By using the data from 15 countries in Asia, this study aims to improve the current global flood risk assessment methods in the aspects of vulnerability proxy selection and a risk calculation formula. In estimating global flood risk, the current methods treat vulnerability in a very simplistic manner. Based on recent literature and empirical findings, this study classifies vulnerability into susceptibility (in terms of marginalized groups, unplanned urbanization, and weak governance), and coping capacity. Each of the four components is, in light of global data availability, expressed by eight proxies, namely, age-related dependency ratio, undernourishment prevalence, urbanization growth rate, deforestation, corruption perceptions index, and three core scores from the Hyogo Framework for Action. Regarding the risk calculation formula, this study tries to break through the limitations of the multiple regression, which is commonly used for estimating coefficients and parameters, by applying the partial least squares regression (PLSR) method. The PLSR method makes it possible to include many proxies in the formula without lowering the explanatory power, even when the proxies are highly correlated.

Acronyms

  • AQUASTAT

    FAO's global information system on water and agriculture

  • CPI

    Corruption perceptions index

  • CRED

    Centre for Research on the Epidemiology of Disasters

  • DRR

    Disaster risk reduction

  • EM-DAT

    Emergency disasters database

  • FAO

    Food and Agriculture Organization of the United Nations

  • GDP

    Gross domestic product

  • GFDRA

    Global flood disaster risk assessment

  • GIS

    Geographic information systems

  • HFA

    Hyogo Framework for Action

  • IPCC

    Intergovernmental Panel on Climate Change

  • MR

    Multiple regression

  • NIPALS

    Non-linear iterative partial least squares

  • PCA

    Principal component analysis

  • PLS

    Partial least squares

  • PLSR

    Partial least squares regression

  • TI

    Transparency International

  • UNISDR

    United Nations Office for Disaster Risk Reduction

  • VIP

    Variable importance in the projection

  • WHO

    World Health Organization

Introduction

After the World Conference on Disaster Reduction held in 2005, numerous global resolutions and expert opinions expressed the view that flood management should make a paradigm shift from conventional practices relying on post-event reconstruction, and humanitarian aid to greater investment in preventive actions based on the disaster risk reduction concept (UNISDR, 2011; ADB-IED, 2012). As a consequence, many methods for global flood disaster risk assessment (GFDRA) have been developed to compare the risk between countries in a comprehensive, integrated, multidisciplinary approach, and they encourage globally consolidated efforts on disaster risk reduction (DRR). The United Nations Office for Disaster Risk Reduction (UNISDR) (2004, 2013) requires scientific methods to satisfy multiple purposes: (i) providing the reference level of global or countrywide risk in order to establish the UN-level targets; (ii) helping inter-governmental development banks and private sectors understand the need to protect people and assets in a policy-neutral manner; and (iii) stimulating risk-prone countries to establish national agendas, institutions, and policies, to launch more detailed planning and engineering, and to strengthen community-based capacity-building programmes. Therefore, it can be said that GFDRA methods are meaningful only when they adequately identify reference levels of flood risk, quantify human-induced risk drivers, and monitor governments' efforts toward DRR.

Problem definition

No existing GFDRA method has received sufficient methodological agreement. Recent studies (Barredo et al., 2007; IHP, 2012; ICHARM, 2013) have pointed out that GFDRA methods are largely challenged in terms of terminologies, data availability, flood impact models for hazard assessment, vulnerability proxy selection, and risk calculation formula. Among these issues, this study specifically attempts to justify the selection of vulnerability proxies and then develop a risk calculation formula.

This study views flood risk as expected death tolls due to flood disasters. Previous studies evaluating flood fatalities on a global basis include UNDP-BCPR (2004), Dilley et al. (2005), and Peduzzi et al. (2009), which commonly have direct or indirect relations to the development of the UN's global platforms. Moreover, these studies more or less follow UNDP-BCPR's approach to selecting vulnerability proxies, and deriving the risk calculation formula. However, this approach has the following two important, interrelated problems.

