Flood Hazard Assessment Through AHP, Fuzzy AHP, and Frequency Ratio Methods: A Comparative Analysis

Abstract

Floods are the biggest hydrometeorological disaster, affecting millions annually. Thus, flood hazard assessment is crucial and plays a pivotal role in rational water management. This study was undertaken to evaluate flood hazards through the application of MCDM methods and a bivariate statistical model integrated with GIS. The methodologies applied were AHP, fuzzy AHP, and the frequency ratio. Eight flood-related criteria were considered—elevation, flow accumulation, geology, slope, land use/land cover (LULC), distance from the drainage network, drainage density, and rainfall index—for the construction of a Flood Hazard Map for each methodology, with the aim to delineate the regions within the study area most prone to flooding. The results demonstrated that around 34% of the Chalkidiki regional unit presents a high and very high hazard to the occurrence of floods. The comparison of the maps generated using DSC demonstrated that all models are capable of delineating high and very high hazard areas with overlap values varying from 0.8 to 0.98. The validation results indicated that the models exhibit sufficient performance in flood hazard mapping with AUC-ROC scores of 66.6%, 65.7%, and 76.5% for the AHP, FAHP, and FR models, respectively.

1. Introduction

Extreme weather conditions are intensifying, leading to more frequent and more destructive events. Global warming, accelerated by deforestation and industrial activities, has intensified irregular rainfall patterns, causing considerable damage to both property and human life, especially in developing countries. As cities expand, the probability of flooding increases within urban areas [1], underscoring the essential role of forest ecosystems in flood prevention. Apart from that, inadequate attention to water drainage, shortcomings in urban planning, and the population’s capacity to cope with disasters can also contribute to the occurrence of extreme event-induced hazards in urban areas [2]. Flood magnitude is a key factor, with heightened damage being linked to urbanization, population growth along rivers, and the reduction of forested areas [3]. The severity of a flood plays a key role in shaping its impact [4]. Flash floods, for example, that frequently lead to secondary disasters like landslides, sinkholes, and erosion, are more complicated, and their accurate prediction is very challenging [5].

According to a survey conducted by the World Economic Forum for the Global Risks Report of 2025, extreme weather events are ranked second in global risks at a two-year level and first at a decade level [6]. Floods are natural disasters that cause loss of life, property, and infrastructure [7]. Flood events result in impacts such as loss of life, damage to properties, and the spread of waterborne diseases, all of which affect communities in multiple ways [8]. Based on EM-DAT (The International Disaster Database), 2/3 of disasters recorded in it are related to natural hazards. Between 2000 and 2022, more than a billion people have been affected by flood events worldwide [9]. More specifically, as stated in the EM-DAT 2024 leaflet, “Floods are the most frequent disasters and affect the largest number of people, accounting for 25% of the database content and impacting more than 1.8 billion people since 2000.”

Floods occur at different intervals with varying durations [10]. The occurrence and severity of floods are determined by various factors, including climatic conditions, geomorphological features, and other environmental variables. Floods are also influenced by several natural and human-induced factors [11]. Therefore, flood hazard estimation based on multiple criteria is more accurate and dependable than one based on a single criterion [12]. Flood management issues are complex, multi-dimensional, and time-sensitive, and multi-criteria decision-making (MCDM) systems are designed to handle this complexity and aid in making informed, rational decisions. Multicriteria analysis allows for the evaluation of multiple factors that impact flood events, and the MCDM approach is a popular method employed in decision-making across a range of fields [13].

The combination of GIS and multi-criteria analysis is particularly widespread. GIS has significantly advanced the environmental sector, making it easier to create maps, analyze areas, and derive results from them. GIS has been broadly used in flood assessment analyses [14,15,16,17,18] because of its strong ability to process spatially distributed data. GIS offers the capability to map areas at risk of flooding, serving as a tool to help protect specific regions from such disastrous events. Remote sensing and GIS tools have been extensively utilized for mapping flood risk and vulnerability. The biggest advantage is that a wide range of models can be integrated into the GIS environment to process various inputs [12]. GIS-based MCDM approaches for flood hazard mapping are particularly valuable in areas with limited available data [19]. The primary benefit of combining GIS and MCDM techniques is that the final product is an easy-to-read map providing useful information to locals and authorities. Flood hazard maps are a tool for early warning systems and can be used to prevent and mitigate future flood events [17].

A variety of methods and techniques have been applied to assess flood hazards [13]. Over the years, hydrological modeling and spatial data analysis have been extensively used to evaluate the dynamics and extent of flooding. One key element in future flood hazard management is the development of flood hazard maps, which are instrumental in identifying areas vulnerable to inundation [20]. Enhancing the precision of flood forecasting and mapping is crucial for mitigating the adverse impacts of flood events [11]. A sustainable and proactive approach to reducing flood-related risks involves identifying flood-prone areas through geospatial analysis [21]. Accurate delineation of flood-prone areas is essential for the effective prevention and management of future floods [22]. Recognizing flood-prone zones and applying targeted structural and non-structural interventions in these locations can substantially reduce casualties, property damage, and economic losses. Therefore, identifying flood-prone areas remains a cornerstone of flood mitigation strategies. A considerable amount of research has focused on the assessment of flood hazards and the identification of vulnerable areas [23,24,25,26,27]. Furthermore, flood hazard mapping plays a key role in comprehensive risk assessments by integrating social, economic, and geophysical dimensions [28].

In recent years, floods have increased dramatically, and as climate change intensifies, they tend to increase further. Europe has often been impacted by a variety of severe and damaging flood events [14]. Floods in Greece have become more severe and frequent over time. More specifically, it has been calculated that floods in Greece between 2000 and 2023 have affected thousands of people [9]. Greece is one of the European countries experiencing a high number of flood events, along with some of the most significant damages [28], and they have been following an increasing trend in recent decades. Therefore, an integrated flood management system is essential as it affects the lives of tens of thousands of people. Statistical methods are broadly recognized and demonstrate high reliability in flood hazard assessment [29]. At the same time, the integration of GIS and RS data in flood hazard mapping is of equal significance, given their capacity to efficiently manage large-scale spatial and temporal data [30].

In this framework, AHP, FAHP, and FR models were chosen to assess flood hazard in the Chalkidiki regional unit. MCDM methods and statistical approaches are broadly selected in flood vulnerability mapping due to their straightforward implementation and compatibility with spatial tools and machine learning models. Researchers are increasingly turning to MCDM methods due to their ability to manage complex decisions involving multiple conflicting criteria, allowing for more comprehensive evaluations [31]. Flood hazard mapping using the AHP MCDM method was chosen, as it allows for integrating multiple flood-related parameters, and it is simple to implement. Its limitation is that it is based on the decision-makers’ opinions, which can lead to bias and compromise the consistency of the results [31,32]. This limitation of AHP is due to the “subjective” nature of priorities established by the decision-makers; its fuzzy extension, FAHP, was chosen, as it is also employed in related spatial applications to address the uncertainty. Lastly, the FR model has been proven by many as effective for flood hazard representation [33,34,35], as it can process nonlinear and uncertain relationships, and it has been proven to be accurate in hydrological hazard assessments [7]. A set of three methodologies was examined to enhance the reliability and the robustness of the results.

Another very commonly used method for flood hazard assessment is through hydraulic modeling [36,37,38,39,40,41]. Ref. [36] studied dam break modelling and flood hazard assessment in a hypothetical scenario of dam failure in northern Greece. They used a two-dimensional numerical model for the simulation of the dam break process, and the routing of the wave was utilized through HEC-RAS. In their study, ref. [37] used hydrodynamic modeling to assess flood hazard in a small-scale area, a village in Indonesia. Ref. [38] developed a simulation model of surface runoff in the Teesta Watershed in India. In their study [39], they used HEC-HMS and HEC-RAS for flash flood hazard assessment and prediction in two drainage basins (An-Nawayah and Al-Rashrash) in southeastern Cairo, Egypt. As [40] states, hydrodynamic models are commonly used to conduct comprehensive simulations of flood behavior and are predominantly associated with forecasting, flood mapping, and the evaluation of different flood scenarios. The key differences between hydraulic and GIS-based models primarily concern the type of input data required and the methodological framework [41].

