An Automated Python Language-Based Tool for Creating Absence Samples in Groundwater Potential Mapping

Abstract

Although sampling strategy plays an important role in groundwater potential mapping and significantly influences model accuracy, researchers often apply a simple random sampling method to determine absence (non-occurrence) samples. In this study, an automated, user-friendly geographic information system (GIS)-based tool, selection of absence samples (SAS), was developed using the Python programming language. The SAS tool takes into account different geospatial concepts, including nearest neighbor (NN) and hotspot analyses. In a case study, it was successfully applied to the Bojnourd watershed, Iran, together with two machine learning models (random forest (RF) and multivariate adaptive regression splines (MARS)) with GIS and remotely sensed data, to model groundwater potential. Different evaluation criteria (area under the receiver operating characteristic curve (AUC-ROC), true skill statistic (TSS), efficiency (E), false positive rate (FPR), true positive rate (TPR), true negative rate (TNR), and false negative rate (FNR)) were used to scrutinize model performance. Two absence sample types were produced, based on a simple random method and the SAS tool, and used in the models. The results demonstrated that both RF (AUC-ROC = 0.913, TSS = 0.72, E = 0.926) and MARS (AUC-ROC = 0.889, TSS = 0.705, E = 0.90) performed better when using absence samples generated by the SAS tool, indicating that this tool is capable of producing trustworthy absence samples to improve groundwater potential models.

1. Introduction

Different approaches such as data-driven, statistical, and machine learning models can be used to model groundwater potential. They are based on a statistical assumption that the past and present situations and state of a phenomenon are key to determining and predicting its future situation and state. The models use two different data samples as the dependent variable: occurrence samples (also known as presence or positive samples) and non-occurrence samples (also known as absence or negative samples) [1,2]. Beside the dependent variable, different geo-environmental factors are considered as independent variables. In other words, the spatial modeling approach requires an inventory of occurrences and non-occurrences and a set of geo-environmental attributes related to groundwater spring [3,4]. Presence samples are usually obtained by conducting field surveys and analyses of high-quality aerial photographs and satellite images. They are thus usually more reliable than absence samples, because they are based on proof of existence of the given phenomenon. Absence samples are typically selected as individual pixels outside the occurrence areas (i.e., spring-free areas), using a simple random sampling method [5,6]. Therefore, determining absence samples (i.e., non-spring) is usually a challenging task and can be a key source of model uncertainty, strongly affecting model performance [7,8].

The quality of both presence and absence samples is extremely important in the modeling process because any error in selection of these samples can lead to a significant error in the final modeling or analysis process. Generally, two main errors can arise in the modeling results: Type I error and Type II error [9]. Considering the example of landslide susceptibility, Type I error, also called ‘false positive’, indicates areas without risk being classified as unsafe. This error may lead to exclusion of these areas from development plans and cause many social and economic problems. On the other hand, Type II errors, called ‘false negative’, involve areas that are unsafe being classified as safe. This error can cause some severe problems in the real world, such as economic damage and loss of life, since using maps produced with Type II error can lead to structures or developments being placed in areas that are unstable or unsafe [9]. Both presence and absence samples strongly influence these error types and, consequently, the predictive performance of the model [10,11]. A performance improvement of only a few percent can lead to more efficient water resources and environmental management [12]. Therefore, powerful standard approaches are required to select absence and presence samples with high accuracy.

Because of lack of reasonable and trustworthy techniques, most spatial modeling studies reported in the literature use a simple random method to select absence samples in different fields, for example, groundwater potential [3,5,10,13,14,15,16], landslide susceptibility [1,17,18,19,20,21], gully erosion susceptibility [22,23,24,25], land subsidence susceptibility [26,27,28,29,30,31], and flood susceptibility [18,32,33,34,35,36,37]. However, the random sampling method has some drawbacks. First, this method does not pay attention to the distribution pattern of absence samples, and therefore the absence samples generated are sometimes significantly clustered and do not provide overall information on the entire study area [34,38]. Second, absence samples may be very close to presence locations, resulting in confusion in the model and also increasing an error in the final output [39]. It is important that absence samples are selected from areas that are reasonably far from the area of the presence samples. Therefore, studies should seek to systematically reduce uncertainties associated with absence samples.

