vvEPA
United States Atmospheric Sciences Research
Environmental Protection Laboratory
Agency Research Triangle Park NC 27711
EPA/600/3-85/069
Jan. 1986
Research and Development
EPA Complex
Terrain Model
Development:
Fifth Milestone
Report—1985
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EPA/600/3-85/069
EPA COMPLEX TERRAIN MODEL DEVELOPMENT
Fifth Milestone Report - 1985
by
Donald C. DiCristofaro
David G. Strimaitis
Benjamin R. Greene
Robert J. Yamartino
Akula Venkatram
Daniel A. Godden
Thomas F. Lavery
Bruce A. Egan
ENVIRONMENTAL RESEARCH & TECHNOLOGY, INC.
696 Virginia Road, Concord, Massachusetts 01742
Contract No. 68-02-3421
Project Officer
Peter L. Finkelstein
Meteorology and Assessment Division
Atmospheric Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
ATMOSPHERIC SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
4, T prr-»-,-.otion Agency
ff.C. r:-'rr-^>~'\-;.. _., f ,
~ ' ' ' ' . .+ Hocio 1670
Chicago,
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NOTICE
The information in this document has been funded by the
United States Environmental Protection Agency under Contract
No. 68-02-3421 to Environmental Research and Technology,
Inc. It has been subject to the Agency's peer and
administrative review, and it has been approved for
publication as an EPA document.
Mention of trade names or commercial products does not
constitute endorsement or recommendation for use.
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PREFACE
The Atmospheric Sciences Research Laboratory (ASRL) conducts
intramural and extramural research programs in the physical sciences
to detect, define, and quantify air pollution and its effects on
urban, regional, and global atmospheres and the subsequent impact on
water quality and land use. The Laboratory is responsible for
planning, implementing, and managing research and development programs
designed to quantify the relationships between emissions of pollutants
for all types of sources with air quality and atmospheric effects, and
to uncover and characterize hitherto unidentified air pollution
problems. Information from ASRL programs and from the programs of
other government agencies, private industry, and the academic
community are integrated by the Laboratory to develop the technical
basis for air pollution control strategies for various pollutants.
The Complex Terrain Model Development (CTMD) program is designed
to develop reliable atmospheric dispersion models that are applicable
to large pollutant sources located in complex terrain. Three major
field studies were conducted during this six-year program. The first
field measurements were collected at Cinder Cone Butte near Boise,
Idaho during the fall of 1980. The second experiment was conducted at
the Hogback Ridge near Farmington, New Mexico in October 1982. The
third series of experiments were conducted in November 1983 and August
1984 at the Tracy Power Plant near Reno, Nevada. Data from these
field studies along with measurements of fluid modeling simulations
performed in the EPA Fluid Modeling Facility are being used to
quantify the effects of terrain obstacles on stable plume dispersion.
A series of annual milestone reports have been issued to describe the
development of the Complex Terrain Dispersion Model (CTDM) to contrast
the performance evaluation of the CTDM against existing complex
terrain dispersion models. This Fifth Milestone Report describes the
August 1984 field experiment. It discusses the continuing development
of the CTDM and evaluates model performance using impingement data
sets from the three experiment sites.
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ABSTRACT
The Complex Terrain Model Development (CTMD) project is being
sponsored by the U.S. Environmental Protection Agency to develop
atmospheric dispersion models to simulate air pollutant concentrations
in complex terrain that result from emissions from large sources. The
emphasis of the program is to develop models with known accuracy and
limitations for simulating 1-hour concentrations in complex terrain
during stable conditions.
This Fifth Milestone Report documents work accomplished from June
1984 through May 1985. It describes in detail the August 1984 Full
Scale Plume Study, including its setting, the experimental design, and
the resulting data base. The FSPS produced a 128-hour data set of
SFg and CF3Br concentrations, ground-based and airborne lidar
measurements, photographs, 8-mm movies, videotapes, and extensive
meteorological data. The highest ten SFg and CF3Br concentrations
and a modeling analysis of 14 hours are discussed in this report.
The refinement of the HBR meteorological data base is essentially
complete. The HBR data have been used to show that the path of the
oil-fog plume centerline was predicted well by assuming the layer of
air below the dividing streamline to be "dead" and by incorporating
the effects of temperature stratification. Boundary layer similarity
relationships simulated satisfactorily the winds and temperature
measured at CCB and HBR up to an altitude of about 10L (ten times the
Monin-Obukov length).
This milestone report also discusses the highest ground-level
tracer concentrations measured at the CCB, HBR, and FSPS sites. The
meteorological characteristics of the concentration events and the
differences among the sites are discussed.
The further development of CTDM is described. Mathematical
descriptions of the modifications to the model are presented. The
latest version of the model has been tested using a subset of
impingement hours from the CCB, HBR, and FSPS data bases. The initial
14-hour FSPS data base was also used to test four existing complex
terrain models—COMPLEX I and II, Valley, and RTDM.
IV
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An EPA Fluid Modeling Facility report describing towing tank
simulations to characterize the effects of stability on the horizontal
and vertical deflections around an isolated hill is included as an
appendix.
This report was submitted in partial fulfillment of contract
68-02-3421 by Environmental Research & Technology, Inc. under the
sponsorship of the U.S. Environmental Protection Agency. This report
covers the period June 2, 1984 to June 1, 1985.
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CONTENTS
1. Introduction 1
2. Full Scale Plume Study 5
2.1 Geographic and Meteorological Setting 5
2.2 Preliminary Experiment 6
2.3 FSPS Experimental Design 10
2.4 Preliminary Evaluation of FSPS and Database ... 28
3. Data Analysis 31
3.1 Refinement of HBR Meteorological Tower Data ... 31
3.2 HBR Streamline Analysis 58
3.3 Representativeness of Stable Boundary Layer
Similarity Theory 75
3.4 Analysis of oz(t) Observed During FSPS 91
4. Analysis of Highest Ground-Level Concentrations at
Each Site 108
4.1 Cinder Cone Butte 108
4.2 Hogback Ridge 117
4.3 FSPS 136
4.4 Comparison of Field Sites 152
5. Model Development and Applications to CTMD
Experimental Data 153
5.1 Description of the Current Version of CTDM .... 153
5.2 Simulations of Impingement Cases 170
5.3 Modeling Freon Releases at HBR 175
5.4 Modeling Tracy 188
6. CTDM — Improvements and Modifications 218
6.1 Stratified Airflow Over a Three-Dimensional Hill 218
6.2 Connection between the Hunt and Mulhearn (1973)
Approach and CTDM 221
6.3 Applicability of CTDM to Other Sites 225
7. Summary, Conclusions and Recommendations for Further
Study 229
7.1 Principal Accomplishments and Conclusions .... 229
7.2 Recommendations for Further Study 233
References 236
Appendix: Streamline Trajectories in Neutral and Stratified
Flow Over a Three Dimensional Hill 240
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FIGURES
Number Page
1. The region around the Tracy Power Plant 7
2. Plant site 8
3. View of the Tracy Power Plant looking east from
"Old Lonesome." "Target Mountain" and "Beacon Hill"
can be seen at the eastern end of the valley 9
4. FSPS field experiment layout 12
5. Tracer gas sampling sites 19
6. FSPS data acquisition system for 150-m tower 21
7. Time series of sonic (....) and propeller ( )
ow data from 40 m, Tower A during Experiment 6 37
8. Time series of sonic (....) and propeller ( )
ow data from 40 m, Tower A during Experiment 12 38
9. Time series of sonic (....) and propeller ( )
<3w data from 5 m, Tower A during Experiment 6 39
10. Time series of sonic (....) and propeller ( )
ctw data from 5 m, Tower A during Experiment 12 40
11. Time series of sonic ( ) and propeller ( )
crv data from 40 m, Tower A during Experiment 12 41
12. Differences between prop-derived wind direction D
and sonic-derived wind direction DS vs. DS for
Experiments 4 to 6 from 40 m, Tower A 43
13. Differences between vane (DX) and sonic (DS) wind
direction vs. DS for Experiments 4 to 6 from 40 m,
Tower A 44
14. Differences between vane (DX) and prop (D) wind
direction for Experiments 4 to 6 from 40 m, Tower A .... 45
15. Differences between prop speeds (S) and sonic
speeds (SS) as fraction of SS vs. sonic direction
for Experiments 4 to 6 from 40 m, Tower A 46
vm
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FIGURES (Continued)
Number Pag
16. Differences between cup speeds (SX) and sonic speeds
(SS) as fraction of SS vs. sonic direction for
Experiments 4 to 6 from 40 m, Tower A 47
17. Differences between prop speeds (S) and cup
speeds (SX) as fraction of SX vs. vane direction
for Experiments 4 to 6 from 40 m, Tower A 48
18. Differences between vane (DX) and sonic (DS) wind
direction vs. DS for Experiment 8 from 40 m,
Tower A 50
19. Differences between cup speeds (SX) and sonic
speeds (SS) as fraction of SS vs. sonic wind
direction for Experiment 8 from 40 m, Tower A 51
20. Differences between prop direction (D) and sonic
direction (DS) vs. DS for Experiments 10 to 14
from 40 m, Tower A 52
21. Differences between vane direction (DX) and sonic
direction (DS) vs. DS for Experiments 10 to 15
from 40 m, Tower A 53
22. Differences between vane direction (DX) and prop
direction (D) vs. DX for Experiments 7 to 14 from
40 m, Tower A 54
23. Differences between cup (SX) and sonic (SS) wind
speeds as a fraction of SS vs. sonic direction
for Experiments 10 to 15 from 40 m, Tower A 55
24. Differences between prop (S) and sonic (SS) wind
speeds as fraction of SS vs. sonic direction for
Experiments 10 to 14 from 40 m, Tower A 56
25. Differences between prop (S) and cup (SX) wind
speeds as fraction of SX vs. vane direction for
Experiments 10 to 14 from 40 m, Tower A 57
26. Differences between vane direction (DX) and prop
direction (D) vs. DX for Experiments 9 to 15 from
40 m, Tower A, preliminary data base 59
27. Differences between vane direction (DX) and prop
direction (D) vs. DX for Experiments 9 to 15 from
40 m, Tower A, refined data base 60
IX
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FIGURES (Continued)
Number Page
28. The relationship between the initial (H) and the
final (n) height of the streamline, the
dividing-streamline height (Hc), half the hill
height (A/2), and half the hill breadth at A/2
(L) . H is measured a distance xc from the center
of the hill ........................ 62
29a. Height of the source streamline (n) above the
crest of HBR for various source heights (H) .
Values are scaled by the height of HBR (A) ........ 65
29b. Height of the source streamline (YI) above the
crest of HBR for various effective source heights
(H - Hc) . Values are scaled by the effective hill
height (H*) ........................ 65
30. Predicted versus observed plume centerline standoff
distance (ETA) at the crest of HBR using the empirical
equation (5) ....................... 68
31. Predicted versus observed plume centerline standoff
distance at the crest of HBR using the "outer-layer"
solution (Eq. 20) of Hunt et al. (1980) that includes
stratification but neglects shear ............. 72
32. Predicted versus observed plume centerline standoff
distance at the crest of HBR using equation (7)
that includes both stratification and shear.
The shear was computed using spline interpolated
values of u(Hc) and u(H) , the assumption B=a^,
and a local parabolic determination of a ......... 74
33. Comparison of the observed wind speed at 40 m with
that estimated from surface-layer similarity theory
and Rit, (10 m) at CCB ................... 78
34. Comparison of the observed potential temperature
difference between 10 m and 40 m with that estimated
from surface-layer similarity theory and Ri^
(10 m) at CCB ....................... 79
35 . Comparison of the observed wind speed at 40 m with
that estimated from the Webb extension to the
surface-layer similarity theory and Ri^ (10 m)
at CCB .......................... 80
36 . Comparison of the observed potential temperature
difference between 10 m and 40 m with that estimated
from the Webb extension to the surface-layer
similarity theory and Ri^, (10 m) at CCB .......... 81
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FIGURES (Continued)
Number Paj
37. Comparison of the observed wind speed at 40 m with
that estimated from the van Ulden/Holtslag
extension to the surface-layer similarity theory
and Rifc (10 m) for those data contained in
Figure 33 83
38. Comparison of observed potential temperature
difference between 10 m and 40 m with that estimated
from the van Ulden/Holtslag extension to the
surface-layer similarity theory and Rij, (10 m)
for those data contained in Figure 34 84
39. Comparison of the observed wind speed at 40 m with
that estimated from the van Ulden/Holtslag
extension to the surface-layer similarity theory
and Rib (10 m) for all stable hours at CCB 85
40. Comparison of the observed potential temperature
difference between 10 m and 40 m with that estimated
from the van Ulden/Holtslag extension to the
surface-layer similarity theory and Ri^ (10 m)
for all stable hours at CCB 86
41. Comparison of the observed wind speed at 150 m
with that estimated from the van Ulden/Holtslag
extension to the surface-layer similarity theory
and Rib (10 m) for all stable hours at CCB 88
42. Comparison of the observed potential temperature
difference between 10 m and 150 m with that estimated
from the van Ulden/Holtslag extension to the
surface-layer similarity theory and Ri^ (10 m)
for all stable hours at CCB 89
43. Variation of aw/u* with non-dimensional
height z/L at CCB. Data are obtained at or
interpolated to the release elevation of the
oil-fog plume 90
44. Comparison of values of Monin-Obukhov length L
obtained for HBR using the bulk Richardson number
method and gradients obtained between 2 m and 5 m,
and 2 m and 10 m. The three circled data points
are from hours in which the meteorological tower
is in the lee of HBR 92
45. Comparison of observed wind speed (top) at 40 m and
potential temperature difference (bottom) between
10 m and 40 m with that estimated from the van
Ulden/Holtslag extension to the surface-layer
similarity theory and Rij, (10 m) for all stable
hours at HBR 93
xi
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FIGURES (Continued)
Number
46. Variation of oz/owT with T/TL using the
CTDM formulation for
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FIGURES (Continued)
Number Pa&t
55. One-hour averaged observed SFg concentrations
scaled by emission rate (ys/m^) (CCB, Experiment
206, 10/24/80, 0700-0800 MST) 115
56. Time series of 5-minute calculated dividing-
streamline heights (Hc) and bulk hill Froude
number above Hc (Fr(Hc)) (HER, Experiment 6,
10/13/82, 0700-0800 MDT) 119
57. Time series of 5-minute propeller anemometer data
from Tower B (HER, Experiment 6, 10/13/82,
0700-0800 MDT). Values at CF3Br release height
( ), 5 m ( ), and 30 m ( ) 121
58. Vertical profiles of hourly meteorological data
from Tower A (HBR, Experiment 6, 10/13/82,
0700-0800 MDT) 122
59. Potential temperature and wind measurements cross
section at HBR. The values at each instrument level
are the perpendicular component of the wind to the
ridge (m/s), the parallel component (m/s), and the
potential temperature (°C). The solid lines with
arrows are isentropes and the dashed line represents
the critical dividing-streamline height. (HBR,
Experiment 6, 10/13/82, 0700-0800 MDT) 123
60. One-hour averaged observed CF^Br concentrations
scaled by emission rate (ys/ne) (HBR, Experiment
6, 10/13/82, 0700-0800 MDT) 125
61. Instantaneous photo from Tower A of release
position with plume traveling over the ridge (HBR,
Experiment 7, 10/14/82, 0655 MDT) 126
62. Time series of 5-minute calculated dividing-
streamline heights (Hc) and bulk hill Froude
numbers above Hc (Fr(Hc)) (HBR, Experiment 7,
10/14/82, 0600-0700 MDT) 127
63. Time series of 5-minute propeller anemometer data
from Tower A. (HBR, Experiment 7, 10/14/82,
0600-0700 MDT). Values at SF6 release height
( ), 40 m ( ), and 80 m ( ) 129
64. Turbulence measurements cross section at HBR. The
values at each instrument level are ou, ov,
and ow (m/s). (HBR, Experiment 7, 10/14/82,
0600-0700 MDT) 130
xm
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FIGURES (Continued)
Number Page
65. Vertical profile of hourly meteorological data from
Tower A (HER, Experiment 7, 10/14/82, 0600-0700
MDT) 131
66. Potential temperature and wind measurements cross
section at HER. The values at each instrument
level are the perpendicular component of the wind
to the ridge (m/s), the parallel component (m/s),
and the potential temperature (°C). The solid
lines with arrows are isentropes and the dashed line
represents the critical dividing-streamline
height. (HER, Experiment 7, 10/14/82, 0600-0700
MDT) 132
67. One-hour averaged observed SF* concentrations
scaled by emission rate (ys/nr) (HER,
Experiment 7, 10/14/82, 0600-0700 MDT) 133
68. Instantaneous photo from the crest of HER
showing the plume as it surmounts the hill (HER,
Experiment 7, 10/14/82, 0710 MDT) 134
69. Instantaneous photo from the crest of HER
looking towards the lee where the plume is
impacting (HER, Experiment 7, 10/14/82, 0710 MDT) 135
70. Two-dimensional display of the plume cross section
along the path of the lidar scan (FSPS, 08/26/84,
0800-0900 PDT) 139
71. Time series of 5-minute calculated dividing-
streamline heights (Hc) (FSPS, Experiment 13,
08/26/84, 0800-0900 PDT) 140
72. Top: Time series of cup and vane wind data at
150 m ( ), 100 m ( ), and 75 m ( )
Bottom: Time series of propeller anemometer
turbulence at 150 m ( ), 125 m ( ), and
100 m ( ). (FSPS, Experiment 13, 08/26/84,
0700-0900 PDT) 141
73. Vertical profiles of hourly meteorological data
from Tower A (FSPS, Experiment 13, 08/26/84,
0700-0800 PDT) 143
74. One-hour averaged observed SFt concentrations
scaled by emission rate (ys/ne) (FSPS,
Experiment 13, 08/26/84, 0800-0900 PDT) 144
xiv
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FIGURES (Continued)
Number Page
75. Instantaneous exposure with a polarizing filter
taken from Old Lonesome of the plume as it
interacts with Beacon Hill (FSPS, Experiment 13,
08/26/84, 0800 PDT) 145
76. Instantaneous exposure taken from Clark Mountain
of the plume traveling over the river valley (FSPS,
Experiment 13, 08/26/84, 0845 PDT) 146
77. The lidar measured plume centroid positions (FSPS,
Experiment 13, 08/26/84, 0800-0815 PDT) 147
78. The lidar measured plume centroid positions (FSPS,
Experiment 13, 08/26/84, 0820-0834 PDT) 148
79. The lidar measured plume centroid positions (FSPS,
Experiment 13, 08/26/84, 0840-0854 PDT) 149
80. Time series of 5-minute lidar derived plume
direction measured in degrees from north (FSPS,
Experiment 13, 08/26/84, 0800-0900 PDT) 150
81. Time series of 5-minute lidar derived vertical
displacement of the plume centroid above the stack
(FSPS, Experiment 13, 08/26/84, 0800-0900 PDT) 151
82. Typical streamline patterns in two-dimensional flow
around an elliptical cylinder 155
83. Sketch of the flow around an ideal cylinder of
elliptical cross-section 158
84. Definition of modeling variables, illustrating in
particular the coordinate system in which the Xg-axis
is aligned with the tangent to the stagnation
streamline at the impingement point (the
B-coordinate system) 161
85. Definition of modeling variables for flow above He .... 164
86. Variation of observed-to-modeled ratios of HER
single maximum hourly concentrations with angle
between the stagnation line and line to receptor
(29 hours) 182
87. Variation of observed-to-modeled ratios of HBR
single maximum hourly concentrations with
zr/Hc (29 hours) 183
88. Scatter plot of scaled (C/Q ys/m^) observed and
modeled concentrations (peak 1, top 2, top 5) for 29
hours of HBR data 185
XV
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FIGURES (Continued)
Number
89. One-hour average observed CF3Br concentrations
scaled by emission rate (ys/m3) (Experiment 11,
10/23/82, 0200-0300 MDT) 186
90. One-hour average predicted scaled concentrations
(ys/m3) from the HBR model (Experiment 11,
10/23/82, 0200-0300 MDT) 187
91. One-hour average observed CF3Br concentrations
scaled by emission rate (ys/m3) (Experiment 11,
10/23/82, 0600-0700 MDT) 189
92. One-hour average predicted scaled concentrations
(ys/m3) from the HBR model (Experiment 11,
10/23/82, 0600-0700 MDT) 190
93. One-hour average observed CF3Br concentrations
scaled by emission rate (ys/m3) (Experiment
14, 10/26/82, 0500-0600 MDT) 191
94. One-hour average predicted scaled concentrations
(ys/m3) from the HBR model (Experiment 14,
10/26/82, 0500-0600 MDT) 192
95. One-hour average predicted scaled concentrations
(ys/m3) from COMPLEX I, Stability Class C
(Experiment 13, 8/26/84, 0800-0900 PDT) 200
96. One-hour average observed scaled concentrations
(ys/m3) (Experiment 13, 8/26/84,
0800-0900 PDT) 201
97. One-hour average predicted scaled concentrations
(ys/m3) from COMPLEX I, Stability Class F
(Experiment 13, 8/26/84, 0800-0900 PDT) 203
98. One-hour average predicted scaled concentrations
(ys/m3) from COMPLEX II, Stability Class C
(Experiment 13, 8/26/84, 0800-0900 PDT) 204
99. One-hour average predicted scaled concentrations
(ys/m3) from COMPLEX II, Stability Class F
(Experiment 13, 8/26/84, 0800-0900 PDT) 205
xv i
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FIGURES (Continued)
Number Page
100. One-hour average predicted scaled concentrations
(ys/m3) from RTDM, Stability Class C using
measured turbulence (Experiment 13, 8/26/84,
0800-0900 PDT) 208
101. One-hour average predicted scaled concentrations
(ys/m3) from RTDM, Stability Class F using
measured turbulence (Experiment 13, 8/26/84,
0800-0900 PDT) 209
102. One-hour average predicted scaled concentrations
(ys/m3) from RTDM, Stability Class C using
Briggs rural (ASME, 1979) dispersion coefficients
(Experiment 13, 8/26/84, 0800-0900 PDT) 211
103. One-hour average predicted scaled concentrations
(ys/m3) from RTDM, Stability Class F using
Briggs rural (ASME, 1979) dispersion coefficients
(Experiment 13, 8/26/84, 0800-0900 PDT) 212
104. One-hour average predicted scaled concentrations
(ys/m3) from CTDM (12185) (Experiment 13,
8/26/84, 0800-0900 PDT) 217
xvii
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TABLES
Number Page
1. Summary of ERT FSPS Responsibilities 13
2. Summary of NOAA ARLFRD FSPS Responsibilities 15
3. Summary of NOAA WPL FSPS Responsibilities 17
4. 150-M Tower Sensor Locations and Measures 22
5. Definition of Measures 23
6. FSPS Experiment Hours of Tracer Release and
Concentrations 29
7. Filter Limits for Tower Measurements 32
8. Corrections Made to Instrument Outputs 35
9. HBR Streamline Standoff at Crest Modeling 67
lOa. Ten Highest x/Q Observed SFg Concentrations
at CCB 109
lOb. Ten Highest x/Q Observed CF3Br Concentrations
at CCB 109
lla. Ten Highest x/Q Observed SF^ Concentrations
at HBR 118
lib. Ten Highest x/Q Observed CF3Br Concentrations
at HBR 118
12a. Ten Highest x/Q Observed SFg Concentrations
at FSPS 137
12b. Ten Highest x/Q Observed CF3Br Concentrations
at FSPS 137
13. Comparison of Modeled and Observed Concentrations
for Stable Impingement Hours at CCB 172
14. Modeled Hours from the HBR MDA Applied 174
15. Comparison of Modeled and Observed Concentrations
for Subset of the HBR CF3Br Data Base 176
16. Summary Statistics for HBR Model 179
17. Comparison of Modeled and Observed Concentrations
for 36-hour Subset of the HBR CF3Br Data Base 181
18. Summary of FSPS Model Input Data 194
xv i i i
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TABLES
Number Page
19. Summary x/Q Statistics for VALLEY Calculations 196
20. Summary x/Q Statistics for COMPLEX I
Calculations 198
21. Summary x/Q Statistics for COMPLEX II
Calculations 199
22. Summary x/Q Statistics for RTDM Calculations
Using On-Site Turbulence Data 207
23. Summary x/Q Statistics for RTDM Calculations
Using Briggs-Rural/ASME—1979 Dispersion
Coefficients 210
24. Summary x/Q Statistics for CTDM Calculations 214
25. Comparison of Peak Modeled and Observed Scaled
Concentrations with Centerline Concentrations
Estimated from Plume Spread Parameters from
CTDM 215
xix
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LIST OF SYMBOLS AND ABBREVIATIONS
SYMBOL
a Ratio of a to u.. (Subsection 3.3)
w *
a(z) Radius of an ideal hill circular in horizontal
cross-section
a1 Separation distance of source/sink pair
A Height of hill
a Relaxation scale factor for decrease in terrain effect
away from hill (Section 6)
o Boundary layer profile parameter (Subsection 3.3)
a First derivative of wind speed profile (Subsection 3.2)
a Wind direction at infinity
w
B Boundary layer profile parameter (Subsection 3.3)
B Second Derivative of wind speed profile (Subsection 3.2)
B Rotation angle (Subsection 5.1)
C Concentration
C Mean concentration from many "filament" plumes
m
C Observed concentration
o
C Modeled concentration
X Concentration
d Downwind distance of sampler (Section 4)
d Distance from the centerline of the plume to the
stagnation streamline associated with the mean wind
direction (Section 6)
d Stack diameter
s
D Diffusivity
D Mean diffusivity over the interval s-s
m o
& Scale factor for LIFT-WRAP transition zone (Section 6)
6 Streamline deflection (Subsection 3.2.2)
6 Vertical deflection of the plume streamline
z
6H Scale of transition zone
c
6 Streamline deflection due to stratification only
Ah.Az Plume height change due to buoyancy of emission
Aw Vertical velocity perturbation
Az Plume height above H (Section 4)
XX
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SYMBOL
A(x-x') Dirac delta function
e Error or residual
f Shape of terrain
f(x) Distance function
F Buoyancy flux
Fr Froude number based on hill height
Fr(Hc) Bulk hill Froude number above H
c
F Vertical distribution factor
z
g Acceleration due to gravity
Y Scale factor for the "stable" mixing length
P Scale factor for the "neutral" mixing length
h Terrain elevation above a reference elevation
h Height of the zero-plane above the elevation
defined as zero in the coordinate system
being used
h(x) Terrain function
H Initial streamline height (Subsection 3.2.1
and Section 4)
H Hill height (crest)
H Critical dividing-streamline height
H^ Effective hill height
n Height of plume centroid above terrain
n . Average observed streamline height
i , i ,i Turbulence intensities alongwind, crosswind, and
x y z
vertical
k x wavenumber (Section 6)
k Wave number along flow (Subsection 3.2.2)
k von Karman Constant (Subsection 3.1)
K Diffusivity
1C. Diffusivity in the absence of terrain
K^ Eddy diffusivity for heat
K ,K' Mean diffusivity over the interval s-s .
Prime denotes mean diffusivity in altered flow.
xxi
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SYMBOL
K Eddy diffusivity for momentum
z
6 Wind direction (Section A)
6 Potential temperature (Subsection 3.3)
6^ Scaling temperature
6 Mean wind direction of approach flow
6 Direction from effective receptor position to source
6* Mean wind direction that carries the deflected plume
centerline over the receptor
6*' Value of 0* after being shifted to simulate the
r r
LIFT/WRAP transition region
0 Direction of the stagnation streamline
s
9, Mixing length (Subsection 3.3)
8, y wavenumber (Section 6)
9. Ratio of Brunt-Vaisala frequency to the wind speed
(Subsection 3.2 )
fi. Along-wind breadth of ellipse (Subsection 3.2.1)
B, Neutral mixing length
n
8. Stable mixing length
s
L Monin-Obukhov length (Subsection 3.3)
L Horizontal Scale of hill (Subsection 3.2)
L Hill length approximation
c
X Wavelength of disturbances generated by the hill
X Aspect ratio of hill (Subsection 3.2)
m Slope
m Vertical wave number (Subsection 3.2.2)
m Arithmetic mean
3.
m Geometric mean
g
M Kummer Function
y,w Elliptical coordinates
u Value of v on boundary of ellipse
o
iT , v Elliptical coordinates
Hs' s e
N Brunt-Vaisala frequency
N. Bulk Brunt-Vaisala frequency for a layer
xxii
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SYMBOL
p Power for wind speed profile power law
p Trial function (Subsection 3.2)
p Hill shape profile exponent (Subsection 5.1)
p' Pressure fluctuation
P(9) Wind direction probability distribution function
P(H ) H probability distribution function
c c
P Pressure
. Nondimensional potential temperature gradient
-------
SYMBOL
S „ Component of speed along x0-axis at the source
so D
position
S Wind speed far from hill
CO
SR Component of speed far from hill which lies along the
x0-axis
D
\|/,4r Source stream function
s
0 Standard deviation
0, Standard deviation of H
He c
a Standard deviation of alongwind velocity fluctuations
about the mean wind
a Standard deviation of crosswind velocity fluctuations
about the mean wind
a a value obtained for a sampling duration T
o o value obtained for an infinite sampling duration
\/vo v
0 Standard deviation of vertical velocity fluctuations
0 ,0 Crosswind horizontal and vertical standard deviation of
y z
tracer concentrations
0 *,0 * o and 0 for a plume from point source
y z y z r r
element for the interval s-s
o
0 ,0 Value of 0 and 0 at s = s
yo zo y z o
0 ,0 Effective 0 and a after accounting for all
ye ze y z
terrain effects up to the location of the model receptor
0 Standard deviation of the horizontal meander component
ym
of the wind fluctuations
0 Total 0 including terrain effects (o ) on the
"filament" plume and meander
o „ Total 0 including terrain effects (o ) on the
zT z ze
"filament" plume and H variations
o Plume spread above plume centerline height
0^0 Plume spread below plume centerline height
o resulting f
Z
buoyant plume
Stand
Time
0 . o resulting from entrainment during the rise of a
sue
o Standard deviation of wind direction
0
XXIV
-------
SYMBOL
t. Time of travel from stack to the point at which o .
b zb
is measured
t0 Time of travel below plume centerline height
Xf
t Time of travel to the midpoint of the interval s-s
m o
t Initial time of travel
o
t Time of travel above plume centerline height
t Virtual time
v
T Temperature (Subsection 3.1)
T Time plus virtual time (Subsection 3.5)
T Ambient temperature
O.
T. ,T. Terrain factor for streamline distortion in the
h ho
vertical direction; subscript o denotes value at crest
T. ,T. Terrain factors for turbulence intensity
ly iz '
T.,T. Terrain factor for streamline distortion in the
lateral direction; subscript o denotes value at crest
y
T- Average of T. along the trajectory of the plume
—y
T' Average of T. across the flow from the streamline
that passes over the center of the hill to the
streamline that passes through the source
T Time scale of molecular mixing
m
T Terrain factor for plume transport speed
T ,T Ratios of streamline distortion factor to diffusivity
factor
T Eulerian time scale
E
T Lagrangian time scale
Li
T Lagrangian time scale of the transverse correlogram
Lii.
T Partial height factor (terrain factor)
T^ Scaling temperature
T Factor for the change in mean turbulence in the interval
T .T Terrain factors for diffusivity
Ojr OZ
T Time of travel
u Generic wind speed
XXV
-------
SYMBOL
u
UT(Z')
u'
u*
u
oo
V
ex
(x.y.z)
x
«
06
rB
sep
X
X
XR'yR'ZR
max
z *
r
zf
Wind speed at release height
Total wind speed (incident flow plus perturbation)
Total wind speed (incident flow plus perturbation)
at z'
Downstream velocity perturbation
Friction velocity
Wind speed far from hill
Exit velocity
General Cartesian coordinates
Distance from estimated height of streamline to hill
center
Position of the impingement point along the xD-axis
a
Tracer release coordinates
Position of the receptor along the xfi-axis
Distance of flow separation point from hill crest
Position of the source along the x0-axis
is
Virtual source distance
Receptor coordinates
Height of streamline above H at x
c c
Geometric mean height
Sampler elevation of maximum concentration
Plume release height
Plume centerline height after accounting for wind shear
Height above surface
ABBREVIATIONS
AC
ARLFRD
ASRL
ATDL
Alternating Current
Air Resources Laboratory Field Research Division
Atmospheric Sciences Research Laboratory
Atmospheric Turbulence and Diffusion Laboratory
Freon 13B1
XXVI
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ABBREVIATIONS
CCB Cinder Cone Butte
CTDM Complex Terrain Dispersion Model
CTMD Complex Terrain Model Development
CW Clockwise
DEC Digital Equipment Corporation
EPA U.S. Environmental Protection Agency
EPRI Electric Power Research Institute
ERT Environmental Research & Technology, Inc.
EWS Electronic Weather Station
FFT Fast Fourier Transform
FMF Fluid Modeling Facility
FSPS Full Scale Plume Study
GC Gas Chromatograph
HBR Hogback Ridge
IBM International Business Machines
LASL Los Alamos Scientific Laboratory
LMF Linear Mass Flow Meter
MCO Maximum observed concentration
MCP Maximum predicted concentration
MDA Modelers' Data Archive
MDT Mountain Daylight Time
MRI Meteorology Research, Inc.
MSE Mean Square Error
MSI Meteorological Standards Institute
MSL Mean Sea Level
MW Megawatts
3
ys/m Micro-seconds per cubic meter
NOAA National Oceanic and Atmospheric Administration
ppb Parts per billion by volume
ppt Parts per trillion by volume
PC Personal Computer
xxvn
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ABBREVIATIONS
PDF Probability Distribution Function
PDT Pacific Daylight Time
PG Pasquill-Gifford
PNM Public Service Company of New Mexico
PPG Plume Path Coefficient
PROM Programmable Read-Only Memory
PST Pacific Standard Time
PVC Polyvinyl Chloride
RABAL Radar-tracked Balloons
RTD Resistance Thermometric Device
RTDM Rough Terrain Diffusion Model
RTI Research Triangle Institute
SF Sulfur hexafluoride
6
SHIS Small Hill Impaction Study
SRI Stanford Research Institute International
TPP Tracy Power Plant
TRC TRC Environmental Consultants, Inc.
VAC Volt Alternating Current
WPL Wave Propagation Laboratory
YAG Yttrium-Aluminum-Garnet
xxvm
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ACKNOWLEDGEMENTS
Continuing progress in the EPA CTMD program has resulted from the
dedicated efforts of several scientists from several organizations.
The success of the August 1984 Full Scale Plume Study (FSPS), in
particular, reflects the cooperation of people from ERT, EPA,
Morrison-Knudsen, Inc., the NOAA Air Resources Lab Field Research
Division and Wave Propagation Lab and, of course, Sierra Pacific Power
Company who let us release tracers from their Tracy Power Plant.
Many people—far too many, in fact, to acknowledge here
individually—contributed their talents and energies over the years to
make the CTMD project successful. In particular, we gratefully
acknowledge the special contribution of the following individuals who
helped with the FSPS or the preparation of this milestone report:
• Aaron Mann of Sierra Pacific Power who assisted us
throughout the FSPS;
• Ray Dickson and his staff at NOAA ARLFRD who were
responsible for the flow visualization and tracer
experiments and extensive meteorological measurements;
• Wynn Eberhard and his colleagues at the Wave Propagation
Laboratory who have supplied the lidar data and many
meteorological measurements;
• Norm Ricks of Morrison-Knudsen who managed the photography
program;
• Steve Andersen and Chris Johnson of ERT in Fort Collins who
operated the 150-m meteorological tower and were responsible
for all CTMD logistics at the Tracy Power Plant;
• Prakash Karamchandani, Cynthia Burkhart, and Elizabeth
Rosentel of ERT who performed many of the analyses and model
calculations presented in this report;
• Bill Snyder and his colleagues at the EPA Fluid Modeling
Facility who have performed many towing tank and wind tunnel
simulations in support of the modeling; and
• Julian Hunt for his ideas and recommendations on modeling
stable conditions in complex terrain and with whom we have
had many useful discussions.
XXIX
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Finally, we give special thanks to Frank Schiermeier, George
Holzworth, and Peter Finkelstein (EPA) for their support and
encouragement. Throughout, they have willingly shared with us the
difficult times, and should share in our successes as well.
XXX
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SECTION 1
INTRODUCTION
The Complex Terrain Model Development (CTMD) project is being
sponsored by the U.S. Environmental Protection Agency (EPA) to
develop, evaluate, and refine practical plume models for calculating
ground-level air pollutant concentrations that would result from
emission sources located in hilly or mountainous terrain. The primary
objective of the project is to develop models to simulate 1-hour
average concentrations during stable atmospheric conditions.
These models are to be used in a wide variety of applications,
such as the siting of new energy development facilities and other
sources of air pollution, regulatory decision making, and
environmental planning. Therefore, the models should be easy to
understand, easy to use, and of known accuracy and limitations. The
CTMD project will recommend the types and extent of meteorological
measurements needed to derive input to the models.
The objectives of the program were described by Holzworth (1980)
and generally follow the recommendations of the participants of the
EPA-sponsored workshop to consider the issues and problems of
simulating air pollutant dispersion in complex terrain (Hovind et al.
