<>EPA
United States
Environmental Protection
Agency
Environmental Sciences Research
Laboratory
Research Triangle Park NC 27711
EPA-600/3-82-036
April 1982
Research and Development
EPA Complex
Terrain Model
Development
First Milestone
Report - 1981
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
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The nine series are:
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4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
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This report has been assigned to the ECOLOGICAL RESEARCH series. This series
describes research on the effects of pollution on humans, plant and animal spe-
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ences. Investigations include formation, transport, and pathway studies to deter-
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This document is available to the public through the National Technical Informa-
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EPA-600/3-82-036
April 1982
EPA Complex Terrain
Model Development
First Milestone Report - 1981
by
T.F. Lavery, A.Bass, D.G. Strimaitis, Venkatram,
B.R. Green, P.J. Drivas,
and
B.A. Egan
Environmental Research & Technology, Inc.
696 Virginia Road
Concord, Massachusetts 01742
Contract No. 68-02-3421
Project Officer
Francis A. Schiermeier
Meterology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U S ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
April 1982
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DISCLAIMER
This report has been reviewed by the Environmental Sciences Research
Laboratory, U.S. Environmental Protection Agency, and approved for
publication. Approval does not signify that the contents necessarily
reflect the views and policies of the U.S. Environmental Protection Agency,
nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
ii
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FOREWORD
The Environmental Sciences Research Laboratory (ESRL) conducts an
intramural and extramural research program 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 quantitate the
relationships between emissions of pollutants from all types of sources and
air quality and atmospheric effects and to uncover and characterize hitherto
unidentified air pollution problems. Information from ESRL 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 project is designed to develop
reliable atmospheric dispersion models that are applicable to large
pollutant sources located in complex terrain. The first major field study
of this five-year program was conducted during 1980 at Cinder Cone Butte
near Boise, Idaho. Data from this field study along with measurements of
scaled physical simulations performed in the EPA Fluid Modeling Facility are
being used to quantify the effects of terrain obstacles on stable plume
dispersion. This interim report presents the performance evaluations of
four existing complex terrain models and describes the initial developmental
stages of two proposed new models.
A. H. Ellison
Acting Director
Environmental Sciences Research Laboratory
111
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ABSTRACT
The U.S. Environmental Protection Agency (EPA) is sponsoring the
Complex Terrain Model Development (CTMD), a multi-year integrated program to
develop and validate practical plume models of known reliability and
accuracy for simulating 1-hour average ground-level concentrations downwind
of elevated sources during stable atmospheric conditions in complex
terrain. The first major component of the CTMP was a field program
conducted during the fall of 1980 at Cinder Cone Butte (CCB), a roughly
axisymmetric, isolated 100-meter hill located in the broad Snake River Basin
near Boise, Idaho. The field program consisted of ten flow visualization
experiments and 18 multi-hour tracer gas experiments conducted during stable
flow conditions.
The data base compiled at CCB includes the following components:
• Source information: emission rates, locations, and heights of
SFg, CF^Br, and oil-fog releases.
• Meteorological information: descriptions of the undisturbed
mesoscale valley flow in the vicinity of CCB as well as
information on flow and dispersion on and over CCB itself.
• Hill surface tracer gas concentrations: data from more than
14,000 individual bag samples collected over the 18 days of
experiments from as many as 80 sampler locations in a given
experiment.
• Lidar data: characterizing the plume trajectory\ and plume spread
upwind and over CCB.
• Photographic data: still photographs taken from fixed locations
on and around CCB, aerial photographs taken from an aircraft
flying overhead, and 16 mm movies and videotapes.
IV
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This report presents an overview of the CCB experiment and the results
of the modeling analyses completed through June 1, 1981. The objectives of
the model analyses are to develop and evaluate new models using the CCB data
base and to compare their performance to the following current complex
terrain dispersion models:
© the EPA Valley model worst-case screening algorithm, widely used
in regulatory practice to screen elevated sources in complex
terrain;
• COMPLEX I and COMPLEX II, two new proposed complex terrain
screening models issued by EPA for public testing and evaluation;
and
9 PFM, a potential flow model for turbulent dispersion of plumes in
the presence of simple terrain features.
For these comparisons, 45 case study hours were selected from the 18 field
experiment days. (The PFM model comparisons were made with about half of
these case study hours.)
