NBS BUILDING SCIENCE SERIES 124

Hurricane Wind Speeds

in the United States

U.S. DEPARTMENT OF COMMERCE • NATIONAL BUREAU OF STANDARDS
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NBS BUILDING SCIENCE SERIES 124

HURRICANE WIND SPEEDS

IN THE UNITED STATES

Martin E. Batts^

Martin R. Cordes^

Larry R. Russell^

James R. Shaveri

Emil Simiu^

^Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

^Center for Applied Mathematics

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

^Larry Russell & Associates, Inc. Houston, Texas 77081

Sponsored by:

Department of Energy

Office of Assistant Secretary for Conservation and Solar Applications

Washington, D.C. 20545

and

National Science Foundation Washington, D.C. 20550

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Luther H. Hodges, Jr., Deputy Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology, and Innovation

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued May 1980

KATIOVAL BDRKATJ or rTAKDARDa

uuuBr

APR 25 1980

. USB
Library of Congress Catalog Card Number: 80-600039

National Bureau of Standards Building Science Series 124

Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 124, 50 pages (May 1980) CODEN: BSSNBV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1980

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Price $3.25

(Add 25 percent additional for other than U.S. mailing)
ACKNOWLEDGMENTS

This material is based upon activities supported by the Department of

Energy, Office of Assistant Secretary for Conservation and Solar Applications, and by the National Science Foundation under agreement No.

ENV-7716113. Any opinion, findings and conclusions or recommendations

expressed in this publication are those of the authors and do not necessarily reflect the view of the Department of Energy or the National

Science Foundation. The cover photograph was provided by the National

Oceanic and Atmospheric Administration.

Cover: Sattelite Photo of Hurriaane Frederiok^ September 19^ 1979.

iii
TABLE OF CONTENTS

Page

LIST OF FIGURES vi

NOTATION vii

1. INTRODUCTION 1

2. PROBABILISTIC AND PHYSICAL MODELS 3

2.1 Probabilistic Models 3

2.2 Physical Models 4

2.2.1 Maximum Gradient Wind Speed 4

2.2.2 Wind Speeds at 10 m Above the Ocean Surface ... 8

2.2.3 Storm Decay 10

2.2.4 Reduction of Wind Speeds Due to Friction Over

Land 10

2.2.5 Dependence of Wind Speeds Upon Averaging Time . 10

3. PROBABILITIES OF OCCURRENCE OF HURRICANE WIND SPEEDS, 11

3.1 Theoretical Approach 11

3.2 Numerical Results 13

3.2.1 Extreme Wind Speeds 13

3.2.2 Probability Distributions of Hurricane Wind

Speeds 16

3.3 Mixed Probability Distributions of Hurricane and

Non-Hurricane Wind Speeds 16

4. ESTIMATION ERRORS 21

4.1 Sampling Errors 21

4.2 Probabilistic Modeling Errors 22

4.3 Observation Errors 23

4.4 Physical Modeling Errors 23

iv
Page

5. CONCLUSIONS 27

REFERENCES 29

APPENDIX A - Hurricane Wind Speeds Blowing from Specified

Directions for 10-yr, 50-yr, and lOO-yr Mean

Recurrence Intervals A-1

V
LIST OF FIGURES

Page

Figure 1. Locator map with coastal distance intervals marked

in nautical miles (1 n. mi. - 1.9 km) [5].

Figure 2. Cumulative distribution function of entering hurricane crossing point, milepost 400 n. mi.

(1 n. mi. = 1.9 km).

Figure 3. Cumulative distribution function of entering storm

headings about mean, milepost 400 n. mi.

(1 n. mi. = 1.9 km).

Figure 4. Ratios V(10,r)/V(10,R)

Figure 5. Estimated fastest-mile hurricane wind speeds blowing

from any direction at 10 m above ground in open terrain near the coastline, for various mean recurrence

intervals (1 mph = 0.47 m/s). 14

Figure 6. Estimated fastest-mile hurricane wind speeds blowing

from any direction at 10 m above ground in open terrain at 200 km inland, for various mean recurrence

intervals (1 mph = 0.47 m/s). 15

Figure 7. Weibull probability distribution plot of 1-min hurricane wind speeds, milepost 450 n. mi. 17

Figure 8. Extreme value Type I probability distribution plot

of 1-min hurricane wind speeds, milepost 450 n. mi. 18

Figure 9. Extreme value Type I probability distributions of

fastest-mile wind speeds. 19

vi
NOTATION

dp/dn = pressure gradient

f = Coriolis parameter

K = coefficient

^ = angle between storm track and coastline

p = retardation factor

p^ = standard pressure

P(n,''^) = probability that n storms occur in t years

P(V ^ vin) = probability that the wind speed V in n storms is less than

P(V V

I ''^) = probability that the wind speed V in years is less than \

r = distance from storm center

R = radius of maximum wind speeds

s = hurricane translational speed

t = time, in hrs.