1979). The program was subsequently designed to include model
development efforts based on physical modeling, field experiments, and
theoretical work.
The CTMD project was begun in June 1980. Four major field
experiments have been completed during the last five years to collect
data for development and evaluation of various modeling approaches.
The first field experiment, Small Hill Impaction Study No. 1 (SHIS
#1), was conducted during the fall of 1980 at Cinder Cone Butte (CCB),
Idaho. CCB is a roughly axisymmetric, isolated 100-m tall hill
located in the broad Snake River Basin near Boise, Idaho. SHIS #2 was
performed during October 1982 at the Hogback Ridge (HER) near
Farmington, New Mexico. HBR is a long, 90-m tall ridge located on the
Colorado Plateau near the western slopes of the San Juan Mountains.
Both small hill studies consisted of flow visualization and tracer
experiments conducted during stable flow conditions with supporting
meteorological, lidar, and photographic measurements. At these sites
the tracer gases were released from mobile cranes or a tower.
The third and fourth field experiments were conducted at the
Tracy Power Plant (TPP) located next to the Truckee River east of
Reno, Nevada. The third experiment, performed in November 1983, was
-------
undertaken as a feasibility and design study for the Full Scale Plume
Study (FSPS). It was co-sponsored by the Electric Power Research
Institute (EPRI). The November experiment not only demonstrated the
feasibility of conducting the FSPS at the TPP, but with the expanded
scope made possible by EPRI's participation, it also produced a data
base that itself is useful for modeling purposes. The FSPS was
performed at Tracy in August 1984. It is described in detail in
Section 2 of this milestone report.
The data bases compiled from the CCB, HER, and November Tracy
experiments are available from the EPA Project Officer. The FSPS data
base will be available in late 1985. The data bases compiled from
each of the experiments include the following components:
• Source information: emission rates, locations, and heights
of SFg, CF3Br, and oil-fog releases.
• Meteorological data: measurements of the approach flow as
well as information on flow and dispersion near the terrain.
• Tracer gas concentrations: data from more than 50,000
individual samples collected during the experiments from as
many as 100 sampler locations in each experiment.
• Lidar data (archived at WPL): sections across the plume
characterizing the trajectory and growth of the plume upwind
of, interacting with, and sometimes in the lee of key
terrain features.
• Photographic data: still photographs taken from fixed
locations, aerial photographs taken at CCB and Tracy from an
aircraft flying overhead, and (occasional) 16-mm and 8-mm
movies and videotapes.
During the course of the CTMD project, four Milestone Reports
(Lavery et al. 1982; Strimaitis et al. 1983; Lavery et al. 1983; and
Strimaitis et al. 1984) have been published. These reports
(EPA-600/3-82-036, EPA-600/3-83-015, EPA-600/3-83-101, and
EPA-600/3-84-110), which are available from EPA, describe the progress
in developing and evaluating complex terrain models using the CCB and
HBR data bases. They also describe in detail the two small hill
studies, the November Tracy study, and a series of towing tank and
wind tunnel studies performed at the EPA Fluid Modeling Facility (FMF)
in support of the modeling.
This phase of the CTMD project will end in December 1986. An
initial, partially validated model will be delivered to the Project
Officer by October 1, 1985. A workshop will be held in early 1986 to
present to the scientific community results from the field
experiments, model development activities, and related work done both
within and outside the CTMD project. The final stable plume
impingement model(s) will be delivered in late 1986. A project report
will be published in December 1986.
-------
This Fifth Milestone Report documents work accomplished from June
1984 through May 1985. It describes in detail the FSPS, including its
setting, the experimental design, and the resulting data base. The
FSPS was successful. It produced a 128-hour data set of SFg and
CF3Br concentrations, ground-based and airborne lidar measurements,
photographs, 8-mm movies, videotapes, and extensive meteorological
data. The highest ten SFg and CF3Br concentrations and a modeling
analysis of 14 selected hours are discussed later in this milestone
report.
The refinement of the HBR meteorological data is complete.
Five-minute and one-hour averaged values of meteorological measures
have been calculated from the corrected 1-sec data.
HBR lidar data have been used to compare measured oil-fog plume
centerline heights upwind and over the crest of HBR to streamline
heights calculated from (1) potential flow theory and from (2) a
linearized perturbation analysis. The comparisons suggest that for
releases above Hc at HBR a substantial portion of the streamline
deflection near the crest can be explained by potential flow of the
air above Hc, i.e., by assuming the ridge was "cut-off" above Hc.
The perturbation analysis shows some improvement in the simulation of
the streamline height when stratification is included in the
calculations.
Stable boundary layer similarity relationships were used to
predict wind and temperature data at 40 m and 150 m from data obtained
at 10 m and 2 m. The predictions were compared to measurements taken
at CCB and HBR. They indicate that the similarity relationships
reproduce the observations fairly well to elevations less than about
10L (ten times the Monin-Obukhov length). Above 10L the predictions
have little reliability.
The Complex Terrain Dispersion Model (CTDM) formula for oz
was tested using lidar estimates of az taken from a 14-hour subset
of the FSPS data base. The predicted oz values were all within a
factor of 2 of the lidar estimates although they generally
overestimated the observations.
This milestone report also discusses the highest ground-level
tracer concentrations measured at the CCB, HBR, and FSPS sites. The
meteorological characteristics of the concentration events and the
differences among the sites are discussed.
The further development of CTDM is described. Mathematical
descriptions of the modifications to the model are presented. The
latest version of the model has been tested with a subset of
impingement hours from the CCB, HBR, and FSPS data bases. The initial
14-hour FSPS data base was also used to test four existing complex
terrain models—COMPLEX I and II, Valley, and RTDM.
-------
This report consists of seven sections and one appendix. Section
2 provides a description of the FSPS. Various data refinements and
analyses are presented in Section 3. Section 4 provides an analysis
of the highest tracer concentrations measured at each site. Progress
in developing CTDM and an evaluation of the model for impingement
hours are discussed in Section 5. Future improvements and
modifications to CTDM are discussed in Section 6. Section 7 presents
the summary, conclusions, and recommendations for future work. The
Appendix contains a report prepared by the EPA FMF describing a series
of neutral and stratified flow experiments to determine streamline
trajectories over a three-dimensional hill.
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SECTION 2
FULL SCALE PLUME STUDY
2.1 Geographic and Meteorological Setting
The Tracy Power Plant east of Reno, NV, was selected as the site
of the Full Scale Plume Study (FSPS) after an extensive survey of all
power plants in the western United States located in settings that
could qualify as complex terrain. In its favor were the following
considerations:
• Unit 3 at Tracy is maintained in warm standby status when it
is not in fact producing power for the grid.
• Sierra Pacific Power Co., the owner and operator, was very
cooperative.
• The plant is surrounded by complex terrain, the elevations
of the mountains affording opportunities for plume impact in
many directions.
• The area is very sparsely populated and nearly devoid of
trees.
• It is near a city with good commercial air service, lodging,
and other logistical support.
The principal drawbacks to Tracy were that it is currently gas-fired
so that its plume cannot be tracked by lidar and that its 120-megawatt
capacity and common standby status did not make it representative of
large new sources undergoing regulatory review.
The first of these drawbacks was overcome by production of
"smoke" with corvus oil as had been done in the two CTMD Small Hill
Impaction Studies. Augmentation of the particulate emissions at any
power plant would have been necessary if photographic data were to be
taken, as was ERT's intention. The feasibility of producing an
artificially smokey plume was demonstrated by tests performed by
ARLFRD at Tracy in July 1983. The size of Unit 3 at Tracy was not
regarded as disqualifying for the purposes of CTMD for several
reasons: New power-generation units in the West were tending to fall
into the 250-MW range rather than the 600-MW range more common in the
previous decade; the majority of sources undergoing regulatory review
are better represented by Tracy than a larger power plant at full
load; and the scale of the Tracy stack effluent required less tracer
gas to keep sample concentrations within an analytical range yielding
good chromatographic precision.
-------
The Tracy site is in the Truckee River valley about 17 miles east
of Reno. (See Figure 1). The plant has three units, but only Unit 3
with 120-MW capacity and a 300-foot (91.4 m) stack is operating.
Geographically the site has merit in that stable flows from the west
are fairly common at night. The Sierra Nevada to the west of Reno and
the Pah Rah Mountains to the east define the Truckee Meadows basin in
which the Reno-Sparks urban area lies. The Truckee River has cut a
canyon through the Pah Rah range and drops approximately 200 feet from
Sparks to Tracy. Large-scale downslope winds off the Sierra at night
flow through the canyon and reinforce the drainage down the river.
Photographs of the wood smoke plume from Sparks showed this to be the
case.
At the plant site (Figure 2), the valley broadens to the north
towards the Pah Rah Mountains. To the south, Clark Mountain rises
almost 3,000 feet (910 m) above the stack base in seven km. At about
4.5 km east of the plant, the river swings sharply north through a
narrow gorge between two large obstacles, "Beacon Hill" (5232 ft. MSL,
or about 300 m above stack base) to the west of the gorge and "Target
Mountain" (5764 ft. MSL or about 460 m above stack base) to the east.
These two terrain elements were the principal "target" areas in the
anticipated westerly winds. Figure 3 is a photograph looking east
from the "Old Lonesome" camera site that shows the relationship of the
plant to these two features.
2.2 Preliminary Experiment
A preliminary experiment was performed at Tracy in November 1983;
it is described in the Fourth Milestone Report (Strimaitis et al.,
1984) and will only be briefly summarized here.
The objectives of the preliminary experiment were to assess the
feasibility of the site for the FSPS and to gather information to
assist in the experimental design. As originally conceived, the
November experiment involved only a handful of tracer samplers for
estimation of dilution factors to determine appropriate tracer release
rates. Typical flow patterns were to be investigated by personal
observation and photographs of the oil-fog plume released from the
300-ft stack. The scope of this study was expanded substantially by
the co-sponsorship of the Electric Power Research Institute (EPRI),
however, and this "preliminary" experiment yielded a database useful
for model development and evaluation in its own right. EPRI's
contractors from the Plume Model Validation and Development program
provided sampling at 53 sites, necessary helicopter service, the
tracer concentration analyses and archiving, quality assurance audits
of the tracer and meteorological components of the study, two pibal
teams and equipment, and airborne lidar data by means of the ALPHA-1
system.
ERT erected CTMD's 150-m meteorological tower instrumented at
four levels and supplied a data acquisition system for the tower, two
electronic weather stations, two carbon arc lamps and operators,
cameras and observers, technical and logistical management, and
coordination with Sierra Pacific. The National Oceanic and
-------
Figure 1. The region around the Tracy Power Plant.
-------
0)
-p
•H
CO
J->
CO
f-H
f^
CM
oo
-------
0>
u
•H
fa
-------
Atmospheric Administration's Air Resources Laboratory Field Research
Division (ARLFRD) and Wave Propagation Laboratory (WPL) were the
principal participants on the EPA/CTMD team. ARLFRD was responsible
for SFg and oil-fog tracer releases, two 10-m towers on promontories
and associated telemetry and data logging, one tethersonde, radio
voice communications, and subcontracted photographers. WPL provided a
second tethersonde, two optical anemometers, a doppler acoustic
sounder, and two monostatic acoustic sounders, all with necessary
operational personnel. ERT produced the master data archive and
distributed it to the participants.
The 150-m tower was maintained until after the FSPS to obtain
almost a year of meteorological data as part of ERT's obligations
under CTMD.
The preliminary experiment yielded 68 hours of tracer
concentrations under a variety of nocturnal and morning conditions.
Over half of these hours appear useful for modeling purposes.
The experiment also fulfilled the informational requirements of
CTMD. Tracy was shown to be an appropriate site for the FSPS, and the
plume often interacted with the terrain. But the drainage flow from
the west proved to be neither as reliable nor as persistent as had
been hoped. Not only was the flow influenced by several migrating
weather systems, some accompanied by snow, but also in conditions of
weak gradient winds, the motion in the valley at plume height often
appeared oscillatory with a period on the order of two hours. Because
of this sloshing, the FSPS sampling array was extended to cover areas
to the west and northwest of the plant. The tracer releases into the
breaching of Unit 3 were shown to be satisfactory, and the effluent
flux from the stack with the plant in warm standby with the forced
draft fan on was sufficient to prevent stack-top downwash in the light
wind conditions that normally prevailed during stable hours. The
spatial and temporal variability of the winds in the study area
indicated the necessity for extensive meteorological instrumentation.
2.3 FSPS Experimental Design
The components of the FSPS were basically the same as those used
in the Small Hill Impaction Studies. Two tracers, SF$ and CF3Br
(Freon 13B1), were released simultaneously from two different
locations to give twice the dispersion information at a small increase
in cost. A "smoke" plume was produced by evaporation of corvus oil in
a small jet aircraft engine exhausted into the side of the duct
leading from the power boiler to the stack. SFg was injected into
the same gas stream through a sampling port just upstream of the
breaching into the flue. CF3Br was released from one of three
heights on the 150-m tower.
One-hour samples of ground-level tracer concentrations were
obtained at more than 100 locations in two-liter Tedlar bags. Three
additional samplers were mounted on the tall tower. Analysis of
tracer concentrations was done by gas chromatography with
electron-capture detection.
10
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Ground-based lidar made vertical transects through the oil-fog
plume, usually at five distances downwind, to measure the location and
dimensions of the plume and its proximity to terrain.
The ALPHA-1 airborne lidar tracked the plume to greater
distances. Color photographs of the plume were taken routinely every
five minutes from five locations, and video-tapes were made during
daylight hours. Two carbon-arc lamps panned along the plume for
illumination when natural light was insufficient. ERT's
scientist-observers took additional color slides and, after dawn, 8-mm
time-lapse movies as well.
Meteorological measurements were made from the 150-m tower, four
10-m towers, two electronic weather stations, two tethersondes, and
one monostatic and two doppler sodars. Two radar-tracking balloon
sounding systems were also used. Figure A shows the locations of the
various meteorological sensors, the lidar, and the Command Center.
As at HBR, principal participants in FSPS were ERT, NOAA/Wave
Propagation Laboratory (WPL), and NOAA/Air Resources Laboratory Field
Research Division (ARLFRD). Under subcontracts to ERT, Meteorological
Standards Institute of Fox Island, WA, performed external audits of
the meteorological tower instrumentation and the gas chromatography
laboratory, and Morrison Knudsen Co., Inc., of Boise, ID, provided
five photographers, 35-mm cameras, a video camera, film, an arc-lamp,
and operators for both arc-lamps. Vara Systems, Inc., of Newbury
Park, CA, surveyed the experiment area and produced a topographic map
under contract to ARLFRD. SRI International made airborne lidar
transects with the ALPHA-1 under the sponsorship of the Electric Power
Research Institute.
Responsibilities of the principal participants are summarized in
Tables 1 to 3.
2.3.1 Tracer Data
Tracer Release
Artificial smoke produced by evaporation of corvus oil in the
exhaust of a small jet aircraft engine made the plume from the plant
stack visible for lidar scans, photography, and observers. The
jet-fogger vaporized approximately 60 gallons of oil per hour and
injected it into the duct leading from Unit 3's boiler to the 91.4-m
stack just downstream of the air preheater section. The boiler's
forced draft fan maintained a steady flow of air through the duct
regardless of generating load, and the plume downwashed at the top of
the stack only on the infrequent occasions when the wind at stack-top
exceeded about 6 m/s. There were apparent periods of building-induced
downwash as well during strong winds at the beginning of a few
experiments; these times are identifiable from observer comments,
lidar data, and photographs.
11
-------
o
1
•rH
tJ
0)
0)
•i-l
14-1
w
0,
co
-------
TABLE 1. SUMMARY OF ERT FSPS RESPONSIBILITIES
Experimental Design (with other participants)
Preparation of Quality Assurance Plan
150-Meter Meteorological Tower Reconfiguration
1. Installation of additional levels and sensors
2. Installation of sonic anemometers and temperature sensors
3. Installation of tracer release system to release CF_Br from
three heights — 102.1, 127.4, and 142.1 m
4. Pre/Post-experiment system calibrations and tests
Field Logistics and Site Preparation
1. NOAA/ARLFRD equipment supply (meteorological systems)
2. Command Center supply and installation
3. Telephone and dataline arrangements
4. Command Center power supply
5. Subcontractor support coordination
6. Lidar siting support
7. Area landowners and lease-holder access authorization
8. Agency notifications
Data Collection System for 150-m Tower
1. Design, code, and test data acquisition system for 150-m tower
meteorological data
2. Install Data General C330 computer system in Command Center
3. Install IBM PC/XT and Intel computers in tower shelter
4. Set-up data line for sonic anemometer computer/Command Center
interface
5. Perform and document control tests for meteorological data
collection system
Field Operations
1. 150-meter meteorological tower maintenance
2. Remote electronic weather station (EWS) installation, calibration,
and maintenance
3. Takedown and installation of tower-mounted tracer samplers after
each experiment
4. Field observations, smoke releases (candles), and photography
13
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TABLE 1 (Continued)
5. Site security
6. Portable toilet services
7. General field support
• Project Takedown
1. 150-meter meteorological tower takedown, inventory, and shipping
2. Remote EWS (2) removal and shipping
3. EWS data reduction and reporting
4. Site decommissioning and restoration
5. Complete project equipment inventory
6. EPA equipment refurbishing (as needed)
7. Shipping EPA equipment to FRD
• Archive of 150-m Tower Data
• Development and Distribution of Data Base
• Overall Direction of Experiment Operations
• Provision of Quality Assurance Auditor
14
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TABLE 2. SUMMARY OF NOAA ARLFRD FSPS RESPONSIBILITIES
• Provide an initial quality assurance plan to ERT.
• Complete preliminary field site preparation and equipment installation
and checkouts. Primary contributions were to:
1. Survey sites for ground-level sampling, tower bases, tethersondes,
lidar observations, roadways, and all other locations pertinent to
the experiment; provide surveyed contour map of experiment site.
2. Erect and provide electrical power for the 10-m towers.
3. Attach temperature and wind sensors on the 10-m towers.
4. Provide voice communications for FRD and ERT operations center(s),
lidar crew, chief photographer, and scientific observers.
5. Purchase oil, kerosene, SF, , and CF-Br.
D J
6. Provide for release of oil-fog and gaseous tracers from the 300-ft
stack and the 150-m tower,
7. Provide chairs, tables, refrigerator, and other equipment for NOAA
ARL and ERT Command Center from available NOAA ARL resources.
8. Deploy sequential tracer samplers at 107 pre-selected locations.
9. Provide all telemetry equipment for the 10-m towers.
• Participate in the field measurement program by:
1. Being ready for the initial test on August 6, 1984.
2. Releasing oil-fog and two gaseous tracers provided by FRD.
3. Sampling 128 hours of gaseous tracer releases at 107 predesignated
ground-level sites and the 150-m tower.
4. Trucking bags to Idaho Falls for GC analysis.
5. Analyzing about 440 whole air samples of gaseous tracers for each
of two shakedown experiments.
6. Analyzing about 1,100 whole air samples of gaseous tracers for
each of 12 tracer release test days. Preparing maps of tracer gas
concentrations within about 48 hours.
7. Conducting tethersonde soundings of pressure, temperature,
humidity, wind speed, and direction.
8. Supplying two radars and taking rabal winds, with the data
provided to the command post in real-time during the experiments.
15
-------
TABLE 2 (Continued)
Submit a final record of all meteorological and tracer data on 9 track,
1600 bpi magnetic tape.
Provide a final report on participation in the field measurement
program, including a description of the surveyed sampling grid and
measurement platform sites, the date and times of field measurement
activities, and the information needed to allow correct understanding
of the character and quality of these measurements.
16
-------
TABLE 3. SUMMARY OF NOAA WPL FSPS RESPONSIBILITIES
Provide an initial quality assurance plan to ERT.
Complete field site preparation and equipment installation and
checkouts. Work included:
1. Preparation of the site and installation of power for the lidar
system.
2. Work with ERT on the installation of the sonic anemometer systems,
including the data acquisition component.
3. Installation of the doppler and monostatic acoustic sounder
systems.
Participate in the FSPS by:
1. Having all equipment in place, ready for the initial experiment on
August 6, 1984.
2. Sampling the oil-fog plume with the lidar system.
3. Operating the sonic systems and providing 20-min average data in
real-time to the ERT command center.
4. Operating two doppler acoustic sounders, with data transmitted to
the command center upon request.
5. Operating three monostatic acoustic sounders.
6. Conducting tethersonde soundings of temperature, relative
humidity, wind speed, and direction. Data transmitted routinely
to the command center.
Supply a final record of all numerical meteorological data on 9 track,
1600 bpi magnetic tape.
Submit tapes of processed lidar data. Also, submit narrative
interpretation of simultaneous monostatic sounder data.
17
-------
The smoke plume could generally be tracked visually at least
until its first interaction with terrain except in strong wind,
neutral conditions. The lidars could track it even when it was
invisible to the eye.
SFfc was injected into the stack plume through a sampling port
in the side of the duct work a few feet upstream of the stack. The
second tracer gas, CF3Br or Freon 13B1, was released from the 150-m
tower at one of three levels — 102.1, 127.4 and 142.1 m above the
ground. The tracer was injected into the side of a Climatronics
aspirated temperature shield with the fan motor mounted backwards so
that the air was blown out the nozzle extension of the aspirator. The
intent of this system was to dilute the heavy tracer with a relatively
large volume of air, both to alleviate problems of negative buoyancy
and to force the tracer away from the tower's three elevated samplers,
located at 43.7, 104.8, and 145.4 m above the ground. This system
seems to have worked since only eight of 128 hours of tracer
concentration data have an abnormally high CF3Br reading at the
sampler near the release point. The nozzles of the aspirators were
aimed to the east in anticipation of predominantly westerly flow
during the experiments.
Both tracers were released from cylinders of "pure" gas stored at
the ground. ARLFRD's release metering systems were those used at HER
and the preliminary FSPS and have been described in the Third
Milestone Report (Lavery et al., 1983). SF6 was piped to the port
in the breaching by garden hose; CF3Br was transported up the tower
to the aspirators in PVC tubing. Each tower release point was fitted
with an electrically controlled valve activated from the ground that
directed the flow to the selected height.
Tracer Sampling
Tracer concentrations were sampled at 110 sites, including the
three elevated samplers on the 150-m tower and one at its base, by the
modified AQS-III bag samplers used at the CCB and HBR experiments.
All samplers operated in the 1-hour mode and filled 2-liter Tedlar
bags. Figure 5 is a map of the sampler sites.
Because of the rugged terrain and size of the network, a
helicopter was necessary to ferry the sampler crew and bags around the
network. ARLFRD arranged the loan of a large Bell helicopter and
2-man crew from another branch of NOAA for the duration of the
experiment.
Tracer Analysis
Chromatographic analysis for SFg and CF3Br in the sample bags
was done by ARLFRD in their laboratory in Idaho Falls, ID. The
analytical procedures and equipment were basically identical to those
used in the lab in Farmington, NM.
18
-------
•H
05
60
I
W
to
CO
60
0)
y
CD
t-i
H
0)
U
t>0
19
-------
Boxes of sample bags were shipped to Idaho Falls by contracted
trucks. Analysis was generally completed within 48 hours of the end
of each experiment.
2.3.2 Meteorological Data
Meteorological data were collected from instruments on the 150-m
tower and four 10-m towers, from two tethersondes, two radar-tracked
balloon (RABAL) systems, and one monostatic and two doppler acoustic
sounders. ERT was responsible for the installation and maintenance of
the 150-m tower instruments and data acquisition, archive, and display
of their outputs with analytical presentations like those at CCB and
HBR. ARLFRD was responsible for the same functions with respect to
the four 10-m towers, although no real-time display or analysis were
required; they also provided and operated the two RABAL systems and
one tethersonde. WPL operated one tethersonde and installed,
maintained, and archived data from three sonic anemometers on the
150-m tower and the acoustic systems.
150-m Tower Data
The data acquisition for the sensors on the 150-m tower was an
improved version of the system used at CCB (Greene and Heisler,
1982). It provided onsite analysis and two media for local recording
of reduced data. A block diagram of the system is shown in Figure 6.
The polling of the analog (voltage) outputs of the sensors,
conversion to digital values, and the calculation of 5-min and 1-hr
values of average data and turbulence quantities were done by ERT
DS-00 "data stations," devices designed and coded by ERT and based on
Intel microprocessors. These units, which were used at CCB, were
located in the shelter at the tower base in the same pair of
instrument racks as the Climatronics signal-conditioning equipment in
order to limit the length of wires between the instrument outputs and
the data acquisition equipment in the interest of noise suppression.
The instruments were scanned four times per second by the Intels.
The two "types" of data stations used are distinguished by the
coding of the PROM: a Type 2 device is designed for speed and
direction inputs, as from Climatronics F460 cup-and-vane systems, and
a Type 3 for UVW inputs, as from triaxial propeller anemometers. At
each data sample, the Type 2 resolves speed and direction into U and V
components. From then on, the two types operate in the same fashion
for calculation of turbulence intensities and vector-resultant wind
speeds and directions. (No vertical wind component is measured by the
Type 2.) Additionally the microprocessors serving the F460s calculate
scalar mean speeds and directions and
-------
Q-OCOh-UJOl- — OZ
21
-------
TABLE 4. 150-M TOWER SENSOR LOCATIONS AND MEASURES
10 50
75
Tower Level (m)
U,V,W propeller anemometer
Cup and vane sets
Temperature
Temperature difference
Pyranometer
Net radiometer
U,V,W sonic anemometer
*
*
*
*
*
*
*
*
100
*
*
125
150
*
*
Measures
U.V.W
IXP, 1YP, IZP
SPV, DPV
UCV, VCV
UCS, VCS
SCV, DCV
SCS
DCS
IXC, IYC
SDR
IYS
T
TD
TC
SDS
DVS
SDV
FVC
SVC
SR
NR
o
o
x
o
X
X
o
o
o
o
o
o
o
0
X
0
X
o
X
X
o
o
X
o
o
o
o
o
X
o
o
0
o
X
0
X
o
0
X
o
o
o
o
o
X
o
X
o
o
X
o
o
o
o
X
o
X
o
o
X
o
o
o
o
o
* Indicates a sensor that was scanned four times per second.
o Indicates a "direct" measure calculated by microprocessors from instrument voltage
outputs.
x Indicates a "derived" measure calculated by C330 computer from direct measures.
Note: The sonic data were archived via a separate data acquisition system provided
by WPL. Averaged data were available on a printer in the command post.
22
-------
TABLE 5. DEFINITION OF MEASURES
Measure Code
Definition
Units
U, V, W Vector average wind components - m/s
props
UCV, VCV Vector average wind components - m/s
cup and vane
UCS, VCS Scalar average wind components - m/s
cup and vane
SPV Vector average wind speed - props m/s
DPV Vector average wind direction - degrees
props
SCV Vector average wind speed - m/s
cup and vane
DCV Vector average wind direction - degrees
cup and vane
SCS Scalar average wind speed - cups m/s
DCS Scalar average wind direction - degrees
vane
IXP*, IYP**, IZP*** Alongwind, crosswind, vertical percent
intensities of turbulence - props
Alongwind, crosswind intensities of percent
turbulence - cup and vane
Scalar crosswind intensity of percent
turbulence - vane
Standard deviation of wind degrees
direction - vane
T Ambient air temperature - °C
encapsulated platinum wire
TD Temperature difference - encapsulated °C
platinum wire
TC Calculated temperature, TC = T + TD °C
SDS Standard deviation of wind m/s
speed - cups
IXC*, IYC**
IYS
SDR
23
-------
TABLE 5 (Continued)
Measure Code
Definition
Units
DVS
SDV
FVC
SVC
SR
NR
Scalar average of vane output signal
Standard deviation of vane output
signal
Fixed voltage constant
Standard deviation of fixed voltage
constant
Solar radiation - pyranometer
Net radiation - net radiometer
degrees
degrees
volts
volts
langleys/rain
langleys/min
TV _ rl r (£u) Zu2 + (Zv)2 Zv2 + 2ZuZvZuv (Zu)2 + (Zv)2 ,1/2
1A - t L ~ JJ
N
**
IY , {i [Zu2 + Zv2 -
N
22
22
IV +2IuIvIuv]}l/2 ^ -
*** ? 2
I2 = {Zw2 - (Zw)2}l/2 ^ -f
2 2 1/2
where U = — - ~ — — - is the vector resultant mean wind speed,
N is the number of samples in the calculations, u and v are the
instantaneous wind component speeds from the propeller anemometers or
cup and vane, and w is the vertical instantaneous wind component speed
from the propeller anemometer.
IYS = SDR •
loO
100
24
-------
The digital outputs of the Intels were in turn polled by a "data
concentrator" computer, an IBM PC/XT desk-top computer located in the
instrument shelter. This unit served as the "controller" of the Intel
microprocessors. Its crystal-driven clock determined when the scans
for 5-min and 1-hr averaged direct measures were performed, and it
could store on disk more than 12 hours of tower data in the form of
5-min and 1-hr averages of the direct measures from the Intels. This
archival function was invoked automatically whenever the IBM
determined that communication with the computer in the control center
office was not possible. The IBM was equipped with a CRT console as
well as a line printer, on which messages were printed indicating
problems with data collection or transmission.
After the IBM data concentrator completed a 5-min (or 5-min and
1-hr) scan of the direct measures from the Intels, it interrupted the
central data collector in the experiment control trailer. The data
collector was a Data General C330, a multi-tasking mini-computer that
received the values of the direct measures from the IBM, calculated
the indirect measures, flagged measures that fell outside prescribed
reasonable ranges, and archived all measures on a 25-megabyte hard
disk. Its other functions were tabulation of selected measures on
hard copy as they were received or calculated, production of profiles
of temperature and wind speed and direction by spline-under-tension
algorithms, calculation of flow parameters such as Froude numbers and
heights of critical streamlines, and production of plots of time
histories or profiles on the Tektronix 4114 plotter. Software
developed for the two previous field studies was used by the C330 with
a few modifications to allow incorporation of doppler acoustic and/or
tethersonde data into the profiles.
Communication between the IBM PC in the shelter and the C330 in
the trailer was over a dedicated telephone line about 400 m long. The
accuracy of data transmission was tested by a check-sum on each record.
At the end of each experiment, the data archived on disk was
dumped to two 9-track tapes, one of which was shipped directly to
ERT's office in Concord, MA, while the other remained in the Reno area.
Selected instrument outputs were recorded on strip chart
recorders in the instrument shelter. The chart-recorded measurements
included the following:
150-m W-propeller
150-m F460 speed and direction
100-m F460 speed and direction
10-m F460 speed and direction
10-m temperature
10- to 150-m temperature difference
10- to 100-m temperature difference
25
-------
10-m Tower Data
The four 10-m towers were powered by high energy (approximately
400 amp-hrs) 12-volt storage batteries charged by solar panels.
Instrument output from Towers 1, 2, and 3 was telemetered continuously
to a Monitor Labs data logger in the Command Center via Communitronics
radio links powered by the same batteries. The data logger controlled
the sampling of the instrument outputs at 4-sec intervals and recorded
these raw data on 9-track tape. The tape data were processed after
the experiments were completed by FRD in their offices in Idaho Falls;
5-min and 1-hr averages of wind speed and direction and temperature as
well as standard deviations of speed and direction were calculated.
Additionally, 5-min averages could be printed on paper tape on request
during calibration, system checks, and audit periods; but this
function could not be performed during experiments because of CPU time
constraints. All measurements from Towers 1, 2, and 3 were recorded
on strip charts in the Command Center.
Tower A, the easternmost tower, was inaccessible by the radio
telemetry system, and the data from its instruments were recorded
locally by a battery-powered Mars data logger.
Platinum temperature probes in aspirated radiation shields, cup
anemometers, and wind vanes were mounted at 10 m on Towers 1, 2, and
3. Cups and vanes and aspirated temperatures were deployed at both 1
and 10 m on Tower 4.
Electronic Weather Stations (Target Mt. Draw)
ERT's two Climatronics Electronic Weather Stations were installed
with their cups, vanes, and temperature probes mounted at about 1 m
above the terrain to examine the flow in the large draw on the west
end of the "target" mountain. Data from these instruments were
recorded on multiple-trace chart recorders.
Sonic Anemometers
Sonic anemometer systems, comprising UVW components and very fast
response platinum wire thermistors, were installed by WPL and ERT at
10, 100, and 150 m on the big tower. These instruments were sampled
20 times per second. Vector resultant wind speeds and directions and
alongwind, crosswind, and vertical turbulence (
-------
Tethersondes
Two tethersondes manufactured by A.I.R., Inc., were flown during
experimental periods, one operated by ARLFRD about 0.8 km west of the
stack and one operated by WPL near the big tower about 1.5 km east of
the stack. These sondes were flown to give wind and temperature
profiles upwind and downwind of the stack and were helpful as
complements to the acoustic sounders nearby. The tethersonde data
were printed on roll paper. The WPL tethersonde data were also
recorded on cassette tapes.
Acoustic Sounders
WPL set up and operated three acoustic sounding systems; two were
doppler sodars in monostatic configuration and one a monostatic
sounder. One doppler was a few hundred meters west of the stack and
one at the east end of the valley. The monostatic system was set up
near the Command Center.
Each sounder had its own data acquisition system, the doppler's
being mini-computer based with hard-copy digital output of 20-min wind
and turbulence profiles. All three systems recorded monostatic-mode
analog output on facsimile charts.
RABALS
ARLFRD operated two radar-tracked balloon (RABAL) systems north
of the river to obtain wind profiles up to a few thousand meters
altitude. Each had its own computerized data acquisition system that
calculated wind speed and direction from azimuth, elevation angle, and
range. Balloons were released and tracked every half hour at both
sites.
2.3.3 Smoke Plume Data
Lidar
WPL operated their lidar system from the base of Clark Mountain
about 2.2 km east-southeast of the plant. The lidar was basically the
same as that used at HBR with the yttrium-aluminum-garnet (YAG)
crystal doped with neodymium. It made vertical transects of the
plume, usually at five azimuths ranging from near the stack to the
"target" areas to the east when flow was from the west. When the
plume blew towards the west, it was hidden from the lidar by terrain
after a few kilometers; when the plume blew towards the high terrain
to the northwest, the lidar sections were almost along the axis of the
smoke.
A series of transects was made approximately every 5 mins, the
data being recorded on 9-track tape for later processing. Improved
real-time display of the signal returns gave feed-back on plume
behavior for experimental guidance and understanding.
27
-------
Photography Program
Under subcontract to ERT, Norman Ricks of Morrison-Knudsen
Company, Inc., was responsible for the photography program, as he had
been at HBR. He and five associates took photographs routinely every
5 mins from five positions in the high terrain and operated the arc
lamp. A second arc lamp and its operator were contracted by
Morrison-Knudsen. Each photographer had two cameras, using one for
the routine 5-minute exposures and one for capturing interesting
images of smoke from their viewpoints. In addition, video-tapes were
made of the plume from the camera position near Tower 3 after dawn.
Airborne Lidar
EPRI sponsored the ALPHA-1 airborne downward-facing lidar at FSPS
as they had in the preliminary experiment at Tracy in November 1983.
This system, developed for EPRI by SRI International, was operated by
SRI scientists during FSPS. The aircraft was typically flown in a
ladder pattern back and forth across the plume, making transects from
near the source to about 8 or 10 km distance. The signal returns were
recorded on both tape and facsimile charts.
2.4 Preliminary Evaluation of FSPS and Database
The FSPS comprised 14 tests or experiments and a total of 128
hours of data collection. Table 6 lists the dates and durations of
the 14 experiments. Experiment hours encompassed a variety of
meteorological conditions ranging from very stable with very light
winds to morning inversion breakup and fumigation. On several
evenings early in an experiment, strong winds from the west produced
near-neutral flow in the valley. Prolonged periods of stable plume
impaction on the targeted elevations to the east frequently occurred.
Some light-wind, stable periods may be difficult to model because
the flow at some levels alternated between going down the valley to
the east and up the valley to the west with a typical period of more
than an hour. The dynamics of this "sloshing" motion have not yet
been studied in the database, but the oscillation appeared sometimes
to lift the plume bodily and then let it subside. One effect of this
sloshing was the advection of layers of old plume in the "approach
flow" of subsequent periods. These layers may then have contributed
"background" to sampled concentrations that were in large part caused
by more direct impact of the source plume on receptors.
A tracer concentration database has been received from ARLFRD
containing 11,609 concentrations for either tracer gas. This
indicates a preliminary data capture of 82.5 percent based on 128
possible hours of sampling by 110 samplers.
Most of the meteorological instrumentation performed well and
data capture is good. There were three systems with known problems
however—the eastern doppler sodar, the western tethersonde, and the
28
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TABLE 6. FSPS EXPERIMENT HOURS OF TRACER RELEASE AND CONCENTRATIONS
Release
Concentrations
>erimen1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
t Date (Aug 84)
6
7
9-10
10-11
11-12
15-16
16-17
17-18
20-21
21-22
22-23
25
26
27
Time (PDT)
03-07
03-07
20-06
20-06
20-06
22-08
22-08
22-08
22-08
23-09
23-09
00-10
00-10
00-10
Oil-Fog
4
4
8
10
8
10
10
5
10
7
10
10
10
9
gF6
4
4
10
10
10
10
10
11
10
10
10
10
10
10
CF3Br
4
4
10
10
9
10
10
11
10
10
10
10
10
10
SF6
4
4
10
10
10
10
10
10
10
10
10
10
10
10
CF3Br
4
10
10
10
10
10
10
10
10
10
10
10
10
TOTAL
115
129 128
128
128
Notes: Preliminary assessment pending receipt of final data.