Two new modeling approaches suggested by the experimental evidence have
been formulated and tested. One new model (called the Impingement model) is
used to simulate ground-level concentrations in strongly stable flows in
which plumes go horizontally around the side of CCB; another new model
(called the Neutral model) simulates slightly stable or neutral flows in
which plumes rise over CCB. It must be emphasized, though, that these new
models—which thus far represent only a modest level of effort—are
tentative first steps toward the goal of practical, reliable complex terrain
models. They are not the desired end results and are in no way identified
for routine application at this time.
All models were evaluated by comparing 1-hour average observed
concentrations with 1-hour average calculated concentrations. The results
are encouraging: the two preliminary models appear to simulate maximum
concentrations and spatial concentration patterns more realistically than
the current models.
v
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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 26, 1980 to June 1, 1981, and work was completed as of June 1, 1981.
VI
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CONTENTS
Page
_ , 111
Foreword ...
Abstract • 1V
_.,. ix
Figures
Tables • xv
Symbols and Abbreviations • xviii
Acknowledgements XX1
1. Introduction . .
1.1 Overview of Complex Terrain Model Development ... 1
1.2 Basic Concepts of Plume Dispersion in Stable Flows . 6
2. Overview of Complex Terrain Field Study 10
2.1 Geographic and"Meteorological Setting 10
2.2 Fluid Modeling of Expected Flow Regimes 17
2.3 Experimental Design of Field Study ... 23
2.4 Field Study Res.ults 45
3. Quality Assurance Program 70
3.1 Meteorological Data . . ; 71
3.2 Tracer Data • • 95
4. Air Quality Models Evaluated 103
4.1 Introduction • • 103
4.2 Valley Model 104
4.3 COMPLEX I and COMPLEX II Models 1°6
4.4 Potential Flow Model 109
4.5 New Experimental Models 114
5. Model Performance Using Cindor Cone Butte Field Data . . 128
5.1 Case Hours Selected for Model Evaluations 128
5.2 Data Preparation 129
Vii
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CONTENTS (Continued)
Page
5.3 Model Evaluation Methods 132
5.4 Sample Case Study Results - Case 205, Hour 5 .... 145
5.5 Summary of Model Performance 184
6. Conclusions and Recommendations for Further Analysis and
Development 221
6.1 Accomplishments in Overview 221
6.2 Comparative Model Performance Evaluations 224
6.3 Recommendations for Further Research 227
References 236
Appendices
A. Summary of Tracer Data Analyzed for Tests 201-218 . 239
B. Laboratory Simulation of Stable Plume Dispersion
Cinder Cone Butte 249
C. Use of Model Performance Statistics 302
Vlll
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FIGURES
Number
Page
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Schematic of flow around a three-dimensional obstacle at
Aerial view of Cinder Cone Butte from south
Distribution of wind speed and direction for September
1965-1969 derived from weather observations at
Composite estimates of plume paths based on towing tank
simulations: wind direction 110°, Fr = 0.4 ,
Composite estimates of plume paths based on towing tank
simulations: wind direction 300°, Fr = 0.4 ,
Bag sampling and analysis procedures . . ,
9
11
12
13
14
15
16
21
22
25
28
32
34
36
37
IX
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FIGURES
JNumbe
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
r
Procedures to obtain tracer gas concentrations
Number of samples analyzed for each field experiment ....
Observed SFg concentrations (ppt) for Case 206,
0500-0600
Five-minute exposure; camera location 0-15 (Case 206,
0500 MST)
One-minute exposure looking from northeast (Case 206,
0508 MST)
Five-minute exposure; camera location 0-15 (Case 206,
0530 MST)
One-minute exposure looking from North Peak (Case 206,
0540 MST)
Five-minute exposure; camera location 0-11 (Case 206,
0546 MST)
Observed SFg concentrations (ppt) for Case 211,
0400-0500
Observed CF3Br concentrations (ppt) for Case 211,
0400-0500
One-minute exposure from southwest (Case 211, 0414 MST). . .
One-minute exposure from lee side of Cinder Cone Butte
(Case 211, 0435 MST)
Observed CF3Br concentrations (ppt) for Case 210
0200-0300
Observed SF6 concentrations (ppt) for Case 210, 0200-0300.
