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Extreme wind speeds for various return periods during rainfall
Journal of Wind Engineering and Industrial Aerodynamics, 26 (1987) 105-125
105
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
EXTREME WIND SPEEDS FOR VARIOUS RETURN PERIODS DURING
RAINFALL
SHUZO MURAKAMI 1, YOSHITERU IWASA2, YASUSHIGE MORIKAWA~ and NORIKO CHINO 2
~Institute of Industrial Science, University of Tokyo, Tokyo (Japan) 2Technical Research Laboratory Takenaka Komuten Co., Ltd., Tokyo (Japan) 3Technical Research Institutes, Taisei Corporation, Tokyo (Japan) (Received July 25, 1986; accepted in revised form November 15, 1986)
Summary Extreme wind speeds for various return periods during rainfall at six typical meteorological stations in Japan were estimated using the statistical method for extremes. The annual maximum wind speeds recorded from 1961 to 1980 at these stations were used for analysis. The annual maximum wind speeds were classified according to the amount of precipitation, and they were found to be well modelled by the extreme type-I distribution. Multiple regression AnMysisemploying two parameters, i.e., annual maximum wind speed and hourly precipitation, was used to fit the type-I distribution.
1. Introduction W i n d pressure during rainfall,in addition to the amount of precipitation, affects the water seal of the external wall and roof of buildings. In order to assess the wind environment around tallbuildings,wind speed during rainfall and itsfrequency of occurrence are fundamental data. The value of wind speed and its probability of non-occurrence during any period during rainfall are therefore also important parameters. Extreme wind speeds for a 50 or 100 year return period at differentmeteorologicalstationsin Japan have been reported in severalpapers, e.g.,refs.I and 2, and the frequency of wind speeds during rainfall from 1953 to 1962 have been obtained at twenty meteorological stations [3]. Moreover, a statistical approach for simultaneous occurrence of rain and wind was attempted by Sacre [4 ],and qualitativeresultsusing four categoriesof rain intensitywere obtained. However, a quantitative study of extreme wind speeds during rainfallhas not been made to date as far as we are aware. W e therefore studied extreme wind speeds for various return periods during rainfallusing the statisticaltheory of extremes at six meteorological stations in Japan.
0167-6105/87/$03.50
© 1987 Elsevier Science Publishers B.V.
106
2. Meteorological data and analytical methods
2.1. Meteorological data for precipitation and wind speed In Japanese meteorological stations, hourly precipitations are recorded, together with the daily maximum hourly precipitations. The 10 rain average wind speeds recorded every 1 or 3 h ( the particular cycle used depended on the year and the meteorological station), and daily maximum 10 rain average wind speeds, are also recorded (see Tables 1 and 2). Data obtained at Sapporo, Sendai, Tokyo, Nagoya, Osaka and Fukuoka from 1961 to 1980 were used for analysis. These wind speeds were classified into eight categories according to the amount of hourly precipitation: >t 5, 7, 11, 21, 31, 41 or 51 ram. Here, the simultaneous measurement of precipitation data and wind speed data was a perplexing problem because of the difference of averaging time and cycle used for TABLE1 Example of meteorological data in t h e case when 10 m i n average wind speeds were recorded every hour (6.7.1968, Tokyo) (a) Meteorological data Observation time a
Wind direction
10 rain average wind speed
Hourly precipitation (ram)
Observation time a
Wind direction
(ms -1) 01 02 03 04 05 06 07 08 09 10 11 12
S SE E ENE ENE S W WSW NW WNW W SSW
10 m i n average wind speed
Hourly precipitation (ram)
(ms -~)
4.2 3.2 4.8 4.7 4.0 4.2 4.8 3.5 3.7 4.7 2.7 3.8
0.5 0.5 4.5 11.0 16.5 16.0 4.0 5,0 8,0 0,0 0.5
11.0 15:50
17.5
13 14 15 16 17 18 19 20 21 22 23 24
SSW SW SSW SSW SW N NNW NE NNE N E NNE
8.0 9.0 7.8 8.5 6.8 3.8 3,3 1,0 1.2 2.8 4.8 3.8
0.5 0.0 2.5 4.5 0.0 -
Daily maxima SSW Observation time:
3:47- 4:47
aThe observation time is expressed by J a p a n S t a n d a r d Time ( J S T ) in t h e 24 h system beginning at midnight.
107 (b) Detailed description of observation times for meteorological data Observation time
2:50
10 min average wind speed (m s-I)
t t t t t
Daily meTimum I0 min average wind speed (ms -1)
Hourly precipiration (ram)
Daily maximum hourly precipiration (mm)
- 4.8
3:00 3:50 4:00 4:50 5:00 5:50 6:00 14:50 15:00
15:5016:00
II.0 (3:47) 4.7
t
17.5
16.5
(4:47)
4.0
16.0 4.2
7.8 (15:40) 11.0 (15:50)
1" 8.5
recording precipitation and wind speed; precipitation was an hourly total recorded every hour, whereas the wind speed was a 10 rain average recorded every I or 3 h. In this study, each hourly precipitation and each daily m a x i m u m precipitation was made to correspond to the m a x i m u m value of wind speed recorded every i or 3 h and to the daily m a x i m u m wind speed, the latterobservations being made within 30 rain (for wind speeds recorded every i h) or 60
108 m i n ( f o r w i n d s p e e d s r e c o r d e d e v e r y 3 h ) f r o m t h e o b s e r v a t i o n t i m e of t h e p r e c i p i t a t i o n . F o r e x a m p l e , in t h e case w h e n 10 m i n a v e r a g e w i n d speeds were r e c o r d e d h o u r l y ( T a b l e 1 ), t h e h o u r l y p r e c i p i t a t i o n of 16.5 m m r e c o r d e d a t 5:00, w h i c h w a s t h e t o t a l a m o u n t of p r e c i p i t a t i o n b e t w e e n 4:00 a n d 5:00, w a s m a d e to c o r r e s p o n d to t h e 10 m i n a v e r a g e w i n d s p e e d o f 4.7 m s - 1 r e c o r d e d a t 4:00, w h i c h w a s t h e m a x i m u m v a l u e o f t h e w i n d s p e e d s o b s e r v e d b e t w e e n 3:30 a n d 5:30. T h e daily m a x i m u m h o u r l y p r e c i p i t a t i o n o f 17.5 r a m , w h i c h w a s t h e t o t a l a m o u n t of p r e c i p i t a t i o n b e t w e e n 3:47 a n d 4:47, w a s also m a d e to corres p o n d to t h e 10 m i n a v e r a g e w i n d s p e e d of 4.7 m s - I r e c o r d e d a t 4:00, w h i c h w a s t h e m a x i m u m v a l u e o f t h e w i n d s p e e d s o b s e r v e d b e t w e e n 3:17 a n d 5:17. I n t h e case w h e n 10 rain a v e r a g e w i n d s p e e d s w e r e r e c o r d e d e v e r y 3 h ( T a b l e 2 ) , t h e h o u r l y p r e c i p i t a t i o n of 5.0 m m r e c o r d e d a t 15:00, w h i c h w a s t h e t o t a l a m o u n t of p r e c i p i t a t i o n b e t w e e n 14:00 a n d 15:00, w a s m a d e to c o r r e s p o n d to t h e 10 m i n a v e r a g e w i n d s p e e d of 7.7 m s - 1 , w h i c h w a s t h e m a x i m u m v a l u e o f TABLE 2 Example of meteorological data in the case when 10 min average wind speeds were recorded every three hours (24.10.1976, Tokyo) (a) Meteorological data Observation time a
01 02 03 04 05 O6 07 08 09 10 11 12
Wind direction
10 rain average wind speed (ms -1 )
SSW
5.1
S
1.0
NNE
2.7
N
5.0
Hourly precipitation (ram)
Observation time"
0.0 0.5 0.0 0.5 0.0 O.5 0.0 1.0 2.0 2.5 1.5 2.0
13 14 15 16 17 18 19 20 21 22 23 24
Wind direction
10 min average wind speed (ms -1
N
5.4
NNW
3.9
N
1.4
Hourly precipitation (ram) 2.5 3.5 5.0 2.5 1.5 0.5
0.1
Daily maxima N Observation time:
7.7 14:10
6.0 14:25-15:25
aThe observationtime is expressed by Japan Standard Time (JST) in the 24 h system beginning at midnight.
