A Critical Assessment of the Driving-Rain Wind Pressures Used in CSA Standard CAN\CSA-A440-M90

$A Critical Assessment of the Driving-Rain Wind Pressures Used in CSA Standard CAN\CSA-A440-M90$

by Peter Felix Skerli

Faculty of Engineering Science

Subrnitted in partial fulfillment of the requirements for the degree of Master in Engineering Science

Faculty of Graduate Studies The University of Western Ontario London, Ontario January 1999

O Peter Felix Skerlj 1999 National Library Bibliothèque nationale I+I of,", du Canada Acquisitions and Acquisitions et Bibliographie Services services bibliographiques 395 Wellington Street 395. nie Wellington Ottawa ON KIA ON4 Ottawa ON K1A ON4 canada canada

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Strong winds coinciding with heavy rainfall provide a formidable challenge in the design of safe and serviceable building envelope systems. Rain penetration through the outer layer of a wall cm not oniy Iead to great econornic Iosses associated with structurai repair or replacement but may aiso compromise the hedth and comfoa of the building's occupants.

In Canada, use has been made of the airport weather records archived by the Atmospheric Environment Service of Environment Canada to develop ciimatologicai inputs to the design of waterproof wails. The climatoIogicaI input parameters are five- and ten-year extreme wind pressures derived from wind data reported during hours with rainfail totals equal to or greater than 1.8 mm. The Canadian Standard CANKSA-A440- Mg0 lists the drïving-rain wind pressures for 637 Canadian sites and outiines their usage in the window selection criteria. Documentation on the derivation of the driving-rain wind pressures is provided in a report written by Welsh, Skinner and Morris (1989) entitled A Clirnnrology of Driving Rain Wind Pressures for Canada-

A detailed review of the anaiysis methodology and of the weather data used in the denvation of the driving-rain wind pressures was conducted and three main areas for improvement were identified. First, conventional order statistics on observed annual extreme wind pressures was performed using hourly observed one- or two-minute mean speeds, Le. non-continuous observations, giving rise to uncertainty in the representative averaging time of the extreme wind pressure estimates. Second, prior to about the rnid 19603, anemometers at Canadian airports were often Iocated on rooftops of airport buildings at heights greater than 10 m, which is the reference height implied in the building standard. No attempt was made to standardize the wind data for use in the analysis. Third, one-hour rainfail totals were estimated from six-hour precipitation (rain. freezing rain, snow, etc.) measurements and hourly present weather observations as opposed to using the actuai measured one-hour rainfalls from automatic rain gauges when ..- 111 availabIe and the estimates ody as necessary.

Weather data fkom fourteen Canadian airport sites were examined to address the above uncertainties and to quanti@ the associated errors. For this, a technique was developed to predict extrerne one-hour mean wind pressures From hourly observed short- duration mean wind speeds using a database comprising continuous one-minute average wind speeds. The method was applied to re-evaiuate the driving-rain wind pressures at the fourteen airport sites considering at the sarne time the non-stationary aspects of the wind records and the available one-hour rainfall measurements. Using the ten-year driving-rain wind pressure as the reference, the resuits of the analysis show that, for the fourteen stations examined, the design pressures currentiy used in the standard are on average 55 3 higher than the one-hour mean pressures denved in this study and range from 20 to 97 % higher.

It is recommended that the Canadian driving-rain wind pressures be re-evaluated on a national scale, taking advantage of techniques descnbed in this work and of more than ten years of additionai weather data now available.

Keywords: wind-driven rain, cirivingrain wind pressures, driving-rain index, extreme wind speeds, extreme wind pressures, CAMCSA-A440-Mg0 Acknowledgements

I would like to thank several people for helping me during my joumey to cornpleting this research paper.

To Dr. Dave Surry, for your support, insight. advice and ~bovedl your patience and unders tanding-

To Atmospheric Environment Service, for supplying the data which was key to my research, and especially to Mr. Stapf for your help with the high frequency database and to Mr. Morris and Mr. Welsh for your help with the interpretation of Canada's national weather archives.

To Anna, for your constant s~pportand for being a sounding board without even really understanding what my thesis was about.

To my colleagues, in particular Rob, Darryl and Jim Bob Ray for providing me with the necessary distractions to reenergize myself and keep my sanity.

To my parents, for your financial support. for keeping my freezer stocked hl1 of home cooked rneals, for your unending encouragement. and for keeping the empty picture frame dusted in the hopes that one day it would be filled with my Masters degree. Table of Contents

Certificate of Examination

Abstract

Table of Contents

List of Figures

List of Tables

Nomenclature

Chapter 1.0 Introduction 1.1 Bac kground 1.2 Scope of Research

Chapter 2.0 Published Research 2.1 Introduction 2.2 Driving-Rain 2.3 Extreme Wind Speeds During Rainfali

Chapter 3.0 Description of the Meteorological Data 3.1 Introduction 3 -2 One-Minute Database 3.2.1 Brevoort Island Station 3-22 St. John's Station 3.2.3 Downsview Station 3 -3 One-Hour Database 3.3.1 Wind Data 3.3.2 Rainfall Data Chapter 1.0 On the Uses of Hourly Observed Short-Duration Mean Wind 95 SP~ 4.1 Introduction 95 4.2 Time Series of Mean Wind Speed 97 4.3 Dependence of Spot Wind Speeds on One-Hour Means 100 4.4 Parent Distribution 107 4.5 Extreme Value Distribution 115 4.5.1 Epochd Extremes 116 4-52 Extrernes fiorn the Parent Population 128 4.6 Concluding Rernarks 134

Chapter 5.0 Evaluation of Canadian Driving-Rain Wind Pressures 5.1 Introduction 5.2 Andyses of Canadian DRWPs 5.2.1 Base Analysis - Welsh, Skinner and Moms ( 1989) 5-32 Analysis 1 - Use of Fitered Wind Records 5.2.3 Analysis 2 - Use of Modified Spot Wind Data 5-24 Analysis 3 - Use of Rainfall Measurements 5.2.5 Analysis 4 - Use of Lieblein's BLUE 5.3 Cornparisons of Canadian DRWPs 5.4 Concluding Remarks

Chapter 6.0 Conclusions and Recommendations 185

References 188

Appendix A Relationship Between Wind Speed, Rainfall Intensity 193 and Driving-Rainfall Intensity

Appendix B Parent Wind Speeds During Rainfail 197

Appendix C Extreme Wind Speeds During Rainfdi 213

Vita List of Figures

Orientation of reference area for rainfd intensity and driving-raiddl intensity

Annual mean driving-rain index (m2!s) for the British Isles, from Lacy (1971)

Annual mean driving-rain index (m2/s) for Canada, from Boyd (1963)

Twelve-point compass roses showing annual mean simultaneous drivuig- rain index (m2/s) for 22 locations in the Bntish Mes, from Lacy (197 1)

Sixteen-point compass roses for Toronto International Airport showing a) relative frequency (%) of wind during rainfdl b) sixteen-year simultaneous driving-rain index (% of total) c) relative frequency (%) of wind during all hours, from Robinson and Baker (1975)

Annual mean simultaneous driving-rain index and three-year return period simultaneous drïving-rain spell index (logarithrnic units, scale indicated on figure) for 12 wind directions, from Pnor (1985)

Illustration of the correspondence between precipitation and wind speed data used by Murakami et al. ( 1987) in the case of a) wind speeds recorded every one hour and b) wind speeds recorded every three hours

Annual extrerne wind speeds (ds)during rainfall for Tokyo based on a) the Type4 extreme value distribution and b) Equation 2.5, after Murakami et ai. ( 1987)

Reference 10 m ten-year return period Driving Rain Wind Pressures (Pa), from Welsh et al. (1989)

AnnuaI extreme wind speeds (ds)during rainfall for Mascot based on the Type-LU extreme value distribution, afier Choi (1992)

Annual extreme wind speeds (m/s) during rainfail for Singapore based on the Tme-1 extreme value distribution with V '.after Choi ( 1994) 3.1 Station locations of the One-minute Canadian Data Base

3.2 Photograph of the POSS Doppler radar, after Sheppard (1990)

3.3 Photograph of Brevoort Island Station

3.4 One-hour mean wind speeds at Brevoon Island Station for the month of September, 1994

3.5 One-hour mean wind speeds at Brevoort Island Station for the seven-hour period beginning on Aupst 27, 1994

3.6 One-hour mean wind speeds at Brevoort Island Station for the seven-hour period beginning on October 15, 1994

3.7 Distribution of absent wind data by month at Brevoort Island Station

3.8 Photograph of St. John's Station

3.9 One-hour mean wind speeds at St. John's Station for the month of November, 1994

3.10 One-hour mean data at St. John's Station for the seven-hour period beginning on March 0 1, 1994

3.1 1 One-hour mean data at St. John's Station for the seven-hou period beginning on March 26, 1995

3.12 Distribution of absent data by month at St. John's Station

3.13 One-hou mean wind speeds at Downsview Station for the month of July, 1994

3.14 Distribution of absent data by month at Downsview Station

3.15 Station locations of the One-hour Canadian Data Base

3.16 Sixteen-point compass roses of mean wind speed for Ottawa Int'l. A.

3.17 Sixteen-point compass roses of mean wind speed normalized by that over the filtered wind record (1970-92) for Ottawa Int'I. A- 3- 18 Sixteen-point compass roses of mean wind speed for Montreal Int'l. A.

Sixteen-point compass roses of rnean wind speed normalized by that over the fdtered wind record ( 1964-92) for Montreal int71.A,

Sixteen-point compass roses of mean wind speed for Victoria Int'l. A.

Sixteen-point compass roses of mean wind speed normalized by that over the filtered wind record (1965-92) for Victoria Int'l. A,

Cornparison of the average temporal distribution of measured and estimated one-hour rainfalls for continuous penods of rairifail lasting two, four and six hours

Idealized power spectmm of wind speed, from Davenport (1994b)

One-minute mean wind speeds and corresponding s?ot factors

Two-minute mean wind speeds and corresponding spot factors

Ten-minute mean wind speeds and corresponding spot factors

Histogams of the spot factor - St. John's Station

Histograrns of the spot factor - Brevoort Island Station

Histogams of the spot factor - Downsview Station

Coefficients of variation - St. John's Station (10699 data points per plot)

Coefficients of variation - Brevoort L Station (6497 data points per plot)

Coefficients of variation - Downsview Station (6925 data points per plot)

Coefficients of variation from Equation 4.1 I

Weibuli distributions of parent one-hour mean wind speed

Histogms of parent one-hou rnean wind speed Mean and r.m.s. values of parent wind speed - result from the alternative measurement normalized by uiat from one-hour means

Weibull parameters for parent wind speed - resdt from the alternative measurement normalized by that from one-hour means

Changes in the Weibuii exponent tbrough the use of spot wind data

Extreme one-hour mean wind pressures based on the epochal model - St. John's Station

Extreme one-hour mean wind pressures based on the epochal model - Brevoort Island Station

Extreme one-hour mean wind pressures based on the epochai model - Downsview Station

iMean and r.m.s. values of extreme wind pressure - St. John's Station - result from the alternative measurement normalized by that from one-hour means

Mean and r.m.s. values of extrerne wind pressure - Brevoort Island Station - result from the alternative measurement normalized by that from one- hour means

Mean and r.m.s. values of extreme wind pressure - Downsview Station - result from the alternative measurement normalized by that from one-hour rneans

Type4 parameters for extreme wind pressure - St. John's Station - result from the aiternative measurement normalized by that from one-hour means

Type-1 parameters for extreme wind pressure - Brevoort Island Station - result from the alternative measurement normalized by that from one-hour means

Type-I parameters for extreme wind pressure - Downsview Station - result from the alternative measurement normaiïzed by that from one-hour 4. Ma Extreme wind pressures based on the epochal mode1 - St. John's Station - 161 result from the alternative measurement normaiized by that from one-hour means

4- 14b Extreme wind pressures based on the epochal mode1 - Brevoort Island 162 Station - result from the aiternative measurement normalized by that from one-hour means

4.14~ Extreme wind pressures based on the epochal model - Downsview Station 163 - result from the alternative rneasurernent normalized by that from one- hour means

4.15 Mean cycling rate and parameter N - result from the alternative measurement nomalized by that from one-hour means

4.16 Extreme one-hour rnean wind pressures based on the parent mode1 for fourteen-day epochs

4.17 Extreme wind pressures based on the parent model for fourteen-day epochs - result from the alternative measurernent normalized by that from one-hou means

5. la DRWPs for the 1.8 mm/hr rainfall threshold expressed as a fraction of that 182 derived in the Base Analysis

5. lb DRWPs for the 3.0 mm/hr rainfall threshold expressed as a fraction of that 183 derived in the Base Analysis

5.1 c DRWPs for the 5.1 mmhr rainfd1 threshold expressed as a fraction of that 184 derived in the Base Analysis

xii List of Tables

Annual wall penetration indices for 10 stations in Canada, from Morris ( 1975)

Window ratings and associated standard test pressures, from Canadian Standards Association CANKSA-A440-M90

Station information of the one-minute database

Available one-minute wind data at Srevoort Island Station during the period of Jan. 27/94 to Nov. 06/94

Statistics of the difference in simultaneous one-minute mean wind speeds measured from the Rosemount and Hydrotech anemometers

Available one-minute wind data at St. John's Station during the penod of Jan. O 1/94 to Apr. 30195

Statistics of the difference in simultaneous one-minute mean wind speeds measured from the 78D #2 and Hydrotech anemometers

Available one-minute wind data at Downsview station during the penod of Jan. O 1/94 to Nov. 27/94

Station information of the one-hour database

Anemometer heights above ground level for Ottawa Int'l. A.

Typical precipitation rates associated with present weather observations, from AES ( 1984)

Worked example for estimating one-hour rainfalls

Cornparison of the number of threshold exceedences indicated by the measured and estimated one-hour rainfails

Number of time senes constructed from the one-minute database for each of the three stations Parameters for obtaining representative values of the coefficient of variation from one-hour mean wind speed in rn/s

Averages of Nsover the indicated number of observations based on the one-minute peak factor

Estimates of parameter p

Influence of the reIevant parameters on changes in the mode and dispersion evduated fiom Equations 4-42

Summary of the anaiysis methods used to evaluate the DRWPs

Comparison of the ten-year DRWs evaluated by Welsh, Skinner and Morris (1989) and by the Base Andysis; statistics from ai1 fourteen stations

Influence of the filtered wind records on the ten-year DRWPs; statistics 175 from all fourteen stations

Influence of the modified spot wind data on the ten-year DRWPs; 177 statistics from dl fourteen stations

Influence of using estimated one-hour rainfalls on the ten-year DRWPs: 178 statistics from aU fourteen stations

Distribution of rainfdl data over the filtered wind records 179

Influence of using Lieblein's BLUE on the ten-year DRWPs; statistics 179 from all fourteen stations

Cornparison of the ten-year DRWPs evaluated by Analysis 4 and by the 180 Base Analysis; statistics fiom al1 fourteen stations

Cornparison of the ten-year DRWPs evduated by Welsh, Skinner and 181 Moms (1989) and by Analysis 4; statistics from ail fourteen stations Nomenclature

Type-1 distribution parameter; inverse of dispersion nth amplitude in a Fourier Analysis parameter of Equation 4. i 1 for defining the coefficient of variation, v, {s} coefficient for estimating Type4 mode from Lieblein's BLUE parameter of Equation 4.1 1 for defining the coefficient of variation, v, {r} coefficient for estimating Type-I dispersion from Lieblein's BLUE Type-IIi distribution parameter and Weibull distribution pararneter parameters of extreme value distribution given in Equation 2.5 factor relating dispersion of the Type-I distribution derived from spot wind speed rneasurements to that derived from one-hour mean wind speeds factor relating inverse of parameter k of the Weibull distribution derived from spot wind speed measurements to that denved from one-hour mean wind speeds factor relating pararneter c of the Weibull distribution derived frorn spot wind speed measurements to that derived from one-hour mean wind speeds factor relating upcrossing rate parameter N derived from spot wind speed rneasurements to that derived from one-hour mean wind speeds spot factor parameter, see Equation 4.3 1 factor relating mode of the Type-1 distribution derived frorn spot wind speed measurements to that derived from one-hour mean wind speeds probabiiity density function of variable X joint probability density function of variables X and Y cumulative distribution function of variable X wind speed spot factor wind speed peak factor wind pressure peak factor for continuous z -minute averages wind pressure peak factor for spot z -minute averages total nurnber of sarnples Type-III distribution parameter and Weibd distribution parameter ascending order rank of wind speed sample one-hour mean dynamic wind pressure one-hour mean wind speed nurnber of wind speed samples upcrossing rate pararneter, see Equation 4.38 upcrossing rate of variable X number of one-hour mean dynamic wind pressures within one peak factor of an epochal extreme one-hour mean dynamic wind pressure probability mass hnction of variable X precipitation total mean dynamic wind speed return period or recurrence interval tirne

Type4 distribution pararneter; mode mean wind speed time series of consecutive r -minute average wind speeds time senes of modified spot T -minute average wind speeds time series of spot r -minute average wind speeds time series of the average of two t -minute wind speeds dunng saine hou Type-III distribution pararneter number of upcrossings dummy variable epochal extreme of variable X first time derivative of variable X reduced variate of Type4 distribution dumrny variable height above ground roughness length

xvi Subscripts

i ith minute i jth hour k ktti z - minute period rn mth Largest wind speed sample

P pth extreme one-hour rnean wind pressure rfir threshold amount Greek Letters

Type4 distribution parameter; inverse of dispersion upcrossing rate parameter, see Equation 4-38 rainfali coIlection efficiency standard deviation of variable X standard deviation of r -minute mean wind speeds over an hour wind speed averaging interval in minutes angle between wali normal and approaching wind coefficient of variation of r -minute mean wind speeds over an hour nth frequency in a Fourier Andysis nth phase shifi in a Fourier Anaiysis mean cycling rate, see Equation 4.38 Euler's Constant (= 0.577)

pi (= 3.14)

average root mean square maximum minimum driving-rain wind pressure best Iinear unbiased estimators

xvü Chapter 1.0 Introduction

1.1 Background

The primary hnction of the building envelope (i-e. the roof, walls, windows, doors, etc. that make up the outer shell of the building) is to provide a cornfortable environment within the interior of the building, one wkch is independent of outside conditions. Ln order to satisQ this requirement, the building envelope must be able to remain intact and functional under the impact of naturd elernents such as high wind speeds, precipitation (rain, snow and hail) and extreme air temperatures. The consequences of rain penetration through the building envelope include material corrosion, material saturation (potentialiy leading to a reduction in the thermal insulating properties of the wall system), staining of interior finishes and damage to the building's contents, among others. Thus, isolated or persistent functional failures of a building envelope over its lifetime can not only lead to great economic losses but may aiso compromise the comfort and health of the occupants.

One form of environmentai loading that is, arpably. at the forefront of building envelope damage is the combined action of wind and min. It is a complex probiem. Aside from the need to define the characteristics of wind and rain themselves, on which this thesis focuses, there are further significant factors affecting the building envelope performance. These include the wind-driven min's interaction with the flow field around the building, Ieading to preferred areas of rain impact (Inculet and Surry, 1994; Choi, 1994~)~the way in which water runs off the building surfaces, and the aerodynamic pressures produced that rnay act to drive the rain through the envelope. These pressures Vary si,gnificantly both in tirne and spatially (Skerlj and Surry, 1994; Inculet et ai., 1994) and depend on the building's environment and wind direction. In general, rain penetration through the builcihg envelope can occur in one of two ways. The €nt pertains to wall systems that comprise an outer layer made of a porous materiai, such as brick or block rnasonry, that when exposed to prolonged periods of wetting becorne saturated- This may result in rainwater present dong the inside face should sipificant wetting persist following saturation. The waII thickness. absorption properties and initial moisture content will play key roles into the arnount of wetting required for saturation. The second way in which rainwater cm penetrate the building envelope is by being forced through an opening, such as a poorIy sealed joint in the exterior finish or an intentional wail vent that is not properly shielded from the rain. Capillary forces can be sufficient to move water through very small openings while wind pressure can cause leakage through openings larger than about O. f mm (Lacy, 1976). The pressure drop required to rnove water through an opening is inversely proportional to the size of the opening and can be severai times lower for openings completely bIocked with water compared to those only partidly blocked (Surry et d., 1994a).

Much work has been performed to date on analyzing the meteoroIogical data collected at weather stations and putting them in a form that is useful to building designers. The key rneteorological parameters are wind speed, wind direction and rainfd intensity. Rainfall intensity, as it is typicaüy measured in the field and presented in weather reports, is defined as the volume of rainwater collected on the ground per unit time per unit area, where the orientation of the collection area is parallel to the earth's surface. Under calm wind conditions, raindrops travel dong vertical paths and, in theory, do not directly impinge on to vertical building surfaces. However, when rainfall coincides with a mean airfIow, the raindrops will follow paths having an angle to the vertical (termed the driving-rain angle), owing to the force applied to them by the wind, and impinge ont0 walls facing or partially facing in the upwind direction. RainfaiI carried dong by the wind is referred to as wind-driven rain or driving-rain. Driving-rainfal1 intensity is defined as the volume of rainwater per unit the per unit area, where, in this case, the orientation of the collection area is perpendicular to the earth's surface and facing in the upwind direction. The reference areas associated with rainfdl intensity and driving-rainfall intensity are depicted in Fi,we 1- 1.

Whde dnving-rainfall intensity is an important meteorologicai parameter with respect to rain penetration through vertical building surfaces, its measurement is not cornmoniy made at standard meteorologicai stations. Some research facilities. however, have developed special directional rain gauges to measure driving-rainfall intensity (for example, Lacy, 195 1; Rose and Farbrother, 1960; and Sankaran and Peterson, 1995b).

The two most common design parameters that have been developed fYom standard rneteorolo~caidata for use in the design of rainproof building envelopes are the driving- rain index and the dnving-rain wind pressure. The driving-rain index is the product of mean wind speed and mean rainfall intensity over a cornmon time period. This product is approximately proportional to the mean omni-directionai driving-rainfall intensity or, in other words, the driving-rain index is proportional to the intensity of rainfaü crossing an imaginary vertical surface facing the wind (see Appendix A). For exarnple, during a ten- minute penod when the mean wind speed is 10 mk and the mean rainfail intensity is 2 mm/hr. you could expect roughly half the amount of driving-rain cornpared to a ten- minute period when the mean wind speed and rainfail intensity are 20 mis and 2 rnrdhr or 10 mls and 4 rnm/hr. As the driving-rain index relates to the intensity of rainfall with respect to vertical surfaces, it has found its application in the design of permeable facades, since these types of wall systems are susceptible to rain penetration after prolonged wetting through material saturation. The dnving-rain index has evolved in its method of calculation over about the past thirty years or so. When detailed meteorologicai data were not abundantly available, the index has been calculated as the product of annuai mean wind speed and annual mean rainfall and used as a simple indicator to the potential of driving-rain (Lacy and Shellard, 1962a; Boyd, 1963). More recent studies utilize hourly data to predict extreme values of the surnrnation of hourly dnving-rain indices over individual spells of rainfall for specified wind directions (Prior, 1985). The work descnbed by Pnor (1985) has been used in the developrnent of the British Standard BS 8104 entitled Assessing the exposure of walls to wind-dnnven ruin (British Standards Institution, 1992)-

The second meteorolo@cal parameter used in the design of rainproof building envelopes is the driving-rain wind pressure. The driving-min wind pressure is an extreme value dynarnic wind pressure derived from wind speed data associated with rainfail intensities exceeding a specified threshold. For example, from a data set comprising mean wind speed and mean rainfall intensity per ten-minute period, ten-minute mean driving-rain wind pressures associated with a raidal1 threshold of 2 mmmi- can be denved by considering in the extreme value analysis only the wind speeds coinciding with rainfail intensities equd to or greater than 2 mm/hr. From a design standpoint, this conditional extreme value dynamic wind pressure is relevant to the forrn of rain penetration caused by pressure differences across openings in the building envelope. Openings in the building envelope can include poorly sealed joints in the exterior finish, intentional wall vents exposed to rainwater and gaps resuiting from excessive deflections in building envelope components such as windows, doors and other fenestrations. Studies on driving-rain wind pressures (or wind speeds) have been conducted over different parts of the world, including Japan (Murakami et al., 1987), Canada (Welsh et ai., 1989), Australia (Choi, l992b) and Singapore (Choi, 1994b). The work conducted by Welsh, Skinner and Morris (1989) has been utilized in the Canadian Standard CAN/CSA-A440-Mg0 entitled Windoivs (Canadian Standards Association, 1990) which gives procedures for designing window systems to resist water leakage.

Several items are worth discussing about the driving-rain index. For a particular time interval, the driving-rain index represents a quantity approximately proportional to the volume of rainwater that will cross a unit area of imaginary vertical surface facing the wind. The relating factor varies somewhat with rainfall intensity and, to a lesser extent, with mean wind speed (see Appendix A). For a mean wind speed of 10 mls and a mean rainfall intensity of 2 mm/hr, the driving-rahfall intensity is approximately 4 rnm/hr (this assumes a proportionality constant of 0.2 dm). Now if a building is introduced such that one of its walls is perpendicular to the upwind direction and if the influence of the building on the airflow is neglected, the wall facing the wind will be irnpacted with rainwater at a rate of 4 mrnfhr- In redity. of course, the building will force the air to travel around it and in turn the air will impart forces to the raindrops such that the rauifall intensity ont0 the walI will be reduced on the whole (as some drops will miss the building altogether) and unevenly distributed over its surface. Edge regions of the wall will tend to receive the most rainfail while central regions will tend to receive the least. Many studies have verïfied this behavior including numerical approaches (Choi, 199 1, l992a, 1993, 1994% 1994b, 1994c, 1995; Sankaran and Paterson, 1995a; Karagiozis and Hadjisophocleous, 1995; Rodgers et ai., 1974), wind tunnel simulations (Inculet and Surry, 1994; lnculet et ai., 1994) and full scale measurements (Lacy. 1964, 1965, 1977: Schwarz and Frank, 1973; Couper, 1972; Ishizaki et al., 1970: Hens and Mohamed, 1994)-

The design rnethodology aven in the British Standard BS 8104 estimates the rainfdl received by a verricd building wail in a one-hour period fiom the hourly driving- rain index value, a factor of 0.2 s/m for estimating the unobstmcted mean driving-rainfall intensity and a collection efficiency term which reflects the influence of the building flow aerodynamics on the total wetting. In the above exarnple, the 4 mm/hr driving-rainfall intensity would be reduced to 2.4 mm&r (i.e. a collection efficiency of 60 %), which can be interpreted as the walI receiving an average of 2.4 liters per square meter of its area during the one-hour period. Glancing wind angles are dedt with by considering only the component of mean wind speed normal to the particular wall orientation in the calculation of the driving-rain index. Further, the driving-min indices, which are derived from b'airf~eld"wind speeds (open level terrain, 10 m height), are locally adjusted to the maximum building height considering the terrain and topographical features present at the site. The wetting estimation rnethodology does not consider the influences of either the building geometry or the temporal variations in the wind and rainfall over an hour and discounts any significance associated with the spatial variation of rainfall intensity over a wall. The methodology outlined above reflects the construction practice and the climate of the United Kingdom. That is. rab penetrauon most ofien occm as a result of the Iarge-scale, slow-rnoving mid-latitude cyclones that frequent the United Kingdom from the Atlantic Ocean. These systerns, or muitiple systems in a weather sequence, cm brïng wet and windy weather to a particular location for up to several days and longer (Pnor, 1985). With masonry construction dominating many parts of the United Kingdom, a primary cause of rain penetration during the prolonged spells of "bad" weather is waiI saturation. This is reflected in the fact that the key design parameter used in the building provisions is an estimate of the one in three year quantity of rainwater received by a wali during a single spell of rainfd, with no regard given to the coincident wind loading on the wall.