MCDM methods and statistical models are often preferred over hydrological models as they require a smaller amount of data for their application, rely mainly on spatial data, which are more easily accessible, are easier and faster in their computational processes, and can be scaled up to larger study areas. Hydrological modeling also demands a lot of fieldwork for data collection, something that is time-consuming and requires a substantial budget [42]. In addition, MCDM techniques are applied for strategic planning, in contrast to the hydraulic analyses that are employed for early warning system design.

The objective of this study is to evaluate and delineate areas prone to flooding, comparing three methodological approaches: AHP, Fuzzy AHP, and Frequency Ratio. The resulting maps of those approaches were compared and analyzed to determine the study area’s flood vulnerability. All three methodologies considered the same flood factors and were processed spatially in GIS Pro 3.4.3.

2. Materials and Methods

2.1. Study Area and Datasets

2.1.1. Study Area

The study area chosen is the Chalkidiki regional unit, which is part of the administrative region of Central Macedonia in Greece. The area is located in the northern part of Greece, between Thermaikos and Strymonikos gulfs, and it extends over three peninsulas: Kassandra in the west, Sithonia in the center, and the Athos peninsula in the east, as shown in Figure 1. It borders the Thessaloniki regional unit in the northwest part, while the Aegean Sea washes the rest of its shores.

The Chalkidiki regional unit covers an area of 3183.6 km² and its perimeter is 772 km. The mean elevation and mean slope are 279.1 m and 11.6%, respectively. The urban population of the Chalkidiki regional unit is 101,324 people (98.3% of the total population). The autonomous monastic state of Mount Athos, which is frequently classified within the geographical boundaries of Chalkidiki, recorded an additional 1746 people (1.7% of the total population), according to the 2021 census data (Hellenic Statistical Authority—ELSTAT). Its largest towns are Nea Moudania, Nea Kallikrateia, and the capital town of Polygyros, and their populations are 10,042, 10,144, and 7779 people, respectively. The overall population density of the Chalkidiki regional unit is 32 people per km².

The study area’s climate belongs to the temperate Mediterranean, following the Köppen climate classification. It is characterized by arid, high-temperature summers and cooler, rainier winters. These climates exhibit high temperature fluctuations between the hot and cold seasons, and the majority of precipitation occurs in winter, while summer is mainly dry.

The type of vegetation found in the study area consists primarily of forest areas, shrubs, and agricultural land, and the smallest part consists of pastures, settlements, and barren land. The forest areas of the area mainly include oak, beech, and pine forests and over 200 herbaceous species. The mountainous areas within the Chalkidiki regional unit are covered to a great extent by mixed forests and broadleaf forests, while to a lesser extent by coniferous forests. Intervening areas between forested regions are partially made up of natural pastures and meadows with low vegetation density. The area also contains artificial surfaces, wetlands, and water bodies. The water surfaces and wetlands found in the area are mainly inland waters (rivers, lakes, swamps, etc.), while a small percentage is occupied by transitional waters (river estuaries). Several settlements can be noticed in the coastal areas, while industrial or commercial use is more prominent.

Geomorphologically, the Chalkidiki regional unit consists of narrow valleys and mountainous paths that accelerate the rapid waters of heavy rainfall.

According to data from the Hellenic Meteorological Service, the area has been significantly affected by heavy rainfall in October 2000, in December 2003, in October 2006, by Storm “Medusa” in September 2017, and by heavy rains in June 2023. These severe weather events caused extensive damage in the area, where large amounts of rainfall were recorded.

The Chalkidiki regional unit is of considerable importance for Greece. It is located adjacent to the country’s second-largest city and has high tourist and agricultural activity, factors that underscore its relevance as a focal area for flood assessment.

2.1.2. Datasets

The evaluation of flood hazard within the study area was based on multiple data sets subjected to successive stages of processing. The application of all three models was conducted in a GIS environment, and more specifically, GIS Pro 3.4.3, where the factors considered were processed as thematic maps. All the datasets that were used in this research can be found in

Table 1. Datasets used in this study.

Data	Source	Spatial Resolution	Description
DEM	Hellenic Military Geographical Service	80 × 80	Processed in GIS Pro 3.4.3
Rainfall	Gauge stations in the area		Processed first in Excel and then in GIS Pro 3.4.3
LULC	CORINE Land Cover 2018, EEA (European Environment Agency)	80 × 80	Processed in GIS Pro 3.4.3
Geological data	Hellenic Survey of Geology & Mineral Exploration (H.S.G.M.E.)	80 × 80	Processed in GIS Pro 3.4.3
Historical Flood Data	Hellenic Ministry of Environment and Energy, the online database of the National Observatory of Athens (meteo.gr), and other published reports	80 × 80	Processed first in Excel and then in GIS Pro 3.4.3 to create training and validation maps

.

The parameters’ data were processed as thematic layers in GIS Pro 3.4.3 to develop the Flood Hazard Index Map. Each thematic layer was classified into five hazard degrees (2 = very low, 4 = low, 6 = moderate, 8 = high, and 10 = very high) using the Natural Breaks Jenks Classification method, following [1,15,24,43] so that all classes in all parameters demonstrate uniformity. The natural breaks classification method is effective for mapping unevenly distributed data because it groups similar, clustered values into the same class. This method relies on the inherent patterns or groupings found within the data. Class breaks are created in a way to best group similar values together and emphasize the distinctions between classes [44].

To extract accurate information from the DEM, small imperfections in the initial dataset needed to be removed. This was achieved using the “Fill” tool within the “Spatial Analyst” Toolbox of GIS Pro 3.4.3. All DEM-derived datasets utilized in this study were generated based on the corrected shapefile.

2.1.3. Flood Criteria

Eight flood-related parameters were considered to determine the most vulnerable areas to flooding, based on a previous study [24]. These were elevation (E), flow accumulation (FA), geology (G), slope (S), land use/land cover (LULC), distance from the drainage network (D), drainage density (DD), and rainfall index (RI).

Elevation, flow accumulation, slope, distance from the drainage network, and drainage density were extracted from the DEM of the study area. According to ESRI [45], DEM is “a raster dataset produced from a sample of elevations or depths taken on a regular grid, typically used to represent the bare-earth terrain, void of vegetation and human-made features.” To determine the rainfall index, the Modified Fournier Index (MFI) was applied to processed historical monthly rainfall data collected from local gauge stations. LULC data was extracted from CORINE Land Cover 2018 of EEA (European Environment Agency), and geology data was derived from the Hellenic Survey of Geology & Mineral Exploration (H.S.G.M.E.).

Flow accumulation and elevation were selected as the most important factors and were placed first in the ranking, as equally important, based on literature [24,43,46,47,48]. The predominance of low-altitude areas in the study area highlights the importance of this parameter. Similarly, flow accumulation represents the movement and convergence of water, a factor that is equally critical in the development of flood events.

The second place was given to drainage density, following [1,47], as the proportion of water that either infiltrates the soil or flows over the surface directly influences the likelihood of flooding.

The rainfall index was assigned to the third position in the hierarchy, consistent with findings from [49,50]. Similar to their studies, it was identified as a decisive factor, as the amount of water reaching the ground surface through precipitation directly influences flood occurrence.

The distance from the drainage network was ranked fourth in the hierarchy. This factor affects flood hazard levels, as areas adjacent to the drainage network face higher susceptibility, whereas areas located at greater distances are comparatively less affected.

