NBS

PUBLICATIONS

NBSIR 86-3317

Directional Hurricane Wind Speeds

A11105 510 7 7b

NATL INST OF STANDARDS & TECH R .C.

All 102510776

w«nrfrickaon Erik M/DIrectlonal hurrlcan SciOO U5e NO.86-3317 VI 986 C.2 NBS-PUBErik M. Hendrickson

and

Emil Simiu

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Gaithersburg, MD 20899

September 1985

Issued February 1986

QC ~“>ared for: 200 clear Regulatory Commission

shington, DC 20555

86-3317

1986

C. 2

NBS RESEARCH INFORMATION CENTER

NBSIR 86-3317

DIRECTIONAL HURRICANE WIND SPEEDS

in,

4

Erik M. Hendrickson

and

Emil Simiu

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Gaithersburg, MD 20899

September 1985

Issued February 1986

Prepared for: Nuclear Regulatory Commission

Washington, DC 20555

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige. Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

ABSTRACT

This report presents a simple procedure for estimating coastline

hurricane wind speeds corresponding to any specified set of wind

directions and to any specified mean recurrence interval. The

procedure uses simulated directional hurricane wind speed data as

described in the report Hurricane Wind Speeds in the United

States ( NBS BSS 124). These data are encoded on magnetic tape

for 56 mileposts located along the U.S. Gulf and Atlantic coasts.

The input to the procedure consists of the location along the

coastline and the set of wind directions of interest. The output

consists of the fastest 60-sec wind speeds at 10m above ground in

open terrain corresponding to the set of directions specified in

the input and to various mean recurrence intervals. In addition,

the output includes the parameters of the Weibull distribution

that best fits the hurricane wind speeds.

Key Words: Climatology; hurricanes; statistical analysis;

structural engineering; wind engineering
.
TABLE OF CONTENTS

1. INTRODUCTION

2. PROCEDURE FOR ESTIMATING HURRICANE WIND SPEEDS

3. DESCRIPTION OF COMPUTER PROGRAM

4. ACKNOWLEDGMENTS

5. REFERENCES

6. APPENDIX - PROGRAM LISTING AND EXAMPLES

LIST OF TABLES

Table 1. Compass Directions and Computer Code Numbers

LIST OF FIGURES

Figure 1.

Figure Al.

Figure A2

.

Figure A3

Figure A4

.

Locator Map

Probability Plot, Directions 1-16

Probability Plot, Directions 3-8

Probability Plot, Direction 2

Probability Plot, Directions 12-4

1 . INTRODUCTION

It has previously been shown that predictions of extreme wind

speeds in hurricane-prone regions cannot, in general, be based

upon a statistical analysis of the largest wind speeds recorded

at a given site [1, p. 89]. For this reason, estimates of

extreme hurricane wind speeds at a site are commonly obtained by

indirect methods [2,3,4] from (1) statistical information on the

climatological characteristics of hurricanes, and (2) a physical

model of the hurricane wind structure.

This indirect approach was described in some detail in Ref. 5,

where it was applied to estimate hurricane wind speeds affecting

the United States Gulf and Atlantic coasts. These estimates were

subsequently used by the Subcommittee on Wind Loads, American

National Standards Committee A58 on Building Code Requirements

for Minimum Design Loads on Buildings, to develop the basic wind

speed map included in Ref. 6. The estimated design wind speeds

in Ref. 5 pertain to (1) hurricane winds blowing from any compass

direction and (2) hurricane winds blowing from any direction

within a 22.5° "half-octant" centered about one of the 16 main

compass directions - N, NNE , NE, ENE , E, ESE, SE, SSE, S, SSW,

SW, WSW, W, WNW, NW, and NNW.

The licensing review process for nuclear power plant facilities

may require the estimation of hurricane winds blowing from any

specified set of directions. This need arises where a certain

wind effect is a function of wind direction (e.g., an aerodynamic

load, the storm surge in an estuary, and so forth). The purpose

of this report and of the attendant computer tape is to make

available to the U.S. Nuclear Regulatory Commission a procedure

that allows this estimation to be carried out rapidly and

conveniently.

1
2. PROCEDURE FOR ESTIMATING HURRICANE WIND SPEEDS

We seek the distribution of annual extreme hurricane wind speeds,

F]_(v), so that any N-yr mean recurrence interval wind speed, vN , can be estimated as vN = F]_"^(l - 1/N) . However, the rate of

occurrence of hurricanes at a particular site is almost always

less than one per year. For this reason, Fj_(v) is constructed by

assuming the hurricane arrivals to be Poisson distributed, as

described below.

The probability that V is less than v in t years, PT (V<v), is

equal to the probability that V is less than v in n storms,

Pn

(V< v), times the probability that n storms occur in t years,

P(n,x), summed over all n. Thus:

P T (V<v) = nf0

Pn (V<v)P(n,x ) (1)

The left hand side of Eq. 1 is the cumulative distribution of

extreme hurricane wind speeds in t years:

PT (V<v) = Fx (v) (2)

Assuming that hurricane wind speeds are statistically independent

from storm to storm, P n (V<v) is:

P n (V<v) = [P s (V<v)

]

n (3)

in which P s (V<v) is the probability that V is less than v for one

storm. Note that P s (V<v) is simply the cumulative distribution

of wind speeds for one hurricane:

Ps (V<v) = Fs (v) (4)

The probability that n storms occur in x years, P(n,x), is

assumed to have a Poisson distribution:

P(n,x) = (ux

)

nexp( -ux ) /n! (5)

in which u = rate of occurrence of hurricanes at the mile post,

and in the directions, of interest. For example, if the rate of

hurricane occurrence at a milepost is uQ , and if m hurricanes

are simulated, k of which have nonzero wind speeds in the

2
directions of interest, then u = u Combining Eqs. 2-5, Qk/m.

