DEPTH-AREA-DURATION ANALYSIS IN A KOREAN RIVER BASIN

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1 Annual Journal of Hydraulic Engineering, JSCE, Vol.57, 213, February DEPTH-AREA-DURATION ANALYSIS IN A KOREAN RIVER BASIN Young-a SHIN 1, Kaoru TAKARA 2 and Maja OSTRIC 1 1 Student Member of JSCE, Dept. of Civil and Earth Resources Engineering, Kyoto University (Gokasho, Uji, Kyoto , Japan) 2 Fellow of JSCE, Prof.., Disaster Prevention Research Institute, Kyoto University (Gokasho, Uji, Kyoto , Japan) Assessment of storm is accomplished by the storm area and duration rather than a simple analysis using the rainfall data of the ground rain gauge stations. One of the best expressions for assessing storm is Depth-Area-Duration (DAD) analysis. The DAD analysis provides a powerful, objective, easy-to-understand three-dimensional perspective of storm rainfall, and is applied to estimate probable maximum precipitation (PMP) for the design of hydraulic structures. However, a general DAD analysis is prone to generate subjective errors to divide and accumulate sub-basins. Further it is difficult to understand the impact of recent localized and intensive storms due to the climate change. This research carried out to obtain DAD analysis of high accuracy in the small basin and relieve errors that occur in the analysis. Methods to estimate areal rainfall are the inverse distance weight (IDW) and ordinary kriging (OK), while methods to accumulate area are the box-tracking and the point-tracking. The merits and demerits of these methods are discussed. Key Words: DAD analysis, areal rainfall, interpolation, tracking, storm center 1. INTRODUCTION In recent years, under the influence of climate change such as global warming, El Nino and La Nina, the localized torrential downpours and recorded torrential rains have proliferated more than in the past. These phenomena lead to floods that exceed the design frequency of hydraulic structures such as levees and weirs. Moreover, serious and secondary damages occur. For instance, when Typhoon RUSA hit Korea in 2, the levees of both Dongmak and Janghyun reservoirs in Gangneung broke, and the breaking increased the damage caused by flooding. Thus to reduce and prevent these damages, studies from various perspectives have been carried out to reflect the characteristics of the recent rain phenomena. Since depth-area-duration (DAD) analysis has enabled the designers to recognize the temporal and spatial rainfall pattern to understand a rainfall-runoff system 1), these studies are considered among the important analyses to estimate the flood discharge from the rainfall in the study area. In addition, DAD analysis is utilized to estimate probable maximum precipitation (PMP) and the influence the design and operation of hydraulic structures such as levees, weirs, and dams. PMP is defined as the greatest depth of precipitation for a given duration meteorologically possible for a given size storm area at a particular location at a particular time of year, with no allowance made for long-term climatic trends under World Meteorological Organization (WMO) 2)-4). This implies that although a research about DAD analysis is primarily served as the initial data for estimating PMP the methodology to improve the accuracy of DAD analysis is required. Both Thiessen polygon and Isohyetal method for the DAD analysis were introduced. Takara et al. 5)-7) adopted Constant Area Method (CAM) and Fixed Rainfall Method (FRM) to estimate depth area (DA) relations by using radar raingauge data as well as applied the results of FRM to estimate PMP. Kim and Won 8) performed DAD analysis using a centered event method to consider the movement of rainfall.

