are considered to be fertile and easy to work with; they also provide good drainage. It is further classified as sandy or clay loamy depending on their predominant compositions. These soils are highly permeable which contain good amount of groundwater. The calculated normalized weight for the soil from the comparison matrix is 0.12 and the overall weightages vary from 24 to 48; low weightages indicate less influence in delineation of groundwater zones. Fine smectitic soil was given high rank (4) and deep loamy soil was given lowest ranking (2). Different types of soil have been depicted in Fig. 3e. In the DS model, belief rate varies from 0.31 to 0.53 with uncertainty rate which varies from 0.05 to 0.20. It reflects low groundwater availability with higher disbelief (0.42 to 0.50).

Land use/land cover (LULC)
The LULC map (Fig. 3f) provides information about forests, builtup, impervious surfaces, agriculture, and water bodies etc. The given pie chart (Fig. 3i) illustrates land cover in the Mahoba district. Agriculture accounts for 62% of the total land where commercial activities like mines cover less than 1%. Approximately 16.8% of the district land is covered by wetland followed by barren land, i.e. 9.3%. Water bodies in the district are less than one percentage of the total land cover. Since the district is densely populated, the builtup area accounts for more than vegetation and water bodies, i.e. 6.9%. The calculated normalized weightage from the AHP comparison matrix is 0.08 and the overall weightages vary from 8 to 40. Water bodies and forest cover were given high ranking as 5 and 4 respectively; builtup area was given a low weight as 1. In the DS model, the belief rate varies from 0 to 0.67 while uncertainty varies from 0.06 to 0.51. Here agriculture is associated with higher belief (0.67) indicating occurrence of groundwater.

Drainage density
Drainage density, defined as the total length of drainage channels per unit area, helps to evaluate and understand the characteristics of runoff and groundwater infiltration (Suganthi et al. 2013). The region was classified (Fig. 3h) as very high, high, medium, low, and very low, which are ranked as 1, 2, 3, 4, and 5, respectively. The calculated normalized weight from the AHP comparison matrix was 0.12; overall weightage varies from 12 to 60. In the study area, high runoff density indicates high surface runoff and low infiltration rate, while low and very low runoff density indicates low runoff and high infiltration rate. The percolation of rainwater takes place in low drainage density areas; therefore, occurrence of groundwater is estimated as high rank for the same. In the DS model, belief rates vary from 0.42 to 0.51 and uncertainty rates vary from 0 to 0.07, which indicate low uncertainty rate for presence of groundwater.

Topographic wetness index
Topographic wetness index (TWI) is one of the important factors considered to study the groundwater potential zone; it describes the relationship between the diversion of the water accumulated in the site part and the gravity that pushes the water according to the slope. The following equation is used for the calculation of TWI factor (Moore et al. 1991): where α is the contributing upslope area and β is the topographic gradient at the same point in the terrain. In the present study, TWI map was prepared using a digital elevation model of CartoDEM data. The map is classified into five categories as illustrated in Fig. 3g. The lower wetness index value varies from 3.42 to 6.66 while high values vary from 10.53 to 16.75. According to Davoodi Moghaddam et al.

TWI = ln(α∕tan )
(2015), Rodhe andSeibert (1999) andSahereh et al. (2021) thematic layers representing topographic factors play a conclusive role in the estimation of the groundwater flow zones. Several researchers Falah et al. 2016, Sahereh et al. 2021Pourtaghi et al. 2014) have used topographic wetness index (TWI) for groundwater potentiality mapping. This thematic layer was not considered an effective factor for the groundwater potential under AHP model of investigation because it represents wetness of terrain and varies with topographic gradient (slope) which will be a repetition in multi-criteria decision making.

Elevation
The relationship between groundwater occurrence and altitude, high altitude reduces the ability to recharge groundwater, thereby reducing groundwater potential. Elevation map was prepared using CartoDEM data which has spatial resolution of 30 m. The map altitude value varies from 56 to 288 m. The map is classified into five categories as shown in Fig. 3j. Table 3 shows the results of the spatial relationship between the existence of groundwater and the impressive factors using the Dempster-Shafer theory (doubt, belief, reasonableness, and uncertainty). The integrated result indicates that enormous groundwater potential was found for the region having greater values of belief and small values of disbelief for the incidence. The belief values vary from 1.79 to 4.56 (Fig. 4a) while Disbelief varies from 3.69 to 4.75 (Fig. 4b).

Integrated results of DS model
The uncertainty map (Fig. 4c) illustrates the lack of information that provides real evidence of the spring incidence. High levels of uncertainty appear in areas with low levels of belief. The plausibility map (Fig. 4d) represents a higher degree where both uncertainty and belief are higher. Table 4 shows accumulated weightage for factors of each thematic layer. Lineament density and geomorphology have received high weightage compared to all other factors of thematic layers. Highest weightage count is 120 for very high lineament zones, while the lowest is 12 for Pegmatite in lithology in the study area.