V = maximum gradient windspeed

gx ^ ^

V(z,R) = maximum velocity at z meters above ground at the radius of

maximum winds

V(z,r) = maximum velocity at z meters above ground at the radius r from the eye

V(z,r,®) = velocity at z meters above ground at radius, r and angle

^ from OM

z = height above ground or water surface, in meters

" = coefficient

max

~ pressure drop from periphery of hurricane to its center

p = air density

0 = angle between lines ON and OM

(J) = angle between storm track and coastline

vii
ABSTRACT

A Monte Carlo simulation technique Is used to obtain estimates of

hurricane wind speeds along the Gulf and East Coasts of the United

States. The paper describes the sources of data, the probabilistic

models for cllmatologlcal characteristics of hurricanes, and the physical

models for the hurricane wind speed field used In the estimations.

Estimated values of fastest-mile hurricane wind speeds at 10 m above

ground In open terrain at the coastline and at 200 km Inland are given

for various mean recurrence Intervals. The estimated hurricane wind

speeds were found to be best fitted by Welbull distributions with tall

length parameters y U. Estimates are given of various errors Inherent

In the estimated values of the hurricane wind speeds. Owing to uncertain

ties with respect to the applicability of the physical models used

In this work to locations north of Cape Hatteras, estimated hurricane

wind speeds given for these locations should be viewed with caution.

Key Words: Buildings (codes); climatology; hurricanes; statistical

analysis; structural engineering; tropical cyclones; wind

(meteorology)

Facing page; Damage caused by Hurricane Camille,

viii
1 . INTRODUCTION

It has previously been shown that predictions of extreme wind speeds

in hurricane-prone regions cannot in general be based upon the statistical analysis of the largest annual wind speeds recorded at a given

site [10, p. 84]. For this reason, estimates of extreme hurricane

wind speeds at a site are commonly obtained by indirect methods [1,

4, 11, 12] from (1) statistical information on the climatological

characteristics of hurricanes, and (2) a physical model of the hurricane wind structure. The climatological characteristics of hurricanes

include: (a) rate of hurricane occurrence in any given region; (b)

difference between atmospheric pressures at the center and at the

periphery of the storm; (c) radius of maximum wind speeds; (d) speed

of storm translation; (e) direction of storm motion, and (f) crossing

point coordinate along the coast or on a line normal to the coast.

The physical model of the hurricane wind includes assumptions on:

(a) dependence of surface wind speeds upon difference between atmospheric pressures at center and periphery of the storm, radius of

maximum wind speeds, speed of translation, latitude, and position

of the point being considered with respect to center of the storm;

(b) storm decay as the storm travels over land and its supply of

energy in the form of warm moist air from the ocean surface is

1
thus cut off; (c) reduction

and (d) ratios between wind

of wind speeds due to friction over land;

speeds averaged over various time intervals.

Given the available statistical information on the climatological characteristics of hurricanes, probabilistic models are estimated for each of

these characteristics. A large number of hurricanes is then generated

by Monte Carlo simulation (random sampling) from these probabilistic

models, as will be explained subsequently in the report. The largest

wind speeds occurring within each of these hurricanes at the site of

concern are the data from which the cumulative distribution function

of the hurricane wind speeds at that site is then estimated. This

procedure was first developed by Russell [9], who also developed the

computer program used in this work.

The purpose of this paper is to present estimates of hurricane wind

speeds on the Gulf and East Coasts of the United States based on the

procedure just outlined and on data taken from References 3 and 5. The

probabilistic and physical models used to obtain these estimates will

be described, and an analysis will be made of errors inherent in the

estimates. Estimates of hurricane wind speeds in California [13] are

not treated in this report.

Facing page: Damage to solar collectors, caused by Hurricane Frederick.

2
2. PROBABILISTIC AND PHYSICAL MODELS

2 . 1 PROBABILISTIC MODELS

The following probabilistic models were used:

1. The hurricane occurrence is described by a constant rate

Poisson process.

2. The probability distribution of the pressure difference between

center and periphery of storm, APjjj^jj, is lognormal. To eliminate

values of APjjj^j^ judged, in light of historical data [5], to be

unrealistically high, the distribution is censored so that

AP„o^ < 101.6 mm (4.00 in) of mercury. (Note that APm-,^ LUd^ lUdA

101.6 mm corresponds to the lowest atmospheric pressure ever recorded worldwide [14].) The effect of this censoring will be

commented upon subsequently in this report.

3. The probability distribution of the radius of maximum wind speeds,

R, is lognormal. This distribution is censored so that 8 km < R < 100 km to avoid unrealistically "tight" or "broad" storms [5].

