Extreme Wind Speeds in the Kingdom of

Saudi Arabia

by

A. M. Arafah1, G. H. Siddiqi2 and A. Dakheelallah3

ABSTRACT

Extreme value analysis of wind data in the Kingdom of

Saudi Arabia is described. Probabilistic models of wind

behavior at twenty stations are generated which yield the

basic design wind speeds for a given recurrence interval

in fastest mile units. The models are verified by the Chi-

square and Kolmogorov-Smirnov goodness-of-fit tests at 5

percent significance level. Basic design wind speeds are

calculated at each station and an isotach map of design

speeds for a 50 year mean reccurrence interval is

presented. The information obtained allows evaluation of

design wind loads by the ANSI A58.1 procedure.

___________________

1Asistant Professor, Department of Civil Engineering, College of Engineering, Riyadh, Saudi Arabia.

2Associate Professor, Department of Civil Engineering, College of Engineering, Riyadh, Saudi Arabia.

3Postgraduate Student, Department of Civil Engineering, College of Engineering, Riyadh, Saudi Arabia.

INTRODUCTION

Wind loads, among the other design loads, are crucial

for the design of structures such as tall buildings,

towers, radar and communication antennas. This paper

considers the reliability and homogeneity aspects of the

wind data and studies the distribution of extreme annual

wind speeds over the Kingdom of Saudi Arabia to obtain a

rational basis for the evaluation of wind induced loads

according to American National Standards Institute's Code

for design loads, ANSI A58.1-19821.

RELIABILITY AND HOMOGENEITY OF DATA

In order for the wind speed data to provide useful

information it must be reliable and form a homogeneous

set.

Measured data are considered reliable if the

recording instruments are adequately calibrated and are

not exposed to local effects due to proximity of

obstructions. However, if at any time in future the

calibration is found to be inadequate, it is possible to

evaluate the corrections and adjust the data.

Measured data form a homogeneous set when they are

obtained under identical conditions of averaging time,

height above ground and roughness of the surrounding

terrain.

Averaging Time

The data averaged over short intervals, like highest

gust, 5 second average etc., in certain cases, can be

affected by stronger than usual local turbulence, which

results in distorted picture of the mean winds. Averaging

over longer periods like 5 or 10 minutes is, therefore,

desirable.

Anemometer Height above Ground

Height of 10 m above gorund is considered to be the

standard instrument height. Wind data measured at any

other height are adjusted to the standard height by power

law2 . The values of exponent in the power law for

different "exposures" are available in literature2.

Specifically for meteorological stations, which are

invariably located in open country, the exponent is one-

seventh.

Roughness of Surrounding Terrain

The measured data are affected by the roughness of

the surrounding terrain. In case the roughness around an

anemometer changes significantly during the period of

record under consideration, it is possible to adjust the

measured record to a common terrain roughness by using

similarity model9.

DESIGN WIND FORCES

Basic Design Wind Speed

Basic design wind (BDW) speed is defined as the

maximum expected annual wind speed at the standard height

of 10 meters above ground in open country over a chosen

recurrence interval. This speed is established by extreme

value analysis of the instrumental data of maximum annual

wind collected from meteorological stations over a

geographical region.

American National Standards Institute's code for

design loads, ANSI A58.1-19821, employs fastest mile wind

(FMW) speed as the BDW speed. FMW speed is the maximum

annual wind speed at which a one mile long column of wind

passes by an anemometer.

Isotach Map

An individual extreme value model for a station

predicts the BDW speeds at various recurrence intervals at

the station. The speeds at a network of stations form the

three dimensional input data to a contouring software

which plots isotachs (lines of equal wind speed) over the

geographic region. BDW speed at a chosen location can be

interpolated from this map.

Wind Induced Forces

Most codes translate the BDW speed to an equivalent

static wind load intensity which varies over the height of

a given structure. This procedure accounts for type of

"terrain exposure" facing the structure, shape and form of

the structure, and its "importance" and other related

factors.