In contrast to the driving-rain index, the driving-rain wind pressure used in the Canadian Standard CMSA-A440-Mg0 addresses a different form of rain penetration. Narnely, pressure-driven water penetration through walls. As stated above, the driving- rain wind pressure is an extreme value dynamic wind pressure associated with rainfds exceeding a specified threshold. Welsh, Skinner and Morris (1989) analyzed historical weather data from 188 stations across Canada and constructed maps of the one in five year and one in ten year drivinp-rain wind pressures associated with a rainfall threshold of 1.8 mrn/hr. The standard requires that the driving-rain wind pressure read from the map (using the five- and ten-year values for residential and commercial buildings respectively) is less than the window system's capacity to resist rain penetration as prescribed by a standard water ùghtness test. The test involves applying a spatially uniform pressure drop across the window system for four penods of five minutes each separated by one-minute intervals of zero pressure while water is continuously sprayed ont0 the window. Tests are repeated with a higher pressure until water penetration is observed and the capacity is then chosen as the applied pressure of the last successful run (see Table 2.2 for test pressure increments). The premise of using a rainfall threshold in the derivation of the dnving-rain wind pressures is to iden- wind events deng which the windward facade will become sufficientiy wet so as to provide an ample amount of water at window locations (for example, along window sills) for leakage to be possible. The spatial and temporal variations in the rainfd intensity impinging the particular envelope cornponent is likely not very si,&ïcant in this context so long as water is present, whether it impinges directiy or collects from surface flows, during the extreme wind ioading. Welsh, Skinner and Morris (1989), through discussions with the technical cornmittee of the building standard, assessed that a threshold of 1.8 mrnh is appropriate in this application.

Accepting that an ample arnount of water will be present at a particular window location during the design event (Le. the clirnatological drïving-rain wind pressure). the following factors dl ment consideration when detemiining the in situ pressure loading that can be cornpared to the laboratory test conditions:

the upwind terrain chancteristics defining the vertical profiles of mean wind speed and turbulence intensity,

the presence and proximity of nearby structures and topographical features.

the building geometry and the location of the window system on the building, and

the building envelope air-leakage characteristics.

Items 1 and 2 couid be used to estimate a local value of the driving-rain wind pressure at the roof height of the building for use in assessing an extemai pressure load at the window location given Item 3 and an internai building pressure given Item 4. The net pressure across the window modified by an appropriate gust factor could then be compared to the pressure rating of the window to ensure a sufficient design. The National Building Code of Canada includes provisions to perform this type of assessment as it pertains to the design of cladding elements against pressure fclure. The rnethodology outIined in the Canadian Standard CAN/CSA-A~~O-LM~O addresses the problem in a different manner than that described above. For "small buildings", as defined in Part 9 of the National Building Code of Canada, the window selection is based on a direct cornparison between the ciimatological drivinprain wind pressure and the window pressure rating For "other buildings", as defined in Part 4 of the National BuiIding Code of Canada, the climatologicd driving-rain wind pressure is to be adjusted from 10 rn above ground to the building height using a 217'~ power law velocity profile (representative of open and flat terrain) and otherwise the same window selection criteria is used. Considering the technologies currently in use for other building envelope design applications in Canada and abroad, there is room for improvement in the rnethodology currentiy in use in Canada for assessing the risk of pressure assisted rain penetration through windows.

In order to be able to begin to improve on the window design cnteria outlined in the Canadian Standard CAN/CSA-A440-M90, several uncertainties about the driving- rain wind pressures themselves need to be addressed. In review of the analysis performed by Welsh, Skinner and Moms (1989), two uncertainties stand out. First, the representative averaging time of the driving-rain wind pressures is not readily apparent owing to the use of non-continuous wind records in their analysis. The wind data, from which conventional order statistics on the annuai extremes was performed, compnsed nominal one-minute or two-minute mean speeds observed on the hou. The authors acknowledge this uncertainty. Secondly, no attempt was made to ensure standardized wind records. That is, measurements made by an anemometer located on the rooftop of an airport control tower, for example, were treated one and the same as measurements made by an anernometer fixed to the ground on a ten-meter pole away from any irnmediate obstructions. Clearly, the estimates of the driving-rain wind pressures are subject to errors since they are currently interpreted in the building provisions as to be representative of the standard meteorological exposure (Le. 10 rn above open and level terrain). The impetus of this research is to address the above uncertainties in the driving- rain wind pressures currentiy in use in the Canadian Standard CAN/CSA-A440-M90. It is hoped that the outcome of this snidy wiil prompt a re-evaluation of the Canadian driving-min wind pressures and, in turn, allow for advancements to be made in the design of waterproof building envelopes.

1.2 Scope of Research

Chapter 2 reviews much of the research done to date regarding the development of wind-driven rain parameters and describes, when applicable, tiow these climatological statistics are used by the engineering cornmunity in the design of rainproof building envelopes. Many of the studies described are outside the direct scope of this thesis but are included as a potential information source for other researchers and as a matter of completeness.

Chapter 3 describes the two meteorologicai data sets employed in this study and the procedures used for quality assurance. For three stations across Canada, the frrst data set includes continuous records of one-minute mean wind data for periods ranging from about nine to sixteen months, The second data set comprises historical weather data recorded at fourteen airports stretched across the southern portions of Canada. The fourteen stations are part of the larger network of 426 weather reporting Canadian airports whose data are maintained and archived by the Atmospheric Environment Service of Environment Canada. The wind data recorded at the fourteen weather stations are examined in terms of changes in the anemorneter's exposure over the penods of record (which are mostiy from 19534992). From this andysis, portions of the record that are suitable for use in developing wind related design parameters are found. One-hour rainfall totals are continuously recorded at many of the weather stations using automatic rain gauges. However, the automatic rain gauges are taken out of service during the co1d season at many of the stations. This can be a significant deficiency of the weather records for coastal stations as a substantial portion of the annual rainfail is experienced during the Iate fa11 through early spring. The procedure used by Weish, Skinner and Moms (1989) to estimate one-hour rainfaii amounts from meteorological data available year-round is aiso evahated in Chapter 3-

In Chaptcr 4, the hi& frequency continuous wind data (one-minute means) are put to use to explore the representative averaging times of extreme wind pressures derived from wind records of hourly observed short-duration mean wind speeds. Wind speed averaging times of one, two and ten minutes are considered and two statisticai approaches for estimating extreme values are examined. A technique is deveioped for estimating extreme one-hou mean wind pressures from these types of non-continuous wind records.

In Chapter 5, the drïving-rain wind pressures are estimated at the fourteen airport sites in a systematic manner that highlights the influences of three andysis issues applicable to the driving-rain wind pressures derived by Welsh, Skinner and Moms ( 1989). The issues are:

the errors associated with using wind measured over non-standard exposures,

the influence of using hourly observed one- or two-minute mean wind speeds on the representative averaging time of the resulting extreme wind pressures, and

the errors associated with using the estimated one-hour rauif.1 arnounts compared to using the one-hour rainfalI measurements when available and the estimates only as necessary.

The final driving-rain wind pressure estimates are compared with the estimates given by Wekh, Skinner and Morris (1989) for the same fourteen stations-

Chapter 6 gives conclusions of the study and recommends areas for future study. Rainf" Intensity: I = Rainwater Volume/Area/Time Driving-Rainfall Intensity : I,, = Ralnwater VolumdAredTirne

Figure 1.1 Orientation of reference area for rainfall intensity and dnving-rainfall intensity Chapter 2 Published Research

2.1 Introduction

Wind and rainfall measurernents made at standard meteorologïcal stations provide a means for studying the CO-occurrenceof wind and rain. These standard data have been used in different ways over the years for assessing geographicdly the relative severity of wind-driven rain. This chapter reviews the different ways in which wind and rainfd data have been employed and, when applicable, how results may relate to the degree of exposure of buildings to rain penetration. Section 2.1 reviews general studies on the severity of wind-dnven rain. Most of these studies have been performed in the United Kingdom. Section 2.2 focuses on the studies involving extreme wind speeds during rainfall.

2.2 Driving-Rain

hterest in wind-driven rain began from as eariy as the 1950's when Hoppestad (1955) produced five maps of annual average driving-rain for Norway - one representing total driving-min and the others representing driving-rain from each of the four cardinal directions. The maps were developed by correlating measured vdues of driving-min (which had been collected ;Ji free-standing cirivingrain gauges consisting of four vertical apertures facing North, East, South and West) with simultaneous measured vdues of wind speed, wind direction and rainfd at four locations in Norway. Hoppestad utilized the relationship to evaluate annual driving-rain totals for the four cardinal directions at 70 locations throughout Norway.

Lacy and Shellard (1962a) consmicted a map showing the geographical variation of the severity of dnving-rain over the British Isles. In the onset of their work, the rainfall impinging a vertical building surface was shown to be proportional to the product of rainfall and the component of wind speed perpendicdar to the building surface. For this, a direct cornparison was made between measured values of rainfall dnven ont0 a building wail in Glasgow and measured values of wind and rainfall at a nearby site. For each hour in which rainfall occurred, the component of the mean wind speed perpendicular to the wall was multiplied by the horizontal rainfall arnount and their daily sums were found to be proportional to the corresponding daily catches of the wall-rnounted rain gauge. Based on this result, Lacy and Shellard felt that values of annual mean rainfail multiplied by annual mean wind speed during rainfall could serve as a simple index to compare the severity of driving-rain between different locations. This proposed empirical extension is vaiid provided one-hour rainfall totals and one-hour mean wind speeds are not temporally correlated,

At the time of their study, wind speeds during rainfall were not widely available and, as a result, overall average wind speeds were used to cornpute values of the index for use in the map- This was rationaliz~dby showing that the ratio of annual mean wind speed during rainfall to that of dl hours remained approximately constant across the British Isles (ratios evaluated at three well separated locations varied €rom 1.20 to 1.40). They ielt, therefore, that the contours denved with overall mean wind speeds would produce a sirnila. picture to those derived with mean wind speeds during rainfall. The term adopted for the product of annual mean wind speed and annual mean rainfall was driving-rain index. To ensure the values were comparable, "basic" wind speeds (i-e. representative of 10 m above ground in open and fîat surroundings) were employed. The preparation of the map was accomplished by simply combining previously established contour maps of annual mean wind speed and annual mean rainfall. The contours were given in units of m% corresponding to wind speed in m/s and rainfall in m. The map is shown in Figure 2.1 (this being a more detailed version with additional contours prepared later by Lacy (1971) as described above). Driving-rain is shown to be most severe dong the West coast of Scotland with index values in excess of 20 m2/s while values below 5 m2/s are typical dong the east coast and throughout the majority of Enpland. Three exposure gradings, indicated on the map by the shaded areas, were suggested by Lacy and Shellard (1962b) according to the index as follows: sheltered, < 3 rn2/s: moderaie, 3 to 7 m2/s; and heavy, > 7 m2/s. These roughiy divided the British Mes into areas corresponding to different levels of building performance with respect to rain penetration.

Boyd (1963) prepared a similar rnap showing the distribution of the driving-rain index across Canada. The map is shown in Figure 2.2. Contours were drawn from the products of annuai mean wind speed and annual mean rainfall evaluated at 14 1 stations. Index values larger than 5 m2/s occur in Pacific and Atlantic coastal regions only. Vancouver Island is shown to have the largest degree of exposure to driving-min with indices up to 13 &/S. The three exposure gradings descnbed above were also adopted in this study and are indicated on the map.

Lacy and ShelIard noted that the dnving-rain index pertains to a vertical surface which is always facing the wind. Also considered relevant was the wall orientations most susceptible to driving-rain and how these varied from location to location and, further, whether the critical directions coincided with the prevailing wind direction in a given area. A further study was undertaken by Lacy and Shellard ( 1962a) to gain sorne insight into these factors for 20 stations across the British Isles- The data available were ten-year records of wind force, wind direction and present weather observed ihree or four urnes daily depending on the station. The present weather information described the precipitation intensity in broad categories of slight, moderate or heavy and the wind force was given in terms of the Beaufort Scaie. At each location, the frequency of occurrence was determined for the different combinations of wind force and precipitation class which were then multiplied by a weighting factor approximately proportionai to the product of mean wind speed and mean rainfail rate for the paaicular category. The weighted frequencies were separately totaled for eight ranges of wind direction (centered on N, NE, E, etc.) and then expressed as a percentage of the &-direction total. The ratios approximated the portion of the driving-rain index attributable to winds from the different directions. Aithough this analysis was only very approximate due to the limitations of the data base, the results for three of the stations were in reasonable agreement with the directional distributions derived directly from hourly instrumental observations of wind and raïnfall over a ten-year period- The results indicated that buiiding walis facing the prevaiiing wind direction in a &en area were not necessariiy the most exposed in terms of driving-rain.

The pioneering work by Lacy and Shellard has served as a major reference for research in the area of wind-driven min. A more detailed version of the driving-rain index map for the British Mes was prepared by Lacy (1971) (see Figure 2.1). As the indices were denved with "basic" mean wind speeds, Lacy proposed ,&delines for locally adjusting the exposure grading obtained on the map for local site conditions which may increase the "basic" wind speed. Adjustment rules were provided for sites near coasts, sites on isolated hills and for high buildings relative to the local surroundings. A conservative approach was thus taken where exposure gradings obtained from the map could be changed Iocally only to a higher grade (Le- slight to moderate, slight to severe, or rnoderate to severe) under specified conditions or combinations thereof. This work was employed by the British Standards Institution ( 1973) in a publication entitled Walling (PanI Brick and block rnasonry) as a general guideline for assessing exposure to wind- driven rain.

Lacy (1971) aiso utilized hourly instrumental observations of wind and rainfall recorded from the pied 1957 to 1966 at 22 stations across the British Ides to further investigate the directional aspects of the annual driving-rain index. For this, annuai totds of the product of hourly rainfd and coincident wind speed were deterrnined separately for twelve directional sectors of wind and then averaged over the ten-year period. To distinguish between the product of the annuai means (Le. the dnving-rain index) and the annual total of hourly products, the latter is defined here as the simultaneous driving-rain index ("simultaneous" indicating that only wind speeds dtuing rainfall are considered). The results for each station were then surnmarized using a twelve-point compas rose, each "petal" representing the simultaneous driving-rain index attributable to wind from the indicated direction, and plotted on a rnap of the British Mes (see Figure 2.3). In contrast to the previous study by Lacy and Shellard (1962a), the directional indices were not normaiized by the total index of the particular location (this being done previously since their absolute values were not considered reliable) so as to aUow cornparisons to be made between stations. Results indicate that building walls facuig south through West are likely to experience the most wetting, this being especially me dong the West coast, and values of the total simultaneous dnving-rain index (sumation of ail twelve "petals") are generaiiy larger dong the West coast. The latter observation is also indicated in the omni- directionai rnap of driving-rain index shown in Figure 2.1.

Directional aspects of dnving-rain in Canada were studied by Morris (1975) in a different marner. He suggested that rain penetration through building wails primarily occurs during prolonged penods of rain (twelve hours or more) where the wind direction remains approximately constant over its duration. Presumably, the fonn of rain penetration considered in this study is that resulting from saturation of permeable facades. For ten locations, using hourly wind and rainfali data available between 1953 and 1972, ail such "storms" were identified for the eight cardinal wind directions and their duration and mean wind speed were determined. Moms considered the rainfail intensity during the "storrn" not an important factor so long as a sufficient quantity of rainwater was provided to saturate the wall, although a reasonable minimum threshold was not set as a cnteria for checking this. For each "storm", the duration (hr) was multiplied by the square of the mean wind speed (km2&) and the annuai averages of this quantity, referred to as the annual wall penetration index (krn2/hr), were determined for the eight cardinal wind directions for aii ten stations. Moms considered the wind pressure during the storm an important factor and therefore used the square of the wind speeds in the index. Results are shown in Table 2.1. Clearly walls king South are not subject to the prolongd wetting events while for walIs facing Northeast and East the opposite is consistently true for al1 10 stations. Maritime locations show high waii penetration indices relative to the other locations and for a wide range of directions. Station Period Annuai indices ( * LOO krn'lhr)

Victoria, J3.C. 1953-1972 3 23 34 611 O 13 24 15 Vancouver, BC 1953-1972 O 191 972 218 O O 6 LO Calgary, Alta. 1953-1972 246 15 26 26 O O 41 377 Winnipeg, Man. 1953-1972 302 208 114 85 O O 34 81 Toronto, Ont, 1953-1972 124 88 229 50 O 5 1 21 Montreal, Que. 1953-f972 141 399 44 151 O 78 37 16 Quebec City, Que. 1957-1966 13 959 761 O O 70 50 O Halifax, NS 1953-1972 327 947 1474 226 O 103 15 35 Sydney, NS- 1953-1972 642 423 9 18 753 O 243 1 90 St.John's,Nfld- 1953-1972 1403 1350 815 749 O 696 127 528

Table 2.1 Annual wdl penetration indices for ten stations in Canada, from Morris ( 1975)

Robinson and Baker (1975) explored the directionai aspects of the driving-rain index for 16 compass points using data recorded at the Toronto International Airport. The data included the frequency of occurrence of wind for specified ranges of speed and direction during rainfall for a sixteen-year period ending in 1968. The frequency of occurrence of wind for 16 directions during rainfall is shown in Figure 2.4a dong side the directional distribution of the simultaneous driving-rain index (expressed as a percentage of the dl-direction total) shown in Figure 2.4b. The frequency of occurrence of wind during al1 hours is aiso included in Figure 2.4~. Wind directions during rainfail are shown to have trends different than those during ai1 hours.

The Building Research Establishment Report written by Lacy in 1976 provided a large-scale map (1:625000) of the annual mean driving-rain index for the British Mes. It was prepared similarly to those prepared by Lacy and Sheilard ( l962a) and Lacy (197 1) with the exceptions that more recent wind and rainfall data were used and that an altitude correction was applied to the "basic" mean wind speeds. The altitude correction accounts for the generd increase in wind speed over large land masses. The report was introduced as follows: "To meet the urgent need for a more precise detemination of the driving-rain index at individual localities, a new large-scale rnap of the mua1 mean index has been prodziced, with proposed niles for adjrsting the 'rnap vnl~ie'to allow for local topogruphic variation and terrain roughness. These are intended tu give local vnl~iesof the inde-r which correspond to the behnviour in practice of cavily wahfilled with insulating foam- ", Incy ( 1976)

The proposed guidelines for iocally adjusting the indices taken from the map were to a large extent more thorough than those given by Lacy (1971). Rules were provided to adjust the index numerically, as opposed to simpiy rnodifying the exposure gading, and accounted for non-level terrain, surface roughness, altitude and building height. With this new system of corrections, Lacy re-defined the limits of the three exposure gradings (Le. sheltered, < 3 rn2/s; moderate, 3 to 7 m%; and heavy, > 7 rn2/s) to correspond with local index values. This was done by considering a house in a suburban environment with a 7.5 rn high gable-end wall as being the most comrnon situation and applying the appropriate corrections to the previous limits of 3 and 7 m2/s to obtain the new limits of 1.3 and 3.1 m2/s. Consider, for exarnple, a large city in a flat part of the country where the dnving-rain index read from the rnap has a value of 4 m2/s. A house (5 m high) located in the center of the city would be classified as having a "sheltered exposure (local index = 1.2 rn2/s) while a simiiar house located in open farmiand some few kilometers from the city would be classified as having a "moderate" exposure (local index = 2.9 m2/s). The more conservative approach outlined by Lacy (1971) would have classified both houses as having a "moderate" exposure.

This work was intended to provide a more practical use of the index as it allowed designers to compare a location where the performance of a wall design was known to the location of a proposed building. Lacy was careful to outiine the type of wall whose susceptibility to rain penetration could be related to the index; narnely, cavity walls with an outer layer made of a porous material. Their performance largely relates to the quantity of rainwater reaching the outer surface, since the more rainwater the more likely the outer absorbent wall will become saturated and result in water present dong the inside face. Lacy proposed that the adjusted values of the index be used specificdly to assess whether cavity-fil1 is to be employed in such a wall design, the significance king that cavity-fill may provide a "bridge" for water to cross the cavity and produce undesirable darnpness of the inner layer (see, for example, Newman (1988) where potential routes of rain penetration across masonry cavity walls have been outiined for three types of insulation fiII). This work was utilized by the British Standards Institution (1978) in a publication entitled Thennal insulation of cavity waiis (with masonry inner and outer Zenves) byjZing with urea-fomaldehydefoarn.

The ornni-directional maps of driving-rain index descnbed to this point are based on the product of annual mean rainfdl and annual mean wind speed (di hours). Caton of the UK Meteorological Office (whose work was reported by Prior (1982) and Mer described by Pnor (1985)) analyzed the simuitaneous driving-rain index roses prepared by Lacy (1971) to compare the total simultaneous index with the conventional dnving- rain index used in the then current national map of the British Mes. He found that the ratio of the former to the latter ranged from 0.8 1 to 1.54 at 22 locations (the locations are those seen in Figure 2.3). The ratio in effect gives the ratio of mean wind speed during rainfall to that of al1 hours, thus, values Iarger than 1-00 (which was the case for 18 of the 22 stations) indicate mean wind speeds during rainfdl to be higher. The more significant result was the variabiIity in the ratio, which indicated that the national map presented a "distorted" picture of the relative severity of driving-rain across the country. Caton noted, however, that the overall characteristics of the variations were similar for both annual indices. Caton felt that improvements could be made to the then current representation of the annual driving-rain index through the use of hourly data so consideration would only be given to the wind speeds during rainfall and, in addition. the directional aspects could also be assessed more generally. His work is now described.

At the onset of Caton's work, one-hour mean wind velocities and one-hour ninfall amounts were available at 20 UK airport stations over the period 1959 to 1973. For twe1ve wall orientations, Caton determined annual totals of hourly PVcosû values where P is rainfall, Vis rnean wind speed and 8 is the deviation of the mean wind direction frorn the normal of the wdI orientation considered, Values of 8 iess than 90" were only used and thus V cos 6 represents the component of wind speed approachîng the given watt. The simultaneous driving-rain index was taken as the average of the 15 annuai totals, which resulted in twelve directional indices for each of the 20 stations. At an additional 32 stations over the same period, one-hour mean wind velocities were available together with annuai rainfall and present weather observed every three hours (these, again, indicating precipitation intensity in categories of slight, moderate or heavy). In order to simulate hourly rainfalls, use was made of the 20 stations initidly andyzed, which also recorded present weather on a bee-hourly basis- Each present weather observation made in the 15-year record was associated with the correspondhg measured three-hour rainfall amount and these rainfalls were then averaged separately for each present weather category and used as a calibration factor. This procedure was performed separately at al1 20 stations for different seasons and wind directions. For the 32 additional stations, the three-hou penod associated with each present weather observation was allotted the appropriate three-hour "calibrated" rainfall arnount (a third given to each hour) from the nearest topographically sirnilar "calibrated" station. Caton then used the approximated hourly minfails to evaluate the simultaneous index for the 12 wall orientations, as described above, together with total annuai rainfall. The directional indices were then multiplied by the ratio of measured annual mean rainfall to that approxirnated fiom the present weather code. Prior ( 1985) later showed that the indices derived frorn hourly wind and rainfall data from 2974 to 198 1 for five of the stations were within about 15 % of those estimated by Caton.

Economic reasons necessitated that a single map be used to present the results of al1 twelve wail orientations. As a guide for interpolation, Caton assumed that the derived indices were proportional to the product of mean annual rainfall and wind speed exceeded 25 5% of the time. This percentile value was chosen since it roughly equals 1.4 times the overail mean wind speed and thus fell in the range of the ratios discussed above (established UK maps were available for both quantities). Geographicai variations applicable to ail directions were fust established by preparing separate maps for each waH orientation showing the directional index relative to a standard level, The UK was divided into 28 regions, each having at least one meteorologicai station. and a map showing the geographical corrections were prepared for each. The regional maps comprised sub-regions that roughly exhibited uniform directional distributions and thus a single simultaneous index rose was provided for each sub-region. An exarnple of a regional rnap is shown in Fiawe 2.5. The dashed lines indicate sub-regional boundaries (this particular map having five sub-regions - PB 1 through PB5) and solid lines separate the various geographical corrections. Taking a West-facing wall in Boston, for example, the sub-region is indicated as PB 1 and its driving-rain rose (left side of Figure 2.5) shows an index of 6 units. The geographical correction indicated on the map for Boston is + 1 unit, thus the driving-rain index for a West-facing wall in Boston becornes 7 units or 1-12 m2/s. A logarithmic scale was used so the corrections could simply be added or subtracted and to avoid decirnd vaIues in the map.

In addition to preparing irnproved (directionai) annual driving-rain indices, a second objective of Caton was to derive annual extreme driving-rain indices associated with individual spells of rainfall. This statistic was considered more appropriate for assessing the risk of rain penetration and Caton suspected that it might not be proportional to the annual rnean index. Caton's original work on the driving-rain speIl index was slightly rnodified by Prior (1985) and the latter is presented here. The definition adopted for a spell of driving-rain was a penod less than 96 hours where the summation of hourly EPV cos 0 vdues exceeded a pre-defined threshold (ex. 0.0 12 m2/s) for a given wall orientation together with dl successive periods of no more than 96 hours where the threshold was again exceeded for the sarne wall orientation. The variable & is a collection eficiency term that accounts for the reduction in the total wetting of a wall caused by raindrops being deflected by the wind to miss the building. A spell of driving- rain was thus bounded by periods of 96 hours where the threshold was not exceeded and the driving-rain spell index was determined as the sum of @Vcose vaiues over the spell. The 96-hour period was considered appropriate to capture al1 the depressions in a weather sequence. Based on results kom various full scale studies (as those descnbed by Lacy

1965, 1977), E was taken to be a function of perpendicular wind speed as follows:

E = 02- (V cos6 - 2), O I E 5 0.6, where V is to be specified in m/s- Pnor determined al1 driving-rain spells at 16 UK sites over a 15 or 23 year penod for 12 wall orientations and then used a graphical technique to predict the one-, three- and ten-year return period values. The three-year return period spell indices were mapped and corrections were provided to convert these to one- or ten-year remperiod values. The mapping was achieved by developing a relationship between the annual mean index and the one in ihree year spell index considering both geographicai and directional variations. Spell index roses were prepared for each sub-region (shown on the right side of Fiapure 2.5) and it was found possible to use the same geographical corrections as those used for the annuai mean index. A different logarithmic scale was used since the spell indices were significantly smailer. Considering Boston again as an exarnple. a West facing wall is shown to have a one in three year driving-rain spell index of 15 + 1 units or 0.089 m2/s.

Prior considered the annuai mean indices "relevant to the weathering and staining of building facades" and considered the three-year return period spell indices "usehl for assessing the risk of rain penetration through masonry wails and building features". This work was utilized by the British Standards Institution (1984) in the Draft for Development Methods for assessing exposure tu wind-driven min which included rules for locally adjusting the values read from the map for terrain roughness and topography. This Iater developed into the British Standard Code of Practice Assessing rhe exposure of ~vnilstu cvind-driven rain (British Standards Institution, 1992).

2.3 Extreme Wind Speeds During Rainfall

The ftrst study of extreme wind speeds during rainfall, to the author's knowledge, was reported by Murakami, Iwasa, Monkawa and Chino in 1987. Data from six meteorological stations in Japan (located at Sapporo, Sendai, Tokyo, Nagoya, Osaka and Fukuoka) over a twenty year period ending in 1980 were used to estimate annual extreme wioc: speeds occdng during rainfalls exceeding selected threshold rainfall rates. The data base comprised ten-minute average wind speeds recorded every one or three hours, one-hour precipitation totals recorded every hour and daily maximum values of both the above.

Due to the variable averaging periods and recording rates of the data, Murakarni et al. made the hourly precipitation amounts correspond to the largest ten-minute average wind speed recorded within 30 or 60 minutes of the precipitation occurrence for wind speeds recorded every one or three hours respectively. As an example, a six hour segment of data during which precipitation occurred in four consecutive hours is illustrated in Figure 2.6. Figure 2.6a depicts wind speeds recorded every one hour and Figure 2.6b every three hours. The wind speeds, V, and the precipitation totals, P, are subscnpted with their time of observation and the averaging periods are approximately indicated by the bar heights. The arrows in the illustration indicate the ten-minute average wind speeds which fail within the necessary time frame of the particular one-hour precipitation arnount. Refemng to Figure 2,6a, PI? would have been made to correspond to the largest wind speed observed between 10:30 and 1230 (Le. the iarger of VII and Vl2), while in Figure Lob, Pl? would have been made to correspond to the largest wind speed observed between LO:OO and 13330 (Le. the larger of Vlo and V13). The daily maximum ten-minute average wind speed (in this example averaged over about 7:35 and 7:45 and denoted as V,,) would have been made to correspond to P9 for both of the wind speed recording rates since it would be larger than the other wind speeds considered in either case. In addition to these, each daily maximum one-hour precipitation total, which may have occurred over any continuous one-hour period, was also made to correspond to a ten-minute average wind speed according to the sarne requirements.

