Urban Flood Risk Assessment and Mapping Using GIS-DEMATEL Method: Case of the Serafa River Watershed, Poland

Abstract

This paper develops a method integrating Geographic Information Systems (GIS) and the Decision-Making Trials and Evaluation Laboratory (DEMATEL) for the analysis of factors influencing urban flood risk and the identification of flood-prone areas. The method is based on nine selected factors: land use/land cover (LULC: the ratio of built-up areas, the ratio of greenery areas), elevation, slope, population density, distance from the river, soil, Topographic Wetness Index (TWI), and Normalized Difference Vegetation Index (NDVI). The DEMATEL method is used to determine the cause–effect relationship between selected factors, allowing for key criteria and their weights to be determined. LULC and population density were identified as the most important risk factors for urban floods. The method was applied to a case study—the Serafa River watershed (Poland), an urbanized catchment covering housing estates of cities of Kraków and Wieliczka frequently affected by flooding. GIS analysis based on publicly available data using QGIS with weights obtained from DEMATEL identified the vulnerable areas. 45% of the total catchment area was classified as areas with a very high or high level of flood risk. The results match the actual data on inundation incidents that occurred in recent years in this area. The study shows the potential and possibility of using the DEMATEL-GIS method to determine the significance of factors and to designate flood-prone areas.

1. Introduction

Climate change and rapid urbanization are causing more frequent pluvial floods [1,2], and changes in precipitation pattern lead to frequent and long-lasting droughts and heavy rains [3]. According to the World Meteorological Organization [4], the probability of the occurrence of a large-scale extreme event has increased worldwide due to anthropogenic climate change. Extreme rainfall and flooding created significant hazards, causing severe damage and casualties in the decade 2011–2020 [4]. The increase in sealing caused by new developments and the reduction in green areas increased the effects of rainfall and contributed to reduced water infiltration into the ground. The combination of these two factors can have a negative impact, causing flooding and similar environmental damage [5].

EU countries assess flood risk and plan actions to reduce it in accordance with the Floods Directive [6]. The assessment of flood hazard and risk is carried out by preparing hazard maps and risk maps, and then risk management plans can be developed [7]. However, in many countries, including Poland, analyses do not include the risk of pluvial floods [2,8]. Therefore, it is necessary to develop an approach that allows these type of threats to be estimated. Pluvial flood risk determination studies are performed using both hydrologic modeling and other approaches, depending on the scale. Hydrological modeling usually concerns the microscale, while at larger scales, the most common approach is the analysis of factors influencing the threat combined with Geographic Information Systems (GIS). Multicriteria decision-making analysis (MCDM) is often used to analyze factors influencing the occurrence of flood susceptibility and combine the information that they provide. The most commonly used MCDM method is the Analytic Hierarchy Process (AHP) [9,10,11,12,13], and its modification—fuzzy AHP (FAHP) [14,15,16], Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) [17,18,19], VlseKriterijumska optimizacija I Kompromisno Resenje (VIKOR) [19,20,21], and Decision-Making Trial And Evaluation Laboratory (DEMATEL) (in classic form or in combination with other techniques) [16,22,23,24]. Other approaches used are machine learning techniques, either used alone or in combination with MCDM. Among the frequently used ones are as follows: artificial neural networks (ANN) [25,26,27] random forest (RF) [18,25,26,27], Naive Bayes Tree (NBT), and Naive Bayes (NB) [21]. Other approaches include the following: gradient boosting decision tree (GBDT) and gradient boosting decision tree (GBDT) [26], extreme gradient boosting (XGBoost) [28], and the boosted generalized linear model (GLMBoost) [29].

As mentioned above, many previous studies used the combination of GIS and AHP: Duan et al. used 18 factors to assess the risk of urban waterlogging disasters in Changchun (China) [30], Roy et al. analyzed urban waterlogging risk in Siliguri (India) (17 factors) [31], Hussain et al. a high number of factors in the AHP-GIS analysis to carry out flood vulnerability mapping in Khyber Pakhtunkhwa (Pakistan) [32], Shuaibu et al. assessed flood risk in the Hadejia River Basin (Nigeria) (13 factors) [33], and Das and Gupta carried out flood mapping in the Subarnarekha basin (India) (12 factors) [34]. Other studies integrating AHP and GIS to identify and map flood-prone areas include [11,12,35,36,37,38,39,40,41,42,43,44,45,46,47]. The studies differ in the number and type of factors that were included in the analyses, ranging from 5 to 18 in the above-mentioned Duan et al. study [30]. The most frequently analyzed factors in the conducted studies were the following: elevation, slope, land use land cover (LULC), rainfall, distance from rivers, soil, drainage density, Topographic Wetness Index (TWI), Normalized Difference Vegetation Index (NDVI), population density, aspect, lithology, curvature of the land surface, flow accumulation, geology, Stream Power Index (SPI), geomorphology, distance to roads, Topographic Roughness Index (TRI), and others. A brief review of the literature on the factors used in the research is presented in Section 2.4.

