Embed Size (px)
Citation preview
WIND ENGINEERING RESEARCH FIELD LABORATORY
SITE CHARACTERIZATION
by
JILL ANN CAMPBELL, B.S.C.E.
A THESIS
IN
CIVIL ENGINEERING
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE
IN
CIVIL ENGINEERING
Approved
Accepted
December, 1995
ACKNOWLEDGMENTS
I would like to express my sincere thanks to Dr. Douglas A. Smith, chairman of
my committee, for the encouragement and guidance throughout my entire graduate career.
Special thanks is extended to Dr. Kishor C. Mehta for serving on my thesis committee. I
would also like to express my thanks to the members of the wind research team for their
help with my research, with special thanks to Dr. Richard E. Peterson, Praveen Sandri,
Steve Weinbeck, and Staci Page.
Financial support was provided by the National Science Foundation to the
Colorado State University/Texas Tech University Cooperative Wind Engineering Program
Grant I CES-8611601 and IICMS-9409869. This support is acknowledged and
appreciated.
My deepest appreciation is reserved for my parents. Without their love,
encouragement, and financial assistance I would never of had the courage to make it this
far in my educational career.
Finally, I would like to thank Mr. Alan J. Reed, Jr. for his unconditional love,
support, and patience. The past year and half has been difficult and stressfiil at times.
Now that this project is complete we can begin our life together.
11
TABLE OF CONTENTS
ACKNOWLEDGMENTS ii
ABSTRACT vii
LIST OF TABLES ix
LIST OF FIGURES xi
LIST OF SYMBOLS xvi
CHAPTER
I. INTRODUCTION 1
1.1 Objectives 3
II. LITERATURE REVIEW 5
2.1 Mean Wind Speed Models 9
2.1.1 Power Law 10
2.1.2 Logarithmic Law 13
2.2 Turbulence Characteristics 18
2.2.1 Turbulence Intensity 18
2.2.2 Integral Scale of Turbulence 22
2.2.3 Power Spectra 28
2.3 Effects of Factors on Wind Profile Parameters and Turbulence Statistics . . .28
III. DATA COLLECTION 33
3.1 Data Acquisition System 33
111
3.2 Meteorological Instrumentation and Tower 35
3.3 Collected Data 39
3.3.1 Summary Statistics 40
3.3.2 Profile Parameters 41
3.3.3 Shear Velocity 42
3.3.4 Turbulence Intensity 42
3.3.5 Stationarity 44
3.4 Data Validation 44
3.5 Mode 15 Database 47
3.6 Censoring the Mode 15 Database 48
IV. ANALYSIS AND RESULTS 52
4.1 Site Average Flow parameters 55
4.1.1 Alpha 56
4.1.2 Surface Roughness 59
4.1.3 Shear Velocity 60
4.1.4 Longitudinal Turbulence Intensity 64
4.1.5 Lateral Turbulence Intensity 66
4.1.6 Statistical Analysis of Overall Site Flow Parameters 68
4.2 Mean Wind Direction 70
4.3 Mean Wind Speed 79
4.3.1 Overview of Effects of Mean Wind Speed in the Five Flow Regions 79
IV
4.3.2 Region 1 84
4.3.3 Region 2 84
4.3.4 Region 3 85
4.3.5 Region 4 86
4.3.6 Region 5 87
4.4 Stationarity 90
4.4.1 Stationarity by Flow Region 90
4.5 Storm Type 92
4.5.1 Overview of Effects of Storm Type in the Five Flow Regions . . . .92
4.5.2 Region 1 94
4.5.3 Region2 95
4.5.4 Region 3 96
4.5.5 Region 4 97
4.5.6 Region 5 98
4.6 Time of Day 99
4.6.1 Overview of Effects of Time of Day in the Five Flow Regions . 1 0 0
4.6.2 Region 1 100
4.6.3 Region 2 101
4.6.4 Region 3 104
4.6.5 Region 4 105
4.6.6 Region 5 106
4.7 Time of Year 108
4.7.1 Overview of Effects of Time of Year in the Five Flow Regions .108
4.7.2 Region 1 109
4.7.3 Region 2 110
4.7.4 Region 3 Il l
4.7.5 Region4 113
4.7.6 Region 5 114
V. CONCLUSIONS AND RECOMMENDATIONS 115
5.1 Conclusions 115
5.2 Recommendations 116
LIST OF REFERENCES 117
APPENDIX
A. MODE 15 DATABASE 121
B MODE 15 DELETED RECORDS 127
C. COMPLETE MODE 15 DATABASE 132
D. FLOW PARAMETERS VERSUS STATIONARITY 133
E. FLOW PARAMETERS VERSUS STATIONARITY 137
F. TYPICAL PLOTS OF PARAMETERS VERSUS TIME OF YEAR 143
VI
ABSTRACT
Wind flow parameters obtained from the field data are simulated in the wind tunnel
for studying wind effects on structures. The wind flow parameters include power law
exponent (a), surface roughness (zo), shear velocity (u*), and longitudinal, lateral, and the
vertical turbulence intensity (lu, Iv, and I ). The results of the wind tunnel study depend
on the reliability of wind flow parameters measured in the field and the simulation
technique. The objective of this work is to investigate the characteristics of the wind flow
parameters at the Wind Engineering Research Field Laboratory (WERFL) in light of the
factors which may affect the parameters. The factors investigated include: mean wind
direction, mean wind speed, stationarity, atmospheric conditions, time of day a record was
collected, and time of year a record was collected.
The National Science Foundation has sponsored a Colorado State
University/Texas Tech University Cooperative Wind Engineering Program at the Texas
Tech University Wind Engineering Research Field Laboratory (WERFL) to study wind
effects on low-rise buildings. Wind and meteorological data are collected on a 160 ft high
meteorological tower. The data collected for this project includes wind speed and wind
direction at four levels on the meteorological tower. Wind speed and direction were used
to assess the wind parameters and perform the characterization of the terrain.
Vll
The scope of this project is limited to data collected between April of 1991 and
June of 1992 (Mode 15 data). A total of 465, 15-minute records were collected of which
454 records were found to be acceptable for analysis.
The analysis of the data included plotting of the parameters versus the factors,
estimation of probability density functions for the parameters, and nonparametric statistical
testing. Interpretation of the analyses and observations from the data analysis revealed
wind from all directions does not yield the same mean and variance of the parameters.
The wind parameters show that stationarity is not an important factor for the site
characterization. Shear velocity is a function of wind speed.
VIU
LIST OF TABLES
2.1 Power Law Exponents in Different Codes 12
2.2 Average Wind Profile Parameter Values 13
2.3 Average Longitudinal Turbulence Intensity Values 21
2.4 Longitudinal Integral Scale of Turbulence at 33 ft 24
2.5 Average Longitudinal Integral Scale of Turbulence Values 25
2.6 Longitudinal and Lateral Integral Scales for Data Group 1 26
2.7 Longitudinal and Lateral Integral Scales for Data Group 2 26
2.8 Comparison of the Results Obtained by Chok and Lui 27
3.1 Wind Speed and Wind Direction Stationarity 44
3.2 Mode 15 Wind Summary Database 50
3.3 Mode 15 Add-On Database 51
4.1 Power Law Exponents 57
4.2 Surface Roughness Values 59
4.3 Shear Velocity Values 62
4.4 Comparison of Chok and Mode 15 lu at 13 ft 64
4.5 Nonparametric Test Results Considering the Entire Site 69
4.6 Duncan's Multiple Range Analysis for zo 75
4.7 Azimuth Angles for the Various Flow Regions 76
4.8 Duncan Grouping for the Wind Flow Parameters 76
IX
4.9 Results of Kruskal-Wallis Test for the Overall Site for the Factor Flow Region . 78
4.10 Original Speed Ranges 79
4.11 Duncan's Multiple Range Analysis for zo 81
4.12 Combined Speeds 82
4.13 Nonparametric Test Results for Mean Wind Speed 83
4.14 Nonparametric Test Results for Stationarity 91
4.15 Nonparametric Test Results for Storm Type 93
4.16 Nonparametric Test Results for Time of Day 100
4.17 Nonparametric Test Results for Time of Year 109
A.1 Mode 15 Database Titles 122
B.l Mode 15 Deleted Records 128
LIST OF FIGURES
1.1 Field Site and Surrounding Terrain 3
2.1 Typical Profiles and Gradient Height (Disaster Research, 1995) 6
2.2 Wind Speed Profile 7
2.3 Power Law for Mode 15 Run 25 11
2.4 Surface Roughness Parameters (ESDU, 1981) 15
2.5 Log Law for Mode 15 Run 25 16
2.6 Turbulence Intensity 22
2.7 U-Spectrum with the Blunt Spectral Models (Tieleman, 1991) 29
2.8 Longitudinal Velocity Spectra at Roof Height (Thomas, 1993) 30
2.9 Lateral Velocity Spectra at Roof Height (Thomas, 1993) 30
2.10 Lateral Velocity Spectra at Roof Height (Thomas, 1993) 31
3.1 Orientation of the UVW Anemometers (Maloney, 1994) 36
3.2 Meteorological Tower (Chok, 1988) 38
3.3 Time History for Ml5N025 at 33 ft 40
3.4 Time History for Record M15N025 at 33 ft 43
4.1 Power Law Exponent versus Mean Wind Direction at 13 ft 58
4.2 Histogram for Alpha 58
4.3 Zo versus Azimuth Angle 60
4.4 Histogram for ZQ 60
XI
4.5 Comparison of Mode 15 Values with ESDU (ESDU, 1991) 61
4.6 u, versus Azimuth Angle 63
4.7 Histogram for u» 63
4.8 lu at 13 ft versus Azimuth Angle 65
4.9 Histogram for ly 65
4.10 Comparison of lu Models and Mode 15 Data 66
4.11 ly versus Azimuth Angle 67
4.12 Histogram for ly 68
4.13 ly versus lu 69
4.14 WERFL Field Site with Respect to Sectors 71
4.15 ZQ versus Sector 72
4.16 WERFL Field Site 73
4.17 WERFL Field Site with Respect to Flow Regions 77
4.18 ZQ versus Speed 80
4.19 u*33 versus Speed 80
4.20 Zo versus Speed for Overall Site 82
4.21 Zo versus Speed for Region 1 84
4.22 Zo versus Speed for Region 2 85
4.23 Zo versus Speed for Region 3 86
4.24 Zo versus Speed for Region 4 87
Xll
4.25 Zo versus Speed for Region 5 88
4.26 Lateral Turbulence at 33 ft versus Speed for Region 5 89
4.27 u,33 versus Speed for Region 5 89
4.28 Zo versus Station for Flow Region 5 91
4.29 a versus Storm for Overall Site 93
4.30 a versus Storm for Region 1 94
4.31 a versus Storm for Region 2 95
4.32 a versus Storm for Region 3 96
4.33 a versus Storm for Region 4 97
4.34 a versus Storm for Region 5 98
4.35 Lateral Turbulence Intensity at 33 ft versus Storm for Region 5 99
4.36 Zo versus Time of Day for Region 1 101
4.37 Zo versus Time of Day for Region 2 102
4.38 Iv at 13 ft versus Time of Day for Region 2 103
4.39 lu at 13 ft versus Time of Day for Region 2 103
4.40 Zo versus Time of Day for Region 3 104
4.41 Lateral Turbulence Intensity at 33 ft versus Time of Day for Region 3 105
4.42 Zo versus Time of Day for Region 4 106
4.43 Zo versus Time of Day for Region 5 107
4.44 Iv at 33 ft versus Time of Day for Region 5 108
4.45 Zo versus Time of Year for Region 1 110
Xlll
4.46 Zo versus Time of Year for Region 2 Il l
4.47 Zo versus Time ofYear for Region 3 112
4.48 Zo versus Time ofYear for Region 4 113
4.49 ZQ versus Time ofYear for Region 5 114
D. 1 a versus Sector 134
D.2 Zo versus Sector 134
D.3 u* versus Sector 135
D.4 u«33 versus Sector 135
D.5 Iui3 versus Sector 136
E. 1 a versus Stationarity 138
E.2 Zoversus Stationarity 138
E.3 u* versus Stationarity 139
E.4 u*33 versus Stationarity 139
E.5 Station versus ZQ for Region 1 140
E.6 Station versus Zo for Region 2 140
E.7 Station versus ZQ for Region 3 141
E.8 Station versus ZQ for Region 4 141
E.9 Station versus Zo for Region 5 142
F. 1 a versus Time ofYear 144
F.2 Zo versus Time ofYear 144
XIV
F.3 u* versus Time ofYear 145
F.4 u*33 versus Time ofYear 145
F.5 Lateral Turbulence Intensity at 13 ft versus Time ofYear 146
F.6 Longitudinal Turbulence Intensity at 13 ft versus Time ofYear 146
XV
LIST OF SYMBOLS
C A constant
hi Height, ft at time i
Iu,v,w Longitudinal, lateral, or vertical turbulence intensity
k von-Karman constant
kd Surface drag coefficient
n Sample size
rms Root mean square = standard deviation of the data
s Standard deviation
u Fluctuating component of the longitudinal wind speed
U Mean wind speed in the longitudinal direction
u* Shear velocity
u»8 Shear velocity at 8 ft based on the u-w correlation
u»33 Shear velocity at 33 ft based on the u-w correlation
IJ^ Mean wind speed at height zi
U^ Mean wind speed at height Z2
U(z) Typical wind speed at height z above the ground
V^ Mean wind speed at time i
Xi Observation at time i
x" Mean value
XVI
w Fluctuating component in the lateral wind speed
z Height above the surface
Zo Surface roughness length
zi Standard reference height at 10 m
a Alpha
Standard deviation o f longitudinal, lateral, or vertical wind speed
Ou Standard deviation o f wind speed
p Air density
T Surface stress
»u,v,w
XVll
CHAPTER I
INTRODUCTION
Describing and predicting wind induced loads on buildings are the primary
missions in wind engineering. The vast majority of this work is performed in wind tunnels
using scale models where researchers have positive control over the wind environment.
To measure meaningful wind-induced pressures on the model, wind tunnel researchers
must match, with appropriate scaling, the wind flow characteristics expected in the field.
The characteristics of the wind which influence mean and fluctuating wind loads on
a building include the mean velocity profile and its associated turbulence. The mean
velocity profile is described by the log law or the power law. Turbulence in the wind is
commonly described by spectra, integral scales of turbulence, and turbulence intensities.
Reliable results in the wind tunnel are only possible when the wind flow is properly
simulated.
Currently, wind tunnel technology for low-rise buildings is not fully developed.
The pressure coefficients obtained from the wind tunnel are not completely representative
of pressures measured in the field for several reasons. Among these are: Reynolds number
effects, sampling frequency of pressures on the models, and inadequate simulation of the
wind characteristics near the ground.
The need for better understanding of the wind effects on low-rise buildings has led
to a research project on a fiill-scale field facility at Texas Tech University. The project,
sponsored by the National Science Foundation, acquires wind characteristics and
associated wind-induced pressures on a full scale low-rise building. Figure 1.1 shows the
Wind Engineering Research Field Laboratory (WERFL) and the surrounding terrain.
WERFL consists of a 30 ft x 45 ft x 13 ft high metal building and a 160 ft high
meteorological tower. Instruments for wind speed, wind direction, temperature, relative
humidity, and barometric pressure, are installed at various levels of the tower. Wind-
induced pressures on the surface of the buildmg are measured with differential pressure
transducers.
WERFL wind data is used to assess wind characteristics at the site. Chok (1988)
has reported the site characteristics at WERFL, however, his analysis is based on a limited
number of data records. Factors which can afifect the flow characteristics such as mean
wind speed; wind speed and wind direction stationarity; storm type; time of year; and
time of day were not considered in this characterization. A complete understanding of the
approach flow and the factors that affect it is required to correctly interpret the wind
pressure data collected at WERFL.
Figure 1.1. Field site and surrounding terrain.
1.1 Objectives
The objective of this study is to investigate the characteristics of the wind flow at
WERFL m light of the factors which may affect the wind flow parameters. The
characteristics of the wind flow which are investigated include the roughness length, the
shear velocity, the power law exponent, and the turbulence intensities. The factors which
can affect these flow parameters are the mean wind direction, mean wind speed, wind
speed and direction stationarity, storm type, time of day, and time of year.
The scope of this study is limited to Mode 15 data collected at WERFL. The
collection of Mode 15 data began in April of 1991 and was completed in June of 1992
with 465 records collected. This study will also incorporate other WERFL research on
integral scales (Lui, 1994) and spectra (Thomas, 1991) for completeness.
The following chapter contains a brief review of the existing knowledge about
mean flow models and turbulence. A detailed discussion of the data, the collection
system, the validation process, and a description of the database are presented in Chapter
ni. The data analysis and resuhs are presented in Chapter TV. Chapter V gives the
conclusions of this study. The appendices contain supporting information related to the
study.
CHAPTER n
LITERATURE REVIEW
As the wind blows over the surface of the earth a turbulent boundary layer is
developed. This boundary layer is called the atmospheric boundary layer. In the boundary
layer the mean wind speed varies with height. The variation of the mean wind speed with
height is termed the wind profile. The depth of the boundary layer and the wind profile
are functions of the surface roughness. Figure 2.1 shows the variation of wind speed with
height for flow over different terrain roughness. Two models are commonly used to
represent the wind profile: the power law and the logarithmic law. These models are
discussed in Section 2.1.
Figure 2.2 shows wind speed time histories collected simultaneously at different
heights for wind flow over an open terrain. Inspection of these tune histories shows that
in addition to the variation of mean wind speed with height there are fluctuations about the
mean. These fluctuations about the mean wind speed are interpreted as turbulence.
Turbulent flow is strongly rotational, three dimensional, chaotic, and apparently random in
both space and time (Kancharia, 1987).