In light of these problems, it is necessary to develop a robust novel tool for selecting absence samples with high accuracy and precision. The main objectives of the present study were thus to: (1) develop an automated, user-friendly tool for selection of absence samples using the Python programming language to select absence samples; (2) apply the selected absence samples in two different machine learning models, random forest (RF) and multivariate adaptive regression splines (MARS), to analyze groundwater potential; (3) evaluate the model accuracy using two common statistical methods; and (4) compare the results of models using absence samples generated by the SAS tool and by a simple random method. The RF and MARS models were chosen because they have been commonly used by different scholars for groundwater potential mapping and their capabilities have been proven [3,10,15,40,41]. This allowed us to investigate only the efficiency of the developed tool, selection of absence samples (SAS). Another reason for selecting these two models is that in terms of model structure they are very different. It should be pointed out that there are a number of other machine learning models, but comparison of their performance was outside the scope of this paper. The novel feature of this study was to develop a suitable framework for selecting absence samples and statistically comparing their performances against those of the ordinary random methods used by previous researchers.

2. Development of the SAS Tool

2.1. Technical Background

In order to create a robust absence sample dataset, different precondition analyses were considered. The conceptual architecture of our approach for selection of absence samples (the SAS tool) is illustrated in Figure 1. In the following subsections, the three-step process is explained in detail.

Step 1: Determining a buffer for presence samples

One of the main problems with selecting absence samples based on a random paradigm is that the absence samples selected may be at or very close to presence samples, which can cause different errors in the model results. In the random sampling method, absence and presence samples may be selected from regions with completely similar properties in which the triggering factors are in a similar condition. Consequently, the modeling approach may encounter a serious misunderstanding about the related process. Therefore, the first step in the SAS tool is to create a buffer zone around the presence samples. This method has been used previously to define absence samples for landslide susceptibility mapping by extracting absence samples from randomly distributed circles [7]. This buffer causes the absence and presence samples to be selected reasonably far from each other. In the SAS tool, the radius of the buffer can be determined by the user and depends on the nature of the phenomenon under study.

Step 2: Average nearest neighbor

Another important issue in absence sample selection is their distribution in the study area. An efficient method for determining the distribution pattern of samples is the average nearest neighbor (NN) approach [42,43]. This algorithm measures the distance between the centroid of each object and the centroid of its nearest neighbor using a nearest neighbor index. The average of all these nearest neighbor distances is then calculated. An average nearest neighbor ratio less than 1 indicates that the samples are clustered, while an average nearest neighbor ratio greater than 1 indicates dispersion of samples [44,45]. This algorithm compares average distance with average distance for a hypothetical random distribution. The nearest neighbor (NN) index is calculated as [41]:

$$NN=\frac{{\overline{D}}_O}{{\overline{D}}_E}$$

(1)

where ${\overline{D}}_O$ is the observed mean distance between each feature and its nearest neighbor, calculated using Equation (2), and ${\overline{D}}_E$ is the expected mean distance for a hypothetical random distribution, calculated using Equation (3) [41]:

$${\overline{D}}_O=\frac{{\sum }_{i=1}^n{d}_i}{n}$$

(2)

$${\overline{D}}_E=\frac{0.5}{\sqrt{\frac{n}{A}}}$$

(3)

where d_i equals the distance between feature i and its nearest neighboring feature, n corresponds to the total number of features, and A is the area of a minimum enclosing rectangle around all features or a user-specified area value. The average nearest neighbor z-score can be also calculated as:

$$z=\frac{{\overline{D}}_O-{\overline{D}}_E}{SE}$$

(4)

$$\mathrm{where}SE=\frac{0.26136}{\sqrt{\frac{n^2}{A}}}$$

(5)

Figure 2 shows a schematic illustration of the relationship between distribution pattern of samples and NN index. As can be seen, low values of NN index correspond to a clustered distribution and high values of NN index correspond to a dispersed distribution of samples [46,47].

Step 3: Hotspot analysis (Getis-Ord Gi*)

Hotspot analysis is an efficient way to calculate the Getis-Ord Gi* statistic, which indicates where features cluster spatially [48]. This algorithm considers an object or feature related to its neighboring features. A feature is only considered a significant hotspot when it has a high value and is also surrounded by other features with high values [49]. In this way, the local sum for each feature and its neighbors is calculated. This local sum is then compared against the sum of all features. If the local sum is considerably greater than the estimated local sum and cannot have resulted from random chance, it can be considered a significant hotspot [46,50]. In this study, hotspot analysis was carried out using the Getis-Ord Gi* statistic for each sample in the presence inventory, calculated as [51]:

$$G_i^{*}=\frac{{\sum }_{j=1}^n{w}_{i,j}{x}_j-\overline{X}{\sum }_{j=1}^n{w}_{i,j}}{S\sqrt{\frac{\left[n{\sum }_{j=1}^n{w}_{i,j}^2-{\left({\sum }_{j=1}^n{w}_{i,j}\right)}^2\right]}{n-1}}}$$

(6)

where x_j is the attribute value for feature j, w_i,j is the spatial weight between feature i and j, n is equal to the total number of features, and:

$$\overline{X}=\frac{{\sum }_{j=1}^n{x}_j}{n}$$

(7)

$$S=\sqrt{\frac{{\sum }_{j=1}^n{x}_j^2}{n}-{\left(\overline{X}\right)}^2}$$

(8)

Figure 3 shows a schematic diagram of hotspot analysis. As can be seen in the diagram, there are some points with high values that are not considered hotspots, because the surrounding features have low values [20]. Hotspot areas not only include presence samples with high values, but all samples in these areas are also characterized by high values. Hotspot samples with high values, where the surrounding objects also have high values, are shown in red in Figure 3.

