Application of GIS-based models of weights of evidence, weighting factor, and statistical index in spatial modeling of groundwater

Groundwater is considered to be one of the most essential natural resources worldwide, which saturates the pore space of geologic formations, and is used for drinking, agricultural, and industrial activities (Fitts 2002; Todd & Mays 2005; Pradhan 2009; Manap et al. 2013, 2014; Nampak et al. 2014). Moreover, it supplies the greatest proportion of water demand in arid and semi-arid areas. The main source of groundwater formation is rainfall or snowmelt that percolates through the soil to the underlying formation or water table (Banks & Robins 2002). The level of use of groundwater has increased due to population growth and surface water drought and limitation, as well as groundwater's constant temperature, better quality, lower vulnerability to pollution, and being widespread, which make it available to tap when required (Jha et al. 2007; Manap et al. 2013). The existence of groundwater beneath the Earth's surface is the result of interaction among some climatic, hydrological, soil, geological, and physiographical factors.

Iran is an arid country with two-thirds of its area covered by desert without any green pasture as only 10% of the country has enough rainfall; thus, groundwater is the only safe source for drinking, agricultural, and industrial purposes (Pourghasemi & Beheshtirad 2015; Khosravi et al. 2018a, 2018b). The three most common sources for the use of groundwater in Iran are wells, springs, and qanats. Thus, identification of areas with high potential for the existence of groundwater resources is the most important issue in proper groundwater resources management and long-term planning. Groundwater potential assessment and mapping is one of the most substantial aspects of groundwater studies, which helps to better exploit and manage the resources of groundwater (Naghibi et al. 2016).

Among three groundwater indicators, namely, wells, spring, and qanats, wells are best in the identification of groundwater yield. Traditional methods of groundwater identification, including drilling, geophysical, geological, and hydrogeological methods, are time-consuming and costly (Nampak et al. 2014; Khosravi et al. 2018c). Preparation for groundwater potential assessment is mainly through ground survey (Ganapuram et al. 2009). Nowadays, application of geographic information system (GIS) as a powerful tool brings insight into the water resources management field. Moreover, some GIS-based bivariate models of frequency ratio (Naghibi et al. 2015; Razandi et al. 2015; Al-Abadi et al. 2016; Balamurugan et al. 2016; Falah et al. 2017; Kim et al. 2018), Shannon entropy (Naghibi et al. 2015; Khosravi et al. 2016b), weights of evidence (Lee et al. 2012; Tahmassebipoor et al. 2016; Ghorbani Nejad et al. 2017), multivariate logistic regression (Ozdemir 2011; Zandi et al. 2016), multiple criteria decision making of analytical hierarchy process (AHP) (Chenini et al. 2010; Agarwal et al. 2013), and machine learning methods including decision tree (DT), random forest (RF), support vector machine (SVM), naïve Bayes (NB), and hybrid adaptive neuro fuzzy inference system (ANFIS) with meta-heuristic algorithms (Chenini & Mammou 2010; Naghibi et al. 2017; Naghibi & Dashtpagerdi 2017; Lee et al. 2018; Khosravi et al. 2018b, 2018d) have been used in the field of hydrology and water resources, especially for recognition of groundwater.

On the one hand, as machine learning algorithms are new, and although they have widespread uses in most of the sciences, some of them have some weaknesses; thus, researchers have combined them with other methods to solve problems (Tehrany et al. 2014, 2015; Khosravi et al. 2018b, 2018d). On the other hand, their accuracy depends on high-resolution data and, in some cases, bivariate models are more accurate than them. For example, Rahmati & Pourghasemi (2017) compared bivariate method of evidential belief function (EBF) with two machine learning methods, namely, RF and boosted regression trees (BRT), in recognition of flood-prone areas and, eventually, revealed that the EBF method had a higher prediction power than two machine learning methods. Also, they stated that bivariate methods were simple tools with high prediction power.

As shown in a literature review, researchers have applied different methods in different fields of study and, generally, there is no framework that identifies which method is better than others. The accuracy of any model is completely dependent on distribution of the used data, case study characteristics, and model structure. The present research study is mainly aimed at comparing prediction power of the three bivariate models of weights of evidence, weighting factor (WF), and statistical index (SI), which are rarely used in groundwater potential mapping, although their prediction power has been confirmed in other fields of study, such as flood susceptibility mapping (Khosravi et al. 2016a) and landslide susceptibility assessment (Yalcin 2008).