109 (b) Detailed description of observation times for meteorological data
Observation time
I0 rain average wind speed (m s- i)
Daily maximum 10 rain average wind
Hourly precipitation (ram)
speed ( m s -1)
Daily maximum hourly precipitation (ram)
11:50 5.0 12:00 2.5 13:00 3.5 14:00
t
14:10
14:50
15:00
t
7.7
5.0
5.4 2.5
16:00 1.5
(14:25)
t
17:00 17:50
18:00
t
0.5 3.9
the wind speeds observed between 13:00 and 16:00. The daily maximum hourly precipitation of 6.0 ram, which was the total amount of precipitation between 14:25 and 15:25, was also made to correspond to the 10 min average wind speed of 7.7 m s-1, which was the maximum value of the wind speeds observed between 13:25 and 16:25. Annual maximum wind speeds in each precipitation class were then extracted from these data. Tables 3-8 show data sets comprising twenty observed annual maximum wind speeds in each precipitation class at six meteorological stations. These
110 TABLE 3 Annual maximum wind speed ( m s -~) reduced to values at a height of 10 m during rainfall (1961-1980, Sapporo) Rank
Probability
i
F(Vi)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.9750 0.9250 0.8750 0.8250 0.7750 0.7250 0,6750 0,6250 0,5750 0.5250 0.4750 0.4250 0.3750 0.3250 0.2750 0.2250 0.1750 0.1250 0.0750 0.0250
Hourly precipitation H (mm) H~>5
H>~7
H>~ll
H>~21
H~>31
13.7 10.4 10.2 9.5 9.4 9.0 8.8 8.6 8.5 8.4 7.7 7.6 7,4 7,2 7,2 6.9 6.3 5.5 5.0 4.6
10.4 10.2 9.1 8.6 8.3 7.6 7.4 6.9 6.7 6.7 6.3 6.2 5.7 5.7 5.0 5.0 4.6 4.3 3.5 3.2
10.4 9.1 8.6 8.6 8.1 6.3 5.7 5.4 5.3 5.1 5.0 3.4 3.2 3.1 3.0 2.5 2.0 1.8 1.8 -
8.6 8,1 5.3 3.1 2.3 2.0 1.8 1.7 1.5 1.2 1.2
0.9
H>~41
H>~51
TABLE 4 Annual m a x i m u m wind speed ( m s -~) reduced to values at a height of 10 m during rainfall (1961-1980, Sendai)
Rank Probability Hourly precipitation i
F(V/)
1 2 3
4 5 6 7 8
0.9750 0.9250 0.8750 0.8250 0.7750 0.7250 0.6750 0.6250
H (mm) H>~5
H>~7
H>~11
H>~21
H~>31
H>~41
H>~51
14.5 12.9 11.4 10.5 10.0 9.1 8.9 8.7
14.5 12.9 11.4 10.0 9.1 8.9 8.2 7.8
12.9 11.4 10.0 8.9 7.0 6.7 6.7 6.6
11.4 10.0 6.6 6.4 4.9 4.7 4.2 4.0
10.0 6.6 6.4 4.9 3.0 2.8 2.6 2.3
6.4 3.0 2.6 -
6.4 -
-
111 TABLE 4 (continued) Rank i
9 10 11 12 13 14 15 16 17 18 19 20
Probability F(V~)
0.5750 0.5250 0.4750 0.4250 0.3750 0.3250 0.2750 0.2250 0.1750 0.1250 0.0750 0.0250
Hourly precipitation H (ram) H>~5
H>~7
H>~ll
7.8 7.7 7.2 6,7 6.7 6.5 5.8 5.8 5.6 5.6 5.1 4.2
7.8 6.7 6.7 6.7 6.0 5.8 5.6 5.3 4.7 4.6 4.5 4.2
5.8 5.4 5.2 5.1 4.7 4.6 4.5 4.5 4.2 4.2 4.0 3.6
H>~21
H~>31
3.9 2.8 2.6 2.5 2.3 0.7 0.3 -
0.3 -
H>~41
H~>51
TABLE 5 A n n u a l m a x i m u m w i n d speed ( m s - 1 ) reduced to values at a h e i g h t of 10 m d u r i n g rainfall (1961-1980, T o k y o ) Rank i
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Probability F(Vi)
0.9750 0.9250 0.8750 0.8250 0.7750 0.7250 0.6750 0.6250 0.5750 0.5250 0.4750 0.4250 0.3750 0.3250 0.2750 0.2250 0.1750 0.1250 0.0750 0.0250
Hourly precipitation H (ram) H>~5
H>~7
H>~ll
H>~21
H>~31
H>~41
H>~51
14.8 14.1 13.3 12.8 12.8 11.6 11.2 11.1 9.8 8.8 7.9 7.7 7.7 7.6 7.5 7.5 6.3 6.3 5.6 5.6
14.8 14.1 13.3 11.6 11.2 11.1 10.4 8.3 7.7 7.6 7.5 7.5 7.5 6.3 6.3 5.6 5.0 4.9 4.8 4.3
14.1 13.3 11.6 11.1 9.5 8.3 7.7 7.7 7.5 7.5 7.3 7.3 6.9 6.3 5.8 5.6 5.0 4.9 4.8 3.6
11.1 10.9 8.8 8.3 7.3 6.6 6.5 5.8 5.0 5.0 4.9 4.7 4.6 4.3 4.2 3.7 3.5 1.8 -
11.1 10.9 6.5 5.9 4.9 4.7 4.6 3.4 3.2 2.9 2.1 2.1 1.4 -
6.6 6.5 4.9 4.7 4.6 3.4 2.6 -
6.5 4.9 3.4
112 TABLE 6 A n n u a l m a x i m u m w i n d s p e e d ( m s - i ) r e d u c e d to v a l u e s a t a h e i g h t o f 10 m d u r i n g rainfall (1961-1980, N a g o y a ) Rank i
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Probability F(V,)
0.9750 0.9250 0.8750 0.8250 0.7750 0.7250 0.6750 0.6250 0.5750 0.5250 0.4750 0.4250 0.3750 0.3250 0.2750 0.2250 0.1750 0.1250 0.0750 0.0250
Hourly precipitation H(mm) H>~5
H>~7
H>~ll
H>~21
H>~31
H~>41
H~>51
26.5 17.3 15.0 13.6 13.1 12.9 12.0 11.7 10.4 10.2 10.2 9.4 9.2 9.0 8.0 7.3 7.3 6.8 6.0 5.7
26.5 17.3 15.0 13.6 13.1 12.9 12.0 11.7 10.4 10.2 9.4 8.8 8.6 8.0 7.3 7.2 6.8 6.0 5.4 5.3
15.0 13.6 13.1 12.9 12.2 11.7 11.2 10.4 10.2 9.4 8.6 8.3 8.0 7.7 7.3 7.0 6.8 5.7 5.4 5.3
15.0 13.6 11.5 10.6 9.4 9.0 8.3 7.6 7.3 5.5 5.4 5.3 5.1 4.9 3.9 3.7 3.5 3.4 2.0 1.6
15.0 10.6 9.4 9.0 5.5 5.2 3.9 3.9 3.7 3.4 3.4 3.0 3.0 -
15.0 9.4 5.5 5.2 4.5 3.9 3.7 3.4 3.0 3.0 2.0 -
9.4 5.5 5.2 3.7 3.0 3.0 -
TABLE 7 A n n u a l m e x i m u m w i n d s p e e d ( m s - 1 ) r e d u c e d to v a l u e s a t a h e i g h t of 10 m d u r i n g rainfall (1961-1980, O s a k a ) Rank i
1 2 3 4 5
6 7 8
Probability F(Vi)
0.9750 0.9250 0.8750 0.8250 0.7750 0.7250 0.6750 0.6250
Hourly precipitation H (ram) H>~5
H~>7
H~>ll
H~>21
H~>31
H>~41
H>~51
22.0 16.2 15.0 14.8 14.7 14.6 11.7 11.3
22.0 16.2 14.8 14.7 14.3 12.2 11.3 11.3
22.0 16.2 14.7 12.2 11.3 10.9 9.5 9.5
16.2 9.5 9.3 8.5 - 7.0 6.6 4.9 4.5
16.2 9.5 7.0 6.6 4.1 3.9 3.4 3.4
6.6 6.5 4.1 3.4 2.1 1.7
6.5 3.4 1.7 -
-
113
T A B L E 7 (continued) Rank
Probability Hourly precipitation
i
F(Vi)
9 10 11 12 13 14 15 16 17 18 19 20
0.5750 0.5250 0.4750 0.4250 0.3750 0.3250 0.2750 0.2250 0.1750 0.1250 0.0750 0.0250
H (ram) H~>5
H~>7
H>~ll
11.3 10.9 10.2 10.1 9.5 8.7 8.5 8.2 8.1 7.6 5.6 5.4
10.9 10.1 9.5 9.3 8.7 8.5 8.1 7.6 7.1 5.6 5.4 4.9
9.3 8.5 8.2 8.1 7.1 6.2 5.8 5.6 4.9 4.5 4.1 3.4
H~>21
H~>31
4.1 3.8 3.4 3.4 3.4 2.6 2.5 2.1 2.0 1.7 -
2.6 2.1 1.7 -
H>~41
H~>51
TABLE 8 Annual meximum wind speed (m s-I) reduced to values at a height of I0 m during rainfall (1961-1980, Fukuoka) Rank i
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Probability F(V,)
0.9750 0.9250 0.8750 0.8250 0.7750 0.7250 0.6750 0.6250 0.5750 0.5250 0.4750 0.4250 0.3750 0.3250 0.2750 0.2250 0.1750 0.1250 0.0750 0.0250
Hourly precipitation H(mm) H>~5
H~>7
H>~ll
H~>21
H>~31
H>~41
H~>51
21.5 16.6 16.0 15.2 13.6 13.4 13.0 13.0 13.0 11.6 11.2 11.1 10.5 9.9 9.6 9.4 8.5 8.4 7.9 6.8
21.5 16.0 15.2 13.6 13.4 13.0 12.3 11.6 11.2 10.5 9.9 9.6 9.4 8.9 8.4 7.8 7.3 6.8 6.3 5.0
16.0 15.8 15.2 13.6 13.4 13.0 11.6 11.2 10.8 9.2 8.9 8.7 7.2 6.7 6.7 6.3 5.8 5.5 5.5 5.0
16.0 15.8 15.2 13.0 11.2 9.2 9.1 8.9 6.4 5.9 5.7 4.8 4.7 4.7 4.6 4.1 3.8 3.8 3.1 3.0
9.2 9.1 6.4 5.7 4.8 4.8 4.6 3.4 2.9 2.3 1.8 1.8 1.8 1.6 -
9.1 4.1 3.4 2.9 2.7 1.8 0.4
2.5 1.2 0.4
-
114
wind speeds were converted to values at a height of 10 m, using the 1/7 power law of eqn. (1)
Vm = V, (lO/z) ~/7
(1)
where Vlo is the wind speed at a height of 10 m and Vz is the wind speed observed at a height of z m. These extreme data were rearranged into decreasing order from largest to smallest and the empirical probability, F (Vi), was assigned to each data, using the method of Hazen-plot in eqn. (2) F(Vi) = 1 - (2i-1)/2N
(2)
where V~ is the ith largest wind speed and N is the number of extreme data (=20).
2.2. Estimation o[ extreme wind speed during rain[aU The extreme wind speed for T years, VT, is defined by eqn. (3) 1 - F ( V T ) =I/T
(3)
where F (V) is the cumulative distribution function for the parent population, V. Of the "three types" of asymptotic extreme distributions, the Fisher Tippett type-I [5] has been widely used for extreme wind speed modelling (see, e.g., refs. 1 and 2 ). The type-I distribution is given by eqn. (4) F ( V ) = e x p ( - e -y)
(4)
y=a(V-b) where a and b are constants. Extreme data, i.e., annual maximum wind speed during rainfall, were plotted on extremal probability papers, and were found to agree well with the Fisher Tippett type- I distribution. The parameters a and b were determined by the method of least squares of eqn. (5):
a=Zy/Zv b= ~z-~/a
(5)
where V and 37are the mean values given by eqn. (6) N
rC= l / N 2 Yi i=1 N
= 1/N i=l
Sv and Sy are the standard deviations given by eqn. (7)
(6)
115
Sv=~/i~=,(Vi
~)2/N
-
(7)
Sy= ~Q//__,~(y,-y)'/N and Yi = - I n { - I n [ F ( Vi)] }
(8)
In this study, we first used this method for annual maximum wind speeds in each precipitation class, but the straight line for the annual maximum figures in one precipitation class sometimes crossed with that of another class (see Fig. 1 ). T h i s m e a n s that the results o f the analysis were contradictory because,
as the precipitation class was divided by the lower limit of the amount of precipitation (hourly precipitation >t 5, 7, 11, 21, 31, 41, and 51 mm), the extreme wind speed for T years in one precipitation class must be higher than that in a higher precipitation class. For example, the annual maximum wind speed in the class where hourly precipitation >/5 mm is greater than or equal to that in
l. O01
1.5
5
I0
Return period 20 50 I(I0
(years)
500
25
>
211 ~t
Ell
I I IIIJ
I ~*~/,.I~[/TI/.,L~H;~21
mm ]5 ~i=I•x lO
5
0 1.0 lO.O 50.0 80.090.095.0 ..... , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . --2 --1 0 1 2 3
99.099.5 ~F(V) . - , . , ......... L . . . , . . . . I ..... 4 5 6 7 ~y
x I oo
y--I.(--I.F(V))
Fig. 1. Results of least square analysis for extreme wind speeds during rainfall (1961-1980, Tokyo).