DATA PROCESSING

The data comprising of the largest annual wind speeds

available with the Meteorological and Environmental

Protection Agency (MEPA) include records varying over

periods of three to thirty three years measured at twenty

eight stations well distributed over the Kingdom. Twenty

of these stations have records over a continuous duration

of fifteen or more years which is desirable for the

probabilistic analysis involved here. These stations

along with the anemometer heights and duration of their

record are listed in Table 1 and considered in this study.

It is presumed that the anemometers at all the

weather stations in the Kingdom are situated in open

country environments throughout their period of commission

and that they are well maintained and adequately

calibrated. However, if at any time in future, it is

determined that the calibration was not adequate, height

of instrument or the

Table 1. Profile of Wind Monitoring Stations in the Kingdom

-------------------------------------------------------- Station Station Anemometer Years of No. Name Height (m) Continuous Records -------------------------------------------------------- 1 Badanah 6 19 2 Bisha 6 20 3 Dhahram 10 26 4 Gassim 7 23 5 Gizan 8 22 6 Hail 8 26 7 Jeddah 10 19 8 Jouf 7 19 9 Kamis Mushit 9 23 10 Madina 10 26 11 Najran 8 15 12 Hafer-Albatian 8 19 13 Riyadh 10 26 14 Rafah 12 18 15 Sulayel 10 20 16 Tabouk 9 26 17 Taif 8 26 18 Turaif 8 17 19 Wajeh 10 26 20 Yanbu 10 23 21 AL-Ehsa 10 4 22 Abha 10 8 23 Baha 10 6 24 Gurayat 10 5 25 Jeddah (KAIA) 10 7 26 Mekkah 10 9 27 Riyadh(KKIA) 10 5 28 Sharurah 10 5 ------------------------------------------------------

terrain roughness did change, the corrections can be

evaluated and the data adjusted accordingly.

The measured annual wind speeds at all the stations

are averaged over ten-minute duration. The ten-minute

speed in knots is converted to ten-minute speed in miles

per hour. The averaging time for conversion of this speed

to FMW speed is obtained by an iterative procedure, and is

used to derive the desired fastest mile2. This speed, in

case of non-standard instrumental heights, is then reduced

to the standard height by power law.

EXTREME VALUE ANALYSIS

Extreme Value Distributions

The theory of extreme values has been successfully

used in civil engineering applications. Floods, winds,

and floor loadings are all variables whose largest value

in a sequence may be critical to a civil engineering

system3. In case of well behaved climates (i.e. ones in

which infrequent strong winds are not expected to occur)

it is reasonable to assume that each of the data in a

series of the largest annual wind speeds contributes to

the probabilistic behavior of the extreme winds.

The design wind speed can be defined in probabilistic

terms, where the largest wind speed in a year is

considered as a random variable with its cumulative

density function characterizing its probabilistic

behavior.

A commonly used distribution in extreme value

analysis is the double exponential distribution in which

an annual wind speed record, Xi, is considered to be a

random variable in the i-th year. For n successive years,

variables Xi are assumed to be mutually independent and to

have identical distributions. Supposing that random

variables Xi are unlimited in the positive direction and

that the upper tail of their distribution falls in an

exponential manner then variable V, the largest of n

independent variables Xi, has Type I (Gumbel) extreme

distribution, FV (υ) , as follows,

FV (υ) = exp [ - exp ( - خطأ! ) ] , (1)

where α and u are the scale and location parameters and estimated from the observed data at each station. The

distribution function FV(υ) is the probability of not

exceeding the wind speed υ.

The Type II (Frechet) extreme-value distribution also

arises as the limiting distribution of the largest value

of many independent identically distributed random

variables. In this case each of the underlying variables

has a distribution which, on the left, is limited to zero.

The Type II distribution function, FV (υ) , is,

FV (υ) = exp [ - ( خطأ! )خطأ! ] , (2)

where the parameters ω and γ are estimated from the

observed data at each station. The parameter, γ , is known

as the tail length parameter3.