2.2. Designing the SAS Tool

The SAS tool was developed using Python, a powerful, high-level, object-oriented, and structured general-purpose programming language. The ArcPy library, which builds on the successful ArcGIS scripting module, was used in this study. Using this programming language, an extension was provided that can be added to the Arctoolbox in the ArcGIS software. The main SAS tool coding and structure design tasks were to develop an automated procedure for generating absence samples that met the three technical conditions described in Section 2.1.

A view of the SAS tool and its components is presented in Figure 4. As can be seen, this tool has several different parts, including inputs and outputs.

Table 1. Input parameters and files for the Selection of Absence Samples (SAS) tool.

ID	Setting	Description
1	Input a layer of presence samples	The layer of presence samples (positive points) showing the location of occurrences for a given phenomenon should be input in this field. For example, a spring file (include locations and groundwater discharge) should be introduced here.
2	Weight of presence samples	Each presence sample has a value or weight. For example, springs have groundwater discharge.
3	Radius of circles (Buffer for presence samples)	Buffer for presence samples should be determined. These buffer/circles do not allow random absence samples to be placed inside them. Therefore, absence samples are placed in an area that is free of the given phenomenon (e.g., landslide-free area, spring-free area).
4	Hotspot circles (buffer for hotspots)	After determining hotspot locations, users should determine a buffer for them that does not allow absence samples to be placed there.
5	Number of absence samples	In general, the number of absence samples is equal to the number of presence samples. The number of absence samples usually influences the model output.
6	Boundary of the study area	The SAS tool needs a specific area such as a study area to determine the permitted sites for producing absence samples. Users can introduce the study area file for this field.

lists the SAS input parameters and files. In the first part, the presence samples layer is imported by the user. These presence samples (positive points) are the location of occurrences for a given phenomenon in shape file format. This layer can be produced using inventory maps, aerial photographs, satellite images, or field surveys. An example is the location of springs in a specific region. The next part is to assign a value (weight) to the presence samples. Here, the user must define the field that includes values related to the presence samples. For example, the amount of discharge from springs can be imported in this input parameter. Another input parameter in the SAS tool is the radius of circles or the buffer for presence samples. This radius value determines the buffer zone in which absence samples cannot be created. After hotspot samples are calculated, hotspot buffers should be produced for each. As done for the presence samples, the user must determine a buffer zone for the hotspot points. Number of absence samples can be determined in the next field. Generally, the number of absence samples should be equal to the number of presence samples. Finally, the SAS tool needs a boundary of the study area. This boundary helps the tool to determine the permitted sites for producing absence samples.

The SAS tool provides three main outputs, which are listed in

Table 2. Output files of the Selection of Absence Samples (SAS) tool.

ID	Setting	Description
1	Absence samples layer	This file is the main output of the SAS tool, and explains the location of absence samples in the study area. These absence samples are produced based on average nearest neighbor and hotspot analyses. This approach for producing absence samples is better than the simple random method.
2	Hotspot and coldspot layer	This file shows the result of hotspot analysis. It classifies presence samples into three groups: coldspot, medium, and hotspot. This type of classification is based on the value of presence samples (e.g., groundwater discharge) and their distance from each other.
3	Significant hotspot samples	This layer explains which presence samples are significant hotspots in comparison with other presence samples. The selection of hotspot samples depends on both z-score and p-value in hotspot analysis based on the Gi* metric.

. The first output is the absence samples layer, which contains the locations of the absence samples. These samples are selected according to the buffer of presence samples, average nearest neighbor, and hotspot analyses. The second main output of the SAS tool is the ‘hotspot and coldspot’ layer, where SAS classifies the presence samples into three classes, namely coldspot, medium, and hotspot, according to their values. The final output is the significance information from hotspot analysis, which shows presence samples that are significant hotspots in comparison with other presence samples. It is worth mentioning that the aim of the SAS tool is simply to produce an absence sample layer. However, the results of hotspot analysis on presence samples can provide useful information, and therefore we retain them as one of the main model outputs.