Resulting wind speeds were then sorted based on their associated one-hour precipitation total into the following categories: 1 5, 7, 11, 21, 31, 41 and 51 mm. Annuai extremes were extracted from the data in each precipitation category and converted to wind speeds at a height of 10 m for dl six locations, Murakami et al. used the series of annual maximum wind speeds to estirnate the parameters of the Type4 extreme value distribution, wtiich has the following cumulative fom;

where rr is the mode of the distribution and 1/ a is a measure of the dispersion. Solving for V in Equation 3.1 gkes the following Linear form;

in which the reduced variate, y, is given by:

The cumulative probabilities were approximated using;

where V', is the mth largest annuai extreme wind speed and M is the totai number of years in which the annual extremes were extracted. The mode and dispersion were estimated for each precipitation category based on the least squares fit of the data in the form shown in Equation 2.2.

Results for the Tokyo station are shown in Figure 2.7a where the estimated regression iines have been plotted for each precipitation threshold category. The plot indicates physical impossibilities when a line representing a certain precipitation threshold yields a higher annual extreme wind speed than a line representing a lower precipitation threshold at an equai probability level. As an example, the annuai maximum wind speeds for return periods longer than about 50 years are shown to be higher during hourly precipitations 2 3 1 mm than during hourly precipitations h 21 mm. This should not be possible since the wind speeds experienced during the higher precipitation threshold would ais0 be experienced during the Iower precipitation threshold and, therefore, the annual extreme wind speeds would have been as ieast as high in the latter as they were in the former.

To rectie this problem, Murakami et al. employed a new mode1 in which the annual extreme wind speeds were assumed to be proportional to both the reduced variate and the one-hour precipitation threshold, Pk. The relationship is;

where Co, Ci and C2 are constants- In cornparison to the Type-1 distribution in the form shown in Equation 3.2, Co+C,Ph, is equivdent to the mode and Ci to the dispersion, the latter now being equal for all precipitation thresholds, thus eliminating the anomaly shown in the previous simple regession andysis. The least squares criterion was used to estimate the mode1 constants for each station and the results for Tokyo are shown in Figure 2.7b- Murakami et al. found that the multiple correlation coefficient exceeded 0.95 at dl six locations.

Welsh, Skinner and Morris (1989) studied annual extreme wind pressures during rainfall for Canada. Available data from 188 meteorological stations, mosdy from 1957 to 1985, were used to predict annual extrerne wind pressures dunng rainfalls exceeding threshold rates of 1.8, 3.0 and 5.1 mrnh. These have been given the term driving-rain wind pressures (DRWPs). The data base included one-minute average wind speeds recorded hourly (or two-minute averages beginning in 1985), six-hour precipitation totals recorded four times daily and hourly notes regarding precipitation type (rain, rain showers, freezing min, snow, etc.) and intensity (light, 4 2.5 mrn/hr: moderate, 2.6 to 7.5 mm/hr; and heavy, 2 7.6 mm/hr). The six-hou precipitation totals were used to estimate one-hour average rainfall rates based on the hourly notes and typical relative precipitation rates of the different precipitation types and intensities. The simultaneous wind speed for a particular one-hour rainfdl was taken as the one- or two-minute average wind speed obsenred at the beginning of that hour. Three series of annual maximum wind speeds were extracted at each station from the hours in which the rainfalls exceeded the three chosen threshold rates and then converted to wind pressures. The method of moments was used to estimate the parameters of the Type-1 extreme value distribution for each series and annual maximum wind pressures were then evaluated for retum periods of 2, 5, 10 and 30 years.

The DRWPs associated with rainidls exceeding 1.8 mm/hr are currentiy used in the Canadian Standards Association CANKSA-A44O-Mg0 as a guide for selecting the appropriate performance Ievel of windows with regard to water tightness. The performance level is based on a standard test which cails for a constant pressure applied for four consecutive five minute penods, separated by one-minute intervals of zero pressure, while water is continuously sprayed ont0 the outside surface. The test pressure is incremented as showo in Table 2.2 until water penetration occurs and the window rating is then chosen according to the applied pressure of the last successful nin. Five- and ten-year return period DRWPs, applicable for residential and commercial buildings respectively, are directly cornpared with the test pressures in order to select the appropriate performance level of windows. Welsh et al. expanded the available data for use in the cornparison by plotting the results of the five- and ten-year return penod DRWPs frorn the 188 Canadian sites on maps and drawing in contours, from which, suitable values for 637 sites have been codified. The nationd map of ten-year return period DRWPs is shown in Figure 2.8. Values taken from the map (or from the data tables) require adjustment for buildings higher than 10 m above the ground as follows:

design DRWP = reference DRWP - (building heightIl0 m)'" (2-6)

A 40 m high commercial building in London, for example, should have windows with at least a B4 rating. The logic is as follows: the ten-year retum period reference DRWP in London at 10 rn is 220 Pa which results in a design DRWP at 40 m of (220) - (40/10)'" = 330 Pa. In contrat, the test pressure associated with the B4 rating is 400 Pa and is the firsst vdue larger than that required. Window rating Pressure differential, Pa For use in small buildings For use in other buildings S torrIl - O l3L B1 150 B2 B2 300 B3 B3 250 - B4 400 - BS 500 - B6 600 - B7 700

Table 2.3 Window ratings and associated standard test pressures, from Canadian Standards Association CAN/CSA-A4440-M90

Choi (I992b) analyzed annuai maximum wind speeds from four Australian stations located in Sydney, Mascot, Richmond and Bankstown. The available record lengths dated back to 19 13 for the Sydney station, 1930 for the Mascot station and 1968 for both the Richmond and Bankstown stations. The wind speed records provided ten- minute average values recorded every three hours and the rainfall records gave cumulative amounts at time intervals of at least one hour and more frequently during "heavy" periods of rainfall, One-hour average rainfall intensities were evaluated and made to coincide with an appropriate ten-minute average wind speed (no hrther information was provided in the report). Series of annual maximum wind speeds were then assembled for each station considering al1 hours and those hours during which the average rainfall intensity matched or exceeded the following threshold values: 10, 20. 30, 40 and 50 rnmh.

Initially, each data set was fitted separately to the Type-I extreme value distribution. The resulting regression lines (Le. V plotted as a hnction of y) were not pardel which indicates the contradiction discussed earlier when the lines cross one another. As a result of this, Choi adopted the mode1 used by Murakami et ai. (Le- Equation 2.5) to produce a series of paralle1 straight tines with different intercepts to represent the annual extreme wind speeds of each data set. It was found that the data poorly fit the resulting muItiple regression lines and, in addition, it was observed that the data formed curves with slopes that decreased with increasing values of the reduced variate. This prornpted Choi to use the Type-III extreme value distribution which is suitable for a random variabte that is iimîted by an upper bound, as was indicated by the flattening of the curves. The Type-III cumulative distribution function is;

F(V)= exp - (:I:T].- Vslv

where k, c and ,v are constants. The constants were evaluated separately for each data set using a ciwi-linear curve fitting technique and the results from the Mascot station are show in Fieme 2.9. Choi found that the data were well represented by the Type-III distribution,

More recentiy, Choi (1994b) studied annual extreme wind speeds at a site located in the east-central portion of Singapore Island. The available data were used to consmct simultaneous pairs of hourly mean wind speed and hourly rainfall intensity. The annual extreme wind speeds were extracted for hourly rainfaii thresholds ranging from 2 5 rnrn/hr to 2 110 rnm/hr together with the annual extremes based on ail hours. The series of wind speeds again indicated curved lines when plotted with V as the abscissa and y as the ordinate. Based on this observation, Choi fitted the square of the wind speeds to the Type-I extreme value distribution and converted the resulting extremes to wind speeds (see Figure 2.10). Annual extreme values of V ' as opposed to V have been shown to converge much quicker to the Type-I asymptote due to the difference in the form of the upper tails of the parent distributions (Cook, 1985).

A common feature seen in the four studies reviewed in this section is that the wind data available for developing statistics on extreme wind speeds during rainfdl were non-continuous observations. The frequency of observation was either one hour or three hours, while the averaping times ranged from one to ten minutes. Since each of the studies employed conventional order statistics on the observed annuai extremes, the representative averaging times of the resulting extreme value estimates are not readily apparent but certainly lower than that over which the wind speed observations were made. This problem is often avoided when derïving overall extreme wind speeds since use cm be made of the observed daily peak speeds (usually gusts) that are often archived in the meteorologicd records maintained at airports. The use of non-continuous wind data, which is the form most commonly available in the weather records maintained at morts, for developing extremes is partiy the impenis for this research. Figure 2.1 Annual mean dnving-raùi index (m2/s) for the British Mes, frorn Lacy (1971)

Figure 2.3 Twelve-point compas roses showing annual mean simultaneous cirivingrain index (m2/s) for 22 locations ùi the British Lstes, fiom Lacy (197 1) en- E = 3 --3 O 'CI=

/ 4 ; one-hour ten-minute 1 one-hou ten-minute i precipitation average ; precipitation average j total wind speed 1 total wind speed hour MC hour 1 7. 7.

Figure 2.6 Iitustration of the correspondence between precipitation and wind speed data used by Murakami et al. (1987) in the case of a) wind speeds recorded every one hour and b) wind speeds recorded every three hours return period (years) 2 5 10 20 50 100 200 500 1 I l l I I 1 I 1 altype-1 extreme valuedistribution P13lmm

-2 -1 O 1 2 3 4 5 6 7 reduced variate, y

return period (years) 2 5 10 20 50 IO0 200 500 h 1 b) mode1 shown in Eauation 2.5 a a al g 20- u C .C. P

Ee, L 4 10- a PZ21mm -. ta ~r31mrn 3 C C @s P 2 51 mm

O I 1 l I I I I -2 - 1 O L 2 3 4 5 6 7 reduced variate. y

Figure 2.7 Annual extreme wind speeds (mk) during rainfaii for Tokyo based on a) the Type4 extreme value distribution and b) Equation 2.5, after Murakami et al. (1987)

return period (years) 2 5 10 20 50 100 30 I I I I i &~e-III extreme value distribution

reduced variate, y

Figure 2.9 Annual extreme wind speeds (ds)during rainfd for Mascot based on the Type-III extreme value distribution, afier Choi (1992) return period (years)

ty~e-lextreme value distribution with v2

I I i l -2 -1 O 1 2 3 4 reduced variate, y

Figure 2-10 Annual extrerne wind speeds (ds) du~grainfail for Singapore based on the Type4 extreme value distribution with V ', after Choi (1 994) Chapter 3 Description of the Meteorological Data

3.1 Introduction

This chapter descnbes the meteorological data employed in this study and the procedures used for their quality assurance.

The Atmospheric Environment Service (AES) of Environment Canada Iocated in Downsview, Ontario provided two databases for use in this research. The first was provided by the Test and Evaiuation Section of the Technology Division and comprises wind and precipitation data rccorded each minute for two sites and wind data recorded at the same frequency for an additional site. This database will be referred to as the one- minute database and is described in Section 3.3. The second database was extracted frorn the Digital Archive of Canadian Climatological Data rnaintained by AES and includes 40 years of hourly wind and rainfall information for fourteen stations. These data are described in Section 3.3 and will be referred to as the one-hour database.

3.2 One-Minute Database

The Test and Evduation Section of AES currently record meteorological data at a one-minute frequency at several stations in Canada. The data have been used to study the effects of king on the performance of a variety of commercially available anemorneters (Redekopp, 1994). In the present study, meteorological data h-orn three of the Canadian sites have been used. Table 3.1 Lists the site locations together wiih their record periods and the type of meteorological data available. Figure 3.1 shows the site locations on a map of Canada. Location Record period vai il able data S tart End Duration Wind Precipitation Brevoort 1, Jan, 27/94 Nov. 06/94 9.4 months X St. John's Jan. 0 1/94 Apr. 30/95 16 months X X Downsview Jan. 0 1/94 Nov, 27/94 10.9 months X X

Table 3.1 Station information of the one-minute database

The meteorological data were remrded each minute and describe the weather during the one-minute penod preceding the time of observation. The wind data comprise the following:

1. rnean wind speed,

2. mean wind direction and

3. peak f'ïve-second pst speed.

The peak gust for a particuiar one-minute penod is the largest of the twelve five-second rnean wind speeds (i.e. averaged from O to 5 seconds, 5 to 10 seconds. etc.) as opposed to being the largest mean speed during any continuous five-second period within the minute. The precipitation data include:

1. mean precipitation intensity and

2. precipitation type.

In addition to these data, the air temperature was also recorded at St. John's and Downsview during the minutes precipitation occurred. The mean wind speed, wind direction and precipitation intensity were di averaged over the fuIl minute.

The wind data were recorded with eleven anemometers in total for ail three stations and of these four different models were used:

1- AES 78D anemometer (78D), 2. Hydro-Tech ice-resistant anemometer (Hydrotech),

3. Rosemount ice-resistant anemometer (Rosemount) and

4. Metrex Instruments de-iceable mernometer (Dragsphere).

The 78D comprises a direction vane and a three-cup rotor speed sensor. Based on pre- defrned cdibrations, wind speeds are deterrnined from the number of revolutions experienced by the cupwheel. The Hydrotech also consists of a rotor anemometer (six radial cups) and direction vane. The Hydrotech sensors are elecuically heated and thus suited for colder climates where exposed rneteorological instruments are susceptible to ice accretion. The remaining two anemometers listed above are also ice-resistant. The Rosemount is a pressure anemometer that measures mean dynamic pressures in both the North-South and East-West directions from which corresponding wind velocities are caiculated. The Dragsphere operates on the force-balance principle where a vertical shaft is free to pivot about its center of gravity in the two orthogonal directions and has attached to it a sphere openly exposed to the wind. The motion of the lower end of the sh&, resulting from wind-induced drag force applied to the sphere, triggers an intemal mechanism that rapidy generates balancing forces to oppose the motion. The measured forces are used to calculate a resultant wind vector.

The precipitation data were measured using a smdl Doppler radar system developed by AES known as the Precipitation Occurrence Sensor System (POSS) and is descnbed in detail by Sheppard and Wu (1985). This automated system measures the Doppler velocity spectrum of scatterers in a smaU volume of air immediately above the sensor from which the spectral mode and the spectral density are used to determine precipitation type and intensity respectively. A photograph of the POSS is shown in Figure 32 Sheppard (1 990) compared POSS rainfdl measurements with measurements made by two conventional gauges: a tipping bucket and a Belfort Weighing Rain Gauge- For a seven-hour period of rainfall in King City, Ontario, ten-minute average rainfall rates measured with the POSS were found to be in reasonable ageement with those measured by the conventiooal gauges; the differences being of the same order as those exhibited between the two conventional gauges. The total rainfali measured in the seven-hou period was 22.2 mm, 22.3 mm and 20.1 mm for the POSS, tipping bucket and Belfort Weighing Rain Gauge respectively.

The POSS divides precipitation type into one of the foilowing categories:

2. rain,

3. snow,

5. precipitation.

When the requirements of the fvst four categones are not met, category 5 is indicated. This category may represent periods when the precipitation comprised a mixture of both liquid and frozen States. Another possibility is that the Doppler radar was erroneously stimulated and, for exarnple, the signal was generated by the passage of debris or by human activity in close proximity to the equipment. The POSS is aiso instrumented to measure air temperature. In the present database, air temperatures were available during the minutes precipitation was detected.

The next three sub-sections describe the data for each individual station in tenns of availability and quality. The procedures used to develop a single wind record from the data of ail available anemometers at a particular site are ouùined.

3.2.1 Brevoort Island Station

Brevoort Island is located in the Northwest Territories just off the Coast of Baffin Island at approximately 63"N latitude and 64"W longitude (see Figure 3.1). A photograph of the site is provided in Fi,we 3.3 where the topography of the surrounding terrain is shown to be moderately sloped and otherwise generally level. The wind instruments are shown to be openly exposed to the wind from ail directions.

The database for Brevoort Island Station comprises measurements of wind data fiom four instruments. Refemng to Figure 33, these include a Hydrotech anemometer (direction sensor lower lefi and speed sensor lower right), a Dragsphere anemometer (rniddle left), a Rosemount anemometer (rniddle right) and a 78D anemometer (background). The instrument Iocated at the top of the pole in the foreground is a U2A anemometer and its measurements were not part of the database used in the present study. The 78D memorneter is fixed to a pole 10 m above gound and is roughly 50 m from the other instruments. The Dragsphere and the Rosemount anemometers are approxirnately 4 rn above ground level and the Hydrotech sensor is roughly 1 m lower. The logging equipment comprises a single timer and thus the measurements from al1 four instruments were simultaneous,

The relative completeness of the four wind records over the period of observation is shown in Table 3.2. The Dragsphere anemometer was not functioning properly &ter the original installation and it was not until towards the end of Aupst that the necessary repairs were made. The Hydrotech anemometer expenenced technical problems for about a four-month stretch beginning in late April resulting in a loss of more than 40 % of its data. The wind records of the remaining two anemometers are more than 90 % complete. The last row in Table 3.2 shows the maximum attainable level of completeness if the data recorded by each instrument were considered interchangeable.

Liemorneter Available winddata 78D 97.0 9% Rosemount 91.5 % Hydrotech 57.5 % Dragspbere 26.4 % at least one of the above 97.1 %

Table 3.3 Available one-minute wind data at Brevoort Island Station during the period of Jan. 27/94 to Nov. 06/94 As there are up to four wind observations for each minute, it was necessay to decide which data would be used to construct a single time senes. An important consideration was to minimize the arnount of missing data while at the same time it was desirable to use data from a single instrument so as to have a wind record which is representative of uniform conditions - i.e. a constant height, location and instrument calibration, Refemng to Table 3.2, data from the 78D anemometer alone provides a time history which is 97.0 % complete, compared to the maximum of 97.1 % when dl four instruments are considered, and thus adheres to the above stipulations. Ho wever, another important consideration was the quality of the data. In Brevoort Island the winters are typically long and cold and the summers short and cool. Thus, for a large portion of the year exposed anemometers are susceptible to ice accretion. The Rosemount, Hydrotech and Dragsphere anemorneters are designed to prevent ice buildup through interna1 heating and therefore are more suited, in cornparison to the 78D anemometer, for colder climates such as that of Brevoort Island.

To assess whether the performance of the 78D anernometer was adversely affected by ice accretion and, at the sarne time, to obtain an overall picture of the relative wind speeds recorded by the four instruments, one-hour mean wind speeds were calculated and plotted on similar axes. Figure 3.4 shows the plot for the month of September (note that the plotting algorithm discontinued lines when data were not available - i.e- data were absent from al1 instruments for a period of severd hours during the last day of the month). For roughly the last ten and a hdf days and for several shorter penods earlier in the month, the 78D anemometer showed Lttie to no wind while the speeds measured by the three ice-resistant sensors remained sia~ficantlyhigher. The 78D anemometer did not report wind speeds larger than O dsuntil roughly one week into October. This type of behavior was observed in eight of the eleven months. Redekopp (1994) analyzed the sarne wind data up to mid-June together with data frorn two ice accretion sensors. It was found that during "icing conditions" the 78D anemometer would significantly under- report the wind speed compared to the other instruments and often stop running al1 together. To avoid the difficult task of detennining which perïods the 78D anemometer was affected by icing, it was decided to onIy use the data from the ice-resistant sensors.

The Rosemount data, being the most complete of the ice-resistant anemometers, were chosen for the wind record at Brevoort Island Station. The the history is 9 1.5 % complete- During the periods when data were not available from the Rosemount sensor (excluding the times when al1 four instruments were not functioning), data from the Hydrotech anemometer were present and utilized to increase the compteteness of the time history to the maximum level of 97.1 96- The Rosemount and Hydrotech anemometers are fixed to the sme pole at approximately 4 and 3 rn above ground level respectively (see Fiapre 3.3). Provided the instruments were equally calibrated, the Rosemount wind speeds should, on average, be marginally higher than the Hydrotech wind speeds based on their relative heights. An increase of 4 to 5 % cmbe expected if a power law profide is assumed with an exponent of 0.15; this exponent being representative of open country terrain. Table 3.3 shows the average and standard deviation of the difference in corresponding measured one-minute mean wind speeds (Rosemount speed - Hydrotech speed) for seven wind speed and four wind direction categories based on the Hydrotech data The number of observations in each category is also shown.

The first row of data in Table 3.3 shows that when the Hydrotech memorneter indicated no wind the Rosemount anernometer indicated. on average, a wind speed of 1.76 ds. This is likely a result of the wind speed threshold associated with overcoming the frictionai forces in the Hydrotech rotor anernometer to initiate rotation. For lighter winds (5 10 ds), as indicated by the Hydrotech data, the mean speed differences show the Rosernount anemometer to indicate higher wind speeds and as the winds become stronger, again as indicated by the Hydrotech data, the opposite is shown to be increasingly me. These resuits sugest that simple ratio relating the two wind speeds may not be appropriate. It is unknown to the author as to the reason(s) for this apparent trend since detaiied information on the calibration of both wind instruments was not available and thus no explanation is offered. It is, however, noted that Redekopp (1994) dso found that the Hydrotech anemometer at Brevoort Island under-predicted the wind speed during "Light winds" by comparïng measurements with the 78D anemometer. No trends in the relative measured wind speeds appear to be associated with wind direction as indicated by the last four rows of Table 3.3.

-- -- Hydrotech wind speed (ds) Wind speed difference (Rosemount - Hydrotech) > -< Average (ds) St- Dev. (mis) No. of obs. - O 1.76 0.9 1 37568

- -- ~ydrotech wind dirëction North 0.59 1.92 59414 East O. 14 1.53 39202 South 0-96 1.23 342 17 West 0.68 1.O9 420 17

Table 3.3 Statistics of the difference in simultaneous one-minute mean wind speeds measured from the Rosemount and Hydrotech anemometers

The approach taken to relate the measured Hydrotech one-minute mean wind speeds with those of the Rosemount anemometer was to assume a Iinear relationship (the measured Hydrotech speeds being the independent variable). A least squares fit was performed on the simultaneous one-minute mean speeds and the coefficient of correlation was found to be 0.96. The resulting regression Iine is:

Rosemount wind speed = 0.906 - Hydrotech wind speed + 1.196 (mls) (3.1)

Data not considered in the fit were the large number of occasions that the Hydrotech anemometer indicated no wind and the Rosemount sensor indicated wind to be present. This was the case for ail but 25 of the observations shown in the fü-st row of Table 3.3. hcluding these events would have increased the y-intercept and decreased the slope compared to values shown in Equation 3.1 and result in a less representative fit to the data for wind speeds > O mls. When the Hydrotech wiiid speeds were available to increase the wind record provided by the Rosemount sensor, they were adjusted according to the regression line shown in Equation 3.1 but not taken to be lower than 1-76 ds(Le. the average difference shown in Table 3.3 for Hydrotech speeds = O mk). The latter stipulation only came into effect when the Hydrotech anemometer indicated wind speeds less than about 0.6 ds.

As an example, roughiy a four day penod begm towards the end of Aupst where the Rosemount sensor did not provide wind data- Fi-we 3.5 shows the time series of one-hour mean wind speed (caiculated from the one-minute means) for the seven day penod approximately centered on this event The vertical dashed lines identify the period when the Rosemount data were not available and the adjusted Hydrotech wind speeds were used. The plot at the top of the figure shows ail available wind data and the one below shows the single wind record used in the present study. In addition to increasing the available data, the Hydrotech data were used on one other occasion. In mid-October, the Rsemount data were not available for about a one-day period and directly foilowing this. for roughly a fourteen-hour penod, the Rosemount anemometer significantly under- predicted the wind speed compared to the three other anemometers (one-hou mean wind speeds were up to 10 dslower). During this event, adjusted Hydrotech wind speeds were used in place of the Rosemount speeds. A seven-day period comprising the event is shown in Figure 3.6.

In surnrnary, the wind record at Brevoon Island Station was taken as the data measured by the Rosemount ice-resistant anemometer which was located roughly 4 m above gound level. During the occasions when these data were not available (and for the additional penod described above), the adjusted Hydrotech wind speeds and the Hydrotech wind directions were used. This resulted in a wind record which was 97.1 % complete during the penod begiming on Jan. 27/94 and ending on Nov. 06/94. The adjusted Hydrotech data were used for less than 6 % of the total period. From this point forward, references to the wind record at Brevoort Island Station will refer to these data, The distribution of absent wind data by month is shown in Fiapre 3.7. Notable periods were roughiy a three and one day stretch occurrîng in July and a two day event in Aupst.

3.2.2 St. John's Station

The meteorolo@cal station in St. John's, Newfoundland is situated in open and level terrain. A photopph of the site that shows four wind instruments is provided in Fiawe 3.8. Mounted on the same structure roughly 4 to 5 m above ground Ievel, the instruments are (front to back) a 78D anemometer, a Dragsphere anemometer, a Rosemount anemometer and a Hydrotech anemometer. In addition to these, not shown in the photograph, is a 78D anemometer fixed to a pole 10 m above gound. To distinguish between the two 78D anemometers, the former wil be referred to as 78D #l and the latter as 78D #2. One-minute precipitation data were also available at this station via the POSS Doppler radar.

The database comprises observations made from January, 1994 through April, 1995 inclusive. The relative compIeteness of the wind records from the five anemometers is shown in Table 3-4 together with the maximum level of completeness indicated in the last row. Bath of the 78D anernorneters provided data for more than 90 % of the record period, The Rosemount anemometer only provided wind information for roughly four and a half months enciing in mid-June. Hydrotech data were available for the sarne penod and additionally for about the last six months of the record. The Dragsphere anemometer provided data for most of the record starting approximately one week into March.

It was observed from rnonthly plots of one-hour mean wind speed that, intermittently throughout the record, the Dragsphere anemometer would become unresponsive to changes in wind strength, as was indicated by the other anemometers. Wind speeds were often under-predicted during strong winds and over-predicted during light winds. On severd occasions the Dragsphere anemometer indicated a near constant wind speed for periods up to a few days and longer. An example of this behavior is shown in Figure 3.9 where one-hour rnean wind speeds have been plotted for the month of November (during this month Rosemount data were not available and the Hydrotech anemometer began to hinction towards the end of day 9). On two separate occasions during the first week, each lasting about thirty hours, the wind speeds measured by the Dragsphere anemometer remained near constant. Aiso shown on this plot is the tendency of the Dragsphere anernometer to over-predict and the Hydrotech anemometer to under- predict the wind speed during light wïnd conditions compared to the wind speeds indicated by the 78D anemometers (i.e. du~gday 14 and on severai occasions proceeding day 26).

Anemometer Available wind data 78D #1 93.4 % 78D #2 96.8 % Rosemount 27.5 % Hydrotec h 62.8 % Dragsphere 83.7 % at least one of the above 96.8 %

Table 3.4 Availabie one-minute wind data at St. John's Station dunng the period of Jan. 0 1/94 to Apr. 30/95

The data chosen to represent the wind record at St. John's Station was that of the 78D #2 anemometer. Favorable characteristics of this data set are that, first, it alone provided the maximum attainable level of completeness and, secondly, the wind speeds were observed at a standard. 10 m height. In terms of quality, however, the 78D anemometer is more likely to expenence problems due to ice accretion than are the ice- resistant sensors. The alternative of only considering data from the three ice-resistant anemometers would allow for a wind record which is roughly 92 % complete. Roughly one-third of this wind record would have had to be supplied by the Dragsphere anemometer which, as described above, occasionally provided suspect data. It was felt that the use of wind data from the 78D #2 anernometer was a better choice with the provision that an attempt be made to identim conditions of icing during which wind data from a more suitable instrument could be used; this task being more manageable at St. John's than it would have been at Brevoort Island since the winters at St. John's are milder and shorter and thus, in a given year, fewer occasions are likely to occur where the 78D anemometer is susceptible to ice accretion.

Redekopp (1994) analyzed the wind data at St. John's for March and April together with data from an ice accretion sensor. During this period, it was observed that "si,pificant" events of ice buildup were a result of freezing drizzle or fieezing rain. It was also noted that the 78D anemorneter continued to nin dunng these penods but often recorded lower wind speeds compared to the ice-resistant sensors. Unfortunately, Redekopp did not explicitly identiS the dates during which the 78D anemometer was adversely influenced by ice accretion.

