The assessment of flood risk is important for policymakers to evaluate damage and for disaster preparation. Large population densities and high property concentration make cities more vulnerable to floods and having higher absolute damage per year. A number of major cities in the world suffer from flood inundation damage every year. In Japan, approximately USD 1 billion in damage occurs annually due to pluvial floods only. The amount of damage was typically large in large cities, but regions with lower population density tended to have more damage per capita. Our statistical approach gives the probability of damage following every daily rainfall event and thereby the annual damage as a function of rainfall, population density, topographical slope and gross domestic product. Our results for Japan show reasonable agreement with area-averaged annual damage for the period 1993–2009. We report a damage occurrence probability function and a damage cost function for pluvial flood damage, which makes this method flexible for use in future scenarios and also capable of being expanded to different regions.
The assessment of the available water resources and their temporal and spatial distribution, as well as the analysis of flood and drought risk, are of great importance for the health of societies and environmental systems (Lehner et al., 2006). A world bank report (Dilley et al., 2005) recorded that earthquakes, floods and drought-like natural hazards continue to cause tens of thousands of deaths, hundreds to thousands of injuries and billions of dollars in economic loss every year around the world. Flooding is one of the major causes of physical loss in the world and is continually increasing in trend. Globally, flood damage had increased from an average USD 7 billion per year in the 1980s to more than USD 20 billion per year at the end of 2000s (Kundzewicz et al., 2013). 35 % of physical loss over the past 40 years in the Asia–Pacific region were due to flooding (Asian Development Bank, 2013). Moreover, occurrence of floods was the most frequent of all natural disasters (Jha et al., 2011). Recent large-scale and record-breaking flooding events in terms of physical loss caused world leaders and policymakers to pay serious attention to proper planning and management of flood control infrastructure and the formulation of future adaptation strategies. China, in 2010, experienced the largest flood damage of USD 51 billion in one single year and the 2011 flood in Thailand caused the most expensive insurance loss ever, worldwide, with total liability estimated at around USD 15 billion (Kundzewicz et al., 2013). Flooding events in Germany and central Europe in May and June 2013 were the most expensive, costing around USD 16 billion (Wake, 2013). Economic loss due to floods is higher in developed countries, whereas the economic loss expressed as a proportion of gross domestic product is much higher in developing countries (Handmer et al., 2012). Even though a huge investment in the improvement of flood control infrastructures has been made, flooding remains a serious problem throughout the Europe (Kundzewicz et al., 2013) and the case of Japan is also similar. Annual expenditure for flood control in the government budget in Japan is nearly USD 10 billion (about JPY 1 trillion) as reported in Kazama et al. (2009). The high potential of flood damage in Japan is basically due to the fact that approximately 9 % of its land is flood-prone, but contains 41 % of population and 65 % of the national assets (Kundzewicz et al., 2013).
Flooding related to rainfall is usually divided into large-scale floods due to high discharge of rivers and streams (fluvial flood), and local or urban floods that occur due to excessive rainfall that overwhelms local drainage capacity (Pluvial flood) (Bouwer, 2013). Even though published flood damage events were often from fluvial flooding, the share of pluvial flooding cannot be underestimated. Pluvial flood damage, particularly in densely populated urban areas and in areas with poor drainage facilities, was recorded to be very high not only during heavy rainfall but also during moderate to low rainfall events. Rapid urbanization with inadequate engineered inner-city drainage infrastructures increases the damage, not only to the economy but also to human lives (Kundzewicz et al., 2013). The Ministry of Land, Infrastructure, Transport and Tourism (MLIT) of Japan had shown that 86 % of total economic flood damage in the Tokyo metropolitan during 1998–2007 was only due to pluvial floods (MLIT, 2008b). The flood damage in Kochi in September 1998 (Yamamoto et al., 1999) was largely due to pluvial floods, and the failure of inner drainage systems also led to the higher flood damage in the 2000 Tokai flood (Ikeda et al., 2007). Average annual economic damage to residential property attributable to pluvial floods in Japan was approximately USD 1 billion (JPY 100 billion) (about 45 % of annual flood damage of the same kind) during 1993–2009 (MLIT, 2009). Figure 1 shows the historical total national fluvial and pluvial flood damage to general property in Japan. Here, general property implies housing, household appliances, depreciable business properties, business inventory properties, depreciable agriculture/fisheries and agriculture/fisheries inventory property. The figure reveals that annually, pluvial floods causes significant damage, and efforts for pluvial flood damage control seem ineffective. Even a well-prepared city in terms of flood defence infrastructures, like Tokyo, suffers frequent pluvial flood damage. Rapid urbanization with an ageing population, a decline in preparedness of local communities to fight flood disaster and an increase in new exposed facilities make cities more vulnerable than before (Ikeda et al., 2007). Smaller cities and towns are typically more severely affected by pluvial floods, perhaps due to less-developed flood defences, as pluvial flood damage per capita in those areas was reported to be higher than in bigger cities. Pluvial flood impacts on the UK and many European cities were also recorded as very high in recent years (Morris et al., 2009; Van Riel, 2011; Spekkers et al., 2013). The scenarios in the present warn us for the future as well, since small changes in rainfall intensity can lead to a rapid increase in loss in urban areas due to the highest concentration of capital (Bouwer, 2013; Morita, 2011; Zhou et al., 2012). Pluvial floods seem very serious and contribute to high physical loss all over the world; however, relatively few studies have been reported on this issue for present and also future climate (Seneviratne et al., 2012).