2 Fig.1 Location of the Yongdam dam basin and ground rain gauge stations. This study aimed to develop a method to enhance the accuracy of the DAD analysis considering a temporal and spatial distribution of the rainfall field. The methods are the point tracking and the box tracking based on the grid concept. 2. STUDY SITE AND DATA (1) Study site The study area (Fig. 1) is the Yongdam basin, located in the uppermost region of the Geum River in the southwest of South Korea. The area which accounts for about 9.5% of the Guem River basin area is 93.4 km 2, a relatively small area. A total of 11 stations, Jucheon, Ancheon, Bugwi, Deokyubong, Donghyang, Gyebuk, Sangjeon, Jinan, Janggye, Cheoncheon and Jangsu were selected as ground gauging stations within the basin. These stations are controlled by the Korea Water Resources Corporation (K-Water) and Automatic Weather System (AWS) of Korea Meteorological Administration (KMA). Typhoons affect Korea during from July to September, leaving damages almost every year across the country, including Typhoon RUSA in 2, MAEMI in 3, NABI in 5, NARI in 7 and BOLAVEN in 212, etc 9). Typhoon RUSA's recorded casualties were 217 dead and 29 missing, and the typhoon recorded the biggest property damages at billion WON ( billion USD), and daily maximum rainfall was 87.5 mm at Gangneung 1). This typhoon was selected as a study event for DAD analysis of Yongdam dam basin. Although the typhoon RUSA landed in southwest South Korea, and went out the northeast from 3th August to 1st September 2, hourly rainfalls from 11 ground rain gauge stations over 31 hours from 1 p.m. on 31st August to 7 p.m. 1st September were used because the rain concentrated during the period in the study watershed. (2) Data Looking at the hourly rainfall data, it gradually Fig. 2 Typical DAD curves and Isohyet map divided into Thiessen polygons 12). started to rain heavily from the afternoon of 31st August 2. It became the strongest over night and came to a sharp lull at dawn on 1st September 2. The hourly rainfalls had a distribution roughly from mm/hr to 33 mm/hr. The heaviest rainfall was observed at Deokyubong station, a value of 33.5 mm/hr. In this research, hourly rainfalls obtained from stations within the domain were converted into 31 grid-based areal rainfalls every hour by ArcGIS 11), considering interpolation methods and grid sizes. The details of interpolation methods are described later (Chapter 4, Section (1)). The Yongdam dam basin from domain of converted grid-based areal rainfalls was extracted and areal rainfalls of Yongdam basin were converted into ASCII form. The maximum areal average rainfalls were estimated according to increasing area size over various lasting times by using the ASCII data. Methods to increase area size are described in the following section. 3. METHODOLOGY (1) Existing DAD analysis The procedure for obtaining DAD curve is as follows: (a) Collect continuous rainfall data of the greatest magnitude separately from all the ground rain gauge stations within the basin. (b) Divide the entire basin into sub-basins (a number of parts) by using Isohyet. (c) Calculate each area of sub-basin. (d) Calculate an average of rainfall of each sub-basin (areal average rainfall). Then the area divided by Thiessen is put into weighting. (e) Calculate accumulated areal average rainfall by adding the sub-basin one by one from the storm center. Then the area of sub-basin is put into weighting. (f) Calculate the areal average rainfall for particular durations such as 1 hr, 6 hr and 12 hr. And search the maximum areal average rainfall for each area and duration.

3 (g) Plot the results of step (f) on semi-logarithmic graph. A typical DAD curve (Fig. 2) indicates that if the objective area in the certain duration increases then the maximum areal average rainfall decreases, and if the duration in the certain objective area increases then the maximum areal average rainfall increases. Area: Cell 1 1 Area: Cell 2 2 Searching Area Searched Area Maximum Rainfall (2) DAD analysis methods proposed As described in the chapter 3, section (1), Thiessen polygons and Isohyets method are generally applied to accumulate area. However, this method cannot search the maximum areal rainfall in segmented areas in more detail. Although CAM and FRM methods suggested by Takara et al. 5)-7) are based on grid, those methods were only applied in radar raingauges, and the maximum areal rainfalls about several areas were searched by manual calculations. DAD equation was optimized to envelop the points after searching. In this study, a method which can consider more accurate actual distribution of rainfall is programmed by complementing both CAM and FRM to search the maximum areal rainfall in segmented areas in more detail by using hourly rainfall based on grid. The following describes the methods to accumulate area. a) Box-Tracking This method (Fig. 3 (a)) is to search the maximum areal average rainfall (MAAR) over the entire grid covering study basin in a designated duration by using square-shaped box. The areal rainfall is given in each grid-cell. Firstly, MAAR is searched by moving the box whose size is the same as one grid-cell in the entire basin. At this point, accumulated time period with the MAAR also is considered. For instance, when duration is 2 hr, there are a total of 3 duration layers such as 1-2 hr, 2-3 hr, 3-4 hr,, 3-31 hr from a total of 31 hourly rainfall data. These layers are called sub-duration in this paper. Then the box calculates MAAR by searching all 3 sub-durations for the 2 hr duration. Seeing Figure 3 (a), when the cell area is 1 1, the MAAR is searched in sub-duration 29-3 hr and when the area is 2 2, the MAAR is searched in sub-duration 3-31 hr. Like this, the MAAR is searched by increasing the box size from 1 1 to N N. N is the smaller number of rows and columns. Then the sub-duration is considered simultaneously. These processes are repeated for other durations to obtain a series of DAD relations. b) Point-Tracking This method (Fig.3 (b)) is firstly, to search one grid-cell with MAAR over the entire grid covering study basin, to compare neighboring cell values of Area: Cell 1 Area: Cell 2 Area: Cell 3 Fig. 3 (a) Box-tracking method (duration: 2 hr). Fig. 3 (b) Point-tracking method (duration: 2 hr). below, above, right and left sides and lastly, to add a newly searched grid-cell with the maximum value to area in a designated duration. The concept of sub-duration is also considered in point-tracking. Whenever the area is accumulated in the designated duration, MAAR is calculated by searching all sub-durations. Seeing Figure 3 (b), when the area is cell 1, MAAR is searched in the sub-duration 1-2 hr. And neighboring cell values of below, above, right and left sides in the sub-duration 1-2 hr are compared and the above grid-cell with maximum value of them is selected when sub-duration is 29-3 hr. The above grid-cell is added as a new area. When the area is cell 2, the neighboring 2 grid-cell values of below, above, right and left sides are compared again. The maximum value of them is searched in left side of secondly found grid-cell of sub-duration 1-2 hr. These steps are repeated up to grid-cells corresponding to the entire basin area. All of the processes are repeated for other durations to obtain a series of DAD relations.