The generation of atmospheric turbulence is a complicated process. The fiictional
drag of the earth's surface and any protruding bodies cause a reduction in the wind
velocity. The fiictional forces at the earth's surface are transmitted through the boundary
layer by shear forces and the exchange of momentum. The exchange of momentum leads
a E d UJ UJ a. </)
o z
o o m
o o o o o
ex E
< a: or I I I h-
7 UJ
n o h-<
1 M.
UJ o < u. a: CO
cr U I H-< ^
J C
b O o>
lO
o. E
>
be
y 8;
-§) '53 a:
I S
o
cd o
o. E
.c o. E a.
E
II
8 4>
o o o o lO ""t ro CM
qdui *p9dds
4>
o
o o o • ^ fO eg
qdui "poads
o o o o o o o o "<t n eg T-
i(dui "pood
o o o n eg T-
qdui "poods
JC
o. £
1 I
m
O
I a. c
<N
NO
<N
O O O 00
O vO
(y) iqSBH
lenc to the generation and decay of eddies termed atmospheric turbulence. Atmosph(
turbulence is three dimensional, with a horizontal, vertical, and transverse component.
Naturally occurring turbulence in the ABL has turbulent eddies in the range in the
order of a milluneter to several kilometers is size (Simiu and Scanlan, 1986). There are
two types of eddies: convectional and mechanical. Convectional eddies are created by the
vertical temperature changes in the atmosphere. Mechanical eddies are created by the
fiiction of the earth's surface on the wind. Mechanical turbulence tends to decreases with
height and the convective turbulence gains importance with height for any combination of
ground roughness and wind speed (Tieleman and Mullins, 1979). For this project,
convective turbulence is neglected since data with 15-minute average mean wind speed
below 13.0 mph at 13 ft are not used (Maloney, 1994).
Turbulence exhibits the following properties: nonlinearity, mixing ability, and
diffusive power (Kancharia, 1987). In some instances turbulence has the following special
characteristics: homogeneity which implies that the turbulence statistics do not vary in
space; stationarity which implies that the statistical properties of the turbulence does not
change with time; and isotropy which implies that the statistics of the turbulence are
invariant to changes in directions of the coordinates (Kancharia, 1987). In this study,
homogeneity of the turbulence within a 15-minute data run is assumed. Isotropy and the
effects of stationarity are investigated.
8
In a three-dimensional turbulent flow the properties are a random function of space
and time. There tends to be a correlation between turbulence measured at a point at
different time intervals and between turbulence components measured at two different
pomts in space. The correlation decreases as the time lag or separation distance between
the two points increases. Since the properties are random functions it is necessary to use
statistics to describe the turbulence characteristics. The most common statistics used to
characterize the wind flow are: turbulence intensity, integral scales of turbulence, and
spectra. These topics are discussed in Sections 2.2.1 through 2.2.3, respectively.
Wind profile and turbulence characteristics measured in the field may be affected
by the mean wind direction (if the terrain is nonhomogeneous), the mean wind speed, wind
speed and dkection stationarity, the time of day, the time of year, and storm types. The
effects of these factors on the wind profile parameters and the turbulence intensities are
discussed in Section 2.3.
2.1 Mean Wind Speed Models
For engineering purposes (which implies neutral stability of the atmosphere) the
mean wind speed profile is usually represented by the power law and/or the logarithmic
law (ESDU, 1981). The power law and the logarithmic law for the case of neutral
atmospheric stability are discussed in Sections 2.1.1 and 2.1.2, respectively.
2.1.1 Power Law
The power law represents the wind profile over a horizontally homogeneous
terrain. It is an en^irical equation widely used by engineers because of its simplicity. The
power law relates the wind speed at two different heights as (Simiu and Scanlan, 1986): ••Itt^T
(2.1) ^1
x^iJ
where:
t/j = mean wind speed at height zi;
C/2 = mean wind speed at height Z2; and,
a = power law exponent.
The power law contains a single model parameter, a, termed the power law exponent.
The power law exponent is dependent on ground surfece roughness and averaging time
(Chok, 1988). When using the power law it is assumed that: (1) a is constant up to the
gradient height; and, (2) the gradient height is a function of a (Davenport, 1965).
The power law exponent is obtained by linear regression of the natural log of the
height and the natural log of the wind speed. Figure 2.3 shows a typical wind speed
profile obtained at WERFL with the power law regression line superimposed. As seen in
Figure 2.3, the power law exponent is the slope of the regression line. Thus a is given by:
10
\
CO
JC
a.
a. CO
m .S
c
o crj
SO * n Tj- r* rsl'
(y *iq«»H)ui
00
O
O
11
^ ( n \
i '=1 \i=\ J\i:i J
a 2 / „ N 2 (2.2)
a = 0.144 (for Run M15N025)
Table 2.1 gives the power law exponents for the four terrain categories used in
various national codes. Inspection of the values in this table indicate the power law
exponent is dependent upon the roughness of the terrain and averaging time. The
exponent increases with increases in terrain roughness and in averaging time. Table 2.2
provides the power law exponents for the Wind Engineering Research Field Laboratory
(WERFL) (Chok, 1988). These 15-minute average a values are comparable to open
terrain power law exponents in the ANSI Standard and NRCC Code.
Table 2.1 Power Law Exponents in Different Codes
Terrain Category
Big City Centers Urban, Suburban Areas Open Terrain Flat Unobstructed Coastal Areas
a 3-sec gust speed h Fastest-mile vmd speed c Mean-hourly wind speed
Australian Codea
(SAA, 1983) 0.20 0.14 0.09 0.07
ANSI Standard^
(ANSI, 1982) 0.33 0.22 0.14 0.10
Canadian Codec
(NRCC, 1980) 0.36 0.25 0.14
• • •
12
Table 2.2 Average Wind Profile Parameter Values (Chok, 1988)
a
0.137* (0.10-0.17) V
0.041 (0.002-0.124)
u« (mph) 1.643
(1.21-2.11) * Average value
V Range of minimum to maximum
2.1.2 Logarithmic Law
The logarithmic law (log law) is developed from physical laws. It is widely
accepted by meteorologists. For neutrally stable atmospheric conditions, the log law is
given by (Simiu, 1973):
k In
^z^
y^oJ (2.3)
where:
U(Z) = typical wind speed at height Z above the ground;
u* = shear velocity;
k = von-Karman constant;
z = height above the surface; and,
Zo = roughness length.
13
The shear velocity is defined for homogeneous terrain as u. = I— evaluated
with surface stress, T and air density, p. The u* value is the average value over the
height range where the wind speed is measured. The value of the von Karman constant, k
is not agreed upon. Tennekes (1973) recommended that the k value be 0.35 + 0.02 for
smooth terrain. Schotz and Panofsky (1980) suggest that k be 0.35 for smooth terrain.
The classical k value is assumed to be 0.4. For this study, the classical k value was used
to calculate the shear velocity.
The roughness length, zo , is a measure of the retarding effect that the surface has
on the wind speed near the ground (ESDU, 1981). It is determined empirically and is a
function of the nature, height, and distribution of the roughness elements. For this project
Zo is obtained experimentally. Figure 2.4 gives typical roughness lengths over uniform
terrain. The values listed in this figure are intended for use in structural engineering
calculations.
The log law provides a good description of the wind profile up to an elevation of
30-50 m (Simiu and Scanlan, 1986) and is a good representation of the wind profile in a
horizontally homogeneous surface (Suniu, 1973). It is suggested by Garratt (1978) that
the logarithmic law in no longer valid at heights < IOZQ, since conditions below this height
are not horizontally homogeneous because of the effects of individual roughness elements.
14
TeffOin <)escription
y n„Qif,4 Kiiit UHCU ( « = M 7 I )
10-
}
2 -
C«f>l'«t • ( l«r«« lownt. (•i>«t
C«nU«« of HMOli town*
S«tu«b«
Many lr««(, Md««t . f«« buildingi
F«« lrM«, Mnwi«r t in*
toolaUd ITM*
F«r«tU
foirlr itvtl aoedad CAuotff
>- f«rmlond
Z o m a x = 0 . 1 2 4
-B" I 7
i^ = 0.041 t ^ nrar^
L««g«>«(« («0'(M«i)c#«p«
r«« l *Mt , mntor I
CMtfTM* (vO-OSai)
N«U)«I *«•« Mfff CM (foimlond)
> Foirlf l»««l f r « M ptaiM
21-
10
Zo„.n = 0.002 '
K)
Alrpofta ( f — a i araa)
> L«r«* »»»aMii cT aalar ( • • • E q u i n a ( t . l ) )
( M l )
OMai • » • • M«
d(m)
Ii «• 2 3
AU 10
O U 2
? 4 •
Id'
! • » « - <«««««4 f t«U«
t M . • « « nau
Figure 2.4 Surface Roughness parameters and Field Site Parameters
(ESDU, 1981 and Chok, 1988)
IS
o
00 og
JZ
^ 6
<U
CO
c
<N 5
o
oo
t o vo o ^
f
O
:z:
O
Urn
e cd
00
o vr> C M
<L> Urn
00
16
The log law contains two parameters: the shear velocity and the roughness length.
These two parameters are obtained by linear regression of the natural log of height and the
wind speed. As shown in Figure 2.5, the roughness length is the y-intercept of the
regression line and the shear velocity is obtained from the slope of the regression line. The
roughness length is computed using the expression:
Vln/2.
2o = exp n
n
1 ^^'
2.5w, n (2.4)
z = 0.016 ft (for Run M15N025)
and the shear velocity computed using:
u,=
ni(vj(inh,)-(|:F,)(i:in/,, J
"Slf ) -\i^^' 1=1 1=1 y
-1 (2.5)
*0.4
u» = 1.301 mph (for Run M15N025)
where the variables are as defined above.
17
Table 2.2 provides a list of ZQ and u* values from the initial WERFL site
characterization (Chok, 1988). The ZQ values computed by Chok are superimposed on the
ESDU (1981) values given in Figure 2.4 for comparison purposes.
2.2 Turbulence Models
Turbulence in the wind is typically characterized by turbulence intensities, integral
scales of turbulence, and spectra. Integral scales of turbulence and spectra are beyond the
scope of this work. However, results from previous investigations of these topics using
WERFL data are presented to aid the reader. Turbulence intensity, integral scales, and
spectra are discussed in Sections 2.2.1 through 2.2.3, respectively.
2.2.1 Turbulence Intensity
Turbulence intensity is the most commonly used parameter to quantify turbulence
in the wind. Turbulence intensity is defined as the standard deviation of the longitudinal
(u(t)), lateral (v(t)), or vertical (w(t)) wind speed normalized by the mean longitudinal
component of the wind. It is expressed as:
/ - ?^^ (2.6)
I ^^ = longitudinal, lateral, or vertical turbulence intensity;
a = standard deviation of longitudinal, lateral, or vertical wind speed; and,
U = mean wind speed in the longitudinal direction.
18
The value of the turbulence intensity decreases with height since the standard deviation of
the wind speed decreases with height while the mean wind speed increases with height.
Turbulence intensity can be estimated for a site using several different empirical
equations. These equations estimate the turbulence intensity at a given height using the
wind profile parameters (Lumley and Panofsky, 1964; Davenport, 1961a, 1961b). The
equations were developed for engineering purposes.
The log law equation can be modified by replacing u» with o^ / C (Lumley and
Panofsky, 1964). The suggested C value is 2.5. Making this substitution the equation
becomes:
^(^)=S (2.7)
where:
o = The standard deviation of wind speed;
k = von-Karman constant;
z = Height above the surface;
ZQ = Roughness length; and
C = a constant.
19
Using Equation 2.7, turbulence intensity can be computed as:
U(z) \ = l=Ck 1 fz^
In —
(2.8)
Davenport (1961b) developed a turbulence intensity equation based on the theory
that fiiction velocity is proportional to the mean wind speed at a fixed height of 10
The equation is written as:
m.
/ . . = _ 2 .45V^
^ ^ -
V ,.
(2.6)
where:
z = Height above the surface;
Zj = Standard reference height of 10 m;
kj = Surface drag coefficient; and
a = Power law coefficient.
Davenport, (1977) recommends that k values of 0.005, 0.015, and 0.05 and a values of
0.16 for open terrain, 0.28 for suburban terrain, and 0.40 for built-up terrain.
20
As shown above, turbulence intensity can be obtained from measuremem using
Equation 2.3 and from empirical models using the wind speed profile parameters using
Equations 2.5 and 2.6. Table 2.3 provides a list of average turbulence imensity values
obtained from the mitial WERFL site characterization (Chok, 1988). The mean and range
of the WERFL turbulence intensities obtained by Chok are plotted in Figure 2.6 along
with the empirical expressions given by Equations 2.6 and 2.8 for comparison purposes.
For Equation 2.8 a site average zo value of 0.15 was used to determine the turbulence
intensity. A kd value of 0.005 and a value of 0.16 were used to calculate the turbulence
intensity using Equation 2.6. This plot indicates that the empirical expressions provide
reasonable models for the WERFL data.
Table 2.3 Average Longitudinal Turbulence Intensity Values (Chok, 1988)
13 ft Turbulence Intensity 33 ft 70 ft 160 ft
0.185* (0.17-0.22)^
0.172 (0.15-0.20)
0.154 (0.12-0.18)
0.136 (0.11-0.16)
* Average value of 31 15-minute records V Range of minimum to maximum
21
Height, ft
Turbulence Intensity based on:
1 - Lumley and Panofsky (1964) 2 - Davenport (1961a, 1961b) 3-Chok(1988)
Minimum-Average-Maximum
0.25 0.30
Turbulence Intensity 0.35 0.40 0.45
Figure 2.6 Turbulence Intensity
2.2.2 Integral Scale of Turbulence
Integral scales of turbulence are measures of the average size of turbulence eddies
(Simiu and Scanlan, 1986). They are an important scaling factors in determining how
rapidly gust properties vary in space. Similarly, the time scales characterize the average
duration of the effects of a gust at a point. The integral length scales are determined by
integrating the appropriate space or autocorrelation functions.
22
There are three integral length scales of turbulence, corresponding to the three
dimensions of the eddies (longitudinal, lateral, and vertical) associated with the
longitudinal wind. The lateral and vertical integral scales of turbulence are approximately
one-third and one-half the longitudinal integral scale.
The integral scales of turbulence display a large degree of variability. The
variability is a result of the dependence of the integral scales of turbulence on the
atmospheric stability condition, height above the ground, and the terrain characteristics.
The integral scales tend to increase with height and wind speed and decrease with surface
roughness. In general, the sizes of the integral scale of turbulence increases with smoother
terrain and height above the ground. The length scale increases asymptotically at gradient
height. Integral scales also decrease slightly with increasing atmospheric stability (Moore,
1985).
Four different methods for evaluating the longitudinal integral scale of turbulence
are commonly used by researchers. The methods are:
1. The direction integration of the autocorrelation fiinction method (Teunissen,
1979).
2. The spectral method, which used the frequency at which the power spectrum is
at its maximum (Teunissen, 1979).
3. The exponential fiinction method (Teunissen, 1979).
4. The direction integration of a best fit fiinction method (Mackey and Lo, 1975).
The best fit function is an exponential function.
23
Different values of longitudinal integral scale of turbulence at 33 ft computed using
different methods by several investigators are shown in Table 2.4 (Chok, 1988). The
different terrain and the different computational methods provide a wide variation of
integral scale values. Table 2.5 provides average longitudinal integral scales obtained
from the initial WERFL site characterization (Chok, 1988).
Table 2.4 Longitudinal Integral Scale of Turbulence at 33 ft (Chok, 1988)
Reference Choi (1978) Duchene-Marullaz (1975) ESDU" (1975) Mackey & Lo " (1975) Sethuraman (1979) Shiotani & Iwatani " (1979)
Teunissen (1979)
Terrain Coastal Area Suburban
Flat& Open Sea
Sea
Sea Flat& Open Flat& Open
Method 1 • • •
75 m
70 m
116m
195 m 135 m
130 m
Method 2 . . .
62 m
Method 3 . . .
. . .
124 m
Method 4 190 m*
210m
Typhoon wind. * From longitudinal integral scale of turbulence model.
24
Table 2.5 Longitudinal Integral Scale of Turbulence Values at WERFL (Chok, 1988)
13 ft Height Above Ground 33 ft 70 ft 160 ft
338* (125-662)^
477 (179-843)
623 (278-1015)
* Average value, ft. V Range of minimum to maximum , ft.
876 (266-1480)
Additional investigations of the integral scales at the WERFL site have been
reported by Lui (1994). In this investigation integral scales of turbulence were
investigated using the correlation integral technique and the exponential fit technique
discussed above. Two sets of records were collected for the investigation. Group 1 was
collected with winds generally from the azimuth angle of 176 degrees, the Group 2 had an
average azimuth angle of approximately 298 degrees. The sample sizes for Group 1 and
Group 2 were 3 and 21, respectively. The average roughness lengths for the two data
groups was 0.01 ft and 0.02 ft for Group 1 and Group 2, respectively. Longitudinal,
lateral and vertical integral scales for Group 1 data computed using the correlation integral
and the exponemial fit techniques are given in Table 2.6. Longitudinal and lateral integral
scales for Group 2 data are given in Table 2.7.