The first step taken to identify periods where the 78D #2 anemometer was affected by icing was to examine plots of one-hou mean wind speed and visually identib the occasions during which wind speeds were under-predicted by the 78D #2 sensor relative to the availabie ice-resistant instruments. For most of the record period, the wind speeds rneasured by the 78D #2 anemometer were as Least as high as those rneasured by the other instruments, this being expected since measurements of the former were made roughly 5 to 6 m higher above ground. The plot shown in Figure 3.9 is representative of what was most comrnonly observed in this respect (not including, of course, the two penods where the Dragsphere anemometer indicated near constant wind). It is likely that using this method may result in shorter periods, perhaps of an hou or less, being rnissed. However, it was the intention to identiQ periods of several hours or more where the 78D #2 anemometer under-predicted speeds to the extent that the varïability of the instruments could be ruled out as a cause of the event. Tentative thresholds were set at a duration of 3 hours and a differential speed of 3 to 4 m/s. An additionai requirement was that at least two ice-resistant sensors were present and indicating comparable speeds.

Eight periods were identified during which it was suspected that the 78D #2 anemometer was under-predicting the wind speed due to ice accretion- For seven of the eight events data were also available from the 78D #I anernometer. A common feature found was that both of the 7SD mernometers, for the most part, were infiuenced at similar tirnes and under-predicted the wind speed to a comparable extent- This fact lends credence to the assurnption that the periods were a resdt of ice buildup; the reason being that similar instruments exposed to similar temperature and precipitation events would likely expenence comparable intensities of ice accretion. During these periods, the available precipitation and temperanire data measured by the POSS were also indicative of conditions during which ice accretion may potentially occur. Two examples are given in Fiawes 3.10 and 3.1 1-

Fiame 3.10 shows one-hour mean data for the seven day period beginning on Mar. 01/94 during which both of the 78D anemometers under-predicted the wind speed compared to the Rosemount and Hydrotech sensors for about a seven hour period (indicated by the two vertical dashed lines). At the top of the fiapre, one-hou mean wind speeds have been plotted from ai1 avaiIable data (the Dragsphere anernometer was not functioning during this time). The one-hour mean wind speeds measured by both of the 78D anemometers were as much as 5 m/s lower than those indicated by the ice-resistant sensors. The middie plot shows the precipitation and temperature data measured by the POSS. Temperatures were only available for those minutes that the POSS detected precipitation and thus, in a given hou, the temperature indicated on the plot is an average of al1 available one-minute observations during that hour. One-hour precipitation totals are shown with three different symbols; each representing a different precipitation type observed by the POSS (see the top three items in the legend of the middle plot). 'ne symbols were chosen such that they would remain identifiable when plotted al1 on a single point. ln a given hour, the symbols were used done or in any combination to represent the composition of the precipitation occurring in that hour. When both of the 78D anemometers began to show slower winds compared to the two ice-resistant sensors and for severai hours pnor, both rain and snow were detected and the air temperatures ranged from about -3 to O OC. When the temperature increased to above O OC, the 78D anemometers retumed to recording comparable wind speeds. It is likely that the event was a result of ice buildup ont0 the 78D anemometers. The plot located at the bottom of the figure shows the single wind record chosen for this study (see more details below).

Fiawe 3.11 shows another example of a period where it was suspected that the 78D #2 anemometer was adversely influenced by ice accretion- Towards the end of Mach, the 78D #2 anemometer stopped running for roughly three days and during this time plus about an additional day and a half, the 78D #1 anemometer showed sirnilar behavior. The temperature and precipitation data, shown in the middle plot, were indicative of icing conditions. The scatter shown in the relative wind speeds during day 6 and about half of day 7 was typical during light winds. As mentioned previously, the Dragsphere anemometer normally indicated the strongest wind speeds followed by the 78D sensors and then by the Hydrotech anemometer. In this case, however, the 78D #1 cupwheel was likely stilI af5ected by icing and thus was showing little to no wind.

The cumulative duration of the eight periods where icing was suspected is approximately 17 days. Wind data were available from the Hydrotech anemometer in al1 cases. To improve the quality of the data and, at the same time, maintain the maximum level of completeness, Hydrotech wind speeds were adjusted and used in place of the 78D #2 wind speeds for these occasions. Table 3.5 shows the mean and r.m.s. of the difference in measured one-minute mean speeds (78D #2 speed - Hydrotech speed) with the same format used in Table 3.3. Data from the eight periods during which icing conditions were suspected were not included in the analysis. The results are sirnilar to those found when the Rosemount and Hydrotech sensors at Brevoort Island were cornpared. The Hydrotech anemometer, being a newer mode1 than was at Brevoort Island, frequently indicated no wind whiIe the wind speeds measured by the 78D #2 anemometer were on average 1.55 m/s. This result is likely due to the high starting threshold apparent with the Hydrotech sensor combined with the fact that the 78D #2 anemometer measured wind speeds 5 to 6 m higher above ground level. The overail tendency was for the 78D #2 speeds to be higher except when wind speeds larger than about 20 m/s were indicated by the Hydrotech anemometer. Hydrotech wind speed (ds) Wind speed difference (78D #2 - Hydrotech) > -c Average (ds) St- Dev. (ds) No. of obs. - O 1.55 0-66 16839

Hydrotech wind direction North 0.88 0.85 96676 East 0.88 0-95 60 144 South 1.26 0.88 8828 1 West 0.63 1-10 150639

Table 3.5 Statistics of the difference in simultaneous one-minute mean wind speeds measured from the 78D #2 and Hydrotech anemometers

A least squares fit of the simultaneous measured data was again used to relate the two wind speeds. The resulting regession Iine is;

78D #2 wind speed = 1.014 - Hydrotech wind speed t 0.774 (ds) with a correlation coefficient of 0.97. Sirnilar to the previous analysis, the data not used in the fit were the large number of observations where the Hydrotech anemometer indicated a speed = O m/s and the 78D #2 anemometer indicated a speed > O ds. The adjusted one-minute rnean wind speeds were not taken to be lower than 1.55 mls as this was the average wind speed recorded by the 78D #3 anemometer dunng the times the Hydrotech sensor indicated no wind. The plots located at the bottom of Figures 3.10 and 3.1 L show the one-hour mean wind speeds calculated from the adjusted Hydrotech one- minute mean wind speeds.

It was found that of the eight occasions where icing was suspected, the 78D #2 direction vane appeared to be influenced oniy once; measured directions remained constant for several days and thus it was Likely that ice buiidup prevented any movement of the direction vane during this period. The wind directions measured by the Hydrotech anemometer were used in their pIace for this event.

in surnmary, the wind record at St- John's Station was taken as the data measured by the 78D #2 anemometer. The cupwheel and direction vane were located 10 m above the ground in open and level surroundings. Adjusted Hydrotech wind speeds were used in place of those rneasured by the 78D #2 anemometer on eight separate occasions (adding to about 17 days of data) when wind speeds were under-reported by the latter. Corresponding temperature and precipitation data suggest the events to be a result of ice buildup. Hereafier the St. John's wind record will refer to these data. The wind record is 96.8 % cornpiete for the 16-month record period. Data were absent for scattered perïods no longer than a day in lena& with two exceptions: nearly a four day period in December and roughly a five day period spanning April and May. Figure 3.12 shows separately the amount of wind and precipitation data absent during each month together with the amount of time that one or both of the above were not available. Clearly, begiming in November, sipificant portions of the precipitation data were not available. Most of these absent data occurred in long continuous perïods. The more significant are about seven days in November, four days in December and 25 days spanning January and Febmary.

3.2.3 Downsview Station

The station in Downsview, Ontario is located at AES headquarters. Unlike the previous stations, which were set up to study the performance of various anemometers with respect to ice accretion, only wind data from two 78D anemometers were available. The fnst, which will be referred to as 78D #1, is located on a 10 rn pole to the south of the AES office building. The second, which will be referred to as 78D #2, is situated on top of the three-storey office building fixed to a pole about 7 m above the roof line. The nearby surroundings consist mainly of one and two-storey commercial buildings. In addition to the wind data, precipitation data were available from the POSS Doppler radar. The penod of record for the Downsview Station spans from Jan. 01/94 to Nov. 27/94, The relative completeness of the two wind records is shown in Table 3.6. Data from the 78D #l anemometer were not available for about the first four months and for the last month of the record period. An exarnple the relative wind speeds measured by

the MO anemometers is shown in Figure 3-13 where the one-hour mean wind speeds have been plotted for the month of July.

Anemometer Available wind data 78D #l 53.3 9% 78D #2 96.8 % at Ieast one of the above 96.8 %

Table 3.6 Available one-minute wind data at Downsview Station during the period of Jan, O 1/94 to Nov. 27/94

The data from the 78D #2 anemometer were chosen for the wind record. This data set provided the maximum attainable level of completeness on its own (see last row of Table 3.6) and therefore data from the 78D #f anemometer were not considered.

As shown in the previous sections when compared to various ice-resistant anemometers, 78D anemometers are likely to slow and sometimes stop when subject to icing. The present database onIy inchdes data from two 78D anemometers and thus it is difficult to assess the frequency and degree of such behavior. With the anernorneters being located at AES headquarters, as opposed to the more remote sites described above, prolonged icing is likely minimized since the instruments are more accessible to those responsible for their maintenance. Plots of one-hour mean wind speed show that only on one occasion did the 78D #2 anemometer stop ninning for a significant period of time (severai periods of less than a few hours were observed but these occurred when the temperatures were well above the freezing point). During the last two days of the record, there was roughly a one day period where the 78D #2 anemometer showed Little to no wind and, at the sarne the, light precipitation was observed intermittently and temperatures were fluctuating around OSC. It is possible that the 78D #2 anemometer was under-predicting the wind speed during this occasion (data from the 78D #I anemometer was not available dilring this period for cornparison).

More si-gnificant than the potential effects of king at this station, the rneasurements taken from both the mernometers may be biased due to Local influences on the arnbient wind by the AES office building and other nearby obstructions. These data are recognized as being limited in this respect.

Hereafier the Downsview wind record will refer to the data measurec! by the 78D #2 anemometer. The wind record is 96.8 % complete and the available precipitation data at this station comprises 9 13 8 of the observation period. The disuibution of absent data by month is shown in Figure 3.14. Wind data were mostly absent for the fmt three months and during the frfih month of the record. The sipifkant penods of absent precipitation data are a four-day span in March and a nine-day stretch towards the end of June.

3.3 One-Hour Database

Wind data and other meteorological information are observed across Canada at 426 airport sites (Yip et al.. 1995). The rnajority of the stations fall south of 55" N. The network includes 3 14 sites that record wind data on an hourly basis. Digital archives of these meteorological data are maintained by AES. In the present study, hourly data were extracted from the AES archives for the fourteen stations listed in Table 3.7 (the stations are shown on a map of Canada in Fi-pre 315). The penods over which the data were available are also shown (see Section 3.3.1 regarding the filtered record periods for the wind data). The wind and rainfail data are described below together with the procedures used for their quality assurance. Station Acronym Wind record Rainfall record Original Filtered (rain gauge data) Victoria Int'l, A., BC WC 1953-92 Vancouver Int'I, A-, BC VAN Calgary Int'I- A., ALTA CAL Regina A-, SASK REG Winnipeg Int'l. A., MAN WIN London A-, ONT LON Toronto Int'l. A., ONT TOR Ottawa Int'l. A., ONT OTT Montreal Int'l. A.. QUE MON Saint John A., NB STJ Halifax Int'l. A., NS HAL Charlottetown A., PEI CFA Port Aux Basque, NFLD POB St. John's A., NFLD SJS * rainfdl data only available during the warm season

Table 3.7 Station information of the one-hour database

The meteorological data employed in the present snidy include:

one or two-minute mean wind speed observed on the hour,

one or two-minute mean wind direction observed on the hour,

consecutive one-hou rainfall totais,

present weather observed on the hour (qualitative),

consecutive six-hour precipitation totals and

consecutive daily rainfall totals.

The Iast three items listed were used to estimate one-hour rainfali totais when the direct measurements frorn automatic rain gauges (Item 3) were not available. This is described further below. 33.1 Wind Data

Missing wind data in the AES archives are very few- Of the fourteen stations listed in Table 3.7, no single year of record had more than 1 % of the hourly wind observations missing with the exceptions of 1979 for Charlottetown and 199 1-92 for Pon Aux Basque. Missing data for these three years were roughly 3,6 and 4 % respectively.

HourIy wind velocities observed at airport sites across Canada (archived as HLYOl wind by AES) represent a nominal one-minute average. Starting in 1985, the averaging interval was increased to two minutes. The instrument typicdIy in use before about the mid 1960's was the 45B anemometer with a flashing light indicator. Observers counted the number flashes in a minute to determine the mean wind speed. During the mid 1960's, most stations began using the U2A anemometer. Observers assessed one- minute mean wind speeds (or two-minute means starting in 2985) directiy from dial or digital indicators or from analog chart output, depending on what was in use at the particular station. In practice, however, variabiiity in the averaging interval arises due to the different habits of observers (Moms, 1996). The one and two-minute averaging intervals rnay be better thought of as upper bounds to the actuai periods over which the archived wind velocities were averaged. A lower bound, perhaps, may be of the order of 30 seconds. nie ability to derive statistics of tme one-hour mean wind speeds from this type of data set is explored in Chapter 4.

Anemorneters are ideally located over open and level terrain with no immediate obstructions nearby which rnight influence the arnbient wind velocity. Nso, open and level terrain extending in al1 directions for an adequate distance is necessary in order for the mean boundary layer fiow to be developed at the point where the rneasurements are taken. When the above holds me, mean wind speeds measured at 10 m above ground level reflect (the so-cailed) standard conditions. Meteorological records, however, often reflect conditions which deviate from those described above and, particularly for long records, reflect conditions which change over tirne. To correctly assess the clirnatoIogical properties of wind frorn such a record, the data wouid fnst need to be adjusted to refiect standard conditions. The analysis wodd otherwise lead to less meaningful results.

For the present database, and for the majority of the stations in the AES archives, there are two sources of inforrnation kept by AES describing site conditions. The fxst Iists changes in anemometer height and instrument type over the station's history. The second describes general surroundings of the instrument site and changes thereof over the record period; references to nearby obstructions, such as buildings or trees, that may have infiuenced the wind measurements are occasionaily made. The site descriptions, depending on the station, Vary in both detail and completeness. Based on the two information sources, the qudity of the wind data for the initial portion of the records is typically poor in that the anemometers at (at ieast) ten of the fourteen stations were Iocated on the rooftops of aircraft hangars. control towers or other airpoa buildings. The measured velocities, therefore, may be biased due to building influences. Nso, early in the wind records, the anemometers were typically about 15 to 20 m above ground level. During the mid 1960's, corresponding to the movement towards the U2A anemometer, most stations reiocated their wind sensor to an exposed area on a standard 10 rn pole. On the whole, the site descriptions indicate that the wind records as archived require some form of adjustment to account for the variable anemometer exposure. Using Ottawa's wind record by way of example, the approach taken here is now descnbed.

An excerpt from the AES site description of Ottawa Int'I- A. is as follows:

"The instrzment site is located 152 rn north of the Administration ~uildingin a grassed triangle borrnded by roads. The area is free of obstntctions except for a few ornamental rrees. There is a row ofaircrafi hangars 600 rn to the West northwest, with single hangars 600 rn to rlze north and 326 m northeast- The anemometer is at the standard height of IO rn and is locared between rrlnways at a distance of 816 rn south of the Administration Building." This particular description ody indicates the current site conditions and not those effective earlier in the station's history. The listed anemometer heights over the station's history are @en in Table 3.8.

Hei-ht Date Effective 18.8 m May 19, 1944 19-5 m Feb. 10, 1951 9.9 m May 18, 1960 10 rn May 14, 1969

Table 3.8 Anemorneter heights above gound level for Ottawa Int'l. A.

The fmt step taken was to identiQ ail periods when the anemometer height and location remained unchanged according to the available information. These will be defined here as stationary penods. According to Table 3.8, over Ottawa's record penod of 1953 to 1992, there were tLhree different anemometer heights- Also, as can be seen frorn the excerpt above, information regarding anemometer relocations was not given for this station (the changes in height, however, may be an indication to changes in the anemometer location). Thus, this station was identified as having three stationary periods with the transition dates given in Table 3.8. The Iast stationary period (Le. May 14, 1969 and forward) corresponds to the description given above.

The next step was to calculate the mean wind speed for sixteen compass directions (22S0 sectors centered on N, NNE, NE, etc.) separately for each stationary period. The results of this analysis, shown is Figure 3.16 for Ottawa Int'l- A., were used to visuaily assess whether or not the anemometer exposures were comparable over the different periods. The calculations were performed on the archived wind speeds and on adjusted wind speeds. The adjustments were made according to the anemometer height by factoring the speeds to be representative of 10 m above ground levei using the logarithmic Iaw with a roughness lena& of 0.03 m. In absence of the detailed information required for anaiyticat estimations, this roughness length was chosen as an average value for the class of terrain typically found at meteorolopical stations. According to the generd classifications given by Cook (L985), a roughness length of 0.0 I m corresponds to 'Vat gassland, parkland or bare soil, without hedges and with very few isolated obstmctions" whiie a roughness Iene@ of 0.1 rn is appropriate for "fannland with fiequent high boundary hedges, occasional srnall farm structures, houses or trees". Assurning that the surrounding terrain of the meteorologicd stations fds within these two categones, the choice of 0.03 m as the roughness length would approximateiy split the difference in terms of the height correction factors. For example, errors of the order of t 7 4o of the mean wind speed would apply to speeds adjusted from 20 to 10 m above gound level.

The results for Ottawa's wind record (see Fiame 3.16) indicate differences between the exposures for the three periods. The fact that ten of the fouteen site descriptions explicitiy stated that anemometers were initiaily located on rooftops would possibly suggest the sarne to be me for Ottawa- This would explain the differences between the wind speed roses since the 80w around a building can be significantly different than the unobstructed upstrearn flow. Depending on the location relative to the building, the dimensions and shape of the building and the wind direction, the mean flow may be faster, slower or from a different direction than that at a sirnilar height upstream. If the only difference between the exposures during the three stationary periods were the memorneter height, the shapes of the mean wind speed roses would be comparable and, depending on the accuracy of the roughness length used to account for the height differences, the adjusted mean wind speeds would be comparable in magnitude. Since thk clearly is not the case, the assessrnent made at this point was to only use the data from 1970 forward - i.e. ai1 the full years within the last stationary period. These data will be referred to as the fdtered wind record,

The Iast step was to constmct wind speed roses, this time normalizing the directional mean wind speeds by those calculated from the filtered wind record, for consecutive intervals of time over the record period. The intervals were mostly four years in lena@, however, to accornrnodate the starting year of the filtered wind record, they were sometimes five or three years long. The intention was to identiq any significant changes in exposure, other than those assessed from the two sources of information, and to himght any graduai changes possibly due to urbanization in areas around the sites. The latter, however. would be more difficult to disiinguish from reai ciimatological trends. The height corrected wind speeds were used for this andysis. The plots for Ottawa ht'L A. shown in Figure 3.17 reved the fdtered wind record ( 1970-92) to be quite stationary over its entire duration. Also, based on this perspective, the variations in the mean wind speed from 1953 to 1969 clearly appear ta be a result of non- clirnatological factors. The final assessment was to oniy use the data from 1970 to 1992 for Ottawa's wind record.

This type of subjective analysis was performed on the data from each station to arrive at the filtered wind records shown in Table 3.7.

At each rneteorological site, the anemometer during the final stationary period was fixed to a 10 m pole located on the ground surface (at Port Aux Basque the anemometer was marginally higher at 10.7 m). For eight of the fourteen stations, only the wind data from the final stationary penods were used as the earlier portions of the wind records qualitatively showed sirnilar discrepancies to that illustrated above for Ottawa. For the six other stations, additional data were utilized in the filtered wind records, This is illustrated in Figures 3.18 and 3.19 for the Montreal station where the data from 1964 to 1992 were taken as the filtered wind record. Afier applying the height correction, the measurements made at 18.9 m above ground compare quite favorably to those over the final stationary period.

The procedures described above were employed simply to arrive at wind records that are more suitable for analysis. That is, the intention was to elirninate, for example, the cornparison between wind speeds measured within an accelerated flow region over a building with those measured under conditions comparable to the meteorological standard. The degree by which the resulting filtered wind records represent standard conditions, on the other hand, is a rnatter that would require more detailed information to assess. A likely scenario applicable to many meteorological sites is a gradua1 change in the character of the upstrearn surroundings due to the encroachment of buildings, trees and other obstructions- This would have the effect of decreasing the mean wind speed over time for the applicable range of wind directions.

The trend of decreasing rnean wind speed with time was evident at several of the stations, but was most pronounced at Victoria Int'l. A. (mean wind speed roses simiIar to those previously presented are given in Figures 3.20 and 3.21 for this station). The instrument site is located about 26 km north of the city of Victoria. The anemometer was initidiy on the roof of a hangar at a total height of 2 1.8 rn above ground level until early in 1964 when it was relocated to an area about 600 m from the instrument site at a standard 10 rn height- The filtered wind record was taken as the data from 1965 to 1992. Over this period, the shape of the mean wind speed roses remained somewhat stable but their average magnitude tended to decrease with the totd range beinp approximately 120 % of the overall mean (see Figure 3 -2 1). If this trend were a result of a gradua1 increase in surface roughness, then it would appear that the changes were directionally uniform. For stationq gradient winds, an increase in roughness length from 0.0 1 to 0.1 m would result in roughly a 20 % decrease of the mean wind speed at 10 m above ground level (Le. about half of the observed range). However, without knowledge about the character of the terrain and changes thereof over time, long-term changes in the wind clirnate cannot be ruled out as a cause, in fact, the filtered wind record for Vancouver Int'l. A., a close neighbor, showed simi1a.r trends but to a lesser extent. This wodd possibly support the idea that some portion of the decrease in mean wind speed was due to climatological factors. No corrections were made for the slowly changing mean wind speed observed at some of the stations-

An alternative method for arriving at a filtered wind record under the above circumstances is to start at the end of the record and move backwards in time until an unacceptable degree of stationarity is observed based on the computed mean wind speed roses. However, unless the filtered wind record cm be justified through historical site information, this method is considered to be overly subjective and inappropriate from a scientific point of view. The technique described above was thus adhered to for ali stations.

3.3.2 Rainfall Data

Hourly rneasurements of one-hour rainfall arnounts are available at many of the airport sites across Canada from automatic rain gauges, The standard instrument is the Tipping Bucket Rain Gauge. Often, however, the gauges are only in service during the warm season which, depending on the region, would typically be from April or May through October or November. For the present database, hourly rainfall data were available for the penods indicated in Table 3.7. Missing data over these periods ranged from roughly 1 to 15 % with an average of about 6 %.

As cm be seen from Table 3.7, the houriy rainfail measurements were generally not available until about the 1960's and, for several of the stations, were not available during the cold season for al1 or part of the record periods- The latter is a sib@ficant deficiency, particularly for coastal regions, since substantial rainfdls may occur during the Iate fa11 through the early spring. Welsh. Skinner and Moms (1989) developed a method to estimate one-hour rainfall totals from data that are available year-round and are available from early on in the records with very few missing observations. Following their method, time senes of one-hour rainfall amounts were constructed for each station and used to fil1 in the missing portions of the time series of measured amounts. The technique is described below,

Present weather observations are routinely made on the hour at Canadian weather stations. When precipitation is present at the time of observation, the type and intensity are reported. The intensities are reported as either light, moderate or heavy. The rates of faU corresponding to the three intensity categones depend on the precipitation type. For exarnple, in the case of rain or rain showers, the following divisions are used (AES, 1996): 1. 1- 1 to 2.5 mm/hr for light,

2, 2.6 to 7.5 mm/tir for rnoderate and

3, 7.6 mm/hr or greater for heavy-

Liquid precipitation fiing at a rate of 1.0 mm/hr or Iess is classified as drizzle. The divisions in this case are:

1. less than 0.2 mmhfor light,

2. 0.2 to 0-4 mm/hr for moderate and

3. 0.5 to 1.O mrnh for heavy.

In the event of rain or rain showers, the observer chooses an intensity category according to instrument data if available or based on qualitative observations otherwise. When instrument measurements are available, the mean rainfall rate over a short period (five minutes, for example) prior to the time of observation is used to choose the intensity level according to the ranges shown above. Qualitative guidelines, such as how fast puddes form or how individuai drops are perceived, are followed in order to c1assiQ the intensity when a rain gauge is not present at the site. The intensity class for frozen precipitation and drizzle, on the other hand, are mostly assessed through visibility criteria. A light intensity, for example, is reported when the visibility is 5/8 mile or greater. Direct measurements (considering the water equivalent of frozen precipitation), as described above, are used when the visibility is influenced by other factors such as fog.

The typical relative precipitation rates are listed in Table 3.9 for the thirteen different precipitation types reported. The method ernployed by Welsh et al. (1989) to estirnate one-hour rainfall arnounts utilizes the present weather observations described above, the precipitation rates shown in Table 3.9 and six-hour precipitation arnounts. The latter are routinely rneasured at the meteorologicai stations year-round and represent the total precipitation amount regardless of the composition (Le. liquid, freezuig and/or frozen). In addition to the three items used by Welsh et al., the procedure outlined here also utilizes 24-hour rainfd amounts, which are dso routinely measured year-round.

Intensity Precipitation rate (mdhr), equivaient water values Rain Rrùn Drïzzie Freezing FmPng Snow Snow Ice Icr Ice Snow Snow Hail showen rain dnzzic gains cryst;ils Pellets pellet showcrs pellets Light i-8 1.8 0.1 1.8 0.1 0-6 0.6 0.0 1.8 1.8 0.6 0.6 1.8 Moderate 5-1 5-1 0.3 4.0 0.3 1.3 1.3 0.0 5.1 5.1 1.3 1.3 5.1

Table 3-9 Typical precipitation rates associated with present weather observations, fiorn AES (1984)

The method for estimating one-hour rainfdl amounts will be ilustrated by way of the worked example show in Table 3.10. The table shows one day of data where the ody two precipitation types obsewed were rain and snow. The first column shows the hou of the day. the second shows the 24-hou rainfall, the third shows the six-hour precipitation and the fourth and fifth show the present weather codes for rain and snow respectively (codes 1, 2 and 3 represent the Light, Moderate and Heavy intensities respectively while O indicates the precipitation type was not observed) together with their associated rates of fdl taken from Table 3.9. The first five colurnns are the archived data from which the estimated one-hour rainfalls shown in the Iast coiurnn are denved.

The first step was to divide the six-hou precipitation amounts into six one-hour amounts via the precipitation factors shown in Colurnn 6, which are based on the typical intensities associated with the present weather code. For exarnple, the precipitation factor for hour 0 1 was calculated as 1.8/(1.8+1.8t5.1+1.8+0+0) = 0.17 1 while for hour 17 ic was calculated as 1.2/(0+0+ 1.8+1.8+ 1.2+ 1.3) = 0.197. The value of 1.2 associated with hour 17 is the average intensity of the two precipitation types observed for that hour - i-e. (1.8+0.6)/2 = 1.2. The next factor applied to the six-hour precipitation amounts is the rain factor shown in Column 7 which again is based on the typical intensities associated with the present weather code. For a given hour, this factor will be unity when only Hour 24hour Six-hour Eksent weather code/ Precip. Rain Tord One-hour rainfdl P~P- typid prm'pitacion factor factor rain rainfdl imm) (mm) intensity (rnmlhr) from factor atimre Table 3.9 (mm) Rain Snow

Total 35

Table 3-10 Worked exarnple for estimating one-hour rainfalis liquid precipitation is observed, zero when only frozen precipitation is observed and somewhere in between when both types are observed. In the above example, the rain factor for hour 17 is 1.8/(1.8+0.6) = 0.750. This factor reflects the portion of the one- hou precipitation which feil as liquid and is based on the assumption that al1 the precipitation types observed in a given hour occur for an equai portion of the time. Findly, the total rauifall factor shown in Colurnn 8 is applied so the total estimated rainfail matches the 24hour measured amount It is ody applied to the estimates within the six-hour periods where both liquid and frozen precipitation occurred. in the above example, the estimated rainfall during hours 13 through 18 added to 1 1.1 mm before the total rainfall factor was applied and to 10 mm afier it was applied, thus making the total estimated rainfdl(25t10 mm) match the 34-hour measured amount (35 mm). During the fxst six-hour period, the total rain factors are unity since the 25 mm of precipitation was ody composed of rain as indicated by the present weather code.

In the report by Welsh, Skinner and Morris (1989), the procedure oudined for estimating the one-hour rainfall amounts was illustrated through a simple exarnple comparable to the first six-hour penod shown in Table 3.10. It is therefore not known how the mixed precipitation events were treated in their analysis and whether the 24-hour rainfall measurernents were used in a similar or aiternative manner compared to that described above.

