Comparison of weighting methods of multi-criteria decision analysis (MCDA) in evaluation of �ood hazard index

Preparing a map of �ood hazard susceptibility is an important step in �ood risk management. Therefore, it is necessary to use methods that reduce errors and increase accuracy in identifying �ood hazard areas. This study was conducted with the aim of preparing a map of the �ood hazard index (FHI) and evaluating subjective and objective multi-criteria decision analysis (MCDA) weighting methods. Talar basin on the north of Iran has been investigated as a case study for this research. Seven ood-inuencing factors including elevation, slope, �ow accumulation, distance from the river, rainfall intensity, land cover, and geology were used to create a �ood hazard map. The weighting of these factors has been performed by Analytical Hierarchy Process (AHP), sensitivity analysis of AHP (AHPS), Shannon Entropy (SE), and Entropy-AHP. The maps created with the data of past �oods were validated with ROC and Kappa index methods. The results showed that the FHI-SE method was more accurate than other methods with an accuracy value of 0.979. FHI-SEA, FHIS, and FHI methods were placed in the next priorities, respectively. Based on the SE method, the factors of distance from the river, elevation, and slope respectively have obtained the highest weight value in creating the �ood hazard index map. Different classi�cations of distance from river variables separately for mountains and plains can reduce the overestimation of �ood hazard areas in mountainous areas. The objective weighting method has provided more accuracy than the subjective weighting method such as AHP.


Introduction
Floods are the most destructive natural hazards that have caused many human and economic losses worldwide in the last century.According to the reports of Emergency Events Database (EM-DAT), although the deaths caused by oods have decreased, the socio-economic damages are increasing throughout the world.Vulnerability to riverine ooding is growing as a result of increasing exposure of people and infrastructure to ood-prone areas (Kundzewicz et al. 2014;Wilhelm et al. 2018).The severe ood of 2019 in Iran is an example of this event that affected more than 10 million people and the amount of damage is reported to be equal to 1% of GDP (https://ourworldindata.org).Several factors including meteorological, hydrological, geomorphological, soil and vegetation characteristics, economic-social characteristics, and infrastructures are contributed to the formation of oods and cause the complexity of managing this risk (Dung et al. 2022).Therefore, preparing a map of ood-prone areas can be an important step in ood management.
Various methods are used to prepare the ood hazard map, which are divided into three main groups including Physical, Numerical, and Empirical (Mudashiru et al. 2021).Physical models predict ood hazard based on physical experiments from the real world.These tests are performed with advanced and expensive equipment.The use of experimental models has decreased in recent years and numerical models have replaced physical models (Mudashiru et al. 2021).
Numerical models have two subgroups, hydrodynamic modeling and hydrological simulation.
Hydrodynamic models are performed in 1, 2, and 3-dimensional forms (Merwade et al. 2008; Patel et al. 2017; Rong et al. 2020), and the ood hazard map is quanti ed based on the ood depth and ow velocity (Maranzoni et al. 2022).
In hydrological methods, simulation is made based on the characteristics of rainfall, in ltration, and runoff in the river basin area (Chen et al. 2015).Hydrodynamic models are usually employed on a small scale (Kanani-Sadat et al. 2019) and due to costly and lack of su cient data, the use of these models is limited, especially in developing countries.(Samela et al. 2018;Dung et al. 2022).Therefore, index-based methods are applied instead of numerical methods to prepare ood risk maps (Kazakis et  Analytic Hierarchy Process (AHP) is the most widely used MCDM method, which is performed by the subjective weighting of criteria (De Brito and Evers 2016).The important advantages of the AHP method are its openness and exibility and the unlimited number of variables for judgment.In addition, this method can be used for large river basins and data-scarce areas.Several studies with AHP method accomplished to identify ood-prone areas (Rahmati et (Stefanidis and Stathis 2013).In some studies, the weights of criteria obtained from AHP method were evaluated by sensitivity analysis and validated with historical ood data.The results of these studies show that the effective weights obtained from the sensitivity analysis (Kazakis et al. 2015;Hammami et al. 2019;Toosi et al. 2019) have provided better accuracy.
Shannon's Entropy is another widely used technique in the MCDA method to prepare a ood hazard map, in which the weights of the criteria are objectively evaluated.Hence, the existence of an information layer of the areas that were ooded is necessary for this work.In most of the studies that have used this method, the weights of the criteria have been calculated based on the frequency ratio (FR) of ooded areas in each class of variables (Khosravi et  Vanolia and Jalukhani Niarki (2021) produced a ood hazard map by combining two subjective-objective weighting methods based on the Ordered Weighted Averaging (OWA) model.The result showed that the combined method is more accurate than the subjective method.
In the current research, ood hazard maps were prepared and evaluated by indexing variables and using subjective, objective, and combined weighting methods.Therefore, the most important aims of this study are: Preparation of ood hazard index map (FHI) with MCDA methods Evaluation and comparison of subjective, objective, and combined (subjective-objective) weighting methods of MCDA in preparation of ood hazard map Analysis of effective variables in creating a ood hazard map based on different weighting methods