Only whole hours counted.
Tracer releases often began 1/2 hour before start of sampling.
29
-------
sonic anemometers, all of which suffered from difficulties with data
acquisition systems. ALPHA-1 gave airborne lidar coverage during 75
experiment hours. WPL's lidar operated reliably except for a few
brief periods.
Four of the five meteorological towers, the two electronic
weather stations, and the tracer analysis laboratory in Idaho Falls
were audited by Meteorological Standards Institute of Fox Island, WA,
under subcontract to ERT. The meteorological systems checked out very
well except for a few correctible problems with instrument
alignments. The results of the audits of the GC lab were also
excellent provided that the instrument responses were calibrated with
polynomials to account for non-linearities. One potential problem was
revealed by the audit in regard to the Mars data logger that had to be
used at the No. 4 10-m tower: when this portable system was used to
take data during the audit, it showed apparent inaccuracies in
analog-to-digital conversion. Unfortunately, Tower 4 was not audited
because of time constraints, and the impact of the A-D conversion
problem on the measurements was therefore not evaluated. Estimates of
the quality of data from this tower will have to be largely subjective
for these reasons.
Very high CF3Br concentrations were sometimes measured in
samples from the base of the 150-m tower; only rarely did they occur
aloft at the tower-mounted samplers. This pattern suggests the
possibility that sometimes Freon leaked from the release system
somewhere near the ground. However, an initial examination of
concentrations sampled throughout the grid indicated no apparent
effect from Freon leaks.
The photography contractor has submitted an archive of more than
11,700 35-mm color slides and 14 VHS videotapes.
Examples of initial analyses of the tracer concentration,
photographic, and meteorological data from 20 FSPS hours are given in
Section 4. Initial modeling of 14 FSPS hours is described in
Section 5.
30
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SECTION 3
DATA ANALYSIS
3.1 Refinement of HER Meteorological Tower Data
In September 1983, ARLFRD submitted to ERT a database of 1-hr and
5-min values from the tower data acquisition system. The
meteorological measurements in this database contained noise. The
problems of noise in the raw 1-sec data have been described by Lavery
et al. (1983); and the consistent and direction-dependent differences
between wind speeds and directions derived from collocated
cup-and-vane and propeller anemometer sets have been shown by
Strimaitis et al. (1984). In October 1984, ERT decided to process the
data using the results of wind tunnel studies of propeller anemometer
calibrations and corrections for non-cosine response (Strimaitis
et al., 1984) to see if some of the apparent biases could be
alleviated at the same time instrument outputs were corrected for
alignment errors revealed by the audit performed by TRC Environmental
Consultants at HER. These refinements and examples of their results
are discussed here.
3.1.1 Filtering and Flagging Raw Data
ERT filtered and flagged the raw counts data in an effort to
reduce the effects of noise on the calculated measurements. The
following noise identification procedures were used:
1) Channel-skipping. If the output (in counts) of channels 15
and 16 of a 16-channel multiplexer were the same in a scan,
a channel-skip was suspected, and a procedure was invoked to
find the channel (from 1 to 15) at which the skip started.
This involved calculating the sum of squares of differences
between counts in the current scan and the previous scan
channel-by-channel, assuming that the skip started at
channel 15, then 14, then 13, etc., and finding the channel
for which the sum is a minimum. The data were then moved
sequentially one channel number higher. The datum from the
channel at which the skip started was lost, set to -1 count,
and flagged "L."
2) "Reasonable" limits. The range limits of reasonable
instantaneous values of instrument outputs are listed in
Table 7. This filter captured big spikes.
31
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TABLE 7. FILTER LIMITS FOR TOWER MEASUREMENTS
Range Limits
Instrument
type
U, V prop
W prop
F460 cups
F460 vane
Fast thermistor
Temperature (RTD)
AT (RTD)
Lower Limit
Counts Units
880
1400
10
0
1100
1100
40
-14.0 m/s
-3.0 m/s
0.13 m/s
0 degs
-8.0° C
-8.0° C
-4.8° C
Upper Limit
Counts Units
Rate-of-change Limit
Counts Units
3120 14.0 m/s 85 1.06 m/s
2800 4.0 m/s 100 0.50 m/s
1120 14.0 m/s 45 0.56 m/s
4000 540 degs 130 17.55 deg
3100 32.0° C 40 0.80° C
3100 32.0° C 30 0.60° C
3960 14.8° C 120 0.60° C
32
-------
3) Simple derivative filter, designed to trap short noise
bursts by comparison of current value with previous value.
If the difference exceeded a pre-set rate-of-change limit
for that type of instrument, the datum was flagged "R." The
rate-of-change limits are listed in Table 7.
4) Tower noise limit, designed to trap "high-frequency" noise,
which looked similar to a sinusoidal oscillation
superimposed on the sequence of instrument signals in a scan
from a tower. For the data not otherwise flagged as bad,
the sum of the absolute values of changes of each channel's
output in one scan from that in the previous scan was
accumulated, averaged, and compared with a preset limit for
the tower. If the average difference exceeded the limit,
all the data from that tower and scan were flagged "T."
The limits used in the rate-of-change filter, shown in Table 7,
are acknowledged to be generally higher than could be reasonably
expected in light of the mechanical and electronic response of the
instruments to likely changes in the atmosphere, particularly for the
steel-encapsulated platinum resistance temperature probes (RTDs),
whose time constant probably exceeds five seconds. The limits are
rather the result of trial and error with less lenient filters that
removed excessive amounts of data because of continuous high-frequency
"ripple" in the signals; in short, they are compromise values.
The filtering and flagging process produced a new 1-sec database
of flagged values in counts, which has been retained in tape copies by
ERT. The flags and their meanings follow:
" " (blank) good data
"0" Over maximum range limit
"U" Under minimum range limit
"L" Lost (first affected channel in channel-skip)
"M" Moved (reassigned from previous channel by
skip-correction)
"T" Tower noise limit exceeded
"S" Several (more than one) flags from the above
Only the " " and "M" flags indicate good data.
Some noise remains in the 1-sec data even after the filtering
procedure. In the Tower A data for Experiments 4 through 6, there is
probably a ripple having an amplitude on the order of 0.1 VAC, which
overpowers the variability in most of the instrument signals and
degrades the usefulness of the turbulence data. The data from the
other towers seem not to be so affected, perhaps because they were
communicated to the central collector by radio rather than cable.
33
-------
3.1.2 Correction of Signals
Corrections to the tower instrument signals have been made on the
basis of the audit results and the cosine response characteristics of
the fixed axis propeller (UVW) anemometers (Strimaitis et al., 1984).
No corrections have been made to either the propeller or cup data on
the basis of wind tunnel calibrations of these instruments since they
appear to be within a few percent of the manufacturer's standard
transfer functions used in the signal processing. Neither have
corrections been made for tower wake effects, although these are
certainly substantial, apparently amounting to up to 40 percent speed
deficit for Tower A (See SHIS #1 QA Report). Instruments were mounted
on the towers on booms extending in directions away from wakes when
winds were blowing from the release area to the ridge so that the data
would not be adversely affected during "modelable" hours. However,
the lower levels (up to 5 m; sometimes higher) on Towers A and B often
showed decoupled drainage winds in strongly stable periods even when
the winds aloft were blowing towards the Hogback, and consequently
these instruments were sometimes in wakes.
Table 8 lists changes made to instrument output during
calculation of 5-min and 1-hr average values to improve their accuracy
by correcting for electronic misalignment and audited errors in
orientation to true north. Tower C propeller data were not corrected
for orientation because audit results conflicted with visual
observations. Both agreed that errors were less than 3 degrees in any
case. The propeller anemometer data were corrected by iterative
applications of the cosine response corrections at every 1-sec scan,
provided both horizontal props showed good data. The iterations were
terminated when the wind direction resolved from the corrected
components changed less than one degree from one iteration to the
next. The W-prop signal was corrected similarly after the horizontal
wind was corrected to provide a basis for estimating angle of attack.
3.1.3 Calculation and Flagging of Averaged Measures
Five-minute and one-hour averaged values of 250 measures were
calculated from the corrected and flagged 1-sec data. Only "good"
data, flagged " " or "M," were used in these calculations, and all
instrument inputs to each measure had to be "good" for a scan to be
used in the measure's averaged value.
Measures were calculated according to the formulas given in the
SHIS #2 Work Plan with one exception for wind direction variability.
The standard deviation of wind direction from the F460 vanes was
calculated in two ways. One method, denoted "sdx2," was a simple
standard deviation of the voltage signal; the other, "sdxl," followed
the procedure recommended by Yamartino (1984), a single-pass method
which accounts for discontinuities in vane output and retains its
precision when variability is high. The simple method was used only
to provide data for comparison with Yamartino*s method for periods
when the vane's range was less than 180° and it didn't switch
potentiometers. Standard deviation of wind direction from propeller
anemometers, "sd," was calculated only by the Yamartino method.
34
-------
TABLE 8. CORRECTIONS MADE TO INSTRUMENT OUTPUTS
Tower A
Tower B
Tower C
Tower P
Level (m)
2
5
10
20
30
40
60
80
100
150
Level (m)
20
40
60
Level (m)
5
20
30
Level (m)
1
10
30
Level (m)
2
5
10
Level (m)
9
18
61
U-prop
-.06 m/s
-.09
-.04
-.07
-.06
-.05
-.05
-.12
-.06
-.09
Cups
-.02 m/s
-.03
-.02
U-prop
-.21 m/s
-.23
-.19
Cups
-.18 m/s
-.20
-.22
U-prop
-.15 m/s
-.16
-.18
Cups
-.02 m/s
0.00
V-prop
-.06 m/s
-.08
-.08
-.04
-.06
-.02
-.05
-.07
-.06
-.08
Vane
1 deg
-1.5
3.5
V-prop
-.18 m/s
-.17
-.18
Vane
-1 deg
0
0
V-prop
-.14 m/s
-.16
-.17
Vane
1.5 deg
6
W-prop
0.00 m/s
-.03
-.04
-.01
-.05
-.01
-.02
-.05
-.02
-.05
W-prop
-.09 m/s
-.09
-.10
T or AT
-.04° C
-.05
-.13
W-prop
-.04 m/s
-.08
-.09
T or AT
.09° C
-
.06
Orientation T or AT
-2 deg
1
1
0
-1
-2
-6
-6
-5
-3.5
Orientation
1 deg
1
1
-.07'
0.00
-.08
-.05
-.05
-.04
-.05
-.04
-.04
-.08
AT
-.16*
-.13
-.13
Orientation T or AT
0
0
0
-.03°
-.09
-.03
35
-------
Flags were assigned to the averaged data values on the basis of
the number of "good" data points in the values. For 5-min data, there
are a possible 300 points; for 1-hr data, 3600. A value was flagged
"E" (Excellent) if it incorporated at least 97 percent of the possible
1-sec values; " " (blank or good) if between 75 and 97 percent; "S"
(Suspect) if between 50 and 75 percent; and "B" (Bad) if less than 50
percent.
3.1.4 Comparison of Measures from Collocated Systems
Plots of measures from collocated systems are useful for
comparison of instrument performance in terms of low-speed response,
relative precision, and in the case of HBR, the effects of noise on
the output values. Plots of this sort are shown in this section, and
inferences are made in regard to data quality. Only 5-min averaged
data flagged "blank" or "E" are used in these comparisons.
Figure 7 is a time series plot of ow both from the sonic and
from the propeller anemometer sets at 40 m on Tower A during
Experiment 6. The propeller anemometer trace shows no particular
correlation with the sonic, which it quite generally exceeds by about
0.2 m/s. This increase in variance corresponds to roughly 0.07 VAC
RMS or 0.1 VAC amplitude, the "AC ripple" noted by field personnel at
the time. Figure 8 is a similar plot of data from Experiment 12,
which was conducted after the completion of the noise suppression
work. Here the two traces correspond much more closely. ERT's field
people at the time reported an AC ripple of about 3 mV amplitude,
which corresponds to only about .01 m/s in ow. The noise
remaining in the prop output from all sources no longer overpowers the
atmospheric component, and the trace follows the sonic trace quite
well. One may infer from these plots that the turbulence data from
the Tower A props are of no practical use in Experiments 4 through 6
but provide a reasonable basis for estimation of atmospheric
turbulence thereafter.
Figures 9 and 10 correspond to 7 and 8 but are traces of the
ow's from 5 m on Tower A rather than 40 m. For the earlier
experiment (Figure 9) the large up and down movements in the prop
traces at 5 m track those at 40 m (Figure 7) very well, as would be
expected if the bursts of noise are consistent on Tower A. Figure 10
shows that the fraction of the vertical turbulence measured by the
props is smaller at the lower level. This effect is probably due to
the suppression of low frequency eddies by the closeness of the
ground; a larger percent of the spectral energy is in high frequency
motions to which the propeller systems don't respond.
These plots imply that the quality of the turbulence data from
the propeller anemometers could be improved substantially by
application of corrections to bring them into better agreement with
the sonic data. Such corrections have not been applied to the values
submitted in the data base so that individual users may make
adjustments at their own discretion. A correction factor of 1.5 or so
would seem to get the data within about 20 percent of the sonic values
almost all the time, at least for this experiment. A somewhat smaller
correction would be appropriate at 40 m.
Figure 11 is a plot of the av data at 40 m during Experiment
12 and corresponds therefore to the ow plot in Figure 8. The
fraction of crosswind turbulence captured by the props is shown to be
36
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Differences between vane and sonic directions and between cup and
sonic speeds at 40 m are plotted in Figures 18 and 19 respectively for
Experiment 8. Prop and sonic comparisons are similar for this
experiment. These plots show a larger degree of scatter than those
for the earlier experiments in spite of the reduction of high
frequency noise in the central data system evidenced in the a^ and
aw values. The prop and cup-and-vane data agree with each other
quite well for this experiment, so the problem might be in the sonic
data.
The success of the noise reduction efforts in improving the
quality of the mean tower measurements is clear in the plots of data
from the later experiments (10 through 14). Figures 20 through 22
correspond to the earlier plots in Figures 12 through 14. With a few
exceptions, even the data for speeds less than 1 m/s agree within
about 10 deg for all three systems. There is an apparent relative
bias of about 3 to 5 deg between the sonic and cup-and-vane systems,
with the sonic system yielding the larger wind direction. With this
bias removed, the great majority of the points for speeds above 1 m/s
and for "modelable" periods (winds from 60 to 150 deg) indicate a
relative uncertainty of about 5 deg or less.
Wind speed comparisons for the later experiments are plotted in
Figures 23 through 25. In very light winds, the cups' speeds were up
to 80 percent higher than the sonics1 speeds (Figure 23). As the
speed increases, the agreement between the two systems improves as
expected, until the relative uncertainty is reduced to about 5 percent
in the "modelable" directions. The differences between the prop and
sonic speeds are similarly scattered (Figure 24). The props yield a
smaller fraction of the sonic speed as the speed decreases. At higher
speeds, the prop data tend to be about 5 to 10 percent lower than the
sonic. The comparison of cup and prop speeds in Figure 25 shows that
the cup speeds are almost universally higher than the props. In very
light winds, the cup speeds may be as much as twice as high as the
props. At higher speeds and in "modelable" directions, the difference
reduces to about 10 percent, as it does in the comparison of sonic and
prop speeds.
If it is assumed that the sonic data are generally the most
accurate of the outputs from the three collocated systems because the
sonic sensors are the most responsive (and may have suffered least
from noise), then it would appear that the propeller data are up to 10
percent low at speeds of about 3 m/s or more. The cups, on the other
hand, are generally more accurate at the highest range of speeds.
Part of the overestimate by the cups at low speeds is due to the zero
offset of 0.22 m/s in the cup transfer function; it is likely that the
winds at the Hogback were frequently lighter than this, at least for
some times during a 5-min averaging period. In fact, in the data
presented here, some of the 5-min vector averages from the sonic
anemometers are below 0.1 m/s. Nonetheless, the cups' offset alone
doesn't account for their averaged responses being consistently higher
than the props', nor do the calibrations used. This discrepancy
between cup and prop speeds corroborates the inference drawn from
comparison of sonic and prop speed; that is, prop speeds may be low.
49
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The reader should note that the comparisons and inferences in the
preceding discussion really relate only to data from the 40-m level of
Tower A. Data from other instruments, however, were processed in the
same way and the results are comparable.
The improvement in consistency between collocated measurements in
the refined data over the preliminary data is demonstrated in
Figures 26 and 27, in which the differences between vane and prop wind
directions are plotted as a function of vane direction for the
instruments at 40 m on Tower A during Experiments 9 through 15. The
distinct trends in direction differences in the preliminary data
evident in Figure 26 have been removed in Figure 27. The improved
consistency in the refined data results from the use of the wind
tunnel calibrations and cosine-response corrections for the props and
probably only to a minor extent from the data-filtering described
above; the raw data were also subjected to substantial filtering in
the production of the preliminary database.
An overall assessment of the quality of the HER meteorological
(and tracer gas) data base can be found in the Quality Assurance
Project Report (Greene, 1985). It presents estimates of the precision
and accuracy of all the measurements. The bottom line of this
assessment is that the data from Experiments 9 through 15 are
completely useful for modeling purposes. The data from the other
experiments are still somewhat noisy, especially the turbulence data
from Experiments 4, 5, and 6.
3.1.5 Remaining Problems in the Tower Data
Certain propeller anemometers showed intermittent lack of
response at HBR as they had at CCB, in spite of the installation of
new bearings. A systematic appraisal that will identify all such
faulty prop data has not yet been completed. When this has been done,
5-min and 1-hr averaged measures calculated from the affected
propellers will be flagged "F" (for Faulty, Failure, Friction, or
Frozen). Some periods of suspect temperature outputs have also been
identified; these too will be flagged.
3.2 HBR Streamline Analysis
In modeling the maximum ground-level concentration of material
from an elevated plume released upwind of a hill, one important aspect
of the flow that must be considered is the vertical deflection of the
plume relative to the surface of the terrain. When the flow is stably
stratified, air nearer the surface possesses a greater potential
density than that at greater elevations. Using a "parcel" argument,
Sheppard (1956) suggested that this air may pass over the top of a
hill only if there is sufficient kinetic energy. Because the denser
air near the surface often possesses insufficient kinetic energy, only
air above a "critical" dividing-streamline height, Hc, is able to
pass over the hill. The flow below Hc must pass around the sides of
the hill, or it may be "blocked" if the hill is an infinite ridge.
Streamlines above Hc will therefore pass closer to the surface of
the hill so that a plume in this flow will travel nearer the surface
58
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of the hill and will produce greater ground-level concentrations.
Diffusion models that explicitly account for this two-layer flow
structure are said to incorporate the "cut-off" hill approach to
simulating the flow above Hc. In this section of the report the
vertical deflection of a streamline in the flow above Hc as it
passes over the crest of HBR is discussed. These deflections are
known to depend on the initial height of the streamline above Hc, on
the shape of the hill above Hc, on the stratification of the flow,
and on the wind speed profile.
In the first subsection, the height and shape dependencies are
considered through potential flow theory. The second subsection
extends the analyses through a perturbation analysis using a
linearized form of the Navier-Stokes equations. Here stratification
and wind speed shear are considered. In both subsections, model
calculations of stand-off distance are compared to lidar measurements
of the height of the oil-fog plume centerline above the crest of HBR.
3.2.1 Representativeness of Potential Flow above Hc
Lidar data received from WPL have been used to compare estimated
streamline heights upwind and over the crest of HBR to calculations
from potential flow theory. Heights of the centerline of oil-fog
plumes have been assumed to represent streamlines. This information
has been used to examine the extent to which the field data collected
at HBR support the "cut-off" hill approach to calculating the flow
above the dividing streamline height. In this modeling approach, the
layer of air below Hc is presumed to remain below the hill top and
the flow above Hc is presumed to behave as potential flow (a
surrogate for weakly stratified flow) over a hill of reduced height.
This analysis makes use of the lidar data obtained at the section
nearest the release point (but after the plume had reached its
approximate equilibrium height), and at the section nearest the crest
of HBR. The centroid of the distribution of backscatter intensity in
each section is assumed to mark the same streamline during each
five-minute period. Meteorological data associated with each of the
streamlines are the five-minute average data for the standard
five-minute interval containing both centroid observations.
Furthermore, of all the periods for which lidar data were available,
only those periods were selected in which the transport wind direction
was fairly steady, and in which the lidar section nearest the crest
lay on the windward side of HBR. This subset of the database is best
suited to study the relationship between the elevation of the plume
above the surface and the incident flow.
The relationship between the initial (H) and final (n) height
of the streamline, the dividing-streamline height (Hc), the hill
height (A), and half the hill breadth at A/2 (L) is presented in
Figure 28. The estimated height of the streamline above Hc measured
at a distance xc from the center of the ridge is denoted zc.
Lidar measurements close to the source are used to estimate zc.
61
-------
u
Figure 28.
The relationship between the initial (H) and the final
(n) height of the streamline, the dividing-streamline
height (Hc), half the hill height (A/2), and half the
hill breadth at A/2 (L). H is measured a distance xc
from the center of the hill.
62
-------
The oil-fog plume centerline height H is used to approximate the
streamline height at x = «>. Calculations of potential flow over an
elliptical cylinder were used to estimate H(x = <») for each of the
lidar measurement periods and the results were quite similar to
H(x = xc). For example, during Experiment 10 at 0801, H is measured
to be 86 m at xc equal to 517 m from the center of the ridge with
Hc calculated at 42 m. H(x = ») is calculated to be 85.1 m, a
negligible difference of only 0.9 m. Larger differences occur if the
lidar measurement of H is made over the edge of the ridge. For
example, during Experiment 7 at 0351, H is 56 m at xc equal to 245 m
from the center of the ridge with Hc calculated at 28 m. H(x = «>)
is calculated to be 48 m. The lidar measurement is over the leading
edge of the ridge where an ellipse is not a good approximation.
Three different types of cylinders (circular, 2-D Rankine, and
elliptical) are used for the potential flow calculations. The flow
over a circular cylinder,
* = - uH (1 - 2 2) (1)
x + H
is the simplest potential flow solution, but its results may be
unrealistic because it does not account for the aspect ratio of HBR.
The along-wind (at 117 degrees) breadth (190 m) of HBR at half its
maximum elevation (45 m) is used to calculate the aspect ratio (4.2,
i.e., 190/45). A hill with an aspect ratio of 4.2 is likely to cause
a greater degree of deflection of streamlines over its crest than a
semicircular hill with an aspect ratio of 1.0 because the semicircular
hill has a steeper slope. (See the discussion in Section 2 of the
Second Milestone Report.) Thus, an aspect ratio of 4.2 is used to
solve the potential flow solutions for a 2-D Rankine cylinder,
* = - uH - m tan"1 (3 - ~^ - 5 — ) (2)
x + H - a'
2
where m = — u a' (—2 -1)
* a'
8, = 190 m = along-wind breadth of the hill at A/2
a' = 347 m = half the distance between the source/sink pair
and an elliptical cylinder,
¥ = - uA(l+X) sinh (y-yo) sin v (3)
63
-------
where y and v are elliptical coordinates, X is the aspect ratio,
and
"o = ln
The heights of observed 5-minute plume centroids (n) above the
crest of HBR for various effective plume heights H (lidar measured
oil-fog plume centerline heights at x = xc) are presented in
Figure 29a. The values are scaled by A, the height of HBR. The
figure includes computed curves of n/A. versus H/A derived from
potential flow over a circular cylinder, an elliptical cylinder, and a
2-D Rankine cylinder. A majority of the points lie well below the
circular cylinder curve, i.e., the measured plumes pass much closer to
the ridge than is expected on the basis of potential flow estimates
that ignore Hc.
The variation of the height of the observed plume centroid
above the crest of HBR for various effective plume heights in excess
of Hc (H-HC) is presented in Figure 29b. Hc is included because
it is expected that the layer of air below Hc does not pass over
HBR. The values are scaled by the effective hill height (H* =
A-HC). The data now better fit the curves that represent potential
flow over a cylinder. This result supports the "cut-off" hill
modeling approach in conjunction with the assumption that the flow
above Hc is essentially neutral. The majority of the data lie above
the circular cylinder curve, suggesting that a measure of the ridge,
shape, e.g., the along-wind aspect ratio, should be included. The
fact that the majority of points lie between the elliptical and
circular curves suggests that streamlines are typically deflected to a
larger extent than would be modeled by potential flow over an
elliptical cylinder with an aspect of 4.2. Although in principle some
other terrain shape may better fit the data, it is likely that a
measure of density stratification or wind speed shear or both needs to
be taken into account in specifying the flow above Hc.
3.2.2 Effects of Stratification and Shear on Streamline
Deflections
An Empirical, Neutral Flow Base Case
The results of the previous subsection indicate that for releases
above Hc, a substantial portion of the streamline deflection can be
understood in terms of neutral potential flow of the air above Hc
over an appropriate hill shape. In fact, a least squares minimization
of the predicted versus observed centerline standoff distance, n,
modeled as
n = m • (H-HC) , (5)
yields a slope, m(=0.68), that represents a hill shape somewhere
between the circular and elliptical cylinders. This fact and the
64
-------
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1 .6
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.8
.7
.6
.5
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.3
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Figure 29a. Height of the source streamline (n) above the crest of
HBR for various source heights (H). Values are scaled by
the height of HBR (A).
c-
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Figure 29b. Height of the source streamline (n) above the crest of
HBR for various effective source heights (H - Hc).
Values are scaled by the effective hill height
65
-------
associated statistical performance measures presented in Table 9 are
important in that they provide a "base case" for judging the
improvements gained through inclusion of stratification and shear. It
is interesting that Equation 5 provides a significantly better fit to
the lidar centerline data than a comparable model that ignores Hc
(i.e., Hc = 0 yielding an m = 0.34) and is slightly better in mean
square error (MSB) than RTDM, which uses a somewhat different formula
for those cases (i.e., 20 of the total 94) where H exceeds the hill
height, h. A scatterplot of predicted versus observed n values for
this potential flow base case is shown in Figure 30.
Streamline Deflection Theory
A number of researchers, e.g., Scorer (1949), Long (1953),
Wurtele (1957) have used perturbation analysis to reduce the
Navier-Stokes equations of motion to (1) a single equation of the
displacement, 6(x,y,z), that a fluid particle at point x,y,z has
experienced; or (2) as an equation in the vertical velocity
perturbation Aw. In two dimensions (i.e., infinite in y direction)
these equations are:
2af^ + (N/u)2S = 0 (6)
and
[V2 + (N/u)2 - B]Aw = 0 (7)
... . _ 1 du . _ 1 d2u . 02 32 32
respectively, where a - - — , B = - ^j , and 72 = — 2 + — 2
Since the w velocity can be computed from & as
Aw = u , (8)
Equations 6 and 7 should yield identical results, but this is only
obvious when shear is negligible (i.e., a = 6 = 0).
Models Incorporating Stratification Only
In the case where shear is negligible Equation 6 may be solved by
first taking the Fourier transform of the equation with respect to x.
Defining
00
{«} = J dx 6(x,z)e-lkx , (9)
Equation 6 reduces to the ordinary differential equation
{6}" + U2 - k2){6} = 0 (10)
66
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TABLE 9. HER STREAMLINE STANDOFF AT CREST MODELING
% MSB % MSB Corr.
Equation 11 MSB* As Bias Stochastic Coeff. (r)
TH — ^— ^— — — ~—
Empirical
n = m • (H-HC) 24.2 38.5 2.0 97.7 0.707
m = 0.68
n = m • H 24.9 45.3 0.8 82.9 0.530
m = 0.34
RTDM 24.2 40.2 2.1 96.6 0.712
Stratification Only
Queney See Eq. 18 24.6 35.7 0.7 98.5 0.733
Hunt Eq. 20 23.4 37.8 8.3 91.4 0.732
Stratification and Shear
Eq. 27 and B = a2 23.9 34.8 4.3 95.6 0.736
Eq. 29 25.0 38.7 0.04 97.5 0.729
"n-jHisthe average value of the streamline height above crest
(in meters) for the 94 cases considered. The average observed
streamline height (HOBS) *s 25.1 m.
*MSE is mean square error in m2.
67
-------
-------
where 9, = N/u and the prime denotes differentiation with respect
to z. Equation 10 has the solution
{6} = e+imz (6(0)} , (11)
where the + sign ensures outgoing waves (i.e., the radiation
condition) and where
tn
= (I2 - k2)1/2 (12)
is the solution of the algebraic equation that results when
Equation 11 is inserted into 10. Determination of the solution
6(x,z) also involves satisfying the lower boundary condition
6(x,h(x)) = h(x) , (13)
which constrains the streamline at the surface to follow the surface.
This non-linear condition is usually linearized as
«(x,0) = h(x) (14)
so that the final solution can be written as
00
«(x,z) = J dk {h} eimz eikx (15)
where {h} is the transform of the terrain function h(x). If
however we rewrite the exp(imz) term in Equation 15 as exp(imz'),
where z' = z - h(x), the resulting expression satisfies the non-linear
condition (13), although Lilly and Klemp (1979) caution that such a
simplistic adjustment will disturb the radiation condition at z = -H».
Irrespective of this point, the main difficulty in evaluating
Equation 15 is the "branch cut" singularity created by m.
Queney (1947) obtained a solution to Equation 15 in the
hydrostatic limit (i.e., k2 « B,2, so that m « 8,) for the case
of the inverse polynomial hill function,
h(x) = h/(l+ (x/L)2) , (16)
chosen because of its simple transform,
{h} = hLe- . (17)
69
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Inserting Equation 17, along with the simplification m = I, into
Equation 15 yields the solution
6(x,z) = h[e cos lz' - (x/L) sin «.z']/[e2 + (x/L)2] , (18)
where c = 1 in Queney's work but is set to e = 1 + z'/L here in
order to recover the exact solution in the neutral limit where 8, = 0
and imz = -kz. Perhaps the only drawback of Equation 18 is that for a
known source height H, one must solve Equation 18 iteratively to find
n E z', subject to the constraint
h(x) + z' - 6(x,z') = H (19)
It should also be noted that for the case of a cutoff hill,
H* = h - Hc, the hill length is approximated as Lc = (H*/h)L
and the effective source height becomes H - Hc. Results of applying
these Equations 18 and 19 at the crest (i.e., x = 0) of the cutoff HBR
are presented in Table 9. What is striking is that for this
parameter-free model, both MSB and r are superior to an empirical
model; thus indicating the value of a model that explicitly includes
the influence of the stratification, 8. = N/u+, in the layer
between Hc and H.
Since a goal of this project is to include effects predicted by
successful theories of stratified flow over terrain into pollutant
dispersion models, a model component developed by Hunt and co-workers
for the "outer flow" region was also tested. For flow over a 2-d
ridge, the standoff height n at the crest may be approximated from
mass conservation as
n = (H - HP)/(1 + Au) (20)
where Au is the dimensionless speed perturbation given as
Au = (H*/LC)(1 + 0.5 s log(s)) (21)
for small s, for the inverse polynomial, cutoff hill, and
s = NLc/u. Despite the fact that Hunt et al. (1981) indicate that
the long "skirted" inverse polynomial hill is an inappropriate shape
for the cutoff hill problem and that the upper level solution,
Equation 21, should be accompanied by a properly matched inner
boundary layer (and possibly a shear dominated middle layer), the
results presented in Table 9 indicate that this simple, upper layer
approximation performs nearly as well as the more complex, iterative
+Both N and speed u were evaluated at z = H. Results obtained using
the wind component perpendicular to the ridge were poorer for all
models considered.
70
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model of outer layer flow previously described. The scatterplot of
predicted versus observed lidar standoff heights is shown in Figure 31.
Before considering the added effect of wind speed shear, several
features of the "stratification only" results are worth considering.
• For centerline standoff measurements made at the crest
(i.e., x = 0), the Equation 18 with e = 1 solution is
independent of the hill width L and, in fact, is completely
independent of the hill shape function assumed. Addition of
the neutral limit case inserts the e = 1 + z'/L
dependence, but this is a small correction for the small
standoff (i.e., z'/L « 1) cases of principal interest. In
comparison, the Hunt relations appear more sensitive to hill
shape and hill length, though an exhaustive study has not
been performed.
• The 94 cases considered here span an s(= NLc/u) range of 0
to = 2.5; thus, one is reasonably sensitive to the
explicit s dependence in Equation 21, although it should be
noted that Equation 21 was derived for small values of s.
An alternative expression suggested by Hunt et al. (1981)
reduces to Au = (HC/LC)/(1 + s2) at the crest of the
inverse polynomial hill and yields a 40% higher MSB than
Equation 21. An accompanying drop in r to 0.60 suggests
that this alternative expression induces s » 1 asymptotic
behavior too quickly.
• Consideration of "stratification only" yields a mean
streamline height that is just 0.5 m (1.75 m for
Equation 20) below the observed mean standoff height and
r.m.s. errors of about +6 m. With event dependent lidar
resolutions of order few meters, greatly improved model
performance cannot be expected to result from using more
sophisticated approaches (e.g., multiple layers) or adding
additional dependencies (e.g., shear).
Inclusion of Wind Shear
Based on various measures of the first (a) and second (8)
derivatives of the wind speed profiles for the HBR events being
considered, the effects of shear might be expected to dominate
stratification effects characterized by 8. = N/u; however, the
previous subsection has indicated that models without shear appear to
adequately model streamline standoff distances measured at the crest.
To understand the influences of shear, it is convenient to return to
Equation 6, take the Fourier transform with respect to x, and
hypothesize a solution of the form
, (22)
where {6o(z)} becomes the new unknown function with the
governing equation
71
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0
OBSERVED ETA (M)
Figure 31. Predicted versus observed plume centerline standoff
distance at the crest of HBR using the "outer-layer"
solution (Eq. 20) of Hunt et al. (1980), that includes
stratification but neglects shear.
72
-------
{60}" -H 2(a - p')U0}' + (P'2 - P" - 2
-------
70
60 -
50 -
-------
additional 0.75 m below the Queney solution without shear, the
increase mean bias is offset by a reduced MSE and increased r. All
other attempts to include shear led to a poorer result (i.e., higher
MSE) than the stratification only results.
One of the more interesting of these attempts involved assumption
of a linear incident wind profile, u(z) = u(H) + a(z-H), in
Equation 27. If the incident profile is assumed to follow the terrain
and the perturbation to the wind field is included, so that
UT(Z«) = u(z') tl- g^f] , (28)
then the streamline deflection can be written as,
6(x,z) = ^f?y *Q
-------
extent as it traveled away from the source. The growth of a plume due
to buoyancy is typically modeled (Pasquill, 1976) as
(30)
where Az is the plume rise. The plume will collapse if az^ is
less than ow/N. In this case this "bubble" of plume material will
not only seek its equilibrium height in the stratified atmosphere, it
will also spread out at this level to reduce the potential energy of
the initial configuration.
For plume heights less than or equal to L, it may be possible to
infer the meteorology (wind and temperature structure as well as the
turbulence) at plume elevation from near-surface measurements. This
has obvious implications for the type of meteorological data needed
for dispersion modeling. In applying a model, one would need to know
when data obtained below the elevation of the plume are likely to be
representative of the flow at plume elevation and above.
This section of the report addresses this issue and describes an
analysis of data from CCB and HER performed to see to what extent
surface boundary layer similarity theory can be used to characterize
the data measured at these two complex terrain sites.
CCB Meteorological Data
The scaling length L was not determined at CCB by measuring the
momentum flux and heat flux near the surface. Rather, it was
estimated from wind speed and temperature measurements near the
ground. With wind speed measured at 10 m, and temperature measured at
2 m and 10 m, the bulk Richardson number might be computed as
R. = fc_ v~10 "2,,x» -/ (31)
D 0 ~ "'™' -"• ••""'-—-
where g is the acceleration due to gravity, 6 is the potential
temperature, and zg is the geometric mean height of the layer
between 2 m and 10 m. When the non-dimensional temperature gradient
(4>h) is set equal to the non-dimensional wind shear (ni), a
reasonable assumption in the stable atmospheric boundary layer
(Panofsky and Dutton 1984), L is related to the gradient Richardson
number (Ri) by
z 5i (32)
L 1 - BRi k '
where S is approximately 5. Ri is defined
Ri = T—T, 03)
6 (du/dz)2
76
-------
Upon writing the temperature difference and the wind speed profile in
terms of 4^ = 1 + Bz/L, Ri^ can be related directly to L, and a
quadratic equation is obtained for L.
The condition that L be positive for stable stratification places
the following restriction on Ri^ for the 2- and 10-m heights used at
CCB:
Rib < (zg/10)2/B (34)
This is equivalent to the condition
Ri < 1/B = 0.2 (35)
From Equation 32, we see that the similarity profiles require that
z » L as Ri -> 0.2. In essence, the production of turbulence by
shear is found to expire when the Richardson number is greater than
approximately 0.2. For the CCB database, the bulk Richardson number
from 2 m to 10 m exceeds the critical value for sustaining turbulence
in approximately half of the hours. Presumably, the value of L in
these cases is less than 2 m.
