Increasing Global Flood Risk in 2005–2020 from a Multi-Scale Perspective

: In the context of global climate change, ﬂoods have become one of the major natural disasters affecting the safety of human life, economic construction, and sustainable development. Despite signiﬁcant improvements in ﬂood risk and exposure modeling in some studies, there is still a lack of evidence on the spatiotemporal distribution patterns associated with ﬂood risk across the globe. Meanwhile, numerous studies mostly explore ﬂood risk distribution patterns based on speciﬁc spatial scales, ignoring to some extent the fact that ﬂood risk has different distribution patterns on different scales. Here, on the basis of hazard–vulnerability components quantiﬁed using game theory (GT), we proposed a framework for analyzing the spatiotemporal distribution patterns of global ﬂood risk and the inﬂuencing factors behind them on multiple scales. The results revealed that global ﬂood risk increased during 2005–2020, with the percentages of high-risk areas being 4.3%, 4.48%, 4.6%, and 5.02%, respectively. There were 11 global risk hotspots, mainly located in areas with high population concentration, high economic density, abundant precipitation, and low elevation. On the national scale, high-risk countries were mainly concentrated in East Asia, South Asia, Central Europe, and Western Europe. In our experiment, developed countries accounted for the majority of the 20 highest risk countries in the world, with Singapore being the highest risk country and El Salvador having the highest positive risk growth rate (growing by 19.05% during 2015–2020). The ﬁndings of this study offer much-needed information and reference for academics researching ﬂood risk under climate change.


Introduction
Floods have become a global issue affecting most parts of the world and are one of the most serious natural disasters worldwide. Over the past 40 years, flood events are estimated to have caused damages worth more than 1 trillion USD, while in the past 20 years, floods influenced more than 1.65 billion individuals [1]. Studies show that in recent years, floods occurred more often than other natural hazards, such as earthquakes, extreme precipitation, and droughts [2,3], and floods have become one of the major disasters affecting people's lives and property all over the world [4]. In fact, in the context of a warming climate and thus the intensifying of the hydrological cycle [5,6], the global flood risk may increase in the future [7,8]. For instance, studies show that even under an optimistic climate change scenario, the sea levels is expected to rise by 0.55 m by 2100, putting coastal cities, particularly large ones, at risk [9]. By 2100, the flood frequency is likely to increase significantly in Southeast Asia, East and Central Africa, and much of Latin America [10]. In response to the growing challenge of flooding, a framework from Sendai Framework for Disaster Risk Reduction 2015-2030 (SFDRR) was presented that temporal evolution of global flood risk were analyzed in terms of multiple scales (grid scale, hotspots, national scale, and continental scale). Against the background of growing international focus on preventing disasters and reducing the associated losses, the results of our study can provide a theoretical and technical foundation for policy makers in various countries and regions across the globe to set flood prevention and mitigation targets and measures in specific areas.

Data
In this study, the basic research unit was the grid cell with a 0.15 • × 0.15 • resolution (approximately 18 km × 18 km), and the spatiotemporal distributions of global flood risk were explored from three perspectives: hotspot regions, national scales, and continental scales. The data used were, among others, global administrative boundary data, hydrometeorological data, topographic and geomorphological data, and socio-economic data. The global administrative boundary data were collected from Resource Environment Science and Data Center (https://www.resdc.cn/ accessed on 19 October 2021), while the other data, divided into hazard data and vulnerability data, are explained in the sections below.

Global Flood Hazard Data
After considering the reviews presented by relevant studies [28,33,34] and the availability of data, we used six kinds of data in this study: precipitation, land use, NDVI, river density, soil texture, and DEM (Table 1). Precipitation data were obtained from the GPM project of NASA. In this study, we took 5 years as the time scale to extract the maximum 5-day precipitation (M5DP) of these 5 years. Due to the availability of data, the precipitation index of 2020 could only use the precipitation data of three years, from 2018 to 2020. The river density data and the soil data were gained from OpenStreetMap (OSM) and Agriculture Organization (FAO), respectively. The two hazard indexes (elevation and slope) were extracted from the DEM data, collected from SRTM. Table 1 presents more details. Since, throughout history, hazard factors have been measured on different scales [35], we needed to unify the indicators into the same dimension. Meanwhile, the results of several studies show that the quantile breakpoint method has good applications for unifying the dimensionality of the factors [35,36]. Thus, after literature reviews [35,37], we used the quantile method to classify the hazard factors on the basis of their contribution to flood probability into five categories, 1 (very low hazard), 2 (low hazard), 3 (moderate hazard), 4 (high hazard), and 5 (very high hazard), as shown in Table 2. Table 2. Classes of flood hazard factors and their ratings.

