THA 2019 International Conference on“Water Management and Climate Change towards Asia’s Water-Energy-Food Nexus and SDGs”
23– 25 January 2019, Bangkok, Thailand.

Estimating Probability Distribution of Benefit from Flood Control
Projects
Keita Kobayashi1,a,*Abstract Frequencies of severe flood events are
expected to increase due to a changing climate.
Therefore, it becomes more and more important toimplement suitable flood defenses based on
quantitative benefit analysis of flood control projects
such as dam construction and embankment. In
general, the benefit from flood control projects isdefined as the sum of expected value of annual
reduced damage cost over the evaluation years,
considering discount rate of each year. Since flooding
is low-frequency events especially in highly protectedareas, it is highly uncertain whether actual reduced
damage cost is distributed around its expected value,i.e. benefit calculated from the expected value does
not necessarily occur frequently. The probability
distribution of reduced damage cost would provide
more comprehensive information for decision making.
This study redefined benefit from a flood control
project as a reduced damage cost, which is actually arandom variable, and developed its probability
distribution by applying an extreme rainfall generation
method. Then, we demonstrated the presented method
under several scenarios of dam construction projects.
The estimated probability distribution was skewed
leftwards, and had a long tail. It reveals large
variability of reduced damage cost. From theprobability distribution, we can extract several
statistics in addition to the expected value, which
provide more information to discuss the characteristicsof actual reduced damage cost by flood control
projects.

Introduction
It is concerned that frequencies of intense
rainfall events will increase due to climate change. To
implement adaptation measures against the expected
severe flood events, countermeasures should be taken,
and fundamental measures are constructing flood
defenses such as embankment and dam. In Japan, costbenefit analysis is utilized from 1997 to evaluate theefficiency of public works, where benefit corresponds
to reduced inundation damage cost by installing flood
defenses, and the efficiency of flood control projects
are measured by comparing it with the cost for
construction and maintenance. According to themanual issued by the Ministry of Land, Infrastructure,
and Transport (hereinafter called “MLIT”) [1], thebenefit from flood control projects is defined as thesum of the expected value of annual reduced damage
cost over the evaluation years, considering discountrate of each year.
Theoretically, annual reduced damage cost isactually a random variable; accordingly, the sum ofannual reduced damage cost is also random variable.
Therefore, the benefit defined above is equivalent to
the expected value of the sum of annual reduced
damage cost over the evaluation years when neglecting
discount rate. According to central limit theorem,
actual reduced damage cost is normally distributed
around the benefit calculated from the expected value
when evaluation period is long enough. However, thisis not guaranteed for an actual evaluation period due tothe low frequency of flooding. In other words, it ishighly uncertain whether actual reduced damage costis distributed around its expected value, i.e. benefit
calculated from the expected value does notnecessarily occur frequently. These facts show that theabove deterministic approach to decision making offlood control projects based on cost-benefit analysis
includes the uncertainty of the probabilistic
characteristics of reduced damage cost. If we canestimate the probability distribution of reduced
damage gained over evaluation period, we can get
more comprehensive information from the distributionin addition to the expected value, e.g. the probability
with which actual reduced damage cost becomes larger
than expected value. These will help advanced
decision making of flood control projects based on
multiple criteria.
In a literature, several uncertainties forbenefit calculation have been discussed, e.g. theuncertainty of risk evaluation process including flood

Keywords benefit from flood control projects,
probability distribution, uncertainty
1

Kyoto Universityakobayashi.keita.55e@st,kyoto-u.ac.jp

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THA 2019 International Conference on“Water Management and Climate Change towards Asia’s Water-Energy-Food Nexus and SDGs”
23– 25 January 2019, Bangkok, Thailand.