The performance of the rainfall estimating technique was assessed by comparing the number of times the estimated rainfall exceeded four pre-chosen threshold amounts with the number of times the rneasured rainfall exceeded the same four thresholds. Data were only considered in a given hour if both the estimate and measurement were available, thus, due to the sparseness of the hourly measurements, the results given in Table 3.1 1 are presented as overall totals as opposed to annual averages. In cornparison to the results from the rneasured rainfall, it cm be seen from the last row of Table 3.11 that the estimated one-hour rainfdl amounts predict on average approximately 12 % more hours with rainfall regardless of the intensity and approximately 18, 22 and 18 % Iess hours with at least 1.8, 3.0 and 5.1 mm of rainfd respectively. These results prompted further study as described below. Station Number of hours with total rainf'l exceedin~threshold Measured rainfdls Estimated rainfails >Omm 21.8mrn 23.0m1-n 15-lm >Omm 21.8mm L3.0m 15.Imm VIC VAN CAL REG UrIN LON TOR OTT MON STJ HAL CHA POB SJS Average 15779 3784 1795 667 17673 3105 1399 548

Table 3.1 1 Cornparison of the nurnber of threshold exceedences indicated by the meaured and estirnated one-hour rainfalls

The series of plots in Figure 3.22 show the average temporal distribution of the measured and estimated one-hour rainfalls over storms with durations of two, four and six hours. Here, stoms are defined as continuous penods of rainfall, as indicated by the measured one-hour arnounts, followed and preceded by at least four dry hours. Al1 storms occurring at the fourteen stations were identified and sorted according to their duration. Then, both the measured and estimated one-hour rainfalls for a particular storm were normalized by the Iargest one-hour rainfall measurement during the sarne storm. The normalized one-hour rainfalls were then averaged for al1 stoms having a similar duration separately for the measured and estimated data Clearly apparent in the plots is that the rainfall estimating technique tends to spread out and skew towards the right the distribu~onof the one-hour rainfalls over a stonn relative to the distribution based on the measured amounts. The former tendency would explain why the rainfd estimates predict more wet hours overall than indicated by the measurements on the one hand and

Iess hours for the higher rainfaii thresholds on the other hand (see Table 3.1 1).

The tendency for the total rainfd over a storm to be spread over a larger number of hours through the use of the estimating technique results because the estimated rainfalls are based on -'spot" observations. For example, if Light-intensity rainfall was observed at a particular hour (or within, say, + 5 minutes of the hour, depending on the practice of the observer) when the bulk of the rainfall occurred outside the corresponding one-hour period, an erroneous amount of rainfall would be allotted to that hou. In hm, this would lead to a reduction in the total rainfdl during @e period over which it actually occurred.

The tendency for the temporal distribution of estimated one-hou rainfalls to be skewed to the right relative to that of the measured rainfds follows frorn allotting the rainfall estimate to the hour following (or to the right of) the time of the present weather observation. For example, if rain had fallen h-om 06: 15 to 07:05, the rainfall estimate based on the present weather observation made at 07:00 would be placed between hours 07:OO and 08:OO while most of the rainfall would have occurred between hours 06:OO and 07:OO. One way to avoid this would be to base the rainfall estimate for a particular hour on the average of the nominal intensities (those associated with the present weather codes) at the top and bottom of that hour and otherwise perform a similar analysis to that illustrated above. While this technique would eliminate the rightward skew in the temporal rainfall distributions, it would dso spread the one-hour rainfall amounts over even more hours. A cornparison of the two estimating techniques showed that the approach outiined in Table 3.10 gives better estimates of the number of hours with rainfall exceeding the threshold amounts shown in Table 3.1 1.

In summary, the strength of the one-hour rainfall amounts estimated from the measured six-hour precipitation totals and the hourly present weather observations is that they are derived fiom data that are available year round with very few missing observations, However, the inherent deficiencies associated with the estimation methodology give good reason to only rely on the estimates in absence of the more accurate measured one-hour rainfail totals-

Figure 3.2 Photograph of the POSS Doppler radar, after Sheppard (1990) Figure 3.3 Photograph of Brevoort Island Station (s/ur) paads pu!^ (s/u) paads pu!& (s/ur) paads purA in--

(s/ur) paads pu!& (s/ur) paads put~

Figure 3.8 Photograph of S t John's Station (s/w) paads pu^^

(S/UI) paads pup~(wu) uo!~et!d!sa~d(s/u~) paads pu!^

(s/ur) paads PUFM

height (m): 19.5 9.9 10.0 date(yy/mrn): 53/01 60/05 69/05 .-.-*--...--.

Figure 3.16 Sixteen-point compas roses of mean wind speed for Ottawa Int'l. A. Fi,we 3-17 Sixteen-point compas roses of mean wind speed normaiized by that over the fdtered wind record (1970-92) for Ottawa Int'l. A. height (m): 23.2 18.9 10.0 date (yy/mm): 53/01 63/02 78/07 --..*--.-....

Figure 3-18 Sixteen-point compass roses of mean wind speed for Montreal Int'l. A. Figure 3.19 Sixteen-point compass roses of mean wind speed normaiized by that over the filtered wind record (1964-92) for Montreai Int'l. A. height (m): 21.8 10.0 date (yy/mm): 53/01 64/02

Figure 3.20 Sixteen-point compas roses of mean wind speed for Victoria Int'l. A. Figure 3.21 Sixteen-point compass roses of mean wind speed normalized by that over the fdtered wind record (1965-92) for Victoria Int'l. A. 1.0 two-hour storrn duration

four-hour storm duration ?f 1

i- 1 six-hour storrn duration

tirne (hours)

Figure 3.22 Comparison of the average temporal distribution of measured and estimated one-hour rainfalls for continuous periods of rainfall lasting two, four and six hours Chapter 4 On the Uses of Hourly Observed Short-Duration Mean Wind Speeds

4.1 Introduction

The AES Digitai Archive of Canadian Climatoiogical Data includes wind data observed at 426 airport sites. A total of 3 14 of the stations make observations each hour of the day (Yip et al., 1995). The wind data include one-minute mean speed and direction observed each hour for periods up to and including 1984 and two-minute mean speed and direction observed each hour thereafter. The wind observations are primarily used for weather forecasting and for aviation purposes.

From a wind engineering standpoint, this particular statistic does not lend itself to easy appiication. A cornmon representation of the wind for engineering purposes is given in terms of a mean velocity together with superimposed gusts- The retationship of the latter to the former is often given in terms of a gust factor which allows the peak pst speed to be estimated from the representative mean wind speed. An example of the scaling-up of the rnean wind speed cmbe found in the National Building Code of Canada (1990) wtiere procedures are outlined with various degrees of complexity to account for the faster winds over shorter periods as it pertains the design of structures. For structures, this is Eurther complicated by the spatial structure of gusts. Nonetheless, the statisticd description of the mean wind speed alone is often adequate. The choice of a suitable averaging period for descnbing mean wind speeds is customarily ten minutes to one hour. The reason for this can be iliustrated through the idealiled wind speed spectrurn given in Figure 4.1 which shows a low energy region for the range of penods mentioned above. The significance of the so-called spectral gap is that its location represents periods during which the wind can be considered adequately stationary (stationarity being an important assumption when reIating peak gus& to mean wind speeds) and therefore provides an appropriate duration for defining mean winds. A suitable wind record wodd therefore be a senes of consecutive one-hou means or a series of consecutive ten-minute means- From such series. extreme value theory can be employed to estimate rnean design wind speeds for appropriate retum periods to be used as the foundation to many engineering problems-

Assurning the statistical properties of one-hour mean wind speeds are of interest, the obvious shortcornin,o with a data set comprising wind speeds averaged over the last one or two minutes of each hour (referred to here as spot wind speeds) is that it is an incompIete wind record. In a piven hour the prevalent wind speed is not captured with a reasonable level of certainty based on a one- or two-minute spot measurement. Refeming again to the ideaiized wind speed spectrum show in Figure 4.1, this is iiiustrated by the distribution of high frequency energy which shows a somewhat broad peak at penods in the range of about three minutes to about hdf a minute. Physically, this implies that consecutive one or two-minute sarnples will fluctuate at a relatively significant Ievel and therefore any one sample is not necessarily representative of the mean speed over the given hour. Naturaily this effect becomes less pronounced as the averaging time of the spot wind speed is increased. Ofien wind archives comprise hourly sarnples of ten- minute averages: such a wind record is stiU incomplete but the ten-minute mean wind speeds are certainly more representative of the corresponding one-hou values.

It should also be noted that deriving, for example, statistical distributions (or other forms of statistical properties) of one-minute mean wind speeds from a database comprising one-minute means observed hourly should not be taken for granted, particularly when extremes are of interest. In the case of the parent distribution, the derived fit is likely to be representative of that which would be obtained if al1 sixty one- minute means were available for each hour provided the database covered an adequate period of time. However, when one is concerned with the distribution of extreme one- minute mean wind speeds, a database containing only one measurement per hour is far from ideal. In a parricular hour, the one observation has a one in sixty chance of being the largest in that hou. It foliows that. if the short-duration wind speeds are observed hourly, they be considered to paralle1 one-hour mean wind speeds so as to emulate a complete wind record. The increased variability uitroduced by this will likely move the predicted extreme by an unknown distance from that averaged over one-hour towards that averaged over one-minute in keeping with the same example.

It is the intent of this chapter to assess, in an exploratory fashion, the abiiity to estimate statistical distributions of one-hour mean wind speed from hourly observed short-duration spot samples. As rnentioned above, spot wind speeds are defined here as hourly observed wind speeds that are averaged over a penod of much less than an hou. The motivation of this chapter stems from the fact that the aviation sites of the AES digital archive presently record two-minute spot wind speeds and pnor to 1985, one- minute sarnples were observed hourly. In order to take advantage of this large Canadian database in tems of deriving statistics for one-hour mean winds, these averaging times are the focus of this chapter. In addition, ten-minute spot wind speeds are aIso considered as this averaging period is often utilized in other national weather archives.

The one-minute database descnbed in Section 3.3 was used for this portion of the study. The varîous time senes of mean wind speed constructed from this database are described in Section 4.2. Section 4.3 describes the dependence of spot wind speeds on their corresponding one-hour means. The performance of predicting the parent distribution of one-hour mean wind speeds from spot measurernents is investigated in Section 4.4 and similarly, the extreme distribution in Section 4.5. Sumrnary remarks are presented in the final section,

4.2 Time Series of Mean Wind Speed

The one-minute database comprises consecutive measurements of one-minute mean wind speed for three locations. Record lengths range from about nine to sixteen months. Three different types of time series of mean wind speed have been constructed from these data and fom the bais of this chapter.

First, time senes comprising consecutive and non-overlapping measurements of mean wind speed have been consmcted- These will be referred to as the '"full'' time senes and denoted as V, {r}where represents the duration in minutes over which the speeds were averaged. For each station, three full time series were constnicted corresponding to two-. ten- and sixty-minute averaging intervals; rnaking a total of four upon inclusion of the original one-minute mean data. As an example, V, {Oz} represents a time senes of consecutive and non-overlapping two-minute mean wind speeds.

The second type of data series derived was that of hourly observed wind speeds averaged over one, two and ten minutes or, in other words, one-, two- and ten-minute spot wind speeds. The notation used to represent the "spot" tirne series is V, (z) where r is similarly defined as above. Three separate series of spot wind speeds were constructed for each averaging interval corresponding to observation times of on the hou, at the two- thirds hour point and at the one-third hour point. Defining y-, as the wind speed averaged over the ith minute in the jth hour, the three spot time series were constructed as follows:

1 1. spot dataseries 1, V'{r], =-xy+, i=6 1-r

1 '- 2. spot data series 2, V, {r}, = - v . ir '-1

1 3. spot dataseries 3, V,{s), =- ZV.. t-J ri=zl-r each for 7 equal to one, two and ten minutes. The corresponding one-hour mean wind speed for the jth hou was simply the average of al1 sixty one-minute means. The purpose of constructing three spot data series for each averagïng interval was to better assess their performance in predicting statistical properties of one-hour mean wind speed. The idea is that the three measurements in a particular hour represent independent fluctuations about the same one hou mean wind speed and the results korn each of the time senes can therefore be used as an indication of the possible variability involved when analyzing this type of data,

The third type of data set consuucted will be referred to as the "modified spotT' time senes and denoted as V'{r}. As indicated by the narne, the wind speeds of this series are fomiulated directly fmm the spot measurements by averaging consecutive values. That is, for the jth hour V,, {T } = (V, {T } +, + V, {z 1 ) / 2. The modified spot time series were constmcted from each of the spot time senes described above. As will 5e shown. the modified data result in better estimates of the statistical propertïes of one-hour mean wind speed compared to those estimated from the original data senes of spot rneasurements, particularly for the one- and two-minute averaging intervals.

Table 4.1 sumarizes the 22 different time senes constnicted from the one- minute database for each of the three locations. As on occasion wind observations were missinp from the original data sets, one-hour mean wind speeds were only accepted if a minimum of 54 observations were present and sirnilady ten-minute means if a minimum of 9 observations were present (i.e, a threshold of 90 %). Two-minute mean wind speeds were used only when both of the one-minute averages were available. AH of the 66 wind speed time series are between 95.4 and 97.1 % complete.

Type of data set Nurnber of time series z = 60 min. r = 10 min. z = 2 min. .r: = 1 min. hl1 data series, V, {s } 1 1 1 1 spot data series, V, {r} - 3 3 3 modified spot data series, V,, {r} - 3 3 3

Table 4.1 Number of time series constructed from the one-minute database for each of the three stations The statistical properties derived from the senes of one-hour mean wind speed will be used as the reference by which the related properties derived from the other time series will be cornpared. As mentioned above, the record lengths of the three stations range from about nine to sixteen months and are not particularly long. At a given station. the statistics and estirnated distribution parameters for the one-hou mean winds are representative for the record period and not necessarily for the station in general owing to the short sarnple. Results from the other time senes are compared to indicate the ramifications of their use when the statistics of one-hour mean speeds are of interest. The fact that the record lengths do not extend over a long penod of thne is less of a sia+ficant factor in this regard since fnst, it is common to al1 the time series for a particular station and secondly, this portion of the study is airned at exploring trends.

4.3 Dependence of Spot Wind Speeds on One-hour Means

Consider a single hour of wind where V; represents the average wind speed over the ith minute. The non-dimensional variable g, can be defined as:

where m, and O,, are respectively the average and standard deviation of over the one- hour penod (m, will be used hereafter in place of V, (60)). It follows that the average of g, is;

and the standard deviation is: Normalking the wind this way on an hour by hour basis, using always the local values of m, and q,,results in g being a stationary random variable of time with an average and standard deviation as indicated above- This representation is certainly not new and has ofien been used for predicting peak short-duration wind speeds, mostly psts of the order of a few seconds, in relation to the mean wind and intensity of turbulence (see, for example, Davenport, 1964).

Here the variable g is given the term spot factor and represents the number of standard deviations a randomly observed short-duration wind speed mers fiom the one- hour mean. This cm be di~tin~~shedfrom the so called peak factor (often denoted as g,) which relates the average number of standard deviations the Iargest short-duration wind speed (or other quantities such as the response of structures to wind) will differ from the mean. An example of the transformation of a time senes of one-minute rnean wind speeds to a tirne series of one-minute spot factors is shown in Figure 4.2a. The sarnple of wind used in the figure was taken from St. John's station and covers a period of ten hours during which one-hour rnean wind speeds were in the range of about 6 to 12 ds. Several items are shown on the upper plot dong with the tirne series of one-minute mean wind speed. Firstly, one-hour mean wind speeds are shown by thickened horizontal lines and secondIy, above or below the right end of each of these Iines are solid circles highlighting the one-minute spot wind speeds (these emulate the data available from aviation sites of the AES digital archive prior to 1985). The latter are also represented on the lower plot which shows the one-minute spot factors resulting from the transformation described above.

Before discussing the ~i~gnificanceof the spot factors, it is apparent from the upper plot in Figure 4.2a that the differences between one-minute spot wind speeds and their corresponding one-hour means are significant and random. In ody this ten-hour period, the differences (expressed as a percentage of the corresponding one-hour mean) range fiom roughly + 27 % to - 30 %. Sùnilar plots are shown in Figures 4.2b and 4.2~for two- minute mean wind speeds and for ten-minute mean wind speeds over the same ten-hour period. In both cases the spot factors were refomulated based on the new hourly values of o, (Le. calcuiated frorn the thirty samples of two-minute means and from the six sarnpIes of ten-minute means respectively for each hour). In this short sample of wind, the use of two-minute spot wind speeds ody shows a marginal improvement in terms of better representing the corresponding one-hou means. In the case of ten-minute spot wind speeds, the differences sirnilar to those expressed above are si,pïficantly smailer and range from about + 10 % to - 15 %.

The ~i~gificanceof the spot factor becomes more apparent when Equation 4.1 is rearranged into the foilowing general hm;

where u, (T)is the coefficient of variation given by:

and:

With the expression given in Equation 4.4 we can relate, in terms of probabilities, spot wind speeds to coincident one-hour means. The assumptions involved and the relevant parameters are now descnbed.

Assuming the coefficient of variation to be a known function of the mean wind speed for a given value of T , Equation 4.4 involves two random variables: narnely the one-hour mean wind speed and the spot factor. The assumption made here is that the two variables are independent. The time series of the spot factors presented in Figures 4.2, being derived from one-hour mean wind speeds ranging from about 6 to 12 ds, are certainiy in support of tiis assumption. Accepting the variables to be independent, it follows that their joint probability can be given by;

where f (m,) and f (g ) are the individual probability density functions. Thus, the probability that a spot wind speed will fa11 within a smail interval centered on V, {r}is simply the sumrnation of the right-hand-side of Equation 4.7 for ail the values of m, and g which satisfy Equation 4.4. As such, the probability distribution of the spot factor and representative values of the coefficient of variation need to be defined. in the above order, these two items are now discussed-

To this point the spot factor has been shown to be a stationary random variable with a mean of O and a standard deviation of 1- To be able to relate a spot measurement of wind to its one-hour mean in terms of probabilities, the statisticd distribution of g is required. For this. consider a continuous record of wind over a one-hour penod that is non-dimensionalized as in Equation 4.1 so V, becomes V(r). Using a Fourier analysis, V(t)cm be represented by the following sumrnation;

where a,, onand #n are corresponding values of the amplitude, angular frequency and phase respectively. It follows from the Centra. Lirnit Theorem that if N is large and the phases are random, the probability density function of V(t) is Gaussian (Davenpon, 1994a) and given by: From Equations 4.1 and 4.9, the probability density function of g(t) is also Gaussian and given by:

If V(r) is replaced with V, (t), , the kth short-dr ration wind speed averaged over duration T in a @en hour, the above will be strictiy tnie as tends to zero. Lqer vdues wiZl result in the extent of the relevant frequencies of the spectral representation to diminish, hence decreasing N and the applicability of the Central Limit Theorem.

To investigate the distribution of g associated with various wind speed averaging intervals, histograms were constructed for T = 1, 2 and 10 minutes. For this, the full time series of V, {Ol}, V, (02) and V, (10) were each transformed to a time series of spot factors in the manner previously described. Only the hours in which al1 wind speeds were greater than zero were considered to ensure no lower bound on the fluctuations. The histograms are presented in Figures 4.3 for the three stations. The standardized normai distribution given in Equation 4.10 is also presented in a similar discrete fashion for comparison. Results show diat the distribution of one- and two-minute spot factors closely resembles that of the normal distribution for al1 three locations. In the case of the ten-minute spot factors, however, the distribution is more uniform for central values and drops off more rapidly comprising a smaller range. The calculated rnean and standard deviation of the spot factors in ail cases were O and 1 respectively as this fact is inherent in their definition,

Another requirernent for relating a short-duration wind speed to its corresponding one-hou mean is the local value of the standard deviation or, in its norrnalized form, the coefficient of variation. Scatter plots of the latter versus one-hour mean wind speed are shown in Figues 4.4 for the three stations examined. Values were determined again for z = 1, 2 and 10 minutes and ploned separately on logaritiimic axes, each data point representing one hour of wind. Again, hours comprising only non-zero short-duration wind speeds were considered and otherwise no attempt was made to filter out any of the data according to either wind speed or directional aspects. The employment of these data is with respect to parent winds (see the following section) and it was felt thar the full range of data shouId be considered. In contrast, ofien great care is taken in choosing appropriate averaging penods for the mean wind speed in order to minunize trends in both the speed and direction so as to ensure a reasonable level of stationarity (Wieringa, 1973)- This is in the interest, however, of fine tuning the relationship between peak gusts and mean winds.

The general tendency is for the coefficient of variation to decrease with increasing mean wind and, at a given wind speed, to be spread over a range of up to an order of magnitude in size and larger. The latter is more evident in the case of ten-minute mean wind speeds compared to the one- and two-minute averaging intervals. The coefficients of variation presented are, in effect, a coarse representaûon of turbulence intensity at a single point within the atmospheric boundary layer. The data most relevant from a practical standpoint are those cdculated for St. John's station since the height of the wind instrument and the surrounding terrain at this site are consistent with the standard present at most meteorological stations, which are typicdy located in open airfields 10 m above ground Ievel. Some general cornparisons will, however, be made on the results of the other stations-

The wind measurements at Brevoort Island were made at about 4 m above ground Ievel in open surroundings. Apart from the scatter at low mean wind speeds, the coefficients of variation cdculated at this site were the lowest on average of the three stations, With al1 else being equal, turbulence intensity in the atmospheric boundary Iayer increases as the ground is approached provided its origin is predominantly mechanical, as opposed to being thermally induced. The fact that this is not reflected in the results for St. John's and Brevoort Island suggests a difference in surface roughess at these sites. Referring to Figures 3.3 and 3.8, the ground at St. John's comprises mostly coarse grave1 while at Brevoort Island snow cover is likely dominant for most of the year. According to the six roughness classifications gïve by Cook (1985), the latter is rated with a smoother surface- It is aIso seen by comparing Figure 4-4b with Figures 4.4a and 4.42 that the coefficients of variation rneasured at Brevoort Island exhibit a larger degree of scatter compared to the other stations. Possible factors are again with respect to the snow cover at Brevoort Island station in that the ground snow Ievel rnay Vary in depth over the course of a season and intermittently local snowdrifis rnay develop, possibly causing peculiarities to the fiow field.

On average the coefficients of variation computed at Downsview are the highest of the three stations- The anemometer at Downsview is frxed to a pole at about 7 m above the roof iine of a three-storey office building and is higher than its nearby surroundings, which consist mainly of one and two-storey commercial buildings. Apart from the greater surface roughness characterized by the terrain, the increased standard deviation for a given rnean wind speed is possibly a result of local influences by the building on which the anemometer resides.

The apparent linearity seen in the data plotted in Fi--es 4.4 suggest that representative values of the coefficient of variation can be given by;

where a{r} and b{r)are positive constants for a given value of r. Based on the least squares criteria, the constants have been derived and are presented in Table 4.2. The corresponding cuves are plotted on linear axes in Figure 4.5 for reference- The dependence of the coefficients of variation on the wind speed averaging interval is clearly indicated in the plots.

The assumptions and relevant parameters presented in this section are utilized in the subsequent section in a numencal approximation of the parameters for describing parent spot wind speeds from those applicable to one-hou means. -. . - - .- - Station Parameters for Equation 4- 1 1

St- John's 0.309 0.3 12 0-286 O -453 0.525 0.698 Brevoort 1. 0.43 1 0.413 0.3 12 0.74 1 0.788 0.845 Downsview 0.28 1 0.270 0220 0-28 1 0.34 1 0.5 15

TabIe 4.2 Parameters for obtaining representative values of the coefficient of variation from one-hour mean wind speed in m/s

4.4 Parent Distribution

In temof the probability density function appropnate for omni-directional mean wind speed. the folIowing Weibdi distribution has long been accepted;

or, in its cumulative forrn;

where k and c are the distribution's parameters. From Equation 4.13, it can be shown that the parameter c represents the wind speed that is exceeded about 37 % of the time and is therefore indicative of the tocation of the distribution. The exponent k reflects the spread in that lowering its value results in probabilities that extend over a wider range of mean wind speed.

Equation 4.13 can be rearranged to the foiiowing form: This would allow similarly transformed data to be compared with a straight line. Estimates of F(m,) can been obtained through an analysis of order statistics. This involves sorting the observed wind speeds in ascending order and applying the following expression;

where (m,), is the mth largest wind speed and M is the total number of observations in the record.

Based on Equation 4.15, cumulative probabilities were estimated for each of the 22 time series for the three stations. Estirnates of the Weibull parameters were made by transforrning the data into the form shown in Equation 4.14 and applying the least squares criteria to define a representative straight line. For a particular case, only 50 of the data points were used in the fit corresponding to equal increments of wind speed starting at 1 m/s and ending rit the extent of the data.

Plots showing the observed data in comparison to the Weibull fit are given in Figure 4.6 for the one-hour mean wind speeds. The observed wind speeds at Downsview are well represented by the straight Line while those for Brevoort Island do not conform as well and tend to form an S-shaped curve. The quality of the fit at St. John's fdls somewhere between in comparison. Histogams for the same three cases are presented in Figure 4.7 showing also the mean and r.m.s. values of the parent populations. The Weibuli parameters and population statistics given in the two figures will be used as the reference by which similar results frorn the other time series are compared. The comparative results from the spot and modified spot data sets are given in Figures 4.8 and 4.9. The mean and r.rn.s. values are sumrnarized in the array of nine plots shown in Figure 4.8 and the estimated Weibull parameters are similarly presented in Figure 4.9. Al1 values are expressed as a ratio of the corresponding result denved from the one-hou mean wind speeds at the saine station. Also shown in Figure 4-9 are estimates of the variation in the Weibull parameters associated with spot rneasurements using an analytical approach described later in this section.

Consider, for example, if the histograrn @en at the top of Fiame 4.7 was constnicted from one-minute spot wind speeds as opposed to the corresponding one-hour means. Assurning that each frequency bin would loose a constant portion of its observations to adjacent bins as a resdt of the increased scatter, the net effect would be for the central bins to decrease in size and for the outer bins to increase, thus spreading out the distribution and at the sarne time not significantly altering the central Iocation. In terms of the parameters of the fitted Weibull distribution, this scenario would decrease the exponent k and likely have little effect on the parameter c.

The resuits shown in Fiapre 4.8 support the above ideas. Focusing only on the statistics derived from the spot data series (symbol "x"), the tendency is for the population mean to rernain close to that derived from one-hou mean wind speeds and for the population r.m.s. to be comparatively larger. As expected, the latter is shown to be increasingly true as the averaging intervd of the spot measurement decreases since this corresponds to larger fluctuations about the one-hour rneans. Now, refening to Figure 4.9 and again only to the resuIts from the spot data series, similar tendencies are seen. That is, changes in the pararneter c are typically small and changes in the exponent k consistently tend to the negative and increasingly so for shorter spot wind speed averaging intervals.

The consistent increase in the r.m,s. values (which translates to a decrease in the Weibull exponent k) is a result of the scatter associated with spot wind speeds about corresponding one-hour means. It was show in the previous section that the deviations from the one-hour rnean wind speed can be related to the coefficient of variation through the spot factor (Le. Equation 4.4). To justifjr the use of the modified spot data series over the spot data series consider, for exmple, if two short-duration wind speeds were available for each hour where the observation times were adequately separated such that their deviations from the one-hour mean wind speed could be regarded as independent. It foüows from Equation 4.4 that the average of the two rneasurements in a given hour (denoted here as VS2{I) ) can be represented by the foilowing expression:

where g, and g, are individual values of the spot factor. Based on the assumption that the two spot factors are independent, it is easily shown that probability density function of the new variable. (g, + g, ) / 2, is also Gaussian with a mean of O and a standard deviation of L / fi,the latter being reduced by roughiy 30 %. It follows that a senes comprising hourly observations of V,, {s) would exhibit less scatter about corresponding one-hour mean wind speeds than an othemise sirnilar series compnsing hourly observations of V, {s} and, in tum, the former would resdt in a better prediction of the Weibull exponent applicable to one-hou mean wind speeds.