Study area
Talar basin is located on the northern of Iran with an area of 2582 km 2 , between 35° 45′ N to 36° 45′ N latitudes and 52° 35′ to 53° 23′ E longitudes (Fig. 1).The mean elevation of the basin is 1960 m with a minimum of -27 m and maximum of 4003 m.Talar River originates from Mount Alborz and ows from south to north and enters the Caspian Sea.The mean annual precipitation in the basin is 677 mm and its spatial variation ranges from 300 mm in the southern parts to 1000 mm in the northern parts.The lithology of the basin is mainly composed of limestone, dolomite, shale, sandstone, and alluvial sediments.The dominant land cover is pasture and forest, which cover 40.7% and 29.6% of the area of the basin, respectively.To prepare the ood hazard map in this study, seven factors were used, which include elevation, slope, rainfall intensity, ow accumulation, distance from the river, land use/land cover (LU/LC), and geology (Fig. 2).The elevation, slope and ow accumulation layers were extracted from the Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) with a resolution of 30 meters.The criterion of rainfall intensity was obtained based on the Modi ed Fournier Index (MFI) (Kazakis et al. 2015;Toosi et al. 2019).This index is calculated with Eq. 1 (Morgan 2005).
where P i is the average monthly precipitation for month i (mm), and P is the average annual precipitation (mm).
The value of MFI was calculated for meteorological stations and rain gauges in the basin and its surroundings, and the values were interpolated by the Inverse Distance Weighting (IDW) method.The distance from the river was determined separately in mountainous and plain areas.In mountainous areas, due to the low ratio of valley width to depth, buffers were determined with smaller distances, and in plains and low-altitude areas, larger distances were de ned for buffers.The LU/LC layer was extracted from the land cover map of Iran with a resolution of 10 meters.This map was produced by processing Sentinel 1 and 2 images on Google Earth Engine (GEE) cloud platform in 2017 (Grobanian et al. 2020).The lithology was extracted from the geological map with a scale of 1:100,000 of the region (Geological Survey of Iran).
Continuous data were classi ed into 5 classes by the Natural Break method in Arc GIS and discrete data such as LU/LC and geology were classi ed based on environmental and local conditions.The classes of each factor were rated according to their effects on ooding on a scale of 2 (minimum) and 10 (maximum).

Flood inventory map
Identifying the areas that were ooded can greatly help ood modeling and model validation.In this study, based on the reports of past oods, the location of 80 ood points has been determined on the map.Also, to evaluate the model, 80 non-ood points were identi ed.To build the model, ood and nonood data were randomly divided into two training (70%) and testing (30%) groups (Fig. 3).Where CI: the consistency index, λ max : the maximum eigenvalue of the comparison matrix, n: the number of criteria, CR: the consistency ratio, and RI : the random index.
If the value of the consistency ratio(CR) is less than 0.1, it indicates that the judgments are con rmed.
Sensitivity Analysis of AHP: Sensitivity analysis evaluates the effect of each criterion in the method (Kazkis et al. 2015).One of the sensitivity analysis methods is the single-parameter analysis technique, which was rst used by Napolitano and Fabri (1996).In this method, the effective weight is calculated with Eq. 4 and replaces the weight obtained by AHP.