LULC is a critical factor, especially in regions with rocky terrain or areas with sparse vegetation. The majority of the study area is covered by forests and/or agricultural land. Nevertheless, due to the presence of certain burnt and urbanized areas, LULC was assigned the fifth place of importance.

Geology is associated with soil permeability and, by extension, surface water drainage. It is generally considered a significant factor in smaller catchments; however, given the large extent of the study area and the inclusion of multiple watersheds, it has been assigned the sixth position in the hierarchical ranking.

Last in the parameters’ ranking was slope, since it is indirectly incorporated through elevation.

Elevation expresses the distance of a point from the sea surface and is measured in meters. Areas with lower elevation values, such as floodplains or valleys, are more likely to flood, as water naturally flows downhill and tends to accumulate in these regions. The highest point in the study region reaches 1918 m, while the lowest, located near the coast, lies at 5.75 m above sea level.

Elevation’s classification and its equivalent hazard degrees can be found in

Table 2. Elevation values and their hazard degrees.

Elevation (m)	Hazard Degree
943–1918	2
568–943	4
351–568	6
163–351	8
6–163	10

.

Flow accumulation refers to the quantity of water that moves into each cell from its neighboring cells and eventually collects within it. In the study area, flow accumulation follows the hydrographic network and was extracted according to the flow direction. Using the raster that was made with the “Fill” tool, the Flow direction was extracted using the tool “Flow Direction” of the Toolbox “Hydrology,” and then with the tool “Flow Accumulation” of the Toolbox “Hydrology”, Flow Accumulation raster was created. Areas with higher flow accumulation represent areas with concentrated water flow and correspond to a greater flooding hazard. The highest hazard levels within the study area are observed near estuaries and streams, while the level of hazard progressively decreases with increasing distance from these locations.

The classes of flow accumulation and their corresponding hazard degrees are given in

Table 3. Flow Accumulation values and their hazard degrees.

Flow Accumulation (m)	Hazard Degree
0–1.173	2
1.173–4.589	4
4.589–11.962	6
11.962–30.535	8
30.535–65.229	10

.

Geology is a parameter that can be significant based on the geological formations occupying an area. It influences groundwater and surface water availability, movement, and quality. Areas that, in their subsurface, consist of permeable formations show increased infiltration and subsurface flow, less surface runoff, and, as a result, less flooding. Conversely, impermeable formations exhibit low filtration rates while favoring the accumulation of surface water and the occurrence of surface runoff.

Geology’s categories and their hazard degrees are displayed in

Table 4. Geology categories and their hazard degrees.

Geology Categories	Hazard Degree
Alluvial	2
Quaternary deposits	4
Neogene sediments	6
Carbonate rocks	8
Crystalline rocks	10

.

The slope is a parameter that expresses the deviation found in the elevation at any point on the ground surface. It typically indicates the degree of incline relative to the horizontal plane and can be measured in degrees and percentages. The slope in the study area varies from 0 to 126.8%, where the lowest slope values are found in flat urbanized and coastal areas. Those areas are more prone to flooding because the water accumulates in them, contrasting with the steeper areas where water can flow towards the gentler ones.

Slope’s values, its classification, and assignment to hazard degrees are presented in

Table 5. Slope values in percentage and their hazard degrees.

Slope (%)	Hazard Degree
47.2–126.8	2
26.9–47.2	4
15.4–26.9	6
6.4–15.4	8
0–6.4	10

.

LULC is a criterion that provides the state of the land regarding the type of exploitation found in it. It presents information about vegetation cover, urbanization, and how the land is used and is considered one of the parameters that influence hydrological processes, such as runoff and infiltration. Land use categories with their hazard degrees and spatial distribution are given in

Table 6. LULC categories and their hazard degrees.

LULC Categories	Hazard Degree	Distribution, %
Forests, Transitional woodland-shrublands, Sclerophyllous vegetation	2	57.07
Non-irrigated-arable land	4	13.17
Vineyards, Olive groves, Natural pastures	6	10.10
Meadows, Sports, and recreation facilities	8	0.89
Coastal marshes, Water bodies, Industrial or commercial zones, Urban development, Mines	10	18.77

. Forests and vegetation cover the most significant part of the area, as shown in Table 6, and those two types of land use exhibit low flood hazard. They are essential for soil cohesion, and their presence reduces soil erosion and degradation.

Distance from the drainage network refers to the measurement from the riverbed to the basin outlet where the water is discharged. Areas near the streambed are considered the most vulnerable, and the hazard decreases as we move further from them. The safety zones were calculated along the drainage network at limits of 200, 500, 1000, 2000, and above 2000 m, following previous studies [24,46]. Areas within 200 m were classified as near the drainage network and were considered very high hazard, whereas the flood hazard degree decreased as the distance increased.

Table 7. Distance from drainage network values in percentage and their hazard degrees.

Distance from Drainage Network (m)	Hazard Degree
>2000	2
1000–2000	4
500–1000	6
200–500	8
<200	10

provides the classification of this factor and the corresponding hazard degrees.

Drainage density refers to the cumulative length of channels per unit area and is typically measured in meters [51]. Higher drainage density values suggest reduced infiltration, which results in increased surface runoff and a greater susceptibility to flooding in the area. The lower the drainage density values are, the higher the infiltration, and as a result, the flooding risk is decreased. Its values were derived from the DEM of the study area and classified into five hazard classes, as shown in

Table 8. Drainage Density values and their hazard degrees.

Drainage Density (km/km2)	Hazard Degree
0–0.073	2
0.073–0.189	4
0.189–0.313	6
0.313–0.472	8
0.472–0.776	10

.

The amount of rainfall a surface receives is quite influential in flood hazard assessments. It directly affects the volume of water that can accumulate in an area. Intense or prolonged rainfall can overwhelm drainage systems, leading to surface runoff, river overflow, and flash floods. The amount, duration, and intensity of rainfall determine how quickly water can penetrate the ground or flow overland, impacting flood risk in a given area. In this study, the rainfall index was chosen to represent the precipitation in the study area, and it was calculated using the MFI as given in Equation (1). This index processes rainfall data from rain gauge stations in an area and estimates the MFI values for each station.

$$\mathrm{MFI}={\displaystyle \sum _{\mathrm{i}=1}^{12}\frac{{\mathrm{p}}_{\mathrm{i}}}{{\mathrm{P}}_{\mathrm{t}}}}$$

(1)

where MFI is the Modified Fournier Index, i is the month, ${\mathrm{p}}_{\mathrm{i}}$ is the mean monthly precipitation (mm), and ${\mathrm{P}}_{\mathrm{t}}$ is the mean annual precipitation (mm). The five hazard classes and their hazard degrees are given in

Table 9. Rainfall Index values and their hazard degrees.

Rainfall Index	Hazard Degree
15.62–34.85	2
34.85–46.43	4
46.43–56.18	6
56.18–68.03	8
68.03–82.78	10

.

The final thematic rainfall index map was developed using the Spline interpolation method in GIS Pro 3.4.3, which is preferred for areas where available precipitation data comes from a small number of rain gauge stations [52].

All thematic maps of the criteria studied are illustrated in Figure 2.

These thematic layers were superimposed in GIS Pro 3.4.3 to implement the proposed methodological framework and develop the Flood Hazard Maps. The complete sequence of steps followed in this methodological approach is depicted in the flowchart shown in Figure 3.

2.1.4. Flood Inventory Map

The FR model application requires historical flood events from the study area. Historical flood records are crucial for the assessment and prediction of future flood scenarios [10,53]. The flood inventory data are also valuable for validating the final flood hazard map [10,54].

