Development of Nomogram for Debris Flow Forecasting Based on Critical Accumulated Rainfall in South Korea

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Article Development of Nomogram for Debris Flow Forecasting Based on Critical Accumulated Rainfall in South Korea

Dong-Ho Nam, Suk-Ho Lee and Byung-Sik Kim *

Department of Urban Environment & Disaster Management, School of Disaster Prevention, Kangwon National University, 346 Joongang-ro, Samcheok-si Gangwon-do 25913, Korea; [email protected] (D.-H.N.); [email protected] (S.-H.L.) * Correspondence: [email protected]; Tel.: +82-33570-6819

Received: 16 September 2019; Accepted: 16 October 2019; Published: 19 October 2019

Abstract: Climate change causes extreme weather events worldwide such as increasing temperatures and changing rainfall patterns. With South Korea facing growing damage from the increased frequency of localized heavy rains. In particular, its steep slope lands, including mountainous areas, are vulnerable to damage from landslides and debris flows. In addition, localized short-term heavy rains that occur in urban areas with extremely high intensity tend to lead a sharp increase in damage from soil-related disasters and cause huge losses of life and property. Currently, South Korea forecasts landslides and debris flows using the standards for forecasting landslides and heavy rains. However, as the forecasting is conducted separately for rainfall intensity and accumulated rainfall, this lacks a technique that reflects both amount and intensity of rainfall in an episode of localized heavy rainfall. In this study, aims to develop such a technique by collecting past cases of debris flow occurrences and rainfall events that accompanied debris flows to calculate the rainfall triggering index (RTI) reflecting accumulated rainfall and rainfall intensity. In addition, the RTI is converted into the critical accumulated rainfall (Rc) to use rainfall information and provide real-time forecasting. The study classifies the standards for flow debris forecasting into three levels: ALERT (10–50%), WARNING (50–70%), and EMERGENCY (70% or higher), to provide a nomogram for 6 h, 12 h, and 24 h. As a result of applying this classification into the actual cases of Seoul, Chuncheon, and Cheongju, it is found that about 2–4 h of response time is secured from the point of the Emergency level to the occurrence of debris flows.

Keywords: rainfall intensity; debris ﬂow forecasting; rainfall triggering index (RTI); critical accumulated rainfall (Rc); nomogram

1. Introduction Global warming-initiated, extreme weather events receive great attention worldwide. South Korea, in particular, has faced such events, including increasing temperature and rainfall and a growing number of heavy rain days, for the recent 100 years [1], which has led to natural disasters such as localized heavy rainfall, wind and waves, droughts, and heavy snows. Notably, the summer season from June to September shows a tendency of having an increased number of debris flows [2]. Debris flows are a type of natural disaster that occurs by a complex interaction between flooding from heavy rainfall and ground soil, as well as by a wide range of other factors such as thawing during spring, indiscriminate logging, and forest fire. They are also, commonly, secondary damage from typhoons and localized heavy rains, with the latter being their main cause because of how heavy rainfall brings an increase in flow speed, soil loss, and large-scale movement of rocks that lead to huge disasters [3].

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In South Korea, damage from debris flows has been reported frequently nationwide, with examples such as Inje County and Pyeongchang County of Gangwon Province in 2006; Seoul, Chuncheon City, and Pocheon City in 2011; Samcheok City in 2012; Busan Metropolitan city in 2014; and Cheongju City and Cheonan City in 2017. For this study, debris flows are seen as mainly from localized heavy rains. In this regard, it requires a thorough understanding of the characteristics of rainfall events that cause debris flows, when establishing an early-warning system for debris flow damage and related planning, maintaining, or managing disaster prevention facilities. In South Korea, studies on forecasting of debris flows and landslides are mainly about using the related standards provided by the Korea Forest Service and the Korea Meteorological Administration to review their relevance with an analysis of rainfall events that cause debris flows and landslides or to quantitatively calculate the standards. However, studies on debris flow forecasting based on rainfall events have not been actively conducted [4–10]. Tables1 and2 show the forecasting standards for landslides and rainfall, provided by the Korea Forest Service and the Korea Meteorological Administration, respectively. Such standards mainly defined rainfall and accumulated rainfall separately.

Table 1. Landslide forecasting standard (Korea Forest Service).

Maximum Hourly Daily Rainfall Continuous Rainfall Rainfall (mm) (mm) (mm) Landslide warning 20–30 80–150 100–200 Landslide alarm >30 >150 >200

Table 2. Rainfall forecasting standard (Korea Meteorological Administration).

3 h Rainfall (mm) 12 h Rainfall (mm) Rainfall warning >60 >110 Rainfall alarm >90 >180

South Korea forecasts landslides and debris flows by analyzing rainfall and basin characteristics and using models to calculate the triggering factors. With the current advancement in radar technologies, studies are continuously conducted for forecasting using radar data [11–21]. Therefore, the study attempted to establish a method that considers rainfall intensity and accumulated rainfall not as an independent factor but a function. To this end, it modified the RTI calculation method developed by Jan and Lee [22] to support the forecasting of debris flows potentially caused by rainfall. The study used past rainfall data from 80 stations located at the areas that experienced damage from debris flows from 2012 to 2013 for rainfall intensity and accumulated rainfall for each rainfall duration. Based on this, it classified debris flow damages to estimate the rainfall triggering index (RTI). In addition, it calculated the average intensity of the rainfall that causes debris flows. For debris flow forecasting, the study classified the forecasting standards for accumulated rainfall into ALERT (RTI from 10 to 50%), WARNING (RTI from 50 to 70%), and EMERGENCY (RTI from 70% or higher). The 10%, 50%, and 70% RTIs were divided by the average rainfall intensity to estimate the critical accumulated rainfall (Rc) and its curve by duration. The calculated Rc was applied to the actual cases of Umyeon Mountain of Seoul, Chuncheon of Gangwon County, and Cheongju City of Chungcheongbuk Province, where damage actually occurred, to make the debris flow forecasting for 24 h of the rainfall triggering such, which aims to determine its applicability for debris flow forecasting.

2. Materials and Methods To analyze the influence from the interlinkage between accumulated rainfall and rainfall intensity, the study collected the rainfall data of 80 areas that experienced debris flow damage in Gangwon Province from 2012 to 2013 and used the rainfall amount by duration with a maximum of 24 h in Water 2019, 11, 2181 3 of 23 whichWater 2019 debris, 11, x flowsFOR PEER occurred. REVIEW Based on this, the RTI, an index for accumulated rainfall and rainfall3 of 23 intensity was calculated for 6 h, 12 h, and 24 h, respectively. Furthermore, the study estimated an rainfall intensity was calculated for 6 h, 12 h, and 24 h, respectively. Furthermore, the study average rainfall intensity at the time of debris flow occurrence before using the RTI equation to calculate estimated an average rainfall intensity at the time of debris flow occurrence before using the RTI Rc for each duration (6 h, 12 h, and 24 h). The Rc of 10%, 50%, and 70% was then used with the equation to calculate 𝑅 for each duration (6 h, 12 h, and 24 h). The 𝑅 of 10%, 50%, and 70% was occurrence probability to define the three risk levels. In addition, based on actual damage cases, then used with the occurrence probability to define the three risk levels. In addition, based on actual the study developed a nomogram for continuous rainfall to verify its applicability for debris flow damage cases, the study developed a nomogram for continuous rainfall to verify its applicability for forecasting (Figure1). debris flow forecasting (Figure 1).