4
Where, W: the effective weight of each factor, P r : the parameter's rating, P w : the factor weight, and, V: the total value of the applied index.Shanon Entropy (SE): Shannon developed an entropy model based on information theory (Pourghasemi et al. 2012).Determining the weight of criteria by Shannon's entropy method has been widely used in natural hazards such as landslides and oods.Here, the recorded ood points were randomly divided into training (70%) and testing (30%) groups.Flood training points were placed on the effective ood information layers and the values of each layer were extracted at the location of each ood point.Then a matrix of 7 criteria and 56 ood points (options) was prepared and the weight of each layer was calculated using Eqs.
where a ij : the value of the j th attribute of the i th alternative; P ij : the normalized value of each attribute, E j : entropy value (SE) of the j th criterion; m: the number of alternatives; K = 1/ln(m) is a constant that causes the weight to be between 0 and 1, w j : the weight of the j th attribute; n: the number of attributes, d j : the degree of heterogeneity of the information contained in each attribute.
Shannon entropy (SE) -AHP: In the Shannon entropy method, it is possible to adjust the weight obtained from the Shannon entropy using predetermined weights.Here, the calculated weights of the AHP method were used to adjust the entropy weight, which is calculated by Eq. 10. 10 Where W J : entropy weight, λ j : AHP weight Subsequently, determining the weights of the criteria by different methods, the rating layers were multiplied by the weight of each variable, and the nal ood hazard index map was obtained in Arc GIS by calculating Eqs.11-14. ( FHI: ood hazard index, r i : the rating of the parameter in each pixel, n: the number of the criteria, and w: the weight of each parameter.W AHP : weights of AHP, W AHPS : weights of single-parameter sensitivity analysis of AHP, W SE : weights of Shanon Entropy, W SEA : weights SE-AHP.

Validation of models
The ood hazard maps were validated with two methods, the receiver operating characteristics (ROC) and Cohen's kappa coe cient.The accuracy index of ROC analysis and the Kappa index value are calculated with Eqs. 15 and 16.

Results
The classes of effective factors in the ooding of the Talar basin (Fig. 4) were rated based on the characteristics of the ooded areas.Areas with low altitude and low slope have the most ood conditions.Therefore, more scores were assigned to the classes with lower height and slope (Table 1), and for other classes, the scores have been reduced accordingly.The factor of LU/LC was scored based on permeability and previously ooded areas; on this basis, water and paddy elds were assigned the highest score and forests had the lowest score.The lithology factor is studied based on the degree of permeability and the creation of runoff during oods.However, here the characteristics of ooded areas have been taken into consideration.Therefore, most scores have been assigned to uvial and alluvial sediments.Alluvial deposits of rivers represent an unwritten ood record (Jones et al. 2010).Proximity to the river has more potential for ooding.Therefore, the distance from the river was classi ed into several buffers based on past oods.This factor was categorized into ve classes 0-50, 50-100, 100-150, 150-200, and > 200 meters in the mountainous region.The distance buffers from the river in the plain region were categorized into ve classes: 0-100, 100-300, 300-500, 500-1000, and > 1000 meters.The buffers near the river were assigned the most scores, and with the increase in the distance, the rating decreased (Table 1).

Flood Hazard Index (FHI) maps
The weight of the ood-effective factors in the FHI was determined by a pairwise comparison of criteria.The value of CR: 0.04 was obtained, which indicates the consistency of judgment of the factors.The ow accumulation factor with a weighted score of 0.34 and the distance from the river with a weighted value of 0.23 had the greatest effect on the FHI map.The FHI map was classi ed into 5 hazard classes including, very low (2-3.6),low (3.6-4.7),medium (4.7-5.6), high (5.6-7.3), and very high (7.3-9.3).In this method, 1.65% of the area of the basin is in two hazard classes of high and very high (Fig. 5A).
The FHI map was analyzed by the single-parameter sensitivity method and the effective weight of the factors was determined.The parameters of slope (0.26), ow accumulation (0.208), elevation (0.177) and MFI (0.166) have the most weighted values in creating the FHIS map.Spatial distribution of ood hazard classes shows that 20.7% of the area of the basin lies in very high and high classes.The spatial distribution of ood hazard classes in FHIS shows that 20.7% of the area of the basin lies in very high and high classes, and the entire plain area is also in these classes (Fig. 5B).
Factors affecting ood in the FHI-SE method were weighted with the Shannon Entropy technique.The variables of distance from the river, elevation, and slope have the greatest effect on the FHI-SE map with weighted values of 0.477, 0.365, and 0.123, respectively.High and very high classes include 4.55% of the basin area and 76% of the basin area in very low and low classes (Table 2; Fig. 5C).The weighting of the criteria in the FHI-SEA method has been combined and the weights obtained from the SE method have been adjusted with the weights obtained from the AHP method.The factors of distance from the river (0.642), elevation (0.235), and slope (0.108) have gained the most weight compared to other criteria.According to this map, 3% of the area of the basin lies in the high and very high classes, and the low and very low classes covered 94.5% of the area (Table 2; Fig. 5D).