Vulnerability is over-simplified in estimating flood risk

In the case of targeting a large-scale area such as a country, it is very hard to define the vulnerability processes aggravating fatalities (Robert et al., 2009). In addition, using authorized data applicable to global flood vulnerability is a big challenge (IHP, 2012). The sources of such data are mainly confined to global statistics of the UN system, such as the World Development Indicators, although there have been scientific efforts, for example, the Global Rural-Urban Mapping Project conducted by the Columbia University Center for International Earth Science Information Network, in order to digitalize socio-economic statistics. It is therefore accepted that vulnerability is simplified to a certain extent in GFDRA methods. Nevertheless, considering poverty as a factor of vulnerability is certainly problematic. UNDP-BCPR (2004), Barredo et al. (2007) and Peduzzi et al. (2009) adopted individual purchasing power, that is, gross domestic product (GDP) per capita, as the proxy for vulnerability. Similarly, Dilley et al. (2005) used the national wealth index as a yardstick to determine vulnerability. These studies might inform flood-prone countries that poverty should be solved to eliminate human-induced risk drivers. Poverty is obviously related to flood vulnerability, because poverty is the root cause of most issues of less developed countries. Nevertheless, ‘not all poor people are vulnerable to disasters, nor are the poor all vulnerable in the same way, and some people who are not poor are also vulnerable’ (Hilhorst & Bankoff, 2004). In addition, eradicating poverty is one of the most difficult goals for all mankind (Wisner, 1993; Wisner et al., 2004). As far as poverty is concerned as a first-hand factor of vulnerability, GFDRA methods become less useful in that they entirely keep silent about what risk drivers are manageable and how enthusiastically governments strive to reduce such drivers (Barredo et al., 2007; Paul, 2011). It should be noted that the purpose of measuring vulnerability is ‘to help bridge the gaps between the theoretical concepts of vulnerability and day-to-day decision making’ (Birkmann, 2007).

The multiple regression method is technically inadequate to combine hazard and vulnerability into flood fatalities

Previous studies have truly attempted to take various socio-economic proxies into consideration. These proxies include age-related dependency ratios, the number of physicians, the number of hospital beds, life expectancy, literacy rates, and the number of radios as well as poverty. However, the studies have had technical problems in translating these proxies into fatalities. Since the work by UNDP-BCPR (2004), multiplicative equations, such as Equations (1)–(3) below, have been used to explain flood fatalities from proxies. (Using these equations is a very common way to handle situations where the effect of predictors on response is neither necessarily linear nor necessarily independent of one another. The model structure in Equation (3) is thus relatively free of assumptions, encouraging parameters to be specified analytically. It should be noted that Equation (3) requires predictors to be positive and dimensionless. Therefore, predictors need to be expressed in terms of standardized values.) 
formula
1
 
formula
2
 
formula
3
where R is the number of flood fatalities, E is the number of affected people, vj is a proxy selected for the jth attribute of vulnerability, c and C are the statistical coefficients for factors not to be considered, a is the parameter for affected people, and bj is the jth vulnerability proxy. Previous researchers have preferred using the multiple regression (MR) method to obtain the values of coefficients and parameters in Equation (3). However, an important problem still remains unsolved: MR requires independence between all predictors on the right side. If the independence condition is not satisfied, MR picks out few predictors to avoid the multicollinearity (known as a statistical phenomenon in which two or more predictors are highly correlated so that the response is erratically sensitive to small changes in the values of predictors). Equation (3) is fitted with a few predictors, yet to the maximum, by using the ordinary least squares estimation. Due to these characteristics, previous studies using the MR have failed by including many vulnerability proxies. For instance, Peduzzi et al. (2009) tested five vulnerability proxies but finally chose GDP per capita solely. Then, they just added that ‘we cannot place two indicators (proxies) that are strongly correlated in the same model’.

In addition, previous studies have not examined the possibility that a multiplicative formula might vary depending on flood severity. For example, let us consider an area where a flood is not severe, affecting only a few residents. In this case, a simple expectation is that most fatalities might occur in marginalized groups. In other words, people might not be killed if they are able to behave without support from others and physically handle the inundation depth. If people are sufficiently provided with disaster-related education, they should be able to take effective actions to reduce fatalities. On the contrary, let us consider another area where a flood is very serious, affecting a large proportion of the population, and where a state of emergency has been declared. When flooding occurs on this scale, it matters little whether people are young or old, or how well they are educated about disasters. Instead, how easily they can evacuate to safer zones might be more important to reduce fatalities. In this sense, it is necessary to ascertain whether the multiplicative formula should be differently defined according to flood severity.

Purpose and scope

This study was conducted as an attempt to solve the aforementioned problems. Thus, it had the following two purposes:

  1. This study addressed the problem that vulnerability is over simplified by a few vulnerability proxies related to poverty. Vulnerability was structured and defined in terms of proxies contextually meaningful for fatality-causing flood disasters. In addition, this study tried to statistically justify the importance of the defined proxies.

  2. This study addressed the problem that the MR method cannot incorporate various vulnerability proxies into risk calculation formula because of a high correlation among the proxies. The MR method (as the existing method) and a new method (as an alternative method) were applied to develop the multiplicative formula individually. After comparing merits and demerits between the two methods, the new method proved to be more useful in developing the formula.