Historical general property damage due to pluvial and fluvial floods in Japan for the period 1993–2009. The fluvial flood damage shows its high fluctuation annually; however pluvial flood damage is much more constant over the period.
In regard to the above discussion, a proper way of assessing pluvial flood damage amount for each hazard event on a local to a global scale for the present and the future is a demanding task for scientific communities. An accurate estimate of economic damage is now indispensable for decision makers so that economic viability of proposed infrastructure development, mitigation and/or adaptation plans for flood defence can be justified and can be used in overall flood risk management strategies (Lavell et al., 2012; Merz et al., 2010).
A wide range of methodologies have been developed and applied for assessing flood damage risk over the last few years; however most of these models were developed for fluvial flooding. A diverse approach has been applied for flood risk assessment by many researchers and organizations. Many conceptual models which provided the different vulnerability or risk indices for spatial comparison were developed for a local to global scale. Some popularly known indices are event-based disaster risk index (DRI) (UNDP, 2004), hazard index for megacities (HIM) (Munich Re, 2004), prevalent vulnerability index (PVI) (Cardona, 2007), discharge probability index (DPI) (Yoshimura et al., 2008), flood vulnerability index (FVI) (Hara et al., 2009) and advance flood risk index (AFRI) (Okazawa et al., 2011). Each index has their own criteria and spatial resolution (local to global scale) for calculating indices for risk or vulnerabilities. This index-based approach might be suitable for assessing relative risk distribution; however as discussed earlier, a decision maker requires an absolute damage amount in monetary terms so that economic viability of a proposed infrastructure development plan for flood defence can be justified.
The direct flood damage estimating models developed so far have basically utilized two different submodels: first, to evaluate hydrological parameters (e.g. flood velocity, flood duration and flood depth), based on some physically based hydrologic modelling techniques (hydrological models), and second, to evaluate absolute/relative damage amount based on a susceptibility function usually derived from empirical analysis (loss models), which relates the hydrological parameters to damage amount. The basic features of hydrological models are to estimate hydrological parameters for a hazard event generally defined by its exceedance probability (return period). On the other hand, a loss model is a central idea for flood damage estimation (Merz et al., 2004) and the most common way of estimating direct damage amount is the use of depth–damage functions often termed as a susceptibility function or a vulnerability function (Dutta et al., 2003; Glade, 2003; ICPR, 2001; Jongman et al., 2012a; Kazama et al., 2009; Kelman and Spence, 2004; Kreibich et al., 2010; Rodda, 2005; Schmidt-Thomé et al., 2006; Smith, 1994; Ward et al., 2013). Some loss models are multi-parameter models based on several hazard parameters (flood depth, flow velocity, contamination etc.) and resistance parameters (flood-prone object type and/or size, mitigation measures etc.) for example, HAZUS-MH (FEMA, 2003), multi-coloured manual model (Penning-Rowsell et al., 2005), FLEMOps (Apel et al., 2009) and FLEMOcs (Kreibich et al., 2010).