One-minute exposure looking from South Peak (Case 210,
0209 MST)
One-minute exposure looking from southwest (Case 210,
0535 MST)
Page
38
40
42
44
49
52
54
55
56
57
58
60
61
62
63
65
66
67
68
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FIGURES
Number
35 Observed SFg concentrations (ppt) for Case 205,
0400-0500 69
36 Example of a data file. 92
37 Example of an edited data file • 93
38a PFM geometry for Cinder Cone Butte calculations 112
38b Illustration of the relationship between the tracer release
height and important reference surfaces at CCB 113
39 Geometry used in formulating Impingement model for low
Froude number flows
40 Geometry used in formulating Neutral model for high Froude
number flows
41 Dependence of lidir-derived Oz on downwind distance
for 15 case hours «
42 Relationship between model inputs, single concentration
observations, and the set of possible concentrations
described by model inputs 138
43 Relationship between an observed concentration and estimates
of this concentration from models A and B when these
models accurately simulate the ensemble mean
concentration • • 139
44 Relative performance of different models. . ... 144
45 Observed SFg concentrations for Case 205, 0400-0500 ... 146
46 COMPLEX I: calculated SFg concentrations for Case 205,
Hour 5, Stability Class D . . • 1*8
47 COMPLEX I: calculated SFg concentrations for Case 205,
Hour 5, Stability Class E . 149
48 COMPLEX I: calculated SFg concentrations for Case 205,
Hour 5, Stability Class F ... 150
49 COMPLEX II: calculated SFg concentrations for Case 205,
Hour 5, Stability Class D 151
50 COMPLEX II:. calculated SFg concentrations for Case 205,
Hour 5, Stability Class E 152
xi
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FIGURES
Number
Page
51 COMPLEX II: calculated SFg concentrations for Case 205,
Hour 5, Stability Class F 153
52 COMPLEX I and II: calculated SFg concentrations versus
observed SFg concentrations for Case 205, Hour 5,
Stability Class D 155
53 COMPLEX I and II: calculated SFg concentrations versus
observed SFg concentrations for Case 205, Hour 5,
Stability Class E 156
54 COMPLEX I and II: calculated SFg concentrations versus
observed SFg concentrations for Case 205, Hour 5,
Stability Class F 157
55 PFM: calculated SFg concentrations for Case 205,
Hour 5, Stability Class D 169
56 PFM: calculated SFg concentrations for Case 205,
Hour 5, Stability Class E 170
57 PFM: calculated SFg concentrations versus observed SFg
concentrations for Case 205, Hour 5, Stability Class D. . 172
\
58 PFM: calculated SFg concentrations versus observed SFg
concentrations for Case 205, Hour 5, Stability Class E. . 173
59 Neutral model: calculated SFg concentrations for
Case 205, Hour 5 179
60 Neutral model: calculated SFg concentrations versus
observed SFg concentrations for Case 205, Hour 5. ... 180
61 Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations calculated
by Valley 187
62 Variation of modeled—to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations
calculated by Valley (centerline) 188
63 Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations
calculated by COMPLEX I (Stability Class D) 192
64 Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations
calculated by COMPLEX I (Stability Class E) 193
xii
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FIGURES
Number
65 Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations
calculated by COMPLEX I (Stability Class F) ....... 194
66 Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations
calculated by COMPLEX I (Appropriate Stability Class -
Turner Scheme) .............«•••.••••.•• 195
67 Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations
calculated by COMPLEX II (Stability Class D) ....... 196
68 Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations
calculated by COMPLEX II (Stability Class E) 197
69 Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations
calculated by COMPLEX II (Stability Class F) 198
70 Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations
calculated by COMPLEX II (appropriate stability class -
Turner Scheme) 1"
71 Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations
calculated by PFM (Stability Class D) ...... 202
72 Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations
calculated by PFM (Stability Class E) 203
73 Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations
calculated by the Impingement model 206
74 Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations
calculated by the Neutral model 208
75 Relative performance of mpdels tested with 45 case hours
of data from CCB with model performance based on ratios
of maximum calculated and observed hourly SFg
concentrations 212
76 Relative performance of models tested with 45 case hours
of data from CCB with model performance based on residuals
of maximum calculated and observed concentrations. . . • • 213
xiii
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Number
77
78
79
FIGURES
Relative performance of models tested with 45 case hours
of data from CCB with model performance based on residuals
of calculated and observed hourly SFg concentration
at all samplers* 214
Relative performance of models tested with 23 case hours
(release height > Hcr^t) of data at CCB with model
performance based on ratios of maximum calculated and
observed SF$ concentrations
Relative performance of models tested with 23 case hours
(release height > Hcr£t) of data at CCB with model
performance based on residuals of maximum calculated
and observed SFg concentrations
80
Relative performance of models tested with 23 case hours
(release height > Hcrit) of data at CCB with model
performance based on residuals of calculated and
observed SFg concentrations at all samplers
217
218
219
xiv
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TABLES
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Prevailing Wind Direction and Frequency at Mountain
Home AFB (October 1964-1970)
SFg and CF3Br Release Rates. » •
Sample Analysis Programs Available Onsite.