4 OK (Box) 1hr OK (Box) 6hr OK (Box) 12hr OK (Box) 18hr OK (Box) 3hr IDW (Box) 1hr IDW (Box) 6hr IDW (Box) 12hr IDW (Box) 18hr IDW (Box) 3hr Fig. 4 DAD analysis by IDW and OK (box-tracking). OK (Point) 1hr OK (Point) 6hr OK (Point) 12hr OK (Point) 18hr OK (Point) 3hr IDW (Point) 1hr IDW (Point) 6hr IDW (Point) 12hr IDW (Point) 18hr IDW (Point) 3hr Fig. 5 DAD analysis by IDW and OK (point-tracking). 4. RESULTS AND DISCUSSIONS (1) Interpolation In the existing DAD analysis, areal rainfall is estimated in a manner that the basin is divided into constant sub-basins by Thiessen polygon and Isohyetal method 13)-14) ; then, to calculate average rainfall of the sub-basin, a constant weight is assigned at the observation points (Kim and Won) 7). However, due to low reliability about assigning weight this method merely analyzes a large amount of data quickly, but accuracy cannot be guaranteed. Therefore, it is essential to appropriately determine a spatial interpolation technique for converting point rainfalls (values observed from ground rain gauge stations) into areal rainfall. To obtain simple, but more accurate DAD analysis results, we examined the Inverse Distance Weight (IDW) and Ordinary Kriging (OK) functioned in ArcGIS. We analyzed all the 31 data sets. If 31 data sets are shown in one graph, it is difficult to identify the results. Therefore representative durations at 1 hr, 6 hr, 18 hr and 3 hr are described in Figs. 4, 5, 9 and 1. Figures 4 and 5 show that the values of IDW (a dotted line) are smaller than those of OK (a solid line) when the duration is 1 hr. The difference is 1.39 mm (box-tracking) and 2.48 mm (point-tracking) on average. However, the values of IDW are greater than that of OK, except for some part within km 2 at the duration 6, 12, 18 and 3 hr. Further, the values of IDW steeply decrease within 1 km 2 and there is difference of maximum 17.8 mm between IDW and OK at duration 3 hr. Meanwhile, rainfall data of 12 hr (from 13: to 24: on 31st August 212) among the results of areal rainfall converted by IDW and OK are compared because the magnitude of data is the biggest at that time. Figure 6 shows that the results of the IDW commonly indicate the pattern of rainfall distribution as a circle. The positions where the circle appears are ground rain gauge stations. It means that the values of areal rainfall are prominently concentrated around the ground rain gauge stations. In other words, spots closest to the ground rain gauge stations are strongly affected by the rainfall of the ground rain gauge stations. As a result, IDW's values tend to partially overestimate or underestimate as a whole. We analyzed that DAD analysis can be more reliable and sophisticated when the areal rainfall is calculated by using OK, which aims to minimize the error variance and is estimated by a weighted linear combination of the available data 15). (2) Initial grid-cell size Kim et al. 8) used 26 km 2 (5.1 km 5.1 km) as the initial area. The 26 km 2 is the governing area of point rainfall proposed in WMO (1986) 3). Takara et al. 5)-7) analyzed DAD relations by using radar data sets of 2.25 km 2 (1.5 km 1.5 km), the grid size of the radar data itself as the initial grid-cell size. In this study, however, to consider an influence according to the initial grid-cell size, DAD analysis is performed by dividing the size of the initial grid into: Case 1: 1 km 2 (1 m 1 m, 4 49); Case 2:.25 km 2 (5 m 5 m, 8 89); and Case 3:.625km 2 ( m m, ) In the box-tracking, the rainfall values in all of the cases are almost equal up to duration 14 hr (see the series of red lines in Fig. 7). But, the rainfall values of Case 3 at duration 15 hr begin to higher than in the other two cases (see the series of black lines in Fig. 7). The rainfall values of Case 3 at duration 3 hr are bigger 9 mm on average than those of the other two cases (see the series of green lines in Fig. 7). In the point-tracking, the rainfall values in all of the cases are almost equal up to duration 14 hr (Fig. 8). But, the values of Case 3 at duration 15 hr begin to diverge. A difference of the values between Case 3 and other cases at duration 3 hr is 9.7 mm on average. The results from both methods commonly show initial grid-cell size had a bigger effect if the area and the duration are increasing.