3
4. The average correlation coefficient between R and A Pmax

approximately -0.3 (see Reference 5, pp. 68 and 69). All other

climatological characteristics are assumed to be statistically

independent

5. The probability distribution of the speed of translation, s, is

normal. This distribution is censored so that 2 km/hr < s < 65

km/hr [5]

6. The cumulative distribution function of the hurricane crossing

point along the coast is a curve matching the historical data

as recorded in Reference 5. Separate distribution curves are defined for entering, exiting, upcoast heading, and downcoast

heading storms. The length of coast being considered for

entering and exiting storms includes a 470 km segment downcoast

of the location under investigation, and a 370 km segment upcoast of that location, the influence of storms not crossing

these segments being negligible for practical purposes.

The downwind and upwind segments are unequal because, owing

primarily to the presence of the translational speed of the

storm, the hurricane wind structure is asymmetrical. As an

example, the distribution curve assumed for entering storms

affecting coastal milepost 400 n. mi. (740 km) [see Figure 1]

is shown in Figure 2.

7. The crossing points on a line normal to the coast are assumed

to be uniformly distributed between 110 km and 280 km from the

coast in the case of upcoast heading storms, and between 110 km

and 360 km in the case of downcoast heading storms.

8. The cumulative distribution functions of heading (direction of

storm translation) for entering storms are curves matching the

historical data recorded in Reference 5. As an example. Figure 3

shows the distribution of the storm headings about their mean

value for milepost 400 n. mi. (740 km). For exiting storms and

for storms crossing a line normal to the coast, the distributions

are assumed to be uniform between + 30° of the mean. The mean

values of the storm headings are obtained from the data of

References 3 and 5. In all cases it was assumed that the path

of the storm motion is a straight line.

2.2 PHYSICAL MODELS

2.2.1 Maximum Gradient Wind Speed

The maximum gradient wind speed can be written as

V _ Rf + dp^l/2 (1) Vgx . -J

^ ^-

4
Figure 1. Locator map with coastal distance intervals marked

in nautical miles (1 n. mi. = 1.9 km) [5].

5
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(see Reference 10, p. 18), where f = Coriolis parameter, dp/dn = pressure

gradient, P = air density, and R = radius of maximum wind speeds. It is

reasonable to assume ^ = «^Pmax (2) an

where « is a coefficient determined empirically. It then follows from

Equations 1 and 2

Vgx = K V Apmax - ^ (3)

1/2 where the notation K = [R "/P] is used. Values of K consistent with

those determined empirically by the Hydrometeorological Branch (National

Weather Service, National Oceanic and Atmospheric Administration) and

used in,Reference 8 vary approximately between 6.97 m/s/mm , (77.5

mph/in^^ ) at latitude 23°N to 6.93 m/s/mm^' (77.0 mph/in-""^ ) at

latitude 45° N. [These values may be used in conjunction with the

assumption that the pressure at the periphery of the storm is p^ = 765 mm (29.77 in).]

2.2.2 Wind Speeds at 10 m Above the Ocean Surface

The maximum wind speed at 10 m above the ocean surface, averaged over

10-min, is assumed to be given by the empirical relation [8]

V(z=10,R) = 0.865 V + 0.5 s (4) gx

Let the center of the storm be denoted by 0, and let a line OM be

defined that makes an angle of 115° clockwise from the direction of

motion of the storm. The 10-min wind speed at 10 m above the ocean

surface at a distance r from 0 along the line OM is denoted by V(z=10,

r). The ratio V(z=10,r)/V(z=10,R) , is assumed to depend on r as shown

in Figure 4 [8] . Let now the angle between a line ON and line OM be

denoted by 6. The 10-min wind speed V(z=lO,r,0) at 10m above the

surface at a distance r from the storm center on line ON is assumed

to be given by the expression [8]

V(z=10,r,e) = V(z=10,r) -^(1 - cos 6) (5)

The wind velocity vector has a component directed toward the center of

the storm. The angle between that vector and the tangent to the circle

centered at 0 is assumed to be between 0° and 10° in the region

0 < r < R, between 10° to 25° in the region R 1 r < 1.2R, and 25° in

the region r 1 1 .2R [8]

8

2.2.3 Storm Decay

The storm decay was assumed to result from a decrease with time of the

difference between pressure at the center and at the periphery of the

storm, given by the following relation

^p(t) = - 0.02 [1+sin f]t (6)

where t = travel time in hours, ^p(t) and ^p^^^ are given in inches,

and 't' = angle between coast and storm track < <t> < 180"). As shown

subsequently in this paper, results based on this model were compared

with results based on Malkin's model, which is consistent with measurements reported in Reference 7. This comparison appears to support the

validity of Equation 6 as a conservative approximation.