From a series of hourly observed spot wind speeds. a time series of V,, {r}cm be constructed in effect by simpiy averaging consecutive observations (as was done in the Formu1ation of the modified spot tirne series, V,, {z})- in a given hour, the fact that the spot measurement is averaged with that occurring at the end of the previous hour (as opposed to using another sarnple from the hour in question) is likely insignificant, particularly when dealing with averaging intervais of one and two minutes. Another difference between a time series of Vs2 {s}and a tirne senes of V,, {s) is that consecutive values of the latter are correlated. That is, V, {T),is used in calculating both V,, (T},and

V { Noting the two differences, the argument presented in the previous paragraph

is likely applicable, at least in a qualitative sense, to the modified spot data senes.

Refemng back to Figure 4.8, it can be seen that the performance of the modified spot wind speeds (symbol "O") is si,@icantly better in terms of predicting the population r.m.s. applicable to one-hour mean wind speeds and that the averaging interval is less of a significant factor. The population means are no different than those determined frorn the spot data sets (however, since one missing data point in the spot the series leads to two missing points in the modified version, the results show smdI differences). The modified spot data series dso favorably influence the predicted Weibull exponents compared to the estimates frorn the spot data series as is seen in Figure 4.9. The ratios of the parmeter c, which tended to be marginally Iess than unity for the spot data senes, likewise show improvements through the use of the modified spot data sets.

At each of the three Locations, the time series of modified ten-minute spot wind speed consistently resulted in population r.m.s. values which were Iower (although only marginally) than the respective value computed from the one-hour mean wind speeds (this, in tum, resulted in higher Weibull exponents for seven of the nine data sets). This is probably a result of using the ten-minute mean wind speed occurring in the previous hour as opposed to using another observation from the hour in question. To this end, a time series of V,, (IO) was consmcted for each station by averaging the ten-minute mean at the beginning of the hour with that at the end of the hour. The population r.m.s. in each of the three cases was found to be nearly equal but slightly higher than the respective vdue computed from the one-hour mean wind speeds (Le. the ratios were slightly greater than unity as opposed to being slightly smaller). It appears that a tirne series of V,,, {IO) parallels that of hourly observed mean wind speed averaged over a penod of slightly longer than an hour thus leading to the varïability being reduced beyond that exhibited by the one-hour mean wind speeds.

On the whole, the discrepancies involved when predicting Weibull parmeten appropriate for one-hour mean wind speed from a database comprising hourly observed spot measurements are small for the parameter c and more sipificant in the case of the exponent k. The results clearly indicate that estimates of the Weibull exponent obtained from spot wind speeds are lower than those appropriate for one-hour means and that irnproved estimates can be obtained through the use of modified spot wind data that are probably within the other uncertainties. Significant factors in this respect are measurement errors associated with anernometers, the variabiiity introduced through the data analysis, the degree by which the data conforms to the mode1 and how the outcome will differ in terms of the eventud use of the parameter estimates.

To be able to assess the differences arising through the use of spot data more generally, a simple analytical exercise was undertaken based on the ideas presented in the previous section. The mode1 is outlined below and results are compared with those from the spot data of the three stations.

The cumulative distribution function of parent spot wind speeds can be estimated by the following expression;

where the region of integration represents all values of m, and g that result in a spot wind speed greater than V,[z) according to Equation 4.4, Taking m, and g to be independent and placing in the appropriate limits, the above expression becomes:

Based on Equations 4.4 and 4.1 1, the Iower lirnit of the integral in braces is given by the solution of m, from the foliowing expression:

In words, the integral in braces represents the probability that the one-hour mean wind speed takes on a value greater than q, (V,(71, g) and thus, its solution foilows from the cumulative distribution function aven in Equation 4.13. Upon expansion, Equation 4.18 becornes; where k and c are the Weibull parameters for the one-hour mean wind speeds. In the above expression f (g) was taken to be Gaussian with a mean of O and a standard deviation of 1. By evaluating numerically Equation 4.30 for an may of vaiues of V, (r), probabilities cm be generated for estimating the Weibull pararneters associated with spot wind speeds given those associated with one-hour means.

To test the expression, Weibull parameters were estimated for one-, two- and ten- minute spot wind speeds for the three locations. The input data in each case were the Weibull pararneters denved fiom the time series of one-hou- mean wind speed (Le. those shown in Figure 4.6) together with the constants a{z)and b{z)given in Table 4.2, In each case, Equation 4.30 was evaiuated for fifty equally spaced wind speeds. The maximum was determined from the given Weibull distribution of one-hour means by setting the probability of exceedence to 0.001 and solving for the corresponding wind speed- This method ensured that the data points covered the bulk of the distribution. In al1 cases exarnined. the least squares correiation coefficient for the generated data was found to be unity to fou signifiant digits.

Results are shown in Figure 4.9 by the dashed lines and compare quite favorably to the trends exhibited by the Weibull parameters derived directly from the spot data sets. More often than not, it is shown for both the Weibull parameters thac the predictions from the model fall within the range of the estimates from the three spot data senes in a given case. The cornparisons lend support to the anaificd approach and the inherent assumptions.

To assess how the use of spot data wilI influence different parent populations of one-hou means, a similar analysis was performed for a range of k and c values comprising those typicaily found in practice. The constants air) and b(~)for relathg the coeEcient of variation to mean wind speed were taken as the values determined from the database of St- John's station. As described above, this station is consistent with rnost standard meteorologicd stations in tenns of anemorneter height and surrounding terrain, namely 10 rn above ground in open and level surroundings (see photograph in Fipe 3.8). The Weibull panmeters used as input to the anaiysis were 3 to 15 m/s for c (with a step size of 1 ds)and 1.3 to 2.7 for k (with a step size of O. 1). Corresponding values were generated in each case for one-, two- and ten-minute spot wind speeds.

Some aspects of the results are best described in terms of the straight-line representation of the cumulative distribution hction (see Equation 4.14). The line defining the probabilities of the one-hour mean wind speeds is influenced through the use of spot data by an increase in the dope, llk. The change in the parameter c depends on this and on the point of intersection of the two lines. For larger fluctuations and ail else being equai, the point of intersection moves away from the tail and towards the y- intercept (which defines the parameter c) and the change in dope is greater. The former of the two would explain why the change in the parameter c was most sibcrIUficant for the Brevoort Island data (see Figure 4.9) since there the fluctuations were least pronounced and therefore the point of intersection tended to be Westfrom the y-intercept. In al1 the cases considered in the simulation, the absolute difference in corresponding values of the parameter c was found to be less than 0.1 m/s with the fractionai values ranghg from 0.97 to 1.00. The point of intersection in these instances tended to be near but to the right of the y-intercept.

The changes in the Weibull exponent simulated in the analysis are summarized graphicaily in Figure 4.10. For clarïty, ody curves corresponding to the input values of c = 3,4,7 and 15 m/s have been included and, for the same reason, the curves for the two- minute spot wind speeds were not included as they were only margindy higher than those for the one-minute interval (about half the thickness of each curve would overlap for a given value of c). Results show larger percent decreases when one-hour mean wind speeds are distributed with either a higher k or a lower c. With dl else constant, one or both of the above will change the distribution to a more peaked cwe compared to the given originai shape. It foiiows that one-hour mean wind speeds which exhibit Little variance in the fust place are more susceptible to the scatter introduced through the use of spot data and. in tum, are more susceptible to discrepancies in the Weibull exponent. The influence of the averaging interval T is aiso clearly indicated on the plot.

Consider, for example, a database comprising hourly observed one-minute mean wind speeds measured 10 m above ground in open Ievel surroundings- If the Weibull parameters were estimated to be 1.9 and 7.0 ds, an estimate of the Weibull exponent associated with one-hour mean wind speeds could be obtained from Figure 4- 10 based on the assumption that the parameter c would not significantly change. The procedure would be to simply locate the above point on the plot (interpolate where necessary) and read the corresponding Weibull exponent associated with one-hour means from the horizontai axis. In the above example, the Weibull exponent for one-hour mean wind speeds is estirnated to be roughly 2.0. The figure, more simply, could be used as an aid in deciding whether modified spot data need be applied according to an estimated error. It should be kept in mind that larger errors are probable for spot wind speeds observed over rougher terrain where the fluctuations about the mean are greater.

For engineering purposes, more significant than the parent population of one-hour mean wind speeds, aithough not unrelated, is the population of extremes. The following section deals with predicting extreme one-hou mean wind speeds from a database, again, consisting of hourly-observed spot measurements.

4.5 Extreme Value Distribution

Two different methods for predicting extreme one-hour mean wind speeds from spot measurements are assessed in this section, The fxst is the traditional approach of fitting epochal extremes to the Type4 extreme value distribution (Gumbel, 1958) and the second involves the parent distribution and an expression for the average upcrossing rate of a stationary random variable (Rice, 1954). The latter approach has been studied by Davenport (1967), Gomes and Vickery (1977), and Twisdale and Vickery (1992, 1993). The two approaches are dealt with separately in the following two sections. The theory of each approach is frrst outhed and then resuits of the relevant parameters and predicted extremes from the various time series are presented and differences among them

4.5.1 Epochal Extremes

Provided the parent distribution of wind speed is of the exponential fom, which is the case for the Weibdl distribution, the statistical distribution of the largest wind speed occurring in a fmed interval of time (or an epoch) follows the Type4 extreme value distribution (Gumbei, 1954). The cumulative form of this distribution is of the double exponential type;

F (ri&, ) = exp[- exp[-a(&, - cr)]]

where fi, denotes the epochal extreme and a and 14 are the distribution parameters. The parameter rc is the mode (that is, the expected or most frequent value) and the inverse of the parameter a is termed the dispersion. The latter, as suggested by its name, reflects the spread of the distribution in that larger values (or smaller values of a) resuït in the bulk of the distribution being spread over a wider range of the variate.

Conforrnity of observed data to the mode1 can be indicated by the degree of linearity after taking the double natural logarïthm of Equation 4.21 and rearranging as follows: Cumulative probabiLities can be derived through an anaiysis of order statistics on the observed extremes (see Equation 4.15). The mode1 panmeters may then be estimated by applying the least squares cntena to the transformed data. Another approach. which produces estimates that are unbiased and exhibit minimum variance, is that outlined by Lieblein (1974). In general, the method involves estimating the parameters through a Linear combination of the order statistics which reflects the unequal confidence in the data based on the rank (as opposed to the least squares method where each data point is 0 ven equal weight). Errors are thus rninirnized in the instances, for exarnple, when a 50-year wind speed is found in a set of 30 annuai maxima; in which case the exceedence probability of the "high" value would be over-predicted. The form of the estimators is:

where rn is the rank and M is the total number of epochal extremes. Lieblein's estimators are termed the Best Linear Unbiased Estimators (BLUE). The coefficients A, and B, depend on the nurnber of extremes. Lieblein (1974) tabulates values appropriate for sample sizes up to and including sixteen and provides a rnethod for their determination

O therw ise.

Extreme wind speeds are often associated with a mean recurrence interval, R, measured in epochs (also referred to as the renirn period). It is the wind speed which is expected to be exceeded on average once every R epochs or in any one epoch with a probability of 1/R. Therefore. 1-1/R may be equated to the cumulative probability to obtain;

which, for R greater than about ten, can be approximated by: The extreme value theory requires that (Gumbel, 1958):

1. the maxima are drawn from identicaily distributed sampies of equd size,

2. the maxima are independent, and

3. the epochs are suffrciently large so as to dlow convergence to the extreme value distribution.

In the case of wind, the above requirements are usually met for epochs equd to one year. With respect to item 1, one-year epochs are appropriate in order to enclose the trends associated with different seasons. The criterion of independence (item 2) will be met from one-year to the next unless, on the rare occasion, adjacent annual extrernes both result from an intense storm occurring through the New Year. The last criterion has been tested by Cook (1982) for two cases of the Weibuil distribution (see Equation 4.13). Namely the Rayleigh distribution (k = 2) and the Exponential distribution (k = 1). The first is often appropriate for representing wind speed and thus it follows that the second is appropriate for the square of the wind speed, or dynarnic pressure. The results showed that the Rayleigh distribution converged at a rnuch slower rate than did the Exponentiai distribution. The result was justified by making reference to the fact that both the Exponential and Type-I extreme value distributions have upper tails of similar form. Cook (1982) assessed that in the case of an epoch size equal to one year, extrernes drawn from a parent Exponentid distribution will have converged fully while those taken from a parent Rayleigh distribution will have not converged and be in ertor to the consenrative (in tems of wind ioading, the Rayleigh distribution over-estimates the 50-year extreme by roughly 10 %). The faster convergence of the Exponential distribution is a good reason for fitting the square of the extreme wind speeds or the dynamic pressures to the Type4 distribution and is the approach adopted here. In light of the above review and the task at hand, the question arises as to how would the annuai extremes extracted fiom a time series of one-hour mean wind speed differ from those extracted fiom a time series of short-duration spot wind speed- ClearIy, if it were assumed that both maxima occurred in the same hour from year to year, then differences would likely be sirnilar to those found with respect to the parent population in the previous section- That is, the annual extremes wouid be comparable on average but those associated with the spot measurements would exhibit more variance. The fact is, however, that the two maxima are not necessarily from the sarne hour. Consider. for exampie, if in a gven year the largest one-hour mean wind speed was 25 m/s and that there were nine other hours (independent or otherwise) over which the mean wind speed was within, say, 10 % of this value. Odds are that the largest spot wind speed would come from the same hour over which the average was the highest but it is not necessarily the case. It is likely, however, that the largest spot measurement in the ten hours would be greater than 25 m/s. It is best to think of this scenario in terms of the distribution of the spot factors which was shown to follow that of the standard normal distribution. It can be shown that the mean value of the largest of ten independent samples taken from the standard normal distribution is roughiy 1.5. Taking the coefficient of variation appropriate for the short-duration measurements to be 0-1 for the "high mean wind speeds then, through Equation 4.4, it follows chat during one of the ten hours the spot measurement will be 15 % (Le. 1+1.5*0.1) higher on average than the corresponding one- hour mean. Thus, regardIess of which hou the peak spot factor occurs, the corresponding spot measurement would be greater than 25 mis. It is hypothesized that epochal extremes taken from a time senes of spot wind speeds will not only exhibit more variance but aIso show a higher average than otherwise sirnilar extremes taken from a time series of one- hou means.

Owing to the shortness of the data series for the three locations, the hypothesis could not be tested with regard to mual extremes. hstead, an analysis was performed for epochs of 7, 14 and 21 days in length, For each location, the extreme wind speeds were extracted from al1 the time series for epochs with at lest 85 % of the data present. The extreme wind speeds were subsequently converted to dynamic pressures using the retationship given in The National Building Code of Canada (1990). That is;

q [Pa] = 0-65.(V [rn / SI)' where q is the dynamic pressure. For each senes of extrerne wind pressures, the mean and r.m.s. were cdculated and the mode and dispersion of the Type4 extrerne value distribution were estimated using Lieblein's BLUE- The results for the one-hour means are given in Figures 4.1 1, Relevant parameters are shown within each of the plots,

It is noted here that the Type4 extreme value distribution may not be appropriate for the extreme wind pressure data owing to the short epoch durations (see the requirements for the theory listed above together with the subsequent discussion) but the results should still serve to hdicate trends associated with the use of spot data. The fact that the epoch sizes and the record periods are common to the analysis of each time series at a given location and that the ody difference is the type of wind observation, the results and trends among them will provide qualitative insight in this respect. Quantitatively, however, an analysis performed on otherwise similar series of annual extreme wind pressures (i-e. epochs equal to one year) may lead to different results. This is mer discussed below.

The mean, rems. and Type4 parameters shown in Figures 4.1 1 are the reference by which the corresponding resuits from the other time series are compared. Figures 4.12 summarize the rnean and r.m.s. values resulting from the other time series as fractions of the corresponding value derived from the one-hour means. Ratios of the estimated mode and dispersion are similarly presented in Figures 4.13. In addition to showing the results from the three spot and three modifïed spot data sets, each plot also shows the resdts from the full data senes (Le. consecutive measurements of r -minute average wind speed) for a further reference. Both the mean and r.m.s. of the epochal extreme wind pressures taken from the spot data sets (symbol "x" in Figures 4.13) are shown in nearly al1 cases to be higher than those taken from the one-hour mean data sets, the few exceptions being for the r.m.s. value. For either of the two quantities, the relative increase tends to be greater for shorter averaging intervals of the spot wind speed measurement. This result is expected since the same phenornenon is taking place in each case but to a larger scale for the shorter averaging intervals. Fwther, the mean and r.m.s. values resulting from the analysis of the Ml data series tend to act as upper bounds to the increases experienced by those resulting from the spot data sets.

Refemng to the results from the modified spot data sets (symbol "O" in Figures 4-12)? both the mean and r.rn,s. values are shown to be consistently Iower than the corresponding values from the spot data sets and often result in ratios nearer unity. It

should be noted that the frrst symbol "O" in each half of a given plot corresponds to the fust symbol "x" in the same half and sirnilarly for the second and third syrnbois (by "correspond" it is meant that they both represent the same spot data series; one as is and the other as the modified version). Cornparisons as such show the modified spot wind pressures to consistently result in lower mean and r.m.s. values. The result is necessary for the means since the highest spot rneasurement in a given epoch will aiways be averaged with a comparatively lower adjacent value to make up the modified spot measurement, For St- John's and Brevoort Island, most often for the ten-minute averaging interval, the mean and r.m.s. values from the modified spot pressures show ratios less than unity to a comparable extent by which they are Iarger based on the spot data. This is not apparent at Downsview station as the ratios on the whole are somewhat shified upward owing to the higher level of fluctuations of the spot measurements as indicated in Figure 4.5.

The ratios resulting from the three spot data sets in a given plot are quite scattered in the case of the r.m.s- values and are somewhat more stable for the means- The variability, in peneral, scales with the level of the fluctuations (which corresponds to the averaging interval and the characteristic surface roughness of the recording station). The scatter in the ratios from the three modified spot data series in a given plot qualitatively show similar trends but often to a lesser scale. With regards to changes in epoch size, it shouId frst be noted that the number of extreme pressure data decrease considerably for the longer epochs (see Figures 4.11) and thus any indicated trends may be questionable due to the lack of control of the number of epochs available in each case. With this in mind, the larger epochs tend to ampw the scatter associated with r.m.s. ratios in a given plot and appear to have little influence over the mean ratios on the whole.

In the interest of understanding how the above trends will influence predicted extreme wind pressures, we tum to the estimated Type4 parameters shown in Figures 4.13. Generally, the changes in the mode and dispersion are similar to those found for the mean and r.m.s. values respectively. By taking, moments of the Type4 extreme value distribution, it can be shown that the mean and r.m.s. are aven by;

where y is Euler's constant (= 0.577). The close correspondence in the ratios presented in Fibiges 4.12 and 4.13 follow from the above relationships together with the fact that the percent increases in the mean and r.m.s. values were typically close in magnitude.

Several exceptions to the above trend were found for the data at Brevoort Island station (see, for example, the lower nght plot in Fiowes 4.12b and 4.13b where the r.m.s. ratios are shown to be sipificantIy higher than those of the dispersion) and are briefly discussed here to illustrate the effectiveness of Lieblein's BLUE in elirninating bias due to outliers found in extreme data. The beginning of the record period at Brevoort Island comprised a severe wind stonn where the Iargest one-hour mean wind speed was in excess of 25 m/s and the largest one-minute mean speed was slightly Iess than 33 m/s. The short-duration extremes found in this event are likely associated with a return penod Ionger than the record lena@ as they significantly faIl outside the range of the other epochd extremes. The r.m.s. vaiues were more influenced by the extreme wind pressures in this event than were the dispersion vaiues since they were aven less weight in the case of the latter- This wodd help explain the discrepancies seen between the ratios.

Moving fonvard, we find that both the mode and dispersion tend to increase through the use of spot data compared to those appropriate for one-hou mean data and thus, noting Equation 4.24, predîcted extremes wili similarly increase. If the mode and dispersion appropriate fcr one-hour mean wind pressures are IL and l/a and if those for the alternative wind pressure measurement differ by a factor of Cu and Cil, respectively, the ratio of the predicted extremes cm be aven by;

(4-28)

The above expression has been plotted for al1 the data sets (Le. ? = F, S and MS) for R ranging from 5 to 100 epochs (see Fiagres 4.14). The first observation is that the wind pressure ratios appear for the most part to be only marginally influenced by R to the extent that a proportional relationship with the mean would appear to be appropriate (the relating constant, of course, would depend on the intensity of the fluctuations), This is to be expected in the case of the extrernes from the fui1 data sets since the highest short- duration speeds in a given hou in relation to the mean are typically charactenzed by peaked distributions (Davenport, 1964). In the case of the spot wind pressures, the variability among the results of the three data sets in a given plot is quite si,dficant (typically 10 and as high as 20 7%) and in general increases for the shorter duration spot measurements. Some of this variability may be attributable to the srnall sampIe sizes in the cases of the larger epochs. The scatter among the modified spot wind pressures shows sirnilar trends but often to a lesser scale. Quantitatively, the use of spot data clearly leads to significant errors and it appears that extreme one-hour mean wind pressures are better assessed through the use of modified spot data. Although, for the ten- minute averagîng interval, the over-predictions from the spot data tend to be of the sarne order as the under-predicûons from their rivai; the former may be preferred in the interest of conservatism.

The question arïses as to how would the above results be different if the anaiysis were performed on a set of annual extreme spot wind pressures. The qualitative picture is Iikely the sarne but the percent differences so presented rnay or rnay not be comparable. The relevant factors are the Ductuating process (descnbed by the coefficient of variation of the short-duration rneasurement about the mean) and the nature of the extreme one- hour means. The latter is important because consideration must be given to al1 the "high" winds occurring over the year; whether they result frorn the same event or an independent one. The more mean wind speeds occurring in a given epoch which are comparable to the overall extreme will result in the largest spot rneasurement being higher on average than if there were fewer comparatively high wind speeds (Le. there would be more opportunity to measure a "high" spot sarnple). Since the fluctuating process is the same regardless of the epoch size, the difference in the results presented here to those appropriate for one-year epochs couid be assessed based on the relative number of "high winds. To this end, the number of hours over which the mean wind pressure was within a certain percentage of the extreme one-hour mean was determined for various epoch sizes. The average peak factor for wind pressures;

GF{2)=- 4F@} fi, determined from Type-1 fits of the previous analysis was used to define the percentage threshold for each station. Thus, the number of one-hour mean wind pressures, Ns, larger than the given epochal extreme divided by G,{r} was detedned on an epoch to epoch basis. %y way of example, the anaiysis was performed for epochs ranging fkom half a month to twelve months based on the one-minute peak factor, GF{O l} . Results are presented in Table 4.3. The values of N' for a aven epoch size and station are averages of those obtained from al1 available epochs over the record period. The results are quite different behueen the three stations. Firstly, the values of N' for Brevoort Island are smallest for the Iongest two epochs (Le. six and nine months) since the record period compnsed a single stonn which was dominant over dl others. In this cype of circurnsrance Ns is certain to be small and the largest spot rneasurement wiIl likely not significandy bias to the high side of the largest one-hour mean. At St. John's, the number of mean wind pressures within one peak factor of the extrerne was quite stable and only increased marginaily for the twelve-month epoch duration. If this was typical over the long run then results presented in Figure 4.14a would likely apply to annual extremes. Lastly, the results at Downsview show a good correlation between epoch size and Ns,in which case, the largest spot measurement would tend to move further away from the peak one-hour mean for longer epochs and closer to the overall extreme short- duration wind pressure. A possible indication to the nature of N' would be the mode of

the distribution of the pth extreme one-hour mean wind pressure, M,, which relates to the Type-I parameten of the overall extreme by (Gumbel, 1958):

Thus, when the dispersion is smail relative to the mode (those for the overd extreme) we could expect more wind pressures nearer the overail maxima since the relative decrease in u,, would be faster otherwise.

A distinct picture presented in Figure 4.14 is that the predicted spot wind pressures correlate well with those resuiting from the full data sets. That is, they typicaily fa11 in between the predicted one-hour mean and the predicted overd short-duration mean at roughly the one-third point (Le. they lie roughly one-third of the distance between the unity line and the uppermost line). In this regard, the following parameter is relevant: From the data shown in the 27 plots of Fiame 4.14, the mean and standard deviation of Cswas calculated to be 0.30 and 0.18 respectively. The thickened vertical line shown in each plot is centered vertically on this mean value and extends one standard deviation in either direction. In tems of their location. the extreme spot wind pressures appear to correlate weii with the locations of the vertical bars for ail the various scales of fluctuation.

Station Quantity Epoch statistics 0.5 mo, 1 mo. 3 mos. 6 mos. 9 mos. 12 mos. St. John's No. of obs, 30 16 5 2 1 1 Ns 13 15 14 12 15 22 Brevoort 1, No. of obs. 17 9 3 1 1 O Ns 18 15 23 9 9 - Downsview No- of obs. 20 11 3 L 1 1 Ns 2 1 30 46 105 108 132

Table 4-3 Averages of Ns over the indicated number of observations based on the one-minute peak factor

If the statistical distribution of Cs could be established more generally as it rnight apply to one-year epochs, it would provide a simple means for estimating the errors associated with the use of spot data. That is, substituting;

and G, {rJ into Equation 4.3 1 gives; Thus, we couid predict the expected value of Gs {r) , analogous to the peak factor but for spot wind pressures, given that of GF{c ) , the latter of which has been established more generally. For example, expressions from which GF{r } could be estimated are:

and:

where 2 and are the height above ground and roughness length respectively. Equation 4.35 (modified here sornewhat ro match terrns) was proposed by Cook (1985) and gives the average factor for relating the peak short duration wind speed to the coincident one- hour mean. The relationship is qualitatively based on the work of Wieringa (1973) but modified empiricaily in the interest of simplification. The predictions based on Equation 4.35 were found to be in excellent agreement with the anaiytical approach presented by Greenway ( 1979).

The use of Equation 4.33 is only speculative and would require a Iarger database to establish foundation. The present results from the lirnited database do support such an idea however, It makes intuitive sense in well-behaved climates, where the rate of occurrence of intense depressions is reasonably constant, that the parameter Cs would be somewhat stable from one epoch to the next. This is more likely mein the case of one- year epochs so as to encompass seasonai trends and have a more constant distribution from which the extremes are taken. Further, some of the inevitable scatter associated with spot data is suppressed, in effect, through the process of ordering the extremes and estimating the parameters of the Type-1 distribution according to Lieblein's BLUE. In the end, it appears reasonable that estimated extreme spot wind pressures would correlate well relative to the one-hour mean value and the overall short-duration value. However, until this can be expressed in more definitive terms, the use of modified spot data provides a practicd means for obtaining reasonabie estimates of extreme one-hou mean wind pressures based on a set of epochd extremes.

An alternative approach to establish more generally the behavior of extremes is to utilize the parent distribution in a manner as descnied below.

4.5.2 Extremes from the Parent Population

The Iink between parent wind speeds and extremes foIIows from the expression of the average upcrossing rate of a stationary rmdom process aven by Rice (1954). Regarding the process to be one-hour mean wind speed, the mean upcrossing rate of rn~is given by;

where ri+, is the derivative of mean wind speed with respect to time and f (ni,,+) is the joint probability function of the two variables. If the mean speed and accelention are independent and if the former fol10ws the Weibd distribution then Equation 4.36 becornes: Regarding the above parameters to be known (see more details below), extreme wind speeds can be estimated from Equation 4.37 in severai ways. The fxst, as suggested by Davenport ( 1967). would be to regard the upcrossings of very high mean wind speeds as rare events that follow the Poisson distribution. This gives the probability of s upcrossings in a period of duration Tas:

nie cumulative distribution of the largest mean wind speed in penod T cm be equated to the probability of zero upcrossings - Le. p(x = O). Setting T = 1 year and the cumulative probabiiity to 1-UR, where R is the rempenod in years, gives:

Another approach, employed by Gomes and Vickery (1977), is to set the upcrossing rate given in Equation 4.37 to 1/R (Le. one upcrossinp in R years). This leads to a sirnilar relations hip:

The above two expressions are approximately the same for R larger than about ten. The difficulty with either of them is that they require some type of numencal or iterative scheme to obtain a solution for the extreme wind speed and thus lack practicai usability. Equation 4.4 1 was simplified by Gomes and Vickery by assuming that 4 (R) was a linear function of InR with a slope as evduated at R = 1 epoch. The solution for & (R) was thus analogous to that from the Type-1 extreme value distribution (see Equation 4.25) where estimates of the mode and dispersion ate given by: -1 =-(ln~)IM-'c l+-- k-l -k-lz1n(ln~) a k [ XlnN ( k ) lnN ]

Resulting extreme wind speeds from the above approximation were found to be in excellent agreement with those determined directly frorn Equation 4.41 for the Austraiian data analyzed by Gomes and Vickery-

The employment of the above theory requires estimates of the parameters shown in Equations 4.38. Estimates of k, c and C, can be obtained from a record of rnean wind speed (see Section 4.4 with regard to the Weibull parameters) while V,termed the mean cycling rate, and P require additional knowledge on the statistics of acceleration. riz,. An alternative approach for deriving the mean cycling rate would be to utilize the Iong-term power spectnim of wind speed (see, for exarnple, Davenport, 1967 or Gomes and Vickery, 1977)-

In the present study, the time series of one-hour mean wind speed for the three locations were transformed to a tirne series of acceleration by way of the eighth-order centered finite-divided-difference formula (which is developed from the Taylor senes expansion and cm be found in most text books describing standard numericd procedures). From the transformed time series, the relevant statistics were determined as follows:

where J is the total number of sarnples in the particular time series. The above expressions are based on the assumption that the statisticai distribution of rir, is symrnetrïcal about zero. The second expression above was evaluated over the full range to account for any slight asymmetries due to the short record periods. The estirnates so determined were used together with those of k, c and o, obtained in Section 4.4 to arrive at values for p. v and N (see Equations 4.38) appropriate for one-hou mean wind speeds at the three stations. An identical analysis was perforrned on the time series of spot and modified spot wind speed for the three averaging intervals.