Data at 2 m and 10 m were used to obtain estimates of L and u*,
the friction velocity. For those cases in which L could be obtained,
the applicability of the flux-profile relations was evaluated by
estimating the wind speed at 40 m (the next measurement height on the
tower) and the temperature difference between 10 m and 40 m. The
results are presented in Figures 33 and 34. The upper portion of
Figure 33 shows the predicted wind speed versus the observed wind
speed, and the lower portion shows the corresponding ratio of the two
versus z/L. The predicted speeds lie quite close to those observed
when z is less than or approximately equal to L. At greater
non-dimensional heights, the speeds are overestimated by 50% or more.
The predicted and observed temperature differences between 10 m and
40 m shown in Figure 34 also show that better predictions are obtained
when z/L is less than or approximately equal to 1. Similar results
have been reported by others (Webb (1970), Skibin and Businger (1985)).
The behavior of the wind speed and temperature residuals for z
greater than L suggests that neither the speed nor temperature
increases with height as fast as 4^ = (1+Bz/L) would indicate.
This too has been reported by others. Webb (1970) suggests that a
reasonable median profile is obtained if ^ = 1+B for z/L greater
than 1. This assumed profile allows the gradient Richardson number to
increase with height, and Webb suggests that this profile should be
most representative for Ri less than 1.0. Figures 35 and 36 show the
results obtained when the "Webb extension" is applied to the data in
Figures 33 and 34. The extension improves the predicted profiles
considerably, and reasonable correspondence is now obtained at heights
in excess of 10L.
Another method of extending the profiles of wind speed and
temperature above z = L has been discussed by van Ulden and Holtslag
77
-------
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4.5
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3 5 7 9 11
DBS WIND SPEED 40M (M/S)
13
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1.00 5.00 10.00 50.00 100.00 300.00
Z/L
Figure 33. Comparison of the observed wind speed at 40 m with that estimated
from surface-layer similarity theory and Ri^ (10 m) at CCB.
78
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UJ
I—
(_>
a
LU
5.00
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.0C
.50
.01
3 5 7 9 11
DBS WIND SPEED 40M (M/S)
13
.10
1.00 5.00 10.00 50.00 100.00 300.00
Z/L
Figure 35. Comparison of the observed wind speed at 40 m with that estimated
from the Webb extension to the surface-layer similarity theory and
Rib (10 m) at CCB.
80
-------
DBS DELTA THETA (K)
12.50
18.00-
7.50-
5.00-
2.50-
o LOO
>
'LU ..f.
co .50
m
o
n
UJ
a
LU
.10
.01
***
.10
1.00 5.00 10.00 50.00 100.00 300.00
Z/L
Figure 36. Comparison of the observed potential temperature
difference between 10 m and 40 m with that estimated from
the Webb extension to the surface-layer similarity theory
and Rib (10 m) at CCB.
81
-------
(1985). They suggest that the dimensionless wind shear should have
the form
4^ = 1 + (4.93 z/L) exp (-.29 z/L) (36)
This profile mimics the traditional 4^ for z less than L, but
allows ^ to approach a constant value at greater heights. If we
assume that 4>h should have the same form, then we obtain a
temperature profile similar to that reported by Stull (1983) and
Yamada (1979), provided that we assume that the height at which the
temperature gradient reaches 2% of the total gradient through the
depth of the ground-based inversion is between 3 and 4 times L. With
this choice of the dimensionless wind speed shear and temperature
gradient profiles, the bulk Richardson number provides a
transcendental equation for L. The results of using this expression
with the data presented in Figures 33 and 34 are presented in
Figures 37 and 38. The performance is nearly the same as that
obtained with the Webb extension, but the computed values of L are not
as small for Richardson numbers approaching 0.2.
The relationship between Ri|j and L obtained by assuming
Equation 36 is valid for all z does not require that the Richardson
number be less than some critical value. Consequently, an estimate
for L can be obtained for all stable hours in the CCB modeling
database (i.e., all Ri^). Figures 39 and 40 contain the results of
comparing observed with predicted values of wind speed and temperature
difference at 40 m for all stable hours.
All of the points in Figures 39 and 40 that were not included in
Figures 37 and 38 appear at z/L greater than approximately 20.
Because z is taken to be 40 m in these plots, z/L = 20 is equivalent
to L = 2 m, which is the lower height for the data used to calculate
Rib- The ability of these extended profiles to match the observed
profiles beyond z = 10L deteriorates as z/L increases. This is
especially true for the temperature profile. In fact, the behavior of
the residuals seen in Figure 40 suggests that there is a systematic
problem with the assumed temperature profile.
The expression for the temperature difference is
u* 6.,^ B.n (z2/za) + 17 [exp (-.29 zx/L) - exp (-.29 Z2/L)]
62-61 = ~^L { In (za/ZQ) + 17 [1- exp (-.29 z^L)]}2 (37)
The subscript 1 denotes data at 10 m, and the subscript 2 denotes data
at 40 m. If the 10-m wind speed is held constant, 62-6^
begins to drop sharply at Z2/L = 20, and does not recover again
until Z2/L is greater than approximately 400. Its minimum value is
approximately one tenth its value for z/L =: 400, and this apparently
accounts for the factor of 10 underestimation seen in Figure 40. No
alternate temperature profile assumptions have been tested as yet, but
it seems that the observed wind speed and temperature well above L for
very small L are the best indicators of speeds and temperatures at
even greater heights, and the "correct" form of the profiles as scaled
82
-------
or
CL
13
11 -
9
Q
UJ 7
Ul
Q_
CO
o
1 -
0
01 3 5 7 9 11
DBS WIND SPEED ( M/S)
13
5.5 T
5.0-j
4.5
4.0
3.5-
3.0"
2.5-
o
LU
g 2.0-
CO
CD
O
CJ
I—I
a
a;
o_
1.5
.01
100 5.0010.00 5000100.00300.00
Z/L
Figure 37. Comparison of the observed wind speed at 40 m with that
estimated from the van Ulden/Holtslag extension to the
surface-layer similarity theory and Rij, (10 m) for those
data contained in Figure 33.
83
-------
13-
LU
F—
cr
i--
ce
CL
0 1
3 5 7 9 11
OBS DELTA THETA (K)
13
to
CD
O
30.00
20.00
15.00-
10.00
7.50
5.00
2.50-
1.00'-
.50
CJ
H
O
a:
Q.
.10-
.01
.01
.10
1.00 5.0010.00 50.00 ' 100.00 300.00
Z/L
Figure 38. Comparison of observed potential temperature difference
between 10 m and 40 m with that estimated from the van
Ulden/Holtslag extension to the surface-layer similarity
theory and Ri^, (10 m) for those data contained in Figure 34.
84
-------
*.« *+
01 3 5 7 9 11
DBS WIND SPEED (M/S)
13
5.00
4.50
4.00'
3.50
3.00
2.50
2.00
1.50-
a:
LU
CO
GO
CD
\
CD
LU
GC
DL
1.00
.50
.10
.01 .10 100 5.001000 100.00 1000.00
Z/L
Figure 39. Comparison of the observed wind speed at 40 m with that estimated
from the van Ulden/Holtslag extension to the surface-layer
similarity theory and Rij, (10 m) for all stable hours at CCB.
85
-------
-------
by surface properties (L, u*, 9*) are relatively unimportant
beyond z/L values of about 10. Profiles in this region should not be
estimated from surface properties.
These results at 40 m are reproduced at greater heights as well.
Figures 41 and 42 illustrate the performance of the profiles in
estimating wind speed and temperature at 150 m from data measured at
2 m and 10 m. The wind speed estimate for z/L less than 10 shows
somewhat greater scatter, but the real difference in performance is
seen at greater values of z/L. There is a strong tendency to
underestimate wind speed with increasing z/L. Perhaps this is because
the structure of the nocturnal jet is not accounted for.
For z/L < 1, the temperature is estimated less well at 150 m than
it is at 40 m, there being a tendency to underestimate the observed
temperature difference. However, the behavior of the residuals at
greater z/L is reproduced. Note that the region of greatest
underestimation has shifted toward somewhat greater z/L. Note also
that the scatter about this systematic trend is nearly the same in
both datasets, which suggests that a different extrapolation method
for the temperature profile stands a chance of performing better.
With these encouraging results for the applicability of the
extended similarity profiles for wind speed and temperature up to
heights of order z = 10L, what should we expect of the vertical
turbulence velocity (ow)?
Within the lower part of the surface layer, ow is typically
constant with height (i.e., this is the constant flux layer) and
proportional to the surface friction velocity (u*);
-------
Q_
CO
a:
Q_
22
20-
18
16
14-
12-
10
8
6-
4-
2-
5.00-1
4.50
4.00
3.50
3.00
2.50-i
cc
LU
CO
CO
a
LU
LU
a:
o_
1.00
.50
.05
4 6 8 10 12 14 16 18 20 22
DBS WIND SPEED (M/S)
.01 .10 1.00 5.0010.00 100.00 1000.00 10000.00
Z/L
Figure 41. Comparison of the observed wind speed at 150 m with that estimated
from the van Ulden/Holtslag extension to the surface-layer
similarity theory and Ri^, (10 m) for all stable hours at CCB.
88
-------
n:
i—
-------
15
13"
11-
8-
7-
3-
1-
* + ,«
+ +
.01
.10
1.00 10.00 100.00 500.00 2600.00
Z/L
Figure 43. Variation of ow/u* with non-dimensional height z/L
at CCB. Data are obtained at or interpolated to the
release elevation of the oil-fog plume.
90
-------
be obtained for the layer between 2 m and 5 m as well as for the layer
between 2 m and 10 m.
Wind speeds measured on the 150-m tower at HBR were generally
smaller than those measured at CCB. Given the limitation that Ri^
must be less than about 0.2 (see Equation 34), the HBR data base
produces 16 values of L for Ri^ (2-10 m), and 26 hours for Ri^
(2-5 m) out of a total of 127 hours.
Figure 44 shows a comparison of those values of L obtained from
Rib (2-5 m) and RiD (2-10 m). There is a definite bias towards
larger values when Ri^ (2-5 m) is used to obtain L, and with the
exception of four data points well to the right of the 1:1 line, the
greatest relative difference between the two estimates of L occurs for
small values of L (say, 5 m or less). Of the four "outliers," three
points are from hours in which the flow at all levels of the main
tower was coming from the "backside" of HBR; that is, the tower was in
the lee of HBR.
Residual plots of the wind speed and temperature predicted for
40 m are presented in Figure 45. They show the result of using the
profile of Equation 36 (assuming <^ = 4^) to estimate L and
thereby the meteorology at the 40-m elevation from the 10-m data.
Better estimates of the wind speed are generally obtained for z/L less
than 10, as was found at CCB (Figure 39). But notice that the scatter
is considerably greater at HBR. Beyond z/L = 10, Figure 45 also
displays the trend toward underestimating the speed with increasing
z/L.
The temperature residuals also tend to follow the pattern
observed in the CCB data, but the scatter is very great.
In general, the utility of attempting to extend the surface
similarity profiles to heights in the neighborhood of z/L = 100 and
greater is dubious.
One reason for the poorer comparison of the profile estimates at
HBR is the presence of the low-level flow away from or parallel to HBR
that was frequently observed during the experiments. In effect, the
surface similarity scaling parameters are calculated for a
locally-generated flow that would be expected to exert very little
influence on the flow at greater heights. As at CCB, it is probably
better to consider the structure of the elevated flow separately from
that at the surface when L is very small. Indeed, this is what the
surface similarity theory would advocate. The overall results of
these analyses of the CCB and HBR observations indicate that the
similarity relationships reproduce the observations fairly well (to
within a factor of 2.0) to elevations less than about 10 L. Above
10 L the predictions have little reliability.
3.4 Analysis of oz(t) Observed During FSPS
One of the most critical quantities for an air quality model to
predict accurately in a stably-stratified atmosphere is the growth of
91
-------
50'
40-
30-
O
*~
.o
of
E
o
20-
10-
0
©
10
20 30
L From R;(, (5m)
40
50
Figure 44. Comparison of values of Monin-Obukhov length L obtained
for HBR using the bulk Richardson number method and
gradients obtained between 2 m and 5 m, and 2 m and 10 m.
The three circled data points are from hours in which the
meteorological tower was in the lee of HBR.
92
-------
200.00
100.0
10.00
7.50
1 6°°
2 2.50
STJ
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\ w
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S c
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II
1.00
.50
.10
.05-
.01
1.(
10 10.0 100.0 1000.0
Z/L
10000.0 100000.0
10.0
100.0
1000.0
10000.0 100000.0
Z/L
Figure 45. Comparison of observed wind speed (top) at AO m and
potential temperature difference (bottom) between 10 m and
40 m with that estimated from the van Ulden/Holtslag
extension to the surface-layer similarity theory and
(10 m) for all stable hours at HER.
93
-------
a plume in the vertical (
-------
h = a + B z/L (40)
Venkatram et al. (1984) suggested that the length scale for diffusion
in the vertical could be constructed as
'*
This assertion is not necessary. Virtually the same result is
obtained directly from the flux-profile relationships. Assume that
passive material diffuses in the same way as heat in a turbulent flow
so that Kz = KH and
u*kz awkz
K = — — * ~- (42)
2 * a *
Therefore the length scale is defined as
I . JS. = *?_ , *2 . (43)
a a. a(a + Bz/L)
w h
z/L is related to the gradient Richardson number and hence to N/0W
by assuming that aw = au*:
E - !r~ Ri - (!r^X
L
-------
This derivation relies only on the appropriateness of the
flux-profile relations for the surface layer and on the assumption
that ow is proportional to u*. Beyond the surface layer, the
length scale for turbulent mixing still should scale with
-------
statistics (e.g., centroid position and the moments 0y and oz)
to be obtained.
This analysis of plume growth focuses on the hourly-average lidar
data and thereby avoids problems in trying to work out the
relationship between instantaneous plume cross-sections obtained for
times-of-travel varying from a few minutes to a half hour or more, and
it also avoids the problem of identifying the meteorology that most
influences each of the scans . Use of the average data also reduces
the variability associated with the discrete sampling, and provides a
measure of time-averaged plume spread that includes any vertical wave
motions.
A total of 14 FSPS experiment-hours were selected from those
hours processed by WPL and from the subset of the FSPS defined by the
top one-third of the entire SFg concentration data set. These same
hours were also used in the Tracy modeling analysis which is presented
in subsection 5.4. They represent stable, plume impingement
conditions when the plume was transported towards the Beacon Hill or
Target Mountain areas.
The initial growth of the plume due to entrainment associated
with the buoyant rise of the plume (ozfc) was estimated from the
hourly-averaged lidar scan made nearest the stack, once the plume had
leveled off. Typically, ozt, was estimated for a distance of 700 m
from the stack. The lidar scans taken downwind of this distance were
then used to evaluate the subsequent growth of oz.
WPL provided maps of the plume centroid position for each
scanning plane during each hour. Those scans obtained when the plume
was in the vicinity of Beacon Hill or Target Mountain for more than
half of the hour were not included in this analysis because we wanted
to evaluate the evolution of the plume before terrain effects became
important. A total of 43 observations were used in this
analysis — with the downwind distance of the plume centroid ranging
from 293 to 4944 m from the stack.
3.4.3 Comparison of Model Predictions with Observations
Figure 46 shows a plot of crz/owT versus T/TL, where the
Lagrangian time-scale is
w r ' r w
where y = 0.52, T = 0.36, and zr is the effective height of the
plume. Both ow and N are calculated from data collected at the
150-m level of Tower A. The time T is taken to be
T = t + tv (48)
where tv is the virtual time-of-travel given by
97
-------
1 .50
1 .00
.70
.50
.30
I
9
«
O -10
bN .07
.05
.03
.02
10
10 20 30 50 70 100 200 300 500 700 1000
T/TL
20 30 50 70 100 200 300 500 700 1000
Figure 46. Variation of oz/owT with T/TL using the CTDM
formulation for oz.
98
-------
2TT^ *
'„ - - sr— - s <«>
T
L
where tj, is the travel time from the stack to the point at which
crzjj is measured. The travel time t is taken to be x/ur where
ur is the wind speed at zr, i.e., 150 m for the 14 hours.
The solid line in the figure is the relationship given by
o T
«, = - W o.5 (50)
which is the equation for az used in CTDM. Each of the 14 hours
is labeled by a number. The number for each hour corresponds to the
oztj value estimated from the lidar data for that hour. It was set
to fit the model for az exactly. The subsequent values for each
hour (represented by the dashed lines) compare the model estimates to
the observed values. For the entire ensemble the model estimates of
az (and T^) are roughly within 50 percent of the observed
values. Note however that the observed data tend to fall below the
model line. This indicates that the subsequent growth of oz
beyond az^ is actually overestimated, in general, by the model.
This tendency of the observed plume growth to be overestimated by
the model could result from modeling TL incorrectly, not screening
out the wave contribution to ov, or not accounting for a collapse
of the plume in the vertical after plume rise. None of these
possibilities has been investigated in detail as yet. Currently, a
method for estimating y2 using vertical temperature flux and crw
data is being tested in the CTDM oz-algorithm. This method, which
is based on the theory of Pearson et al. (1983) does not depend on
whether the crw measurements include waves.
Figure 47 presents the ratios oz (observed)/oz (predicted)
versus time-of-travel. The triangles in this figure represent the
azt, value estimated from the lidar data for that hour which
correspond to the numbers in Figure 46. From this figure, the
predicted values are generally seen to lie within a factor of 1.5 of
the observed values. That is, the predictions lie in the range az
(observed) /1. 5 to 1.5 <*z (observed),
Several existing complex terrain dispersion models use the P-G
curves to simulate plume growth. It is informative to ask how well do
estimates of
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2 .00
1 .00
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-------
To find out, the oil-fog plume observations were compared with az
(P-G) where
a2 (P-G) = a . 2 + (0.362 x°'55 -2.7)2 for x < 1000 m (51)
Z ZD
a2 (P-G) = a . 2 + (33.6 x °'14 -75)2 for x > 1000 m (52)
Z ZD
This is the formulation that is used by COMPLEX I, which adds in
quadrature the initial buoyancy-enhanced plume spread to the growth
expected due to ambient turbulence for very stable (Class F)
conditions. The results of the comparison are displayed in Figure 48
(top).
These results are quite similar to those of Figure 47.
Apparently, the slow growth rate prescribed by the Class F P-G curves
provides a reasonable (± 50%) estimate of the observed growth rate
for this particular data set (14 hours). Note that the points for
0Zb (the triangles) do not lie along the perfect prediction line.
This results from adding the buoyancy-induced spread to the ambient
spread in quadrature. A more direct comparison can be made with
Figure 47 if the virtual source method of including oz^ is used.
The results are contained in the lower portion of Figure 48. The
similarity between these estimates of oz, relying on the observed
0Zb and the Class F P-G curves, and those obtained by the CTDM
algorithm, relying on the observed crzt), N, ow, u, and the
surface similarity flux-profile description of diffusion in the stable
boundary layer, primarily reflects the dominance of the
buoyancy-enhanced growth.
The P-G curves have been interpreted as a description of the
growth of a plume with distance for a representative turbulence
intensity, i.e., az = ow x f(x) where x is the downwind
distance, f(x) is a function of distance (e.g., the straight line in
Figure 46), and ow is the representative turbulence intensity.
The form of the distance function and the value of the turbulence
intensity is specified for each stability class. RTDM has adopted
this interpretation as a means for including measurements of
turbulence intensity in calculating oy and
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70 100
200 300 500 700 1000
TIME (SEC)
A AA A A A
A A A
A A A
70 100
200 300 500 700 1000
TIME (SEC)
2000
+ T + +
2000
Figure 48. Variation of oz (observed)/oz (predicted) with
travel-time using the PGT formulation. The upper plot
corresponds to predicting az by adding the buoyancy
enhanced and the ambient turbulence az portions in
quadrature, while the lower plot uses the virtual source
approach.
102
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1 .00
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70 100
200 300 500 700 1000
TIME (SEC)
2000
i r
t i
A A AA A
A A A A
70 100
200 300 500 700 1000
TIME (SEC)
2000
Figure 49. Variation of az (observed)/az (predicted) with
travel-time using the RTDM formulation with measured
turbulence. The upper plot corresponds to predicting
oz by adding the buoyancy-enhanced and the ambient
turbulence az portions in quadrature, while the lower
plot uses the virtual source approach.
103
-------
If the measured ow data contain a significant wave component,
and if this is thought inappropriate for the RTDM algorithm, then
"default" values of the turbulence intensity might be substituted.
The default turbulence intensity for Class F is 0.016 (i.e., the
Briggs (1973) expression). The algorithm performs much better when
the default turbulence values are used, as shown in Figure 50. This
nearly matches the performance of the buoyancy-enhanced P-G algorithm.
This comparison suggests that the turbulence intensity that
drives the plume growth should be very small in very stable conditions
if the stability-class-dependent distance function is used. What
happens if the turbulence intensity of 0.016 is used in the CTDM
algorithm, and how does this compare with the assumption that plume
growth in excess of o^ might be ignored? Figure 51 contains the
results. The CTDM algorithm overestimates plume growth in only three
scans, and the bias has certainly shifted toward underestimating plume
growth. In fact, when iz is set equal to 0.016, the resulting
predictions of az are nearly equal to oz^ (i.e., no growth).
This is reflected in the degree of similarity between the two plots in
Figure 51. Apparently, the inclusion of a turbulence time-scale based
upon measurements of N and
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200 300 500 700 1000
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Figure 50. Variation of az (observed)/oz (predicted) with
travel-time using the RTDM formulation with Briggs rural
(ASME, 1979) dispersion coefficients. The upper plot
corresponds to predicting oz by adding the
buoyancy-enhanced and the ambient turbulence
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200 300 500 700 1000
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Figure 51. Variation of oz (observed)/oz (predicted) with
travel-time using the CTDM formulation with iz = 0.016
(upper plot), and variation of az (observed)/ozb
with travel time (lower plot).
106
-------
(RTDM)) does as well as the az model that uses meteorological data
obtained near plume elevation. However, realistic simulations of
sequences of hourly concentrations should rely upon observed
meteorology rather than worst-case modeling assumptions. To this end,
the performance of the CTDM algorithm for oz provides
encouragement that observed meteorology can be effectively
incorporated.
107
-------
SECTION 4
ANALYSIS OF HIGHEST GROUND-LEVEL CONCENTRATIONS
AT EACH SITE
The purpose of this section is to describe the meteorological
conditions that produced the highest ground-level concentrations
during each field experiment. In particular, the applicability of the
dividing-streamline concept to describe stable flow in complex terrain
is assessed. For each field experiment, the top ten SFg and CF3Br
concentrations are presented along with the meteorological conditions
estimated for the release heights. Detailed analyses of four
experiment hours are presented to illustrate plume behavior above,
below, and near the dividing-streamline height. These four case
studies represent the highest ground-level concentrations at each
field site. Each case-study analysis includes a description of the
observed concentration distribution and meteorological data. Also, a
calculated centerline concentration is compared with the observed
maximum concentration. Finally, a comparison of the concentration
events observed at each of the three field sites is made.
The CCB tracer and flow visualization experiments are described
in detail in the First Milestone Report (Lavery et al., 1982). The
HER studies are discussed in the Third Milestone Report (Lavery et al.,
1983).
4.1 Cinder Cone Butte
The ten highest observed SFg concentrations scaled by the
emission rate (shown as x/Q in units of ys/m-^) measured at CCB
are presented in Table lOa. The net release height (zr),
dividing-streamline height (Hc), and sampler elevation (Zj^jj);
wind speed (u), sigma-v (ov), sigma-w (
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ground-level concentrations. Only 2 of the 29 releases below Hc
produced concentrations listed in the top ten. Plumes above Hc
tended to flow up and over the hill and produced concentrations near
the top or on the lee side of CCB. Only 3 of the 60 releases above
Hc produced x/Q values listed in the table.
Table lOb lists the ten highest normalized observed
concentrations measured at CCB along with the appropriate release and
meteorological information. At CCB, approximately 88% of the CF3Br
releases were made at heights above Hc, about 10% near Hc, and 2%
below. Most of the time CF3Br was released at a height higher than
the SFg release height. As expected, the highest CF3Br
concentrations occurred when the release height was above the
calculated dividing-streamline height, typically at elevations higher
than the release height. Four of the highest ten concentrations were
observed during the neutral Experiment 217 (Hc=0) . Evidently, as
shown by the relatively large values of ow, there was enough
mixing to bring the CF3Br plume to the hill surface on the windward
side.
Of the ten highest observed concentrations, there is only one
release (Experiment 210 Hour 3) near Hc. The results of this case
are similar to CF3Br releases above Hc in that the highest
concentrations occurred at an elevation higher than the release height.
4.1.1 Experiment 206, Experiment-Hour 8 (0700-0800 MST)
The SFg tracer gas and oil-fog were released southeast of the
hill at a release height 35 m above the ground. Local terrain
elevations near the release point are estimated to be 5.5 m below the
base elevation of the hill coordinate system, so the net release
height corresponds to the 29.5-m height level on the hill. Although
the SFg release terminated early at 0753, there was nearly a full
hour of tracer impact on the hill because the travel time from the
source to the hill center at 1.8 m/s was about 5 minutes.
Wind and temperature data measured at Tower A during this hour
were used to characterize the flow in terms of Hc. Because the
v-component of the 40-m wind set was missing, wind speeds at this
height were estimated before Hc was calculated. The data from the
80-m wind set and the good u-component measured at 40 m were used to
infer the 40-m wind speeds.
Time series plots of the calculated 5-minute Hc and bulk hill
Froude numbers above Hc (Fr(Hc)) for this experiment-hour are
presented in Figure 52. The dashed line represents the SFg tracer
gas release height. At the beginning of the hour Hc is 27 m but
quickly rises to above 40 m. Hc falls steadily to below 30 m during
the latter half of the hour. Fr(Hc) during the same period exhibits
a similar pattern, rising as high as 3.6. The hourly averaged Hc
value is 33 m; thus, this hour represents transport along streamlines
very near Hc.
110
-------
o
X
70
60
50
30
20
10
0
Release Height
Time (Hour)
8
3.5
3.0
2.5
2.0
Time. (Hour)
Figure 52. Time series of 5-minute calculated dividing—streamline
heights (Hc) and bulk hill Froude numbers above Hc
(Fr(Hc)). (CCB, Experiment 206, 10/24/80, 0700-0800
MST).
Ill
-------
Time series plots of the 5-minute propeller anemometer data
measured at Tower A are presented in Figure 53. The Tower A data
along with the reconstructed 40-m winds are "splined under tension" to
the tracer gas release height and these release height values are
represented by the solid line.
The 10-m winds were light and variable during this hour, whereas
the winds at 80 m were quite steady. The plume at 35 m was observed
to be flowing toward the hill so that the direction shear must have
occurred below this height. The 40-m wind speeds decreased
significantly during the first half-hour causing the rise of Hc.
The relatively large vertical turbulence intensities are
corroborated by observations that strong eddies appeared to bring the
plume down to the ground. The eddies gave the plume a rotating
appearance as one observer looked back at the source along the plume
axis.
An hourly average of the 5-minute temperature and propeller wind
data measured during this hour at Tower A were used to construct
vertical profiles. A "spline under tension" method was used to
interpolate the meteorological variables for every 5 m between
instrument levels. The vertical profiles of hourly averaged wind
direction, wind speed, and temperature are presented in Figure 54.
The large directional wind shear below the release height is clearly
evident. The wind speeds were also quite light below the release
height.
The distribution of the observed hourly averaged normalized
concentrations (x/Q in ys/m3) is shown in Figure 55. Hill
height contours in 10-m intervals starting at 5 m are also shown. The
5-minute average wind flow vectors estimated at the tracer gas release
height are drawn at the release position. The length of each flow
vector is proportional to the 5-minute wind speed. The 1-hour average
flow vector, derived from a vector average of the 12 5-minute wind
vectors, is depicted by the long dotted line emanating from the
release position.
Observations indicate that the plume mixed down to the hill
surface near the base of the draw on the southeast side of CCB
producing the maximum observed SFg concentration (164 ys/m-*) at
an elevation (25.3 m) less than Hc. This is the highest observed
normalized concentration found at the CCB field experiment.
Concentrations are also found on the northeast and north sides of the
butte. Plume material was mixed to the surface of the hill and then
advected directly over and around the hill.
A centerline concentration was calculated by means of the
one-hour average meteorology estimated at the tracer gas release
height. A comparison of the highest observed concentration with the
estimated centerline concentration provides information on plume
dilution and the reasonableness of the oz and
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114
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OBSERVED
Exp: 206-8
Zr = 35 m Gas: SF6
Q = .062 g/s Hour: 800
-------
method used to calculate oz (Venkatram et al. 1984) at d + xv is
as follows:
a (d + x )
°z = JT (d + x ) -, 1/2 <54)
where x is a virtual source distance defined as
AB + / ( AB) + B (55)
l 2 w2
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w
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and the initial spread of the plume (
-------
physical causes of the eddies; nor have we analyzed the meteorological
data to predict their occurrence.
4.2 Hogback Ridge
The ten highest normalized SFg concentrations measured at HBR
are presented in Table lla. Hc and the meteorological parameters
were estimated from Tower A data. The highest concentrations
generally occurred when zr > Hc. At HBR the SFg was released
coincidentally with the oil-fog through the nozzle of the jet fogger.
Except for two hours, the CF3Br was never released at a greater
height than the SFg. Because of the very light winds that were
typical below the crest of the ridge and the thermal buoyancy of the
oil-fog release, the coincidental SF$ and oil-fog plumes frequently
rose well above Hc. As observed at CCB, plumes above Hc flowed up
and over'the ridge, producing the highest concentrations at
Zr» typically near the top or on the lee side of the ridge.
Table lib lists the ten highest normalized observed
concentrations measured at HBR along with the appropriate release and
meteorological information. In this table the meteorological
parameters and Hc were estimated from Tower B data. For CF3Br,
the highest concentrations occurred when zr < Hc. Releases below
Hc tended to stagnate, producing high concentrations on the windward
side of the ridge at typically Hc > z^^^ > zr. Occasionally
plume material was slowly transported up and over the ridge after
impingement on its windward side. However, if the winds near the
release had a substantial component parallel to the ridge, then most
of the plume material stayed below the crest.
The CF3Br emissions released well below Hc produced the
highest concentrations observed during the three field experiments.
The results at HBR are quite different from those experienced at CCB.
At HBR the flow below Hc was impeded by the ridge and the tracer gas
pooled against the ridge and subsequently was either lifted over the
top or was transported parallel to the ridge line to the south. At
CCB the flow well below Hc traveled around the sides of the hill,
and consequently tracers released well below Hc produced relatively
low concentrations.
4.2.1 Experiment 6, Experiment-Hour 9 (0700-0800 MDT)
The CF3Br tracer gas was released 100 m from the base of the
ridge at a release height 20 m above the ground. The release base
elevation was 17.4 m above the zero elevation of the hill coordinate
system, so the net release height corresponds to the 37.4 m height
level on the ridge.
The 5-minute Hc and Fr(Hc) time-series plots are presented in
Figure 56. The 5-minute temperature and propeller anemometer wind
data measured at Tower B (1, 5, 10, 20, 30 m) near the base of the
ridge were used in conjunction with Tower A (80, 100, 150 m) data to
characterize the flow in terms of Hc. If the wind direction was not
within a defined sector of HBR (117° ± 45°), the projected
117
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Figure 56. Times series of 5-minute calculated dividing-streamline
heights (Hc) and bulk hill Froude number above Hc
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119
-------
(Equation 60) wind speed was used. If the projected wind speed was
less than zero, then the wind speed was set to zero for that
particular level. The effective height of HER was taken to be 85 m.
The 5-minute values of Hc are all greater than the release height,
except for two periods when Hc drops to zr. The sudden decreases
in Hc correspond to decreases in the Tower A temperatures measured
at 80 to 150 m. The average of the 5-minute Hc values over the hour
is 56 m; thus, this hour is representative of flow below Hc.
Fr(Hc) slowly decreases during the hour, with the exception of the
two sharp decreases.
The propeller anemometer data from Tower B, the 30-m tower near
the base of HBR, are used to represent the flow at the release
height. The trend in wind speeds and directions at 5, 20, and 30 m is
shown in Figure 57. The local release height corresponds with the
20-m level on Tower B. The winds at the release height are less than
1 m/s, and there is a gradual shift in direction from 10° at the
beginning of the hour to 240° by the end of the hour. Tethersonde
measurements of wind direction at the release height also show a shift
in wind direction through the hour.
The trends in iz and ow values during the hour are also
shown in Figure 57. The values of iz and ow estimated at the
release height vary from 18 to 32% and 0.10 to 0.16 m/s respectively.
The one-hour value for
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.4. I .1r 4 .9
HOGBACK RIDGE. NM
TOWER MEASUREMENTS CROSS SECTION
EXPERIMENT: 6
TIME: 800
z.a. -.e
Z.3. -.3
a.8. -.5
H,
Figure 59. Potential temperature and wind measurements cross section
at HBR. The values at each instrument level are (left to
right) the perpendicular component of the wind to the
ridge (m/s), the parallel component (m/s), and the
potential temperature (°C). The solid lines with arrows
are isentropes and the dashed line represents the
dividing-streamline height. (HBR, Experiment 6, 10/13/82,
0700-0800 MDT).
123
-------
components indicate that at the lowest levels of Tower A (2-10 m) the
flow is from the northwest, and at the lowest levels of Tower B (1-5
m) the flow is from the northwest to southwest or down the slope of
HBR. Above this layer, the flow is predominantly from the southeast
or up the slope of HBR.
This cross section corroborates previous analyses which suggested
that releases below Hc tended to stagnate with the tracer gas
impinging against the ridge. These meteorological conditions and
release height produced the highest concentrations that were observed
on the windward side of HBR.
The distribution of the observed hourly averaged normalized
CF3Br concentrations over the surface of the ridge is shown in
Figure 60. The largest concentrations are found near the bottom half
of the sampler array at an elevation that is less than Hc. The
maximum observed concentration (445 jis/m-^) is found 7 m below the
net release height at an elevation of 30.4 m. This is the largest
observed normalized concentration found in the CTMD modeling data
set. This maximum concentration is confirmed by a collocated sampler
which measured 425 ys/m3 for the same period. A sharp decrease of
observed tracer concentrations is found above the mean Hc surface
(1656 MSL) although some CF3Br was transported above Hc to the
crest of the ridge.
Using the method presented in subsection 4.1.1, oy is
calculated to be 168.3 m and az is calculated to be 9.4 m with the
initial size of the plume set to zero. From this, a centerline
concentration is calculated to be 202 ys/m3. Because the
propeller anemometer winds estimated at the tracer release height are
so light and variable during the hour, there is a great deal of
uncertainty in calculating a one-hour average centerline concentration.
If the hourly averaged sonic anemometer data are used to estimate
«*y» °z» anc^ u (see the Fourth Milestone Report for a
discussion of this experiment-hour using the sonic data), then a
centerline concentration is calculated to be 278
4.2.2 Experiment 7, Experiment-Hour 6 (0600-0700 MDT)
The SF$ tracer gas was released 100 m from the base of the
ridge at a release height 15 m above the ground. Figure 61, a photo
taken at 0655 MDT from the 150-m tower, shows the smoke plume
traveling from the release crane over the ridge. The oil-fog
generator produced enough heat flux to cause a thermally- induced rise
in the oil fog and collocated SFg plumes. Lidar measurements taken
near the source, meteorological profiles, and photographs were used to
estimate a 32-m plume rise. Thus, the effective plume elevation after
plume rise is 47 m above the ground. Local terrain elevations near
the release point are estimated to be 17.4 m above the base elevation,
so the net release height corresponds to the 64.4-m level on the ridge.
Time series plots of the 5-minute Hc and Fr(Hc) values are
presented in Figure 62. The 5-minute temperature and propeller wind
data measured at the 150-m tower were used to characterize the flow in
124
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Figure 62. Time series of 5-minute calculated dividing-streamline
heights (Hc) and bulk hill Froude numbers above Hc
(Fr(Hc)) (HER, Experiment 7, 10/14/82, 0600-0700 MDT).
127
-------
terms of Hc. For the first forty minutes of the hour, Hc
decreases from 59 m to 30 m before slowly rising. The average of the
5-minute Hc values over the hour is 41 m; thus , this hour represents
flow above Hc. The trend in Fr(Hc) values correlates with the
trend of Hc. Fr(Hc) starts off at 2.4, decreasing to 1.5 before
slowly rising.
Time series plots of the 5-minute propeller anemometer data from
Tower A are presented in Figure 63. The data at 80 m (dotted lines)
and 40 m (dashed lines) are presented along with the data "splined
under tension" to the tracer gas release height (solid lines). The
splined values are close in value to the measured 60-m values which
are not presented in this figure. The wind directions at all three
levels are quite steady. Tethersonde measurements of the wind
direction at the release height indicate winds ranging from 70° to
130°. The wind speeds at the release height slowly increase from
1 m/s to more than 3 m/s during the first forty minutes, before slowly
decreasing. This coincides with the trend in 5-minute Hc values
mentioned above.