frequency analysis [3] and risk premium. For example,
in the field of urban planning, it is discussed thatwillingness to pay becomes higher than the expectedvalue of reduced damage cost because of risk aversion[4]. Risk premium is induced from the probability
distribution of reduced damage cost; therefore,
estimating the probability distribution of benefit isimportant to explicitly incorporate the idea of risk
premium into in the process of decision making fordisaster prevention investment.
On the other hand, recent studies havedeveloped methods for estimating a flood risk curve,
i.e. the probability distribution of annual maximum
inundation damage cost, considering influential factorsof risk evaluation such as rainfall time-space
distribution and/or hydrograph variations [2], [5]. For
instance, Tanaka et.al. [5] showed that considering therainfall time-space distribution makes it possible toenhance the accuracy of evaluating flood disaster risk.
This study demonstrates the derivation of theprobability distribution of T-year cumulative reduceddamage cost by generating huge number of rainfall
events in consideration of rainfall time-space
distribution.
From these backgrounds, the purpose of thisstudy is estimating the distribution of T-year
cumulative reduced damage which is defined as sumof annual reduced damage cost over Tyears, andquantifying the probability with which we can actually
benefit from flood control projects. The study area is
Yodo River basin (8,240km2) and several construction
scenarios of the existing dams in the Kizu River basin(Takayama Dam, Murou Dam, Shorenji Dam, Hinachi
Dam, Nunome Dam) are evaluated. For each project,
we estimate the probability distribution of T-year
cumulative reduced damage cost at conjunction area of
three tributaries, Kizu River, Uji River, and Katsura
River, and analyze its stochastic characteristics. The
impact of design of projects and evaluation period on
the estimated distribution is also examined.

On the other hand, we define T-year cumulative
reduced damage cost ‫ୖܦ‬ǡୟ୪୪ ሺܶሻ as follows.
‫ୖܦ‬ǡୟ୪୪ ሺܶሻ ൌ ‫ܦ‬ୠǡୟ୪୪ ሺܶሻ െ ‫ܦ‬ୟǡୟ୪୪ ሺܶሻ

where ‫ܦ‬ୠǡୟ୪୪ ሺܶሻ and ‫ܦ‬ୟǡୟ୪୪ ሺܶሻ are cumulative damage
cost before and after investment, and denoted as‫ܦ‬ୠǡୟ୪୪ ሺܶሻ ൌ σ்௧ୀଵ ‫ܦ‬ୠǡ௧ ǡ ‫ܦ‬ୟǡୟ୪୪ ሺܶሻ ൌ σ்௧ୀଵ ‫ܦ‬ୟǡ௧ ǡEൣ‫ୖܦ‬ǡୟ୪୪ ሺܶሻ൧=E[‫ܦ‬ୠǡୟ୪୪ ሺܶሻ]-E[‫ܦ‬ୟǡୟ୪୪ ሺܶሻ]ൌ σ்௧ୀଵ ൣ‫ܦ‬ୠǡ௧ െ ‫ܦ‬ୟǡ௧ ൧ ൌ σ்௧ୀଵ ൣ‫ୖܦ‬ǡ௧ ൧ ൌ σ்௧ୀଵ ܾǡ

Methodology
DistributionofEstimating

Probability

In this research, we take a Monte Carloapproach to obtain enough number of samples of Tyear cumulative reduced damage cost, by generating
enormous number of extreme rainfall events. Assume
rainfall events follow the following three assumptions
which were used by Tanaka et.al. [5].
Assumption 1. When rainfall occurs, possible
rainfall pattern is limited to the ܰ patterns.
Pattern ߦ௜ ሺ݅ ൌ ͳǡʹǡ ǥ ǡ ܰሻ occurs with probability
pi. Denote rainfall duration time of pattern ߦ௜ asdi.
Assumption 2. Basin averaged total rainfall
rafollows the conditional cumulative distributionfunction (CDF) ‫ܩ‬ோ౗ȁ஽ ሺ‫ݎ‬ୟ ȁ݀௜ ሻgiven di.
Assumption 3. Annual number of occurrences ofrainfall events follows the Poisson distribution
with occurrence ratio ofμa.