The estimates of parmeter p were generally not influenced by the type of hourly wind observation. This is show in Table 4.4 where the value resulting from the time series of one-hour mean wind speed are compared with the average and r.m.s. of those resulting from the other time series. A value of 0.37 would appear appropriate for al1 three stations. This can be compared with 0.36 which was the estimate obtained by

Gomes and Vickery (1977) in their analysis of Aus~aliandata and with 1I (= 0.40) which would be the value if the accelerations were taken as normally distributed.

Station Parameter B From time series of m, from al1 remaining tirne series mean r.ms. St. John's 0.369 0.376 0.003 Brevoort 1, 0.367 Downsview 0.373

Table 4.4 Estimates of parameter P

The mean cycling rates based on the one-hour mean wind speeds were found to be roughly 440, 300 and 510 cycles/year for St. John's, Brevoort Island and Downsview respectively. In contrat to the parameter P, the cycling rates were significantly influenced by the type of wind observation as is shown in Figure 4.15. Firstly, the fact that the cycling rates are higher for the spot measurements is not surprising since the changes in wind speed from one observation to the next ofien become amplified for measurements taken over shorter durations. We find at St. John's that the increases range from about 20 to 40 % for the ten, two and one-minute averaging intervals respectively. At Brevoort Island the increases are comparable and at Downsview they are somewhat higher as the upper range increases to about 50 %. The modified spot data sets typically result in ratios near unity for the one and two-minute averaging intervals and show roughly a 10 % decrease in the case of the modified ten-minute spot wind speeds. The quantitative results should be indicative to those which would be obtained from an othenvise sirnilar analysis perfomed on Iqer databases since they reflect the parent process.

The changes in the parameter N (shown in the nght half of each of the plots given in Figure 4.15) generally mirror those previously discussed for the cycling rate. This results from the fact that both the parameter P and the ratio ko,/c are quite stable for the different type of wind observations- With regard to the latter, this can be seen by taking the second central moment of the Weibull distribution and then muitiplying the result by Mc. This would give the following relationship;

where r denotes the gamma function. Thus, for k rangïng from 1.5 to 2.5 the ratio is found to only change marginaiiy from about 0.92 to 0.95.

Predicted extreme wind speeds based on the mode and dispersion given in Equations 4.42 are influenced by N, llk and c. If the factors by which the three parameters change are CN,CIR and Cc, the ratio of the mode resulting from the alternative measurement to that from one-hour mean wind speeds, Cu,cm be adequately represented b y;

while the similar factor for the dispersion cmbe given by: The above expressions cm be used to assess the degree by which the parameters influence the estimates of the mode and dispersion and therefore of the predicted extremes, Typical values are shown in Table 4.5. Firstiy, the actual value of N over the relevant range does not ~i~gnificantiyinfluence the ratios of either the mode or dispersion and was teft constant while the WeibuiI exponent k has some influence and was varied as shown in the table. Cc was taken as just less than unity (as was found most often the case in Section 4.4) and was not varied as its influence on both ratios is readily apparent from the above expressions. We see from Table 4.5 that a 6 % increase in I/k has more of a impact on the predicted mode and dispersion than a 40 % increase in N; these being typical variations found at St. John's for the one-minute spot wind speeds. Their combined effect is perhaps more relevant, since both changes should exist in the case of spot wind speeds; this is shown in the last row.

cc cm CN Changes in the mode and dispersion k = 1.5, N = 900 /year k = 2.5, N = 900 /year

Table 4.5 Influence of the relevant parameters on changes in the mode and dispersion evduated from Equations 4.42

The mode and dispersion has been evaiuated from Equations 4.42 for the entire lot of data sets. The mean cycling rates. given in cycles/year, were first converted to represent fourteen-day epochs to allow the cornparison of results with observed values. The derïved speeds were converted to dynamic pressures using Equation 4.26 to maintain a consistent presentation with that previous. Results are shown in Fi,we 4.16 for the one-hour mean datz. The estimate of the mean cycling rate is shown in each of the plots. In ail cases the model appears to represent the data quite well with the exception of St- John's where the dispersion appears to be somewhat low.

Extreme wind pressure ratios based on the Type4 parameters for fourteen-day epochs are shown in Fi,we 4-17 for the spot and modified spot data sets. The ratios show sirniiar trends to those presented in Figures 4.14 (note that the vertical scales are diffèrent). This simply follows from the fact that the parent model fits well the sarne data that were used to calibrate the Type4 parameters in the previous analysis. With regard to the scatter among the results of three spot data sets in a given plot (or modified spot data sets), the parent method is found to render a more consistent result in cornparison to the method of epocfial extremes. It is clear that, for either type of analysis, however, the ernployment of modified spot wind data would be advantageous when the interest is in predicting one-hour mean extremes-

The parent mode1 cm be used to assist in answe~gthe question posed earlier. Narnely, how would the results given in Section 4.5.1 be different if an othenvise sirnilar analysis was performed on a set of annual extreme spot wind pressures. The parent model would suggest that there would be a marginal increase in the ratios, That is, if the plots in Fi,pre 4.17 were constructed for one-year epochs, as opposed to fourteen-day epochs, the ratios so presented would be slightly higher on the whole (in terms of the percentage value, the typical increase wouId be about 1 %).

4.6 Concluding Remarks

This chapter has shown that use can be made of national weather archives comprising hourly spot measurements for estimating parent and extreme value statistics of one-hour mean speeds or pressures. The procedure is to generate a new wind speed time series by simply averaging the adjacent spot measurernents. This has the effect of reducing the variability of the houriy speed about the one-hour mean value. The results from the wind speed data recorded at St. John's, which were measured over open and flat terrain at a height of IO m, showed that the direct use of one-minute mean spot wind speeds leads to extrerne wind pressures that are typicaiiy about 15 to 20 % hïgher than one-hou rnean vaiues. Using Equations 4.34 and 4-35, this translates to roughly a 10- to 20-minute mean pressure assuming a roughness len,~ of the order of 0.01 m. The use of the modified spot wind data increased the averaging times of the resulting extreme wind pressures, which are estimated to range from about 40 to 60 minutes assurning the same roughness length. The use of the modified spot hvo-minute speeds in the extreme value anaiysis resuited in wind pressures that correspond to roughly a 50- to 70-minute average. These averaging times cm be compared to the 20- to 30- minute wind pressures resulting from the direct use of two-minute spot wind speeds.

I I O ln O in C CU 4 c. (s/ru) paads pu~~ (S/UI) paads pu^^

0.20 1 based on one-minute mean wind soeeds I

0.20 based on two-minute mean wind speeds

0.20 based on ten-minute m-ean wind speeds - normal dist-

-4.0 -3.2 -2.4 -1.6 -0.8 0.0 0.8 1.6 2.4 3.2 4-0 spot factor, g

Figure 4.3a Histogarm of the spot factor - St. John's Station based on one-minute mean wind speeds 1 --I

0.20 based on two-minute rnean wind speeds

0.20 - based on ten-minute mean wind speeds normal dist.

spot factor, g

Figure 4.3b Histograrns of the spot factor - Brevoort Island Station based on one-minute mean wind s~eeds

based on two-minute mean wind s~eeds

0.20 based on ten-minute mean wind speeds - normal dist, I

spot factor, g

Figure 4.3~ Histograms of the spot factor - Downsview Station 1 based on one-minute mean wind s~eeds

3 1 based on two-minute mean wind s~eeds 1 4

1 0.01 , 61i Ili 1 1 1 tI1.1 1 0.3 0.6 1 3 6 10

i based on ten-minute mean wind s~eeds

one-hour mean wind speed (4s)

Figure 4.4a Coefficients of variation - St. John's Station (10699 data points per plot) 3 - based on one-minute mean wind speeds

-1 based on two-minute rnean wind speeds

1 0.01 ! 1 1 i 114 1 1 i 1111 i

based on ken-minute mean wind speeds

0.3 0.6 3 - ._ 3 O 1 10- - _. - one-hour mean wind speed (m/s)

Figure 4.4b Coefficients of variation - Brevoort Island Station (6497 data points per pw 1 based on one-minute mean wind s~eeds

t 0.01 l i 1,II' I t i 11.1 I O.3 0.6 1 3 6 10 3

1 based on two-minute mean wind speeds

1 0.01 i 1 1 18Ili I I i I1!1 L 0.3 O. 6 1 3 8 10 3 O

speeds c 1 based on ten-minute mean wind

1 1 0.01 1 1 I Li[il l I 1 L 1 Ili1 1 O. 3 O. 6 1 3 6 10 3 one-hour rnean wind speed (rn/s)

Figure 4.4~ Coefficients of variation - Downsview Station (6925 data points per plot) 0.3 St. John's

one-minute means two-minute means ten-minute means

1 Brevoort Island 1

ten-minute means

0.3

f Downsview

1 I I 1 4 10 1 G 20 25 one-hour mean wind speed (m/s)

Figure 4-5 Coefficients of variation fiom Equation 4.1 1 c = 4-72 rn/s -

- - - x Data - Weibull fit I I I 0.0 1 0.1 0 0 -50 O .'9 9 probability of non-exceedence

Figure 4.6 Weibull distributions of parent one-hour mean wind speed 0 -4 St. John's mean = 7-11 r-ms. = 3.53

Brevoort Island mean = 6.19 0.3 r.m.s- = 4.57

0 -4 Downsview

4 8 12 16 20 24 one-hour mean wind speed (m/s)

Figure 4.7 Histograms of parent one-hour rnean wind speed

Weibull exponent k for one-hour mean wind speeds

Figure 4.10 Changes in the Weibull exponent through the use of spot wind data 600 7-dav e~ochs mean = 153.0 r-rns. = 65-7 400- mode = 123-6

600 14-dav epochs mean = 181.3 r-ms. = 67.7 4001 mode = 149.1

,600 a P. 21 -day epochs w 2 rnean = 202.6Pa 3 r-m-S.= 67.4 Pa $ 400- mode = 169.4Pa al aL disp. = 57.8 Pa Tl C *d 5 200- UJ E al L 4 x Data X - vpe-1 fit a10 1 I l I l 1 2 5 10 20 50 1C return period (epochs)

Figure 4.1 la Extreme one-hour mean wind pressures based on the epochal mode1 - St. John's Station 600 7-day e~ochs rnean = 174.9 r-rns. = 84-6 mode = 133.8

mode = 178.1 X '"1 disp. = 75.8 i /

,600 (Q CL 21 -day epochs V Q) mean = 248.7 Pa S. 3 r.ms = 73.7 Pa

X xData - vpe-1 fit 1 1 1 l 1 2 5 10 20 50 1C return period (epochs)

Figure 4.1 1b Extreme one-hour mean wind pressures based on the epochal mode1 - Brevwrt Island Station 7-day ,epochs mean = 66-1 r-m-S. = 24.6 mode = 54.3 = 20.8

14-day e~ochs mean = 77.8 r-m-S.= 25.0 mode = 65.6 disp. = 21.3

a a 21 -dav epochs P) mean = 87.5 Pa -L 3 1l r.rn.s. = 22-8 Pa mode = 75.8 Pa disp. = 21.0 Pa

X - o! I I I vpe-1, fit 2 5 10 20 return period (epochs)

Figure 4.1 lc Extrerne one-hour mean wind pressures based on the epochal mode1 - Downsview Station

ten-minute spceds

14-day epochs

2î-dsy epochs lp41

moan

Figure 4.12~ Mean and r.m.s. values of extreiiie wind pressure - Downsview Station - result froin the alternative ineüsureinent normalized by thut from one-hour means Fu

m 1::: i 1::: I t::: r 1::: n 1::: n I ::y n I ::: a r ::: U 1 ::: Il 1 1:: Il 1 ::: T=l 13: 1 13- 1 15. O.Y

Ki/III 1

LI/111III N :::i t Ici III O :::[ --

1 1 1: I I a: ItLi1 l 1:

O Ili:: - Ill :: III :: Ill :: 111 1: III :: _I .Y I I :: I I :: I I :: 1 l:: 1 I :: 1 l:: l t :: 1 c:: l c:: 1 i:: 1 t::: 1 c:: l 11: P 1: :: t 1: :: 1 1: :: 1 1:: I 1:: 1 1:: I 1:: 1 1:: 1 1:: l 1:: 1 :: I :: 1, I - O 1 IL : 1 lt .: I li :: 1 IL :: l IL :: l 11: :: - l 11: :: 1 11::: l 11::: 1 11::: 1 Il: :: 1 11::: 1 II: :: w :: 111::: - l Il: :: 111::: 1 Il : :r 141:: 111:: - 1 u:: 1 in:: II:: r i :: 1 r :: II ::. . 111b11

1 Il #: Ill : Ill : III I III : Ill : Ill : Ill : Ill : rrr: Ill : III : Ill : 111 : lit : &il: Ill 5 Ill r Ili I Ill : 11 1 1I II l 9

600 Brevoort Island mean cycling rate = 297

,300 1 a P. Downsview w 0 mean cycling rate = 508 cycles/year L I VI rn 200- cl L a -a .-E: 100-

E xxXxxx QI L -4 xData X - Eqns. 4.42 0o I 1 i 1 L l 2 5 10 20 50 1 I return period (epochs)

Figure 4.16 Extreme one-hour mean wind pressures based on the parent mode1 for fourteen-day epochs 1 111 .I rit :: i lit :: III :: 1 III r: Ill :: - I III :I Ill :: I III :: Ill :: j 118 :: III :: i III --- - I III .1:- - 1 11 -. 1 1 11 ! III i.-. -i 1 ! Ilt -- 1 .- II1 .--- II1 -* - f 1 11 .- 1 11 - ! 1 11 t 1 11 l Il .- j 1 II r Il , 1 I

1 Il :: : 111 :: : III :: : tll :: : Ill :: : f II :: : iIr :: : Ill :::I

I il III IIl III 1 Il I Il l II 1 II 1 Il I II 1 11 1 tl IIl 111 1 11 1 11 1 11 4 II I U IO In Ia Iu 1 I Chapter 5 Evaluation of Canadian Driving-Rain Wind Pressures

5.1 Introduction

Welsh, Skinner and Moms (1989) constructed maps showing the geographicd variation of drivingrain wind pressures (DRWPs) across Canada for use in the CSA Standard CANKSA-A440-M90. The Standard requires that a DRWP read from the design map is less than the window's capacity to resist rain penetration as prescnbed by the water tightness test. The test involves applying a spatially uniform pressure drop across the window for four periods of five minutes each separated by one-minute intervals of zero pressure while water is continuously sprayed onto the window. Tests are repeated with a higher pressure until water penetration is observed and the window capacity is then chosen as the applied pressure of the Iast successful run. The test pressure increments are shown in Table 2.2.

An essential requirement for relating the water penetration test conditions to in- situ driving-rain conditions is knowledge of the extreme wind climate during rainfalI for the patticuiar site Iocation. The wind events of interest are those that occur during rainfails that sufflciently wet the windward building surface so as to provide an ample arnount of water at window Iocations or at the Iocations of other envelope components prone to water penetration. In this context, the spatial and temporal variations in the intensity of rainid impinging ont0 a building surface over a storm may not be of importance so long as water continues to reside at the locations of the envelope susceptible to rain penetration (for exarnple, dong window sills or construction joints). Welsh, Skinner and Moms (1989), through discussions with the technicd comrnittee of the CSA Standard, suggested that a minimum one-hour mean rainfall intensity of 1.8 mm/hr could be used as a tbreshold for identifying the wind events during which suffrcient water would be avaiiabIe on the windward facade for infiltration to be possible.

To be of practical use and to allow for their interpretation, the DRWs wouid have to represent a known averaging time and be based on a common terrain exposure and height above ground. This would dlow for the mean values to be rnodified for different exposures and heights above ground. Also, appropriate gust factors could then be applied to adjust the mean DRWs to represent an averaging tirne comparable to the duration of the applied pressure used for the window test, for exarnple, or to other durations as seen fit for different applications.

In review of the analysis performed by Welsh, Skinner and Morris (1989), two uncertainties in their DRWP estimates were evident. Fust, the representative averaging time of the DRWPs were not readily apparent owing to the use of non-continuous wind records in their analysis. The wind data, from which conventionai order statistics on the annual extrernes was performed, comprised nominal one-minute or two-minute mean speeds observed on the hour. The authors acknowledged the uncertainty in the averaging time of their DRWP estimates. Secondly, no attempt was made to ensure standardized wind records. That is, measurements made by an anemorneter located on the rooftop of an airport control tower, for exarnple, were treated one and the same as measurements taken from an anemorneter hxed to a ten-meter pole on the gound surface away from any imrnediate obstructions. To be able to compare results from one location to the next would require that al1 measurements be based on a similar exposure and height above ground. It appears from the fourteen stations examined in this study that about the fust five to ten years of the records andyzed by Welsh, Skinner and Moms (1989), which were mostly 29 years long, were to various extents incompatible with data refiecting a standard exposure (i.e- 10 meters above open and flat terrain).

The two items discussed above are addressed through a re-evaluation of the DRWPs for fourteen of the stations examuied by Welsh, Skinner and Moms (1989). The averaging time issue is dealt with through the use of the modified spot data technique presented in the previous chapter and the non-stationary aspects of the AES wind records are dedt with by using the fdtered wind records developed in Section 3.3.1. In addition, several other andysis issues that may give rise to errors are considered and will be discussed in the following section.

5.2 Analyses of the Canadian DRWPs

Five different methods were used to evaluate DRWPs for the fourteen stations listed in Table 3.7. The first method emulates the andysis performed by Welsh, Skinner and Moms (1989) whiie each of the following four methods rnodiQ a certain aspect of the analysis. The issues are addressed separateIy in order to highiight each of their influence on the resuiting DRWs. In the opinion of the author, the final analysis leads to DRWPs that are more readiIy interpretable in terms of averaging time and terrain exposure and thus more suited to a wider range of applications.

5.2.1 Base Analysis - Welsh, Skinner and Morris (1989)

The first method for estimating DRWPs foiiowed that used in the work of Welsh, Skinner and Morris ( 1989). One-hour rainfall amounts were estimated from six-hour precipitation (rain, freezing rain, snow, etc.) totds and hourly present weather observations as described in Section 3.3.2. The wind speed associated with a given one- hour rainfall total was taken as the nominal one-minute or nominal two-minute rnean observed at the beginning of that hour. For example, if 3 mm of rainfall were estimated between hours 1200 and 13:00, the associated wind speed would be that averaged over the one or two minutes ending at hour 12:OO. The wind speeds associated with one-hour rainfdls 2 1.8 mm, 2 3.0 mm and 2 5.1 mm were then collecteà and the annual extremes from each subset were extracted and converted to dynamic pressures using Equation 4.26. The Method of Moments (Equations 4.27) was then applied to determine the mode and dispersion of the Type4 extreme value distribution and the DRWPs were evaluated for a aven return penod using Equation 4.24. The record penods of this analysis are the same as those anaiyzed by Welsh, Skinner and Moms (1989) for each of the fourteen stations. The penods of record for the HAL and POB stations are 196 1-1985 and 1966-1985 respectively. For the remaining ttveive stations, the record penods are 1957-1985. Also, similar to their analysis, the archived wind speeds were used directiy with no modification for the different memorneter heights and exposures.

5.2.2 Anaiysis 1 - Use of Filtered Wind Records

In Canada, it was not recognïzed until about the mid 1960's the importance of locating anemometers away from the immediate influence of nearby obstructions. At this time, the anemometers located at many Canadian airports were relocated (often from the rooftops of airport buildings) to open areas on standard ten-meter poles. The wind records used in the Base Analysis and by Welsh, Skinner and Moms (1989) spanned this transition period and, at the same time, al1 measurements were ueated equal in the analyses. Here, the method is comparable to that described in the previous section with the exception that the filtered wind records developed in Section 3.32 were used. The periods of the tiltered wind records (see Table 3.7) start on average about 8 years later and extend 7 years longer compared to those used in the Base Analysis.

5.2.3 Analysis 2 - Use of Modifed Spot Wind Data

Here, the modified spot wind data were incorporated into the analysis, which is othenvise sirnilar to Analysis 1. For example, if 3 mm of rainfali were estimated between hours 1200 and 13:00, the associated wind speed in this case would be the average of the short-duration means observed at hour 12:OO and at hour 13:OO. As shown in Section 4.5, this process leads to extreme value estimates that better represent one-hour means compared to the extrerne values derived from a record comprising one short-duration observation per hour. 5.2.4 Analysis 3 - Use of Rainfaii Measurements

The issue addressed through this analysis is how the accuracy of the DRWPs is infIuenced through the use of thz raiddl estirnates as opposed to the more accurate rainfall measurements. The premise for using the estimated amounts is that the meteorological data from which they are based are consistently avaiiable year round. On the other hand, the rainfall rneasurements from the automatic rain gauges are often only available during the warm season. Rainfalls during the Late fa11 through early spring, which are not uncomrnon for coastal regions, may coincide with strong winds and thus need to be considered in the analysis. In review of fourteen stations lisced in Table 3.7, it is seen that ten stations have rainfdl rneasurements year round, two stations have rainfall measurements year round over most of the record penod and four stations have rainfall measurements during the wani season ody. In this analysis, the rainfall estimates were only used when the measurements were not available and otherwise the measurements were used. Apart from this difference, this analysis is sirnilar to Analysis 2.

5.2.5 Analysis 4 - Use of Lieblein's BLUE

In this Analysis, the Type-1 parameters were estimated with Lieblein's BLUE (Lieblein, 1974) as opposed to the Method of Moments. Lieblein's approach gives the correct weight to each of the extrema according to their rank. This andysis is otherwise sirnilar to Analysis 3.

5.3 Cornparisons of Canadian DRWPs

A summary of the five different methods described above is given in Table 5.1. The changes in the analyses are highlighted in the table. The DRWP estimates are plotted in Fiewes S.la, 5.lb and 5.k for the 1.8 mm, 3.0 mm and 5.1 mm one-hour rainfall thresholds respectively. All DRWPs are expressed as fractions of the corresponding value denved using the Base Analysis. Aiso shown on the plots are the DRWP estimates obtained by Welsh, Skinner and Morris (1989). Appendùt D plots results of Analysis 4. Andvsis Record Period Wind Data Rain Data Analvsis Base Welsh, Skinner Spot Es tirnated Method of and Morris ( 1989) observations Moments 1 Fiitered Spot Estimated Method of observations Moments - -- 2 ~iltered Modified spot Es timated Method of observations Moments 3 Filtered Modified spot Measured Method of observations Estimated Moments 4 Fiitered Modified spot Measured/ LieMein's observations Estimated BLUE

Table 5-i Surnmary of the analysis methods used to evaluate the DRWPs

The fxst result that stands out in Figures 5.1 is the large differences between the DRWPs estimated in the Base Analysis (shown as un@ on the plots) and the DRWPs estimated by Welsh, Skinner and Morris (1989). For example, for the 1.8 mm/hr rainfd threshold, the 30-year DRWP estimated by Welsh, Skinner and Moms ( 1989) at SJS is 55 % higher and, at MON, their DRWs are at lest 30 % higher for al1 the return periods pIotted. In contrast, their values are about 5 % Iower at VAN and practically equal at VIC, CAL and HAL. The overall trend is that the DRWPs estimated by Wekh et al. are higher than those derived in this study using the Base Analysis with the differences decreasing for the higher rainfall thresholds. This trend is highiighted in Table 5.2 where the ratios of the ten-year DRWPs have been summarized.

Rainfall Ten-year DRWPs - Threshold Welsh et ai. / Base Analysis avg. r.m.s. max. min. 1.8mmk 1-15 0-15 1.42 0-94 3.0mm/hr 1.10 0.12 1.38 0.90 S.lmm/hr 1-04 0.06 1.19 0.94

Table 5.2 Cornparison of the ten-year DRWPs evaluated by Welsh, Skinner and Morris (1989) and by the Base Analysis; statistics from al1 fourteen stations The above discrepancies are disturbing because both of the analyses were based on the same elements of the AES digital archives. Assuming, therefore, that the wind data used in both analyses were the same, the dii-ferences wouid have to be attributed to differences in the rainfall estimates between the two studies; the estimates being based on hourly present weather obsenrations, six-hour precipitation arnounts and 24-hour rainfall arnounts (see Section 3-32). For exarnple, if one of the procedures lead to an average of 400 hours per year during which the raidal1 exceeded 1.8 mm and the other procedure Iead to an average of 500 hours per year during which the same threshold was exceeded, the mnuai extremes would tend to be higher in the Iatter case due to the increased population size (assurning that the statistics of each population were not si-eficantly different), Further, if the average number of hours per year were 40 and 50 respectively for the 5.1 mm one-hour rainfall thresholdTan increase in the annual extreme would also be applicable but to a Iesser extent. This idea would explain the differences shown in Table 5.3 if the rainfall estimating procedure used by Welsh, Skinner and Morris (1989) tended to produce a larger number of rainfall events than in this study.

An example of where the rainfail estimating procedures may have been different is in the treatment of mixed precipitation events. In this study, care was taken to distinguish between the different precipitation types over a given six-hour period and to adjust the rainfail estimates accordingly to match the measured 24-hour rainfall arnount. This is illustrated in the exarnple calculations given in Table 3.10. This modification tended to decrease the one-hou rainfall estimates. If this adjustment was not used in the analysis performed by Welsh, Skinner and Moms (1989), then their estimated rainfalls would tend to be higher for the mixed precipitation events, which would lead to a larger number of rain-fali threshold exceedences compared to this study.

Several different variations in the rainfall estimating technique were exercised in an attempt to arrive at DRWPs similar to those derived by Welsh, Skinner and Moms (1989). One of these did not include the modification factor to resolve the mixed precipitation events as described above. Another variation in the anaiysis included matching the one-hour rainfaii arnounts with the short-duration mean wind speeds observed at the bottom of the hour as opposed to matching them with the speeds measured at the top of the hour. However, the differences in the DRWPs codd not be resolved as none of the alternative analyses produced DRWPs ~i,~cantiydifferent than those derived in the Base &aiysis.

Another possible explmation of the differences between the DRWPs developed by Welsh, Skinner and Morris (1989) and those derived in this study using the Base Analysis is that the wind databases were different in the two studies. This is indicated based on the wind record at POB- Welsh, Skinner and Morris (1989) only utilized annuai extremes if more than 90 9% of al1 the relevant data were available over the aven year. The same provision was foIlowed in this study. Of the 20 years of data analyzed for POB, 19 years were found to have a sufficient amount of data in this study whiie al1 20 years apparently passed the criteria in their study. The annual extremes from 1966 were not considered in this study since more than 40 % of the wind data during this year are missing from the database.

Unfortunately, despite direct dialogue with L. E. Welsh, the differences between the two sets of DRWPs could not be resolved. This issue needs to be resolved and it is an area recornmended for future research.