Sero Plain in the west of West Azerbaijan Province, which covers about 52 km², is selected as the case study, where groundwater resources supply the greatest proportion of water demand for drinking and agricultural sectors (see Figure 1).

It is located between 44 37 30 to 44 43 30 E and 37 41 to 37 47 N. Altitude varies from 1,490 m to 1,697 m above the mean sea level. Slope varies between 0 and 26 degrees. According to Urmia Regional Water Authority reports, the mean annual rainfall is about 440 mm. Sero Plain is mostly covered by Inceptisol soil and agriculture land-use covers about 94% of the study area. Geologically, Quaternary and Permian cover about 58% and 18% of the study area, respectively. Average storage coefficient for the study area is about 5%, for Quaternary formation (Qt1 and Qbv) is about 6% and for Eosin and Cambrian is about 4%.

Well inventory mapping is necessary for determination of the spatial relationship of the well locations with each conditioning factor in the case study. Recognition of spatial groundwater with higher potential is performed through wells with higher groundwater yield (Nampak et al. 2014). In this study, the threshold of 11 m³/h was considered according to the reports of Urmia Regional Water Authority and a literature review for groundwater yield, and the wells with groundwater yields higher than 11 m³/h were considered for modeling (Nampak et al. 2014). In the study area, only 75 well locations had groundwater yields higher than 11 m³/h. These wells were grouped into two categories randomly with 70% (53 well locations) in the training dataset and 30% (22 well locations) in the testing dataset. The training dataset was used to build the model and the testing dataset was used to evaluate and compare it with other ones (Nampak et al. 2014; Khosravi et al. 2018b). The locations of wells and their groundwater yields were obtained through Urmia Regional Water Authority.

Ten conditioning factors of ground slope, altitude, aspect, curvature, distance from river, distance from fault, lithology, land-use, rainfall, and soil media were considered for groundwater spatial modeling based on a literature review and the available data (Nampak et al. 2014; Khosravi et al. 2018b).

A digital elevation model (DEM) was obtained for the area under study from ASTER Global DEM with a spatial resolution of 30 m; then, factors of ground slope, slope aspect, altitude, and curvature were achieved directly from a DEM using ArcGIS10.2 software. Altitude factor was divided into five classes of 1,491–1,548, 1,548–1,573, 1,573–1,599, 1,599–1,633, and 1,633–1,697 m (Figure 2(a)). Ground slope of the area under study was classified into five categories including 0–3.1, 3.2–5.7, 5.8–8.7, 8.8–12.8, and 12.9–26.7 by quantile scheme classification method (Figure 2(b)). According to a literature review, quantile scheme classification method was applied in the present research to classify all the performed maps (Tehrany et al. 2014, 2015; Khosravi et al. 2018b, 2018c). The plan curvature factor was divided into three classes of less than −0.05 (or concave), −0.05 to 0.05 (or flat), and more than 0.05 (or convex) (Figure 2(c)) (Pham et al. 2017). This factor shows surface topography of the Earth. Slope aspect of Sero Plain was classified into nine categories of flat, north, northeast, east, southeast, south, southwest, west, and northwest (Figure 2(d)).

Average annual rainfall in 20 years for 4 rain-gauge stations was utilized in the production of the rainfall map. This factor is considered as one of the most substantial conditioning factors in groundwater resources occurrence, as groundwater forms by deep percolation of rainfall or snowmelt. The rainfall map was extracted by Kriging method, because of low RMSE, and divided into five rainfall groups of 400–424, 425–446, 447–467, 468–488, and 49–510 mm (Figure 2(e)). Soil characteristics have a direct effect on groundwater resources in water infiltration. 1:50,000 soil map of West Azerbaijan Province in (.shp) format, provided by Iranian Water Resources Department (IWRD), was applied in the preparation of the case study soil. Three soil types of Inceptisols, rock outcrop/Inceptisols, and rock outcrop/Entisols cover the Sero Plain (Figure 2(f)).

Land-use/land-cover map of the case study was produced by using Landsat 7 (ETM+) through supervised image classification techniques. Images were received from the US Geological Survey (USGS). Finally, the prepared land-use map was divided into three classes of irrigated land and agriculture, dry farming, and moderate rangeland (Figure 2(g)). Geology factor can affect groundwater resources due to different infiltration rates of different lithological formations (Pradhan 2009; Adiat et al. 2012). This factor was identified by GSI. Moreover, the formation of geology, including Qt1, Qbv, E2c, E2s, Pr, and Pgn (Figure 2(h)), were considered. Fault layers of Iran in (.shp) format, provided by Geological Survey of Iran (GSI) at a scale of 1:100,000, were utilized for identification of the fault layer in the area under study. Faults and rivers in the area under study were used in the identification of the two most substantial conditioning factors of distance from fault and distance from river. Finally, these factors were divided into five classes of 0–100, 100–200, 200–500, 500–1,000, and >1,000 m (Figure 2(i) and 2(j)) (Khosravi et al. 2018b).

