京都大学防災研究所年報 第 56 号 B 平成 25 年 6 月
Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No. 56 B, 2013

A Basin-scale Spatial Distribution of Probable Maximum Precipitation for the
Yodo River Basin, JapanNor Eliza Alias(1), Pingping LUO and Kaoru TAKARA(1) Graduate School of Engineering, Department of Civil and Earth Resources Engineering, Kyoto
University (Permanent address: Faculty of Civil Engineering, Universiti Teknologi Malaysia)
Synopsis
The objective of this paper is to analyze the extreme rainfall in term of the PMP
estimates for the Yodo River basin. The PMP are estimated using the Hershfieldstatistical method. Since the method uses statistical approaches, long recorded data
available in Japan were able to be fully utilized. A limitation by using the Hershfieldstatistical method is that only point PMP are estimated. Using the point PMP estimates,
a spatial PMP of 1-day, 2-day, 3-day, 5-day, and 7-day rain were developed. The paper
describes the methodology used to produce the spatial PMP and discuss on the PMP
distributions over the basin area. Comparison between the spatial PMP and previous
flood historical records were also conducted. Good agreement were observe from thecomparison confirming reasonable spatial PMP distribution were constructed.
Keywords: Probable maximum precipitation, Hershfield statistical method, extreme
rainfall, spatial distribution

1.

Introduction

Global warming have been claimed to produce
higher intensity and long period of rainfall acrossthe globe. This includes Japan. Lying on prone
typhoon area, exposed to the Pacific Ocean on the
East and located near to the Siberian land mass on
the West, heavy rainfalls are regularly expected
especially during the summer (Jun to August). The
rains are observe to becoming more intense andfrequent. In order to understand the extreme rainfall,
an upper boundary or limit of possible extreme
rainfall could be estimated. The estimates is called
the probable maximum precipitation (PMP). The
PMP estimates can be use for flood disastermanagement (hazard map, dam operation, flood
control, irrigation, etc.). World MeteorologicalOrganization (WMO, 2009) defines the PMP as"the greatest depth of precipitation for a given
duration meteorologically possible over a given size
storm area at a particular location at a particulartime of the year, with no allowance made forlong-term
climatic
trends"(WMO,
2009).
Previously, research on PMP are not very popularin Japan probably due to PMP estimates are usuallyused for dam designs. However, more research are
currently being conducted and of high interest.
Huge dams are usually constructed forhydro-electricity projects, whereas Japan useshydro-electricity powers about 10% , 30% from
nuclear power plant (before the Fukushima nuclear
plant incident) and mainly from coal.
This research conducts PMP estimation for oneof the river basins in the Kansai region of Japan, theYodo river basin. The Yodo river basin extends
over six prefectures of Mie, Shiga, Kyoto, Osaka,― 65 ―

Hyogo and Nara with an area of 8,240 km2. It is thelargest river basin in the Kansai region. The basin
area includes Lake Biwa and several main rivers(Katsura, Seta-Uji, Kizu and Yodo rivers) whichflow towards the Osaka bay. The population in thebasin has been increased since the Edo period(1700) to Taisho period (1925), from 2 million to
4.73 million people. In 2002 the population havereached 14 million (Shiga Prefectural Government,
2007; Kinki Regional Development Bureau, 2002).
Various hydrological studies have been
conducted within the Yodo river basin before. Luo
et al. (2012) analyzed land use change under the
paleo- environment (1843 to 1976) to explore theeffects of human activities on hydrologic response.
Kim et al. (2008) developed a numerical model forhydrological and climate change analysis.
Combination of the Global Climate Model (GCM)
and a hydrological model investigated the possible
impacts of climate change from the hydrological
viewpoint. Other researches were more focused
towards the water quality analysis and water
resources management especially in the Lake Biwa
of Yodo river basin. Even though, several statisticalresearches have been conducted using data fromstations within the Yodo river basin (Takara andTosa, 1999; Takara and Stedinger, 1994; Takasao etal.,1986), extreme rainfall analysis and PMP
estimates using whole data of the basin has yet tobe conducted.
The objective of this paper is to analyze theextreme rainfall in term of the PMP estimates for
the Yodo River basin. The PMP are estimated using
the Hershfield statistical method. Since the method
uses statistical approaches, long recorded data
available in Japan were able to be fully utilized. A
limitation by using the Hershfield statistical method
is that only point PMP are estimated. To obtain anaerial PMP estimates, depth area duration curve isneeded. This paper however will not discuss on theareal PMP. Using the point PMP estimates, a spatial
PMP of 1-day, 2-day, 3-day, 5-day, and 7-day rain
could be generated. The paper will describe themethodology used to produce the spatial PMP using
1-day rainfall.