Groundwater potential zones
The groundwater potential maps were prepared using the relative importance of several thematic layers; each thematic layer was divided into several categories for estimation of relative weightages. Thematic layers, viz. geomorphology,   lineament density, lithology, slope, soil, LULC, drainage density, altitude, and topographic wetness index, were used under overlay analysis to delineate groundwater potential zone map. The map shown in Fig. 5a represents groundwater potential zones using AHP model and Fig. 5b represents groundwater potential zones using DS model. Both the maps were classified into very high, high, medium, low, and very low groundwater zones.
In AHP model groundwater potential zone map, it is evident that the northwest side of the study area (Fig. 5a) has high groundwater potential which is classified as very high zone; this zone has an area of 209 km 2 . High groundwater zones constitute an area of 931 km 2 and followed by medium zone of 1306 km 2 which cover the majority of the study area. Low zone has an area of 460 km 2 while very low zone 12 km 2 .  5 Groundwater potential zone maps: a groundwater potential zones using AHP model, and b groundwater potential zones using DS model In the DS model (Fig. 5b), the northwest and south part of the study area has high and very high groundwater potential zones which cover 34% and 17% (Table 5) of the study area respectively. while southeast part has medium and low groundwater potential zones; the similar trend is also observed in the AHP model. In DS model, high zones constitute an area of 1004 km 2 while low zone has an area of 432 km 2 .
All the channels of watersheds contain a good amount of groundwater relative to the other regions of study area. High zone regions are influenced by stream channels. Jaitpur and Panwari blocks of the Mahoba district have high groundwater potential relative to Charkhari and Kabrai blocks.

Validation
According to Tehrany et al. (2013), in the ROC curve sensitivity is plotted against true positive and true negative value of groundwater occurrence and the area under the curve (AUC) shows the distribution performance of the models. Here AUC equals to zero indicates a noninformative model while perfect condition represents AUC equals to one. The AUC for the AHP model is 76% while it is 79% for the DS model; therefore, the DS model is more accurate than the AHP model (Fig. 6). This is because the weight value of TWI and altitude data layers has influenced belief rate, while removing the same results in lower accuracy. In AHP model, these two layers were not considered to avoid over-estimation of weightages on similar parameters. The accuracy of the delineated groundwater potential zones in different watersheds under the study area was validated by analysing the bivariate relationship between the groundwater potential zones and the 16 wells yield data. The validation result indicates that wells having high discharge (> 1500 L/min) lie in high and very high groundwater potential zones whereas wells having low discharge (< 500 L/min) lie in moderate and low groundwater zones. Using analytical hierarchy process and Dempster-Shafer model, certainty of the findings related to groundwater potential zones has been improved.

Sensitivity analysis of the thematic layers
In AHP model, frequency distribution of overall weightages varies from 8 to 456 (Fig. 7). The most influential thematic layer is found to be lineament density and least was drainage density as well as LULC. Sensitivity analysis of lineament density shows minimum weightage as 24 and maximum as 128 respectively (Table 6).

Limitations
The accuracy obtained through both the models is more than 75% and limitation lies with pixel size of a particular class. Because different classes constitute different pixel sizes, belief and importance rate may differ slightly from what was taken in consideration for the delineation of the groundwater potential maps.

Conclusion
The groundwater potential zones (GWPZs) of Mahoba District of Uttar Pradesh were delineated by an integrated approach using AHP and Dempster-Shafer model with the help of remote sensing data under GIS framework. Normalize weightage for parameters, viz. geomorphology (0.38), lineament density (0.19), lithology (0.13), slope (0.10), soil (0.08), LULC (0.06), and drainage density (0.05), were considered in the AHP. Comparison matrix was also calculated. The groundwater potential map on the basis of DS model also corroborates the findings of AHP model regarding delineation of groundwater potential zones. The northwest side of the study area is characterized by very high groundwater potential zone while the northeast and southeast side of the region is characterized as medium and low groundwater potential zone. With AHP model, very high groundwater potential zone constitutes an area of 209 km 2 while very low groundwater zone has an area of only 12 km 2 .
In the DS model, Belief, Disbelief, Uncertainty, and Plausibility were equated using well locations, and taking the cognizance of several thematic layers, the groundwater potential map illustrates that the northwest and south part of the study area has high and very high groundwater potential zones while southeast part has medium and low groundwater potential zones.
The study has been validated using field data pertaining to yield of wells. The receptor operating curve (ROC) method was used to validate the result which shows DS model is more accurate than the AHP model. According to spatial distribution of groundwater potential zones, both the models show minor differences to each other due to quantitative and qualitative change in AHP and DS models respectively. The findings of the present research will provide a roadmap to planner and user of groundwater.
Author contribution Hemant Kumar Pandey has contributed in introduction and methodology section, and Vishal Kumar Singh has contributed in numerical analysis and software application while Sudhir Kumar Singh has contributed in result and discussion section of the manuscript.
Funding This work was supported by Natural Resources Data Management System (NRDMS), Department of Science and Technology, Govt. of India (Grant numbers: NRDMS/01/267/019).

Data availability
The data will be made available on request.

Declarations
Ethics approval Not applicable.

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Competing interests The authors declare no competing interests.
Interest statement The present research work does not have any conflict of interest with the researchers who have done the work in this  area. The findings of the present research work will provide a road map for making the plan for water management.