Fuzzy analysis for borehole site selection

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Hydrogeology JournalOfficial Journal of the InternationalAssociation of Hydrogeologists ISSN 1431-2174 Hydrogeol JDOI 10.1007/s10040-014-1166-5

Site selection for drinking-water pumpingboreholes using a fuzzy spatial decisionsupport system in the Korinthia prefecture,SE Greece

Andreas K. Antonakos, KonstantinosS. Voudouris & Nikolaos I. Lambrakis

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Site selection for drinking-water pumping boreholes using a fuzzy

spatial decision support system in the Korinthia prefecture,

SE Greece

Andreas K. Antonakos & Konstantinos S. Voudouris & Nikolaos I. Lambrakis

Abstract The implementation of a geographic informa-tion system (GIS)/fuzzy spatial decision support system inthe selection of sites for drinking-water pumping bore-holes is described. Groundwater is the main source ofdomestic supply and irrigation in Korinthia prefecture,south-eastern Greece. Water demand has increased con-siderably over the last 30 years and is mainly met bygroundwater abstracted via numerous wells and boreholes.The definition of the most “suitable” site for the drilling ofnew boreholes is a major issue in this area. A method ofallocating suitable locations has been developed based onmulticriteria analysis and fuzzy logic. Twelve parameterswere finally involved in the model, prearranged into threecategories: borehole yield, groundwater quality, andeconomic and technical constraints. GIS was used tocreate a classification map of the research area, based onthe suitability of each point for the placement of newborehole fields. The coastal part of the study area iscompletely unsuitable, whereas high values of suitabilityare recorded in the south-western part. The studydemonstrated that the method of multicriteria analysis incombination with fuzzy logic is a useful tool for selectingthe best sites for new borehole drilling on a regional scale.The results could be used by local authorities anddecision-makers for integrated groundwater resourcesmanagement.

Keywords Groundwater management . Productionboreholes . Multicriteria analysis . Fuzzy logic . Greece

Introduction

In many countries, groundwater is the primary resourcefor irrigation and domestic supply. For this reason,preserving its availability and quality is crucial for thefuture (UNESCO 1998). One of the major issues thatneeds to be addressed by hydrogeological researchconcerns the definition of the most suitable sites for thedrilling of new boreholes, especially in areas where waterresources are scarce or under environmental pressure.Thus, the selection of sites for drinking-water pumpingboreholes should be based on the analysis of a largeamount of high-quality data. The most often used methodsfor site selection consist of analog approaches, regressionmodels, location allocation models, and checklistmethods. In addition, artificial intelligence techniquessuch as artificial neural networks (Lee et al. 2004) andfuzzy logic (Ercanoglu and Gokceoglu 2002) have beenused in site selection.

Decision support systems (DSS) are computerizedsystems, which include models and databases that areused in decision-making. They are useful tools that helpscientists and administrators in choosing the best (eco-nomic, social or environmental) and/or alternative solu-tions (Leung 1997; Manos et al. 2007).

Geographic information systems (GIS) and decisionsupport systems (DSS) offer strong facilities for ground-water resources management (Manos et al. 2007). DSSfeaturing mechanisms for the input and use of spatialinformation, as well as for the output of thematic maps,are known as spatial decision support systems (SDSS)(Vacik and Lexer 2001). The SDSS could be based onmultiple criteria decision-making techniques (Hwang andYoon 1981; Zhu et al. 1998).

Models used for the site selection process are usuallyprescriptive. These models involve the application of a setof criteria that are set out as good engineering practice andmay result from a blend of scientific, economic and socialfactors. In the case of site selection for the drilling of newboreholes, there are several criteria and, in most cases,they are independent. The most important of these criteriarelate to the productivity of the aquifer system (hydrauliccharacteristics, recharge, groundwater balance, etc.),groundwater quality, aquifer pollution potential, and

Received: 5 November 2013 /Accepted: 20 June 2014

* Springer-Verlag Berlin Heidelberg 2014

A. K. Antonakos :N. I. LambrakisDepartment of Geology,University of Patras, Patras, Greece

K. S. Voudouris ())Lab. of Engineering Geology & Hydrogeology,Department of Geology,Aristotle University, 54124 Thessaloniki, Greecee-mail: [email protected]

Hydrogeology JournalDOI 10.1007/s10040-014-1166-5

Author's personal copy

economic and technical issues (the site accessibility,expected drilling depth, etc.). Most of these criteria canbe expressed geographically, since they can be counted ascontinuous spatial distributions (Zhu et al. 1998).