The collection, preparation, and development of a historical flood database is the foundation of flood hazard studies [55]. The flood inventory map of the study area was created with data collected from various sources. These sources are the Hellenic Ministry of Environment and Energy, the online database of the National Observatory of Athens (meteo.gr), and other published reports. The data collected consisted of 148 historic flood occurrences that transpired in Chalkidiki from 1980 to 2018, as shown in Figure 4. The dataset consists of the flood events recorded in the area with their coordinates, the number of flood events, and the date they occurred. Based on literature [54,56,57,58,59], the inventory map was divided into a ratio of 70–30%, which is the most frequently used. Thus, the total historical flood events were separated into two maps. The first included 70% (training map) of the total records and was used for model training, and the second contained the remaining 30% (validation map) of the past floods and was used for the validation of the results. The flood events that occurred in the study area were randomly divided into two datasets, and both maps were created in GIS Pro 3.4.3. The Flood Inventory map had a spatial resolution of 80 × 80, the same as the rest of the inputs.

2.2. AHP

AHP was selected as the first methodology to be employed to estimate the parameters’ weights. It is a multicriteria decision-making technique that offers a systematic approach to integrating and evaluating the impact of various factors involving various levels of dependent or independent qualitative and quantitative information [60]. AHP is considered the most widely used methodology for flood hazard assessment [22,23,24,46,61], and it is preferred by the majority of scientists because it is very easily applied, and it can be combined with GIS and remote sensing. The use of the AHP decision-making technique for mapping flood vulnerability and risk by combining various flood-related factors is commonly employed [14].

The Analytic Hierarchy Process (AHP) is a method for multi-criteria decision-making, where the criteria are structured hierarchically. The central part of AHP is the pairwise comparison to examine the importance of each criterion concerning each of the others. An assessment of their relative importance is carried out to classify the criteria from the least important to the most important, giving them a value from 1 to 9, respectively, according to their relevance. The numerical scale developed by [62] and used in this study is presented in

Table 10. Saaty’s pairwise comparison scale.

Definition	Numeric Value
Extremely important	9
	8
Very strongly more important	7
	6
Strongly more important	5
	4
Moderately more important	3
	2
Equally important	1

.

An 8 × 8 comparison matrix is used, where all diagonal entries equal 1. In this matrix, the factors are placed hierarchically based on their importance, and each row illustrates the relationship between the two parameters in terms of flood hazard. The final matrix was created based on the “approximate method” [63] that demands the normalization of the initial matrix.

Next in the process, a Consistency Check is required, which was completed by deriving the numerical consistency ratio CR, as given by Equation (2):

$$\mathrm{C}\mathrm{R}={\displaystyle \frac{\mathrm{C}\mathrm{I}}{\mathrm{R}\mathrm{I}}}$$

(2)

where CR is the Consistency Ratio, CI is the Consistency Index, and RI is the Random Index, whose values are given in

Table 11. Random Index (RI).

n	RI
1	0.00
2	0.00
3	0.58
4	0.90
5	1.12
6	1.24
7	1.32
8	1.41
9	1.45

and depend on the number of criteria.

The consistency index CI was calculated using Equation (3):

$$\mathrm{C}\mathrm{I}={\displaystyle \frac{{\mathrm{\lambda }}_{\max }-\mathrm{n}}{\mathrm{n}-1}}$$

(3)

where CI is the Consistency Index, ${\mathrm{\lambda }}_{\max }$ is the maximum eigenvalue of the comparison matrix, and n is the number of criteria.

The acceptable values of CR are up to 0.10. If this ratio is greater than 0.10, an inconsistency is detected, and the original comparison table must be reviewed.

Subsequently, the Flood Hazard Index map was obtained using Equation (4):

$$\mathrm{F}\mathrm{H}\mathrm{I}={\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{i}}\times {\mathrm{r}}_{\mathrm{i}}}$$

(4)

where FHI is the Flood Hazard Index, ${\mathrm{w}}_{\mathrm{i}}$ is the weight of each criterion i, ${\mathrm{r}}_{\mathrm{i}}$ is the rating of each criterion, and n is the number of criteria.

2.3. Fuzzy Sets and FAHP

The FAHP method is an extension of the AHP [62] that uses fuzzy logic for decision-making under uncertainty. AHP is considered the most widely used methodology for flood hazard assessment due to its simple implementation and combination with GIS software [24]. However, it introduces an amount of uncertainty, since it is based on objective criteria [13]. The degree of subjective importance is biased, which leads to uncertainties in the assessment weights [64]. In order to overcome this level of uncertainty, researchers have applied the FAHP method [28,64,65,66,67] because it can reduce the impact of this uncertainty.

Numerous fuzzy AHP techniques have been studied by many scientists [68,69,70,71]. The FAHP method applied in this study is the one that Buckley proposed [70]. This approach is followed by many scientists in various scientific fields [65,72,73,74].

Zadeh presented fuzzy sets in 1965 [75], and since then, they have been used in many fields of study. He introduced Fuzzy Logic (FL) as an alternative to the traditional Boolean logic, which relies on binary values (0, 1). FAHP retains the structure of classical AHP through pairwise comparisons but distinguishes itself by integrating fuzzy logic to assign weights, thereby incorporating uncertainty into the process [14].

A Triangular Fuzzy Number, TFN, $\tilde{\mathrm{\alpha }}=\left(\mathrm{l},\mathrm{m},\mathrm{u}\right)$ is a fuzzy set established over the domain of real numbers, $ℝ$. A TFN function’s membership function is described as follows:

$${\mathrm{\mu }}_{\tilde{\mathrm{\alpha }}}\left(\mathrm{x}\right)=\left\{\begin{array}{cc}\left(\mathrm{u}-\mathrm{x}\right)/\left(\mathrm{u}-\mathrm{m}\right),\hfill & \mathrm{if}\mathrm{m}\le \mathrm{x}\le \mathrm{u}\\ \left(\mathrm{x}-\mathrm{l}\right)/\left(\mathrm{m}-\mathrm{l}\right),\hfill & \mathrm{if}\mathrm{l}\le \mathrm{x}\le \mathrm{m}\\ 0,\hfill & \mathrm{if}\mathrm{x}>\mathrm{u}\mathrm{or}\mathrm{x}<\mathrm{l}\end{array}\right.$$

(5)

where l, m, and u are the lower, middle, and upper bounds of the triangular fuzzy number $\tilde{\mathrm{\alpha }}=\left(\mathrm{l},\mathrm{m},\mathrm{u}\right)$, respectively.

As [66] states, integrating the fuzzy AHP and TFN offers a novel scientific method for assessing flood hazard, making the evaluation results more rational and thorough.

Buckley’s approach applies TFNs, aligning them with Saaty’s precise numerical values and linguistic scale. The linguistic significance scale is converted into TFNs, as illustrated in

Table 12. Fuzzy AHP comparison scale and its definitions, adopted by [76].

Definition	Numeric Value	Triangular Fuzzy Number	Fuzzy Reciprocal
Extremely important	9	(9,9,9)	(1/9,1/9,1/9)
Intermediate value	8	(7,8,9)	(1/9,1/8,1/7)
Very strongly more important	7	(6,7,8)	(1/8,1/7,1/6)
Intermediate value	6	(5,6,7)	(1/7,1/6,1/5)
Strongly more important	5	(4,5,6)	(1/6,1/5,1/4)
Intermediate value	4	(3,4,5)	(1/5,1/4,1/3)
Moderately more important	3	(2,3,4)	(1/4,1/3,1/2)
Intermediate value	2	(1,2,3)	(1/3,1/2,1)
Equally important	1	(1,1,1)	(1,1,1)

.

Step 1. An 8 × 8 comparison matrix was created where the flood criteria were placed hierarchically following a previous study [55], and a pairwise comparison table was created.

Step 2. The comparison was made, but each number in the decision matrix was replaced by three numbers, l, m, and u, that represent low, middle, and upper values of the triangular fuzzy numbers.

