A New Framework for Comprehensive Flood Risk Assessment Under Non-Stationary Conditions Using GIS-Based MCDM Modeling

Abstract

Flood risk has been increasing due to the effects of climate change, frequent rainfall, and urbanization. Therefore, flood risk assessments in urban areas are important issues for the mitigation of flood disaster and sustainable development. Although there has been an increase in studies on flood risk, there remains a scarcity of research examining the effects of rainfall at different return periods on flood risk under non-stationary conditions in Geographic Information System (GIS) - and multi-criteria decision-making model (MCDM)-based flood risk assessments. To address this gap, this study integrated MCDM-based flood hazard mapping techniques with rainfall quantiles calculated for different return periods under non-stationary conditions to identify and prioritize flood risk areas in Izmir, Türkiye. Firstly, to analyze the current flood risk, the Analytical Hierarchy Process (AHP) was integrated into the GIS and the VIseKriterijumsa Optimizacija I Kompromisno Resenje (VIKOR) approach was used to determine the flood risk priority of 165 points. The results showed that Buca, Menderes, Bornova, Kemalpaşa, Çeşme, Torbalı, Menemen, Seferihisar, and Çiğli were identified as high-flood-risk areas. The VIKOR results indicate that the highest-flood-risk points are R91 (Çeşme), R153 (Buca), and R93 (Çeşme). For a thorough flood risk assessment, the rainfall estimates obtained with the Generalized Additive Models for Location, Scale, and Shape (GAMLSS) at 10-, 20-, 50-, and 100-year return levels under non-stationary conditions were re-weighted with AHP and were incorporated into the hazard criteria, and flood risk analyses were performed for four scenarios. The results showed that as return periods increase, high-risk areas expand, while low-risk areas shrink. Specifically, the proportion of very-low-risk areas declined from 15.12% for the 10-year return period to 13.92% for the 100-year return period, whereas the proportion of very-high-risk areas increased from 6.73% to 7.53% over the same return period levels. VIKOR results, unlike the VIKOR findings for the current case, revealed that points R55, R56, and R54 in Kemalpaşa had the highest flood risk in four scenarios.

1. Introduction

Natural disasters have become one of the most significant threats facing humanity [1]. Among these disasters, flooding is one of the most destructive, widespread, familiar, and regular events [2,3,4]. Human exposure to catastrophic floods increased from 20% to 24% between 2000 and 2021, and projections of current climate change indicate that this rate will increase [5]. Urban floods have increased significantly in recent years due to intense urbanization and climate change [6,7]. Heavy rainfall caused by climate change [8], integrated with changes in hydrological processes such as infiltration and evapotranspiration due to the increase in impermeable surfaces in urban areas, accelerate the formation of runoff and expose cities to the risk of severe flooding [9]. Hence, flood risk assessments in dense urban areas are of utmost importance for the development of effective flood mitigation strategies and the protection of human settlements.

Flood risk is determined by combining flood hazard and vulnerability [10,11]. Flood hazard is defined as the geographic and frequency distribution of the intensity analysis of natural disaster events in any region [12]. Vulnerability can be expressed as sensitivity and fragility to an expected hazard and is also a dynamic concept that evolves over time [13]. Flood risk assessments are critical for assessing, preventing, and responding rapidly to floods in the sustainable risk management of urban areas. In many countries, there are studies using physically based and empirical approaches or methodologies for various flood hazard, vulnerability, and risk prediction [14]. Physically based techniques utilize computer-based hydraulic models, which are either manually or automatically calibrated to simulate synthetic flood events and produce flood hazard maps [15]. One of the major challenges with the developed model is to validate it across different study areas, increasing its reliability, and effectively calibrating it. Additionally, it is crucial to conduct a comprehensive sensitivity analysis of the parameters to ensure model continuity [16]. Furthermore, with limited data, applying these models becomes challenging, especially in urban areas where detailed inputs are crucial [17]. Flood risk assessments using empirical methods include various statistical and data-driven strategies for black box approaches, artificial intelligence models, multi-criteria decision-making (MCDM) frameworks, and machine learning techniques [18,19,20]. A detailed flood risk assessment for a region is quite complex because many parameters and variables must be included [21]. MCDM is successful in tackling these complex issues due to its ability to handle different factors that have conflicting and competing relationships [22]. Geographic Information Systems (GISs) and various MCDM methods, such as the Analytic Hierarchy Process (AHP) method, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and VIseKriterijumsa Optimizacija I Kompromisno Resenje (VIKOR), have been frequently used by researchers for flood risk analyses [23,24,25,26,27,28,29,30]. For instance, ref. [31] conducted a study considering ten criteria for the assessment of flood risks in Port Louis, Mauritius. While the AHP method was used in weighting the criteria, GIS was preferred in creating spatial analysis maps of the criteria and deriving the risk map. Flood trends were evaluated in separate analysis maps as physical, social, and economic. Ref. [32] conducted a flood risk assessment in Barguna, Bangladesh, using eight hazard and eleven vulnerability criteria. Criteria prioritization was conducted with the AHP method and spatial analysis maps of criteria were created with GISs. According to the results obtained in the GIS environment, 37.65% of the study area was found to have high flood risk levels. Ref. [33] performed a flood risk assessment along the Tapi River using six hazard and three vulnerability criteria. The AHP method was used to determine the superiority of the criteria in the risk assessment. The spatial analysis maps of the criteria and the derivation of the final risk map were created with the GIS. It was found that approximately 3.331 km² of the study area had a high risk level. In the study conducted by [25], a flood risk assessment was carried out using seven hazard and seven vulnerability criteria. Separate risk maps were created in the GIS environment with the criterion weight values obtained from AHP and TOPSIS. According to the results, 5.67% (0.55 km²) of the AHP map and 2.31% (0.34 km²) of the TOPSIS map were found to be at very high risk. A flood risk assessment study by [34] was carried out in the Bongoigoon district of India. Topographic, hydrological, geo-environmental, population, infrastructural, ancillary main criteria, and sub-criteria were weighted with AHP. According to the final risk map obtained in the GIS environment, 28% of the district is under flood risk. Ref. [35] conducted a study on social vulnerability to flood risks. Three main criteria (exposure, sensitivity, and adoptability) and eighteen sub-criteria were used in the study. A statistical performance comparison according to the criteria was conducted by considering 10 districts in Nanjing.

Recent research suggests that extreme rainfall events will increase in frequency and intensity for each degree increase in the planet’s temperature [36]. Flood events caused by extreme rainfall are among the most destructive natural disasters globally, capable of causing significant economic losses and negative impacts on human lives [37,38]. Thus, investigating the effects of rainfall events at different return levels on hazard mapping has become an important task in sustainable flood risk assessments and in the prevention of potential damage to urban areas. Studies investigating the effects of extreme rainfall on flood risk for different return levels with MCDM-based approaches are quite limited. For example, Ref. [39] constructed a regional flood risk assessment model based on a combination of subjective and objective multi-weight methods. Flood risk assessments were carried out for 10-, 50-, 100-, and 200-year return periods by fitting different precipitation indices to the P-III distribution. They emphasized that with the increase in return periods, the overall spatial extent of medium-to-very-high-risk areas progressively decreases, while the distribution of very-high-risk areas gradually shifts towards the south. Ref. [40] carried out a flood hazard assessment using 12 hydro-geomorphological factors with AHP and an Analytical Network Process (ANP)-based GIS method. They calculated rainfall at 20-, 50-, and 100-year return levels using four distribution functions (i.e., two-parameter lognormal, Pearson type III, log Pearson type III, and Gumbel) for flood hazard. According to its results, the hazard map for the 100-year return period shows that a total of 0.71 million of the population is at “very high” risk of flood exposure. Ref. [41] evaluated the flood risk for arid and semi-arid regions based on spatial AHP and GIS integration. In the study, rainfall values were calculated with Log Pearson type III distribution at different return levels for flood risk assessment. The results of the study showed that as the return period level increased, the medium-, high-, and very-high-risk areas increased, and the low- and very-low-risk areas decreased. It is necessary to compare different probability distribution functions and choose the more appropriate one for the precipitation data [42,43].