25
Table 2.6 Longitudinal and Lateral Integral Scales for Data Group 1 (Lui, 1994)
Statistic
Maximum Minimum Average
Standard Deviation
Wind Direction^ (degrees)
181.50 169.70 176.30 3.88
Wind Speed^ (mph)
20.10 16.20 17.90 1.32
''U' (ft)
510 172 357 113
X^ (ft)
383 151 249 82
'U' (ft)
11 48 60 10
^ '
(ft)
37 20 28 9
Wind direction at 13 ft ^ 15-minute mean wind speed at 13 ft
Longitudinal integral scale at 13 ft using correlation integral technique * Longitudinal integral scale at 13 ft using exponential fit technique
Lateral integral scale at 13 ft using exponential fit technique Vertical integral scale at 13 ft using exponential fit technique
Table 2.7 Longitudinal and Lateral Integral Scales for Data Group 2 (Lui, 1994)
Statistic
Maximum Minimum Average
Standard Deviation
Wind Direction* (degrees)
319.1 284.9 298.0
9.5
Wind Speed^ (mph)
26.3 17.7 21.6
2.5
"U' (ft)
819 191 501 149
""U' (ft)
781 142 409 143
'U' (ft)
111 37 74 23
'U' (ft)
63 30 48 10
Wind direction at 13 ft ^ 15-minute mean wind speed at 13 ft ^Longitudinal integral scale at 13 ft using correlation integral technique "^ Longitudinal integral scale at 13 ft using exponential fit technique ^ Lateral integral scale at 13 ft using exponential fit technique ^ Vertical integral scale at 13 ft using exponential fit technique
26
A comparison of the results obtained by Chok and Lui listed in Tables 2.8 for the
longitudinal integral scales at 13 ft showed that the different methods used are
comparable. The correlation mtegral technique provided the widest range of values. Lui's
results using the exponential fit technique and Chok's results are similar for Group 1 and
Group 2 data.
Table 2.8 Comparison of the Results Obtained by Chok and Lui
Data (Azimuth Angle)
Chok, 1988 160°-210° Lui, 1994 Group 1
(169.7°-181.5°)
Chok, 1988 270°-70° Lui, 1994 Group 2
(284.9°-319.1°)
Integral Scale
""U
"Lu
""U' V V V
Average
274
357 249 60 28
324
501 409 74 48
Maximum
304
510 383 77 37
647
819 781 111 63
Minimum
256
172 151 48 20
125
191 142 37 30
* Longitudinal integral scale at 13 ft using correlation integral technique ^ Longitudinal integral scale at 13 ft using exponential fit technique ^ Lateral integral scale at 13 ft using exponential fit technique * Vertical integral scale at 13 ft using exponential fit technique
27
2.2.3 Power Spectra
Wind tunnel modeling of the turbulence should not only include the simulation of
the distribution of the turbulence intensities, but also the duplication of the spectral
densities (Tieleman, 1991). For high wave number ranges, the spectral densities vary with
wave number, dissipation, and viscosity. The gain of turbulent energy from the mean flow
governs the energy-containing range. Tieleman (1991) compares the different spectrum
models. This comparison is reproduced in Figure 2.7. This figure shows an observed u-
spectrum from Boulder Atmospheric Observatory (BAO) with the Tieleman blunt spectral
models representing flat, smooth, uniform terrain and slightly perturbed terrain and the
Kaimal and Davenport spectrum. Further theoretical aspects of the power spectrum is
beyond the scope of this project.
Thomas et al. (1993) has compared longitudinal and lateral spectra obtained at
WERFL with those obtained in the Colorado State University wind tunnel. Figure 2.8-
2.10 provide the comparison of the longitudinal and lateral spectra. A good agreement
between the longitudinal spectra is observed. The lateral velocity spectra at the roof
height shows a deficit in lateral turbulence in the wind tunnel.
2 3 Effects of Factors on Wind Profile Parameters and Turbulence Statistics
The factors (mean wind direction, mean wind speed, stationarity, storm type, time
of day, and time of year) have specific effects on the WERFL wind profile parameters and
turbulence statistics. Each parameter and the turbulence statistics can be changed by a
single factor or a combination of factors. For this project, the only combination of factors
investigated were the flow regions (azimuth angle) in conjunction with either mean wind
speed, stationarity, storm type, time of day, or time of year. The flow regions are
discussed in Section 4.2.
28
o o
o
I
o
I
CO
I
o o
o
I
I
0^ I
-o c (/) a> C o orj <u <—< cd
CJ c
t 00
c c O) C/3 4>
a .
OC
o
cd «<-i i :
(2-*n/(")nsu)3oi
o o. or) ••-• c
•5 a H
a. C/5
0
O
o c o (A
•c to a. E o U <N 4> (-•
%
29
<N
V3
a
CO
c
0.001
0.01
O.OOOOl 0.0001
" nz/U [cycles]
— 1:100 RII @ CSU _^ Full Scale (M15N545) 2 ( m | is robr height. U |niA| b »xlocity >i z and o h frojoency [HzJ.
Figure 2.8 Longitudinal Velocity Spectra at Roof Height (Thomas, 1993)
I •—• a i
<
aooi CO c
0.0001
.L
/ f ^ v ^ t / i l ^
/
f Q f i ^ f P
likiter ^lv"vrJy
v :
oixxni 0.0001 nz/U [cycles] 10
1:100 RII @ CSU _^ Full Scale (M15N545) With Random B b d c MoUoa; z (mj b roof hei(bi, U {mh\ b vclociiy ai z and n b ttcqutacj (Hz]
Figure 2 9 Lateral Velocity Spectra at Roof Height (with random blade motion) (Thomas, 1993)
30
0 1
<
to
E 001
00 OUJI
0 0001 000001 0.0001 aooi T r °^* 1 ®-*
nz/U [cycles] 1:100 RU @ CSU _^ Full Scale (M15N545)
No BUdc Moi ion; z |n i | is roof height, U |m/s| B velocity al Z and n b (rcqueiKy (Hz]
Figure 2.10 Lateral Velocity Spectra at Roof Height (no blade motion) (Thomas, 1993)
31
The flow regions are defined by the surrounding terrain. The different terrains
have distinctive surface roughness and thus unique surface roughness lengths (z ). The
rougher the terrain the higher the ZQ value. The different terrains also affect a which,
increases as the surface roughness increases.
The 15-minute duration mean wind speed is used to calculate the flow parameters
and turbulence statistics. The mean wind speed can experience extreme changes
associated v th different storm types. The surface roughness decreases with increasing
mean wind speed (ESDU, 1991). Higher wind speeds have the opposite effect on a and
u,, they increase with increasing wind speeds. Turbulence statistics are controlled by the
standard deviation of either the longitudinal, lateral, or vertical wind speed and the mean
wind speed in the along-wind direction.
Atmospheric conditions, classified as storm types, can affect the mean wind speed
and standard deviation of the wind speed, these factors in turn affect the wind flow
parameters and turbulence statistics.
The heating and cooling trends of the day can have an effect on the turbulence
statistics. The time of day at which a record was collected can be an important factor.
Convective turbulence is created by the heating of the earth's surface and affects the
turbulence statistics. Convective turbulence is however, neglected for this project
(Maloney, 1994) since mean 15-mmute wind speeds below 13 mph at the 33 ft height are
not used.
During the fall and winter the surface roughness will decrease because of the lack
vegetation surrounding WERFL. Thus the time of year affects the surface roughness and
in turn the turbulence statistics. The surface roughness and the mechanical turbulence is
affected by the time of year based on seasonal terrain characteristics.
32
ClL\PTERin
DATA COLLECTION
In an attempt to obtain reliable wind load data, researchers at Texas Tech
University have constructed a permanent laboratory to measure wind effects on structures
in the field (Levitan, 1989). The Wmd Engineering Research Field Laboratory (WERFL)
consist of a one-story experimental building and a 160 ft. meteorological tower located in
Lubbock, Texas. WERFL is located two miles from the main campus of Texas Tech
University. The site tends to experience strong winds at different times throughout the
year. The WERFL building and pressure measuring system reference is discussed below,
fiirther details are given by Levitan and Mehta (1991a, 1991b).
3.1 Data Acquisition System
The WERFL data acquisition system consist of a micro-computer with an analog
to digital (A/D) converter. In data acquisition mode 15, which includes the data for this
work, an 80386-based PC (with 8 MB RAM and math co-processor) with an internal 20
megabyte hard drive was used to collect the data (the system has been periodically
upgraded since this data was collected. As of the spring of 1995, the system uses a
Pentium 60 to collect the data). The PC is enhanced with a 12 MHz 80286 accelerator
card with a math co-processor. A MetraByte DAS-8 high speed A/D converter converts
the analog vohages, from the instruments, to digital form. The DAS-8 has a continuous
over-voltage of ±30 volts without damage, and an input range of ±5 volts. Four
MetraByte EXP-16 expansion submultiplexers used in conjunction with the DAS-8
handles 64 individual input channels (expandable to 128 channels). The EXP-16 provides
33
signal amplification, filtering, and conditioning. It is important to note that the computer
equipment has since been upgraded.
A software package called Labtech Notebook controls the data acquisition system.
The software features a real-time display of incoming data and elaborate triggering
mechanisms. The system also allows for different channels to be set up with different
characteristics. When wind speeds reach a preset threshold level Labtech will trigger
automatically. The standard setup calls for 36 channels sampling each at 10 Hz, for a
continuous period of 15 minutes. The system can record data at a rate upward of 3600
samples per second. Due to the enormous amount of data, the data is copied from the
internal hard drive to a 600 MB erasable optical cartridge drive. The optical cartridge is
transported to the Wmd Engineering offices on the Texas Tech campus where the data is
processed, plotted, and stored for fiiture analysis.
Wind speed is monitored continuously and the system triggers automatically when
the one-minute mean speed (at the building roof height) exceeds a preset threshold value,
typically, 20 mph. Once the system is triggered a 20 sec pretest calibration run for
transducer zero drift is performed. After the transducer zero drift run, the primary
acquisition program acquires data for a 15-minute duration. Upon completion of the 15-
minute run, a post-test zero calibration run is performed and the triggering program is
restarted.
34
3.2 Meteorological Instrumentation and Tower
The Mode 15 meteorological instrumentation includes: sbc wind speed
anemometers, two wind direction vanes, two temperature sensors, a relative humidity
sensor, and a barometric pressure sensor. The instrumentation is mounted on a 160-ft,
three-legged truss tower. The tower is located 150 ft west of the test building. The
instruments are installed a sk levels: 3, 8, 13, 33, 70,160 ft.
There are two different types of R. M. Young anemometers in use, three-cup and
UVW. The Gill 3-cup anemometers, model 12102, are located at the 3, 13, 70, 160 ft
levels. These anemometers produce an analog output voltage proportional to the wind
speed. They have a maximum range of 112 mph and a 8.9 ft distance constant. An
additional 3-cup anemometer is placed at the top of a 13-ft pole located halfway between
the tower and the field site building. This instrument allows for redundancy of wind speed
measurement at the roof height of the building.
Two Gill Micro-vanes, model 12304, are located at 13 and 160 ft levels. For the
wind direction sensors the rated delay distance is 3.6 ft. Two three-component
anemometers Gill UVW, model 27005, are installed at 8 and 33 ft levels.
The UVW anemometers have an optional carbon fiber thermoplastic propeller.
Model 08254. These have a maximum range rated at 90 mph and have a distance constant
of 6.9 ft. The orientations of the UVW anemometers is not uniform. The instruments are
placed so that the U component anemometer points toward the northeast, the V
component anemometer points toward the northwest, and the W component anemometer
point upward. Figure 3.1 shows the orientation of the UVW anemometer. The 33 ft level
anemometer is oriented so that V and W components are tilted at 35° from the vertical
axis The UVW at 33 ft was titled for the entire Mode 15 data collection according to the
Mode 15 Daily Log. This placement results in a more accurate measurement of the
35
Figure 3.1 Orientation of the UVW Anemometers (Maloney, 1994)
36
vertical wind speed by having part of the vertical component measured by two different
instruments. When the vertical wind speed is measured by a single anemometer pointed
upward, errors can result due to the inertia of the propeller when the vertical wind
switches direction.
The additional meteorological instrumentation is provided by Teledyne
Geotech. Thebarometricpressureisrecordedby a model BP-100 sensor. The
rated resolution for the BP-lOO is 0.01 in Hg. The temperature readings are
recorded at a sampling rate of 10 Hz. A model RH-200 sensor is used to measure
the relative humidity. A platinum temperature sensor is built into the RH-200,
which is rated ±0.2°F. The temperature, barometric pressure, and relative
humidity sensors are mounted at the 13 ft level of the tower. A temperature
sensor is also mounted at the top of the tower.
In order to reduce the towers interference with the wind measurements, the
anemometers are mounted on 6-ft booms, see Figure 3.2. The booms are oriented to the
west northwest, 300° azimuth. The winds from the north, west, and south have a clear
approach to the instrumentation. Tower interference is expected to occur within the range
of 80° - 160°. Since, most extreme winds come from the north, west, and south in the
Lubbock area, tower interference affects few records.
The instruments and data acquisition system are constantly checked and
maintained in order to insure that the data collected is of the highest quality level. These
checks verify proper operation of the acquisition system and instrumentation. The
equipment is also maintained according to a set schedule.
37
160 ft—I S,D,T
70 ft-
33 ft-
13 ft-
(a)
S,D
S, T, H, P
8 ft- S.D
3f t - | S
N
LEGEND S Wmd Speed D Wind Direction T Temperature H Relative Humidity P Barometric Pressure
Figure 3 2 Meteorological Tower (Chok, 1988)
(a) Instrument Boom
(b) ln.struments on the Tower
^x
3.3 Collected Data
The meteorological data collected on the tower of interest for this thesis are the
15-minute duration wind speed and wind direction time histories. The data is collected at
3, 8, 13, 33, 70, and 160 ft using a 3-cup or UVW anemometer or a wind vane. Detailed
descriptions of the instrumentation and locations of the instruments are provided above.
The wind speed and wind direction time histories are processed to yield
longitudinal, lateral, and vertical components of wind speed. Summary statistics which
include the mean, standard deviation, minimum and maximum values are computed from
the wind speed, wind direction, longitudinal, lateral, and vertical time histories measured
at each elevation. The calculation of these summary statistics are discussed in Section
3.3.1.
In addition to the summary statistics, parameters which describe the wind profile
are computed using the mean speeds at the sbc heights. Shear velocity computed at a
single height is computed directly from the time histories. Turbulence intensity, which is a
measure of the level of turbulence in the wind field, is also computed from the summary
statistics. The procedures used to compute the profile parameters, shear velocity at a
single height, and turbulence intensities are given in Section 3.3.2 through 3.3.4,
respectively.
Stationarity of a time history is examined for each wind speed and wind direction
time history. Stationarity checks used for the data are discussed in Section 3.3.5.
39
3 3 1 Summary Statistics
The summary statistics computed for the wind data, includes the mean, standard
deviation (rms), minimum and maximum values for each time histories The mean is the
expected value of a random variable. The root mean square (rms) is the standard
deviation of the data. The minimum and maximum observations convey information
concerning the amount of variability present in the data. Figure 3.3 shows a time history
of M15N025 at 33 ft with its associated summary statistics.
Speed, mph
40. O-30. O-20 o-^ 1 0. o
\ t ^
0. O 2 0 0 . 400. 600. Time, seconds
800.
F33=25.1 mph
Minimum33 =12.9 mph
Maximum33 = 38.9 mph
rms33= 4.53 mph
Figure 3.3 Time History for M15N025 at 33 ft
The mean wind speed varies with height above the ground and with averaging
time. As the length of the time interval increases the mean wind speed corresponding with
the interval decreases. The averaging time for this project is 15 minutes. The mean is
calculated using:
I-. X -
; = 1 (3.1) / ;
where:
Xj = observation at time i, and
n - sample size (9000 for wind data)
40
Figure 3.3 show the time history at 33 ft for record M15N025 with mean wind speed of
25.1 mph.
The standard deviation is the most generally used measure of variation (Miller,
1990). The rms is used to determine stationarity and turbulence intensity. The rms value
is calculated using:
R Rms = (=1
n - l (3.2)
/
where:
Xi = observation at time i,
X = mean, and
n = sample size.
For the time history shown in Figure 3.3, the rms values is 4.53 mph
3.3.2 Profile Parameters
The profile parameters include a, zo, and u*. The value of a is calculated using
Equation 2.2. This equation is the slope of the regression line of the power law. For
Ml 5N025, a is 0.144. The surface roughness is computed using Equation 2.4. This
equation is the linear regression expression for y-intercept of the linear regression line for
the log law. For M15N025, ZQ is 0.017 ft. Shear velocity is determined using Equation
2.5, which is the linear regression expression for the slope of the regression line from the
log law incorporating the final steps to get u« For M15N025, u* is 1.307 mph.
41
3.3.3 Shear Velocity
Shear velocity is computed using the turbulence observations where u*
is V ^ (Tieleman, 1991). Shear velocity for 8 ft and 33 ft is computed from the u and w
time histories for the WERFL data. Figure 3.4 (a) and (b) illustrate the u and w time
histories for the 33 ft height, u g and u»33 is calculated according to Equation 3.3.
9000
"*=J-^Z^ (3-3)
where:
n = sample size,
u = fluctuating component of the longitudinal wind speed,
w = fluctuating component of the lateral wind speed.
For record Ml5N025: u»g = 0.665 mph and
u«33 = 1.753 mph
3.3.4 Turbulence intensity
The turbulence intensity is the coefficient of variation of the wind speed. It is the
most conmionly used parameter to define turbulence in a time domain. Chapter II gives
detailed discussion of turbulence intensity. Equation 2.6 is used to compute the
turbulence intensity values for the WERFL data, l^^^ uses the mean wind speed in the
longitudinal direction and the standard deviation of the longitudinal, lateral, or vertical
wind speed from the sunmiary statistics. For record M15N028 at 33 ft height the
longitudinal turbulence is 0.209, the lateral turbulence mtensity is 0.177, and the vertical
turbulence is 0.078.
