Environ Earth Sci DOI 10.1007/s12665-014-3109-9

ORIGINAL ARTICLE

Using combined AHP–genetic algorithm in artificial groundwater recharge site selection of Gareh Bygone Plain, Iran Saeed Rahimi • Majid Shadman Roodposhti Rahim Ali Abbaspour

•

Received: 1 October 2013 / Accepted: 27 January 2014 Ó Springer-Verlag Berlin Heidelberg 2014

Abstract Flood spreading is one of the suitable strategies to control and benefit from floods which in turn improve the groundwater recharge, makes soil more fertile, and increases nutrients in soil. It is also a method for reusing sediment, which is usually wasted. Thus, selection of suitable areas for flood spreading and directing the flood water into permeable formations are amongst the most effective strategies in flood spreading projects. Having combined analytic hierarchy process (AHP) of multi-criteria decision analysis and genetic algorithm (GA) of artificial intelligence approaches, this paper addresses the problem of finding the most suitable area location for flood spreading operation in the Gareh Bygone Plain of Iran. To this end, the nine effective geodata layers including slope, alluvium thickness, geology, morphology, electrical conductivity, land use, drainage density, aquifer transmissivity, and elevation were prepared in geographic information system environment. This stage was followed by elimination of the exclusionary areas for flood spreading while determining the potentially suitable ones. Having closely examined the potentially suitable areas using the proposed methodology, the land suitability map for flood spreading was produced. The AHP and GA were used for ranking all the alternatives and weighting the criteria involved, respectively. The results of the study showed that most suitable areas for the artificial groundwater recharge are located in Quaternary Qft2 and Qsf geologic units and in morphological units of pediment and Alluvial fans with slopes not exceeding 2 %. Finally, further evidence for the acceptable efficiency of the integrated AHP–GA method in locating most suitable flood spreading areas have been S. Rahimi  M. Shadman Roodposhti  R. Ali Abbaspour (&) College of Engineering, University of Tehran, Tehran, Iran e-mail: [email protected]

provided by such significant spatial coincidence between the produced map and the control areas located near Kowsar research station, where the earlier flood spreading projects were successfully performed. Keywords Flood spreading  AHP  Genetic algorithm  Gareh Bygone Plain

Introduction Artificial groundwater recharge is the planned infiltration of effluents from sanitation systems (e.g. waste stabilization ponds, surface, horizontal flow or vertical flow constructed wetlands), storm water or surface runoff into the aquifer to increase the natural replenishment of groundwater resources. Groundwater recharge is increasing in popularity as groundwater resources are being depleted and as saltwater intrusion is becoming a greater threat to coastal communities (Tilley et al. 2008). In recent years, researchers in watershed engineering and other fields have become increasingly interested in using geographic information system (GIS) to fulfill artificial groundwater recharge site selection. Along with GIS, remote sensing and the technology of satellite data processing with access to up-to-date and diverse information are broadly used to deal with management problems (Saraf and Choudhury 1998). Accordingly, the main purpose of using remote sensing, GIS, and multi-criteria decision making (MCDM) together in an integrated approach is to provide scientific evidence for the site selection processes. Many studies have found evidence for the efficiency of the combination of the satellite data, GIS, and MCDM in locating the optimal zones for flood spreading and other ground water recharge methods (Krishnamurthy and