2.

Study site and data

62 stations were chosen for the extreme rainfall
analysis and PMP estimation. 31 stations inside the
Yodo river basin and 31 stations outside of thebasin boundary. The stations outside the Yodo river
basin were considered as additional margin for the
PMP estimation and spatial distribution analysis for
the Yodo river basin. The data were obtained fromthe Japan Meteorological Agency (JMA). Long
historical data (1880 - 2012) belongs to the surface
weather observation network, while the rest arefrom the Automated Meteorological Data
Acquisition System (AMeDAS) (1976 - 2012) of
JMA. Fig.1 shows the locations of stations selected
for the analysis. Distances among each station areabout 20 to 30 km.

Fig. 1 Locations of the Yodo river basin and
AMeDAS stations
selected for the statisticalanalysis and PMP estimation
3.

MethodThe 1-day rainfall obtained by JMA was used toderived the 2-day, 3-day, 5-day and 7-day rainfall
using Fortran codes developed by the writers. To
obtain the rainfall data directly from JMA are time
consuming and costly since 62 station were used,thus a Fortran program was written to generate the2-day, 3-day, 5-day and 7-day data. From there,
the annual maximums of all the periods wereextracted also using the same Fortran program. The― 66 ―

2-day, 3-day, 5-day and 7-day rainfall of one of thestations were compared with the data from JMA for
validation. Similar rainfall data were obtained, thus
assuring the quality of the derived rainfalls (2-day,
3-day, 5-day and 7-day annual maximums).
Using the annual maximums of the rainfalls,
Hershfield statistical method was used for
estimating the PMPs. Hershfield method is being
used widely (Deshpande et al., 2008; Koutsoyiannis,
1999; Durbude, 2008; Desa et al., 2001; Desa et al.,2007). It was considered in the manual on
estimation of probable maximum precipitation by
the World Meteorological Agency (WMO, 2009)
after it had been modified and developed by
Hershfield (Hershfield, 1961a; Hershfield 1961b).
It is also believed to be closely comparable to thoseobtainedbytheconventional
moisturemaximization and storm transposition methods(Deshpande et al., 2008). More comparison
betweenthestatisticalmethodandhydro-meteorological method however are stillneeded. The essence of the Hershfield statisticalmethod is storm transposition, but instead oftransposing the specific rainfall amount of one
storm, an abstracted statistic Km is transposed(WMO, 2009). The Hershfield method for
estimating the PMP value for a station uses thefollowing equations.

where, XPMP is the PMP estimates for a station,
Xn is the mean of the annual extreme series, Sn is thestandard deviation of the annual extreme series, Km
is the frequency factor which depends on theavailability of data period, Xmax is the highest
rainfall value at the station, Xn-1 is the mean of theannual extreme series without the largest value, andSn-1 is the standard deviation of the annual extreme
series without the largest value.
First, the parameters Xn, Sn and Km arecalculated. Then, Km values for all stations areplotted against the Xn values respectively and an
envelope curve is drawn (Fig.2). The new Km value
is picked up from the envelope line for eachstation's Xn. Finally, the PMP values for eachstation is calculated using Eq.1 by replacing Km
with the new value.
According to the WMO (2009) envelopment is aprocess for selecting the largest value from any setof data. Several researchers applied similarenvelopment technique currently used for this paper(Desa et al., 2007;Metreata, 2006). Fig.2 shows the
Km plots against Xn and its envelope lines. All theKm values despite various rainfall periods have Km
values less than 20. It was mentioned by Hershfieldthat the maximum values of Km obtained using 2700
stations (most stations were in the US) used forprevious climatological observation programme is
20 (WMO, 2009). In this study, the average valuesof the transposed Km are around 13 to 15. It wasstated by Hershfield also that for areas of heavy
rainfalls the value of 15 could be too high and too
low for arid areas. This study however found thatthe value 15 was obtained for an area of highrainfalls, contributing to the information for the Km
according to its climate characteristics. The two
extreme Km values comes from Hikone andMiyagawa. A more smooth an accurate envelope
could be obtained if longer records and higher
number of extreme rainfalls were recorded.
Spline interpolation method in ArcGIS 10
Spatial analyst tool box were used for theinterpolation of the point PMP. The method waschosen due to its low interpolation error and its
approach in preserving the point value whereby theinterpolated surface goes through the data points.
The Spline technique is considered as adeterministic and global method where acontinuously differentiable surface is fitted to all
the data. The technique used to interpolate the dataassumes that the data are error free and hence theinterpolated data goes through the data points.
Spline technique is one of the interpolation
technique that are generally recommended forhydrologic applications since it is robust,
operationally straightforward to use and represents
quite well the spatial distributions of hydrologicalparameters (Bloschl and Grayson, 2000).