In AHP, factors are analyzed by comparing them in pairs and determining how much more important a given factor is than the compared factor. In this paper, the DEMATEL method is used, which similarly uses pairwise comparisons of factors, but assesses cause-and-effect relationships, because by comparing factors in pairs, the extent to which a given factor influences the others can be determined [22,48]. Through mathematical operations, it is possible to determine both the direct and indirect influence of individual factors and, based on the assessment of the total influence, determine the key factors and their weights [49]. DEMATEL, unlike AHP, is not so commonly used in flood susceptibility assessment, but there are several studies that have used it in other contexts. Taherizadeh et al. [22] combined DEMATEL with a GIS-based analytic network process to evaluate flood vulnerability in Golestan province (Iran). Fourteen factors were implemented (elevation, slope, aspect, vegetation density, soil moisture, flow direction, river distance, rainfall and runoff, flow time, geomorphology, drainage density, soil type, lithology, and land use). Zheng et al. [16] created a new method G-DEMATEL-AHP (combining Grey-DEMATEL with AHP) and applied it to assess the flooding risk in urban areas of mega-cities (case study Zhengzhou city). Thirteen factors were considered, divided into groups that characterized the following: (1) the natural environment (slope, elevation, rainfall, river density, river proximity, drainage capacity), and (2) the vulnerability (LULC, population density, metro line density, metro line proximity, location of metro station, road network density, road network proximity). The results of two methods, G-DEMATEL-AHP and fuzzy AHP, were compared and it was found that G-DEMATEL-AHP is more effective in identifying the highest risk sites than FAHP. Ali et al. [24] developed an approach to identify flood-prone areas in the Topl’a river basin (Slovakia) using a geographic information system (GIS), multi-criteria decision making (MCDM), bivariate statistics (Frequency Ratio (FR), Statistical Index (SI)) and machine learning (Naïve Bayes Tree (NBT), Logistic Regression (LR)). DEMATEL method combined with analytical network process (ANP) was used to evaluate the relationships and interdependencies between factors. The analyses showed that the DEMATEL-ANP model was the most effective algorithm with the highest accuracy, followed by LR, NBT-SI and NBT-FR [24].

The aim of this study was to develop a method combining GIS and DEMATEL to assess the urban flood risk. This is an important problem in Poland because so far, despite 12 years of conducting flood risk analyses based on the Flood Directive, the problem of pluvial floods has not been addressed. We conducted a review of research in this field and developed a relatively simple method (a method from the MCDM group, based on publicly available spatial data and using the free QGIS software (Desktop 3.36.3)) so that it could also be used by, for example, city authorities. The review, to the best of the authors’ knowledge, also shows that most of this type of research was conducted for case studies from China, countries from South Asia, as well as countries from the Near East and Africa. Therefore, this work can be valuable also because of the approach to the problem from the point of view of the problems of European countries. The catchment area of the Serafa River (including densely populated residential districts of the city of Krakow and Wieliczka town, Poland) was selected for implementation. The catchment area is highly urbanized and at risk of flooding, in recent years particularly significant losses were caused by floods caused by the occurrence of water from the riverbed in 2010 and 2019 [50,51]. In addition, pluvial floods and flash floods occur almost every year [52,53,54]. Data provided by the State Fire Service showed 629 interventions in the years 2018–2024 that were undertaken due to flooding or inundation of private and public property or communication infrastructure. The analysis is carried out in three stages. The first one is based on the GIS analysis of the acquired data and the transition from different spatial scales to a common hexagon layer, in which the values from each factor will be included. The second stage includes cause-and-effect analysis (DEMATEL method), in which calculations are carried out successively, the result of which is the determination of the weights of individual factors. The last stage is the multiplication of the normalized values obtained in the GIS analysis with the weights of the factors.

2. Materials and Methods

2.1. Study Area

The case study area covers the Serafa River watershed, which is located in the southern part of Poland in the Małopolska Province, and includes a part of the city of Kraków and the town of Wieliczka (Figure 1). The Serafa River is a right tributary of the Vistula River [55]. The Serafa catchment area is bounded by 49°57′31″ and 50°03′02″ north latitudes and 19°57′19″ and 20°06′54″ east longitudes and covers an area of 72.4 km². According to the Hydrographic Division Map of Poland (MPHP) [55], it comprises 15 elementary catchments, including eight streams: Serafa, Drwina Długa, Drwinka, Malinówka, Krzyszkowice, Grabówka, Potok Miodówka, and Zabawka. The Serafa River flows from the northern slopes of the Wieliczka Foothills, its sources are located at an altitude of 230.00 m above sea level, the river flows through Wieliczka, then Kraków (Bieżanów district) flowing into the Vistula at km 93 + 500 at an altitude of 188.63 m a. s. l. The average catchment slope is 3.1%, and the average river slope is 0.3% [54]. In the years 1991–2020, at the Kraków synoptic weather station the average annual air temperature was 8.9 °C, and annual precipitation was 673 mm [56]. Built-up areas (residential, industrial and communication areas) constitute 43% of the catchment area, agricultural areas 7% and greenery areas 48%. In the Serafa catchment area, three dry reservoirs were commissioned in 2023—Malinówka 1, Malinówka 2 and Serafa 2—whose purpose is to reduce the risk of flooding [52].