Eq. 1 is rewritten as:

ft (v) = n

£ 0 [F s (v)

]

n (UT) nexp(-ux)/n!

or, by noting that

nSg x

n/n! = exp(x),

FT

( v ) = expOutd - F s

( v) ) ]

( 6 )

(7)

At this point, two approaches are possible. First, we can assume

that FT

( v ) plots linearly on Weibull probability paper, but with

an intercept shifted away from the origin. Indeed, for v = 0,

F s (v) = 0 so that Ft (v) = exp(-ux).. In this case, the speeds Vj_

are plotted against exp[- (ux ) (m+l-i ) / (m+1 ) ] and the wind speed

with mean recurrence interval N is:

A second approach is to assume that F s (v) has a Weibull

distribution. In this case, Vj_ is plotted against i/(m+l) and

the wind speed with mean recurrence interval N is:

A comparison of results obtained using Eqs. 8 and 9 for milepost

2400 and various directions indicated that there is no

significant difference between the two approaches. Since the

first approach was the one originally developed in connection

with the work reported in Ref. 5, it was used in the computer

program described in the following section.

vN = Ft

" 1 (1 - 1/N) ( 8 )

VN

= Fs" 1

^ 1 + ( 1/u) ln( 1 - 1/N)] (9)

3
3. DESCRIPTION OF COMPUTER PROGRAM

The purpose of the computer program presented herein is to

estimate coastline hurricane wind speeds corresponding to any

specified set of wind directions and to any specified mean

recurrence interval.

The program is written in FORTRAN and consists of a main routine

and two subroutines called WEIB and SORT. A listing of the

program appears in the Appendix. The program has been written on

magnetic tape along with 56 data files containing the simulated

directional hurricane wind speed data. These data were obtained

by using the procedure and information described in Ref. 5.

A locator map for the Gulf and Atlantic coasts, where mileposts

in nautical miles are shown for the various locations along the

coasts, is given in Fig. 1. Corresponding to each milepost is a data file containing hurricane wind speeds from 16 directions for

999 simulated hurricanes. The program user interested in

estimating wind speeds at the location of the third milepost

would attach the third data file to the program run.

The input to the computer program consists of the location along

the coastline and the set of wind directions of interest. The

directions are specified in terms of adjacent half-octants , each

centered about one of the 16 main compass directions, identified

in Table 1, along with their respective code numbers.

Table 1. Compass Directions and Computer Code Numbers

Direction Code Direction Code

NNE 1 SSW 9

NE 2 SW 10

ENE 3 WSW 11

E 4 W 12

ESE 5 WNW 13

SE 6 NW 14

SSE 7 NNW 15

S 8 N 16

4
For example, if the directions of interest sweep the 22.5° angle

centered about the NNE direction, the input to the program is

specified as 1,1. If the directions of interest sweep the four

adjacent 22.5° angles centered about the S, SSW, SW, and WSW

directions, the input to the program is specified as 8,11. If

the directions of interest sweep the two adjacent half -octants

centered about the N and NNE directions, the input to the program

is specified as 16,1. Note that the order of the directions

input to the program corresponds to a clockwise sense. A sample

interactive session using the program appears in the Appendix.

The output of the program consists of the fastest 60-sec wind

speed over open terrain (Exposure Category C as described in ANSI

A58-1982 [6]), at the coastline, at 10m above ground,

corresponding to the specified directions and to the 10-yr,

25-yr , 50-yr, 100-yr, 500-yr, 1000-yr, and 2000-yr mean

recurrence intervals. In addition, the output includes the

parameters of the Weibull distribution that best fits the

hurricane wind speed data. Knowledge of these parameters allows

estimates to be made of speeds corresponding to any mean

recurrence interval. The user may also select an optional

graphical output consisting of the probability plot of the

simulated hurricane wind speed data. Examples of probability

plot output are included in the Appendix.

Once the estimated 60-sec wind speeds at 10m elevation, over open

terrain, v

Qpen ' are known, it is possible to estimate the

corresponding 60-sec wind speeds at 10m elevation over water,

vwater ' as follows

vwater

" 1,26 v

open (10

60-sec wind speeds at elevations different from 10m can be

estimated as in Ref. 7. To obtain wind speeds averaged over time

intervals different from 60 seconds, see Ref. 1, p. 62.

5
The results obtained by this program could in some instances

exhibit minor differences with respect to the results of Ref. 5.

Such differences are due to sampling errors inherent in the Monte

Carlo simulations on which the respective results are based. The

quality of the estimates obtained by the computer program

presented here is the same as for the estimates of Ref. 5. Owing

to the relatively small climatological data samples upon which

the hurricane wind speed estimates at locations north of Cape

Hatteras are based, these estimates should be viewed with

caution. For comments on the errors in the estimation of

hurricane wind speeds, the reader is referred to Ref. 5.

6
4. ACKNOWLEDGMENTS

The writers wish to thank R.D. Marshall and Bruce Ellingwood,

Center for Building Technology, National Bureau of Standards, for

their helpful suggestions. We would especially like to thank Dr.