Figure 1.1. Flowchart for debris ﬂowflow forecasting.

3.3. Theoretical Background

3.1.3.1. Debris Flow AA debrisdebris flowflow refers refers to to the the dynamic dynamic phenomenon phenomenon where where soil, soil, rocks, rocks, and an floatingd floating substances substances flow downflow down a slope a slope by gravity by gravity with changeswith changes in their in shapetheir shape and sizes. and sizes. Sharpe Sharpe [23] di [23]fferentiated differentiated debris debris flows fromflows debris from debris avalanches avalanches in his United in his United States–based States–based studies, studies, with the with former the asformer a movement as a movement of soil and of rockssoil and saturated rocks withsaturated water atwith a water water channel at a water with achannel steep slope, with and a thesteep latter slope, as a phenomenonand the latter where as a fragmentedphenomenon soil where of an fragmented upper layer soil at a steepof an slopeupper flow laye fast,r at a similar steep toslope a snow flow avalanche. fast, similar As to shown a snow in Figureavalanche.2, the As path shown of debris in flowsFigure comprises 2, the path three of zones: debris initiation, flows transportation,comprises three and zones: deposition initiation, [ 24]. Sincetransportation, debris flows and have deposition pressure [24]. 4–5 Since times debris higher flows than have that pressure of flooding 4–5 water, times givenhigher that than they that are of mixedflooding with water, soil given and rocks, that they their are external mixed forcewith issoil 10 and times rocks, higher their than external that of force flooding is 10 times water higher when conflictingthan that of with flooding facilities water [25 when]. conflicting with facilities [25]. Major factors that have influence on the occurrence of debris flows include topographic factors (slope angle, slope impact, and facilities to reduce the flow of pumice stones and soil), geographical factors (depth of soil layers and characteristics of top soil), and hydrological factors (amount of rainfall). Among such factors, rainfall increases pore water pressure and soil weight and leads to erosion and scour of the surface. The analysis of scales and accumulated rainfall indicates that an area with 200 mm or higher of rainfall and 20 mm/h of rainfall intensity will face severe damage with increasing frequency (Figure 3). This result suggests that areas with low vulnerability may experience a higher probability of debris flow occurrence, in a rainfall episode with a certain level

Water 2019, 11, x FOR PEER REVIEW 4 of 23

Waterand intensity.2019, 11, 2181 Therefore, for the rainfall that triggers a debris flow, it is standard to consider 4both of 23 accumulated rainfall and rainfall intensity observed at the time of its occurrence.

Water 2019, 11, x FOR PEER REVIEW 4 of 23 and intensity. Therefore, for the rainfall that triggers a debris flow, it is standard to consider both accumulated rainfall and rainfall intensity observed at the time of its occurrence.

Figure 2. Initiation, transportation, and depositiondeposition of debris ﬂowsflows [[25].25].

Major factors that have influence on the occurrence of debris flows include topographic factors (slope angle, slope impact, and facilities to reduce the flow of pumice stones and soil), geographical factors (depth of soil layers and characteristics of top soil), and hydrological factors (amount of rainfall). Among such factors, rainfall increases pore water pressure and soil weight and leads to erosion and scour of the surface. The analysis of scales and accumulated rainfall indicates that an area with 200 mm or higher of rainfall and 20 mm/h of rainfall intensity will face severe damage with increasing frequency (Figure3). This result suggests that areas with low vulnerability may experience a higher probability of debris flow occurrence, in a rainfall episode with a certain level and intensity. Therefore, for the rainfall that triggers a debris flow, it is standard to consider both accumulated rainfall and rainfall intensity observedFigure at the 2. time Initiation, of its occurrence.transportation, and deposition of debris flows [25].

Figure 3. Accumulated rainfall and rainfall intensity at the time of debris flow occurrence [6].

3.2. Estimation of Critical Accumulated Rainfall Using RTI The RTI model developed by Jan and Lee [22] was designed to forecast debris flows triggered by rainfall in real time. For the RTI calculation, rainfall intensity (I) and accumulated rainfall (𝑅) are used as follows.

RTI = 𝐼 × 𝑅 (1)

In the equation above, I indicates rainfall intensity (mm/h) and 𝑅 is the accumulated rainfall (mm) observed shortly before the occurrence of debris flows. Among of the rainfall episodes for up to seven days, the one that continues for 24 h with a direct influence on debris flows is considered as antecedentFigureFigure rainfall. 3. 3. AccumulatedAccumulated The study rainfall rainfall used and and the rainfall rainfall rainfall intensity intensity accumulated at at the the time time for of of durationdebris debris flow ﬂow 6 occurrence h, 12 h, and [6]. [6]. 24 h to estimate the RTI. Since rainfall has a direct impact on the occurrence of debris flows, especially its 3.2. Estimation of Critical Accumulated Rainfall Using RTI 3.2.accumulation Estimation ofand Critical intensity, Accumulated the existing Rainfall system Using RTIfor forecasting landslides uses forecasting for The RTI model developed by Jan and Lee [22] was designed to forecast debris ﬂows triggered by accumulatedThe RTI modelrainfall developed and rainfall by intensityJan and Lee and [22] daily was rainfall, designed whereas to forecast the RTIdebris is calculatedflows triggered with rainfallaccumulated in real rainfall time. For and the rainfall RTI calculation, intensity to rainfall consider intensity both (theI) and amount accumulated and intensity. rainfall However, (Rt) are used the by rainfall in real time. For the RTI calculation, rainfall intensity (I) and accumulated rainfall (𝑅) are as follows. used as follows.