2.2. Methodological Approach

The proposed approach to estimating flood susceptibility using DEMATEL and GIS is shown in Figure 2. The first stage was a literature review of the criteria/factors used in similar analyses in other countries—presented in Section 2.4. Upon identification, the most frequently used factors were verified in terms of data availability in publicly available open databases. In stage 2, the collected data were prepared and indicators derived from the original data were determined. Spatial layers of individual factors were also prepared in a common hexagonal grid. The description of the adopted indicators can be found in Section 3.1. In step 3, DEMATEL was used to determine the relationships between factors and factor weights. In stage 4, a final assessment was made using the weighted sum method with weights determined using the DEMATEL method, and then maps of the susceptibility of individual areas to pluvial floods were made on a catchment scale. To assess the correctness of the adopted procedure, a layer was used with marked locations of actual flooding that occurred in this area, developed on the basis of data on interventions undertaken by the State Fire Service during flooding.

2.3. DEMATEL Method

Decision-Making Trial and Evaluation Laboratory (DEMATEL) analyses the cause-and-effect relationships between the analyzed factors, identifying key factors and determining their weights [49]. The calculations are performed in the following sequence [48]:

• Determining the direct-influence matrix;
• Normalizing the direct-influence matrix;
• Obtaining the total-relation matrix—direct and indirect impact;
• Determining the cause–effect diagram or the influential relation map (IRM);
• Determining the weights of factors.

Step 1. Study of the relationships between $n$ factors $F$, leading to the construction of the direct-influence matrix $D$. Relationships between factors were examined by comparing them in pairs using a defined scale regarding the level of impact of individual factors. Originally, the method used a 4-degree scale [57], but different scales can be used, e.g., 4 degrees [48], 5 degrees [49,58,59,60,61]. In this study, a 5-point scale was used, where the influence of factor $F_i$ on factor $F_j$ is quantified on a 0 to 4 scale (i.e., 0 = no influence, 1 = low influence, 2 = moderate influence, 3 = high influence; and 4 = very high influence) [22,58,62].

The direct-influence matrix A [49]:

$$A=\left[\begin{array}{cc}\begin{array}{ccc}\begin{array}{c}0\\ a_{\mathrm{2,1}}\\ a_{\mathrm{3,1}}\end{array}& \begin{array}{c}{a}_{\mathrm{1,2}}\\ 0\\ a_{\mathrm{3,2}}\end{array}& \begin{array}{c}{a}_{\mathrm{1,3}}\\ a_{\mathrm{2,3}}\\ 0\end{array}\end{array}& \begin{array}{cc}\begin{array}{c}\cdots \\ \cdots \\ \cdots \end{array}& \begin{array}{c}{a}_{1,n}\\ a_{2,n}\\ a_{3,n}\end{array}\end{array}\\ \begin{array}{ccc}\begin{array}{c}\cdots \\ a_{n,1}\end{array}& \begin{array}{c}\cdots \\ a_{n,2}\end{array}& \begin{array}{c}\cdots \\ a_{n,3}\end{array}\end{array}& \begin{array}{cc}\begin{array}{c}\cdots \\ \cdots \end{array}& \begin{array}{c}\cdots \\ 0\end{array}\end{array}\end{array}\right],$$

(1)

where:

$a_{i,j}$—influence of factor $F_i$ on factor $F_j$, i = 1, 2, …, n; j = 1, 2, …, n.

Step 2. Determine of the normalized direct-influence matrix $X$ as follows [49]:

$$X={\displaystyle \frac{1}{s}}A,$$

(2)

where

$$s=max\left(\underset{1\le i\le n}{\mathit{max}}\sum _{j=1}^n{a}_{i,j};\underset{1\le j\le n}{\mathit{max}}\sum _{i=1}^n{a}_{i,j}\right),$$

(3)

Step 3. Attain the total-influence matrix T by summing the direct effects and all indirect effects. According to [22,63], in order to calculate the total relation matrix T, the condition given in the Formula (4) must be satisfied, which guarantees convergent solutions to the matrix inversion:

$$\begin{gathered} X^2,X^3,\dots ,X^{\infty } \\ \underset{m\to \infty }{\lim }{X}^m={\left[0\right]}_{n\text{×}n} \\ {\left[0\right]}_{n\mathrm{x}n}\mathrm{i}\mathrm{s}\mathrm{a}n\times n\mathrm{n}\mathrm{u}\mathrm{l}\mathrm{l}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{x} \end{gathered}$$

(4)

$$T=X+X^2+...+X^{\mathrm{\infty }}=X{(I-X)}^{-1},$$

(5)

in which $I$ is denoted as an identity matrix.

Step 4. Determine the influential relations map (IRM), which consists of determining the vectors $R$ and $C$, which are the sum of the row and column values of the total-influence matrix $T$, according to the formulas [49]:

$$\begin{gathered} R={\left[r_i\right]}_{n\times 1}={\left[\sum _{j=1}^n{t}_{i,j}\right]}_{n\times 1} \\ C={\left[c_j\right]}_{1\times n}={\left[\sum _{i=1}^n{t}_{i,j}\right]}_{1\times n}, \end{gathered}$$

(6)

The value r_i of the total influence (impact) shows the total direct and indirect influence transmitted by the i-th factor to the other factors. The value c_j of the total influence shows the total direct and indirect influence received by the i-th factor from the other factors [49].

