a full-scale investigation of roughness lengths wind

A FULL-SCALE INVESTIGATION OF ROUGHNESS LENGTHS

IN INHOMOGENEOUS TERRAIN AND A COMPARISON OF

WIND PREDICTION MODELS FOR TRANSITIONAL FLOW REGIMES

by

ANNA G. GARDNER, B.S.C.E., M.S.Arch.

A DISSERTATION

IN

CIVIL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

DOCTOR OF PHILOSOPHY

Approved

Chairpersonofme'Committee

Accepted

Dean of the Graduate School

May, 2004

ACKNOWLEDGEMENTS

1 would like to express appreciation to my committee chairman. Dr. Chris

Letchford, for his patience and constructive and enthusiastic guidance. Without his

encouragement this dissertation would simply not have been possible. I would also like

to thank Dr. Kishor Mehta for introducing me to the Wind Science and Engineering

Research Center and supporting me through every step of meeting and exceeding my

educational goals. Dr. McDonald and Dr. Douglas Smith's encouragement during the

course of this research and my academic career is very much treasured. I would like to

express my gratitude to John Schroeder for sharing his expertise in this research.

Special recognition should go to Chris Lubke, an undergraduate at the time of this

research, for his hard work and expert Labview programming that collected and

processed the data in this research. The support of the entire Wind Engineering

Department, professional, financial and personal, has been instrumental to the completion

of this dissertation.

Rebecca Pagan, a dearest friend, is thanked for her continued support, guidance,

and assistance in completing various stages and processes in the dissertation journey.

My deepest appreciation is to my family. My parents always encouraged me to

seek my dreams and take advantage of every opportunity. My grandparents were always

available with words of encouragement and support. And mostly for my husband Tom

and daughter Isabella endured the long hours of study and the extreme grumpiness that

often accompanied those many years.

TABLE OF CONTENTS

ACKNOWLEDGEMENTS ii

ABSTRACT vii

LIST OF TABLES viii

LIST OF FIGURES x

NOMENCLATURE xiii

CHAPTER

I. mTRODUCTION 1

II. BACKGROUl^D 3

2.1 Introduction 3

2.1.1 Atmospheric Boundary Layer 3

2.1.2 Internal Boundary Layer (IBL) 9

2.1.3 Internal Boundary Layer Models 11

2.1.3.1 Atmospheric Observations 12

m. DISPLACEMENT HEIGHT AND ROUGHNESS LENGTH 19

3.1 Introduction 19

3.2 Conceptual Explanations 21

3.2.1 Displacement Height 21

3.2.2 Roughness Length 21

3.3 Roughness Element Derived Models 22



3.4 Wind-Field Derived Models 30

3.4.1 Best-Fit Log-Law Derived Models 31

3.4.2 Conservation of Mass Derived (COM) Models 31

3.4.3 Turbulence Intensity Derived Models 34

3.5 Summary 35

W. EXPERIMENT DETAILS 36

ni

4.1 Introduction 36

4.2 Equipment, Instrumentation, and Facilities 37

4.2.1 Anemometers 37

4.2.2 WEMITE Units 38

4.2.2.1 WEMITE 1 39

4.2

4.2

4.2

4.2

2.2 WEMITE 2 40

2.3 WEMITE Meteorological Equipment 41

.2.4 Data Acquisition 41

.2.5 Data Processing 42

4.2.3 WERFL Meteorological Tower 42

4.2.3.1 WERFL Data Acquisition 42

4.2.3.2 WERFL Data Processing 43

4.2.4 Computer Synchronization 43

4.2.5 Experiment Setups 43

4.2.5.1 Experiment Setup 1 43




WEMITE 2 IN THE RESIDENTIAL COMMUNITY 60

5.1 Roughness Element Derived Models 60

5.1.1 Roughness Element Parameters 60



5.2 Wind-Field Derived Models 65

5.2.1 Introduction 65

5.2.2 Best-Fit Log-Law Derived Models 66

5.2.3 Conservation of Mass (COM) Derived Models 71

5.2.4 Turbulence Intensity Derived Roughness Length 76

5.3 Discussion 80

IV

5.3.1 Roughness Element Derived Models 80

5.3.1.1 Displacement Height 80

5.3.1.2 Roughness Length 81

5.3.2 Wind-Field Derived Models 82

5.3.2.1 Reliability of Data 90

5.4 Conclusions 90

5.4.1 Roughness Element Derived Models 90

5.4.2 Wind-Field Derived Models 91

VI. WEMITE 1 IN THE AGRICULTURAL FIELD 93

6.1 Introduction 93

6.2 Discussion 93

6.3 Conclusions 94

VIL TRANSITION FLOW REGIME MODELS 102

7.1 Background 102

7.1.1 Change of Terrain Roughness Experiment Parameters 104

7.1.2 Discussion 105

7.1.2.1 Gust Change of Terrain Models 106

7.1.2.2 Mean Change of Terrain Models 107

7.2 Conclusions 115

Vm. CONCLUSIONS 116

8.1 Conclusions 116

REFERENCES 118

APPENDDC

A. ROUGHNESS ELEMENT DERTVED DISPLACEMENT HEIGHT CALCULATIONS 129

B. ROUGHNESS ELEMENT DERIVED ROUGHNESS LENGTH CALCULATIONS 132

C. ACTUAL PROFILE INTEGRATION ERROR 136

D. COM PROBABILITY DISTRIBUTION 139

E. zo VERSUS WS 141

F. Zo, upper VERSUS WS 143

G. TRANSITIONAL FLOW REGIME RUNS 145

VI

ABSTRACT

Models for estimating the mean and gust wind speeds in the transitional flow

regime are investigated and compared to full-scale measurements. Displacement heights

and roughness lengths are also investigated for each data collection location. Roughness

lengths are calculated from fiill-scale data using conservation of mass and turbulence

intensity methods. These values are compared to wind tunnel, visual inspection and

roughness element based methods. The displacement height is also estimated from

conservation of mass and compared to roughness element based methods.

vi i

LIST OF TABLES

2.1. Full-Scale Experiments for Internal Boundary Layer Growth 16

3.1. Coefficients for Moore (1951) and Perry and Jouberf s (1963) Zd models (Equation 3.3) 22

3.2. Coefficients for Counihan (1971), Lee and Soliman (1977), and Hussain's (1978) Zd models (Equation 3.4) 23

3.3. Coefficients for Kutzbach (1961) and Raupach et al.'s (1980) displacement height models (Equation 3.5) 24

3.5. Coefficients for ZQ Models of Nikuradse (1950), Fang and Sill (1992), Saxton et al. (1974), and Houghton (1985) 26

3.6 Coefficients for ZQ Models of Tanner and Pelton (1960), Sellers (1965), and

Kung(1961, 1963) 27

4.1. Anemometer Details for WEMITE 1 40

4.2. /êmometer Details for WEMITE 2 40

4.3. WEMITE Meteorological Instrument Details 41

4.4. /êmometer Details for WERFL 42

4.5. WERFL Meteorological Instrument Details 42

5.1. Defmition of Roughness Element Derived Zd and zo Model Parameters 62

5.2. Kondo and Yamazawa( 1986) Fetch Area Parameters 63

5.3. Roughness Element Derived Zd Models Based on HêanRand HpeakR 63

5.4. Roughness Element Derived zo Models (Directionally Independent) based on HmeanR 6 4

5.5. Roughness Element Derived ZQ Models (Directionally Dependent) based on

5.6. Roughness Element Derived zo Models (Directionally Independent) Based on HpeakR 65

5.7. Roughness Element Derived ZQ Models (Directionally Dependent) Based on

HpeakR 65

5.8. Raupach et al.'s (1980) hitermediate Layer Height Ranges 66

5.9. Mean R^ and Associated OR2 From the Ln(Height) versus Mean Wind Speed Data for the 3 Flow Regions 67

Vll l

5.10. Average Zd, zo. and associated as From De Bruin and Moore's (1985) COM Method for Each Flow Region Associated With WEMITE 2 in the Residential Community 73

5.11. Comparison of ZQ'S and associated a's Calculated from TI and De Bruin and Moore (1985) for Each Flow Region Associated With WEMITE 2 in the Residenfial Communhy 79

5.12. Roughness Element Derived Zd Models that Are Within a 95% Probability of Occurrence Based on COM Zd Model 80

5.13. Roughness Element Derived zo Models that Are Within a 95% Probability of Occurrence Based on COM Zd Model 82

6.1. Flow Region ZQ stafistics for WEMITE 1 Located in the Agriculture Field 101

7.1. WERFL Insufficient Fetch Gust and Mean Correction Multipliers 108

7.2. Transition Region Beginning and Ending 115

A.l. Counihan (1971), Lee and Solimon (1977), and Hussain (1978) Zd Calculations. 130

A.2. Kutzbach (1961) and Raupach et al. (1980) Zd Calculations 131

A.3. Abtew et al.'s (1989) zd Calculations 131

B.l. Nikuradse (1933. 1950), Fang and Sill (1992), Saxton et al. (1974), and Houghton's (1985) ZQ Calculations 133

B.2. Tanner and Pelton (1960), Sellers (1965), and Kung's (1961,1963) zo

Calculations •. 133

B.3. Abtew et al.'s (1986) ZQ Calculations 133

B.4. Lettau's (1969) ZQ Calculations 134

B.5. Busmger's (1975) ZQ Calculations 134

B.6. Counihan's (1971) zo Calculations 134

B.7. Kondo and Yamazawa's (1983) zo Calculations 135

B.S. Kondo and Yamazawa's (1986) ZQ Calculations for Ru = 1520m (5000ft) 135

C.l. Log-Law Velocifies Used in s^^^ Estimation 137

C.2 Estimation Parameters for e^^^ 138

G.l. Change of Terrain Runs 146

IX

LIST OF FIGURES

2.1. Structure of the ABL 5

2.2. Isolated Roughness Flow 7

2.3. Wake Interference Flow 7

2.4. Skimming Flow 8

2.5. Flow Regime by Roughness Element Density 8

2.6. Conceptual Structure of the Transitional and Equilibrium IBL Growth 10

2.7. Conceptual Comparison of Stress and Velocity Defined IBL Growth 10

2.8. Atmospheric Observations of Smooth to Rough IBL Growth 17

3.1. Graphical Illustrafion of Zd and ZQ in the Log-Law 20

3.2. Wind Profiles Over Smooth and Rough Surfaces 21

3.3. Abtew et al.s (1989) Effective Height of a Sphere 25

3.4. Illustration of Marunich s (1971) Model for Zd (Tajchman 1981) 32

3.5. Illustration of De Bruin and Moore's Model for Displacement Height, Zd

(De Brum and Moore,1985) 33

4.1. Experiment Terrain and Data Collection Locations 36

4.2. Prop Anemometer 38

4.4. UVW Anemometer 38

4.3. Prop-Vane Anemometer 38

4.5. Sonic Anemometer 38

4.6. Photograph of WEMITE 1 39

4.7. Meteorological Instrumentation 41

4.8. Experiment Setup 1: Site Survey of WEMITE 1 and WEMITE 2 at WERFL 44

4.9. Experiment Setup 2 45 4.10. Experiment Setup 2: Site Survey of WEMITE 1 & WEMITE 2A in the

Agriculture Field 46

4.11. IBL Growth for Experiment Setup 2 and 230°-260° Wind Direction 46

4.12. IBL growth for Experiment Setup 2 and 50°-85° Wind Direction 47

4.13. Aerial Photograph of Flow Regions for WEMITE 1 for Open Country Fetch 48

4.14. Aerial Photograph of Flow Regions for WEMITE 2 for Open Country Fetch 49

x

4.15. Aerial Photograph of Flow Regions of WERFL Open Country Fetch Lines 50

4.16. Fetch of Open Country Terrain, WEMITE 1 in the Agriculture Field (m) 51

4.17. Fetch of Open Country Terrain, WEMITE 2A in the Agriculture Field (m) 51

4.18. Fetch of Open Country Terrain, WERFL (m) 52

4.19. Experiment Setup 3 53

4.20. Experiment Setup 3. Site Survey of WEMITE 2 in the Rushland Residential Community (measurements in feet) 54

4.21. Aerial Photograph of Flow Regions for WEMITE 2 in the Residential Community 55

4.22. Fetch of suburban terrain for WEMITE 2 in the Residential Community (m) 56

4.23. IBL growth for Experiment Setup 3 and 230°-260° Wind Direction 57

4.24. IBL growth for Setup 3 and 50°-85° Wind Direction 58

4.25. Experiment Setup 4: WEMITE 1 and WEMITE 2 back at WERFL 59

5.1. Roughness Element Parameters Photograph (Picture taken April 6, 1998) 61

5.2. Aerial Photograph of a Rushland Residential Block 61

5.3. Aerial Photograph of ASCE 7-2002 Exposure B (ASCE 7 2002) 66

5.4. Example Profiles of ln(z) versus Mean Wind Speed for Each Flow Region Associated With WEMITE 2 Located in the Residential Coimnunity 68

•J

5.5. Variation of R with Zdfor In(z-Zd) vs V and Perry and Joubert (1963) 69 V

5.6. Raupach et al.'s Variation of Zd to the Slope of In(z-Zd) vs— 70 lit

5.7. De Bruin and Moore's (1985) COM Profile Comparison 72

5.8. Variation of Zd and Zo Derived From COM Method with Wind Direction 74

5.9. Variation of ZQ Derived by COM and Log-Law Methods with Wind Direction and Fetch 75

5.10. Variation of Ou to u* for Flow Region 3 of WEMITE 2 Located in the Residential Community 77

5.11. Comparison of ZQ Calculated From TIu and COM to Wind Direction and F 78

5.12. Variation of Ou, u*, and Their Ratio C at 15m in the Residential Community

with Fetch Downwind of a Smooth to Rough Roughness Change 84

5.13. Aerial Photograph of Surface Roughness Irregularities in the Suburban Terrain.. 85

5.14. Turbulence Parameters u* and Ou for WEMITE 2 in the Residential Community. 86

5.15. Turbulence Ratios, TIu and C, for WEMITE 2 in the Residential Community 87

xi

5.16. Close-Up Aerial Photograph of Residential Site and Local Flow Influences 89

6.1. Comparison of z,, Calculated from the Wind Profile Using All, Lower, and Upper Instruments to Wind Direction and Fetch for WEMITE 1 in the Agriculture Field 95

6.2. IBL Layers for WEMITE 1 in the Agricultural Field for 135° Wind Direction 96

6.3. Variation of Profile Derived Roughness Lengths to Fetch for WEMITE 1 in the Agriculture Field for Wind Direcfions Between 140° and 270° 97

6.4. TIu derived ZQ Compared to zoupper and zoiowei Versus Wind Direction for

WEMITE 1 Located in the Agricultural Field 98

6.5. TIu at 15m versus Wind Direction 99

6.6. Aerial Photograph Close-Up of WEMITE 1 Located in the Agricultural Field 100

7.1. Change of Terrain 10-minute Mean Wind Speed Profiles 109

7.2. Change of Terrain 3-second Gust Wind Speed Profiles 110

7.3. 3-second Gust Change of Terrain Multipliers 111

7.4. 3-second Gust Change of Terrain Mean Multipliers 112

7.5. Mean-Hourly Change of Terrain Multipliers 113

7.6. Mean-Hourly Change of Terrain Mean Multipliers 114

D.l. COM Probability Distribution, Zd (De Bruin and Moore 1985) 140

D.2. COM Probability Distribufion, zo (De Bruin and Moore 1985) 140

E.l. Zo vs. WS 142

F . l . Zo.upperVS. W S Z... 144

Xll

NOMENCLATURE

a constant

acent centrifugal acceleration

acor Coriolis acceleration

^.4a„ai actual wind profile area

A ^ area of open terrain

Ag area of woody terrain

Af. area of large building sites

Aj, area of small building sites (Category D) suburban

A ^ fetch area

4og-iaw area of the log-law wind profile

Ag area of roughness element

^s silhouette area of the average roughness element perpendicular to the wind

direction

Agjj.^ area of the site

^„ area upwind

Ajf. windward surface area (Aw=Af for bluff bodies)

b constant

c constant

C constant

D distance between roughness elements

Dp distance between roughness elements parallel to the wind direction

^gradient gradient height or atmospheric boundary layer height

S^ internal boundary layer height

S , stress-equilibrium internal boundary layer height

S„,.^^^ stress-transitional internal boundary layer height

xiii

<>> e„„l

I mm.

velocity-equilibrium internal boundary layer height

velocity-transitional internal boundary layer height

F Fetch

^c fraction of the plan surface area covered by roughness elements

f the component of the earth's rotation perpendicular to the surface

[2 Qsin O]

hi developed height of the inner layer

H average roughness element height

H^ effective height of roughness element

^peak PS^k height of roughness element

K von Karman's constant

Kz gust velocity pressure exposure factor

Kzi downstream velocity pressure exposure factor at height z

Kioi downstream equilibrium velocity pressure exposure factor at height 10m

Kio,2 upstream factor at 1 Om

/ roughness element breadth perpendicular to the wind direction

MA asymptotic peak gust velocity multipliers in the upwind terrain A

MB asymptotic peak gust velocity multipliers in the downwind terrain B

MBX non-dimensional gust wind speed in the transition region

Mx non-dimensional wind speed multiplier

Mo upstream wind speed multiplier

Mz, cat downstream equilibrium wind speed multiplier

n number of roughness elements

Q. earth's rotational speed

O latitude of the location of interest

^ ^ dimensionless wind speed gradient

R radius of curvature of flow

Rpt radius of curvature of plant top

XIV

P density of the air

SA projected frontal area on a plane normal to wind direction (silhouette area)

cr„ standard deviation of longitudinal component of mean wind speed

<T ,, standard deviation of vertical fluctuations downstream of roughness

change

TIu longitudinal turbulence intensity

r shearing stress

TQ surface shearing stress

M* friction/shear velocity, m/s T ^

W» =

\P/

u,^, friction velocity upstream of change of terrain

«.p fi-iction velocity downstream of change of terrain

u,Q surface shear stress

V wind speed or velocity

' rodienr wlud spced Or velocity at gradient height

V mean wind speed or velocity at height z

X distance fi-om ground to center of curvature of plant top

Xi distance downstream of change in terrain

z instrument height

z* viscous layer height

Zg roughness length

z roughness length downstream of roughness change

z roughness length upstream of roughness change

Z* height of the transition sub layer

Zj displacement height

Z . min imum instrument level

XV

Z,„ j maximum instrument level

Z, transitional flow boundary layer height

Z^ equilibrium flow boundary layer height, m

xvi

CHAPTER 1

INTRODUCTION

The log-law is used to model the change of the mean wind speed with height.

