Extreme Hydrological Events: Precipitation, Floods and Droughts (Proceedings of the Yokohama Symposium, July 1993). IAHS Publ. no. 213, 1993. 75 Some characteristics of heavy rainfalls in the Yamato river basin found by the principal component and cluster analyses M. KADOYA & H. CHIKAMORI Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji, Kyoto 611, Japan T. ICHIOKA Sogochosasekkei Co., Ltd., Umedakita building, Shibata 1-8-15 Kita-ku, Osaka 530, Japan Abstract In this paper, characteristics of spatial distribution of heavy rainfalls causing floods in the Yamato River basin located in the Kinki district are examined by applying the techniques of both principal component and cluster analyses. The result of the principal component analysis shows that rain gauge stations in this basin can be arranged into eight groups from the common characteristics of rain storms. On the other hand, the result of cluster analysis differs slightly from the former, but supports it in the practical sense. Finally, the correlations of flood peak discharges at Kashiwara with 12-, 24-, and 48-hour maximum rainfalls averaged over a basin are examined. The result shows that the flood peak discharges have strong correlation with areal 12-hour rainfalls, especially with those in new urbanized areas along the main channel. INTRODUCTION Clarifying the characteristics of heavy rainfalls is the fundamental importance in the planning of flood control or the design of river structures. In this paper, the Yamato River basin located in the Kinki district is chosen as an objective research basin, and the relation between characteristics of heavy rainfall in the basin and flood peak discharges at Kashiwara is examined by applying the techniques of both principal component and cluster analyses to the rainfall data obtained in the basin. First, the technique of principal component analysis is applied for the spatial distribution pattern of the data of maximum 12-, 24-, and 48-hour rainfalls observed in and around the basin, and regionalization of this basin and grouping of rain storms are performed on the basis of characteristics of spatial distribution of rainfall. Next, regionalization of this basin and grouping of rain storms are also performed by the cluster analysis, and their results are compared with those of the principal component analysis. Finally, the correlation of flood peak discharge at Kashiwara with areal rainfall for a given duration is investigated and the effect of characteristics of spatial distribution of rainfall is clarified. RESEARCH BASIN AND RAINFALL DATA The Yamato River rises from the Kasagi Mountainous Zone, flows through the Nara and the Kawachi Plains, and goes down into the Osaka Bay. Since the basin of this 76 M. Kadoya et al. river has so large area as 1070 km2, the flood formation process is not simple. In this basin, flood risk has been increased because the middle zone of the basin has been urbanized rapidly in recent three decades. This basin suffered severe flood disaster caused by a record heavy rainfall in 1-3 August 1982. We use the data of 12-, 24-, and 48-hour maximum rainfalls observed at 26 points in and around the basin (Fig. 1) for 19 rain storm cases for which flood peak discharges at Kashiwara were over 1000 m3/s or 2 days rainfalls over 100 mm were observed at Nara during 1966-1985. In which, all of the duration time of rain storm are defined at Nara. Unrecorded data of rainfall are substituted by the data estimated from isohyetal maps. Moreover, the hourly rainfall data unrecorded at Sakai before 1974 are substituted by those at Otori located near the Sakai station. Fig. 1 Locations of rain gauge stations in and around the Yamato river basin. PRINCIPAL COMPONENT ANALYSIS Interpretation of principal components In this analysis, rain gauge stations are treated as individuals and rainfalls as variables. Fig. 2 shows the distributions of scores of principal components for 12-hour rainfall. In this figure, the Yamato River basin is divided into 26 polygons using the Thiessen method, and the darker the polygon governed by a gauging point, the higher the score Characteristics of heavy rainfalls in the Yamato river basin 77 Fig. 2 Distributions of scores of principal components for 12-hour rainfall, (a) for the first, (b) for the second, (c) for the third, (d) for the fourth. of the principal component at this point. In general, the first principal component is said to be an index of magnitude. This tendency is well seen in Fig. 3. That is, Fig. 3(a) shows the relation between scores