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Srinivas 1995; Krishnamurthy et al. 1996; Saraf and Choudhury 1998; Han 2003; Chowdhury et al. 2010; Jamali et al. 2013). Using GIS and spatial decision support systems, Ghayoumian et al. (2002, 2005 and 2007), Zehtabian et al. (2001), Alesheikh et al. (2008) and Sargaonkar et al. (2011) have located suitable sites for the artificial recharge of aquifers. Kheirkhah Zarkesh (2005) has developed a decision support system for flood spreading site selection and a conceptual model of flood spreading schemes in the semi-arid areas. Moreover, many studies have been conducted to find appropriate conditions for ground water recharge site selection (Al-Assa’d and Abdulla 2010; de Laat and Nonner 2012). Regarding the fact that the groundwater has long been believed to be the single most important water resource in many regions of Iran, this is considered as a major historical limitation in the social and economical development of the country. Recent studies on the management of water resources in Iran have shown that out of the 430 billion m3 of the annual precipitation in the country, 20 % is lost during sudden floods which flow into the playas, lakes, and seas (Foltz 2002; Mohammadnia and Kowsar 2003). While several groundwater recharge methods have been developed including the direct surface recharge, direct subsurface recharge, and indirect recharge techniques (Oakford 1985), the direct surface recharge method is one of the most cost-effective, simple, and commonly used techniques employed for the artificial recharge of aquifers. The direct surface recharge method contains the surface spreading of floodwater and is helpful in areas with widely available land, highly permeable soils, and a shallow unconfined aquifer (O’Hare et al. 1986). In this regard, there are at least two major questions to successively utilize the direct surface recharge approach. First, ‘‘which land is the most suitable for artificial groundwater recharge in the region?’’, while the second and most important question concerns, ‘‘to what extent it is considered as the most suitable geographic location?’’ As an essential domain, the site selection methods have always performed a significant role in spatial decisionmaking processes. Traditional methods used at the beginning of necessity for site selection appearance, developed relatively by analysts and specialists based on multi-criteria methods. A main disadvantage of these methods relates to dependency of the final results to personal privy of participant experts. In addition, using different multi-criteria methods for one problem could make different results, not a unique or even similar result. To resolve these issues, artificial intelligence and soft computing methods were used for site selection problems, in the context of GIS GeoComputing. However, these methods have still their own drawbacks such as the process of problem solving is a black box to the users and the final result is sensitive to the

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objective function. In this paper, selection of optimal sites for flood spreading involves integrating several complicated parameters, which necessitates the use of GIS in combination with multi-criteria decision analysis (MCDA) and optimization methods. This study presents an integrated strategic framework with emphasis on structuring the decision problem including careful selection and weighting of criteria and alternative evaluation. Accordingly, using AHP technique the qualitative judgment can be quantified to make geodata layer comparison more intuitionistic using pairwise comparison process. Moreover, a number of favorable characteristics of the AHP method could enhance optimization methods, namely at the level of structuring of the decision problem and of the determination of weights. Finally, this article introduces an approach that integrates AHP with GA of Artificial Intelligence, which could be a useful geospatial tool for integrating multiple features/attributes that affect the artificial ground water recharge process. It also should be mentioned that to the best of our knowledge, nonetheless, the AHP–GA method has not been applied to the flood spreading site selection thus far.

General situation of the region The Gareh Bygone Plain (28°300 to 28°450 N and 53°450 to 54°010 E) is located in the south part of Fars province of Iran (Fig. 1). The mean elevation of the area is 1,476 m above mean sea level. According to the De Martonne climate classification, the area represents arid to semi-arid climate type with the average annual rainfall of 259 mm, the average annual potential evaporation rate of 2,934 mm and the average annual temperature of about 20.6 °C. Gareh Bygone is an area located in the folded Zagros Mountains stretching like a folded belt from the northeast to the southwest of the country. In this area, only signs of the last two geological eras are found. The Mesozoic formation constitutes mountains and hill units and contains sandstone, limestone, clay stone, siltstone and conglomerate. The Cenozoic formation is composed of alluvial deposits (with the average depth of 30 m), which in the forms of alluvial fans and pediments play the major role in the formation of the aquifers of the basin. The source of the water of the Gareh Bygone Plain is of both subsurface and surface types. Bishezard and Chahghuch seasonal rivers are the surface sources of water, with the former having a length of 28 km and being the major recharge source of the aquifers of the region and the latter having a less significant role. Finally, it should be mentioned that the small amount and unbalanced distribution of precipitation both spatially and temporally can lead to serious problems. In other words, high-intensity rainfalls which result in destructive

Environ Earth Sci

Fig. 1 Locator map of the study area

floods bring about serious damages to downstream towns, roads, and agriculture, and sometimes even cause casualties (Hayati et al. 2006). Flood spreading on aquifers by artificial recharging of the aquifers, is an efficient strategy for controlling floods and managing water shortage and water resources in the region (ASCE 2001).