James A. Lechner of the Center for Applied Mathematics, National

Bureau of Standards, for his enlightening discussions and for his

valuable and patient help.

7
5.

REFERENCES

1. Simiu, E. , and Scanlan, R.H., Wind Effects on Structures , Wiley-Interscience, New York, 1978.

2. Russell, L.R., "Probability Distributions of Hurricane

Effects, " Journal of the Waterways, Harbors, and Coastal

Engineering Division , ASCE, Vol. 97, No. WW1, February, 1971.

3. Tryggvason, B.V., Surry, D. , and Davenport, A.G. , "Predicting

Wind Induced Response in Hurricane Zones," Journal of the

Structural Division , ASCE, Vol. 102, No. ST12, December, 1976.

4. Gomes, L. , and Vickery, B.J., On the Prediction of Tropical

Cyclone Gust Speeds Along the Northern Australian Coast , Research

Report R278, School of Civil Engineering, University of Sydney,

February, 1976.

5. Batts, M.E., et al. Hurricane Wind Speeds in the United

States, NBS Building Science Series 124, National Bureau of

Standards, Washington, D.C., May, 1980.

6 . American National Standard Minimum Design Loads for Buildings

and Other Structures , ANSI A58.1, American National Standards

Institute, New York, 1982.

7. Bietry, J., Sacre, C., and Simiu, E. , "Mean Wind Profiles and

Change of Terrain Roughness," Journal of the Structural Division , ASCE, Vol. 104, No. ST10, October, 1978.

8
Figure 1 Locator Map
6. APPENDIX - PROGRAM LISTING AND EXAMPLES

This appendix includes (1) a listing of the FORTRAN program

described in this report, (2) an example interactive computer run

using the program, and (3) example graphical output obtained from

the program. The examples presented were run to solve the

following problem:

Problem: Find (1) the parameters of the Weibull distributions of

largest annual hurricane wind speeds and ( 2 ) the wind speeds

corresponding to various mean recurrence intervals for milepost

2400 (Delaware Bay). Consider winds blowing from (1) all

directions, (2) directions ENE, E, ESE, SE, SSE, and S, (3) just

direction NE, and (4) all directions from W to E going clockwise.

The graphical output consists of the probability plots for each

problem described and was obtained using a Tektronix graphics

terminal

.
PROGRAM LISTING

oooo

oooo

ooooo

PROGRAM WINDS (TAPE5,OUTPUT=/1000)

c the purpose of this program is to estimate coastline hurricane wind speeds

C CORRESPONDING TO USER SPECIFIED DIRECTIONS AND MEAN RECURRENCE INTERVALS.

C THE PROGRAM CONSISTS OF THIS MAIN ROUTINE AND TWO SUBROUTINES CALLED

C 'WEIS’ AND ’SORT'. INPUT DATA FOR THE PROGRAM ARE ON 56 DATA FILES CONC TAINING SIMULATED DIRECTIONAL HURRICANE WIND SPEED DATA AS DESCRIBED IN C REF. 1. THERE IS ONE DATA FILE FOR EACH OF 56 STATIONS OR MILEPOSTS

C DEFINED ALONG THE GULF AND ATLANTIC COASTS. THE FIRST STATION IS MlLEC POST 150 AT PORT ISABEL. TEXAS AND THE LAST STATION IS MILEPOST 2900

C JUST NORTHEAST OF PORTLAND. MAINE. INTERMEDIATE STATIONS ARE LOCATED

C AT 50 NAUTICAL MILE INTERVALS BETWEEN MILEPOSTS 150 AND 2900. A LOCATOR

C MAP SHOWING THE EASTERN SEABOARD AND THE GULF COAST AND THEIR MILEPOSTS

C IS IN FIG. 1 OF THE REPORT (ALSO. IN REF. 2).

C THIS PROGRAM HAS BEEN WRITTEN ON MAGNETIC TAPE. ALONG WITH 56 DATA FILES

C CONTAINING SIMULATED HURRICANE WIND SPEED DATA. THE FIRST FILE ON THE

C TAPE IS THIS FORTRAN PROGRAM. THE 2ND THROUGH 57TH FILES ARE THE DATA

C FILES CORRESPONDING TO MILEPOSTS 150 TO 2900 (STEP 50), IN ORDER. FOR

C EXAMPLE. TO ESTIMATE HURRICANE WIND SPEEDS AT MILEPOST 500. COPY THE FIRST

C FILE (THE PROGRAM) AND THE (500-1 50)/50 + 2 = 9TH FILE FROM THE TAPE.

C THEN RUN THE PROGRAM USING THE SELECTED DATA FILE.

C IF THE STATION OF INTEREST IS NOT LOCATED AT AN INTEGER MULTIPLE OF 50

C NAUTICAL MILES. THE DATA FILE CORRESPONDING TO THE NEAREST MILEPOST

C SHOULD BE SELECTED. FOR EXAMPLE. IF IT IS DESIRED TO ESTIMATE HURRICANE

C WIND SPEEDS AT CAPE HATTERAS - MILEPOST 2170 - THEN THE DATA FILE CORC RESPONDING TO MILEPOST 2150 SHOULD BE SELECTED.

IT IS SUGGESTED THAT HURRICANE WIND SPEEDS BE ESTIMATED FOR A PARTICULAR

MILEPOST BY RUNNING THE PROGRAM FOR THE MILEPOST OF INTEREST, AND FOR THE

TWO MILEPOSTS TO EITHER SIDE OF THE SELECTED STATION. THE MEAN RECURRENCE INTERVAL WIND SPEEDS CAN THEN BE CALCULATED AS THE AVERAGE OF THE

THREE VALUES OBTAINED.