Number Hazard Index Classes Rating
Gridded global datasets for Gross Domestic Product and Human Development Index over 1990-2015 [38] and (2) 2020 economic data from Global dataset of gridded population and GDP scenarios [39].

Flood Risk Index System
Flooding is a result of rainfall generated by abnormal atmospheric activity. Many studies have been conducted on flood risk; however, no unified system has been formed for the selection of indexes [40]. Here, flood risk assessment indexes were considered in terms of hazard and vulnerability. The flood risk index system was generated on the basis of the hazard system theory (three conditions for the formation of floods: disaster-causing factor, disaster-pregnant environment, and hazard-affected body) [41], the principles of index selection [42], and the research results of domestic and foreign scholars [25] (Figure 1). In such a theory, the system only provides a general framework for global flood risk assessment and has a certain reference value. In actual application, it is essential to take into account the unique environmental and socioeconomic conditions of the study area and consider the index system in combination with the resolution and accessibility of data.

Methods
After collating sufficient theoretical knowledge related to flooding, the relevant flowchart was built ( Figure 2). Firstly, the basic data were collected and an index system based on the hazard-vulnerability framework was generated. Then, the index weighting method to be used in this study was determined, i.e., the game theory weighting method (a combination of the TFN-AHP and the EM method) was chosen. Finally, based on the regional integrated flood risk grade (RIFRG) model, the global flood risk assessment and spatiotemporal difference patterns were conducted from multiple perspectives and scales. Figure 1. The index system of global flood risk. Note: M5DP, maximum 5-day precipitation; LU, land use; RD, road density; ST, soil texture; SL, slope; EL, elevation; PD, population density; ED, economic density; BD, building density; FD, farmland density; FPD, female population density; CPD, child population density; EPD, elderly population density; IS, impervious surface; RD, road density; SD, shelter density; HD, hospital density; GPC, GDP per capita.

Methods
After collating sufficient theoretical knowledge related to flooding, the relevant flowchart was built ( Figure 2). Firstly, the basic data were collected and an index system based on the hazard-vulnerability framework was generated. Then, the index weighting method to be used in this study was determined, i.e., the game theory weighting method (a combination of the TFN-AHP and the EM method) was chosen. Finally, based on the regional integrated flood risk grade (RIFRG) model, the global flood risk assessment and spatiotemporal difference patterns were conducted from multiple perspectives and scales.

The Triangular Fuzzy Number-Based Analytic Hierarchy Process
Traditionally, the AHP is weighting method commonly used to assess flood risk. The original AHP method uses pairwise comparisons to represent the relative importance of the assessment factors. However, such pairwise comparisons are somewhat subjective [18]. To reduce the subjectivity to some extent, we invoked fuzzy theory to replace clear numbers. In the TFN-AHP theory, the median value of the triangular fuzzy number represents the maximum likelihood of the assessment model, while the maximum and minimum values refer to the fuzziness corresponding to the maximum likelihood [43,44]. More detailed theoretical presentations and calculation procedures can be found in some stud-

The Triangular Fuzzy Number-Based Analytic Hierarchy Process
Traditionally, the AHP is weighting method commonly used to assess flood risk. The original AHP method uses pairwise comparisons to represent the relative importance of the assessment factors. However, such pairwise comparisons are somewhat subjective [18]. To reduce the subjectivity to some extent, we invoked fuzzy theory to replace clear numbers. In the TFN-AHP theory, the median value of the triangular fuzzy number represents the maximum likelihood of the assessment model, while the maximum and minimum values refer to the fuzziness corresponding to the maximum likelihood [43,44]. More detailed theoretical presentations and calculation procedures can be found in some studies [43,44].

Entropy Weight
Throughout history, entropy was first applied to information theory in 1948 by entropy researcher Shannon as a way to measure the order of a system [45]. Many methods have evolved from entropy theory, such as the maximum entropy algorithm [46][47][48] and the entropy power method [49]. Entropy weighting is an objective, multi-criterium decisionmaking method for optimizing decisions under a set of qualitative, quantitative, and sometimes conflicting factors [49]. As an objective weighting method, based on the information entropy theory, the entropy weight (EW) is reflective of the content of helpful information provided by indicators. The specific calculation steps can be found in previous research studies [50,51].