Materials and methods Influencing data layers First of all, the artificial groundwater recharge site selection in this study started with the selection and preparation of nine geodata layers of the study area including slope,

alluvium thickness, geology, morphology, electrical conductivity (EC), land use, drainage density, aquifer transmissivity, and elevation (Fig. 2) which were selected based on the similar earlier studies (Krishnamurthy and Srinivas 1995; Krishnamurthy et al. 1996; Saraf and Choudhury 1998; Han 2003; Chowdhury et al. 2010; Nasiri et al. 2013). Then, a questionnaire was designed to collect necessary information required for artificial groundwater recharge site selection of Gareh Bygone Plain, including local experts’ opinions to ensure the practicality and integrity of the selected geodata layers and also the importance (weight) of the approved ones. In other words, weights of the approved geodata layers were subsequently calculated using pairwise comparisons, based on the local expert responses to the questionnaires.

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Fig. 2 Nine input geodata layers involving: a slope (°), b alluvium thickness (m), c geology, d morphology, e electrical conductivity (lmhos/ cm), f land use, g drainage density (km/km-2), h aquifer transmissivity (m2/day) and i elevation (m)

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Slope Surface runoff velocity is directly related to land slope. Hence, slope is one of the most effective factors in the artificial groundwater recharge site selection (Alesheikh et al. 2008). National and international studies show that the areas with slope range from 1 to 5 percent are suitable for flood spreading (Krishnamurthy et al. 1996; Nasiri et al. 2013). Consequently, the slope map of the study area is prepared from the 30 m SRTM DEM and is shown in Fig. 2a. Alluvium thickness The thickness of alluvium is another major factor in flood spreading and groundwater recharge. In general, the greater the thickness of alluvium, the larger the amount of groundwater storage. In other words, if all the parameters are appropriate except the alluvium thickness, flood spreading may cause saturation of the recharged layer (Ghayoumian et al. 2007; Nasiri et al. 2013). The alluvium thickness map of the study area is shown in Fig. 2b.

hills. Floodplain, alluvial fans, and pediment constitute 5.1, 3.3, and 33.6 % of the area, respectively, while hills and rocky outcrops comprise the remaining 58 % (Fig. 2d). Electrical conductivity Electrical conductivity is a measurement of total dissolved solids (TDS), or the total amount of dissolved material in an aqueous solution, which relates to the ability of the material to conduct electrical current through it. This implies the quality of groundwater which demonstrates the amount of chemicals and biological impurities and is a major factor in specifying water for certain uses (Nasiri et al. 2013). Consequently, in the present study, EC has been employed as a parameter for assessing water quality index (Fig. 2e). It also should be mentioned that although both EC and TDS were measured and their maps provided, only EC was used as the water quality index, hence TDS and EC showed the same trend of change. Land use

Geology Since different geological units have different suitability values or potential for flood spreading and groundwater recharge, geology is one of the important factors for artificial groundwater recharge site selection. Therefore, geology and the types of geological formations in the region have important roles in selecting flood spreading sites (Fig. 2c). Because of enjoying good permeability, transmissivity and high water storage capacity, limestone and coarse alluviums present good conditions for recharging aquifers. Coarse (sand and gravel) and pervious or karstic formations typically enjoy better hydraulic conductivities and aquifer transmissivity, and the regions with young alluvial are known to be suitable sites for flood spreading (Nasiri et al. 2013). Morphology Morphological maps are one of the most important end products of investigations made by geomorphologists on a territory. Moreover, at the present moment, in places where no subsurface information could be obtained, geomorphological maps can be used as an appropriate criterion for artificial groundwater recharge site selection (Nasiri et al. 2013). Vast plains with moderate slopes, pediments, and alluvial fans are considered the best locations for developing artificial aquifer recharge projects. The area under study includes geomorphological units of floodplains, alluvial fans, pediments, rocky outcrops, and

Land use is also one of the key factors in the artificial groundwater recharge site selection. From the land use point of view, the Gareh Bygone Plain includes river bed, residential areas, range land, and irrigated and dry farming (Fig. 2f). Undertaking artificial recharge projects is feasible in areas with an appropriate density of vegetation coverage because these regions not only recharge water into aquifers but also prevent the surface soil erosion. Poor rangelands, on the other hand, are not proper places for artificial recharge projects due to the increasing rate of soil erosion (Alesheikh et al. 2008; Nasiri et al. 2013). Drainage density Drainage density is the total length of all the streams and rivers in a drainage basin divided by the total area of the drainage basin and calculated through the following formula: P Li l¼ ; ð1Þ A where L is the length of each stream segment and A is the area of drainage basin. There is an inverse relationship between drainage density and permeability. Moreover, it is clear that the higher the permeability, the lower the drainage density, and vice versa. Accordingly, drainage density can be considered an indirect indicator of the suitability of an area for artificial groundwater recharge (Nasiri et al. 2013). Drainage density for all the

