Estimation of Real-time Flood Risk on Roads Based on Rainfall Calculated by the Revised Method of Missing Rainfall

Recently, flood damage by frequent localized downpours in cities is on the increase on account of abnormal climate phenomena and the growth of impermeable areas due to urbanization. This study suggests a method to estimate real-time flood risk on roads for drivers based on the accumulated rainfall. The amount of rainfall of a road link, which is an intensive type, is calculated by using the revised method of missing rainfall in meteorology, because the rainfall is not measured on roads directly. To process in real time with a computer, we use the inverse distance weighting (IDW) method, which is a suitable method in the computing system and is commonly used in relation to precipitation due to its simplicity. With real-time accumulated rainfall, the flooding history, rainfall range causing flooding from previous rainfall information and frequency probability of precipitation are used to determine the flood risk on roads. The result of simulation using the suggested algorithms shows the high concordance rate between actual flooded areas in the past and flooded areas derived from the simulation for the research region in Busan, Korea.


Introduction
The frequency and intensity of natural disasters are increasing due to global warming and climate change.Even if the related technique for weather forecasting is very developed, flooding damage from localized torrential rain and typhoons, due to climate change and the growth of impermeable areas by urbanization, is not shrinking in the world.Most cities have important infrastructures, such as roads, and they also have high population densities.For this reason, cities are severely damaged if inundation occurs in the cities.As a typical example, the torrential rain that poured in Seoul, Korea, between 26 July 2011 and 27 July 2011, caused 62 deaths and resulted in 980 flood victims and 19,215 inundated homes, according to official figures [1].
Because of repeated flood damage like this, many studies in the world are being conducted regarding methods that can be used to reduce flood damage and establish proper countermeasures.In this study, we are focused on flooding on roads, which is the basis of all means of transportation.
Many researchers are engaged in studies relating to flooding.Research on the development of a flood risk index is representative of these kinds of studies.The flood risk index was originally developed for an indicator, which is analysis of the death toll by flooding.Today, the flood risk index has been used as a criterion to give priority for solving flood damage.It has established the set-up for flood prevention measuring in many countries.Many international organizations, including OECD (Organization for Economic Cooperation and Development), UNDP (United Nations Development Program), UNCSD (United Nations Commission on Sustainable Development) and UNEP (United Nations Environment Program), have developed the risk assessment index for natural disasters, such as flooding, and have given the risk information to each country.These risk indexes are used to help Third World countries by offering assistance from the UN [2].Furthermore, many countries are heavily invested to establishing ways to prepare for floods at a government level.In particular, Japan faces the most danger for natural disasters, such as earthquakes and typhoons.The government of Japan developed a flood vulnerability index and uses it to establish flood prevention measures.Many scholars abroad have had their research related to flood risk published.Connor and Hiroki proposed a method for assessing flood vulnerability caused by climate change in order to help make decisions for structural and non-structural countermeasures to reduce flood vulnerability [3].Birkmann proposed a strategy to reduce the vulnerability of flooding by analyzing factors for environmental, social and economic risk [4].
However, a flood risk index should be comprised not of national factors, but rather of local factors, because regional characteristics can affect the type of flooding that occurs in a particular area.In other words, it is hard to apply the flood risk index of one country to another country, because flooding is affected by regional characteristics.Many studies are being carried out regarding the flood risk in Korea, which is the object of this study.Similarly to the government of Japan, in Korea, the potential flood damage concept was introduced in the Water Vision 2020, which was planned by the Ministry of Land, Transport and Maritime Affairs (MLTMN).In this concept, the flood risk index is calculated based on the possibility of damage for each region [5].Lim et al. [2] suggested a method to define and apply an appropriate index that can measure the risk of regional flood damage and used the pressure-state-response structure to develop the flood risk index.Kim et al. [6] quantitatively analyzed the severity of flash floods by estimation of a flash flood index from probability rainfall data in a test basin.Jo et al. [7] developed a new flood index that measures the severity of floods in small ungauged catchments for use in local flood predictions by regression analysis between the new flood index and rainfall patterns.
Looking into previous research, most of the studies are about flood preparation for large units, such as a city or a large basin.There is a lack of research on sudden local flooding for a small area (unit), which has occurred with higher frequency recently [7].
Todays, research on a real-time system is trending in computer science, and studies for automation and real-time systems are being carried out in many areas, such as e-Learning [8], e-Meeting [9], GPS [10,11], and so on.Accordingly, we are interested in estimating rainfall in real time for a specific location, not a given time period.
The ultimate goal of this study is to develop a flood risk index of an intensive type targeted at roads as a part of a study about sudden local flooding.To calculate the real-time accumulated rainfall, which is a decisive factor of the flood risk index on a road link, the inverse distance weighting method (IDW) is used along with the real-time accumulated rainfall observed directly at the Automatic Weather System (AWS) and updated in real time through the web.In addition to this factor, the flooding history of roads, the rainfall range causing flooding, calculated from accumulated rainfall information when flooding has arisen in the past, and standard frequency probability precipitation for road design are selected as factors to determine the flood risk index for roads.