The theoretically based log-law is based on neutrally stable atmospheric wind flow over

an infinite, horizontal, and homogeneously rough surface. Under neutrally stable

atmospheric conditions and flat topography, the main influence on the log-law is the

surface roughness, characterized by the log-law's parameter: roughness length, zo. Again

the Zo is based on an infinite homogeneous surface roughness. Rarely in the built

environment do infinite homogeneous surface roughness conditions exist. Whether it is

urban sprawl adjacent to undeveloped open terrain, the ocean meeting land, or open park

areas within neighborhoods, surface roughness changes and irregularities are the norm

and not the exception.

In 2002 the US wind load standard, ASCE 7, incorporated a process to estimate

how a change of surface roughness will affect the design wind speed used to predict wind

loading on buildings. The Australian/New Zealand wind load standard, AS/NZS 1170.2,

has incorporated the effects of surface roughness changes since 1989. Both standards

were developed from wind tunnel studies. While wind tunnel studies provide useful

means to understand and parameterize problems, full-scale validation is always sought.

Full-scale measurements were obtained using two instrument mobile towers

(WEMITE-Wind Engmeering Mobile Instrumented Tower Experiment) 1 and 2 and the

Wind Engineering Field Laboratory (WERFL). WEMITE 2 was placed within a

suburban community, while WEMITE 1 was placed in an agriculture field, between

WEMITE 2 and WERFL, approximately 30m from the edge of the suburban community.

The objectives of this study were:

1. Investigate the effects thatinhomogeneous surface roughness has on z o derived

fi:om conservation of mass (COM) and longitudinal turbulence intensity (TI^).

2. Estimatethe z o and displacement height, Zd, in the suburban community and

compare with ZQS and ZdS obtained from correlations with physical characteristics

of the suburban roughness elements, such as house height and plan area density.

3. Obtain full-scale wind speed measurements in the transition region.

4. Compare transition region full-scale wind speed measurements to models given in

ASCE 7 and AS/NZS 1170.2.

The accomplishment of these objectives is described in the following 7 chapters.

• Chapter II focuses on the background information and literature search to describe

the atmospheric boundary layer and means of modeling. A summary of previous

full-scale change of terrain experiment is also given.

• Chapter III describes the wind field and roughness element derived models used

to obtain zo and Zd values.

• Chapter IV gives a full description of the experimental setups, their surrounding

terrain, meteorological equipment and data acquisition systems used to obtain the

full-scale data.

• Chapter V gives the zo and Zd values obtained in suburban terrain derived

sunultaneously from De Bruin and Moore's COM model. The COM derived zo's

are compared to TIu derived zo's. The wind field derived ZQS and ZdS

measurements are then compared to values obtained from physical characteristics

of the roughness elements.

• Chapter VI discusses resuhs from ZQ measurements obtained in the agricultural

field for various fetches.

• Chapter VII provides a brief background discussion on ASCE-7 (2002) and

AS/NZS 1170.2's (2002) change of terrain models and compares the full-scale

transifional velocity measurements to ASCE-7 (2002) and AS/NZS 1170.2

(2002).

• Chapter VIII gives the conclusion and recommendation resuhing from this

research.

CHAPTER II

BACKGROUND

2.1 Introduction

Wind is air in motion. On a macro scale, wind resuhs from the movement of air

fi-om high-pressure areas to low-pressure areas in an attempt to reach a state of

thermodynamic equilibrium. Differences in atmospheric pressures are referred to as

pressure gradients. Pressure gradients are caused by the varying amounts of solar heat

absorbed by the earth's surface and atmosphere.

High above the Earth's surface in the free atmosphere, the wind is mamly

influenced by the curvature of the flow (centrifugal acceleration, ace„t) and the rotation of

the Earth (Coriolis acceleration, acor) defined, respectively, by Equation 2.1 and Equafion

2.2.

acent = V ^ / R (2 .1 )

acor = 2 Qsin O V (2.2)

where V is the velocity, R is the radius of curvature of flow, 2 Qsin O is the

component of the earth's rotation perpendicular to the surface, where Q is the earth's

rotational speed and O is the latitude of the location.

Winds close to the Earth's surface are influenced by the physical and thermal

properties of the earth's surface and atmosphere. The height where the winds are no

longer influenced by the earth's surface is called the gradient height, (Jg , „,. The

gradient height defines the top of the atmospheric boundary layer (ABL), also referred to

as the planetary boundary layer (PBL).

2.1.1 Atmospheric Boundarv Layer

A boundary layer is the region in which the effects of the boundaries of flow are

noticeable (Elliott 1958). The boundaries of flow of the ABL are the physical and

thermal properties of the Earth's surface and atmosphere and the dynamics and

thermodynamics of the lower troposphere (Arya, 1995). It is generally expected that

when the hourly-mean wind speed exceeds 10 m/s (22 mph) or 3-sec gust wind speed

exceeds 15 m/s (33 mph) the turbulence produced by the mechanical mechanisms of air

flow over surface roughness dominate any thermal effects, thereby allowing the ABL to

be considered adiabatic or neutrally stable' (Cook, 1985). Most strong winds that are

considered design events in structural design occur in neutrally stable conditions^ (Harris

and Deaves, 1978).

The mean winds that occur in the ABL can be divided into three layers: an outer

layer, an inner layer^ and a viscous layer (see Figure 2.1). The velocity at a specific

height in the outer and inner layers is dependent on the surface shear stress, the gradient

height and the density of the air. The non-dimensional expression of this flow

dependence is known as the velocity defect law and is given in Equation 2.3:

gradient z />

"*0 ^ gradient j

(2.3)

where Vgradient is the wind speed at gradient height; z is the height; V is the mean

wmd speed at z; u^^ is friction velocity, a measure of the surface shear stress

{U,Q=^TQI p) and / is some function to be determined.

^ The stability of air reflects the susceptibility of rising air parcels to vertical motion, i.e., giving rise to buoyancy forces. Stability is a fiinction of the vertical distribution of the atmospheric temperature. The atmosphere is considered to be neutrally stable when the vertical change of ambient temperature, the adiabatic lapse rate, is approximately equal to -1° C/100 m.

" Excluded from this statement are winds with intense thermal components, which can include winds at tropical and temperate latitudes, mountain slope winds, seacoast wind, dovmbursts and tomadic winds (Harris and Deaves, 1978).

^Also known as the inertial sublayer, the constant-flux layer and the wall region

JS

o

C3 o 3

C/3

3

o II

But unlike the outer layer, the velocity in the inner layer is also dependent on the

roughness of the earth's surface. The parameter used to scale the roughness of the earth's

surface is the roughness length, zo. The non-dimensional expression of the inner layer's

flow dependence on ZQ is known as the "law of the wall," given by Equation 2.4:

" • 0 (2.4)

K-o J

where / is some function of Z/ZQ.

The inner layer is characterized by being high enough to apply the velocity-defect

law but also low enough to apply the law of the wall. Using an asymptotic process to

match these two laws results in a dimensionless wind speed gradient, ^^ , equal to unity

(Equation 2.5).

J. is= dV .,

<t>M= ^ - = 1 (2.5)

The mtegration of (j);^ results in a logarithmic profile known as the log-law given

by Equation 2.6. The inner layer under neutrally stable conditions and dynamic

equilibrium can be modeled using the log-law, which produces a mean velocity profile

dependent on height (z), surface roughness (Zo), friction velocity (u*), zero-plane

displacement (zd), and von Karman's constant ( K ).

K(r; = i^ ln K

f ___ \

V - 0 y (2.6)

The application of the log law sets an upper limit of the inner layer of

approximately 0.1 S^^^^j^^, to 0.2 5^„^f^„, and the application of the velocity defect law sets

a lower limit of approximately 20zo to 50 zo(Weiringa 1993).

The mean flow in the viscous layer varies three-dimensionally and depends on

wake diffusion, not turbulence (Wiring 1993). Flow within the viscous layer is affected

' Dynamic equilibrium ideally exists over a homogeneous surface roughness with an infinite fetch.

by local flow around individual roughness elements.^ There are 3 types of physical flow

behaviors over roughness elements: isolated roughness flow, wake interference flow and

skimming flow (Morris 1955).

Isolated roughness flow, referred to as semi-smooth flow by Weiringa (1993),

occurs when there is enough space between roughness elements that the wake and

separation bubble develop and reattach before flow reaches the next roughness element

(Figure 2.2).

I winH>

Figure 2.2. Isolated Roughness Flow.

Wake interference flow occurs when the spacing between the roughness elements

is not sufficient to allow the separation bubble to completely develop (Figure 2.3). Jia et

al. (1998) found that the roughness length reaches a maximum at the begirming of wake

interference flow.

Figure 2.3. Wake Interference Flow.

Skimming flow develops when the roughness elements are located so close to

each other that stable vortices develop between the roughness elements and the flow

^ The elements of the surface that make the surface rough are known as roughness elements. Roughness elements can vary greatly in shape and size (grains of sand, ocean waves, vegetation, buildings, etc.).

7

seems to skim over the roughness elements creating a roughness sub layer (Figure 2.4).

Jia et al. (1998) found that when skimming flow develops the roughness length decreases

with increasing density.

Iwinty

Figure 2.4. Skimming Flow.

Lee and Solimon (1977) used results from wind turmel testing to define the

various flow regimes for normal and staggered pattems of elements by the roughness

element density. Isolated roughness flow for normal and staggered pattems was found to

exist when the roughness element density was less than 8% and 16 % respectively. Wake

interference flow developed when the roughness element density was between 8% and

44% for normal pattems and between 16% and 40% for staggered pattems. Skimming

flow developed for roughness element densities above 44% and 40% for the normal and

staggered pattems, respectively (see Figure 2.5).

Isolatf

0

:d <

1 10

•^

Wake Interference

H—1—1~ 20 30 40

• Skimming

• f 1 1 50 60 70

•

1 80

1 90

100 %

Figure 2.5. Flow Regime by Roughness Element Density.

The viscous layer can be divided into two layers: a displacement height layer and

an intermediate layer. The displacement height layer (see Figure 2.1) exists between the

surface of the earth and up to a level where the log-law can theoretically be applied. The

remainder of the viscous layer is deemed the intermediate layer. Experiments show that

wind speeds in this layer do not fit the log-law because they are still being influenced by

the localized flow fi-om the roughness elements (Weiringa, 1993; Lo, 1990; Raupach et

al., 1980).

The height of the viscous layer, z*, has been estimated by Wieringa (1993) and

Tennekes (1973, 1982) and are given in Equations 2.7 and 2.8.

z* = Zd + 20zo (2.7)

z* s 20zo to 50zo (2.8)

2.1.2 Intemal Boundarv Layer (IBL)

When wind flow encounters a discontinuity in surface conditions, such as a

change in surface roughness (mechanical) or temperature and/or humidity (thermal), a

new boundary layer or intemal boundary layer (IBL) is formed. Since this research

assumes neutral stability (eliminating thermal effects) and surface roughness is the main

mechanism influencing the ABL, it is of great interest to examine the effect of a change

in surface roughness on the ABL wind profile. When surface roughness increases or

decreases, the surface shear stress (r^) increases or decreases with a consequent change

in the amount of fi-iction force momentum the wind flow must overcome, i.e. a slowing or

speeding up of the wind near the surface. This results in an altered velocity profile in the

zone affected by the change as the flow strives to reach a new equilibrium with the new

surface roughness.

The altered profile may be considered the combination of two profiles separated

by a transition region. The upper part is still govemed by the upstream surface roughness

and is thus essentially part of the old BL (upstream equilibrium flow), while the lower

part is govemed by the new surface roughness and forms the new BL or IBL. Between

the two profiles exists a transitional flow regime or blending region (Figure 2.6).

upstream

equlibrium flow

•"^^ - new BL, IBL

downstream

equilibrium flow roueh terrain smooth terrain

Figure 2.6. Conceptual Structure of the Transitional and Equilibrium IBL Growth.

The IBL height, 6,, is the level where the influence of the roughness change

begins to be noticeable. Defining how the change begins to be noticeable can be and has

been approached several ways. IBL definitions have been based on stress and velocity.

The basis of the definition is important because velocity profiles adjust to new surface

conditions much slower than stress profiles, i.e., a stress based IBL is thicker than a

velocity based IBL with a consistent fetch, F (distance downstream of the surface

roughness change), as illustrated in Figure 2.7. Shir (1992) estimated that a stress-

defined IBL would be roughly twice the height of a velocity-defined profile. Stress-

defined IBL profiles are considered to be superior estimators since stress has greater

variation across the region of influence as opposed to velocity profiles (Deaves, 1980).

wind >

rough terrain ' smooth terrain

Figure 2.7. Conceptual Comparison of Stress and Velocity Defined IBL Growth.

10

2.1.3 Intemal Boundary Layer Models

Researchers have attempted to model the intemal boundary layer growth by

theoretical means (Elliott, 1958; Taylor, 1962; Logan and Jones, 1963; Panofsky and

Townsend, 1964; Townsend, 1965; Plate and Hidy, 1967; Nickerson, 1968; Taylor, 1969;

Blom and Wartena, 1969; Peterson, 1969; Shir, 1972; Rao et al., 1974; Mulheam, 1977;

Jensen, 1978; Schlichting, 1979; Beljaars et al., 1987; Deaves, 1981) and observafional

means in wind tunnel studies (Antonio and Luxton, 1972; Raupach et al., 1980; Wood,

1982; Cheng and Castro, 2002; and atmospheric studies Kutzbach, 1961; Steams, 1964;

Steams and Lettau, 1963; Blackadar et al., 1967; Bradley, 1968; Panofsky and Peterson,

1972; Munro and Oke, 1975; Peterson et al., 1976; Karlsson, 1985; and Jegede and

Foken, 1999). Elliot's theoretical model has been the most influenfial, utilized, and

substanfiated. Therefore a brief review of his model follows. This dissertation's

experiment collected full-scale atmospheric data; a literature review of atmospheric

observation studies is presented in Section 2.1.3.1.

Elliott (1958) assumed log-law wind profiles and modified Karman's integral

equation to derive the height of the intemal boundary layer, 5^, as a function fetch.

Elliott's solution was easily approximated by Equation 2.8.

5^=aX" (2.8)

where a = 0.75 - 0.03 In w; and m = "^y^ , resulting in a varying between 0.6-/ --0(7

0.9. The value of n was found to 0.8 and constant regardless of the value of o. It is

important to note that Elliott's model assumes that the friction velocity is a function of

fetch but is constant with height. This constant stress assumption implies that the

momentum flux at the top of the boundary layer is piu^^, and is pu,j^ at the bottom of the

boundary layer. Also the upstream BL and downstream BL or new BL wind speeds are

assumed equal at the top of the new BL which implies a discontinuity in stress. Elliott

recognized this was theoretically unrealistic, and a transitional zone is likely to exist. But

the discontinuity in stress is indicative of a very narrow transition zone and therefore

11

would be a reasonable assumption. For expansion of Elliott's model to include a

transifion region see Panofsky and Townsend (1963) and Taylor (1962).

2.1.3.1 Atmospheric Observations

In 1961, the University of Wisconsin's Department of Meteorology began a series

of atmospheric experiments to study the modification of wind profiles over different

surface roughness fetches. These experiments were set up on the smooth ice surface of

frozen Lake Mendota using bushel baskets and Christmas trees to form a controlled

surface roughness. Kutzbach (1961) measured velocity profiles over bushel baskets

ahering fetch and roughness element height and density. In 1963, Steams and Lettau

measured velocity profiles above Christmas trees. Steams (1964) repeated his 1963

experiment making several improvements; one of the most important being the addition

of more anemometers to better define the wind profile shape. Due to the limited height

of the measurements, these experiments are most useful in the evaluation of the effects of

roughness element geometry and density on the wind profile structure. Therefore data

relevant to the IBL growth is minimal and questionable.

Blackadar et al. (1967) measured velocity profiles for rough (unmown hay) to

smooth (mown hay) flow transitions in Lawrence Township, New Jersey. Blackadar

compared wind profiles to the equilibrium upstream wind profiles, concluding that the

growth of the transitional velocity IBL was in reasonable agreement with Elliott (1958).

The method used by Blackadar et al. to determine the IBL height could not be ascertained

from the source.

Bradley (1968) performed one of the best-known atmospheric experiments.

Bradley measured both rough to smooth and smooth to rough transitions using spikes,

grass and tarmac to create the transitions. Bradley measured the surface stress variation

and velocity profiles downwind of a surface roughness change and concluded that the

transitional velocity IBL grows according to a 4/5 power law and that the equilibrium

stress IBL can be approximated by a height to fetch ratio of 1:200. Bradley determined

the IBL height by plotting the height of the instruments measuring the mean wind speed

on a log axis against the mean horizontal wind speed on a linear axis. The height of the

12

IBL is the level where a kink appears in the profile. Bradley also found that for S-R

changes the surface shear stress immediately after the change increases to about twice the

equilibrium value and for R-S changes stress immediately after the change is about half

the equilibrium value.

Panofsky and Peterson (1972) measured wind velocity profiles at the Danish

Atomic Energy Commission at Riso, Denmark, over a surface roughness change from

water to land (smooth to rough). Kinks in the velocity profile are used to define the

velocity IBL growth rate. Panofsky and Peterson concluded that their observations were

in good agreement with Elliott (1958). In 1974, Peterson et al. (1976) set up another

experiment at Riso to study the effect of abrupt surface roughness changes on the wind

field. Three masts measured wind speeds, on at the transition change (the water and land

interface) and two others at 53m and 124m inland. The velocity profiles of these towers

were compared to upstream conditions. Peterson et al. concluded that the velocity

transitional IBL grows at a height to fetch ratio of 1:10.

Munroe and Oke (1975) measured wind profile transitions from smooth (tobacco

seedlings) to rough (winter wheat) terrain. The growth of the equilibrium IBL value

matched Elliott's (1958) growth rate and Peterson's (1969) conclusion that only 10% of

the lower IBL layer is in equilibrium with the new surface. Munroe and Oke utilized a

velocity difference and a fi-iction velocity method to identify the IBL height. The

velocity difference method involved finding the difference between the actual wind

profile and the best-fit log profile. The velocity differences were plotted with respect to

fetch and height. Large velocity differences indicate flow not in equilibrium. A straight

vertical line indicates equilibrium flow and deviations from this line indicate the

transition region. The friction velocity method uses the ratio of friction velocities to

downstream equilibrium friction velocities and compares these values at different

elevations at the same fetch. If the profile is in equilibrium, the ratio will be one

indicating the momentum flux is constant; and therefore in equilibrium, but if the ratio

differs from unity, this indicates the presence of a transition region.

13

Karlsson (1985) measured wind profiles at the urban-rural border of Uppsala,

Sweden. Power law profiles were applied to the upstream and downstream profiles. The

intersection of these profiles was used to estimate the velocity IBL height. Karlsson

found that the velocity IBL grew with fetch according to a 0.63 power law.