THE PROGRAM PROMPTS THE USER FOR INPUT TO SPECIFY THE DIRECTIONS OF INTERES

FOR THIS PROGRAM, THE COMPASS IS DIVIDED INTO 16 HALF-OCTANTS, EACH WITH

A 22.5 DEGREE ANGLE CENTERED ABOUT ONE OF THE 16 PRINCIPAL COMPASS

DIRECTIONS LISTED BELOW (WITH THEIR RESPECTIVE CODES).

1—

NNE 5— ESE

2- NE 6- SE

3—

ENE 7-SSE

4- E 8- S

9-SSW 1 3—WNW

10- SW 14- NW

1

1

WSW 1 5—NNW

12- W 16- N

C FOR EXAMPLE, IF THE DIRECTION OF INTEREST SWEEPS THE 22.5 DEGREE ANGLE

C CENTERED ABOUT THE NNE DIRECTION, THE INPUT TO THE PROGRAM IS ’1.1’.

C IF THE DIRECTIONS OF INTEREST SWEEP THE FOUR ADJACENT 22.5 DEGREE ANGLES

C CENTERED ABOUT THE S, SSW, SW. AND WSW COMPASS POINTS. THE INPUT TO

C THE PROGRAM IS ’8.11’. IF THE DIRECTIONS OF INTEREST ARE FROM N TO NNE.

C THE INPUT IS ’16,1’. NOTE THAT THE ORDER OF DIRECTION INPUT CORRESPONDS

C TO A CLOCKWISE SENSE OF ROTATION.

C THE OUTPUT OF THE PROGRAM CONSISTS OF THE FASTEST 60-SECOND WIND SPEED

C OVER OPEN TERRAIN AT THE COASTLINE AT 10 METERS ABOVE GROUND. CORRESC PONDING TO THE SPECIFIED DIRECTIONS AND TO 10-. 25-, 50-. 100-, 500-.

C 1000-, AND 2000-YEAR MEAN RECCURENCE INTERVALS. IN ADDITION, THE OUTPUT

C INCLUDES THE PARAMETERS OF THE WEIBULL DISTRIBUTION THAT BEST FIT THE

C HURRICANE WIND SPEED DATA, ACCORDING THE MAXIMUM PROBABILITY PLOT

C CORRELATION COEFFICIENT CRITERION OF BEST FIT.

C IT IS POSSIBLE TO OBTAIN THE 60-SECOND WIND SPEEDS BLOWING OVER OPEN

C WATER BY MULTIPLYING THE DATA BY A SUITABLE FACTOR. IT IS SUGGESTED

C THAT A FACTOR OF APPROXIMATELY 1.26 BE USED (REF. 3).

C TO OBTAIN WIND SPEEDS AT ELEVATIONS OTHER THAN 10 METERS,

C ABLE FACTOR CAN BE USED TO MODIFY THE DATA (SEE REF. 3).

AGAIN A SUITC WIND SPEEDS AVERAGED OVER TIME INTERVALS DIFFERENT FROM 60-SECONDS (FOR

C EXAMPLE, 1-HOUR) CAN BE CALCULATED BY INCLUDING A FACTOR AS DISCUSSED

C IN REF. 4. P. 62.
C NOTE THAT THE RESULTS 08TAINED BY THIS PROGRAM WITH THE ASSOCIATED DATA

C FILES COULD DIFFER INSIGNIFICANTLY FROM THOSE IN REF. 1 BECAUSE OF THE

C SAMPLING ERRORS THAT ARISE WHEN DIFFERENT MONTE CARLO SIMULATIONS ARE

C PERFORMED.

C THIS PROGRAM HAS BEEN WRITTEN WITH THE INTENT THAT IT BE EASY TO

C MODIFY TO SUIT THE PARTICULAR USER'S NEEDS.

C REFERENCES:

C 1. BATTS, M.E., ET AL, "HURRICANE WIND SPEEDS IN THE UNITED STATES,"

C BUILDING SCIENCE SERIES BSS-124, NATIONAL BUREAU OF STANDARDS.

C WASHINGTON, DC. 1980.

C 2. BATTS, M.E., RUSSELL, L.R., SIMIU, E. , "HURRICANE WIND SPEEDS IN C THE UNITED STATES." JOURNAL OF THE STRUCTURAL DIVISION, ASCE,

C VOL. 106, NO. ST1 0 , OCTOBER. 1980.

C 3. BIETRY, J., SACRE, C.. SIMIU, E. , "MEAN WIND PROFILES AND CHANGE

C OF TERRAIN ROUGHNESS," JOURNAL OF THE STRUCTRUAL DIVISION. ASCE,

C VOL. 104, NO. ST10, OCTOBER. 1978.

C 4. SIMIU, E.. SCANLAN, R.H., WIND EFFECTS ON STRUCTURES, JOHN WILEY ic SONS,

C NEW YORK. 1978.

DIMENSION V( 1000, 16) ,VMAX( 1000) ,X( 1000) ,Y( 1000)

DIMENSION F(7) ,MRI (7) . VMRI (7) , XX(2) ,YY(2)

REAL LOC LOGICAL PLTFLAG

DATA MR I /1 0,25, 50, 100,500, 1000,2000/

PLTFLAG = .FALSE.