― 67 ―

Fig. 2 Km distribution of the 24-hr PMP for Yodo river basin

600

500

Rainfall (mm)

400
300
200

100
0
1880

1900

1920

1940

1960

1980

2000

2020

Year

Fig. 3 Distribution of the annual maximum 24-hour rainfall observation in the Yodo river basin.
4.

Results and discussions

4.1 Maximum 24-hour rainfall time series
Fig.3 illustrates the annual maximum 24-hour
rainfall distribution of stations within the Yodoriver basin from 1880 to 2012. The observed data
ranges from 29 years to 132 years. The longest
observation data were obtained from Kyoto, Osakaand Hikone stations which have 132, 130 and 119
years of observation respectively, while the others
have only up to 37 years. This corresponds to thecommencing of AMeDAS in 1974. Information ofeach station’s data and the parameters for the PMP
estimation are presented in Table 1.
4.2 Probable maximum precipitation (PMP)
estimates
Table 1 shows the PMP estimates and its
rainfall statistical properties (Xn and Xmax) of eachstation. The results show stations with higher Xmax

values tends to has higher PMP estimates indicating
good correspondence between them.
The Hershfield statistical method uses atransposed frequency factor Km for its PMP
estimation; which considers the average maximum
rainfall, Xn of one station instead of just the largest
maximum rainfall, Xmax. Thus, for this case Soni
station has the highest estimated PMP value due toits high Xn even though Hikone's Xmax is muchhigher. Hikone station has 118 years data compared
to Soni station with 36 years data, resulting into
Hikone's Xn being much less than Soni's. Therefore,
the PMP value in Soni is overestimated due to its
less numbers of observations. More accurate PMP
estimates could be obtained from longer data
records.
Generally, both highest range of PMP value andmaximum rainfalls are observed at Soni, Hikone
and Shimogahara (PMP values higher than 1000
mm, and Xmax higher than 300 mm for the 1-day― 68 ―

rainfall case), followed by Nabari, Ueno,
Kasatorayama and Toyonaka (PMP values higher
than 800 and Xmax higher than 250 mm).
4.3 Spatial probable maximum precipitation(PMP)
A spatial PMP for the Yodo river basin ispresented in Fig.4. The PMP spatial distributions
presented include 100-mm interval isohyetal lines.
PMP values at any point in the river basin could be
estimated from the isohyetal lines. The isohyetal
lines clearly show the range of PMP values. The
highest PMP observed is around the Hikone andShimogahara stations which are from 900 to 1040
mm (1-day PMP), while the lowest is at the northside of Lake Biwa around Yanagase and Torahime
where the isohyetal lines are less than 500 mm. At
the south-east of the basin, areas around Soni,
Nabari Ouda and Ueno also show quite high PMPvalues (800 to 1300 mm). In general, similar
distribution of the high and low PMP estimates areobserved for all periods (2-day, 3-day, 5-day and7-day rainfall). In addition, the PMP estimates areas
around Hanasetogi seems to increase and become
significant as the rainfall period increase from1-day to 7-day. This could show that Hanasetogi
has higher risk of extreme rainfall for storms withlonger period.
By comparing the PMP distribution against theDEM (Fig.4f) of the basin, we could see that areas