RTI = 𝐼 × 𝑅 (1)

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RTI = I Rt (1) × In the equation above, I indicates rainfall intensity (mm/h) and Rt is the accumulated rainfall (mm) observed shortly before the occurrence of debris flows. Among of the rainfall episodes for up to seven days, the one that continues for 24 h with a direct influence on debris flows is considered as antecedent rainfall. The study used the rainfall accumulated for duration 6 h, 12 h, and 24 h to estimate the RTI. Since rainfall has a direct impact on the occurrence of debris flows, especially its accumulation and intensity, the existing system for forecasting landslides uses forecasting for accumulated rainfall and rainfall intensity and daily rainfall, whereas the RTI is calculated with accumulated rainfall and Water 2019, 11, x FOR PEER REVIEW 5 of 23 rainfall intensity to consider both the amount and intensity. However, the RTI can be difficult to understandRTI can be difficult for communities to understand where debrisfor communities flow–related where damage debris is expected, flow–related as it isdamage only a combinationis expected, ofas rainfallit is only intensity a combination and accumulated of rainfall intensity rainfall andand accumulated does not directly rainfall deliver and thedoes information not directly about deliver a riskthe levelinformation of debris about flow. a Therefore, risk level the of RTIdebris was flow. converted Therefore, into critical the RTI accumulated was converted rainfall into (Rt )critical to aid understanding in the provided forecasting. Since the RTI focused on damage in Taiwan during the accumulated rainfall (𝑅) to aid understanding in the provided forecasting. Since the RTI focused on country’sdamage in developed Taiwan during stage, itthe showed country’s a gap developed for the rainfall stage, and it intensityshowed a of gap South for Korea. the rainfall Therefore, and theintensity study of changed South Korea. the level Therefore, to 10%, the 50%, study and 70%,changed taking the intolevel consideration to 10%, 50%, theand flood 70%, forecastingtaking into standardsconsideration provided the flood by theforecasting Han River standards Flood Control provided Offi byce [the26]. Han Figure River4 shows Flood the Control definition Office of RTI[26]. and Rc. Figure 4 shows the definition of RTI and 𝑅.

Figure 4. ConceptConcept of of RTI RTI and R𝑅c𝑐 [[22].22].

4.4. Result and Discussion 4.1. Analysis of Debris Flow-Triggering Rainfall Data 4.1. Analysis of Debris Flow-Triggering Rainfall Data In South Korea, mountainous areas account for 60% of its territory. Since most of them are In South Korea, mountainous areas account for 60% of its territory. Since most of them are concentrated in Gangwon Province, debris flow damage is frequently reported for the province. In this concentrated in Gangwon Province, debris flow damage is frequently reported for the province. In regard, the study collected data on the debris flow–triggering rainfall from 80 stations for 2012 to this regard, the study collected data on the debris flow–triggering rainfall from 80 stations for 2012 2013 in Gangwon Province, where debris flows easily occur, and calculated accumulated rainfall and to 2013 in Gangwon Province, where debris flows easily occur, and calculated accumulated rainfall rainfall intensity at the site of damage occurrence (Table3). Figure5 shows the points of debris flows and rainfall intensity at the site of damage occurrence (Table 3). Figure 5 shows the points of debris and the current status of rainfall monitoring stations. Figures6 and7 show dispersion of the maximum flows and the current status of rainfall monitoring stations. Figure 6 and Figure 7 show dispersion of accumulated rainfall and rainfall intensity for 6 h, 12 h, and 24 h at the 80 stations in the damaged areas. the maximum accumulated rainfall and rainfall intensity for 6 h, 12 h, and 24 h at the 80 stations in the damaged areas.

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Figure 5. Positions of debris flow damage. Figure 5. Positions of debris ﬂowflow damage.

Figure 6. Box plot of accumulated rainfall used in this study. Figure 6. Box plot of accumulated rainfall used in this study. Figure 6. Box plot of accumulated rainfall used in this study.

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Figure 7. BoxBox plot plot of rainfall intensity used in this study.

Table 3. Analysis of accumulated rainfa rainfallll and rainfall intensity.

Accumulated Rainfall (mm) Rainfall Rainfall Intensity Intensity (mm/h) (mm/h) ClassiﬁcationClassification Min Ave Ave Max Max Min Min Ave Ave Max Max 6 h 38 98.24 162 6.33 16.37 27 6 h 38 98.24 162 6.33 16.37 27 12 h 39 133.18 232 3.25 11.10 19.33 12 h 39 133.18 232 3.25 11.10 19.33 24 h 39 164.31 300 1.63 6.85 12.5 24 h 39 164.31 300 1.63 6.85 12.5

4.2. Development of Nomogram for Debris Flow Forecasting, Using RTI and 𝑅 4.2. Development of Nomogram for Debris Flow Forecasting, Using RTI and Rc The study used rainfall information from the 80 stations mentioned above to calculate the RTIs The study used rainfall information from the 80 stations mentioned above to calculate the RTIs by phase (ALERT, WARNING, and EMERGENCY) for each rainfall duration (6 h, 12 h, and 24 h). by phase (ALERT, WARNING, and EMERGENCY) for each rainfall duration (6 h, 12 h, and 24 h). The RTIs were estimated as 600 (10%), 1350 (50%), and 2321 (70%) for the 6 continuous hours; 494 The RTIs were estimated as 600 (10%), 1350 (50%), and 2321 (70%) for the 6 continuous hours; 494 (10%), 1496 (50%), and 1900 (70%) for the 12 hours; and 570 (10%), 950 (50%), 1442 (70%) for the 24 (10%), 1496 (50%), and 1900 (70%) for the 12 hours; and 570 (10%), 950 (50%), 1442 (70%) for the hours. Table 4 summarizes the calculated RTIs and accumulated rainfall and rainfall intensity for 24 hours. Table4 summarizes the calculated RTIs and accumulated rainfall and rainfall intensity for each duration. each duration. Table 4. Estimation of rainfall triggering index. Table 4. Estimation of rainfall triggering index. ① Accumulated Rainfall ② Rainfall Intensity O1 Accumulated Rainfall (mm) O2 Rainfall Intensity (mm/h) ① × ② RTIO1 O2 RTI No. No. (mm) (mm/h) × 6 h6 h 12 h 12 h 24 h 24 h 6 6 h h 12 12 h h 24 h 24 h 6 h 12 6 hh 24 12 h h 24 h 1 591 59 98.5 98.5 136.5 136.5 9.83 9.83 8.21 8.21 5.69 5.69580 580809 776 809 776 2 592 59 98.5 98.5 136.5 136.5 9.83 9.83 8.21 8.21 5.69 5.69580 580809 776 809 776 3 513 51 70 70 116 116 8.5 8.5 5.83 5.83 4.83 4.83434 434408 561 408 561 4 624 62 77 77 150 150 10.33 10.33 6.42 6.42 6.25 6.25640 640494 937 494 937 5 625 62 77 77 150 150 10.33 10.33 6.42 6.42 6.25 6.25640 640494 640 494 640 6 776 77 93 93 147 147 12.83 12.83 7.75 7.75 6.13 6.13988 988720 900 720 900 7 777 77 93 93 147 147 12.83 12.83 7.75 7.75 6.13 6.13988 988720 900 720 900 8 87.5 95.5 121 14.58 9.55 5 1276 912 610 8 87.5 95.5 121 14.58 9.55 5 1276 912 610 9 134 134 134 22.33 11.17 5.58 2992 1496 748 9 134 134 134 22.33 11.17 5.58 2992 1496 748 10 134 134 134 22.33 11.17 5.58 2992 1496 748 11 13410 134 134 134 134 134 22.3322.33 11.17 11.17 5.58 5.582992 29921496 748 1496 748 12 13411 134 134 134 134 134 22.3322.33 11.17 11.17 5.58 5.582992 29921496 748 1496 748 13 3912 134 39 134 39 134 6.522.33 11.17 3.25 5.58 1.632992 1496 253 748 507 63 14 10413 39 104 39 104 39 17.33 6.5 3.25 8.67 1.63 4.33253 1802507 63 901 450 15 72.514 104 89.5 104 128 104 12.0817.33 8.67 7.46 4.33 5.331802 876901 450 667 712 16 4715 72.5 72 89.5 105 128 7.83 12.08 7.46 6 5.33 4.38876 368667 712 432 459 17 72.516 47 89.5 72 128 105 12.08 7.83 67.46 4.38 5.33368 876432 459 667 682 17 72.5 89.5 128 12.08 7.46 5.33 876 667 682 18 72.5 89.5 128 12.08 7.46 5.33 876 667 682