Jegede and Foken (1999) performed field experiments for the Meteorological

Observatory of the German Weather Service in Lindenberg, Germany in 1996 and 1997.

The Lindenberg area is made of varying terrains which consist of forests, small lakes,

meadows and farmlands. A 10m mast was used to measure mean wind speed profiles.

The fetch for various terrain changes varied, depending on direction, between 140m and

315m. Jegede and Foken found that the IBL growth agreed well with Elliott's (1958)

theoretical IBL growth model (Equation 2.8), with the height of the equilibrium stress

layer being estimated with values a = 0.3 and b = 0.5 and the height of the transitional

stress layer having an a = 0.4 and b = 4/5.

Jegede and Foken (1999) used a similar technique as Elliott (1958) to determine

the IBL height. They plotted the wind speed against the square root of the height.

Summarized by Jegede and Foken (1999), Foken (1990) presents a method of plotting the

instrument height on a log axis against the normalized wind speed on a linear axis. Again

the presence of a kink in the profile will identify the IBL height. Foken (1990) reviews

various techniques and their merits and downfalls (Jegede and Foken, 1999);

unfortunately this German document could not be found in an English translation and

therefore was not reviewed.

The atmospheric experiments are listed in Table 2.1 along with the maximum

anemometer height, the type of roughness change (S-R and/or R-S), the fetch and the

type of roughness elements. Figure 2.8 and Figure 2.9 show the data from these

experiments (when available) and compares the data to Elliott (1968). To compare data

to Elliott (1958), roughness lengths of 0.005m for the smoother surface and 0.02m for the

rougher surface were used, since most of the terrain in the atmospheric experiments fit

the classifications of exposures C and D given by the ASCE 7 (2002) commentary. For

14

correct comparisons of IBL heights any displacement height was subtracted from the IBL

elevations.

15

o

o

J

c

o CQ "TO c !U

c S

X

w "3 o

on

3 I J H

E

s

ejD s o

en VI

C SI

.s s 3 X! O V

£ X

4i

O

O

c ra

'5 — 3 o

Pin -a e ra -a <L» 00 4)

V~i 00 ON

S3 O en tn

"^ ra t^

s n

o ^

ao *"

C/2 J =

© O N

§

' ^ -o & ra ^ —

T3

§

c

o u ra > g "3) H c O C/3

• 'S

tu g

o 2 ra ra

V-1

Pi I

t/3

U ON

u OB c ra

J3

U

ON

O -o ra o

o o

Pi

r<-> (-•4

ON

0) 0-

O S3 ra

• a c ra

pa

c o (N o >^ ra

E M~l o o

a: p < o E c P

S o ON

NO

1/3 I

Pi

NO

U

E " o en 1) ^ en ra m CL p. 3 3

I

IZ3

NO

ra ra a . 00

. o w o

ra T3

o ra

S

NO ON

NO ON

3 ra

:

16

100

0.01

0.01 0.1 10 100 1000

F(m) A Peterson et al. (1976) O Kutzbach (1961) • Munroe and Oke (1975)

Elliott (1968)

• Stearns and Lettau (1963) D Panofsky and Peterson (1972) A Bradley (1968) - Jegede and Foken (1999)

Figure 2.8. Atmospheric Observations of Smooth to Rough IBL Growth.

17

1000

100

J 3 • l - l

CQ

0.01

0.01 0.1

D Blackadar et al. (1967)

A Bradley (1968)

1 10 100

fetch, F (m)

- Jegede and Foken (1999) X Karlsson (1985)

Emott(1968)

1000

Figure 2.9. Atmospheric Observations of Rough to Smooth IBL Growth.

18

CHAPTER III

DISPLACEMENT HEIGHT AND ROUGHNESS LENGTH

3.1 Introduction

The physical meanings of the displacement height, zj, and the roughness length,

zo, have not been clearly established outside of their empirical purpose in the log-law (De

Bruin and Moore 1985). The zo is derived from a wind profile by plotting the natural log

of the instrument height, zi, versus the mean wind speed, v,. A best-fit line is then fitted

to the points. If a Zd does not exist, then the zo is equal to the exponential of the y-

intercept.^ Equation 3.1 gives the zo derived from wind profile measurements when a Zd

is not present (Campbell, 1995). Equation 3.2 gives the value of the zo when a Zd is

present. Defined empirically relative to the log-law, the Zd is a correction factor for the ZQ

(Figure 3.1).

exp

ZM--,) TK 1=1 (3.1)

-0 = exp

X1B(--,--.) Z^' /s' ,=\ (3.2)

where zo = roughness length

z = instrument height

n = number of measurement heights

K = von Karman's constant

u* = shear velocity

^When fitting a best-fit line, the procedure minimizes the error relative to a particular axis, typically the y-axis.

19

I = mean wind velocity

Zd = displacement height.

2.5

-?- 2

t ° 1.5

'c'

0.5

R = 0,9995^,^^-*'''''''^

' 1 1 1 1

4 6 8

Mean Wind Speed (m/s)

10 12

Figure 3.1. Graphical Illustration of Zd and Zo in the Log-Law.

The Zo influences the shape of the wind profile and height of the boundary layer

and Zd dhectly affects the accuracy of ZQ. Figure 3.2 shows conceptual wind profiles over

a smooth and rough surface. As the surface becomes rougher, ZQ, Zd, and Sgradiem become

larger.

20

Height (m) Height (ft)

6 0 a _ 2000-Gradient Height. 6p.,ai,„,

>00 1500^

400 I -

300 IOOOL-

200 500- r

100 z

0 0~ . .

ti Gradient Height, \,,^^^

a "1

1 r i 4 4n-lnn

Gradient Height, Sjradfcni

1 •• ' /

r ^ O ^ , ,

\^^ Velocity / Profile

A Figure 3.2. Wind Profiles Over Smooth and Rough Surfaces

3.2 Conceptual Explanations

3.2.1 Displacement Height

Sutton (1949) hypothesized that the Zd is the depth of still air trapped among the

roughness elements. After all, the log law is undefined for z < Zd. Similar to Suttons

belief, Marunich (1971) defined the Zd as the vertical displacement of a parcel of air as it

passes fi-om a smooth reference surface, where Zd = 0, to a rougher surface, where Zd > 0.

Thom (1971) believed that the Zd represented the elevation at which the mean drag (the

surface shear stress) acts on the roughness elements.

3.2.2 Roughness Length

Panofsky and Dutton (1984) believed that the zo represents the size of the eddies

produced from the wind moving over a rough surface: the larger the eddies the larger the

Zo and vice versa.

21

3.3 Roughness Element Derived Models

If the Zd and ZQ are considered dependent on the characteristics of the surface, then

they should be a function of roughness element size, shape and density. Models based

roughness element parameters have been developed to estimate both Zd and ZQ. on


Moore (1951) and Perry and Joubert's (1963) wind tunnel studies found that the

Zd was proportional to the roughness element height, H (Equation 3.3). Their resuhs

produced similar coefficients (Table 3.1) which, if averaged, resuhs in a commonly used

rule of thumb estimate of Zd = 0.75H.

Zd = cH (3 3)

Table 3.1. Coefficients for Moore (1951) and Perry and Joubert's (1963) Zd models (Equation 3.3).

Reference Moore(1951)

Perry and Joubert's (1963)

c 0.7 0.8

In wind tunnel experiments, Counihan (1971). Lee and Soliman (1977), and

Hussain (1978) found a relationship between the Zd and the roughness element height, H

and the fraction of plan area covered by the roughness elements, Fc. All three researchers

used Perry and Joubert's (1963) method to estimate the Zd which is described in further

detail in section 3.4.1. Counihan used Lego™^ blocks, 15.9mm in width and length and

9.5mm in height, and varied their density; Lee and Soliman (1977) used normal and

staggered patterned roughness element arrays of different densities made up of 20mm

cubes; Hussain (1978), working from previous work by Solimon (1976) and Lee and

Solimon (1977), estimated the displacement height over arrays of roughness elements

with 75mm widths and lengths and 36mm heights. Due to criticism of Soliman's

experimental set-up, in particular the depth of boundary layer relative to the roughness

element height and limited fetches, Hussain established ratios of boundary layer thickness

to roughness element height more reflective of atmospheric conditions and used greater

22

fetches to ensure equilibrium conditions. Hussain's results agree well with Counihan.

Hussain attributes Counihan's slightly lower constant to Counihan's use of the average of

measurements taken at different locations among his roughness elements (at the block

centeriine and the street centeriine). Equation 3.4 and Table 3.2 show the Zd model and

coefficients derived by Counihan, Lee and Solimon, and Hussain's experiments.

z,=cHF^

H = height of the roughness elements

Fc = fraction of the plan surface area covered by the roughness elements

c = constant.

Table 3.2. Coefficients for Counihan (1971), Lee and Soliman (1977), and Hussam's (1978) Zd models (Equation 3.4).

(3.4)

Reference Counihan (1971)

Lee and Soliman (1977) Hussain (1978)

c 1.5 2.5 1.6

Raupach et al.'s (1980) wind tunnel studies of flow over normal and staggered

patterned arrays of cylinders (6mm in diameter and 6mm in height) resuhed in an

exponential relationship between the Zd and Fc (Equation 3.5). Raupach et al. modified

Perry and Joubert's (1963) method to identify the Zd. This modified method is further

discussed in section 3.4.1.

Kutzbach (1961) performed atmospheric studies over varying densifies of bushel

baskets (42cm base radius, 37cm top radius, 30cm in height) and also found an

exponential relationship between the Zd and Fc. Kutzbach used a least-squares error

technique to estimate the Zd. Details of the least-squares error technique employed are

not discussed in Kutzbach's paper. Kutzbach's experiment may have been negatively

impacted by the experiment setup. It is questionable that all instruments were located in

the inner layer and if the fetch was sufficient to simulate equilibrium conditions.

Equation 3.5 shows the Zd model derived from Kutzbach and Raupach et al.'s

experiments and Table 3.3 lists their associated coefficients.

23

c and a = constants.

Table 3.3. Coefficients for Kutzbach (1961) and Raupach et al.'s (1980) displacement height models (Equation 3.5).

Reference Kutzbach (1961)

Raupach etal. (1980)

c •1.09 1.47

a 0.29 0.33

The majority of research for determining Zd has been performed in wind tunnels

with bluff-body rectangular-shaped roughness elements. Common roughness elements

found in suburban exposures include homes with varying roof shapes, trees, berms,

fences, cars, etc. These roughness elements are often irregularly shaped and therefore the

height used in the wind tunnel models may not correspond well with the peak or

maximum heights of the suburban roughness elements.

Abtew et al. (1989) addressed this issue by fitting common geometrical forms to

the irregular shaped roughness elements to come up with an effective height parameter,

Heff, used to estimate a Zd for a roughness made up of various shapes. The Heff is defined

by Abtew et al. as the effective roughness element height. He uses spheres in his

example and, since the spheres are assumed to be touching at their edges and therefore

the wind is assumed not to see the lower half of the sphere, the average height will be the

average height of the upper half of the sphere plus the radius of the sphere, Rsphere- Abtew

et al. gives the average height of the upper half of the sphere as Rspheresin45° which is

distance from half the height of the sphere to the point located half-way on the quarter

circle arc (Figure 3.3).

24

HciT =Rsrhc,c+RsriuTcSin45' 0.5R

Figure 3.3. Abtew et al.'s (1989) Effective Height of a Sphere.

Abtew et al.'s Zd model also depends on the Fc, but a H ff that depends on the

roughness element shape is used instead of the actual roughness element height (Equation

3.6).

Zd = HeffFc (3.6)

Heff = the effective height of an individual roughness element

For a surface roughness made up of varying roughness element shapes, a Zd is

calculated for each shape and all the ZdS are added together to estimate the overall Zd for

an area. Table 3.4 gives the estimates of the Heff for various roughness elements

presented by Abtew et al. Note that the Heff given for buildings in Table 3.4 is for

buildings with flat roofs and does not take into account varying roof slopes found in most

residential single-family homes located in the United States.

For homes with sloped roofs, the Heff was estimated as the eave height plus one-

half the height of the roof slope. This estimation is based on Abtew et al.'s

approximation of Heff for triangular shapes, where Heff = 0.5Hpeak- Note that adding 0.5

times the roof height to the roof eave height results in the same mean roof height

calculation used in the wind load design standard ASCE 7.

25

Table 3.4 Estimates of Heff for Various Roughness Elements (Abtew etal. 1989)

Roughness element Broad leaf trees Bemis, ridees

Everereen trees Buildings (flat root)

Effective height (0.71R„+X)

0.5H„ (0.51 l+X)

I W

Rpt = radius of curvature of plant top

X = distance from ground to center of curvature of plant top

Hpeak = peak height of roughness element

For any roughness element height used in a model, it is important to note that the

rigidity of the roughness element can also contribute to the H or Heff. High winds may

cause non-rigid elements, such as trees and other vegetation, to bend over resulting in a

reduced H or Heff.


Nikuradse (1933, 1950) was one of the first researchers to derive a zo based on

roughness element parameters. By measuring water flowing through pipes luied with

sand grains, he found that the ZQ for sands could be estimated by a ratio of 0.033H

(Equation 3.7). Through wmd turmel studies, Saxton et al. (1974), Houghton (1985), and

Fang and Sill (1992) found a similar linear relationship between the zo and the H. Fang

and Sill concluded that this ratio was only applicable for uniformly shaped, sized and

spaced roughness elements, such as crops or forest and the zo's correlation with H only

exists for more controlled situations and was not applicable for many natural conditions.

The coefficients for each reference are listed in Table 3.5.

=,=cH (3.7)

c = constant

Table 3.5. Coefficients for zo Models of Nikuradse (1950), Fang and Sill (1992), Saxton et al. (1974), and Houghton (1985).

Reference Nikuradse (1950)

Fang and Sill (1992), Saxton et al. (1974). Houghton (1985)

c 0.033

0.1

26

Tanner and Pelton (1960), Kung (1961, 1963), and Sellers (1965) found more

complex logarithmic relationships between z„ and H (Equation 3.8) which are dependent

on twocoefficients. The coefficients for each reference are listed in Table 3.6.

logZg^a + blogH (3 3)

a and b = constants

If the logarithmic principle: log, .4" = «log„ ^ is applied. Equation 3.8 becomes

Equation 3.9:

log-o = « + log//*. (3 9)

Taking the exponential of each side results in the simplified equation. Equation 3.10: a i r b Zo=10'H

Simplifymg further by assigning c = 10\ gives Equation 3.11.

= c / / '

(3.10)

(3.11)

Table 3.6 Coefficients for zo Models of Tanner and Pelton (1960), Sellers (1965), and Kung (1961, 1963).

Reference Tanner and Pehon (1960)

Sellers (1965) Kung (1961 and 1963)

a -0.883 -1.385 -1.24

c 0.131 0.041 0.058

B 0.997 1.417 1.19

From simple intuitive investigation, the relationship of zo to H alone is

questionable. According to the models discussed, the zo is independent of roughness

element density. For example, an area that contained 100 roughness elements and an

equal area that contained 1000 roughness elements of the same height would have the

same ZQ. This contradicts wind tunnel observations of the three flow behaviors: isolated

roughness flow, wake interference flow, and skimming flow, discussed in Chapter II.

As suggested by Lettau (1960), the element shape and spacing must be governing

factors. Through analysis of wind turmel data and the atmospheric experiments of

Kutzbach (1961), Lettau (1969) suggests that zo is dependent on H and the ratio of the

projected frontal area on a plane normal to the wind direction (silhouette area), SA, and

27

the specific density^ or area of site, Asue, divided by the number of roughness elements, n.

Lettau's zo model is given below in Equation 3.12.

n

: „ = 0 . 5 / / — ^ (3.12)

SA - projected frontal area on a plane normal to the wind direction (silhouette area) Ague = area of the site

n = number of roughness elements on the site

SA

•^sile /

Lettau states that his model is limited when / " approaches unity and for large

horizontal sizes or scales of As.te (i.e., a regional or continental scale). Busmger (1974)

and Seginer (1974) concluded that Lettau's model is only vahd for moderately

inhomogeneous situations due to the effect of changing effective drag and any increase in

sheltering effects. Fang and Sill (1992) applied Lettau's model to both atmospheric and

wind tunnel experiments and found that Lettau's model correlated well with both data

types. It should also be noted that Fang and Sill proposed an alteration of Lettau's

method by suggesting the use of an effective height, Heff (Equation 3.13), which depends

on a windward surface area parameter: Aw

^sile/ ^ i v / «

Abtew et al. (1986) also proposed that the ZQ is dependent on H and Fc (Equations

3.14-3.16). Substituting in Abtew et al.'s Zd relationship (Equafion 3.6) into Equation

3.14 yields Equation 3.15. which simplifies to Equation 3.16.

^ Lettau uses the term specific area.

^ Note that for a cube, with the wind hitting normal to one side the the cube Aw = SA. But if a wind is hitting a cylinder 3mm in height with a 1mm diameter, then SA = (cylinder height)(cylinder diameter) = (3mm)(lmm) = 3mm^ and Aw = (half-circle

perimeter)(height of the cylinder) = —(iww?) (3OTW) = 4.71mm''.

28

=o=0.13(«,,^-.-^) (3.14)

ro=0.13(//.,, -// ,„F,). (3.15)

ro=0.13//,,,(l-FJ. (3.16)

Businger's (1975) ZQ model is based on the average distance between roughness

elements parallel to the wind direction. Dp, and the H (Equation 3.17).

--"•'f ' l - 0 . 5 - ^ ' (3.17)

Dp = distance between roughness elements parallel to the wind direction

From atmospheric measurements taken on a 200m AMeDAS tower located in the

Tahoku and Kanto districts of Japan, Kondo and Yamazawa (1986) developed a ZQ model

that used Digital National Land Information of the Geographical Survey Institute,

Ministry of Construction of Japan (Equation 3.18). Digital images were analyzed

according to the area occupied by types of site or roughness elements: AA - open areas,

AB - wooded areas, Ac - larger building areas. AD - smaller building areas. The validity

of this model is limited to ZQS between 0.2m and 1.5m.

Zo=(40a + 125b + 200c + 110d-30)100 (3.18)

where a = "^^Z. , b = ^^Z , c = ^ ^ 7 . and ^ = ^ y ^ and a+b+c+d=l

AA = area of open terrain

AB = area of wooded terrain

Ac = area of larger building terrain

AD = area of smaller building terrain

Au = area upwind

For the Au, Kondo and Yamazawa suggest using a fan shaped 45 degree area with a

radius of lOOH or use a complete circle when one direction is not of particular interest.