Through the improvement of the GFDRA method, this study is expected to make two contributions. First, it has identified which proxies are statistically significant for flood fatalities. Hence, the results imply political recommendations about what actions are necessary to reduce the anthropogenic aspect of flood risks. Second, a risk calculation formula is suggested, although it will obviously require further refinements. The authors believe that the importance of the formula lies in its practicality; the formula will be a good tool to enhance various stakeholders' understanding of flood risks in terms of widely used proxies and the indicator correlated with real consequences, such as death tolls. In addition, it can be used to operationalize the complexity arising from the relations among the risk components, choose significant vulnerability factors to be considered, and then specify countries at risk. It is therefore expected that the formula will give the first risk indication necessary to stimulate more elaborate risk assessments.

The aforementioned problems will be addressed in relation to Asian cases. Asia is well known as a flood-prone region; therefore, there have been intensive endeavours in the region to establish flood forecasting and early warning systems. Although it seems that the trend of flood fatalities in the region is declining slightly, based on 2000–2010 global disaster records (EM-DAT, the emergency disasters database), Asia still recorded about 70% of global death tolls due to flood (that is, 3,949 out of 5,678 persons per year).

Global flood disaster risk assessment

Basic concepts used in the GFDRA method

Because of a special focus on flood disaster, terminologies in the disaster risk discipline are adopted. Thus, risk is considered not as a purely probabilistic term but as ‘the expected losses from a particular hazard to a specified element at risk’ (United Nations Disaster Relief Organization, 1979). This study selected flood fatalities as ‘the expected losses’. Hence, the definition is specifically expressed as ‘the expected fatalities from flood hazard to people at risk’. In the 1970s, O'Keefe et al. (1976) and Wisner (1977) stated that disasters are caused by internal, human-induced conditions as well as external, natural phenomena. Since then, flood disaster risk has been perceived as a product of hazard and vulnerability. Hazard is often estimated by the frequency of occurrence of an event generating the hydrological impact beyond a specified level, as in UNDP-BCPR (2004). However, it is said that vulnerability is multidimensional, and that its measurement requires an integrated understanding of physical, social, economic, and institutional factors inherent in the areas. Recently, experts have shown a tendency to separate demographical factors, that is, population or population density, from other vulnerability attributes, and then designate them as the exposure coefficient. According to Robert et al. (2009), it is, on one hand, because the exposure concept is clearer compared with other vulnerability factors, and also because it is easy to quantify the exposure coefficient from national statistics or the geographic information systems (GIS)-based population distribution data. On the other hand, when the exposure coefficient is multiplied by hazard occurrence frequency, it is possible to infer the expected number of affected people in the hazardous areas.

The remaining attributes of vulnerability are conceptually obscure, yet they are becoming more and more important in GFDRA methods. For example, Peduzzi et al. (2009) state that the ‘least developed countries represent 11% of the population exposed to hazards but account for 53% of casualties’. This inequality is a matter of great concern in relation to global DRR, and can be analysed by vulnerabilities other than hazard. According to the dualistic structure of vulnerability (Wisner, 2002), some attempts have been made to divide these vulnerability attributes into internal conditions increasing or decreasing disaster risks. The former is susceptibility encompassing difficulties in overcoming the negative impacts of hazardous events, whereas the latter is coping capacity related to positive resources to deal with them. Hence, susceptibility and coping capacity correspond well to human-induced risk drivers and governments' efforts toward DRR.

Selection of proxies for vulnerability

On a large scale such as for a country, whether vulnerability is adequately handled largely depends on the selection of proxies. After extensively reviewing previous studies on flood vulnerability and examining global data availability, the authors decided to select vulnerability with eight proxies for this study.

Susceptibility: marginalized groups

It is well known that certain groups are particularly vulnerable to natural disasters. Regarding flood fatalities, marginalized groups in age and health have been seriously discussed (UNISDR, 2009). This is because they often have less access to information and serious difficulty in taking individual actions to prepare for a flood. At the time of inundation, people in these groups often need support from other groups for evacuation. Accordingly, they often experience disproportional fatalities. For marginalized groups, two proxies were used: age-related dependency ratio (%), and undernourishment prevalence (%). The age-related dependency ratio was originally defined by Shryock & Siegel (1975) to compare the population structure and measure productivities related to the age distribution. It is defined by the ratio of those typically not in the labour force (people with ages ≤ 14 or ≥65 are considered to be dependents) and those in the labour force (people aged 15–64 as productive). In this ratio, the term ‘dependents’ does not refer to bodily weakness; rather, it refers to exclusion from the labour force. For this reason, special caution should be taken when this proxy is interpreted from the GFDRA viewpoint. Since this proxy has been regularly announced as one of the World Development Indicators, the data have been available from the online database of the World Bank. Undernourishment prevalence was alternatively chosen because the global data necessary to estimate the number of patients were unavailable. Hence, in using this proxy, it is assumed that the number of patients would increase with undernourishment. Indeed the World Health Organization (WHO) considers undernourishment to be heavily responsible for infectious diseases, such as malaria and diarrhoea, in less developed countries, saying that ‘malnutrition is the single most important risk factor for disease’ (Nutrition for Health and Development, 2000). Along with the World Food Programme, the Food and Agriculture Organization of the United Nations (FAO) (2009) first defined undernourishment prevalence as the ‘probability that an individual randomly selected from a population is found to be undernourished’ and evaluated the intake adequacy through benchmarking studies on dietary energy requirements. The results are available in the AQUASTAT online database.