Step 3. Once the comparison matrices were constructed, the Fuzzy Geometric Mean of the values in each row was calculated using Equation (6):

$${\tilde{\mathrm{r}}}_{\mathrm{i}}={\left({\displaystyle \prod _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{x}}_{\mathrm{i}\mathrm{j}}}\right)}^{\left(1/\mathrm{n}\right)}$$

(6)

where ${\tilde{\mathrm{r}}}_{\mathrm{i}}$ is the fuzzy geometric mean, ${\mathrm{x}}_{\mathrm{i}\mathrm{j}}$ is the product of each row of the matrix, and n is the number of parameters.

Step 4. The fuzzy weights were computed using the following three steps:

Step 4.1. For each ${\tilde{\mathrm{r}}}_{\mathrm{i}}$ (low, middle, upper bound), the sum of the vectors was calculated.

Step 4.2. For each fuzzy triangular number that was calculated in Step 4.1, the (−1) power was determined.

Step 4.3. The final fuzzy weights were computed by multiplying each ${\tilde{\mathrm{r}}}_{\mathrm{i}}$ with its reverse vector, following Equation (7):

$${\tilde{\mathrm{w}}}_{\mathrm{i}}={\tilde{\mathrm{r}}}_{\mathrm{i}}\times {\left({\tilde{\mathrm{r}}}_1+{\tilde{\mathrm{r}}}_2+\dots +{\tilde{\mathrm{r}}}_{\mathrm{n}}\right)}^{-1}=\left(\mathrm{l}{\mathrm{w}}_{\mathrm{i}},\mathrm{m}{\mathrm{w}}_{\mathrm{i}},\mathrm{u}{\mathrm{w}}_{\mathrm{i}}\right)$$

(7)

Step 5. The final weights were calculated by incorporating, firstly, the Center of Area (CoA) defuzzification method and, secondly, the normalization of ${\mathrm{D}}_{\mathrm{i}}$, using Equations (8) and (9), respectively:

$${\mathrm{D}}_{\mathrm{i}}={\displaystyle \frac{\mathrm{l}{\mathrm{w}}_{\mathrm{i}},\mathrm{m}{\mathrm{w}}_{\mathrm{i}},\mathrm{u}{\mathrm{w}}_{\mathrm{i}}}{3}}$$

(8)

$${\mathrm{w}}_{\mathrm{i}}={\displaystyle \frac{{\mathrm{D}}_{\mathrm{i}}}{{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{D}}_{\mathrm{i}}}}}$$

(9)

For the formation of FAHP’s map, the weights ${\mathrm{w}}_{\mathrm{i}}$ obtained by Equation (9) were inserted in GIS’s raster calculator using Equation (4), and the Flood Hazard Index Map was generated.

2.4. Frequency Ratio (FR)

MCDM techniques like AHP and fuzzy AHP are based on decision-makers, which means that their precision and effectiveness are dependent on the expertise of the professionals involved. In contrast, bivariate methods like frequency ratio (FR) rely on historical flood data to forecast the likelihood of future flooding in a specific area. The fact that they utilize past events enables them to generate valuable results [4].

Bivariate statistical analysis refers to the interpretation and examination of the relationships between dependent and independent variables, and the FR model is among the most widely utilized bivariate statistical models for predicting vulnerability to natural hazards [55,57,77]. In recent years, many researchers have used the frequency ratio model in flood assessment studies to highlight flood-prone areas [53,56,57,77,78].

The frequency ratio is a bivariate statistical model that can be easily paired with GIS software. It assigns values to each criterion class and evaluates their influence on flooding occurrence [34]. Remote sensing and GIS offer an efficient and convenient method for creating flood hazard maps using the Frequency Ratio model [79]. The frequency ratio is suitable for flood susceptibility mapping as it can be quickly and easily applied to regions with limited map data and is cost-effective. It is regarded as one of the most widely used and accurate methods for evaluating hazard strategies [80]. These models are straightforward in their implementation and provide realistic maps for flood hazard analysis [81].

The frequency ratio model is based on historical flood data from flood recording databases. Methodologies based on historical data and not on personal opinions have proven to be more representative and objective. Using past flood events for flood forecasting is essential and provides more robust results.

For the model training, each flood-conditioning factor was divided into five classes. The flood inventory map was overlaid with each flood-conditioning factor layer using GIS Pro 3.4.3 tools. That way, the model could count the number of flood occurrences that fall within each class of each factor and the total area of each class within the entire study area. The spatial relationships between different flood occurrence locations and each contributing factor were determined by applying the frequency ratio model to delineate flood vulnerability zones in the study area. As a result, the frequency ratio was calculated for each class within all eight conditioning factors using Equation (10) [21].

$$\mathrm{F}{\mathrm{R}}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{\%\mathrm{flooded}\mathrm{area}\mathrm{surrounded}\mathrm{by}\mathrm{particular}\mathrm{class}\mathrm{of}\mathrm{a}\mathrm{criterion}}{\%\mathrm{of}\mathrm{overall}\mathrm{area}\mathrm{surrounded}\mathrm{by}\mathrm{class}}}$$

(10)

where $\mathrm{F}{\mathrm{R}}_{\mathrm{i}\mathrm{j}}$ is the frequency ratio of class i of criterion j. FR values at each factor’s class vary between 0 and 1, where 1 represents the existence of flooding and 0 depicts flood absence over the area.

Subsequently, the relative frequency was computed as the normalized value of the frequency ratio values according to Equation (11):

$$\mathrm{R}{\mathrm{F}}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{\mathrm{F}{\mathrm{R}}_{\mathrm{i}\mathrm{j}}}{{\displaystyle \sum \mathrm{F}{\mathrm{R}}_{\mathrm{i}\mathrm{j}}}}}$$

(11)

where $\mathrm{R}{\mathrm{F}}_{\mathrm{i}\mathrm{j}}$ is the Relative Frequency of class i of criterion j, $\mathrm{F}{\mathrm{R}}_{\mathrm{i}\mathrm{j}}$ is the frequency ratio of class i of criterion j and ${\displaystyle \sum \mathrm{F}{\mathrm{R}}_{\mathrm{i}\mathrm{j}}}$ denotes the total values of FR of all classes of criterion j. This value represents the relationship between the classes and the historical flood events.

Ultimately, the prediction rate had to be estimated to create the Flood Hazard Index Map. The prediction rate aids in recognizing the correlations among the flood criteria, and it was computed using Equation (12).

$$\mathrm{P}{\mathrm{R}}_{\mathrm{j}}={\displaystyle \frac{\left(\mathrm{M}\mathrm{a}\mathrm{x}\mathrm{R}{\mathrm{F}}_{\mathrm{j}}-\mathrm{M}\mathrm{i}\mathrm{n}\mathrm{R}{\mathrm{F}}_{\mathrm{j}}\right)}{\mathrm{M}\mathrm{i}\mathrm{n}\left(\mathrm{M}\mathrm{a}\mathrm{x}\mathrm{R}{\mathrm{F}}_{\mathrm{j}}-\mathrm{M}\mathrm{i}\mathrm{n}\mathrm{R}{\mathrm{F}}_{\mathrm{j}}\right)}}$$

(12)

where $\mathrm{P}{\mathrm{R}}_{\mathrm{j}}$ is the prediction rate value of criterion j, $\mathrm{M}\mathrm{a}\mathrm{x}\mathrm{R}{\mathrm{F}}_{\mathrm{j}}$ is the maximum value of RF among all classes of criterion j, $\mathrm{M}\mathrm{i}\mathrm{n}\mathrm{R}{\mathrm{F}}_{\mathrm{j}}$ is the minimum value of RF within all classes of criterion j, and $\mathrm{M}\mathrm{i}\mathrm{n}\left(\mathrm{M}\mathrm{a}\mathrm{x}\mathrm{R}{\mathrm{F}}_{\mathrm{j}}-\mathrm{M}\mathrm{i}\mathrm{n}\mathrm{R}{\mathrm{F}}_{\mathrm{j}}\right)$ is the minimum value from all values of $\mathrm{M}\mathrm{a}\mathrm{x}\mathrm{R}{\mathrm{F}}_{\mathrm{j}}-\mathrm{M}\mathrm{i}\mathrm{n}\mathrm{R}{\mathrm{F}}_{\mathrm{j}}$ between all criteria.

