On Hypsometric Curve and Morphological Analysis of The Collapsed Irrigation Reservoirs

To identify the drought and flood control functions of an irrigation reservoir, research on hydrological analysis and its impact needs to be conducted. To this end, geographical 21 characteristics, such as the cross section of the reservoir, are important, but such information is insufficient. Therefore, this study aimed to identify the topographic and morphological 23 characteristics of reservoirs without measured data using their geographical information. In addition, an attempt was made to identify the morphological characteristics of reservoirs that had 25 collapsed due to aging and the increased frequency of occurrence of strong rainfall intensity 26 caused by climate change. Ten reservoirs, including the Ga-Gog Reservoir located in Miryang 27 city, Gyeongsangnam province, South Korea with measured data, were selected as target 28 reservoirs. The topographic information of the target reservoirs was constructed using 29 topographical maps and GIS techniques. Based on the information, the volume (V)-area (A)-depth 30 (H) relationship and the hypsometric curve (HC) according to the relative height (h/H) and relative 31 area (a/A) were created. When the volume of each reservoir estimated using topographic 32 information was compared with the measured volume, the error rate was found be between 0.23 33 and 14.27%. In addition, two reservoirs that had collapsed near Miryang city were added, and the 34 V-A-H relationship and HCs were created based on the topographic information. In addition, the 35 morphology index, storage-area of full water-levee height relationship, and storage-area of full 36 water relationship were analyzed to identify the morphological characteristics of the reservoirs. The analysis results showed that the collapsed reservoirs had a relatively high water depth and a 38 large area. In addition, similar types of reservoirs were grouped by conducting cluster analysis using basic specifications, such as the reservoir watershed, storage, and area of full water. When the cluster analysis results were analyzed based on HC, the reservoirs were grouped into three shapes: convex upward shape (youthful stage), relatively flat shape (mature stage), and convex downward shape (old stage). The HCs of the collapsed reservoirs exhibited the convex downward 43 shape (old stage), indicating that they were subjected to considerable erosion due to aging. In 44 other words, considerable erosion makes the allowable storage capacity insufficient due to the 45 large amount of sediment accumulated in reservoirs and reduces their flood control capacity, 46 which may cause them to collapse during heavy rainfall. Therefore, it is expected that identifying 47 the potential causes of reservoir collapse through the morphological characteristics and HCs of 48 reservoirs will support the operation and management of reservoirs for reducing flood damage. 49


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The precipitation by heavy rainfall, monsoon rains, and typhoons, which occur during the 54 summer rainy season, is stored and used in the next year. To this end, water is secured and water 55 resources are managed through hydraulic facilities, such as dam reservoirs for various types of 56 water and irrigation reservoirs for agriculture. Owing to the increasing variability of precipitation 57 under the influence of climate change and an imbalance in precipitation by region, however, 58 reservoirs are becoming more vulnerable to droughts and floods depending on the region. In 59 is not possible to accurately express the geometry of a reservoir with a cross section. In this study, 125 it was assumed that the A-h and V-h relationships can be expressed with inverse functions. In 126 addition, a basic mathematical theory was developed based on previous studies to induce first-127 order equations for these relationships. Here, it can be inferred that the A-h and V-h relationships 128 are interdependent. Thus, based on this, the equations were induced (Hayashi et al, 2000;Kim et 129 al, 2002). (1) 138 139 where η is an arbitrary variable for water depth, V is the volume of the reservoir, h is the water 140 depth from the lowest point of the reservoir to the water surface, ℎ 0 is the water depth to the 141 infinitesimal area of the reservoir, and A is the surface area of the wetland. 142

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A is assumed to be flat and can be obtained considering the wetland slope between dh, which can 144 be expressed as Eq. (2). 145 (2) 147 148 where y is the altitude of the ground surface corresponding to h, 0 is the unit altitude of the 149 ground surface, r is the radius of the wetland, 0 is the radius of an arbitrary infinitesimal area of 150 the wetland, and p is the shape factor for the side slope of the wetland. 151

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Since the area is A = π 2 if it is obtained using a conventional method without considering the 153 slope of the reservoir, the change in area depending on the water depth is π 0 2 ∝ ℎ 0 and π 2 ∝ 154 ℎ 0 . Therefore, Eq.

Morphology index 182
The morphology index of a reservoir is quantified using the average depth and area of full water of the reservoir.

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According to Leonard and Crouzet (1999), a morphology index of 10.5 or higher belongs to a deep lake and a 184 morphology index of 0.6 to 10.4 represents a normal lake. A morphology index of 0.5 or less is classified as a shallow 185 lake. Eq. (9) shows the morphology index applied to reservoirs.

Storage-area of full water-levee height relationship 190
195 196

Storage-area of full water relationship 197
Takeuchi (1997) estimated the storage-area of full water relationship for reservoirs in the world with an area of full water of 198 36.1 2 or high and a storage of 0.5 3 〗 or higher as shown in Eq. (11).