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Table 4. Cont.

O1 Accumulated Rainfall (mm) O2 Rainfall Intensity (mm/h) O1 O2 RTI No. × 6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h 18 72.5 89.5 128 12.08 7.46 5.33 876 667 682 19 51 70 116 8.5 5.83 4.83 433 408 560 20 51 70 116 8.5 5.83 4.83 433 408 560 21 80 144 179 13.33 12 7.46 1066 1728 1335 22 87.5 95.5 121 14.58 7.96 5 1276 760 610 23 60 86 117 10 7.17 4.88 600 616 570 24 60 86 117 10 7.17 4.88 600 616 570 25 60 86 117 10 7.17 4.88 600 616 570 26 91.5 111.5 151 15.25 9.29 6.29 1395 1036 950 27 91.5 111.5 151 15.25 9.29 6.29 1395 1036 950 28 38 65 83 6.33 5.41 3.49 240 384 287 29 78 79 119 13 6.58 4.96 1014 520 590 30 141 160 187 23.5 13.33 7.79 3313 2133 1457 31 141 160 187 23.5 13.33 7.79 3313 2133 1457 32 141 160 187 23.5 13.33 7.79 3313 2133 1457 33 141 160 187 23.5 13.33 7.79 3313 2133 1457 34 141 160 187 23.5 13.33 7.79 3313 2133 1457 35 90 106 141 15 8.83 5.88 1350 936 828 36 90 106 141 15 8.83 5.88 1350 936 828 37 90 106 141 15 8.83 5.88 1350 936 828 38 141 160 187 23.5 13.33 7.79 3313 2133 1457 39 141 160 187 23.5 13.33 7.79 3313 2133 1457 40 100 123 150 16.67 10.25 6.25 1666 1260 937 41 120 197 231 20.00 16.42 9.63 2400 3234 2223 42 147 185 209 24.50 15.42 8.71 3602 2852 1820 43 117 146 173 19.50 12.17 7.21 2282 1776 1247 44 119 199 232 19.83 16.58 9.67 2360 3300 2243 45 119 199 232 19.83 16.58 9.67 2360 3300 2243 46 118 202 238 19.67 16.83 9.92 2321 3400 2360 47 85 131 166 14.17 10.92 6.92 1204 1430 1148 48 98 139 187 16.33 11.58 7.79 1601 1610 1457 49 155 188 216 25.83 15.67 9.00 4004 2945 1944 50 89 130 143 14.83 10.83 5.96 1320 1408 852 51 96 136 139 16.00 11.33 5.79 1536 1541 805 52 78 138 161 13.00 11.50 6.71 1014 1587 1080 53 87 167 190 14.50 13.92 7.92 1262 2324 1504 54 96 136 139 16.00 11.33 5.79 1536 1541 805 55 96 136 139 16.00 11.33 5.79 1536 1541 805 56 134 176 198 22.33 14.67 8.25 2993 2581 1634 57 162 222 300 27.00 18.50 12.50 4374 4107 3750 58 73 84 88 12.17 7.00 3.67 888 588 323 59 78 138 161 13.00 11.50 6.71 1014 1587 1080 60 88 135 175 14.67 11.25 7.29 1291 1519 1276 61 88 135 175 14.67 11.25 7.29 1291 1519 1276 62 88 135 175 14.67 11.25 7.29 1291 1519 1276 63 88 135 175 14.67 11.25 7.29 1291 1519 1276 64 88 135 175 14.67 11.25 7.29 1291 1519 1276 65 125 178 191 20.83 14.83 7.96 2604 2640 1520 66 68 129 138 11.33 10.75 5.75 771 1387 794 67 68 129 138 11.33 10.75 5.75 771 1387 794 68 89 120 186 14.83 10.00 7.75 1320 1200 1442 69 89 120 186 14.83 10.00 7.75 1320 1200 1442 70 145 232 265 24.17 19.33 11.04 3504 4485 2926 71 107 151 180 17.83 12.58 7.50 1908 1900 1350 72 107 151 180 17.83 12.58 7.50 1908 1900 1350 73 97 138 162 16.17 11.50 6.75 1568 1587 1094 74 73 103 131 12.17 8.58 5.46 888 884 715 75 73 103 131 12.17 8.58 5.46 888 884 715 Water 2019, 11, 2181 9 of 23

Table 4. Cont.

O1 Accumulated Rainfall (mm) O2 Rainfall Intensity (mm/h) O1 O2 RTI No. × 6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h

Water76 2019, 11, x 112 FOR PEER REVIEW 154 174 18.67 12.83 7.25 2091 1976 12629 of 23 77 145 232 265 24.17 19.33 11.04 3504 4485 2926 78 14577 145 232 232 265 265 24.17 24.17 19.33 19.33 11.04 11.043504 4485 3504 2926 4485 2926 79 13278 145 213 232 241 265 22.00 24.17 19.33 17.75 11.04 10.043504 4485 2904 2926 3781 2420 80 13279 132 213 213 241 241 22.00 22.00 17.75 17.75 10.04 10.042904 3781 2904 2420 3781 2420 80 132 213 241 22.00 17.75 10.04 2904 3781 2420 Prior to forecasting debris flow, related standards should be established. In South Korea, flood forecastingPrior isto made,forecasting wherein debris flood flow, levels related are standards standardized should with be 50established. to 70% of In the South project Korea, flood flood water levels,forecasting in general, is made, applied wherein for the flood warning levels are and standa alerting.rdized As with explained 50 to 70% above, of the the project study referredflood water to the levels, in general, applied for the warning and alerting. As explained above, the study referred to the flood forecasting standards of the Han River Flood Control Office [26], with the following set for each flood forecasting standards of the Han River Flood Control Office [26], with the following set for level: 10 to 50% of the occurrence possibility for ALERT, 50 to 70% for WARNING, and 70% or higher each level: 10 to 50% of the occurrence possibility for ALERT, 50 to 70% for WARNING, and 70% or for EMERGENCY. Furthermore, the study classified three forecasting levels for the durations of 6 h, higher for EMERGENCY. Furthermore, the study classified three forecasting levels for the durations 12 h, and 24 h. Figure8 shows events of the 80 stations in relation with RTIs, whereas Figures9–11 of 6 h, 12 h, and 24 h. Figure 8 shows events of the 80 stations in relation with RTIs, whereas Figures show9–11 graphs show graphs of the RTIof the estimations. RTI estimations.