Susceptibility: unplanned urbanization

Urbanization has adverse effects on the environment, especially when the urban growth rate does not co-evolve with carrying capacity, including management capabilities, natural resources, and basic service supplies. These effects are related to several mechanisms increasing vulnerability to flood, which are collectively called ‘unplanned urbanization’ (UNISDR-AP, 2012). First, fast growth of urban population leads to environmental deteriorations, such as increased surface imperviousness and deforestation, which makes peak discharges intensive and rapid. Second, residential districts expand to potential flood inundation zones, which leads to greater risk of flood disasters that will affect illegal settlements and socially weak persons. Third, urban expansion lowers local governments' motives for protecting marginalized groups from flood disaster. This is well illustrated by Fernandez & Sanahuja (2012), who reveal the increasing demarcation between the rich and the poor, and the decreasing investment in protecting socially weak persons in Latin America.

This study considered two proxies in measuring unplanned urbanization. The first was the urbanization growth rate (annual %), which refers to the population growth rate in urban areas set by national statistical offices. The data are regularly announced as one of the World Development Indicators of the World Bank. The second was deforestation defined as the percentage of land area not covered by forest (natural or planted stands of trees of at least 5 m). The proxy can be calculated from forestation data in the Millennium Development Goals Database of the United Nations Statistics Division.

Susceptibility: weak governance

It is often argued that more corrupt countries experience higher fatalities than less corrupt ones (for example, Ferreira, 2011). Even if a government operates hazard monitoring instruments, and stipulates high-level building codes and strict land uses, the fatalities do not naturally decrease unless its governance is transparent and accountable. More importantly, people say that countries with weak governance often consume the budget prepared for flood defence for other political purposes. For example, a country established a flood control agency for effective flood management projects and assigned around US$75 billion for the period 1977–2010. In spite of the huge investment a newspaper (The Nation, 2010) reported that ‘progress to control flooding remains at zero level, as most of the projects did not witness any physical work on the ground’. It also added that large parts of the budget were not ultimately allocated to construction costs.

The authors decided to use the corruption perceptions index (CPI), which Transparency International (TI) estimates through expert assessments and opinion surveys. This index refers to ‘the misuse of public power for private benefit’ (TI, 2010). It should be noted that CPI values were adjusted to assign 0 and 100 scores to best and worst countries, respectively (because original CPI values are the opposite).

Coping capacity: governments' efforts toward disaster risk reduction

Along with the projections of the Intergovernmental Panel on Climate Change (IPCC) and the Hyogo Framework for Action (HFA), many experts (Gleick, 2003; Pahl-Wostl, 2007; Lee et al., 2011; Schelfaut et al., 2011) have contended that adaptation and resilience should be revisited to cope with the uncertainties in forecasting hydrological hazards. Consequently, they have suggested that flood risk reduction be addressed by improving coping capacity ‘more softly’ or with non-structural means. In particular, early warning systems, community solidarity, and disaster-related education have received a great deal of attention as measures of governments' efforts toward DRR, especially for the purpose of reducing flood fatalities. It is obvious that early warning systems are important to save lives when floods occur (Rogers & Tsirkunov, 2010; UNISDR, 2010). These systems assist local authorities in evacuating residents at risk to shelters or other safer places with adequate timing, water infrastructure managers in shifting from the standard operation rules, and hospitals and aid agencies in perceiving needs for preparations. The importance of community solidarity was well documented by ADPC (2002) and Iglesias (2011). They showed that because a community is the basic unit reacting first to the occurrence of a flood hazard, community solidarity helps residents share information channels and then make well-organized decisions to implement damage mitigation behaviour. Regarding disaster-related education, it is easily found that capacity-building programmes have enabled local authorities and residents to wisely reduce flood damage (for more details, see Osti & Miyake (2011), who compiled experiences in Asia). To quantify the level at which a country has made these efforts, this study used three HFA core scores: P2-C3 score (the capacity for risk assessment and early warning), P1-C3 score (the community participation and decentralization in DRR), and P3-C2 score (the DRR in education and training). To monitor governments' achievements in the five priority areas specified in HFA, the UNISDR regularly requests governments to submit national progress reports, and reviews them for two years. After that, UNISDR evaluates the countries according to 20 core scores on a 5-point scale (1 = minor achievement, 5 = comprehensive achievement). It should also be noted that any proxies related to structural means, including dams, dykes, and floodwalls, were not selected because it was impossible to collect authorized and insightful data over many countries.