The Flood Hazard Index Map using the FR model was produced, following Equation (13), by utilizing the FR weights, which were determined by normalizing the PR values for each criterion.

$$\mathrm{F}\mathrm{H}\mathrm{I}={\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}\mathrm{P}{\mathrm{R}}_{\mathrm{i}}\ast {\mathrm{r}}_{\mathrm{i}}}$$

(13)

where FHI is the Flood Hazard Index, $\mathrm{P}{\mathrm{R}}_{\mathrm{i}}$ is the prediction rate of each criterion i, ${\mathrm{r}}_{\mathrm{i}}$ is the rating of each criterion, and n is the number of criteria.

3. Results

In this paper, the FR statistical model, AHP, and FAHP multi-criteria analyses were applied to estimate the flood-susceptible areas within the study area. The factors taken into account were elevation, flow accumulation, slope, rainfall index, geology, LULC, distance from the drainage network, and drainage density. The parameters were processed by GIS Pro 3.4.3 and visualized as thematic maps.

3.1. AHP Outcomes

AHP was applied for the estimation of the relative weights of the parameters under consideration. The relative weights reflect the importance of a parameter regarding the problem under consideration. The initial parameter ranking adopted based on the study area’s characteristics was as follows: flow accumulation and elevation were selected as the most important factors and were placed first in the ranking. The second place was given to drainage density, whereas the third was given to the rainfall index. The fourth place in the hierarchy was given to the distance from the drainage network, the fifth place was appointed to LULC, and the sixth to geology. Last in the parameters’ ranking was slope.

Table 13. AHP pairwise comparison matrix. Abbreviations used in the table are described in the corresponding section.

	E	FA	DD	RI	D	LULC	G	S
E	1	1	2	3	4	4	5	7
FA	1	1	2	3	4	4	5	7
DD	1/2	1/2	1	2	3	4	5	6
RI	1/3	1/3	1/2	1	2	3	4	6
D	1/4	1/4	1/3	1/2	1	2	3	5
LULC	1/4	1/4	1/4	1/3	1/2	1	2	3
G	1/5	1/5	1/5	1/4	1/3	1/2	1	2
S	1/7	1/7	1/6	1/6	1/5	1/3	1/2	1

gives the pairwise comparison based on the hierarchical ranking of the factors examined, as mentioned in the criteria section.

The next step of the AHP methodology is to examine for inconsistencies. Equations (2) and (3) were followed to perform the inconsistency check. The Consistency Ratio’s (CR) value was estimated to be 0.03, a value that meets the requirements of the consistency check and verifies the stability of the weights extracted.

The final Flood Hazard Index map following the AHP method was created using Equation (4) in the raster calculator, where the parameters were inserted as thematic maps, and it is portrayed in Figure 5.

The flood hazard distribution of the study area is presented in

Table 14. Flood hazard and its distribution in the study area, based on the AHP method.

Flood Hazard Degree	Area, km2	Flood Hazard
2	402.20	Very Low
4	756.45	Low
6	894.84	Moderate
8	741.11	High
10	389.03	Very High

, and the corresponding chart is depicted in Figure 6.

The map created to highlight the most perilous areas encountered in the study area indicates that the areas showing very high hazard cover a rate of 12.2%, while high hazard is met in 23.28% of the total area. A significant part of the study area is characterized as moderate hazard and covers 28.11% of the total area. The riskiest areas are located mainly in the western part of the Chalkidiki regional unit, which borders the Thessaloniki regional unit. In this area, intense urbanization and coastal tourist facilities are located, and many flooding events have occurred. Before the Kassandra Peninsula, another high-hazard area is located in the southern part of the study area. This specific area extends along the coastal zone to the east of the Kassandra Peninsula of Chalkidiki and receives torrential runoff from the upstream mountain range. Additionally, in the northern and northwestern part of the Sithonia Peninsula, high-hazard areas can be found, which have flooded in the past due to water volumes deriving from the Chavrias River.

3.2. FAHP Outcomes

FAHP was employed to evaluate the relative significance of the analyzed parameters.

Table 15. FAHP pairwise comparison matrix using TFN. Abbreviations used in the table are described in the corresponding section.

	E	FA	DD	RI	D	LULC	G	S
E	(1,1,1)	(1,1,1)	(1,2,3)	(2,3,4)	(3,4,5)	(3,4,5)	(4,5,6)	(6,7,8)
FA	(1,1,1)	(1,1,1)	(1,2,3)	(2,3,4)	(3,4,5)	(3,4,5)	(4,5,6)	(6,7,8)
DD	(1/3,1/2,1)	(1/3,1/2,1)	(1,1,1)	(1,2,3)	(2,3,4)	(3,4,5)	(4,5,6)	(5,6,7)
RI	(1/4,1/3,1/2)	(1/4,1/3,1/2)	(1/3,1/2,1)	(1,1,1)	(1,2,3)	(2,3,4)	(3,4,5)	(5,6,7)
D	(1/5,1/4,1/3)	(1/5,1/4,1/3)	(1/4,1/3,1/2)	(1/3,1/2,1)	(1,1,1)	(1,2,3)	(2,3,4)	(4,5,6)
LULC	(1/5,1/4,1/3)	(1/5,1/4,1/3)	(1/5,1/4,1/3)	(1/4,1/3,1/2)	(1/3,1/2,1)	(1,1,1)	(1,2,3)	(2,3,4)
G	(1/6,1/5,1/4)	(1/6,1/5,1/4)	(1/6,1/5,1/4)	(1/5,1/4,1/3)	(1/4,1/3,1/2)	(1/3,1/2,1)	(1,1,1)	(1,2,3)
S	(1/8,1/7,1/6)	(1/8,1/7,1/6)	(1/7,1/6,1/5)	(1/7,1/6,1/5)	(1/6,1/5,1/4)	(1/4,1/3,1/2)	(1/3,1/2,1)	(1,1,1)

presents the fuzzy pairwise comparison matrix, maintaining the same hierarchy in the parameters as previously.

In the last step of the methodology, the parameter weights were converted from fuzzy weights into crisp values to be inserted in the raster calculator in GIS Pro 3.4.3. Equation (4) established the Flood Hazard Index map, which is pictured in Figure 7.

Substantial vulnerability appears in the western coastal areas and on the borders with the Thessaloniki regional unit, where intense urbanization can be found, at the estuaries of the Olynthios and Chavrias rivers, in the northeastern part of the regional unit in the areas where influence is exerted from downstream of Lake Volvi, in the northwestern area of the Athos Peninsula in the Gomati area, as well as on the northeastern coasts where the lowland areas of Olympiada and Kalyvia Varvaras are located.

The methodology’s outcomes reveal that areas with high and very high hazards exceed 34% and are located mainly in the western and central parts of the Chalkidiki regional unit. Moderate hazard can be found in 28.12% of the Chalkidiki regional unit, whereas the lowest hazard areas cover a percentage of 13.10%.

Table 16. Flood hazard and its distribution in the study area, based on the FAHP method.

Flood Hazard Degree	Area, km2	Flood Hazard
2	417.05	Very Low
4	782.62	Low
6	895.24	Moderate
8	713.72	High
10	374.99	Very High

provides the distribution of flood hazard in the study area for each hazard class, and the distribution chart is displayed in Figure 8.