Thus, when j = i, the sum (r_i + c_i) is an index representing the total effect both transmitted and received by the i-th factor. In other words, (r_i + ci) shows the degree of importance that the i-th factor plays in the system. In contrast, the difference (r_i − c_i) shows the net effect that the i-th factor contributes to the system. When (r_i − c_i) is positive, the i-th factor is a net sender, and when (r_i − c_i) is negative, the i-th factor is a net recipient.

Step 5. Determine the weights ${\omega }_i$ of the factors are determined based on the indicators r_i and c_i [49]:

$${\omega }_i={\displaystyle \frac{r_i+c_i}{\sum _{i=1}^n\left(r_i+c_i\right)}}.$$

(7)

The final result (flood risk level $FRL$) for each analyzed catchment fragment was obtained using the weighted linear combination WCL (also called simple additive weighting SAW). A hexagonal grid was used to divide the catchment, created in QGIS using the “Vector” and “Research Tools” tools. In the “Create Grid” command, a hexagonal grid type of 100 m was selected. A WLC is conducted by multiplying values of factors $f$ by the corresponding weights and aggregating all weighted factors. The following equation was used [13,64]:

$$FRL=\sum _{i=1}^n{\omega }_i·f.$$

(8)

2.4. Factors Used in Assessing Flood Risk—Literature Review

The selection of factors used in this study was made based on the results collected from literature reviews published in recent years (

Table 1. The most frequently considered factors in assessing the risk of flooding.

Reference	Slope	LULC	Elevation	Rainfall	Drainage Density	Distance from River	Soil	TWI	NDVI	Population Density	Other Factors Used
[30]	x	x	x	x	x	x		x	x	x	geomorphology, road density, GDP, NDMI, and others
[17]	x	x	x	x	x		x	x			aspect, lithology, curvature, SPI, and others
[32]	x	x	x	x		x				x	distance to emergency services, literacy rate, distance to education facilities, irrigated area, and others
[31]	x	x	x	x	x	x	x		x	x	flow accumulation, geomorphology, road density, distance to emergency services, and others
[21]	x	x	x	x		x	x	x	x		aspect, geology, curvature, SPI, and others
[25]	x	x	x	x	x	x		x	x		SPI, flow accumulation, distance to road, geomorphology, and others
[65]	x	x	x	x	x	x	x	x	x		lithology, SPI, TRI, plan curvature, and others
[15]	x	x	x	x	x	x	x	x			lithology, curvature, SPI, flow accumulation, and others
[66]	x	x	x		x	x	x		x	x	aspect, geology, distance to road, plan curvature, and others
[33]	x	x	x	x	x	x	x			x	flow accumulation, road density, literacy rate, employment rate, and others
[16]	x	x	x	x		x				x	distance to road, road density, river density, metroline density, and others
[34]	x	x	x	x	x	x	x	x			geology, curvature, geomorphology, TRI, and others
[67]	x	x	x	x		x	x	x			aspect, curvature, SPI, STI, and others
[26]	x	x	x			x	x	x	x		aspect, curvature, SPI, normalized differences built-up index, and others
[20]	x	x	x		x	x	x	x			aspect, curvature, flow accumulation, STI
[27]	x	x		x			x	x			aspect, curvature, SPI, distance to road, and others
[35]	x	x	x	x	x	x	x	x			curvature, flow accumulation, metroline proximity
[22]	x	x	x	x		x	x				aspect, lithology, geomorphology, vegetation density, and others
[68]	x	x	x	x	x	x			x	x	road density, GDP, building density
[18]	x	x	x	x	x	x					aspect, distance to road, distance to urban drainage, CN
[69]	x	x					x	x			aspect, lithology, SPI, profile curvature, and others
[70]	x	x					x	x			aspect, lithology, plan curvature, profile curvature, and others
[36]	x	x	x	x	x	x		x			geology, hydraulic conductivity, groundwater table
[37]		x								x	distance to emergency, proportion of vulnerable population; dependent population (age), low rise buildings, and others
[12]	x		x	x		x		x	x	x	distance to road, distance to emergency services, NDWI
[71]	x	x	x	x		x	x		x		flow accumulation, distance to road
[72]	x	x	x	x	x	x	x	x		x	-
[73]	x	x	x	x	x	x	x				geology
[38]	x	x	x	x	x	x	x				lithology
[74]	x	x	x	x	x	x	x				geology
[75]	x	x		x	x	x	x			x	flood depth
[39]	x	x	x	x	x		x	x			flow accumulation
[23]	x	x	x	x	x	x	x				-
[40]	x	x	x	x	x	x	x				-
[41]	x		x	x	x				x		geomorphology, NDWI
[45]	x	x	x	x	x		x				-
[14]	x	x	x		x	x					profile curvature
[11]	x	x	x	x	x		x				-
[42]	x		x		x			x			CN, direct runoff depth at 50-year return period
[43]	x	x	x	x	x		x				-
[44]	x	x	x	x	x	x					-
[46]	x	x	x		x		x				-
[47]	x	x	x		x		x				-
Total	42	40	38	33	31	30	30	19	11	11

Note: “x” means that a factor was taken into account in the analysis.