(1)

Define‫ݎ‬ሺ‫ݔ‬ǡ ‫ݕ‬ǡ ‫ݐ‬ሻ as rainfall intensity at a location ሺ‫ݔ‬ǡ ‫ݕ‬ሻand time ‫ݐ‬, and rainfall pattern ߦ௜ is defined aswhere b is expected value of annual reduced damage; r
is discount rate; and T is evaluation period. Denoting
annual flooding damage before and after flood control
investment as Da and Db, respectively, b is definedwith annual reduced damage ‫ ୖܦ‬ൌ ‫ܦ‬௕ െ ‫ܦ‬௔ asܾ ൌ ሾ‫ ୖܦ‬ሿ ൌ ሾ‫ܦ‬ୠ ሿ െ ሾ‫ܦ‬ୟ ሿǤ

(5)where ‫ୖܦ‬ǡ௧ is reduced damage cost of year t.

According to the manual of cost-benefit analysis
issued by MLIT [1], benefit of flood defenses over ܶ
years ‫ܤ‬ሺܶሻ is defined as௕

(4)respectively, where ‫ܦ‬ୠǡ௧ and ‫ܦ‬ୟǡ௧ are flooding damage
costs of year t before and after flood control
investment. In this study, we estimate probability
distribution of ܶ-year cumulative reduced damage
cost ‫ୖܦ‬ǡୟ୪୪ ሺܶሻ defined in (3). In addition, weinvestigate impact of evaluation period T length on theprobability distribution of ‫ୖܦ‬ǡୟ୪୪ ሺܶሻ. Note that
expected value of T-year cumulative reduced damage
cost is obtained from (1) and (4), and we can confirm
that benefit ‫ܤ‬ሺܶሻ used in the manual [1] corresponds
to the mean value of ‫ୖܦ‬ǡୟ୪୪ ሺܶሻ when neglecting
discount rate, i.e.

Basic Concept of Estimating
Probability
Distribution of TYearcumulative Reduced Damage
Cost‫ܤ‬ሺܶሻ ൌ σ்௧ୀଵ ሺଵା௥ሻ೟షభǡ(3)‫ݎ‬ሺ‫ݔ‬ǡ ‫ݕ‬ǡ ‫ݐ‬ሻ ൌ ‫ݎ‬ୟ ߦሺ‫ݔ‬ǡ ‫ݕ‬ǡ ‫ݐ‬ሻǡ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ‫ܣ א‬ǡ Ͳ ൑ ‫ ݐ‬൑ ݀ǡ

(6)where A is the targeted watershed. ߦሺ‫ݔ‬ǡ ‫ݕ‬ǡ ‫ݐ‬ሻ isnormalized to satisfy the following equation:

(2)

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THA 2019 International Conference on“Water Management and Climate Change towardds Asia’s Water-Energy-Food Nexus and SDGs”
23– 25 January 2019, Bangkok, Thailand.
ௗ‫׭‬஺ ቀ‫׬‬଴ ߦሺ‫ݔ‬ǡ ‫ݕ‬ǡ ‫ݐ‬ሻ݀‫ݐ‬ቁ ݀‫ ݕ݀ݔ‬ൌ ܵǡ

for five actual dams along the Kizu River(TakayamaDam,
MurouDam,
ShorenjiDam,
HinachiDam, NunomeDam), whhose locations are
displayed in fig. 1. According too Tanaka et.al. [6],when flood beyond design level occurs, the river
overflows around the three tribu
utaries’ conjunction
area, and the overtopping probability of downstream
Yodo River becomes very low. Heence we analyze theeffect of dams from the reduced damagedcost at threetributaries’ conjunction area ind
dicated by the redcolored box in fig.1. In the flood siimulation, we do notconsider dyke breach, and only consider damage fromovertopping.