Game Theory
Subjective weighting (SW) and objective weighting (OW) are the two main types of weighting methods involving indexes. Previous studies indicate that SW and OW methods have their own strengths and weaknesses in different scenarios [52]. In such a theory, the SW method can reflect the subjective preferences and experiences of decision makers. The OW method, on the other hand, has a strong mathematical theoretical foundation and is based on the characteristics of the data themself, avoiding subjectivity to a certain extent. Therefore, a suitable model is needed to combine the advantages of SW and OW. Game theory (GT), a mathematical model of strategic interaction between rational and irrational subjects, specializes in resolving conflicts among two or more participants [53], since it allows the weight information of subjective or objective weights and the most satisfactory weight, also known as the combined weight (CW), to be efficiently used. In this study, the SW method and the OW method were considered as two participants in the flood risk assessment methodology; more details can be found in the two studies [52,54]. The specific calculation process was as follows: (1) We obtain I weights for n indexes according to I categories of weighting methods, since ω i = [ω i1 , ω i2 , . . . , ω im , . . . , ω in ], i = 1, 2, . . . , I, and m = 1, 2, . . . , n. Therefore, we can construct a weight vector: W = {[ω 1 , ω 2 , . . . , ω I ]}; (2) The possible combined weight, ω * = ω * 1 , ω * 2 , . . . , ω * m , . . . , ω * n , is achieved by collecting and combining information on multiple weighting approaches. From this, we can see that ω* is denoted by W, as shown in Equation (1): (3) Suppose there exists a most appropriate linear combination of coefficients α*, such that the deviation between ω* and ω i (i = 1, 2, . . . , I) is minimized to achieve a compromise between the I weights. Thus, the optimization function is to minimize the deviations between ω* and ω i : Moreover, based on the differential nature of the matrix, the terms for the best firstorder derivatives are obtained using Equation (3): Remote Sens. 2022, 14, 5551 8 of 21 Next, Equation (3) is presented in matrix form: (4) The weight coefficients are calculated and then normalized to obtain α*: Eventually, ω* can be obtained as:

Flood Risk Calculation and Gradation
In this study, we quantified the flood hazards using Equation (7). As shown in Table 4, the index weights for 2005, 2010, 2015, and 2020 were obtained using three methods: TFN-AHP, EW, and GT. The equation used is as follows: where H is the flood hazard, A i is the degree of affiliation of each indicator, and ω i is the weight value of each index. Vulnerability, as defined in the IPCC report [55], is the degree to which a system is susceptible to and unable to cope with adverse effects (climate change). In such a theory, the key parameters of vulnerability are exposure, sensitivity, adaptability, and coping capacity. Additionally, the index weights of vulnerability for 2005, 2010, 2015, and 2020 were obtained, as shown in Table 5. The specific equation of flood vulnerability is as follows: where V is flood vulnerability, E is exposure, S is sensitivity, and C is coping capacity.  Flood risk is a comprehensive result of the interaction between the flood (hazard) and the disaster-bearing body (in terms of its vulnerability in relation to its socio-economic conditions, resilience, and mitigation capacity against the flood). Considering this point, the specific definition of flood risk is as follows: where R is the flood risk, H is the flood hazard, and V is the vulnerability to the flood. Referring to some ecological approaches, a risk index that reflects the combined degree of sub-regional flood risk was used. The index was compiled by reclassifying the risk level of each grid into a quantitative value: very low risk = 1, low risk = 2, medium risk = 3, high risk = 4, and very high risk = 5. Specifically, the definitions of the regional integrated flood risk grades (RIFRGs) were calculated using Equation (10): where RIFRG i is the regional integrated flood risk grade for region i, G j is the risk value for grade j, A j is the area of flood risk grade for j in region i, and S j is the entire area of region j.