). The following databases were used for the literature review: SCOPUS, Science Direct, Web of Science, and Google Scholar.

A review of 43 articles from the last 4 years revealed at least 11 publications (25% of all analyzed articles) showed factors that were used to assess flood susceptibility. The analysis of available data and assessment of the possibilities of their determination led to the elimination of the factors: rainfall and drainage density. Rainfall—due to the small area covered by this work, this factor was not used, and there are no IMGW meteorological stations located in the Serafa River catchment area. Drainage density—this was not used due to the lack of complete public data on the drainage network. According to the report [76], the main factors influencing floods are the insufficient capacity of riverbeds, other water courses and drainage systems resulting from the intensive development of the catchment area in the last few decades. The built-up area in the catchment area has increased significantly at the expense of green and agricultural areas. An additional problem is the shaping (flattening) of the northern part of the catchment area (the Vistula River valley), and the occurrence of impermeable soils in this area. Ultimately, the following factors were selected for analysis: slope, elevation, LULC, distance from river, soil, TWI, NDVI, and population density.

3. Results

3.1. Factors

3.1.1. LULC

Land use and land cover is one of the most frequently used indicators in flood risk analyses. The map showing LULC was created based on publicly available data from the National Geoportal (the Topographic Objects Database (BDOT 10k)) [77].

From the collected data, 15 LULC classes were created. Figure 3 shows the diversified LULS resulting from the location of the Serafa catchment area, the north-western part of which is located in the area of Kraków city, while the south-eastern part is located in the area of Wieliczka town and small villages surrounding it. However, for the further stages of analysis, land use was classified into three classes (Figure 4):

• Built-up areas: single-family housing, multi-family housing, sealed and unsealed roads, sealed and unsealed squares, railway areas, landfills, and other built-up areas;
• Greenery areas: allotment gardens, agricultural areas, low-greenery areas, and high-greenery areas;
• Surface water.

For the analyses using GIS, a 100 m hexagonal grid was used. The LULC data were used in the analyses in the form of two numerical criteria that were defined for each hexagon:

• the ratio of built-up areas,
• the ratio of greenery areas.

3.1.2. Elevation

Elevation was developed based on the Digital Elevation Model (DEM) from the National Geoportal in the form of the most up-to-date grid from 2023 (1 m × 1 m mesh) [77].

Figure 5 shows a slight variation in the terrain in the northern part of the catchment, at the mouth of the Serafa river to the Vistula and near the accompanying area. Significant elevations are noticeable only in the central part of the catchment, which increase towards the south. The elevation values range from 188.63 to 430.37 m above sea level.

3.1.3. Slope

Slope was developed based on the DEM, in QGIS, using the ‘GDAL’ plugin. The result is given in percentage values. Figure 6 shows significant differences in slope, most visible at road and rail infrastructure facilities, as well as on the slopes of the elevations in the southern part of the catchment. The slope values range from 0 to 50%.

3.1.4. Population Density

The population density factor was developed on the basis of data from the Geostatatistis Portal of Statistic Poland [78]. Population density data in the form of a vector layer for the entire country are published in a 1 km × 1 km grid. Figure 7 shows the layer clipped to the study boundaries. There is a noticeable high population density in the city of Krakow, where the multi-family housing estate of the Bieżanów district is located, with a population density ranging from 10,000 to 13,000 per 1 km².

3.1.5. Distance from River

The distance from the river was determined based on the hydrological network created from the data of the Map of Hydrographic Division of Poland [55]. Using the ‘BUFFER’ function in the QGis program, the distances from designated streams and rivers were developed. Figure 8 shows distances from 10 m to 100 m (every 10 m), from 100 m to 500 m (every 50 m). For further analysis, the value of 600 m was assigned to the remaining area.

3.1.6. Soil

The soil map (Figure 9) was developed based on the sheets of the Detailed Geological Map of Poland 1:50,000 downloaded from the Central Geological Database of the Polish Geological Institute—National Research Institute [79]. The analysis used map sheets of Kraków, Myślenice, Niepołomice and Wieliczka. The results were processed by georeferencing the sheets to the index grid and then outlining the soil classes. Due to the use of four different sheets, the soil types differ slightly, but for the purposes of the analysis, similar soil types were aggregated.

3.1.7. NDVI

The Normalized Difference Vegetation Index (NDVI) determines the vegetation cover of an area and its impact. The scale of values for this index is from −1 to 1. A negative value indicates the presence of surface water, values close to 0 indicate no vegetation cover, while values close to 1 indicate lush vegetation cover [41].

Data for analysis were downloaded from the platform of the United States Geological Survey (USGS) [80]. The NDVI development included the analysis of data from May 2023, and these data were selected to be as reliable as possible in terms of vegetation since vegetation develops during the spring season. The “Raster calculator” function in the QGis program was used to calculate the NDVI. The downloaded Band 4 and Band 5 files were loaded, then the calculation for Landsat 8 was performed as follows [12]:

$$NDVI={\displaystyle \frac{(Band5-Band4)}{(Band5+Band4)}}$$

(9)

The result of the calculation was a raster layer, as shown in Figure 10. The NDVI values within the Serafa river catchment range from −0.1 to 0.6. The map shows that in highly urbanized areas there is a lack of vegetation cover; in the northern area negative values are shown by surface waters, while the values closest to 1 occur in the most altitude-diversified terrain, covered with intensive vegetation.