Moving forward, the influence of using the fdtered wind records to denve the DRWPs can be gauged by comparing the results from Analysis 1 and Analysis 2 in Figures 5.1 (see also Table 5.3 where the ratios for the ten-year recurrence interval have been summarized). The results show that the overaii trend is for the DRWPs to decrease through the use of the filtered wind records and that the amunt in which they decrease cm be related to the extent and duration that the anemometer exposures deviated from standard conditions. At REG, for example, the fust ten years of wind data were measured from an anemometer located on a rooftop at a height of 20.4 m above ground (1957- 1960/09) and from an anemometer fixed to the Control Tower at a height of 26.8 m above ground (1960/10- 1966). Beboinning in 1967, the measurements were taken from an anexnometer Iocated more than 0.5 km from the Tenninal Building and fixed to a pole at a height of 9.1 m. The height was later increased to 10 m. The record periods used in the Base Analysis and in Analysis 1 were 1957-1985 and 1967-1992 respectively- The omission of the fust ten years of wind data resulted in DRWPs that were about 20 5% Iower for this station. In contrat to this example, the results for WIN show only small differences (< 5%) between the two sets of DRWs for ali three rainfall thresholds. The anemometer at this station was moved to a standard pole (10 m above ground) towards the end of 1963 from the roof of a hangar, where it was a total of 9.8 rn above ground level. The data from 1957 through to 1963 were not used in the filtered wind record as a directionai analysis of the rnean wind speeds indicated that the measurements were somewhat biased due to the flow aerodynarnics around the aircraft hangar. However, the extent and duration of the non-standardized portion of the wind record were much Iess for WIN than they were for REG. This is reflected by the much smaller change between the DRWPs derived in the Base Anaiysis and in Analysis 1.

Rainfdl Ten-year DRWPs - Threshold Analysis 1 / Base Analysis avrr- rems, max. min.

Table 5.3 Influence of the filtered wind records on the ten-year DRWPs; statistics from al1 fourteen stations

Anoth~rfactor that may have contributed to the differences between the two sets of DRWPs is that an additionai seven years (19864993) of data were used in the filtered wind records. This effect is Likely srnail in cornparison to the impact of discarding potentidiy biased wind data and may have produced either an increase or decrease in the estimates of the DRWPs. On the whole, the results for the fourteen stations examined illustrate that it is very important to investigate the memorneter's exposure over the station's history and to use only those data representative of standard conditions- As discussed above, the DRWPs evaluated by WeIsh, Skinner and Morris (1989) are based on records comprising hourly-observed one- or two-minute mean wind speeds (the transition for the AES hourly wind archives was at the start of 1985). Using the one- minute averaging interval by way of example, it was shown in the previous chapter that extreme wind pressures denved from such non-continuous records would typically fdin between a one-hour mean and a peak one-minute mean at roughly the one-third point. It was also shown that by averaging the consecutive one-minute mean wind speeds to create a new time senes, the predicted extreme wind pressures would approach a one-hour rnean within about 5 % for an open exposure at 10 m above ground (see Figure 4.14a or the results for St. John's in Figure 4-17], and be generaily on the conservative side.

To assess the influence of ernploying the modified spot data, the DRWPs derived fiom Analysis 2 can be compared with those derived from Analysis 1 in Figures 5.1. A summary of the ratios of the two sets of ten-year DRWPs is presented in Table 5.4. The clear trend is for the DRWPs denved from the modified spot data to decrease relative to those derived from the original hourly spot data. The decrease does not appear to be sipnificantly influenced by the rainfdl threshold nor does it appear to depend on the rempenod. As cm be seen in Table 5.4, the ten-year DRWPs decrease on average by 14 % for the two Iower rainfdl thresholds and by 17 % for the 5.1 mrn/hr rainfall threshold. These percent decreases can be compared with both 10 % and 12 % which are the average decreases for the one- and two-minute mean wind pressures respectively for the St. John's data analyzed in Chapter 4. The lower percentages indicate that the surface roughness at the St. John's memorneter site (see Figure 3.8: anemometer height = 10 m) is less than the average or typical surface roughness at the fourteen airpon sites considered in this chapter.

Overall, the DRWPs derived through the use of the modified spot data compared to those derived from the original spot data are significantly lower as shown in Table 5.4. In no case was an increase observed since a decrease is inherent in the averaging technique. The DRWs denved from the modified spot wind data cm be interpreted as siightly consenrative estimates of one-hour rnean DRWs. Depending on the surface roughness characteristics of the site and the averaging intervals of the hourly observed speeds, which are nominally one or two minutes but may vary due to the actual practice of the weather observers, it is estimated that the DRWPs derived from the modified spot data may be up to 10 % higher than a one-hour mean DRWP but more typicaily less than 5 % higher. Either a greater surface roughness or a shorter wind speed averaging time will make the DRWPs denved from modified spot wind data Iarger relative to a tme one- hour mean DRWP.

RainfalI Ten-year DRWPs - Threshold Anaivsis 2 / Analvsis 1

Table 5.4 Influence of the modified spot wind data on the ten-year DRWPs; statistics from al1 fourteen stations

The DRWPs examined to this point have been derived using the one-hour rainfall estimates. As was shown in Section 3.3.2, the time series of one-hour rainfall derived through the estirnating technique consistently indicated a fewer nurnber of hours during which the rainfall thresholds were exceeded compared to the nurnber of hours indicated by the time series of one-hour rainfail measurements. For the 1.8, 3.0 and 5.1 mmhr thresholds, it was shown that the number of threshold exceedences decreased by an average of about 20 % for the fourteen stations exarnined.

An evaluation of how the use of the estimated rainfalls influences the DRWPs can be made by comparing the DRWPs derived by Analysis 2 and Analysis 3 in Figures 5.1. A summary of the ratios for the ten-year recurrence interval is siiown in Table 5.5, where it cm be seen that the tendency is for the DRWPs to increase by about 4 to 5 % when the rainfall measurements are utilized in the analysis. Based solely on the fact that the number of exceedences of a particular rainfall threshold is higher when the rainfaIl measurements are used, an increase in the DRWPs wouid be expected since extremes increase when the size of the population from which they are extracted increase (i-e. there is more opporninity for an extreme to occur). .However, in view of the range of ratios gïven in the last two columns of Table 5.5, this effect does not always dorninate as the DRWPs based on the rainfaii measurements sometimes decrease compared to those based on the estimated rainfalls. ClearIy, in addition to their size variation, there can be si,dficant differences between the two conditional wind speed populations that give rise to the differences shown in Table 5.5-

Rainfall Ten-year DRWPs - Threshold Analysis 3 1 Andysis 2 avg. r-m.s. max. min. 1-8 mmh 1-04 0-11 1.32 0.89 3.0mm/hr 1.04 0.08 1.18 0.91 5-lmm/hr 1-05 0.12 1.18 0.73

Table 5.5 influence of using estimated one-hou rainfds on the ten-year DRWPs; statistics frorn al1 fourteen stations

In ail, the results show that it is important to utilize the measured rainfalls from the automatic rain gauges since the accuracy of the DRWPs may otherwise be compromised. The measured vaiues, however, are not consistently available year-round and the estimates must therefore be used to fil1 in the rnissing data, meaning that some degree of error may still exist in the DRWPs derived in Analysis 3 (and in Analysis 4). The distribution of estirnated and measured rainfalts for the fourteen stations is shown in Table 5.6 over the penods of the filtered wind records. Note that for CAL, REG, WIN and CHA. the large percentage of estimated rainfdls are for the winter months.

In the final analysis, the technique used to estimate the mode and dispersion of the Type4 extreme value distribution was changed from the Method of Moments to Lieblein's BLUE. The latter approach gives estimates of the Type4 parameten, in the form of a Iinear combination of the order statistics, that are unbiased and have minimum variance (Lieblein, 1974). As can be seen in Figures 5.1 and Table 5.7, the differences between the DRWPs resulting fkom Analyses 3 and 4 are generally small and tend to be more variable for the higher rainfdl thresholds. Among the other uncertainties, the method for estimaUng the Type-1 parameters is likely not very sipificant.

Station Record Available rainfd data (%) Period Measured Estimated WC VAN CAL REG WIN LON TOR OTT MON STJ HAL CHA POB* SJS * 0.5 % of the rainfall data is missing

Table 5.6 Distribution of rainfall data over the filtered wind records

Rainfall Ten-year DRWs - Threshold Analysis 4 / Anaiysis 3 avg. r.m.s. mm. min. 1.8 rnm/hr 1-00 0.04 1.06 0.94 3.0mmkr 1-00 0.05 1.06 0.91 5.1 mm/hr 0.98 0.07 1.09 0.85

Table 5.7 Influence of using Lieblein's BLUE on the ten-year DRWPs; statistics from ail fourteen stations

5.4 Concluding Remarks

The Canadian Standard CANKSA-A440-Mg0 currently utikes both five and ten-year DRWPs associated with a one-hour rainfall threshold of 1.8 mm as critena for selecting windows and other cladding components to resist rain penetration. The derivation of these DRWPs is reported by Welsh. Skinner and Morris (1989). The results presented in this chapter, which are based on data from fourteen of the stations examined in their study, show that the DRWs currently used in the building standard are subject to errors associated with the use of non-standardized wind records and the use of one-hour rainfall estimates. Also, the DRWPs lack interpretation with respect to their representative averaging time owing to Ihe use of hourly observed wind speeds that are nominaily averaged over one or two minutes.

The finai analysis (Analysis 4) cm be compared with the Base Analysis, which emuiates that used by Welsh, Skinner and Moms (1989), to gauge the overall impact of the issues listed above (see Figures 5-1 and Table 5.8). The overall tendency is for the DRWPs derived in Analysis 4 to be significantly lower than those derived in the Base Analysis. In review of the results for the ten-year recuence interval shown in Table SA1 the average decrease is about 25 % for each of the three rainfall tiiresholds- The variation between the ratios for the fourteen stations, as indicated by the last three columns in Table 5.8. is also very significant; showing more than a 40 % drop in some cases and more than a 5 % rise in others.

Rainfall Ten-year DRWPs - Threshold Analvsis 4 / Base Analysis avo- r.m.s. max, min.

Table 5.8 Cornparison of the ten-year DRWPs evaluated by Analysis 4 and by the Base Analysis: statistics from dl fourteen stations

The final comparison that wiLI be made, which is perhaps the most relevant, is between the DRWPs evaluated by Welsh, Skinner and Morris (1989) and by the final analysis conducted in this study (Analysis 4). The DRWPs derived in Analysis 4 are considered to be the best possible estimates of one-hour mean DRWPs that are obtainable frorn the data availabIe in the Canadian weather archives, The results shown in Table 5-9 cleady indicate that it wodd be a worthwhile effort to re-evaiuate the DRWPs that are currently uçed in the Canadian Standard CANKSA-A440-Mg0 using the techniques summarized in this chapter. This wodd gîve the engineering community a design wind pressure that is more readily interpetable in ternis of averaging time and exposure and thus more suited for a wider range of design applications involving wind, rain and the building envelope.

ThreshoId Welsh et al. / Anaiysis 4 avg. r.m.s. max, min,

Table 5.9 Cornparison of the ten-year DRWPs evaiuated by Welsh, Skinner and Morris (L989)and by Anaiysis 4; statistics frorn al1 fourteen stations

Chapter 6.0 Conclusions and Recommendations

This thesis evaluates dnving-min wind pressures (DRWPs) at fourteen airport stations stretched across Southem Canada and compares them with the DRWPs currently in use by the Canadian Standards Association as a ,pide for desi,~ng waterûght windows in residentiai and commercial buildings located in Canada (CSA Standard CANKSA-A440-M90). Results tiom this study lead to the foilowing conclusions:

1. The DRWPs given in the current building standard are not necessarily representative of the standard meteorologïcal exposure (Le. a height of 10 m above open and flat terrain). From the fourteen stations considered in this study, the ten-year DRWPs (associated with the 1.8 mm one-hour rainfall threshold) are estimated to be on average 16 % higher than those representative of the standard rneteorologicai exposure. The errors, however, are station dependent and are estimated to range from O to 47 90 for the fourteen stations examined-

The DRWPs given in the current building standard are subject to errors owing to the use of estimated one-hou rainfalls in their derivation. The technique used to estimate the one-hour rainfalls consistently leads to fewer hours during which the rainfall total exceeds thresholds of 1-8, 3.0 and 5.1 mm and does not necessarily capture the wind climate associated with these rainfdl thresholds. From the fourteen stations considered in this study, the ten-year DRWPs (associated with the 1.3 mm one-hour raidail threshold) are estimated to have errors approxirnately ranging From + 12 to - 24 % with an average error of approximately - 4 9%.

3. The representative averaging time of the DRWPs given in the building standard is not known with great certain@ owing to the use of non-continuous wind data in their denvation (i.e. hourly-observed speeds averaged over nominally one or two minutes). From the fourteen stations considered in this study, the ten-year DRWPs (associated with the 1.8 mm one-hour rainfd threshold) are estimated to be 2 to 32 Z higher than one-hou mean values and on average 16 % higher than one-hour mean values. These percentages are ody approximate since the estimates of the one-hour mean DRWPs used as the reference for cornparison are only appr~~ate.The stated percentages are considered to be slightly low. 4. The DRWPs given in the buiiding standard are subject to apparent errors of unknown or@n The reference DRWPs taken as the "correct7' values are estimated in this study through an anaiysis that emdates that described by Welsh, Skinner and Morris (1989), who give details on the derivation of the DRWPs that are used in the building standard. From the fourteen stations considered in this study, the ten-year DRWs (associated with the 1.8 mm one-hour rainfall threshold) are estimated to have apparent errors ranging from t 42 to - 6 % with an average error of + 15 7%.

First and foremost, a recommended area of future research would be to resolve the differences in the DRWPs discussed in the fourth conclusion above. The differences are disturbing because the archived weather elements, the record periods and the analysis techniques are apparently the same in this study as they were in the study conducted by Welsh, Skinner and ~Moms(1989). This has been confiïed to a reasonable level through direct discussions with L. E. Welsh.

Based on the four conclusions Iisted above, it is considered to be a worthwhile effort to re-evaluate the DRWPs for the entire network of Canadian airports that maintain weather records. The analysis should employ the modified spot wind data described in Chapter 4 so as to arrive at extreme wind pressures that cm be interpreted as (nominal) one-hour rneans, which could then be factored to represent different averaging times as seen fit for different applications. Further, the anemometer's exposure history should be carefutly examined to identiS portions of the wind record that are incompatible with standardized data, should they exist. When information about the station's history is lirnited to the short descriptions available in this study, an analysis similar to that described in Section 3.3.1 cm be used to fdter incompatible data. Finaily, use should be made of the one-hour rainfall measurements from the automatic rain gauges when available to ieduce the potential errors associated with using the one-hour rainfall estirnates (see Section 3.3.2)-

It is recognized that the translation of estimated DRWPs into design practice is itself an approximate process. Tests on building envelope components are typicaily carried out with steady, spatiaily uniform pressures and a basic threshold quantity of water- Nevertheless. given that the DRWPs so detennined could be more accurately interpreted as standardized one-hou mean values, improvements made with respect to acctual design issues couId then be justified. Potential areas of improvement in the window selection criteria outlined in the CSA Standard CANKSA-A440-Mg0 are discussed in Chapter 1 (see Pages 7 and 8).

Another area worthy of future research is the study of the directional characteristics of the DRWPs- For the fourteen weather stations considered in this thesis, plots are included in Appendix B and AppendYc C which show the directional aspects of the overall wind climate and the directional aspects of the wind climate associated with rainfall intensities equal to or greater than 1.8 rnmh. Referring to the lower right hand polar plot in Figure C.3, it can be seen that at Caigary International Airport the DRWPs approaching from the NNW are approximateiy three times larger than those approaching from the SW through S to SE. From an engineering standpoint, this type of information cmlead to economicaiiy efficient building envelope designs.

Surry et al. (1994b) suggested that, for a particdar region, the extreme wind climate dunng rainfdl might be predicted based on the overail extrerne wind climate and the mean nurnber of hours during a year that rainfail occurs. The approach assumes that the underlying parent distribution of wind speed during rainfall is reasonably comparable to that of the overall wind clirnate (Le. wind speed is not significantly correlated with rainfall). The results presented in Appendix B show that during rainfall the parent distribution of O&-directional wind speed differs significantly from the overd parent distribution of omni-directional wind speed. For example, for the fourteen stations examined, the Weibull parameters k and c are on average 26 and 34 % higher when derived from the wind speed data associated with the 1.8 mm/hr rainfall threshold compared to when derived from al1 the wind speed data. Thus, this attractive proposd appears unlikely to succeed in practice. References

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Skerlj, P.F. and Suny, D. ( 1994), "A Study of Mean Pressure Gradients, Mean Cavity Pressures, and the Resulting Residual Mean Pressures Across a Rainscreen for a Representative Building", BLWTL-SS23- 1994, The Boundq Layer Wind Tunnel Laboratory, The University of Westem Ontario. Surry, D.. hculet, D.R., Skerlj, P.F., Lin, J-X., and Davenport, A.G. (1994a), "Wind, Rain and the Building Envelope: A Status Report of Ongoing Research at the University of Westem Ontario", Journal of Wind Engineenng and Indusuial Aerodynamics, 53, pp. 19-36. Surry, D., Skerlj, P-F- and Mikitiuk, M.J. ( 1994b), "An Exploratory Study of the CIimatic Relationships Between Rain and Wind, BLWTL-SS22-1994, The Boundary Layer Wind Tunnel Laboratory, The University of Westem Ontario. Twisdale, L.A. and Vickery. P.J. (1992), "Research on Thunderstom Wind Design Panmeters", Journal of Wind Engineering and Industrial Aerodynamics, 41, pp. 545-556. Twisdaie, LA. and Vickery, P.J. (1993), "Anaiysis of Thunderstom Occurrences and Windspeed Statistics", Proceedings of the 7h US. National Conference on Wind Engineering, Los Angeles, USA. Welsh, L.E., Skinner, W.R. and Morris, R.J. (1989), "A CIimatoIogy of Driving Rain Wind Pressures for Canada", Climate and Atmospheric Research Directorate Drafi Report, Environment Canada, Atmosphenc Environment Service, Canada. Wiennga, J. (1973), "Gust Factors Over Open Water and Built-up Country", Boundary- Layer Meteorology, 3, pp. 424-44 1.

Yip, TC, Auld, H. and Dnes, W. (19951, "Recomrnendations for Updating the 1995 National Building Code of Canada Wind Pressures", Proceedings of the 9" International Conference on Wind Engineering, New Delhi, India, pp. 187 14877 Appendix A Relationship Between Wind Speed, Rainfall Intensity and Driving-Rainfaii Intensity

Rainfdl intensity, as it is typicdy measured in the field and presented in weather reports, is a measure of the volume of water that irnpinges the ed's surface per unit time per unit area, where the orientation of the reference plane is horizontai (Le. perpendicular to the force of gravity). This measure dong with a measure of the mean wind speed can be used to esùmate the intensity of wind-drïven rain. The intensity of wind-driven rain is defined as the volume of water per unit time per unit area, where, in this case, the reference plane is orîented vertically and facing in the upwind direction. An example of the relationship between the two rainfail intensities and the mean wind speed will be given below for the case of a steady and uniform flow field-

Under calm wind conditions, raindrops wiil fall vertically and vavel at a speed equal to their terminal velocity. The tenninal velocity is reached when the gravitational force acting on the raindrop is equal to the sum of the buoyancy and aerodynamic forces. As each of the above forces depends on the size of the raindrcp, so to does the temiinal velocity. The stagnant air rainfall intensity can thus be given as the summation of the contributions from each drop radius as follows;

where r is the drop radius, G(r)is the volume of water comprîsed of drops with radii Iess than and equal to r per unit volume of air and V[(r)is the temiinal velocity of draps with radii equal to r. Gum and Kinzer (1948) have measured the terminal velocities of water droplets in stagnant air. They found that drops having radii less than 0.04 mm obey Stokes' Law. which yields the following expression for terminal velocity;

2d(P- Pu, V,(r)= - 9~uir

where p and p denote densiry and viscosity respectively and g is gravity- Markowitz (1976) developed an expression for terminal velocity that matches the data of Gunn and Kinzer for drops having radii Iarger thm 0.15 mm (Inculet and Suny, 1994). The reIationship is;

where r is to be specified in mm. For the purpose of the analysis, the above two models will be used over the indicated ranges in r and a straight Iine joining the two models at their limits will be used for drop radii between 0.04 and 0.15 mm.

The distribution of raindrop sizes within a given rainfd1 has been studied by Best (1950). It was found that the portion of drops having a radius iess than or equal to r cm be expressed in terrns of a Weibull distribution where the location parameter is proportionai to the rainfail intensity raised to the power 0.232. Et was also found that the totd volume of water per unit volume of air scdes to the intensity of rainfall raised to the power of 0.846. The Best mode1 leads to the following expression for G(r);

where r and 1, are to be specified in mm and mm/hr respectively. Setting arbitrarily I, to 1, 5, 10 and 50 mmlhr, the numerical evaluation of Equation A.1 yields values of I. equal to 1.01.5.12, 10.2 and 47.7 mm/hr respectively, aU of which are within 5 % of their target; proving the consistency of the above rnodels.

If a uniform and steady flow is introduced, the horizontal movement of air past the raindrops will Iead to forces on the drops and accelerate thern in the direction of the wind. When equilibnum is reached (i.e. when the relative speed between the drops and the wind is zero), the raindrops will move at a horizontal speed equai to the wind speed and at a vertical speed equal to their terminal velocity. The straight-line path followed by the raindrops can be defined by the driving rain angle;

where U is the wind speed. The rainfall intensities relative to a horizontal plane, I, and relative to a vertical plane facing the wind, Idr, can be given by:

These expressions have been solved numerically to produce the plot shown in Figure A. 1.

The cirivingrain index has often been used as a meteoroIogicd indicator to the intensity of wind-driven min. It is defined as the mean wind speed rnultiplied by the coincident mean rainfall intensity. The calculation of the driving-rain index is typically performed using a one-hour rainfall arnount and the mean speed over the same hour, but this mîy vary depending on the available meteorologicd data. The premise of the driving-min index is that it will represent a quantity that is roughly proportional to the dnving-rain intensity, and therefore wiii reflect the potentid of rain impacting vertical building surfaces. For the case of uniform and steady flow, the resuits given in Figure A.1 indicate that the driving rain index, IU, relates to the dnving rain ktensity, Idr, by a factor that depends on the rainfalI intensity. These results suggest that a map showing the geographical variation in the driving-rain index (perhaps in the form of annual extreme one-hour mean values) might represent a somewhat distorted picture compared to one that represents drivinprainf' intensity.

Figure A.1 Driving-rainfall intensity, Idr, nonnalized by the dnving-rain index, lu, versus rainfall intensity, I Appendix B Parent Wind Speeds During Rainfail

This appendix presents plots of omni-directionai wind speed versus exceedence probability and plots of wind direction versus frequency of occurrence. Plots are presented for each of the fourteen stations of the one-hour database. The wind data used in the analysis are the modified spot wind speeds over the filtered wind records. The rainfall data are a combination of the measured and estimated one-hour totals; the latter were only used when the former were not available.

The omni-directional parent wind speed distributions are shown on the left sides of the figures. For a given location, the analysis was perfonned using the entire wind speed population and the populations associated with one-hour rainfail totals equd to or greater than 1.8, 3.0 and 5.1 mm. The fitted Weibull distribution is also shown in each case together with the estimates of the distribution parameters (Le. c and k). The rnean number of hours per year that a particular one-hour raïnfail threshold was exceeded (denoted as &) is dso given where appropriate. The wind roses (Le. wind direction versus frequency of occurrence) for the entire wind speed population and the population associated with the 1.8 mm rainfaiI threshold are shown on the right sides of the figures. The directional plots show the chances that wind will approach from 22.5" sectors centered on N. NNE,NE, ENE, E, etc,

For the conditional populations (Le. those associated with a one-hour rainfall threshold), the tme probability of exceeding a given wind speed or of the wind approaching from a particular directionai sector can be obtained by multiplying the probabilities shown in the plots by the probability of exceeding the rainfall threshold. For exarnple, at Victoria International Airport (Fi,we BA), the probability that the mean wind speed will be greater than 4 m/s and the one-hour rainfall total wiii be at least 1.8 mm is approximately: Also, at the same location, the probability that the mean wind will approach from the south (k 1 1.25O) during an hour with at least 1.8 mm of rainfd is approximately:

:,cHP= = 6,.3d4 10.9 hours/yoar

*Data 1 - Weibull fi 0.8 e O .'O O o:ao oh exceedence probability

Figure 8.2 Oinni-directional wind speed versus exceedence probiibility (left) und probabiliiy of wind approaching frorn 22.5" directional sectors (right) for Vancouver Int'l A. (VAN) - conditional probiibilities are presented for the rainfall cases r: data - Weibui! fit 1 E 1 I -- k O .'O 9 O .'9 O 0.01 exceedence probabilily directional variation

Figure 8.3 Omni-directional wind speed versus excecdence probiibility (Iell) iind probabiliiy of wind iippmüchiiig Irom 22.5" O directional sectors (right) for Calgary Int'l. A. (CAL) - condiiional probabilities are presented for the rainfnll cases w O O n -O O O n O -0 -0 O O d CI - 'm - n - O - (s/ur) paads pa~wuaaur (s/nr) paads pu!& uaatu (s/m) paads pu!& uaam @/KI) paads pu!^ uearrr (s/ur) paads pn!~uaaru (s/u) paads pa~~ueau (s/m) paads pu!m ueau (s/u~) paads palfi uvaux (s/ru) paads puln uwaur IO.?,Na-

(s/ur) paads pu!& uaaur (sp) paads pu!& uuaaru Appendix C Extreme Wind Speeds During Rainfall

This appenh presents plots of omni-directionai wind speed and directional wind speeds versus retum period. Plots are presented for each of the fourteen stations of the one-hour database. The wind data used in the analysis are the rnodified spot wind speeds over tbe fdtered wind records- The rainfall data are a combination of the measured and estimated one-how totals: the Iatter were ody used when the former were not available.

The omni-directional extreme wind speed distributions are shown on the left sides of the fiopres. For a given location, the analysis was performed using the entire wind speed population and the populations associated with one-hour rainfall totals equd to or greater than 1.8, 3.0 and 5.1 mm. Three distributions are compared to the observed annual extreme wind speeds in each case. The solid line shows the distribution derived from fitting the observed annual maximum wind pressures to the Type-I extreme value distribution using Lieblein's BLUE (Le. Analysis 4 of Chapter 5). The resulting mode and dispersion (denoted as u and lia respectively) are aven in each of the plots. Note that since wind pressures were used, the mode and dispersion have units of Pa. The dotted Lines represent the distributions derived using the parent approach descnbed in Section 4.5.2 (Le. Equations 4.42). The upcrossing rate parameter N is given in each of the plots. It was observed from this analysis that the mode and dispersion estimated using Equations 4.42 are highiy erratic for N smaller than about 10 per year. This prompted the direct use of Equation 4.41 for estimahg the extreme speeds according to the parent model. The resulting distributions are shown with dashed lines. The solutions of Equation 4.4 1 are plotted in Figure C. 15 for reference.

The directional anaiysis was performed using both the overall wind population and the population associated with one-how rainfalls equd to or larger than 1.8 mm. The directional extreme wind speeds were denved using the Type-1 distribution with the distribution parameters estirnated fkom Lieblein's BLUE. 1 ~qns.4,42 I I t 2 b 10 20 I relurn period (years) return periods - 6, 10 and 30 years

Figure C. 1 Omni-directionül wind speed versus return period (left) und five-, [en-, and thirty-yeür wind specds upprouching from td 22.5" directional sectors (right) for Victoria Int'l A. (VIC) I; (s/m) paads pn~muaaur

(S/LU) paads pu!^ uaaur (s/ru) paads patm ueau

(s/m) paads pa!~usau (sp) paads puf~ueaut

(s/ur) paads pu!& uoaur (S/UI) paads ~UIMuaaur

(s/u.I) paads pu!^ ueam (sp)paads pu!& uaatu

($/ut) paads pu!& ueau t

(sp) paads pu~nruaaur 1 ~qns.4,42 t I I 2 6 10 20 return period (years) return perlods = 6, IO and 30 years

Figure C.8 Oinni-directional wiiid speed versus reiurn period (lefi) and rive-, ten-, and thiriy-yeür wind speeds approuching fro~n 22.5' directionul sectors (right) for Ottawa Int'l. A. (OTT) (sp) paads PU~Munam

(S/UI) paads pu+ uaaar (s/ur) paads pu!^ uaaru

(s/ar) paads pa!M uuaaar (s/m) paads pur^ rreaur

O w

(s/ru) paads pu!^ uearu (s/ur) paads putw ueau

(s/u~) paads pul~uaam Figure C.15 SoIutions to Equation 4.4 1