2.2.4 Reduction of Wind Speeds Due to Friction Over Land

The factor for reducing overwater to overland surface wind speeds used

in Refej^ence 8 is 0.78 for wind speeds over 37 m/s. In Reference 2, the

ratio V (10)/v"(10), where V(10) = 10-min mean speed at 10 m above the

surface, and the superscripts w and ^ indicate "overwater" and "overland'

respectively, is given as

V^(IO) ^ 1 (7)

10

V^(IO) P

where the retardation factor p = 0.83 and the roughness length Zq = 0.005 m, so that V (10)/V^(10) = 0.79, i.e., this ratio has almost

exactly the same value as in Reference 8. Note that Equation 7 is based

on similarity relations applicable to storms in which the gradient wind

may be regarded as geostrophic, so that its applicability to hurricane

winds is uncertain, at least in the region of maximum wigd speeds. In

this work it was therefore assumed conservatively that V (10)/V^(10)

=0.85.

2.2.5 Dependence of Wind Speeds Upon Averaging Time

Research results concerning the ratios of hurricane wind speeds corresponding to different averaging times do not appear to be available.

In the absence of such results, it was judged reasonable to use wind

speed ratios obtained for non-tropical storms by Durst which are summarized, e.g., in Reference 10, p. 62. For example, the ratio between

the fastest one-minute and the fastest 10-minute speed at 10 m above

open terrain was assumed to be 1.18.

Facing page: Trees uprooted by typhoon in Manila (The Philippines),

10
3. PROBABILITIES OF OCCURRENCE OF HURRICANE WIND SPEEDS

3.1 THEORETICAL APPROACH

To estimate probabilities of occurrence of hurricane wind speeds, one thousand hurricanes were assumed to hit the area adjoining each of the

56 sites being investigated. (Recall that this area was defined previously in the section "Probabilistic Models", items 6 and 7.) Four

categories of storms were considered: entering hurricanes (i.e., hurricanes moving inland), exiting hurricanes (i.e., hurricanes headed

toward the ocean after moving over land), upcoast heading hurricanes

(i.e., hurricanes whose center remains offshore and moving upcoast),

and downcoast heading hurricanes. For each location, the ratios between

the number of hurricanes belonging to each of these categories and the

total number of hurricanes affecting that location were estimated from

the information given in References 3 and 5.

The climatological data for each of the one thousand hurricanes were determined from the respective probability distributions by Monte Carlo

simulation (random sampling). Associated with each hurricane is a wind

field, and a set of wind speeds at the site of interest which depend

11
upon the position of the moving hurricane center with respect to the

site. These wind speeds were calculated for a sufficiently large

number of such positions (6 or 7, depending on track). The largest

among these speeds represents the maximum wind speed caused by the

hurricane at the site. A set of one thousand such wind speeds is

thus obtained, which is used as the basic set of data for the estimation of the probability of occurrence of hurricane wind speeds

at the site. (This procedure was applied to estimate extreme wind

speeds without regard to direction, as well as extreme wind speeds

blowing in specified directions.) The wind speeds are ranked by magnitude, and the probability of occurrence of the i-th ranking wind

speed, v^, in a set of m wind speeds (m = 1,000 in the work reported

herein) is obtained as follows.

Let the probability that the wind speed in any one storm is less than

V be denoted by F^. The probability that the highest wind speed V in n storms is less than v can be written as

n ^ (8) P(V < v|n) = (F^)" = F

V

Let the probability that V < v in t years be denoted by P(V < v, x).

It is possible to write

P(V < V, t) = Z p(v < v|n) P(n, t) (9)

n=0

where P(n,T) denotes the probability that n storms will occur in t years. If a Poisson process is assumed to describe P(n,T), and if use

is made of Equation 9,

°° ( VT ) ^ —VT

P(V < V, t) = Z F'^ ®

n=0 ^ n!

" (vtF )^

= e" ^"^ Z ^

'^=0 n! _ VT VT^

= e e V

VT = e (l-Fv^ (10)

where the Poisson parameter ^' = annual rate of occurrence of hurricanes

in the area of interest for the site being considered. For t = 1,

P(V < V, t) = probability of occurrence of wind speeds less than

V in any one year

12
Consider now the wind speed . Its probability of occurrence can be

written as

Thus

P(V < VI, 1) = e ^ (12)

The estimated mean recurrence interval of the speed v^^ is then

N i (13)

1-e

3.2 NUMERICAL RESULTS

3.2.1 Extreme Wind Speeds

Hurricane fastest-mile wind speeds at 10m above ground over open terrain

were estimated for 58 mileposts (from 150 through 3000 in increments of

50 - see Figure 1) at the coastline, and at 25 km, 50 km, 100 km and

200 km inland. The results of the calculations were smoothed as follows.

For each milepost the average was calculated of the fastest-mile wind

speeds at that milepost and at its two neighboring mileposts [located

each at 50 n.mi. (93 km) from it]. This averaging was done, for each

milepost, at the coastline, as well as at 25 km, 50 km, 100 km, and

200 km inland. A least-squares straight line was fitted at each milepost to the five averages thus obtained. The ordinates of this line at

the coastline and at 200 km inland represent the values given by the curves of Figures 5 and 6, respectively. Extreme fastest-mile speeds

at distances inland of less than 200 km from the coastline may be

obtained by linear interpolation between Figures 5 and 6. It is noted

that the values of Figures 5 and 6 differ by at most a few percent from

the corresponding unsmoothed values originally calculated for the coastline locations.