3. Case Study

In a case study, the SAS tool was applied to generate an absence sample layer for the Bojnourd watershed, North Khorasan province, Iran (37°15′–37°35′ N, 57°03′–57°40′ E) (Figure 5). The aim in the case study was to model groundwater potential, and an absence sample layer was needed, while presence samples (i.e., groundwater springs) were readily available, as shown in Figure 5. The elevation of the study area ranges between 875 and 2968 m, mean annual precipitation is 272 mm, and mean annual temperature is 13 °C (Khorasan Shomali Meteorological Organization). Groundwater is one of the main water resources in the area. From a geomorphological viewpoint, the region is classified as mountainous and there are several faults and folds that play a significant role in the development of springs. North Khorasan province has around 17,000 km² of karst masses, which supply around 88% of the water demand in the province.

3.1. Application of the SAS Tool

Both the simple random sampling method and the newly developed SAS tool were used to produce absence samples in order to model groundwater potential in the study area. The absence samples generated using the common random method are shown in Figure 6a, and those produced using the SAS tool are shown in Figure 6b. In order to highlight the difference between the random method and the SAS tool, the absence samples they produced are overlaid (Figure 6). In the diagrams, blue circles represent the hotspot buffers and red points the absence samples. As can be seen in the zoomed-in parts of the map, the simple random method created several absence samples that were very close to each other (i.e., had a clustered distribution pattern) and also fell within the hotspot buffers (i.e., blue circles). In contrast, the SAS method created absence samples that were reasonably far from each other (i.e., had a dispersed distribution pattern) and, more importantly, that did not fall within the hotspot buffers. Moreover, with the use of the random method, several parts of the study area had no absence samples, while numerous absence samples were unreasonably concentrated in some other parts. In contrast, the SAS tool met all three preconditions (no absence samples on or near presence samples, dispersed absence samples, no absence samples in hotspot buffers). Therefore, the method used for selection of absence samples had a considerable influence on the absence samples.

3.2. Groundwater-Affecting Factors

Groundwater-affecting factors (GAFs) contribute in the modeling process as independent variables. Since there are no universal guidelines for selecting GAFs, previous studies have considered different geo-environmental and topo-hydrological factors [43,52,53]. Based on the literature, sixteen GAFs were selected in the present study to spatially predict groundwater spring potential. These were altitude, slope, aspect, profile curvature, plan curvature, land use/cover, lithology, soil, distance from fault, distance from stream, stream density, relative slope position (RSP), topographic wetness index (TWI), topographic position index (TPI), terrain roughness index (TRI), and convergence index (CI) (Figure 7 and Figure 8).

Both remote sensing and geographical information system (GIS) techniques were used to produce groundwater-affecting factors. First, a digital elevation model (DEM) was produced using the airborne LIDAR (light detection and ranging) system, which is an effective and reliable means of collecting topographical data in large areas. The triangular irregular network (TIN) generated was converted to an ArcGIS grid of 1 m pixel resolution using a TOPOGRID algorithm. In order to achieve homogeneity with other predictive maps and to increase efficiency in terms of manipulation and storage, the high-resolution DEM produced was coarsened to 10 m resolution. This resolution was considered to create topography-related predictive factors, including altitude, slope, aspect, profile curvature, plan curvature, distance from fault, distance from stream, stream density, RSP, TWI, TPI, TRI, and CI. In addition, in order to create an accurate land use map, Landsat-8 Operational Land Imager (OLI) images in 2018 were used. Atmospheric corrections were performed using the FLAASH module in ENVI software. Next, the Gram-Schmidt pan-sharpening module was used for the fusion of panchromatic and multispectral satellite images. In addition, a supervised classification approach with the maximum likelihood algorithm was carried out. Finally, in accordance with the resolution of other DEM-extracted factors, the land use map produced was resampled with a spatial resolution of 10 m in ENVI software.