42
I ong i 1 ,,ri i ,?• I.I i r c! speed a' 33 ft ( M P H )
30 OH
0. O 1 00. O 200 C 300 O 400 0 500 O 600. O 700 O BOO 0
Time, seconds
(a)
o / ^ , 0 0 O 200 0 JOO. 0 - • O O ^ 5 0 0 0 6 0 0 O 700 O 6O0 0
Time, seconds
(b)
Figure 3 4 Time Histories for Record M15N025 (a) u-component (b) w-component
43
3.3.5 Stationarity
Stationarity is one of the most important statistics generated. A stationarity check
is run for all levels. A time series is determined to be stationary when its properties are
invariant of time. It is important to assess the stationarity of the time series because
almost all time series analysis procedures in the current practice assume that the data being
analyzed is stationary (Jenkins and Watts, 1968).
There are two stationarity conditions for wind data, stationary and nonstationary.
Wind speed, wind direction, longitudinal, lateral, and vertical time histories at 13 ft are
used to classify the stationarity of a record. Each 15-minute record is divided into 18
intervals for testing. The mean and variance for the 18 sectors is calculated then trend and
reverse arrangement nonparametric tests are performed on both the mean and variance of
the sectors (Levitan, 1993). Table 3.1 shows the number of Mode 15 records for each
wind speed and wind direction stationarity classification.
Table 3.1 Wind Speed and Wind Direction Stationarity
Speed Stationary
Nonstationary
Direction Stationary
226 83
Nonstaionary 101 44
Total Number of Records = 454
3.4 Data Validation
Certainly the single most important task for Texas Tech researchers is that of data
validation and quality assurance (Levitan, 1992). There are three main components: a
daily check of the field laboratory, frequently scheduled instrument calibrations and
maintenance, and analysis of the data collected.
44
The daily check of the field laboratory consist of one of the researchers making a
trip to the field site. The check includes a list of about 20 items. Anything out of the
ordinary is noted in the daily log.
The instrumentation calibration and maintenance is a major item in the quality
assurance program. The anemometers are calibrated and wind tunnel tested at least three
times per year. The bearings in the anemometers are replaced at least once per year. The
calibration of all other meteorological instrumentation is checked once per week.
The validation of the data collected is imperative due to the special nature of the
data collected. The validation is performed in a three step process; the steps are termed
Stage 1, Stage 2, and Stage 3 validation. The validation allows for the early detection of
problems with the instrumentation and data acquisition system. The raw data is processed
by several custom written analysis programs. A preprocessor converts the raw A/D
integer counts into equivalent voltages and then into engineering units. The processing
program provides summary statistics and time history plots for each instrument.
The Stage 1 validation is started once the data is printed and plotted. Stage 1
validation involves checking the following items:
1. Initial zero readings,
2. Summary of zero readings,
3. Multiplexor noise levels,
4. Pressure coefficients,
5. Wind speed data,
6. Wind direction and corrected UVW data,
7. Meteorological and miscellaneous data.
45
The process is usually completed within a month from the time the data was originally
collected.
Stage II validation provides a review of the summary statistics and the time history
plots. This process is based on an understanding of the site, instrumentation, and the flow
characteristics around the WERFL test building. It also is a double check of certain
aspects of the Stage I process and addresses any issues identified during Stage I
validation. Stage II validation involves checking the following items:
1. Re-check the wind direction and computation of wind angle of attack.
2. Address any question noted during Stage I validation.
3. Check for reasonability of pressure coefficient values.
4. Double check the wind direction data.
5. Check the values of the velocity profile parameters.
6. Check reasonableness of meteorological data.
Stage II validation provides a general review and the determination of the final validity of
the data.
Stage III is the final validation step. This process provides a review of all the
collected data. During Stage III the Mode 15 summary statistics and computed values,
discussed in Section 3.3, are imported into Mode 15 Wind Database and Add-On
Database. The database records are edited to remove data identified in Stage I and II
validation as bad. The edited records in the database are plotted and outliers identified.
The records which contain the outliers are pulled and re-examined. Outliers are either
46
deleted or retained based on an examination of the data. With the completion of Stage III
validation process the data is available for further study.
3.5 Mode 15 Database
The Mode 15 Database is assembled from the summary files. The database
contains the following information:
»8
1. Wind Flow Parameters
a. a
b. 2„
c. u*
d. u*s
e. u«33
2. Wind Data at all Levels
3. Meteorological Values
a. Temperature at 13 ft
b. Barometric pressure
c. Relative humidity
d. Air density
4. Stationarity
47
5. Other
a. Lateral displacement of roof purlin
b. Vertical displacement of roof purlin
c. Door sensor
d. Window sensor.
The column locations of the Mode 15 Wind Database information are listed in
Table 3.2. Table 3.3 lists the additional information obtained by the Add-On Database.
A SAS program, M15db.sas, merges the individual databases, by appending the Add-On
Database and the Wind Database, to create a single database. The merged database will
be referred to as Mode 15 Database from this point onward. The Mode 15 Database
contains 465 runs. Appendix A contains the printout of the database.
3.6 Censoring the Mode 15 Database
To further insure that only appropriate data is included in this site characterization
the Mode 15 database was thoroughly inspected and censored. This censoring process
included plotting all Database information with respect to the run number. If a data point
fell outside the norm or typical data it was classified as an outlier. The SAS program
M15db.sas contains a section that identifies the outliers and prints them with respect to
run number and parameter. The hard copies of the records were pulled from the files and
examined by hand. Records were deleted for the following reasons: the instrumentation
was not working correctly, the data that was classified as bad through the validation
48
process, human error allowed the bad data to pass through Stage I and Stage II of the
validation process, and the time history plots showed unusual spikes or time histories that
can not be explained within the scope of this project. The records that were deleted due
to unusual spikes or time histories are classified as "Special Cases" and are marked
accordingly in order to allow for further examination at a later date. The "Special Case"
data has nothing wrong with the data it is just not the typical case. Appendk B Table B. 1
details the deleted records and the specific information that is deleted. If the
instrumentation at a certain height was bad then the data at that height was deleted along
with any values calculated using the bad data. The reasons for deleting a specific height
are the same as those for deleting an entire record.
49
Table 3.2 Mode 15 Wind Summary Database
Information General
Meteorological (Mean, rms. Max., Min., Turb/Range)
General Meteorological (Mean, RMS. Max., Min.)
Column 1 2 3 4 5
6-10
11-15 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70 71-75 76-80 81-85 86-90 91-95 96-100 101-105 106-110
111-114 115-118 119-122 123-126 127-130 131-134 135-138 139-141 142-145
Data Run Number Run Date Run Time Building Position Angle of Attack
Wind Speed at 3 ft (3 cup)
Wind Speed at 8 ft (UVW) Wind Speed at 13 ft from the Pole (3 cup) Wind Speed at 13 ft from the Tower (3 cup) Wind Speed at 33 ft (UVW) Wind Speed at 70 ft (3 cup) Wind Speed at 160 ft (3 cup) Longitudinal Wind at 8 ft (UVW) Longitudinal Wind at 13 ft (3 cup) Longitudinal Wind at 33 ft (UVW) Longitudmal Wind at 160 ft (3 cup) Lateral Wind at 8 ft (UVW) Lateral Wind at 13 ft from the Tower (3 cup) Lateral Wind at 33 ft (UVW) Lateral Wind at 160 ft (3 cup) Vertical Wind at 8 ft (UVW) Vertical Wind at 33 ft (UVW) Wind Direction at 8 ft (UVW) Wind Direction at 13 ft from the Tower (vane) Wind Direction at 33 ft (UVW) Wind at Direction 160 ft (vane)
Temperature at 13 ft Barometric Pressure Relative Humidity Air Density (Slugs/ft^) Air Density (Kg/m^) Lateral Displacement Vertical Displacement Door sensor Window Sensor
50
• " rmtm
Table 3.3 Mode 15 Add-On Database
Information
General
Wind Speed Stationarity
Longitudinal Wind Speed
Lateral Wind Speed
Vertical Wind Speed
Wind Direction
Velocity Profile Parameters
Column
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
25
26
27
28
Data
Run Number EditA^erified Status 3 ft (3 cup) 8 ft (uvw) 13 ft from the Pole (3 cup) 13 ft from the Tower (3 cup) 33 ft (uvw) 70 ft (3 cup) 160 ft (3 cup) 8 ft (uvw) 13 ft from the Tower (3 cup) 33 ft (uvw) 160 ft (3 cup) 8 ft (uvw) 13 ft from the Tower (3 cup) 33 ft (uvw) 160 ft (3 cup) 8 ft (uvw) 33 ft (uvw) 8 ft (uvw) 13 ft from the Tower (vane) 33 ft (uvw) 160 ft (vane)
Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary Stationary
Alpha
Zo
u*
U*8
^*33
51
CHAPTER IV
ANALYSIS AND RESULTS
The objective of this project is the investigation of the effects of the mean wind
direction, mean wmd speed, stationarity, storm type, time of day, and time of year (termed
here as factors) on the power law exponent, shear velocity, roughness length, longitudinal
turbulence intensity and lateral turbulence intensity (referred here as parameters) measured
at the Wind Engineering Research Field Laboratory (WERFL). A total of 465 records of
15-minute duration, collected in the field during the period from April, 1991 to June,
1992, are used for the assessment. Of the 465 records 454 records were used for
statistical analysis. These records contain the typical wind data collected at WERFL,
which is discussed in detail in Chapter HI. The Mode 15 Database used in this analysis,
which contains the 454 records, is provided on disk in ASCII format in Appendix C.
In addition to the summary statistics computed from the field data, several
categorical variables are added to the database for the analysis. These variables include
flow regions, stationarity, speed, storm type, time of day, and month. The added
categorical variables facilitate a complete statistical analysis on the approach flow
parameters and the factors that affect them. The statistical analysis of the data provides a
visual and statistical representation of the WERFL data.
The methodology used for the analysis is based on commonly available and easily
interpretable statistical procedures. Statistical testing to determine if a factor has a
52
significant effect on a flow parameter is accomplished using the commercially available
Statistical Analysis System (SAS) software (SAS, 1990). Analysis procedures include
plotting the data, generating histograms for the parameters, and performing both
parametric and nonparametric tests to detect significant differences in the flow parameters
due to the effects of the various factors.
Visual representation of the data involved producing various types of plots such as
X-Y scatter graphs, box plots, and stem-and-leaf charts. The X-Y scatter graph and box
plot were produced for each parameter and factor or selected combination of factors. X-
Y scatter graphs provided a visual picture of the data distribution. The stem-and-leaf
chart was only used for the initial examination of the wind direction. Stem-and-leaf charts
present the same information as a histogram except the original information is retained.
The box plot effectively portrayed comparisons among sets of observations.
Histograms of the flow parameters were evaluated to determine if the data was
normally distributed. A histogram provides a visual display of the data that conveys an
idea of the shape of the probability density fiinction of the random variable (Miller,
Freund, and Johnson, 1990).
The parametric test used in the data analysis is the Duncan's multiple range test.
Duncan's test is one of the oldest methods for comparing means currently in use (Milton
and Arnold, 1990). The test compares the range of any set of means with an appropriate
least significant range. In this study, a significance level of 0.01 (one percent) is used. The
assumptions underlying the Duncan multiple-range test are (Milton and Arnold, 1990):
53
1. The samples represent independent samples drawn from a specific populations
with unknown means.
2. Each of the populations is normally distributed.
3. Each of the populations has the same variance.
These assumptions are essentially the same as those used in a one-way analysis of variance
that has equal sample sizes. Typically, the data is not normally distributed. Therefore, the
results of this parametric test was not weighed equally with the results of the
nonparametric test.
The nonparametric test used in this work is the Kruskal-Wallis test. The Kruskal-
Wallis test statistic is a function of the ranks of the observations in a combined sample
(Conover, 1980). The following are assumptions made when using the Kruskal-Wallis
test (Conover, 1980):
1. All samples are random samples from their respective populations.
2. In addition to independence within each sample, there is mutual independence
among the various samples.
3. The measurement scale is at least ordinal.
4. Either the population distribution functions are identical, or else some of the
populations tend to yield larger values than other populations do.
54
The Kruskal-Wallis test is a nonparametric alternative to the t-test. The test is sensitive to
differences among means in the sample. Thus, the null hypothesis is stated as (Conover,
1980):
Ho: All of the population distribution functions are identical.
HI: At least one of the populations tends to yield larger observations than at least
one of the other populations.
The WERFL wind data is examined first for the overall site in Section 4.1.
Analysis of the data with respect to mean wind direction is presented in Section 4.2. This
analysis indicates that the site can be subdivided into five regions for further study. The
effects of the mean wind speed, stationarity, storm type, time of day, and time of year on
the flow parameters are investigated for each of these five regions in Sections 4.3 through
4.7, respectively.
4.1 Site Average Flow Parameters
The WERFL field site can be considered to be located in flat, open terrain. As the
first step in the analysis of the data, site average flow characteristics are investigated and
compared with the published results presented in Chapter HI. Site average values for the
power law exponent (a), surface roughness length (zo), shear velocity (u»), the
longitudinal turbulence intensity (lu), and the lateral turbulence intensity (Iv) are given in
Sections 4.1.1 through 4.1.5, respectively. The results of the Kruskal-Wallis testing for
the effects of the factors on the overall site flow characteristics is presented in Section
55
4.1.6. Site average values presented here include both stationary and nonstationary data
from all azimuth angles. Of the 454 records approximately fifty percent are classified as
stationary in both wind speed and wind direction (see Table 3.1). Since both stationary
and nonstationary records used for this analysis, the site average may not be appropriate
for wind turmel modeling purposes.
4.1.1 Power Law Exponent, a
The overall site power law exponent, a, as a function of mean flow direction at 13
ft (azimuth angle) is shown in Figure 4.1. This plot includes both stationary and
nonstationary data. As can be seen in this figure, there is a wide range of a values
measured at WERFL. A histogram of the a values with the associated summary statistics
is shown in Figure 4.2.
A comparison of the Mode 15 WERFL data to the values given in the ANSI
Standard (ANSI, 1982), Canadian Code (NRCC, 1980), and Australian Code (SAA,
1983), and the previous site characterization by Chok (1988) is given in Table 4.1. The
WERFL a values from both Chok (1988) and from this analysis are slightly larger than the
values specified in the codes. Chok's (1988) results are based on only stationary records
that are in neutral stable conditions. However, since the Mode 15 data contains both
stationary and nonstationary data, this may not be a completely accurate comparison.
56
The comparison of the a values from Chok (1988), the codes, and Mode 15 values
showed that a for open terrain listed in the codes lies within the ranges of the data obtain
by Chok and in this study (Mode 15). SAA has the lowest a value, this is due to the fact
that a in this case is based on a 3-second averaging time. The ANSI, NRCC codes and
Chok (1988) a values are approximately equal. The a value for Mode 15 was higher than
that of ANSI, NRCC, and Chok (1988) which is possibly due to that both stationary and
nonstationary records were used to calculate the average a value.
Table 4.1 Power Law Exponents
Code ASCE7-93^
NRCC, 1990^ SAA, 1983 ^ Chok, 1988*
Mode 15 Values*
Terrain Category Open Open Open Open
Open
a 0.14 0.14 0.09 0.14
(0.10-0.17) 0.16
(0.11-0.25) ^ Fastest-mile averaging time ^ Mean houriy averaging time ^ Three second gust averaging time * 15-minute averaging time
57
a, ft
0.26
0.24
022
0.20
0.18
0.16
0.14
0.12
0.10
" ^
• . - I * * < ^ • • •
40 80 120 160 200 240
Mean Wind Direction 280 320 360
Figure 4.1 Power Law Exponent versus Mean Wind Direction at 13 ft
60
50 —
40
Number of 30
Observations
20 _
10 —
0 0.10
Mean =0.159 s = 0.0231
Mininum = 0.114 Maximum = 0.247
n =454
Jl 1 JI 0.12 0.14 0.16 0.18 0 20 0 : ;
a
Figure 4.2 Histogram for a
24
58
41.2 Surface Roughness, ZQ
The Mode 15 surface roughness values as a function of azimuth angle are shown in
Figure 4.3. The histogram for zo along with the associated summary statistics is shown in
Figure 4.4. Similar to the a values presented in Section 4.1.1, the zo values show a large
scatter. The mean value of the roughness length is 0.043 ft. As shown in Figure 4.5, this
compares well with the published values from ESDU (1991) for runway areas which are
classified as open terrain. The range of zo is 0.002 to 0.288. The values lie within the of
dessert (flat) terrain to fairly level grass plains.
The Mode 15 surface roughness values are compared to Chok's (1988) in Table
4.2. The comparison of Chok and Mode 15 ZQ values show that the mean and minimum
value of ZQ are comparable. Mode 15 data exhibits a larger range than reported by Chok
(1988).
Table 4.2 Surface Roughness Values
^ • ^ • ^ ^ ^ ^
Chok, 1988
Mode 15 Values
Zo
(ft) 0.041*
(0.002-0. 124)A 0.044
(0.002-0.288) * Average value
A Range of minimum to maximum
59
0.25
0.20
0.15
Zo
0.10
0.05
0.00 80 120 160 200 240 280 320 360
Azimuth Angle, degrees
Figure 4.3 ZQ versus Azimuth Angle
120
100 —
Number 60 of
Observations 40
Mean = 0.043 s = 0.036
Minimum = 0.002 Maximum = 0.212
n = 454
I I il I H I J • n nl 0.10
Zo 0.15 0.20 0.25
Figure 4.4 Histogram for ZQ
60
T«fiQtn ( ) (scr ipt ioo
V R«qai« Mil, Uoohi (« :^ I? I )
}
} 10
9 e 7 -« 5
ZQ ma\~ 0.288 ^
-2 K)
"z; = 0.044
Ton)
K)
Zo = 0.002
S«»«Nta
Monr !>•««, M d « « t . Urn bwiWMi^*
taolaU<< lfM« Uncul fra«
Ftw I f M t , «nnUr tMa«
O i l f r a u i « 0 - 0 3 « i )
•taiwol tA«« M<1«c« ( tar
r«r««u
foJelf it««< «ae4«« cevnif
>- F«>mlan« L«na«ra«< (*<0 O^iBlcrap*
>• M r l f l«v«( f rVM ptadw
10
10
CMai • » • • • • *
AiryerU Im—ay mm»)
>• L«rt* l i » l M i i «( M U r ( M i C « M l l « « ( C . I ) )
0*Mrt ( l l«0
t > f - <««*c«4 pl«la«
le t . <••« <••(•
5U 10
0 U 2
Figure 4.5 Comparison of Mode 15 Values with ESDU (ESDU, 1981)
61
4 1.3 Shear Velocity
The shear velocity (u») as a function of azimuth angle and the histogram for the
shear velocity is shown in Figures 4.6 and 4.7, respectively. Shear velocity for the overall
site is compared to the results of Chok's (1988) initial site characterization in Table 4.3.