All of the previous models assume equilibrium conditions and do not account for

a limited fetch. Through wind tunnel experimentation, Counihan (1971) developed a

model dependent on fetch. But Counihan's model is restricted to a range of

0.10 < F, < 0.25. Counihan used various arrangements of Lego bricks (9.5mm (0.375in)

29

in height and 15.9mm (0.625in) square) attached to Lego™ base boards that had 1.6mm

(0.0625in) protrusions. Counihan's model is shown in Equation 3.19 and note that in

h equilibrium condhions (an infinite fetch > 0 ) it simplifies to Equafion 3.20.

--o = //[8.2/7//- + 1.08f;-0.08] (3.19)

F = upstream distance to surface roughness change, fetch

--o=H[1.08F,-0.08] (3.20)

He found that the ZQ will increase until F^. « 0.25 and then begins to decrease when

F, >0.25. When 0.10<F , <0.25, Counihan suggests that the roughness elements are

producmg the maximum contribution to the production of turbulent energy, i.e. wake

interference flow (refer to section 1.5) is occurring, and when F, >0.25 the mixmg effect

of the roughness elements becomes gradually more suppressed by their closeness to each

other, i.e., skimming flow (refer to section 1.5) is occurring. The beginning development

of skinmiing flow atF, >0.25. contradicts Lee and Solimon's (1977) findings that

skimming flow begins when F > 0.40 . Counihan did not investigate the flow behavior

forF^ >0.25, but states that 0.10<F^ <0.25 is representative of most suburban and urban

areas. After assessing suburban areas in the Lubbock community, it was found that most

suburban areas had F >0.25 which contradicts Counihan's statement or assumption.

3.4 Wind-Field Derived Models

Displacement height, Zd, and ZQ models based on wind-field profiles have been

proposed by Lettau (1957, 1971), Perry and Joubert (1963), Marunich (1971), Raupach et

al. (1980), Molion and Moore (1983), De Bruin and Moore (1984), Lo (1990), and

Peterson (1996).

Perry and Joubert (1963), Lettau (1971), and Raupach et al. (1980) used graphical

best-fit methods to estimate Zd from wind profile measurements and then substhuted the

Zd's mto the log-law to find the zo, whereas Marunich (1971), Molion and Moore (1983),

30

De Bruin and Moore (1984), Lo (1990), and Peterson (1996) employed conservafion of

mass principles to calculate Zd and zo simultaneously.

3.4.1 Best-Fit Log-Law Derived Models

Lettau (1957) introduced a sum of squares error technique to determine the

roughness parameters. Weighted mean wind difference values are calculated with and

without a Zd. The ratio without the Zd is subtracted from the ratio including the Zd and the

sum of squares error is computed until a Zd value is established that minimizes the error.

Robinson (1962) gives a detailed explanation and presents several examples on how to

apply Lettau's method.

Perry and Joubert (1963) introduced a method for determining Zd by plotting V fu*

against In(z-Zd). If a constant stress layer exists, then the plotted data should be linear.

Successive values for the Zd are used until Pearsori Correlation Coefficient, R^ is

maximized, resulting in the best-fit line.

Raupach et al. (1980), slightly modified Perry and Joubert's method. Like Perry

and Joubert, Raupach et al. plotted V/u* against In(z-Zd). Various values of Zd were

trialed until the slope of the best fit line equaled 0.4 (von Karman's constant for

equilibrium flow).

3.4.2 Conservation of Mass Derived (COM) Models

As previously stated, Marunich (1971) theorized that the ZQ was the vertical

displacement of a parcel of air as it passes from a smooth reference surface to a rougher

surface (Tajchman 1981). Marunich equated the amount of mass transported from

ground level to the gradient height, zigradient, over open terrain without a Zd to the amount

of mass transported from the ground to the gradient height, zogradiem, for a rougher terrain

with a Zd (Lo 1990) (Equafion 3.21). Marunich's model equates the Zd to the

displacement of a trajectory from zi to Z2 (Figure 3.4) (Tajchman 1981). This method has

two significant flaws. Marunich's model does not account for the existence of a

transition sub layer, z* (Lo 1990) and Marunich's model depends on the roughness length

value chosen for the smoother terrain profile (Molion and Moore 1983).

31

•^Igradieiii ^^gradienl

j V,(z)dz= JV,(z)dz 0 0

where Zigradiem = gradient height over open or smooth terrain with no Zd

Z2gradient = gradient height over rougher terrain with a Zd

I, = mean wind velocity over open or smooth terrain with no Zd

I, = mean wind velocity over rougher terrain with a Zd

(3.21)

.J. 'rn riT Figure 3.4. Illustration of Marunich's (1971) Model for Zd (Tajchman 1981).

De Brum and Moore (1985), like Marunich (1971), assume conservation of mass

conditions. Unlike Marunich, De Bruin and Moore equate the amount of mass

transported by the measured wind profile to the mass transported by a log-law fitted

profile, by adjusting the Zd to achieve conservation of mass conditions. By equating the

mass flow in the actual profile to that in a log-profile with a Zd, De Bruin and Moore are

physically implying that any mass within the roughness elements is subtracted from the

mass flow of a log- profile above Zd + zo (Equation 3.22 and Figure 3.5). The subtraction

of this mass flow from the log-profile corresponds to the height of the intermediate layer,

where the log-law is not valid, but must be applied to match wind speeds in the itmer

layer. From this assumption illustrated in Figure 3.5, areas A and B should be equal.

Although De Bruin and Moore improved the theoretical basis of the mass conservation

approach, the practicality of application of deriving Zd and zo separately depends on a

direct measurement of u* in the irmer layer.

32

j r , .w(^) ' t=7- In dz -0 J

(3.22)

'acuai = actual mean wind velocity from measured profile

^

7 7 — I

inner layer V;

1

IB' I ' 1

Zo+Zd

Stn 1 S t n :

Figure 3.5. Illustration of De Bruin and Moore's Model for Displacement Height, Zd (De Bruin and Moore, 1985).

Lo (1990) extended De Bruin and Moore's (1985) mass conservation model by

using a relationship between the logarithmic profile and surface characteristics so that a

direct measurement of u* was unnecessary. To establish this relationship, two wind

speed measurements are necessary within the inner layer, instead of the one required by

De Bruin and Moore (1985). Lo applies the logarithmic profile at twcpoints n and n+1

(Equafions 3.23 and 3.24).

K

— II* ,

v.. = — hi

- H + l

- 0

'-d

- 0

(3.23)

(3.24)

Lo non-dimensionalized (signified by an apostrophe superscript) all his variables

with Un+i or Zn+i and solved for zo and Zd usmg the equations 3.25 and 3.26.

I ( - H ~ - r f ) - 0

(3.25)

(l--.y

33

F(rrf) = 0 = ( l - / ( - . - , / ) l n ( l - . - / ) - ( l - . - / ) + (.4-l + . - / ) .

[aln(-„'-.-/)-/Jln(l-.-/)]+'-"' -'''* (3 26) (I---/) / '

where 1 a =—=-1-r,.'

fi: '

1

A =

0

lv(=')ct='

Peterson (1997) modified Lo's model so that it used more than twodata points

(wuid speeds) which would inherently help minimize errors associated with using only

two points. Peterson proposed plotting the velocity profile (In(z-Zd) vs F ) to solve for u*

and Zo. Then Zd is kerated until the F(zd) function (Equation 3.26) is minimized. By

usuig the velochy profile any number of points in the irmer layer can be incorporated into

the calculation.

3.4.3 Turbulence Intensity Derived Models

Roughness length can also be calculated from the longitudinal turbulence

intensity, TIu. The TIu is the standard deviation of the longitudinal component of the

mean wind speed, o-„ divided by the mean wind speed, V (Equation 3.27). From

experiments under neutral conditions it has been shown that the standard deviation of the

longitudinal component of V is proportional to the shear velocity, u* (Equation 3.28)

(Lumley and Panofsky, 1964). Solving the log-law for u* produces Equafion 3.29. By

substituting Equation 3.28 into Equafion 3.29, the zo can be estimated from TIu

(Equations 3.30 and 3.31).

r / „ = ^ (3.27)

V

TIu = longitudinal turbulence intensity

0-,, = standard deviation of the longitudinal component of the mean wind speed

34

o-„ = Ciu

C = constant

(3.28)

In V - 0 ;

^ = TI=. I'

Cv

In - J

(3.29)

(3.30)

V - 0 ;

Rearranging, Equation 3.30 becomes Equation 3.31.

. _ -~-d - 0

exp 'CK-^

TI

(3.31)

If C is not assumed to be a constant, C can be calculated for each mn from

Equafion 3.28. Substituting Equation 3.28 into Equafion 3.31, results in the original log-

law (Equafions 3.32 and 3.33).

exp u.

TI

(3.32)

exp K exp

'VK^ (3.33)

V "* J

3.5 Summary

Although the physical meaning of Zd and ZQ is not clearly understood, both

parameters play an important role in estimating the wind speeds a structure might

experience in a particular terrain. Both parameters can be estimated from the roughness

elements' height, shape, and density or from experimental and theoretical methods that

employ measurements of the shear velocity and mean wind speed wind profile.

35

CHAPTER IV

EXPERIMENT DETAILS

4.1 Introduction

Full-scale wind measurements in open, suburban and transitional flow regimes

were captured in Lubbock. TX using the Wind Engineering Mobile Instrumented Tower

Experiment (WEMITE) units, WEMITE 1 and WEMITE 2, and the Wind Engmeering

Research Field Laboratory (WERFL) meteorological tower. Wind measurements were

collected at WERFL, an agricuhural field southwest of and adjacent to WERFL, and in

the suburban in the single-family residential community of Rushland located west of

Quaker Avenue and south of 4* Street (Figure 4.).

Figure 4.1. Experiment Terrain and Data Collection Locations

36

4.2 Equipment, Instrumentation, and Facilities

4.2.1 Anemometers

Four types of anemometers were employed to capture wind measurements: prop,

prop-vane, UVW, and sonic anemometers. A prop anemometer (Figure 4.2) consists of a

stationary propeller that measures wind speed in a particular direction, where a prop-vane

anemometer (Figure 4.3) consists of a propeller, which measures the wind speed,

attached to a rotating vane that measures wind direction. A UVW anemometer (Figure

4.4) consists of three stationary prop anemometers set in an array to provide wind

velocities in three orthogonal directions. Sonic anemometers (Figure 4.5) measure wind

speed and direction by transmitting and receiving sonic signals and outputs the wind

measurements in three orthogonal directions. Sonic Anemometers determine wind speed

and direction by measuring the effect of wind flow on sound waves passed between sonic

sensors. An improvement over mechanical wind sensors like cup, propeller, or vane

types, sonic anemometers have no moving parts and thus respond more quickly to wind

flow fluctuations. The sonic anemometer measures wind velocity components along

three axes simultaneously by transmitting and receiving sound waves between pairs of

orthogonal sensors. These sound waves are affected by the movement of wind between

the sensors, and microcomputer electronics compute true wind speed and direction from

the received sonic data. Sonic anemometers respond linearly and are free from

contamination of measurements due to pressure, humidity, and temperature, and

interference from other velocity components.

37

Figure 4.2. Prop Anemometer Figure 4.4. UVW Anemometer

Figure 4.3. Prop-Vane Anemometer Figure 4.5. Sonic Anemometer

4.2.2 WEMITE Units

The WEMITE units are customized trailers with retractable towers instrumented

to measure wind speed, wind direction, barometric pressure, relative humidity, and

temperature (Figure 4.6). Aluminum extensions were added to the top of both WEMITE

towers to extend each tower from a maximum measurement height of 10 m. (33ft.) to

15.2m (50 ft).

38

Figure 4.6. Photograph of WEMITE 1.

4.2.2.1 WEMITE 1

WEMITE 1 collected wind data at 3.0, 6.1. 9.1, and 15.2m. (10, 20, 30, and 50ft.)

above ground level. R.M. Young prop anemometers measured vertical wind speed at 3.0

and 9.1m. (10 and 30ft.) above ground level. R.M. Young prop-vane anemometers

measured wind speed and wind direction at 3.0, 6.1, and 9.1m. (10, 20, and 30ft.) above

39

ground level. An R.M. Young sonic anemometer captured wind speed and direcfion data

at the highest measurement level of 15.2m. (50ft.). Table 4.1 summarizes WEMITE 1

anemometer heights, type, and model numbers.

Table 4.1. Anemometer Details for WEMITE 1.

WEMITE 1

HEIGHT

3 m. (10 ft.)

6.1m. (20 ft.)

9.1m. (30 ft.)

15.2 m. (50 ft.)

TYPE

Prop-Vane Vertical Prop

Prop-Vane

Prop-Vane Vertical Prop

Sonic

MODEL #

R.M. Young Wind Monitor-MA 05106 Gill Prop Anemometer 27106

R.M. Young Wind Monitor-MA 05106

R.M. Young Wind Monitor-MA 05106 Gill Prop Anemometer 27106

Gill Sonic Anemometer

4.2.2.2 WEMITE 2

WEMITE 2 collected wind data from 2.1, 4.0, 6.1, 10.0, and 15.2m. (7, 13, 20,

33. and 50ft.) above ground level. R.M. Young^ro^ anemometers collected vertical wind

speed data at 4.0 and 10.0m. (13 and 33ft.) above ground level and a UVW anemometer

collected wind speed and direcfion data at the 10.0m. (33ft.) level. R.M. Young prop-

vane anemometers measured wind speed and direction at the 2.1,4.0, 6.1, and 10.0m. (7,

13. 20, and 33ft.) heights and an R.M. Young sonic anemometer collected wind speed and

direction data at the 15.2m (50ft.) height. Table 4.2 summarizes WEMITE 2 anemometer

heights, type, and model numbers.

Table 4.2. Anemometer Details for WEMITE 2

WEMITE 2

HEIGHT 2.1m. (7ft.)

4 m. (13 ft.)

6.1m. (20 ft.)

10 m. (33 ft.)

15.2 m. (50 ft.)

TYPE Prop-Vane Prop-Vane

Vertical Prop Prop-Vane Prop-Vane

UVW Vertical Prop

Sonic

MODEL # R.M. Young Wind Monitor-MA 05106 R.M. Young Wind Monitor-MA 05106

Gill Prop Anemometer 27106 R.M. Young Wind Monitor-MA 05106 R.M. Young Wind Monitor-MA 05106

3 Gill Prop Anemometers 27106 Gill Prop Anemometer 27106

Gill Sonic Anemometer

40

4.2.2.3 WEMITE Meteorological Equipment

Each WEMITE unit is equipped with meteorological instruments that measure

temperature, barometric pressure, and relative humidity (Figure 4.7). Meteorological

instruments on both towers are located at Im. (3ft.) above the ground. Meteorological

instrument type and model numbers are listed in Table 4.3.

Figure 4.7. Meteorological Instrumentation

Table 4.3. WEMITE Meteorological Instrument Details.

INSTRUMENT TYPE

Barometer Relative Humidity & Temperature Sensor

MODEL #

R.M. Young 61201 R.M. Young 41372VC

4.2.2.4 Data Acquisition

The WEMITE data acquisition systems use a Fujitsu laptop and a LabView

program to continuously sample signals and store data from the instruments at a rate of

lOHz for periods of 30 minutes. The data was copied daily to a 100 MB Zip drive and

transferred to a desktop PC where it was burned to a CD for storage and processing.

41

4.2.2.5 Data Processing

Data was processed using LabView software. Data was collected for 30 minute

periods or runs. The mean wind speed was calculated for each run. The 3-second peak

gust was obtained for each run by taking the highest 3-second average using a 3 second

moving average technique for the entire run. All instrument data was plotted and visually

inspected or validated.

4.2.3 WERFL Meteorological Tower

The WERFL meteorological tower employs UVW anemometers to collect wind

data fi-om 2.5, 5.8, 10.0, 21.0, and 49.0m. (8, 13, 33, 70, and 160ft.) above ground level.

Table 4.4 lists anemometer height, type, and model number.

Table 4.4. Anemometer Details for WERFL

WERFL HEIGHT

2.5 m. (8 ft.) 5.8 m. (13 ft.) 10 m. (33 ft.) 21m. (70 ft.) 49 m. (160 ft.)

TYPE UVW Anemometer UVW Anemometer UVW Anemometer UVW Anemometer UVW Anemometer -

MODEL # R.M. Young Gill Anemometer 27005T R.M. Young Gill Anemometer 27005T R.M. Young Gill Anemometer 27005T R.M. Young Gill Anemometer 27005T R.M. Young Gill Anemometer 27005T

Barometric pressure, temperature, and relative humidity instruments are located at

the 5.8m. (13ft.) level. Table 4.5 lists meteorological instrument types and model

numbers.

Table 4.5. WERFL Meteorological Instrument Details

INSTRUMENT TYPE MODEL #

Barometer R.M. Young 61201 Relative Humidity & Temperature Sensor R.M. Young 41372VC-VF

4.2.3.1 WERFL Data Acquisition

The WERFL data acquisition system uses a desktop PC located in the center

control room of the WERFL building to continuously sample signals and store data from

the instruments at a rate of 30 Hz for periods of 60 minutes at a time. The data was

42

copied daily to a 1 GB Jazz drive and transferred to a desktop PC, offsite, where it was

burned to a CD for storage and processing.

4.2.3.2 WERFL Data Processing

WERFL's data is collected in 1 hour runs. During this experiment, WEMITE was

in data collection Mode 52. The mean wind speed is calculated for each run and the peak

3 second gust is measured using a moving average technique. All WERFL instrument

data used in the change of terrain models were plotted and visually inspected and

validated. It is important to note that during this experiment's time period the WERFL's

tower and laboratory was imdergoing a re-instrumentation and data collection system

changes. For details on the data validation process refer to Gardner et al. (1998).

4.2.4 Computer Synchronization

Data was collected daily from WERFL and the WEMITE units, hi order to keep

the computers synchronized relative to time, WERFL's time was transferred to the

computers on WEMITE 1 and 2 daily when any time discrepancies existed.

4.2.5 Experiment Setups

4.2.5.1 Experiment Setup 1

Experiment setup 1 involved setting up both WEMITE units at WERFL for

mstrumentation testing and calibration with the WERFL tower. Figure 4.8 shows details

on the layout of setup 1.

43

WERFL TOWER HEIGHT IflO'

WEMITE I t " '

INSTBlJl

WERFL SLAB

[NSrmiJMEHTAI. NORTH

WEMITE 2 IKaTRUMENTAL NORTH

. ALL MTlASIIRTtMFWTS r.IVBH IH FEET

Figure 4.8. Experiment Setup 1: Site Survey of WEMITE 1 and WEMITE 2 at WERFL


Once calibrated and tested, the WEMITE towers were placed just east of the

Rushland community into an agriculture field to collect wind flow measurements

adjacent to the change in surface roughness (Figure 4.8). On March 26*** 2000, WEMITE

1 was moved from WERFL to the agriculture field 31.3m (102.6ft.) east of the edge of

the Rushland residential community and 250.2m. (821.1ft.) south of 4th Street. On April

4* 2000, WEMITE 2 was placed 90.5m. (297ft.) east of WEMITE I, 121.8m. (399.6ft.)

east of the residential community and 228.9m. (750.9ft.) south of 4* Sti-eet (Figure 4.9).