In order to manage the uncertainty, fuzzy logicapproaches have been adopted (Uricchio et al. 2004).Use of GIS for site selection involves finding locations orzones that satisfy a set of criteria. If the criteria are definedas a set of deterministic rules, the model consists ofapplying Boolean operators to a set of input maps, and theoutput is a binary map, because each location is eithersatisfactory or not. Alternatively, each location may beevaluated according to weighted criteria, resulting in aranking on a suitability scale. The subsequent selectionprocess then benefits from the ability to assess suitabilityrankings, rather than simply presence/absence, and fromthe knowledge of spatial patterns of suitability. Sitesuitability is calculated by the weighting and combiningof multiple sources of evidence.

The assignment of weights can either be carried outwith statistical criteria, by use of an actual study region toestimate the spatial relationships between predictor mapsand the response map calibrated by known places suitablefor the placement of new boreholes, the weights can beestimated on the basis of expert opinion. These two typesare usually called “data-driven” and “knowledge-driven”models, respectively. In data-driven modeling, the variousinput maps are combined by use of models such as logisticregression, weights of evidence or neural network analy-sis. Knowledge-driven models include the use of fuzzylogic or Bayesian probability (Stoms et al. 2002;Pourghasemi et al. 2012).

A “data-driven” model is difficult to apply in the caseof site selection for the placement of new boreholesbecause it is very difficult to define what is “suitable” orwhat can be distinguished as “unsuitable”, as can be done,for example, with mineral potential mapping, whereplaces of existent ore deposits can be distinguished as“suitable”, or in the case of aquifer pollution potentialwhere places with concentration of a pollutant above acertain limit can be distinguished as “unsuitable”. Among“knowledge-driven” methods, that of fuzzy logic allowsflexible combinations of weighted maps, and can bereadily implemented with a GIS modelling language.The method applied in this study is based on a subjectiveempirical model, with the fuzzy membership values beingassigned subjectively, using a knowledge of the processinvolved to estimate the relative importance of the inputmaps.

The aim of the present study is to apply themulticriteria analysis within a GIS environment, in orderto create a classification map of the research area inGreece, based on the suitability of each point for theplacement of new borehole fields. Firstly, the paperdescribes a hydrogeological survey, the results of whichenabled, amongst others, identification of the aquifersystem that exists within the study area, acquisition ofgroundwater quality data, and a vulnerability assessmentof the aquifer system to pollution. Secondly, the criteria

are discussed and the final choices are introduced. Finally,a fuzzy spatial decision support system approach for siteselection of drinking-water pumping boreholes in a GIScontext is presented.

Although fuzzy DSS have been developed to supportlocal authorities and decision makers for groundwaterresources management, and for vulnerability and pollutionrisk assessments (Süzenm and Doyuran 2003; Voudouriset al. 2010), such investigations are limited, as deducedfrom international literature. The proposed method can beapplied in other areas with different hydrogeologicalconditions.

Description of the study area

General characteristicsThe study area is in the north-eastern part of the Korinthiaprefecture in NE Peloponnesus, Greece, covering an areaof 902 km2 (Fig. 1). The study area is drained mainly byfour torrents: Asopos, Zapantis, Rachianis and Xerias. Thetopographic relief is gentle from north to south and variesfrom 0 to 1,600 m above sea level (a.s.l.).

The study area is characterised by Mediterraneanclimatic conditions and non-homogeneous distribution ofrainfall and water resources. The mean annual precipita-tion in the study area for the period 1975–2004 is594 mm, which corresponds to mean annual rainfall watervolume of 536×106 m3. Precipitation (P) is directly relatedto altitude (h) by the relationship: P=0.34h+468. Thewater balance parameters have been computed accordingto the procedures described by Thornthwaite and Mather(1957). A major amount of the annual precipitation,approximately 361×106 m3 (67.5 %), is lost via evapo-transpiration, while 103×106 m3 (19.1 %) infiltrates andrecharges groundwater. The remaining amount of water,72×106 m3 (13.4 %), discharges to the sea as surfacerunoff (Voudouris et al. 2007).