The profile of HER with the locations of the three meteorological
towers and the appropriate instrument levels are shown in Figure 64.
The numbers shown at each instrument level are the propeller derived
au, dv, and 0W values in units of m/s. On Tower A, the
values of ow begin to decrease above the 80-m level. The
turbulence found at the top of the ridge at Tower C is much lower than
that at the equivalent level of Tower A.
The one-hour average profiles of the 5-minute temperature and
propeller wind data measured at Tower A are presented in Figure 65.
There is more than 90° of wind direction shear below 40 m. Above this
level, the wind directions are fairly uniform with height. There is
also a marked increase in wind speed above the 40-m level.
The isentropic cross section for this hour is presented in
Figure 66. The isentropes represented by the solid lines with arrows
show that the flow above Hc travels up and over the ridge; whereas
the flow below Hc is blocked, forming a recirculating flow. It is
expected that the highest concentrations will occur at an elevation
greater than the release height near the top or on the lee side of the
ridge. The wind components indicate that at the lowest levels of
Towers A and B the flow is from the northwest to southwest, or
downslope. Above this layer, the flow is from the northeast to
southeast, or upslope.
The distribution of the observed hourly averaged normalized
concentrations is shown in Figure 67. As expected, the maximum
observed concentration (91 ys/m^) is found in the lee of HER. The
concentrations are much lower below the mean Hc level (1658 MSL) ,
indicating that the bulk of the plume material was transported above
Hc up and over the ridge. Figures 68 and 69 are instantaneous
photos taken at 0710 MST from atop the ridge. The plume is
surmounting the ridge as shown in Figure 68 and ground-level impact
occurs in the lee of the ridge as shown in Figure 69.
128
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8.8. Z.8r 6 .7
HOGBACK RIDGE. NM
TOWER MEASUREMENTS CROSS SECTION
EXPERIMENT: 7
TIME: 708
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Figure 66. Potential temperature and wind measurements cross section
at HBR. The values at each instrument level are the
perpendicular component of the wind to the ridge (m/s),
the parallel component (m/s), and the potential
temperature (°C). The solid lines with arrows are
isentropes and the dashed line represents the
dividing-streamline height. (HBR, Experiment 7, 10/14/82,
0600-0700 MDT).
132
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The hourly averaged lidar scans made at an along-plume distance
of 60 m from the source yield an estimate of initial plume size
(ozo) of 12.9 m. By the method discussed in subsection 4.1.1, the
virtual source distance is calculated to be 904.3 m and <5z(d+xv)
is 16 . 7 m. The lidar-measured value of ay at a distance of 60 m
from the source is 32.6 m, and at a distance of 127 m from the source
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A plot of the hourly averaged lidar scan closest to the source,
which was used to estimate plume rise, is presented in Figure 70,
This is a two-dimensional display of the plume cross-section along the
path of the lidar scan. The darkest and largest symbols indicate
where the signal from the plume is strongest. The x-axis represents
the horizontal distance in meters from the lidar, and the y-axis
represents the vertical height in meters relative to the lidar. The
profile drawn from the y-axis is a vertical profile of the plume
signal in the scan plane, which is found by integrating the array
horizontally. The profile drawn from the x-axis is a horizontal
profile of the plume signal in the scan plane, which is found by
integrating the array vertically. From these analyses, it can be seen
that the average plume is reasonably well-defined and coherent; hence,
the lidar-derived height of the plume is a good estimate of the plume
rise.
The 5-minute Hc and plume height time series plots are
presented in Figure 71. Because the travel time to the receptor of
maximum concentration is approximately one hour, the meteorology from
the previous hour is used to calculate Hc. Hc is first calculated
from
Hc = H - (u/N) (63)
where H is the effective height of the terrain towards which the plume
is directed. If Hc is calculated to be less than 150 m, then Hc
is recalculated by means of the integral formula presented in the CTMD
First Milestone Report (Equation 4). The 5-minute temperature data
measured at six levels of Tower A (10, 50, 75, 100, 125, 150 m) and
the 5-minute cup-and-vane wind data measured at four levels of Tower A
(10, 75, 100, 150 m) are used to characterize the flow in terms of
Hc. The cup-and-vane data are used in this analysis because the
cosine response corrections have not yet been applied to the propeller
anemometer data. If the vane wind direction is not towards Beacon
Hill or Target Mountain (197 to 307°), the wind speed is set to zero
for that particular level. The average of the 5-minute Hc values
over the hour is 225 m and the hourly average height of the plume is
211 m; thus, this hour is representative of transport along
streamlines near Hc.
In Figure 72, the top two plots are two-hour time series of
cup-and-vane wind data measured at 150 m, 100 m, and 75 m. Because
the wind speeds are less than 2 m/s, the travel time to the receptor
of maximum concentration is approximately one hour; thus, the
meteorology from 0700 to 0800 is believed to be more representative.
During this time period, there is more than 60° of wind direction
shear between the winds at the release height (estimated from the
150-m level) and at 100 m.
The bottom two plots in Figure 72 are two-hour time series of
propeller anemometer vertical turbulence intensities and
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8
Time (Hour)
Figure 71. Time series of 5-minute calculated dividing-streamline
heights (Hc) (FSPS, Experiment 13, 08/26/84, 0800-0900
PDT).
140
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estimated at the release height from the 150-m level is .148 m/s
(iz = 9%). The vertical profiles of the one-hour average of Tower A
temperature and cup-and-vane wind data measured during hour ending
0800 are presented in Figure 73.
The hourly-averaged observed normalized SF6 concentration
(ys/m^) distribution is presented in Figure 74. The wind flow
vectors drawn at the release position are from the cup-and-vane data
measured during the preceding hour. Observations and photographs
indicate that as the plume approached "Beacon Hill," it split and
traveled around the sides of the hill to the north and south. There
was impingement on the southeast flank of Beacon Hill where the
maximum observed concentration (8.3 ys/m^) was measured. The
plume also impinged to the north of Beacon Hill where the second
highest concentration (8.0 vs/m-*) for the hour was observed.
Figure 75 is an instantaneous photo taken with a polarizing filter at
0805 from a location west of the plant. As seen in this photo,
filaments of plume material traveled up toward the summit of Beacon
Hill. The plume can be seen to split as it approaches Beacon Hill and
travels around the sides of the hill. Half-way through the hour, the
plume shifted so that the main segment passed over the southern
portion of Beacon Hill and the valley. Figure 76 was taken at 0845
from the camera position at Clark Mountain and shows the plume now
traveling over the river valley. Notice the downward wisp of
turbulent plume material in the vicinity of the Tracy stack.
The lidar measured plume centroid positions for approximately
every five minutes during the hour are presented in Figures 77 through
79. It should be noted that the lidar cannot sample oil-fog on the
north side of Beacon Hill; hence, the centroid positions are based
only on "seen" plume material. Lidar measurements and observer
comments (including those from the scientists who operated the lidar)
indicate that during the first half of the hour, the plume is
traveling northeast with considerable horizontal dispersion.
Observations suggest some of the oil fog is lingering against the
north side of the river basin west of Beacon Hill, and some of the
plume is splitting off and passing to the north of the hill. The
lidar does measure a. considerable amount of plume material as it
impacts the south shoulder of Beacon Hill. As the plume exits the
Beacon Hill area, the plume appears to be drawn down the river cut.
As the hour progresses, the plume trajectory shifts clockwise, and by
0845, there is little or no plume material against the north basin
slope.
A time series plot of the plume direction measured in degrees
from north is shown in Figure 80. As the hour progresses, the plume
shifts clockwise (from Beacon Hill towards the river valley) at all
five measuring azimuths of the lidar. A time series plot of the
vertical displacement of the plume centroid above the stack is
presented in Figure 81. As the plume approaches Beacon Hill during
the first half of the hour, the plume centroid increases in
elevation. However, during the last half of the hour, as the plume
travels clockwise toward the river valley, the plume centroid
decreases by more than 50 m in elevation.
142
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36 m and a horizontal plume size (
-------
SECTION 5
MODEL DEVELOPMENT AND APPLICATIONS TO
CTMD EXPERIMENTAL DATA
5.1 Description of the Current Version (12185) of CTDM
This section describes changes that have been made to CTDM since
preparation of the Fourth Milestone Report (Strimaitis et al. 1984).
CTDM (12185) is the first version that can be readily applied to the
three experiment sites. It has been run using "impingement" subsets
of the three data bases and some of the results are reported here.
5.1.1 Terrain Description
To simplify the structure of the code, previous versions of CTDM
had modeled the terain obstacle as either an isolated axisymmetric
hill or an isolated two-dimensional ridge section. This required two
separate terrain treatments in the model to handle both CCB and HER.
For general application, CTDM needs to be able to accommodate hill
shapes intermediate between these two idealizations.
CTDM now simulates all isolated hills or hill segments as if they
were ellipses in horizontal cross-section. At any height between the
base of the hill and the crest, the hill shape is characterized by the
lengths of its major and minor axes. However, the vertical
cross-section of the hill is not assumed to be elliptical.
A height profile, h, along each "axis" of the hill is presumed to
have the form:
h = H + h (64)
l+(x/L)P
where H is the height of the crest of the hill above a zero-plane
(i.e., H is the relief height of the hill), x is the distance from the
crest along the axis, L is the horizontal scale of the hill that
equals the value of x at the point on the hillside where h = 0.5 H, p
is an exponent whose value is chosen to give an adequate
representation of the hill shape in profile, and h0 is the height of
the zero-plane above the elevation defined as zero in the coordinate
system being used. For a particular hill, L and p may have values
that differ from the major axis to the minor axis. For example, CCB
is represented by the choices
153
-------
H = 105 m h0 = -10 m
L(major) = 280 m L(minor) = 225 m
p(major) =3.3 p(minor) =4.0
Also needed in this terrain specification is the orientation of the
major axis relative to north. For CCB, it is 127° clockwise (CW) from
north.
This method for describing the terrain features to the model
allows the model to treat CCB and HER with the same algorithms. The
terrain parameters for HER are:
orientation = 27° CW from north
H = 90 m h0 = 1599 m
L (major) = 10,000 m L(minor) = 150 m
p (major) = 10.0 p(minor) =1.8
Note that the test-section of HER is essentially a two-dimensional
ridge, so that the major axis is specified by a very large length
scale. Also, heights at HER are referenced to sea level, whereas
heights at CCB are referenced to 945 m MSL; hence ho differs
markedly between the two locations.
5.1.2 WRAP
Characteristics of Two-Dimensional Flow Around an Ellipse
A particle in a steady two-dimensional flow around an ellipse
will experience both accelerations and decelerations as it passes by
the ellipse. The magnitude of these changes in speed depends upon how
close the particle is to the stagnation streamline of the flow.
Maximum changes occur for particles on the stagnation streamline.
Furthermore, the spacing between adjacent streamlines varies in
inverse proportion to these changes in the speed along streamlines.
Figure 82 is a representation of a typical streamline pattern for
flow around an ellipse when the incident flow is at an angle to the
axes of the ellipse. The speed along a particular streamline reaches
a minimum near the stagnation zone along the upwind face. It then
increases to a maximum at some point near the apex of the boundary,
beyond which the speed slows once again to a minimum before resuming
the speed of the incident flow.
A plume in this steady flow (with some small-scale turbulence)
will follow the streamline patterns, spreading slowly across adjacent
streamlines. However, as streamlines spread apart (or contract) the
plume size in the horizontal will expand (or shrink) to the same
extent. In the absence of diffusion, these kinematic changes in the
horizontal size of the plume will not alter the concentration of
material within the plume. Changes to the horizontal scale of the
plume are balanced by changes in the flow speed so that the flux of
material is unchanged. With the addition of small-scale diffusion,
the rate of plume growth in the horizontal can be altered by changes
in streamline spacing (Hunt and Hulhearn, 1973). However, based on
154
-------
Stagnation Zone
Stagnation Streamline
Figure 82. Typical streamline patterns in two-dimensional flow
around an elliptical cylinder.
155
-------
the observations at CCB and Tracy we choose to ignore the effects of
small-scale diffusion on concentrations in the WRAP component of
CTDM. The observations suggest that kinematic effects dominate short
averaging times and that low frequency turbulence — meanders —
control crosswind plume growth over hourly averaging times.
Plume growth in the vertical increases to the extent that the
time-of-travel to a particular receptor increases compared to that in
the absence of the hill. In principle, if plume material is traveling
toward the hill along the stagnation streamline, it will take an
infinite amount of time for that material to reach the hill (the speed
along the stagnation streamline goes to zero at the stagnation
point). This of course also gives diffusion an infinite amount of
time to act on this material and remove it from the stagnation
streamline. This idealization, of course, doesn't occur; but recent
fluid modeling studies (Hunt, 1985), have shown the importance of the
effect of travel-time on the vertical growth of plumes.
WRAP Reformulation
To simulate ground-level concentrations due to dispersion of
releases below Hc in complex terrain settings, CTDM must approximate
the key features of steady two-dimensional flow around an ellipse that
were described above. Two key approximations in the WRAP component
are (1) lateral diffusion is insensitive to accelerations in the flow
(i.e., the kinematic deformation of the plume has no effect on the
diffusion rate), and (2) vertical diffusion increases with increases
in travel-time caused by terrain-induced alterations in the flow
speed. Furthermore, the mean flow for the averaging period (one hour)
is considered steady, while all of the variability in the flow over
the period, including that due to meandering, is considered
"turbulence."
This approach differs from that previously adopted in WRAP, in
which some allowance had been made for alterations in lateral
diffusion caused by the kinematic deformations in the flow while no
allowance had been made for travel-time effects in the rate of
vertical growth of the plume. Furthermore, a distinction had been
made between fluctuations in the direction of the wind on the
time-scale of the vertical turbulence and fluctuations on the
time-scale of meanders in the flow so that concentrations on the
surface of the hill depended upon the dilution of material in the
"filament" plume, and the frequency (over the averaging period) that
the wind came from a direction very near to the stagnation wind
direction. Note that the effects of flow distortion on lateral
diffusion only altered the rate of spread of the narrow "filament"
plume and had no effect on the meander of the "filament" plume.
The change in WRAP has been motivated in part by the scale of the
FSPS compared to that of SHIS #1 or SHIS #2. With the very light
transport speeds typically associated with flows with impingement
potential, transport times from the source to terrain frequently
exceeded an hour at the FSPS site. Consequently, the travel-time
could readily exceed the meander time-scale. When this occurs, the
156
-------
path taken by a puff or plume segment is not straight, and plume
material can be advected toward a hill along a number of potential
stagnation streamlines rather than the single one for a flow that is
steady over the travel time to the hill. This situation would appear
to be better approximated by a wide plume in a steady flow.
A second reason for the change in the WRAP model was the observed
tendency toward overestimating impingement concentrations at CCB
(SHIS #1). Photographs of the plume during several primary
impingement episodes showed a rather striking rate of plume growth in
the vertical near the hill. In other words, the travel-time factor is
important and should be included in the model.
With these approximations and assumptions in mind, the "filament"
plume equation (Equation 33) presented by Strimaitis et al. (1984) for
receptors beyond the impingement point was modified to include the
total lateral turbulence measured during the averaging period,
neglecting distortion effects. The Equation (33) now becomes
" 9 Exp(-0.5(d/o^)2) (1 -I- sign(yjErf ^g Vg )
yo y
(65)
4«u a a -. r
co y z yo y
z -z z +z
(B.Exp(-0.5( r )2) + B,Exp(-0.5(-£—
\ o i o
z z
where
b,-b^+b0 b,+b0-b.
B = Erf( . - ") + Erf( * - ")
2 b b
o o
(66)
b,-b^-b^ b.-fb^+b,.
and
. = Erf( ) + Erf(
1 b b
o o
b0 =
bi = Hcoz2
b2 = zR°zo2
b3 = zraz*2
The subscript R denotes the receptor location, and the subscript r
denotes the source location (see Figure 83). The distance from the
stagnation streamline associated with the mean wind direction to the
centerline of the plume is denoted as d, the total sigma-y (for
horizontal spread of the mean plume) as O, and the total sigma-z
157
-------
Stagnation
Streamline
Figure 83. Sketch of the flow around an ideal cylinder of elliptical
cross-section. The section shown is taken either at the
elevation of the centerline of the plume (zr), or at
Hc, depending on which is smaller, and it indicates the
relationship between the streamline through the source
(i|/s), the stagnation streamline (^o=0), and the
coordinate system with x-axis aligned with the mean wind
direction.
158
-------
(for the vertical spread) as oz. The amount of plume spread
experienced over the distance to the stagnation point is denoted as
azo and <*yo, and the rate of plume growth beyond the
stagnation point to the receptor is denoted as oz* and Oy*,
where
(67)
The size of the ellipse that is used to estimate the flow below
Hc is taken from the horizontal cross-section of the hill at the
minimum of the following two elevations: either the elevation of the
center-line of the plume, or the elevation of Hc. In this way the
shape of the hill selected is associated with the peak concentration
of plume material found within the layer of fluid below Hc. As a
consequence, the position of the impingement point (or the stagnation
point) is also associated with the peak concentration of plume
material below Hc.
Concentrations at receptors located on the hillside upwind of the
stagnation point (see Figure 83) are estimated as if the receptor sits
on a pole of height equal to the receptor elevation above the base of
the stack. Furthermore, the lateral distance between the plume
centerline and the receptor is set equal to d, so that concentrations
at all of these receptors are controlled by the amount of material on
the stagnation streamline. In this way plume material below Hc and
below plume centerline height follows streamlines around the hill, and
only material which diffuses onto the stagnation streamline impinges
on the hill. The equation for estimating these concentrations is:
z -z zw"*~z
C = r—9 Exp(-0.5(d/o )2){Exp(-0.5(-^—-)*) + Exp(-0.5(~5—-)*)}
2vu
-------
Incident Flow: The wind speed and direction measured at a tower
near a hill may be influenced by the presence of the hill, so that the
observed mean speed and direction must be estimated at infinity to
determine the incident flow. This is calculated from the theory of
two-dimensional potential flow around an ellipse. Denote this speed
and direction by S^ and -o^, where the direction is measured
counter-clockwise from the major axis of the ellipse (Figure 84).
Source Streamline: Once the size and shape of the ellipse and
the incident flow angle relative to the major axis of the ellipse are
known, the source position can be converted to the elliptical
coordinates (vs»vs^ an<* *-he stream function through the source
(«|/s) can be calculated from
«|f = -S (a + b) sinh(y ) sin (v + a ) (69)
S oo S S W
where a is the semi -major axis of the ellipse, and b is the semi -minor
axis (Batchelor, 1967). Note that jT equals y-yo in
Batchelor's notation so that tT = 0 on the surface of the ellipse.
For an ellipse whose major axis lies along the x-axis, the
relationship between (v, v) and (x,y) is given by
(70)
2222 2
x = (a - b ) cosh (y + y ) cos (v)
°
2222 2
y = (a - b ) sinh (y + y ) sin (v)
Rotated Coordinate System: Distance is tracked along the
xg-axis, which is parallel to the stagnation streamline at the
stagnation point. This coordinate system is needed to provide a
convenient Cartesian coordinate system that allows the streamline
through the source to be a single-valued function of x for all
aw. The rotation angle, 6, is given by
tan B = - tan(a ) (71)
b w
Source Streamline Offset (d): The distance between the
streamline through the source (<|»s) and the stagnation streamline
(i|/o = 0) far from the hill is related to the value of «|/s and
the wind speed at infinity, So,. Because the speed of the flow
equals the gradient of the stream function far from the hill, we find
d =
However, because av may be measured closer to the hill, the speed
at the source is substituted to estimate d near the source.
Time~of -Travel: Denote the component of the speed along tys
that lies along the xg-axis as Sg. Then the time that it takes to
travel from the source to the neighborhood of the impingement point, a
distance xog - xsg, is given by the integral of 1/Sg over that
160
-------
Impingement Point
Figure 84. Definition of modeling variables, illustrating in
particular the coordinate system in which the xg-axis
is aligned with the tangent to the stagnation streamline
at the impingement point (the fl-coordinate system). The
coordinates along the xg-axis of the source are denoted
by xsfi, xoB, and xrB, respectively.
161
-------
interval. Furthermore the ratio of the time-of-travel in the presence
of the hill to that in the absence of the hill, a time-of-travel
factor, is given by the average of Sgo/Sg over the interval.
The quantity Sgn/Sg is given by
S0 ((ra-l)sin2u + (r sinh u + cosh y)2)(l + r tan2o )
BOO W
_ _ — — —
B r(r+l)((sin v + cos v tan a )2 + sinh2 y(l + tan2a ) + sinh u cosh y(l+r2tan2a w/r))
w w ™
(73)
where r = a/b. In practice, a time-of-travel factor is obtained by
numerically integrating Equation 73 over the interval to find its
average value.
Sigma-z: Changes to the flow speed along the plume centerline
and the horizontal size of the plume due to kinematic effects do not
alter the concentration of material in the modeled plume. Therefore,
the total Oy appearing in Equation 65 (or 68) is expressed in
terms of the travel time given by (xrg - xsg)/Sga> where xrg
is the position of the receptor along the xg-axis, and xsg is that
of the source. Sigma-z does depend on the changes to the
time-of-travel. If the receptor lies upwind of the impingement
position x0g, the time-of-travel is given by
(XrB - XsB> ,X°B SB» 1
T = - - J - dX - -
B» x . B sB~oB
SB
If the receptor lies beyond x0g, then the time-of-travel is given by
XrB~XoB , ,__.
T - -j— + — J -dx (75)
sB
where Ssg is the component of the flow along the xg-axis at the
source position. In this way all travel-time in the interval between
the source and the impingement position is adjusted by the
time-of-travel factor for the entire interval. This augmented
time-of-travel is used to calculate az by means of Equation 50.
Note that UQ, in Equations 65 and 68 is set equal to So,.
Two points need to be stated regarding the use of this modeling
procedure. First, these adjustments to the flow and dispersion
properties are invoked only when the centerline of the plume is less
than or equal to the elevation of Hc plus oz at xog, plus the
length
-------
travel primarily in the flow above Hc from those that have a
substantial fraction of their material in the flow below Hc.
Second, the time-of-travel is never computed for a mean wind
direction that places the source on the stagnation streamline. As
discussed earlier, the flow is not expected to be truly steady so
plume material will experience a finite residence time on the
stagnation streamline. A measure of this residence time is the
crosswind turbulence intensity, iy. For larger values of iy, the
wind direction is less likely to place the source on the stagnation
streamline for a long enough period of time to bring it very close to
the hill. Therefore, in calculating the time-of-travel, the value of
oty, used is never allowed to be any closer to vs than one half
iy. The choice of the factor one-half is arbitrary at this point in
the CTDM development and should receive additional attention in future
work.
5.1.3 LIFT
Changes have been made to the LIFT portion of CTDM to simplify
the treatment of the horizontal deflection of the plume, to include an
estimate of how the turbulence changes over the hill, and to
accommodate hills with horizontal cross-sections that are elliptical
in shape. Descriptions of these changes are presented below in that
order.
Horizontal Deflection; The description of LIFT given by
Strimaitis et al. (1984) on page 15 uses one lateral distortion factor
to quantify the lateral deflection of a streamline in the flow over a
hill as well as to specify changes in the lateral spacing of
streamlines. This leads to an expression for the horizontal
distribution of plume material in Equation 12 that is not correct.
However, a correct specification of the lateral deflection is given in
a subsequent section of that report in the discussion of the effective
receptor location (section 2.1.3). This situation is rectified in the
development presented below.
Hill-induced changes to the horizontal spacing of streamlines are
represented by the horizontal distortion factor Tj_. This factor
does not give the amount of lateral deflection experienced by a
particular streamline. LIFT requires the average streamline spacing
over the interval s-so as well as the lateral position of the plume
centerline at the distance s downwind of the source. The former is
the average of Tj along the flow over (s-so), denoted as
T^ x. The latter involves the average of T^, at the downwind
distance s, across the flow from the streamline that passes over the
center of the hill to the streamline that passes through the source,
denoted as "fj" y. With this notation, the lateral position of the
shifted plume centerline becomes T& vyr(Figure 85) and the
horizontal spread of the plume becomes T^ x
-------
Receptor
Deflected
Plume Centerline
Source
Figure 85. Definition of modeling variables for flow above Hc.
164
-------
cr 2 = a 2 + o*2/T 2 (76)
ye yo y y
and Ty is now defined (see Section 2.1.2 in the Fourth Milestone
Report) as
Ty = T$/Tay (77)
In a coordinate system centered on the hill with the x-axis aligned
with the incident flow (see Figure 85), yr is the lateral position
of the plume center-line before deflection. The horizontal
distribution function (HDF) then becomes
y
2
HDF = 6 T
f* «ye
where yjj is the lateral position of the receptor. This is the
function that simulates a "filament" plume. The equation for
concentrations due to a. meandering plume becomes
F (6*) s (6 -6 *)
c « _S_JL. Exp _0.5 ( r m r )» (79)
V V
where Fz is the vertical distribution factor, sr is the distance
from the source to the receptor, Gm is the mean wind direction for
the averaging period, 0* is the wind direction that carries the
deflected plume centerline over the receptor, and
o* = a2 (s ) + a2 (s ) (80)
yT ye r ym m v '
Note that 0ytn(sm) denotes the lateral "meander" plume size at a
distance sm, which is the projection of the distance to the receptor
(sr) onto the trajectory of the 1-hour average plume centerline.
This conforms to the usual definition of downwind distance to a
receptor. The lateral size of the "filament" plume contains all of
the deformation induced by the hill, so that if the meander is large
(i.e., if the 1-hour turbulence intensity iy is dominated by wind
direction fluctuations on a time-scale greater than 5 to 10 minutes)
-------
center-line of the def lected__plume and the receptor is given by
Equation 78 as yR(l-TY JO/Tg, x. Because we want the deflected plume
to pass over the receptor, we must shift the wind direction an amount
that "cancels" the deflection given above. Therefore,
r(9r - 6*) =
or
where 6r is the direction from the receptor to the source in the
undistorted flow, y^ is the lateral position of the receptor for a
wind direction equal to 9r, and "T"jT ^ is evaluated for a path
along the direction 6r.
Diffusivity Factor Tq,; In assessing the flow above Hc, we
assume that the hill slope is small enough that time-of-travel effects
can be ignored. Then the relationship between plume spread and
diffusivity is
o|(t) = 2K(t) (82)
and so (see Equations 9 and 10 in Strimaitis et al. 1984)
K'
• r <">
m
where % represents the mean diffusivity over the interval s-so.
Because oz has the form
a t
= W t (84)
the diffusivity is given the approximate form
K = W (85)
•L
so that
4 - C[ 11 tm/v 3 (86)
m L
166
-------
Where tja is the time-of-travel to the mid-point of the interval
s-s0 in the undisturbed flow. Also,
? + (87>
and T^ is the factor for the change in the mean turbulence in the
interval .
The turbulence factor can be estimated from rapid distortion
theory (RDT) in certain circumstances. RDT describes the effects of
straining flows on the turbulence when the straining takes place on a
time-scale shorter than the turn-over time of a characteristic eddy.
If the straining occurs on a time-scale longer than this, RDT does not
apply. In neutral flow, this means that RDT does not apply near the
surface in the inner boundary layer. However, in highly stratified
flow, the eddy time-scale is inversely proportional to N, so that it
grows shorter with increasing stratification. Consequently, there is
a point at which RDT is no longer applicable in the outer layer as
well. When RDT is applicable, Britter et al. (1981) report an
approximate result obtained by Townsend (1976) that is equivalent to
T = 1 + /0.8 (T - 1) . (89)
ow u
With the use of this relationship, Ttfz is expressed solely as a
function of Tu and T^ (See Fourth Milestone Report).
If the bulk of the plume is within the inner layer, and if the
hill has a moderate slope (say H/L > 0.3, where L is the half-length
of the hill at 0.5 H), then
TOW - Tu (90)
That is, the turbulence intensity remains unchanged over the hill.
Britter et al. (1981) estimate the depth of the inner layer as 6:
* in (6/z0) = 2k2 L (91)
where zo is the roughness length and k is von Karman's constant.
For CCB, L ~ 250 m and zo ~ 5 cm so that 5 is approximately
14 m. If we expect that T^ < 0.5 for CCB, plumes released below
30 m may be influenced by this inner layer. However, the model
currently assumes RDT applies to all plumes.
Elliptical Hill Shapes; CTDM has been constructed in a way that
allows the degree of flow deformation over a hill to be specified or
scaled by the deformation at the crest of the hill. For an
167
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axisymmetric hill, the deformation at the crest does not depend upon
the direction of the flow. This is not the case for non-axisyiranetric
hills.
For an elliptical shape, the deformation or magnitude of
terrain-effect depends on the angle of the wind to the major axis of
the ellipse. Because the flow is currently modeled on the basis of
potential flow calculations, the flow field components along the major
and minor axes may be superimposed to obtain the net flow field. For
an incident wind speed S^, along the major axis, the speed over the
crest is defined to be Tuoa S^. For a wind along the minor
axis, the speed over the crest is Tuob S^. Therefore, the speed
at the crest of the hill (denoted as Sc) for an incident flow of
speed So, and direction 9m, is given by
Sc2 = T2uoaSro2 cos2(6m - 6H) + T2uobSm2 sin2(em - 0H) (92)
so that the speed factor for a particular wind direction (Tuo =
SC/SCQ) is
Tuo2 = Tuoa2 +
-------
When the coordinate system is rotated through an angle 6 so that the
x-axis points into the wind,
— --
T(x',y',zr) = 1 + (To(zr) -1) exp[-( aa - ( b
where the primes denote the location of the point in the rotated
system, and
s = sin 6 c = cos (6) (97)
Re-arranging the argument of the exponential function in Equation 96 ,
y>Rx 2
T(x',y',zr) = 1 + (To(zr)-l) e-
, (98)
x'+ y'scR (1/b2 - I/a2)
or
x'R
T(x',y',zr) = 1 + (To(zr)-l) e-
j (99)
y' + x'scR (1/b2 - I/a2)
_ 2 a2b2
where R = • , 2 =—r
x b2c2 + a2s2
2 a2b2
y = b2s2 + a2c2
With moderate stratification, xgep is no longer zero, and the
T-field is shifted and elongated in the direction of the flow to
simulate the appearance of weakly stratified flow.
The elongation and shift now occur in the x' coordinate. The
amount of this change, xsep, is added to the length scale in the x*
direction to elongate the field (i.e., the denominator of the argument
of the exponential function containing x' increases, and this reduces
the rate at which the T-factor approaches unity with increasing
distance from the crest along x'). And xsep is subtracted from the
coordinate position x' to shift the position of the extreme value of
the T-factor in the downwind direction:
y'R
T(x',y',zr) = 1 + (T0(zr> -1> exP t^^rtT12*
(100)
6XP - a (R + x )
x sep
169
-------
or
x1 - x
T(x',y',z) = 1 -f- (T(z) -1) exp {-[
or - -
«r + W
+ x'scR 2 ( -
exp {-
Although Equations 100 and 101 are not equivalent, the former is more
Convenient when T(x',y',zr) must be integrated along x' to obtain
Tx, while the latter is convenient for integrating along y' to
obtain "ry.
5.1.4 LIFT/WRAP Interface
Plumes that approach a hill at elevations less than or slightly
greater than Hc are expected to experience a greater horizontal
deflection and greater travel time to the hill than are plumes at
elevations well above Hc. The WRAP portion of CTDM always computes
the horizontal deflection for plume material below Hc, but computes
an increased time-of-travel only when the plume center-line is below or
near enough to Hc that a significant portion of the plume extends
below Hc by the time the plume reaches the hill at the elevation of
Hc.
The LIFT portion also incorporates an increased time-of-travel
whenever the WRAP portion does. Furthermore, it uses the wind
direction computed at "infinity" whenever the time-of-travel is
incorporated. Beyond this, LIFT also allows material close to Hc to
deflect around the hill if the stagnation streamline at Hc is not
directed toward the hill. This adjustment had also been made in the
previous version of the model.
In the present version of LIFT, the shift to the side of the hill
is introduced into the concentration calculation by changing 6r*
(Equation 79). 6r* is replaced by 8r*' , where
e *• = e * + (e - e *) exp «H - Z_)/*H ) (102)
r r sr cRc
and where 9S is the stagnation wind direction and &HC is the
scale of the transition zone. Equation (102) has a form identical to
that used in the previous version of the model.
5.2 CTDM Simulations of Impingement Cases
The current version of CTDM described in Section 5.1 has been
applied to the "impingement" hours within the CCB and HER data sets.
The intent of this analysis is to see how the changes made to CTDM,
and the WRAP portion in particular, affect model performance.
The "impingement" portion of the CCB data set includes those hours
in which the SF6 plume was released below Hc, or in which it was
170
-------
released no more than 10 m above Hc. In the terminology of the
Fourth Milestone Report, these comprise the impingement (release
height = Hc ± 10 m) and stable (release height < Hc - 10 m)
hours. Refer to the Fourth Milestone Report for a discussion of the
meteorological data for these hours.
For HER, only the CF3Br data set from experiment 8 onwards has
been considered. Within this data set, we have selected hours in
which the mean wind direction is toward the sampler array or in which
several 5-minute average wind directions are toward the array.
5.2.1 CCB
The specification of terrain parameters for CCB is noted in
Section 5.1. Two other user-provided parameters have been chosen to
be consistent with those used in the Fourth Milestone Report. These
include the length scale factor for the LIFT-WRAP transition zone
(6 = 0.1), and the horizontal scale factor for the terrain-factor
fields (a = 0.67). The terrain factors for the speed at the
hill-crest and the deformation of streamlines in the vertical are:
Tuoa = !-16 Thoa = 0.50
Tuob = 1-22 Thob = °-52
The 'a' quantities are for flow along the major axis, whereas the 'b'
quantities are for flow along the minor axis.
These values of the terrain factors at the crest are estimated
from calculations of potential flow over the crest of an ellipsoid.
The ellipsoid is determined by matching its shape to the approximate
shape of CCB at an elevation of one half its total height. Such an
ellipsoid reproduces L along each axis (L = 280 m, 225 m; see 5.1.1).
The aspect ratios for the chosen ellipsoid are 3.6 and 2.9.
COMPLEX/PFM contains a look-up table of results of calculations of
flow over the crest of ellipsoids with aspect ratios of 1, 2, 5, and
10. These results for ellipses described by the cross-wind and
along-wind aspect ratio pairs (2,2), (2,5), (5,2), and (5,5) have been
used to estimate the factors for CCB. Note that the CCB database
primarily contains wind directions aligned approximately with the
minor axis so that Tuotj and T^0^ will be most important in
estimating the flow above Hc. The representative values chosen in
the Fourth Milestone Report (Strimaitis et al. 1984) for modeling CCB
are T^o = 0.5 and Tuo = 1.25.
Modeling results are presented in Table 13. These results were
obtained by averaging the 5 highest observed concentrations (scaled by
the emission rate) and the 5 highest modeled concentrations for each
hour. Results are presented for the latest version (12185) of CTDM as
well as for the version (03184) discussed in the Fourth Milestone
Report. The columns labeled Co and Cp are based on the average of
the 5 greatest concentrations. The columns labeled Co/Cp (Max)
show the ratios of the peak observed concentration to the peak modeled
concentration. These results essentially reflect the ability of the
model to predict the magnitude of the higher concentrations for the
hours in which they are observed, but do not reflect the ability of
the model to predict the exact locations of the peak observed
concentrations.
171
-------
TABLE 13. COMPARISON OF MODELED AND OBSERVED CONCENTRATIONS
FOR STABLE IMPINGEMENT HOURS AT CCB (SF, TRACER)
o
Exp-Hr
201-4
201-5
201-6
203-2
203-3**
203-8
205-8
206-6
206-7
206-8
209-3
209-8
211-2
2H-3**
211-5
211-6
211-7**
214-4
215-1**
215-5
204-1
204-2
204-5
204-6
204-7
204-8
205-7
213-5
213-6
213-7
213-8
214-2
214-3
215-4
215-6
C°*3
(ys/mj)
13.9
19.1
14.9
4.8
2.1
30.4
11.9
86.5
67.2
101.0
4.7
15.2
5.0
2.2
74.1
34.9
6.1
43.2
16.7
27.4
7.4
8.2
2.9
9.5
7.0
15.1
6.6
19.6
13.6
11.0
4.2
19.3
37.2
14.4
7.6
CTDM (03184)
cp* co/cp
(ys/m3)
35.8
54.0
31.3
12.8
1.2
44.6
39.8
99.6
167.1
345.6
35.1
113.7
15.3
17.6
39.2
18.0
5.6
31.2
14.5
15.0
15.7
12.6
3.4
29.6
35.7
20.3
20.5
28.2
39.2
18.6
21.0
38.8
19.4
19.8
18.1
0.41
0.40
0.51
0.42
1.99
1.51
0.30
0.82
0.39
0.35
0.14
0.14
0.36
0.15
2.30
2.37
1.46
1.38
1.07
2.11
0.75
0.63
1.34
0.59
0.21
0.70
0.60
0.97
0.45
0.87
0.29
0.63
2.84
0.80
0.49
CTDM (12185)
cp* co/cp
(ys/m3)
36.2
44.7
15.1
9.5
0.9
46.4
31.2
94.6
115.4
230.9
26.7
69.4
21.5
9.9
41.5
13.5
0.6
25.6
14.1
16.1
16.2
0.2
0.8
16.4
33.0
16.4
11.9
15.4
29.3
16.2
7.9
10.1
12.4
16.7
9.4
0.39
0.49
0.77
0.65
2.31
1.14
0.31
0.82
0.39
0.53
0.15
0.26
0.25
0.30
2.16
2.78
12.70
1.70
1.23
1.82
0.67
24.04
2.60
0.92
0.23
0.34
0.93
1.51
0.52
0.91
0.58
1.10
4.01
1.01
0.91
*Average of the 5 greatest scaled concentrations (ys/m3) for the hour.