Spatiotemporal Variations in Global Risk on the Grid Scale
With respect to the three major drivers of floods (disaster-causing factor, disasterpregnant environment, and hazard-affected body), we selected 19 indexes to build the index system on the basis of the hazard-vulnerability framework. Then, combined with the quality and availability of data and other comprehensive considerations, we generated the global flood risk distribution map (2005-2020). Based on the natural breakpoint method, we classified the global flood risk during 2005-2020 into five levels, namely, very low, low, medium, high, and very high ( Figure 3). To verify the accuracy of the proposed model and flood risk results in this study, we performed ROC curve validation based on the global flood location dataset, which we downloaded from the Dartmouth Flood Observatory website (http://floodobservatory.colorado.edu/ accessed on 19 October 2021). The relationship between model performance and the AUC could be classified into four levels [56]: poor (<0.6), moderate (0.6-0.7), good (0.7-0.8), and very good (0.8-1). The validation results showed that the GT model and the flood risk results had a high accuracy, with AUC values of 0.871 (Figure 4). the global flood location dataset, which we downloaded from the Dartmouth Flood Observatory website (http://floodobservatory.colorado.edu/ accessed on 19 October 2021). The relationship between model performance and the AUC could be classified into four levels [56]: poor (<0.6), moderate (0.6-0.7), good (0.7-0.8), and very good (0.8-1). The validation results showed that the GT model and the flood risk results had a high accuracy, with AUC values of 0.871 ( Figure 4).  Since the differences in the spatial distribution of flood risk during 2005-2020 are not obvious, the distribution of flood risk in 2005 was taken as an instance to demonstrate the spatial distribution pattern of global flood risk. In accordance with the results of Fang et al. [16], the global flood risk distribution is closely related to population, economy, and precipitation. As shown in Figure 3, the regions at higher flood risk were primarily located in regions that had high population concentrations, high economic density, abundant precipitation, and low elevation, for example, North China Plain in China, the northern part of India, the Indus River Basin in Bangladesh, the central cities in Indonesia, and Nile River Basin in Egypt. the global flood location dataset, which we downloaded from the Dartmouth Flood Observatory website (http://floodobservatory.colorado.edu/ accessed on 19 October 2021). The relationship between model performance and the AUC could be classified into four levels [56]: poor (<0.6), moderate (0.6-0.7), good (0.7-0.8), and very good (0.8-1). The validation results showed that the GT model and the flood risk results had a high accuracy, with AUC values of 0.871 ( Figure 4).  Since the differences in the spatial distribution of flood risk during 2005-2020 are not obvious, the distribution of flood risk in 2005 was taken as an instance to demonstrate the spatial distribution pattern of global flood risk. In accordance with the results of Fang et al. [16], the global flood risk distribution is closely related to population, economy, and precipitation. As shown in Figure 3, the regions at higher flood risk were primarily located in regions that had high population concentrations, high economic density, abundant precipitation, and low elevation, for example, North China Plain in China, the northern part of India, the Indus River Basin in Bangladesh, the central cities in Indonesia, and Nile River Basin in Egypt.  [16], the global flood risk distribution is closely related to population, economy, and precipitation. As shown in Figure 3, the regions at higher flood risk were primarily located in regions that had high population concentrations, high economic density, abundant precipitation, and low elevation, for example, North China Plain in China, the northern part of India, the Indus River Basin in Bangladesh, the central cities in Indonesia, and Nile River Basin in Egypt.
With respect to the temporal variations in global flood risk, the RIFRG was used for the statistics. As shown in Table 6, the global flood risk showed a gradual upward trend.  1.867 (2015), and 1.935 (2020), which indicated that the risk of global flood increased. A study from World Resources Institute shows that by 2030, as many as 750 million people worldwide are expected to be in 100-year flood zones [14]. In addition, some studies using climate models for future global flood risk projections indicate that global economic losses from floods grow more rapidly than the global economy (as indicated by the proportion of losses to GDP) and that on a global scale, absolute damage could increase 20-fold by 2100 if no action is taken [57].