5 Annual Journal of Hydraulic Engineering, JSCE, VOL.57, 213, February Method 13hr 14hr 15hr 16hr 17hr 18hr 19hr 2hr 21hr 22hr 23hr 24hr OK IDW Fig. 6 Spatial rainfall distribution pattern estimated by OK and IDW for a period of 12 hours from1: p. m. on August 31st 2. Point 5m 1hr Point 5m 6hr point 5m 12hr point 5m 18hr point 5m 3hr 24 box 5m 1hr box 5m 6hr box 5m 12hr box 5m 18hr box 5m 3hr Box 1m 3hr Box 1m 15hr Box 1m 14hr 22 Box 5m 3hr Box 5m 15hr Box 5m 14hr Box m 3hr Box m 15hr Box m 14hr Fig. 7 Comparison DAD analysis according to initial grid-cell size in Cases 1, 2 and 3 (box-tracking) Fig. 9 Comparison of point-tracking and box-tracking in Case 2 (initial grid-cell size: 5 m 5 m) Point m 1hr Point m 6hr point m 12hr point m 18hr point m 3hr box m 1hr box m 6hr box m 12hr box m 18hr box m 3hr Point 1m 3hr Point 1m 15hr Point 1m 14hr Point 5m 3hr Point 5m 15hr Point 5m 14hr Point m 3hr Point m 15hr Point m 14hr Fig. 8 Comparison DAD analysis according to initial grid-cell size in Cases 1, 2 and 3 (point-tracking). (3) Comparing box- and point-tracking methods There is no significant difference of the rainfall values in Case 1 and Case 2 (both box- and point-tracking). This indicates that even if we compare the reuslts of Case 1 (1 km 2 ) with those of Case 2 (.25 km 2 ) by initial grid-cell sizes, it will not significantly affect DAD analysis. Therefore, the tracking method comparison is carried out in Case 2 and Case 3. Figures 9 and 1 show that box-tracking (dotted line) represents the smaller rainfall values than those of the point-tracking (solid line) as area increases. The longer the duration is, the more the difference of values of the box- and point-tracking methods increases. In particular, the rainfall estimated from Fig. 1 Comparison of point-tracking and box-tracking in Case 3 (initial grid-cell size: m m). the area, 9 km 2 in the duration 3 hr differ up to approximately 45 mm. The reason is the features of both box- and point-tracking. The point-tracking extend the area only around the maximum value which found at the first; in other words, although there is similar value in the spot located far away from the maximum value, the similar value cannot be searched by the point-tracking. This means that the point-tracking can consider the shape of strong rainfall area from only one storm center. Meanwhile, the box-tracking searches the maximum value through the whole basin whenever the area is added. This means that the box-tracking can consider several storm centers, but cannot consider the shape of strong rainfall area.