(a) 6 h

(b) 12 h

Figure 8. Cont.

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(c) 24 h (c) 24 h Figure 8. Determination of RTI values according to risk level (a) 6 h; (b) 12 h; (c) 24 h. FigureFigure 8. Determination 8. Determination of of RTI RTI values values according according to risk levellevel ((a)a) 6 6 h; h; ( b(b)) 12 12 h; h; (c (c)) 24 24 h. h.

(a) ALERT (a) ALERT

(b) WARNING (b) WARNING

Figure 9. Estimation of rainfall triggering index (6 h): (a) ALERT; (b) WARNING; (c) EMERGENCY. Water 2019, 11, x FOR PEER REVIEW 11 of 23

Water 2019Figure, 11 , 9.x FOREstimation PEER REVIEW of rainfall triggering index (6 h): (a) ALERT; (b) WARNING; (c) EMERGENCY.11 of 23 Water 2019, 11, 2181 11 of 23 Figure 9. Estimation of rainfall triggering index (6 h): (a) ALERT; (b) WARNING; (c) EMERGENCY.

(a) ALERT

(b) WARNING

Figure 10. Estimation of rainfall triggering(c) EMERGENCY index (12 h): (a) ALERT; (b) WARNING; (c) EMERGENCY. FigureFigure 10. Estimation10. Estimation of rainfall of rainfall triggering triggering index (12 index h): (a) ALERT;(12 h): (b(a)) WARNING; ALERT; (b (c)) EMERGENCY.WARNING; (c) EMERGENCY.

(a) ALERT

Figure(a) ALERT 11. Cont.

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(b) WARNING

FigureFigure 11. Estimation11. Estimation of rainfall of rainfall triggering triggering index (24 index h): (a) ALERT;(24 h): (b()a) WARNING; ALERT; ( (bc)) EMERGENCY.WARNING; (c) EMERGENCY. RTIs are not information obtained directly from rainfall. Moreover, most people ﬁnd RTIs diﬃcult to understandRTIs are and not use. information Therefore, obtained the study directly converted from RTIs rainfall. to Rc to Moreover, aid understanding. most people To estimate find RTIs values,difficult average to understand rainfall intensity and use. wasTher usedefore, for the each study duration. convertedR cRTIsthat to corresponds 𝑅 to aid understanding. to the average To rainfallestimate intensity values, is average shown in rainfall Table5 intensity. Figure 12 was shows used RTIs for each for 10%, duration. 50%, and𝑅 that 70% corresponds calculated from to the Figuresaverage9–11 rainfall and R c intensityestimation is graphs.shown in Table 5. Figure 12 shows RTIs for 10%, 50%, and 70% calculated from Figures 9 to 11 and 𝑅 estimation graphs. Table 5. Estimation of critical accumulated rainfall (Rc).

Rc (mm) Classiﬁcation WARNING (up to EMERGENCY (up to ALERT (10% and over) 50% and over) 70% and over) 6 hr 37 82 142 12 hr 45 135 171 24 hr 83 139 211

The study developed a nomogram for debris flow forecasting by rainfall duration, using the critical accumulated rainfall (Rc) for each occurrence possibility (10%, 50%, and 70%) and duration (6 h, 12 h, and 24 h). As shown in Figure 13, a nomogram is a graph of debris flow forecasting levels for the rainfall accumulated from the start to 24(a) hRTI of 6 the h duration. For each duration, the debris flow forecasting levels (ALERT, WARNING, and EMERGENCY) are classified with different colors to aid the visual expression of each level by duration of accumulated rainfall.

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(b) WARNING

Figure 11. Estimation of rainfall triggering index (24 h): (a) ALERT; (b) WARNING; (c) EMERGENCY.

RTIs are not information obtained directly from rainfall. Moreover, most people find RTIs

difficult to understand and use. Therefore, the study converted RTIs to 𝑅 to aid understanding. To estimate values, average rainfall intensity was used for each duration. 𝑅 that corresponds to the Wateraverage2019, 11 ,rainfall 2181 intensity is shown in Table 5. Figure 12 shows RTIs for 10%, 50%, and13 of 2370%

calculated from Figures 9 to 11 and 𝑅 estimation graphs.

Water 2019, 11, x FOR PEER REVIEW (a) RTI 6 h 13 of 23

(b) RTI 12 h

Figure 12. Estimation of rainfall triggering index (RTI) and critical accumulated rainfall (𝑅𝑐): (a) RTI 6 Figure 12. Estimation of rainfall triggering index (RTI) and critical accumulated rainfall (Rc): (a) RTI h; (b) RTI 12 h; (c) RTI 24 h. 6 h; (b) RTI 12 h; (c) RTI 24 h.

Table 5. Estimation of critical accumulated rainfall (𝑅𝑐).

𝐑𝐜 (mm) Classification ALERT WARNING EMERGENCY (10% and over) (up to 50% and over) (up to 70% and over) 6 hr 37 82 142 12 hr 45 135 171 24 hr 83 139 211

The study developed a nomogram for debris flow forecasting by rainfall duration, using the

critical accumulated rainfall (R) for each occurrence possibility (10%, 50%, and 70%) and duration (6 h, 12 h, and 24 h). As shown in Figure 13, a nomogram is a graph of debris flow forecasting levels for the rainfall accumulated from the start to 24 h of the duration. For each duration, the debris flow forecasting levels (ALERT, WARNING, and EMERGENCY) are classified with different colors to aid the visual expression of each level by duration of accumulated rainfall.

Water 2019, 11, 2181 14 of 23

Water 2019, 11, x FOR PEER REVIEW 14 of 23

FigureFigure 13. 13.Debris Debris ﬂowflow Nomogram. Nomogram.