Moreover, in existing studies that conduct MCDM-based risk assessments for different return levels, precipitation data are considered to be stationary. However, due to climate change and human activities, statistics of precipitation series exhibit complex and non-stationary changes [44]. Thus, the assumption that the mean and variance of the distributions in the frequency analysis of hydrological variables will remain constant over time is questionable [45]. Numerous studies have reported that hydrological time series are no longer stationary [46,47,48,49]. Hence, different techniques and concepts for non-stationary frequency analyses of time series have been proposed in the literature. To improve the performance of non-stationary models for any variable, researchers have employed physically significant covariates, including atmospheric oscillation indices and time series from hydrological and meteorological data [50]. Among these, large-scale oscillations are one of the most critical explanatory variables for the non-stationary modeling of precipitation series [51]. To incorporate external covariates, the Generalized Additive Models for Location, Scale, and Shape (GAMLSS), developed by [43], has been successfully applied in hydrological studies in different parts of the world [44,45,46,47].

Therefore, this study constructs a decision-making approach to develop a regional flood risk assessment model by considering the effects of rainfall at different return periods on flood risk under non-stationary conditions. The present study aims to (1) obtain the weight values for the hazard and vulnerability criteria by the AHP method, taking into account a comprehensive literature review and expert opinions; (2) perform the hazard index importance ranking of potential flood areas obtained from the flood risk map with the VIKOR method; (3) determine the most appropriate probability distribution functions, including gamma (GA), logistic (LOGIS), two-parameter lognormal (LOGNO), and Weibull (WEI), for rainfall data by including atmospheric oscillation indices such as the West Mediterranean Oscillation (WeMO), the Southern Oscillation (SO), and the North Atlantic Oscillation (NAO) as explanatory variables with the GAMLSS technique and then to obtain rainfall at 10-, 20-, 50-, and 100-year return levels under non-stationary conditions; (4) re-weight the hazard criteria for four different rainfall scenarios by including the rainfall criteria obtained at different return levels, ultimately producing four separate hazard maps; (5) to generate four flood risk maps by conducting a weighted overlay analysis of the current vulnerability map with four different hazard maps and to compare the results with the existing flood risk map; (6) evaluate the importance order of the flood hazard index for four flood risk maps with the VIKOR method and to compare the results with those of the existing VIKOR method; and (7) discuss the advantages of the new integrated approach. To the best of the authors’ knowledge, there is no study that considers the effects of rainfall at different return periods on flood risk under non-stationary conditions in GIS- and MCDM-based flood risk assessments. Thus, the proposed new perspective can increase the capacity to assess the disaster risk for various study areas and provide comprehensive information to decision-makers regarding sustainable flood risk management.

2. Materials

This study aims to conduct a flood risk assessment in Izmir province by considering flood hazard and vulnerability criteria. Additionally, it introduces a novel approach to comprehensive risk assessment by including rainfall at different return levels in the flood hazard maps. The flow chart of the study is shown in Figure 1.

In order to carry out the flood risk analysis, the AHP method was preferred in weighting the hazard and vulnerability criteria by utilizing the opinions of the decision-making team. The spatial analysis of the criteria was carried out with the ArcGIS software (version 10.8), and spatial layers were created for each criterion. Hazard, vulnerability, and flood risk maps were created by performing a weighted overlay analysis with the criteria weights obtained from AHP. The areas with the highest risk were determined with the VIKOR method. Then, rainfall at various return levels (10, 20, 50, and 100 years) was estimated using the GAMLSS technique, including physical explanatory variables as covariate variables under non-stationary conditions. AHP was used again for weighting, and overlap analysis was performed in the GIS environment to generate four different risk maps. VIKOR was applied to assess alternatives in the risk maps obtained from four different scenarios for comprehensive flood risk management.

2.1. Study Area

İzmir, situated in the Aegean Region of Turkey, is the third-most-populous city in the country, covering an area of 12.012 km². The region experiences the Mediterranean climate, which consists of hot, dry summers and mild, rainy winters. The Mediterranean climate is more dominant in the coastal areas; however, due to the topographic structure of the region, the Mediterranean climate is also experienced in the interior areas. Based on data from 1938 to 2023, İzmir experiences an average of 77.8 rainy days per year, with an average monthly total rainfall of 712.1 mm and an average annual temperature of 18 °C [52]. İzmir consists of 30 districts and its total population is 3.701.733 as of 2023 [53]. The developing economy and population growth have led to rapid urbanization, causing land use and land cover changes in the region, and therefore it is one of the regions of Turkey that has been subject to frequent and severe floods throughout its history. Almost every year, there have been major heavy rains and floods. In November 1995, heavy rains and torrential downpours occurred in Izmir, causing serious flooding in cities and agricultural lands. As a result of this disaster, 65 people lost their lives. On 2 February 2021, due to heavy rainfall, floods and inundations occurred in many parts of Izmir province, and urban life was seriously affected. As can be seen from the records, Izmir province has been exposed to various flood events. For this reason, it was chosen as the study area. Figure 2 illustrates the study area along with its water sources.

2.2. Defining the Evaluation Criteria

This research considered the flood risk concept under two headings: hazard and vulnerability. The criteria triggering flood hazard and vulnerability are identified by evaluating the literature as well as academic and expert insights. The decision-making team includes two academics specializing in hydrology as well as three experts from the General Directorate of State Hydraulic Works. The scope of the study was expanded by adding new vulnerability criteria used for the first time in the literature. Two main criteria and ten sub-criteria were set for the flood hazard analysis, while three main criteria and nine sub-criteria were chosen for the vulnerability analysis.

Table 1. Detailed descriptions of the criteria, data sources, and references.