Method

Defining the multiplicative formula and test cases

Using the selected vulnerability proxies and the multiplicative formula, Equation (4) hypothetically presents how many fatalities would occur in the ith test case (see Table 1 for notation and data sources): 
formula
4
Table 1.

Definition of a test case Ti.

Notation Proxies Units Data sources [access] 
Ri Flood risk (flood fatalities) persons/1,000 km2/year Calculated from disaster statistics in the EM-DAT of the Centre for Research on the Epidemiology of Disasters (CRED) [http://www.emdat.be/
Ei Affected people persons/1,000 km2/year 
 Age-related dependency ratio World Development Indicators of the World Bank [http://data.worldbank.org/data-catalog/world-development-indicators
 Undernourishment prevalence AQUASTAT of the FAO [http://www.fao.org/nr/aquastat/
 Urbanization population growth %/year World Development Indicators of the World Bank [http://data.worldbank.org/data-catalog/world-development-indicators
 Deforestation Calculated from forestation data in the Millennium Development Goals Database [http://data.un.org/
 CPI 0–100 scale 2011 corruption perceptions index of the TI [http://www.transparency.org/
 Community solidarity score 1–5 scale Prevention Web of UNISDR [http://www.preventionweb.net/
 Early warning score 1–5 scale 
 DRR education score 1–5 scale 
Notation Proxies Units Data sources [access] 
Ri Flood risk (flood fatalities) persons/1,000 km2/year Calculated from disaster statistics in the EM-DAT of the Centre for Research on the Epidemiology of Disasters (CRED) [http://www.emdat.be/
Ei Affected people persons/1,000 km2/year 
 Age-related dependency ratio World Development Indicators of the World Bank [http://data.worldbank.org/data-catalog/world-development-indicators
 Undernourishment prevalence AQUASTAT of the FAO [http://www.fao.org/nr/aquastat/
 Urbanization population growth %/year World Development Indicators of the World Bank [http://data.worldbank.org/data-catalog/world-development-indicators
 Deforestation Calculated from forestation data in the Millennium Development Goals Database [http://data.un.org/
 CPI 0–100 scale 2011 corruption perceptions index of the TI [http://www.transparency.org/
 Community solidarity score 1–5 scale Prevention Web of UNISDR [http://www.preventionweb.net/
 Early warning score 1–5 scale 
 DRR education score 1–5 scale 
As in Table 1, flood fatalities and affected people were re-scaled to the same area, or 1,000 km2. This was intended to equalize them in land area, which largely differs among countries. The ith test case (ith test pattern) Ti was defined as (Equation (5)): 
formula
5

The following conditions were used in collecting the test cases:

  1. The study sites were confined to 15 countries with consideration of data availability for selected indicators: Bangladesh, Cambodia, India, Indonesia, Japan, Kazakhstan, Korea, Laos, Nepal, Pakistan, the Philippines, Tajikistan, Thailand, Turkey, and Vietnam.

  2. The temporal range was confined to the period 2007–2012.

  3. The cases where there had been no fatalities or affected people were excluded. Because EM-DAT is used to build the multiplicative formula, zero values do not necessarily mean no death, or no influence (Paul, 2011). Those cases were considered as suspicious.

Based on these three conditions, 64 cases were collected in total (i = 15 countries × 6 years − 26 suspicious cases). Among all cases, 41 cases where the number of affected people had been more than 263 persons per 1,000 km2 were used to build the multiplicative formula for major flood severity, whereas the 23 remaining cases were used for minor flood severity. The traditional way to measure flood severity is estimating return periods for hydrological characteristics, for example, peak river discharge. On the country scale, however, the return period concept becomes unclear because spatial heterogeneity is very high (Barredo et al., 2007). Alternatively, this study conducted a clustering analysis for affected people in 64 cases because affected people is the only predictor related to flood severity in Equation (4). As a result, this study analysed that the number of affected people, that is, a threshold of 263 persons per 1,000 km2, could be used to clearly categorize the 64 cases into two groups. Therefore, throughout this paper, it should be noted that flood severity refers to the relative number of people who were affected by a flood. Nevertheless, flood severity is, in principle, relative. Although a certain level of flooding implies a disastrous hazard for some countries, it can be just a seasonal phenomenon for other countries. Using the threshold, this study was limited in ‘standardizing’ countries that are very different in hydrological conditions. The authors previously ascertained that the number of affected people and the values of the five proxies for susceptibility were positively correlated to the number of flood fatalities, but the values of the three proxies for coping capacity were the opposite.