4.3. Review4.3. Review on Applicability on Applicability of Debrisof Debris Flow Flow Nomogram Nomogram withwith Actual Actual Cases Cases Figure 13. Debris flow Nomogram. To reviewTo review applicability applicability of of the the debris debris flow flow nomogramnomogram that that the the study study developed, developed, it applied it applied the the nomogram4.3. Review onto Applicabilitycases of damage of Debris caused Flow in Nomogram the past wibyth debris Actual flows. Cases The representative cases include nomogram to cases of damage caused in the past by debris flows. The representative cases include Umyeon Mountain of Seoul Seoul Metropolitan City, the capital of Korea in 2011, Chuncheon City To review applicability of the debris flow nomogram that the study developed, it applied the Umyeonof Gangwon Mountain Province of Seoul in 2011, Seoul and Metropolitan Cheongju City City, of Chungcheongbuk the capital of Korea Province in 2011, in 2017. Chuncheon The study City nomogram to cases of damage caused in the past by debris flows. The representative cases include of Gangwonestimated Province the response in 2011, time and before Cheongju the damage City ofoccurrence Chungcheongbuk by forecasting Province debris inflows 2017. with The the study Umyeon Mountain of Seoul Seoul Metropolitan City, the capital of Korea in 2011, Chuncheon City estimated the response time before the damage occurrence by forecasting debris flows with the actual actualof Gangwon rainfall Province data for inthe 2011, cases. and The Cheongju case of Umye City ofon Chungcheongbuk Mountain where debrisProvince flows in 2017. occurred The studyat 10:00 rainfallinestimated data27 July for 2011,the the response cases.resulted The timein case18 before deaths of Umyeon the and damage the Mountain evacuation occurrence where of 400by debris people.forecasting flows In 2011, debris occurred Chuncheon flows at 10:00with City the in of27 July 2011,Gangwonactual resulted rainfall inProvince 18 data deaths for experienced the and cases. the The evacuationdebris case flowsof Umye ofthaton 400 occurred Mountain people. at where In 24:00 2011, debris and Chuncheon caused flows occurred 13 deaths City at of 10:00and Gangwon 26 Provinceinjuries.in 27 experienced July The 2011, case resulted of debris Cheongju in flows 18 deaths City that of occurredand Chungcheongb the evacuation at 24:00uk and ofProvince 400 caused people. occurred 13 In deaths 2011, at 11:00 andChuncheon 26on injuries. 16 July City 2017, of The case of CheongjucausingGangwon Citytwo Province deaths. of Chungcheongbuk experiencedFigure 14 shows debris Provincethe flows photos that occurred of occurreddamaged at 11:00at areas 24:00 ontaken and 16 Julyatcaused those 2017, 13times. causingdeaths and two 26 deaths. Figureinjuries. 14 Theshows Theresults thecase of photos of debris Cheongju offlow damaged Cityforecasting of Chungcheongb areas with taken the nomogram atuk those Province times. the occurred study developed at 11:00 on are 16 as July follows. 2017, Thecausing results two ofdeaths. debris Figure flow 14 forecasting shows the photos withthe of damaged nomogram areas the taken study at those developed times. are as follows. The results of debris flow forecasting with the nomogram the study developed are as follows.

Figure 14. Photo of damage areas in this study. (A) Seoul Metropolitan City; (B) Chuncheon City; (C) Cheongju City. Water 2019, 11, x FOR PEER REVIEW 15 of 23 Water 2019, 11, x FOR PEER REVIEW 15 of 23

Figure 14. Photo of damage areas in this study. (A) Seoul Metropolitan City; (B) Chuncheon City; (C) Figure 14. Photo of damage areas in this study. (A) Seoul Metropolitan City; (B) Chuncheon City; (C) Cheongju City. Cheongju City. 4.3.1. Case 1: Umyeon Mountain, Seoul 4.3.1. Case 1: Umyeon Mountain, Seoul For the case of Umyeon Mountain of Seoul, the capital of Korea, it started raining at 17:00 on 26 For the case of Umyeon Mountain of Seoul, the capital of Korea, it started raining at 17:00 on 26 July and recorded the maximum accumulated rainfall 307 mm (Figure 15) until 16:00 on 27 July with WaterJuly and2019, recorded11, 2181 the maximum accumulated rainfall 307 mm (Figure 15) until 16:00 on 27 July15 with of 23 damage occurring at 9:00 on 27 July. The debris flow forecasting results were ALERT for 18:00 on 26 damage occurring at 9:00 on 27 July. The debris flow forecasting results were ALERT for 18:00 on 26 July, WARNING for 19:00 of the same day, and EMERGENCY for 5:00 on 27 July (Figure 16). Based July, WARNING for 19:00 of the same day, and EMERGENCY for 5:00 on 27 July (Figure 16). Based on4.3.1. this, Case it can 1: be Umyeon assumed Mountain, that damage Seoul occurs after the EMERGENCY level. Therefore, it is estimated on this, it can be assumed that damage occurs after the EMERGENCY level. Therefore, it is estimated that 4 h of response time is secured prior to damage occurrence. When forecasting is made that For4 h theof caseresponse of Umyeon time is Mountain secured ofprior Seoul, to thedamage capital occurrence. of Korea, itWhen started forecasting raining at 17:00is made on additionally for the WARNING level, the response time that can be secured is estimated as 7 h. 26additionally July and recordedfor the WARNING the maximum level, accumulated the response rainfall time that 307 can mm be (Figure secured 15 is) estimated until 16:00 as on 7 h. 27 July Regarding the comparison analysis with the alerting standards of the Korea Forest Service and withRegarding damage occurring the comparison at 9:00 on analysis 27 July. with The the debris alerting ﬂow standards forecasting of resultsthe Korea were Forest ALERT Service for 18:00 and the Korea Meteorological Administration, the former provided the same level of risk; however, it onthe 26Korea July, Meteorological WARNING for Administration, 19:00 of the same the day, former and EMERGENCYprovided the same for 5:00 level on of 27 risk; July however, (Figure 16 it). produced the Alarm level for 18:00 of 26 July and 2:00 of 27 July, which are some hours before the Basedproduced on this,the Alarm it can belevel assumed for 18:00 that of damage26 July and occurs 2:00 after of 27 the July, EMERGENCY which are some level. hours Therefore, before itthe is damage occurrence, with its response time delayed for an hour. On the other hand, the latter estimateddamage occurrence, that 4 h of responsewith its timeresponse is secured time priordelayed to damage for an occurrence.hour. On the When other forecasting hand, the is madelatter provided the Alarm level for 19:00 of 26 July, which is some hours before the damage occurrence, additionallyprovided the for Alarm the WARNING level for 19:00 level, of the 26 responseJuly, which time is thatsome can hours be secured before isthe estimated damage asoccurrence, 7 h. and issued the alert for 24:00, which is 3 h passed the actual damage occurrence (Table 6). and issued the alert for 24:00, which is 3 h passed the actual damage occurrence (Table 6).

Figure 15. Hyetograph (Case 1). Figure 15. Hyetograph (Case 1).