Flood damage assessment methodology and their results further depend on the defined spatial boundary (Apel et al., 2009). To date, several studies have been done from a very local municipal level (Baddiley, 2003; Grünthal et al., 2006), catchment scale (Dutta et al., 2003, 2006; ICPR, 2001), national scale (Hall et al., 2005; Kazama et al., 2009; Rodda, 2005) and regional scale (Schmidt-Thomé et al., 2006) to the global scale (Jongman et al., 2012b; Ward et al., 2013). Winsemius et al. (2013) also provided a framework for global river flood risk assessment. Due to the increasing need for national-scale and even larger scale flood damage assessment (Winsemius et al., 2013), macro-scale studies are getting much popular.
Most of the damage assessment models that have been discussed so far were primarily developed for fluvial flooding; however, the loss model could be a common component for both fluvial and pluvial flood damage assessment. A few studies on pluvial floods and their associated damage have also been reported. Zhou et al. (2012) described a framework for economic pluvial flood risk assessment considering future climate change which quantifies flood risk in monetary terms as expected annual damage in different return periods of rainfall. Escuder-Bueno et al. (2012) presented a methodology for assessing pluvial flood risk using two different curves, one for societal risk and the other for economic risk; however both were limited to a local scale.
The flood damage assessment models to date contain a number of uncertainties in both hydrological and loss models. Hydrological models possess uncertainties regarding extreme value statistics used, stationary and homogeneity of data series, consideration of physical properties (e.g. dikes and drainage systems) of a location, and calibration and validation of model output etc. (Apel et al., 2009). However, the largest sources of uncertainties in damage modelling were associated with prescribed depth–damage functions (Apel et al., 2009; Hall et al., 2005; Jongman et al., 2012a; Merz et al., 2004, 2010; de Moel and Aerts, 2010). A reason for uncertainty in loss models is their crude assumption of the relationship between damage and flood depth only in most cases. Moreover, these models were generally developed for some specific location using past flood records and their validation are always a critical issue for their temporal and spatial transferability. Uncertainty related with the property types and their values is also critical in many cases. There is still a need for better understanding of different processes leading to damage so that they can be modelled appropriately (Meyer et al., 2013). A special report of the Intergovernmental Panel on Climate Change (IPCC), often called IPCC SREX (IPCC, 2012), also focused on the need for more empirical and conceptual efforts to develop robust damage assessment methodology.
In regard to the present situation, this study is motivated towards a development of a simple but robust statistical model as integral of hazard, vulnerability and exposure, based on a historical database in Japan for pluvial flood damage assessment, that could be used for all regions irrespective of their individual characteristics of pluvial flooding. Moreover, the model described in this paper overcomes several uncertainties regarding both hydrological and vulnerability models and is capable for estimating total annual damage on a national scale in simple and rapid way. Our method for damage assessment is a macro-level statistical model that focuses on pluvial floods and considers all daily precipitation events in a year, thereby calculating annual damage. In this study, each daily rainfall event is characterized by its exceedance probability based on the Gumbel distribution. We report two different functions, namely, the damage occurrence probability function and the damage cost function. The former represents the relationship of exceedance probability of rainfall and its corresponding damage probability, and the latter represents the relationship of exceedance probability of rainfall and relative damage cost of a particular location. These two functions were further used to calculate annual damage and thereby average annual damage (AAD) for the whole of Japan due to pluvial flooding. We also examined uncertainties associated with daily damage data and their preparation. A popular bootstrap method was applied for uncertainty analysis. Sensitivity tests were also performed to examine robustness of the model. We believe this model helps decision makers to estimate annual damage for short-term planning and to estimate average annual damage for long-term planning with a reasonable level of confidence. As a macro-level study, we use readily available data, including population density, elevation and national annual gross domestic product (GDP), which make this method more flexible for use in future climate scenarios and also make it extendable to global assessment. The next section describes the methodology, including forcing data and theory. The subsequent section presents the results for annual damage, along with uncertainty analysis. The final section concludes the paper.