Socioeconomic stability of the studied area is based onwater-resources availability, which ensures adequate agri-cultural production and tourism development (Voudouriset al. 2007). A major part of the study area, 49.9 %, iscovered with intensive cultivations (vineyards, fruit trees,olive groves), which are widely spread throughout thestudy area. The use of inorganic fertilisers in thesecultivations has a great polluting effect on groundwater.The spread of irrigated land increased greatly in the lastfew decades to meet demand, as indicated by the numberof wells and boreholes (~500 in 1990 to ~2,500 in 2006).The average depth of production boreholes increased from18 m in the late 1970s to 40 m in the 1990s. In the lastfew decades many deep boreholes have been opened andmany shallow irrigation water-supply boreholes have rundry (Voudouris 2006).

The water needs in the coastal zone of the study areaare predominantly covered by the exploitation of coastalaquifers, through a large number of boreholes.Overexploitation causes a deficient groundwater balancein many coastal aquifers, triggering saline water intrusion,

Hydrogeology Journal DOI 10.1007/s10040-014-1166-5


which has negative consequences on the socioeconomicdevelopment of the area. In recent years, seawaterintrusion has been more evident, owing to high rates ofurbanisation and increased agricultural activities(Panagopoulos et al. 2002).

Geological and hydrogeological settingThe study area is characterised by a complex geologicalstructure (Fig. 2). The geological bedrock consists of thecarbonate sediments of the Trapezona sequence (atransition zone between Pindos and Pelagonian geotec-tonic zones) in the south-eastern part of the study area andthe carbonate sediments and flysch of the Pindos andTripolis zones in the south-western part of the study area(Katsikatsos 1992).

The Trapezona carbonate sequence consists of platedlimestones of Triassic to Upper Jurassic age with nodulesand thin bands of chert. In Middle Jurassic, this sequencewas interrupted by shales and cherts formations made upof bedded sandstone clay and marl with ophiolithic bodiesin them.

The Tripolis zone consists of a dolomitic limestone tolimestone series of Upper Jurassic to Eocene age whichare unconformably overlaid by the Tripolis zone flyschformation. The Pindos zone formation in the study areaconsists of Upper Cretaceous platy limestones which areunconformably overlaid by the Pindos zone flyschformation. The Pindos zone is geotectonicallyoverthrusted on the Tripolis zone with a general NE–SWthrust direction.

The main part of the study area is covered by post-orogenic sediments of Pliocene to Holocene age whichunconformably overlay the bedrock formations. They

consist of Pliocene lacustrine marls interbedded with thinlayers of conglomerates and sandstones, cemented fluvial(proximal and distal) conglomerates of Calabrian age, seaterraces of Tyrrhenian age, alluvial deposits consisting ofalternations of red sand, clay, sandy loam and looseconglomerates of Pleistocene age and finally recentalluvial deposits and talus cones (Fig. 2).

From a hydrogeological point of view six majorhydrogeological units (aquifers) can be distinguished:

& The carbonate aquifers of the bedrock which are fullykarstic for the Trapezona sequence and Tripolis zone andpartly karstic for the Pindos zone. They are highlyproductive aquifers with an average thickness of 100–400m and hydraulic conductivity values varying from 1 to775 m/day (Mastoris et al. 1971; Morfis and Zojer 1986).

& The flysch formations of Tripolis and Pindos zones aswell as the shales-cherts formations of the Trapezonasequence can be distinguished as impermeable units.

& The Pliocene marl aquifer that develops in the thinbeds of sandstones and conglomerates interbeddedwithin the marl formation. It is a confined aquifer withan average thickness of 2–10 m and low hydraulicconductivity values (below 1 m/day; Mastoris et al.1971).

& The Calabrian conglomerates aquifer with an averagethickness of 50–100 m and high values of hydraulicconductivity (129 m/day; Zervogiannis 1991).

& The aquifer that develops within the alluvial and seaterrace formations, with an average thickness of 30–50 m and medium to high hydraulic conductivityvalues (2 m/day; Mastoris et al. 1971).

& The aquifer that has developed within recent alluvialand talus cone deposits with an average thickness of40–60 m and hydraulic conductivity values varying

Fig. 1 Geographic orientation map of the study area in Greece



from 8 to 69 m/day (Koumantakis et al. 1999). Thisaquifer is in most cases in hydraulic contact with theunderlay aquifer of alluvial deposits and sea terraceformations from which it is laterally recharged(Stamatis and Voudouris 2003).