116
the class where hourly precipitation >t 7 mm, because the wind speed in the class where hourly precipitation >I7 mm is also contained in the lower precipitation class, i.e., the class where hourly precipitation >/5 ram. In order to prevent the crossing of the straight lines for each precipitation class, they must be parallel to one another, or else as the precipitation class is higher, the slope of the line must be smaller, i.e., the value of a in eqn. (4) must be greater, and the abscissa at which the ordinate is zero must be greater. To overcome this contradiction, we used multiple regression analysis according to the model of eqn. (9)
V=Co+C~y+C2H
(9)
where Co, C~ and C2 are the regression coefficients. It was supposed in eqn. (9) that the annual maximum wind speed during rainfall, V, was linear with the hourly precipitation, H, and with the reduced variate y ( = - In{ - In [ F (V) ] } ), and that all the straight lines for each precipitation class were parallel to one another. The linearity of the annual maximum wind speed during rainfall, V, and the hourly precipitation, H, was supposed as it is the most simple model, and the relationship between the two parameters, i.e., V and H, is a problem to be examined in the future. Return 1.001 , . .
.
.
1.5 . .
.
5 10 , ........
2()
of least squares --Result5 by t h e method Of m u l t i p l e regression
analysis
......
Results by of multiple multiplied
period (years}
50 l(}(} , ..........
500
,.I,
TOKYO (1961
--1980 )
the method regression analysis by the coefficient.].(}9
2¢(1
/. >
LI
III ;,; i t l,..t;X
_ !
1.0 50.0 80.090.095.0 99.099.5 ~FIV)× ..... i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . , . . . - ......... , . - , , . . . . , ..... --2 -- 1 0 1 2 3 4 5 6 7
I 0o
Fig. 2. Extreme value analysis for wind speeds in the case when hourly precipitation reached 5 mm or more (1961-1980, Tokyo).
117 3. Results A comparison between the results of least square analysis and those of multiple regression analysis for the data at Tokyo meteorological station is shown in Figs. 2-5. These figures show the results in the case when hourly precipitation reached 5, 11, 31, and 51 mm, or more. It appeared that there were no distinct differences between these two methods. Figures 6-11 show the results of multiple regression analysis at Sapporo, Sendai, Tokyo, Nagoya, Osaka and Fukuoka in Japan. The regression coefficients and correlation coefficients are shown in each figure, and correlation coefficients at each station were higher than 0.95. This method may therefore be considered to be very effective. Furthermore, it was considered logical that estimated values for a high precipitation class were obtained by referring to annual maximum wind speeds for a low precipitation class, because there were not many annual maximum wind speeds in high precipitation classes. The figures also show the results of multiple regression analysis multiplied Return period 1.001 1.5 i . . . . . . . . .
5
10 ,,,,
20 50 100 . •., ..........
(years) 500 ,.,,
by t h e imethod TOKYO squares --Results by t h e method (1961 of ~ltiple regression -1980) analysts = ...... Results by t h e m e t h o d of multiple reqression analysis multiplied by t h e c o e f f i c i e n t , l . 0 9 ------Results 7 of least
! /.
ij•
--
Hour
I y
T" '
1.010.0 --1
1~)
precipitation:=
~'~
--2
J I
50.0 0
80.090.095.0 1
2
99.099.5
:~
1
~y
5
5
~F(V)xtoo 6
7
y=I.,--I.F~V))
Fig. 3. Extreme value analysis for wind speeds in the case when hourlyprecipitation reached 11 mm or more (1961-1980, Tokyo).
118 Return 1.OOl .
,
.
.
1.5
.
.
.
5
.
It)
.,,,,,
20 .
period
50
I 1 ' t ' 1,1' I ' l l I ' I u i ' " ' r ' " l ' ' ' ' I i i n I I ------Results by the m e t h o d ~of least squares
E --Results
lyears}
IUO
500
. . . . . . . . . . .
,.,..
I"''['
'
'
TOKYO (1961
bY t h e method
reqression --1QRfI~ "------" Results by t h e m e t h o d o f multiple reqresslon analysis IKIltiplied by the coefficient,l.09
~-
of m u l t i p l e
analysis
L
......
~,
i;O
25
,/,.-'"/ ¢-
>
.~
/
_
f" / I
x
.ourly precipitation:
5
I 1.010.
50.0
--I
2
0
80.090.095,0 1
2
9,q. O 9 9 . 5 ~ / " ~ V ) ×
:{
4
5
~y
6
y--l,,~
1o o ,
I,,F
l ))
Fig. 4. Extreme value analysis for wind speeds in the case when hourly precipitation reached 31 m m or more (1961-1980, Tokyo). Return 1.0()1 ,
.
.
.
.
|.5
.
.
5
.
10
,,,,
20
. . . . .
50
period
(years}
100
50O
, . . . . . . . .
------Results by the method o f least squares --Results by the method of multiple reqression
,.,.,,
TOKYO {1961
analysis
-1980)
...... Results by the method of multiple recJression analysis multiplied by the coeffieient,l.09
25
>
2O ! 3
"~: •
[
Hourly 5 precipitation::H_~5lnm
/ . ~
1.0 2
090.095.0 1
0
1
'2
1,,
,"
3 ~y
99.099.5~FIV)xloO
4 y=
5
6
7
I.~.-I.F(V))
Fig. 5. Extreme value analysis for wind speeds in the case when hourly precipitation reached 51 m m or more (1961-1980, Tokyo).
119 l.t)Ol
Return period ( y e a r s ) 7) lo 2o 5(J loo 5o()
1.5
ll"l'l'l'l'l'l'l'r""""l""ll I'I ' I""I' ' ' R e s u l t s by the method of n u l t | p l e analysis . . . . . . R e s u l t s bY of IRlltiple multiplied
C2
-1980)
the method regression analysis by t h e c o e f f i c i e n t , l . O 9 I
I
"~5 ~n -
coefficient :
correlation
~:o.,5,6
I II
+..
IH~
-
:>
-
I I
.:"+
; ....
7In
.+
"../ /
AH:~ limb A H 2" 2 i n l l [] H
:',t}
- 0 . 4055
Multiple
F
(1961
reqression
RegressiOnciC0 = 8.6837coefficient1. i[ 8670 :
~
SAPPORO
o f l e a s t squares R e s u l t s bY the method
- -
.
.+~ ,+
-I
..".-"
+3,_- -
.
I llllJ
"
t"
"
.
l:J
" ]
Fll I IIIII[ ;I I I1 1 F/I
H~':
I;i+"~,-~;pm;,]~
!10
., ! :.t P..+(!!.t !., .+}.).~+.(!....8!!:it.! .'~.!'.}.!.'~.~: .t.!....... ~ ~: J~1,~ ).:1['1~d{'[i'. ~"I'x -,
-i
o
l
~
:+ ~I
,~
s
'~
I00
v
(;
~ = - - l,,~ - - l,,l"+ | ' ) )
Fig. 6. Multiple regression analysis for extreme wind speeds during rainfall (1961-1980, Sapporo). 1.001
1.5
5
Return period ( y e a r s ) 10 20 50 ltX) 500
-I1+_________' 1 ' I'1'1'1'1' iofanaOfResul Iml tlpys lemJltsOfResul ItIipsl'ebybybYsquareSt ler~""l'"' asttsResulonregressi°n ts IRt llint heteIhtethhodl'l hod ere
30
m u l t i p l i e d by the c o e f f i c i e n t , 1 . 0 9 Reqression c o e f f i c i e n t : [ ] CO ffi 7.7655 i CI 2.3474 •
-~5 >
C2
- 0 . 2428
MultiPle c o r r e l a t i o n R = 0.9745 @H• AR~"
coefficient:
' ~",'~'~,~
7mB
~
lmt
. ".":
"7.
H~,'"
x x~51,..
v ,,;:i
~
"
•
A.
|
+==
..... 1.0 I0.0 80.090.095.0 99.099.5--F(V)x 1 o o ........... . ............. ,...... ................ , ....., .............................. --2 --1 O 1 2 3 4 5 6 7 '
~y
J
'
0
y=--I.(--I.F(V))
Fig. 7. Multiple regression analysis for extreme wind speeds during rainfall (1961-1980, Sendal).
120 1.5
I-t)ol
Return period 20 30 I00
510
(years) 500
ll'"rl,'prplTi+FPVFl I I'"'I'"'I,,,'I I l ' l ' I " " I ' ' ' T - - ' ~ -----Results by the method o f least s q u a r e s TOKYO -I --Results by t h e method ( l g 6 1 ~ Of multiple regression - ----= _ i analysis --1980) . . . . . . Results bY the method ~., of multiple regression analysts ~ ,it) Imltiplied bY t h e c o e f f l c i e n t , l . 0 9 ~ 2ecJression coefficient : I ] I ~
co :
a.asaa
/ I
I
-~1
a
CI = 2.3498 Ft I --:'~:~ 25 C2 = - 0 . 2 i 4 0 --I t .-;-'..-~ > Multiple correlation coefficient: ,':-'+/.X'/~] R = 0. 9722 -' ; ; / ,'"
,,,,,
-~-
I
OH" 5ram t ~ - tt Al#iiliil ~ 7
~---;~.1-1,
.-~-t)
11.45-~-;~""7mm."
I
m-.=2,-I :l_JJ_ E l H , 3 1 m m
t /~.+'~-
I i k:~Fy~,~R~..-,.11mmL'~,
:l[
f l,i i l ~ i ~ l d ~ _ V L i ~ . , , l l l . . .
xHl511
. "
-
.-
.
L- i-lis~,.,.
50, 0
0
i
i
i
~ ~..'~_.~X.I.~'I
i. ~ io.:(i
- ?"'
I
I
i131mm
-ll~~.~+.i? - i>'"
],5
~,
80. t)90. 0 95. 0
?
1
9+). 0 9 9 . 5 ~ / - ' ~ l ' ) × i o
:4
I
7>
fi
T
y~--l.,--[.FW)
',
Fig. 8, Multiple regression analysis for extreme wind speeds during rainfall (1961-1980, Tokyo). 1.001
1.5
5
10
Return Period (years} 20 50 100 500
2 of least squares n " i Results by the method (1961 : of multiple re
.'~'~
i
c 2 = -o. 24m
1 L .I,";.",t.,<~" ]> 5ram" J
=Multip: .... relation i,v-iD~-¢~ii~, .,~, x 7mill/," : ~,~: ~.. ..a
l .,t;>2~"~2%-2~'" ~'/ l,';'~sn/']'tY, #)~'i'<~'.]~H'21mm-
7,- I I
i FI,21ml
II
..r.,~l~'l."J~_,'w'u.'wl, . .-l'/
l.t'~lO.t)
- ""
-- 1
~i.(i-
t)
";
JY,G.~TV./'LJ~/~H>31mm:
I Ht51mm
99. t)99.,3~1: l ' x l O O
80. tigo. t)95. o 1
"2
1
:~
~
lO i
5
(;
y=l,, --I,,1"" l"
Fig. 9. Multiple regressionanalysisfor extreme wind speeds during rainfall(1961-1980, Nagoya),
121 Return I. iX)I 1,5 , . . . . . . .
5 I() 2 o ,.,, . . . . .
5i) Ioo , ........