3.3. FR Model Outcomes

The FR method evaluates the same parameters but applies different weights and priorities. The priorities of the factors depend on their prediction rate (Equation (12)), which exhibits the connections between the factors contributing to a flood. The normalization of the PR values for each parameter constitutes the final stage of the method, where the final values of the weights were derived. It should be noted that the higher the PR value in the FR model, the more critical the role of the factor in flood vulnerability assessment.

After evaluating the PR values, the ranking of the parameters was determined as follows: flow accumulation was identified as the most important factor, followed by elevation. Slope ranked third in importance, followed by LULC in fourth place. Drainage density and geology were considered equal in the fifth place, while the rainfall index was sixth. Finally, the distance from the drainage network was last in the parameters’ hierarchy.

The Flood Hazard Index map was developed using Equation (13) and is illustrated in Figure 9.

The FR model’s outcomes denote that the most dangerous areas cover 12.11% of the study area, and the least dangerous 12.75%. High and very high hazards can be found in 34% of the Chalkidiki regional unit, mainly concerning low-altitude areas, steep areas, and areas bordering the Thessaloniki regional unit. 27.76% of the area is characterized by a moderate hazard percentage, corresponding to 883.76 km² of the area.

In comparison to the AHP and the FAHP, the frequency ratio model highlighted as very high hazard certain areas that the other two characterized as high hazard. Predominantly, it concerns the area of Koumitsa in the eastern part of the Athos peninsula, the area of Nea Potidea in the Kassandra peninsula, the Sykia area in the eastern part of the Sithonia peninsula, and the coastal region of Ierissos within the eastern part of the study area.

The distribution of flood hazard in the Chalkidiki regional unit based on the FR model can be found in

Table 17. Flood hazard and its distribution in the study area, based on the FR model.

Flood Hazard Degree	Area, km2	Flood Hazard
2	405.79	Very Low
4	811.63	Low
6	883.76	Moderate
8	696.97	High
10	385.47	Very High

and its related graph in Figure 10.

3.4. Validation of Flood Hazard Maps

Conducting a validation check of the applied methodology is a standard and necessary practice in all studies. Validating the method is critical to ensure the chosen approach is appropriate for achieving the intended goals. The validation of the results was implemented to assess the impact of different parameters and their weights on the final outputs.

In order to check the robustness of the methodologies applied, the following validation checks were performed: Initially, validation of the FR outcomes with the validation map created from the historical data containing 30% of the past flood events; furthermore, validation of the findings was implemented using the ROC-AUC model, and ultimately, comparison of the outcomes of all three methodologies with the results of the 1st Review of the Flood Hazard Management Plans of the Hellenic Ministry of Environment and Energy. Furthermore, a spatial overlap analysis of the produced maps was performed to assess the level of agreement between the results.

3.4.1. FR Model Validation

In the first step of validation, the FR model’s performance was examined. The validation map, consisting of 30% of the historical data, was used to confirm the results. As shown in Figure 11, the flood hazard map has identified as hazardous and highly hazardous those areas where at least one historical flood event has been recorded. More specifically, it was calculated that 75% of the historical floods occurred in areas the map pointed out as high and very high hazard. This confirmation rate is quite satisfactory, and the map can be considered relatively accurate and representative.

3.4.2. ROC-AUC

In the second part of the validation procedure, the validation of the models was conducted using the Area Under the Curve in the Receiver Operating Characteristics (ROC) curve (AUC-ROC) method. The AUC value serves as an indicator of how accurately the forecasting system predicts predefined events and has been employed by many studies [29,53,82,83,84]. AUC can take values between 0 and 1, with 1 indicating perfect prediction.

The ROC curves produced are depicted in Figure 12.

Based on the ROC curve analysis, the FR model’s map, with an AUC score of 0.765, demonstrates greater reliability compared to the AHP and FAHP models, which achieved AUC values of 0.666 and 0.656, respectively. The FR model’s ROC value indicates a better agreement between the predicted dangerous areas and the actual distribution of flood-prone areas. AHP and FAHP values are acceptable for flood hazard mapping [33]; however, they reveal an opportunity for further improvement by incorporating higher-resolution datasets and a more detailed flood inventory map.

These AUC values demonstrate a satisfactory correspondence between the predicted flood locations and the actual flood occurrences. These rates indicate that the applied methodologies show sufficient accuracy in their results and can be utilized for flood hazard assessment.

3.4.3. Comparison of the Flood Hazard Maps and the National Flood Risk Management Plans

In the last step of the validation, a comparison was made between the Flood Hazard Maps created and the results of the 1st Review of the Flood Risk Management Plans of the Hellenic Ministry of Environment and Energy. The Flood Risk Management Plans of the Hellenic Ministry of Environment and Energy defined the areas with the most significant probability of flooding and are essentially more vulnerable to flooding as Potentially High Flood Hazard Zones. The Potentially High Flood Hazard Zones were established throughout the entire Greek territory. For the Central Macedonia Region, the highlighted areas as Potentially High Flood Hazard Zones are presented in Figure 13.

The zones that are presented in Figure 13 are

• EL10APSFR001—The Coastal Zone of Chanioti-Polydrosso Areas of the Southern Kassandra Peninsula;
• EL10APSFR002—The Coastal Zone of Agios Nikolaos Area and other low-lying areas of Western Sithonia;
• EL10APSFR003—The Low Zone of Stream Basins of Moudania, Agios Mamas, and Northern Part of Kassandra Peninsula, Chalkidiki;
• EL10APSFR004—The Low Zone of Stream Basins of Nea Irakleia Prefecture—Kallikrateia Prefecture and Coastal zone of Epanomi;
• EL10APSFR006—Low-lying areas of the lakes Koroneia—Volvis and the Richios River watershed;
• EL10APSFR008—The Low-lying basin zone of the T66 regional ditch, the Loudias and Axios rivers, including the area of the former Lake Artzan and Gallikos, lakeshore areas of Lake Doirani, low-lying zone of the Thessaloniki urban complex, and Anthemountas stream;
• EL10APSFR009—Lowland zones of the Chavrias catchment basin and streams of the Municipality of Aristotelis.

These zones are considered potentially vulnerable to flooding, and as Figure 14 shows, all maps created indicate the same areas as dangerous. These are territories located near river estuaries, sites influenced by lake streams, low-altitude coastal areas, and nearshore zones where torrential runoff from the upstream mountain range ends up.

Observing the map representing the Potentially High-Hazard Zones in contrast to the maps created by AHP, FAHP, and the FR model, we conclude that the results of all methods converge quite well. All areas characterized as perilous by the three maps of this study belong to the potentially high flood hazard zones and cover approximately 34–36% of the total area of the study area.

3.4.4. Dice Similarity Coefficient (DSC)

Finally, to evaluate the spatial agreement between the three Flood Hazard Maps, the Dice Similarity Coefficient (DSC) was calculated, focusing on the high- and very-high hazard areas (classes 8 and 10). DSC is a spatial overlap index that ranges from 0, indicating no spatial overlap between two sets of binary segmentation, to 1, indicating complete overlap [85,86].

The DSC, which serves as the overlap metric, is determined using Equation (14):

$$\mathrm{D}\mathrm{S}\mathrm{C}\left(\mathrm{A},\mathrm{B}\right)={\displaystyle \frac{2\left|\mathrm{A}\cap \mathrm{B}\right|}{\left|\mathrm{A}\right|+\left|\mathrm{B}\right|}}$$

(14)

where $\left|\mathrm{A}\cap \mathrm{B}\right|$ represents the number of pixels of the intersection between sets A and B, and $\left|\mathrm{A}\right|+\left|\mathrm{B}\right|$ represents the total pixel number of sets A and B, respectively.

The results revealed a strong pairwise overlap, with DSC scores ranging from 0.807 to 0.981, as shown in

Table 18. Pairwise scores obtained for maps’ spatial overlap.

Map Pair	DSC
AHP VS FAHP	0.981
AHP VS FR	0.814
FAHP VS FR	0.807

.