Sub-Criteria	Brief Description	Data Source	Literature Source
H1.1. Annual Average Maximum Rainfall	Heavy rainfall in urban areas is likely to cause flooding. In the study, due to the insufficient number of observation stations, ERA5-Land rainfall data were taken from 13 points distributed homogeneously in the study area. The data were acquired daily between 1960 and 2021 and then the annual average maximum rainfall was calculated.	https://cds.climate.copernicus.eu/ (accessed on 5 August 2025)	[14,54,55,56]
H1.2. Flow Accumulation	Flow Accumulation is an important parameter that indicates important flood-prone regions. Higher values denote increased flood risk.	DEM	[25,57]
H1.3. Drainage Density	The drainage density represents the proportion of the total length of river channels to the area of the drainage basin. The risk of flooding is higher in areas with high drainage density.	DEM	[58]
H2.1. LULC	LULC offers comprehensive information on the land use and land cover uses of an area over time due to human impact or natural occurrences, especially in the non-homogeneous land cover of urban areas, infiltration capacity, and runoff vary. This causes the flood risk to vary from region to region.	livingatlas.arcgis.com (accessed on 10 August 2025)	[59,60]
H2.2. Proximity to River	Distance to a river is important in determining an area’s exposure to flooding. Areas farther from a river are less likely to be affected by flood hazards than those closer to it.	OpenStreet Map	[61,62]
H2.3. Elevation	The lowest elevation areas are the areas at high risk of flooding because water flows from higher to lower ground; thus, it is natural for areas at low elevations to become inundated due to flooding.	earthdata.com/DEM (accessed on 8 August 2025)	[55,63]
H2.4. Slope	Another important criterion affecting the risk of flooding is the slope of the land. Flat slopes are more easily inundated than higher slopes.	DEM	[22,55,64,65]
H2.5. Curvature	Curvature refers to the rate of change of a slope in a given direction. Negative values indicate concavity, zero values represent flat surface, and positive values indicate convex curvature. Concave terrains are a hazard for flood risk, while convex terrains are the least hazardous areas.	DEM	[8,66,67]
H2.6. NDVI	Vegetated lands play a protective role against flood events by reducing the acceleration of the flow and functioning as a natural barrier. This vegetation cover is depicted using the normalized difference vegetation index (NDVI), with values between −1 and +1. Negative NDVI values represent an area that is highly susceptible to flooding.	Satellite Image Landsat 8	[68,69]
H2.7. TWI	Topographic Wetness Index (TWI) is an index used to determine the wetness potential of a land. TWI is important in determining flood risk zones. High positive values indicate humidity while low negative values indicate drought.	DEM	[70,71]
V1.1. Public Transportation Station	Public transportation stations can significantly increase the risk of flood vulnerability because they areas where people gather. In this study, all bus, metro, and IZBAN stations of the Izmir province were considered.	https://acikveri.bizizmir.com/ (accessed on 8 July 2025)	[72]
V1.2. Road Networks	The distance of people to the road is an important factor in the flood response and evacuation process. The situation of roads at risk of flooding increases the severity of the flood.	OpenStreet Map	[22,55]
V2.1. Population Density	Population density directly increases the risk of exposure to floods. In densely populated areas, the risk of vulnerability to flooding events is high.	Turkish Statistical Institute	[25,73]
V2.2. Household	Household refers to the number of families at risk of flooding and can have a key role in amplifying the impact of flooding.	Turkish Statistical Institute	[74,75]
V2.3. Education Level	Education can increase people’s awareness of flooding and is considered a vulnerability assessment indicator.	Turkish Statistical Institute	[76]
V2.4. Socio-Economic Development Level	People with higher socio-economic development levels, such as education levels, may be more aware of the effects of flood risk.	sanayi.gov.tr (accessed on 20 July 2025)	Pilot Study
V3.1. Health Centers	Providing easy access to healthcare is essential to protecting the health and well-being of residents in the event of flooding. Therefore, damage caused by flooding may vary depending on the location of healthcare facilities.	https://acikveri.bizizmir.com/ (accessed on 8 July 2025)	[77]
V3.2. Disaster and Emergency Assembly Areas	The spread of assembly areas for use in the event of disasters and emergencies throughout the city can affect the extent of damage caused by events such as floods. The distribution of these areas can change the risk of residents’ exposure to hazards during emergencies.	https://acikveri.bizizmir.com/ (accessed on 8 July 2025)	Pilot Study
V3.3. Emergency Stations	Emergency facilities show the capacity of a city to respond to and cope with hazards. Rapid rescue and assistance are critical during the hazard; therefore, the density of emergency facilities increases resilience to flood events.	https://acikveri.bizizmir.com/ (accessed on 8 July 2025)	[78]

provides concise statements of the criteria, reasons for their selection, data formats, sources of the data, and references from the literature.

2.3. Atmospheric Oscillations

There are many studies indicating that large-scale atmospheric systems such as the West Mediterranean Oscillation (WeMO), the Southern Oscillation (SO), and the North Atlantic Oscillation (NAO) have impacts on hydrological and meteorological variables in Turkey [79,80,81]. Hence, annual and seasonal WeMO, SO, and NAO indices were employed as covariates to determine the temporal variability of annual average maximum rainfall series. The values of SOI, NAOI, and WeMO were taken from the University of East Anglia Climate Research Unit [82]. Seasonal time series were calculated for each oscillation index, including winter, spring, summer, and autumn, along with annual datasets.

Table 2. Brief description of the climatic covariates.

Covariates	Code	Covariates	Code
Annual NAO	x1	Summer SO	x9
Winter NAO	x2	Autumn SO	x10
Spring NAO	x3	Annual WeMO	x11
Summer NAO	x4	Winter WeMO	x12
Autumn NAO	x5	Spring WeMO	x13
Annual SO	x6	Summer WeMO	x14
Winter SO	x7	Autumn WeMO	x15
Spring SO	x8

provides a summary of the climatic covariates used in the study.

3. Methodology

In flood risk analyses of urban areas, MCDM (weighting only) and GIS techniques are frequently combined. As a flood risk analysis involves a multi-layered and multi-criteria approach, the AHP and VIKOR methods were used for weighting and ranking. Considering the non-stationary conditions, rainfall data for different return periods were produced with the GAMLSS technique. Visual inspection of criteria layers, spatial analysis of the criteria, and risk analysis in different return scenarios were conducted in a GIS platform. Details about the methods employed were arranged according to the following categories.

3.1. Analytical Hierarchy Process (AHP)

The AHP method, presented as a semi-quantitative technique, is an effective method used by researchers in areas such as risk analysis, vulnerability analysis, site selection, geographical evaluations of regional areas. It provides the user with the criterion relationships between thematic layers and is used in solving multi-criteria problems [55,83,84,85,86]. AHP contributes to obtaining more effective results in the solution process by integrating the decision maker’s judgment into the hierarchical structure in a scientific and systematic way in complex decision-making problems [87]. AHP is useful for including many parameters that are not compared with each other in terms of units in the decision process and decision-solving processes [88]. Within the AHP framework, pairwise comparison matrices are basically established to compare the criteria. The method includes many process steps and applications [87,89].

Step 1. Defining the problem related to the decision-making process.

Step 2. Selecting the criteria impacting decision-making processes through a literature review and with the suggestions of the established decision-making team.

Step 3. Creation of AHP hierarchical structure and establishment of pairwise comparison matrices (each decision-making team member creates a separate pairwise comparison matrix).

In pairwise comparison matrices, each criterion is compared with all other criteria in order. In this way, quantitative and qualitative features can be compared in the same matrix and included in the decision-making process. The number of comparisons of the criteria can be calculated with the help of “n(n − 1)/2”, and the Saaty [1,2,3,4,5,6,7,8,9] scale is used while making comparisons [90].

Step 4. To maintain consistency in the matrix, the vector normalization presented in Equation 1, frequently used in the AHP method, is performed.

$${r\prime }_{ij}={\displaystyle \frac{r_{ij}}{\sum _{i=1}^n{r}_{ij}}}$$

(1)

Step 5. Priority vector values reflecting the weight values are obtained with the formulation in Equation (2).

$$w_i=\left({\displaystyle \frac{1}{n}}\right){\sum }_{j=1}^n{r\prime }_{ij} i,j,=1, 2, 3, \dots , n$$

(2)

Step 6. In order to test the accuracy and usability of comparison matrices, a consistency analysis is performed using the formulations presented in Equations (3) and (4).

$$CR={\displaystyle \frac{CI}{RI}}$$

(3)

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

(4)

In order to determine that the comparison matrices are usable, the consistency ratio (CR) must yield a result less than 0.1. If this is not achieved, the relevant comparison matrix is rebuilt and the CR value is recalculated.