Data was collected by WEMITE 1, WEMITE 2, and WERFL simuftaneously

from April 4, 2000 to April 19, 2000. Wind data utilized in the change of terrain models

are limited to a southwest wind direction (230° to 265°) and a northeast wmd direction

(50° to 85°). Figure 4.10 shows details on the layout of experiment setup 2. Figure 4.11

and Figure 4.12 show the expected IBL heights relative to all three towers for the

southwest and northeast wind directions.

44

The fetches or distances to a surface roughness change for WEMITE 1, WEMITE

2 and WERFL are shown in aerial photographs in Figure 4.13, Figure 4.14, and Figure

4.15, respectively. The surrounding terrain was classified into three regions based on

fetch: Flow region 1 is defined as having a fetch of I km or less, flow region 2 is defined

as having a fetch between I km and 2km, and flow region 3 is defined as having a fetch

greater than 2km. Specific fetch values are shown in Figure 4.16, Figure 4.17, and Figure

4.18, respecfively.

Figure 4.9. Experiment Setup 2

45

PENCE

- 102.

WEMITE 1 r—

^^•^•^llklKNTAL NORTH

rl * _BLDU_ 1 1 BLDG,

;-j;o.;

,-*>

INSTRUUENTAI- NORTH.— -- - T

J MAGNETIC NORTH

- . WEMITE 2A

; " ' J MAGNETIC NORTH

. , 1. K ' F ; ! = n R E U F N T S CIV^U l N ~ r F F T

EMPTY LOT 1 GAS STATION

OUAKEH AVE. 750.3

N-^-:>,,

AGRICULTURE FIELD

r/.

X

0

G

1

1

n

1

1

1

G

1

g

G

1

Figure 4.10. Experiment Setup 2: She Survey of WEMITE 1 and WEMITE 2A in the

Agriculture Field

180

160

140

120

^ 100 H

I 80-1 60

40

20 i

0.

Wmd Diiection (230-260)

WERFL

WEMITE.r ' WEP-TE-? •

g g Q Q ^ SubuibMiTenain Agiicultme Field

-100 0 100 200 300 400 500 600 700 800

fetch (m)

sbess fiansitional IBL (EUoitt 1968) velocity transitional IBL equiHbrium IBL

Figure 4.11. IBL Growth for Experiment Setup 2 and 230°-260° Wind Direcfion

46

180

160

140

120

I 80 60

40

20

0

Wind Direction (50°-85°)

WERFL1 ' s .

WEMTTE 1 " - •-

i iWEMTTEZA : • ' " >^ciD a o ' Agriculture Field

-1800 -1300 -800 fetch, m

-300

Subui-ban Terrain

200

sti-ess ti-ansitional IBL (EUoitt 1968)

equilibrium IBL

velocity t ransi t ional IBL

Figure 4.12. IBL growth for Experiment Setup 2 and 50°-85° Wind Direction

47

Figure 4.13. Aerial Photograph of Flow Regions for WEMITE 1 for Open Country Fetch

48

Figure 4.14. Aerial Photograph of Flow Regions for WEMITE 2 for Open Country Fetch

49

(lkm> fetch <2km)

r~l Flow region 3 (fetch > 2km)

•3E"T*ai«iT.

Figure 4.15. Aerial Photograph of Flow Regions of WERFL Open Country Fetch Lines

50

Figure 4.16. Fetch of Open Country Terrain, WEMITE 1 in the Agriculture Field (m)

190 170 180

Figure 4.17. Fetch of Open Country Terrain, WEMITE 2 A in the Agriculture Field (m)

51

}5i]m 10 , ,

190^ mo 180

Figure 4.18. Fetch of Open Country Terrain, WERFL (m)


On April 19. 2000, WEMITE 2 was moved to the residential community to

collect wind data representative of the suburban terrain (Figure 4.19). WEMITE 2 was

placed in a empty residential lot at 3912 13* Street in the Rushland Community. Data

was simuhaneously collected by WEMITE 1, WEMITE 2, and WERFL from April 19

2000 to May 11, 2000. The site was surrounded by fences, houses, and trees (Figure

4.20). The flow regions for WEMITE 2 located in the residential community are shown

in Figure 4.21 and the fetch values are shown in Figure 4.22. Wind data utilized in the

change of terrain models are limited to a southwest wind direction (230° to 265°) and a

northeast wind direction (50° to 85°). Figure 4.23 and Figure 4.24 show the expected IBL

heights relative to all three towers for these southwest and northeast wind directions.

52

Figure 4.19. Experiment Setup 3

53

HOITSF

BACK ALLEY

I . . . 37.6 ;_

TALL TRBIS

r 1

mSTRUUEUUL NORTH

\ 37l6

4J I 3EGR'

'umjsK gEGRT TEHH3

.V

HiCKETlO MOKIE N . 13 TH ST.

TALL TREES

(20 to 30 ft in height) HOUSK

Figure 4.20. Experiment Setup 3. Site Survey of WEMITE 2 in the Rushland Residential Community (measurements in feet).

54

V j " n ' n • i ,

i-':.

n

Flow region 1 (fetch < 1km)

Flow region 2 (lkm> fetch <2km)

Flow region 3 (fetch > 2km)

t -

'' •*

c

^ ^ ^ . .jtsfissfcfaij^u:!

Figure 4.21. Aerial Photograph of Flow Regions for WEMITE 2 in the Residential Community.

55

350 0

Figure 4.22. Fetch of suburban terrain for WEMITE 2 in the Residential Community (m)

56

180

160

140

120

a ' 100

I 80 60

40

20

Wind Direction (230-260)

WERFL

WEMITE 2 WEMlTg'1 ^-

3C3 O Q Q O O p O Q QCQ OOQ O O O OQ, Suburban Terrain

•800 -600 -400 -200

i.-— 0

fetch, m

Agriculture Field 200 400 600 800

stress transitional IBL (Elloitt 1968) velocity transitional IBL equilibrium IBL

Figure 4.23. IBL growth for Experiment Setup 3 and 230°-260° Wind Direction.

57

180

160

140

120

a ' 100

I 80 60

40

20

0

Wind Dii'ection (SC-SS")

WERFL

WEMITE 2 •N. WEMITE 1

Q O O P O D O Q Q 3 Q C T i r Q - Q - 0 - . ii Suburban Terrain

-800 -600 -400 -200 0

fetch, m

— stress transitional IBL (Elloitt 1968) equilibrium IBL

Agiiculture Field 200 400 600

velocity transitional IBL

800

Figure 4.24. IBL growth for Setup 3 and 50°-85° Wind Direction


Towers were moved to WERFL to validate instrument performance. WEMITE 1

was moved from the agriculture field back to WERFL on May 11* 2000. WEMITE 2

followed on May 15. Details on experiment setup 4 are given in Figure 4.25.

58

WERFL TOWER

MAQNKTIC NORTH

WEMITE 1

INSTRUMENTAL NORTH

WERFL SLAB

• tLL MEASnilEllMITE BUSH IM raST I

Figure 4.25. Experiment Setup 4: WEMITE 1 and WEMITE 2 back at WERFL

59

CHAPTER V

WEMITE 2 IN THE RESIDENTIAL COMMUNITY

5.1 Roughness Element Derived Models

5.1.1 Roughness Element Parameters

In Chapter III, it was shown that most roughness element based models for

displacement height, Zd, and roughness length, ZQ, are derived from wind tunnel testing

employing rectangular roughness elements. Almost all Zd and ZQ models presented are a

function of roughness element height. But this relationship to rectangular roughness

element height may not be effective when applied to suburban exposures which have

irregularly shaped roughness elements, such as homes and vegetation. Therefore two

roughness element heights were investigated for the Rushland Community: peak roof

height (HpeakR = 6.0m (20ft)) and mean roof height (HmeanR = 4.3m (14ft)), with the

exception of Abtew et al.'s (1986) model, which gives a procedure to estimate an

effective height for irregular shaped roughness elements (Figure 5.1). The mean roof

height is the eave height plus half the roof height. The average lot size, Asue (Figure

5.2a). is 1420m' (15285ft') and the average home footprint area, AR, is approximately

306.6m- (3300 ft^). The fracfion of cover / A,

4 ^site J

, based only on the homes of the

community, is 0.22. Initially models are evaluated using a Fc based only on the homes.

If the model results in a Zd or zo value significantly lower than the values obtained

directly from wind field measurements (discussed later in this chapter), then a Fc value

including homes and trees is employed. An exception is Abtew et al.'s (1986) model

which gives a procedure developed specifically to address trees, and so trees are included

in the Fc parameter used in their model. The Rushland community is an older community

and has many large mature trees. The trees are highlighted in Figure 5.2b by green

circles and are estimated to cover approximately 30% of the she mcreasing Fc from 0.22

to 0.52. Tables 5.1 and 5.2 define the value of each parameter used in the various

roughness element based Zd and zo models.

60

•| HpeakR = 6.0m (20ft) ™^.

Figure 5.1. Roughness Element Parameters Photograph (Picture taken April 6, 1998).

CcO^

I'lS.i'j I'^v' O <9 «» .»

a ' O ^^^^

Figure 5.2. Aerial Photograph of a Rushland Residenfial Block.

61

Table 5.1. Definition of Roughness Element Derived Zd and ZQ Model Parameters.

Parameter

Ax

A„ A,.

A„

AR

A.,.c

Au

A«

Dp

F,

rinieanR

HpeakR

n

Rpc

SN

X

Description ai ca of open terrain upwind of site

aiea of wooded terrain upwind of site area of larger building terrain upwind

of site area of smaller building terrain

upwind of site

area of roughness elements on site

area of site( allowances for streets and alleys are included in the estimate)

area of upwind of a 4?° fan with a

radius, R „ of lOOHpeak wetted windward surface area of

roughness elements on site distance between roughness elements

parallel to the wind direction (allowances for streets and alleys are

included in the estimate)

fraction of the site area that roughness elements cover F^ = AR/As,te

average height of the roughness elements

peak height of the roughness elements

number of roughness elements on the site

radius of a plant canopy

projected frontal area (silhouette area) of the roughness elements on the site

on a plane normal to the wind direction

distance from the ground to the center of curvature of the tree canopy

Value

refer to Table 3.9

AR =

306.6m-homes only

AR = 426.0m-trees only

AR =

732.6m-trees and

homes

As,te= 1420m-

Au = 906.832m-Ru= 1520m

for rectangular shapes

Dp = 30.5m N a n d S

Fc = 0.22 homes only

Dp= 12.5m E a n d W

F, = 0.30 trees only

Dp = 26.7m SE, SW. NE, and

NW F, = 0.5

homes and trees

HmeanR = 4 . 3 m

homes only

HpeakR = 6.0m homes only

n = l homes only Rpc = 4.7m

SA=137m-N a n d S

homes only

SA=160m-E a n d W

homes only

SA=155m-SE. SW, NE, and

NW homes only

X = 3.6m

62

Table 5.2. Kondo and Yamazawa (1986) Fetch Area Parameters.

0° 45° 90° 135° 180° T>;^o

270° 315°

R„ = 1520m (5000ft) AA, m-

0.50 0.16 0.53 0.07

0 0.19 0.04 O.U

AH, nr 0 0 0 0 0 0 0 0

A C m-0 0

0.04 0 0 0 0 0

AD, m' 0.50 0.84 0.43 0.93 LO

0.81 0.96 0.89


Table 5.3 shows the ZdS calculated from each model relative to HmeanR and HpeakR-

All calculations of the ZdS in Table 5.3 are shown in Appendix A.

Table 5.3. Roughness Element Derived Zd Models Based on HmeanR and HpeakR-

Reference Kutzbach (1961)

Coumhan (1971)

Lee and Solimon (1977)

Hussam (1978)

Raupach etaL( 1980) Abtew etal. (1986)

Zd, m (HmeouR)

3.0 1.4 3.4 2.4 5.6 1.5 3.6 3.8 4.5

Zdi m (HneakR)

2.0 4.7 3.3 7.8 2.1 5.0 4.2 5.5 n/a

Fe based on homes only

homes and trees homes only


homes and trees homes only homes only

homes and trees


Tables 5.4-5.5 and 5.6-5.7 show the ZQS calculated from each model relative to

HmeanR and HpeakR, respectively. All calculafions of the zos in Tables 5.5-5.8 are shown in

Appendix B.

63

Table 5.4. Roughness Element Derived zo Models (Directionally Independent) b a s e d o n HmeanR-

Reference Nikuradse (1933, 1950)

Tanner and Pelton (1960) Kung (1961. 1963)

Sellers (1965) Counihan (1971)

Abtew etal. (1986)

Kondo and Yamazawa (1983, 1986)

Fang and Sill (1992), Saxton et al. (1974), and Houghton (1985)

Zo, m 0.14 LO

0.33 0.18 0.68 0.46

0.24

0.56

0.43

Fc based on n/a n/a n/a n/a

homes only homes and trees

homes only

homes and trees

n/a

Table 5.5. Roughness Element Derived ZQ Models (Directionally Dependent) b a s e d o n HmeanR-

Reference

Lettau (1969)

Businger (1975)

* Kondo and Yamazawa

(1986)

Wind Direction

0° 45° 90° 135° 180° 225° 270° 315°

z„, m

0.21

0.15

0.80

0.23

0.15

0.80

0.24

0.05

0.79

0.23

0.15

0.80

0.21

0.15

0.80

0.23

0.15

0.61

0.24

0.05

0.78

0.23

0.15

0.80

*Kondo and Yamazawa's (1986) method does not use height as a parameter.

64

Table 5.6. Roughness Element Derived ZQ Models (Directionally Independent) based on HpeakR-

Reference Nikuradse (1933. 1950)

Fang and Sill (1992). Sa.\ton ct ;il. (1974), and Houghton (1985)

Tamier and Pelton (1960) Sellers (1965)

Kung(1961. 1963) Counihan (1971)

Kondo and \aniazawa (1983)

Zo, m 0.20

0.60

1.7 0.25 0.49 0.95 0.33 0.78

Fc based on n/a

n/a

n/a n/a n/a

homes only homes only

homes and trees

Table 5.7. Roughness Element Derived ZQ Models (Directionally Dependent) based on HpeakR-

Reference

Lettau (1969) Businger (1975)

Wind Direction

0° 45° 90° 135° 180° 225° 270° 315°

Zo, m

0.29 0.10

0.33 0.07

0.34 0.27

0.33 0.07

0.29 0.10

0.33 • 0.07

0.34 0.27

0.33 0.07

5.2 Wind-Field Derived Models

5.2.1 Introduction

As described in Chapter TV, WEMITE 2 was placed in a smgle-family residential

community to capture full-scale wind measurements. Three different flow regions based

on fetch of suburban terrain were defined and wind profile parameters were investigated

for each flow region (Figure 5.3).

From a visual inspection of aerial photographs, ASCE 7-2002 would classify this

community as exposure B: suburban residential area with mostly single-family dwellings

with category B terrain around the she for a distance greater than 457m (1500ft) or ten

times the height of the structure, whichever is greater, in any wind direction (Figure 5.3).

65

Figure 5.3. Aerial Photograph of ASCE 7-2002 Exposure B (ASCE 7 2002).

ASCE 7-2002 gives zo values for exposure B between 0.15-0.7m (0.49-2.3ft) with

a typical value of 0.3m (1.0ft) (Table 5.8). If this ZQ value range is substituted into the

range of the Raupach et al.'s (1980) expected intermediate layer height, z* = 20zo to 50zo

(Equation 2.8) it can be seen that the height of the intermediate layer, i.e., the begirming

of the inner layer is expected to occur anywhere from 3 to 35m (10 to 115ft) aboye the

surface (Table 5.8).

Table 5.8. Raupach et al. s (1980) Intermediate Layer Height Ranges.

lower limit typical

upper limit

Zom (ASCE 7-2002)

0.15 0.30 0.70

z* m (Raupach et al. 1980)

z* = (20-50)zo 3.0-7.5

6.0-15.0 14.0-35.0

5.2.2 Best-Fh Log-Law Derived Models

Using a log-profile best-fit method, the Pearson Correlation Coefficient, R ' . and

associated standard deviation, 0R2, were calculated for all 5 instruments, the top 4

66

instruments, and the top 3 insfruments on WEMITE 2 in the residential community.

Table 5.9 gives the average R" and 0R2 values for each flow region. The upper three

instruments give the best fit, i.e. the maximum R^ but it can be argued that the R will

improve with the elimination of points due to the limited number of instruments.

However, the plot of the natural log of the height, ln(z), versus the mean wind speed, V,

shows a distinct kink in the profile occurs at the 6.1m instrument height for each flow

region indicating a flow behavior change: a change from the viscous layer to an

intermediate layer. This kink consistently appears at the 6.1m height through out the data

collected in the residential communhy. Example runs are shown for each flow region in

Figure 5.4. From Figure 5.4, h is not clear if the wind flow behavior at 6.1m is consistent

with the viscous layer flow or the intermediate layer flow.

Table 5.9. Mean R" and Associated 0R2 From the Ln(Height) versus Mean Wind Speed Data for the 3 Flow Regions.

flow region

1 2

3

fetch (m)

1 km< \ 1 km < .\ < 2 km

x > 2 k m

all instruments

mean R" o ^

0.897 0.055 0.879 0.062 0.854 0.045

top-4 instruments

mean R- ( j ^

0.941 0.035 0.937 0.039 0.917 0.024

top-3 instruments

mean R- (JR^

0.973 0.013 0.971 0.020 0.968 0.016

67

0.5 1.5 2 2.5 3 mean wind speed, m/s

3.5

o flow region 1 (run 46 4/26/2000 12:53 PM) - B - flow region 2 (run48 4/23/2000 11:00 AM) -A-flow region 3 (run 13 4/22/2000 5:30 PM)

4.5

Figure 5.4. Example Profiles of ln(z) versus Mean Wind Speed for Each Flow Region

Associated With WEMITE 2 Located in the Residential Community.

To find the value of Zd, the In(z-Zd) vs V was plotted and Zd was varied until the

value that gave the best-fit line, i.e., the maximum R" . was achieved. Figure 5.4 shows

an example run of this method. Dropping the bottom 2 instruments and leaving the top 3

instruments results in a better fit than including the top 4 or all the instmment heights.

For all runs, the maximum R^ value converged on a Zd = 4m (Oft).

An example run of employing Perry and Joubert's (1963) Zd model is also

illustrated in Figure 5.5. For every run Perry and Joubert's method converged to a

maximum R ' when the Zd = 6m (20ft). Raupach et al.'s (1980) method always converged

to a slope or K = 0.4 when the Zd = 3.9m (13ft) (Figure 5.6). Lettau's method produced

umeasonable resuhs for suburban terrain, giving values of Zo that were greater than the Zd

due to the limited number of heights.