Three bivariate models of weights of evidence, SI, and WF were applied in spatial modeling of groundwater resources. A flowchart of the present research is presented in Figure 3.

SI is another bivariate model that was introduced for the first time by Van Western in 1997 for identification of landslide-prone areas (Khosravi et al. 2016b). Performance of this method can be summarized as: (1) classification of each conditioning factor; (2) overlaying of the groundwater well location and each conditioning factor; (3) calculation of density of wells in each class of factors; (4) calculation of the weight of each conditioning factors class; and, finally, (5) calculation of the algebraic sum of all conditioning factors to produce the map of groundwater well potential. The SI method, similar to other bivariate models, is on the basis of the spatial relationship of groundwater well distribution with the characteristics of each conditioning factor (Yalcin 2008).

E_ij is defined as the groundwater well density of the class i of factor j, and E shows the total groundwater well density of the case study. L_ij reveals the number of groundwater well locations for the class i of factor j, and L_T is considered as the sum of the groundwater wells in the case study. Also, P_ij shows the amount of pixels in the class i of factor j and P_L is the total number of pixels in the case study.

The positive and negative values for W_SI show the strong and weak relationships, respectively, between each class of factors and groundwater occurrence. It is noteworthy that the more the positive value, the greater the correlation will be; it is the opposite for negative values.

Model evaluation is the crucial step to determine the quality of the achieved maps. In the present research, two criteria, namely, receiver operating characteristic (ROC) method and Friedman test, are investigated for model evaluation and comparison.

ROC method is the well known and most popular method of evaluation based on visual attractiveness (Fawcett 2006; Powers 2011; Tehrany et al. 2013; Pham et al. 2017). There are two types of ROC curves, including success rate and prediction rate. Success rate is constructed by training dataset; thus, it only shows how the model fits the training data and it cannot be utilized in model validation. As a result, testing dataset, which cannot be used in model building, is applied for model validation. It shows how good the applied model predicts the groundwater well potential. Area under the ROC curve method (AUC) reveals the prediction power of the model, quantitatively.

Friedman is a well-known, non-parametric statistical test, introduced by Friedman (1937), and used to determine the statistical significance of differences between groups (prediction power of the models) (Beasley & Zumbo 2003; Khosravi et al. 2018b). Our null hypothesis is that there are not differences in prediction power of the models in mapping of the groundwater well potential. If P-value and chi-square are less than 0.05 and more than 3.84, respectively, then the null hypothesis is rejected (Chapi et al. 2017; Khosravi et al. 2018b, 2018c).

One of the most substantial steps in any spatial modeling is to determine whether there is multi-collinearity between independent variables or not (Pourghasemi & Beheshtirad 2015). Multi-collinearity shows that there exists high correlation between independent variables and one of them can be predicted by another one; thus, it must be removed. Multi-collinearity diagnosis is measured by two indices that are called tolerance and variance inflation factor (VIF) (O'Brien 2007). Tolerances less than 0.2 or 0.1 and/or VIFs of 5 or 10 and/or more indicate multi-collinear problems (O'Brien 2007). According to Table 1, the smallest tolerance and the largest VIF are 0.300 and 3.331, respectively. Thus, no multi-collinearity exists between independent factors in the study area.