3.2. VIKOR

The VIKOR method is an approach designed for complex systems for the MCDM processes. It is a multi-qualified method developed to include criteria with different or immeasurable units in decision-making problem solutions [91]. The compromise ranking list is created by employing the weights calculated through AHP. The ideal proximity value is used to rank the VIKOR method results [92,93]. The VIKOR method involves multiple procedural steps [91].

Step 1. Producing the decision matrix.

Step 2. The best ($f_i^{*}$) and worst ($f_i^{-}$) efficiency metrics are calculated for each criterion used in decision-making. When determining the best ($f_i^{*}$) and worst ($f_i^{-}$), whether the criteria are benefit- or cost-oriented is considered.

$$f_i^{*}=\underset{i}{\max } x_{ij}, f_i^{-}=\underset{i}{\min } x_{ij}; Benefit criteria$$

(5)

$$f_i^{-}=\underset{i}{\min } x_{ij}, f_i^{*}=\underset{i}{\max } x_{ij}; Cost criteria$$

(6)

Step 3. The ($S_i$) and ($R_i$) values are acquired using Equations (7) and (8). ($S_i$) indicates the maximum group benefit and the minimum of the $S$ values of the various options. ($R_i$) represents the worst performance value of the relevant alternative or candidate value [94].

$$S_i=\sum _{j=1}^n{\displaystyle \frac{w_j(f_i^{*}-x_{ij})}{(f_i^{*}-f_i^{-})}}$$

(7)

$$R_i=\underset{j}{\max }\left[{\displaystyle \frac{w_j(f_i^{*}-x_{ij})}{(f_i^{*}-f_i^{-})}}\right]$$

(8)

Step 4. The $Q_i$ metric used to order the alternatives is derived via Equation (9).

$$Q_i=v\ast {\displaystyle \frac{S_i-S^{*}}{S^{-}-S^{*}}}+\left(1+v\right)\ast {\displaystyle \frac{R_i-R^{*}}{R^{-}-R^{*}}}$$

(9)

where $Q_i$ is the priority rule, $S^{-}=\underset{i}{\max } S_i$, $S^{*}=\underset{i}{\min } S_i$, $R^{-}=\underset{i}{\max } R_i$, $R^{*}=\underset{i}{\min } R_i$, and $v=0.5$.

Step 5. To comprehensively rank the options, $S_i$, $R_i$, and $Q_i$ values are sorted from smallest to largest.

Two criteria must be satisfied to assess efficiency of $Q_i$, as follows:

$$C1=Q\left(A_2\right)-Q\left(A_1\right)\ge {\displaystyle \frac{1}{N-1}}$$

(10)

$A_1$ and $A_2$ represent the first and second values of the $Q$, respectively, and $N$ indicates the number of criteria.

$$C2=\left(A_m\right)-Q\left(A_1\right)<{\displaystyle \frac{1}{N-1}}$$

(11)

3.3. GAMLSS Model

The Generalized Additive Models for Location, Scale, and Shape (GAMLSS) proposed by [95] is a powerful and popular framework for regression models with time-varying distribution parameters. GAMLSS allows for modeling the parameters of distributions as a function of explanatory variables. These explanatory variables can be, for example, time- or physically based covariates [96]. Recently, the GAMLSS framework has been effectively applied in non-stationary frequency analyses of hydrological and meteorological series [81,97,98,99]. In this study, four widely used distribution functions are chosen to model the annual average maximum rainfall series (

Table 3. A summary of the probability distribution functions utilized in this study.

Code	Dist. Type	Probability Density Function (PDF)
WEI	Weibull	$f_y\left(\left.y\right|\mu ,\sigma \right)={\displaystyle \frac{\sigma y^{\sigma -1}}{{\mu }^{\sigma }}} exp\left\{-{\left({\displaystyle \frac{y}{\mu }}\right)}^{\sigma }\right\}$
		$y>0, \mu >0, \sigma >0$
LOGNO	LogNormal	$f_y\left(\left.y\right|\mu ,\sigma \right)={\displaystyle \frac{1}{\sqrt{2\pi {\sigma }^2}}}{\displaystyle \frac{1}{y}}exp\left\{-{\displaystyle \frac{{\left[\log \left(y\right)-\mu \right]}^2}{2{\sigma }^2}}\right\}$
		$y>0, \mu >0, \sigma >0$
GA	Gamma	$f_y\left(\left.y\right|\mu ,\sigma \right)={\displaystyle \frac{1}{{\left({\sigma }^2\mu \right)}^{1/{\sigma }^2}}}{\displaystyle \frac{y^{\frac{1}{{\sigma }^2}-1}{e}^{-y/\left({\sigma }^2\mu \right)}}{г\left(1/{\sigma }^2\right)}}$
		$y>0, \mu >0, \sigma >0$
LOGIS	Logistic	$f_y\left(\left.y\right|\mu ,\sigma \right)={\displaystyle \frac{1}{\sigma }}exp\left\{{\displaystyle \frac{x-\mu }{\sigma }}\right\}+\left\{1+exp{\left\{{\displaystyle \frac{x-\mu }{\sigma }}\right\}}^{-2}\right\}$
		$y>0, \mu >0, \sigma >0$

): gamma (GA), logistic (LOGIS), two-parameter lognormal (LOGNO), and Weibull (WEI). In addition to the traditional time-varying non-stationary models, physically based non-stationary models including mu, sigma, or both mu and sigma have been developed within the scope of the study.

In the present study, the approach of [51] was adopted in developing the non-stationary models. Four potential models were evaluated for the analysis of the rainfall series frequency: (Model 1) is a model in which parameters (mu and sigma) remain constant over time, (Model 2) is a non-stationary model where the mu parameter (μ) varies as a function of any of the oscillation indices, (Model 3) is a non-stationary model where the mu parameter (μ) and the sigma parameter(σ) vary as functions of an oscillation index, and (Model 4) is a non-stationary model where the mu parameter (μ) varies as a function of oscillation index combinations.

3.4. Model Selection and Assessment

The optimal distribution was determined by using the Akaike information criterion value [100]. The distribution with the lowest AIC value was selected as the best-fitting model. The AIC can be computed simply, as

$$AIC=-2L_{max}+2p$$

(12)

Here, $L_{max}$ indicates the maximized value of the log-likelihood function for the fitted model and $p$ represents the total number of model parameters. To further investigate the efficiency of the chosen model, the Filliben coefficient [101], which quantitatively expresses the agreement between the observed and theoretical quantiles, was examined, and the independence and normality of the residuals were visually tested using a worm plot [102]. As stated by [103], a Filliben coefficient exceeding 0.97 in the model indicates that the model is suitable. An important consideration in selecting the most successful models is that adding more explanatory variables to the model may generate a lower AIC score. However, this enhancement may lack statistical significance. Therefore, the likelihood ratio (LR) test [104] is used to determine if the addition of a new explanatory variable results in a significant improvement. The LR test statistic is as follows:

$$LR=2(L_1-L_0)$$

(13)

Here, $L_1$ and $L_0$ represent the maximized values of the log-likelihood function under models $M_1$ and $M_0$, respectively. The test result was evaluated at a significance level of α = 0.05. If the α value calculated according to the test result was greater than 0.05, the complex model was not selected. All operations were performed on the R platform using the freely available gamlss package [95].