Spatiotemporal Variations in Global Risk Hotspots
In this study, on the basis of the global flood risk assessment results on the grid scale, 11 global risk hotspot regions were identified using the hotspot analysis tool of ArcGIS. Assuming that each grid had one element, the condition for this grid to be a hotspot was that it had a high value itself and was surrounded by other elements that also had a high value [58]. In other words, for a statistically significant z-score, the higher the z-score was, the tighter the clustering of high values (hotspots) was. In this study, taking the distribution map of risk hotspot regions in 2005 as an example ( Figure 5), there were 11 risk hotspot regions in the world, namely, (1) Japan Sea coast, (2) North China Plain, (3) the Jakarta region in Indonesia, (4) Ganges River Basin, (5) Eastern Mediterranean countries, (6) both sides of the English Channel, (7) Nile River Basin in Egypt, (8) countries around the Gulf of Guinea, (9) Ethiopia region, (10) Mid-Atlantic-Great Lakes region in the United States, and (11) the Rio de Janeiro region in Brazil.
It can be discovered from Figure 5 that global flood risk hotspots were mainly concentrated in Asia, as 5 of these 11 hotspots were in Asia, especially in East and South Asia. The remaining hotspots were scattered across other continents, while Oceania was the only continent without any hotspots. To some extent, precipitation is the main cause of high-risk aggregation, especially in East, Southeast, and South Asia [33,59]. For instance, the Japan Sea coast is located in the western Pacific Ocean and is affected by typhoons all year round, and the probability of flooding due to typhoons and heavy rainfall is much higher here than in other parts of Asia. Both sides of the English Channel are located in the westerly wind belt. According to incomplete statistics, there are more than 200 rainy days throughout the year. Thus, precipitation is abundant. Additionally, the coastal countries are highly developed capitalist countries, so the probability of flooding in the region and the resulting damage are higher than in other parts of Europe. In addition to precipitation, the disaster-pregnant environment and the hazard-affected body itself are also constraints on flood risk. As with most basins, the Nile River Basin is the economic and population concentration of Egypt. As expected, the risk of flooding and erosion is higher in the highly built-up and urbanized coastal areas, with the Nile Delta region being the most flood-prone area along the Egyptian coast [60]. the westerly wind belt. According to incomplete statistics, there are more than 200 rainy days throughout the year. Thus, precipitation is abundant. Additionally, the coastal countries are highly developed capitalist countries, so the probability of flooding in the region and the resulting damage are higher than in other parts of Europe. In addition to precipitation, the disaster-pregnant environment and the hazard-affected body itself are also constraints on flood risk. As with most basins, the Nile River Basin is the economic and population concentration of Egypt. As expected, the risk of flooding and erosion is higher in the highly built-up and urbanized coastal areas, with the Nile Delta region being the most flood-prone area along the Egyptian coast [60]. To explore the changing pattern of global flood risk hotspot regions in a time series, we presented statistics at the different levels of risk and the change in RIFRG values in each hotspot region ( Figure 6). Generally, the pattern of risk change in hotspot regions was consistent with the pattern of global risk change, with a gradual increase in the trend. Especially, the most obvious trends of increasing risk were concentrated along the Japan Sea coast (Figure 6a  To explore the changing pattern of global flood risk hotspot regions in a time series, we presented statistics at the different levels of risk and the change in RIFRG values in each hotspot region ( Figure 6). Generally, the pattern of risk change in hotspot regions was consistent with the pattern of global risk change, with a gradual increase in the trend. Especially, the most obvious trends of increasing risk were concentrated along the Japan Sea coast (Figure 6a have been conducted in recent years on the flood risk in Ethiopia [62]. Additionally, the RIFRG values of the hotspots in the Jakarta region in Indonesia (Figure 6c) and Ganges River Basin (Figure 6d) were the highest among the 11 hotspots, which meant that these two hotspots were at higher flood risk. Meanwhile, the distribution of the different levels of flood risk in these two hotspots was also even, with the other hotspots being mainly dominated by areas at very low risk (i.e., the Japan Sea coast, Eastern Mediterranean countries, and Nile River Basin in Egypt) ( Figure 6).  In relative terms, the countries around the Gulf of Guinea (Figure 6h), the Ethiopian region (Figure 6i), and the Rio de Janeiro region in Brazil (Figure 6k), all showed varying degrees of increasing and then decreasing flood risk. In particular, the Ethiopian region had the highest increase in risk among these three hotspot regions. Throughout history, floods have been among the most prominent disasters in Africa. However, few studies have been conducted in recent years on the flood risk in Ethiopia [62]. Additionally, the RIFRG values of the hotspots in the Jakarta region in Indonesia (Figure 6c) and Ganges River Basin (Figure 6d) were the highest among the 11 hotspots, which meant that these two hotspots were at higher flood risk. Meanwhile, the distribution of the different levels of flood risk in these two hotspots was also even, with the other hotspots being mainly dominated by areas at very low risk (i.e., the Japan Sea coast, Eastern Mediterranean countries, and Nile River Basin in Egypt) ( Figure 6).
It is challenging for global government agencies to mitigate the risk from increasing instances of flooding. The current rapid expansion of urban flood risk suggests that previous urban designs have not given sufficient attention to the management of flood risk, particularly in the Asian region [61]. Thus, future policies should prioritize land use planning in flood-exposed areas to minimize construction in flood-prone areas; mitigate damage from unavoidable flooding; and encourage urban growth and expansion, including migration and redevelopment, in flood-safe areas. Some initiatives may contribute to these goals, for instance, the government could take additional measures to strengthen flood prevention and mitigation to safeguard crucial urban infrastructure, such as shelters, hospitals, and railroads. Even in times of no flooding, the government should take measures to raise awareness of flood risk among residents [63]. Additionally, implementing flood insurance may be an effective means of controlling economic losses from floods [64].