Building the multiplicative formula for the GFDRA

To solve the aforementioned problem of the MR method in deriving the multiplicative formula, it might be possible to conduct a principal component analysis (PCA): that is, prior to the MR, integrating a large number of predictors into a small number of latent factors. This combination of PCA and MR has the advantage of losing fewer predictors. However, the PCA does not answer the question of how latent factors should be defined to better explain the response (flood fatalities). As a result, this combination succeeds in incorporating sufficient predictors into the formula, but it often results in acquiring inaccurate responses.

As an alternative, this study used the asymmetric partial least squares (PLS) method, the so-called PLS regression (PLSR). Figure 1 illustrates conceptual differences between MR and PLSR (for the state of the art, refer to Geladi & Kowalski (1986) and Rosipal & Krämer (2006)). Basically, the PLSR adopts the non-linear iterative partial least squares (NIPALS) algorithm (Wold, 1975) to subtract latent factors from predictors. This algorithm is formulated by iterative optimization procedures: (i) obtaining latent factors for predictors through the PCA; (ii) calculating values of latent factors by using test cases for predictors; (iii) determining weights in latent factors with reference to the response value; (iv) comparing calculations and test cases for the response; (v) repeating the whole procedure until the comparison results in convergence. Therefore, the NIPALS algorithm provides one way to maximize the covariances of latent factors (algebraic vectors integrating affected people and vulnerability proxies) with the response (flood fatalities). Owing to the ‘supervised’ manner to subtract latent factors, the PLSR can be said to be superior to the combination of PCA and MR.

Fig. 1.

Conceptual schemes of the two methods for building the multiplicative formula. (a) Multiple regression (MR) method. (b) Partial least squares regression (PLSR) method. Note: the MR was implemented by the IBM SPSS ver.19.0, while the PLSR additionally required using the IBM PLS extension command.

Fig. 1.

Conceptual schemes of the two methods for building the multiplicative formula. (a) Multiple regression (MR) method. (b) Partial least squares regression (PLSR) method. Note: the MR was implemented by the IBM SPSS ver.19.0, while the PLSR additionally required using the IBM PLS extension command.

The PLSR determines the importance of predictors on the basis of the VIP (variable importance in the projection) value. This value, defined in Equation (6), conceptually stands for the extent to which the variance of the response is explained by that of each predictor: 
formula
6
where is the VIP value of the lth predictor in the kth latent factor, is the sum of squares for the response, is the weight of the lth predictor in the kth latent factor, p is the total number of predictors, and d is the total number of chosen latent factors. If predictors are loaded in a single latent factor, that is, d = 1, the VIP value for a predictor is directly proportional to its weight obtained from the PLSR: . Despite continuous discussions between statisticians, any absolute criteria of VIP lack theoretical background (Boulesteix & Strimmer, 2006). Hence, what the VIP value reveals should be interpreted as the relative importance of predictors.

Results and discussion

Results of deriving multiplicative formula

Box 1 shows the results of applying the two methods individually to build the multiplicative formulas for minor flood severity. Even though the values of all vulnerability proxies have been previously confirmed to be properly correlated with flood fatalities, the MR merely includes two predictors, that is, undernourishment prevalence and urbanization population growth, due to high multicollinearity. In addition, the significance of urbanization population growth is not clearly revealed; in fact, the P-value (0.078) of the parameter is slightly higher than the widely predetermined significance level (0.010 or 0.050). Noticeably, even the number of affected people is not included in the formula. This is a very serious problem because flood fatalities do not occur without affected people (accordingly, the authors attempted to build the formula again by unconditionally incorporating affected people into the formula. This trial resulted in low statistics of parameters and incorporation of no vulnerability proxies). These problems seemed to be effectively solved by the PLSR. The NIPALS algorithm discovered a latent factor integrating affected people and six vulnerability proxies as predictors. Also, the factor was analysed to be highly significant for the fatalities: the p-value is close to zero.

Box 1.
Derived multiplicative formulas: minor flood severity (n = 21).

• When using the MR,

Equation: 
formula
 
formula

• When using the PLSR,

Equation: 
formula
8
 
formula
 
formula
9
 
formula
10

Note: R = flood risk (persons/1,000 km2/year); LF = latent factor; E = affected people (persons/1,000 km2/year); v1 = age-related dependency ratio (%); v2 = undernourishment prevalence (%); v3 = urbanization population growth (annual %); v4 = deforestation (%); v5 = CPI (0–100 scale); v6 = community solidarity score (1–5 scale); v7 = early warning score (1–5 scale); v8 = DRR education score (1–5 scale); α and β = standardized values of predictors; the P-value denotes the probability that the predictor-response relation could be explained by chance, and not by the calculated parameter.