located at the foot of the mountainous lines (ex:Hanasetoge, Ktoto, Soni, Shimogahara)
havehigher PMP distributions. This show the orographic
effects taking place in those areas. Orographic
barriers tend to enhance rainfalls. In the case of
Hikone and Shimogahara (North East of the basin)
areas which have the highest PMP distributions,additional moisture sources could come from winds
blowing through the Lake Biwa thus contributing
high PMP distribution. From records, maximum
winds recorded in Hikone and Shimogahara stations
are mostly from the North-West directions.
4.4 Comparison of PMP with historical flood
eventsExtreme rainfalls have been proven to influence
the discharge within the Yodo river basin (Luo etal., 2012), therefore the spatial PMP distribution of
the Yodo river basin is compared with previous
flood records. Table 2 presents flood disasters in
the Yodo river basin according to the main rivers’
maximum flow and the Yodo river's maximum
water level. During every flood event the Kizu riverfrequently has the largest maximum flow comparedto Katsura and Uji rivers. Generally, this agrees
with the estimated spatial PMP distribution in
Fig.5 which shows areas around Kizu river having
higher PMP range (800 mm to 1300 mm) compared
to areas around Katsura and Uji rivers (600 mm to
800 mm).

(a) 1-day PMP(b) 2-day PMP(d) 5-day PMP(e) 7-day PMP(c) 3-day PMP(f) DEM

Fig. 4 Spatial PMP (a) 1-day (b) 2-day (c) 3-day (d) 5-day (e) 7-day and (f) DEM for the Yodo river basin― 69 ―

Table 1 Statistical properties of the annual
maximum 24-hour rainfall and PMP values (mm) of
the selected 62 stations.
No

Stations(Years)

Xn

Xmax

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62

Arakawa(28)Hakusan (34)
Hanasetoge(34)Hari(37)
Higashiomi(37)Hikone(119)
Hirakata(34)Hokusei(37)Ibigawa(34)Ikomayama(37)Imajo(37)
Imazu(37)
Jubusan(34)Kameyama(37)Kamiishizu(37)Kasatoriyama(37)Katsuragi(31)Kawachinagano(37)Kayumi(37)Keihoku(37)Kiraramine(32)Kyotanabe(37)Kyoto(132)
Mihama(37)Minamikomatsu(36)Mino(34)
Miyagawa(35)Miyama(37)Nabari(37)Nagahama(37)Nagaokakyo(37)Najio(30)
Nara(60)
Nose(37)
Obama(37)Oi(37)
Omihachiman(37)Osaka(130)
Otsu(37)
Ouda(37)
Ozu(26)
Rokkosan(30)Sakai(37)
Sanda(37)
Sekigahara(37)Shigaraki(37)Shimogahara(30)Shitsukawa(37)Shuchi(31)Soni(37)
Sonobe(34)Suijo(37)
Takami(29)Tawaramoto(37)Toyonaka(34)Tsu(124)
Tsuchiyama(37)Tsuruga(25)Ueno(76)
Yanagase(37)Yokkaichi(37)Yoshino(22)

(1-d)
111
145
123
98
91
98
91
141
160
93
97
91
93
138
141
161
85
93
195
104
170
93
105
104
110
102
324
104
105
78
113
110
90
103
99
113
99
91
104
95
173
100
83
88
147
102
128
108
98
158
112
103
172
79
96
136
122
88
105
99
126
106

(1-d)
223
324
215
220
174
597
172
310
354
275
141
164
204
242
290
259
196
213
498
209
394
200
289
269
188
259
764
269
295
120
239
269
182
221
232
261
183
251
158
235
421
175
163
188
265
235
341
232
206
370
259
249
449
191
272
427
231
165
287
157
295
226

PMP
1-d
796
1018
757
630
555
1004
599
807
975
761
473
529
671
833
1042
849
573
678
1297
717
918
605
734
863
571
746
870
863
904
419
758
870
602
720
765
886
629
631
548
741
1173
648
641
698
857
704
1066
813
714
1134
854
757
1382
591
853
938
790
580
886
445
849
769

2-d
1089
1173
1185
801
738
1273
868
1045
1141
920
701
812
855
1035
1403
1161
759
874
1765
957
1247
851
956
1098
832
945
1628
1098
1073
707
1029
1090
723
916
1068
1277
770
847
688
920
1513
861
769
898
1259
808
1165
1039
980
1576
1045
931
1706
635
1022
1197
967
763
983
700
1069
1338