(7)

where S means the catchment areea of targetedwatershed. Rainfall duration time d is defined asfollows.
݀ ൌ ሼ‫ݐ‬ȁߦሺ‫ݔ‬ǡ ‫ݕ‬ǡ ‫ݐ‬ሻ ൐ Ͳǡ ‫׌‬ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ‫ܣ א‬ǡ ‫ ݐ‬൐ Ͳሽ(8)Definingthe starting time of rainfall ass 0, d indicatesthe maximum time until which rainnfall lasts at a
certain point in the watershed.
Following these assumptionss, we generateimmense samples of T-year cumullative reduced
damage cost, following the steps shownn below.
Step 1. Generate the annual number off occurrencesof
rainfall events ݊ from the Poisson ddistribution
Step 2. Prepare ܰ past rainfall evennts and extract
rainfall patterns ߦ௜ ሺ‫ݔ‬ǡ ‫ݕ‬ǡ ‫ݐ‬ሻ normaalized by total
rainfall amount. Note that tsatisffies inequality,Ͳ ൑ ‫ ݐ‬൑ ݀௜ ǡ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ‫ ܣ א‬where di. is the rainfall
duration time of pattern ߦ௜ ሺ‫ݔ‬ǡ ‫ݕ‬ǡ ‫ݐ‬ሻ; Ais thecatchment area. Generate one paattern with theprobability ͳȀܰ, i.e. randomly.
Step 3. By following Step 2, thhe conditional
CDF‫ܩ‬ோ౗ ȁ஽ ሺ‫ݎ‬ୟ ȁ݀௜ ሻ correspondingg with thegenerated rainfall pattern ߦ௜ ሺ‫ݔ‬ǡ ‫ݕ‬ǡ ‫ݐݐ‬ሻis determined.
Generate total rainfall amouunt‫ݎ‬ୟ from theconditional CDF‫ܩ‬ோ౗ȁ஽ ሺ‫ݎ‬ୟ ȁ݀௜ ሻ. Fromm the obtained
total rainfall amount ‫ݎ‬ୟ and its spatiotemporal
pattern ߦ௜ ሺ‫ݔ‬ǡ ‫ݕ‬ǡ ‫ݐ‬ሻ, one rainfa
fall event isdeterminedmodel and an
Step 4. Running a rainfall-runoff m
inundation model, calculate damage costs
with/without investment, Db andd Da, f. Then,calculate the reduced damage cost for thegenerated rainfall event.
Step 5. Repeating Steps 2 to 4 for ݊ times, sum
reduced damage costs of each rainnfall events andobtain one sample of annual reeduced damage
cost‫ ୖܦ‬.
Step 6. Repeating Steps 1 to 5 for T times, sum
annual reduced damage and get onne sample of Tyear cumulative reduced damage ccost‫ୖܦ‬ǡୟ୪୪ ሺܶሻ. In
this research, discount rate was eliminated to
focus
the
discussiononprobabilistic
characteristics of reduced damage ccost.
Step 7. Repeat Step6 for ‫ ܯ‬times annd estimate theprobability distribution of T-yeear cumulative
reduced damage cost from the many samplesof‫ୖܦ‬ǡୟ୪୪ ሺܶሻ.

Fig. 1. Figure of Yodo Riiver basin.
We used the condition
nal CDF of basinaveraged rainfall on duration ‫ܩ‬ோ౗ȁ஽ ሺ‫ݎ‬ୟ ȁ݀௜ ሻ on the
Yodo River basin and rainfaall-runoff/inundation
models estimated/constructed by Tanaka.
T
et al. [6] asfollows. Rain gauge data for 35 years
y(1980 to 2014)at 156 stations were used in analy
ysis. They extracted
spatiotemporal rainfall patterns of the 1,317 rainfall
events observed over 35 years, i.ee. ܰ ൌ ͳǡ͵ͳ͹. Fromthe basin-averaged rainfall and durationdtime of the
1,317 rainfall events over 35 yearss, they estimated theconditional probability distributiion of one basinaveraged rainfall on duration timee. One rainfall event
is defined as a series of rainfall events without dry
period longer than 5 hours. In order to estimate
conditional probability distributioon, the generalized
Pareto distribution and two-vaariable exponential
distribution were fitted to the marginal distribution ofbasin-averaged rainfall ‫ܩ‬ோ౗ ሺ‫ݎ‬௔ ሻ an
nd rainfall durationtime‫ܩ‬஽ ሺ݀ሻ, respectively. Their correlationcstructureC(‫ܩ‬ோ౗ ሺ‫ݎ‬௔ ሻǡ ‫ܩ‬஽ ሺ݀ሻ) was modelled byb using the normal
copula. According to the Theorem of Sklar[7], thisnotation
indicatesthesimultaneous
distribution‫ܩ‬ோ౗ ǡ஽ ሺ‫ݎ‬௔ ǡ ݀ሻ. Finally, the conditional
cumulative distribution was obtaineed as‫ܩ‬ோ౗ȁ஽ ሺ‫ݎ‬ୟ ȁ݀ሻ ൌଵడ௚ವ ሺௗሻ డௗ‫ܩ‬ோ౗ ǡ஽ ሺ‫ݎ‬௔ ǡ ݀ሻǤ