READ (5,100) MPOST.N. URATE

100 FORMAT (2I10.F10.0)

NSAVE = N URATES = URATE

DO 110 I = 1 ,

N

110 READ (5,120) (V(I,J), J=1 ,16).VMAX(I)

120 FORMAT (16F7.3.F8.5)

130 N = NSAVE

WRITE (*.140)

FORMAT (//,' ENTER THE INTEGER CODE FOR THE BEGINNING AND’ ./,

1

’ ENDING DIRECTIONS (GOING CLOCKWISE) ' ,/, 2

’ 0. 0-STOP' ./. 3 ’ 1-NNE 5-ESE 9-SSW 1 3—WNW ’ ./, 4 * 2- NE 6- SE 10- SW 14- NW' ,/. 5 ’ 3-ENE 7-SSE 1

1 -WSW 1 5—NNW ' ,/. 6 ' 4- E 8- S 12- W 16- N ’

)

READ (*,•) JBGN.JEND

IF ( JBGN .LE. 0) THEN WRITE (*.150)

150 FORMAT (/,' EXIT FROM PROGRAM')

IF (PLTFLAG) CALL DONEPL

STOP

END IF

C THE BASIC WIND SPEED ON THE TAPES IS IN KNOTS. AT 10 METERS ABOVE

C GROUND. AT THE SHORELINE (0 MILES FROM SHORE), OVER OPEN TERRAIN, AND

C AVERAGED OVER 1 MINUTE.

C WE WANT SPEED IN MPH , AT 10 METERS HEIGHT. AT THE SHORELINE.
oooooo

ooo

oooooooooo

C OVER OPEN TERRAIN. AND AVERAGED OVER 1 MINUTE.

CUN ITS = CONVERSION FACTOR FOR CONVERTING BASIC SPEED TO SPEED IN UNITS OF MILES PER HOUR

CHIGHT = CONVERSION FACTOR FOR CONVERTING BASIC SPEED TO SPEED AT SPECIFIED HEIGHT

CSNDRE = CONVERSION FACTOR FOR CONVERTING BASIC SPEED TO SPEED AT SPECIFIED DISTANCE INLAND FROM THE SHORE

CROUGH - CONVERSION FACTOR FOR CONVERTING BASIC SPEED TO SPEED OVER

SPECIFIED TERRAIN WITH A SPECIFIED ROUGHNESS

CTIME - CONVERSION FACTOR FOR CONVERTING BASIC SPEED TO SPEED AVERAGED

OVER A SPECIFIED PERIOD OF TIME

CUNITS = 1.152

CHIGHT *1.0

CSHORE *1.0

CROUGH =1.0

CTIME =1.0

C * CUN ITS ‘CHIGHT *CSHORE«CROUGH*CTlME

IF (JBGN .EQ. 1 .AND. JEND .EQ. 16) THEN

DO 160 I = 1 ,N 160 X(I) = C*VMAX(I)

ELSE IF (JBGN .EQ. JEND) THEN

DO 170 I = 1 ,N 170 X(I) * C‘V( I , JBGN)

ELSE IF (JBGN .GT. JEND) THEN

DO 200 I = 1 ,N X(I) = 0.0

DO 180 J = JBGN, 16 180 X(I) = AMAX1 (C‘V(I ,J) , X( I )

)

DO 190 J = 1 .JEND

190 X(I) = AMAX1 (C»V(I ,J) ,X(I))

200 CONTINUE

ELSE

DO 220 I = 1 ,N X(I) = 0.0

DO 210 J = JBGN. JEND

210 X(I) = AMAX1 (C*V( I .J) , X( I )

)

220 CONTINUE

END IF CALL SORT (X.N.X)

VCUT =0.0

WRITE (‘.230)

230 FORMAT (/, * ENTER THE CUT-OFF VALUE OF WIND SPEED’)

READ (...) VCUT

DO 24-0 I = 1 , N

IF (X(I) .GT. VCUT) GO TO 250

2*0 CONTINUE

250 NCUT =1-1

N = N - NCUT

WRITE (*.260) NCUT

260 FORMAT (’ THE NUMBER OF EXCLUDED WIND SPEEDS =’ 15)

WRITE (*.270)

270 FORMAT (/, ' ENTER BEGIN AND END INDICES OF X(I) TO BE PRINTED’)

READ (.,•) I BGN . I END WRITE (*.280) (X(I). I = I BGN , I END)
C 280 FORMAT (7F10.2)

URATE = (REAL(N)/REAL(NSAVE) ) *URATES

DO 290 I = 1 ,N X(I) = X ( I+NCUT

)

Y( I ) = EXP(—URATE* (N+1— I )/(N+1 )

)

290 CONTINUE

CALL WEIB (N,X,Y, SCALE. SHAPE. LOC)

WRITE (*.300) MPOST.JBGN.J END, SHAPE, SCALE, LOC

300 FORMAT (/,

1

* RESULTS OF FITTING A THREE PARAMETER WEIBULL DISTRIBUTION’ ./. 2 * TO EXTREME DIRECTIONAL WIND SPEED DATA’,//,

3 ’ MILEPOST’. 15,/,

4 ’ FROM DIRECTION NUMBER’ , 13./.