Validation of ood hazard map
The results of the ROC accuracy index show that all the methods used have good e ciency in preparing the ood hazard map.But the FHI-SE method with a value of 0.979 has the highest accuracy value compared to other methods (Table 3).The value of this index for FHI, FHIS, and FHI-SEA methods was 0.874, 0.937, and 0.957, respectively.According to Cohen's index, FHI-SE, and FHI-SEA methods lie in the excellent group with values of 0.958 and 0.917, and FHI and FHIS methods are in the good group with values of 0.75 and 0.837.

Discussion
The problem of weighting variables in the occurrence of complex phenomena such as oods is a In the SE method, which is objective and based on past oods, the factors of distance from the river, elevation, and slope were assigned a higher weight.The ood hazard assessment in the adjacent basin (Tajen basin) of the study area, which was carried out with the objective method and correlation matrix, shows that the variables of slope, distance from the river, and elevation are the most important factors affecting oods (Avand et al. 2021).The weight of the geological factor was the lowest in all the methods used in this study.Placing all ood points in one lithology has reduced the weight of this factor.The results of the work of Khosravi et al. (2016) in the Haraz basin (North of Iran), which was carried out using Shannon's entropy method, showed that the variable distance from the river and geology had the greatest and least in uence on the ood hazard map.
In the SEA method, the order of the weights is the same as in the SE method, but their values have changed.Considering the average weight of these four methods, the weight of the variables of distance from the river, elevation, and slope had a greater effect on the ood hazard assessment in the Talar basin (Fig. 6).The studies conducted worldwide show the difference in weight of variables with environmental conditions.
Figure 6: Weights of effective criteria in oods with different MCDM methods Most previous studies that have used the SE method for ood hazard assessment have used the frequency ratio (FR) method.This method was initially used in the present study, but it displayed an exaggerated weight for the accumulation ow variable, which practically made it impossible to use this method.Although, in other research related to this topic (Shannon Entropy), the ow accumulation variable was not used.
The spatial distribution of the very high class in the FHI map is mainly limited to the main bed of the river, and the high hazard zone is located at a maximum distance of 300 meters from the river.The effective factor in this map is the accumulation ow variable, which has a high weight; so, only the pixels of the ow path are placed in the very high susceptible class.This factor has caused some of the observed ood areas to be located further away from the river channel and in medium and low-class zones.
In the FHIS map, the weight of the slope factor was higher than other criteria.This factor caused the plain area, which has a slope of less than 5 degrees, lie in the high susceptible class, and even up to a few kilometers from the river, which according to reports and evidence has no oods, are also in this class.
Therefore, it seems overestimated in identifying the highly susceptible class.The factor of distance from the river has attained more weight than other variables in the FHI-SE map.Therefore, the buffers of 300 meters and 300-1000 meters from the main channel of the river, are placed in the very high and high susceptible class.Generally, in the Shannon Entropy method, the greater the dispersion of the values of an attribute, the higher the weight.The factor of distance from the river in the FHI-SE method is given a higher weight due to the distribution of ood points at distances further from the river.The effect of the elevation factor is also seen as the second most effective variable in this map, so that the elevation classes of > 1500 meters and 200-1500 meters, except for the rivers, lie in the very low and low hazard classes, respectively.The weight of the distance from the river was increased in the FHI-SEA map compared to the FHI-SE map.This factor caused buffers < 100 and 100-400 meters to be placed in very high and high classes, respectively.
In this study, the variable distance from the river was considered different for mountainous and plain areas.To investigate the effect of this variable in mountainous areas, in another map, the classi cation of the distance from the river was considered the same for the entire basin (mountains and plains).
Based on this new classi cation, the nal ood hazard map was prepared with the FHI-SE method.In several places as examples, valley cross-sections are drawn in a very high and high ood zone (Fig. 7).
The depth of the valley in these cross-sections varied from 50 to 150 meters and the width of the valley was 200 meters at most.Considering the depth of the valley, the area of the catchment area, and river discharge in oods, this depth will never be at risk of ooding in the current climatic conditions.However, in the ood hazard map, which is displayed in two dimensions, this area is placed in the high-risk class.
This issue leads to the exaggeration of ood zones in the mountainous region.In the original FHI-SE map, the sum of two very high and high susceptible zones was 4.5%.While by applying the distance from the river in the same way in the mountains and plains, the area of these classes has increased to 7.1%.
Therefore, by making a difference in the classes of the distance from the river according to the ratio of the depth to the width of the valley, it is possible to reduce the exaggerated areas in the very high and high-hazard classes.
Figure 7: In this map, the distance from the river (buffers) is considered the same for mountainous and plain areas.Sample cross-sections were drawn from very high and high-hazard zones.