:_.,== o~f i ~l e' a~s t' ~ ' rs q. uea"r ;e~~ ' Results
by the
of . u l t i p l e
(years)
period
51)0 ,.,,,,
' OSX~ ~ • , (1961
method
,'~
,;'~
-1980)"','.'~
regression
aria I yS I S
, ,/, ,/y/x:~ Results by t h e m e t h o d I :{I) of meltlple re~resslon I ~-/f//,'-I analysis molttplled by I /',~'~/~." the coefftclent,l.09 I J'*-'~'~/,'/" ~ ee~resslon coefficient :It I ,4.','/Z// " • CO = 1 0 . 8 2 6 3 J I I I.•/Iz'~X"Y'/ I "'12= CI : 3.4116 II / ~ . ~ ( ~ H Z / . ' : J ">
[.';':¢'/A
......
/~
IV ~ i ' ~ ; , : ~
~lultiple correlation :coefficient : R = 0 9811
]
•
/ ", ,': m.'~ '-)0 ~
i'L.'L~A/~.Y /~'~ ,14/~'2f~" J,
I / . ,.; ~-V / '~ t~" . ' ", "
HZ
//-:
o., ~. II I I ,,~,~/~),~'~':m ,~ . ..-Ill ~ ~ , . ; ~ ..<:
e H = ~ 7ira A :~
• , , •
"
• H:~21mml I ~ UH~31nn t~7~'/ H 4 1 m m l t/);'~i
•
"
..mst-J6~Da',,Y , ,t ~ I.,'/I ./XI I , ' Y V / ' t ~ , ~
II ~ # , ' ~ l ~ t ~
0
1
2
I
3
4
;2
.~
"51"mm-~..:"' <~
3
~y
,
: ~)
...}.:}!..[~)...}!....... ~!:.!!.8!!:~.!.?!!:!,75.%...~.::.,..:!...2~t~ . ,~, " --1
•
/L/rl ,1/ [(,/I"H~" . I ,'/I J/,,l/ A / ' - t , ' , 3 1 r a m : I,'/ll/]/t .,I:-~." " >34 Y / I , ' ~ 4 1 m m '
,,
--2
-
" 21mm/
.x i o o
6
y = l , - - l~l'" V , ,
Fig. 10. Multiple regression analysis for extreme wind speeds during rainfall (1961-1980, Osaka). Return period 5 10 2 0 50 100 ,,,, . . . . . , ........
1.001 1.5 , . . . . . . .
------11-'7'[~esults'l'l'l' I ' II ' rb~t "h"yel " " m e t ~ ( i l ' l of
least
,
i,,,, i , , ,
FUKUOKA (1961
squares
Results by the method of Imltlple regression analYSis Results by the method of multiple reqresslon analYSiS Multiplied by the coefficlent.l.09 , ~eqression coeff(cient : CO = 12. 1240
-1980) ,'~"
......
ci = ~.9639 c2 = -0.3422
I i
dultiple correlation coefficient : R : 0.9738
] I
o Ha
• "="
5=nll I I ~" ....
A H~" l l l m
|
"'/--~
30
~f, | ,:"[,zYXT~,~
~:'~2~.'al
II I I , ~ " D ~ , ~ g I ! l,C,'/r//~'=d
~ -
,d
2~ >
~f.,"/",~.~.~/ ~'--'~ /'" IA:.rq),r/'-/r-~,-1 / / / 3 "[.1.,~A/cJ,.~"'.,-V ./ / " 1 9 )
L,"]4kfA"
,-,-
(years) 500 ,.,..
4 ,,/'1~'~
"t'/'.YL4".- . / / L ~ ". / q , =H~> / :
,,'-'1 ""
1 H : ~ 4 1 n n I I,:1".:'~71 /1.Y1 / A -F/'Ha~. x H~'Slnll M ) ~ l q f J / ' / r ] l - ' J / [",Z['¢"~ 31mm
.~ s
g.~'r~2dr N.I II [/_'1 U ~ ~ l l l ~ l I I 1.010.0 --2
--1
50.0 0
80.090.095.0 1
2
3 ~
o
99. 0 99. 5 ~ F ( V ) x 4 5 6 ~=--I.(--I.y(V))
I O0
7
Fig. 11. Multiple regression mmly~i~ for extreme wind speeds during rainfall ( 1961-1980, Fukuoka ).
122 b y a coefficient of 1.09 ( d o t t e d line ). T h i s coefficient was u s e d to c o r r e c t t h e s e results to t h o s e of m o r e a n n u a l m a x i m u m d a t a for two reasons: (1) T h e n u m b e r of e x t r e m e data, w h i c h was t w e n t y in this study, was n o t sufficient for t h e e x t r e m e value analysis. I n addition, a n n u a l m a x i m u m w i n d speeds have t e n d e d to decrease in r e c e n t y e a r s in J a p a n . (2) Usually, in t h e case of building design in J a p a n , t h e m a x i m u m value e s t i m a t e d f r o m d a t a over t h e p a s t several decades is used as a design criteria o f e n v i r o n m e n t a l load. T h e coefficient of 1.09 was o b t a i n e d f r o m eqn. (10), w h i c h was p r o p o s e d b y Fujino et al. [6] on the basis o f a n n u a l m a x i m u m w i n d speed d a t a collected f r o m 1929 to 1977 ( 49 y e a r s ) at 130 m e t e o r o l o g i c a l s t a t i o n s in J a p a n . E q u a t i o n (10) was derived f r o m a c o m p a r i s o n b e t w e e n e x t r e m e values d e t e r m i n e d w i t h TABLE 9 Extreme wind speeds (m s- i) for various return periods at a height of I0 m during rainfall Hourly Return period Sapporo Sendai Tokyo precipitation (years) H (mm)
Nagoya
Osaka Fukuoka
H~>5
20 50 100
13.2 15.0 16.6
14.7 17.1 18.9
16.1 18.5 20.4
20.6 24.0 26.3
21.1 24.5 27.1
20.7 24.0 26.2
H>~7
20 50 100
12.4 14.0 15.8
14.2 16.6 18.4
15.7 18.1 20.0
20.2 23.3 25.8
20.0 23.3 26.1
20.0 23.2 25.3
H>~ll
20 50 100
10.5 12.1 13.9
13.2 15.6 17.4
14.8 17.2 19.0
19.0 22.2 24.7
18.9 22.0 25.0
18.5 21.8 23.7
H>~21
20 50 100
6.2 8.0 9.5
10.8 12.8 14.8
12.4 14.7 16.5
16.4 19.5 22.0
15.2 18.5 21.2
15.0 18.5 20.1
H~>31
20 50 1~
1.7 3.7 5.0
7.8 10.2 11.9
9.0 12.5 14.2
13.6 16.8 19.2
11.6 15.0 17.5
11.0 13.9 16.2
H~>41
20 50 100
-
5.2 7.8 9.6
7.9 10.4 11.9
11.5 14.3 16.7
7.8 11.3 14.0
7.0 10.0 12.5
H>~51
20 50 100
-
2.8 5.0 7.0
5.7 8.0 9.5
8.5 11.7 14.0
3.5 8.0 9.0
3.5 6.5 8.7
-
123 this data, and those determined with data for the latestn years (n = 10, 20, 30, 40). V~. = ~ . V . ~n = --0.255 I n ( n ) +1.85
(I0)
where V~. = extreme value determined with 49 year data, V. = extreme value determined with data collected over the last n years, ~. = correction factor due to the tendency of annual wind speeds in Japan to decrease, n = n u m b e r of data. Table 9 shows extreme wind speeds for a 20, 50 and 100 year return period classified according to the amount of hourly precipitation. These results were obtained using multiple regression analysis and multiplication by a coefficient of 1.09. From this analysis, we found a tendency for the extreme wind speed during rainfall to decrease in the order Nagoya, Osaka, Fukuoka, Tokyo, Sendai and Sapporo. Figure 12 shows the extreme wind speeds for a 20, 50 and 100 year return period, and Fig. 13 shows the annual amount of precipitation and the number of days with daily precipitation >i 30, 50, and 100 mm at the six meteorological stations.These stations are arranged in the order of decreasing extreme wind speed during rainfallin both figures. It isevident on comparing the two figuresthat the order of stationsaccording to extreme wind speed is not equal to that according to precipitation.This can be understood because storms and torrential rains, which arise from extratropical cyclones, typhoons and fronts in Japan, do not always arise at the same time. OExtreme wind s p e e d for 2 0 - Year return period •
5 0 - year return period
,,
x
year return period
100-
40
E v
X
x
X
0
0
0
3O
10
I Nagoya
I OQeka
I
Fukuoka
I
Tokyo
I Sendal
I SaPPoro
Fig.12.Extremewind speedsat Sapporo,Sendai,Tokyo,Nagoya,Osaka and Fukuoka.
124 m ["-'-] Ir//,,".l
Annual a m o u n t of precipitation Number of days with daily precipitation;; 3 0 r a m " :~ 5 0 m m " ~lOOmm
A 2000
20
v
o
•
11i
!/I
"
soo[- •
°LI 0
Nagoya
0 Osaka
Fukuoka
Tokyo
Sendai
SaplPoro
Fig. 13. Annual amount of precipitationand number of days with dailyprecipitationi>30, 50, and 100 m m at Sapporo, Sendai, Tokyo, Nagoya, Osaka and Fukuoka.
In this study, the order of the six stations according to extreme wind speed during rainfallwas equal to that according to the extreme wind speed. 4. Conclusion
Annual m a x i m u m wind speed during rainfallat six typical meteorological stations in Japan was analysed using observed rainfall and wind data from 1961 to 1980. W e concluded as follows: (1) The extreme values of annual m a x i m u m 10 min average wind speeds, which were classifiedfor an hourly precipitation,could be closely fittedto a Fisher Tippett type-I distribution. (2) Multiple regressionanalysis,which assumed that annual m a x i m u m wind speed during rainfallwas a linear function of a reduced variate and of hourly precipitation,was very effectivein fittingthe type-Idistribution.In thismethod, we could eliminate the contradictionmentioned in section2.3,and could obtain the wind speed for any return period relatedto an arbitraryhourly precipitation. (3) In this study, we found a tendency for the extreme wind speed during rainfallto decrease in the order Nagoya, Osaka, Fukuoka, Tokyo, Sendai and Sapporo.
125
References 1 Annual maximum wind speed (1929-1966) in Japan, Technical Data Series,No. 34, Jan. 1971, published by the Japan Meteorological Agency, Tokyo (in Japanese ). 2 M. Nakahara, Annual maximum wind speed forvariousreturn period,Kenchiku Kenkyu Shiryo, No. 26, March 1981, published by Building Research Institute,Ministry of Construction (in Japanese). 3 T. Shoda, T. Terasawa and T. Katayama, Experimental study on air and water tightness of metal window sashes, Report of the Instituteof Industrial Science, the University of Tokyo, Vol. 20, No. 2, Aug. 1970 (in Japanese). 4 Christian Sacre, Concomitance de la pluie et du vent en France, approche statistique,Cah. Cent. Sci. Tech. Batim., 232 (1982) 1792. 5 E.J. Gumbel, Statisticsof Extremes, Columbia University Press, N e w York, 1958. 6 Y. Fujino, M. Ito and T. Sakai, Basic design wind speeds based on yearly maximum wind speeds, Proc. Japan Society of CivilEngineers, No. 305, Jan. 1981 (in Japanese).