The results shown in Figures 5 and 6 represent smoothed estimates of

hurricane wind speeds without regard to direction. As previously

indicated, similar results were obtained for winds blowing in specified

directions. Estimates of coastline fastest-mile hurricane wind speeds

at 10 m above ground over open terrain, smoothed by averaging results

obtained for three consecutive milestone positions, are plotted in

Appendix A as a function of direction. Note that the number of storms

associated with strong winds blowing in specified directions is in

certain cases very small. It was therefore not possible in those cases to estimate wind speeds corresponding to relatively short mean recurrence intervals. This is reflected by the blank portions of some of the curves of Appendix A.

13
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Errors in the estimation of extreme hurricane wind speeds are dealt

with in the subsequent section. It is noted here that these errors increase as the mean recurrence interval increases. Therefore, estimates of wind speeds corresponding to mean recurrence intervals

exceeding 100-yr, say, may contain significant errors. Nevertheless,

such estimates obtained by the procedure used in this paper are of

interest as they provide the only available basis for assessing the

validity of wind load factors currently being used for structural

design purposes in hurricane-prone regions.

3.2.2 Probability Distributions of Hurricane Wind Speeds

The results obtained from the calculations were used to estimate probability distributions of hurricane wind speeds (blowing from any direction). It was found, by using the probability plot correlation

coefficient method, that in all cases the best fitting distribution

for the 1-minute speeds was the Weibull distribution with tail length

parameter Y > 4 (for practical purposes Y = 4 can be assumed, the

differences between results based on Y = 4 and Y > 4 being negligible).

As an illustration, the results obtained at milepost 450 [1-minute

wind speeds at coastline over water, in knots (1 knot ~ 1.9 km/hr)] are plotted on Weibull(Ys4) and Extreme Value Type I probability paper

on Figures 7 and 8, respectively. It is seen that the results fit

the Extreme Value Type I distribution poorly, i.e., the results do

not fit a straight line on Fig. 8, as they do on Fig. 7.

3.3 MIXED PROBABILITY DISTRIBUTIONS OF HURRICANE AND NON-HURRICANE

WIND SPEEDS

Mixed probability distributions of hurricane and non-hurricane fastestmile (as opposed to 1-minute) wind speeds were estimated by using the

following expression:

P(V < V) = Pjj (Vjj < v)-Pnh(Vnh < V) (14)

in which Pjj (Vjj < v) = cumulative distribution of hurricane wind speeds

Vjj, and Pj^jj ^^NH ^ ^) ~ cumulative distrtibution of non-hurricane wind

speeds, Vjj^j. The distribution Pj^ was determined as shown in this report.

For the distribution Pfjjj, an Extreme Value Type I distribution was

assumed. The parameters of Pjjjj were estimated at various locations from

maximum annual wind speed data that did not include hurricane wind

speeds. The results of the calculations showed that the effect of the

non-hurricane winds is negligible for mean recurrence intervals of the

order of 50 years or more (see Fig. 9). For mean recurrence intervals

of about 20 years, the estimated wind speeds that include the effect

of non-hurricane winds exceed the estimated hurricane speed by about

5%. Note that these conclusions are not applicable north of Cape

Hatteras, where non-hurricane wind may control the design at certain

locations

16
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19
Facing page: Damage caused by Cyclone Taray in Darwin, Australia.

20
4. ESTIMATION ERRORS

The errors in the estimation of hurricane wind speeds by the procedure

used in this work may be divided into four categories: (1) sampling

errors , due to (a) the limited size of the data sample used in making

statistical inferences on the climatologogical characteristics of

hurricanes (in the United States these data samples correspond to

lengths of record of 75 to 100 years), and (b) the limited number of

hurricanes generated by the Monte Carlo simulation; (2) probabilistic

modeling errors , due to the imperfect choice of the distribution

functions to which the climatological data are fitted (e.g., assuming

that a lognormal distribution holds when in fact a normal distribution

would be more appropriate); (3) observation errors , due to the imperfect measurement or recording of the true values of the climatological

characteristics; and (4) physical modeling errors , due to the imperfect

representation of the dependence of the wind speed upon the various

climatological characteristics and micrometeorological parameters.

4.1 SAMPLING ERRORS

As shown in some detail in Reference 1, the standard deviation of the errors associated with the limited size of the climatological data

samples (corresponding to about 75 to 100 years of record) is of the

21
order of 6% to 10% of the estimated wind speeds, while the standard

deviation of the errors due to the limited number, m, of hurricanes

used in the simulation is of the order of a few percent for m j, 1,000.