of the first principal component and the mean point rainfalls defined as mean rainfall of every storm at a given point, and Fig. 3(b) the one between factor loadings and the coefficients of correlation defined by the mean and the mean point rainfall. On the other hand, it is found in Fig. 2(a) that scores of the first principal component tend to increase to the north part of this basin. Thus we conclude that the first principal component also represents the variation of rainfall in the south-north direction. The score of the second principal component increases to the west part of this basin, as seen in Fig. 2(b). The score of the third principal components tends to decrease near the main channel of the Yamato River, as seen in Fig. 2(c), and the score of the fourth principal components tends to increase near Nara and the east mountainous area. However, the tendencies of the third and the fourth principal components are not clear compared with the ones of the first and the second principal components. (b) -*3 " D 1 I - 12 -4-20246 -1 0 I Score of 1st P.C. Factor Loading of 1st P.C. Fig. 3 Scatter diagram about the first principal components for 12-hour rainfalls; (a) score to mean rainfall at each point, (b) factor loading for the coefficient of correlation between point and mean rainfalls of every storm at given points. 78 M. Kadoya et al. Table 1 shows that the cumulative contribution reaches almost 80% by the fourth principal component, thus we conclude that characteristics of heavy rainfalls in this basin can be explained fully using the scores of principal components from the first to the fourth. Table 1 Cumulative contributions of principal components (%). Duration of Princip il Compc nent Rainfall(hr) 1st 2nd 3rd 4th 5th 12 42.3 59.3 72.0 81.0 84.8 24 41.8 56.9 68.4 77.5 82.1 48 41.6 57.7 71.0 78.9 83.8 On the basis of the interpretation of the principal components mentioned above, we discuss the regionalization of this basin due to the difference of characteristics of heavy rainfalls. Fig. 4(a) shows the relation between scores of the first and the second principal components and Fig. 4(b) the relation between those of the third and the fourth. Rain gauge stations can be classified into six groups, I to VI, as shown in Fig. 4(a). Since the rain gauge 15 is far from the other stations belonging to the group III in Fig. 4(b), it is separated from the group III and treated as another group. The group III can be divided into two groups, stations (4, 5, 10) and (6, 18, 19), because these two groups are far from each other, as seen in Fig. 4(b). Thus they are treated as the different ones. Furthermore, the group VI can be divided into two parts according to whether the sign of scores of the third principal component is positive or negative. As the result, rain gauge stations are arranged into 9 groups for 12-hour rainfall. We also investigate the distribution of scores of the principal components for 24- and 48-hour rainfalls in the same way as mentioned above for 12-hour rainfall, then the basin is regionalized into 7 regions for 24-hour rainfall, and 8 regions for 48-hour rainfall. The difference among these regionalizations is summarized as follows. a) Regions 8 and 9 in Fig. 5 are contained in one region for 24-hour rainfall, while (a) (b) 1 H i i o - : v j» i a.' 21 ID," 22CP - |9 H •*4 —ïêa-rfsji-u- kv n>' D2 q D OD,| 6 p u u _._>ÏÏ5 ~ 4t§f3 21 -•^8247n "23 ! rv îm n>4 : vi | 1300 j i i i 111 1 1 li 1 1 1 i i i i 1 1 ! 1 1 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 Score of 1st P.C. Score of 3rd C. Fig. 4 Scores of principal components for 12-hour rainfall: (a) relations between the first and second principal components; (b) relations between the third and fourth principal components. Characteristics of heavy rainfalls in the Yamato river basin 79 Fig. 5 Regions divided by the principal component analysis of 12-hour rainfall. this region is divided into two different regions for 48-hour rainfall, that is rain gauge station No. 20 and a region consisting of 5 stations (21, 22, 24, 25, 26). b) Regions 2 and 3 in Fig. 5 are contained in one region for both 24- and 48-hour rainfall. c) Station No. 3 belonging to the region 4 in Fig. 5 joins in the region 5 located in the upper stream of the main channel for 24-hour rainfall. However, in order to provide the useful information to the planning of flood control, it is desirable that the regionalization for expressing characteristics of heavy rainfalls is summarized to only one type eliminating the effect of rainfall duration.