(9)As a rainfall-runoff model used was 1KDHM [8], a distributed rainfall runnoff model based ona kinematic wave flow approx
ximation. 1K-DHM
calculates the slope runoff and riiver routing at eachcell at around 1km (30 sec) resolution over a twodimensional domain. Slope runofff is simulated withthe continuity and momentum equations of the

Application to the Dam Construction Projects
A. Rainfall generation and Damage cosst calculation
The above presented method was applied tofour different scenarios of dam constrruction projects
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THA 2019 International Conference on“Water Management and Climate Change towards Asia’s Water-Energy-Food Nexus and SDGs”
23– 25 January 2019, Bangkok, Thailand.

kinematic wave theory, considering saturated andunsaturated subsurface flows and surface flow with thefollowing discharge-storage relation.

calculation of T-year cumulative reduced damage costfor ‫ ܯ‬ൌ ͳͲͲǡͲͲͲ times, we estimated the probability
distribution of the benefit of each scenario.
B. Trial Calculation Results of 50 years total reduced
damage cost.

௛ ఉ‫ݒ‬௖ ݀௖ ቀ ቁ ሺͲ ൑ ݄ ൑ ݀௖ ሻ
ௗ೎

‫ݍ‬ൌ൞

‫ݒ‬௖ ݀௖ ൅ ‫ݒ‬௔ ሺ݄ െ ݀௖ ሻሺ݀௖ ൑ ݄ ൑ ݀௔ ሻߙሺ݄ െ ݀௖ ሻ௠ ൅ ‫ݒ‬௔ ሺ݄ െ ݀௖ ሻ ൅ ‫ݒ‬௖ ݀௖ ሺ݀௔ ൑ ݄ሻ

(10)Among the five dams, we first set project J:
there is no dam on the Kizu River and construct
Takayama Dam on the basin. Figure 2 shows thehistogram of simulated T-year cumulative reduced
damage cost. Red line indicates the expected value.
JPY is converted to USD at a rate of 100 yen per
dollar. Obviously, the distribution is skewed leftwards
with a long tail. The probability with which the benefit
is equal to or over the expected value is about 10-20%,
and one with which benefit is obtained is about 55%.
On the other hand, extremely large benefit values
much larger than the median value occurs with acertain probability. These indicated that the expectedvalue integrated different types of benefit and made itdifficult to grasp the whole characteristic of the benefitof the project. By estimating the distribution of
reduced damage cost as fig.2, more detailed
information as demonstrated above becomes available,
which is expected to support more rational decision
making.

where, q is the slope runoff discharge per unit width; his the water depth; da and dc are the water depth
corresponding to the maximum water content ofsaturated and unsaturated soil layers, respectively; va
and vc are the water velocity of saturated andunsaturated soil layers, respectively; ߙ ൌ ݊Ȁξߠ; nis the roughness coefficient; and ߠ is the slope
gradient. River flow is simulated with a kinematicwave model. All dams in Yodo basin are modeled inaccordance with their operation rules, and rainfallrunoff before/after a project is represented by
excluding/including the corresponding dam models.
Overflow inundation over the floodplain wasmodelled with one dimensional local inertial equation
for river routing and two dimensional one forfloodplain simulation. One dimensional local inertial
equation is denoted as
డ஺
డ௧
డொ
డ௧

൅ ݃‫ܣ‬

൅డሺ௛ା௭ሻ
డ௫

డொ
డ௫

(11)