4. Results

4.1. Evaluation of AHP Findings

The criteria weights used in the flood risk analysis were established through the AHP method, based on the opinions of the decision-making team. The pairwise comparison matrices were constructed via the Saaty [1,2,3,4,5,6,7,8,9] scale. For the main and sub-criteria,

Table 4. Hazard criteria and sub-criteria weights.

Hazard
Main Criteria and Sub-Criteria		Criteria Weights	Main Criteria and Sub-Criteria		Criteria Weights
	Annual Average Maximum Rainfall (mm)	0.246	Topographic	Elevation (m)	0.082
Meteorological and Hydrological	39.83–42.79	0.064		0–409.5	0.358
	42.80–45.74	0.12		409.6–843.8	0.271
	45.75–48.70	0.182		843.89–1278.2	0.206
	48.71–51.66	0.264		1278.3–1712.6	0.107
	51.67–54.62	0.37		1712.7–2147	0.058
	Flow Accumulation (pixels)	0.133		LULC	0.194
	0–1.7 × 105	0.059		Water	0.32
	1.7 × 105–7 × 105	0.099		Urban	0.237
	7 × 105–1.6 × 106	0.144		Bareland	0.167
	1.6 × 106–2.9 × 106	0.219		Crops	0.125
	2.9 × 106–4.5 × 106	0.479		Trees	0.101
	Drainage Density (km/km2)	0.02		Rangeland	0.05
	0.001–0.20	0.073		TWI	0.027
	0.21–0.30	0.132		2.23–6.89	0.084
	0.31–0.40	0.159		6.90–11.55	0.148
	0.41–0.80	0.24		11.56–16.22	0.194
	0.81–1.67	0.396		16.23–20.88	0.256
Topographic	Slope (degrees)	0.06		20.89–25.54	0.318
	0–10	0.342		Proximity to River (m)	0.164
	10.1–20	0.262		<500	0.334
	20.1–30	0.21		500–1000	0.265
	30.1–45	0.121		1000–1500	0.189
	45.1–72.77	0.065		1500–2000	0.143
	Curvature	0.041		>2000	0.069
	Concave	0.558		NDVI	0.033
	Flat	0.32		<0	0.353
	Convex	0.122		0.01–0.20	0.268
				0.21–0.40	0.184
				0.41–0.60	0.123
				0.61–0.99	0.072

depicts the flood trigger parameters in different categories. According to the various weighting results generated for the hazard criteria, the factor with the highest weight on flood occurrence in the study area is H1.1. Annual Average Maximum Rainfall, with a weight of 0.246, followed by H2.1. (0.194), H2.2. (0.164), H1.2. (0.133), H2.3. (0.0.82), H2.4. (0.06), H2.5. (0.041), H2.6. (0.033), H2.7. (0.027), and H1.3. (0.02). A consistency analysis was performed to validate these results. The consistency ratio (CR) was below the 0.1 threshold, indicating a high level of consistency, which confirms that the proposed weights are acceptable.

The flood vulnerability factors determined in the study and the calculations for all of them along with their sub-classes are shown in

Table 5. Vulnerability criteria and sub-criteria weights.

Vulnerability
Main Criteria and Sub-Criteria		Criteria Weights	Main Criteria and Sub-Criteria		Criteria Weights
Transportation	Public Transportation Stations	0.076	Urban	Socio-Economic	0.055
	<0.870	0.086		0.29–1.23	0.307
	0.871–3.50	0.117		1.24–2.10	0.248
	3.51–8.660	0.196		2.01–3.0	0.189
	8.661–15.770	0.273		3.01–4.0	0.142
	15.771–24.82	0.328		4.01–6.91	0.114
	Road Networks (m)	0.171	Proximity	Health Centers	0.103
	<250	0.099		0–0.020	0.313
	250–500	0.156		0.021–0.130	0.24
	500–1000	0.184		0.131–0.340	0.209
	1000–1500	0.242		0.341–0.60	0.153
	>1500	0.319		0.61–0.92	0.085
Urban	Population Density	0.204		Disaster and Emergency Assembly Areas	0.141
	12,094–80,000	0.081		0–0170	0.313
	80,000.01–140,000	0.136		0.171–0.50	0.295
	140,000.01–200,000	0.226		0.51–1.15	0.183
	200,000.01–300,000	0.256		1.151–2.12	0.116
	300,000.01–522,738	0.301		2.121–3.38	0.093
	Household	0.088		Emergency Stations	0.125
	2.23–2.55	0.092		0–0.013	0.343
	2.56–2.74	0.181		0.014–0.050	0.25
	2.75–2.87	0.213		0.051–0.13	0.189
	2.88–3.00	0.248		0.131–0.30	0.154
	3.01–3.28	0.266		0.31–0.47	0.064
	Education Level	0.037
	862–12,000	0.335
	12,000.01–24,000	0.253
	24,000.01–40,000	0.192
	40,000.01–60,000	0.146
	60,000.01–122,932	0.074

. In the calculation of vulnerability criteria, V2.1. Population was selected as the most significant factor and weighted at 0.204. This is followed by V1.2. (0.171), V3.2. (0.141), V3.3. (0.125), V3.1. (0.103), V2.2. (0.088), V1.1. (0.076), V2.4. (0.055), and V2.3. (0.037), respectively.

4.2. Evaluation of AHP-Based GIS

In this part of the study, the hazard and vulnerability criteria that trigger flood risk were transferred to the GIS environment. An appropriate interpolation method was selected to create the layer map of each criterion (i.e., Slope, Kernel Density, and IDW spatial analyses) and then reclassification was performed with equal interval and natural break methods, according to the type of data, to determine appropriate interval categories [105,106,107]. The spatial distribution maps of the ten hazard and nine vulnerability indicators used in this study are shown in Figure 3 and Figure 4, respectively.

The sub-criteria weights acquired from AHP were adapted to the criterion layers in the GIS environment. Subsequently, all criterion layers were converted to raster data to create raster maps with 25 m × 25 m pixel spatial resolution. The weighted overlay analysis was implemented for hazard and sensitivity criteria in the GIS environment using the main criterion weights obtained from AHP.

The relative hazard map is obtained by the given formula

$$\begin{array}{ll}Hazard index=& H\mathrm{1.1.}\times 0.246+H\mathrm{1.2.}\times 0.133+H\mathrm{1.3.}\times 0.02+H\mathrm{2.1.}\times 0.194+H\mathrm{2.2.}\times 0.164+H\mathrm{2.3.}\times 0.082\\ & +H\mathrm{2.4.}\times 0.06+H\mathrm{2.5.}\times 0.041+H\mathrm{2.6.}\times 0.033+H\mathrm{2.7.}\times 0.027\end{array}$$

(14)

The relative flood vulnerability map is derived using the following formula:

$$\begin{array}{ll}Vulnerability index=& V\mathrm{1.1.}\times 0.076+V\mathrm{1.2.}\times 0.171+V\mathrm{2.1.}\times 0.204+V\mathrm{2.2.}\times 0.088+V\mathrm{2.3.}\times 0.037\\ & +V\mathrm{2.4.}\times 0.055+V\mathrm{3.1.}\times 0.103+V\mathrm{3.2.}\times 0.141+V\mathrm{3.3.}\times 0.125\end{array}$$

(15)

The ultimately derived expressions for $Hazard index$ and $Vulnerability index$ are written in Equations (14) and (15), and the associated spatial maps (i.e., flood hazard map and flood vulnerability map) are depicted in Figure 5 and Figure 6, respectively. The natural break approach was used to identify risk areas.