In some cases, say, at Jacksonville, Florida, the poorly understood

and seemingly anomalous occurrence histories may lead to larger errors

than are typical of the model overall. Part of the sampling errors due

to the limited number of hurricanes used in the simulation is eliminated by the use of the smoothing procedure described previously.

4.2 PROBABILISTIC MODELING ERRORS

To assess the effect of various probabilistic models used in the simulation, calculations were carried out at mileposts 400, 1450 and 2100

(see Figure 1) under the following assumptions:

a. Distribution of aP is normal. This assumption results in a max decrease of the 50-yr, 100-yr, and 400-yr wind speeds with respect to the corresponding values based on the assumption of

lognormality by about 5%, 5%, and 8%, respectively.

b. Distribution of R is normal. This assumption results in an increase of the 50-yr, 100-yr, and 400-yr wind speeds with

respect to their corresponding values based on the assumption

of lognormality by about 1%, 2%, and 6%, respectively.

c. Distributions of APmax ^ both normal. This assumption

results in a decrease of the 50-yr, 100-yr, and 400-yr wind

speeds with respect to their corresponding values based on the

assumption that APmax ^^'^ ^ both lognormally distributed

by about 3%, 3%, and 4%, respectively.

d. Distribution of s is lognormal. The differences between estimates of wind speeds based on this assumption on the one hand,

and on the assumption that s is normally distributed on the

other hand, are negligible for practical purposes.

e. Distribution of ap is not censored. The censoring of the ^ max ° distriibution of APmax ^ ^^max 101 -6 mm) reflects the writers'

belief that this upper bound is dictated by physical considerations, and that an unbounded distribution would thus be

physically unrealistic. Nevertheless, calculations were carried

out for five stations in which it was assumed that the lognormal

distribution of ap is unbounded. It was found that the max estimated hurricane wind speeds and their cumulative distribution

functions were for practical purposes the same regardless of

whether the condition .p 101.6 mm was assumed or not.

22
A final observation with regard to the choice of probabilistic models

concerns the representation of the hurricane occurrences as a Poisson

process. It can be shown that this model could be replaced, e.g., by

a geometric probability model, without any significant effect upon the

estimated results, particularly for winds with mean recurrence intervals of the order of 20 years or more.

4.3 OBSERVATION ERRORS

To assess the effect of possible errors in the measurement (or re- cording) of the parameters ^P„„„ and R, calculations were carried out

at mileposts 400, 1450, and 2100 (Figure 1) in which it was assumed

that the mean and/or standard deviation of ^P^iax ^ larger

than those estimated from the data of Reference 5. Increasing both

the mean and the standard deviation of ^p by a factor of 1.1 resulted

max

in an increase in the estimated values of the 50-yr, 100-yr, and 400-yr

winds of about 5% at milepost 400, 8% at milepost 1450, and 10%

at milepost 2100. Leaving the mean unchanged and increasing the standard deviation by a factor of 1.1 resulted in an increase of the estimated speeds of the order of a few percent. The effect of increasing

or decreasing the mean and/or the standard deviation of the radii of

maximum wind speeds, R, by a factor as high as 1.5 was of the order

of a few percent at most<

As previously indicated, the data used in this report were obtained

from Ref . 5. The estimation of hurricane wind speeds at various locations could presumably be improved by using additional sources of

climatological information, e.g., those available in the archives

of the Corps of Engineers. The writers believe that this is the case particularly for South Texas, Louisiana, southwest Florida and Jacksonville .

Note that estimated hurricane wind speeds are lower at mileposts 1000

and 1750 (Figures 1, 5, and 6) than in the regions adjacent to these

mileposts. This may be due to the relation between configuration of

the coast and the hurricane paths. However, it may be that hurricanes

at and near these mileposts were underreported in the past. It appears

therefore prudent to increase the wind speeds calculated at mileposts

1000 and 1750 by about 5 mph or 10 mph. Finally, it was found that

the storm decay overland was very weak at mileposts 650 and 2250.

This is due, at least in part, to the configuration of the coast at

these mileposts, although the spurious occurrence of strong simulated

storms may also have contributed to this result.

4.4 PHYSICAL MODELING ERRORS

The coefficient K in Equation 3, the coefficients of Equation 4, and

the dependence of wind speeds upon radius represented in Figure 4,

have been determined empirically by the National Weather Service on

23
the basis of careful correlations of pressure and wind speed measurements. Clearly, the corresponding physical model of the hurricane wind

field is, nevertheless, imperfect. It is the writers' belief, based,

e.g., on information from Reference 6, that the standard deviation of

the errors inherent in this model is of the order of 5% to 10%.

It was noted previously that the coefficient K assumed in this work may

be used in conjunction with the value p^ = 756 mm (29.77 in). To check

the effect on the calculated results of the assumption p^ = 760 mm

(29.92 in), calculations based on this assumption were carried out at

mileposts 400, 1450, and 2100. It was found that differences between

results based on p^ = 756 mm and p^ = 760 mm were of the order of 3%.