Based on the method of order statistics developed by

Lieblein13, the values of cumulative density function,

FV(υ), corresponding to a series of extreme annual wind

speeds, can be estimated as follows,

FV(υ) = (3) !خطأ

where n is the number of years of record and m(υ) is rank

of the event, υ, in the ascending order of the magnitudes.

The inverse function of FV(υ) is known as the

percentage point function (PPF) which gives the value of

wind speed υ at a sellected value of FV(υ). For Type I

(Gumbel) extreme distribution the PPF is,

υ(F) = u + α y(F) (4)

which is a linear relation between υ(F) and the

intermediate variate y(F) which is given by,

y(F) = - ln(- ln F) (5)

Relation between the Two Distributions

The Type II distribution with small values of tail

length parameter results in higher estimates of the

extreme wind speeds than the Type I distribution. It can

be shown that for values of parameter γ equal to 15 or more the two distributions, Type I and II , are almost

identical4. It can also be shown that if V has Type II

distribution then Z = ln V has the Type I distribution

with parameters u = ln ω and α = ( 1/γ ). This relationship affords use of Type I probability paper for Type II

distribution also3.

Errors in Prediction of Wind Speeds

Errors are inherent in the process of wind speed

prediction. Besides the errors associated with the

quality of the data, there are sampling and modeling

errors.

The sampling errors are a consequence of the limited

size of samples from which the distribution parameters are

estimated. These errors, in theory, vanish as the size of

the sample increases indefinitely9. A sample size of 15 or

more, at a station, employed in this study is adequate in

this regard.

The modeling errors are due to inadequate choice of

the probabilistic model. Chi-square and K-S Test are

performed to choose the best fitting model.

Probabilistic Wind Models in Use

One major question that arises in the wind speed

extreme value analysis is the type of probability

distribution best suited for modeling the behaviour of the

extreme winds. Thom5 studied the annual extreme wind data

for 141 open country stations in the United States. The

Type II distribution was chosen to fit the annual extreme

wind series giving isotach maps for 2, 50 and 100-year

mean recurrence intervals.

Thom6 also developed new distributions of extreme

winds in the United States for 138 stations. New maps were

drawn for 2-year, 10-year, 25-year, 50-year and 100-year

mean recurrence intervals. In his study, Thom used the

Type II (Frechet) distribution. He indicated that

examination of extensive non-extreme wind data indicated

that such data follow a log-normal distribution quite

closely, which reinforces the choice of the Type II

distribution.

Simiu7 presented a study in which a 37 year-series of

five- minute largest yearly speeds measured at stations

with well-behaved climates were subjected to the

probability plot correlation coefficient test to determine

the tail length parameter of the best fitting distribution

of the largest values. Of these series, 72% were best

modeled by Type I distribution or equivalently by the Type

II distribution with γ=13; 11% by the Type II distribution with 7<γ<13; and 17% by the Type II distributions with

2<γ<7. Simiu8 obtained the same percentages from the

analysis of 37 data sets generated by Monte Carlo

simulation from a population with a Type I distribution

which indicates that in well-behaved climates extreme wind

speeds are well modeled by Type I rather than Type II

distributions.

Simiu4 showed that the Type I distribution of the

largest values is an adequate representation of extreme

wind behaviour in most regions not subjected to hurricane-

force winds. Simiu9 indicated that for hurricane-prone

regions the Type II distribution with a small value of the

tail length parameter may give better estimation of

extreme wind speeds.

The ANSI #A58.1-821 wind load provision is based on a

wind speed contour map developed by Simiu10. The wind

speeds in the map were established from the data collected

at 129 meteorological stations in the contiguous United

States. The Type I (Gumbel) distribution is used in the

analysis. Simiu used data only for locations for which a

minimum of 10 years of continuous records were available11.

The provisions of National Building Code of Canada12

are also based upon the assumption that extreme wind speed

is best modeled by the Type I distribution.