3.1.8. TWI

The Topographic Wetness Index (TWI) (Figure 11) is commonly applied to assess the impact of topography on overflow production and flow cumulation at any point in a stream watershed [39]. The TWI is the function of slope and the upstream contribution area, it helps to identify the potential increase in the regional rainfall runoff model, soil water content and water areas, according to the area every pixel size of the water [67]. DEM and slopes were used to determine the index. The analysis used the “SAGA” plug-in and its function “Flow accumulation (qm of esp) in which the DEM raster was recalculated, resulting in flow accumulation. The next step was to calculate it in the “Raster Calculator” function, using the following formula [12]:

$$TWI=\ln \left({\displaystyle \frac{a}{tan\beta }}\right),$$

(10)

where

$a$—flow accumulation layer multiplied by the pixel size that makes up the raster;

$tan\beta$—the local slope.

3.2. Factor Analysis Using the DEMATEL Method Determining Factor Weights

The factors adopted for analysis were compared with each other and the mutual influence of the indicators on each other was assessed. A 5-point scale was adopted for the calculations: 0 = no influence, 1 = low influence, 2 = moderate influence, 3 = high influence; and 4 = very high influence. The direct-influence matrix is presented in

Table 2. The direct influence matrix.

Factor		F1	F2	F3	F4	F5	F6	F7	F8	F9
Slope	F1	0	0	2	2	3	4	1	2	1
Elevation	F2	4	0	3	4	1	4	3	1	2
LULC—the ratio of built-up areas	F3	2	0	0	4	4	3	4	0	2
LULC—the ratio of greenery areas	F4	0	0	4	0	4	3	4	0	1
NDVI	F5	0	0	0	0	0	1	0	1	2
TWI	F6	0	0	0	2	2	0	0	0	2
Population density	F7	2	0	4	4	4	1	0	1	1
Distance from river	F8	1	0	2	3	2	1	2	0	4
Soil	F9	1	0	2	2	4	0	2	1	0

.

The normalized direct-influence matrix was used to further calculate the total influence matrix $T$ (

Table 3. The total influence matrix.

Factor		F1	F2	F3	F4	F5	F6	F7	F8	F9	R
Slope	F1	0.032	0.000	0.154	0.175	0.253	0.233	0.117	0.107	0.126	1.197
Elevation	F2	0.222	0.000	0.265	0.326	0.277	0.304	0.257	0.091	0.203	1.945
LULC—the ratio of built-up areas	F3	0.123	0.000	0.117	0.277	0.342	0.222	0.256	0.042	0.174	1.554
LULC—the ratio of greenery areas	F4	0.047	0.000	0.244	0.116	0.314	0.202	0.242	0.032	0.127	1.325
NDVI	F5	0.010	0.000	0.022	0.027	0.039	0.054	0.021	0.049	0.104	0.326
TWI	F6	0.011	0.000	0.035	0.109	0.136	0.027	0.034	0.013	0.108	0.473
Population density	F7	0.123	0.000	0.259	0.272	0.331	0.150	0.111	0.076	0.137	1.459
Distance from river	F8	0.083	0.000	0.180	0.226	0.244	0.125	0.177	0.034	0.238	1.308
Soil	F9	0.073	0.000	0.152	0.160	0.276	0.072	0.150	0.068	0.069	1.020
	C	0.724	0.000	1.428	1.688	2.211	1.389	1.366	0.513	1.287

) (the convergence condition presented in Formula (4) was verified checked and met).

In the next step, the values of the sum indices (r_i + c_i) were calculated, showing the degree of importance of the i-th factor in the analyzed system, and the differences (r_i − c_i) showing the net influence that the i-th sensor brings to the system. The resulting values of these indicators are presented in

Table 4. Total impact and net impact indicator values.

Factor		ri + ci	ri + ci
Slope	F1	1.921	0.472
Elevation	F2	1.945	1.945
LULC—the ratio of built-up areas	F3	2.981	0.126
LULC—the ratio of greenery areas	F4	3.013	−0.364
NDVI	F5	2.536	−1.885
TWI	F6	1.862	−0.916
Population density	F7	2.825	0.093
Distance from river	F8	1.821	0.795
Soil	F9	2.307	−0.267

and Figure 12.

Figure 12 allows for a cause-and-effect analysis of the factors and shows their degree of prominence and relationship. The figure shows that F1, F2, F3, F7, and F8 are factors that most influence the other factors since they present R − C values above 0. F5, F6, and F9 are affected clusters because they have R − C values below 0. The R + C axis is prominent, and the most important factors in the model have the highest R + C values, and the least important factors have the lowest.

The strongest cause factors are the elevation (F2) with the value R − C equal to 1.945, distance from river (F8) R − C = 0.795 and slope (F1) R − C = 0.472. In contrast, NDVI (F5) and TWI (F6) (with the lowest R-C values) are strongly influenced by the above-mentioned influence factors (slope, elevation, distance from river).