The impermeable layer underlying all the aquifers ofthe post-orogenic sediments is the lacustrine marls of thePliocene marl formation, as can be seen in the geologicalcross-section of Fig. 2.

Groundwater qualityBased on previous hydrochemical investigations(Voudouris et al. 2000; Panagopoulos et al. 2002), thewater of the study area is of various hydrochemical types:Ca–HCO3 is the predominant water type in freshwatersnear the recharge zones of the aquifer system. This type ofwater occurs along the southern part of the studied area.Na–HCO3 type, as well Na–SO4 and Na–Cl types areapparent downstream of the recharge zones indicatingexcessive mixing and ion exchange processes and seawa-ter intrusion.

The distribution of chloride shows a general increase ofconcentration down gradient, to the north towards thecoastline. So far, saline water intrusion is mainly exhibitedat specific zones along the coastline and especially theLecheo and Vrachati areas. Nitrate pollution is the second

major source of groundwater degradation in the studyarea. High nitrate is noticeable throughout the entireregion, rendering most of the samples unsuitable fordrinking, as concentrations far exceed 50 mg/L (CouncilEU 1998). High nitrate concentrations are attributed toseveral sources, the most important of which are the“irrational” application of fertilizers, septic tanks, and thedisposal of untreated domestic effluent into abandonedwells (Voudouris et al. 2004).

Methodology

Choice of the criteriaThe architecture and main components of the SDSS areshown in Fig. 3. Twelve parameters were finally involvedin the model, prearranged in three categories:

1. Criteria of borehole yield2. Criteria of groundwater quality3. Economic-technical criteria

The choice of the criteria included in the model wasbased on the particular hydrological, hydrogeological andhydrochemical conditions of the study area. The firstcategory of criteria indicates that in order for a site to beappropriate for the drilling of a new borehole, it must

Fig. 2 Geological map and geological cross section of the study area



ensure a satisfactory yield compared to adjacent sites andregarding the intended use (municipal, private).

The yield (productivity) of a borehole depends on thetechnical completeness, as well as the hydraulic charac-teristics and the recharge of the aquifer system.Transmissivity values were used to approximately esti-mate the possibility of groundwater abstraction (Krásný1993). Calculation of the transmissivity was based onresults from pumping test analyses, applying Theis, Jacoband recovery methods (Todd and Mays 2005).Furthermore, the calculation of transmissivity can bebased on the specific capacity, which has been consideredthe most representative parameter for productivity whenpumping test data are not available (Neves and Morales2007). Specific capacity (Q/s) is defined as the ratio ofdischarge (Q) to drawdown (s) at the pumping boreholefor a given time (Jalludin and Razack 2004). In addition,an extra criterion of yield was used, and that is the densityof the existing boreholes, which increased in areas wherehigh yield values were ascertained.

Groundwater recharge in the aquifer occurs via thefollowing mechanisms:

& Direct infiltration of rainfall& Seepage from surface-water bodies (rivers and lakes)

through river-lake beds, mainly in the nearby area andin cases where the aquifer is hydraulically connected tothe surface-water bodies

& Lateral subsurface inflows

Furthermore, return flow of water applied to the land asirrigation is also essential to the system’s replenishment(Voudouris 2006). Consequently, as criteria for thesufficiency of recharge of the aquifer, both the quantity

of the infiltrated water in the area and the distance fromthe adjacent surface water bodies must be used.

Based on the previous considerations, four criteriaconcerning the yield of the borehole were defined:

1a. The transmissivity of the aquifer, as determined by thepumping tests or estimated from specific capacityvalues

1b. The productivity of the aquifer, as determined by thedensity of the operating boreholes

1c. The direct recharge of the aquifer, as determined bythe quantity of infiltration

1d. The induced recharge of the aquifer, as determined bythe distance from the adjacent surface water bodies(Todd and Mays 2005; Voudouris 2006)

Spatial distribution of these criteria for the study area ispresented in Fig. 4. The choice of the second category ofcriteria is based on the assumption that groundwater fromany borehole must attain certain water quality standards,which will appoint it as appropriate for any particular use(domestic, irrigation, industrial). Apart from the existingquality conditions of the aquifer, the expected qualityconditions of the aquifer must also be considered, basedon the assessment of the aquifer’s vulnerability topollution. Vulnerability refers to the sensitivity of anaquifer system to deterioration due to human activities(Al-Zabet 2002).