Daily precipitation data were used as an external forcing for hazard in this
study since they are a strong external loading for pluvial floods (Zhou et al., 2012). Daily precipitation
data were obtained from the Auto Meteorological Data Acquisition System
(AMeDAS), which cover all areas of Japan at an interval of about
20
The population size of a location has a strong influence on flood risk
(Kundzewicz et al., 2013). Increasing population in a flood-prone zone
increases exposure; and therefore total damage amount increases with
increasing population (de Moel et al., 2011; Morita, 2011). The case of Japan
is even more serious as a large number of the population live in a relatively
small flood-prone area (Kundzewicz et al., 2013). However, population size is
not a sole component for determining flood risk. Residents of small cities or
towns are often far more vulnerable to disaster than residents of megacities
(Cross, 2001). Three population density classes (low: 0–250 persons per
km
Damage data are always a critical issue in flood damage assessment. A lack of
reliable, consistent and comparable data is a major obstacle (Hall et
al., 2005; Handmer, 2003; Handmer et al., 2012; Kundzewicz et al., 2013; Merz
et al., 2010; Meyer et al., 2013) to formulating a robust methodology and to
validating it. Moreover, the level of uncertainty in damage estimation is
mainly dependent on available data (Escuder-Bueno et al., 2012; Handmer,
2003). Several international flood damage databases which archive the flood
damage data from all over the world along with duration (start and end date)
and location exist, for example EM-DAT, Dartmouth flood observatory, Munich
Re and Swiss Re etc. Since all databases have their own criteria of damage
recording, local-scale little damage (Meyer et al., 2013), and in some cases
great damage, was often not recorded because the total annual damage recorded
in these database was much smaller than that recorded in respective national
damage databases. However, such national-level damage databases are only
available for a few developed countries. In this study, daily damage data due
to pluvial floods for the period 1993–2009 based on economic damage to
tangible general property (housing, household appliances, depreciable
business property, business inventory property, depreciable
agriculture/fisheries property, agriculture/fisheries inventory property)
from MLIT's flood disaster statistics were used. The various characteristics
of this database are well described in Mouri et al. (2013). These data
include the name of the city or town where a disaster happened, the type of
disaster (fluvial or pluvial), the type of damaged assets, the start and end
date of flooding, and the total amount of damage. Further disaggregation of
these data into temporal and spatial resolution was a really big challenge.
For this study, the first day of damage onset was considered the damage day
and the total recorded damage amount was assigned to that single day. These
damage data were further interpolated onto the
Assets value is another important component of economic damage assessment.
Current models for economic flood damage estimation possess high uncertainty
regarding the assets value used (Jongman et al., 2012a; de Moel and Aerts,
2010). For regionalization of a model, the integrated asset value, which has
a uniform definition for all regions, is essential. For a macro-scale study,
an aggregated asset value is more appropriate to make it flexible for
expanding to other regions (Merz et al., 2010) and in the absence of real
assets data in present situation, GDP can be a powerful candidate in this
regard (Jongman et al., 2012a). The proposed model was also developed in view
of its application on a global scale in which GDP could be a very useful
indicator for asset value. In this study, GDP data were used as an asset
value, and macro-economic vulnerability is defined as the ratio of damage to
GDP at a location, which will be described more in a later section. National
annual GDP data for 1993–2009 were taken from the International Monetary
Fund (IMF) world economic outlook database of April 2012. Prefectural GDP
data were taken from the Statistics Bureau, Ministry of Internal Affairs and
Communications (MIC), government of Japan. These data, shown in Fig. 2,
reveal that the GDP of each prefecture is approximately proportional to the
population (these data are for 2003, but the trend was similar in other
years). The national-level annual GDP was hence distributed onto each grid
proportional to the grid population (Chan et al., 1998; Jongman et
al., 2012b; Ward et al., 2013) as given in Eq. (1):
GDP as a function of prefectural population in Japan for the year 2003. The data show that the population–GDP relation follows a linear fit except in a few cases.
Many geological and topographical characteristics contribute to the flood
risk (Kundzewicz et al., 2013). The topographical characteristic
fundamentally determines the flooding extent, its depth and velocity, which
ultimately govern flooding impact at a location. In most of the reported
methodology (Dutta et al., 2003; Kazama et al., 2009; Zhou et al., 2012), the
topographical slope was implicitly used in their hydrological models. In some
models, direct elevation data were used to estimate flood water depth, for
example in Feyen et al. (2012). We also evaluated the topographical
dependency in damage occurrence at a location. To preserve the impact of
topographical characteristics in flooding, we used the slope as one of the
parameters in our damage occurrence probability function, the details of which
will be described later. Topographical slope data were prepared based on
GTOPO30 data sets (USGS, 1996). GTOPO30 is a global digital elevation model
(DEM) with horizontal grid spacing of 30
Extreme events interacting with exposed human resources and economic
activities can lead to disaster. To this end, various definition of risk can
be found in different literatures. Smith (1996) defined the risk simply as a
probability of a specific hazard occurrence. Davidson and Shah (1997) further
elaborated the risk as a product of hazard, exposure, vulnerability, capacity
and measures. Hall et al. (2005) specifically defined flood risk as the
product of the probability of flooding and the consequential damage, summed
over all possible flood events. As per the definition of United Nation
International Strategy for Disaster Reduction (UNISDR) (UNISDR, 2009),
disaster risk is a product of hazard, vulnerability and exposure, and hence
can be simply written as
Different components of damage assessment and their interrelationships. Damage occurrence probability appears to be more dependent on exposure, whereas damage cost seems to be dependent on susceptibility in a particular location.