Spatiotemporal Distribution of Flood Risk on the National Scale
Using the RIFRG model, the global flood risk on the national scale was calculated and then classified into five levels with reference to the natural breakpoint method (Figure 7). As shown in Figure 7, most countries were at low and very low risk, with high-risk countries (RIFRG values greater than 2.5) being concentrated in East and South Asia and Central and Western Europe. Specifically, Japan, North Korea, South Korea, Vietnam, the Philippines, India, Bangladesh, Pakistan, Italy, Germany, and the Netherlands had higher RIFRG values. In addition, five countries (India, Bangladesh, Pakistan, the Netherlands, and Madagascar) were at very high risk for the period 2005-2020, indicating that these five countries were among the countries with the highest risk of flooding during this 15-year period globally.
instances of flooding. The current rapid expansion of urban flood risk suggests that previous urban designs have not given sufficient attention to the management of flood risk, particularly in the Asian region [61]. Thus, future policies should prioritize land use planning in flood-exposed areas to minimize construction in flood-prone areas; mitigate damage from unavoidable flooding; and encourage urban growth and expansion, including migration and redevelopment, in flood-safe areas. Some initiatives may contribute to these goals, for instance, the government could take additional measures to strengthen flood prevention and mitigation to safeguard crucial urban infrastructure, such as shelters, hospitals, and railroads. Even in times of no flooding, the government should take measures to raise awareness of flood risk among residents [63]. Additionally, implementing flood insurance may be an effective means of controlling economic losses from floods [64].