The existing quality of the groundwater can becharacterized by a general index of the chemicalcomposition such as the total dissolved solids (TDS) orthe electrical conductivity (EC), or by the use ofindividual indicators such as the concentration ofparticular ions. As was mentioned before, high

Fig. 3 Architecture and main components of the SDSS



concentrations of nitrate (NO3–) and chloride (Cl–) ions

are recorded in the study area. In this work, the use of ageneral index such as electrical conductivity was decidedupon, because in most parts of the study area, qualitydeterioration is the result of high concentrations of morethan one element.

The expected groundwater quality in the study area isdetermined mainly from the aquifer specific vulnerabilityto pollution, as estimated using the methods described byAntonakos and Lambrakis (2007), and also from theseawater intrusion potential, as seawater intrusion is aphenomenon that occurs extensively in both porous andkarst aquifers in the study area.

Aquifer specific vulnerability was determined by usingthe modified DRASTIC method (Aller et al. 1987), firstdescribed by Panagopoulos et al. (2005), and evaluated forthe study area by Antonakos and Lambrakis (2007). Theacronym DRASTIC corresponds to the initial of theincluded seven parameters: Depth, Recharge, Aquifermedia, Soil media, Topography, Impact of the vadosezone media, hydraulic Conductivity of the aquifer.Determination of the DRASTIC index involves

multiplying each parameter weight by its site ratingand summing the total (Aller et al. 1987). Themodification of the DRASTIC method is based uponsimple statistical procedures, involving revision of therating scale and relative weight of each parameterparticipating in the vulnerability assessment equationand addition or subtraction of parameters, based ondescriptive statistics, simple statistical tests and correla-tion to nitrate concentration. As deduced from theaforementioned investigations, this particular methodseems to have certain advantages compared with theoriginal DRASTIC method (Antonakos and Lambrakis2007). Seawater intrusion potential in the absence ofother data is determined from the distance from thecoastline and from the groundwater electrical conductiv-ity, which in the coastal zone of the study area is mainlyaffected by seawater intrusion.

On the basis of previous considerations, three majorqualitative criteria were deduced:

2a. The existing groundwater quality, as expressed by theelectrical conductivity

Fig. 4 Maps of the study area showing the distribution of the four parameters concerning borehole yield: a parameter 1a: aquifertransmissivity, b parameter 1b: borehole density, c parameter 1c: aquifer recharge, d parameter 1d: distance from river network



2b. The vulnerability of the aquifers, as expressed by theapplication of the modified DRASTIC method

2c. The seawater intrusion potential, as expressed fromthe distance of the coastline

Spatial distribution of these criteria in the study area ispresented in Fig. 5. The influence of the third category ofcriteria is based on the fact that the chosen site for theconstruction of a new borehole must have economicadvantages (mainly drilling and pumping cost) in com-parison with alternative favourable sites based on thequantitative and qualitative criteria, and also must becompatible with certain restrictions such as the distancefrom existing boreholes, both for observance of legalrestrictions and also for conservation of the aquiferbalance. The major factor which affects the cost of aborehole is the expected drilling depth, which is deter-mined mainly by the thickness of the vadose (unsaturated)zone.

Other factors that influence the construction cost of aborehole include ease of access to the construction site,which is determined by distance to the existing road

network, and finally the morphology of the site, sincesites with high surface slopes are difficult to accessand need extra configuration works before the drillingprocedure.

Finally, due to legal constrictions that exist in the studyarea regarding the minimum distance between newboreholes and existing ones or new boreholes and springs,the suitability of a site from a legal point of view isdetermined by the distance of the site from existingboreholes, and also from physical discharges (springs) ofthe aquifers (constrained areas). There were no other legalconstrictions for the drilling of new boreholes in the studyarea, but if they were, the constrained areas would havebeen excluded from the analysis or treated as no-dataareas. From these assumptions, five economical-technicalcriteria were produced:

3a. The drilling cost, as expressed by the thickness of thevadose zone

3b. The ease of access as expressed by the distance fromthe road network

3c. The morphology, as expressed by the surface slope

Fig. 5 Maps of the study area showing the distribution of the four parameters concerning groundwater quality and vadose zone thickness:a parameter 2a: groundwater electrical conductivity (EC), b parameter 2b: aquifer specific vulnerability, c parameter 2c: distance from thecoastline. d parameter 3a: vadose zone thickness



3d. The distance from the existing boreholes or wells3e. The distance from physical discharges of aquifers

(springs)

Spatial distribution of these criteria for the study area ispresented in Fig. 6.