Based on the VIP value, Figure 2(a) depicts the relative importance of each predictor. These results imply that, under the minor severity condition, fatalities occur for various reasons including marginalized groups, unplanned urbanization, and low coping capacity, as well as affected people. It is found that the affected people predictor is less important than other predictors: VIP = 0.495 (because the PLSR selected a single latent factor and six predictors, Equation (6) shows that the VIP for affected people is its weight multiplied by the square root of six. The PLSR also generated 0.202 for the weight value. Hence, the VIP value is ). Hence, floods in which the number of affected people is less than 263 persons per 1,000 km2 were not deemed to be purely natural disasters. Moreover, except for deforestation and the CPI, the formula takes into consideration all predictors (affected people and six vulnerability proxies) used in the flood risk definition. This formula seems to be open to many DRR actions. It is also noticeable that the selected proxies are influenced by attributes at various governance levels. Communities or municipalities usually have the responsibility to improve the community solidarity score and DRR education score; municipalities or provinces take key roles in solving problems related to the urban population growth and age-related dependency ratio; and the early warning score is connected with activities under national disaster management policies.

Fig. 2.

Relative importance of predictors in the multiplicative formula. (a) VIP values at the minor severity condition. (b) VIP values at the major severity condition.

Fig. 2.

Relative importance of predictors in the multiplicative formula. (a) VIP values at the minor severity condition. (b) VIP values at the major severity condition.

Box 2 shows the results of applying the two methods for major flood severity. Again, the PLSR seems to be much better than MR. In calculating flood fatalities, the PLSR can make use of affected people, urbanization population growth, CPI, and the early warning score, but MR cannot consider any proxies for susceptibility. The PLSR can thus be said to make the flood risk assessment more insightful. Moreover, the extracted latent factor showed high significance for fatalities: the P-value is close to zero. For the multiplicative formula obtained by MR, the significance of the early warning score was less satisfactory; the P-value was larger than 0.010 or 0.050.

Box 2.
Derived multiplicative formulas for GFDRA: major flood severity (n = 43).

• When using the MR,

Equation: 
formula
11
 
formula
12

• When using the PLSR,

Equation: 
formula
13
 
formula
14
 
formula
15
 
formula
16

Note: R = flood risk (persons/1,000 km2/year); LF = latent factor; E = affected people (persons/1,000 km2/year); v1 = age-related dependency ratio (%); v2 = undernourishment prevalence (%); v3 = urbanization population growth (annual %); v4 = deforestation (%); v5 = CPI (0–100 scale); v6 = community solidarity score (1–5 scale); v7 = early warning score (1–5 scale); v8 = DRR education score (1–5 scale); α and β = standardized values of predictors; the P-value denotes the probability that the predictor-response relation could be explained by chance, and not by the calculated parameter.

Figure 2(b) shows the relative importance of each predictor. Based on the VIP, it is possible to say that when flood severity is relatively large, flood fatalities are dominated by the number of affected people. Improving governments' responsibility (CPI) and solving the adverse effects of fast urbanization growth are helpful to a certain extent. Nonetheless, they were analysed to be less effective than the establishment of early warning systems. This seems to suggest that, for a disastrous flood, a core question is how to keep people away from flood waters with proper timing. Besides, it is noticeable that the proxies selected for floods with major severity are mainly related to attributes at the top governance level, because the early warning score and CPI are manageable, depending on the central government's efforts.

 Figure 3 shows the results of comparing observed and estimated fatalities over all 64 cases. Even though R2 is almost unchanged, the PLSR makes use of affected people and seven vulnerability proxies as predictors. The fact that the explanatory power is not lowered while important predictors are not lost is said to be a unique strength of the PLSR (Geladi & Kowalski, 1986). This leads the coefficient and individual parameters in the multiplicative formula to be less over-fitted. The model parameters are therefore expected not to change very much when test cases are newly taken.

Fig. 3.

Comparison of fatalities between observations and estimations. (a) When using the MR. (b) When using the PLSR.

Note: The MR calculated flood fatalities with four predictors (affected people, undernourishment prevalence, urbanization population growth, and early warning score), whereas the PLSR used eight predictors (affected people, age-related dependency ratio, undernourishment prevalence, urbanization population growth, CPI, community solidarity score, early warning score, and DRR education score).

Fig. 3.

Comparison of fatalities between observations and estimations. (a) When using the MR. (b) When using the PLSR.