**Modeled with the meteorological tower placed 10 km from CCB at a bearing
of 127°.
172
-------
The current CTDM version generally shows a reduction in its
tendency to overestimate the observed concentrations. But note that
there are now a few hours that are underestimated to a larger degree.
Two hours stand out in this regard: 211-7 and 204-2. Apparently, the
modeled deflection of the mean flow around the hill keeps the plume
too far from the hill. The performance of the models for the
remaining hours is as follows:
CTDM Version "Impingement Hours" "Stable Hours"
03184 mg, sg = 0.54, 2.52 nig, sg = 0.49, 1.84
12185 nig, Sg = 0.66, 2.35 mg, sg = 0.84, 2.17
5.2.2 HER
CTDM has been applied to the CF3Br dataset from HBR in much the
same way as it had been applied to CCB. The scale factors 6 and a
remain at 0.1 and 0.67, respectively, and the terrain factors for
vertical deformation and velocity speed-up at the crest of HBR are:
TUOa = 1-0 Thoa = 1-°
Tuob = 2.0 Thob = 0.5
These values are obtained from potential flow solutions for flow
around a cylinder of circular cross-section. These calculations
predict that the streamline that lies along the boundary of the
cylinder (ty = 0) is associated with a speed-up factor (Tu) of 2.
Because the flow is two-dimensional, the product T^TU must be
unity so that T^ = 0.5 We have used these values of Tu and Tb
to approximate those for HBR in this application of CTDM. No attempt
has been made as yet to incorporate the results discussed in Section 3
of this milestone report, but this would have a relatively small
impact on modeling CF3Br tracer-hours at HBR because during these
hours the plume was virtually always at an elevation less than Hc.
Thirty-six hours were selected from the CF3Br database at HBR.
The principal criterion for selecting an hour was that some of the
5-min average winds be directed toward the sampler network. Of this
subset of hours, a few were not modeled because very low CF3Br
concentrations were measured on the ridge.
The 36 hours are listed in Table 14. The highest and
second-highest measured CF3Br concentrations, the hourly averaged
Hc value, the release height above local terrain, and the release
location are listed. For all but seven of the hours, the release
height is below Hc.
Tower A meteorological data in the Modeler's Data Archive were
used for the modeling. However, both propeller and sonic measurements
were utilized. The values of ow measured by the sonic anemometer
were used in combination with the wind speeds and directions measured
by the props. For releases at locations 203 and 215, model input
parameters were interpolated from the Tower A data to the height of
the release above sea level rather than height above the ground.
173
-------
TABLE 14. MODELED HOURS FROM THE HER MDA
Exp-Hr
8-1
8-2
8-5
8-6
8-7
8-8
8-9
10-3
10-5
10-6
10-7
10-8
10-9
10-11
11-1
11-4
11-7
11-8
11-9
11-10
12-2
12-3
12-9
12-10
14-5
14-6
14-7
14-8
14-10
14-12
15-4
15-5
15-7
15-8
15-9
15-11
Time
(MDT)
2300-0000
0000-0100
0300-0400
0400-0500
0500-0600
0600-0700
0700-0800
0200-0300
0400-0500
0500-0600
0600-0700
0700-0800
0800-0900
1000-1100
2300-0000
0200-0300
0500-0600
0600-0700
0700-0800
0800-0900
0200-0300
0300-0400
0900-1000
1000-1100
0200-0300
0300-0400
0400-0500
0500-0600
0700-0800
0900-1000
0300-0400
0400-0500
0600-0700
0700-0800
0800-0900
1000-1100
Measured CF3Br
Concentration (ys/m-*)
High 2nd High
57
34
329
61
72
44
74
19
47
36
42
22
40
11
52
166
9
52
21
9
15
10
23
17
38
117
109
63
6
31
17
58
22
26
36
14
40
33
124
48
69
40
41
13
42
34
39
20
27
9
48
166
7
46
20
8
15
9
18
16
33
105
95
61
5
29
15
48
20
24
32
14
(m)
84
82
65
55
43
45
31
44
63
40
43
47
42
1
77
62
39
28
36
26
50
37
1
1
43
36
39
34
43
25
50
47
39
41
47
1
zr
(m)
20
10
30
25
25
30
15
30
30
30
30
30
30
30
20
20
25
25
10
10
40
50
40
40
20
20
20
20
35
35
40
40
40
40
40
40
Release
Location*
215
215
215
215
215
215
215
A
A
A
A
A
A
A
203
203
A
A
A
A
A
A
A
A
203
203
203
203
A
A
A
A
A
A
A
A
*See Figure 49 in Third Milestone Report.
174
-------
Only data from Experiments 8 through 15 were considered for
selection in this model evaluation because no <*w data from the
sonic anemometers are available from Experiment 7 and because noise in
the data from Tower A in the earlier experiments swamped the
turbulence information. Efforts to reduce the noise were at least
partially successful by Experiment 7 but were not completed until
Experiment 10.
Table 15 shows the results of running CTDM (12185) at HBR. The
data are partitioned into two sets: data for plumes released from
Tower A; and plumes released from site 203, located near the
intersection of the road to Tower A and "Hogback Highway," the road
which parallels HBR at the foot of the ridge, or site 215 which is
located roughly one third of the way from the base of HBR down the
road toward Tower A. The reasons for making this partition are
(1) the meteorological data appropriate to the plume origin are better
known for the releases from Tower A, and (2) the Tower A plumes travel
roughly twice as far to reach the hillside.
The results presented in Table 15 indicate that the model
performs better for the Tower A group than it does for the other
group. The geometric mean and standard deviation (nu and sg) for
the Tower A group are 0.91 and 2.01, respectively, whereas those for
the other group are 1.97 and 2.63, respectively. Measuring the
meteorological data right at the source position may be partially
responsible for this result, but other factors can also be important.
For example, the meteorology may not be similar: one of the hours in
the Tower A group has a mean wind direction away from the hill, and a
simulation of this hour required modeling each 5-minute period. Three
hours in the other group had to be simulated in this way.
Excluding these four hours, the modeling results for the Tower A
group remain better than those for the releases nearer the hill. The
mg and sg values for the remaining 22 hours in this group are 0.83
and 1.71, respectively. Those for the 10 hours of releases closer to
the hill are 1.53 and 2.22, respectively.
The performance of CTDM (12185) can be compared with the
performance of the semi-empirical model (see Table 17) discussed in
Section 5.3. When the four hours are removed, values of nu and sg
from the semi-empirical model for the Tower A group are 0.93 and 1.99,
respectively; and those for the other group are 0.77 and 1.78.
Therefore CTDM exhibits the least scatter (sg = 1.71) for the
Tower A group, whereas the semi-emipirical model exhibits the least
scatter for the other group (Sg = 1.78). These results indicate
that although the semi-empirical algorithms do not appear to offer
improved modeling performance for the Tower A group, a substantial
improvement is seen for those hours in which the plume is released
closer to HBR.
5.3 Modeling Freon Releases at HBR
5.3.1 Introduction
In modeling the dispersion of releases around HBR we have adopted
two approaches, CTDM (discussed earlier in Section 5.2) and a
semi-empirical model that is discussed later in this section. The
175
-------
TABLE 15. COMPARISON OF MODELED (CTDM) AND OBSERVED CONCENTRATIONS
FOR SUBSET OF THE HBR CF Br DATA BASE
Exp-Hr
10-3
10-5**
10-6
10-7
10-8
(10-9)
(10-11)
11-7
11-8
11-9
11-10
12-2
12-3
(12-9)
(12-10)
14-10
14-12
15-4
15-5
15-7
15-8
15-9
15-11
Tower A Releases
C0* Cp* C0/Cp
(ys/m-3) (ys/mj)
13.1
39.5
33.0
38.3
18.8
26.9
8.3
6.3
43.5
17.5
7.8
14.7
8.3
18.3
14.2
5.6
23.6
14.6
47.9
18.5
24.9
30.0
13.8
20
5
73
20
30
48
12
16
37
10
12
25
14
12
11
13
16
40
39
26
33
16
10
.1
.3
.5
.0
.0
.9
.4
.0
.7
.3
.0
.9
.0
.0
.0
.3
.4
.3
.3
.1
.0
.0
.1
0.
8.
0.
2.
0.
0.
0.
0.
1.
1.
0.
0.
0.
1.
1.
0.
1.
0.
1.
0.
0.
1.
1.
(Max)
63
47
48
08
70
82
70
54
30
75
66
44
66
50
33
39
87
34
43
80
83
68
10
Exp-Hr
8-1
8-2**
8-5**
8-6
8-7
8-8
8-9
11-1
11-4**
14-5
14-6
14-7
14-8
Releases
C0*
(ys/mj)
26.2
30.0
160.5
48.8
63.7
40.3
45.3
39.8
157.2
28.1
90.2
94.0
56.0
Closer to Ridge
Cp* Co/Cp
(ys/m3)
62
23
27
42
22
18
53
54
12
18
24
16
45
.7
.5
.1
.3
.8
.6
.9
.6
.3
.4
.0
.7
.4
0
1
10
1
2
1
1
0
12
1
4
6
1
(Max)
.86
.04
.99
.38
.85
.88
.18
.94
.65
.63
.50
.22
.24
* Average of the 5 greatest scaled concentrations (ys/m3) for the hour.
** Concentrations estimated from simulating all 5-minute periods during the hour.
() Turbulence data from the sonic anemometers are incomplete; data from propeller
anemometers are substituted.
176
-------
semi-empirical approach extends the work discussed in Section 4.3 of
Fourth Milestone Report. Although the applicability of the
semi-empirical model is limited to the observations and complex
terrain data used to develop it, the combined use of CTDH and the
semi-empirical model can help in understanding dispersion at a ridge
site. In particular, the variety of output from CTDM can be used to
develop parameterizations required to extend the range of
applicability of the semi-empirical model. In short, the model for
HBR described in this section should be viewed as a complement of
CTDM. It will be improved as we gain more understanding of the
behavior of the observations through the more theoretically based
model and application of the semi-empirical model to the CCB and Tracy
sites.
The basic model is not very different from that described by
Strimaitis et al. (1984). The significant modification is related to
the use of a probability density function to describe the wind
direction and speed data. This change was motivated by the observed
variability of the winds measured at Tower A during the majority of
the study hours. The next section describes the current version of
the semi-empirical model.
5.3.2 The Modified HBR Model
The initial semi-empirical HBR model (Strimaitis et al. 1984) can
be represented by the equation,
C(x,y,o) =
2Q
mi (a .+a )a
r zB. zu y
T 2 z 2 y 2
exP I- p r ] exp [- __R_]
2tf * 20 2
(103)
In Eq. 103, C(x,y,o) is the ground-level concentration, Q is the
emission rate, ur is the hourly averaged mean wind speed at the
source height, ay is the crosswind spread, az^ and ozu
are the parameters that describe the vertical diffusion of the lower
and upper portions of the plume, zr is the release height, and the
plume height factor Tp depends upon zr, Hc, and the
source-receptor geometry. Its formulation was described in
Subsection 4.3.3 in the Fourth Milestone Report.
The first modification we made was to replace the concept of an
hourly averaged mean wind by a probability or frequency distribution
derived from the 5-minute averaged wind speeds, directions, and
standard deviations. Then, the crosswind term in Eq. (103) becomes
u
y r
exp -
P(0)
U6r
(104)
In Eq. 104, P(6)d6 is the probability that the wind blows in the
angle d6 surrounding the direction 9, u$ is the wind speed
associated with 9, and r is the source-receptor distance. Notice
that this formulation avoids defining a mean wind direction.
177
-------
Furthermore, it accounts for the observed distribution of wind
directions rather than assuming a Gaussian distribution. The model
uses 5-minute average wind directions to construct a probability
distribution in 1-degree sectors. In addition, the average wind speed
for each sector is calculated and used by the model rather than using
the hour-averaged wind speed. The 5-minute average
-------
TABLE 16. SUMMARY STATISTICS FOR HER MODEL
Experiments 8-15 36 hours
Top 1 Top 2
Model mg Sg r2 nu sg r2
Flat Terrain 2.45 3.60 0.130 2.39 3.64 0.126
Cut-Off Hill 0.46 2.55 0.446 0.47 2.44 0.449
HER 1.05 2.14 0.347 1.01 2.11 0.350
Top 5
mg sg r2
2.31 3.73 0.111
0.48 2.41 0.409
0.95 2.12 0.331
Experiments 10-15 29 hours
Model
Flat Terrain
Cut-Off Hill
HER
"S
2.37
0.50
1.02
Top 1
S8
3.57
2.51
1.97
0
0
0
r2
.167
.456
.413
m
2
0
1
6
.34
.51
.00
Top 2
ss
3.72
2.43
2.01
r2
0.150
0.443
0.388
•s
2.30
0.52
0.96
Top 5
S6
3.88
2.38
2.05
r2
0.130
0.412
0.362
179
-------
deviations are approximately 2.0. Although the same cases were not
considered in the Fourth Milestone Report, it is clear from an
examination of Table 16 and Table 14 (Fourth Milestone Report) that
the present model represents a significant improvement over the
previous formulation. Clearly, this improvement is directly related
to the use of the distribution of 5-minute winds, instead of the
Gaussian distribution, to calculate the horizontal concentration
distribution. The mean of the 5 greatest observed and modeled
concentrations for each of the hours is listed in Table 17, along with
the ratio of the peak observed to the peak modeled concentration for
each hour.
Table 16 also shows the performance of the empirical Tp
formulation relative to a flat-terrain (Tp=l) equation and that
corresponding to a cut-off hill, i.e.,
Tp = (zr-Hc)/zr; zr > Hc
(108)
=0 ; zr < Hc
As expected, the flat terrain model underpredicts concentrations while
the cut-off hill model overpredicts concentrations. However, note
that the cut-off hill model results produce r^-values which are
similar to those from the semi-empirical model results. This suggests
that the simple device of bringing the plume closer to the hill's
surface goes a long way towards explaining the variance of the
observed concentrations on the ridge.
Figures 86 and 87 are examples of the behavior of the residuals
from the semi-empirical model (the 29-hour subset) as a function of
model inputs. In general, the residuals are uncorrelated with the
model inputs, which suggests that for the data set and inputs
considered, we can do little to improve the performance of this
particular model formulation.
Our analysis of the CF3Br concentration measurements made at
HBR suggests that hill "effects" on ground-level concentrations can be
accounted through a factor which effectively lowers the plume towards
the surface of the hill. Of course, model performance is also
affected by the other parameterizations in the model, as evidenced by
the improvement of the performance of the HBR model when the Gaussian
distribution is replaced by a wind distribution which accounts for the
large meandering typical of the wind during stable conditions. The
point needs to be reiterated that during stable conditions there is
considerable meandering of the wind, and this has to be accounted for
in calculating
-------
TABLE 17. COMPARISON OF MODELED (EMPIRICAL) AND OBSERVED CONCENTRATIONS
FOR 36-HOUR SUBSET OF THE HBR CF Br DATA BASE
Exp-Hr
10-3
10-5
10-6
10-7
10-8
10-9
10-11
11-7
11-8
11-9
11-10
12-2
12-3
12-9
12-10
14-10
14-12
15-4
15-5
15-7
15-8
15-9
15-11
Tower A Releases
GO* "Cp* Co/Op (Max)
(ys/rn3) (ys/m3)
13.1
39.5
33.0
38.3
18.8
26.9
8.3
6.3
43.5
17.5
7.8
14.7
8.3
18.3
14.2
5.6
23.6
14.6
47.9
18.5
24.9
30.0
13.8
40.9
10.1
42.1
22.8
27.9
45.1
14.0
20.4
46.2
5.5
18.7
8.1
11.4
10.6
10.7
17.0
12.1
21.9
27.2
29.5
23.0
11.9
10.0
.37
4.54
.82
1.76
.71
.84
.66
.35
1.04
3.36
.45
1.74
.87
1.82
1.38
.30
2.15
.71
1.60
.72
1.20
2.06
1.19
Exp-Hr
8-1
8-2
8-5
8-6
8-7
8-8
8-9
11-1
11-4
14-5
14-6
14-7
14-8
Releases
C0*
(ys/m3)
26.2
30.0
160.5
48.8
63.7
40.3
45.3
39.8
157.2
28.1
90.2
94.0
56.0
Closer to Ridge
Cj> CO/CP (Max)
(ys/m3)
66.2
126.2
38.5
76.7
38.7
34.1
45.5
128.7
67.1
59.7
71.3
69.8
95.7
.76
.20
8.22
.78
1.61
1.21
1.55
.40
2.09
.61
1.51
1.30
.56
* Average of the 5 greatest scaled concentrations (ys/m3) for the hour.
181
-------
o
r»
o
01
o
o
o
n
o
ft
o
CM
00 .C
C -P
•H
w C ^
QjJ fl) (fl
« at u
0) O
Q-i fO .C!
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^j jj ^
I -P -H
•O C -I
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182
-------
-------
The performance of the model is summarized through the
scatterplots of Figure 88. These good results have to be tempered by
the fact that the model is only applicable to the limited data set
considered in this analysis. This is the limitation of any
semi-empirical model. Before the model can provide general guidance
on dispersion in complex terrain, it has to be applied to the CCB and
Tracy data bases. Furthermore, we have to provide further
justification, even if it is only partial, of the formulation for
Tp. This has to come from the theoretical models being developed in
this project.
5.3.5 Selected Case-Study Results
To provide more information about the modeling than can be
derived from the summary of the results, selected hours are described
in more detail in this section. The hours are:
• Experiment 11, 0200-0300 MDT
• Experiment 11, 0600-0700 MDT
• Experiment 14, 0500-0600 MDT
These hours were selected because they represent a variety of
dispersion conditions and include examples of model underprediction
and over-prediction.
Experiment 11. Experiment-Hour 4 (0200-0300 MDT)
The tracer gas was released 100 m from the base of the ridge at a
release height 20 m above the ground. The winds were light, 1.7 m/s
or less, for the entire hour. Four of the 5-minute average wind
directions were toward the hill, though only two were within ±60° of
the stagnation angle to the ridge. The average value of Hc for this
hour was 62 m. The av and
-------
1.00
1.00
80. 100. 120. 140. 160. 180.
p (,us/m3)
200.
100.
60.
40.
•C 20.
N
O 6.0
4.0
2.0
1 00
1.00 2.0 4.0 6.0 10.0 20. 40 60. 100.
Cp (/*/m3)
180.
160
140.
120
100
80.
60.
40.
20.
0.
200.
20. 40. 60. 80. 100. 120. 140 160. 180.
Cp U«/m3)
1.00
1.00
60. 80. 100. 120. 140. 160. 180.
C
Figure 88. Scatter plot of scaled (C/Q ys/m3) observed and
modeled concentrations (peak, top 2, top 5) for 29 hours
of HBR data.
185
-------
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187
-------
Experiment 11. Experiment-Hour 8 (0600-0700 MPT)
This release was made from Tower A at a height of 25 m. The
5-minute average wind speeds varied from 0.8 to 1.8 m/s; all 12 of the
5-minute average directions were toward the hill. The hourly-averaged
value of Hc was 28 m, which is approximately equal to the release
height. The hourly-averaged values of
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192
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Because the non-cosine response corrections have not yet been
applied to the propeller anemometer data, the hourly vector-averaged
cup and vane anemometer data from the 150-m level of Tower A are used
to represent the wind speed and direction at the height of the plume.
In addition to CTDM, three conventional complex terrain models (RTDM,
Complex I and II) were run. Wind data collected at 150 m were used,
rather than the 10-m wind data extrapolated to stack top with a power
law relationship.
The stability class was calculated from net radiation and wind
speed data by means of the method of Williamson and Krenmayer (1980).
The hourly scalar-averaged wind speeds measured by the cups at the
10-m level on Tower A and the hourly averaged net radiation data
measured at the 1-m level on Tower A were used to compute the
stability.
The vertical turbulence (ow) used to represent dispersion
conditions at plume height was obtained from the hourly averaged 150-m
vertical intensity of turbulence measured by the props and the hourly
vector averaged propeller wind speed measured at the 150-m level on
Tower A. The prop response correction suggested by Horst (1973) has
been applied to the hourly averaged estimate of ow.
The local Brunt-Vaisala frequency (N) was estimated at the
release height by using the hourly averaged temperature difference
between the 125-m and 150-m level on Tower A. The critical
dividing-streamline height (Hc) was calculated by the method
discussed in Subsection 4.3.1.
The observed concentration distribution, the wind data estimated
at plume height, and the travel time to the location of the observed
maximum concentration were used to determine whether the meteorology
representative of the experiment-hour should be shifted in time. A
one-half to one-hour shift of the 5-minute meteorology was applied to
11 of the modeling hours based on an examination of the concentration
pattern, wind direction, and travel time. An appropriate one-hour
average was then calculated from the shifted 5-minute data.
Table 18 lists for each experiment-hour all of the inputs to the
models that were tested with the FSPS data in this report. The
experiment number, date, and hour ending for each of the 14
experiment-hours are followed by the effective plume elevation above
the base of the stack (zr + Ah), the critical dividing-streamline
height (Hc), the 150-m hourly average wind speed and direction, the
Brunt-Vaisala frequency (N), sigma-w (
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194
-------
Complex II were run using stability class F as well. Predicted
concentration plots for both stability classes are presented in the
next subsection.
5.4.2 Application of Conventional Complex Terrain Models
Valley
The maximum 1-hour tracer concentrations (scaled by the emission
rate) from the EPA Valley screening model are presented in Table 19
for each of the 14 case hours. The observed maximum concentrations
and the ratios of the hourly calculated to observed concentrations
paired in time but unpaired in space are also included. Two sets of
predicted concentrations are presented for each experiment-hour. The
first set includes Valley calculations without buoyancy enhancement
and the second set is based on a buoyancy enhanced estimate of
cz. Equation 52 was used to calculate the ambient 0za. The
constants used in this equation are applicable for P-G stability
Class F over a distance greater than 1,000 m, which includes all of
the downwind distances for the 14 case hours. For the buoyancy
enhanced Valley calculations,
«zb - 57s (108)
where Ah is the lidar-derived hourly averaged plume rise. The
resultant value of az2 is then expressed as the sum of the squares of
the ambient and buoyant oz components oz2 = oza2 4- <*zt>2.
The non-buoyancy enhanced Valley concentrations appreciably
overestimate the maximum observed normalized concentrations for all
case-hours. Valley overestimates by as much as a factor of nine for
two case-hours. The closest the non-buoyant Valley prediction comes
to the maximum observed concentration is for Experiment 13-9 where the
(C0/Cp) Max is 0.42.
Similarly, the buoyancy enhanced Valley concentrations also
overestimate the maximum observed normalized concentrations for all
case-hours. However, three of the case-hour predictions are now
within a factor of two of the maximum observed. For Experiment 13-9,
(C0/Cp) Max is now 0.74. In any event, both sets of Valley
calculations substantially overestimate the observed SF$
concentrations.
COMPLEX I and COMPLEX II
COMPLEX I is a univariate Gaussian plume model with 22.5° sector
averaging in the horizontal, while COMPLEX II computes off-plume-
centerline concentrations according to a bivariate Gaussian
distribution function. Terrain treatment in the COMPLEX models varies
with stability class. A 0.5 terrain adjustment is used for neutral
and unstable classes, while no terrain adjustments (with a 10-m "miss"
distance) are used for stable classes.
195
-------
TABLE 19. SUMMARY x/Q STATISTICS FOR VALLEY CALCULATIONS
Experiment
Number
2
2
2
2
3
5
6
6
7
11
13
13
13
14
Hour
Ending
4
5
6
7
6
4
5
7
7
6
7
8
9
3
Max C
o
(vs/m3)
3.4
8.0
3.2
5.1
3.2
5.1
3.7
2.7
5.5
7.5
4.1
6.7
8.3
2.4
Max C
P
(ys/m8)
24.7
26.4
25.5
24.3
22.0
23.5
28.3
25.1
24.2
21.4
20.1
20.3
19.8
22.4
(C /C )
o p
Max
0.14
0.30
0.13
0.21
0.15
0.22
0.13
0.11
0.23
0.35
0.20
0.33
0.42
0.11
Max C *
P
(ws/m3)
18.8
22.9
20.4
17.7
14.2
16.4
27.4
19.6
17.7
12.8
11.5
11.7
11.2
14.5
(Co/CP}
Max
0.18
0.35
0.16
0.29
0.23
0.31
0.14
0.14
0.31
0.59
0.36
0.57
0.74
0.17
*Buoyancy Enhanced.
196
-------
In order to use the buoyancy induced dispersion option, the model
must first calculate the plume rise. The hourly averaged lidar-
ob served plume rise (Ah) and a constant stack temperature (Ts) are
used to estimate the exit velocity as
AT F
V = . -,!! ,. . (109)
ex gds2(Tg-Ta)
where g is the acceleration due to gravity, ds is the stack
diameter, and Ta is the ambient temperature. Given measured values
of plume rise (Ah) and meteorological parameters, the buoyancy flux
for stable conditions can be estimated from
F = ()3 (110)
where u is the 150-m wind speed and 36/3Z = .035 °K/m for
stability class F. For unstable conditions, the buoyancy flux is
F = ( )4/3 F < 55 mVs3 , (111)
21 . 42.)
F = ()4/3 F > 55 mVs3 (112)
Thus, the exit velocity input to the model is specified such that the
modeled plume rise will match the lidar-observed plume rise. This
plume rise is then used to calculate the buoyancy induced dispersion
as Ah/3.5.
The performance statistics for the average of the top two
concentrations paired in time but unpaired in space for the COMPLEX
models are presented in Tables 20 and 21. Because there are a limited
number of samplers in the area of the maximum observed concentration,
the top two statistics are used rather than the top five statistics.
The average of the highest two observed and predicted normalized
concentrations, their residuals, the maximum predicted concentrations,
and the ratios of maximum observed to the maximum predicted are
listed. Experiment 13-9 was modeled using stability classes C and F.
The average top-two COMPLEX I concentrations are in fair
agreement with the average top-two observed concentrations. The
average top-two residuals indicate that COMPLEX I overpredicts for 11
of the case-hours. The ratio of the maximum observed to predicted
concentrations indicate that 10 of the case-hours lie within a factor
of two.
The COMPLEX I predicted concentration distribution (as normalized
X/Q in units of vs/m^) for Experiment 13-9 using stability class
C is presented in Figure 95. The observed concentration distribution
(as normalized x/Q) is presented in Figure 96. The 5-minute vector
averaged wind distribution estimated at the height of the plume is
197
-------
TABLE 20. SUMMARY x/Q STATISTICS FOR COMPLEX I CALCULATIONS
Experiment
Number
2
2
2
2
3
5
6
6
7
11
13
13
13
13
14
Hour
Ending
4
5
6
7
6
4
5
7
7
6
7
8
9
9*
3
C
o
(vs/m3)
3.4
7.3
3.0
4.8
2.5
4.7
3.0
2.6
5.0
5.9
3.5
4.5
8.2
8.2
2.0
C
P
(ys/m3)
6.5
5.8
8.0
10.5
5.4
14.5
2.9
4.9
6.6
9.3
4.9
8.9
1.5
6.0
4.1
C -C
o p
(vis/m3)
-3.1
1.5
-5.0
-5.7
-2.9
-9.8
0.1
-2.3
-1.6
-3.4
-1.4
-4.4
6.7
2.2
-2.1
MaxCp
(ys/m3)
6.7
6.0
8.2
10.8
5.9
14.9
3.1
5.1
6.8
9.3
5.5
9.3
1.5
6.2
4.9
-------
TABLE 21. SUMMARY x/Q STATISTICS FOR COMPLEX II CALCULATIONS
Experiment
Number
2
2
2
2
3
5
6
6
7
11
13
13
13
13
14
Hour
Ending
4
5
6
7
6
4
5
7
7
6
7
8
9
9*
3
C
o
(ys/m3)
3.4
7.3
3.0
4.8
2.5
4.7
3.0
2.6
5.0
5.9
3.5
4.5
8.2
8.2
2.0
CP
(ys/m3)
14.1
8.6
21.9
15.9
4.5
40.5
5.4
14.1
7.4
39.0
10.5
34.8
2.1
23.4
13.3
C -C
o p
(ys/m3)
-10.7
-1.3
-18.9
-11.1
-2.0
-35.8
-2.4
-11.5
-2.4
-33.1
-7.0
-30.3
6.1
-15.2
-11.3
MaxCp
(ys/m3)
17.4
14.8
27.6
22.9
4.7
42.9
6.9
15.0
8.1
44.8
13.0
46.1
2.5
28.8
14.1
(Co/Cp)
Max
0.20
0.54
0.12
0.22
0.68
0.12
0.54
0.18
0.68
0.17
0.32
0.15
3.35
0.29
0.17
Refer to Table 19 for Max C values.
o
*Modeled with Stability Class F.
199
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201
-------
drawn at the stack position. The hourly vector averaged wind
direction is depicted by the long dotted line. Using stability class
C, COMPLEX I grossly underpredicts the maximum observed
concentrations. The predicted COMPLEX I concentration distribution
using stability class F is presented in Figure 97. The predicted
concentrations are now more than four times larger than those
COMPLEX I calculations using stability class C. However, the peak
predicted concentrations are still less than the maximum observed
concentrations. Also, the predicted concentration distribution shows
a horizontal spread that appears too small.
The COMPLEX II results indicate an overprediction of all
case-hours except for Experiment 13-9 when stability class C was
used. The residual statistics indicate that four of the case-hours
have predicted concentrations within 2 ys/m-*; however, nine of the
case-hours show overpredictions of more than 10 ys/m^. The ratios
of the maximum observed to predicted concentrations show that only
four of the case-hours lie within a factor of two.
The COMPLEX II predicted concentration distribution (as
normalized x/Q in units of ys/m-*) for Experiment 13-9 using
stability class C is presented in Figure 98. The predicted
concentrations are much lower than the observed concentrations. When
stability class F is used, as shown in Figure 99, COMPLEX II grossly
overpredicts the maximum observed concentrations. Also, the spatial
distribution pattern shown in the COMPLEX II run is much narrower in
the crosswind direction (than the observed scatter).
RTDM
The Rough Terrain Diffusion Model (RTDM) is a sequential Gaussian
plume model designed to estimate ground-level concentrations in rough
(or flat) terrain in the vicinity of one or more collocated point
sources (ERT, 1982). It is specifically designed for applications
involving nonreactive gases and is best suited for evaluation of
buoyant plume behavior within about 15 km of the source.
Rather than assuming full reflection (Valley-like computations)
for cases of plume impingement, RTDM uses a partial plume reflection
algorithm that takes into account the slope of the terrain. Off-plume
centerline concentrations are computed according to a bivariate
Gaussian distribution.
In stable conditions, the dividing-streamline height (Hc) is
computed from the wind speed, the terrain height, and the strength of
the ground-based inversion. Plumes below Hc are allowed to impinge
on the terrain. During neutral or unstable conditions, or above Hc
in stable conditions, a "half-height" correction simulates the effect
of terrain-induced plume modifications on ground-level concentrations.
As used in the COMPLEX I and COMPLEX II analysis, the hourly
averaged lidar-derived plume rise (Ah) and a constant stack
temperature are used to estimate the exit velocity. Thus, the exit
202
-------
to (j
C 0)
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205
-------
velocity input to RTDM is such that the modeled plume rise will match
the lidar-derived plume rise. This plume rise is then used to
calculate the buoyancy-induced dispersion as Ah//T0~.
RTDM was first run using the hourly values of the vertical and
horizontal components of the turbulence intensity estimated at plume
height to calculate 0y and az. The top-two normalized
concentration statistics paired in time but unpaired in space for this
version of RTDM are presented in Table 22. The average top-two
concentrations underpredict the observations for all case-hours. The
ratio of the maximum observed to predicted concentrations indicate
that none of the case-hours lie within a factor of two.
The RTDM predicted concentration distribution (as normalized
X/Q in units of ys/m^) for Experiment 13-9 using the measured
turbulence data and stability class C is presented in Figure 100. The
observed concentration distribution was presented in Figure 96. For
unstable conditions, RTDM sets Hc to zero and az is only a
function of the vertical intensity of turbulence and downwind distance
expressed as
o = ix . (113)
RTDM grossly underpredicts the maximum observed concentrations. The
results do not change much when stability class F is used, as shown in
Figure 101. As discussed in Subsection 3.4.3, the values of oz
are overpredicted when the measured values of turbulence are used in
conjunction with the RTDM expression for stable az.
RTDM was then tested using the Briggs rural (ASME, 1979)
dispersion coefficients and these results are presented in Table 23.
The top-two average predicted concentrations are now much larger than
those predicted from RTDM's algorithm that use the measured turbulence
data. The ratios of the maximum observed to predicted concentrations
indicate that six of the case-hours now lie within a factor of two.
The RTDM predicted concentration distribution (as normalized
X/Q in units of tis/m-*) for Experiment 13-9 using the ASME
dispersion parameters and stability class C is presented in
Figure 102. RTDM still underpredicts the maximum observed
concentrations. The predicted concentrations increase substantially
when stability class F is used, as presented in Figure 103. The
(C0/Cp) Max is now 0.92; however, the maximum concentration occurs
much further downwind than the maximum observed concentration. Also,
compared to the observed concentrations, the spatial distribution
pattern is extremely narrow in the crosswind direction.
5.4.3 Application of CTDM
CTDM (12185) has been applied to the initial modeling dataset.
All but one of the 14 hours has been included; only "Beacon Hill"
receptors have been explicitly included in the modeling, so the single
hour of the dataset in which "Target Mountain" was the primary impact
zone was not modeled.
206
-------
TABLE 22. SUMMARY x/Q STATISTICS FOR RTDM CALCULATIONS
USING ON-SITE TURBULENCE DATA*
Experiment
Number
2
2
2
2
3
5
6
6
7
11
13
13
13
13
14
Hour
Ending
4
5
6
7
6
4
5
7
7
6
7
8
9
9*
3
C
o
(ys/m3)
3.4
7.3
3.0
4.8
2.5
4.7
3.0
2.6
5.0
5.9
3.5
4.5
8.2
8.2
2.0
C
P
(ps/ro3)
0.9
1.0
1.0
0.8
0.8
0.8
0.9
0.5
1.5
0.6
1.1
0.4
0.6
0.7
0.7
C -C
o p
(ys/m3)
2.5
6.3
2.0
4.0
1.7
3.9
2.1
2.1
3.5
5.3
2.4
4.1
7.6
7.5
1.3
Max C
P
(vs/m3)
1.0
1.4
1.1
0.8
1.1
1.1
0.9
0.5
1.8
0.7
1.1
0.4
0.6
0.7
0.8
(W
Max
3.4
5.8
2.9
6.1
2.9
4.8
4.1
5.3
3.1
11.3
3.7
16.7
12.9
11.6
2.9
Refer to Table 19 for Max C values.
o
*Modeled with stability class F.
207
-------
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o
w
•o
» oo
4J
•O -H •>
O ft
•H Cd *>
T3 -U C
4) CO 0)
^j PJ
CL •• »H
* u
fl) Q Q)
60 H p.
cd « X
u w
0) B ^-^
> o
cd u a)
u
3 —
OP1
o
g
0) m U
C 3. 3
6 ~ -P
o
o
2
3.
208
-------
•o •
0) -^
(J H
3 Q
co CL,
CO
CO
jj
§
u
§
o
60 O
C I
•H O
W O
3 CO
o
to
M <•
M 00
ed v.
r-l \D
o CM
^
>» oo
en
a>
4J -H iH
o .0
•r-l 0) *>
T3 -U C
0)000)
u e
0) Q 0)
60 H PI
CO IK! X
U tO
0) E >-'
> o
cd u o)
iu o
u c
3^0)
on -i
X B 3
I ^ .0
0) 01 U
C 3- 3
O ^^ -P
-------
TABLE 23. SUMMARY x/Q STATISTICS FOR RTDM CALCULATIONS USING
BRIGGS-RURAL/ASME - 1979 DISPERSION COEFFICIENTS"*"
Experiment
Number
2
2
2
2
3
5
6
6
7
11
13
13
13
13
14
Hour
Ending
4
5
6
7
6
4
5
7
7
6
7
8
9
9*
3
C
o
(ys/m3)
3.4
7.3
3.0
4.8
2.5
4.7
3.0
2.6
5.0
5.9
3.5
4.5
8.2
8.2
2.0
°P
(ys/m3)
3.5
3.6
12.5
9.5
4.1
16.4
1.1
4.4
5.4
19.5
7.7
17.3
1.2
8.4
6.4
C -C
o p
(ys/m3)
-0.1
3.7
-9.5
-4.7
-1.6
-11.7
1.9
-1.8
-0.4
-13.6
-4.2
-12.8
7.0
-0.2
-4.4
Max C
P
(ys/m3)
5.1
5.6
14.2
12.9
4.5
22.0
1.1
4.9
6.7
25.7
9.6
23.0
1.4
9.0
7.1
(Co/Cp)
Max
0.68
1.44
0.23
0.40
0.72
0.23
3.48
0.55
0.82
0.29
0.43
0.29
5.84
0.92
0.34
Refer to Table 19 for Max C values.
o
*Modeled with stability class F.