Spatiotemporal Distribution of Flood Risk on the National Scale
Using the RIFRG model, the global flood risk on the national scale was calculated and then classified into five levels with reference to the natural breakpoint method ( Figure  7). As shown in Figure 7, most countries were at low and very low risk, with high-risk countries (RIFRG values greater than 2.5) being concentrated in East and South Asia and Central and Western Europe. Specifically, Japan, North Korea, South Korea, Vietnam, the Philippines, India, Bangladesh, Pakistan, Italy, Germany, and the Netherlands had higher RIFRG values. In addition, five countries (India, Bangladesh, Pakistan, the Netherlands, and Madagascar) were at very high risk for the period 2005-2020, indicating that these five countries were among the countries with the highest risk of flooding during this 15year period globally. To explore more deeply the changes in the risk values over the time series for individual countries, the RIFRG values on the national scale were reclassified into five categories, with changes greater than or equal to one level being considered significant. Figure  8 indicates that flood risk showed the following trend: significantly increasing, leveling off, and then significantly increasing again. From 2005 to 2010 (Figure 8a), more than 10 countries were at significantly increased risk (Kazakhstan, Tajikistan, Ukraine, Sweden, Norway, Angola, South Africa, Ecuador, etc.), while a few countries were at significantly To explore more deeply the changes in the risk values over the time series for individual countries, the RIFRG values on the national scale were reclassified into five categories, with changes greater than or equal to one level being considered significant. Figure 8 indicates that flood risk showed the following trend: significantly increasing, leveling off, and then significantly increasing again. From 2005 to 2010 (Figure 8a), more than 10 countries were at significantly increased risk (Kazakhstan, Tajikistan, Ukraine, Sweden, Norway, Angola, South Africa, Ecuador, etc.), while a few countries were at significantly decreased risk, namely, Ireland, Denmark, and Turkmenistan. Subsequently, in 2010-2015, the number of countries at a significantly increased risk was about the same as the number of countries at a decreased risk (Figure 8b). However, the trend in risk change for the period of 2015-2020 returned to an increasing trend (Figure 8c), and the increasing trend was even greater than that for the period of 2005-2010 (Figure 8a). Specifically, these countries at significantly increased risk were mainly located in Asia and Europe, while countries at significantly decreased risk were mainly located in Africa (Figure 8c). decreased risk, namely, Ireland, Denmark, and Turkmenistan. Subsequently, in 2010-2015, the number of countries at a significantly increased risk was about the same as the number of countries at a decreased risk (Figure 8b). However, the trend in risk change for the period of 2015-2020 returned to an increasing trend (Figure 8c), and the increasing trend was even greater than that for the period of 2005-2010 (Figure 8a). Specifically, these countries at significantly increased risk were mainly located in Asia and Europe, while countries at significantly decreased risk were mainly located in Africa (Figure 8c). From the above elaboration, there were significant differences among countries affected by floods at the global level. Therefore, we investigated the relationship between RIFRG values and national income levels for each country from 2005 to 2020. According to the World Bank classification, countries are classified into four income levels: low in- From the above elaboration, there were significant differences among countries affected by floods at the global level. Therefore, we investigated the relationship between RIFRG values and national income levels for each country from 2005 to 2020. According to the World Bank classification, countries are classified into four income levels: low income, lower-middle income, upper-middle income, and high income. The results presented in Figure 9 showed two trends in global flood risk on the national scale. Firstly, these results indicated that overall flood risk increased for all the countries in the world between 2005 and 2020, with the most pronounced increase in the period of 2015-2020 in particular. Secondly, a country's flood risk was positively correlated with the country's income level; in short, the flood risk of high-income countries was much higher than that of low-income countries, and the gap between the two tended to increase over time. Meanwhile, some studies suggest that globally, absolute damage from flooding could increase 20-fold by 2100 if no action is taken [57]. Thus, regardless of the income level, more efforts should be invested in future flood prevention and management, especially in high-income countries. sented in Figure 9 showed two trends in global flood risk on the national scale. Firstly, these results indicated that overall flood risk increased for all the countries in the world between 2005 and 2020, with the most pronounced increase in the period of 2015-2020 in particular. Secondly, a country's flood risk was positively correlated with the country's income level; in short, the flood risk of high-income countries was much higher than that of low-income countries, and the gap between the two tended to increase over time. Meanwhile, some studies suggest that globally, absolute damage from flooding could increase 20-fold by 2100 if no action is taken [57]. Thus, regardless of the income level, more efforts should be invested in future flood prevention and management, especially in high-income countries. In this study, the top 20 countries with the highest RIFRG values were counted in order to assess the distribution of countries at the highest global flood risk. As shown in Table 7, the country at the highest risk of flooding was Singapore, with RIFRG values of 4.987, 4.987, 4.993, and 4.993 for 2005, 2010, 2015, and 2020, respectively. According to statistics, among these 20 countries, 11 were developed countries, namely, Singapore, Mauritius, Netherlands, Bahrain, Belgium, Liechtenstein, Trinidad and Tobago, Japan, South Korea, Germany, and Israel. This showed that the risk of flooding was closely correlated with the distribution of population and the economy of each country, and generally speaking, the more densely populated and economically developed countries were at a higher risk of flooding.
In terms of changes in the time series, the flood risk for these 20 countries showed an increasing trend over the period of 2005-2020, consistent with the trend on the grid scale. The two countries with the highest rate of change in risk in 2015-2020 were Haiti and El Salvador, with Haiti having the highest negative growth rate of −13.48% (2015-2020) and El Salvador having the highest positive growth rate of 19.05% from 2015-2020 (Table 7). Meanwhile, some studies point out that between 1986 and 2013, El Salvador experienced increased flood risk in many areas due to urbanization, and in the 2030 scenario, urban coverage would be more than double the urban coverage in 2013 [65]. Critically, due to the existing level of urbanization in El Salvador, current flood protection measures and plans may not be sufficient to mitigate future flood risks [65]. In addition, Vietnam was the only one of these 20 countries where the flood risk continued to grow in all three phases, and the growth trend kept rising, increasing from 0.11% in 2005-2010 to 1.92% in In this study, the top 20 countries with the highest RIFRG values were counted in order to assess the distribution of countries at the highest global flood risk. As shown in Table 7, the country at the highest risk of flooding was Singapore, with RIFRG values of 4.987, 4.987, 4.993, and 4.993 for 2005, 2010, 2015, and 2020, respectively. According to statistics, among these 20 countries, 11 were developed countries, namely, Singapore, Mauritius, Netherlands, Bahrain, Belgium, Liechtenstein, Trinidad and Tobago, Japan, South Korea, Germany, and Israel. This showed that the risk of flooding was closely correlated with the distribution of population and the economy of each country, and generally speaking, the more densely populated and economically developed countries were at a higher risk of flooding. In terms of changes in the time series, the flood risk for these 20 countries showed an increasing trend over the period of 2005-2020, consistent with the trend on the grid scale. The two countries with the highest rate of change in risk in 2015-2020 were Haiti and El Salvador, with Haiti having the highest negative growth rate of −13.48% (2015-2020) and El Salvador having the highest positive growth rate of 19.05% from 2015-2020 (Table 7). Meanwhile, some studies point out that between 1986 and 2013, El Salvador experienced increased flood risk in many areas due to urbanization, and in the 2030 scenario, urban coverage would be more than double the urban coverage in 2013 [65]. Critically, due to the existing level of urbanization in El Salvador, current flood protection measures and plans may not be sufficient to mitigate future flood risks [65]. In addition, Vietnam was the only one of these 20 countries where the flood risk continued to grow in all three phases, and the growth trend kept rising, increasing from 0.11% in 2005-2010 to 1.92% in 2010-2015 and to 2.89% in 2015-2020. This is due, in large part, to Vietnam's rapid population expansion, accelerated urbanization, and industrial growth in recent years [66]. In relative terms, the flood risk in Asia increased, which meant that Asia is expected to be one of the continents most prone to and most affected by floods in the future. Compared to Asia, North America was the continent at the lowest risk (with RIFRG values of 1.717, 1.735, 1.760, and 1.837 for 2005, 2010, 2015, and 2020, respectively). Meanwhile, Europe was the continent with the second lowest flood risk, in the sense that the flood prevention infrastructure could be strengthened through a booming economy and advanced technology, greatly improving human response to floods and thus reducing human casualties and economic losses due to floods [31]. Among these six continents, Africa was at low risk due to its low flood hazard [67], with the most significant reduction in risk from 2010 to 2015 (RIFRG reduction of 0.051, Table 8).