5

’ TO DIRECTION NUMBER ’,13,//,

6 ’ SHAPE PARAMETER =’,G15.5,/,

7 ’ SCALE PARAMETER =’,G15.5,/,

8 ’ LOCATION PARAMETER =’ .G15.5)

RSHAPE = 1.0/SHAPE

DO 310 I = 1 .7 F( I ) = 1.0- 1 . 0/MR 1(1)

VMRI(I) = LOC + SCALE* (-ALOG(1 .0 - F( I ) )

) . *RSHAPE

310 CONTINUE

WRITE (*,320) (VMRI(I), 1=1,7)

320 FORMAT (//,

1

’ MEAN RECCURENCE INTERVAL WIND SPEEDS’. /.

2

’ 10 25 50 100 500 1000 2000’./,

3 7F8.1)

C THE FOLLOWING SUBROUTINE CALLS WILL PLOT A CUMULATIVE FREQUENCY

C DIAGRAM FOR THE DATA ON WEIBULL PROBABILITY PAPER, AND WILL PLOT

C THE BEST FIT WEIBULL DISTRIBUTION AS DETERMINED IN SUBROUTINE WEIB.

C THE SUBROUTINES ARE PART OF THE DISSPLA PLOTTING SOFTWARE LIBRARY. WRITE (*.330)

330 FORMAT (’ SELECT ONE’,/.’ 0-NO PLOT’,/,’ 1-PLOT’)

READ (*,*) I

A

IF (IA .EQ. 1) THEN

IF (NOT. PLTFLAG) CALL TEKALL (4014,960,0,1,0)

PLTFLAG = .TRUE. CALL PAGE (15.0.12.0)

CALL HEIGHT (0.25)

CALL AREA2D (13.0.8.0)

CALL XNAME (’WIND SPEED (MPH)$’,100)

CALL HEIGHT (0.35)

CALL CARTOG

CALL MX1ALF (’STANDARD’, ’•’)

CALL MX2ALF (’INSTRU’, ’ 7. ’) CALL YNAME (’( ZM5*LN JJM0P 1 • N25G 1 E 1 M0 .-3EXM0* )2M7H0 . 5E* 1 /G$ ’

, 1 00)

CALL HEIGHT (0.18)

CALL MESSAG ( ’ N%G1 E1M0*-3EX* = MEAN RECURRENCE INTERVAL IN YEARS$

’

• .100,2.0,9.0)

CALL MESSAG ( ’%M7*G%M0* = WEIBULL DISTRIBUTION TAIL LENGTH PARAMET

•ER$’ , 100,2.0,8.5)

XMAX =0.0

YMAX =0.0

YMIN = 100.0

DO 340 I = 1 ,

N

Y( I

)

= ( —A LOG (1.0 - Y(I)))*. RSHAPE

YMAX = AMAX 1 ( Y (

I ) , YMAX

)

YMIN = AMIN1 ( Y(

I ) , YMIN) XMAX = AMAX1 (X( I ) .XMAX)
340 CONTINUE

XMAX = 25.0*REAL(INT (XMAX/25 . 0 + 0.99))

YSTEP = (YMAX - YMIN)/5 .

0

CALL GRAF ( 0 . 0 . 25 . 0 , XMAX , YMI N , YSTEP . YMAX

)

CALL CURVE (X.Y.N.0)

XX(1) = 0.0

YY( 1 ) = -LOC/SCALE

IF ( YY( 1 ) .LT. YMIN) THEN

YY( 1 ) * YMIN

XX(1) = SCALE*YMIN + LOC END IF

XX(2) = XMAX

YY(2) = (XMAX- LOC) /SCALE

IF (YY(2) .GT. YMAX) THEN

YY(2) = YMAX

XX(2) = SCALE»YMAX + LOC

END IF CALL CURVE (XX,YY,2,0)

CALL ENDPL (0)

END IF

GO TO 130

END SUBROUTINE WEIB (N , X , Z , SC , SH . LP)

REAL LP DIMENSION X(1000) , Y( 1 000) ,Z(1000)

DIMENSION GAMTA8(42) ,CC(42) .SL0PE(42) ,YINT(42)

DATA GAMTAB

1 / 1 ..0. 2 .0. 3,.0, 4. 0. 5..0, 6..0, 7..0, 8..0. 2 9. 0, 10..0. 1 1 ,.0. 12..0, 13,.0, 14,.0. 15..0. 16 .0. 3 17..0, 18 .0, 19 .0, 20,.0. 21 .0. 22 .0, 23,.0. 24 .0. 4 25,.0. 30 .0. 35 .0, 40 .0. 45 .0, 50..0, 60..0, 70 .0. 5 80 .0. 90 .0, 100 • 0, 150,.0, 200 • 0. 250 .0, 350 .0, 500 .0. 6 750.0,1000.0/

DO 140 I = 1,42

A = 1 . 0/GAMTAB( I

)

DO 110 J = 1 ,

N

110 Y(J) = (—ALOG( 1 . 0 - Z(J)))**A

CALL PPCCAN (N , X , Y , SLOPE( I),YINT(I),CC(I))

140 CONTINUE

C FIND THE DISTRIBUTION WITH THE MAXIMUM PPCC

.

I SAVE = 1 CCMAX = CC(1)

DO 400 I = 2,42

IF (CC(I) .GT. CCMAX) THEN

I SAVE = I CCMAX = CC(I)

END IF 400 CONTINUE

SH = GAMTAB (I SAVE)
SC = SLOPE(ISAVE)

LP = YINT( I SAVE)

RETURN

END SUBROUTINE PPCCAN (N , X ,Y . SLOPE , YINT , CC)

DIMENSION X(1000) ,Y(1000)

RN = FLOAT (N)

SUM1=0 .

0

SUM2=0 .

0

DO 120 J = 1 .