68

R- vs Zj

(run 13 4/22/2000 5:30 pm - in flow region 3)

top 2 instruments

1 2 3 4 5 6

—ln(z-z^) vs wind speed —Perry and Joubert (1963) [

Figure 5.5. Variation of R" with Zdfor In(z-Zd) vs V and Perry and Joubert (1963).

69

0.6

» 3

> -O

N N

O. O

0.5

0.4

0.3

0.:

Raupach et al. (1980) Model (run 13 4/22/2000 5:30 PM)

=" 0.1 -

Zd, m

Figure 5.6. Raupach et al.'s Variation of Zd to the Slope of In(z-Zd) vs—

The best-fit log-law methods were originally developed and used in wind tunnels,

where muhiple data heights were available. Caution is advised when using these

methods with only a few wind speed collection heights, the best fit may simply be

occurring due to the elimination of points. Therefore, the best-fit log-law methods are

not well suhed for many atmospheric experiments. For this experiment these methods

may not have been effective due to the limited number of data collection points and/or an

msufficient number data collection points located in the inner layer. The reliability of the

experimental data relative to the number of data points will be further discussed m

section 5.3.2.1.

70

5.2.3 Conservation of Mass (COM) Derived Models

Applying Peterson (1990) and Lo's (1990) methods to the top 2 and 3 instruments

on WEMITE 2 yielded unrealistic values for zo and Zd. Since the methods depend on

having at least 2 or more points in the inner layer, it was deduced that the methods may

be failing because there is only one data point in the inner layer: the 15.2m (50ft)

instrument. Since u* was measured at the 15.2m (50ft) height, it was possible to apply

the conservafion of mass (COM) principle with only one instrument located in the inner

layer by using De Bruin and Moore's (1985) model (Equafion 3.22). The actual profile's

area is set equal to a log-law profile's area (Equation 5.1) generated from the 15.2m

(50ft) measurements of friction velochy, u*, and V . The log-law is rearranged (Equation

5.2) and inserted into the integral of the log-law (Equation 5.3): leaving 1 term to solve

for: Zd- The Zd is varied until the area of the log-law profile is equal to the area of the

actual profile. Figure 5.7 shows an example of this method applied to a data run. Notice

that areas A and B are equal. The Zd is calculated and substituted back into the log-law

(Equation 5.2) to solve for ZQ. A discussion and estimation of the approximate error

associated with the integration method of the actual profile is discussed Appendix C.

^acliial - Aiog-im' (-'-O

ZQ =exp \n(z-:a)-V —

K

([(-,5„, - -dN--,5„, - - - , ) -1])] - --,„„ in(-o))-

([(-<,--</N-o)-i])]+-'X-o))

(5.2)

(5.3)

71

Conservafion of Mass Example Profiles From Flow Region 3 (WEMITE 2 in the Residential Community)

(run 10 4/22/2000 3:59 PM) 18.0

4 6

wind speed, m/s

10

• actual profile log-law profile

Figure 5.7. De Brum and Moore's (1985) COM Profile Comparison.

Figure 5.8 shows the variation of the Zd and zo calculated from COM method

relative to wind direction and fetch, F. Flow region 3 is of particular interest since it has

the longest fetch and should be most representative of equilibrium conditions for the

suburban terrain. Flow region 3 has a mean Zd = 3.6m (12ft) with a standard deviation, a,

equal to 0.42 and a mean ZQ = 0.60m (2ft) with a a = 0.20. The mean Zd, ZQ, and their

associated standard deviations for each flow region are listed in Table 5.10. Probability

distributions for COM results are given in Appendix F. Appendix F shows the variation

of zo with wind speed for daytime (5:00 a.m.-9:00 p.m.) and night time (9:00 p.m.-5:00

a.m.) measurements. There was no noticeable relationship between ZQ and the magnitude

of wind speed or time of day. The influence of the Zd on zo is obtained by comparing the

72

Zo calculated from the log-law without a Zd and with a Zd = 3.6m (12ft). Ignoring the Zd

results in a 30% overestimation of zo(Figure 5.9).

Table 5.10. Average Zd, ZQ, and associated as From De Bruin and Moore's (1985) COM Method for Each Flow Region Associated With WEMITE 2 in the Residential

Community.

Flow region

1

• >

j>

F (km)

F< 1 1 < F <

1 2 < F

Zd(m)

3.1

3.6

3.6

o

0.42

0.47

0.42

min Zd (m) 2.4

2.7

2.9

max Zd . (m) 4.2

5.0

5.4

zo(m)

0.33

0.56

0.60

a

0.22

0.25

0.20

min Zo (m) 0.10

0.13

0.21

max Zo(m) 0.91

1.1

1.1

#of runs 91

153

357

73

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74

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75

5.2.4 Turbulence Intensity Derived Roughness Length

Using the average Zd = 3.6m obtained from COM, the ZQ was calculated using the

longitudinal turbulence intenshy, TKi (Equation 3.31). The constant value for C in

Equation 3.31 was obtained by plotting the standard deviation of the longitudinal velocity

component, Ou, versus u* for flow region 3 (the flow region most representative of

equilibrium conditions) and fitting a line to the data through the origin (y-intercept = 0).

The value of C is equal to the slope of the line. From Figure 5.10, h can be seen that C =

2.8 for the flow region 3. Although the Pearson Correlation Coefficient indicated a rather

poor fit, the value of C is used to derive ZQS for all wind directions. This value is identical

to the constant obtained by Deaves (1981) of 2.8 for fully developed neutral equilibrium

flows. Lumley and Panofsky (1964) listed several values of C obtained by various

researchers that ranged from 2.1 to 2.9. Substituting in C = 2.8 and K = 0.4, Equation

3.31 becomes Equation 5.4.

^1.12^ exp TT

Figure 5.10 compares the variation of zo calculated from TIu (Equation 5.4) and

COM to wind dhection. The average Zo derived from TIu for flow region 3 was 0.66m

which agrees quhe well with COM average zo = 0.60m. The data and probability

distributions for TIu derived ZQ'S are given in Appendix E. Table 5.11 compares the mean

Zo and a of the TIu and COM methods for with each flow region.

76

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79

5.3 Discussion

5.3.1 Roughness Element Derived Models

5.3.1.1 Displacement Height

Hussain s (1978) model, usmg HmeanR and an Fc based on both homes and trees

resulted in a zj = 3.6m (12ft) agrees with the results obtained from COM which estimated

the average Zd = 3.6m (121ft). For a 95% probability of occurrence in flow region 3 (the

flow region most representative of equilibrium flow), Zd (calculated from COM method)

had to be in the range of 3.0m (lOft) to 4.6m (15ft) (Appendix D). Counihan's (1971)

and Abtew et al. s (1986) models based on H„eanR and a F based on home and tree

coverage and Raupach et al. (1980) and Kutzbach's (1961) models based on HmeanR and

Fc based only on homes also gave resuhs within this 95% probability of occurrence

range. For models based on HpeakR. only Lee and Solimon (1977) and Kutzbach (1961)

both based on a Fc that considers only homes gave resuhs within the 95% probability of

occurrence range, hiterestingly, Kutzbach's (1961) Zd model using H„,eanR and HpeakR

with a Fc based on homes only spans the 95% probability of occurrence range quite well

and his model was the only one that was directly derived from fiill-scale atmospheric

experiments. Table 5.12 summarizes only the roughness element derived models that

produced Zd estimates in the 95% probability of occurrence range.

Table 5.12. Roughness Element Derived Zd Models that Are Within a 95% Probability of Occurrence Based on COM Zd Model.

Reference

Kutzbach (1961)

Counihan (1971) Lee and Solimon (1977)

Hussain (1978) Raupach etal. (1980) Abtew etal. (1989)

Zd, m (ft) 3.0 4.2 3.4 3.3 3.6 3.8 4.5

H based on '^iiieanR

HpeakR

^meanR

HpeakR

^meanR

^meanR

^meanR

Fc based on

homes only



homes and trees

80

5.3.1.2 Roughness Length

The following models produced ZQ'S the closest to the average zo =0.60m (1.97ft)

obtained from De Bruin and Moore's (1985) COM method:

a. Counihan (1971): using HmeanR and Fc based on homes only,

b. Kondo and Yamazawa (1983): using HmeanR and Fc based on homes and trees,

and

c. Fang and Sill (1992) - Houghton (1985) - Saxton et al. (1974) - : using HpeakR.

The 95% probability of occurrence range of COM zo was 0.32-l.Om (1.1-3.3ft).

The following models including those listed above produced ZQ values in the 95%

probability of occurrence range:

a. Kung (1961, 1963): using HmeanR and HpeakR,

b. Lettau (1969): using HpeakR (note for wind direcfions 0° and 180° this method

falls just below the lower limit of the 95% probability of occurrence range).

c. Counihan (1971): using HpeakR and Fc based on homes only,

d. Kondo and Yamazawa (1983 and 1986): using HpeakR and Fc based on both

homes only and homes and trees,

e. Abtew et al. (1986) using HmeanR and Fc based on homes and trees, and

f Fang and Sill (1992) - Saxton et al. (1974) - Houghton (1985): usmg HmeanR.

Table 5.13 summarizes all the roughness element derived models that produced zo

estimates in the 95% probability of occurrence range.

81

Table 5.13. Roughness Element Derived zo Models that Are Within a 95% Probability of Occurrence Based on COM Zd Model.

Reference

Kung (1961. 1963)

Lettau (1969)

Counihan (1971)

Kondo and Yamazawa (1983)

Abtew etal. (1986)


Fang and Sill (1992), Saxtonetal. (1974), and

Houghton (1985)

z„, m (ft)

0.33

0.49

0.29-0.34*

0.68

0.95 0.56 0.33 0.78

0.46

0.61-0.80*

0.43

0.60

H based on

^mcaixR

HpeakR

HpeakR

l^meajiR

HpeakR

^nicanR

HpeakR

.l^meanR

n/a

l^meanR

HpeakR

F,. based on

n/a

n/a

homes and trees

homes only

homes and trees

n/a

n/a

* direction dependent

5.3.2 Wind-Field Derived Models

The best-fit log-law and COM methods simultaneously derive the Zd and ZQ.

There were an insufficient number of data points across the wind profile to successfully

apply the best-fit log-law methods. Lo (1990) and Peterson's (1990) COM models were

applied to the top 2 and 3 instrument heights of WEMITE 2 in the residential communhy.

Both models resuhed in uru-ealistic Zd and Zo values, often resuhing in ZQ'S greater than

the ZdS. These resuhs suggest that only the top instrument, at 15.2m (50ft), was in the

inner layer.

Therefore, De Bruin and Moore's (1986) COM model was applied to the data

obtained from the 15.2m instrument and resuhed in an average Zd = 3.6m and an average

Zo = 0.6m for the region of flow most indicafive of equilibrium condifions: flow region 3.

Next Lumley and Panofsky's (1964) TIu method was used to solve for zo using Zd = 3.6m

(12ft). From the comparison between the TIu and COM ZQS, for wind directions in region

1 (approximately 15°-90°), there is a distinct separafion (Figure 5.11). The ZQS estimated

82

from the COM method are significantly lower than those obtained from the TIu method.

This separation is most likely due to the smaller fetch found in flow region 1 which has

an average fetch of 700m (2300ft). The Tl„ model appears to have reached equilibrium

with the suburban roughness, producing for flow region I an average ZQ = 0.62m, but the

COM model appears to be influenced by the upstream smoother agricuhure field terrain

producing zo = 0.15m (0.5ft) between the 15°-90° wind direcfions.

Recall, that a constant value of C = 2.8, which is based on neutral equilibrium

flow conditions and is proposed by Deaves (1981) to be independent of terrain was used

in the TIu model. Assuming C independent of terrain, the remaining variables in the TIu

model, Ou and F, should dictate whether zo reflects the upstream smoother terrain or the

local suburban terrain. Note that F is a parameter in both models, suggesting that Ou is

the main influence on the TIu model producing the rougher ZQS. The turbulence

parameters, GU, U*, and their ratio, C, have been plotted against fetch and compared to a

turbulence parameter model presented by Deaves (1981) for smooth to rough roughness

changes (Figure 5.12). The turbulence parameters of the u* and Ou and C and TIu are

plotted agamst the wmd direction and shown in Figures 5.14 and 5.15, respectively. Both

u* and Ou values scatter for wind directions greater than 200°, where for wind directions

between 90° and 200° data collapses which coincides with a fetch approximately greater

then 7000m. This trend does not appear to exist in the TI and C data, where the data

appears consistently collapsed for all wind directions.

Another interesting difference in behavior between the ZQS calculated from COM

and TIu occurs between approximately 200°-260° wind directions. The TIu ZQS begin to

scatter and drop below the COM ZQS (Figure 5.11). If we look at the terrain between 200°

and 260°, there are two open areas or smooth patches: Rush School and Higginbotham

Park (Figure 5.13). The Rush School is approximately 29,400m^ (316,000ft^) and 230m

(750ft) upsfream of WEMITE 2 and the Higginbotham Park is approximately 98,000m^

(l,050,000ft^) and 570m (1900ft) upstream of WEMITE 2.

83

0 0

CD > ea a

a c o c 5

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ness

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84

Figure 5.13. Aerial Photograph of Surface Roughness Irregularhies in the Suburban Terrain.

85

u r j

J3

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(U o 3 ;-! 3 H

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86

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87

These open patches appear to influence Tl„ ZQS, while not impacting the COM ZQS.

This brings up 2 questions.

1. How large does a surface roughness irregularity have to be to begin to

influence the TIu zo?

2. At what distance upstream will a surface roughness irregularhy begin to

influence the TIu zo?

Since TIu ZQS in flow region I with an average fetch of 600m appears to be in

equilibrium with the new surface roughness and Higginbotham Park is approximately

600m upstream, h is suspected that only Rush School is influencing the TIu ZQS.

Therefore the distance at which surface roughness irregularities of approximate area

29.400m"- (316,000ft-) begin to influence TIu zo's is believed to occur at some distance

less than 600m upstream. Surface roughness irregularities approximately 1500m or more

away from WEMITE 2 with an area in the order of 120,000m' (I,300,000ft^) or less do

not influence the TIu ZQS.

There is a playa lake and a large park within 1,600m (6,562ft)) of WEMITE 2 that

might help answer the previous quesfions. The playa lake is located 1,486m (4,875ft)

upwmd at 200° and is approximately 117,580m^ (l,265,625ft^) and Maxey park is

located 1,600m (5,250ft) upwind at 150° wmd direction and is approximately 209,032m-

(2,250,000ft ). Neither one of these parks or open areas appear to be influencing the ZQS

estimated by TIu or COM methods (Figure 5.11).

The next phenomenon that needs to be addressed is the undulation of ZQS which

occurs in both the TIu and COM models (Figure 5.11). Originally it was thought that the

undulation of ZQS may be due to the grid layout of the streets, but upon closer inspection

the peaks and valleys did not correspond closely enough to N, S, E and W orientation of

the road grid. The peaks at 140° and 250° and the valleys at 50° and 190° might

correspond to peaks and valleys in the fetch, but this same behavior is not consistent for

the peak at 0° and the valley at 300° (Figure 5.11).

Next the possibility of local flow influences was investigated as being the possible

cause of the ZQ undulafions. Figure 5.16 is a close-up aerial photograph of the lot in

88

which WEMITE 2 was located in the Rushland residential community. The white arrows

represent valleys-smooth ZQS and the blue arrows represent peaks-rougher ZQS. Regions

of rougher and smoother ZQS are shaded accordingly. The directions where the zo tend to

peak or become rougher (signified by the blue arrows and shading) appear to correspond

to directions where taller trees or a home are located within 20m (70ft) of the WEMITE 2

tower. The directions where the ZQ become smoother, valleys (signified by the white

arrows and striped shading) appear to correspond to directions where there are no tall

trees or structures within 45m (150ft) the WEMITE 2 tower. Therefore, the undulating

pattems of ZQ appear to be the result of local flow pattems.

Figure 5.16. Close-Up Aerial Photograph of Residential She and Local Flow hifluences.

89

5.3.2.1 Reliability of Data

It is very important to note that the validity of the wind-field based models

depends on the assumption that the 15.2m (50ft) insfrument is located in the inner layer.

Weiringa (1993) gives a minimum height for profile measurements to be collected as:

and the maximum height for profile measurements to be collected as

-max ~ O.OIF . ^5 g-j

Estimating z,n,n from Equation 5.5 and substituting in the average ZQ (ZQ = 0.6m

(2ft)) and Zd (zd-3.6m (12ft)) for flow region 3 derived from COM model, z™„, is equal to

15.6m, which places the highest instrument at 15.2m (50ft) just below the inner layer, ft

is possible that the 15.2m (50ft) instrument is not in the inner layer, ft is suspected that if

measurements taken a meter or two higher would resuh in an average ZQ closer to the

typical zo value given in ASCE 7 (2002) of 0.3m. But if this is true and we substitute a ZQ

= 0.3m (1ft) and a Zd = 3.6m (50ft) into the z„u„ equafion, then z m = 9.7m (32ft), placing

the 15.2m (50ft) mstrument well into the inner layer. Weiringa also recommends a

mmimum of 3 levels of profile measurements over high roughness (ZQ ~ Im (3ft)) and a

minimum of 4 profile levels over moderate roughness (ZQ ~ 0.1m (0.3ft)) for accurate

estimates of ZQ derived a profile fitting methods.

5.4 Conclusions

The specific conclusions for this chapter are listed below.

5.4.1 Roughness Element Derived Models

1. There were several roughness element derived models that estimated reasonable ZdS.

Kutzbach's (1961) model appears to be the most promising, because it produced ZdS

that spanned the 95% probability of occurrence obtained by COM wind-field model

usuig a Fc based only on homes with either HmeanR or HpeakR-

90

2. There were several roughness element derived models that estimated reasonable ZQS.

Kondo and Yamazawa (1983) was the only model with Fc based on homes only that

produced ZQS in the 95% probability of occurrence obtained by COM wind-field

model. Their ZQ model, using HmeanR and HpeakR, also spanned 95% probability of

occurrence obtained from COM wind-field zo model.

5.4.2 Wind-Field Derived Models

1. From investigation of COM methods, it was deduced that only the top instmment at

15.2m (50ft) of WEMITE 2 located in the residential community was at the very

bottom edge of the inner. Assuming the inner layer begins at 15.2m (50ft), both

ASCE 7 (2002) and AS/NZS 1170.2's (2002) assumption that for suburban terrain the

mner layer begins at 10m (33ft) is too low.