105
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
EXTREME WIND SPEEDS FOR VARIOUS RETURN PERIODS DURING
RAINFALL
SHUZO MURAKAMI 1, YOSHITERU IWASA2, YASUSHIGE MORIKAWA~ and NORIKO CHINO 2
~Institute of Industrial Science, University of Tokyo, Tokyo (Japan) 2Technical Research Laboratory Takenaka Komuten Co., Ltd., Tokyo (Japan) 3Technical Research Institutes, Taisei Corporation, Tokyo (Japan) (Received July 25, 1986; accepted in revised form November 15, 1986)
Summary Extreme wind speeds for various return periods during rainfall at six typical meteorological stations in Japan were estimated using the statistical method for extremes. The annual maximum wind speeds recorded from 1961 to 1980 at these stations were used for analysis. The annual maximum wind speeds were classified according to the amount of precipitation, and they were found to be well modelled by the extreme type-I distribution. Multiple regression AnMysisemploying two parameters, i.e., annual maximum wind speed and hourly precipitation, was used to fit the type-I distribution.
1. Introduction W i n d pressure during rainfall,in addition to the amount of precipitation, affects the water seal of the external wall and roof of buildings. In order to assess the wind environment around tallbuildings,wind speed during rainfall and itsfrequency of occurrence are fundamental data. The value of wind speed and its probability of non-occurrence during any period during rainfall are therefore also important parameters. Extreme wind speeds for a 50 or 100 year return period at differentmeteorologicalstationsin Japan have been reported in severalpapers, e.g.,refs.I and 2, and the frequency of wind speeds during rainfall from 1953 to 1962 have been obtained at twenty meteorological stations [3]. Moreover, a statistical approach for simultaneous occurrence of rain and wind was attempted by Sacre [4 ],and qualitativeresultsusing four categoriesof rain intensitywere obtained. However, a quantitative study of extreme wind speeds during rainfallhas not been made to date as far as we are aware. W e therefore studied extreme wind speeds for various return periods during rainfallusing the statisticaltheory of extremes at six meteorological stations in Japan.
0167-6105/87/$03.50
© 1987 Elsevier Science Publishers B.V.
106
2. Meteorological data and analytical methods
2.1. Meteorological data for precipitation and wind speed In Japanese meteorological stations, hourly precipitations are recorded, together with the daily maximum hourly precipitations. The 10 rain average wind speeds recorded every 1 or 3 h ( the particular cycle used depended on the year and the meteorological station), and daily maximum 10 rain average wind speeds, are also recorded (see Tables 1 and 2). Data obtained at Sapporo, Sendai, Tokyo, Nagoya, Osaka and Fukuoka from 1961 to 1980 were used for analysis. These wind speeds were classified into eight categories according to the amount of hourly precipitation: >t 5, 7, 11, 21, 31, 41 or 51 ram. Here, the simultaneous measurement of precipitation data and wind speed data was a perplexing problem because of the difference of averaging time and cycle used for TABLE1 Example of meteorological data in t h e case when 10 m i n average wind speeds were recorded every hour (6.7.1968, Tokyo) (a) Meteorological data Observation time a
Wind direction
10 rain average wind speed
Hourly precipitation (ram)
Observation time a
Wind direction
(ms -1) 01 02 03 04 05 06 07 08 09 10 11 12
S SE E ENE ENE S W WSW NW WNW W SSW
10 m i n average wind speed
Hourly precipitation (ram)
(ms -~)
4.2 3.2 4.8 4.7 4.0 4.2 4.8 3.5 3.7 4.7 2.7 3.8
0.5 0.5 4.5 11.0 16.5 16.0 4.0 5,0 8,0 0,0 0.5
11.0 15:50
17.5
13 14 15 16 17 18 19 20 21 22 23 24
SSW SW SSW SSW SW N NNW NE NNE N E NNE
8.0 9.0 7.8 8.5 6.8 3.8 3,3 1,0 1.2 2.8 4.8 3.8
0.5 0.0 2.5 4.5 0.0 -
Daily maxima SSW Observation time:
3:47- 4:47
aThe observation time is expressed by J a p a n S t a n d a r d Time ( J S T ) in t h e 24 h system beginning at midnight.
107 (b) Detailed description of observation times for meteorological data Observation time
2:50
10 min average wind speed (m s-I)
t t t t t
Daily meTimum I0 min average wind speed (ms -1)
Hourly precipiration (ram)
Daily maximum hourly precipiration (mm)
- 4.8
3:00 3:50 4:00 4:50 5:00 5:50 6:00 14:50 15:00
15:5016:00
II.0 (3:47) 4.7
t
17.5
16.5
(4:47)
4.0
16.0 4.2
7.8 (15:40) 11.0 (15:50)
1" 8.5
recording precipitation and wind speed; precipitation was an hourly total recorded every hour, whereas the wind speed was a 10 rain average recorded every I or 3 h. In this study, each hourly precipitation and each daily m a x i m u m precipitation was made to correspond to the m a x i m u m value of wind speed recorded every i or 3 h and to the daily m a x i m u m wind speed, the latterobservations being made within 30 rain (for wind speeds recorded every i h) or 60
108 m i n ( f o r w i n d s p e e d s r e c o r d e d e v e r y 3 h ) f r o m t h e o b s e r v a t i o n t i m e of t h e p r e c i p i t a t i o n . F o r e x a m p l e , in t h e case w h e n 10 m i n a v e r a g e w i n d speeds were r e c o r d e d h o u r l y ( T a b l e 1 ), t h e h o u r l y p r e c i p i t a t i o n of 16.5 m m r e c o r d e d a t 5:00, w h i c h w a s t h e t o t a l a m o u n t of p r e c i p i t a t i o n b e t w e e n 4:00 a n d 5:00, w a s m a d e to c o r r e s p o n d to t h e 10 m i n a v e r a g e w i n d s p e e d o f 4.7 m s - 1 r e c o r d e d a t 4:00, w h i c h w a s t h e m a x i m u m v a l u e o f t h e w i n d s p e e d s o b s e r v e d b e t w e e n 3:30 a n d 5:30. T h e daily m a x i m u m h o u r l y p r e c i p i t a t i o n o f 17.5 r a m , w h i c h w a s t h e t o t a l a m o u n t of p r e c i p i t a t i o n b e t w e e n 3:47 a n d 4:47, w a s also m a d e to corres p o n d to t h e 10 m i n a v e r a g e w i n d s p e e d of 4.7 m s - I r e c o r d e d a t 4:00, w h i c h w a s t h e m a x i m u m v a l u e o f t h e w i n d s p e e d s o b s e r v e d b e t w e e n 3:17 a n d 5:17. I n t h e case w h e n 10 rain a v e r a g e w i n d s p e e d s w e r e r e c o r d e d e v e r y 3 h ( T a b l e 2 ) , t h e h o u r l y p r e c i p i t a t i o n of 5.0 m m r e c o r d e d a t 15:00, w h i c h w a s t h e t o t a l a m o u n t of p r e c i p i t a t i o n b e t w e e n 14:00 a n d 15:00, w a s m a d e to c o r r e s p o n d to t h e 10 m i n a v e r a g e w i n d s p e e d of 7.7 m s - 1 , w h i c h w a s t h e m a x i m u m v a l u e o f TABLE 2 Example of meteorological data in the case when 10 min average wind speeds were recorded every three hours (24.10.1976, Tokyo) (a) Meteorological data Observation time a
01 02 03 04 05 O6 07 08 09 10 11 12
Wind direction
10 rain average wind speed (ms -1 )
SSW
5.1
S
1.0
NNE
2.7
N
5.0
Hourly precipitation (ram)
Observation time"
0.0 0.5 0.0 0.5 0.0 O.5 0.0 1.0 2.0 2.5 1.5 2.0
13 14 15 16 17 18 19 20 21 22 23 24
Wind direction
10 min average wind speed (ms -1
N
5.4
NNW
3.9
N
1.4
Hourly precipitation (ram) 2.5 3.5 5.0 2.5 1.5 0.5
0.1
Daily maxima N Observation time:
7.7 14:10
6.0 14:25-15:25
aThe observationtime is expressed by Japan Standard Time (JST) in the 24 h system beginning at midnight.