Summary of Tracer Data Analyzed. ...
Audit Results: Climatronics Temperature System
Audit Results: Climatronics Delta Temperature System. . . •
Audit Results: Climatronics UVW Wind Systems
Audit Results: F460 Wind Speed System
Audit Results: Climatronics F460 Wind Direction
Audit Results: Climatronics F460 Wind Direction
Linearity Test
Audit Results: Orientation of V Propeller Crossarm
Audit Results: F460 Wind Direction Systems Errors
Audit Results: Landmark and North Stake Orientation
18
26
31
46
47
74
75
76
78
79
80
81
82
83
XV
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TABLES
Number
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Classification Criteria and Data Quality Flags for
Hour-Averages Produced from 5-Minute Data . . .
Recount Statistics
Co-Located Sampler Statistics
Sample Degradation Test . . .
TRC Audit Results
Comparison of Oz Derived from Lidar Observations with
Predicted a.
Data Estimated at Source Height for Case Hours Selected
for Model Comparisons
Descriptive Statistics and Associated Analyses.
Frequency Distributions of SFg Concentrations for
COMPLEX I and II Models (Case 205, Hour 5, Stability
Class D). . .
Frequency Distributions of SF6 Concentrations for
COMPLEX I and II Models (Case 205, Hour 5, Stability
Class E)
Frequency Distributions of SFg Concentrations for
COMPLEX I and II Models (Case 205, Hour 5, Stability
Class F)
Observed Versus COMPLEX I Paired Concentrations (Case
205, Hour 5, Stability Class D) <
Observed Versus COMPLEX I Paired Concentrations (Case
205, Hour 5, Stability Class E)
Observed Versus COMPLEX I Paired Concentrations (Case
205, Hour 5, Stability Class F)
Observed Versus COMPLEX II Paired Concentrations (Case
205, Hour 5, Stability Class D) •
Observed Versus COMPLEX II Paired Concentrations (Case
205, Hour 5, Stability Class E)
Observed Versus COMPLEX II Paired Concentrations (Case
205, Hour 5, Stability Class F) . . .
94
97
97
99
100
125
133
136
158
159
160
161
162
163
164
165
166
xvi
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TABLES
Number
32
33
34
35
36
37
38
39
40
41
42
43
44 •
45
46
47
48
Summary Statistics for COMPLEX I and II (Case 205,
Hour 5)
Frequency Distributions of SF6 Concentrations for
PFM (Case 205, Hour 5, Stability Class D) . . .
Frequency Distributions of SFg Concentrations for
PFM (Case 205, Hour 5, Stability Class E) . . .
Observed Versus PFM Paired Concentrations (Case 205,
Hour 5, Stability Class D)
Observed Versus PFM Paired Concentrations (Case 205,
Hour 5, Stability Class E). . .
Summary Statistics for PFM (Case 205, Hour 5)
Frequency Distributions of SF6 Concentrations for
Neutral Model (Case 205, Hour 5)
Observed Versus Neutral Paired Concentrations (Case 205,
Hour 5) • '
Summary Statistics for Neutral Flow Model (Case 205,
Hour 5) '
Summary C/Q Statistics for Valley and Centerline Valley
Calculations •
Summary C/Q Statistics for COMPLEX I Calculations ....
Summary C/Q Statistics for COMPLEX II Calculations. . . .
Summary C/Q Statistics for PFM Calculations
Summary C/Q Statistics for Impingement Model Calculations
Summary C/Q Statistics for Neutral Model Calculations . .
Summary of Analysis of C/Q Residuals - All Case Hours . .