Annual maximum daily rainfall was assumed to follow a two-parameter Gumbel
distribution. The annual maximum daily rainfall data for the period
1976–2009 were used to calculate the Gumbel parameters. Gumbel distribution
is one of the extreme value statistical distributions which has widely been
adapted for hydrological events (Hirabayashi et al., 2013; Mouri et
al., 2013; Ward et al., 2013; Yoshimura et al., 2008). Mouri et al. (2013)
showed the applicability of Gumbel distribution for AMeDAS daily
precipitation for the whole of Japan using a standard least-squares criterion.
We also evaluated the goodness of fit of the Gumbel distribution to annual
maximum daily rainfall using the probability plot correlation coefficient
(PPCC) (Hirabayashi et al., 2013; Vogel, 1986) test, which revealed that
about 94 % grids have a PPCC value greater than the critical PPCC
(0.95532 for 34 samples), corresponding to 5 % significance
level, proving its applicability. Based on the Gumbel distribution extreme value theory, the
cumulative distribution function for the annual maximum daily precipitation,
The damage occurrence probability (DOP) is the probability of damage at a
given location (i.e. grid point) in response to a rainfall event. To
calculate damage occurrence probability at each location, some “bins” of
exceedance probability were prepared. The width of each bin was fixed as
per its sensitivity regarding the number of daily rainfall events and the number of
damage events. Several trials were performed to fix the bin size, especially
for lower exceedance probability bins. The number of damage events for each
bin for all three population density classes is shown in Fig. 4a. The figure
reveals that the number of damage events was very low in smaller
exceedance probability bins (i.e. higher return period); however the number of
damage events in higher exceedance probability bins (i.e. smaller return
period) was surprisingly higher. The damage events in frequent rainfall
events were often neglected in previous damage modelling techniques, although
this damage could have a considerable share in the total damage amount. The DOP
was calculated as a ratio of damage events (
The damage occurrence probability as a function of the exceedance probability of rainfall for different population density classes. Higher population density exhibits higher damage occurrence probability and vice versa.
The damage occurrence probability as a function of the exceedance
probability of rainfall for different topographical slopes for population
density class
Damage occurrence parameter values for Japan in all three population density classes.
Vulnerability parameters values in Japan for all three population density classes. The 90th (upper) and 10th (lower) percentile values were derived from the means of 10 000 bootstrap samples.
The damage cost function describes the degree of damage associated with each daily rainfall event and hence also can be termed as vulnerability. As described earlier, the most common way of estimating direct damage amount so far was the use of a depth–damage function. A depth–damage function shows the relationship between flood depth and relative damage associated with it. Total damage amount due to a flood event is not only dependent on water depth but also on other factors like flow velocity, duration of inundation, sediment concentration etc. (Kundzewicz et al., 2013; Merz et al., 2004), resistance parameters (type, size, shape and property of objects) (Kreibich et al., 2010) and the level of preparedness of a society (Merz et al., 2004). Another main issue related to depth–damage functions is their spatial and temporal non-transferability especially for national-level and global-level damage assessment, because they were often developed from local municipality scale or catchment scale. Asset values at a location also always create a large uncertainty, which is largely dependent upon various building characteristics. In this study, we introduce a damage cost function that relates the exceedance probability of rainfall to the average damage per GDP (DpG) for each population density class. The GDP was taken as an asset value which indicates the asset, irrespective of the individual characteristics of a location; and hence its applicability to all regions is widened.