STEPS OF EXTREME VALUE ANALYSIS

The determination of appropriate distribution type

involves the following steps,

1) the annual extreme wind speeds records at each

station are first corrected for the standard

anemometer height, terrain exposure, and the

averaging time,

2) the data, for each station, are then arranged in an

ascending order. The corresponding values of the

CDF are calculated from Eq.3 ,

3) the intermediate parameter, y, is calculated using

Eq. 5,

4) linear regression analysis is performed between

values of υ and the corresponding values of y, to estimate values of parametrs u and α in Eq. 4. such an analysis for Madian is shown in Fig. 1 as a

sample,

5) the Chi-Square ,χ 2, test with 95 percent confidence level is performed for model verification,

6) steps 4 and 5 are repeated using ln (V) in place of

V,

7) based on the distribution of the data on the

modified extreme Type I probability paper and on

the minimum value of χ 2 , the more appropriate

model for the wind speed data is selected, and

8) in case of the Type II distribution, the parameters

ω = eu and γ = (1/α) are also calculated.

RESULTS OF EXTREME VALUE ANALYSIS

The extreme value analysis is performed on the wind

speed data of the 20 stations which have fifteen or more

years of continuous record. The extreme distribution models

obtained are presented in Table 2. As seen in the table, at

fifteen stations wind speed data are best modeled by the

Type I distribution and the remaining five stations they

follow the Type II distribution.

As a specific example of analysis, Fig. 1. presents the

fastest mile annual extreme wind speed data for Madina

Station ploted on the Extreme Type I propability paper.

The appropraite model is found to be,

V = 45.34 + 9.75 y

Table 2 Extreme Value Models of Fastest Mile Speed in Mile per Hour at 20 Stations in the Kingdom of Saudi Arabia

----------------------------------------------

Station Type u (ω) α (γ)

(1) (2) (2)

----------------------------------------------

Badana I 59.54 11.37

Bisha I 51.16 8.73

Dhahran I 45.95 4.90

Gassim I 63.19 11.59

Gizan I 53.48 11.59

Hail II 53.52 7.99

Jeddah I 48.59 6.44

Jouf I 56.88 7.09

Khamis-Mushiat I 42.05 7.58

Madina I 45.34 9.87

Najran II 47.94 8.03

Hafer-Albatin I 57.46 6.66

Riyadh II 51.98 7.57

Rafah I 55.26 7.27

Sulayel II 51.22 6.55

Tabuk II 54.54 8.05

Taif I 51.36 8.68

Turaif I 56.53 8.19

Wajh I 47.17 8.21

Yanbu I 46.58 6.68

---------------------------------------------- (1) Extreme value distribution type. (2) In case of the Type II distribution, the values

listed belong to the parameters within the parentheses in the column heading.

which means,

FV(υ) = exp [ - exp ( - ( خطأ! ) ) ]

On the other hand, in Riyadh, the fastest mile annual

extreme wind speeds were found to be best modeled by

extreme Type II given by,

Fv(υ) = exp [ - ( خطأ! )خطأ! ]

MODEL VERIFICATION

The models obtained are checked by the Chi-square and

Kolmogorov-Smirnov (K-S) goodness-of-fit tests at 5 percent

significance level. The calculated values of the statistic

D1 for the Chi-Square and D2 for Kolmogrov-Smirnov

goodness-of-fit tests are listed in Table 3 along with the

corresponding critical values, D1c and D2c , at 5 percent

significance level. The results indicate that the

calculated values of D1 are below the critical values at

sixteen stations. At the remaining four stations, Dhahran,

Jouf, Hafer Al-batin and Yanbu, they however, exceed the

critical limits. Such a result, when several events are

clustered in one wind speed interval, is expected in Chi-

square analysis. On the other hand, the calculated values

of statistic D2 are less than the critical values at all

the stations which indicates that the models are acceptable

at 95 percent confidence level.

Table 3 Calculated and Critical Values of Statistics D1

and D2 at 5 percent Significance Level.