Conclusion
In this study, Flood Hazard Index (FHI) was evaluated with four weighting methods AHP, AHP-S, SE, AHP-SE.Among the mentioned methods, the SE method, which is an objective weighting method, has been more accurate than other methods.The SE method requires the existence of past ood data, which can be obtained from various sources, including eld evidence, satellite images, or existing reports.In general, obtaining these data is associated with problems.The variables of distance from the river, elevation, and slope respectively have been assigned more weight in the FHI-SE map.
The application of MCDA methods such as AHP and SE in the preparation of ood hazard maps and their validation shows that these methods have been approved by various researchers.However, identifying the method that takes priority or has more accuracy in ood assessment, depends on the available layers of information and the environmental conditions of the region.
Some variables such as geology, land cover, and the amount and intensity of rainfall play an important role in creating runoff.But during river ooding, when water leaves the main river bed and ows in the surrounding areas, the diversity of these factors plays a minor role in ooding.Instead, factors such as slope, height, distance from the river, and ow volume are considered as the main and in uential factors.Therefore, the role of topography and digital elevation model with appropriate pixel size and high accuracy can play a more important role in identifying ood zones.One of the reasons for using the distance classes from the river separately in the mountains and the plains has been to prevent the creation of exaggerated zones in the ood hazard map in mountainous areas.
The results of the comparison of MCDA weighting methods in this study show that the weight of factors affecting the ood for the preparation of the FHI map is different for the following reasons: The difference in subjective and objective weighting methods that provide different results even on the basin scale.
The difference in subjective and objective weighting methods that provide different results even at the scale of a catchment The    Weights of effective criteria in oods with different MCDM methods al. 2015; Dash and Sar 2020).Empirical models are divided into three subgroups (Mudashiru et al. 2021) including 1-multi-criteria decision analysis (MCDA) methods (Arabameri et al. 2019; Akay 2021; Shahiri Tabarestani et al. 2023) 2-Statistical methods (Tehrani et al. 2014; Khosravi et al. 2016) and 3-Machine learning (Tehrani et al. 2015; Xiong et al. 2019; Khosravi et al. 2019) and arti cial intelligence (Falah et al. 2019; Jahangir et al. 2019; Khoirunisa et al. 2021).Among these, the MCDA technique is the most common technique that evaluates complex decision-making systems with a set of criteria (Wu et al. 2022).De Brito and Evers (2016) studied the application of MCDA methods in ood risk management in a review article.Determining the weight of the criteria in the MCDM method is performed with two objective and subjective weighting methods (Sitorus and Brito-Parada 2020).The subjective weighting method is based on expert judgment and paired comparison of variables (Sitorus and Brito-Parada 2020).The objective weighting of the variables is obtained from the mathematical evaluation of the criteria and does not require an expert opinion (Mahmoody Vanolya and Jelokhani-Niaraki 2019).Therefore, it reduces uncertainty and increases the effectiveness of the evaluation process (Mudashiru et al. 2021).

Figure 1 :
Figure 1: The location of Talar basin in Iran Methodology

Figure 4 :
Figure 4: Map of factors affecting oods in Talar basin; A: Elevation, B: Slope, C: Flow accumulation, D: MFI, E: LU/LC, F: Geology, G: Distance from the river

Figure 5 :
Figure 5: Flood hazard maps of Talar basin, A: FHI, B: FHIS, C: FHI-SE, D: FHI-SEA challenging issue.In previous research, several variables have been used to evaluate oods.The use of variables depends on the environmental conditions and the availability of data (Du et al. 2022).The criteria of ow accumulation, distance from the river, slope, and elevation respectively have obtained the most weight in the AHP method.In the AHPS method, the factors of slope, ow accumulation, elevation, and MFI have obtained the highest weight values and the weight of the factor of distance from the river has been greatly reduced.Previous studies carried out with similar environmental conditions in Iran, which were weighted by AHP method, show that the two factors of slope and distance from the river are the most important in uencing variables in ooding in the region(Arabameri et  al. 2019; Shahiri Tabarestani and Afzalimehr 2021; Mousavi et al. 2022).

Figure 4 Map
Figure 4

Table 1
Classi cation of effective factors in ooding, rating scores, and weight values with different methods

Table 1 :
Classi cation of effective factors in ooding, rating scores, and weight values with different methods

Table 2 :
Area (percentage) of ood hazard classes in ood hazard maps of Talar Basin

Table 3 :
ROC accuracy index and Cohen's kappa index for ood hazard maps in Talar basin