Implications and Limitations
To the best of our knowledge, current global flood risk studies mainly take into account population mortality and economic loss rates [31]. This method ignores to some extent the interactions between the intrinsic factors of hazard and vulnerability, and the results present only a crude spatial distribution of the global flood risk on the national scale. On the basis of the studies on flood risk, in this study, we constructed a framework for analyzing the multi-scale spatiotemporal patterns of global floods. In this framework, we tried to start from the conditions of flood risk generation (disaster-causing factors, disaster-pregnant environment, and hazard-affected body) based on the grid scale and also integrated the components and interactions of the factors within hazard and vulnerability. Subsequently, we comprehensively considered the spatial and temporal distribution patterns of global flood risk, the underlying patterns and causes from multiple perspectives based on the RIFRG model. In relative terms, our results had high precision, validated using ROC curves (AUC value of 0.871 for risk results), EM-DAT data comparison, literature comparison, and other methods. The findings demonstrated that global flood risk was still on the rise under the current disaster prevention measures. From these results, patterns in the spatial distribution and temporal evolution of global flood risk highlighted the variations between disasters and natural hazards defined by human behavior, providing a much-needed perspective on the risk of human influence on climate [68,69]. The framework presented here can provide a reference and basis for other scholars to investigate the spatiotemporal distribution patterns of large-scale flood risk.
Although progresses and findings were obtained, here, some limitations still remained. Firstly, due to the difficulty in data collection, some of the data were sourced differently between 2005-2015 and 2020. Despite the fact that the data used in this study had a high degree of accuracy in previous studies, they may have also resulted in incomprehensiveness and loss of some accuracy in flood risk assessment. Then, to some extent, we may have somehow overlooked spatial heterogeneity due to the large size of the study area, and some common flood indexes were not taken into account (i.e., aspect, extreme precipitation data, and some normalized difference water indexes). Additionally, the simulation and prediction of future global flooding based on the CMIP6 model is a current hot topic, and relevant research can be conducted in the future.

Conclusions
Based on the hazard-vulnerability framework, this study explored the spatiotemporal patterns of the global flood risk on four scales for 2005-2020: the grid scale, hotspots, the national scale, and the continental scale. As per the results, the global flood risk increased during 2005-2020, and the high-risk areas were mainly located in areas with a high population density, a high economic density, abundant precipitation, and low elevation. The hotspot analysis showed that there were 11 risk hotspot areas globally, mainly located in the capital city areas where the population is concentrated and economically developed and around several major basins in the world. Specifically, East Asia, Southeast Asia, and South Asia were among the regions at the highest flood risk, with four risk hotspots in these regions. From the national-scale perspective, the high-risk countries (RIFRG values greater than 2.5) were concentrated in East Asia, South Asia, and Central and Western Europe. Generally, the flood risk of a country was positively proportional to the country's income level, with the risk in low-income countries being much lower than the risk in highincome countries, and the gap between the two tended to increase over time. Additionally, developed countries accounted for most of the 20 countries of the world at the highest flood risk. The countries with the highest rate of change in risk from 2005 to 2020 were Haiti and El Salvador, with Haiti having the highest negative growth rate of (−13.48% in 2015-2020) and El Salvador having the highest positive growth rate (19.05% in 2015-2020).