Flood hazard and vulnerability zones were delineated after reclassifying them into five zones: ‘very low,’ ‘low,’ ‘moderate,’ ‘high,’ and ‘very high’. Flood hazard zones cover the following areas: ‘very low’ 18.31%; ‘low’ 32.66%; ‘moderate’24.78%; ‘high’ 18.10%; and ‘very high’ 6.15% (Figure 5). From Figure 5, the flood hazard areas categorized as “very high” and “high” are concentrated in the central parts of the city and in the Çeşme district located in the west of the city. For vulnerability, the areas with ‘very low,’ ‘low,’ ‘moderate,’ ‘high,’ and ‘very high’ risk of cover, respectively, constituted 8.41, 23.30, 31.34, 22.49, and 14.46% of the İzmir city (Figure 6). It was found that many districts in the study area, including Menemen, Kemalpaşa, Buca, and Menderes, were located in these vulnerable areas. A flood risk map was created by combining the vulnerability and hazard maps [108]. Therefore, in order to perform a comprehensive flood risk assessment within the scope of the study, the Weighted overlay analysis was repeated by assigning equal weights to the vulnerability and hazard criteria, resulting in the generation of the flood risk map (Figure 7).

As shown in Figure 7, the ratios of the ‘very low,’ ‘low,’ ‘moderate,’ ‘high,’ and ‘very high’ flood risk levels are 16.57, 30.57, 27.68, 18.82, and 6.36%, respectively. Buca, Menderes, Bornova, Kemalpaşa, Çeşme, Torbalı, Menemen, Seferihisar, and Çiğli are districts identified to be at high and very high flood risk. To compare the risk levels, random zones were chosen from the high-risk areas. The performance values for these regions were used to evaluate and rank the risk zones through the VIKOR method.

4.3. Risk Assessment with the VIKOR Method

This study evaluated 165 points in Izmir province to evaluate and prioritize flood risk. Hence, the VIKOR approach was applied for different selected points. Firstly, in the VIKOR method’s application phase, the criteria, along with their benefit and cost aspects, were identified. To rank the flood risk, the values of $S_i$, $R_i$, and $Q_i$ were listed from smallest to largest. Conditions $C1$ and $C2$ were included among the requirements that needed to be met. The results obtained from the VIKOR method are presented in

Table 6. Top 20 points with high flood risk.

Rank	1	2	3	4	5	6	7	8	9	10
Point	R91	R153	R93	R90	R92	R110	R32	R31	R97	R28
$Q_i$	0.884	0.768	0.754	0.752	0.722	0.715	0.706	0.703	0.691	0.657
Rank	11	12	13	14	15	16	17	18	19	20
Point	R163	R22	R115	R117	R151	R2	R100	R1	R114	R33
$Q_i$	0.652	0.627	0.619	0.603	0.599	0.589	0.576	0.576	0.564	0.556

. The ranked order of flood risk across regions in Table 6 shows that The R91 point in the Çeşme district has the highest flood risk score of 0.884, followed by the R153 point in the Buca district, R93, R90, and R92 in Çeşme with the scores of 0.768, 0.754, 0.752, and 0.722, respectively.

4.4. Modeling with GAMLSS and Comprehensive Risk Assessment Under Non-Stationary Conditions

Models were created using annual maximum rainfall data from 13 stations, with both stationary and non-stationary models using the 15 potential covariate variables specified in Table 2. In the creation of the models, four two-parameter distributions were considered, namely, gamma (GA), logistic (LOGIS), lognormal (LOGNO), and Weibull (WEI). As mentioned in Section 4.3, models were created using the GAMLSS method in different scenarios and the most appropriate distributions were selected according to the AIC criteria.

Table 7. Summary of the fitted models with AIC values, Filliben coefficients, and LR test p value.

Station No	Model	AIC Values	Filliben Coefficients	LR Test p Value
1	LOGNO(μ,σ)	496.79	0.99
	LOGNO(μ ∼x1,σ)	491.8	0.99	0.008
	LOGNO(μ∼x1 + x14,σ)	487.99	0.99	0.015
2	LOGNO(μ,σ)	512.9	0.99
	LOGNO(μ∼x2,σ)	511.86	0.99	0.01
	LOGNO(μ∼x2 + x12,σ)	507.88	0.99	0.014
3	GA(μ,σ)	461.7	0.99
	GA(μ∼x1,σ)	455.09	0.99	0.003
4	LOGNO(μ,σ)	474.87	0.98
	LOGNO(μ∼x1,σ)	468.71	0.99	0.004
5	LOGNO(μ,σ)	484.35	0.99
	LOGNO(μ∼x14,σ)	483.56	0.98	0.094
6	LOGNO(μ,σ)	459.25	0.97
	LOGNO(μ∼x5,σ)	456.23	0.97	0.024
7	GA(μ,σ)	485.64	0.99
	GA(μ∼x10,σ)	482.53	0.99	0.023
8	LOGNO(μ,σ)	476.27	0.99
	LOGNO(μ∼x10,σ)	471.4	0.99	0.008
9	LOGNO(μ,σ)	484.24	0.99
	LOGNO(μ∼x1,σ)	481.3	0.99	0.02
	LOGNO(μ∼x1 + x10,σ)	478.8	0.99	0.03
10	LOGNO(μ,σ)	470.74	0.97
	LOGNO(μ∼x1,σ)	466.7	0.98	0.014
11	GA(μ,σ)	472.07	0.99
	GA(μ∼x10,σ)	469.3	0.99	0.03
12	LOGNO(μ,σ)	472.51	0.99
	LOGNO(μ∼x10,σ)	470.6	0.98	0.04
	LOGNO(μ∼x10,σ∼x10)	468.34	0.99	0.03
13	LOGNO(μ,σ)	445.37	0.98
	LOGNO(μ∼x5,σ)	442.78	0.98	0.03

The bold LR test p value indicates that the complex model was not selected at the 5% significance level.

summarizes the selected distributions, mathematical models of the distribution parameters, AIC values, Filliben coefficients, and LR test p values. In addition, a comparison of four different probability distributions for stationary models at each station is presented in Supplementary Table S1. As can be seen from Table 7, LOGNO and GA distributions were selected as the best distributions at 10 and 3 stations, respectively. WEI and LOGIS distributions were not selected as the best-performing distributions at any station. According to the LR statistical test results, adding more explanatory variables at station number 5 does not lead to a statistically significant improvement in the AIC value at the 5% significance level. Therefore, the non-stationary model at that station was not considered for further analysis. Upon evaluating the model distributions, the independence and normality of the residuals of the most successful models were evaluated within the scope of the study. Table 7 shows that the best-performing models have Filliben coefficients greater than 0.97. This assessment indicates that the selected models are suitable. Furthermore, worm graphs were plotted based on the most suitable distributions identified for the stations in Figure 8. For the example of worm plots, results for only four stations are presented. The standardized residuals for all models stayed within the 95% confidence interval, showing that these models are valid.

Table 7 also emphasizes that, except for one station, the non-stationary models where only the location parameter is represented by oscillation indices are mostly more successful. NAO and SO are key covariates for modeling annual average maximum rainfall, while WeMO is the primary covariate for modeling annual average maximum rainfall at a few stations.