3-d
1060
1282
1244
1147
818
1378
968
1166
1165
1165
776
849
1039
1140
1535
1274
1114
1163
1975
1029
1293
955
1027
1078
914
1009
1914
1078
1358
838
1076
1198
956
966
1089
1263
891
933
805
1249
1598
1016
1043
934
1376
988
1228
1076
996
1830
1055
1020
1859
978
1055
1246
974
741
1095
799
1246
1433

5-d
1161
1411
1363
1194
992
1567
1142
1538
1266
1271
1011
913
1131
1384
1902
1411
1231
1290
2322
1158
1611
1094
1191
1096
1121
1257
2060
1096
1446
934
1245
1341
1129
1120
1192
1278
1119
1042
1016
1397
1852
1218
1196
1064
1657
1110
1452
1187
1116
2134
1139
1081
1926
1085
1183
1396
1340
839
1289
860
1475
1485

7-d
1141
1513
1526
1172
975
1512
1153
1673
1274
1214
1117
946
1138
1522
1849
1497
1242
1242
2325
1133
1805
1120
1253
1114
1205
1331
1934
1114
1361
893
1309
1339
1109
1159
1114
1156
1150
1115
1038
1354
1914
1297
1219
1087
1620
1110
1351
1207
1097
2066
1124
1044
1941
1064
1197
1415
1331
864
1201
918
1561
1406

Table 2 Flood disasters in the Yodo river basin(Shiga Prefectural Government, 2007)

Date
25/09/1952
27/09/1955
27/08/1957
14/08/1958
27/09/1959
30/08/1960
28/10/1961
17/09/1965
17/09/1972
02/08/1982

Maximum flow (m3/sec)
Kizu Katsura
Uji
Yodo
River
River
River River
5800
2700
1780 7800
3850
810
670
4610
3650
790
525
4030
3900
2500
1270 6800
6200
1700
885
7200
770
2600
310
3840
5220
2100
1000 7800
5170
2500
900
6870
3250
2320
810
5230
3980
1950
990
6260

Max. waterlevel (m)
Yodo
River
6.97
5.49
5.07
6.5
6.69
4.7
6.95
6.75
4.64
4.65

5.

Summary and Conclusions

The PMP estimated using the statistical
Hershfield methods corresponds reasonably with
the Xmax of each stations respectively. Generally thehighest ranges of PMP value and maximum
rainfalls are observed around Soni, Hikone,
Shimogahara, Nabari and Ueno with a 1-day PMP
value around 1000 mm . However, PMP value inSoni is overestimated due to its few numbers ofobservations. More accurate PMP estimates could
be obtained from longer data records.
From the PMP spatial distribution andisohyetal lines the highest observed PMP is aroundthe Hikone and Shimogahara stations which arefrom 900 to 1040 mm, while the least is around the
Yamagase and Torahime stations. However areas
near Hanasetogi has higher risk of extreme rainfall
for storms with longer period since the PMP
estimates becomes significantly higher as the rain
period increases.
In term of comparison with historical floodrecords, The PMP illustrate a good correspondencewith the previous flood events. It is estimated thatthe area around Ueno, Nabaki and along the Kizu
river has a high 1-day PMP value (800 mm to1300 mm) compared to areas around Katsura andUji river (600 mm to 800 mm) corresponding well
to areas with the highest river discharge.
Generally, the paper highlights one of themethodology that can be used to estimate the PMP
values and producing a spatial PMP estimates.
Since Japan has long rainfall records, the statisticalmethods are appropriate and fully utilizes therecords. Spatial distribution of the PMP presented
in this paper will be useful as a background material
in identifying area with the most extreme rainfall
possible to occur in the Yodo river basin with aperiod of 1-day, 2-day, 3-day, 5-day and 7-day.
Comparisons as well as inputs to numerical models
can also be conducted using the results obtained.
PMP studies are one of the steps to determine theprobable maximum flood (PMF). PMF studies are
crucial for basins with high population and exposed
to various kinds of water related natural disasters.

― 70 ―

Fig. 5 Yodo river basin main rivers and spatial
1-day PMP.
Acknowledgements
This
study
was
supportedbytheMonbukagakusho (MEXT), Postdoctoral fellowshipof Japan Society for the Promotion of Science(P12055), JSPS KAKENHI Grant Number
24∙02055, and the Kyoto University Global COE
program on “Sustainability/Survivability Science
for a Resilient Society Adaptable to Extreme
Weather Conditions”. The authors wish to thank theJapan Meteorological Agency (JMA) for providing
the data.
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