The achieved weights by WOE model are presented in Table 2. In terms of altitude, the first class, i.e., 1,491–1,548 m, has the highest weight (4.14) and the greater the altitude, the lower would be the weights or the lower the groundwater well potential probability. Results show that 41.5% of the wells have been drilled at the altitude of 1,491–1,548 m. Slopes between 0 and 3.1 degrees show the highest probability of groundwater occurrence and with increase in ground slope, the probability of groundwater occurrence is reduced. The reason is that with increase in the slope, runoff generation gets higher and infiltration lower; thus, the probability of groundwater occurrence decreases. This is in accordance with the results of Khosravi et al. (2018b), Naghibi et al. (2015, 2016), and Nampak et al. (2014). Regarding plan curvature, flat curvature has the highest effect on groundwater (4.35) and the other two curvatures, namely, convex and concave, do not have significant effects on groundwater occurrence. This is because water infiltration is greater in a flat curvature than in other curvatures. North aspect has the highest effect on groundwater occurrence (2.71), followed by southwest (1.08) and east (0.13); however, other aspects do not have significant impacts. This is because north aspect gets the lowest amount of solar radiation among all aspects. Only the rainfall class of 446–467 mm has a positive effect (1.38) on groundwater potential probability and other classes are not effective. Theoretically, the more the rainfall, the higher the probability of groundwater occurrence; however, our case study does not follow this theory; this is because other factors which have significant effects on the groundwater occurrence control the condition. As most of the area under study is covered by Inceptisol soil and the other two types of soil encompass a very small proportion of the area, all the wells are located in Inceptisol soil. Also, as the case study is mostly covered by agricultural lands, all the wells have been drilled in this type of land use. Although 52% of the wells have been drilled in the Qt1 Quaternary-period formation, because large areas are covered by the formation of this period, it does not have a significant impact and the geologic period of Permian (Pcgn) has the highest impact (2.46) on groundwater occurrence; moreover, other geologic units do not have significant effects on groundwater potential. Permian-period formation (Pcgn) consists of sandstone and lime.

The prepared map has been categorized based on quantile classification scheme into five classes of very low (VL), low (L), moderate (M), high (H), and very high (VH) groundwater potential. This method is used in the field of geosciences when data have skewness (Khosravi et al. 2018a, 2018b).

Results of success rate show that the SI model has the highest AUC (0.747), that is, this model better fits the training dataset, followed by WF (AUC = 0.742) and WOE (AUC = 0.737) (Figure 5(a)).

Results of prediction rate reveal that, similar to success rate, the WOE model has the highest prediction power (AUC = 0.798) with accuracy of 79.8%, followed by SI (AUC = 0.795) and WF (AUC = 0.791) (Figure 5(b)).

The highest prediction power of the WOE model can be related to the fact that WOE model benefits from the Bayesian-based theorem in a log-linear form. Also, the WOE model is utilized when sufficient dataset is in hand to predict the relative significance of evidential themes by statistical tools (Bonham-Carter 1994).

According to Yesilnacar (2005), all the performed models have good prediction power. Results of Friedman test (Table 3) reveal that P-value (0.913) and chi-square (0.182) are more than 0.05 and less than 3.84, respectively; thus, the null hypothesis is accepted, i.e., the difference between performances of the models is not statistically significant.

Results of the WOE model, as the best model in prediction of groundwater well potential, show that VL, L, M, H, and VH cover about 20.03, 20.05, 20, 19.95, and 19.95% of the study area, respectively (Figure 6). This result for the SI model is close to WOE but for the WF model is not similar. The WF model has an overestimate in the H class and an underestimate in the VL class.

The result of this research is not in accordance with the results of Falah et al. (2017), in which, FR had a higher prediction power in comparison to SI and WOE, and Ghorbani Nejad el al. (2017), where EBF had a higher efficiency. However, our result is in accordance with the result of Arabameri et al. (2019), that the WOE model outperforms RF and technique for order preference by similarity to ideal solution (TOPSIS) multi-criteria. There is a lot of research about groundwater potential mapping which has applied different types of models in the aforementioned literature review, but there is no universal guideline as to which model is better or has a higher prediction power (Chen et al. 2019). Khosravi et al. (2018d) suggested that as each model has advantages and disadvantages and we cannot find the model that has the highest prediction power with most of the data, some popular models should be applied and finally the best one be selected for further analysis. This is related to the mode structure and type of data (Khosravi et al. 2018c).

One of the major causes of today's water crisis is the lack of integrated water resources management and long-term planning for drought stress, especially in developing countries. A principal step towards this aim is identification of the existence of water and groundwater resources. In the present study, three GIS-based models of weights of evidence, SI, and WF were applied in spatial identification of groundwater resources. Outcomes show that all the models showed good results; however, WOE had the highest prediction capability, followed by SI and WF. According to the SI and WOE models, most of the groundwater was identified in the altitude of 1,491–1,548 m, ground slope of 0–3.1 degrees, flat curvature, north aspect, rainfall of 446–467 mm, Inceptisol soil, agricultural land use, Permian geologic period, and 0–100 m distance from fault and rivers. According to the WF model, altitude had the highest impact on groundwater occurrence and rainfall had the lowest. According to the WOE model, 39% of the area under study, located in the southeastern part, had high and very high potential for groundwater. Results of this research study are helpful for Urmia Water Regional Company to sustainably manage groundwater resources.