109 (b) Detailed description of observation times for meteorological data
Observation time
I0 rain average wind speed (m s- i)
Daily maximum 10 rain average wind
Hourly precipitation (ram)
speed ( m s -1)
Daily maximum hourly precipitation (ram)
11:50 5.0 12:00 2.5 13:00 3.5 14:00
t
14:10
14:50
15:00
t
7.7
5.0
5.4 2.5
16:00 1.5
(14:25)
t
17:00 17:50
18:00
t
0.5 3.9
the wind speeds observed between 13:00 and 16:00. The daily maximum hourly precipitation of 6.0 ram, which was the total amount of precipitation between 14:25 and 15:25, was also made to correspond to the 10 min average wind speed of 7.7 m s-1, which was the maximum value of the wind speeds observed between 13:25 and 16:25. Annual maximum wind speeds in each precipitation class were then extracted from these data. Tables 3-8 show data sets comprising twenty observed annual maximum wind speeds in each precipitation class at six meteorological stations. These
110 TABLE 3 Annual maximum wind speed ( m s -~) reduced to values at a height of 10 m during rainfall (1961-1980, Sapporo) Rank
Probability
i
F(Vi)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.9750 0.9250 0.8750 0.8250 0.7750 0.7250 0,6750 0,6250 0,5750 0.5250 0.4750 0.4250 0.3750 0.3250 0.2750 0.2250 0.1750 0.1250 0.0750 0.0250
Hourly precipitation H (mm) H~>5
H>~7
H>~ll
H>~21
H~>31
13.7 10.4 10.2 9.5 9.4 9.0 8.8 8.6 8.5 8.4 7.7 7.6 7,4 7,2 7,2 6.9 6.3 5.5 5.0 4.6
10.4 10.2 9.1 8.6 8.3 7.6 7.4 6.9 6.7 6.7 6.3 6.2 5.7 5.7 5.0 5.0 4.6 4.3 3.5 3.2
10.4 9.1 8.6 8.6 8.1 6.3 5.7 5.4 5.3 5.1 5.0 3.4 3.2 3.1 3.0 2.5 2.0 1.8 1.8 -
8.6 8,1 5.3 3.1 2.3 2.0 1.8 1.7 1.5 1.2 1.2
0.9
H>~41
H>~51
TABLE 4 Annual m a x i m u m wind speed ( m s -~) reduced to values at a height of 10 m during rainfall (1961-1980, Sendai)
Rank Probability Hourly precipitation i
F(V/)
1 2 3
4 5 6 7 8
0.9750 0.9250 0.8750 0.8250 0.7750 0.7250 0.6750 0.6250
H (mm) H>~5
H>~7
H>~11
H>~21
H~>31
H>~41
H>~51
14.5 12.9 11.4 10.5 10.0 9.1 8.9 8.7
14.5 12.9 11.4 10.0 9.1 8.9 8.2 7.8
12.9 11.4 10.0 8.9 7.0 6.7 6.7 6.6
11.4 10.0 6.6 6.4 4.9 4.7 4.2 4.0
10.0 6.6 6.4 4.9 3.0 2.8 2.6 2.3
6.4 3.0 2.6 -
6.4 -
-
111 TABLE 4 (continued) Rank i
9 10 11 12 13 14 15 16 17 18 19 20
Probability F(V~)
0.5750 0.5250 0.4750 0.4250 0.3750 0.3250 0.2750 0.2250 0.1750 0.1250 0.0750 0.0250
Hourly precipitation H (ram) H>~5
H>~7
H>~ll
7.8 7.7 7.2 6,7 6.7 6.5 5.8 5.8 5.6 5.6 5.1 4.2
7.8 6.7 6.7 6.7 6.0 5.8 5.6 5.3 4.7 4.6 4.5 4.2
5.8 5.4 5.2 5.1 4.7 4.6 4.5 4.5 4.2 4.2 4.0 3.6
H>~21
H~>31
3.9 2.8 2.6 2.5 2.3 0.7 0.3 -
0.3 -
H>~41
H~>51
TABLE 5 A n n u a l m a x i m u m w i n d speed ( m s - 1 ) reduced to values at a h e i g h t of 10 m d u r i n g rainfall (1961-1980, T o k y o ) Rank i
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Probability F(Vi)
0.9750 0.9250 0.8750 0.8250 0.7750 0.7250 0.6750 0.6250 0.5750 0.5250 0.4750 0.4250 0.3750 0.3250 0.2750 0.2250 0.1750 0.1250 0.0750 0.0250
Hourly precipitation H (ram) H>~5
H>~7
H>~ll
H>~21
H>~31
H>~41
H>~51
14.8 14.1 13.3 12.8 12.8 11.6 11.2 11.1 9.8 8.8 7.9 7.7 7.7 7.6 7.5 7.5 6.3 6.3 5.6 5.6
14.8 14.1 13.3 11.6 11.2 11.1 10.4 8.3 7.7 7.6 7.5 7.5 7.5 6.3 6.3 5.6 5.0 4.9 4.8 4.3
14.1 13.3 11.6 11.1 9.5 8.3 7.7 7.7 7.5 7.5 7.3 7.3 6.9 6.3 5.8 5.6 5.0 4.9 4.8 3.6
11.1 10.9 8.8 8.3 7.3 6.6 6.5 5.8 5.0 5.0 4.9 4.7 4.6 4.3 4.2 3.7 3.5 1.8 -
11.1 10.9 6.5 5.9 4.9 4.7 4.6 3.4 3.2 2.9 2.1 2.1 1.4 -
6.6 6.5 4.9 4.7 4.6 3.4 2.6 -
6.5 4.9 3.4
112 TABLE 6 A n n u a l m a x i m u m w i n d s p e e d ( m s - i ) r e d u c e d to v a l u e s a t a h e i g h t o f 10 m d u r i n g rainfall (1961-1980, N a g o y a ) Rank i
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Probability F(V,)
0.9750 0.9250 0.8750 0.8250 0.7750 0.7250 0.6750 0.6250 0.5750 0.5250 0.4750 0.4250 0.3750 0.3250 0.2750 0.2250 0.1750 0.1250 0.0750 0.0250
Hourly precipitation H(mm) H>~5
H>~7
H>~ll
H>~21
H>~31
H~>41
H~>51
26.5 17.3 15.0 13.6 13.1 12.9 12.0 11.7 10.4 10.2 10.2 9.4 9.2 9.0 8.0 7.3 7.3 6.8 6.0 5.7
26.5 17.3 15.0 13.6 13.1 12.9 12.0 11.7 10.4 10.2 9.4 8.8 8.6 8.0 7.3 7.2 6.8 6.0 5.4 5.3
15.0 13.6 13.1 12.9 12.2 11.7 11.2 10.4 10.2 9.4 8.6 8.3 8.0 7.7 7.3 7.0 6.8 5.7 5.4 5.3
15.0 13.6 11.5 10.6 9.4 9.0 8.3 7.6 7.3 5.5 5.4 5.3 5.1 4.9 3.9 3.7 3.5 3.4 2.0 1.6
15.0 10.6 9.4 9.0 5.5 5.2 3.9 3.9 3.7 3.4 3.4 3.0 3.0 -
15.0 9.4 5.5 5.2 4.5 3.9 3.7 3.4 3.0 3.0 2.0 -
9.4 5.5 5.2 3.7 3.0 3.0 -
TABLE 7 A n n u a l m e x i m u m w i n d s p e e d ( m s - 1 ) r e d u c e d to v a l u e s a t a h e i g h t of 10 m d u r i n g rainfall (1961-1980, O s a k a ) Rank i
1 2 3 4 5
6 7 8
Probability F(Vi)
0.9750 0.9250 0.8750 0.8250 0.7750 0.7250 0.6750 0.6250
Hourly precipitation H (ram) H>~5
H~>7
H~>ll
H~>21
H~>31
H>~41
H>~51
22.0 16.2 15.0 14.8 14.7 14.6 11.7 11.3
22.0 16.2 14.8 14.7 14.3 12.2 11.3 11.3
22.0 16.2 14.7 12.2 11.3 10.9 9.5 9.5
16.2 9.5 9.3 8.5 - 7.0 6.6 4.9 4.5
16.2 9.5 7.0 6.6 4.1 3.9 3.4 3.4
6.6 6.5 4.1 3.4 2.1 1.7
6.5 3.4 1.7 -
-
113
T A B L E 7 (continued) Rank
Probability Hourly precipitation
i
F(Vi)
9 10 11 12 13 14 15 16 17 18 19 20
0.5750 0.5250 0.4750 0.4250 0.3750 0.3250 0.2750 0.2250 0.1750 0.1250 0.0750 0.0250
H (ram) H~>5
H~>7
H>~ll
11.3 10.9 10.2 10.1 9.5 8.7 8.5 8.2 8.1 7.6 5.6 5.4
10.9 10.1 9.5 9.3 8.7 8.5 8.1 7.6 7.1 5.6 5.4 4.9
9.3 8.5 8.2 8.1 7.1 6.2 5.8 5.6 4.9 4.5 4.1 3.4
H~>21
H~>31
4.1 3.8 3.4 3.4 3.4 2.6 2.5 2.1 2.0 1.7 -
2.6 2.1 1.7 -
H>~41
H~>51
TABLE 8 Annual meximum wind speed (m s-I) reduced to values at a height of I0 m during rainfall (1961-1980, Fukuoka) Rank i
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Probability F(V,)
0.9750 0.9250 0.8750 0.8250 0.7750 0.7250 0.6750 0.6250 0.5750 0.5250 0.4750 0.4250 0.3750 0.3250 0.2750 0.2250 0.1750 0.1250 0.0750 0.0250
Hourly precipitation H(mm) H>~5
H~>7
H>~ll
H~>21
H>~31
H>~41
H~>51
21.5 16.6 16.0 15.2 13.6 13.4 13.0 13.0 13.0 11.6 11.2 11.1 10.5 9.9 9.6 9.4 8.5 8.4 7.9 6.8
21.5 16.0 15.2 13.6 13.4 13.0 12.3 11.6 11.2 10.5 9.9 9.6 9.4 8.9 8.4 7.8 7.3 6.8 6.3 5.0
16.0 15.8 15.2 13.6 13.4 13.0 11.6 11.2 10.8 9.2 8.9 8.7 7.2 6.7 6.7 6.3 5.8 5.5 5.5 5.0
16.0 15.8 15.2 13.0 11.2 9.2 9.1 8.9 6.4 5.9 5.7 4.8 4.7 4.7 4.6 4.1 3.8 3.8 3.1 3.0
9.2 9.1 6.4 5.7 4.8 4.8 4.6 3.4 2.9 2.3 1.8 1.8 1.8 1.6 -
9.1 4.1 3.4 2.9 2.7 1.8 0.4
2.5 1.2 0.4
-
114
wind speeds were converted to values at a height of 10 m, using the 1/7 power law of eqn. (1)
Vm = V, (lO/z) ~/7
(1)
where Vlo is the wind speed at a height of 10 m and Vz is the wind speed observed at a height of z m. These extreme data were rearranged into decreasing order from largest to smallest and the empirical probability, F (Vi), was assigned to each data, using the method of Hazen-plot in eqn. (2) F(Vi) = 1 - (2i-1)/2N
(2)
where V~ is the ith largest wind speed and N is the number of extreme data (=20).
2.2. Estimation o[ extreme wind speed during rain[aU The extreme wind speed for T years, VT, is defined by eqn. (3) 1 - F ( V T ) =I/T
(3)
where F (V) is the cumulative distribution function for the parent population, V. Of the "three types" of asymptotic extreme distributions, the Fisher Tippett type-I [5] has been widely used for extreme wind speed modelling (see, e.g., refs. 1 and 2 ). The type-I distribution is given by eqn. (4) F ( V ) = e x p ( - e -y)
(4)
y=a(V-b) where a and b are constants. Extreme data, i.e., annual maximum wind speed during rainfall, were plotted on extremal probability papers, and were found to agree well with the Fisher Tippett type- I distribution. The parameters a and b were determined by the method of least squares of eqn. (5):
a=Zy/Zv b= ~z-~/a
(5)
where V and 37are the mean values given by eqn. (6) N
rC= l / N 2 Yi i=1 N
= 1/N i=l
Sv and Sy are the standard deviations given by eqn. (7)
(6)
115
Sv=~/i~=,(Vi
~)2/N
-
(7)
Sy= ~Q//__,~(y,-y)'/N and Yi = - I n { - I n [ F ( Vi)] }
(8)
In this study, we first used this method for annual maximum wind speeds in each precipitation class, but the straight line for the annual maximum figures in one precipitation class sometimes crossed with that of another class (see Fig. 1 ). T h i s m e a n s that the results o f the analysis were contradictory because,
as the precipitation class was divided by the lower limit of the amount of precipitation (hourly precipitation >t 5, 7, 11, 21, 31, 41, and 51 mm), the extreme wind speed for T years in one precipitation class must be higher than that in a higher precipitation class. For example, the annual maximum wind speed in the class where hourly precipitation >/5 mm is greater than or equal to that in
l. O01
1.5
5
I0
Return period 20 50 I(I0
(years)
500
25
>
211 ~t
Ell
I I IIIJ
I ~*~/,.I~[/TI/.,L~H;~21
mm ]5 ~i=I•x lO
5
0 1.0 lO.O 50.0 80.090.095.0 ..... , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . --2 --1 0 1 2 3
99.099.5 ~F(V) . - , . , ......... L . . . , . . . . I ..... 4 5 6 7 ~y
x I oo
y--I.(--I.F(V))
Fig. 1. Results of least square analysis for extreme wind speeds during rainfall (1961-1980, Tokyo).
