بررسی و مقایسۀ کارایی روش‎¬های FAHP و GCA برای مکان¬یابی پخش سیلاب در محیط GIS (مطالعۀ موردی: حوضۀ آبریز گربایگان)

Introduction
One of the main principles in the process of spreading floodwater is use of the water in arid and semi arid areas for an efficient utilization of both the water and the soil. Executing more than one decade research plans on floodwater spreading in the realm of Iran aquifers have proved that the plains and deserts have got a great potentiality in order to supply water and to prevent the irreparable damages of flood and desertification. The first and the most important step in executing a floodwater spreading project is a suitable zonation for water spreading and to penetrate it into underground water tables. It is impossible to use Geographical Information Systems (GIS) in order to site select potential zones for floodwater spreading without using Multi-criteria Decision Making system (MCDM). Floodwater spreading plan except to gather water and transfer waste water to nourish the aquifers by the purpose of reducing soil erosion and improving the vegetation is studied with a multi-purpose attitude. One of the most appropriate tools in site selection for certain zones is the application of computerized conceptual models in the Geographic Information System (GIS) environment. Because there are a variety of models in this field, identifying and introducing the best model is one of the most essential actions in executing these operations or plans. We have tried in this research to observe the important factors and criteria such as: geocentric factors (geology, geomorphology and soil), hydrology, geohydrology, slope and physiographic characteristics of basin and also discussing certainty or uncertainty of effective locative data in site selection of the potential zones to spread floodwater. On the other hand we have attempted to identify and introduce the most suitable model in site selection of the potential zones to spread floodwater in the Garabaygan aquifer basin in Fars, Iran. FAHP model and GCA with some of their operators are the selective models in this research.
 
Methodology
Study area:
Garabaygan region in the Fasa is located in 190 Km away from southeast Shiraz in lat. from 28° 41' to 21° 41' N and long. from 53° 53' to 45° 57' E.  Also it's located at 1120 to 1160 above sea level.
 
Methodology
Firstly in this research we calculated nine effective factors including geomorphology, geology, slope, height, land use, alluvium thickness, drainage density and electrical conductivity in floodwater site selection by using FAHP and GCA models and then we provided and classified the information layers of these nine factors by using Arc GIS 9.3. Considering the weights of every factor and the scores that they have been assigned, we made the final map of zonation based on these models by classifying them into five classes: very unsuitable, unsuitable, average, suitable, very suitable.
 
FAHP Method:
The analytic hierarchy process (AHP) is one of the extensively used multi-criteria decision-making methods. One of the main advantages of this method is the relative ease with which it handles multiple criteria. The use of AHP does not involve cumbersome mathematics. AHP involves the principles of decomposition, pairwise comparisons, and priority vector generation and synthesis.
A major contribution of fuzzy set theory is its capability of representing vague data. The theory also allows mathematical operators and programming to apply for the fuzzy domain. A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function, which assigns to each object a grade of membership ranging from zero to one. Essentially, the uncertainty in the preference judgments gives rise to uncertainty in the ranking of alternatives as well as difficulty in determining consistency of preferences. These applications are performed with many different perspectives
and proposed methods for fuzzy-AHP. In this study, Chang’s (1992) extent analysis on fuzzy-AHP is formulated for a selection problem.
In the fuzzy-AHP procedure, the pairwise comparisons in the judgment matrix are fuzzy numbers that are modified by the designer’s emphasis.
To deal with vagueness of human thought, Zadeh first introduced the fuzzy set theory, which was oriented to the rationality of uncertainty due to imprecision or vagueness.
A triangular fuzzy number (TFN)  is shown in Fig. 1. A TFN is denoted simply as( The parameters  and  respectively denote the smallest, possible and the largest promising value, and the largest possible value that describe a fuzzy event.
 
 
Fig. 1. A triangular fuzzy number
 
GCA Method:
 The most important function of the theory (GCA) is proposing a modern method to study and survey systems in the uncertainty situation which is based on the gray sequence, creation of a collection of gray numbers provided that values of gray numbers are not known, but the area in which those values lie is given. Gray systems are named after colors of the concerned topics. With the purpose of clarity, in this theory information and data are displayed as indicators of the degree of darkness of the colors (color sequences from white to black). The word "black" is assigned to the information and data which their inner structure and relations are totally unknown and hardly possible to be encoded. GTS is one of the mathematical which helps much in solving problems in the three following situations: 1. Uncertainty 2. Discontinuous data 3. Insufficient data.
 
Results and Discussion
In this research we have used nine effective factors including geomorphology, geology, slope, height, land applying, alluvium thickness, drainage density and electrical conductivity in floodwater site selection. In this study some criteria (i.e., geology, slope, drainage density and alluvium thickness,) have maximal effects whereas some others (i.e., elevation, landuse, and geomorphology) have minimal effects.
Final map of both methods are supplied in 5 classes from completely suitable to unsuitable. Completely suitable class in FAHP model has an area of 17.101 hectares and in GCA model has an area of 12.195 hectares of total area (7946 hectares) of the province. The table 1 shows the results.
Table 1. findings of functional models





capa coefficient


Area of a region in ha


Accuracy of the model


functional models




-.0897


17.101


%47.37


FAHP




.0943


12.195


%52.63


GCA




 


30.296


%100


total





 
Conclusion
In this study, FAHP and GCA were used in combinative approach with GIS in order to determinate appropriate areas for flood spreading in Garbaigan plain. The findings show that susceptible regions for flood spreading are in quaternary units like: Qc2, Mm-1, Qb, Qgsc, Qscg, and PLQb. Also according to geomorphology and land uses, cone carters, plains and low density pastures are the totally appropriate zones for flood water spreading. These zones are in correspondence with the location of the Kosar floodwater spreading station. They have the special characteristics for spreading floodwater. On the other hand, according to this, our obtained results is the best reason for choosing the Fuzzy model and Gray System Theory for evaluating the quality of data in comparison with other applied models. Also comparison of finding obtained from this two models show that GCA model is more accurate than FAHP model to find susceptible regions for flood spreading.