------------------------------------------------------------- Chi-Square Test Kolmogorov-Smirnov Test ---------------------------------------------- Station D D D D 1 1c 2 2c-------------------------------------------------------------

Badana 2.087 11.07 0.0835 0.300

Bisha 1.493 11.07 0.0791 0.290

Dhahran 19.110 11.07 0.1541 0.256

Gassim 4.163 11.07 0.0748 0.272

Gizan 5.247 11.07 0.1414 0.278

Hail 5.903 11.07 0.1177 0.256

Jeddah 3.169 11.07 0.1569 0.300

Jouf 16.558 11.07 0.1368 0.300

Khamis-Mushiat 9.310 11.07 0.0929 0.272

Madina 3.661 11.07 0.1529 0.256

Najran 7.949 11.07 0.1625 0.340

Hafer-Albatin 22.741 11.07 0.1346 0.300

Riyadh 10.215 11.07 0.2198 0.256

Rafah 9.255 11.07 0.1463 0.310

Sulayel 7.234 11.07 0.1074 0.290

Tabuk 10.376 11.07 0.1054 0.256

Taif 5.345 11.07 0.1122 0.256

Turaif 4.313 11.07 0.1136 0.320

Wajh 4.547 11.07 0.1377 0.256

Yanbu 17.608 11.07 0.1228 0.272

-------------------------------------------------------------

EXTRAPOLATION OF WIND SPEED MODELS

At any station, the extreme wind speed at a particular

annual probability of exceedance, Pa, can be calculated

using the corresponding wind speed model. The mean

recurrence interval or return period, N, is defined as

N = (6) !خطأ

If a structure has a life span of n years, then for a

specific wind with a return period of N years, the

percentage risk, which expresses the probability that this

design wind is exceeded at least once during the lifetime

of the structure, is given by

Pr = 1 - [ 1 - Pa ]

n = 1 - [ 1- خطأ! ](7) !خطأ

If the return period is taken to be the same as the

lifetime of the structure, there is always a risk of

63% that this speed is exceeded at least once during the

lifetime of the structure.

The mean recurrence interval or the return period for

specified accepted risk percentage and design service

lifetime of the structrue is given as,

N = (8) !خطأ

ANSI A58.1-821 specifies that a basic design wind speed

corresponding to a 50-year mean recurrence interval should

be used in designing all permanent structures. However,

the structures with an unusually high degree of hazard to

life and property in the case of failure, are to be

designed for a 100-year mean recurrence interval while the

structures having no human occupants or where there is

negligible risk to human life, are to be designed for a

25-year mean recurrence interval.

Based on a given set of observed annual wind speeds, the

principal output from this procedure is the estimated wind

speeds, VN, for various mean recurrence intervals. Wind

speeds at 25, 50, 100, and 475 years return period are

listed in Table 4. The return period of 475 is calculated

using 50 year design lifetime of the structure and 10

percent accepted risk.

PLOTTING OF ISOTACHS

Isotachs for given recurrence intervals are plotted over

the geographic map of the Arabian peninsula from the

estimated extreme winds of twenty stations. A contouring

software is employed to plot the isotachs. The software

first generates information on a regularly spaced grid

from the irregular grid information supplied to it and

then develops a best fitting surface over the grid. The

fifty year return period wind speed contour map is plotted

in Fig.2.

CONCLUSIONS

In this study, appropriate extreme wind distribution

models for the largest yearly fastest-mile wind speed at

20 weather stations in the Kingdom are developed. The

analysis of the data revealed that the probabilistic

behavior of the series of the largest annual winds at

fifteen of the twenty stations can be described by the

Type I extreme distribution while at the remaining

stations by the Type II distribution. An isotach map for

50-year recurrence intervals is developed

Table 4. Fastest-Mile Design Wind Speed (MPH) at

Weather Stations for Different Mean Recurrence

Intervals.