The highest agreement was observed between AHP and FAHP maps (0.98), indicating a very high degree of consistency in identifying the most flood-prone areas, while the lowest was between the FAHP and FR maps (0.807). These findings indicate that the maps largely agree on the locations of critical flood-prone areas, suggesting strong alignment in identifying key areas vulnerable to flooding. All three methods demonstrate comparable effectiveness in representing flood hazards, and their combination as a set of methodologies for addressing flood hazard assessment problems can enhance the reliability of the results. The study concludes that these approaches successfully map flood hazard and can be applied to other regions with similar characteristics.

In conclusion, the flood hazard maps produced will aid authorities and planners in pinpointing high-hazard areas within the Chalkidiki regional unit, enabling them to take appropriate mitigation actions to safeguard lives, infrastructure, and property and steer development away from these hazard zones.

4. Discussion

This analysis evaluates and compares the outcomes of three methodological frameworks applied for flood hazard assessment. The results indicate the presence of numerous high-hazard zones within the study area that are prone to flooding. In particular, specific locations are currently experiencing flood events and are likely to remain at risk in the absence of appropriate mitigation measures. Across all three approaches, high and very high flood hazard areas are predominantly identified in low-lying urban and coastal regions.

All three methods exhibit only minor variations in their results, reinforcing the reliability of the findings. Notably, several historical flood events have occurred in areas that, according to the generated maps, demonstrate moderate to very high levels of flood susceptibility. Specifically, the regions identified as hazardous and vulnerable by the applied methodologies have been subjected to flooding in the past, in some cases on multiple occasions.

More precisely:

• 57% of the historical flood events occurred in areas designated as high or very high hazard by the AHP model;
• 52% of all recorded flood events took place in regions classified as high or very high hazard by the FAHP model;
• 72% of historical floods within the study area are located in zones identified as high and very high hazard by the FR model.

As a spatial metric, the DSC was implemented to quantify the spatial overlap between the generated maps, yielding results indicative of an exceptionally high degree of concordance with values ranging from 0.8 to 0.98. Such values demonstrate strong reliability of the findings and substantiate the robustness of the models applied. The flood hazard maps also revealed that the most vulnerable areas in the study area are those located near urban areas, at coastal locations, and near water bodies. The coastal part of the Chalkidiki regional unit, along with its western part that borders the Thessaloniki regional unit, is among the areas that exhibit greater hazard compared to the rest of the study area. This is attributed to the fact that the area is predominantly residential and urbanized, highlighting the significant impact of the absence of forested land.

The hazard distribution within the study area for all three approaches is presented in Figure 6, Figure 8 and Figure 10, and an examination of these reveals that

• According to the AHP model, 35.5% of the study area is classified as very high and high flood hazard, 36.39% as very low and low hazard, while 28.11% of the study area falls under moderate hazard.
• Based on the FAHP model, very high and high flood hazard zones cover 34.2% of the study area, very low and low hazard zones account for 37.68%, and 28.12% of the area is categorized as moderate hazard.
• Based upon the FR model, 34% of the study area is designated as very high and high hazard, 38.24% as low and very low hazard, and 27.76% is classified as moderate hazard.

The percentage distributions of flood hazard zones are similar, and it is apparent that the factors selected for the flood hazard assessment are representative and have the potential to assess the flood hazard degree of an area. Regarding the parameters’ ranking, the main differences are observed in the ranking of the slope, the rainfall index, and the distance from the drainage network. Slope is estimated by the FR model as being of greater importance and was placed third; the rainfall index, according to the FR model, belongs to a lower ranking than in the other two methodologies, and the distance from the drainage network was placed last in the ranking by the FR model, while it had been prioritized when applying the AHP and FAHP approaches.

This study showed that AHP and FAHP present similar hazard rates in the study area; however, according to the validation, AHP slightly outperforms FAHP. This aligns with previous studies that applied similar statistical models. Similar results have also been observed in [72], who compared AHP and FAHP methods for flood vulnerability mapping and concluded that AHP performed slightly better than FAHP. The fact that AHP and FAHP show similar results has also been pointed out by [19], who compared the two methods. Regarding AHP and FR models, our results also confirm [25,61], who evaluated the same models. They determined that the FR model performed better than the AHP and that both models presented similar accuracy in flood hazard mapping. Finally, [84] examined the FAHP and the FR methods and concluded that both methods are efficient when it comes to flood hazard assessment and that the FR model performed better than the FAHP, as in our study.

It is essential to point out that all methods present certain limitations. While AHP is easy and relatively reliable, it introduces uncertainties due to its reliance on subjective opinions when prioritizing parameters. As for FAHP, despite the added complexity, it may lead to similar results to the traditional AHP in some cases when it follows the AHP ranking, and the FR model introduces some degree of uncertainty due to its reliance exclusively on inventory data, meaning that in areas where historical data is lacking, this approach poses challenges, and its application is limited. The precision of flood records is crucial for assessing the FR model. Another important limitation arises from the limited availability of observed flood inventory data. The lack of observed information significantly constrained the thorough validation and critical evaluation of the proposed methods.

Therefore, future research could adopt a bigger input data set, such as a more updated flood inventory map, satellite, or higher-resolution data, to improve accuracy and precision in urban and rural areas. It could also integrate advanced machine learning techniques to improve flood prediction models by incorporating more complex data patterns and enhancing forecasting accuracy.

5. Conclusions

Numerous studies in hydrology and environmental science have shown that climate change, unsustainable water resource use, and various natural and human-induced factors have already contributed to a rise in extreme weather events, including increased flooding. Unfortunately, this increase is expected to intensify in the years to come. Thus, protecting human lives, infrastructures, crops, and the environment is imperative. Predicting all areas prone to flooding is a great asset and can allow all local and state authorities to develop a flood mitigation strategy.

This study employed the AHP, FAHP, and Frequency Ratio GIS-based methods to delineate potential flood-prone zones by integrating eight flood-related parameters. The results demonstrate that all three methodologies effectively identified areas of high flood hazard, with notable agreement among the produced flood hazard maps.

Specifically, the AHP model delineated high and very high hazard zones that have historically experienced over 55% of recorded flood events, while the FAHP model identified susceptible areas that encompass more than 50% of historical floods. The FR model exhibited the strongest alignment with historical data, accurately identifying zones where over 75% of past flood events occurred.

The findings highlight the applicability of all three methodologies for flood hazard assessment, providing valuable tools for regional decision-makers and water resource managers. Notably, AHP and FAHP can be utilized even in regions lacking comprehensive flood records, whereas the FR model demonstrates high predictive capacity where historical data are available. The validation of the models revealed that the outcomes provided satisfactory precision and effectively portrayed flood hazard areas.

It is important to note that the results of all three methodologies primarily converge. This study’s results point out the capability of the methodologies implemented to highlight an area’s flood vulnerability and can be an effective tool for identifying flood-prone areas. The adopted methodological framework demonstrates that all three models effectively delineate areas potentially vulnerable to flooding. Given that the study area is particularly sensitive to floods, accurately identifying such high-hazard zones is of critical importance.

The results can serve as a foundation for water resource specialists, regional decision makers, and local governments to develop adaptation and mitigation strategies to reduce future flood-related losses. Flood hazard maps can become a particularly valuable tool for authorities and policymakers to develop strategies to mitigate all negative consequences by following the principles of sustainable development, with the ultimate goal of protecting human life and the environment. Flood-vulnerable areas can be treated with both soft and hard measures. The soft ones should focus on enhancing public education to ensure that individuals possess adequate knowledge of self-protection and appropriate response protocols during flooding events. The hard ones should aim to safeguard flood-prone areas. This can be achieved with both hydraulic flood-control infrastructure, like levees and dams, and erosion-control measures such as revetments and riparian buffers.