The most important factors are LULC greenery areas (F4)—for which the R + C value of 3.013—as well as population density (F7) and LULC for built-up areas (F3), for which prominence values are also very high (F7 2.825; F3 2.981).

The values of the indicators (r_i + c_i) were used to determine the weights ${\omega }_i$, to determine the importance of individual factors in shaping the flood risk. The weight values were calculated based on Formula (7). The resulting values of the weights of individual factors are presented in the

Table 5. The weights of factors.

Factor		ri + ci	${\mathit{\omega }}_{\mathit{i}}$
Slope	F1	1.921	15%
Elevation	F2	1.945	16%
LULC—the ratio of built-up areas	F3	2.981	24%
LULC—the ratio of greenery areas	F4	3.013	24%
NDVI	F5	2.536	20%
TWI	F6	1.862	15%
Population density	F7	2.825	23%
Distance from river	F8	1.821	15%
Soil	F9	2.307	19%

. In the next stage, the values of the calculated weights were used to create a summary assessment for individual hexagons and were used to illustrate the final results.

The weight values indicate the key criteria that have the greatest impact on the occurrence of a hazard, these are mainly LULC and population density. The factors that have the least impact include slope, TWI, and distance from the river.

3.3. Designation of Areas at Risk of Flooding in the Serafa River Catchment Area

To determine the level of urban flood risk, a weighted sum was determined for each hexagon using the weights presented in Table 5, after previously normalizing the values of all factors. The final result of the GIS analyses is presented in Figure 13.

Highly urbanized areas are the most vulnerable to floods; the highest level of risk (marked in red) is in the north-western part of the catchment (these are densely built-up areas of housing estates in Krakow). A high risk is also present in the southern part of the catchment area, where the built-up areas of the town of Wieliczka are located. Areas not exposed to flooding, with very low or low flood risk level, account for 6 and 22% of the total catchment area, respectively. Areas with moderate flood risk level cover 28% of the area, and areas with high or very high flood risk cover 32 and 13% of the total catchment area (

Table 6. The area share of flood susceptibility classes in the Serafa catchment.

Flood Risk Level		Area
		(km2)	(%)
Very low	0.41–0.61	4.2	6%
Low	0.61–0.82	15.8	22%
Moderate	0.82–1.02	19.9	28%
High	1.02–1.23	22.8	32%
Very high	1.23–1.43	9.7	13%
Total		72.4	19%

).

In order to assess the accuracy of the obtained results, the locations of actual flooding and inundation incidents from 2018 to 2024 were also marked on the map. The data were provided by the State Fire Service (SFS), which is responsible for interventions in such cases. The actual incidents mostly match the obtained analysis result. The largest number of SFS interventions took place in the southern part of the catchment area in the town of Wieliczka. The high risk shown in the north-western part of the catchment (areas of multi-family housing estates in Krakow) does not correspond to the actual interventions. This is likely due to the efficiently functioning drainage systems in this area. This indicates the limitations of this study and the direction of future research: in urban areas with varying degrees of drainage equipment, with sometimes insufficient capacity of these systems, factors such as distance from drainage, drainage capacity, drainage density should be included.

According to SFS data, the largest number of interventions caused by the rising water in the river took place in the area of the Malinówka stream tributary to the Serafa, which was likely one of the reasons for undertaking the construction of three dry reservoirs mentioned in the case study description.

4. Discussion

The urban flooding process is influenced by a number of factors. As observed in the literature review presented in Section 2.4, this study considered nine commonly used factors contributing to flooding (slope, elevation, LULC: the ratio of built-up areas and the ratio of greenery areas, NDVI, TWI, population density, distance from river, and soil). A similar or even smaller number of factors were included in other studies [11,38,40,41,42,44,46,47,73]. A number of studies were also conducted based on the analysis of a much larger number of factors [15,17,21,22,30,31,32,33,65,66].

Factor analysis using the DEMATEL method indicated that the most important factors are LULC and population density, among others due to the nature of floods that occur in this analyzed area. Pluvial floods occur in Poland in urbanized areas due to high exposure to floods (these factors represent it), high rainfall intensity and inefficiency of drainage systems. The DEMATEL method assigned them high weights because, taking into account the interrelationships of factors, the ratio of built-up areas and population density, in addition to the direct impact on flood risk (high exposure), indirectly affects other factors, usually leading to unfavorable changes in the ratio of greenery areas, TWI and NDVI, and also affects changes in slope and soil (leveling of areas, sealing, etc.). The DEMATEL method approach provides a different perspective on the significance of factors influencing flood risk than other multi-criteria decision support methods. In our opinion, it is worth attention and dissemination, and it may also be valuable to compare the results given by DEMATEL and, for example, the widely used AHP method, which will also be the subject of our future research.

A similar indication of LULC as the factor with the highest weight was indicated by, among others, Nkonu et al. (weight 0.438, five factors analyzed) [47]. The second position with a weight of 0.179 (right after the slope) was determined using LULC by Hagos et al. [70] in an analysis with 10 factors. Chaulagain et al. indicated the distance from river (weight 0.32) as the most important criterion, followed by rainfall; LULC was ranked third with a weight of 0.22 (out of five indicators) [44]. A very similar result was also obtained by Waqas et al., the order of the criteria in the analysis: distance from river, rainfall, geology, LULC with a weight of 0.15 on four positions out of eight analyzed factors [73].