Note: The MR calculated flood fatalities with four predictors (affected people, undernourishment prevalence, urbanization population growth, and early warning score), whereas the PLSR used eight predictors (affected people, age-related dependency ratio, undernourishment prevalence, urbanization population growth, CPI, community solidarity score, early warning score, and DRR education score).

Conclusions

Starting with ongoing discussions on GFDRA methods, this study addressed problems in selecting vulnerability proxies and relating them to flood fatalities. Hence, an attempt was made to carefully divide vulnerability into marginalized groups, unplanned urbanization, weak governance, and coping capacity, and then select eight proxies based on a consideration of empirical literature and data availability. Moreover, as an alternative to the MR, the PLSR was applied to include vulnerability proxies as predictors for global flood risk and explain fatality records satisfactorily. It is thus concluded that this study can enhance the methodological aspect of GFDRA, which is necessary to consider anthropogenic factors and important to gain a practical understanding of flood risk. Perhaps the real outcome of this study might not be the findings presented so far but rather the methodological challenges identified for further studies; experts have recently started to realize the need for this comprehensive, integrated, multidisciplinary approach (after UN Resolution 60/195 was endorsed in 2005). Before anything else, the authors contend that the following points should receive much attention.

  • How finely should global flood risk be identified? The country scale is considered to be important in the GFDRA because national governments have primary responsibility to announce vulnerability-related data. However, spatial variations are excessively hidden, especially when a single risk is assigned to the large-size country, such as India. For risk assessments on a finer scale, feasibility studies should be launched to investigate which vulnerability proxies can be disaggregated into the watershed basin or local administrative unit.

  • How should deforestation be considered in the GFDRA? Because of a low correlation between deforestation data in the Millennium Development Goals Database and flood fatality data in the EM-DAT, this study could not demonstrate deforestation to be an important proxy for vulnerability, even by using the PLSR. This contradicts the findings of flood-deforestation interaction studies, especially Bradshaw et al. (2007), who found evidence in the 1990–2000 data of 56 developing countries. Our results do not indicate that deforestation should be interpreted as a minor cause for flood risk. Rather, it seems that deforestation should be estimated on a finer scale. Further studies will be conducted to estimate deforestation within potentially or repeatedly inundated areas and then analyse its relation to flood fatalities across various watershed basins.

  • How should the effectiveness of structural means be considered in the GFDRA? This study did not select any proxy for structural means, including dams, dykes, and floodwalls, because authorized data were not globally available. Nevertheless, this study showed that reducing the number of affected people is very important to mitigate flood fatalities at the major severity condition, which implicitly raises the need for preventive investment in structural means. In order to derive this message in a more rigorous manner, the authors take note of digital water atlas projects, which are currently being conducted by the UN-Water, FAO, and Global Water System Project. If these projects provide global distribution data about structural means, it is necessary to quantify the effectiveness of structural means as proxies for coping capacity and include these proxies into the risk calculation formula. These efforts will make the formula more reliable and informative.

  • How should more reliable disaster records be collected for more accurate vulnerability assessment? In this study, multi-source disaster records in the EM-DAT were essential to analyse the statistical importance of vulnerability proxies to flood fatalities and obtain the empirical risk calculation formula. As a global disaster data source, the EM-DAT is irreplaceable now for vulnerability assessment. However, it should be noted that these multi-source records very often show large differences from statistics officially announced by governments. Therefore, the authors feel it necessary to conduct a similar study with official statistics if disaster situation reports are sufficiently collected from national emergency management authorities.

  • How should future perspective on flood risks be investigated? Undoubtedly, risk assessment is a tool to be used for building a safer future. Hence, utmost attention should be paid to uncovering future flood risks. Many experts very often argue that flood risks are likely to increase over time. Although it is still disputable that climate change will pose bigger threats, many countries show clear trends toward accelerated population density in floodplains, ageing society, and uncontrolled urbanization. All these trends, related to the dynamics of progression of vulnerability, raise the strong possibility that human losses in the future will be greater than those at present under a given flood condition. In this sense, further studies need to build scenarios of the vulnerability factors selected in this study and use the risk calculation formula in appraising the magnified level of future risks. Those studies will offer political insights about why certain countries, particularly some of the less developed countries, will have difficulties in attaining an acceptable level of risk, and why they need to receive global support today to enhance their coping capacities.

Acknowledgements

This study was made possible in part by the project of the ADB and ICHARM, ‘Technical Assistance for Supporting Investments in Water-Related Disaster Management (TA7276-REG)’. We would like to express our sincere appreciation to the editor and three reviewers for constructive criticism. We are also thankful to Dr Tanaka of the Kyoto University, Dr Osti of the Asian Development Bank, Dr Yasuda, Mr Sawano, Dr Shrestha, Dr Gusyev, Ms Hagiwara, and Mr Okubo of the ICHARM for providing their comments.

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