Altitude in the study area varies from 877 to 2967 m. A slope map with range from 1% to 736.3% was produced using the DEM generated. The slope aspect classes are shown in Figure 7c. The CI is a terrain parameter that reflects the structure of the relief as a set of divergent areas (ridges) and convergent areas (channels). If the CI value is positive, then the pixel is defined as divergent, while convergent pixels have a negative CI [54,55]. In this study, the CI map was produced in SAGA (System for Automated Geoscientific Analyses) software and the CI value ranged from −99.5 to 99.6 (Figure 7d). The minimum and the maximum ‘distance from fault’ values were calculated to be 0 and 3277 m, respectively (Figure 7e). ‘Distance from streams’ values calculated for the study area varied between 0 and 2324 m (Figure 7f). To analyze the stream density in the study, the Kernel density tool was used. The minimum and maximum stream density values in the study area were 0 and 2.8, respectively (Figure 8a). The RSP map was generated in SAGA software, and its values ranged from 0 to 1 (Figure 8b). TPI measures the difference between elevation at the central point and average elevation around it within a predetermined radius [11]. Negative TPI values show that the central point is located lower than its average surroundings, while positive values indicate a position higher than the average. In this study, TPI values varied between −136.6 and 130.3 (Figure 8c). TRI, produced in SAGA software, was also used as a measurement of terrain heterogeneity. It ranged from −99.5 to 99.6 in the study area (Figure 8d). TWI is one of the secondary topographic factors and is calculated based on the specific catchment area and the local slope. TWI is a relative measure of the soil moisture availability of a given site in the watershed [56]. TWI values ranged from 0.42 to 21.27 in the study area, which indicates significant variation in spatial patterns of saturated areas (Figure 8e). A lithological map of the study area was digitized from a geological map of Khorasan province published by the Geological Survey of Iran (GSI) (Figure 8f). A detailed description of lithological classes can be found in

Table 3. Lithology of the study area.

Era	Period	Lithology
Cenozoic	Quaternary (Q)	Low level piedmont fan and valley terrace deposits
Cenozoic	Neogene (N)	Red marl, gypsiferous marl, sandstone, and conglomerate
Mesozoic	Cretaceous (C)	Olive green glauconitic sandstone and shale
Mesozoic	Early Cretaceous (EC)	Ammonite bearing shale with orbitolin limestone
Mesozoic	Jurassic-Cretaceous (JC)	Pale red argillaceous limestone, sandstone, and conglomerate
Mesozoic	Triassic–Jurassic (TJ)	Subordinate sandy limestone, dark grey shale, and sandstone

.

3.3. Groundwater Potential Modeling

In this study, two state-of-the-art machine learning models, RF and MARS, were used to model groundwater potential, due to their structural flexibility. In the modeling process, two different absence sample types were used: (1) those produced by the simple random method, and (2) those produced by the SAS method (i.e., meeting all three preconditions).

3.3.1. Random Forest (RF)

Random Forest is a non-parametric model introduced as a form of classification and regression tree method [57]. It consists of a combination of tree classifiers, where each tree is created using a random vector sampled independently from the input vector. To classify an input vector, each tree also casts a unit vote for the most popular class. The combination of several classification trees in a forest can improve the performance of predictions. In this approach, a randomized subgroup of variables of interest is used to split the tree, and the average of all tree results is considered the final outcome of the model [53,58]. The random selection of features at each node reduces the correlation between the trees in the forest, thus decreasing the forest error rate. In addition to random feature selection, averaging over numerous trees can also decrease bias and variance [59]. Additionally, RF has vigorous error estimates and higher prediction performance. Other characteristics of RF are random feature selection at each node and a no pruning or stopping rule [60]. Through these, overfitting is significantly reduced. In the RF model, bootstrap samples are used to produce trees. The RF approach rests upon the basic premise that a set of classification trees has better performance than a stand-alone classifier. It has the following advantages [40,53,61]:

• it is relatively robust to noise and outliers;
• it provides an internal unbiased estimate of the generalization error through out-of-bag (OOB) error;
• it estimates the importance of variables in the modeling process (i.e., contribution of variables);
• it can handle numerous input variables (i.e., predictive factors) without variable deletion;
• it efficiently handles large databases; and
• it reduces the computational burden and is computationally lighter than other tree-based models.

In general, design of a tree-based model requires a pruning method and the choice of an attribute selection measure. The Gini index and the information gain ratio are the most frequently used attribute selection measures in tree-based models. RF uses the Gini index to measure the impurity of an attribute. The Gini index allows selection of the split with the lowest impurity at each node [61]. Among the trees in the forest, the class with the maximum number of votes is the predicted class of an observation. In this study, the RF model was implemented using the package ‘randomforest’ in R software.

3.3.2. Multivariate Adaptive Regression Splines (MARS)

The MARS model is a non-parametric form of regression analysis [62]. It combines the mathematical construction of splines, classical linear regression, brute search intelligent algorithms, and binary recursive partitioning to develop a model capable of predicting a target variable [63]. Since MARS uses piecewise basis functions, it can model complex relationships between variables without strong model assumptions. MARS considers each sample as a knot and develops a linear regression model with the candidate feature(s). When implementing a MARS model, knots are selected automatically in a forward stepwise manner. The knot is a key concept in the MARS model and characterizes a point where the behavior of the function changes. In order to define a set of piecewise functions (also known as basic functions, BFs), candidate knots can be placed at any position within the range of each independent variable. In fact, the beginning and end of each BF is determined by a knot. The MARS model selects the knot and its corresponding pair of basic functions at each step, which can significantly decrease the residual sum of squares [64]. The search lasts until all possible BFs have been found. The least important BF is identified and eliminated. Similar to the RF model, MARS is able to analyze the importance of variables and this characteristic is very useful, especially when some potential or new variables are considered. In addition, MARS can save much modeling time when the dataset is huge, because it does not need a long training process [65,66]. It also searches for potential interactions between predictive variables, allowing any degree of interaction to be analyzed in the model building process. Through these characteristics, MARS is able to yield homogeneous final groups in the terminal nodes and minimize prediction errors [67]. In addition, it allows the contribution of predictive variables to be assessed using the generalized cross-validation criterion [66]. The MARS model can be described as follows:

$$\mathrm{Y}={\mathsf{\beta }}_0+\sum _{\mathrm{m}=1}^{\mathrm{M}}{\mathsf{\beta }}_{\mathrm{m}}{\mathrm{h}}_{\mathrm{m}}\left(\mathrm{x}\right)$$

(9)

where Y is the value predicted by the model and can be decomposed into a sum of M terms (each of which is formed by a coefficient β_m and BF h_m(x)) and an initial constant β₀. Detailed background and characteristics of the MARS model can be found in [62]. Therefore, it has considerable advantages in modeling natural processes in data-scarce regions. In this study, the MARS model was implemented using the package ‘earth’ in R software.

3.4. Accuracy Assessment

In order to evaluate the accuracy of the models, a threshold-dependent method (area under the receiver operating characteristic curve, AUC-ROC) and different threshold-independent methods (false positive rate (FPR), true positive rate (TPR), true negative rate (TNR), false negative rate (FNR), the true skill statistic (TSS), and efficiency (E)) [68,69] were used in this study. FPR estimates the probability of incorrectly predicting a non-occurrence location as an occurrence. TPR, also known as sensitivity, indicates the probability of correctly predicting the positives as observed in reality. However, FPR and TPR are insufficient performance metrics, because they ignore false negatives and false positives, respectively [9]. TNR aims to quantify the probability of correctly predicting the negatives as they occur in reality. Furthermore, FNR, also termed miss rate, determines the probability of incorrectly predicting an occurrence location as a non-occurrence. TSS (also called Pierce’s skill score) measures the ability of a predicted value to discriminate between occurrence and non-occurrence. Although researchers have used the kappa coefficient to evaluate model performance, it has some drawbacks, and TSS has been proposed to compensate for these drawbacks while retaining all the advantages of the kappa coefficient [70]. Efficiency E, also known as accuracy, is able to indicate the overall success of the predictive model. These evaluation criteria are commonly applied to investigate model performance [9,70,71,72,73]. All of these evaluation criteria are calculated based on a contingency matrix (

Table 4. Contingency matrix used for evaluation of models.

Observed	Predicted
	Non-Occurrence	Occurrence
Non-occurrence	True negative (TN)	False positive (FP)
Occurrence	False negative (FN)	True positive (TP)

), which includes four components: true positive (TP), true negative (TN), false positive (FP), and false negative (FN). The evaluation criteria are calculated as Equations (10)–(15):

$$\mathrm{TPR}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}$$

(10)

$$\mathrm{FPR}=\frac{\mathrm{FP}}{\mathrm{FP}+\mathrm{TN}}$$

(11)

$$\mathrm{TNR}=\frac{\mathrm{TN}}{\mathrm{TN}+\mathrm{FP}}$$

(12)

$$\mathrm{FNR}=\frac{\mathrm{FN}}{\mathrm{FN}+\mathrm{TP}}$$

(13)

$$\mathrm{TSS}=\mathrm{TPR}-\mathrm{FPR}$$

(14)

$$\mathrm{E}=\frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}}$$

(15)

The ROC curve is produced by plotting the TPR against the FPR [74,75,76]. The area under the ROC curve (AUC-ROC) method is associated with cost/benefit analysis of analytical decision making and can show model sensitivity as a function of information retrieval. The closer the AUC-ROC value is to 1, the better the model performance. All evaluation criteria were calculated using the performance measure tool (PMT) extension [77], which allows learning capability (also termed goodness-of-fit) and predictive performance to be determined based on the training and validation datasets, respectively.

4. Results and Discussion

4.1. Selection of Absence Samples and Accuracy Assessment

The accuracies of the models in the training step (goodness-of-fit) are summarized in

Table 5. Goodness-of-fit of the random forest (RF) and multivariate adaptive regression splines (MARS) models in different sampling strategies.