Figure 16. Debris flow forecasting using nomogram (Case 1). Figure 16. Debris flow forecasting using nomogram (Case 1). Figure 16. Debris ﬂow forecasting using nomogram (Case 1).

Regarding the comparison analysis with the alerting standards of the Korea Forest Service and the Korea Meteorological Administration, the former provided the same level of risk; however, it produced the Alarm level for 18:00 of 26 July and 2:00 of 27 July, which are some hours before the damage occurrence, with its response time delayed for an hour. On the other hand, the latter provided the Alarm level for 19:00 of 26 July, which is some hours before the damage occurrence, and issued the alert for 24:00, which is 3 h passed the actual damage occurrence (Table6). Water 2019, 11, 2181 16 of 23

Table 6. Comparison of debris ﬂow forecasting level results (Case 1).

Occurrence Time of Debris Flow: 27 July 2011, 9:00 Time 17:00 18:00 19:00 20:00 21:00 22:00 23:00 0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 Accumulated 17 51 95 97 100 103 103 103 103 137 152 172 182 201 217 238 275 276 281 289 298 300 304 307 rainfall (mm) Rc (mm) - AL W W W W W W AL W W W EM EM EM EM EM EM EM EM EM EM EM EM KFS (mm/h) - A A- W W W W W A W W W A A A A A A A A A A A KMA (mm/h) - - A W----- W W W W W W W W W W A A W W W ※ ALERT: AL, WARNING: W, EMERGENCY: EM, ALARM: A. Water 2019, 11, 2181 17 of 23

4.3.2. Case 2: Chuncheon, Gangwon Province 4.3.2. Case 2: Chuncheon, Gangwon Province 4.3.2. Case 2: Chuncheon, Gangwon Province In the case of Chuncheon City, located in Gangwon Province, the rainfall started at 1:00 of 27 July, In the case of Chuncheon City, located in Gangwon Province, the rainfall started at 1:00 of 27 and theIn the 230 case mm of maximumChuncheon accumulated City, located rainfall in Gangwon was recorded Province, until 24:00the rainfall of the samestarted day at (Figure1:00 of 1727). July, and the 230 mm of maximum accumulated rainfall was recorded until 24:00 of the same day July,The damageand the 230 occurred mm of at maximum 24:00 of 27 accumulated July, and forecasting rainfall was for recorded debris ﬂows until was24:00 made of the on same 4:00 day for (Figure 17). The damage occurred at 24:00 of 27 July, and forecasting for debris flows was made on (FigureALERT, 17). 19:00 The for damage WARNING, occurred and at 21:00 24:00 for of EMERGENCY27 July, and forecasting (Figure 18 for). Withdebris the flows application was made of theon 4:00 for ALERT, 19:00 for WARNING, and 21:00 for EMERGENCY (Figure 18). With the application 4:00EMERGENCY for ALERT, level, 19:00 it for was WARNING, found that 4 and h of 21:00 response for EMERGENCY time was secured (Figure prior to18). the With damage the application occurrence, of the EMERGENCY level, it was found that 4 h of response time was secured prior to the damage ofand the with EMERGENCY the additional level, forecasting it was found for thethat WARNING 4 h of response level, time a total was of secured 6 h of the prior time to wasthe damage secured. occurrence, and with the additional forecasting for the WARNING level, a total of 6 h of the time occurrence,Regarding theand comparison with the additional analysis withforecasting the alerting for the standards WARNING of the level, Korea a total Forest of Service6 h of the and time the was secured. Regarding the comparison analysis with the alerting standards of the Korea Forest wasKorea secured. Meteorological Regarding Administration, the comparison the analysis former provided with the thealerting same riskstandards level; however,of the Korea it produced Forest Service and the Korea Meteorological Administration, the former provided the same risk level; Servicethe Alarm and level the forKorea 19:00 Meteorological of 27 July and forAdministrati 21:00 of 27on, July the again former before provided the actual the damage same occurrence.risk level; however, it produced the Alarm level for 19:00 of 27 July and for 21:00 of 27 July again before the however,The standards it produced of the latter the Alarm issued level Alarm for from 19:00 1:00 of of27 27 July July, and which for 21:00 is some of hours27 July before again the before damage the actual damage occurrence. The standards of the latter issued Alarm from 1:00 of 27 July, which is actualoccurrence. damage This occurrence. is a level lower,The standards compared of to the the latter actual issued risk level Alarm of Warningfrom 1:00 at of the 27 time July, of which damage is some hours before the damage occurrence. This is a level lower, compared to the actual risk level of someoccurrence hours (Tablebefore7 ).the damage occurrence. This is a level lower, compared to the actual risk level of Warning at the time of damage occurrence (Table 7). Warning at the time of damage occurrence (Table 7).

Figure 17. Hyetograph (Case 2). FigureFigure 17. 17. HyetographHyetograph (Case (Case 2). 2).

Figure 18. Debris flow forecasting using nomogram (Case 2). Figure 18. Debris flow forecasting using nomogram (Case 2). Figure 18. Debris ﬂow forecasting using nomogram (Case 2).

Water 2019, 11, x; doi: FOR PEER REVIEW www.mdpi.com/journal/water Water 2019, 11, x; doi: FOR PEER REVIEW www.mdpi.com/journal/water Water 2019, 11, 2181 18 of 23

Table 7. Comparison of debris ﬂow forecasting level results (Case 2).

Occurrence Time of Debris Flow: 27 July 2011, 24:00 Time 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 24:00 Accumulated 16 18 25 45 70 89 93 97 98 98 98 100 101 101 101 109 114 125 167 178 205 210 248 263 rainfall (mm) Rc (mm) - - - AL AL W AL AL AL AL AL AL AL AL AL AL AL AL W W EM EM EM EM KFS (mm/h) - - - W W------W W W W W W W A W A A A A KMA (mm/h) A A A A A A A A A W W------W W W W W ※ ALERT: AL, WARNING: W, EMERGENCY: EM, ALARM: A. Water 2019, 11, 2181 19 of 23