Table 4.3 Shear Velocity Values
u«
Chok, 1988
Mode 15 Values
1.64* (1 .21 -2 .11 )A
1.33 (0.74-2.60)
* Average value A Range of minimum to maximum
The Mode 15 site characterization exhibits a significantly lower average and a
larger range of shear velocity than that reported by Chok (1988). This maybe the result of
using a small sample size by Chok, the effects of including both stationary and
nonstationary records in the Mode 15 data, or the effects of including records from wind
directions in the Mode 15 data which were not considered by Chok.
62
^ • * . * *
120 160 200 240 Azimuth Angle, degrees
280 320 360
Figure 4.6 Azimuth Angle versus Shear Velocity
50
4 0 -
Number 30 of
Observations
20
10
0 0.6
JUiL 0.8 1.0 1.2 1.4
u«, ni}rfi
Mean =1.337 s = 0.273
Minimum = 0.743 Maximum = 2.603
n = 454
1.6 18 20
Figure 4.7 Histogram for u»
63
4.1.4 Longitudinal Turbulence Intensity
The Mode 15 longitudinal turbulence intensity, lu, values at the 13 ft height as a
fiinction of azimuth angle are shown in Figure 4.8. The histogram for this data along with
the associated summary statistics is shown in Figure 4.9. Comparisons of the Mode 15
data to the analytical models proposed by Lumley and Panofsky (1984) and by Davenport
(1961a, 1961b) and with Chok (1988) is shown in Figure 4.10 and Table 4.4, respectively
(the appropriate values for the analytical models are listed in Section 2.2.1).
The comparison of Mode 15 data to the analytical models shows that the average
turbulence intensity values for Mode 15 lie in-between the analytical models. The range of
the Mode 15 data incorporates both Panofsky (1984) and Davenport (1961a, 1961b)
models (the variable used in the models are listed in Section 2.2.1). A comparison of
Chok (1988) and Mode 15 data show that they are similar. The longitudinal turbulence
intensity from Mode 15 data is slightly higher than reported by Chok (1988). This could
be due to inclusion of both stationary and nonstationary records in the Mode 15 data
and/or due to the sample sizes used to perform the analysis.
Table 4.4 Comparison of Chok (1988) and Mode 15 I at 13 ft
Statistic
Mean Minimum Maximum
Sample Size
lu Chok (1988)
0.18 0.17 0.22 31
Mode 15 0.20 0.14 0.51 454
64
<t5
I I
0.35
0.30
0.25
0.15
0.10
WW :t 40 80 120 160 200
Azimuth Angle, degrees
240 280 320 360
Figure 4.8 ly at 13 ft versus Azimuth Angle
Num ber of
Observat ions
ou
50
40
30
20
10
0 0.
1 1
0 n 0
Mean = 0.201 s = 0.028
M inira um = 0.141 M axim um = 0.342
n = 454
IL JL 0.20 0.25
Longitudinal Turbulence Intensity at 1 3 ft
0 30 0.35
Figure 4.9 Histogram for I
65
160
120
Height, ft
80
40
0.0
Turbulence Intensity based on:
1 - Lumley and Panofsky (1964) 2 - Davenport (1961a, 1961b) 3-Mode 15 Data
Minimum-Average-Maximun
0.1 0.2 0.3 0.4
Longitudinal Turbulence Intensity
0.5 0.6
Figure 4.10 Comparison of ly Models and Mode 15 Data
4.1.5 Lateral Turbulence Intensity
The Mode 15 lateral turbulence intensity, Iv, values at the 13 ft height as a
fiinction of azimuth angle are shown in Figure 4.11. The histogram for this data along
with the associated summary statistics is shown in Figure 4.12. The lateral turbulence
intensity as a fiinction of longitudinal turbulence intensity is given in Figure 4.13. For the
lateral turbulence intensity a comparison between Mode 15 data and Chok is not possible
since Chok did not Hst the lateral turbulence intensity values in his work.
66
0.35
0.30
I 0.25 I V <j
a u •3 % 0.20 H •g u «
0.15
0.10
• •
40 80 120 160 200 240
Azimuth Angle, degrees
280 320 360
Figure 4.11 ly versus Azimuth Angle
70
60
50
g 40 O
.S 30
20
10
0.10 1 Lg JL
Mean = 0.179 s = 0.028
Minimum = 0.112 Maximum = 0.312
n = 454
•• • I H n „i „ 0.15 0.20 0.25
Lateral Turbulence Intensity at 13 ft
0.30 0.35
Figure 4.12 Histogram for ly
67
0.35
0.30
S 0.25
0.20
0.15
0.10'— 0 10
* •
0.15 0.20 0.25
Lxmgitudinal Turbulence Intensity at 13 ft
0.30 0.35
Figure 4.13 ly versus I u
4.1.6 Statistical Analysis of Overall Site Flow Parameters for the Factors
The nonparametric Kruskal-Wallis test is used to determine if the site flow
characteristics (a, zo, u«, lu, and Iv) are affected by the mean wind direction, mean wind
speed, stationarity, storm type, time of day, and time of year. The results of these tests are
shown in Table 4.5. In general, except for stationarity, each of the factors is shown to
have a significant effect on the flow characteristics when the site is considered as
homogeneous. However, this may be due to combined effects (the effect of a mixed data
influencing the test results). Each factor is investigated individually in the following
sections.
68
a> u, • « - »
c W 0)
• • ->
00 c •n a> -a 'ui C o CJ
W3 • « - •
3 en
to H o •c Z
a. c o
>
r»1
>
>
00 >
O
5
00
•
3
• 3
hf
D
t/) CO c/ ly. c/i (X)
to (/) LT) C/O t/) CO
C/) CO ^ CO CO CO
C/3 CO CO C/) CO CO
CO CO ^ CO CO CO
CO CO ^ CO CO CO
CO CO ^ CO CO CO
CO CO CO CO ^ CO ^ CO
CO CO ^ CO ^ CO
CO CO ^ CO CO CO
g CO g CO CO CO
• rx CO C>b CO CO CO
c O -o
D -o H u C T3 .S g c O O
.B ^ -zz t ^ V
g a c/) CO H H 1
a>
c/>
69
4.2 Wind Dirertinn
The mean wind direction at the 13 ft level of the tower is used to investigate the
effects of azimuth angle on the flow parameters. The site is initially divided into 10 degree
increments, termed here as sectors, to perform the analysis. Figure 4.14 shows the 10
degree sectors superposed on a map of the field site and surrounding terrain. The sectors
are numbered 1 to 36 and correspond to 10° increments.
The approach flow characteristics shown in Section 4.1 as a fiinction of azimuth
angle were plotted with respect to sector. Figure 4.15 shows the relationship of a to the
categorical variable sector. These plots provide a good characterization of the data. They
provide information on the number of data runs in each sector, the range of values for the
parameter, and the azimuth angle from which the data was collected. The plots also show
any trends that occur within the data. Plots of all the parameters versus sector are
contained in Appendix D.
The trends seen graphically are correlated with the physical surroundings at the
field site, see Figures 4.15 and Figure 4.16. The ranges are from 20° to 80°, 80° to
130°, 130° to 190°, 190° to 240°, 240° to 270°, and 270° to 20°. These ranges
correspond to: the residential area to the northeast; the hospital to the southeast; the
residential area to the south; the antenna farm to the southwest; the residential area to the
southwest; and the open area from the northwest to the northeast. Due to the limited
amount of data for the range 80° to 130° this range was eliminated from this study
70
19 018 " 5 SCALE - MILE
Figure 4 14 WERFL Field Site with Respect to Sectors
71
0.26
0.24
0.22
0.20
^ 0 . 1 8
0.16
0.14
0.12
0.10
< •
•J •I
. . . .
• # • • • • • • •
• Ml • - h i t . » ? . , . • • • • n i l * • . :
12 16 20 Sector
24 28 32 36
Figure 4.15 a versus Sector
72
Figure 4 16 WERFL Field Site SCALE - MILE
71
Duncan's multiple range (DMR) test was used to investigate the observed
graphical trends with respect to the surrounding terrain. The Duncan's multiple range test
provides a comparison of the mean values for the wind flow parameters (a, ZQ, U*, and
u*33) with respect to the sectors. Table 4.6 provides a listing of the sectors, means, and
the results of the DMR test (Duncan Grouping) for z ,.
The categorical variable, flow region was created using the DMR resuhs from the
analysis using the categorical variable Sector. It combines adjacent sectors which exhibit
mean flow characteristics, which are not significantly different, to form a flow region.
Based on the DMR analysis of all the flow parameters, the sectors are combined to form
five flow regions. The azimuth angles for each region are listed in Table 4.7. Figure 4.17
shows the flow regions superposed on the WERFL site plan. Combining the sectors into
regions increases the sample size within a region which allows for a more accurate
analysis.
DMR testing of the flow parameters in the five flow regions showed significant
differences in the means of the parameters. Regions 1, 2, and 4 are residential areas.
These regions did not show any significant difference in the flow parameters The flow
characteristics from Region 3 are significantly different for all wind flow parameters.
Table 4.8 gives the flow regions, means, and DMR results for this analysis.
74
Table 4.6 Duncan's Multiple Range Analysis for ZQ
1 Sector 1 2 3 4 5 6 7 8
9-13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Sample Size 19 27 39 8 19 23 10 6
2 9 13 7 9 19 17 21 14 5 14 18 26 28 27 15 8 7 2 3 2 20 16
Mean 1.3142 1.4233 1.6135 1.4829 1.1545 1.2554 1.2016 1.1008 N/A
1.3470 1.3622 1.2696 1.2947 1.0986 1.1002 1.2510 1.3691 1.3214 1.1078 1.1372 1.2784 1.3508 1.4105 1.4676 1.4193 1.4469 1.4214 1.0230 1.1383 1.1145 1.2884 1.3473
Duncan Grouping A B C A B A A B
B C A B C
B C B C
N/A A B C A B C A B C A B C
C B C
A B C A B C A B C
B C B C
A B C A B C A B C A B A B A B A B
C B C B C
A B C A B C
75
Table 4.7 Azimuth angles for the various flow regions
Flow Region Overall Site
1 2 3 4 5
Azimuth Angle 0°-360°
20°-80° 130°-190° 190°-240° 240°-270° 270°-20°
Table 4.8 Duncan Grouping for the Wind Flow Parameters
a
ZQ
u«
'^•33
Flow Region
1 2 3 4 5
1
2 3 4 5
1 2 3 4 5
1
2 3 4 5
Sample Size
105 59 71 72 146
105 59 71 72 146
105 59 71 72 146
75 57 63 45 143
Mean
0.15158 0.16364 0.17470 0.16168 0.15284
0.03260 0.04170 0.06649 0.04538 0.04018
1.37569 1.20869 1.26730 1.35594 1.37569
1.29817 0.82872 1.00159 1.35487 1.37990
Duncan Grouping
C B
A B
C
B B
A B B
A B
A B A A
A
C B
A A
76
0 ^ 5 ^ I
SCALE -'"MTLE
Figure 4.17 WERFL Field Site with Respect to the Flow Regions
77
As shown in Section 4.1, the histogram of the flow parameters are not normally
distributed. The Kruskal-Wallis statistical analysis of the flow parameters in each flow
region show a significant difference (at the 1% level of significance) in the parameters
except for ZQ. Table 4.9 provides the results of the Kruskal-Wallis test for each flow
parameter for the factor flow region. Significant difference in the means of all the flow
parameters are detectable at the 5% level of significance.
Table 4.9 Results of Kruskal-Wallis Test for the Overall Site for the Factor Flow Region
Factor
a
ZQ
u*
^•33
^US T %13 T
^U33 T %160 T ^V8 T ^VB T ^V33
IVI60
Result of Kruskal-Wallis Test (1% significance level)
S NS S s s s s s s s s s
Since the flow region is a significant factor that affects the flow characteristics, all further
analysis of the factors will be performed for each of the five flow regions
78
4.3 Mean WinH •<;pAf>fj
Speed is a categorical vahable based on the mean wind speed at the 13 ft level on
the tower. The Speed classification originally assumed values from I to 9. Speed 1 was
assigned mean wind speed values at the 13 ft height that ranged from 0 miles per hour
(mph) to 12 mph. Thereafter, in each speed category the wind speed range increased by 2
mph until Speed 9 which includes any speeds greater than 26 mph. Table 4.10 lists the
wind speed ranges for the categorical variable Speed.
Table 4.10 Original Speed Ranges
Speed Categories 1 2 3 4 5 6 7 8 9
Ranges (mph) 0-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26 >26
4.3.1 Overview of Effects of Mean Wind in the Five Flow Regions
Considering the field site as having homogeneous terrain, the wind flow
parameters were plotted versus the categorical variable speed to provide a visual analysis
of the data. The plots showed that higher flow parameter values tended to occur at lower
79
wind speed for a, ZQ, ly, and ly. Figure 4.18 shows this trend for a typical plot of ZQ
versus Speed. The plots also verify that u« and u*33 are fijnctions of mean wind speed, see
Figure 4.19.
^
0.25
0.20
0.15
0.10
0.05
0.00
t
I I !
Speed (mph)
• t 5
I Ii Figure 4.18 ZQ versus Speed
1 a
2.5
2.0
1.5
1.0
0.5
0.0'
I
4 5
Speed (mph)
I i I t
I
i !
t
Figure 4.19 u»33 versus Speed
80
The speed classifications originally ranged from 1 to 9 but was reduced to five
speed classifications. Speed 1 and 2 were deleted since neutral stability conditions may
not be present when wind speeds are less than 15 mph at the 33 ft height (Malony, 1994).
Conservatively, no wind speeds below 14 mph at the 13 ft height were used in this
analysis. Upon review of the Duncan's grouping of Speed it was determined that there is
no significant difference in the mean parameter values for wind speeds higher than 22 mph.
Therefore, Speed 7, 8, and 9 were combined to a single Speed factor. See Table 4.11 for
list of Duncan's grouping for ZQ.
Table 4.11 Duncan's Grouping for ZQ
Speed 3 4 5 6 7 8
9
Sample Size 15 53 62 43 17 8 2
Mean 0.0334 0.0277 0.0342 0.0432 0.0514 0.0366
Duncan Grouping B B B B
A B
0.0930 A 1
This limits the analysis of the effects of mean wind speed to speeds greater than 14
mph and reduces the analysis of the data in each of the 5 flow regions to only five Speed
categories. The five combined Speed categories with their associated ranges are listed in
Table 4.12. Figure 4.20 shows a typical plot of ZQ versus Speed for the 5 speed
categories.
81
0.25
0.20
Table 4.12 Combined Speeds
Range (mph) 14-16 16-18 18-20 20-22 >22
o N to"
I u
^
0.15
0.10
0.05
0.00
•
I
i I 10
t
I
I
I i
t
20 30 40
Speed (combined ranges)
•
50
Figure 4.20 ZQ versus Speed for Overall Site
82
An analysis of the eff ects of mean wind speed using the categorical variable Speed
for each flow region was performed. The results of the Kruskal-Wallis test for each flow
parameter in each flow region is shown in Table 4.13. In general, the effects of mean
wind speed are significant for the shear velocity but not for the other flow parameters
when considering a specific flow region. However, the effects of mean wind speed
showed significant differences in some of the flow parameters within a flow region. A
discussion of the results of the testing in the five flow regions is presented in Section
4.3.2-4.3.6.
Table 4.13 Nonparametric Test Results for Mean Wind Speed
Region 1 2 3 4 5
1 Interpretation
a
S* NS»*
S NS NS NS
Zo
S NS S
NS NS NS
u* S S
NS S s S
U«33
S NS S
NS S S
lu8
NS NS NS NS NS NS
*U13
NS NS NS NS NS NS
Iu33
NS NS NS S
NS NS
^U160
NS NS NS S
NS NS
lv8
NS NS NS NS S
NS
^V13
NS NS NS NS S
NS
*V33
NS NS NS NS S
NS
^VIM
s NS NS NS NS NS 1
* significant effect at the 1% level of significance ** non significant effect at the 1% level of significance
s.i
4.3.2 Region 1
Figure4.21 provides a typical plot of the data, Zo versus Speed, for Region 1.
Kruskal-Wallis test for the effects of mean wind speed on the wind flow parameters
indicates there are significant differences. Longitudinal and lateral turbulence intensities
are not significantly different with respect to Speed.
Zo,ft
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
S • I
10 20 30 40
Speed (combined ranges)
Figure 4.21 ZQ versus Speed for Region 1
4.3.3 Region 2
50
The flow parameters are not affected by a change in the wind speed for Region 2.
No strong conclusions could be drawn from the plots. See Figure 4.22 for a typical plot
of the data, ZQ versus Speed, for Region 2.