Sampling Strategies	Evaluation Criteria	Models
		RF	MARS
Selection of Absence Samples (SAS) method	AUC-ROC 1	0.944	0.925
	TSS 2	0.891	0.852
	Efficiency (E)	0.946	0.926
	True positive rate (TPR)	0.938	0.921
	False positive rate (FPR)	0.046	0.069
	True negative rate (TNR)	0.953	0.931
	False negative rate (FNR)	0.061	0.078
Simple random method	AUC-ROC 1	0.926	0.898
	TSS 2	0.852	0.789
	Efficiency (E)	0.926	0.894
	True positive rate (TPR)	0.921	0.892
	False positive rate (FPR)	0.069	0.102
	True negative rate (TNR)	0.931	0.897
	False negative rate (FNR)	0.078	0.107

¹ Area under the receiver operating characteristic curve; ² True skill statistic.

. When the RF model used the absence points produced by the SAS method, it had an AUC-ROC value of 0.944, whereas the AUC-ROC value was lower (0.926) in the simple random sampling method. Threshold-dependent evaluation metrics shed more light on the learning capability of the RF model in both sampling strategies and clearly confirmed the higher accuracy of the RF model in the SAS method (TSS = 0.891, E = 0.946, TPR = 0.938, FPR = 0.046, TNR = 0.953, FNR = 0.061) than in the simple random sampling method (TSS = 0.852, E = 0.926, TPR = 0.921, FPR = 0.069, TNR = 0.0931, FNR = 0.061).

For the MARS model, the SAS method also gave a higher AUC-ROC value (0.925) in comparison with the simple random method (0.898). In addition, for the simple random method, the accuracy of the MARS model decreased in comparison with the SAS method based on threshold-dependent criteria (Table 5). The TSS, E, TPR, FPR, TNR, and FNR values in the SAS method were 0.852, 0.926, 0.921, 0.069, 0.931, and 0.078, respectively, while in the simple random method the corresponding values were 0.789, 0.894, 0.892, 0.102, 0.897, and 0.107, respectively. Therefore, there was better agreement between the predictions of both models and reality in the SAS method. However, while goodness-of-fit shows how well the model fits to the training dataset and also reflects the learning capability of the model, the prediction performance of the model cannot be judged by goodness-of-fit because it is measured by the training dataset already used for model calibration [31].

The predictive performances of the RF and MARS models with the different absence sample selection strategies are shown in

Table 6. Predictive performance of the random forest (RF) and multivariate adaptive regression splines (MARS) models in different sampling strategies.

Sampling Strategy	Evaluation Criteria	Models
		RF	MARS
Selection of Absence Samples (SAS) method	AUC-ROC 1	0.913	0.889
	TSS 2	0.72	0.705
	Efficiency (E)	0.926	0.90
	True positive rate (TPR)	0.921	0.905
	False positive rate (FPR)	0.067	0.105
	True negative rate (TNR)	0.932	0.894
	False negative rate (FNR)	0.078	0.094
Simple random method	AUC-ROC 1	0.872	0.833
	TSS 2	0.681	0.67
	Efficiency (E)	0.906	0.86
	True positive rate (TPR)	0.896	0.855
	False positive rate (FPR)	0.082	0.135
	True negative rate (TNR)	0.917	0.864
	False negative rate (FNR)	0.103	0.144

¹ Area under the receiver operating characteristic curve; ² True skill statistic.

. Both the RF (AUC-ROC = 0.913, TSS = 0.72) and MARS (AUC-ROC = 0.889 and TSS = 0.705) models showed better performance when absence samples generated by the SAS tool were used in modeling. When absence samples of the random method were used, the performances of both models were considerably lower, with the RF model showing an AUC-ROC of 0.872 and a TSS of 0.681, and the MARS model an AUC-ROC of 0.833 and a TSS of 0.67.

When the simple random method was used to generate absence samples, the RF model gave E = 0.906, TPR = 0.896, FPR = 0.082, TNR = 0.917, and FNR = 0.103, while MARS gave E = 0.86, TPR = 0.855, FPR = 0.135, TNR = 0.864, and FNR = 0.144. However, when using the SAS method, the RF (E = 0.926, TPR = 0.921, FPR = 0.067, TNR = 0.932, and FNR = 0.078) and MARS (E = 0.9, TPR = 0.905, FPR = 0.105, TNR = 0.894, and FNR = 0.094) models showed better predictive performance. Another important finding in this study was that the RF model outperformed the MARS model, irrespective of the absence sampling method used (Table 6).