Cluster analysis 203
Cluster analysis is a method of classifying data with similar characteristics into groups based on the characteristics methods that use the distance between data, such as shortest connection and longest connection. A representative method for 207 non-hierarchical cluster analysis is K-means clustering. K-means cluster analysis classifies data with similar characteristics 208 into K groups. It is a method of grouping data in the close distance from a centerpoint, which is the average of the data in 209 each cluster. In this study, K-means cluster analysis was conducted to determine optimal clusters by minimizing the distance 210 between data in each cluster based on the centerpoint, and the cluster analysis process was terminated at the stage where the 211 arbitrarily defined centerpoint of each cluster could no longer minimize the error. Figure.

Target basin selection 219
Ten reservoirs, including the Ga-Gog Reservoir located in Miryang city, Gyeongsangnam province, were selected as target 220 reservoirs in this study. They were measured using unmanned water depth measuring equipment by the National Disaster 221 Management Research Institute. The total storage capacity is the height from the reservoir bottom to the full water level.

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Since the dead storage level could not be identified, the total storage was compared and analyzed. In this study, the reservoir 223 data measured by the National Disaster Management Research Institute were used. The locations of the ten reservoirs,

Creation of digital elevation models (DEMs) for the target reservoirs 234
The target reservoirs were modeled based on the digital topographic maps (1:25,000) of Miryang city, Gyeongsangnam 235 province provided by the National Spatial Information Portal. To quantitatively identify the altitude and topographic 236 characteristics of the reservoirs, the procedure of (1) to (6) in Figure. (Table 6).

Analysis of the morphological characteristics of the reservoirs 276
To identify the characteristics of the reservoirs, the morphology index and the storage-area of full water-levee height relationship

Analysis of reservoir characteristics through cluster analysis 328
To identify the characteristics of the reservoirs with different specifications, cluster analysis was conducted using the basic 329 specifications of each reservoir. As shown in Table 8, the specifications of the ten reservoirs, including the Ga-Gog Reservoir, 330 were used as input data. The input data included the basin area, useful capacity, area of full water, levee height, levee length, 331 permissible area, area irrigated, and frequency of drought. As shown in Figure. 10, the cluster analysis classified the reservoirs into two groups: group (I) with reservoirs whose useful 338 capacity and area of full water were large, including R1, R2, and R6, and group (II) with reservoirs whose useful capacity and area 339 of full water were small, including R3, R4, R5, R7, R8, R9, and R10. The results of conducting cluster analysis using the basic 340 specifications of the reservoirs showed that the reservoirs could be classified based on the useful capacity and area of full water, 341 which were identified as indicators that were more influential than other basic specifications in the cluster analysis process.

Morphological analysis of the collapsed reservoirs using cluster analysis and HC 349
HC and the cluster analysis method were applied to reservoirs that had collapsed and caused damage in the past. The reservoirs

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Cluster analysis was conducted using the specifications of the ten target reservoirs as well as the Sandae (11) and Goeyeon (12)

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Reservoirs as input data. The cluster analysis classified the reservoirs into three groups: group (I) with the R3, R4, R5, R7, R8, R9, 364 and R10 reservoirs whose area of full water and useful capacity were relatively small; group (II) with the R1, R2, and R6 reservoirs 365 whose area of full water and useful capacity were relatively large; and group (III) with the Sandae (11) and Goeyeon Reservoirs 366 whose area of full water and useful capacity were largest ( Figure. 11).

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To identify the characteristics of each group, the morphological characteristics of the reservoirs were investigated using their HCs.

Conclusion 384
In this study, the geometry of unmeasured reservoirs was constructed using their topographic information, and 385 morphological analysis was conducted for them. The hypsometric curve (HC) was created for each reservoir to understand 386 their geometry and identify the area by elevation and storage capacity. In addition, the morphology index was quantitatively 387 presented through the analysis of the storage-area of full water relationship for each reservoir. The topographic and 388 morphological analysis of reservoirs that had collapsed due to aging, insufficient management, and flooding were analyzed 389 to identify the potential causes of collapse.

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(1) The area by elevation and volume were calculated for ten reservoirs located in Miryang city, Gyeongsangnam province, 392 including the Ga-Gog Reservoir, using digital topographic maps. When the results were compared with the volumes 393 of the reservoirs measured by the National Disaster Management Research Institute, the error rate ranged from 0.23 394 to 14.27%. The error rate was excellent as its average value was approximately 5.03%. In addition, HC was created 395 for each reservoir using the area by elevation and volume.

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(2) Cluster analysis was conducted to classify similar types of reservoirs into groups using basic specifications, such as the 398 basin area, useful capacity, and area of full water. The cluster analysis classified the reservoirs into two groups: the R1, R2, 399 and R6 reservoirs whose useful capacity and area of full water were large and the R3, R4, R5, R7, R8, R9, and R10 reservoirs 400 whose useful capacity and area of full water were small. The useful capacity and area of full water were identified as 401 indicators that had a larger impact on the cluster analysis results than the other specifications.