The Whole Process
A road is composed of a number of records, which are named road links on map data, because a road has many change points, due to intersections, curves, etc.Therefore, a flood risk index is calculated individually for each road link.The flooding history of each road, the rainfall range causing flooding, dangerous roads for flooding, real-time accumulated rainfall and standard frequency probability precipitation are used as factors for the flood risk index of a road link in this study.Figure 1 shows the flowchart for the process to calculate a flood risk index of a road link.

Flooding History
The collection and analysis of flooding history information is the general work to develop the flood risk index, because areas prone to flooding are exposed to flooding damage easily [12].
The flooded roads are extracted in two ways in this study.First, the flooded regions (inundation trace map) provided as a type of vector (polygon type) and the ones made by the governmental organization (Korea Cadastral Survey Corporation) are used for this work.Road links included in these flooded regions of the research region (Busan, Korea) are extracted.The extraction work of flooded roads is completed by using the system tools provided by ArcGIS Desktop.The road links included in the area are those that the named attribute disaster type has "flooding" as the value by using the Select and Clip tools.From this work, approximately 2398 road links out of 69,408 road links of the research region were extracted.
Second, the road links restricted by flooding are extracted using newspaper reports related to flooding from 2007 to 2011.Fifty-one reports of flooding events were collected, and 534 road links were extracted by identification work with a real map.Finally, approximately 3007 road links out of a total of 69,408 road links of the research region were extracted through these two methods.Figure 2 shows the extracted road links as a map.

Rainfall Range Causing Flooding
To find the rainfall range causing flooding on each road link, the information of accumulated rainfall at AWS stations when flooding has arisen in the past and the IDW method are used.The accumulated rainfall is not actually observed at a road link.For this reason, we regard a road link as a missing rainfall site and use IDW, which is one of the revised methods of missing rainfall, to calculate the probable rainfall on a road link.

The Revised Method of Missing Rainfall
There are many methods to revise missing rainfall.Among them, the arithmetic average method (AA), the inverse distance weighting method (IDW) and the coefficient of correlation weighting method (CCW) are suitable for processing by computer systems, because they do not need an ex ante analysis [13].In this study, the IDW method is selected, because it is the most commonly used method in weather-related systems.Formulas (1) and ( 2) are shown below in relation to the calculation formula of the IDW method.
where   o Z s is the revised rainfall (mm) at o s ,   i Z s is the observed rainfall (mm) at i s , n is the number of observing sites and i w is the weight of i s .
where io d is the distance between i s and o s and p is the degree of weight changes by distances.
Commonly, p is set as 2.0, and also, the result of IDW method is the best when p is set as 1.5 or 2.0 [13].

Rainfall Range Causing Flooding at AWS
The maximum and minimum values of 15-minute and one-hour accumulated rainfalls, respectively, have been extracted at AWS stations for the past five years, from 2007 to 2011.These four values (the maximum of 15 minutes of accumulated rainfall, the minimum of 15 minutes of accumulated rainfall; the maximum of one hour of accumulated rainfall and the minimum of one hour accumulated rainfall) at each AWS site become rainfall ranges causing flooding.Table 1 shows four values used as the rainfall ranges causing flooding at 11 AWS stations in Busan, which is the research region.