6 5. CONCLUSIONS In this study, hourly rainfall data of a total of 31 hours of Typhoon RUSA were acquired from 11 ground rain gauge stations within the target basin. Among the interpolation methods in ArcGIS, Inverse Distance Weight (IDW) and Ordinary Kriging (OK) are compared. The initial grid-cell size is classified into 1 km 2,.25 km 2 and.625 km 2 in order to consider the impact of the initial grid-cell size. Lastly, the box-tracking and point-tracking methods for adding area are programmed and compared. This study's results suggest: (1) When deciding the interpolation technique, Inverse Distance Weight (IDW) and Ordinary Kriging (OK) are compared. It was considered that OK is proper in the target basin. (2) Comparing the results of DAD analysis according to the initial grid-cell size, the rainfall values of 1 km 2 and.25 km 2 were almost identical, its value increased 9 mm on average when using.625 km 2. As a result, the DAD analysis is affected by the initial grid-cell size. (3) The box-tracking can consider multiple storm centers. Although the point-tracking can consider only one storm center, that can reflect more accurately the shape of strong rainfall area. In conclusion, the appropriate method can be determined depending on the characteristic of target basin and event. Although the values of each grid are interpolated from the values of the gauging station, the method is able to be utilized with the radar data in further study. And we will apply a series of this research in other events of this study basin as well as in other regions of Japan where it rained a lot to verify applicability of developed methods. ACKNOWLEDGMENTS: This study was supported by the Kyoto University Global COE Programs: Human Security Engineering for Asian Megacities (HSE) and Sustainability/Survivability Science for a Resilient Society Adaptable to Extreme Weather Conditions (ARS). We thank to everyone for provided comments on this paper. REFERENCES 1) Tye, W., Parzybok, D.M., Hultstrand, E.M., Tomlinson, B.K. and Kappel, W.D.: Real-time depth-area-duration analysis for EAPs and flood warning systems, Association of State Dam Safety Officials (ASDSO) Annual Dam Safety Conference, 9. Annual Journal of Hydraulic Engineering, JSCE, VOL.57, 213, February 2) WMO: Manual for depth-area-duration analysis of strom precipitation, World Meteorological Organization, No.237, ) WMO: Manual for Estimation of Probable Maximum Precipitation, Second Edition, World Meteorological Organization, Operational Hydrology Report, No.1, Geneva, Siwitzerlad, ) WMO: Manual on estimation of probable maximum precipitation (PMP), World Meteorological Organization, No.845, 9. 5) Takara, K., Imamoto, H., Hayashi, T., Nakakita, E., Ichikawa, Y., Hashino, T. and Nakamura, Y.: Storm and flood disaster in the Nakagawa basin in 1998, Disaster Prevention Research Institute, Kyoto University, No. 42, B-2, pp , 1999 (in Japanese). 6) Takara, K. and Hashino, T.: DAD analysis using radar raingages and PMF estimation in the Naka river, Disaster Prevention Research Institute, Kyoto University, No. 43, B-2, pp , (in Japanese). 7) Takara, K., Hasino, T. and Nakao, T.: Application of radar raingage and nonlinear optimization to DAD analysis, JSCE, No.691, 1 (in Japanese). 8) Kim, N. and Won, Y.: DAD analysis on storm movement, Korea Water Resources Association, pp , 4 (in Korean). 9) Kang, M.: Identifying the Damages and Causes of Floods and the Outlook for Future Floods in South Korea, Korea Society of Civil Engineers (KSCE), Vol. 59, pp , 211 (in Korean). 1) Lee, H., Choi, B., Oh, B., Yoon, H., Kim, H. and Jeong, Y.: 2 national flood investigation report, the Korea Water Resources Corporation (K-Water), Chaps.1-2, 2 (in Korean). 11) Kim, N.: GIS Application Data Management and Spatial Analysis using ArcGIS, Hanulacademy, pp , 21 (in Korean). 12) Shaw, E. M.: Hydrology in Practice, third edition, Chapman & Hall, pp , ) Kim, N., Kim, G., Won, Y., Lee, H., Kim, D., Park, S. and Park, M.: Water Resources Management Techniques Research Report 1999: South Korea's major storm, Ministry of Construction and Transportation (Korea Institute of Construction Technology), Vol. 1, pp. 1-77, (in Korean). 14) Kim, N., Kim, G., Won, Y., Lee, H., Kim, D., Park, S. and Park, M.: Water Resources Management Techniques Research Report 1999: Korea Probable Maximum Precipitation Estimates, Ministry of Construction and Transportation (Korea Institute of Construction Technology), Vol. 2, pp , (in Korean). 15) Issaks, E.H. and Srivastava, R.M.: An Introduction to Applied Geostatistics, Oxford University Press, pp , (Received September 3, 212)