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micro-watersheds in the study area ranged from 0.7 to 2.3 km/km2 (Fig. 2g). Aquifer transmissivity Transmissivity, as one of the hydraulic properties of aquifer relates to the ability of an aquifer to transmit water through its entire saturated thickness. It is defined as hydraulic conductivity multiplied with the saturated layer thickness of the aquifer: T ¼ K  D;

ð2Þ

where K is hydraulic conductivity and D is saturated layer thickness. Here, aquifer hydraulic conductivity was assessed through the pumping test, which is the best and the most precise method for the measurement of hydraulic conductivity. This coefficient is indicated by different quantities but it typically ranges from 10 to 10,000 m2/day (Nasiri et al. 2013). Aquifer transmissivity in Gareh Bygone Plain varies as a function of the differences in the thickness of the saturated layer (Fig. 2g). Proposed methodology Proposed methodology has two steps. In the first step, using pairwise comparison process through the analytical hierarchy process (AHP) method, the qualitative judgment has been qualified to make comparison more intuitionistic. In the next step, obtained results have been used as weights of geodata layers in genetic algorithm.

Fig. 3 Flowchart of binary GA (Haupt and Haupt 2004)

representation of the variables, the binary method is presented first. (Haupt and Haupt 2004) The components of the GA are shown as a flowchart in Fig. 3.

General method of genetic algorithm Model implementation The computation of genetic algorithm (GA) is an iterative process which simulates the process of genetic selection and natural elimination in biologic evolution. Candidate solutions are retained and ranked for the each iteration according to their eligibility. Consequently, a fitness function is used to remove unqualified solutions. Genetic algorithms belong to the larger class of evolutionary algorithms (EA), which generate solutions to optimization problems using techniques inspired by natural evolution, such as selection, crossover, and mutation. Such GA operators are then performed on those qualified solutions to estimate new candidate solutions of the next generation. The above process is carried out repeatedly until certain convergence condition is met. Genetic algorithm has two type of representation of variable: Binary and continuous representation. Both algorithms follow the same menu of modeling genetic recombination and natural selection. One represents variables as an encoded binary string and works with the binary strings to minimize the cost, while the other works with the continuous variables themselves to minimize the cost. Since GAs originated with a binary

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Assuming that the artificial groundwater recharge site selection of Gareh Bygone Plain could be based on the proposed methodology, a 3-step procedure has been applied. Step 1, includes necessary data preparation of selected geodata layers to further facilitate the implementation of genetic algorithm. In step 2, hierarchical structure to estimate the weights of geodata layers was constructed employing AHP. In Step 3, preprocessed, weighted geodata layers had been used as input layers, to reach the optimal site for the artificial groundwater recharge using genetic algorithm. These steps are described in detail as the following subsections. Preprocessing and standardizing To facilitate the implementation of GA, it is necessary to perform data preprocessing and standardization. Spatial data models are useful for convenient layer display, but may not be suitable for the implementation of searching

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in genetic algorithm (Yeh et al. 1995). Therefore, the spatial data provided by GIS database need to be preprocessed and re-modeled before they can be used for GA. Accordingly, all derived FS geodata layers were converted into proper raster format with 30 m 9 30 m resolution, and after subsequent data normalization (in an interval of [0,1]), the spatial datasets were processed in ArcGIS. Assessment of weights with AHP To express the relative importance of each geodata layer and to derive the relative weights, the basic idea of performing pairwise comparison is a pedagogical and intuitive participatory approach. The result of interview with local experts expresses that with which intensity aij a geodata layer gi is more or less important than another geodata layer aj, using the fundamental scale of absolute numbers from 1 to 9 (Saaty and Vargas 2001), quantitatively defined and explained (Tables 1, 2).