ൌ Ͳǡ
ொȁொȁ

൅ ݃݊ଶ రΤయ ൌ Ͳǡ
ோ

஺

(12)

where t is the time; x is the location in the downstream
direction; A is the cross-sectional area; Q is thedischarge; z is the elevation; ݃ is the gravity
acceleration; n is the roughness coefficient; and R is
the hydraulic radius. Neglecting the advective term of
the Saint-Venant equation, high speed arithmetic
operation is realized with the same level of accuracy as
the diffusion equation. Damage cost is calculated forhouse, households, and office depreciable/stock assets,
by multiplying exposed asset at each cell of theinundation model by damage ratio which is a functionof maximum flood depth. The function is defined in
the manual of MLIT [1].
In accordance with MLIT’s manual [1],evaluation period T was set as 50 years.. Whendisaggregating a rainfall event into to basin-averaged
cumulative rainfall and its spatiotemporal pattern as inthis study, it is obvious that flood damage costmonotonically increases with basin-averaged rainfall
for a fixed rainfall pattern; therefore, we havedeveloped a relation between cumulative rainfall andresulting flood damage cost for all the rainfall patterns
before Monte Carlo simulation, then in Step 4 to
calculate flood damage cost, flood damage cost for thegenerated rainfall event was calculated by linearlyinterpolating the relation for the generated rainfall
pattern, instead of running rainfall-runoff/inundation
models for all the generated events. Repeating the

Fig. 2. Histgram of 50-years cumulative reduced
damage cost of the project constructing Takayam
Dam. Red line indicates expected value.
Differences of Probability Distribution between
Projects
Among the five target dams, the Takayama
Dam has the largest flood storage capacity. As shownin fig.1, among the other four dams, Nunome Dam islocated on a different tributary river. To examine theimpact of the location of dams on the estimatedprobability distribution, we split the construction
project of the four dams into projects K, and project L:
Project K first constructs three dams except for the
Nunome Dam (Shorenji Dam, Murou Dam, andHinachi Dam), and Project L then constructs the
Nunome dam. Table.1 shows the statistics of threeprojects (J, K, L) gained from their probability
distribution of 50-year cumulative reduced damage
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THA 2019 International Conference on“Water Management and Climate Change towards Asia’s Water-Energy-Food Nexus and SDGs”
23– 25 January 2019, Bangkok, Thailand.

cost. Comparing with Projects K and L, Project L
shows lower skewness and higher probability ofgetting more befit equal to or more than expectedvalue, and the occurrence of benefit.
As shown in fig.1, in the Project K,
Takayama Dam is already constructed in the same
tributary, so dams constructed in Project K canmitigate damage only for flood causing inflow volume
over the storage capacity of Takayama Dam. On theother hand, the Project L constructs Nunome Dam in
the tributary where no dam has been constructed
before; thusNunome dam more frequently shows flood
control effect than dams installed by Project K.
Accordingly, Project L is expected to benefit the target
area more frequently than Project K. As shown in
Table.1, difference between the expected value of
Projects K and L is about 26%. On the other hand, theprobability with which the benefit equal to or morethan its expected value by Project L is 230% larger
than Project K, indicating that using other statistics
provided different characteristics of projects from theexpected value .

Conclusions
In the present benefit evaluation method,
benefit is represented as the expected value of
cumulative reduced damage in evaluation period.
However, flooding is a low-frequency event,especially in highly protected areas; thus,it is highly
uncertain whether actual reduced damage cost is
distributed around its expected value. In this research,in order to quantify stochastic characteristics ofbenefit, we developed an estimation method of T-year
cumulative reduced damage cost probability
distribution, and applied the method to several
scenarios of flood control projects on the Kizu River.
By estimating probability distribution of Tyear cumulative reduced damage cost, we can get
more statistics as well as mean value, and reveal thecharacteristics of each project. Following findings
were obtained in this study:
1. In all the four projects, probability distribution
skewed leftwards, and the probability withwhich we can actually obtain the benefit equal
to or more than the expected value is about 1020%. On the other hand, extremely large
benefit values is expected with a certain
probability. In the process of averaging reduced
damage cost,
2. The expected value of benefit and otherstatistics such as the probability with which
benefitisobtainedshow
different
characteristics depending on projects
3. When we set longer evaluation period, 1000
years, distribution of cumulative reduced
damage approaches normal distribution, andbenefit wasevenly distributed around its
expected value, compared with offsetting
evaluation period to 50 years. This indicatedthat T-year cumulative reduced damage cost
was distorted because the evaluation period
was not long enough to represent the expectedvalue as the benefit due to low frequency offlooding.