210
-------
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01 oo 0)
O *" rS
•HUM
4J IO •+*
co
U 60 0)
.
-U
•O -H
<1) rH
-p >1-l
« ^
•H CO
•O -U
0) CO
01 a";
0) Q I
60 H I
cd X i
u
0 e
S2!
0)
o
o
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*? R
t-i O
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Pi
w o
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^3 c^
o
o
o
CO
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00
3 o ^ CM
OfO v.
^3 e ^ oo
I ^ (0
a) w it -
C 3. 3 CO
O ^-< U H
CM
O
2
•H
fx.
211
-------
•H
(0 U
CO 00 0)
jj-SSJ
-U PQ v^
60 W
C -P
-U
0)
O
O
O
W
3
CO M-l
"O CO 0)
0) CO O
^H -H O
CO O
O C
W >» O
•O -i-l
fl) -t
4-) -H
O .0
•H CO
•O ^->
a) oo
Q) O
eo H
CO «
t-i
a) g
> O
« u
to H
(j Q
0) ft*
O.
W O
.H O
-o o*
o
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r^ O
cr> GO
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-------
"Beacon Hill" is represented in CTDM by the following parameters:
Height (H) = 300 m
Base Elevation (ho) = 1299 m (MSL)
Major Axis Minor Axis
Semi-length (L) 1062 m 708 m
Inverse Polynomial Power (p) 2.5 1.5
Orientation of the major axis (degrees CW from north) is 66°. The
length scale factors for the transition region above Hc and the
terrain factor fields are the same as those used in the modeling of
CCB:
6 = 0.1
a = 0.67
The terrain factors for the vertical deformation and speed-up of the
flow at the crest are taken to be
Thoa = 0.50 Thob = 0.60
Tuoa » 1.15 Tuob =1.30
where "a" refers to flow along the major axis, and "b" refers to flow
along the minor axis. These terrain factors are consistent with what
one might expect for potential flow over Beacon Hill. They are
obtained from estimates of potential flow over an ellipsoid as
discussed in Subsection 5.2.1.
Modeling results are presented in Table 24. CTDM underestimates
all but one of the peak observed concentrations, but six of the
thirteen are within a factor of two. The geometric mean and standard
deviation for this dataset are 2.32 and 1.86, respectively. For
comparison, the geometric mean and standard deviation for the
COMPLEX I results presented in Table 20 (using Class F for Experiment
13-9) are 0.59 and 1.53. Therefore, CTDM tends to underestimate the
observed concentrations to a greater degree than COMPLEX I
overestimates them, and the scatter in the CTDM estimates is somewhat
larger than the scatter in the COMPLEX I estimates.
Approximate centerline values of the x/Q have been calculated
as l/(2iruoytfz) from representative hourly plume spread
parameters from CTDM. They are compared with peak modeled and
observed values of the x/Q ^n Table 25. In most cases, the tendency
for CTDM to underestimate the observed peak concentrations arises from
the size of the computed values of ay and oz, and not from the
impact assumptions. The analysis of Section 3.4 indicates that oz
is generally overestimated by the CTDM algorithm, and so an
improvement in CTDM performance will require better performance from
the <3Z algorithm.
The performance of the Oy algorithm has not been assessed.
This algorithm may also be overestimating the spread of the plume in a
time-averaged sense over an hour, but it is also possible that the use
of a Gaussian distribution for the horizontal spread also leads to an
213
-------
TABLE 24. SUMMARY x/Q STATISTICS FOR CTDM CALCULATIONS"*"
Exp
No.
2
2
2
2
3
5
6
6
7
11
13
13
13
14
Hour
Ending
4
5
6
7
6
4
5
7
7
6
7
8
9
3
C°*3
(ms/m°)
3.4
7.3
3.0
4.8
2.3
4.7
3.0
2.6
4.2
5.9
2.1
4.2
8.2
2.0
Cp*
(ys/m^)
3.3
1.7
3.3
3.7
1.1
2.7
_
0.4
2.4
1.6
1.4
1.5
2.2
0.5
Max Cg
3.4
2.8
3.3
3.8
1.3
2.8
_
0.4
2.7
1.6
1.7
1.7
2.3
0.5
Max
1.02
2.84
0.96
1.33
2.55
1.86
_
6.33
1.60
4.62
1.46
4.07
3.64
4.70
+Refer to Table 25 for Max C values.
o
*Average of the 2 greatest scaled concentrations at receptors near
"Beacon Hill" for the hour.
214
-------
TABLE 25. COMPARISON OF PEAK MODELED AND OBSERVED SCALED
CONCENTRATIONS WITH CENTERLINE CONCENTRATIONS
ESTIMATED FROM PLUME SPREAD PARAMETERS
FROM CTDM
Exp-Hr
2-4
2-5
2-6
2-7
3-6
5-4
6-7
7-7
11-6
13-7
13-8
13-9
14-3
<*z
(m)
30
33
32
28
61
54
70
52
62
32
43
44
90
-------
underestimate of the peak observed concentrations. Consider
experiment 13-9. Modeled concentrations for this hour are shown in
Figure 104, as are the 5-minute average wind vectors used in the
modeling. The distribution of winds is not Gaussian, and exhibits a
dominant lobe towards "Beacon Hill." In effect, this lobe defines a
narrower plume than that estimated by the model, and yet this lobe is
most important in determining the peak observed concentrations for the
hour. Consequently, a type of PDF approach may be important in
modeling the FSPS.
216
-------
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217
-------
SECTION 6
CTDM - IMPROVEMENTS AND MODIFICATIONS
Several modifications to CTDM are under development. These
activities involve the scientific basis of the model and the need for
a practical regulatory tool. They address the need for specifying the
influence of the hill on diffusion in the flow above Hc (i.e., the
LIFT module). It is important for the model to be able to distinguish
among hill shapes and the structure of the incident flow in
calculating the flow deformation caused by the hill. The results
reported in Section 3.2 are encouraging in that streamline heights
observed over the crest of HBR tend to follow theoretical
expectations. Additional aspects of developing the theory for flow
over two- and three-dimensional hills are discussed in 6.1.
In Section 6.2, a connection is made between the terrain factor
for az contained in CTDM and the theory of thin plumes embedded in
a deformed flow presented by Hunt and Mulhearn (1973). A modification
to how the average diffusivity is calculated over the hill allows the
CTDM calculation to simulate the results of the theory.
A discussion of how CTDM, or the basic concepts of CTDM, can be
transferred to other sites is contained in Section 6.3. This
discussion explores several topics raised in contemplating the
eventual use of CTDM in the air quality permitting process.
6.1 Stratified Airflow over a Three-Dimensional Hill
Hunt and Richards (1984) describe a quite general approach for
approximating the flow over arbitrary three-dimensional hills in terms
of multi-layered flows in the neutral, s = NL/u « 1, and strongly
stratified, s » 1, limits. Their results are generally presented in
the form of various convolution integrals over the hill shape function
or its derivative; but these integrals can be quite difficult to
evaluate for hill shapes other than the inverse polynomial hill. On
the other hand, Smith (1980) keeps the integrals in their Fourier
representations and presents approximate, closed-form results for flow
near the surface for a symmetric inverse polynomial hill. In this
section a somewhat intermediate path is taken and results are
developed for an arbitrary hill shape and evaluated for the asymmetric
inverse polynomial hill as well as the bivariate Gaussian hill shape
function
h(x,y) = h exp{-|[(x/o )2 + (y/o )2]} (114)
/. x y
218
-------
where the hill sigmas are related to the more conventional half-widths
at half maximum by
L = aUlitf)1/2 * 1.18 a . (115)
Paralleling the development in Subsection 3.2.2 one can write the
solution for the vertical displacement, S(x,y,z), as
6(x,y,z) = Re(^;)2 J dk J da / dx' J dy'h(x' ,y« )eimz* -
ik(x-x') + U(y-y'), (116)
6
where Re denotes the real part, k, 8. are the x, y wave numbers,
respectively, z' = z - h(x,y), all integrals are over the domain -o°
to +co unless otherwise noted, and
v2 4- 9.2 w2
m2 = < ka ) «•) that
provided reasonable results for HBR lidar measurements in
Subsection 3.2.2,
• reasonable approximation of the integrand maximum
corresponding to 9,/k = Lx/Ly, and
• the ability to evaluate Eq. (116).
It is also worth noting that the errors incurred in the imaginary part
of m are not so critical because the limit z* -» 0 will be invoked
for this part. Inserting (118) into (116) gives rise to two integral
expressions that have simple results in the limit of zf -» 0. These
are
J dk e-kZ> - , A(x-x') + 7 (119)
and i- J di e-|5l|z' - m A(y-y') (120)
219
-------
where A(x-x') is the Dirac delta function and the absence of an
imaginary term in (120) is due to the presence of the absolute value
|I| as contrasted with the k term in Eq. (119). Inserting these
results back into (116) and performing the remaining y1 and x'
integrations yields
6(x,y,z) = Re eim'z'[h(x,y) + J(x,y)] (121)
where J(x,y) is the principal value of an integral that can be
expressed alternatively as
J(x.y) = ; ' . (122.)
or
• °° A
= v I ^7" th(x-x',y) - h(x+x',y)] . (122c)
The latter form is suggestive of the derivative of the hill shape
function term of Hunt et al. (1981). Selection of the particular form
of Eq. (122) depends mostly on the assumed form of h(x,y). For
example, the case of the asymmetric 3-d inverse polynomial hill,
h(x,y) = . 2h . 2 , (123)
1 + x /L x + y /Ly
yields
J(x,y) = i(x/Lx)h(x,y)/(l + y2/!^2)1/2 (124)
after evaluation of either Eq. (122a) or (122b) by contour
integration. It is also encouraging to note that the limit
Ly •* oo gives back the 2-d ridge, and (124) combined with (123)
gives back Eq. (18): the original Queney (1947) result. This result
also shows that Eq. (121) is correct in the limit z'/Lx « 1 and
that correction factors of order (1 + z'/L) could be used to extend
the usefulness of Eq. (121) to larger z'; however, this is not a
critical point since the principal interest is in narrow plumes
approaching close to the hill so that z' « L. The final form for the
vertical deflection for the 3-d inverse polynomial hill is
(x/Lx)
«(x,y,z) = h(x,y)[cos m'z' - (1+ 2/L 2)1/2 sin m'z»] (125)
220
-------
where h(x,y) is given by Eq. (123) and m* is defined by Eq. (118).
The bivariate Gaussian hill function given by Eq. (114) is more
readily evaluated using (122c) and conventional integration techniques
since the integrand is not well behaved at large imaginary values of
x' . After some algebraic manipulation one obtains
4 °° Av' — —(v'/rt ^2
J(x,y) = i h(x,y) 2 J JS 2^* 'V sinh(xx'/o2)
ir x x
= i(2/ir)1/2h(x,y)(x/o
(126)
* i(2/«)1/2h(x,y)(x/ox)
where M is a Rummer function that is then approximated to lowest order
in x/ox. As with the inverse polynomial hill, this result can be
easily combined with Eq. (121) to yield a complete description of
6(x,y,z).
Once the vertical deflections are available, the z' integration
necessary to obtain the pressure fluctuation, p' , is obtained as
p'(x,y,z) = -g - Re-e[h(x,y) + J(x,y)J , (127)
where p(z) is the unperturbed density profile. As discussed in
Smith (1980), this then immediately yields the downstream velocity
perturbation, u', as
u« = -p'/(Pou) . (128)
Computation of lateral velocities and displacements are somewhat more
difficult as successive integrations in the x direction are required;
however, these are not expected to present major problems. This then
provides a complete description of the plume centerline path (or any
other streamline) in stratified flow. The secondary effects of speed
shear with height are then factored in as described in
Subsection 3.2.2. Arbitrary wind directions may be handled by a
rotation of the hill shape function and a slight redefinition of m*.
In addition, an inner boundary layer may be added by displacing the
hill shape function by the desired amount.
6.2 Connection between the Hunt and Mulhearn (1973) Approach and CTDM
In CTDM, the distortion in the flow over a hill and the response
of the diffusion process to that distortion are treated consecutively
to simplify the computation. The mean distortion in the flow along
the path to a particular receptor is specified, and then the diffusion
of plume material in that altered flow takes place with an altered
221
-------
mean diffusivity. Physically, the plume growth is altered locally at
each position along the path, and can be approximated by a line
integral (along the trajectory) involving the diffusivity and the
local straining of the flow (Hunt and Mulhearn 1973). The CTDM
approach can give results more like the line integral by altering the
way the mean diffusivity is calculated.
The streamline height above the ground is denoted by n, where
n(z,t) = z + &z(z,t) - Hf(t) . (129)
The vertical deflection of the plume streamline is 6Z, H is the
height of the hill, and f(t) is the shape of the hill along the wind
direction. Note that the distance coordinate "x" has been transformed
into a time-of-travel, t, and that z denotes the elevation of the
streamline far upwind of the hill. Also note that far upwind of the
hill, f(t) = 0, and 6z(z,t) = 0, so that the spacing between
streamlines in the vertical is a constant:
The key parameter in the vertical distribution factor in the
Gaussian plume equation is the ratio of the plume centerline height
above the ground to the spread of the plume in the vertical. Denote
this ratio as R. For low-slope hills in the limit that the
travel-time is greater than the Lagrangian time-scale (TL) , R can be
written as:
R2 = r" (130)
n2(zc, t)
ah (z.t),
az '
)7 ,fc2 K(t')
z o' X3n (z,1
( 3z
dt1
I\ 2
z }
C
where t is the travel time, zc is the initial height of the plume
upwind of the terrain, and K is the diffusivity. If we take the
straining of the flow On/3z) to be constant with height, as does
Hunt and Mulhearn (1973), but equal to its average value between the
plume centerline and the surface rather than its value at plume
centerline height, then the streamline height above the surface is
approximated by
n(z,t) = z ^^- (131)
so that
222
-------
2 _ Z
R = —7 — s - (132)
J 2K(t') df
,-,.
Assume that the initial time-of -travel "to" takes place before the
hill has a significant influence on the flow. Then
t t
2K(f ?dt = [ 2K_(f )df = 0Z (t ) (133)
T — 77TT 2 j W Z O
O 8n(f ). •'o
where KF is the diffusivity in the absence of the hill. This allows
R to be rewritten as
R2 = - ~ - - 2K(f) dt' (134)
The mean rate-of-strain for the layer of air between the surface
and the center line of the plume is denoted in CTDM by
Th
-------
This equation approximates the diffusion process in the interval
(t-t0) with a mean diffusivity factor Toz and a mean strain
factor T^.
Therefore, the two approaches are consistent if
~T~
(f^>* = f I I 2 (I I, * f 1* 2K_(f) df (139)
•L- I* A_ I ^ • L> J t C
h o h c o
Because Equation (130) is valid for t » TL, Kp is independent of
t in the interval t-t0 so that
. f 2K_(f) df = (t-t ) 2K_ (140)
T» £ Of
O
If we assume that the time dependence of T^(zc,t) is contained in
a function <|>(t) so that
Th (zc, t) = 4>(t) Th (141)
then
K(f ) df
Toz2 =fc t jt *2(t'} - ^~ (142)
°Z K-., tQ K_,
t-t
O
Therefore, the factor~Taz is related to a weighted average of the
diffusivity over the interval (t-to), where the weighting function
is essentially the square of the amount of straining in the flow. The
spatial distribution of the straining of the flow can be obtained from
the analysis presented in 6.1.
An interesting situation arises when the diffusivity is very
small. Mixing of plume material across streamlines towards the hill
surface proceeds at a slow pace even in the presence of hill-induced
distortion. Consequently, the effect of the hill on ground-level
pollutant concentrations appears minimal if the plume is far enough
above Hc (i.e., no impingement potential). However, a new inner
boundary develops over the surface of the hill at elevations above
Hc and if this layer extends high enough to intercept plume
material, pollutant concentrations at the surface can increase
markedly. Under these circumstances, the speed-up of the flow is
important in establishing the depth of this new inner layer, and the
elevation of the plume above the surface in the deformed flow is
important in determining how much plume material can be mixed through
the inner layer to the surface.
224
-------
This type of terrain effect is not included in applications of
the Hunt and Mulhearn theory, and it is not included in CTDM.
However, because of the importance of the elevation of the plume in
the deformed flow relative to the depth of the inner layer, the effect
might be viewed as a plume-height correction analogous to the terrain
correction factor or partial height factor contained in simpler
models. Specification of the inner layer depth is being pursued so
that this concept can be included in CTDM and tested.
6.3 Applicability of CTDM to Other Sites
A fundamental objective of the CTMD project has been to develop a
model which, to the largest extent possible, would be applicable to a
variety of terrain settings where direct impaction of a plume during
stable atmospheric conditions could be expected. The best way to
accomplish this objective is to simulate correctly the dominant
physical processes involved in the transport and diffusion
algorithms. The overall CTMD project design, which called for field
experiments at three different topographic settings, including one at
a "full scale" power plant location, emphasized the importance of
obtaining a physical understanding of the phenomena of importance by
observing plume behavior at different scales and different
topography. The heavy reliance of the CTMD project on the use of
physical modeling results is a further manifestation of the concept
that properly scaled and interpreted results from small scale
experiments can be used to provide insight on the importance of and
effects of specific physical variables. At this point, we have a
clearer understanding of the similarities and differences of flow
behavior observed at small and large physical scales and at the
different topographic settings. It is therefore appropriate to
comment on these findings and how they are related to the
applicability of CTDM to more general locations. It should be stated,
however, that while every effort, within the constraints of the
project, has been made to develop a generalized model, the diversity
of the topography near existing or anticipated emission sources is
large and, generally, one should expect some degradation of the
reliability of the model predictions as one applies CTDM to very
different settings.
In the discussion that follows, we will identify different
physical phenomena that affect the generality of CTDM and provide some
guidance on the proper interpretation of this knowledge to future
applications of CTDM.
6.3.1 Dividing Streamline Height
One of the more important findings of the work performed to date
from the physical modeling and field studies is the general
applicability of the method for estimating Hc, the dividing
streamline height. Snyder et al. (1985) provide a comprehensive and
up-to-date documentation of these findings, including discussions of
cases and circumstances where some modifications of the approach have
been suggested.
225
-------
Towing tank experiments with a model of CCB showed good agreement
of dividing streamline heights normalized by hill height with the
'1-Fr' rule. Experiments with truncated triangular ridges showed
agreement for Fr < .25 but deviation from the rule for greater values
of Fr, This deviation was associated with the formation of an upwind
vortex which produced a downflow on the front face of the ridge. The
experiments confirmed, however, that the dividing streamline height
was independent of the width of the hill. Other experiments with
truncated sinusoidal ridges at various angles to the mean flow provide
further substantiation of the '1-Fr' rule for angles of 60° and 90° to
the ridge axis. At a 30° angle, the streamline followed a '1-.7 Fr'
relationship — indicating that a path of lower potential energy was
found. This is consistent with the notion that the kinetic energy of
a parcel provides a necessary but not sufficient basis for predicting
that the parcel will travel up and over a terrain obstacle. In this
sense the dividing streamline height calculated from the integral
energy equation provides a lower limit to the actual dividing
streamlines.
As discussed elsewhere the use of the dividing streamline height
to define flow patterns has been important to the understanding of
flow at CCB, HER, and at the Tracy power plant. Other investigators
(Rowe et al., 1982 and Ryan et al., 1984) have confirmed the
applicability of the concept to large scale settings. Because it is
applicable to a range of physical scales, the dividing streamline
concept is one of the cornerstones of the general applicability of
CTDM.
6.3.2 Terrain Correction Factors
Previous sections of this report have addressed the formulation
of T-factors that characterize turbulence changes and flow distortion
as a function of the three-dimensional geometry of terrain objects and
characteristics of the incident flow. The development of these
formulations has been based on physical concepts which should be, and
which appear to be, valid for a range of topographic shapes and
scales. Whereas terrain correction factors commonly used in today's
models are arbitrary (e.g., 10 meters in the Valley model) or
oversimplifications (e.g, the half-height concept), the CTDM
formulations represent factors which will adjust the various
parameters in a manner consistent with our knowledge of the physical
processes.
We believe that further work will be required to specify
corrections to the streamline heights, dispersion coefficients, etc.
associated with multiple hill interactions. For example, the present
formulations cannot be expected to give good results in predicting the
peak concentration on the front side of a hill downwind of another
hill unless the plume-terrain interaction for the first hill is weak.
More generally, the sensitivity of the peak predicted concentrations
as a function of specific variations of the topographic descriptors
needs to be explored mathematically and with comparisons to other
applicable data sets.
226
-------
6.3.3 Effects of Upwind Terrain
Both the CCB and HBR experimental sites were selected because of
the existence of relatively flat fetches upwind of the primary terrain
obstacles. It was desirable to study the impingement phenomena
without the complications expected from the effects of upwind terrain
obstacles. On the other hand, at Tracy, the surrounding topography
undoubtedly affected the approach flow to the various terrain
features. It is our view that the effect of upwind terrain is
primarily to (1) affect the horizontal dispersion rates through the
formation of large eddies which subsequently break up in the approach
flow; and (2) creation of lee waves under stable conditions which
affect the vertical motion of the plumes. The magnitude of these
effects is very much site specific — depending upon the shapes,
relative heights, and complexity of the surrounding terrain. For this
reason site specific meteorological measurements are the best way to
quantify their influence on dispersion rates. The first effect, on
horizontal dispersion, can be estimated from wind fluctuation data
just upwind of the source. Such measurements can be directly input to
CTDM and the model calculations will be altered in accordance with the
magnitude of the crosswind dispersion.
How to treat the second effect, the formation of waves, needs
further analyses. Vertically oriented anemometers cannot distinguish
between wave motion and turbulent motions. The wave motions, of
course, have a finite effect on the vertical displacements possible of
fluid parcels while the turbulent motions result in continuous
diffusion. While spectral analysis of the vertical wind fluctuation
data could presumably allow some separation of wave effects from
turbulence effects, it is not clear that this will resolve the
issues. For example, the wave motions will induce vertical motion of
an elevated plume on a hillside where impingement is taking place.
This will, in effect, leave the signature of a plume with greater
vertical dimensions than would be implied from "snapshot" views or by
eliminating the wave motions from the turbulence data. However, the
effect of these motions on time-averaged concentrations will not be as
large as would be implied if the contribution of the waves were
treated as turbulence. Whether spectral analysis should be applied
may depend upon the amplitude of the wave motions encountered. If
their amplitude is large in comparison to the characteristic scale of
the plume resulting from buoyancy induced dispersion, and/or the
ambient turbulence, such analysis will probably be desirable. This is
a technical area which will receive further study this year through
analysis of the Tracy data set. The results will provide further
information on the magnitude of wave effects and on the need to make
adjustments to turbulence data for dispersion model use.
6.3.4 Importance of Drainage Flows
An issue raised in the early design of the CTMD project (Hovind
et al., 1979) was the importance of drainage flows in full scale
topographic settings. There are two aspects to this issue. First of
all is the question of whether stable air flow in mountainous areas
will commonly carry an elevated plume toward high terrain. Because
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drainage winds are shallow compared to terrain heights in many areas
and because such flows will prefer to pass around the sides of a
terrain obstacle rather than to climb up the surface, the question of
whether stable plume impingement occurs in reality is a valid one.
The way to address this issue definitively for any location is through
direct observation of the local flows either through wind measurements
or flow visualization. At the Tracy power plant, drainage flows,
which had origins in the Sierras to the west, clearly were
sufficiently deep to dominate the approach flow to Beacon Hill and
Target Mountain. Similarly, at CCB and HBR, large scale drainage
flows created relatively predictable deep and stable winds toward the
terrain objects. Of course, this was an important aspect of these
areas which made them attractive experimental sites. In fact, this
was the principal reason why they were selected. There are settings
(narrow canyons or valleys) where systematic flow toward the high
terrain (sidewalls) is not expected. Meteorological measurements at
these settings will probably indicate frequent up-down valley flows
and rare cross valley flows.
The second aspect of the drainage flow issue is what the effect
of very local drainage flows, induced by the immediately encountered
terrain, will have on plume trajectories and dispersion. McNider and
Arritt (1984) have outlined some concerns on the transferability of
the dividing streamline concept to large scale topography because of
the increased importance of drainage winds. They argue that if a
terrain feature protrudes above the nocturnal surface inversion,
drainage winds will develop more strongly because the temperature
gradient will not suppress the formation of the drainage flow.
Independent of that effect, large features will develop deeper
drainage flows. From some numerical simulations of a two-dimensional
terrain feature, McNider and Arritt postulate that the drainage flow
from a 1,000 m high hill extended to 250 m in depth. While we feel
that the influence would be much smaller for three-dimensional
features (the drainage flow will be shallower for a three-dimensional
feature), this is clearly an area for further investigation with the
Tracy data.
The influence of such local drainage flows on concentration
patterns observed at CCB and HBR is minimal. These "small hills" are
not tall enough to generate deep slope flows, although very shallow
slope flows at low elevation on these hills were occasionally
observed. Near terrain of greater relief, one would expect drainage
flows to exert & greater influence on the distribution of plume
material, and this was observed at Tracy. However, the effect of
drainage flows, or slope flows, on the peak observed concentrations at
Tracy does not appear to be important. For concentrations averaged
over an hour, peak values are characteristically found near plume
elevation. However, some tracer material from the location of the
higher concentrations is apparently carried downslope and produces
nonzero concentrations at lower elevations. These concentrations are
typically much less than those at plume elevation. The significance
of these concentrations might increase with averaging time, and it
would be interesting to look at available 3-hour averages of the
observed tracer concentrations to see if this is so.
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SECTION 7
SUMMARY, CONCLUSIONS, AND
RECOMMENDATIONS FOR FURTHER STUDY
This Fifth Milestone Report describes in detail the FSPS that was
performed in August 1984 at the Tracy Power Plant. The FSPS produced
a 128-hour data base of SFg and CF3Br concentrations, ground-based
and airborne lidar data, photographs, 8-mm movies, videotapes, and
extensive meteorological measurements. This report describes the
final refinement of the HBR meteorological data base. It also
presents a variety of data analyses that were performed in support of
the model development. The highest ground-level tracer concentrations
measured at the CCB, HBR, and FSPS sites are discussed.
The further development of CTDM is described. Mathematical
descriptions of the modifications to the model are presented. The
latest version of the model has been tested using a subset of
impingement hours from the CCB, HBR, and FSPS data bases. The initial
14-hour FSPS data base was also used to test four existing complex
terrain models — COMPLEX I and II, Valley, and RTDM.
7.1 Principal Accomplishments and Conclusions
Refinement of the HBR Meteorological Data Base
The refinement of the meteorological data collected during SHIS
#2 is now complete. The refinement process involved the filtering and
flagging of the raw 1-sec counts data to reduce the effects of noise
on the calculated measurements. Corrections were also made on the
basis of the audit results and the cosine response characteristics of
the fixed propeller anemometers. Five-minute and one-hour averaged
values of meteorological measures were calculated from the corrected
and flagged 1-sec data. The success of the refinement efforts is
demonstrated by the improvement in consistency between collocated
measurements.
An overall assessment of the quality of the HBR meteorological
(and tracer gas) data base can be found in the Quality Assurance
Project Report (Greene 1985). It presents estimates of the precision
and accuracy of all the measurements. The bottom line of this
assessment is that the data from Experiments 10 through 15 are
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completely useful for modeling purposes. The data from the other
experiments are still somewhat noisy, especially the turbulence data
from Experiments 4, 5, and 6. The HER data base is available from the
EPA Project Officer.
HER Streamline Analysis
Lidar data collected at HBR have been used to compare streamline
heights upwind and over the crest of HBR to calculations from
potential flow theory and from a linearized perturbation analysis.
The comparisons suggest that for releases above Hc at HBR a
substantial portion of the streamline deflection near the crest can be
explained by potential flow of the air above Hc over a cylinder.
This approach assumes the terrain is "cut-off" below Hc. The
perturbation analysis shows some improvement in the simulation of the
streamline height when stratification is included in the calculations.
Representativeness of Stable Boundary Layer Similarity Theory
Modeling the dispersion of an elevated plume requires
meteorological data representative of plume height. Since this
information is not always available, it is useful to consider if
near-surface measurements can be used to infer information at plume
elevations. This issue was addressed by using stable boundary layer
similarity relationships to predict wind and temperature data at 40 m
and 150 m from data obtained at 10 m and 2 m. The predictions were
compared to measurements taken at CCB and HBR. The results indicate
that the similarity relationships reproduce the observations fairly
well to elevations less than about 10L. Above 10L the predictions
have little reliability. Since L is typically a few meters during
stable conditions, near-surface measurements will not be useful for
estimating meteorological conditions above, say, 50 m. Most major
sources generate plumes whose equilibrium heights are well above
50 m. Therefore, proper modeling of these sources will require
meteorological data collected on tall towers or via acoustic sodar.
Strimaitis et al. (1984) demonstrated that the performance of
CTDM deteriorates when the model input data were constructed from
sparse data sets using near-surface measurements, rather than the wind
and temperature profiles available from the 150-m tower. These model
performance tests and the fact that the similarity relationships are
useful to heights of less than 10L corroborate the need for onsite
measurements of turbulence intensity near the release height and
detailed vertical profiles of wind and temperature.
Investigations of Vertical Plume Growth
CTDM uses the expression:
-------
to simulate the vertical diffusion of an elevated plume.
Hourly-average lidar data from 14 FSPS impingement hours were used to
perform an initial evaluation of the expression for az. In
particular, the evolution of ctz after plume rise was investigated.
The initial growth (ozfc) °f tne plume due to entrainment
associated with its buoyant rise was estimated from the
hourly-averaged lidar scan made in the vicinity of the stack, once the
plume had leveled off. Typically, 0zb was measured at a distance
of 700 m from the stack. The lidar scans taken downwind of this
distance were then used to evaluate the subsequent growth of oz.
The observed values of c?z beyond ozb suggest that the
model for TL and az overestimates the lidar estimates of
vertical plume growth. This tendency of the observed plume growth to
be overestimated could be the result of modeling TL incorrectly, not
screening out the wave contribution to ow, or not accounting for a
collapse of the plume in the vertical after plume rise. None of these
possibilities has been investigated in detail as yet.
An Analysis of the Highest Ground-Level Concentrations Observed
at CCB. HBR. and the FSPS
The ten highest SFg and CF3Br concentrations observed at CCB,
HBR, and Tracy were presented in order to illustrate the associated
meteorological conditions. The distributions of the tracer
concentrations and the lidar and photographic data support the concept
of a critical dividing streamline that separates stable air flow into
two layers. At CCB the highest concentrations were observed most
often when the tracer gas was emitted at an elevation near the
calculated dividing streamline height. At the Hogback the highest
concentrations were observed when the tracer gas was released below
Hc. Evidently, at a long ridge setting like HBR, the flow below
Hc is impeded by the ridge, thereby giving the tracer gas an
opportunity to impinge on its windward side. At the isolated,
three-dimensional CCB site the air flow below Hc is not constrained,
but "escapes" by flowing around the sides of the hill, effectively
dispersing the tracer gas. At both sites tracers released above Hc
tended to flow over the terrain and the higher concentrations were
produced near the top or on the lee side.
Initial analysis of the Tracy data base suggests the full-scale
site exhibits dispersion characteristics similar to both small scale
sites. The observed concentrations show that nine of the ten highest
normalized concentrations occurred when the tracer gas was released
below Hc. We have not yet analyzed the meteorological data to
ascertain if the low-level flow at Tracy was blocked or constrained.
For the hours with the ten highest SFg concentrations, five have
estimates of the plume height. All five plume heights (or effective
release heights) are near the calculated height of the dividing
streamline.
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The Complex Terrain Dispersion Model (CTDM)
The Fourth Milestone Report provides a detailed description of
CTDM. Most of the basic structure of the model described therein has
not been changed. The current version (12185) is considered a working
version that has been and will continue to be revised before the
initial submittal to EPA in October 1985. Over the last year the
major revisions include:
• a generalization of the treatment of terrain so that now
hills are simulated as ellipsoids;
• a reformulation of WRAP to simulate the effects of travel
time on vertical plume growth; and
• changes to LIFT to simplify the treatment of the horizontal
deflection of the plume, to include an estimate of how the
turbulence changes over the hill, and to accommodate hills
with horizontal cross-sections that are elliptical in shape.
Upcoming revisions to the model are also discussed in this milestone
report.
The current version of CTDM has been tested using a subset of
"impingement" hours from the CCB and HBR data bases and 13 hours from
an initial 14-hour data set from the FSPS. A comparison of the
modeled concentrations with the values observed at CCB suggests a
reduction in the tendency of the model to overestimate the observed
concentrations (see Table 7 in the Fourth Milestone Report). The
model does reasonably well in simulating the HBR concentrations.
CTDM underestimates the concentrations measured during the FSPS
although many (6 of 13) are within a factor of two. This tendency
toward underprediction arises primarily from the size of the computed
hourly values of ay and oz, and not from the impingement
assumptions. An examination of 5-minute wind vectors for some of the
hours suggests a PDF approach might improve the modeling of the FSPS.
The Semi-Empirical HBR Model
A simple plume model in which the horizontal distribution of
tracer gas is determined by a probability distribution function (PDF)
developed from wind direction observations, and in which wind speed is
associated with wind direction as well, was applied to a subset of
CF3Br cases from HBR. With the vertical terrain correction factor
described in the Fourth Milestone Report and the oz formulation
from CTDM, this model simulated the observed concentrations reasonably
well (i.e. , nig x, 1.0 and sg < 2.0).
Comparative Model Evaluations Using the 14-Hour FSPS Data Base
Valley, COMPLEX I and II, and RTDM were run using the 14-hour
FSPS data set. CTDM was run for 13 of these hours in which the
primary plume impact is on "Beacon Hill." Valley and COMPLEX II
substantially overestimate the observed SFg concentrations.
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The average top-two COMPLEX I concentrations are in fair
agreement with the average top-two observed concentrations paired
hourly. The average top-two residuals indicate that COMPLEX I
overpredicts for 11 of the case-hours. The ratio of the maximum
observed to predicted concentrations indicate that 10 of the
case-hours lie within a factor of two.
RTDM was first run with the hourly values of the vertical and
horizontal components of the turbulence intensity estimated at plume
height to calculate Oy and az. The average top-two
concentrations underpredict the observations for all case-hours. The
ratio of the maximum observed to predicted concentrations indicate
that none of the case-hours lie within a factor of two.
RTDM was then tested with its default Briggs rural (ASME, 1979)
dispersion coefficients. The top-two average predicted concentrations
are now much larger than those predicted from RTDM's algorithm that
uses the measured turbulence data. The ratios of the maximum observed
to predicted concentrations indicate that six of the case-hours now
lie within a factor of two.
Again, CTDM was run using 13 hours of the initial FSPS data
base. The averages of the highest two modeled concentrations for all
but one of the hours underestimated the observations. Six of the
modeled concentrations were within a factor of two of the observations.
7.2 Recommendations for Further Study
7.2.1 Data Analysis and Model Formulation
High priority will be given to expanding the analysis of the
vertical growth of the Tracy plume because it is apparent that a
proper specification of az(and oy) is critical to modeling
concentrations at Tracy. More hours, including a wider range of
meteorological conditions, will be included. It is particularly
important to provide as complete a description of the effects of
waves, as possible. Data from the sonic anemometers will be
particularly important in evaluating the model of Pearson et al.
(1983) for this data set, and in attempting to identify wave-dominated
events.
High priority will also be given to investigating the performance
of a PDF formulation of CTDM. Such a formulation appears important
for adequate simulation of some of the hours in the HER dataset and
may improve the ability to simulate the peak observed concentrations
at Tracy. While formulating the PDF version of CTDM, we will learn
more about the elements of the semi-empirical model that control its
performance at HBR, and how these elements can be related to theory
and incorporated in CTDM.
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Of particular importance at Tracy are the issues of averaging
time and time-of-travel from the stack to the terrain. A 1-hour
averaging period for the concentration field may be too short a period
for many important impingement events in which the time-of-travel to
the impingement zone is nearly equal to or actually exceeds one hour.
Long travel times must be treated carefully if a plume model is to be
applied correctly. To assess this, impingement calculations will be
made for various averaging periods and compared with the corresponding
measured concentration averages. Various lag times for the
meteorological data will also be included in the study, and
comparisons with traditional averages of hourly Gaussian plume
calculations will be made to investigate the significance of averaging
and lag times for current regulatory modeling practice.