The fuzzy logic approach

Fuzzy logic provides an effective conceptual frame-work for dealing with uncertainty (Tanaka 1997;Tsakiris and Spiliotis 2004; Uricchio et al. 2004). Thebasic concept of fuzzy logic is the conversion of eachparameter in a relative scale ranging between 0 and 1and the creation of the pairs defined by one parameterX and one membership function. Thus, if X is aparameter and x the values of X, the fuzzy set is the setof ordered pairs

x;μ xð Þ½ �∀x ∈ Xf g; ð1Þ

where μ(x) is termed the membership function of x and isexpressed by the following formula:

μ xð Þ ¼0; ∀ x ≤aμ xð Þ; ∀a < x < b1; ∀ x ≥b

8<: ð2Þ

where X is the initial parameter, x the values of X, a and bthe min and max values of the parameter X, and μ(x) thefunction of x. The range of μ(x) is [0, 1], where 0expresses non-membership and 1 expresses fullmembership.

The selection of the adaptable membership function isan essential step in order to transform the parameter,taking into account the relative weight of the parameter.The choice remains a subjective decision for thehydrogeologist/researcher and should be based onprolonged studies of the regional conditions. The mem-bership functions have different types (triangular, trape-zoidal, sigmoidal, etc.), depending on the nature of theproblem (Fig. 7).

Fig. 6 Maps of the study area showing the distribution of the four remaining economical-technical criteria: a parameter 3b: distance fromroad network, b parameter 3c: surface slope, c parameter 3d: distance from existing boreholes, d parameter 3e: distance from springs



The sigmoidal membership function is a commonlyused function in fuzzy set theory (Gemitzi et al. 2006;Tsoukalas and Uhrig 1997). In this study, the aforemen-tioned transformation was carried out using the ArcSDM3extension of ArcGIS 9.x software program (Kemp et al.2001; Sawatzky et al. 2004). This software uses thefollowing sigmoidal membership function (Luo andDimitrakopoulos 2003):

μ1 xð Þ ¼ 1

1þ xf 2

� � f 1ð3Þ

μ2 xð Þ ¼ 1

1þ xf 2

� �− f 1ð4Þ

where f1 is the dispersion index of values of x, and f2 is thecentral point of values of x, i.e. the point where μ(x) = 0.5.The first of the preceding equations is characterised as‘large’ and the second one as ‘small’. The fuzzificationalgorithms “small” and “large” are used to indicatewhether small or large values of the crisp set producelarger members of the fuzzy set (Tsoukalas and Uhrig1997). The spread and mid parameters are subjectivelydefined to reflect the expert opinion. Examples of thesmall and large functions and hedges are shown in Fig. 8.Small and large do not work with negative values orvalues of zero; so the user must transform the data topositive values before fuzzification.

Fig. 7 Different types of fuzzy membership functions. X is the initial parameter

Fig. 8 Graphs of the six sigmoidal membership functions



Furthermore, four derivative functions are used in orderto maximise the flexibility of transformation:

μ3 xð Þ ¼ μ1 xð Þ½ �2μ4 xð Þ ¼

ffiffiffiffiffiffiffiffiffiffiffiμ1 xð Þ

p

μ5 xð Þ ¼ μ2 xð Þ½ �2μ6 xð Þ ¼

ffiffiffiffiffiffiffiffiffiffiffiμ2 xð Þ

pð5Þ

The aforementioned functions are respectivelycharacterised as ‘Very large’, ‘Somewhat large’, ‘Very small’and ‘Somewhat small’ (Tsoukalas and Uhrig 1997). Thesefunctions are the fuzzy membership squared (a decreasivefunction) or the square root of the fuzzy membership (anincreasive function). Thus, Very small, which impliessmaller than small, is Small squared; whereas Very large,which is larger than Large, is the square root of Large.Whichone of the preceding equations (μ1 to μ6) was applied for thefuzzy transformation of the 12 parameters, depends on thesemantic implication and it is shown in Table 1.