In this study, we prepared some exceedance probability bins. Mean DpG in
each bin for different damage events was calculated for the period
1993–2002 for all three population density classes. Damage per GDP value
showed very large variation within a bin as seen in Fig. 4b, c and d as
box plots for low, medium and high population density classes respectively. The
lower and higher ends of the box give the 25th and 75th percentile value of the
data, whereas red bars within each box show the median value of the data
within each bin. Larger deviation in each bin is shown by the whisker plot
(dotted line) showing a range of 1.5 times the inner quartile. The green line
joins the mean value of DpG in each bin. The figures (box plots) reveal that
there is a large deviation of damage value with respect to its property
even with similar hazard events. This large variation is partly due to the bin
size itself which constitutes a large variation of hazard frequency, and
partly due to the large uncertainty in damage amount, even with the same hazard
event at a location. Moreover, the mean value of damage per GDP is
significantly higher than its corresponding median value, showing that a low
number of damage events causes a larger share in total annual damage. We
adopted an inverse power law to relate exceedance probability of rainfall
(
As discussed before, a flood damage assessment model possesses a number of uncertainties which always limit its use for future projection. In this study, damage due to an event was computed using Eqs. (9) and (10). Vulnerability parameters were calculated by fitting a power curve with mean DpG value; however as seen from Fig. 4b, c and d, the DpG values in each exceedance probability bin have large variation. The uncertainty related to very large variation of DpG in each bin was evaluated using a bootstrap method (Efron, 1979). Using a bootstrap technique of resampling for the data in each bin, 10 000 bootstrap samples were generated and their means were calculated. 10th and 90th percentile values were taken for these mean values (10 000 in number), assigning lower and upper uncertainty range of the mean for each bin. The parameter values for Eq. (10) were also calculated for these 10th and 90th percentile DpG along with mean DpG. The values of vulnerability parameter for these two percentile DpG are also tabulated in Table 2 along with computed parameter values for mean DpG. The former two hence gave the maximum and minimum limit of our damage estimation with a probable confidence band of 80 %, and the latter one provides the total annual damage.
The damage cost function for different population density classes as a function of the exceedance probability of rainfall derived using mean DpG. The vulnerability varies with population density, and a lower populated area exhibits higher vulnerability.
Total annual pluvial flood damage variation in
Annual damage was calculated from the sum of the daily damage value due to
each rainfall event in a year, which can be given as
Parameters in the DOP and the damage cost function were first computed using the damage data for the period 1993–2002. Damage data for 2003–2009 were used for validation purpose. Only DOP parameters were calibrated during the fine tuning process to estimate better annual damage variation and average annual damage during the periods. The average annual damage and its annual variation were observed while calibrating DOP parameters.
The results of the proposed model were evaluated according to its capability to produce the annual total national damage and average annual damage in both calibration and validation period using the damage occurrence probability function and the damage cost function with mean DpG. Along with total national damage, total annual damage for all three population density classes was also evaluated. Figure 8a, b and c show the annual variation of total calculated damage within low, medium and high population density classes respectively along with the recorded damage variation. The annual variation of total national pluvial flood damage (recorded and calculated) is shown in Fig. 8d. The upper and lower ranges of annual damage were calculated using parameters of damage cost function with 90th and 10th percentile of the means of bootstrap samples, as shown by the shaded area in the figures. Annual variation in the calculated damage compared with the recorded variation in damage shows good agreement in most years, except for 1997 (in low population density class) and 1998 (in medium population density class). As these data were generated using spatial and temporal averaging, the large localized damage in some grids may have been underestimated. For example, the largest recorded damage in 1998 was due to the Kochi flood on 24 September 1998; however, as Iwasada et al. (1999) pointed out, the inundation of the Kochi flood resulted from overflowing water from a part of the Kasumi levee (a traditional Japanese discontinuous levee) along the Kokubu river. It means that this particular inundation was unexpected, given the existing flood mitigation measures. Thus, some of the recorded damage from pluvial flooding may be from river flooding and may therefore be over-recorded.
The annual variation in the total damage during the validation period shows good agreement with the recorded data, which may be due to the absence of any event causing extensive damage in this time period in a particular grid.
The computed average annual national damage (with the financial costs normalized to 2005 levels) during the calibration period 1993–2002 was USD 853.92 million, which is slightly lower than the recorded average annual damage over this period (USD 1011.19 million). Computation of the average annual damage for 2003–2009 using this method gave USD 807.09 million, slightly higher than the recorded average damage in this period (USD 744.61 million). Fukubayashi (2012) also estimated the national average annual damage for flood inundation in Japan during 1993–2009 to be USD 980 million, but did not evaluate the annual variation in the damage.