N

SUM1 = SUM1+X( J)

SUM2 = SUM2+Y ( J

)

120 CONTINUE

XBAR = SUM1/RN

YBAR = SUM2/RN

SUM1 =0.0

SUM2 =0.0

SUM3 =0.0

DO 130 J = 1 ,N SUM1 = SUM1 + (X( J )—XBAR ) • *2 SUM2 = SUM2 + ( Y( J )—YBAR ) • *2 SUM3 = SUM3 + ( X ( J

) —XBAR ) * ( Y ( J

) —YBAR

)

130 CONTINUE

SLOPE = SUM3/SUM2

YINT = XBAR-S LOPE* YBAR

CC = SUM3/SQRT (SUM1 *SUM2)

RETURN

END SUBROUTINE SORT (X.N.Y)

C THIS SUBROUTINE SORTS A VECTOR, X. IN ASCENDING ORDER AND PUTS THE

C RESULT IN VECTOR Y.

C FORMAL PARAMETERS:

C RECEIVED:

C X = VECTOR OF NUMBERS TO BE SORTED,

C N = NUMBER OF VALUES IN X() AND Y(Y) (DIMENSION OF X AND Y)

.

C RETURNED:

C Y = VECTOR OF SORTED NUMBERS.

DIMENSION X(N) ,Y(N) , IU(36) . IL(36)

C CHECK THE INPUT VECTOR FOR OBVIOUS SORTS.

IF (N .LE. 0) THEN

WRITE (*,100) N 100 FORMAT (• ERROR IN SUBROUTINE SORT, N

=

’ , 110)

STOP

END IF

IF (N .EQ. 1) THEN

Y(1) = X(1)

RETURN

END IF

XI = X(1)

Y( 1 ) = XI

DO 110 I = 2 ,

N

IF (X(I) .NE. XI) GO TO 120
Y ( I ) = XI

1 10 CONTINUE

120 DO 130 I = 2 .

N

IF (X(I) .LT. X( 1—1 ) ) GO TO 250

Y(I) = X(I)

130 CONTINUE

C START POINT FOR SORT.

250 DO 260 I = 1 ,N Y( I ) = X(I)

260 CONTINUE

14=1

1 = 1 J=N

305 I F ( I .GE . J )GOTO370

310 K=

I

MID=(I+J)/2

AMED=Y(MID)

I F(Y( I ) .LE. AMED)GOTO320

Y(MID)=Y(I)

Y( I )=AMED

AMED=Y (MID)

320 L=J IF(Y(J) . GE . AMED)GOTO340

Y(MID)=Y(J)

Y(J)=AMED

AMED=Y (MID)

I F ( Y ( I) . LE. AMED)GOTO340

Y (MID)=Y ( I

)

Y(I)=AMED

AMED=Y (MID)

GOTO340

330 Y(l)=Y(K)

Y(K)=TT

340 L= L—

1

I F( Y( L) . GT . AMED)GOTO340

TT=Y(L)

350 K=K+1

I F ( Y ( K ) . LT. AMED )GOTO350

I F ( K . LE . L ) GOT0330

LMI=L—

I

JMK=J—

K

I F ( LM I . LE . JMK)GOTO360

I L(M)=I

IU(M)=L

I=K M=M+1

GOTO380

360 I L ( M

) =K

IU(M)=J

J=L

K4=M-t-1 GOTO380

370 M=M-1

I F(M . EQ . 0)RETURN

1=1 L(M)

J=IU(M)

380 JMI=J—

I

IF(JMI .GE. 11 )GOTO310

I F( I . EQ . 1 )GOTO305

1 = 1-1 390 1=1+1

I F( I . EQ . J )GOTO370

AMED=Y (1+1

)

I F ( Y ( I) . LE . AMED)GOTO390

K=I 395 Y(K+1 )=Y(K)

K=K—

1

I F(AMED . LT . Y(K) )G0T0395

EXAMPLE INTERACTIVE COMPUTER SESSION

fuse 7,np2400

READY >?xqc wlnd.f

ESTER THE INTEGER CODE FOR THE BEGINNING AND

ENDING DIRECTIONS (GOING CLOCKWISE)

O.O-STOP

1-NNE 5-ESE 9-SSW 13-WNW

2- NE 6- SE 10- SW 14- NW 3-ENE 7-SSE 11-WSW 15-NNW

4- E 8- S 12- W 16- N >1,16

RESULTS OF FITTING A THREE PARAMETER WEIBULL DISTRIBUTION

TO EXTREME DIRECTIONAL WIND SPEED DATA

MILEPOST 2400

DIRECTION NUMBER I TO DIRECTION NUMBER 16

SHAPE PARAMETER - 3.0000

SCALE PARAMETER - 95.106

LOCATION PARAMETER - -72.624

MEAN RECCURENCE INTERVAL WIND SPEEDS

10 25 50 100 500 1000 2000

53.0 67.8 77.2 85.6 102.2 108.5 114.4 SELECT ONE

0-

NO PLOT

1-

PLOT

>0

ENTER THE INTEGER CODE FOR THE BEGINNING AND

ENDING DIRECTIONS (GOING CLOCKWISE)

O.O-STOP

1-

NNE

2- NE

3-

ENE

4- E >3,8

5-

ESE 9-SSW 13-WNW

6- SE 10- SW 14- NW

7-

SSE 11-WSW 15-NNW

8- S 12- W 16- N

RESULTS OF FITTING A THREE PARAMETER WEIBULL DISTRIBUTION

TO EXTREME DIRECTIONAL WIND SPEED DATA

MILEPOST 2400 FROM DIRECTION NUMBER 3 TO DIRECTION NUMBER 8

SHAPE PARAMETER - 1000.0

SCALE PARAMETER - 69248.