In Fig. 8 the graphs of the six aforementionedsigmoidal membership functions are illustrated, deducedfrom the ArcSDM3 extension of ArcGIS 9.x softwareprogram. Finally, in Fig. 9 the graphs of membershipfunctions used for all the parameters in the study area arepresented.

There is a variety of aggregation operators in order tocombine the membership values and produce the finaldistribution rating.

These operators are briefly reviewed below:

1. Fuzzy AND (Cartesian product). It is defined asμAND ¼ min μ1;μ2;μ3;…ð Þ

2. Fuzzy OR. It is defined as μOR ¼ max μ1;μ2;μ3;…ð Þ3. Fuzzy algebraic product: μP ¼ ∏

i¼1

nμi

4. Fuzzy algebraic sum: μS ¼ 1−∏i¼1

n1−μið Þ

5. Gamma operator (γ-operator): μγ ¼ μSð Þγ: μPð Þ1−γwhere γ∈[0,1].

The γ-operator is a combination of the algebraic sumand the algebraic product. When γ is 0, this operator is the

same as the algebraic product; when γ is 1, this operator isthe algebraic sum. Judicious choice of γ provides abalance between the strong effects of the algebraic sumand the weak effects of the algebraic product; in otherwords, it produces output values that ensure a flexiblecompromise between the ‘increasive’ tendencies of thefuzzy algebraic sum and the ‘decreasive’ effects of thefuzzy algebraic product (Luo and Dimitrakopoulos 2003).

Fuzzy logic model structure and implementationin the study area

The type of membership function of each parameter, aswell as the indices used for defuzzification of the model’sparameters, is listed in Table 1. The selection of primaryweights of the parameters was based on expert knowledgeand it was decided to enter all parameters in the modelwith equal weights. Furthermore, the selection of theappropriate dispersion indices (f1) and central points (f2)was based on expert knowledge as well as on thedescriptive statistics (mean, median, mode, standarddeviation) of each parameter in the study area. The initialdistributions of the model parameters were transformed infuzzy set, using GIS and the aforementioned membershipfunctions.

The use of the different fuzzy operators is a matter ofthe researcher’s opinion. Nevertheless, each operator isappropriate for a specific combination of parameters andproduces a different impact on the final result. In thepresent model, both the fuzzy AND and fuzzy ORoperators were initially used and the fuzzy gammaoperator was applied to the produced combined factors.

The fuzzy AND operation is appropriate for thecombination of two or more parameters, if they belongto the same category, and they independently define theinfluence of this category, e.g. the parameters thickness ofthe vadose zone and the distance from the adjacent surfacewater bodies, which both independently contribute togroundwater recharge.

The fuzzy OR operation is appropriate for thecombination of two or more parameters, if they belongto the same category, and they accumulatively influencethe result of this category, e.g. the distance from the

Table 1 Dispersion indices and central points of membership functions used by the model

Parameter Membership function Dispersion index f1 Central point f2

Transmissivity (m2/day) μ4(x) 1 5Recharge (net infiltration) (mm/year) μ1(x) 4 250Distance from the surface water bodies (m) μ5(x) 1 500Electrical conductivity of groundwater (μS/cm) μ2(x) 5 1,000Aquifer specific vulnerability μ5(x) 5 80Distance from the coastline (m) μ4(x) 4 1,000Vadose zone thickness (m) μ6(x) 4 30Distance from the road network (m) μ6(x) 3 1,000Surface slope (degree) μ5(x) 5 10Distance from the existing boreholes (m) μ1(x) 5 500Distance of springs (m) μ1(x) 5 1,000Density of boreholes (boreholes/km2) μ1(x) 3 10



existing boreholes and the distance from springs, whichboth advocate the suitability of one site. Seven factorswere created by means of the aforementioned operators,which were combined with the gamma operator (γ=0.95).The evaluation structure of the primary criteria-parametersis shown in Fig. 10.