Population density indicated in our study as an important factor was also ranked high (third position with a weight of 0.11 out of 13 factors) in the study by Abdrado et al. [37]. On the other hand, Harshasimha and Bhatt [72] ranked LULC third from the last position (weight: 0.5) out of nine analyzed indicators, and population density was ranked last with a weight of 0.2.

The selection of factors and their weights depends on the scale of the study and the type of terrain. Rainfall is a significant factor mostly in large-scale studies, Sarkar et al. [13] conducted analysis for Dakshin Dinajpur (Bengal) with an area of 2219 km², using AHP method considered rainfall as the key criterion with the highest weight, its variability was significant (from “<1300 mm” to “>1800 mm”), although also in smaller scale this factor can be significant if it is characterized by significant variability e.g., Chaulagain et al. [44] for Kathmandu metropolitan city area with an area of 49.5 km² but rainfall ranges from 2367 to 3101 mm. In the case of our small-area case study, rainfall does not play a significant role.

In many studies factors such as elevation and slope were given a high rank. Shuaibu et al. [33] conducted flood risk mapping in the Hadejia River basin (Nigeria) and elevation and slope were the most important indicators of flood hazard. Paul and Sarkar [41] identified flood susceptible areas in the Mahananda river catchment (Nepal, India, and Bangladesh) using AHP and found that elevation is the most important factor (before geomorphology, slope, NDWI, drainage density, NDVI, and rainfall). Harshasimha and Bhatt [72] determined flood vulnerability in Kamrup Metropolitan District (Assam) and indicated that slope, in addition to drainage density, TWI, and elevation were the primary flood-causing geo-environmental parameters. The elevation and slope in the case study area, especially in the built-up area, are not characterized by significant variability [33,40,41].

Many studies also indicate the importance of the factor distance from river. In our study, it was the factor with the lowest weight, but it depends on the specificity of flood phenomena. Chaulagain et al. [44] indicated this factor as the most important flood criterion. Also Allafta and Opp [38] gave high weight to the distance from the river (the second most important criterion, rainfall in the first place) in the GIS-AHP analysis for flood prone areas mapping in the trans-boundary Shatt Al-Arab basin (Iraq-Iran).

This study shows the potential and possibility of using the DEMATEL-GIS method to determine the significance of factors and map areas prone to flooding. The developed approach is relatively simple (unlike methods using machine learning), is based on publicly available spatial data and uses free QGIS software (Desktop 3.36.3), so it has the potential for wide application. The developed result maps can be used both in flood management and policy, as well as spatial planning in cities. The analysis of factors also shows the significance of the ratio of green area to NDVI, the total weight of which is 44%, so they can be of significant importance for reducing the level of risk (by increasing the area of greenery areas, especially with trees), which should be the subject of urban policy in the development and promotion of greening of urban areas with a high risk of flooding.

5. Conclusions

Increased urbanization, changes in spatial development and increasing sealing have a strong impact on the increase in the risk of flooding and inundation. This is an important problem, the identification and assessment of which, despite many studies, remains unresolved. In many countries, including Poland, risk maps for pluvial floods are not developed despite the advanced methodology and practice of river flood risk maps. The proposed GIS-DEMATEL approach allows for the assessment of factors and mapping of areas at risk of pluvial floods. The DEMATEL method allows for the analysis of cause and effect of factors and allows for drawing attention to factors that have the greatest impact on others. The weights determined in this way take into account both direct and indirect impacts of factors. The developed approach was implemented in the Serafa River catchment, nine factors were proposed: LULC (the ratio of built-up areas, the ratio of greenery areas), elevation, slope, population density, distance from the river, soil, NDVI and TWI. The factors were analyzed using the DEMATEL method and their weights were determined, and then maps defining the flood risk level were created using GIS analyses. The analysis results indicate that highly urbanized areas are most vulnerable to flooding; the highest level of risk occurs in densely built-up areas of housing estates in Krakow and in the center of Wieliczka. Areas with very high or high flood risk cover 13% and 32% of the total catchment area, areas with moderate flood risk cover 28%, areas with low flood risk cover 22% and areas with very low flood risk cover 6% of the total catchment area.

The developed map can be a useful tool in the integrated strategic planning of flood protection and spatial planning, as well as in the planning and operational activities of rescue services and crisis management. Based on the DEMATEL factor analysis, it is possible to plan actions to limit the impact of the dominant factors determining the risk level (e.g., control of further development and sealing of high-risk areas, increasing the share of green areas with high NDVI parameters, developing recommendations for existing and planned development in terms of maintaining the biologically active surface and its quality, etc.). The analysis also shows the limitations of the proposed method, which results from the lack of use of a coefficient illustrating the drainage system and its capabilities. The high flood risk shown in some multi-family housing estates in Krakow does not correspond to the actual interventions. This is probably due to the efficiently functioning drainage systems in this area. This indicates the direction of future research: in urban areas with varying degrees of drainage equipment, with sometimes insufficient capacity of these systems, factors such as distance from the drainage, drainage capacity, drainage density should be taken into account.