84
0.20
0.15
Zo,ft
0.10
0.05
0.00
i
10
I I 20 30
Speed (combined ranges)
I 40 50
Figure 4.22 ZQ versus Speed for Region 2
4.3.4 Region 3
The wind speed data in Region 3 provided unusual plots. The plots for the wind
flow parameters show a gap in the data. The data in Figure 4.23 exhibits the gap in the
data (plot of Zoversus Speed). The sample size for Speed 40 is five and Speed 50 is two.
If the data was analyzed with respect to flow region and individual Speeds, Speeds 40 and
50 would not be weighted equally compared to the other three Speed classifications
because of their Ihnited sample sizes. The Kruskal-Wallis test determined that a, z^, and
u,33 have a significant difference with increasing speed while, the other approach flow
parameters do not have a difference.
85
0.20
0.15
Zo(ft) 0.10
I •
I I
0.05
0.00 10
i I 1
20 30 40
Speed (combined ranges) 50
Figure 4.23 ZQ versus Speed for Region 3
4.3.5 Region 4
In general, the parameters are not affected by a change in the wind speed for
Region 4. No strong conclusions could be drawn from the plots. Figure 4.24 shows a
typical plot of the data, Zoversus Speed for Region 4. The Kruskal-Wallis test did,
however, show that a significant difference occurs with respect to the mean values of u*,
and longitudinal turbulence intensity at 33 and 160 ft. The change in wind speed does not
have an affect on a, ZQ, U,33, longitudinal turbulence at 8 and 13 ft, and lateral turbulence
at 8, 13, 33, and 160 ft.
86
Zo.ft
0.16
0.12
0.08
0.04
n nn
•
1
1 •
{
t
•
•
•
•
1 • •
* 1
t 1 •
«
•
i •
!
10 20 30 40
Speed (combined ranges)
50
Figure 4.24 ZQ versus Speed for Region 4
4.3.6 Region 5
Figure 4.25 provides a plot of the wind flow parameter for Region 5, ZQ versus
Speed, and Figure 4.26 for a plot of the lateral turbulence intensity at 33 ft versus Speed.
The shear velocity tends to increase with increasing wind speeds, see Figure 4.27 for a
plot of Speed versus u*33. Statistical testing indicates u» at 33 ft, and the lateral turbulence
intensity are affected by the wind speed, a, z^, and the longitudinal turbulence intensity
are not affected by a change in wind speed.
87
0.12
0.10
0.08
Zo, ft 0.06
0.04
0.02
0.001 10
t
J 20 30
Speed (combined ranges)
I t i
t
I 40
I
i
50
Figure 4.25 Zoversus Speed for Region 5
o c V
I <d
• J
0.25
0.20
0.15
0.10
0.05' 10
I *
t
20 30
Speed (combined ranges)
40 50
Figure 4.26 Lateral Turbulence at 33 ft versus Speed
88
2.5
2.0
1.5
1.0 I
I
I t
t
! I
•
I t *
0.5 10 20 30 40
Speed (combined ranges)
Figure 4.27 u*33 versus Speed for Region 5
50
Considering the Kruskal-Wallis test results on the flow parameters for the
categorical variable Speed in each flow region, it can be generally stated that Speed does
not have a significant effect on the flow parameters. The shear velocities are the exception
to this statement.
89
4.4 Stationarity
Stationarity is based on the speed and direction stationarity at 13 ft. A categorical
variable. Station, is defined using the four stationarity conditions:
ss = 1 = stationary speed and stationary direction;
sn = 2 = stationary speed and nonstationarity direction;
ns = 3 = nonstationarity speed and stationary direction; and,
nn = 4 = nonstationarity speed and nonstationarity direction.
Stationarity is an important parameter for wind tunnel modeling. Stationary records are
currently the only records used for wind tunnel simulation. Modelers claim that they can
not accurately model nonstationarity records at this time. Since flow regions have been
shown to be a significant parameter, the stationarity effects are investigated on a flow
region basis.
4.4.1 Stationarity by Flow Region
The results of the nonparametric tests for the effects of stationarity for each flow
region are shown in Table 4.14. Figure 4.28 shows a typical plot of station versus z^ for
flow region 5. z^ shows no trend with respect to stationarity criteria. The parameters lie
within a consistent range. See Appendix E for figures of the zo versus Stationarity for
each flow region. The Kruskal-WalUs test on the parameters in each flow region showed
gnificant difference with respect to the variable station. no SI
90
Table 4.14 Nonparametric Test Resuhs for Stationarity
Region
1 2 3 4 5
Interpretation
a
NS* NS NS NS NS NS
Zo
NS NS NS NS NS NS
u*
NS NS NS NS NS NS
^*33
NS NS NS NS NS NS
^U8
NS NS NS NS NS NS
%13
NS NS NS NS NS NS
^U33
NS NS NS NS NS NS
^U160
NS NS NS NS NS NS
^V8
NS NS NS NS NS NS
^V13
NS NS NS NS NS NS
^V33
NS NS NS NS NS NS
^V16 0
NS NS NS NS s*
NS 1 * significant effect at the 1% significant level ** non significant effect at the 1% significant level
0.12
0.10
0.08
o 0.06
0.04
0.02
0.00
t
I I I t
1.0 2.0
Station
i
3.0 40
Figure 4.28 ZQ versus Station for Flow Region 5
91
4.5 Storm Typp
The categorical variable storm type was added to the database using the Local
Climatological Data Sheets (LCD), (1991-1992). Storm classification enables the data to
be analyzed according to the atmospheric conditions when the run was taken. The runs
were classified as one of the following storm types:
1 = Deep cyclone,
2 = Frontal passage,
3 = Down mixing,
4 = Synoptic,
5 = Thunderstorm.
The storm classification for each run can be obtained from the database contained on disk
in Appendk C in the Mode 15 Complete Database. Plots and the Kruskal-Wallis test
were the only analysis performed for storm type. The analysis of the effects of storm type
for Region 1 through 5 are presented in Sections 4.5.1-4.5.5, respectively.
4.5.1 Overview of Effects of Storm Type in the Five Flow Regions
The resuhs of the Kruskal-Wallis tests performed by region are given in Table
4.15. Figure 4.29 shows a plot of a versus Storm. In general, the storm type does not
have a significant effect on the flow parameters.
92
Table 4.15 Nonparametric Test Results for Storm Type
Region
1 2 3 4 5
Interception
a
N S -NS NS S»
NS
NS
Zo
NS NS NS S s
NS
u.
S
s NS NS
NS
NS
U.33
NS NS NS NS NS
NS
^U8
NS NS NS
S NS
NS
*U13
NS NS NS S
NS
NS
*U33
NS NS NS NS NS
NS
*UI60
S NS NS S
NS
NS
'V8
NS NS NS S
NS
NS
Ivi3
NS NS S S
NS
NS
Iv33 S
NS S
NS NS
NS
*VI60
NS NS S s s s
* significant effect at the 1% significant level ** non significant effect at the 1% significant level
Alpha
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
«
I
i I
•
I !
•
^2 3
Storm
Figure 4.29 a versus Storm for Overall Site
93
4 5 2 Region 1
Storm types that occur in Region 1 are frontal passages and synoptic conditions.
There are no obvious trends in the data. See Figure 4.30 for a plot of a versus Storm.
Based on the Kruskal-Wallis analysis, the flow parameters are not affected by storm type
expect for u,, longitudinal turbulence intensity at 160 ft, and lateral turbulence intensity at
33 ft.
0.19
0.18
0.17
od Xi
0.16
0.15
0.14
0.13
0.12
I !
$
t
I
I
t
Storm
Figure 4.30 a versus Storm for Region 1
94
4.5.3 Region 2
Only two storm types occur in Region 2. The stomi types are synoptic conditions
and thunderstorms. Only eight thunderstorms occurs during Mode 15. Figure 4.31
provides a plot of a versus Storm. The storms do not have an affect on the wind
approach parameters, i.e., the Kruskal-WalHs test shows no significant difference in the
mean values except for u,33. No strong conclusion can be drawn regarding this analysis
due to the small thunderstorm sample size.
0.24
0.22
0.20
| 0 . . 8
0.16
0.14
0.12
Storm
I • I
I I
Figure 4.31 a versus Storm for Region 2
95
4 5.4 Region 3
The storm types that pass through Region 3 are synoptic conditions,
thunderstoims, deep cyclones, and mixing down. However, the only predominant storm
type is synoptic conditions, the other storms have small sample sizes. See Figure 4.32 for
plot of a versus Storm which displays the limited sample size of deep cyclones, mbdng
down, and thunderstorms. Based on the Kruskal-Wallis analysis, the flow parameters are
not affected by storm type expect for I^ at the 13 ft, 33 ft, and 160 ft heights.
0.24
0.22
0.20
Alpha 0.18
0.16
0.14
0.12
t t
3
Storm
9
I
•
I • •
•
•
Figure 4.32 a versus Storm for Region 3
96
4.5.5 Region 4
All five storm types pass through the area of Region 4. Thunderstorms and deep
cyclone conditions are limited in sample size. The plots show that the values lie within a
consistent band of data but do not show any distinctive trends. Nonparametric testing of
the flow parameters with respect to stonn type indicates the stonn type has a significant
effect on a, ZQ, lug, lun. Iui6o> hs, hu^ and Iv,6o but not on u„ u*33,1 33, and Iv33 (Table
4.18). Figure 4.33 illustrates the effect of storm type on a.
Alpha
0.21
0.20
019
018
017
016
015
014
013
012'
t t
t
I t •
t
2 3
St(xm
I
t
I I
•
I
Figure 4.33 a versus Storm for Region 4
97
4 5 6 Region 5
All five of the storm conditions pass through Region 5. The storm classification of
thunderstorm and deep cyclone have limited sample sizes. Only two deep cyclones and
three thunderstorms occur m Region 5 during the collection of Mode 15 data. The plots
show that the values he within a consistent band of data but do not show any distinctive
trends. The nonparametric test indicates that the flow parameters are not affected by
storm type except for Zg and lyieo- Figure 4.34, a versus Storm, and Figure 4.35, Iv33
versus Storm, illustrate the typical effects of storm type.
Alpha
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
I I
3
Storm
Figure 4.34 a versus Storm for Region 5
98
0.25
CO
• 1 - 4
(A c 4^
0.20
0.15
•
I t
0.10
• I
I
I
I I
0.05 3
Storm
Figure 4.35 Lateral Turbulence Intensity at 33 ft versus Storm for Region 5
4 6 Time of Day
The time of day is categorical variable based on the hour the record was collected.
The time is recorded as military time. By dividing the data into hours it can be analyzed
for the affect that heating and cooling of the surface has on the approach flow.
99
4 6 1 Overview of EfFects of Time of Dav in the Five Flow Ret
The results of the Kruskal-Wallis test for the effects of time of day on the flow
parameters for each flow region is provided in Table 4.16. In general, the effects of time
of day are significant for the lateral turbulence intensities at the 13 ft, 33 ft, and 160 ft
heights but not for the other flow parameters when considering a specific flow region.
However, the effects of the time of day showed significant differences in some of the flow
parameters within a flow region. A discussion of the resuhs of the testing in the five flow
regions is presented in Sections 4.6.2-4.6.6.
Table 4.16 Nonparametric Test Resuhs for Time of Day
Region 1 2 3 4 5
Interpretation
*sign
a
NS-S* s
NS NS NS
ificant <
Zo
NS S S
NS NS NS
jffecta
u* S S
NS NS NS NS
tthel
"•33
NS NS NS NS NS NS
%signi
^U8
NS NS NS NS NS NS
ficant
^U13
NS NS NS NS NS NS
evel
^ 3
NS NS NS NS NS NS
^wo NS NS S S
NS NS
Iv8 NS NS S
NS S
NS
lvi3
NS NS S s s s
^V33
NS s s s s S
'vi60
NS NS s s s s
** non significant effect at the 1% significant level
4.6.2 Region 1
The times at which data was collected in Region 1 are scattered and does not
exhibit a set pattern The data does form a band of data. See Figure 4.36 for a plot of ZQ
versus time for Region 1 The highest values tend to happen between four p.m. and
midnight The Kruskal-Wallis analysis showed that no significant difference occurs for
100
any of the parameter except u.. In general the approach flow parameters are not affected
by the different times at which they were collected so, atmospheric stabUity does not have
a strong effect for Region 1.
Zo,ft
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
•
• • •
t : • 1 1 : • . • • • • i
• •
• *
•
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time of Day (hour)
Figure 4.36 ZQ versus Time of Day for Region 1
4.6.3 Region 2
Time of day analysis for Region 2 did not give equivalent resuhs to those of the
Overview and Region 1 analysis. The plots that showed the highest parameters values
between seven p.m. and one a.m. See Figure 4.37 for a plot of ZQ versus Time. It is also
101
important to note the a, z^, and u* values tend to increase throughout the day instead of
peaking in the afternoon. u»33 and the lateral turbulence intensity peaked in the afternoon
between noon and three p.m. See Figure 4.38 for a plot of lateral turbulence intensity at
13 ft versus Time. Longitudinal turbulence parameters were their highest between seven
p.m. and twelve a.m.. Figure 4.39 illustrates the effect of Time on I n- The following
parameters were influenced by the time of day they were collected: a, ZQ, U*, and lateral
turbulence at 33 ft. The other parameters were not affected by the time of day.
0.20
0.15
Zo, ft
0.10
0.05<
0.00
t • • :
• • : * • • • • • s •
* ft: r 1 - T T T T T T m ^ i n n r M 1516 n 1819 20 2122 23 24
TimeofDayOiour)
Figure 4.37 z^ yersus Time of Day for Region 2
102
0.28
ro
Inte
nsity
at
snce
T
urbu
le
Lat
eral
0.26
0.24
0.22
020
0.18
0.16,
0.14'
0.12
•
. : ^
I
• • •
• I
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time of Day (hour)
Figure 4.38 ly at 13 ft versus Time of Day for Region 2
0.28
2 0.26
g 0.24 • 4 - * s ii
J 0.22 I H * H 0.20
00
g 0.18
0.16
• •
• * • •
• • • • :
•
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time of Day (hrs)
Figure 4.39 I, , at 13 ft versus Time of Day for Region 2
103
4 64 Region3
The time at which the data was collected for Region 3 contained some unusual
patterns. The wind flow parameters, a, z , and u, have a distinct gap in the data. See
Figure 4.40 for a plot of ZQ versus Time. The time of the highest values for the lateral and
longitudinal turbulence mtensity were typically from twelve p.m. to five p.m. Figure 4.41
provides a plot of lateral turbulence intensity at 33 ft versus Time. The resuhs of the
nonparametric test showed that the mean values for a, ZQ, and the lateral turbulence
intensity parameters are significantly different and thus are swayed by the time of day the
record was collected. u», u»33, and the longitudinal turbulence intensity are not affected by
the tune of day.
t3
0.25
0.20
0.15
0.10
0.05
0.00
• • • • •
• • t
• • •
•
• «
» . . i n : 1 2 3 4 5 6 7 8 ~ n r T r m n r T 5 i6 n i819 20 2122 23 24
Time of Day (hrs)
Figure 4.40 z^ versus Time of Day for Region 3
104
0.30
:j 0.25
c
o o c 3
3 H "oS i-i
u OS
0.20
0.15
0.10
• •
•
•
• * • *
• • •
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time of Day (hrs)
Figure 4.41 Lateral Turbulence Intensity at 33 ft versus Time of Day for Region 3
4.6.5 Region 4
The time of day data for Region 4 has a distinct gap in the data from seven a.m. to
ten a.m. The approach flow parameters tend to show the widest range of values from ten
a.m. to seven p.m. See Figure 4.42 for a plot of ZQ versus Time for Region 4. The wind
flow and longitudinal turbulence intensity parameters are not affected by time of day.
Lateral turbulence intensity parameters are the only parameters affected by a change in
time for Region 4. Thus, the wind flow and longitudinal turbulence intensity does not
change with time of day, the lateral turbulence intensity does change with time of day.
105
0.16
0.12
o' 0.08
0.04
0.00
: i :
• t
r - • • • *
• I • • ' 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time of Day (hrs)
Figure 4.42 ZQ versus Time of Day for Region 4
4.6.6 Region 5
For Region 5, the time data shows no distinctive trends except for the lateral
turbulence intensities which increase throughout the day. Figure 4.43 provides a typical
plot of the data (ZQ versus Time) and Figure 4.44 is a plot of lateral turbulence intensity at
33 ft versus Time. The Kruskal-WaUis test for the wind flow and longitudinal turbulence
intensity parameters show no significant effect doe to time of day. The lateral turbulence
intensity is affected with respect to collection time.
106
0.12
0.10
0.08
• #
o 0.06 N
0.04
0.02
0.00
I • •
* • : • • ! • •
• I • •
* • •
• • .
f • • • • : • !
I ! I ; I : : • • • t • t • t • • • •
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time of Day (hour)
Figure 4.43 ZQ versus Time of Day for Region 5
0.25
tS 0.20
4>
I 0.10
..
« * « • •
• • •
I
• I
I « • •
0.05' 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time of Day (hrs)
Figure 4.44 ly at 33 ft versus Time of Day for Region 5
107
4.7 Time ofYear
Month is a categorical variable representing the month of the year when the data
was collected. It is simply the month of the year ranging from 1 to 12. The factor Month
allows for the seasonal effect of the approach flow characteristics to be evaluated.
Typically the fields located in the vicinity of the WERFL contain cotton plants from July
to November, httle vegetation exist from December to April, and weeds grow in the fields
from May to June. Extreme winds usually occur from January to June and then from
November to December. See Appendk F for typical plots of the data. The wind
parameters tend to display the highest values during different times of the year. The
largest a and ZQ values are reached during the month of June while, u* and u»33 experience
the highest values during February and May. Lateral and longitudinal turbulence intensity
values tends to remain more constant throughout the year than the wind flow parameters.
