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 Chisquare 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 Engineering, Riyadh, Saudi Arabia.

Civil

Engineering,

College

of

2Associate

Professor, Department of Engineering, Riyadh, Saudi Arabia.

Civil

Engineering,

College

of

3Postgraduate

Civil

Engineering,

College of

Student, Department Engineering, Riyadh, Saudi Arabia.

of

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 oneseventh. 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 evaluated and the data adjusted accordingly.

can

be

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, ‫ ] ) !ﺧﻄﺄ‬,

FV (υ) = exp [ - exp ( -

(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) = where

the

exp

parameters

[

-

(

ω

and

‫!ﺧﻄﺄ‬ γ

)‫] !ﺧﻄﺄ‬

,

(2)

estimated from the observed data at each station. The parameter, γ , is known as the tail length

are

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) =

‫!ﺧﻄﺄ‬

(3)

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) which

is

a

linear

relation

(4) 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 prediction. quality of errors.

are inherent in the process of wind speed Besides the errors associated with the the data, there are sampling and modeling

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