After identifying the best models, the rainfall data related to different return periods (T) for T = 10, 20, 50, and 100 years were computed to assess flood risk. The return period connected with the probability of non-exceedance and is calculated via the general formula T = 1/(1 − F(Pr > pr)). Rainfall quantiles are computed by applying the inverse of this equation. It is necessary to emphasize that quantiles for any return period (T) will vary over time in non-stationary conditions but remain constant in stationary conditions. Within the scope of the study, rainfall quantiles were calculated for 10, 20, 50, and 100 years, and the average values of the quantiles were taken while creating the rainfall map. Hazard criteria were re-weighted with the AHP method, taking into account 10-, 20-, 50-, and 100-year rainfall quantiles, and the weights are given in

Table 8. Main weights for the flood risk assessment at different return periods.

	Return Periods
Criteria	10-Year	20-Year	50-Year	100-Year
H1.1.	0.295	0.334	0.398	0.427
H1.2.	0.124	0.117	0.105	0.088
H1.3.	0.018	0.018	0.017	0.016
H2.1.	0.185	0.172	0.153	0.186
H2.2.	0.152	0.143	0.128	0.107
H2.3.	0.075	0.073	0.066	0.057
H2.4.	0.057	0.052	0.049	0.042
H2.5.	0.038	0.037	0.034	0.031
H2.6.	0.031	0.03	0.027	0.025
H2.7.	0.025	0.024	0.023	0.021

.

A consistency analysis was performed for the results obtained in Table 8. The results found that the CR value was below the threshold of 0.1, indicating that the weights were acceptable.

At this stage of the study, the procedure in Section 4.2 was followed and the rainfall criteria in different return periods were included in the hazard criteria and transferred to the GIS environment. Weighted overlay analyses were re-performed to identify potential hazard areas using the criteria weight combinations in the scenarios. To control the length of the paper, the hazard maps obtained for the four different rainfall scenarios are not included here. To perform a comprehensive flood risk analysis, the current vulnerability and the hazard criteria considered for four different rainfall scenarios need to be considered together. The weighted overlap analysis was performed again by equalizing the weights, and the flood risk maps for four different rainfall scenarios are presented in Figure 9.

As depicted in Figure 9, the spatial distribution of overall flood risk in Izmir City indicates that the central and western areas are at higher risk, while the eastern and northern regions exhibit comparatively lower risk. As an important finding, it was observed that as the return period level increased, the flood risk in the western part of the city increased (Figure 9). The flood risk distribution in İzmir City was determined, as presented in

Table 9. The proportions of the areas exposed to overall flood risk.

Flood Risk Scenarios	Very Low (%)	Low (%)	Moderate (%)	High (%)	Very High (%)
10 Year	15.12	28.26	28.60	21.29	6.73
20 Year	14.91	28.48	27.85	21.69	7.07
50 Year	14.52	28.70	27.80	21.70	7.28
100 Year	13.92	31.59	24.64	22.32	7.53

.

Table 9 shows that with the stepwise increase in return periods, the general spatial pattern of high- to very-high-risk areas in the risk zones increases and the distribution of very-low-risk areas decreases.

At this point in the study, the flood risk assessment and ranking process of 165 points determined from the current flood risk map in Section 4.3 was also carried out for four different scenarios. For this purpose, the VIKOR method was run again for four different scenarios. The VIKOR results for assessing comprehensive flood risk in the Izmir City are presented in

Table 10. Top 20 high-flood-risk points for four different scenarios.

10 Year	Rank	1	2	3	4	5	6	7	8	9	10
	Point	R55	R56	R54	R153	R163	R31	R32	R28	R97	R110
	$Q_i$	0.957	0.770	0.740	0.714	0.678	0.670	0.666	0.626	0.618	0.617
	Rank	11	12	13	14	15	16	17	18	19	20
	Point	R22	R53	R115	R117	R33	R151	R100	R1	R2	R114
	$Q_i$	0.608	0.595	0.587	0.573	0.569	0.568	0.566	0.549	0.545	0.540
20 Year	Rank	1	2	3	4	5	6	7	8	9	10
	Point	R55	R56	R54	R153	R163	R53	R151	R164	R165	R152
	$Q_i$	0.974	0.820	0.804	0.728	0.721	0.700	0.681	0.620	0.616	0.589
	Rank	11	12	13	14	15	16	17	18	19	20
	Point	R50	R155	R156	R37	R154	R41	R31	R32	R159	R157
	$Q_i$	0.585	0.552	0.544	0.533	0.530	0.510	0.503	0.500	0.500	0.500
50 Year	Rank	1	2	3	4	5	6	7	8	9	10
	Point	R55	R56	R54	R153	R53	R163	R151	R164	R165	R152
	$Q_i$	0.979	0.849	0.828	0.753	0.748	0.747	0.709	0.669	0.654	0.642
	Rank	11	12	13	14	15	16	17	18	19	20
	Point	R50	R156	R155	R154	R157	R159	R141	R37	R120	R146
	$Q_i$	0.629	0.598	0.590	0.580	0.555	0.553	0.544	0.539	0.525	0.521
100 Year	Rank	1	2	3	4	5	6	7	8	9	10
	Point	R55	R56	R54	R163	R53	R153	R151	R164	R165	R152
	$Q_i$	0.979	0.855	0.824	0.771	0.763	0.750	0.711	0.678	0.670	0.654
	Rank	11	12	13	14	15	16	17	18	19	20
	Point	R50	R156	R155	R154	R159	R157	R146	R141	R37	R147
	$Q_i$	0.638	0.599	0.589	0.580	0.553	0.552	0.532	0.528	0.522	0.511

The VIKOR results show that for all four scenarios, R55 in the Kemalpaşa district in the north-east of the city has the highest flood risk, followed by the R56 and R54 points in the same district.

5. Discussion

This study presents an approach to assessing the comprehensive flood risk by combining MCDM with risk maps obtained at different return levels under non-stationary conditions. The GAMLSS technique was used to obtain precipitation values at return levels using different physical explanatory variables in non-stationary conditions. MCDM methods and the GAMLSS technique offer excellent potential in assessing flood risk, but their integration in flood risk assessment is first reported in the literature with this study. The assessment results for the current case showed that the three most important criteria for hazard are H1.1., H2.1., and H2.2., respectively. Similarly to this result, refs. [84,109] reported that rainfall was the most important criterion for flood hazard. The three most important factors for vulnerability are V2.1., V1.2., and V3.2, respectively. This finding is corroborated by the research of [110], which identified population density as a primary criterion for vulnerability. Hazard and vulnerability maps were overlapped to perform a comprehensive flood risk assessment. As seen in Figure 7, the Buca, Menderes, Bornova, Kemalpaşa, Çeşme, Torbalı, Menemen, Seferihisar, Çiğli, Bayındır, and Karaburun districts are at high risk of flooding. An analysis of this map shows that abundant rainfall, nearby river bodies, flat slopes, and low elevation profiles, as well as urban development types, contribute significantly to flood risk. This investigation’s outcomes are compatible with the results of recent studies carried out by [111], who highlighted that the Bornova, Kemalpasa, Menderes, Bayındır, and Karaburun districts are critical regions for flooding, and [112] underlined that Torbalı and Çeşme are the most vulnerable districts in terms of flooding. Similarly, a study conducted by [113] emphasized that Bornova, Buca, and Çeşme are highly susceptible to flood risk. A comparative analysis of the findings from flood assessment studies in İzmir confirms the consistency and accuracy of the integrated method proposed in this study.