2. The Zd = 3.6m (12ft) from De Bruin and Moore's (1984) COM model mdicates that

the top of the viscous layer and the bottom of the intermediate layer is at

approximately 3.6m. The conclusion that the inner layer begins at 15.2m (50ft), sets

the height of the mtermediate layer at 15.2m (50ft) and the depth of the intermediate

layer at 15.2m - 3.6m = 11.6m (38ft). The intermediate layer height of 15.2m (50ft)

does fall within height range given by Raupach et al. (1980-Equafion 2.8) of (20-

50)zo=12m-30m.

3. The Zo's from De Bruin and Moore's (1984) COM model for the suburban terrain

flow regions with the maximum fetch, which is most representative of equilibrium

flow varied between approximately 0.3m and 1.0m (0.98ft and 3.2ft). This range is

shnilar to the range of ZQ'S given by ASCE 7 (2002) of 0.15m to 0.7m (0.45ft to

2.3ft). AS/NZS 1170.2's (2002) value of zo = 0.2 for terrain Category 3 falls on the

low side of the ZQ range computed by COM. Since the methods used to calculate ZQ

are based only on the 15.2m instrument and it was concluded this instrument might be

located at the interface of the irmer and intermediate layers, h is beheved that raising

the instrument a few meters may have produced lower zos,which would be closer to

the typical values given by ASCE 7 (2002), typical ZQ = 0.3m (0.98ft) for Exposure B,

and AS/NZS 1170.2 (2002). typical ZQ = 0.2m (0.66ft) for Terrain 3.

91

4. The COM zo's varied between the equilibrium ranges of 0.3m and 1.0m (0.98ft and

3.2ft), except when the upwind fetch was less than I km (3,200ft). For fetches less

than 1km the Zo dropped to approximately 0.15m (0.45ft) and appears to be

influenced by the upstream smoother terrain of the adjacent agriculture field.

5. The TIu Zo's were not influenced by fetches below 1km, and consistently varied

between 0.3m and 1.8m (0.98ft and 5.9ft). This consistency is thought to be due to

the use of a C based on equilibrium flow conditions and the influence of Ou.

6. The TIu ZQS were influenced by smooth patches within the suburban terrain (such as a

school yard), approximately 30,000m- (320,000ft^) in area and within 230m (750ft)

upstteam. This sensitivity is also thought to be due to the influence of Ou. Smooth

patches of approximately 200,000m' (2,000,000ft^) and 1.5km (5,000ft) upstream did

not influence the TIu zoS. Note that COM ZQS were not influenced by the smooth

patches.

92

CHAPTER VI

WEMITE I IN THE AGRICULTURAL FIELD

6.1 Introduction

As described in Chapter 2: Experiment Setup, WEMITE 1 was placed in an

agricultural field 31.3m (102.6ft) east of the suburban low-rise single-family residential

community (Rushland) to capture full-scale wind measurements. Three different flow

regions based on fetch were defined and the ZQS were examined for each flow region

(Figure 4.12).

6.2 Discussion

Using a log-law best-fit method, roughness lengths, zos, were calculated for all 4

instruments, Zoaii, the top 3 instruments, zoupper, and the bottom 3 instmments, zoiower, on

WEMITE 1 located in the agriculture field (Figure 6.1). Appendix F shows the variation

of Zo upper with the wind speed for daytime (5:00 a.m.-9:00 p.m.) and night time (9:00

p.m.-5:00 a.m.) measurements. There was no noticeable relationship between ZQ upper

and the magnitude of the wind speed and time of day. The zoaii, based on all instruments,

follows zoiowei, based on the lower three instruments. Whereas zoupper, based on the top

three mstruments, diverges at a wind direction of 135°, giving much smoother ZQS. This

decrease in zo might be due to a combination of the 9.1m instrument being influenced by

upsfream patches of roughness while the 15.2m instrument is being influence by an

upstream open area just south of Brownfield Hwy at approximately 135° (refer to Figure

4.12). Figure 6.2 shows a conceptual velocity equilibrium IBL growth based on EUiott

(1958) model for the 135° wmd direcfion.

In flow region 1 shown in Figure 6.1, there appears to be an excellent correlation

between ZQ and fetch. Figure 6.3 shows the variation of profile derived zos with increases

in fetch for the wind direcfions between 140° and 270°. The 140°-270° whid direcfion

was chosen due to gradual changes in fetch. The local terrain of WEMITE 1, the

agriculture field, is classified by ASCE 7 (2002) and AS/NZS 1170.2 (2002) as open

93

terrain; these standards give typical ZQ values as 0.03m and 0.02m, respectively. It can be

seen from Figure 6.3 that the zo doesn't approach this value until a fetch of 600m or more

exists.

Next the zo for WEMITE 1 in the agriculture field derived from TIu at 15.2m

(usmg Equation 3.31 with a C = 2.8 and Zd = Om) is compared to the profile derived ZQS

(Figure 6.4). The TIu zos follow the general trend of the profile based ZQS, with the

exception of a drop and scattering of the zos that occurs between 250° and 290°. This

drop and scattering is the result of localized smoother flow resulting from an open area

approximately 270° of WEMITE 1 (Figure 6.4). This trend is also seen in the TI between

250° and 290° in Figure 6.5. Note that the proximity of the open area does not appear to

influence the profile based Zo's. For each flow region the mean, standard deviation, a,

minimum, and maximum values of the various derived zo's are listed in Table 6.1.

6.3 Conclusions

The specific conclusions for this chapter are listed below.

1. Both mean wind speed profile and TIu derived Zos do not give values expected for

open terram until the upwind fetch is greater than 600m for heights up to 15m.

2. The Zo values correlated quhe well with fetch, and collapsed very well for fetches

below 600m.

3. Unlike the profile derived ZQS, the TIu derived ZQS are influenced by local openings

of 50m or smooth patches in the roughness element pattern.

94

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99

Figure 6.6. Aerial Photograph Close-Up of WEMITE 1 Located in the Agricultural Field.

100

Table 6.1. Flow Region zo statistics for WEMITE I Located in the Agricuhure Field.

Flow Region mean o min. max. Z|i all

1 -> 3

0.37 0.08 0.07

0.40 0.17 0.19

0.00255 0.00037 0.00079

2.8 1.6 1.9

z,i lower 1 2 3

0.33 0.06 0.05

0.42 0.13 0.17

0.00291 0.00013 0.00002

2.2 1.2 1.9

Zo upper 1 2 3

0.53 0.14 O.ll

0.52 0.30 0.24

0.00013 0

0.00006

3.9 2.5 2.3

ZoC«i 15m (TIJ 1 -> 3

0.44 O.II 0.10

0.49 0.20 0.18

0.00897 0

0.00005

8.8 1.6 1.2

Zo(5i9.1m(Tl„) 1 2 3

0.53 0.15 0.13

0.63 0.25 0.22

0.00708 0.00003 0.00164

11.4 1.8 1.4

Zo (2 6.1m (TIu) 1 2 3

0.60 0.16 0.14

0.65 0.26 0.24

0.01456 0.00002 0.01002

II.6 1.8 1.5

z,j @ 3.0m (TIu) I 2 3

0.80 0.24 0.21

0.74 0.32 0.30

0.04775 0.00001 0.02288

11.8 2.2 1.8

101

CHAPTER VII

TRANSITION FLOW REGIME MODELS

7.1 Background

The Australian Wind Load Code, AS 1170.2 was one of the first codes to adopt a

pragmatic procedure for calculating the effect that a change of terrain has on both mean-

hourly and 3-second gust velocity profiles. Holmes et al. (1990) discuss the rationale for

the method adopted in ASl 170.2, which draws on the work of Deaves (1981), Wood

(1982), and additional wind tunnel testing. A simple exponenfial model for the transifion

regime was found to match wind tunnel tests for gust speeds. Namely, the non-

dimensional gust wind speed in the transition region, MBX is given by;

M,.,=M,+|(M,-M,)(l-e-^^^iJ (7.1)

where MA and MB are the asymptotic peak gust velocity multipliers m the upwmd terrain

A and the downwind terrain B, respectively, and F is the fetch in meters. In the

codification process, the exponential model was linearized, introducing errors of

approximation of no more than 10%. Results are obtained for a non-dimensional wind

speed multiplier (Mx), which is the ratio of the gust speed at height z in a specific terrain

type to the gust wind speed at 10m in standard open terrain (Zo = 0.02m). ASl 170.2

(1989) defines Mx as:

M=M„ + K . - . . « 0 - ^ o ( ' ^ (7.2)

where Mo is the upstream wind speed multiplier, M(z, cat) is the downstream equilibrium

wind speed multiplier, Mx is the transitional multiplier, L is the linearized transition

length, and F is the distance downstream of the change in terrain to the structure under

consideration (fetch). For mean wind speeds, L was set to 1500m. For gust wind speeds,

L was set to 2500m to take into account the increased length required for gust conditions

to reach equilibrium. The term Xj is the distance downstream from the start of the new

terrain to the developed height of the Intemal Boundary Layer (EBL). The growth of the

102

IBL was described by Wood (Equation 7.3), except the 0.28 constant was rounded to 0.3

(Equation 7.4).

= 0.28 / A° '

.Y

-O.r \-a.r )

X, -

-11.25

h.

0-3_-„,.

(7.3)

(7.4)

where Zo,r= larger of the two roughness lengths

h, = Zi = developed height of the inner layer

x, = distance downstream of change in terrain

Prior to 2002, ASCE 7 did not take into account the effect of terrain change on

velocity profiles. In 2002 an approach based on investigations by ESDU (1983 and

1990), was infroduced into the ASCE 7 commentary. The approach was based on surface

roughness categories and exposure categories. The surface roughness categorization

depends on the type of roughness elements (i.e., build-up, vegetation, open-undeveloped)

upwind. The exposure categorization depends on the surface roughness category and the

distance it continues upwind. For buildings located in transition zones between the

exposure categories an intermediate exposure is permitted and an acceptable method is

given in the conmientary based on ESDU (1983, 1990).

In the model presented in the ASCE 7 (2002) commentary, the gust velocity

pressure exposure factor Kz at a site after a change in terrain/exposure is modified

accorduig to Equation 7.5.

Kz = Kz, + AK [with AK = (Kio,2- Kio.i) (K,i/Kio,i) FAK (x)] (7.5)

Kzi = downstream velocity pressure exposure factor at height z

K]o,i = the downstream equilibrium velocity pressure exposure factor at 10m

Kio,2 = the upstream factor at 10m

FAK(X) is a fetch function allowing transition between exposures given by Equation 7.6:

FAK (X) = logio(xi/x) / logio(xi/Xo) (for Xo < x < x,) (7.6)

FAK (X) = 1 (for X < Xo)

FAK(X) = 0 (forx>xi)

103

X = the distance from the change in terrain (fetch)

The parameter XQ is a "starting^ value and XQ is given by Equation 7.7.

The parameter xi is a "finishing' value for transition, for rough to smooth (R -^ S)

changes (Kio.i > Kio,2) xi = 100 km, while for smooth to rough (S - • R) changes (Kio,i <

Kio,2) xi = 10 km. To compare this model with ASl 170.2 (1989) and the field data, the

square root of Kz must be taken to deal with velocity ratios rather than velocity pressure

ratios.

7.1.1 Change of Terrain Roughness Experiment Parameters

WEMITE 2. WEMITE I, and WERFL were aligned in a southwesterly-

northeasterly wind direction; therefore the data for the change of terrain (rough to

smooth) models were taken from the 230°-250° and 50°-70° wmd direcfions. The number

of high whid speed runs was limited due to the short duration of the experiment. To

increase the sample size, the 30 minute runs were divided into 10-minute segments.

Appendix F lists the runs used in the change of terrain experiments for each direction.

During the experiment, the 33ft anemometer at WERFL was malfunctioning; requiring

the calculation of mean speeds at 10m from a log-law profile fit to the remaining

functioning WERFL instruments and then converted to a 3-second gust wind speed using

the Durst (1960) curve.

For the southwest wind directions 230°-250°, WERFL was used to measure the

equilibrium wind speeds at the 10m (33ft) height in open terrain. According to ASl 170.2

and ASCE 7's models, WERFL must have an upwind fetch of 2.5km and 100km,

respectively, for 3-second gust wind speeds to be considered in equilibrium with the new

surface roughness. For mean hourly wind speeds, ASl 170.2 (1989) requires an upwind

fetch of 1.5km. The upwind fetch from WERFL to the surface roughness change ranges

from 700m to 800m for wind directions of 230°-250° which is below both AS 1170.2 and

ASCE 7's equilibrium fetch requirements (Table 7.1). Therefore, the 10-minute mean

and 3-second gust wind speeds at WERFL must be corrected (mcreased) for each model

104

to consider the insufficient fetch. Table 7.1 gives the insufficient fetch correction

muhipliers, M, for WERFL according to AS 1170.2 (1989) and ASCE 7 (2002). For

example, the 3-second gust wind speed at WERFL for the wind direction of 230°

according to ASCE 7 (2002) would only represent 93% (from Table 7.1) of the expected

equilibrium 3-second gust wind speed. The WERFL lOm 3-second gust wind speeds

were corrected for the ASCE 7(2002) model using Equation 7.8. The same procedure,

using the appropriate muhipliers from Table 7.1, was performed for the ASl 170.2 3-

second and mean wind speed models.

M conecied . . (7.8)

For the northeasterly wind directions, 50°-70°, WEMITE 1 was used to measure

the equilibrium wind speeds at 10m since h is downstream of WERFL. The upstream

fetch of WEMITE I ranged from 1.7 to 2.0km. Again an insufficient fetch for

equilibrium condhions exists for both the ASl 170.2 (1989) and ASCE 7(2002) 3-second

gust models. Therefore, WEMITE I's 10m 3-second gust wind speeds were corrected

(mcreased) to better reflect equilibrium gust wind speeds. Figures 7.1 and 7.2 show an

example run of 10-muiute mean and 3-'Second gust profiles obtained from WERFL,

WEMITE 1 and WEMITE 2 that was used in the change of terrain models.

7.1.2 Discussion

From Figures 7.3 and 7.4, it can be seen that ASl 170.2's (1989) transition region

for both 3-second gust and the mean hourly change of terrain models begins at II9.7m

downstream of the surface roughness change for a 10m height, assuming the code

suggested values for zor = 0.2 and zos =0.02. If the zo measured by WEMITE 2 in the

residential community, zo=0.6m, is used in place of zor, then ASl 170.2's transhion region

for a 10m height is estimated to begin 91m downstream of the surface roughness change.

ASCE 7's (2002) transition region begins 46m downstream of the surface roughness

change. AS 1170.2 assumes that the wind flow reaches equilibrium 2.5km (8200ft)

downstream of the surface roughness. While ASCE 7 assumes that for R ^ S changes

105

equilibrium is not achieved until 100km (328,000ft) downstream. Transition regions are

shown on Figure 7.3 and compared in Table 7.2

7.1.2.1 Gust Change of Terrain Models

The average gust multiplier calculated from the from WEMITE 2's wind speeds

at 15m divided by the wind speed from WERFL at lOm equals 0.79 and the data varies

above and below the both models, agreeing best with the models that assume a za of 3.6m

obtained from a conservation of mass (COM) method discussed in Section 5.2.3 (Figures

7.3 and 7.4- filled triangles). It should be noted that both ASl 170.2 and ASCE 7 omh

the use of a Zd. Therefore the models are artificially adjusted to reflect a Zd. WEMITE

2's wmd speed at 15m, instead of the standard 10m, is used because h was the only

instrument thought to be located in the inner layer (refer to Section 5.2.3).

The average gust multiplier based on the WEMITE I's wind speed at 15m

divided by the equilibrium wind speed estimated by WERFL at 10m equals 0.87 (Figures

7.3 and 7.4— filled squares). The wind speeds at WEMITE 1 agree well with both

models, underestimated by ASl 170.2 and overestimated by ASCE 7 by 2 %, assuming a

Zd of 3.6m (comparing to the solid white and black lines). If no displacement height is

assumed, then ASl 170.2 and ASCE 7 overestimate the wind speed by approximately 3%

(comparing to the dashed white and grey lines).

The average gust multiplier based on WEMITE 1 's wind speed at 10m divided by

the equilibrium wind speed estimated by WERFL at 10m equals 0.73 and all models

regardless of the za overestimated the wind speed by 16% to 26% (Figures 7.3 and 7.4 -

hollow squares).

There are only 4 data points obtained from WERFL's wind speed at 10m divided

by the wind speed from WEMITE 1 at 10m (Figure 7.3 - filled diamonds). The 4 points

average value was 0.97 and varied about both models while approachmg unhy, indicating

that the flow is approaching equilibrium with the new surface roughness at an

approximate fetch of 1.4km (Figure 7.4).

The Hurricane Planetary Boundary Layer (HPBL) data from Hurricane Bonnie

and Floyd (Letchford et al. 2001) give results that range from 45%) underestimations to

106

25%) overestimations of wind speeds, again varying above and below both models

(Figure 7.3 - filled and hollow circles). Although this data scatters, this high wind speed

data is Ul a similar range to the ABL data and their averages agree well with the change

of terrain models (Figure 7.4).

7.1.2.2 Mean Change of Terrain Models

Figure 7.5 shows ASl 170.2's mean change of terrain multipliers compared to

full-scale ABL and HPBL data. Like the gust models, upstream data collected by

WEMFTE 1 and 2 agree best with the model that assumes a Zd of 3.6m. The average

wmd speed at WEMITE 2 at 15m is overestimated by 14% when a Zd of 3.6m is assumed

(Figure 7.6 - red line), and is overestimated by 23%) when no Zd is assumed (Figure 7.6 -

blue dashed line). The muhipliers based on WEMITE I's wind speeds at 15m divided by

WERFL's wmd speeds at 10m (Figure 7.5 - filled squares) overestimates the wind speed

by only 3% (Figure 7.4 - solid red solid line) if a Zd of 3.6 is assumed. If no Zd is

assumed the model overestimates wind speeds by 14% (Figure 7.6 -solid red boxes

compared to the dashed line). Note that at a 30m fetch, WEMITE 1 at 15m agrees quite

well with ASl 170.2's model that assumes a displacement height (Figures 7.5 and 7.6 -

filled squares compared to solid line). Since WEMITE 1 is not in the transition region

defined by ASl 170.2 (Figure 7.5), one would expect data consistent with the upstream

WEMITE 2 measurements. This is not the case and indicates that the transition region

for mean wind flow may be starting at a distance of 30m, instead of the 100m given by

AS 1170.2.

Like the gust models, the mean data from WERFL at 10m divided by the data

from WEMTIE 1 at 10m (Figure 7.5 - filled diamonds) approaches unity at the

approximate fetch of 1.4km suggesting flow is approaching equilibrium. The 10-minute

mean HPBL data (filled and hollow circles) overestimates wind speeds by up to 45% and

underestimates wins speeds up to 25% for the mean' change of terrain models (Figure

7.6). But their average values agree quhe well with ASl 170.2's gust change of terrahi

model.