Relation Between Probability Distribution andCentral Limit Theorem
When evaluation period T is large enough, probability
distribution of T-year cumulative reduced damage costtheoretically converges to normal distribution, so
reduced damage cost is assumed to distribute around
its expected value. Figure.4 shows the variation ofhistogram of Project J when changing the evaluation
period from 50 years to 1,000 years. For comparisonof distribution characteristics, cumulative reduced
damage cost was converged to annual
Table I. Benefit statsitics of each project
Project

J

K

L

Expected value

655

197

157

Standard variarion

2240

804

355

Skewness

38.3

5.44

2.92

Probability with which benefit
becomes larger than expected
value

0.18

0.10

0.23

Occurrence probability of benefit

0.55

0.30

0.74

mean value by dividing evaluation year T. We canconfirm that probability distribution of reduced
damage cost skewed leftwards and have a long tail inlimited evaluation period of 50 years, but the
distribution approaches bilaterally symmetrical and theprobability we can actually get benefit equal to or
more than the expected value increases as theevaluation period becomes larger. This indicated thatthe general evaluation period of 50 years are not quite
enough to represent the annual reduced damage costby its expected value.

Fig. 3.Histgram of 50 and 1,000 years cumulative
reduced damage cost of the project94

THA 2019 International Conference on“Water Management and Climate Change towards Asia’s Water-Energy-Food Nexus and SDGs”
23– 25 January 2019, Bangkok, Thailand.

This study proposed an idea to estimate theprobability distribution of T-year cumulative reduced
damage cost for providing information about various
statistics of reduced damage cost and making morerational decision making. We will discuss how toincorporate this idea into the actual decision making
process for advanced decision making process of flood
control projects.

[5] Tanaka, T., Tachikawa, Y., Ichikawa Y., Yorozu,
K. “A flood risk curve development using
conditional probability distribution of rainfall on
duration”, Journal of JSCE B1 (HydraulicEngineering), Vol. 72, No. 4, I_1219-I_1224,
2016.
[6] Tanaka, T., Ichikawa, Y., Yorozu, K., Tachikawa,Y. “Development of a probablistic flood damage
map and its application to benefit analysis of landraising”, Journal of JSCEJournal of JSCEB1(Hydraulic Engineering), Vol. 72, No. 4, I_1477I_1482, 2018.
[7] Nelsen, R., 2006. An Introduction to Copulas.
Springer, New York.
[8] Tachikawa, Y., Tanaka, T.: 1K-DHM/1K-FRM,
http://hywr.kuciv.kyoto-u.ac.jp/products/1kDHM/1k-DHM.html

Acknowledgment
This study was supported by Kansai Energy
Recycling Foundation.
References[1] The flood control economic survey manual (draft)
pp. 15-62, 2005.
[2] Apel, H., Thicken, A. H., Merz. B. and Blöschl,
G. “A probabilistic modelling system forassessing flood risks”, Nature Hazards,” Vol. 38,
No. 1-2, pp. 79-100, 2006
[3] Falter, D., Schröter, K., Dung, N. V.,
Vorogushyn, S., Kreibich, H., Hundecha, Y Apel,
H., Merz, B. “Spatially coherent flood risk
assessment based on longterm continuous
simulation with a coupled model chain. Journal of
Hydrology, Vol. 524, pp. 182-193 2015.
[4] Yokomatsu, M., Kobayashi, K. “Economic
benefit of physical risk reduction by disasterprevention investment”, No. 660/Φ-49, pp.111123, 2000.

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