Coding and decoding the chromosomes and define objective function The binary GA works with bits. The variable x has a value represented by a string of bits that is Ngene long. If Ngene = 10 and X has limits defined by 1 \X \1024, then a gene with 10 bits has 2Ngene ¼ 1024 possible values (Fig. 5). Here, x and y coordinate of each geodata layer represents chromosome dimensionality. In other words, regarding the total area of study region, data accuracy and data dimensionality each of these two variables (i.e. x and y) has been determined by a 10 bite string composed of binary numbers. Accordingly, Fig. 5 shows structure of a sample chromosome. In our optimization problem, each chromosome is presented in a string of 20 bits that are decoded by Eq. 3 (illustrated in Fig. 6): x¼

w1 X

2i zwi ;

ð3Þ

i¼0

Application of GA in the Gareh Bygone flood spreading After weighting the FS geodata layers, in the next step, the modified GA is implemented to select the most suitable site for FS. Figure 4 shows an overall flowchart of GA implementation for artificial ground water recharge site selection.

where x represents the decoded number, z is the binary string and w is the number of binary characters in that string. To illustrate the working principles of GAs, artificial groundwater recharge site selection of Gareh Bygone Plain is considered as a constrained optimization problem. The linear programming of the problem is as follows:

9 8 h i   > > > > þ 0:149 Alluvium Thickness 0:175 Slope ðx; yÞ ðx; yÞ > > > > > > > > > > > > þ 0:147½Geology > > = < ðx; yÞ  þ 0:140½Geomorphologyðx; yÞ  h i Minf ðx; yÞ ¼ > > > þ 0:122½ECðx; yÞ  þ 0:077½LUðx;yÞ  þ 0:078 Drainage Densityðx; yÞ > > > > > > > > > h i > >   > > > > ; : þ 0:065 AquiferTransmissivityðx; yÞ þ 0:048 Elevationðx; yÞ s.t. 0\Slope\2 0\drainage density\0:25 0\EC\3000

ð4Þ

1120\elevation\1250 400\aquifer transmissivity\600 Alluvium thickness [ 50 Geomorphology ¼ flood plainjalluvial fan Geology ¼ QgjQgscjQscgjQbjQc LU ¼ Low density range;

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where f(x, y) is chromosome costs in problem solving and (x, y) are x and y coordinates of corresponding chromosome in constructed evaluation matrix.

Natural selection

Generate initial population Population size has significant impact on the final result and performance of genetic algorithm. According to the Schema Theorem (Chen 1996), given the population size M, the genetic operators are able to produce M3 schemas. Based on this fact, more and more building blocks can be generated and optimized till the optimal solution is found. Here, in the present study, 100 random chromosomes (Npop) consisting of 20 bits (Nbits) string have been selected using ‘Rand’ and ‘Round’ (Eq. 5). Then, 10 first numbers of each chromosome strings have been used as x coordinate and the rest as y coordinate, respectively (Fig. 5).    Pop ¼ round rand Npop ; Nbits : ð5Þ Find cost for each chromosome A cost function simply generates an output from a set of input variables (a chromosome). The cost function also may be a mathematical function, an experiment, or a game (Haupt and Haupt 2004). Here, variables are x and y in each data layer, then: Cost ¼ f ðP1; P2Þ ¼ f ðChromosomesðx; yÞ in each layerÞ: ð6Þ

Table 1 AHP evaluation matrix of nine geodata layers involving: (a) slope, (b) alluvium thickness, (c) geology, (d) morphology, (e) electrical conductivity, (f) land use, (g) drainage density, (h) aquifer transmissivity and (i) elevation c

d

in this case, P1 and P2 are problem variables that show coordinate of pixels in geodata layers

a

b

E

f

A

1

2.2

1.5

1.3

1.3

3

B

0.45

1

1.1

1.3

1.5

3

C

0.66

0.91

1

1.5

1.4

2.4

D E

0.76 0.76

0.77 0.66

0.66 0.71

1 0.66

1.5 1

F

0.33

0.33

0.41

0.41

G

0.66

0.5

0.5

H

0.66

0.41

0.41

I

0.33

0.41

0.41

g

h

i

1.5

1.5

3

2

2.4

2.4

2

2.4

2.4

2.4 2.8

2.6 2

2.6 2

2 2

0.35

1

1.8

2

2.2

0.38

0.5

0.55

1

2

2.2

0.38

0.5

0.5

0.5

1

2.4

0.5

0.5

0.45

0.45

0.41

1

Inconsistency ratio: 0.04

Natural selection which has been represented by other phrases namely, ‘‘survival of the fittest’’, translates into discarding the chromosomes with highest costs. In this regards, the Npop costs and associated chromosomes are ranked from the lowest cost to the highest in the first step. Then, the best are selected to continue, while the rest of them are deleted. The selection rate, Xrate, is the fraction of Npop that survives for the next step of mating. The number of chromosomes that are kept each generation is (Haupt and Haupt 2004): Nkeep ¼ Nrate  Npop :