An algorithm for calculating the terrain effect factors for the
LIFT portion of CTDM, based on the theory developed and described in
this report, will be formulated and implemented. Included in this
algorithm will be the effects of streamline displacement, flow
deformation, changes in turbulence, and an inner boundary layer over
the top of the hill, on the evolution of the plume, and on the
resulting concentration of plume material at the surface of the hill.
Once implemented, the algorithm will be tested for its sensitivity to
hill shape and the structure of the approach flow.
Work will be performed on the problem of how to "decompose" an
array of hills into hill segments that will reflect the degree of flow
deformation expected in the neighborhood of each receptor in a model
application. This will aid in the generalization of CTDM and its
transferability to arbitrary terrain settings.
The algorithm in LIFT that provides a transition region between
the LIFT and WRAP portions of the code will be modified to reflect the
towing tank data obtained at the EPA FMF, and reported in the
Appendix. Essentially, the issue to be addressed is how quickly the
steering tendency of the terrain below Hc is reduced above Hc.
The WRAP model requires further scrutiny. At present, its
primary effect on concentrations at ground-level arises from its
time-of-travel adjustments, and its "terrain steering" (i.e., the
relationship between the mean streamline through the source and the
stagnation streamline of the mean flow.) Each of these is quite
dependent on the scale of the hill (or hills) in horizontal
cross-section compared to the distance of the source from the hill,
and the suitability of the notion of a steady, mean flow. At HBR,
where the scale of the hill is much greater than the distance from the
hill to the source, the model calculations appear to be too sensitive
to the hill shape, and notions about a mean flow are at times
inappropriate. At CCB, the degree of steering seems to be
overestimated at times. Some of these problems may arise from how
wind directions measured at towers near the hill are "adjusted" to
obtain the wind direction "at infinity."
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Once the modifications to the model are complete, CTDM will
undergo a systematic series of sensitivity studies. These will help
identify the conditions in which the terrain effects contained in CTDM
have the greatest and least impact on the magnitude of the
ground-level concentrations. The effects of uncertainties of the
model input data on concentrations will also be analyzed. These will
include direct input (wind speed, etc.), the various terrain
parameters, and the location of the meteorological tower.
An analysis of the FSPS data will be undertaken to provide a
description of the observed flow throughout the experiment area. The
behavior of the visible plume from the Tracy stack and the
corresponding tracer-gas concentrations measured at the ground will be
characterized as a function of area-wide meteorological measurements.
This analysis will serve to identify the roles of the upper-level flow
and the local drainage flow in determining the character of the flow
and turbulence in the valley.
7.2.2 Development of FSPS Meteorological Data Base
Because the height of the SFg/oil-fog plume at Tracy was often
greater than 150 m, and because the flow in the Truckee Valley was
sheared at these elevations in very stable conditions, meteorological
data relevant to the plume will have to be derived for many periods
from measurements made by tethersonde, Doppler sodar, and rabals. The
tethersonde flown west of the power plant was apparently faulty, and
little data are available from the east Doppler system as well, so the
best sources of data above 150 m are the tethersonde flown near the
tall tower and the west Doppler. Both of these systems can provide
good estimates of wind speed and direction, but vertical turbulence
estimates must come from the Doppler. The rabal data extend the
vertical range of wind observations well above plume height on a
quasi-instantaneous basis and will be most useful for evaluation of
spatial variability within the valley. These considerations imply
that the development of a Modeler's Data Archive for FSPS will be
somewhat more complex than those for CCB and HBR.
The audit of the meteorological tower systems indicated that the
quality of data from these instruments is excellent and no major noise
problems have been discovered. The principal effort in the refinement
of these data will be the correction of the averaged speeds and
directions from UVW propellers for non-cosine response.
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Wurtele, M. 1957. The Three Dimensional Lee Wave. Beitr. Phys. frei
Atmos.. 29: 242-252.
Yamada, T. 1979. Prediction of the Nocturnal Surface Inversion
Height. J. Appl. Meteor.. 18: 526-531.
Yamartino, R.J. 1984. A Comparison of Several "Single-Pass"
Estimators of the Standard Deviation of Wind Direction. J.
Climate and Appl. Met.. 23:1362-1366.
239
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APPENDIX
STREAMLINE TRAJECTORIES IN NEUTRAL AND STRATIFIED
FLOW OVER A THREE-DIMENSIONAL HILL
240
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Streamline Trajectories in Neutral and Stratified Flow
Over a Three-Dimensional Hill
by
William H. Snyder*
Roger S. Thompson
Meteorology and Assessment Division
Atmospheric Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
and
Michael S. Shipman
Northrop Services, Inc.
Research Triangle Park, NC 27709
May 1985
ATMOSPHERIC SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC 27711
*0n assignment from the National Oceanic and Atmospheric Administration, U.S.
Department of Commerce
241
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1. INTRODUCTION
In attempting to predict the maximum ground-level concentration
from a source upwind of a hill, the most important feature of the flow
is the displacement of the mean streamline through the source, because
that displacement determines how near to the surface the centerline of
the plume will reach. The exact path taken by the plume in
circumventing the hill and the plume's closeness of approach to the
hill surface are critical in determining the location and magnitude of
the ground-level concentrations. These displacements are known to be
strongly affected by the hill shape and by the stratification in the
approach flow (Hunt et al., 1979; Hunt and Snyder, 1980; Snyder and
Hunt, 1984; Snyder et al., 1985).
The purpose of the work described herein was to characterize the
effects of stability on the horizontal and vertical deflections of
streamlines around an isolated hill. A large set of streamline
trajectories over an axisymmetric hill was measured using the
stratified towing tank of the EPA Fluid Modeling Facility.
Three-dimensional coordinates of the streamlines (86 independent
trajectories) were determined through stereographic analysis of
photographs of dye streak lines released at a matrix of source
positions (heights and lateral offsets from the hill/flow centerline),
and at stabilities ranging from strongly stable to neutral (Froude
number of 0.6, 1.0, 2.0, and «°). The general features of these
measurements are presented, but the primary value lies in the fact
that a relatively complete data set is available for testing
mathematical models and algorithms of the detailed structure of
stratified flow over hills. As an example use of the data set, a
particular mathematical model using linear theory and a Fast Fourier
Transform (FFT) technique to predict these streamline trajectories is
evaluated.
Section 2 describes the experimental details and the photographic
analysis technique. Example results are presented and discussed in
Section 3, and a description and evaluation of the mathematical model
are presented in Section 4. A data tape containing the coordinates of
the trajectories is available from the authors upon request.
242
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2. APPARATUS, INSTRUMENTATION AND TECHNIQUES
2.1 The Towing Tank
The EPA towing tank (1.2mX2.4mX25m) is elevated
approximately 3.5 m above the building floor. The walls and floor are
made of clear acrylic plastic (2.54 and 3.17 cm thick respectively),
providing maximum visual access. The model hill is mounted on a flat,
square baseplate. This apparatus is turned upside down and suspended
from a towing carriage so that the baseplate is submerged
approximately 6 mm below the water surface. The apparatus is then
towed the length of the tank. Further details may be obtained from
Thompson and Snyder (1976).
Figure A-l shows the arrangement of the model and cameras about
the tank. The coordinate system originates at the hill base center.
The longitudinal coordinate, x, increases downstream from the hill
axis. The cross-stream coordinate, y, is measured from the hill
centerline, positively toward the camera. The vertical coordinate, z,
is taken to be positive downward from the baseplate level. Since the
model is upside down, the depth z is directly interpreted as height in
the atmosphere.
Mixing and distribution systems permit the tank to be filled with
any desired shape of stable density profile. In these experiments,
the maximum uniform density gradient was used—that is, the tank was
initially filled with fresh water at the surface and saturated salt
water at the bottom. The density profile tended to erode toward
neutral at the surface and bottom of the tank because of the towing
operations and molecular diffusion. In order to maintain the desired
stratification in the vicinity of the hill, the neutral layer
(nominally 3 cm) near the surface was "skimmed" off between tows, and
the original level was restored by introducing an additional layer of
saturated brine at the bottom of the tank. Thus, successive
experiments had slightly different density profiles as an increasingly
deep layer of nearly constant density fluid was accumulated at the
bottom. This gradual change in the bottom boundary condition does not
appear to significantly affect the study results, since the depth of
the uniform gradient extended from the surface to at least four hill
heights in elevation. When the depth of the neutral layer reached
40-50 cm, the tank was emptied and refilled. Figure A-2 shows the
evolution of the density profile over a time period of 16 days and a
series of 15 tows.
243
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of the model and cameras.
244
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Figure A-2. Evolution of density profiles over the course of 16 days
and 15 tows.
245
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The tracer used in these experiments was a blue food dye diluted
with sufficient salt water to produce a plume that was neutrally
buoyant at the release height. This mixture was released from a
bent-over stack located near the upstream edge of the baseplate (x =
-7.5H, where H is the hill height). For these experiments, a narrow
plume was desired, so that a thin tube (1.5 mm ID) was used for the
stack and the dye mixture was emitted nearly isokinetically to form a
streamtube.
2.2 The Model
The model used in this study was an idealized representation of
Cinder Cone Butte in Idaho. The axisymmetric model shape is given by
h (r) = (H + c)/[l + (r/L)4] - c,
with H = 15.45 cm, L = 38.75 cm, and c = 0.97 cm. As shown in the
figures, the model had a fairly flat top and a maximum slope of 0.45
or 24.4°. The model was mounted on the towing-tank baseplate such
that the hill blended smoothly into the flat surface at a radius of
5H. Reference circles were painted on the model at various elevations
to aid in the flow visualization.
Density profiles were measured before each tow. Water samples
from various levels in the towing-tank were drawn into test tubes.
The specific gravity of each sample was determined by the weight of a
submerged object relative to its weight in fresh water. The resulting
density profile was used to set the tow speed U to obtain the desired
Froude number
Fr = U/(gHAp/p)1/2,
where Ap is the density difference between the base and top of the
model hill and g is the gravitational acceleration.
The density profile was also used to specify how the refractive
index varied with depth. For this purpose, the density profile, which
was typically measured with a spacing of 2 cm down to 45 cm, and 10 cm
spacing below 45 cm, was filled-in using interpolation techniques; a
detailed profile of refractive index was derived from that. The
refractive index ranged from 1.333 for fresh water to 1.378 for
saturated brine.
2.3 Photographic Technique
The purpose of this section is to describe the technique
developed to measure the three-dimensional plume trajectories
(streaklines). Basically, the technique is an application of the
common stereographic process in which two simultaneous photographs
taken from different vantage points are combined to provide a
three-dimensional representation. The plume centerlines on side- and
bottom-view photographic prints were digitized and input to a PDF
246
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11/44 minicomputer. In reconciling these disparate views, the
computer algorithm accounted for parallax and refraction. Light rays
were bent significantly by the salt water gradient in the tank and at
the water-wall and wall-air interfaces.
Both side- and bottom-view cameras moved with the model as it was
towed so that several photos were obtained during each tow. The
side-view camera was hung from the towing carriage itself. It was
held at the lowest practical level—looking obliquely upwards through
the layers of salt water to avoid internal reflections. The
bottom-view camera was mounted on a second carriage below the tank.
This vertically facing camera was aligned with the model. The cameras
were fired simultaneously by radio command. Both cameras were
equipped with lenses with focal lengths of 43 mm and were operated at
aperture settings of f/5.6.
2.4 Photographic Analysis
In the analysis of the photographs, the camera was treated as a
point source/receptor of light rays which were traced through the
walls of the tank and the layers of salt water. The photographic
print is thought of as a screen between the virtual camera and the
wall of the tank. Together, the virtual camera and a point in the
photograph determine a light ray which can be projected into the tank
to recover the actual location of the feature in question.
The location of the virtual-point camera must be determined.
Also, the orientation angle of the side-view camera must be specified
to greater precision than can be easily measured.
The side-view camera was aimed so that a reference mark on the
wall of the tank was aligned with a hash mark on the model. The
incident angle at the wall of the light ray passing through these two
points was determined by a predictor-corrector method - given the
density profile. This angle was taken as the vertical orientation of
the camera. The line of sight of the side-view camera was assumed to
be perfectly aligned in the x = 0 plane, and the bottom-view camera
was taken to be directly below the hill center.
The location of the virtual-point camera was determined by a
least-squares fitting technique. A grid (10 cm mesh) was photographed
at five lateral positions with the tank (y = -40, -20, 0, 20, 40 cm).
The actual positions of the grid intersections (473 points total) were
compared to the positions projected from the photographs. Both the
virtual-camera location and a scale factor (depending on the relative
positions of the photograph and camera) were varied. The combination
giving the best fit was determined. The virtual location of the side
camera was found to be 199 cm from the centerline and the bottom
camera was found to be 277 cm below the free surface. In comparison,
the physical positions were 209 and 287 cm, respectively.
247
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Generally, six pairs of photographs were taken during each tow.
Depending upon the variability of the plume path, two, three, or four
pairs were selected for processing. Photos from the first half of the
tow were favored as they were believed to be more representative of
the prescribed flow conditions (i.e., less influenced by the
columnar-mode reflections from the upstream end-wall of the tank; see
Snyder et al., 1985).
The centerline of the plume was estimated and marked on each
8 X 10 inch photographic print. Points along this line were digitized
in addition to several reference points. Eight reference points were
used for the side view—three on the model surface and five on
5 cm-long pointers spaced along the model centerline. Eleven
reference points were available for the bottom view—all on the model
surface—although often either the extreme upstream of downstream
point was obscured by a support member.
Given the virtual position and orientation of the camera, the
locations of reference points, and the density profile, the computer
determined the paths of light rays to each of the reference points
using a predictor-corrector method. By computing the points where
these rays intersected an arbitrary plane (perpendicular to the line
of sight of the camera), the positions at which the reference points
were expected to appear on the photograph were determined—to within a
constant scale factor. Figure A-3 illustrates this projection. The
length and slope of line segments connecting reference points were
calculated for the computed digitized sets. The scale factor required
to project points in the photograph to the arbitrary plane was found
by comparing these line lengths. This scale factor was computed
separately for each photograph to allow for possible differences in
the printing process. In a similar manner, a rotation angle and
offset were found to correct for the orientation of the photograph on
the digitizer board. The coordinates of the digitized plume
centerline were transformed by this offset, rotation angle, and scale
factor.
The result of this transformation was that coordinates from the
photograph were properly oriented and projected to a known plane.
Then a ray from the "point camera" through any point of interest on
the photograph was traced as it passed through the water-channel walls
and saltwater layers. The intersection of the rays from a point
observed in both side- and bottom-view photographs is an estimate of
the actual three-dimensional position of the feature.
Combining the two views of the plume centerline was a bit more
complicated because the independently digitized curves were made up of
different points. An interactive procedure was used, interpolating
within both sets of points, to finally find rays that intersected at
the same (x,y,z) coordinates. For convenience, interpolation was
again used to find y and z values for a set of points spaced uniformly
in x.
248
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The streamwise extent of the observed/computed streaklines was
-60 to +60 cm (-4 to 4H), although the range was smaller for plumes
with large lateral offsets, that is, closer to the camera.
In the most stable cases, the plume's behavior was observed to
vary during the tow. Low stacks, just above the dividing-streamline
height (Snyder et al., 1985), were especially sensitive to changes in
flow conditions during the tow. Also, a few plumes in neutral
conditions had some significant meanders (secondary flows in the tank
due to wind tunnel operations and instabilities at the source are
possible explanations for these deviations). In order to increase the
representativeness and smoothness of the derived trajectories, several
trajectories from a single tow were averaged together. Interpolation
was used to obtain y and z values at specified x values. A simple
independent average of the y and z values was used.
As a final step, the averaged trajectory was normalized by the
hill height and expressed in several other coordinate systems. The
parameters listed below were calculated and are listed in the data
tape.
Horizontal radius R = (x2 + y2)l/2
Total deflection D = [(z - zs)2 + (y - ys)2]1/2
Deflection angle 4> = tan~l ((z - zs)/(y - ys))
Horizontal distance to hill R - r(z)
Vertical distance to hill z - h(x,y)
Normal distance to hill surface n
The maximum vertical (z - zs) and lateral (y - ys)
deflections are reported along with the x location at which they
occurred. The plume's closest approach to the hill surface (minimum
n) was also estimated. Finally, the values of D, , and n at
the side of the hill (x = 0) were evaluated. Figure A-4 illustrates
the interpretation of several of these parameters.
2.5 Error Estimates
There are several sources of error in the photo analysis method
used in this study. The geometric treatment using the concept of a
"virtual-point camera" is questionable. The cameras were assumed to
be perfectly aligned, and distortion inherent in the photographic
processing was ignored. Numerically, a fit to derived coordinates of
reference points was used to scale and orient digitized points. The
use of a discrete density profile caused some discontinuity—an
infinitesimal change in position at the side wall that moves a ray
across a density interface causes a finite change in position near the
model. The resolution of the digitizer was 0.01 inch, which
translates to 0.2 cm in the towing tank (bottom view).
250
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A measure of the cumulative magnitude of these errors was
obtained in the fitting process and in independent verifications. A
preliminary experiment was conducted to test the feasibility of
measuring plume trajectories in the towing tank. A different model
hill was used. The "Polynomial Hill" was higher (H = 23.4 cm), and
had a greater maximum slope (45°) than the Axisymmetric Cinder Cone
model. This model had several pointers attached which served as
verification marks independent of the reference points. Specific,
identifiable points were used, but the positions were determined
without extrinsic knowledge. That is, the rays from the side and
bottom views were traced to their intersection and not to a known
plane.
The results of this verification test are shown in Figure A-5.
The relatively large discrepancy shown for one pair of points (near
x=0) was due to difficulty in seeing the pointer against the hash mark
in its background. It should be noted that the "measured" coordinates
were partially determined from the photographs. The radial distance
was physically measured, but the azimuthal angle was taken from the
bottom view photograph because of the difficulty in accurately
measuring such angles on the model. The largest error in the radial
distances of the verification marks was 0.23 cm and the remaining
values were less than 0.1 cm. This test was conducted with the model
stationary. A second test in which the model was towed produced
essentially identical results. This indicates that the disturbed
density field did not dramatically alter the apparent positions of
objects for the chosen vantage points.
These tests showed that the stereographic technique had
sufficient resolution to locate fixed, identifiable points on and near
the model. In practice, other sources of error occurred. First, the
centerline of the plume had to be estimated. Except for a few cases
in which the plume remained quite narrow, this was probably the
greatest source of error. In some cases with meandering or looping
plumes, some smoothing was necessary. The plume centerline was drawn
on the photograph with a felt-tipped pen. Then the curve was traced
with a cursor using the digitizer table. In carefully tracing the
curve, it was impossible to keep the crosshairs from wandering about
the line. When many plumes were digitized at a sitting, the
operator's care may have varied. The variability was estimated to be
on the order of the line width (0.03 inch), which translates to 0.6 cm
at the model.
Also, the curves obtained for the side and bottom views were
digitized independently and therefore were made up of different
points. Interpolation and interaction were required to obtain rays
that could be traced to the same (x,y,z) coordinates.
In conclusion, it is believed that plume trajectories were
measured in the towing tank to within one centimeter. The general
behavior of plumes which closely approached the hill surface confirmed
this conclusion; that is, very few of the measured/computed
trajectories were seen to violate the hill surface.
252
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253
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3. EXPERIMENTAL RESULTS
Figure A-6 shows the source locations in the y-z plane used in
the experiments with the axisymmetric Cinder Cone model. Beginning
with tow number 73, two plumes were released simultaneously, and the
two trajectories were identified with suffixes A and B. The
x-coordinate for all the releases was -7.5H. The major parameters
measured are listed in Tables A-l through A-4. In these Tables, all
lengths have been normalized by the hill height of 15.45 cm.
Figure A-7 shows examples of (a) side- and (b) bottom-view
photographs taken during tow number 51 (F = 0.6, ys/H = zs/H =
0.50).
As mentioned earlier, six pairs of photographs were generally
taken during each tow and, depending upon the variability of the plume
path during the tow, two to four pairs were selected for digitization
and analysis. These individual realizations were then averaged
together to obtain the averaged trajectory. Figure A-8 shows a
typical example of the variations in the trajectories obtained from
the digitization of three pairs of photographs; the variation from one
trajectory to the next is observed to be generally well within 0.1H.
The averaging process, however, was clearly inappropriate in a very
few cases where the plume behavior was not steady during the length of
the tow. Figure A-9 shows an example (F = 0.6, zs = 0.5H, ys = 0)
where the release height was only very slightly above the
dividing-streamline height (Hjj = 0.4H). The plume initially
traveled directly up and over the hill, but perhaps due to secondary
(horizontal) flows in the tank, it was later observed to deviate
widely around the side of the hill. Averaging was done in all cases,
however, as averaging was inappropriate in only a very few cases.
Figure A-10 shows the lateral and vertical displacements and
displacement angles for streamers originating on the centerline at
half the hill height under the various stabilities. The lateral
deflections were essentially zero for all stabilities except for F =
0.6 in which, as shown in Figure A-9 and discussed above, the plume
path was not steady. The vertical deflections show a monotonic
increase with increasing F (decreasing stability). Note that because
of the lateral deflection observed at F = 0.6, the maximum height
reached by that streamer was less than the hill height. The
displacement angle changed sign when the streamer descended below its
initial elevation. Note that this happened in the stratified cases,
but not in the neutral case. In the stratified cases, the streamers
254
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255
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260
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(a) Side view.
t f> f • ,^,' %#. ' ••' • ' § s ,-. •
'•*•""" , "ip^tw^""^™ ^|l^;l
(b) Bottom view.
Figure A-7. Examples of photographs digitized to estimate plume
trajectories in three dimensions. Tow 51, F = 0.6,
ys/h = 0.5, zs/h = 0.5. Flow from left to right.
261
-------
1 i i i i -, —-,—rH i i i i I
0 -f
Figure A-8, Typical example of plume variation during a tow.
Tow 80, F = 0.2, zs/h = 1.0, ys/h = 0.75.
262
-------
X
X
rvi
Figure A-9. Example of experiment during which the plume's path
varied markedly and averaging was perhaps inappropriate,
Tow 8, F = 0.6, ys=0, zs = 0.5.
263
-------
o
I
o
,2
1.5 -f
1 -\
.'5 -:
-0.5 -f
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-2
A NEUTfinL
O F = 2.0
O F = 1..0
D F = 0./6
hill radius
at z = H/2.
-'U
-3 -2
-1 ,0
3.5
3
2,5
2
1.5
1
A .NEUTRflL
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O f = l.D
D F = 0..6
CO
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HJ
oc
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a
UJ
_i
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Z
a:
0 T—'—'—'—L-H—'—'—'—'—I—'—'—'—'—| ' ' ' !l | ' ' ' ' | ' ' '
A NCUTRflL
<> F = 2.0
O F - 1.0
r - O.G
Figure A-10.
IX, N'QN-D
Elevations and lateral displacements and displacement angles for
plumes originating at y = 0, z = 0.5h for various stabilities.
264
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obviously "hugged" the hill surface as they swept down the lee side.
In the neutral case, however, separation occurred on the lee side, and
the streamer remained well aloft of the surface.
Figure A-ll shows similar trajectory parameters, but where the
lateral offset of the source was ys/H =1.0. In this, the lateral
deflections increased dramatically with increasing stability, from
0.35H in neutral flow to 1.6H at F = 0.6 (deflections at hill center,
x = 0). Note that the lateral deflections are roughly symmetrical
fore and aft of the hill in neutral flow, but far from symmetrical in
the stable cases. The vertical deflections are obviously inhibited by
the stable stratification; the maximum vertical deflection at F = 0.6
appears to occur at x = -4H and has a value of 0.1H, whereas the
maximum under neutral conditions occurs near x = 0, with a value of
0.7H.
265
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CD
I
CD
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I
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cc
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2
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[
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.5
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ii
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3
2.5
2
1.5
1
,5
0
A NEUTRnL
O F = 2.0
O F = 1.0
D F = 0.6
hill radius
at z = H/2.
-3 -2 -i 0 1
i — i — i — i — I — i— i — i — i — I — i — i — i — i — I — : — i — i — i — I — i — i — i — i — I — i
i — I — i
A hEUTfiflL
O F •= 2.0
O F = 1.0
D F = 0.6
NELITRflL
O I- = P. 0
O F = i.u
] F = U.G
Figure A-ll.
Vertical and lateral displacements and displacement angle for
plumes originating at y = l.Oh, z = 0.5h for various stabilities.
266
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4. MATHEMATICAL MODEL
A method of predicting streamline trajectories for arbitrary hill
shapes is necessary in the application of complex terrain dispersion
models that use the idea of a Gaussian plume following a streamline
(Hunt et al., 1983). One such method is described and evaluated here,
using the data described in Section 3. This method used linear theory
and the Fast Fourier Transform (FFT) technique.
4.1 Description of Model
A linear theory of stratified flow past a three-dimensional,
isolated hill was presented by Crapper (1959). He applied his theory
to an axisymmetric hill which had a known Fourier transform and
obtained an analytic solution for the vertical deflection of
streamlines. Smith (1980) used Crapper' s ideas but made use of modern
computers in performing FFT calculations to determine the
deflections. Both Crapper and Smith were interested primarily in lee
waves. However, the vertical deflections of streamlines applied to
the flow upwind of the hill, as computed with their techniques, are
directly applicable to plume trajectory estimation.
Although Crapper (1959) allowed a vertical shear in the approach
velocity profile, Smith (1980) did not. Since the flow in the EPA
Towing Tank is for a linear stratification and uniform approach
velocity, all calculations presented here were made assuming such
conditions .
The approach outlined by Smith (1980) can be briefly described as
follows. The steady flow of a stratified Boussinesq fluid can be
described by linearized equations of motion for the perturbation
quantities u, v, w, p, p, and n (where dn/dx = w/U, n is the
vertical displacement of a streamline above its far upstream height).
The system of equations can be reduced to a single equation for r\
[32/3x2] v2n + [H2N2/U2] V2 n = 0,
where N2 = -(g/p)(dp/dz) ,
and all lengths have been normalized by the hill height H. By taking
a double Fourier integral (transformed variable indicated by a ^ ) , the
equation becomes
= 0,
267
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with
m2 = [(k2 + a2)/k2] f(H2N2/U2) -k2] .
For constant N2/U2, the solution is
n(k, I, z) = Q(k, a, 0) eimz.
The boundary condition required for solution is n(x, y, 0) = h(x, y)
which gives, through Fourier transform,
ft(k, 1, 0) = n(k, !l).
This boundary condition requires streamlines originating at z = 0 to
follow the hill surface. The computation method then^ consists of
obtaining the FFT of the hill shape, multiplying by e*-™2 for the
height z of interest, and inverting to obtain the streamline
deflections. Smith provides some suggestions for optimizing the
two-dimensional FFT procedure.
A Digital Equipment Corporation POP 11/44 computer was used for
the numerical computations. The largest two-dimensional array
(actually a pair of arrays for the real and imaginary parts) that may
be easily used for calculations with this machine is 128 X 128, and
this array size was used exclusively. The hill was centered at grid
point (64,64) in this array.
To provide a suitable upstream and downstream area for the flow
to adjust, an interval of A = 0.5H was used; that is, the terrain
extended from 31. 5H upstream to 32H downstream of the hill center.
The digitized representation of the hill cross-section can be seen in
Figure A-12.
Each run of the model, corresponding to a prescribed height z
above the datum, produced an array of the amount the streamlines have
been deflected from their far upstream level z0 to arrive at points
(x,y,z). To obtain streamline trajectories from such data would
require making model runs for several z values and performing some
sort of contouring method for various zo values . Under the
assumption that deflections are small, each model run can be
interpreted as corresponding to a given upstream level zo; that is,
n(x,y,z) ~ n(x,y,z0). Linear theory presumes that deflections
are small, so that this interpretation is warranted. Large
differences between the two interpretations indicate the
inapplicability of the theory. Thus, the result of each model run was
used directly even though some of the deflections were not small.
Smith's solution and numerical method were followed closely.
However, the solution of the differential equation in transform space
has a singular point at longitudinal wave number equal to zero. In
the discrete solution, the Fourier coefficients for k = 0 in the
transform array were arbitrarily set to zero to avoid the difficulties
of the singular behavior. This resulted in a shift of the mean
268
-------
heights of the calculated streamlines which were then adjusted to
originate at the correct level; that is, to pass through the locations
of the point sources in the towing tank experiments (7.5H upstream of
the hill center).
In addition, an equation for the transform of lateral deflections
was derived, and lateral deflections were obtained through the inverse
FFT algorithm. Together, the lateral and vertical deflections
provided predictions of three-dimensional trajectories originating
away from the hill centerline.
4.2 Comparison with Experimental Results
The linear theory was derived for small deflections which can be
expected to result from flow over gentle hills. The axisymmetric CCB
model, however, was quite steep (maximum slope of 0.45 or 24.4°).
Also, very stable flow (Fr = U/NH less than 1.0) is known to divide
and pass around the hill at lower elevations. The linear theory
cannot be expected to be applicable to such situations. Two questions
are to be considered for this relatively steep hill: how well do the
calculated streamlines match the streamlines observed in neutral flow
and how does increasing stability affect the results?
Experimental and predicted streamline trajectories for
streamlines originating directly upstream of the hill center for
neutral flow are shown in Figure A-13. There is very good agreement
between the experimental results and predictions for all heights for
the flow upstream and over the hill top. The heights of the
trajectories are underpredicbed in the lee of the hill where flow
separation was observed. The linear theory cannot predict
separation. The vertical deflection of streamlines originating at
lateral offsets of 1H are shown in Figure A-14. The agreement is not
quite as good as was observed for the centerline cases.
The lateral deflections of the streamlines for neutral flow are
shown in Figures A-15 to A-18 for streamlines that originate at
heights of 0.25, 0.50, 0.75, and 1.0 H, respectively. Overall, the
comparisons with most of the experimental observations are very good.
Where there is a discrepancy between calculated and experimental
result, the neighboring cases usually are in good agreement, which
indicates experimental variability rather than inadequacy of the
calculation technique.
Trajectories were also calculated for stable flow with Fr = 1.0.
Comparison with the towing tank results were poor even on centerline
where the calculated streamlines originating as high as 1.0 H
intersected the hill near the top of the lee side. This low Froude
number in combination with the steepness of the hill was clearly
beyond the capabilities of the linear theory approach.
269
-------
X/H FROM HILL CENTER
Figure A-12. The discrete representation of the hill along the x-axis.
A Hs/H = 0.25 o Hs/H = 1.00
a HS/H = 0.50 A HS/H = 1.25
O HS/H = 0.75 calculated trajectory
X/H FROM HILL CENTER
Figure A-13.
Streamline trajectories for neutral flow over the hill
center; ys/H = 0.
— calculated trajectory
X/H rnOM HILL CENTER
Figure A-14.
Streamline trajectories for neutral flow. Vertical
deflection for streamlines originating at offset of
ys/H = 1.0
270
-------
:>1*^^S3?Swx5w» 1 I
[^^^^^^^^^^
1.0-
.0.5.
_Y f r.y.s/H = 0
X/H FROM HILL CENTER
Figure A-15. Streamline trajectories for neutral flow. Lateral
deflection for streamlines originating at HS/H = 0.25.
1 • U
X/H FROM HILL CENTER
Figure A-16. Streamline trajectories for neutral flow. Lateral
deflection for streamlines originating at HS/H = 0.50.
.ys/H = o j
X/H FROM HILL CENTER
Figure A-17. Streamline trajectories for neutral flow. Lateral
deflection for streamlines originating at HS/H = 0.75.
271
-------
4 Q
ya/H= o
X/H FROH HILL CENTER
Figure A-18. Streamline trajectories for neutral flow. Lateral
deflection for streamlines originating at HS/H = 1.0.
X/H FROM HILL CENTER
Figure A-19.
Streamline trajectories for stable flow, Fr = 2.0, over
the hill center, ys/H = 0.
X/H FROH HILL CENTER
Figure A-20.
Streamline trajectories for stable flow, Fr = 2.0.
Vertical deflections for streamlines originating at
offset of ys/H = 1.0.
272
-------
Comparisons are also made at a Froude number of 2.0. The
vertical deflections of streamlines originating directly upstream of
the hill center and at lateral offsets of ys/H =1.0 and 2.0 are
shown in Figures A-19, A-20, and A-21, respectively. The streamline
trajectories for sources on the centerline show quite good agreement
between the predictions and experimental results, at least upwind of
the hill center. However, the comparisons are not as good for
streamlines originating at laterally offset positions. The predicted
vertical deflections are much too large especially for the streamlines
originating at the lower levels. The lateral deflections, Figures
A-22 to A-25, are underpredicted for this stable flow, again,
especially at the lower levels. The experimental results exhibit
substantially more lateral and less vertical deflection than the
predictions.
4.3 Conclusions
Streamline trajectories calculated using a linear theory model
and FFT computations were compared with those obtained in towing tank
experiments for a three-dimensional hill.
The calculated trajectories compared quite well with the
experimental results for neutral flow. Both vertical and lateral
deflections of the flow as it passed the hill showed good agreement
except in the small region to the lee of the hill where the flow
separated in the towing tank experiments. The model does not handle
separation.
However, for stable flow, Fr = 2.0, the linear theory did not
predict the streamline trajectories well except for those on the
centerline that passed directly over the hill. The calculated
streamlines that originated at points offset from the centerline did
not deflect as much in the lateral and deflected more in the vertical
than the experimentally measured trajectories. That is, the model
results correspond to what would be expected for a less stable
situation.
The approximations made in the linear theory approach are most
appropriate for very large Froude numbers. Smith (1980) provided some
estimations of limiting Froude numbers for which this method should be
applicable. He showed that the linear theory will break down as a
result of a collapse of the vertical distribution of density at Froude
numbers near 2.0. The boundary condition used in the analysis
restricts ground-level streamlines to pass over the hill in a direct
downstream direction, that is, with no lateral deflection. This
boundary condition is consistent with the other approximations made
for shallow hills and small deflections. However, it is known that as
the stability of the flow increases, streamlines near the hill surface
experience larger lateral deflections. The failure of the
computations for Froude numbers of 2.0 in matching the experimental
results are consistent with these approximations. The vertical
deflections over the center of the hill where lateral deflections were
small showed good agreement with experimental results. Streamlines
originating at points offset from the center did not match as well.
273
-------
X/H FROM HILL CENTER
Figure A.-2I.
Streamline trajectories for stable flow, Fr = 2.Q.
Vertical deflections for streamlines originating at
offset of ys/H = 2.Q.
X/H FROM HILL CENTER
Figure A.-22. Streamline deflections for stable flow, Fr = 2.Q.
Lateral deflections for streamlines originating at
HS/H = 0.25.
X/H FROM HILL CENTER
Figure A-23. Streamline trajectories for stable flow, Fr = 2.0.
Lateral deflections for streamlines originating at
HS/H = 0.50.
274
-------
mca
1. 0
0.5
0
X/H FHOM HILL CENTER
Figure A-24. Streamline trajectories for stable flow, Fr = 2.0.
Lateral deflections for streamlines originating at
HS/H = 1.0.
ys/H = l.o.
X/H FROM HILL CENTER
Figure A-25.
Streamline trajectories for stable flow, Fr = 2.0.
Lateral deflections for streamlines originating at
HS/H = 1.25.
275
-------
That the linear theory predicted reasonably well in neutral flow
and showed the correct trends with stability is encouraging. Further
tests of the calculation method should be made for less steep hills
under neutral and stable conditions. For a less steep hill, for which
there is no flow separation, the method may be expected to work quite
well for neutral flow. Hopefully, stable flow results would also
improve for hills with less steep slopes. Finally, further
experimental results in the range 2.0 < F < 10 would prove useful in
delineating the range of applicability of the linear theory.
The streamline trajectories obtained for neutral flow over the
axisymmetric CCB hill can be used to predict ground-level
concentrations using a Gaussian plume following the streamline
approach with the results to be compared with available wind tunnel
data.
276
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REFERENCES
Crapper, G.D., 1959. A Three-Dimensional Solution for Waves in the Lee
of Mountains, J. Fluid Mech.. 6_, 51-76.
Hunt, J.C.R., Leibovich, S. and Lumley, J.L., 1983. Prediction Methods
for the Dispersal of Atmospheric Pollutants in Complex Terrain,
Rpt. No. PPRP-78 to Maryland Power Plant Siting Program by Flow
Analysis Associates, Ithaca, NY, 177p.
Hunt, J.C.R., Puttock, J.S. and Snyder, W.H., 1979. Turbulent
Diffusion from a Point Source in Stratified and Neutral Flows
around a Three-Dimensional Hill: Part I: Diffusion Equation
Analysis, Atmos. Envir.. 13. 1227-39.
Hunt, J.C.R. and Snyder, W.H., 1980. Experiments on Stably and
Neutrally Stratified Flow over a Model Three-Dimensional Hill,
J. Fluid Mech.. 96., pt. 4, 671-704.
Smith, R.B., 1980. Linear Theory of Stratified Hydrostatic Flow Past
an Isolated Mountain, Tellus. 32. 348-64.
Synder, W.H. and Hunt, J.C.R., 1984. Turbulent Diffusion from a
Point Source in Stratified and Neutral Flows around a
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