Summary of Analysis of C/Q Residuals for Hours in which
H > Hcr-[t + 5 m . . •
Page
168
174
175
176
177
178
181
182
183
185
189
190
201
204
207
210
216
xvi i
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SYMBOL
LIST OF SYMBOLS AND ABBREVIATIONS
scat
max
d
36/3 z
3p/3z
D , D
y» z
£
Fr
g
h
H
Hcrit
IX, IY, IZ
A
m
g
Horizontal distortion factor
Scattering coefficient
Concentration
Instantaneous concentration
Maximum hourly averaged concentration
Observed concentration
Modeled concentration
Distance of source to receptor
Vertical potential temperature gradient
Vertical density gradient
Ratio of plume spread in complex terrain to plume spread
over flat terrain
Error or residual
Ratio of streamline spacing at the source to that at a
given downwind distance
Hill factor
Froude number
Acceleration caused by gravity
Hill height
Height of the plume centerline above the ground over flat
terrain
Critical dividing streamline height
Turbulence intensities alongwind, crosswind, and vertical
Vertical length scale of turbulence
Geometric mean
xviii
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N
n
r,6,z
w
a
'
ze
u
s
U, u
X
x
x,,
z.
1
Brunt-Vaisala frequency.
Height of plume centerline over a, terrain feature
Fractional height of plume centerline over a terrain
feature
Angle between stagnation streamline and U
Instantaneous angular plume spread
Tracer emission rate
Surface heat flux
CCB polar coordinate system coordinates
Geometric standard deviation
Standard deviation of distribution of model errors or
residuals
Standard deviation of horizontal wind direction
Standard deviation of vertical velocity fluctuations
Standard deviation of crosswind tracer distribution
Crosswind and vertical standard deviations of tracer
concentrations in flat terrain setting
Standard deviation of vertical tracer distribution
Effective total hourly standard deviation of vertical
tracer distribution derived from lidar sections
Integral time scale
Average temperature
Wind speed at source
Uniform wind speed of flow approaching hill
Stream function
Distance downwind from source
Set of known model input variables
Set of unknown variables affecting plume dispersion
Mixed layer height
Plume release height
ABBREVIATIONS
CCB
DBMS
Cinder Cone Butte
Data Base Management System
xix
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EPA
ERT
FMF
GC
MRI
MST
NAWC
NOAA
NRTS
ppb
ppt
PG
PFM
RTD
TRC
WPL
U.S. Environmental Protection Agency
Environmental Research & Technology
Fluid Modeling Facility
Gas chromatograph
Meteorology Research, Inc.
Mountain Standard Time
North American Weather Consultants
National Oceanographic and Atmospheric Administration
National Reactor Testing Station
Parts per billion by volume
Parts per trillion by volume
Pasquill-Gifford
Potential Flow Model
Resistance Thermometric Device
TRC Environmental Consultants, Inc.
Wave Propagation Laboratory
xx
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ACKNOWLEDGMENTS
Many people—far too many, in fact, to acknowledge here individually—
contributed their talents and energies to making a success of the Cinder
Cone Butte (CCB) experiment. We wish to emphasize the extraordinary efforts
of colleagues without whom the experiment would never have flown. First,
our colleagues at ERT and WSSI: Mike Onorato and Bob Ledwith, who both
worked many long days and nights to configure, program, install, and check
out the data base management system; Jim Wallace, who did much of the
scientific software development; Jim Wagner, Robert Lehmann, Paul Shultz,
and Tom Swafford, who labored literally around the clock to install and
check out the tower instrumentation and data communication links; Dan
Godden, who captained the computer command center through many long
experiments; Bob Hatcher, who devoted many weeks to designing, planning, and
supervising the field execution of the CCB experiment; and especially Norm
Ricks, whose mechanical wizardry, resourcefulness, and sheer persistence in
conquering a myriad of mechanical problems was an inspiration to us all. We
also want to thank Tony Curreri and Jack Beebe, who assembled the modeling
system so quickly; and especially Don DiCristofaro, Jonathan Pleim, and Bill
Adamski, who worked long days and nights to do all the model runs and
analyses, accurately and completely, in truly record time.
Next, we can thank but a few of many other colleagues who struggled
with us to carry this off:
9 Tim Spangler and George Taylor of NAWC, our field general and
deputy field general at CCB, who superbly directed the complicated
logistics of the field operations. Their fortitude, energy, and
unfailing patience throughout many difficulties were crucial to
the harmonious operation of the field program.
xxi.
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• Bill Snyder of the EPA Fluid Modeling Facility, the godfather of
the "small hill" experiment, whose many helpful suggestions in
calling the shots during both phases of the field program were
invaluable and whose pyrotechnic and photographic triumphs at CCB
are truly memorable I
• Wynn Eberhard and colleagues from the NOAA Wave Propagation
Laboratory, who labored with us during Phase II to generate the
lidar data base.
• Julian Hunt, for his many useful suggestions for modeling the flow
regimes at CCB.
