An Enhanced Approach to the Spatial and Statistical Analysis of Factors Influencing Spring Distribution on a Transboundary Karst Aquifer
Abstract
:1. Introduction
2. Proposed Methodology
2.1. Weights of Evidence Technique
2.2. Workflow for the Application of the WofE Technique for Karst Springs
 I
 Q1—where is it possible to find karst springs?
 II
 Q2—where is it possible to identify the permanent karst springs?
 calculation of the prior probability;
 generalisation of the evidential themes, and evaluation of contrast C, weights W^{+} and W^{−};
 evaluation of the statistical and physical significance of the generalised evidential themes; and
 creation of the posterior probability map.
 analysis using the permanent springs as TPs (calculation of the prior probability, generalisation of the evidential themes, evaluation of contrast C, weights W^{+} and W^{−}, statistical and physical significance, and creation of the posterior probability map);
 analysis using all springs as TPs on the generalised evidential themes (evaluation of contrast C, weights W^{+} and W^{−}, statistical and physical significance) and calculation of the prior probability;
 calculation of the adjusted contrast and weights, by subtracting C, W^{+} and W^{−} calculated using all springs as TPs (step 2) from C, W^{+} and W^{−} calculated using the permanent springs as TPs (step 1);
 creation of the adjusted posterior probability map using: (i) the prior probability calculated using all springs and (ii) adjusted weights obtained from step 3;
 reclassification of the posterior probability values in 5 classes, using the geometrical interval classification method; and
 comparison of the adjusted posterior probability map (step 4) with the posterior probability map, obtained using the standard WofE approach (step 1), and their derived reclassified maps, through calibration and validation techniques (Table 1). In this phase, we use the temporary springs, as CPs, for the validation of the adjusted map.
3. Application of the Proposed Workflow
3.1. Geological and Hydrogeological Characterisation of the Study Area
3.2. Evidential Themes
3.3. Response Variables
4. Results
4.1. Location of Springs (Q1)
4.2. Location of Permanent Springs (Q2)
4.3. Validation
5. Discussion
6. Summary and Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Concept  Definition  Operative Translation in... 

Response variable  The phenomenon under consideration (e.g., mineral deposits). The location of occurrences is known. The occurrences are treated as points. Occurrences are subdivided into two sets used for generating the response themes (training set) or performing calibration and validation processes (control set) [17,18].  Examples: mineral deposits (e.g., [17]), landslides (e.g., [19]), contaminated water wells (e.g., [23,31]). Occurrences can be either training points (TPs), being part of the training set, or control points (CPs), as part of the control set. 
Evidential themes or predictors  Factors influencing the location and spatial distribution of the response variable. Evidential themes represent sets of continuous or categorical spatial data [17,18].  Geological, geomorphological and physical factors influencing the presence and spatial distribution of the phenomenon under consideration, for example:

Response theme or predictive probability map  The response theme (i.e., predictive probability map) is the result of the WofE [32].  A response theme (i.e., predictive probability map) is an output data layer showing the distribution of posterior probability values [32]. It represents the relative probability of occurrence of the phenomenon under consideration (e.g., presence of mineral deposits, landslides risk, groundwater vulnerability). 
Prior probability  The probability that a unit area contains an occurrence without considering any evidential themes [17,18].  It is given by the ratio between the number of unit areas containing a TP and the total area [17]. 
Posterior probability  The posterior probability represents the relative probability that a unit area contains an occurrence based on the evidences provided by the evidential themes [17,18].  The posterior probability is calculated by adding a weight for each evidence class to the logit of the prior probability and converting the sum from logit to probability [17]. 
Generalization of the evidential themes  Ordered evidential themes can be generalized during the analysis to improve model results relating the number and location of TPs and the presence of random effects [32].  Generalizing an ordered evidential theme means defining ranges of values that can be grouped into evidence classes, which have a statistically significant spatial correlation with the location of TPs [32]. An objective (semiguided) procedure has been developed by Sorichetta, Masetti, Ballabio and Sterlacchini [16]. 
Weights  Weights establish a spatial association between TPs and evidential themes. Weights are the values assigned to each evidence class [18,32].  Weights are calculated for each evidential theme based on the presence or absence of TPs [18,32]:

Contrast  The contrast is a measure of the usefulness of each evidence class in predicting the location of the occurrences [17,18].  For each class of each evidential theme, the contrast is calculated as the difference between the positive and the negative weight (C = W^{+} − W^{−}). A positive contrast value means a direct correlation between the class and the TPs, and a negative value means an indirect correlation, whereas a value close to zero means low or no correlation [18] 
Statistical significance  A level of significance needs to be established prior the generalization process. This is equivalent to a Student ttest [18,23].  A confidence value for the ratio between the contrast and its standard deviation (i.e., normalized contrast) must be selected to provide a useful measure of the significance of the contrast and, thus, to the respective class of an evidential theme. See [23], for a complete list of confidence values and relative test values. 
Scientific explanation  The pattern distribution of an evidential theme after the generalization process needs some justification by scientific reasoning [16,18,19,23,31,33].  The pattern distribution needs to be justifiable from either a geological (e.g., [34]), geomorphological (e.g., [19]) or hydrogeological (e.g., [31]) point of view. 
Bias  Statistical models generally require the use of random samples of a population. A bias could occur when the spatial distribution of occurrences differs greatly from an ideal random setting. Such condition could occur in mineral exploration researches or hydrogeological studies. For example, sources of exploration bias include land accessibility factors (location of outcrops, roads, lakes, swamps, property boundaries, political boundaries, etc.) and perceived exploration criteria (faults, alteration, geochemical anomalies, etc.); in most hydrogeological settings, biased distribution of monitoring wells is due to land accessibility factors and a tendency to site more monitoring wells in known contaminated areas than in other areas [35,36].  Sorichetta, Masetti, Ballabio and Sterlacchini [16] developed a quantitative methodology that allows sampling bias to be recognized and contrast values to be corrected for sampling bias effects in hydrogeological studies. In an ideal random setting, contrasts calculated using all occurrences (both TPs and CPs) should have values of near zero for all evidence classes. If a bias occurs, the contrast is adjusted by subtracting the contrast calculated using all occurrences from the contrast calculated using either a) the TPs or b) the CPs. This procedure requires that the same classification of the Evidential Themes is used for both the analyses with all occurrences and either the TPs or the CPs. 
Reclassified Predictive Probability Map  Scientifically defensible response themes, expressed as probability maps, require additional interpretation before being usable for most of the enduser purposes. This is due to the excessive number of classes, which is inappropriate in practical purposes (e.g., land use regulations) [37,38,39].  Sorichetta, Masetti, Ballabio, Sterlacchini and Beretta [38], in their study on groundwater vulnerability assessment, have demonstrated the reliability and suitability of the geometrical interval classification method for reclassifying posterior probability values and obtain maps consisting of few classes (5). The geometrical interval classification method which ensures that each class has approximately the same number of different post probability values. 
Calibration & Validation  The meaningfulness, reliability and accuracy of the probability maps need to be checked to improve defensibility of the results and facilitate implementation [19,23,38,40].  Techniques: 
Data  Use  Data Source 

digital elevation model (SRTM, resolution of 3 arcseconds)  evidential theme: DE  [48] 
geological map (1:100,000)  evidential themes: FA and CC  [49] 
sinkhole database (location)  evidential theme: SH  Cadastre of sinkholes (Aggtelek National Park) 
modelled yearly average precipitation map (1000 m resolution)  evidential theme: PC  http://tinyurl.com/ClimateEU 
spring database (location and activity: permanent or temporary)  response variables  [30]; Cadastre of springs (Aggtelek National Park) 
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Iván, V.; Stevenazzi, S.; Pollicino, L.C.; Masetti, M.; MádlSzőnyi, J. An Enhanced Approach to the Spatial and Statistical Analysis of Factors Influencing Spring Distribution on a Transboundary Karst Aquifer. Water 2020, 12, 2133. https://doi.org/10.3390/w12082133
Iván V, Stevenazzi S, Pollicino LC, Masetti M, MádlSzőnyi J. An Enhanced Approach to the Spatial and Statistical Analysis of Factors Influencing Spring Distribution on a Transboundary Karst Aquifer. Water. 2020; 12(8):2133. https://doi.org/10.3390/w12082133
Chicago/Turabian StyleIván, Veronika, Stefania Stevenazzi, Licia C. Pollicino, Marco Masetti, and Judit MádlSzőnyi. 2020. "An Enhanced Approach to the Spatial and Statistical Analysis of Factors Influencing Spring Distribution on a Transboundary Karst Aquifer" Water 12, no. 8: 2133. https://doi.org/10.3390/w12082133