Many studies have highlighted the importance of the combination of GIS and MCDM methods to rank high-risk areas in the effective management of flood risks [56,114,115,116,117]. Furthermore, it is useful for decision-makers to determine the flood risk scores in any area to create suitable flood risk mitigation measures [118]. For this aim, the VIKOR method is frequently used in ranking the flood risks of urban areas [119,120,121]. Table 6 presents the 20 stations with the highest flood risk among 165 stations, as determined by the VIKOR method. The spatial distribution of these stations within the study area is illustrated in Figure 10. R91, the station with the highest flood risk, is located in the Çeşme district. It can be generally observed that the points located in the Çeşme and Buca districts have high risk scores.

Assessing flood risks under rainfall events with different return levels can provide useful information to decision-makers and politicians [122]. Thus, precipitation data were modeled with four different probability distribution functions under non-stationary conditions using the GAMLSS framework, and the most successful models based on various evaluation criteria are shown in Table 7. Results showed that the LOGNO and GA distributions were found to be the most suitable at 10 and 3 stations, respectively. These outcomes are reinforced by the work of [123], which examined a meteorological drought analysis of the rainfall series over Turkey and reported that the most appropriate distribution for duration, which is one of the drought characteristics, is the LOGNO distribution. For constructing non-stationary models, atmospheric oscillation indices were used as explanatory variables at annual and seasonal scales. The findings indicate that using the annual NAO and autumn SO indices as explanatory variables yields successful results. The results of this study confirm the results of previous studies examining the effects of NAO and SO on precipitation variables in Turkey. Ref. [51] concluded that NAO and SO indices are important explanatory variables for precipitation in Turkey.

Previous research using MCDM has not integrated flood hazard mapping techniques with rainfall return periods in non-stationary conditions and has not identified potential hazard areas. Thus, in the study, rainfall values for 10-, 20-, 50-, and 100-year return levels were calculated using the most appropriate probability distribution functions determined by the GAMLSS technique and transferred to the GIS environment to obtain flood risk maps for various scenarios. Comparing the flood risk maps given for various scenarios in Figure 9 with the current risk map in Figure 7, the results showed that with the change in return periods, the high- and very-high-risk areas move stepwise from the east and north to the central parts of the city. Among these, the increase in high-risk areas is more evident, especially in the Çeşme district. When the ratio of high- and very-high-risk areas is compared with the current risk map and the 100-year risk map, it expands from 35.35% to 41.69%, showing that the probability of extreme flooding in these areas increases. Areas of medium and very-high risk are mostly located in Buca, Bornova, Kemalpaşa, Menderes, Çeşme, and Çiğli, where the intensity of flooding is high due to frequent and heavy rainfall and the density of urbanization is also significant. Table 9 indicates the spatial distribution of flood risks in various return periods. Comparing the current flood risk map with the map obtained for 10 years, the areas classified as very-low- and low-risk have diminished, while the moderate-, high-, and very-high-risk areas have expanded. For 20, 50, and 100 years, very-low- and moderate-risk areas decreased compared to 10 years, and the very-low- and very-high-risk areas also increased. The 100-year rainfall scenario is frequently used for the evaluation of flood risk maps [124,125]. To assess flood risk on a district basis, the distribution of very-high- and high-risk areas on the risk map obtained for a return level of 100 years is illustrated in Figure 11. In light of the evaluation conducted for very-high flood risk, the five highest-priority districts were determined as Çeşme (21.37%), Kemalpaşa (17.05%), Buca (10.27%), Urla (8.45%), and Torbalı (7.35), respectively. (see Figure 11).

Finally, the risk assessment of 165 points obtained from the existing flood risk map with the existing VIKOR method was also carried out for the risk maps obtained for different return periods, and the outputs were compared with the existing VIKOR results. The results in Table 10 show that the points with the highest flood risk scores have changed compared to the current VIKOR results. Additionally, Figure 12 illustrates the placement of these stations within the study area.

The points with the three highest flood risk scores on the current flood risk map are R91 (Çeşme district), R153 (Buca district), and R93 (Çeşme district), respectively. However, the top three points with the highest flood risk scores for 10, 20, 50, and 100 years are R55, R56, and R54 in the Kemalpaşa district, respectively. The results also indicate that the Buca district has a high flood risk. In fact, the fourth-highest flood risk point for the 10-, 20-, and 50-year return levels is R153 in the Buca district. The same point has the sixth-highest flood risk score for the 100-year period. The R163 point (Çeşme district), which has the fourth-highest flood risk score for the 100-year period, ranks fifth for the 10- and 20-year periods and sixth for the 50-year period. However, the same point has the eleventh-highest flood risk score in the current VIKOR results.

The comparison of GIS-based flood risk maps with the ranking results produced by the VIKOR method shows that the spatial distribution of high-risk areas is highly consistent across both analyses. This alignment confirms that the performance parameters used in the study accurately capture the underlying spatial reality and that the MCDM framework yields coherent and dependable results. Overall, the findings demonstrate that the GIS-based VIKOR approach is a robust and reliable tool for flood risk assessment.

The study offers a comprehensive flood risk assessment, delivering easily accessible risk data for decision-makers and planners to identify and prioritize the most vulnerable areas. Results from the integrated assessment method can increase the capacity to assess disaster risks in light of different scenarios and offer improved information for decision-making regarding sustainable flood risk management.

6. Conclusions

The proposed study presents a comprehensive analysis examining the effects of rainfall at different return periods (10-, 20-, 50-, and 100-year) on flood risk under non-stationary conditions in GIS- and MCDM-based flood risk assessments for Izmir province. The key findings can be summarized as follows:

(1) GIS-based AHP results showed that the districts of Buca, Menderes, Bornova, Kemalpaşa, Çeşme, Torbalı, Menemen, Seferihisar, and Çiğli have been identified as areas with high and very high flood risk.

(2) Among the 165 homogeneously determined points, the VIKOR results show that R91 (Çeşme district), R153 (Buca district), and R93 (Çeşme district) are the points with the highest flood risk scores, respectively.

(3) Probability distribution functions were applied to the rainfall data to analyze the impact of rainfall quantiles at different return periods on flood risk under non-stationary conditions. The findings showed that the LOGNO and GA distributions were the most suitable distributions for the evaluation criteria at ten and three stations, respectively. Furthermore, using annual NAO and autumn SO indices as explanatory variables yielded successful results compared to other annual and seasonal oscillations.

(4) By determining the most successful distributions with the GAMLSS technique, precipitation quantiles were obtained at 10-, 20-, 50-, and 100-year return levels and weighted overlap analysis was performed in the GIS environment to obtain flood risk maps for different scenarios. The results showed that with the increase in return periods, the high- and very-high-risk areas move stepwise from the east and north to the central parts of the city, and the flood risk in the western part of the city increased. According to the spatial evaluation results, it was determined that as return periods increase, the overall spatial extent of high-to-very-high-risk areas within the risk zones expands, while the coverage of very-low-risk areas declines.

(5) The flood risk scores of 165 points identified on four different flood risk maps were re-analyzed with the VIKOR method to rank them. The results were determined to be different from the VIKOR results obtained for the current flood risk map, showing that in all four scenarios, the R55 point in the Kemalpaşa district, located in the north-east of the city, has the highest flood risk, followed by the R56 and R54 points in the same district.

In the study, a new integrated approach was presented and a thorough flood risk assessment for the Izmir province was performed. The present study can offer ideas for sustainable urban flood risk management in similar plain cities by considering non-stationary conditions for rainfall quantiles in GIS- and MCDM-based assessments.