----------------------------------------------------- Mean Recurrence Interval, years Station ------------------------------------ 25 50 100 475

-----------------------------------------------------

Badana 95.9 103.9 111.8 129.6

Bisha 79.1 85.2 91.3 104.9

Dhahran 61.6 65.1 68.5 76.1

Gassim 99.3 107.2 115.1 132.7

Gizan 90.6 98.6 106.8 124.9

Hail 79.8 87.2 95.2 115.8

Jeddah 69.2 73.7 78.2 88.3

Jouf 79.6 84.5 89.5 100.5

Khamis-Mushiat 66.3 71.6 76.9 88.4

Madiah 76.9 83.83 90.7 106.1

Najran 71.4 77.9 85.0 112.0

Hafer-Albatin 78.8 83.4 88.1 98.5

Riyadh 79.3 87.0 95.4 117.3

Rafah 78.5 83.6 88.7 100.0

Sulayel 83.4 92.9 103.3 131.1

Tabuk 81.1 88.5 96.6 117.2

Taif 79.1 85.2 91.3 104.9

Turaif 82.7 88.8 94.2 107.0

Wajh 73.9 79.7 85.4 98.3

Yanbu 67.9 72.6 77.3 87.7

------------------------------------------------------

Fig. 1 Isotach, in mile per hour, annual fastest-

mile, 33 feet above ground for exposure C,

with 50-year mean recurrence interval.

for use with the ANSI-procedure in developing wind loads.

The maximum basic design wind speed of 107.2 mph, for 50-

year mean recurrence interval, is obtained at Gassim

Station, while the minimum of 65.1 mph is obtained at

Dhahran. The ANSI-prescribed minimum of 70 mph is

exceeded at all stations excepting Dhahran.

REFERENCES

1- American National Standard Building Code Requirements

for Minimum Design Loads in Buildings and Other

Structures, A58.1, American National Standards

Institute, New York, NY, 1982.

2- Wind Loading and Wind-Induced Structural Response,

Report by the Committee on Wind Effects of the

Committee on Dynamic Effects of the Structral Division,

American Society of Civil Engineers, New York, N.Y,

1987.

3- Benjamin, J. R., and Cornell, C.A., Probability,

Statistics, and Decision for Civil Engineers, McGraw-

Hill Book Co. Inc., New York, N.Y, 1970.

4- Simiu, E. and Filliben, J.J., "Probability

Distributions of Extreme Wind Speeds", Journal of the

Structural Division, ASCE, Vol. 102, No. ST9,

September 1976, pp. 1861-1877.

5- Thom, H.C.S., "Distribution of Extreme Winds in the

United States", Journal of the Structural Division,

ASCE, Vol. 86, No. ST4, April, 1960, pp. 11-24.

6- Thom, H.C.S., "New Distributions of Extreme Winds in

the United States", Journal of the Structural

Division, ASCE, Vol. 94, No. ST7, July 1968, pp. 1787-

1801.

7- Simiu, E., and Filliben, J.J., "Statistical Analysis

of Extreme Winds," Technical Note No. 868, National

Bureau of Standards, Washington, D.C., 1975.

8- Simiu, E., Bietry, J. and Filliben, J.J., " Sampling

Errors in the Estimation of Extreme Winds," Journal of

the Structural Division, ASCE, Vol. 104, No. ST3,

March, 1978, pp. 491-501.

9- Simiu, E., and Scanlan, R., Wind Effects on

Structures, Second Edition, Wiley-Interscience

Publication, New York, 1986.

10- Simiu E., Changery, M.J., and Filliben, J.J., "Extreme

Wind Speeds at 129 Stations in the Contiguous United

States," NBS Building Science Series 118, U.S. Dept.

of Commerce, National Bureau of Standards, Mar. 1979.

11- Mehta, K.C., "Wind Load Provision ANSI #A58.1-1982,"

ASCE Annual Convention and Structural Congress, New

Orleans, La., October 1982, pp.769-784.

12- Canadian Structural Design Manual, Supplement No.4 to

the National Building Code of Canada, National

Research Council of Canada, 1970.

13- Lieblein, J., "A New Method of Analyzing Extreme-value

Data", National Bureau of Standards Report No. 2190,

Washington, D.C., 1953.