ð7Þ

Natural selection occurs in each generation or iteration of the algorithm. Of the Npop chromosomes in a generation, only the top Nkeep survive for mating and the bottom Npop - Nkeep are discarded to make pool for the new offspring. Deciding how many chromosomes to keep is somewhat arbitrary. Letting only a few chromosomes survive to the next generation limits the available genes in the offspring. Keeping too many chromosomes allows bad performers a chance to contribute their traits to the next generation. It is common to keep 50 % (Xrate = 0.5) in the natural selection process (Sivanandam and Deepa 2007). Accordingly, in the present study, the population has been sorted by descending fitness values within which the first 50 % were selected as candidates for further examination. Selection GA simulates the ‘‘survival of the fittest’’ theory to make a search process. Therefore, GA is naturally suitable for solving maximization or minimization problems. In this step of GA application in the Gareh Bygone flood spreading, the fitness value of each chromosome (square matrix composed of 23 9 23 pixels) has been determined by the active fitness conditions and retrieved further. Afterwards, two chromosomes were selected from the mating pool of Nkeep chromosomes to produce two new offspring. Pairing takes place using weighted random pairing in the mating population until Npop - Nkeep offspring are born to replace the discarded chromosomes. The probabilities assigned to the chromosome in the mating pool are inversely proportional to their cost. In other words,

Table 2 The calculated weight vector from AHP Slope

Alluvium thickness

Geology

Morphology

EC

LU

Drainage density

Transmissivity

Elevation

0.175

0.149

0.147

0.140

0.122

0.077

0.078

0.065

0.048

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Fig. 4 Flowchart of proposed methodology to determine optimal sites for flood spreading

Fig. 5 Coding the chromosomes with 2 genes (20 bits)

Fig. 6 Decoding of a chromosome with 2 genes (20 bits)

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Environ Earth Sci Fig. 7 Single-point crossover illustration regarding the 7th chromosome as crossover point

a chromosome with the lowest cost has the greatest probability of mating, while the chromosome with the highest cost has the lowest probability of mating. A random number determines which chromosome is selected. This type of weighting is often referred as roulette wheel weighting (Haupt 2004). For this goal, we have used rank weighting method of weighted random pairing that is named roulette wheel ranking squared. This approach is problem independent and finds the probability from the rank, n, of the chromosome (Haupt and Haupt 2004): Pn ¼

ðNkeep ðn þ 1ÞÞ2 ð50  ðn þ 1ÞÞ2 : ¼ PNkeep 2 38025 n¼1 n

ð8Þ

Then, a random number between zero and one is generated. Starting at the top of the list, the first chromosome with a cumulative probability that is greater than the random number is selected for the mating pool. Mating Mating is the creation of one or more child(ren) from the parents selected in the pairing process. The genetic makeup of the population is limited by the current members of the population. The most common form of mating involves two parents that produce two children. A crossover point, or kinetochore, is randomly selected between the first and last bits of the parents’ chromosomes (Haupt and Haupt 2004). After selection of elite parents, there are three possible actions which further evolve the selected population: create a new randomized individual, clone an existing individual or mate a randomly chosen pair of individuals to produce a new individual. Here, in the present study, the latter action was applied to produce a new individual out of the mating pool. Similar to the gene recombination, which plays an essential role during the process of natural biologic evolution, the crossover is the most significant operation in the

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genetic search strategy. It determines the major behavior of optimization process. Several crossover schemes are used, such as one-point crossover, two-point crossover, and multipoint crossover. However, as a common criterion, any crossover operator should ensure that the proper genes of good individuals be inherited by the new individuals of next generation. A big crossover probability may improve genetic algorithms capability to search new solution space, while increase the likelihood of disordering the combination of good genes. However, if the crossover probability is set too small, search process may be trapped in a dull status and is prone to ceasing (Wu and Shan 2000; Wu et al. 2004). To recombine two strings to get a better string, here, one crossover point has been selected as GA operator. As a result, a random number ranging from 1 to 19 has been selected and considered as crossover point. Then, binary string from beginning of chromosome to the crossover point is copied from one parent (father chromosome), the rest is copied from the second parent (mother chromosome) (Fig. 7). Mutation Binary mutations randomly change a bit in a chromosome (Haupt 2004). Mutation is the second way a GA explores a cost surface. A single point mutation changes a 1 to a 0, and vice versa. Mutation points are randomly selected from theNrate. Npop total number of bits in the population matrix. Mutations do not occur on the final iteration (Haupt and Haupt 2004). To add new information in a random way to the genetic search process and ultimately help to avoid getting trapped at local optima, we have used 0.1 mutation probability rate (l = 0.1). It also should be noted that selection of this mutation rate was achieved using a trial-and-error approach. Mutation may cause the chromosomes of individuals to be different from those of their parent individuals (Fig. 8).