LOCATION PARAMETER - -69271.

RECCURENCE INTERVAL WIND SPEEDS

10 25 50 100 500 1000 2000

35.2 58.4 71.9 83.3 104.0 111.4 118.0 SELECT ONE

0-

NO PLOT

1-

PLOT >0
ENTER THE INTEGER CODE FOR THE BEGINNING AND

ENDING DIRECTIONS (GOING CLOCKWISE)

0,0-STOP

1-

NNE

2- NE

3-

ENE 4- E

> 2,2

5-

ESE 9-SSW 13-WNW

6- SE 10- SW 14- NW

7-

SSE 11-WSW 15-NNW

8- S 12- W 16- N

RESULTS OF FITTING A THREE PARAMETER WEIBULL DISTRIBUTION

TO EXTREME DIRECTIONAL UIND SPEED DATA

MILEPOST 2400 FROM DIRECTION NUMBER 2 TO DIRECTION NUMBER 2

SHAPE PARAMETER - 2.0000

SCALE PARAMETER - 53.772 LOCATION PARAMETER - -59.744

.'lt.A.N RECCURENCE INTERVAL WIND SPEEDS

10 25 50 100 500 1000 2000

21.9 36.7 46.6 55.6 74.3 81.6 88.5 SELECT ONE

0-

NO PLOT

1-

PLOT

>0

ENTER THE INTEGER CODE FOR THE BEGINNING AND

ENDING DIRECTIONS (GOING CLOCKWISE)

1-

NNE

2- NE

3-

ENE

4- E >12,4

5-

ESE 9-SSW 13-WNW

6- SE 10- SW 14- NW

7-

SSE 11-WSW 15-NNW

8- S 12- W 16- N

RESULTS OF FITTING A THREE PARAMETER WEIBULL DISTRIBUTION

TO EXTREME DIRECTIONAL WIND SPEED DATA

MILEPOST 2400 FROM DIRECTION NUMBER 12 TO DIRECTION NUMBER 4

SHAPE PARAMETER - 3.0000

SCALE PARAMETER - 90.160 LOCATION PARAMETER - -67.934

MEAN RECCURENCE INTERVAL WIND SPEEDS

1° 25 50 100 500 1000 2000

51.1 65.2 74.1 82.1 97.8 103.8 109.3 SELECT ONE

0-

NO PLOT

1-

PLOT >0

ENTER THE INTEGER CODE FOR THE BEGINNING AND

ENDING DIRECTIONS (GOING CLOCKWISE) O.O-STOP

1-

NNE 5-ESE

2- NE 6- SE

3-

ENF. 7-SSE

4- E 8- S

9-SSW 13-WNW

10- SW 14- NW

11-

WSW 15-NNW

12- W 16- N

> 0,0

EXIT FROM PROCRAM

>
EXAMPLE GRAPHICAL OUTPUT

(

N

N = MEAN RECURRENCE INTERVAL W YEARS

y ~ WEBULL DtSTReUTlON TAiL LENGTH PARAMETER

Figure Al. Probability Plot, Directions 1-16
(

N^)

N = MEAN RECURRENCE NTERVAL (N YEARS

WIND SPEED (MPH)

Figure A2. Probability Plot, Directions 3-8
(

N

/U J)

N = MEAN RECURRENCE WTERVAL M YEARS

7 = WEBULL D6TRBUD0N TAIL LENGTH PARAMETER

Figure A3. Probability Plot, Direction 2
N = MEAN RECURRENCE INTERVAL IN YEARS

y = WElBULL DSTReUTlON TAIL LENGTH PARAMETER

Figure A4. Probability Plot, Directions 12-4
MBS• 1 14A WKV. 2-4CI U.S. DIPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

. PUBLICATION OR

REPORT NO.

NBSIR 86-3317

2. Performing Organ. Report No^ 3. Publication Date FEBRUARY 1986

4. TITLE AND SUBTITLE

Directional Hurricane Wind SDeeds

5. AUTHOR(S)

Erik M. Hendrickson and Emil Simiu

i. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

S. Type of Report & Period Covereo

Research, Final

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. Stote, ZIP)

. Nuclear Regulatory Commission

Washington, DC 20555

10.

SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gnificant

bibliography or literature survey, mention it here)

This report presents a simple procedure for estimating coastline

hurricane wind speeds corresponding to any specified set of wind

directions and to any specified mean recurrence interval. The

procedure uses simulated directional hurricane wind speed data

as described in the report Hurricane Wind Speeds in the United

States (NBS BSS 124) . These data are encoded on magnetic tape

for 56 mileposts located along the U.S. Gulf and Atlantic coasts.

The input to the procedure consists of the location along the

coastline and the set of wind directions of interest. The output consists of the fastest 60-sec wind speeds at 10m above

ground, in open terrain, corresponding to the set of directions

specified in the input and to various mean recurrence intervals.

In addition, the output includes the parameters of the Weibull

distribution that best fits the hurricane wind speeds.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by sem.co . o'-

-

. Climatology; hurricanes; statistical analysis; structural

engineering; wind engineering

13. availability

1_X] Uni imited

I j For Official Distribution. Do Not Release to NTIS

1~

i Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

pt| Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

15. Price

$9.9!