Spatial distribution of average annual damage 0.1
Even though the model was calibrated and validated with bulk national damage data, the performance of the model with different population density classes was also very good, as seen from Fig. 8a, b and c. This led us to present the spatial distribution of the average annual damage and average annual damage per GDP for the period 1993–2009 using Eqs. (9), (10) and (11). The results are shown in Figs. 9 and 10, respectively. The average annual damage distribution reveals very large damage in big city areas, particularly Tokyo, Osaka, Nagoya and Niigata, which is related to the large population density in flatlands. However, the spatial distribution of the average damage per GDP shows an inverse trend. In general, scattered small towns have higher damage per GDP than big cities do, perhaps due to less preparation for pluvial flooding.
The sensitivity of model results due to different horizontal resolution
precipitation input (AMeDAS) and slope computed from a finer DEM (SRTM3) than
the DEM used for model development (GTOPO30) was also evaluated. The annual
variation of total national damage due to the use of 20 and 60 km resolution
AMeDAS precipitation data along with 0.1
Spatial distribution of average annual damage per GDP per
0.1
Annual variation of total national annual pluvial flood damage with AMeDAS precipitation forcing with three different horizontal resolutions. Very little discrepancy is seen for precipitation input with different horizontal resolutions.
Annual variation of pluvial flood damage with the slope derived from GTOPO30 DEM data, in which the model was optimized, and SRTM3 DEM data. The damage estimation with the slope derived from a finer resolution DEM is lower than that of a coarse-resolution DEM.
A MLIT report (MLIT, 2008a) described a significant increase in the daily precipitation rate in Japan over the last 100 years, as well as increases in short-term heavy rainfall over the past 30 years as also revealed in Utsumi et al. (2011). The report further revealed, based on different studies, that future annual precipitation and summer precipitation will increase in most parts of Japan. This is expected to decrease the return period of an event and thereby increase the probability of damage and the size of the damage for a given event. Practical guidelines for strategic climate change adaptation planning for flood disaster prevention (MLIT, 2010) focuses on three main strategic areas: socioeconomically developed and urbanized areas, alluvial plains and regions where flood control measures are currently underdeveloped. The guidelines also highlight the importance of economic damage assessment. The average annual damage estimation for pluvial floods and its regional distribution could be valuable data for any future adaptation or mitigation planning. We believe that our methodology and results can be applied in such studies.
We have described a method to calculate annual pluvial flood damage based on daily precipitation data, and socioeconomic and topographical data. Using this method, we can compute the damage from every event in a year, many of which are typically excluded when computing damage from a low-frequency event only. We observe a significant contribution of high-frequency low-magnitude events in total annual damage, which is included in this method via the probability of damage. The probability of damage at a given location depends on the population density and the topographical slope of the landscape. The damage occurrence probability is higher for a high population density area because of a high concentration of properties.
The damage cost function curves show that damage per GDP was lower in highly populated areas than in areas of low population density at a given frequency of rainfall events. We believe that the damage per GDP in highly populated urban areas reflects the ability to withstand the disaster. The spatial variation in the total damage cost and the damage per GDP across Japan were computed for each grid point using simple relationships. The rapid and simple way for calculating annual damage and average annual damage due to pluvial floods with some uncertainty will be a very useful tool for decision makers for planning, policymaking, budgeting and the management of urban drainage systems. We believe the damage occurrence probability function and damage cost function will be applicable in addressing future climate and socioeconomic changes and can also be applied to other areas or countries. However a precise optimization of parameters might be needed for other nations. The functions and results presented here also provide some insight into the improvement of the present integrated physical hydrological modelling technique for flood damage assessment which might have the capability to assess flood damage associated with even shorter rainfall duration (subdaily scale), which is now much more difficult to incorporate in the presented model due to the temporal and spatial scale of the present damage recording technique.
This study was conducted under the framework of the Precise Impact Assessment on Climate Change of the program for Risk Information on Climate Change (SOUSEI program) supported by the Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT), RECCA/SALSA project, JSPS KAKENHI, Grant-in-Aid for Scientific Research (S) (23226012), Core Research for Evolutionary Science and Technology (CREST) program from the Japan Science and Technology Agency, and the Environment Research and Technology Development Fund (ERTDF) S-10. The first author was financially supported by the government of Japan through the MEXT scholarship program for PhD study at the University of Tokyo and the study was also a part of his PhD dissertation. Edited by: T. Glade Reviewed by: two anonymous referees