Rainfall Range Causing Flooding on Road Links
The rainfall range causing flooding on each road link is calculated using the IDW method and the values from Table 1.For example, in order to find the maximum value of 15 minutes of accumulated rainfall, which is one of four rainfall ranges causing flooding, the distances between a road link and each AWS site are calculated, and then, the final value is calculated by using Formulas (1), ( 2) and the values of the "Max of 15 min" column from Table 1.
These four values of each road link, of course, are calculated automatically in real time by the developed program in this study.As a result, all 69,408 road links have four values used as rainfall ranges causing flooding, which are similar to those in the AWS site in Table 1.

Frequency Probability Precipitation
The frequency probability of precipitation is calculated by the rainfalls, which is relevant to the appropriate interval recurrence of the past maximum rainfalls through probability analysis.It mainly has been used to design hydraulic structures.
The flood risk index of a road link with a flooding history is determined by using the rainfall range causing flooding, which is based on the past rainfall information.However, if there is no flooding history on a road link, then there is no need to measure the range of flood damage rainfall in that area.Table 2 shows the probability precipitation on rainfall frequency for the road design provided from the government office in the research region, Busan, South Korea.

Real-Time Accumulated Rainfall
Fifteen-minute and one-hour accumulated rainfalls at AWS stations are updated and can be acquired every minute through the web page of the Meteorological Administration.Therefore, the real-time accumulated rainfalls at the AWS stations are taken from the web; then, the real-time accumulated rainfall on each road link is estimated using the observed rainfall information at AWS stations and the IDW method.Figure 3 shows the process to calculate the real-time accumulated rainfall on a road link.

Revision of Rainfall-Related Factors
To develop the flood risk index in this study, two kinds of accumulated rainfall data, 15-minute and 1-hour accumulated rainfalls, are used.In order to convert these two accumulated rainfalls into only one value, Formula (3), as below, is used.
That is to say, one minute of accumulated rainfall is calculated respectively from 15-minute and one-hour accumulated rainfalls.The weighted value is approached by the method that is based on the relative importance of the details of each indicator through the preferences of experts and residents of that area.In this method, the fact that there is no difference between the weighted value and non-weighted value in terms of the evaluation results is reported [2].Moreover, the inappropriate weighted value misleads the final results, and because of that, we attempted to use an equally weighted value for each factor.As a result, the minute unit rainfall is acquired by using two kinds of rainfall.Formulas ( 4)-( 6), which are used in order to revise rainfall-related factors, are as follows: where, 0 ≤ α ≤ 1, ACRF is accumulated rainfall and Current_Rain_Index is a sub-index for the real-time accumulated rainfall.
where, 0 ≤ α ≤ 1, FY is frequency years and Frequency_Rain_Index is a sub-index for the frequency probability precipitation.

Levels of Flood Risk Index
In this study, the flood risk index is divided into five levels with reference to the Emergency Action Plan (EAP).The higher the level is, the more dangerous the flooding on a road can be.
EAP is the legal plan to minimize the damage when facilities collapse or when there is a risk of collapse.It will be given for one of five hierarchical categories: "no risk", "attention", "cautions", "alert" and "critical."From among these, "critical" is the highest level, that is to say the most dangerous level [1].

Decision Algorithm of Flood Risk Index
To develop the flood risk index on roads, the algorithm is split into two parts: the road links with flooding history or with no flooding history.If the road has no flooding history, it is considered as a dangerous road for flooding if it is included in the flood expectation map.
If a road link has a flooding history, its flood risk index is determined according to the rate between the index of the rainfall range causing flooding Formula (4) and the index of current rainfall Formula (5).However, if there is no flooding history on the roads, it is divided again by whether the road link is included in the flood risk area of the flood expectation map.Then, its flood risk index is determined according to the rate between the index of the frequency probability precipitation Formula (6) and the index of current rainfall Formula (5). Figure 4 shows the algorithm to determine the flood risk index on roads in real time, as suggested in this study.