Environ Earth Sci Fig. 8 Mutation process illustration

Fig. 9 Schematic representation of proposed FS site selection and suitability analysis

Convergence The number of generations that evolve depends on whether an acceptable solution is reached or a set number of iterations are exceeded. After a while all the chromosomes and associated costs would become the same if it were not for mutations. At this point, the algorithm should be stopped (Haupt and Haupt 2004). In this step, we achieve new offspring with 100 chromosomes. Accordingly, to further achieve our goal, we have examined objective fitness function composed of several weighted fitness conditions. In case the optimal solution could not be found in this generation, this generational process is repeated until a

Fig. 10 Repetition of GA in artificial groundwater recharges site selection of Gareh Bygone Plain

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Fig. 11 Output map of AHP–GA application in artificial groundwater recharge site selection Fig. 12 Resultant 3D output of chromosome cost

termination condition and optimum solution has been reached. Here, we define 2 conditions that algorithm must have one or both of them to stop. The main criterion is that results should not be changed during 50 iterations of algorithm. If this criterion is not satisfied during 300 iterations, the algorithm stops.

Results and discussion The overall process of combined AHP–GA application in the artificial groundwater recharge site selection of Gareh Bygone Plain has been schematically presented in Fig. 9.

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The nine collected geodata layers related to casual FS projects involving slope, alluvium thickness, geology, morphology, electrical conductivity, land use, drainage density, aquifer transmissivity, and elevation were prepared and analyzed in GIS environment in the present work. Having collected the geodata layers according to the flowchart, the nine geodata layers were converted into the raster format in the GIS environment to implement AHP–GA, and the preliminary data preprocessing and standardizing of selected geodata layer were performed on them. Following this, the pixel values of the raster datasets related to the FS site selection criteria were extracted and stored in nine separate spatial matrixes in a database.

Environ Earth Sci

Afterward, to implement artificial groundwater recharge site selection using the proposed methodology, the database was imported into the MATLAB for further programming procedure. The objective function optimization was calculated for all alternatives using MATLAB programming. Finally, the output was converted to a raster dataset which was a square matrix (23 9 23 pixels, equal to 104 hectare) which in fact indicates the most suitable land (Figs. 10, 11, 12). It must be noted that geographical coincidence of Gareh Bygone flood spreading station with the optimum area indicates reliability of the proposed methodology for FS site selection.

Conclusion In the arid and semi-arid areas, rainfall distribution is bimodal and highly skewed with the highest, rainfall amounts, and intensity, being received in the winters and springs. The annual evaporation is high, and exceeds annual rainfall for most part of the year. Therefore, FS can be considered as one of the suitable methods for flood management and water harvesting that increases the groundwater recharge, makes soil more fertile and increases nutrients in soil. Considering the groundwater-based agricultural activities in the Gareh Bygone Plain and the location of the region in the arid zone of Iran, the present study aimed to prevent the water loss in the region by determining suitable flood spreading sites and using the floodwater optimally. Having used combinational AHP–GA methods in GIS environment, the suitable FS areas were located. The AHP method was used to quantify the subjective judgments of FS-related criteria weights, whereas the GA method was employed to further evaluate priorities of available alternatives based on the weights obtained from the AHP. According to the obtained results, the proposed optimal area coincides with parts of Kowsar research station in Gareh Bygone Plain which has been previously used for the artificial ground water recharge through FS projects and already showed the promising result. It is located in pediment and alluvial geomorphological units and quaternary Qgsc geological units where the slope value is not more than 2 degree (5 %). Finally, it can be concluded that the proposed method can be considered as a promising tool for hydrologists in selecting suitable flood spreading sites and in the planning and management of groundwater resources.

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