In this study, both the RF and MARS models showed better performance when based on the newly developed SAS tool, because it overcomes all the disadvantages associated with the simple random method. The results obtained demonstrate that the method and strategy used for production of absence samples significantly influences model prediction accuracy. The most interesting finding was that absence samples created by the SAS tool had a dispersed distribution pattern and were far from hotspot areas. In addition, the average nearest neighbor method resulted in a more even distribution of selected samples, which were more representative of the overall situation in the study area. Since hotspot areas are statistically significant, the end visualization is less subjective. Through these advantages, the SAS tool can enhance the ability of models based on presence–absence samples. However, it is difficult to directly compare the results of this study with those in previous publications, because there is no standard method for producing absence samples in the field of groundwater potential mapping. In landslide susceptibility modeling, a previous study investigated the effects of absence samples on model prediction and suggested that a buffer around presence samples can efficiently increase the accuracy of absence samples [7]. In other environmental fields, sampling strategy has been shown to have a significant influence on model performance [78,79].

Despite this, the simple random method has been widely applied by researchers [24,35,44,80]. Another disadvantage of the simple random method is that each pixel of the study area, even presence locations, has an equal chance of being selected as an absence sample [51]. Moreover, the distribution pattern of the absence samples generated by the simple random method is sometimes clustered and consequently cannot be representative of the population (i.e., pixel values in the study area) [81,82]. When absence samples are not truly representative of the population, the resulting error in the model output is called a ‘sampling error’ [52,83]. Therefore, although the simple random method is easy to use, it does not consider any criteria or essential preconditions. These shortcomings prompted us to develop a new method for creating absence samples based on statistical and spatial analyses.

4.2. Groundwater Potential Mapping

The groundwater potential maps produced by the RF model based on the simple random method and the SAS method for producing absence samples are shown in Figure 9, while the corresponding maps created by the MARS model are shown in Figure 10. The blue color in the maps indicates high groundwater potential values, while red color indicates low values. All maps show high groundwater potential in southern parts of the study area.

Table 7. Statistical characteristics of the probability values obtained from the random forest (RF) and multivariate adaptive regression splines (MARS) models based on the simple random and selection of absence samples (SAS) methods.

Model	Simple Random Method				SAS Method
	Minimum	Maximum	Mean	SD	Minimum	Maximum	Mean	SD
RF	0.002	0.989	0.339	0.228	0.003	0.994	0.351	0.232
MARS	0.010	1.000	0.309	0.307	0.010	1.000	0.287	0.300

SD: Standard Deviation.

shows the statistical characteristics of the probability values obtained from the RF and MARS models based on the simple random and SAS methods. As can be seen from the table, the RF method gave higher mean values and lower standard deviation with both the simple random and the SAS methods. From an aerial viewpoint, southern parts of the Bojnourd watershed have the highest groundwater potential based on both models. In this regard, others have reported a similar pattern for groundwater potential in this study area [43,73].

In this study, the RF and MARS methods were used to produce groundwater potential maps. Both models showed fairly good performance, but RF outperformed MARS based on the AUC-ROC and TSS evaluation criteria. RF is a powerful predictive model that combines several different decision trees to build a forest of trees [72]. In our earlier studies in the Mehran region, Iran, RF also demonstrated excellent performance in predicting groundwater potential [73]. Similar findings have been made in some other studies [10,15,82]. Appropriate determination of groundwater potential can help decision makers and stakeholders formulate effective groundwater policies and strategies [84,85].

5. Concluding Remarks

Sampling strategy is of great importance in groundwater potential modeling. However, selecting appropriate absence samples is a considerable challenge, and researchers often use a simple random sampling technique to deal with this challenge. The random sampling method can be a significant source of error in the groundwater modeling process. Hence, in this study, an automated, user-friendly tool for creating absence samples called selection of absence samples (SAS) was developed using the Python programming language. The SAS tool uses nearest neighbor index and hotspot analysis to produce robust and reliable absence samples. In a case study, the SAS tool was successfully applied to produce absence samples for groundwater potential modeling. The main finding of the study is that both the RF and MARS models showed better predictive performance when based on absence samples created by the SAS method rather than the simple random method. These findings improve understanding of the influence of sampling strategy on model output. Other data obtained in this study suggest that the SAS not only produces a proper distribution of absence samples, but also improves the performance of data mining and machine learning models for groundwater potential mapping. However, further research is needed to identify limitations of the SAS tool. In future investigations, it might be possible to consider topo-hydrological characteristics for selecting absence samples that enhance the efficiency of the SAS tool. Another task for future investigations is to investigate the performance of the SAS tool in a number of spatial modeling sub-fields (e.g., landslide, land subsidence, flooding).

Tool information

Name of tool: SAS (selection of absence samples)

Developers: Samadi, M., Rahmati, O.

Hardware required: General-purpose computer (3 Gb RAM)

Software required: ArcGIS 10.2 (or higher versions)

Program language: Python

Tool size: 5.1 kb

Availability: https://github.com/mahmoodsamadi/SAS

Cost: free of charge