Results

Figure 11 shows the suitability map, expressing thedegree of suitability for drilling new production bore-holes, using fuzzy logic. Suitability ranges from 0 to 1.As shown in Fig. 11, a large part of the study area hassuitability values of 0, indicating that these areas arecompletely unsuitable for drilling new boreholes. Thisresult can be attributed to the fact that in many areas atleast one of the model factors has a value of 0 (e.g. areasvery close to existing boreholes and springs or areas with

high EC values in the coastal region of the study area orareas with very low borehole productivity in the semi-mountainous region of the study area, where aquitardmarl predominates), and because the “gamma” operator isactually a product, if one of the product components takesthe value of 0 then the result of the product (suitabilityscore) is also 0 . This fact must not be considered as amodel failure, because it allows one to focus on reallysuitable areas for drilling new boreholes.

High values of suitability are recorded in the areaWSW of Nemea, where conglomerates are the predomi-nant geological formations, in which important aquifersare developed. Lower suitability values can be observed inthe alluvial aquifers around Xiliomodio and in the aquiferthat develops within the eluvial and sea terraces forma-tions. The coastal alluvial aquifer between Korinthos andKiato seems to be totally unsuitable mainly owing to poorgroundwater quality resulting from intensive agriculturalactivities, urban growth and seawater intrusion, as well as

Fig. 9 Graphs of membership functions used for all the model parameters in the study area



due to the high density of existing boreholes.Nevertheless, along the south and southwest edges ofthe coastal alluvial plain there are some narrow zones ofhigh suitability. This can be attributed to a combination offavorable parameters like the absence of existing bore-holes and springs, the proximity to the road network, thelower EC and aquifer vulnerability values and the smallvalues of vadose zone thickness. The coastal area betweenKorinthos and Kiato is a highly populated area withincreased water demand and has a small percentage ofsuitable areas, so it must cover these demands from nearbyareas. According to the model results, the most suitablenearby areas are the aforementioned narrow areas at theedges of the coastal alluvial plain and the areas in whichthe eluvial aquifer and sea-terrace formation aquiferdevelop.

It should be noted that the presented method has greatflexibility and adaptability. Parameters can be added tothe model or excluded from the model according to the

local hydrogeological and socio-economic conditions ofthe study area. Furthermore, if the raw data for oneparameter of the model are difficult to obtain for acertain study area, the parameter can be substituted byanother parameter for which raw data are available. Forexample, if data for the parameter of aquifer vulnerabil-ity are not available, the parameter of land use, which isa parameter with readily available data and a very goodindicator of pollution potential of an aquifer, can beused.

Finally, with changes in factor weights, or changes inthe type of membership functions or selection of differentfuzzy operators, the results of the model can be tailored tothe priorities of the research. If, for example, the purposeof the research is to identify the most suitable locations forthe drilling of new boreholes for drinking water then theimpact (factor weight) of quality factors should beincreased, while the impact of economic factors shouldbe minimized.

Fig. 10 The evaluation structure of the criteria using aggregation operators



Conclusions and discussion

In the present study, multicriteria analysis was coupledwith fuzzy logic in a GIS environment in order to definethe most suitable sites for the drilling of new boreholes.For this reason, 12 parameters were finally involved in themodel, prearranged in three categories: criteria of boreholeyield, criteria of groundwater quality, and economic-technical criteria.

Based on the aforementioned criteria, a final mapexpressing the degree of suitability for drilling newproduction boreholes was illustrated by the use of fuzzylogic. Suitability ranges from 0 to 1. A large part of thestudy area (the coastal part) has suitability values of 0,indicating that these areas are completely unsuitable fordrilling new production boreholes. High values of suit-ability are recorded in the area WSW of Nemea, whereconglomerates are the predominant geological formationsin which important aquifers are developed.

Finally, the study demonstrated that the method ofmulticriteria analysis in combination with fuzzy logic is auseful tool for selecting the best sites for new boreholedrilling on a regional scale. The method can help the localwater management authorities to focus on really suitableareas for groundwater abstraction on which they canconduct more detailed research in order to define the exactpositions for the placement of new production boreholes.The method requires relatively easy to collect raw data

and can be applied to other areas with similarhydrogeological and socio-economic conditions. Severalimprovements of the proposed method may be consideredin the future concerning the parameters included in themodel and the modification of the fuzzy logic analysiswith the addition of an artificial neural network procedure.

Acknowledgements This research was conducted under the “K.Karatheodoris” project, funded by the Research Committee of theUniversity of Patras. The authors greatly appreciate the valuablecomments of the anonymous reviewers.

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Fuzzy analysis for borehole site selection

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