107

Table 7.1. WERFL Insufficient Fetch Gust and Mean Correction Multipliers.

Direction Fetch (km) ^S 1170.2 (2002) AS 1170.2 (2002) ASCE 7 (2002) (Mean-Hourly) (3-Second Gust) (3-Second Gust)

JO 2^6 1.00 1.000 0.950

10 1.89 1.00 0,954 0944

20 1.89 1.00 0.954 O.944

30 1.43 0.88 0923 0940" jW L23 0.86 , 0.909 0.938

_50 L i i 085 0903 0936 60 1.03 084 0895 0935~

70 097 0.83 0.892 0.934

80 1.03 0.84 0895 0935 90 069 O80 0.872 0929 100 051 0.78 O860 0.924 110 051 078 O860 0.924 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350

0.49 1.54

1.71 1.54 1.03 0.97 097 0.69 O80 091 086 074 0.69 O80 1.43 1.26 1.31 1.37 1.60 2.86 2.06 1.94 3.54 4.06

0.78 089 1.00 0.89 084 083 083 O80 081 082 082 081 O80 081 088 086 087 087 1.00 1.00 1.00 1.00 1.00 1.00

0.858 O930 0.942 0.930 0895 0.892 0.892 0872 O880 0888 0884 0.876 0872 0.880 0.923 0911 0.915 0919 0934 1.000 0965 0.958 1.000 1.00

0.924 0941 0.943 0941 0.935 0934 0934 0929 0931 0933 0932 0.930 0929 0.931 0.940 0938 0.939 0939 0.942 O950 0.945 0.944 0953 0.950

108

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Reference

ASCE 7 (2002) ASl 1702 (2002) Experiment Data

Table 7.2. Transition Region Beginning and Ending.

3-Second Gust Transition Beginning

40m 100m

> 60m

3-Second Gust Transition

100km 2.5km 1.5km

Ending

7.2 Conclusions

The specific conclusions of the chapter are listed below.

1. Three-second gust wind speeds in the suburban terrain may be overestimated by

both ASl 170.2 and ASCE 7 by approximately 6 and 11%, respectively. This is

due to the rougher ZQ = 0.6 obtained from the experiment as compared the typical

values used by the models of 0.2m and 0.3m.

2. The Zd appears to be an important parameter to consider in change of terrain

models. Currently ASl 170.2 and ASCE 7 ignore Zd- Not mcluding a Zd could

result in mean wind speed underestimations as high as 35%.

3. Mean wind speeds in suburban terrahi may be overestimated by AS 1170.2, which

assumes ZQ = 0.2. by approximately 15%.

4. Both 3-second gust and mean hourly wind speeds are approaching equilibrium for

R -^S transhions within 1.5 km downstream of the surface roughness change.

115

CHAPTER VIII

CONCLUSIONS

The objectives of this study were to:

1. Investigate the effects inhomogeneous surface roughness has on roughness length,

Zo , derived fi-om conservation of mass (COM) and longitudinal turbulence

intensity (TIu).

2. Estimatethe z o and displacement height, Zd, in the suburban community and

compare them to ZQS and ZdS estimated from physical characteristics of the

suburban roughness elements, such as house height and denshy.

3. Obtain full-scale transition region wind speed measurements.

4. Compare transhion region full-scale wind speed measurements, to models given

in ASCE 7 (2002) and AS/NZS 1170.2 (1989).

This research successfully completed the above objectives by collecting and

analyzmg data records from the two WEMITE units and WERFL taken between March

26 and May 15, 2000. The specific conclusions from this research are given below.

8.1 Conclusions

1. For suburban terrain De Bruin and Moore's (1984)) conservation of mass (COM)

method gave reasonable values for Zd and ZQ. For the Rushland suburban

communities having an average fraction of cover, Fc, of 0.22 (homes only) or 0.5

(homes and trees) and having a mixture of both one and two story homes with

mature vegetation resulted in a Zd = 3.6m, zo = 0.6m, and viscous layer height of

z* = 15m. Assuming the COM Zd = 3.6m longitudinal turbulence intensity (TIu)

approach gave a slightly higher Zo = 0.66m. This conclusion suggests the level of

constant wind speed above the ground for Terrain Category 3 given by ASl 170.2

should be increased from 10m to 15m. It appears that the 10m height does not

take into account the intermediate layer, z*.

116

2. Several models derived from roughness element physical characteristics predict

reasonable Zd and ZQ values for the suburban terrain. Refer to Chapter V for

models details.

3. For smooth to rough transitions, a fetch of at least 1000m is necessary for zo

obtained from COM to be similar to those obtained in the regions most

representative of equilibrium conditions. A fetch of approximately 600m was not

sufficient for COM ZQ. The limited fetch did not appear to influence the ZQS based

on TIu, suggesting that a fetch of 600m is sufficient for TIu derived ZQS and that

stresses reach equilibrium faster than velocity, agreeing with Shir's (1972)

findings.

4. For rough to smooth transitions (suburban to open terrain) a fetch of at least 600m

is needed for mean wind speed profile and TIu derived ZQS to approach

equilibrium at a 15m height.

5. TIu ZQS are senshive to upstream smooth patches within 230m (750ft) of

approximately 30,000m' (320,000ft^). The upstream length of the open area

measured approximately 230m (750ft). This suggests that TIu zo require a fetch

greater than 230m, but less than 600m, to reach equilibrium at a 15m height with

the local terrain.

6. Transitional regime data generally agreed well with ASCE 7 and ASl 170.2

models. Data varied so extensively that a superior model could not be

determined. Omitting the Zd can result in wind speed overestimations as high as

35%. ASCE 7 (2002) and ASl 170.2 (1989) change of terrain models do not

consider Zd. Including a Zd always improved experiment and model correlation.

7. The transition region for mean wind speeds at 15m may be starting at or before

30m downstream of the surface roughness change.

117

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124

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125

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126

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127

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128

APPENDDC A

ROUGHNESS ELEMENT DERTVED DISPLACEMENT

HEIGHT CALCULATIONS

129

Table A. 1. Counihan (1971), Lee and Solimon (1977), and Hussain (1978) Zd Calculations.

Reference

Couni]ian(1971)

Lee and Solimon (1977)

Hussam (1978)

Zd Equation

l-5"mc'OH«'^i

homes only

••5W „,„„,/; F,, homes and trees

^•^^ peakR^c

homes only 1.5H p^,gi^jfF^

homes and trees

^•-''' meanR''c

homes only

'—^ nieofiR' c

homes and trees

^•^HpeakRl^c

homes only 2.5 H p^^i^nF^

homes and trees

^•^HmeanRpc

homes only

^•s>n mewiR'^c

homes and trees

^•^lipeakRpc

homes only

^•^HpeakR^c

homes and trees

Zj (all directions) 1.5(4.3w)(0.22)

= 1.42m 1.5(4.3w)(0.52)

= 3.35m

1.5(6w)(022)

= I.98m

1.5(6OT)(052)

= 4.68m

2.5(4.3OT)(0.22)

= 2.37m 2.5(4.3w)(0.52)

= 5.59m 2.5(6OT)(0.22)

= 3.33m

2.5(6OT)(0.52)

= 7.80m

1.6(4.3OT)(0.22)

= 1.51m 1.6(4.3OT)(0.52)

= 3.58m 1.6(6OT)(0.22)

= 2.Ilm

1.6(6w)(052)

= 4.99m

130

Table A.2. Kutzbach (1961) and Raupach et al. (1980) Zd Calculations.

Reference

Kutzbach (1961)

Raupach etal. (1980)

Zd Equation

homes only

109// , , , , , /^ ,°-"

homes only

^••^'^^iiwmiRK

homes only

homes only

z,| (ail directions)

1.09(4.3OT)(O22)°-'

= 3.02m

1.09(6.0W)(0.22)' '^^

= 4.22m

I .47(4 .3OT)(0 .22)°"

= 3.84m

1 .47(6W)(0 .22)""

= 5.35m

Table A.3. Abtew et al.'s (1989) zd Calculations.

Reference

Abtew etal. (1989)

Zd Equation

homes and trees

Zd (all directions) (4.3OT)(0.22) + (3.6OT)(4.7W) sin 45°(O30)

= 4.5m

131

APPENDDC B

ROUGHNESS ELEMENT DERIVED ROUGHNESS

LENGTH CALCULATIONS

132

Table B.l. Nikuradse (1933, 1950), Fang and Sill (1992), Saxton et al. (1974), and Houghton's (1985) ZQ Calculations.

Reference

Nikuradse (1933, 1950)

Fang and Sill (1992). Saxton et al. (1974). and Houahton (1985)

Zo Equation

IJ ineanR

30

" peakR

30

IJ '^ nieanR

10

^ peakR

10

Zo (all directions) 4.3OT

30 =014m

6.0m

30 =0.20m

4.3w

10 =.43m 6.0/w

10 = 60m

Table B.2. Tanner and Pelton (1960), Sellers (1965), and Kung's (1961, 1963) Zo Calculations.

Reference

Tanner and Pelton (I960)

Sellers (1965)

Kung(1961.1963)

Tanner and Pelton (I960)

Sellers (1965)

Kung (1961,1963)

ZQ Equation

' " • " meaiiR

i n " W * i " " peiikR

ZQ (all directions)

10-^"4.3/n'^^'

=I.03m

10-' ^=4.3m°-9^^

=018m

\0-'^U.3m'''

=0.33m

\0~^^'6.0m''''

=1.66m

10-^^^=6.0^"^^^

=0.25m

l O ' - ^ 6.0/w'"'

=0.49m

Table B.3. Abtew et al.

Reference

Abtew etal. (1986)

Zo Equation

O.UH^^f(\-F,)

s (1986) Zo Calculations.

Zo

OI3(4.3w)(I-0.2) + OI3(6.45w)(I-0.30) =I03m

133

Table B.4. Lettau s (1969) ZQ Calculations.

Reference Zo Equation Zo (N/S)

Zo (E/W)

Zo (SE, SW, NE, NW)

Lettau (1969)

0 5 / / lueanR 0.5(4.3/;;) 137;//-I423w-

0.5(4.3w) I60w'

= 0.21m i423w^

= 0.24m

0.5(4.3w) 155/w I423w'

= 0.23m

0.5// peokR s.,

0.5(6.0/77) 137 ;// 1423/;;-

= 0.29m

0.5(6.0m) I60w'

I423w-0.34m

0.5(6.0m) I55w'

1423w' = 0.33m

Table B.5. Busmger's (1975) ZQ Calculations.

Referenc e

Businger (1975)

Zo Equation

0 5 -H meojiR

D., 1-05-

H', tiieaiiR

\ D

P J

0 5 -H

f peakR

D^ 1-0.5-

H peakR

ZQ

(N/S)

05 (4.3nO-

305/w

1 - 0 5 (4.3w)

30.5m

2 \

=0.15m

05 (6.0w)-

30.5m

' 1 - 0 . 5 ! ^ : ^ ' 30.5m

=0.10m

Zo (EAV)

05 (4.3/7/)-

12.5m

1 - 0 5 (4.3w)

\2.5m

=0.05m

2 ^ -

0.5 (6.0/77)-

12.5/7/

12.5OT

=0.28m

Zo (SE, SW, NE,

NW)

05 (4.3/77)'

26.7/77

Vo.5^^-^'">''' V

26.7/71

= 015m

0.5^-^^^^. 26.7m

1 - 0 5 (6.O/77) 2 A

26.7/77

= 0.07m

Table B.6. Counihan's (1971) zo Calculations.

Reference

Counihan (1971)

ZQ Equation

^,„»««(108^.-008) homes only

/ /p««(108F, -0.08)

homes only

Zo

4.3/7;(1.08(0.22)-0.08)

=0.68m

6.0/7/(1.08(022)-0.08)

=095m

134

Table B.7. Kondo and Yamazawa's (1983) zo

Reference

Kondo and Yamazawa (1983. 1986)

Zo Equation 0.25//,„,„„«F,

homes only

(^•'-^^flleaiiRFc

iiomes and trees

^•-^f^pcakRp'c

homes only

^•~^flpeakR ^c

homes and trees

Calculations.

Zo (all directions) 0.25(4.3/77 )(0.22)

=0.24m

0.25(4.3/77 )(052)

=0.56m

025(6/77 )(0.22)

=0.33m

0.25(6/77 )(052)

=078m

Table B.S. Kondo and Yamazawa's (1986) zo Calculations for Ru = 1520m (5000ft).

Reference


Zo Equation: Direction

0°

45°

90°

135°

180°

225°

270°

315°

(40fl + U5b + 200c + I lOi/ - 30)100

Calculations (40(0.50) + 125(0) + 200(0) + 110(050) - 30)/100

= 0.80m (40(0.16) +125(0) + 200(0) + 110(084) - 30)/100

= 0.80m (40(0.53) +125(0) + 200(0.04) + 110(0.43) - 30)/100

= 0.79m "

(40(0.07) +125(0) + 200(0) +110(.93) -30)/100 = 0.80m

(40(0) +125(0) + 200(0) + 110(1) - 30)/100 = 0.80m

(40(0.19) + 125(0) + 200(0) +110(081) - 30)/I00 = 0.61m

(40(0.04) + 125(0) + 200(0) + 110(0.96) - 30)/100

= 0.78m (40(0.11) + 125(0) + 200(0) + 110(0.89) - 30)/100

= 0.80m

135

APPENDDC C

ACTUAL PROFILE INTEGRATION ERROR

136

The error associated with the integration of the actual profile, E^^ , was estimated

by fitting a log-law profile to the same instruments heights used in the actual profile

using a Zd = Om (0.0ft) and zo = 0.3m (Ift). The log-law and actual profile are integrated

using Equation 5.3 and Equation C.l, respectively. The error in integrafion of the actual

profile will be approximated by the absolute value of the difference in the integration of a

the log law using Equation 5.3 and Equation C. 1 divided by the integration of the log law

using Equation 5.3 (Equation C.2).

First the mean wind speeds are calculated from the log-law (Equation 2.6) at

heights consistent with the instruments heights used in the actual profile (Table C.l).

Next the mean wind speed values are plugged into Equation A.l to find the associated

area (sample calculation provided in Equation C.3). Equation 5.3 is used to calculate the

standard of comparison area (sample calculation provided in Equation C.4). Table C.2

gives the values of each integral and the error of integration. The error of integration of

the actual profile is approximately 30%.

T a b l e d . Log-Law Velocifies Used in e^^ Estimation.

' , m/s 2.92 3.89 4.52 5.26 5.89

z, m

2.1 4.0 6.1 lOO 15.2

^acliial = Wl5.2mO'l5.2m "-10.0m )^ 2) + WIQ o,„(( = 15.2;» ~ =10 Om ) ' ' ^ + (-10,0m "-=6.1m)' - )

+ "6.1m((=10.0m " =6.1m ) ' ' 2 + ( = 6.1m " =4.0m ) ^ 2) + W4.0m ((=6.1m " =4.0m ) / 2 + (^4 o„, - ^ l . to ) / 2 ) ( C . 1)

-t-"2.1m(( = 4 .0m-=2.1m)/2 + =2.1m''2)

_ "^aciiial ~^log-/OTi' ( C . 2 )

^log-Zon'

Aaciial = 5 .89/77/5((15.2/77-10.0/77) /2)+5.26/7/ / i ( (I5 .2/ /7-I0 .0/77) /2 + (I0 .0 /77-6 .I / /7) /2)

+ 4 .52/77/5((IO0/7/ -6 .1 / /7) /2 + (6.1/77-4.0/77)/2) + 3 .89/7/ /5( (6 .1 / /7-4 .0 /77) /2+ ( C . 3 )

(4.0/77 - 2.1/77) / 2) + 2.91/77 / 5 ( (4 .0 /7 / - 2.1/77) / 2 + 2 .1/ / / / 2)

A^^^_^^^^ =— | ([(l5m -Om[M15m -Oin) -1] ) ] - 15mln(0.3m))-([(Om -Om[ln(0,3/>0-1)]+ Qm\n{fi.im)\ ( C . 4 )

137

Table C.2 Estimation Parameters for £;„,

Integration Error Estimation A„c,u»h m - A | „ g . | „ ^ m - 4^^^^^^^^^ _ ^log-/mr

Equation 3.9 Equation 3.10 ^tnt

^log-IOH-

66.4 50.1 0.32

138

APPENDDC D

COM PROBABILITY DISTRIBUTION

139

Zd (De Bruin and Moore 1985) Histogram

Z d m

1 1 Frequency Cumulative %

100.00% 97.5%

80.00%

60.00%

40.00%

20.00% 2.5% .00%

Figure D.l. COM Probability Distribution, Zd (De Brum and Moore, 1985).

• ^ i / ^ i N o t ^ o o o N ' — I ••—I Tl- »y-~i v.g) r - OO ON • r ^

o > o > C 2 c ? c r > o > < o c ^ c : 5

Zom I Frequency Cutnulative %

f» - 80%

60%

- 40%

- 20%

go|%

Figure D.2. COM Probability Distribution, zo (De Brum and Moore, 1985).

140

APPENDIX E

Zo versus. WS

141

>

T3

•T3

c :S

mea

n

1)

3 .3 a 1

o rr,

 o N

»—H

w o 3 Ofi

ui'oz

142

APPENDDC F

Zo, upper versus. WS

143

t/1

1 o '^ TS

^ c en lU

E OJ

"ti

>

a o

•a c

-o n

C/3

>

3 00

o o

o o o o

(ra) '"^"z

144

APPENDDC G

TRANSITIONAL FLOW REGIME RUNS

145

Table G. I. Change of Terrain Runs.

NE Wind (Res) Time/Date

4/27/00 5:47 PM 4/27/00 5:57 PM 4/27/00 6:07 PM 4/27/00 6:17 PM 4/27/00 6:27 PM

SWWind(Res) Time/Date

4/22/00 5:06 PM 4/22/00 5:16 PM 4/22/00 5:26 PM 4/22/00 5:36 PM 4/22/00 5:46 PM 4/22/00 5:56 PM 4/22/00 6:36 PM 4/22/00 6:46 PM 4/22/00 6:56 PM 4/22/00 7:06 PM 4/22/00 7:16 PM 4/22/00 7:26 PM

4/22/00 11:32 PM 4/22/00 11:42 PM 4/22/00 11:52 PM 4/23/00 12:02 AM 4/23/00 12:12AM 4/23/00 12:22 AM 4/23/00 12:32 AM 4/23/00 12:42 AM 4/23/00 12:52 AM 4/23/00 1:02 AM 4/23/00 1:12 AM 4/23/00 1:22 AM 4/23/00 1:32 AM 4/23/00 1:42 AM 4/23/00 1:52 AM 4/23/00 2:02 AM 4/23/00 2:12 AM 4/23/00 2:22 AM

146

a full-scale investigation of roughness lengths wind

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