4.7.1 Overview of the Effects of Time ofYear in the Five Flow Regions
The results of the Kruskal-Wallis test for the effects of time of year in each flow
region is given in Table 4.17. In general the test results show that the month when a
record was collected does have a significant effect on the flow parameters. The effects of
time of year in each flow region are discussed below.
108
Region
1 2 3 4 5
Interpretation
Table 4.17 Nonparametric Test Resuhs for Time ofYear
a
S* S s s s
Zo
s s s s s
s s
u*
s s s s s s
U*33
s N S -
S S s s
^ 8
s NS s s
NS s
Iui3
NS NS S s
NS NS
'u33
NS NS S s
NS NS
Iui60
s NS S s s s
^V8
S NS NS S s s
Vl3 s
NS s s s s
^ 3 3
s NS s s s s
^V160
s NS s s s s
significant effect at the 1% significant level ** non-significant effect at the 1% significant level
4.7.2 Region 1
For Region 1, the data is typically collected during January, February, March,
April, May, and November. Figure 4.45 provides a plot of ZQ versus Month for Region 1
In general, the approach flow parameters are affected by the different times at which they
were collected except for lun and Iu33. The seasonal changes do have a strong affect in
Region 1.
109
0.14
012
0.10
0.08
0.06
004
002
nnn
•
• •
s 1
•
• •
•
•
s • •
t • • • • •
i • •
•
•
• •
t •
• 1 i 1
4 6 Month
10 12
Figure 4.45 ZQ versus Time ofYear for Region 1
4.7.3 Region 2
The data for Region 2 occurred during January, March, April, May, June, and July.
The highest values for the flow parameters occurred during June. Figure 4.46 provides a
plot of ZQ versus Month. The Kruskal-Wallis analysis indicates significant differences in a,
Zo, and u* with respect to the time of year. The other parameters, however, are not
affected with respect to time of year.
no
o N
U.14
0.12
OlO
008
O06
O04
0.02
onn
•
• • 1 1
I
• •
S • •
•
» •
• • • • • •
i • •
•
•
• •
t •
•
6 Month
10
t
I 12
Figure 4.45 ZQ versus Time ofYear for Region 1
4.7.3 Region 2
The data for Region 2 occurred during January, March, April, May, June, and July.
The highest values for the flow parameters occurred during June. Figure 4.46 provides a
plot of ZQ versus Month. The Kruskal-Wallis analysis indicates significant differences in a,
ZQ, and u* with respect to the time of year. The other parameters, however, are not
affected with respect to time of year.
110
0.20
0.15
4 0.10
0.05
0.00
•
•
•
• •
t
1 ; . ' 1
6
Month
10 12
Figure 4.46 ZQ versus Time ofYear for Region 2
4.7.4 Region 3
Mode 15 data for Region 3 occurred during February, March, April, May, June
and October. Figure 4.47 provides a plot of ZQ versus Month. The Kruskal-Wallis
analysis indicates significant difference for approach flow parameter with respect to the
time of year except for lateral turbulence intensity at 8 ft. The time of year does have a
strong effect on the wind parameters for Region 3.
I l l
o N
0.20
0.15
0.10
0.05
A r\r\ 1 1 1
•
•
•
1
1 1 •
*
0 4 6 8
Time ofYear (month) 10 12
Figure 4.47 ZQ versus Time ofYear for Region 3
112
47 5 Region4
For Region 4 the data typically occur during January, February, March, April,
May, June, November, and December. The records collected in April and June are limited
in sample. The data do not display a specific trend or pattern. The Kruskal-Walhs test
showed no significant effect on the approach flow parameters with respect to time of year
in Region 4. Figure 4.48 illustrates a typical plot of ZQ versus Month.
0.16
0.12
0.08 N
0.04
0.00 0
•
•
i I
I
•
4 6 8
Time ofYear (month)
10
•
t
12
Figure 4.48 ZQ versus Time ofYear for Region 4
113
4.7.6 Region 5
The wind data collected for Region 5 was collected during January-May and
November-December. SeeFigure4.49for a plot of zoversus Month for Region 5. The
Kruskal-Wallis analysis indicates that time of year is a significant effect for a, zo, u., u.33,
and lateral turbulence intensity (see Table 4.20). The longitudinal turbulence intensities,
general, are not affected by the time of year.
r3
0.12
0.10
0.08
0.06
0.04
0.02
0.00' 0
• I I
t •
I
•
i I I •
I i
I i I
4 6 8
Time ofYear (month)
t I
I
10 12
Figure 4.49 ZQ versus Time ofYear for Region 5
114
CHAPTER V
CONCLUSIONS
The purpose of this study is to investigate the characteristics of the wind flow at
WERFL in hght of the factors which may affect the parameters for Mode 15 data. The
characteristics of the wmd flow which are investigated include ZQ, a, u», u»33, ly, and I .
The factors which can affect the flow parameters are the mean wind direction, mean wind
speed, wind speed and direction stationarity, storm type, time of day, and time of year.
Descriptive statistics, plots, and statistical testing were used to examine the field data.
5.1 Conclusions
Based on the observations of the results in this study, the following conclusions are
drawn concemmg the wind flow parameters at WERFL for Mode 15 data:
1. Based on the nonparametric test results for the overall site, the wind flow
parameters in general are affected by all the factors under investigation.
2. Five distinctive flow regions are identified: the regions are 20°-80° (Region 1),
80°-130° (deleted from the database), 130°-190° (Region 2), 190°-240°
(Region 3), 240°-270° (Region 4), and 270°-20° (Region 5). Regions 1, 2,
and 4 include residential areas located approximately one mile from the WERFL
site in the direction specified by the Region. Region 3 incorporates the antenna
farm located less than one-half mile south-west of the WERFL site. Region 5
consists of 110° of open area from the northwest to the northeast of WERFL.
115
4. The flow parameters are different in the five flow regions with the exception of
Zo-
5. Stationarity is not an important factor for the site characterization.
6. The wind flow parameters are not affected by mean wind speed with the
exception of u* and u.33.
7. The wind flow parameters are not affected by the storm type, the exception to
this is Ivi6o- This conclusion is tentative due to the hmited sample sizes.
8. The time of day does not affect the wind flow parameters, the exception is ly.
9. In general, the tune of year has an effect on the wind flow parameters.
5.2 Recommendations
The follov^ng recommendations are made for fiiture studies.
1 Analysis of the of each of the wind parameters with respect to the flow regions should
contain. In conclusion Mode 15, Mode 28, and Mode 38 data would provide more
information of the characterization of the site.
2. This study investigated the wind flow parameters with respect to an individual factor. A
study investigating combined effect of the factors on the wind flow parameters using
Mode 15, 28, and 38 data, would provide a more detailed analysis of a site.
3. For this study it is assumed that convective turbulence can be neglected; this assumption
should be fiirther studied to determine its vaUdity.
116
LIST OF REFERENCES
ASCE 7-93, 1993: "Minimum Design Loads for Buildings and Other Structures," American Society of Civil Engmeers, 347 East 47 Th. St., New York, NY.
Choi, E. C, 1978: "Charaaeristics of Typhoons Over the South China Sea," Journal of Industrial Aerodynamics. Vol. 3, pp. 353-365.
Chok, C. v., 1988: "Wind Parameters of Texas Tech University Field Site," Master's Thesis, Department of Civil Engineering, Texas Tech University, Lubbock, Texas.
Conover, W. J., 1980: Practical Nonparametric Statistics, John Wiley and Sons, Inc., New York.
Davenport, A. G., 1961a: "The Spectrum of Horizontal Gustiness Near the (jround in High Winds," Ouarterly Journal of the Roval Meteorological Society. Vol. 87, April, pp. 194-211.
Davenport, A. G., 1961b: "The AppHcation of Statistical Concepts to the Wind Loading of Structures," Proceedings of Institute of Civil Engineering. Vol. 79, August, pp. 449-471.
Duchene-MaruUaz, P., 1975: "Full Scale Measurements of Atmospheric Turbulence in a Suburban Area," Proceedings of the Fourth International Conference on Wind Effects on Buildings and Structures, pp. 23-31.
ESDU, 1975: "Characteristics of Atmospheric Turbulence Near the Ground," Item No. ' 75001, Engineering Sciences Data Unit, London, England.
ESDU, 1982: "Strong Winds in the Atmospheric Boundary Layer," Item No. 82026, Engineering Sciences Data Unit. London, England.
ESDU 1988 "Integral Length Scales ofTurbulence Over Flat Terrain with Roughness ' changes," Item No. 86035, Fngineering Sciences Data Unite, London, England
Garratt, J. R., 1978: "Flux-Profile Relation Above Tall Vegetation," Quarterly Journal of Roval'Meteorological Society. Vol. 104, pp. 199-211.
Jenkins, G. M., and Watts, D. G., 1968: ^pprtr;.l Analysis and Its Applications, Holden-Day Inc., Oakland.
117
Kancharala, V. R., 1987: "Analysis of Wind Characteristics from Field wind Data," Master's Thesis, Department of Civil Engineering, Texas Tech University, Lubbock, Texas.
Lappe, U.O., and Davidson, B., 1963: "On the Range of Validity of Taylor's Hypothesis an the Kolmogoroflf Spectral Law," Journal of Atmospheric Sciences Vol 20 DO 569-576. ' '^^
Lei, Liu, 1994: "Integral Scales of Wind at Wind Engineering Research Field Site," Master's Report, Department of Civil Engineering, Texas Tech University, Lubbock, Texas.
Levitan, M. L., 1988: "Statistical Analysis to Validate Full Scale Wind and Structural Response Data," Master's Thesis, Department of Civil Engineering, Texas Tech University, Lubbock, Texas.
Levitan, M. L. and Mehta, K. C, 1991: "Texas Tech Field Experiments for Wind Loads Par I: Building and Pressure Measurement System," Journal of Wind Engineering and Industrial Aerodynamics. Vol., 43, pp. 1565-1576.
Levitan, M. L. and Mehta, K. C, 1991: "Texas Tech Field Experiments for Wind Loads Par II: Meteorological Instrumentation and Terrain Parameters," Eight International Conference on Wind Engineering. London, Ontario, Canada, July 8-12, pp. 1577-1588.
Lin, J. X., Surry, D., and Tieleman, H. W., 1995: "The Distribution of Pressure Near Roof Comers of Flat Roof Low Buildings," Department of Engineering Science and Mechanics Virginia Polytechnic Institute and State University, Blacksburg, Virginia.
Lumley, J. L., and Panofsky, H. A., 1964: The Structure of Atmospheric Turbulence. John Wiley and Sons, Inc., New York.
Mackey, S., and Lo, K. L., 1975: "Spatial Configuration of Gusts," Proceedings of the Fourth International Conference on Wind Effects on Buildings and Structures, pp. 41-52.
Maloney, S. P., 1994: "The Effect of Atmospheric Stabihty on Characteristics of Surface Layer Flows," Master's Thesis, Department of Atmospheric Science, Texas Tech University, Lubbock, Texas.
Miller, Irwin, Freund, John E., and Johnson, Richard A., 1990: Probability and Statistics ' for Engineers, Prentic-Hall, Inc., Englewood Cliffs, New Jersey
118
Milton, J. S., and Arnold, J. C, 1986: Introduction to Pmbabilitv and Stati tirg McGraw-Hill, Inc., New York.
Moore, G. E., Liu, M. K., and Shi, L. H., 1985: "Estimates of Integral Time Scales from a 100 m Meteorological Tower at a Plains Site," Boundary Layer Meteorology Vol. 31, pp. 349-368.
NRCC, 1990: "National Building Code of Canada 1980," National Research Council of Canada, Associate Committee of the National Buildmg Code, NRCC No. 17724, Ottawa, Canada.
Panofsky, H. A., and Duttan, J. A., 1984: Atmospheric Turbulence: Models and Methods for Engineering Apphcations. John Wiley and Sons, Inc., New York.
SAA, 1983: "SAA Loading Code," Part 2-Wind Forces (Austrahan Standard 1170, 1983), Standards Association of Australia, North Sydney, Australia
SAS/ETS User's Guide, 1990: Version 6, Fourth Edition, SAS Institute Inc., Cary, N.C.
Sethuraman S., 1979: "Structures ofTurbulence Over Water During High Winds," Journal of Applied Meteorology. Vol. 18, pp. 324-328.
Shoitani, M., and Iwatani, Y., 1979: "(Just Structures Over Flat Terrain and Their Modification by a Barrier," Proceedings of the Fifth International Conference on Wind Engmeering. Vol. 1, pp. 203-214.
Simiu, E., 1973: "Logarithmic Profiles and Design Wind Speeds," Journal of Engineering Mechanics Division. ASCE, October, pp. 1073-1083.
Simiu, E., and Scanlan, R. H., 1986: Wind Effects on Structures: An Introduction to Wind Engineering. John Wiley and Son Inc., New York.
Taylor, G. I., 1938: "The Spectrum ofTurbulence," Proceedings of Royal Society. London, A, 164, pp. 476-490.
Teunissen, H. W., 1979: "Measurements of Planetary Boundary Layer Wind and Turbulence Characteristics Over a Small Suburban Airport," Journal of Industrial Aerodynamics. Vol. 4, pp. 1-34.
Teunissen, H. W., 1980: "Structure of Mean Winds and Turbulence in the Planetary Boundary Layer Over Rural Terrain," Boundary Laver Meteorology. Vol 19, pp. 187-221.
119
Thomas, G., Cochran, L. S., Cermak, J. E., and Mehta, K. C, 1993: "Comparison of Field and Wind-Tunnel Measured Spectra," The Seventh United States National Conference on Wind Engineering. Vol. 7, pp. 793-802.
Tieleman, H. W., 1991: "The Atmospheric Surface Layer and Its Simulation for wind-Load Studies on Low-Rise Structures," Proceedings of the Eighth Coll. on Ind. Aerodyn.. Fachhochschyle Aachen, West Germany, 1989, Part 1, pp. 101-112.
Tieleman, H. W., and Mullins, S. E., 1979: "The Structure of Moderately Strong Winds at a Mid-Atlantic Coastal Site (Below 75m)," Proceedings of the Fifth International Conference on Wind Engineering. Vol. 1, pp.
120
APPENDIX A
MODE 15 DATABASE
(reference Diskette A for database in pocket)
121
Table A. l Mode 15 Database Titles
Titles Run
Number Date Time
Data Observation Number
Record Number Date
Mihtary Time Building Position Building Position Angle of Attack Angle of Attack
S3mean Mean Wind Speed at 3 ft (mph) S3 rms Root Mean Square of the Wind Speed at 3 ft S3max Maximum Wind Speed at 3 ft (mph) S3min Minimum Wind Speed at 3 ft (mph) S3turb Turbulence Intensity of the Wmd Speed at 3 ft /a
SSmean Mean Wind Speed at 8 ft (mph) S8rms Root Mean Square of the Wind Speed at 8 ft n S8max Maximum Wind Speed at 8 ft (mph) n S8min Minimum Wind Speed at 8 ft (mph) ȴ
S8turb S13Pmean S13Prms S13Pmax S13Pmin S13Pturb S13mean S13rms S13max S13min S13turb
S33mean S33rms S33max S33min S33turb
S70mean S70rms S70max S70min S70turb
S160mean S160rms
Turbulence Intensity of the Wind Speed at 8 ft Mean Wmd Speed at 13 ft from the pole (mph) /»
Root Mean Square of the Wind Speed at 13 ft from the pole Maximum Wmd Speed at 13 ft from the pole (mph)
n
I*
Mimmum Wind Speed at 13 ft from the pole (mph) Turbulence Intensity of the Wind Speed at 13 ft from the pole
/ I
Ce
Mean Wind Speed at 13 ft (mph) .>(
Root Mean Square of the Wmd Speed at 13 ft i i
Maximum Wind Speed at 13 ft (mph) Minimum Wind Speed at 13 ft (mph)
J ?