It was also noted that results based on the model for storm decay used

in this work (Equation 6) were compared with results based on Malkin's

model, which is consistent with measurements reported in Reference 7.

The differences between the two sets of results were in all cases small

(of the order of + 2%).

In estimating wind speeds over water immediately off the shoreline it was assumed that the roughness length parameter corresponds to "flow

over water" conditions in all directions (this will be referred to as "surface friction hypothesis I"). In reality, each location immediately

offshore is affected not only by hurricane winds which blow from the

ocean (and for which "flow over water" conditions prevail), but also

by hurricane winds blowing from inland, for which the assumption that

a roughness length corresponding to "flow over open terrain" conditions

may have to be used. The hypothesis that the roughness length depends

upon whether the winds flow from the ocean or from land will be re- ferred to as "surface friction hypothesis II". Whether or not "surface

friction hypothesis II" is warranted is by no means always certain:

indeed, near the shoreline the terrain is likely to be flooded during

the occurrence of hurricanes. Nevertheless, it is of interest to check

the differences between results based on surface friction hypotheses I and II. Calculations carried out at mileposts 400, 850, 1450, 2100, and

2800 showed that estimated wind speeds corresponding to hypothesis II

were lower than those based on hypothesis I by an amount generally not

exceeding 3%.

Local wind intensification due to the presence of rainbands occur at

all locations south of the 30° north parallel. These intensifications

might have to be be accounted for by increasing the wind speeds calculated herein by as much as 10 mph (4.47 m/s) or so.

As previously noted, the physical models used in this report, and

particularly the storm decay model, provide a description of the wind

field that is probably less accurate at sites located north of Cape

Hatteras, N.C., (mileposts 2200 or more, see Figure 1). The numerical

results obtained for these sites should therefore be viewed very

cautiously

24
The physical model of the hurricane wind speeds may be refined by using

a detailed representation of the coastline and Its adjacent bodies of

water. Such refinements may result in an Improvement of hurricane wind

speed estimate by an amount of the order of 5% or so.

Additional refinements might include accounting for slower storm decay

where large bodies of water are present inland, e.g., in the low- lying areas of Louisiana. Additional research is required to develop Improved

storm decay models in such situations.

25

i
Facing page: Damage caused by Hurricane Camille.

26
5. CONCLUSIONS

In this paper, estimates are presented of hurricane wind speeds along

the Gulf and East Coasts of the United States. The paper describes the sources of data, the probabilistic models for the climatological characteristics of hurricanes and the physical models for the hurricane wind

speed field used in the estimations. Estimated values of fastest-mile

hurricane wind speeds at 10 m above ground in open terrain at the

coastline and at 200 km inland are given for various mean recurrence intervals (Figures 1, 5, and 6). Fastest-mile wind speeds at distances

inland of less than 200 km from the coastline may be obtained by

linear interpolation between these values. It was found that the

estimated hurricane wind speeds are best fit by Weibull distributions

with tail length parameters y > A, rather than, e.g., by Extreme Value

Type I distributions. Estimates are given of various errors inherent

in the estimated values of the hurricane wind speeds. The confidence

bands for the estimates were found to be of the order of at least + 10% at the 68% confidence level. It was also noted that, owing to

the possible inapplicability of the physical models used in this work

at locations north of Cape Hatteras, estimated hurricane wind speeds

27
given for these locations should be viewed with considerable caution.

In certain special cases it may be desirable to base estimates of

hurricane wind speeds on more elaborate data, physical models, and

representations of the coastline than those used in this work. Nevertheless, in the writers' opinion, the results presented in this paper

provide a rational and consistent basis for making realistic decisions

on the specification of design wind speeds and load factors in

hurricane - prone regions.

28
REFERENCES

1. Batts, M. E., Cordes, M. R. , and Simiu, E., "Sampling Errrors In

Estimation of Extreme Hurricane Winds," Proc. of the 3rd Engineering Mechanics Division Specialty Conference, Sept. 17-19, 1979,

Austin, Texas.

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

Change of Terrain Roughness," Journal of the Structural Division , ASCE, Vol. 104, No. STIO, October 1978, pp. 1585-1595.

3. Cry, G. W. , Tropical Cyclones of the North Atlantic Ocean-Tracks

and Frequencies of Hurricanes and Tropical Storms , 1871-1963,

Technical Paper No. 55, U.S. Dept. of Commerce, Weather Bureau,

Washington, D.C., 1965.

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, the University of Sydney,

February, 1976.

5. Ho, F. P., Schwerdt, R. W., and Goodyear, H. V., Some Climatological Characteristics of Hurricanes and Tropical Storms, Gulf and

East Coasts of the United States , NOAA Technical Report NWS15,

Washington, D.C., May 1975.