116
the class where hourly precipitation >t 7 mm, because the wind speed in the class where hourly precipitation >I7 mm is also contained in the lower precipitation class, i.e., the class where hourly precipitation >/5 ram. In order to prevent the crossing of the straight lines for each precipitation class, they must be parallel to one another, or else as the precipitation class is higher, the slope of the line must be smaller, i.e., the value of a in eqn. (4) must be greater, and the abscissa at which the ordinate is zero must be greater. To overcome this contradiction, we used multiple regression analysis according to the model of eqn. (9)
V=Co+C~y+C2H
(9)
where Co, C~ and C2 are the regression coefficients. It was supposed in eqn. (9) that the annual maximum wind speed during rainfall, V, was linear with the hourly precipitation, H, and with the reduced variate y ( = - In{ - In [ F (V) ] } ), and that all the straight lines for each precipitation class were parallel to one another. The linearity of the annual maximum wind speed during rainfall, V, and the hourly precipitation, H, was supposed as it is the most simple model, and the relationship between the two parameters, i.e., V and H, is a problem to be examined in the future. Return 1.001 , . .
.
.
1.5 . .
.
5 10 , ........
2()
of least squares --Result5 by t h e method Of m u l t i p l e regression
analysis
......
Results by of multiple multiplied
period (years}
50 l(}(} , ..........
500
,.I,
TOKYO (1961
--1980 )
the method regression analysis by the coefficient.].(}9
2¢(1
/. >
LI
III ;,; i t l,..t;X
_ !
1.0 50.0 80.090.095.0 99.099.5 ~FIV)× ..... i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . , . . . - ......... , . - , , . . . . , ..... --2 -- 1 0 1 2 3 4 5 6 7
I 0o
Fig. 2. Extreme value analysis for wind speeds in the case when hourly precipitation reached 5 mm or more (1961-1980, Tokyo).
117 3. Results A comparison between the results of least square analysis and those of multiple regression analysis for the data at Tokyo meteorological station is shown in Figs. 2-5. These figures show the results in the case when hourly precipitation reached 5, 11, 31, and 51 mm, or more. It appeared that there were no distinct differences between these two methods. Figures 6-11 show the results of multiple regression analysis at Sapporo, Sendai, Tokyo, Nagoya, Osaka and Fukuoka in Japan. The regression coefficients and correlation coefficients are shown in each figure, and correlation coefficients at each station were higher than 0.95. This method may therefore be considered to be very effective. Furthermore, it was considered logical that estimated values for a high precipitation class were obtained by referring to annual maximum wind speeds for a low precipitation class, because there were not many annual maximum wind speeds in high precipitation classes. The figures also show the results of multiple regression analysis multiplied Return period 1.001 1.5 i . . . . . . . . .
5
10 ,,,,
20 50 100 . •., ..........
(years) 500 ,.,,
by t h e imethod TOKYO squares --Results by t h e method (1961 of ~ltiple regression -1980) analysts = ...... Results by t h e m e t h o d of multiple reqression analysis multiplied by t h e c o e f f i c i e n t , l . 0 9 ------Results 7 of least
! /.
ij•
--
Hour
I y
T" '
1.010.0 --1
1~)
precipitation:=
~'~
--2
J I
50.0 0
80.090.095.0 1
2
99.099.5
:~
1
~y
5
5
~F(V)xtoo 6
7
y=I.,--I.F~V))
Fig. 3. Extreme value analysis for wind speeds in the case when hourlyprecipitation reached 11 mm or more (1961-1980, Tokyo).
118 Return 1.OOl .
,
.
.
1.5
.
.
.
5
.
It)
.,,,,,
20 .
period
50
I 1 ' t ' 1,1' I ' l l I ' I u i ' " ' r ' " l ' ' ' ' I i i n I I ------Results by the m e t h o d ~of least squares
E --Results
lyears}
IUO
500
. . . . . . . . . . .
,.,..
I"''['
'
'
TOKYO (1961
bY t h e method
reqression --1QRfI~ "------" Results by t h e m e t h o d o f multiple reqresslon analysis IKIltiplied by the coefficient,l.09
~-
of m u l t i p l e
analysis
L
......
~,
i;O
25
,/,.-'"/ ¢-
>
.~
/
_
f" / I
x
.ourly precipitation:
5
I 1.010.
50.0
--I
2
0
80.090.095,0 1
2
9,q. O 9 9 . 5 ~ / " ~ V ) ×
:{
4
5
~y
6
y--l,,~
1o o ,
I,,F
l ))
Fig. 4. Extreme value analysis for wind speeds in the case when hourly precipitation reached 31 m m or more (1961-1980, Tokyo). Return 1.0()1 ,
.
.
.
.
|.5
.
.
5
.
10
,,,,
20
. . . . .
50
period
(years}
100
50O
, . . . . . . . .
------Results by the method o f least squares --Results by the method of multiple reqression
,.,.,,
TOKYO {1961
analysis
-1980)
...... Results by the method of multiple recJression analysis multiplied by the coeffieient,l.09
25
>
2O ! 3
"~: •
[
Hourly 5 precipitation::H_~5lnm
/ . ~
1.0 2
090.095.0 1
0
1
'2
1,,
,"
3 ~y
99.099.5~FIV)xloO
4 y=
5
6
7
I.~.-I.F(V))
Fig. 5. Extreme value analysis for wind speeds in the case when hourly precipitation reached 51 m m or more (1961-1980, Tokyo).
119 l.t)Ol
Return period ( y e a r s ) 7) lo 2o 5(J loo 5o()
1.5
ll"l'l'l'l'l'l'l'r""""l""ll I'I ' I""I' ' ' R e s u l t s by the method of n u l t | p l e analysis . . . . . . R e s u l t s bY of IRlltiple multiplied
C2
-1980)
the method regression analysis by t h e c o e f f i c i e n t , l . O 9 I
I
"~5 ~n -
coefficient :
correlation
~:o.,5,6
I II
+..
IH~
-
:>
-
I I
.:"+
; ....
7In
.+
"../ /
AH:~ limb A H 2" 2 i n l l [] H
:',t}
- 0 . 4055
Multiple
F
(1961
reqression
RegressiOnciC0 = 8.6837coefficient1. i[ 8670 :
~
SAPPORO
o f l e a s t squares R e s u l t s bY the method
- -
.
.+~ ,+
-I
..".-"
+3,_- -
.
I llllJ
"
t"
"
.
l:J
" ]
Fll I IIIII[ ;I I I1 1 F/I
H~':
I;i+"~,-~;pm;,]~
!10
., ! :.t P..+(!!.t !., .+}.).~+.(!....8!!:it.! .'~.!'.}.!.'~.~: .t.!....... ~ ~: J~1,~ ).:1['1~d{'[i'. ~"I'x -,
-i
o
l
~
:+ ~I
,~
s
'~
I00
v
(;
~ = - - l,,~ - - l,,l"+ | ' ) )
Fig. 6. Multiple regression analysis for extreme wind speeds during rainfall (1961-1980, Sapporo). 1.001
1.5
5
Return period ( y e a r s ) 10 20 50 ltX) 500
-I1+_________' 1 ' I'1'1'1'1' iofanaOfResul Iml tlpys lemJltsOfResul ItIipsl'ebybybYsquareSt ler~""l'"' asttsResulonregressi°n ts IRt llint heteIhtethhodl'l hod ere
30
m u l t i p l i e d by the c o e f f i c i e n t , 1 . 0 9 Reqression c o e f f i c i e n t : [ ] CO ffi 7.7655 i CI 2.3474 •
-~5 >
C2
- 0 . 2428
MultiPle c o r r e l a t i o n R = 0.9745 @H• AR~"
coefficient:
' ~",'~'~,~
7mB
~
lmt
. ".":
"7.
H~,'"
x x~51,..
v ,,;:i
~
"
•
A.
|
+==
..... 1.0 I0.0 80.090.095.0 99.099.5--F(V)x 1 o o ........... . ............. ,...... ................ , ....., .............................. --2 --1 O 1 2 3 4 5 6 7 '
~y
J
'
0
y=--I.(--I.F(V))
Fig. 7. Multiple regression analysis for extreme wind speeds during rainfall (1961-1980, Sendal).
120 1.5
I-t)ol
Return period 20 30 I00
510
(years) 500
ll'"rl,'prplTi+FPVFl I I'"'I'"'I,,,'I I l ' l ' I " " I ' ' ' T - - ' ~ -----Results by the method o f least s q u a r e s TOKYO -I --Results by t h e method ( l g 6 1 ~ Of multiple regression - ----= _ i analysis --1980) . . . . . . Results bY the method ~., of multiple regression analysts ~ ,it) Imltiplied bY t h e c o e f f l c i e n t , l . 0 9 ~ 2ecJression coefficient : I ] I ~
co :
a.asaa
/ I
I
-~1
a
CI = 2.3498 Ft I --:'~:~ 25 C2 = - 0 . 2 i 4 0 --I t .-;-'..-~ > Multiple correlation coefficient: ,':-'+/.X'/~] R = 0. 9722 -' ; ; / ,'"
,,,,,
-~-
I
OH" 5ram t ~ - tt Al#iiliil ~ 7
~---;~.1-1,
.-~-t)
11.45-~-;~""7mm."
I
m-.=2,-I :l_JJ_ E l H , 3 1 m m
t /~.+'~-
I i k:~Fy~,~R~..-,.11mmL'~,
:l[
f l,i i l ~ i ~ l d ~ _ V L i ~ . , , l l l . . .
xHl511
. "
-
.-
.
L- i-lis~,.,.
50, 0
0
i
i
i
~ ~..'~_.~X.I.~'I
i. ~ io.:(i
- ?"'
I
I
i131mm
-ll~~.~+.i? - i>'"
],5
~,
80. t)90. 0 95. 0
?
1
9+). 0 9 9 . 5 ~ / - ' ~ l ' ) × i o
:4
I
7>
fi
T
y~--l.,--[.FW)
',
Fig. 8, Multiple regression analysis for extreme wind speeds during rainfall (1961-1980, Tokyo). 1.001
1.5
5
10
Return Period (years} 20 50 100 500
2 of least squares n " i Results by the method (1961 : of multiple re
.'~'~
i
c 2 = -o. 24m
1 L .I,";.",t.,<~" ]> 5ram" J
=Multip: .... relation i,v-iD~-¢~ii~, .,~, x 7mill/," : ~,~: ~.. ..a
l .,t;>2~"~2%-2~'" ~'/ l,';'~sn/']'tY, #)~'i'<~'.]~H'21mm-
7,- I I
i FI,21ml
II
..r.,~l~'l."J~_,'w'u.'wl, . .-l'/
l.t'~lO.t)
- ""
-- 1
~i.(i-
t)
";
JY,G.~TV./'LJ~/~H>31mm:
I Ht51mm
99. t)99.,3~1: l ' x l O O
80. tigo. t)95. o 1
"2
1
:~
~
lO i
5
(;
y=l,, --I,,1"" l"
Fig. 9. Multiple regressionanalysisfor extreme wind speeds during rainfall(1961-1980, Nagoya),
121 Return I. iX)I 1,5 , . . . . . . .
5 I() 2 o ,.,, . . . . .
5i) Ioo , ........