Simulations
To verify the suggested algorithm for the real-time flood risk index on roads, we collected the flood events for the last six years from 2007 to 2012 and simulated two cases that caused much damage to the research region, Busan, Korea.The date/time and rainfall information at that time are shown in Table 3.In the case of Simulation 1, 310 mm was reported per day in Busan, and this was the most accumulated rainfall in 18 years.It was reported that 10 road regions were flooded.We extracted the 66 road links by comparing the realistic map to flooded roads at the time.For Simulation 2, a maximum of 80 mm per hour and 231 mm per day was recorded in Busan.A total of 17 road regions were flooded at that time, and we extracted 179 road links through the map data.Figures 5 and 6 show the results of the simulation as a map.Table 4 shows the result of the simulation in more detail.The number of links that reached more than Level 4 was 43 out of 66 for Simulation 1 and 166 out of 170 for Simulation 2. To compare the two results, the east and west part of the areas are clearly different from each other.In the case of Simulation 1, the amount of rainfall for the AWS station (923, Gijang) marked to the east of Figure 5 is three times more than Simulation 2. Therefore, road links that are close to this AWS station have a higher level of flood risk index than Simulation 2. For a similar reason, road links near the marked AWS station (921, Gaduck) of Simulation 2 have a higher level than Simulation 1.

Conclusions
In this study, we suggested a method to develop a flood risk index on a road that is of an intensive type.This is a study about sudden local flooding, which has been occurring with greater frequency recently, in contradistinction to a flood risk index for a large unit, such as a city or a large basin, which has previously been researched in general.The aim of this study is the development of a flood risk index on road links using real-time accumulated rainfall to give information for the flood risk of roads to drivers in advance.
Flooding history, the rainfall range causing flooding, real-time accumulated rainfall and frequency probability precipitation are used as factors that determine the flood risk index on a road link in real time.First, we collected the flooding history data of road links from the inundation trace map and newspaper reports and extracted 3007 road links out of a total of 69,408 road links of the research region (Busan, South Korea).Then, every road link is allocated a rainfall range causing flooding calculated by the analysis of past rainfall information at AWS stations and real-time accumulated rainfall using the amount of rainfall at AWS stations updated every minute through the Internet by the Korea Meteorological Administration.In these cases, AWS stations have rainfall information, but a road link has none, because its rainfall is not measured directly.For this reason, we need a method to estimate the amount of rainfall on a road link using observed rainfall at AWS stations.To interpolate rainfall, we consider a road link as an unmeasured missing rainfall site; then, the inverse distance weighting (IDW) method, which is one of the revised methods for missing rainfall, was selected to calculate the probable accumulated rainfall on each road link.The IDW method is a suitable method in a computing system, and it is commonly used to assess precipitation, because of its simplicity.In other words, the IDW method is more appropriate than other revised methods for a real-time computing system, which is our development system environment in this study.Lastly, the frequency probability

Figure 1 .
Figure 1.The flowchart for the development of the real-time flood risk index on roads.AWS, Automatic Weather System.

Figure 2 .
Figure 2. Extracted road links from the flooding history.

Figure 3 .
Figure 3. Process for calculating the real-time accumulated rainfall on each road link.IDW, Inverse Distance Weighting.

Figure 4 .
Figure 4.The algorithm to develop the road's flood risk index in real time.

Table 1 .
Rainfall ranges causing flooding at AWS stations in Busan, Korea.
AWS Code

Max of 15 min Min of 15 min Max of 1 h Min of 1 h
Note: Provided by the Korea Meteorological Administration; Max of 15 min and Min of 15 min are the maximum and minimum values of 15 min of accumulated rainfall values; Max of 1 h and Min of 1 h are in the same vein.

Table 2 .
The frequency probability precipitation (mm) in Busan, Korea.
Note: Provided by the Korea Ministry of Land, Infrastructure and Transport.

Table 3 .
The real-time rainfall information of simulated data (mm).

Table 4 .
The result of simulation in detail.The accordance rate was calculated with links having more than level 4 as Flood Risk Index (FRI).