6. Holliday, C, On the Maximum Sustained Winds Occurring in Atlantic

Hurricanes , Tehnical Memorandum No. WBTM-SR-45, U.S. Dept. of

Commerce, Environmental Sciences Services Administration, Weather

Bureau, Fort Worth, Texas, 1969.

7. Malkin, W. , Filling and Intensity Changes in Hurricanes on Land , National Hurricane Research Project, Report No. 34, U.S. Dept. of

Commerce, Washington, D.C., November 1959.

8. Revised Standard Project Hurricane Criteria for the Atlantic and

Gulf Coasts of the United States , Memorandum HUR7-120, U.S. Dept.

of Commerce, NOAA, June 1972.

9. Russell, L. R. , "Probability Distributions for Hurricane Effects,"

Journal of the Waterways, Harbors, and Coastal Engineering

Division , ASCE, Vol. 97, No. WWl, February 1971, pp. 139-154.

10. Simiu, E., and Scanlan, R. H. , Wind Effects on Structures , WileyInterscience, New York, N.Y. , 1978.

11. Sklarin, J., Stochastic Analysis of Hurricane Wind Loads (Harman,

T.G., and Cornell, C.A., supervisors). Report R77-2, Order No.

563, Department of Materials Science and Engineering, Massachusetts

Institute of Technology, Cambridge, Mass, Jan., 1979.

29

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

Windinduced Response in Hurricane Zones," Journal of the Structural

Division , ASCE, Vol. 102, No. ST12, December 1976, pp. 2333-2350.

Windstorms in California , State of California, Department of Water

Resources, Sacramento, California, Dec, 1979.

Worldwide Extremes of Temperature, Precipitation and Pressure

Recorded by Continental Area , ESSA/PI680032 , Environmental Data

Service, U.S. Department of Commerce, October, 1968.

30
APPENDIX A

HURRICANE WIND SPEEDS BLOWING FROM SPECIFIED DIRECTIONS FOR lO-YR,

50-YR, and lOO-YR MEAN RECURRENCE INTERVALS

Notes

1. For key to mean recurrence interval symbols, see bottom of next page.

2. Ordinates represent estimated fastest-mile mean speeds in mph

(1 mph = 0.4A7 m/s).

3. Abscissas represent clockwise angles of directions from which winds

are blowing with respect to north.

A-1
A-2
A-3
A-4
A-5
A-6

-I 1 1 1 1 1 t > T I t t » I I

I I I I I I I I I I I I M IM

RILE POS-f 19M

Zft 360 NIU POST 2«M

IM

IM

IM

M'

I * ! T T < I I

I < I M lie 87* NIU POST 2tM

-rH

3M 1—I I i 1 I I < t I I I

I I I I PIU POST CiM

tat

tM

IM

IM

M'

MT 1

1 I » I I I I I I < T I I < • M tM 27* «

PIU POST 21M

T 1 1 1—r—T

1 I T I 1 1 I f—r- IM

niU POST IMO

2'>e 3«<

A-8
A-9
A-10
A-11

GOVERNMENT PfilNTING OnCE . 1W 0-31 1-046 (6S)
NBS-114A (REV. 9-78)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

PUBLICATION OR REPORT NO. BSS 124l.Oov't Accessfw No.

4. TITLE AND SUBTITLE

Hurricane Wind Speeds in the United States

5. Publication Date May 1980

$. Perfomifftg Organization Code

7. AUTHOR(S) Martin E. Batts, Martin R. Cordes, Larry R. Russell, James R. Shaver, and Emil Simiu

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

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11. Contract/Grant No. NSF Grant No. ENV77-

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15. SUPPLEMENTARY NOTES

Library of Congress Card Catalog Number: 80-600039

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

16. ABSTRACT (A 200-word or less (actual summary ol most significant information. It document includes a significant bibliography or

literature survey, mention it here,) A Monte Carlo simulation technique is used to obtain estimates of hurricane wind

speeds in the Gulf and East Coasts of the United States. The paper describes the sources of data, the probabilistic models for the climatological characteristics

of hurricanes, and the physical models for the hurricane wind speed field used in

the estimations. Estimated values of fastest-mile hurricane wind speeds at 10 m

above ground in open terrain at the coastline and at 200 km inland are given for

various mean recurrence intervals. The estimated hurricane wind speeds were found

to be best fitted by Weibull distributions with tail length parameters y > U. Estimates are given of various errors inherent in the estimated values of the

hurricane wind speeds. Owing to uncertainties with respect to the applicability

of the physical models used in this work to locations north of Cape Hatteras,

estimated hurricane wind speeds given for these locations should be viewed with

caution.

17. KEY WORDS fsi'x to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons) Building (codes); climatology: hurricanes, statistical analysis;

structural engineering; tropical cyclones; wind (meteorology).

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