:_.,== o~f i ~l e' a~s t' ~ ' rs q. uea"r ;e~~ ' Results
by the
of . u l t i p l e
(years)
period
51)0 ,.,,,,
' OSX~ ~ • , (1961
method
,'~
,;'~
-1980)"','.'~
regression
aria I yS I S
, ,/, ,/y/x:~ Results by t h e m e t h o d I :{I) of meltlple re~resslon I ~-/f//,'-I analysis molttplled by I /',~'~/~." the coefftclent,l.09 I J'*-'~'~/,'/" ~ ee~resslon coefficient :It I ,4.','/Z// " • CO = 1 0 . 8 2 6 3 J I I I.•/Iz'~X"Y'/ I "'12= CI : 3.4116 II / ~ . ~ ( ~ H Z / . ' : J ">
[.';':¢'/A
......
/~
IV ~ i ' ~ ; , : ~
~lultiple correlation :coefficient : R = 0 9811
]
•
/ ", ,': m.'~ '-)0 ~
i'L.'L~A/~.Y /~'~ ,14/~'2f~" J,
I / . ,.; ~-V / '~ t~" . ' ", "
HZ
//-:
o., ~. II I I ,,~,~/~),~'~':m ,~ . ..-Ill ~ ~ , . ; ~ ..<:
e H = ~ 7ira A :~
• , , •
"
• H:~21mml I ~ UH~31nn t~7~'/ H 4 1 m m l t/);'~i
•
"
..mst-J6~Da',,Y , ,t ~ I.,'/I ./XI I , ' Y V / ' t ~ , ~
II ~ # , ' ~ l ~ t ~
0
1
2
I
3
4
;2
.~
"51"mm-~..:"' <~
3
~y
,
: ~)
...}.:}!..[~)...}!....... ~!:.!!.8!!:~.!.?!!:!,75.%...~.::.,..:!...2~t~ . ,~, " --1
•
/L/rl ,1/ [(,/I"H~" . I ,'/I J/,,l/ A / ' - t , ' , 3 1 r a m : I,'/ll/]/t .,I:-~." " >34 Y / I , ' ~ 4 1 m m '
,,
--2
-
" 21mm/
.x i o o
6
y = l , - - l~l'" V , ,
Fig. 10. Multiple regression analysis for extreme wind speeds during rainfall (1961-1980, Osaka). Return period 5 10 2 0 50 100 ,,,, . . . . . , ........
1.001 1.5 , . . . . . . .
------11-'7'[~esults'l'l'l' I ' II ' rb~t "h"yel " " m e t ~ ( i l ' l of
least
,
i,,,, i , , ,
FUKUOKA (1961
squares
Results by the method of Imltlple regression analYSis Results by the method of multiple reqresslon analYSiS Multiplied by the coefficlent.l.09 , ~eqression coeff(cient : CO = 12. 1240
-1980) ,'~"
......
ci = ~.9639 c2 = -0.3422
I i
dultiple correlation coefficient : R : 0.9738
] I
o Ha
• "="
5=nll I I ~" ....
A H~" l l l m
|
"'/--~
30
~f, | ,:"[,zYXT~,~
~:'~2~.'al
II I I , ~ " D ~ , ~ g I ! l,C,'/r//~'=d
~ -
,d
2~ >
~f.,"/",~.~.~/ ~'--'~ /'" IA:.rq),r/'-/r-~,-1 / / / 3 "[.1.,~A/cJ,.~"'.,-V ./ / " 1 9 )
L,"]4kfA"
,-,-
(years) 500 ,.,..
4 ,,/'1~'~
"t'/'.YL4".- . / / L ~ ". / q , =H~> / :
,,'-'1 ""
1 H : ~ 4 1 n n I I,:1".:'~71 /1.Y1 / A -F/'Ha~. x H~'Slnll M ) ~ l q f J / ' / r ] l - ' J / [",Z['¢"~ 31mm
.~ s
g.~'r~2dr N.I II [/_'1 U ~ ~ l l l ~ l I I 1.010.0 --2
--1
50.0 0
80.090.095.0 1
2
3 ~
o
99. 0 99. 5 ~ F ( V ) x 4 5 6 ~=--I.(--I.y(V))
I O0
7
Fig. 11. Multiple regression mmly~i~ for extreme wind speeds during rainfall ( 1961-1980, Fukuoka ).
122 b y a coefficient of 1.09 ( d o t t e d line ). T h i s coefficient was u s e d to c o r r e c t t h e s e results to t h o s e of m o r e a n n u a l m a x i m u m d a t a for two reasons: (1) T h e n u m b e r of e x t r e m e data, w h i c h was t w e n t y in this study, was n o t sufficient for t h e e x t r e m e value analysis. I n addition, a n n u a l m a x i m u m w i n d speeds have t e n d e d to decrease in r e c e n t y e a r s in J a p a n . (2) Usually, in t h e case of building design in J a p a n , t h e m a x i m u m value e s t i m a t e d f r o m d a t a over t h e p a s t several decades is used as a design criteria o f e n v i r o n m e n t a l load. T h e coefficient of 1.09 was o b t a i n e d f r o m eqn. (10), w h i c h was p r o p o s e d b y Fujino et al. [6] on the basis o f a n n u a l m a x i m u m w i n d speed d a t a collected f r o m 1929 to 1977 ( 49 y e a r s ) at 130 m e t e o r o l o g i c a l s t a t i o n s in J a p a n . E q u a t i o n (10) was derived f r o m a c o m p a r i s o n b e t w e e n e x t r e m e values d e t e r m i n e d w i t h TABLE 9 Extreme wind speeds (m s- i) for various return periods at a height of I0 m during rainfall Hourly Return period Sapporo Sendai Tokyo precipitation (years) H (mm)
Nagoya
Osaka Fukuoka
H~>5
20 50 100
13.2 15.0 16.6
14.7 17.1 18.9
16.1 18.5 20.4
20.6 24.0 26.3
21.1 24.5 27.1
20.7 24.0 26.2
H>~7
20 50 100
12.4 14.0 15.8
14.2 16.6 18.4
15.7 18.1 20.0
20.2 23.3 25.8
20.0 23.3 26.1
20.0 23.2 25.3
H>~ll
20 50 100
10.5 12.1 13.9
13.2 15.6 17.4
14.8 17.2 19.0
19.0 22.2 24.7
18.9 22.0 25.0
18.5 21.8 23.7
H>~21
20 50 100
6.2 8.0 9.5
10.8 12.8 14.8
12.4 14.7 16.5
16.4 19.5 22.0
15.2 18.5 21.2
15.0 18.5 20.1
H~>31
20 50 1~
1.7 3.7 5.0
7.8 10.2 11.9
9.0 12.5 14.2
13.6 16.8 19.2
11.6 15.0 17.5
11.0 13.9 16.2
H~>41
20 50 100
-
5.2 7.8 9.6
7.9 10.4 11.9
11.5 14.3 16.7
7.8 11.3 14.0
7.0 10.0 12.5
H>~51
20 50 100
-
2.8 5.0 7.0
5.7 8.0 9.5
8.5 11.7 14.0
3.5 8.0 9.0
3.5 6.5 8.7
-
123 this data, and those determined with data for the latestn years (n = 10, 20, 30, 40). V~. = ~ . V . ~n = --0.255 I n ( n ) +1.85
(I0)
where V~. = extreme value determined with 49 year data, V. = extreme value determined with data collected over the last n years, ~. = correction factor due to the tendency of annual wind speeds in Japan to decrease, n = n u m b e r of data. Table 9 shows extreme wind speeds for a 20, 50 and 100 year return period classified according to the amount of hourly precipitation. These results were obtained using multiple regression analysis and multiplication by a coefficient of 1.09. From this analysis, we found a tendency for the extreme wind speed during rainfall to decrease in the order Nagoya, Osaka, Fukuoka, Tokyo, Sendai and Sapporo. Figure 12 shows the extreme wind speeds for a 20, 50 and 100 year return period, and Fig. 13 shows the annual amount of precipitation and the number of days with daily precipitation >i 30, 50, and 100 mm at the six meteorological stations.These stations are arranged in the order of decreasing extreme wind speed during rainfallin both figures. It isevident on comparing the two figuresthat the order of stationsaccording to extreme wind speed is not equal to that according to precipitation.This can be understood because storms and torrential rains, which arise from extratropical cyclones, typhoons and fronts in Japan, do not always arise at the same time. OExtreme wind s p e e d for 2 0 - Year return period •
5 0 - year return period
,,
x
year return period
100-
40
E v
X
x
X
0
0
0
3O
10
I Nagoya
I OQeka
I
Fukuoka
I
Tokyo
I Sendal
I SaPPoro
Fig.12.Extremewind speedsat Sapporo,Sendai,Tokyo,Nagoya,Osaka and Fukuoka.
124 m ["-'-] Ir//,,".l
Annual a m o u n t of precipitation Number of days with daily precipitation;; 3 0 r a m " :~ 5 0 m m " ~lOOmm
A 2000
20
v
o
•
11i
!/I
"
soo[- •
°LI 0
Nagoya
0 Osaka
Fukuoka
Tokyo
Sendai
SaplPoro
Fig. 13. Annual amount of precipitationand number of days with dailyprecipitationi>30, 50, and 100 m m at Sapporo, Sendai, Tokyo, Nagoya, Osaka and Fukuoka.
In this study, the order of the six stations according to extreme wind speed during rainfallwas equal to that according to the extreme wind speed. 4. Conclusion
Annual m a x i m u m wind speed during rainfallat six typical meteorological stations in Japan was analysed using observed rainfall and wind data from 1961 to 1980. W e concluded as follows: (1) The extreme values of annual m a x i m u m 10 min average wind speeds, which were classifiedfor an hourly precipitation,could be closely fittedto a Fisher Tippett type-I distribution. (2) Multiple regressionanalysis,which assumed that annual m a x i m u m wind speed during rainfallwas a linear function of a reduced variate and of hourly precipitation,was very effectivein fittingthe type-Idistribution.In thismethod, we could eliminate the contradictionmentioned in section2.3,and could obtain the wind speed for any return period relatedto an arbitraryhourly precipitation. (3) In this study, we found a tendency for the extreme wind speed during rainfallto decrease in the order Nagoya, Osaka, Fukuoka, Tokyo, Sendai and Sapporo.
125
References 1 Annual maximum wind speed (1929-1966) in Japan, Technical Data Series,No. 34, Jan. 1971, published by the Japan Meteorological Agency, Tokyo (in Japanese ). 2 M. Nakahara, Annual maximum wind speed forvariousreturn period,Kenchiku Kenkyu Shiryo, No. 26, March 1981, published by Building Research Institute,Ministry of Construction (in Japanese). 3 T. Shoda, T. Terasawa and T. Katayama, Experimental study on air and water tightness of metal window sashes, Report of the Instituteof Industrial Science, the University of Tokyo, Vol. 20, No. 2, Aug. 1970 (in Japanese). 4 Christian Sacre, Concomitance de la pluie et du vent en France, approche statistique,Cah. Cent. Sci. Tech. Batim., 232 (1982) 1792. 5 E.J. Gumbel, Statisticsof Extremes, Columbia University Press, N e w York, 1958. 6 Y. Fujino, M. Ito and T. Sakai, Basic design wind speeds based on yearly maximum wind speeds, Proc. Japan Society of CivilEngineers, No. 305, Jan. 1981 (in Japanese).