></
Turbulence Intensity of the Wind Speed at 13 ft ;> Mean Wind Speed at 33 ft (mph)
Root Mean Square of the Wmd Speed at 33 ft * 7
Maximum Wind Speed at 33 ft (mph) >v
Minimum Wind Speed at 33 ft (mph) i'i
Turbulence Intensity of the Wind Speed at 33 ft Ir
Mean Wind Speed at 70 ft (mph) Root Mean Square of the Wind Speed at 70 ft
Maxmium Wind Speed at 70 ft (mph) fj
Minimum Wind Speed at 70 ft (mph) J v /
Turbulence Intensity of the Wind Speed at 70 ft Mean Wmd Speed at 160 ft (mph)
Root Mean Square of the Wind Speed at 160 ft
122
Table A.1 con't S160max S160min S160turb LgSmean LgSrms LgSmax LgSmin LgSturb
Lg 13 mean Lgl3rms
Maximum Wind Speed at 160 ft (mph) Mmimum Wind Speed at 160 ft (mph)
i ' *
Turbulence Intensity of the Wind Speed at 160 ft Mean Longitudinal Wind Speed at 8 ft (mph)
Root Mean Square of the Longitudinal Wind Speed at 8 ft Maximum Longitudinal Wind Speed at 8 ft (mph) Minimum Longitudinal Wind Speed at 8 ft (mph)
Turbulence Intensity of the Longitudinal Wind Speed at 8 ft Mean Longitudinal Wind Speed at 13 ft (mph) ^1,
Root Mean Square of the Longitudinal Wind Speed at 13 ft Lgl3max Maximum Longitudinal Wind Speed at 13 ft (mph) Lgl3niin Minimum Longitudinal Wind Speed at 13 ft (mph) Lgl3turb Turbulence Intensity of the Longitudinal Wind Speed at 13 ft Lg33mean Mean Longitudinal Wind Speed at 33 ft (mph) n
Lg33rms Root Mean Square of the Longitudinal Wind Speed at 33 ft i^ Lg33max Maximum Longitudinal Wmd Speed at 33 ft (mph) Lg33min Minimum Longitudinal Wind Speed at 33 ft (mph) Lg33turb Turbulence Intensity of the Longitudinal Wmd Speed at 33 ft -
Lgl60mean Lgl60rms Lgl60max Lgl60min Lgl60turb LtSmean LtSrms LtSmax LtSmin LtSturb
Ltl3mean Ltl3rms Ltl3max Ltl3min Ltl3turb Lt33mean Lt33rms Lt33max Lt33mm Lt33turb
Ltl60mean
Mean Longitudinal Wind Speed at 160 ft (mph) Root Mean Square of the Longitudinal Wind Speed at 160 ft
Maximum Longitudinal Wmd Speed at 160 ft (mph) Minimum Longitudinal Wind Speed at 160 ft (mph)
Turbulence Intensity of the Longitudinal Wind Speed at 160 ft. Mean Lateral Wind Speed at 8 ft (mph)
Root Mean Square of the Lateral Wind Speed at 8 ft Maximum Lateral Wind Speed at 8 ft (mph) Minimum Lateral Wind Speed at 8 ft (mph)
Turbulence Intensity of the Lateral Wind Speed at 8 ft Mean Lateral Wind Speed at 13 ft (mph)
Root Mean Square of the Lateral Wind Speed at 13 ft Maximum Lateral Wind Speed at 13 ft (mph) Minimum Lateral Wind Speed at 13 ft (mph)
Turbulence Intensity of the Lateral Wind Speed at 13 ft Mean Lateral Wind Speed at 33 ft (mph)
Root Mean Square of the Lateral Wind Speed at 33 ft Maximum Lateral Wind Speed at 33 ft (mph) Minimum Lateral Wind Speed at 33 ft (mph)
Turbulence Intensity of the Lateral Wind Speed at 33 ft Mean Lateral Wind Speed at 160 ft (mph)
123
Table A. 1 con't Ltl60rms Ltl60max Lt 160mm Ltl60turb VSmean V8rms V8max
Root Mean Square of the Lateral Wind Speed at 160 ft Maximum Lateral Wind Speed at 160 ft (mph) Minimum Lateral Wind Speed at 160 ft (mph)
Turbulence Intensity of the Lateral Wind Speed at 160 ft Mean Vertical Wind Speed at 8 ft (mph)
Root Mean Square of the Vertical Wind Speed at 8 ft Maximum Vertical Wind Speed at 8 ft (mph) ^
V8min Minimum Vertical Wind Speed at 8 ft (mph) - VSturb Turbulence Intensity of the Vertical Wind Speed at 8 ft
V33mean Mean Vertical Wind Speed at 33 ft (mph) *u
V33rms Root Mean Square of the Vertical Wmd Speed at 33 ft 47 V33max Maximum Vertical Wind Speed at 33 ft (mph) i^ V33min Minimum Vertical Wind Speed at 33 ft (mph) *^
V33turb Turbulence Intensity of the Vertical Wind Speed at 33 ft DSmean Mean Wind Direction at 8 ft Oil
D8rms Root Mean Square of the Wind Direction at 8 ft D8max D8min
DSrange D13mean D13rms D13max D13min
D13range D33mean D33rms D33max D33min
D33range D160mean D160rms D160max D160min
D160range Tmean Trms Tmax Tmin
BPmean BPrms
Maximum Wind Direction at 8 ft Minimum Wind Direction at 8 ft
Turbulence Intensity of the Wind Direction at 8 ft Mean Wind Direction at 13 ft
Root Mean Square of the Wind Direction at 13 ft Maximum Wind Direction at 13 ft
47
<f3
Minimum Wind Direction at 13 ft Turbulence Intensity of the Wind Direction at 13 ft
Mean Wind Direction at 33 ft Root Mean Square of the Wind Direction at 33 ft 10!
Maximum Wind Direction at 33 ft Minimum Wind Direction at 33 ft
Turbulence Intensity of the Wind Direction at 33 ft Mean Wind Direction at 160ft
Root Mean Square of the Wind Direction at 160 ft Maxmium Wind Direction at 160ft Minimum Wind Direction at 160 ft
Turbulence Intensity of the Wind Direction at 160 ft Mean Temperature at 13 ft
Root Mean Square of the Temperature at 13 ft Maximum Temperature at 13 ft Mmimum Temperature at 13 ft
Mean Barometric Pressure Root Mean Square of the Barometric Pressure
124
Table A.1 con't BPmax BPmin Rmean Rrms Rmax Rmin
As/ftmean As/ftrms As/ftmax As/ftmin
Ak/ftmean Ak/ftrms Ak/ftmax Ak/ftmin Ltmean Ltrms Ltmax Ltmin Vmean
Maximum Barometric Pressure Minimum Barometric Pressure
Mean Relive Humidity Root Mean Square of the Rehve Humidity
Maximum Relive Humidity Minimum Relive Humidity
Mean Air Density (slug/ft^3) Root Mean Square of the Air Density (slug/ft^3)
Maximum Air Density (slug/ft^3) Minimum Air Density (slug/ft^3)
Mean Air Density (kg/m^3) Root Mean Square of the Air Density (kg/m^3)
Maximum Air Density (kg/m^3) 2*
Minimum Air Density (kg/m^3) i Z l
Mean Lateral Displacement of Purlin Root Mean Square of the Lateral Displacement of Purlin
Maximum Lateral Displacement of Purlm />->
Minimum Lateral Displacement of PurUn Mean Vertical Displacement of Purlin
Vrms Root Mean Square of the Vertical Displacement of Purlin Vmax Maximum Vertical Displacement of Purlin Vmin Minimum Vertical Displacement of Purhn
Dmean Mean Door Sensor Data (volts) Drms Root Mean Square of the Door Sensor Data Dmax Maximum Door Sensor Data (volts) Dmin Minimum Door Sensor Data (volts)
Dmean Mean Window Sensor Data (volts) vj?
Drms Root Mean Square of the Window Sensor Data Dmax Maximum Window Sensor Data (vohs) Dmin Minimum Window Sensor Data (vohs) / f /
S3stat SSstat
Stationarity of Wind Speed at 3 ft li-
Stationarity of Wind Speed at 8 ft Stationarity of Wind Speed at 13 ft from the pole S13Pstat
S13Tstat S33stat S70stat S160stat LgSstat
Lgl3stat Lg33stat
Stationarity of Wind Speed at 13 ft Stationarity of Wind Speed at 33 ft Stationarity of Wmd Speed at 70 ft Stationarity of Wind Speed at 160 ft
Stationarity of Longitudinal Wind Speed at 8 ft Stationarity of Longitudinal Wind Speed at 13 ft Stationarity of Longitudinal Wind Speed at 33 ft
125
Table A. 1 con't Lgl60stat
LtSstat Ltl3stat Lt33stat
Ltl60stat V8stat
V33stat DSstat
D13stat D33stat
Stationarity of Longitudinal Wind Speed at 160 ft Stationarity of Lateral Wind Speed at 8 ft Stationarity of Lateral Wmd Speed at 13 ft Stationarity of Lateral Wind Speed at 33 ft
Stationarity of Lateral Wind Speed at 160 ft Stationarity of Vertical Wind Speed at 8 ft
Stationarity of Vertical Wind Speed at 33 ft Stationarity of Wind Direction at 8 ft
Stationarity of Wind Direction at 13 ft Stationarity of Wind Direction at 33 ft
D160stat Stationarity of Wind Direction at 160 ft a Alpha Zo Surface Roughness (ft) u* Shear Velocity (mph) U*8 Shear Velocity at 8 ft (u-w correlation) (mph) U*33 Shear Velocity at 33 ft (u-w correlation) (mph)
Sector Mean Wind Direction Category (10° increments) Speed Mean Wind Speed Category Day Time of Day (hour)
Station Sum
Month Storm
Stationarity Category Flow Region
Time ofYear (month) Storm Type
126
APPENDIX B
MODE 15 DELETED RECORDS
127
Table B. 1 Mode 15 Deleted Records
Record Number
29 43 52 53 83
Portions Deleted
Wind speed at 13' from the moveable pole (13' P) turb/range Completely Deleted (Special) Wind speed at 13'P turb/range Completely Deleted (Special) Completely Deleted (Special) Completely Deleted (Special)
101 Wind speed at 8' mean and rms. Wind dhection at 8' rms and turb/range
103 Completely Deleted (Special) 104 Wind speed at 8' turb/range. Wind direction at 8' rms and turb/range 107 Wmd speed at 8' mean and rms. Wind direction at 8' rms and
turb/range 108
109
110
111 112 113 115 116 117 121
122
123 125
126 128 130 131 132 133
Wind speed at 8' mean and rms. Wind direction at 8' rms and turb/range Wind speed at 8' mean and rms. Wind direction at 8' rms and turb/range Wind speed at 8' mean and rms, Wind direction at 8' rms and turb/range Wind speed. Wind direction, and Lateral wind at 8' turb/range Lateral wind at 8' turb/range Lateral vyind at 8' turb/range Wind direction at 8' rms and turb/range Completely Deleted (Special) Completely Deleted Lateral wind at 8' turb/range. Wind direction at 8' rms and turb/range. Wind direction at 13' and 160' turb/range Lateral wind at 8' turb/range. Wind direction at 8' rms and turb/range. Wind direction at 13' turb/range Lateral wind at 8' turb/range. Wind direction at 8' rms and turb/range Lateral wind at 8' turb/range, Wind direction at 8' rms and turb/range. Wind direction at 13' turb/range . Completely Deleted (Special) Completely Deleted (Special) ^ Wind direction at 13' and 160' turb/range Completely Deleted Wind direction at 13' and 160' turb/range Completely Deleted (Special)
128
Table B.l con't
134
135
136 138
139
140 142
143 144
145 146 148
Completely Deleted Completely Deleted Wind direction at 13' turb/range Completely Deleted Wind direction at 13' and 160' turb/range Wind speed at 70' mean, rms, max., min., and turb/range Completely Deleted Wind direction at 13' turb/range Wmd direction at 13' turb/range Lateral vnnd at 8' and 13' turb/range. Wind direction at 8' rms Completely Deleted (Special) Wind speed at 70' mean, rms, max., min., and turb/range
149 Completely Deleted 150 Wind direction at 13' turb/range 262 Completely Deleted 267 Completely Deleted 305 Wind direction at 160' turb/range 320 Wind speed and du ection at 33' rms and turb/range. Longitudinal and
Lateral wind at 33' turb/range 329 Longitudinal and Lateral wind at 33' turb/range 351 352
356 391
399
401 405 418
419 420
452
453
516 517 518
519
520 521 522
Wind direction at 13' and 160' turb/range Wmd direction at 8', 13', and 160' turb/range Wind speed at 13' from the pole turb/range Completely Deleted Wind du-ection at 160' turb/range Wind direction at 160' turb/range Longitudinal and Lateral wind at 160' turb/range Wind direction at 13' turb/range Wind du-ection at 160' rms and turb/range Wind direction at 160' rms and turb/range Completely Deleted (Special) Completely Deleted (Special) Completely Deleted (Special) Completely Deleted Completely Deleted Lateral wind at 33' turb/range and Wind direction at 33' rms and turb/range Completely Deleted Completely Deleted Completely Deleted (Special)
129
Table B.l con't 523
525 538 558 559 561 568 572 589 591 592 621 623 624 625 626 633 645 678 696 699 717 732 733 735 736 737 740 741 742 743 744 747 749 750 751 752 753 755 756
Completely Deleted Completely Deleted Completely Deleted (Special) Completely Deleted Completely Deleted Completely Deleted (Special) Completely Deleted (Special) Completely Deleted Completely Deleted (Special) Completely Deleted Completely Deleted (Special) Completely Deleted Completely Deleted Completely Deleted Completely Deleted Completely Deleted Wind direction at 13' turb/range Completely Deleted Completely Deleted (Special) Completely Deleted (Special) Completely Deleted (Special) Completely Deleted (Special) Wind direction at 160' turb/range Completely Deleted Completely Deleted Wind direction at 160' rms and turb/range Completely Deleted Completely Deleted Wind direction at 13' rms and turb/range Wind direction at 13' and 160' rms and turb/range Wind direction at 13' rms and turb/range Wind direction at 13' rms and turb/range Completely Deleted Wind direction at 13' and 160' turb/range Wind direction at 13' and 160' turb/range Completely Deleted Wind direction at 13' and 160' turb/range Completely Deleted Completely Deleted Completely Deleted 1
130
Table B.l con't 759 760 764 111 783 785 786 800
Completely Deleted Completely Deleted Completely Deleted (Special) Completely Deleted Completely Deleted Wind direction at 13' turb/range Wind direction at 13' turb/range Completely Deleted
131
APPENDIX C
COMPLETED MODE 15 DATABASE
(reference Diskette B m pocket)
132
APPENDIX D
PARAMETERS VERSUS SECTOR
133
Alpha
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
t «
ih • t
• » * • •
0
• I l • : : • I
12 24 16 20
Sector Figure D. 1 a versus Sector
28 32 36
0.25
0.20
0.15
Zo,ft
0.10
0.05
0.00
hi *i 0 8
*: r , • • •
t 1 1 •
.ti
• •
12 16 20
Sector 24 28 32 36
Figure D.2 zo versus Sector
134
3.0
2.5
2.0
Ustar, mph
1.5
1.0
: :
•ii=ii'ilijiP * • A A A *
• #
il u
0.5 0
2.5
12 16 20
Sector
24
Figure D.3 u* versus Sector
28 32 36
2.0
1.5
Ustar33, mph
1.0
0.5
! ;
* ! • • I t J
•
0.0 0 12 16 20
Sector
24 28 32 36
Figure D.4 u*33 versus Sector
135
0.35
0.30
Iui3
0.25
0.20
0.15
0.10 10 15 20
Sector 25 30 35 40
Figure D.5 Iui3 versus Sector
136
APPENDIX E
FLOW PARAMETERS VERSUS STATIONARITY
137
Alpha
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
•
1.0
I S 6 ft i
2.0 3.0
Stationarity
I
4.0
0.25
Figure E. 1 a versus Stationarity
Zo,ft
0.20
0.15
0.10
0.05
0.00
I I I i
1.0
I i t
I
2.0 3.0
Stationarity
!
i 1 4.0
Figure E.2 zo versus Stationarity
138
3.0
2.5
2.0
Ustar, mph
1.5
1.0
0.5
2.5
2.0
1.5
Ustar33, mph
1.0
0.5
0.0
•
I 1.0 2.0 3.0
Stationarity
Figure E.3 u* versus Stationarity
1.0 2.0 3.0
Stationarity
Figure E.4 u*33 versus Stationarity
i
I
4.0
*
4.
t «
• « • •
1
•
i 1
i t
1 1 »
4.0
139
Zo,ft
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0.20
t t •
I 1.0
I t
I *
t
2.0 3.0
Stationarity 4.0
Figure E.5 zo versus Stationarity for Region 1
0.15
Zo, ft 0.10
0.05
0.00
t
I
I 1.0
I * *
2.0 3.0 Stationarity
4.0
Figure E.6 zo versus Stationarity for Region 2
140
Zo,ft
0.20
0.15
0.10
0.05
0 00
• •
•
•
1 t
t
•
1
•
: •
•
i
1 1.0 2.0 3.0
Stationarity 4.0
Zo,ft
Figure E.7 zo versus Stationarity for Region 3
0.16
0.12
0.08
0.04
0.00 1.0
t
I t
2.0 3.0
Stationarity
Figure E.8 zo versus Stationarity for Region 4
«
4.0
141
0.12
0.10 •
0.08
Zo, ft 0.06
0.04
0.02
0.00
t
I I
1.0
•
I i t
I
L 2.0 3.0
Stationarity
t
To"
Figure E.9 zo versus Stationarity for Region 5
142
APPENDIX F
TYPICAL PLOTS OF PARAMETERS VERSUS TIME OF YEAR
143
a
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10 0
I !
!
4 6 8
Time ofYear (month)
10
S t t
t •
12
0.25
Figure F. 1 a versus Time of Year
Zo, ft
0.20
0.15
0.10
0.05
0.00
t I I
I I i 4 6 8
Time ofYear (month)
10
t I
• i 12
Figure F.2 zo versus Time ofYear
144
3.0
2.5
2.0
u. , m p h
1.5
1.0
I i I
I I
t
i •
t
0.5 4 6 8
Time ofYear (month)
10 12
Figure F.3 u* versus Time of Day
2.5
u.33, mph
2.0
1.5
1.0
0.5
•
t i I t
i I I I t
I i i •
0.0 4 6 8
Time ofYear (month)
10 12
Figure F.4 u*33 versus Time of Day
145
u
I I IS
0.35
0.30
025
0.20
015
i t
•
•
• • •
i
I I
t
OlO 4 6
Time ofYear (month) 10 12
Figure F.5 Lateral Turbulence Intensity at 13 ft versus Tune ofYear
5
J 3
•e 3 H •a .s •t
035
0.30
025
0.20
015
0.10
•
t I
I
I
i I t
4 6 8
Time ofYear (month)
i !
10 12
Figure F.6 Longitudinal Turbulence Intensity at 13 ft versus Time ofYear
146
PERMISSION TO COPY
In presenting this thesis in partial fulfillment of the
requirements for a master's degree at Texas Tech University or
Texas Tech University Health Sciences Center. I agree that the Library
and my major department shall make it freely available for research
purposes. Permission to copy this thesis for scholarly purposes may
be granted by the Director of the Library or my major professor. It
is understood that any copying or publication of this thesis for
financial gain shall not be allowed without my further written
permission and that any user may be liable for copyright infringement.
Agree (Permission is granted.)
•Student's Signature tudent's Signature Date
Disagree (Permission is not granted.)
Student's Signature Date