Water 2019, 11, x FOR PEER REVIEW 3 of 23 Water 2019, 11, x FOR PEER REVIEW 3 of 23 4.3.3. Case 3: Cheongju, Chungcheongbuk Province 4.3.3. Case 3: Cheongju, Chungcheongbuk Province 4.3.3. Case 3: Cheongju, Chungcheongbuk Province In the case of Chuncheon City, located in Chungcheongbuk Province, the rainfall started at In the case of Chuncheon City, located in Chungcheongbuk Province, the rainfall started at 1:00 1:00 ofIn 16the July, case andof Chuncheon the 290 mm City, of maximumlocated in Chungcheongbuk accumulated rainfall Province, was recorded the rainfall until started 14:00 at of 1:00 the of 16 July, and the 290 mm of maximum accumulated rainfall was recorded until 14:00 of the same sameof 16 July, day (Figureand the 19 290). The mm damage of maximum occurred accumulated at 11:00 of rainfall 16 July, was and recorded forecasting until for 14:00 debris of ﬂows the same was day (Figure 19). The damage occurred at 11:00 of 16 July, and forecasting for debris flows was made madeday (Figure at 8:00 19). for The WARNING damage occurred and 9:00 at for 11:00 EMERGENCY of 16 July, and (Figure forecasting 20). With for debris the application flows was ofmade the at 8:00 for WARNING and 9:00 for EMERGENCY (Figure 20). With the application of the EMERGENCYat 8:00 for WARNING level, it was and found 9:00 that for 2 h ofEMERGENCY response time (Figure was secured 20). priorWith to the the damageapplication occurrence, of the EMERGENCY level, it was found that 2 h of response time was secured prior to the damage andEMERGENCY with the additional level, it was forecasting found forthat the 2 WARNINGh of response level, time a totalwas ofsecured 3 h of theprior time to wasthe secured.damage occurrence, and with the additional forecasting for the WARNING level, a total of 3 h of the time Regardingoccurrence, the and comparison with the additional analysis withforecasting the alerting for the standards WARNING of the level, Korea a total Forest of Service3 h of the and time the was secured. Regarding the comparison analysis with the alerting standards of the Korea Forest Koreawas secured. Meteorological Regarding Administration, the comparison similar analysis tendency with riskthe levelsalerting were standards shown forof the all threeKorea alerting Forest Service and the Korea Meteorological Administration, similar tendency risk levels were shown for standardsService and (Table the 8Korea). Meteorological Administration, similar tendency risk levels were shown for all three alerting standards (Table 8). all three alerting standards (Table 8).

Figure 19. Hyetograph (Case 3). Figure 19.19. Hyetograph (Case 3).

Figure 20. Debris flow forecasting using nomogram (Case 3). Figure 20. Debris ﬂowflow forecasting using nomogram (Case 3).

Water 2019, 11, 2181 20 of 23

Table 8. Comparison of debris ﬂow forecasting level results (Case 3).

Occurrence Time of Debris Flow: 16 July 2011, 11:00 Time 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 24:00 Accumulated 2 2 2 2 5 6 23 109 168 220 288 290 290 290 290 290 290 290 290 290 290 290 290 290 rainfall (mm) Rc (mm) ------W EM EM EM EM EM EM EM EM EM EM EM EM EM EM EM EM KFS (mm/h) ------A A A A A A A A A A A A A A A A A KMA (mm/h) ------A A A A A A A A A A A A A W--- ※ WARNING: W, EMERGENCY: EM, ALARM: A. Water 2019, 11, 2181 21 of 23

5. Conclusions In this study, we collected rainfall data targeting the areas that experienced damage from debris flows from 2012 to 2013, and developed the debris flow nomogram that reflects both accumulated rainfall and rainfall intensity. It used the two elements observed shortly before the occurrence of debris flows to estimate RTIs and set the three levels according to the possibility of debris flow occurrence: 10 to 50% for ALERT, 50 to 70% for WARNING, and 70% or higher for EMERGENCY. In addition, to help the understanding of the residents in the areas where debris flows can occur, the study converted RTIs to actual accumulated rainfall values (Rc) for use in forecasting. In this study, the debris flow nomogram was developed for each duration (6 h, 12 h, and 24 h) and applied to actual cases of debris flow damage for Umyeon Mountain of Seoul, Inje County of Gangwon Province, and Cheongju City of Chungcheongbuk Province. As a result, the use of the nomogram for debris flow forecasting that the study developed could secure sufficient response time for the cases of Umyeon Mountain of Seoul and Chuncheon of Gangwon Province, where rainfall continues for long durations, and the case of Cheongju of Chungcheongbuk Province where heavy rain is localized. Results for each case are summarized as follows. Case 1: In the case of Umyeon Mountain of Seoul, 280 mm of the rain that continued for 17 h caused the occurrence of debris flows. The results of using the nomogram in forecasting debris flows for the EMERGENCY level showed that it could secure 4 h of the response time. When the forecasting was made additionally for the WARNING level, a total of 7 h of the response time could be secured to ensure reactive actions. Case 2: In the case of Chuncheon of Gangwon Province, 260 mm of the rain for about 24 h caused the occurrence of debris flows. The results of using the nomogram in forecasting debris flows showed that it could secure 4 h of the response time. In addition to the forecasting for the WARNING level, a total of 6 h of the response time could be secured. Case 3: In the case of Cheongju of Chungcheongbuk Province, 290 mm of the rain for about 11 h caused the occurrence of debris flows. The results of using the nomogram in forecasting debris flows showed that it could secure 2 h of the response time. With addition to the forecasting for the WARNING level, a total of 3 h of the response time could be secured. The results above suggest that the debris flow forecasting nomogram provided by the study is applicable for the actual forecasting on debris flow damages that can be caused by the long-term increase in rainfall and short-term, localized heavy rain. Meanwhile, in the cases of Seoul and Chuncheon, the forecasting standards of the Korean Meteorological Administration and the Korean Forest Service led to the indiscriminate issuance of alerts at the starting point of rainfall. However, the forecasting with the nomogram of the study is expected to support the understanding of rainfall value by general users with a visual representation of the risk level, and allow a proper forecasting or response system to the situation. Due to the diverse causes of debris flows, rainfall-related factors are not enough in determining debris flow occurrence. Therefore, it is crucial to provide the standards that general people can use to make decisions even without expert knowledge. As rainfall is considered the most common factor that causes debris flows, it is expected that the forecasting on debris flows using the nomogram can support the easier interpretation of general users for debris flows. In addition, the forecasting that uses the nomogram the study developed and radar rainfall information can prevent debris flow damage in real time.

Author Contributions: D.-H.N. and S.-H.L. carried out the survey of previous study and wrote the graph of the data. B.-S.K. suggested idea of study and contributed to the writing of the paper. In addition, we contributed to conducting a reanalysis of the research data responding to the reviewers’ results and providing a clear research result with a solid academic basis that coincides with the research purposes. Funding: This research was supported by a grant(2017-MOIS31-004) from Fundamental Technology Development Program for Extreme Disaster Response funded by Korean Ministry of Interior and Safety (MOIS). This research was supported by a grant (MOIS-DP-2015-05) of Disaster Prediction and Mitigation Technology Development Program Water 2019, 11, 2181 22 of 23 funded by Ministry of Interior and Safety (MOIS, Korea). This study was supported by 2016 research grant from kangwon national university (number-620160136) Also, This paperwork (or document) was financially supported by Ministry of the Interior and Safety as “Human resource development Project in Disaster management”. Conflicts of Interest: The authors declare no conflict of interest.

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