And finally, our special thanks to Frank Schiermeier and George
Holzworth, whose unflagging enthusiasm, support, and warm encouragement
truly made the difference.
xxii
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SECTION 1
INTRODUCTION
1.1 Overview of Complex Terrain Model Development
At a time of growing national pressure to expedite decisions on the
regulatory acceptability of new energy-development facilities and other
major air pollution sources, it is imperative to improve the air quality
models that play critical roles in decision-making—especially when models
in wide regulatory use are regarded as insufficient by many of the modelers
who use them. In particular, problems of plume transport and dispersion in
complex terrain urgently require more reliable models.
The Valley model (Burt 1977), widely used for such problems, is
recommended for preliminary screening analyses only. The U.S. Environmental
Protection Agency (EPA) does not recognize any current model as generally
reliable for refined source analyses in complex terrain.
Recognizing its special responsibility to encourage the development of
more reliable complex terrain models for regulatory decision making, EPA's
Environmental Sciences Research Laboratory convened an expert technical
workshop in July 1979 to address outstanding problems of dispersion model
development for sources in complex terrain (Hovind et al. 1979). The
workshop's specific objective was to make recommendations to EPA for the
design of an extensive research program to support the development of more
credible models for regulatory applications.
The general consensus of the workshop supported EPA's suggested focus
on stable plume impaction and its multiphased approach to progressive model
refinement:
The Workshop participants agreed in principle that EPA should adopt a
two-phased field program approach, starting with a controlled
experiment on a small, isolated hill of simple geometric setting, and
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then proceeding with a large scale program of increased complexity. It
was also recommended that the model development program follow multiple
phases. The initial effort should be oriented towards improvements in
Gaussian-based models, while the final effort should be aimed towards
new model development incorporating complex flow fields in rough
terrain with either Gaussian-based or "K theory" based models.
Physical modeling 'programs should be an integral part of the above
efforts (Hovind et al. 1979).
Proceeding with the workshop recommendations, EPA undertook the
preliminary conceptual design of such a multi-year integrated program in
which paramount emphasis was placed upon the "production of a useful model
(or models) with demonstrated reliability and prescribed applicability"
(Holzx«>rth 1980). During the field measurements and laboratory experiments
throughout the program, the observational needs of the modelers were to be
foremost in importance. The program was perceived as "an integrated and
highly coordinated effort that involves:
(1) model evaluation/improvement/development,
(2) scaled physical modeling in a fluid modeling laboratory,
(3) field measurements/experiments centered on an isolated, simple
hill, and
(4) field measurements/experiments centered on a full-scale
plant....in terrain with opportunities for plume impaction and
other types of plume-terrain interactions" (Holzworth 1980).
In June 1980 a contract was awarded for this program, called the EPA
Complex Terrain Model Development.* The stated goal of this study is to
*The prime contractor for the study is Environmental Research and
Technology, Inc. (ERT). Its principal subcontractors are Western
Scientific Services, Inc. (WSSI), responsible for fixed meteorological
data (towers, instrumentation and data communication), and North American
Weather Consultants (NAWC), responsible for the experimental field program
(tracer and smoke releases, tracer data collection, photography, mobile
meteorology, and field logistics). In allied activities, the EPA Fluid
Modeling Facility (FMF) has provided laboratory fluid modeling support;
the NOAA Wave Propagation Laboratory has supported the field program with
a manned lidar system; and TRC, Inc. has provided independent data audits.
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develop and validate practical plume models of known reliability and
accuracy in order to simulate 1-hour average* ground-level concentrations
during stable atmospheric conditions in complex terrain downwind of elevated
sources. The models must be reasonably economical and easy to use,
and—most importantly-—their accuracies, limitations, and restrictions must
be well understood.
In accordance with EPA's preliminary planning to meet this goal, this
study comprises field observations and measurements, laboratory fluid
modeling, data archiving and analysis, and model development and
evaluation. The primary field measurement data gathered by the contractor
are supplemented by experiments at the EPA Fluid Modeling Facility (FMF),
and the model development and evaluation tasks are guided by complementary
work at the EPA Meteorology and Assessment Division.
The first major field program was conducted during the fall of 1980 at
Cinder Cone Butte (CCB), a roughly axisymmetric, isolated 100-meter hill
located in the,broad Snake River Basin near Boise, Idaho. The field program
consisted of a preliminary, learning phase followed by a second, intensive
measurement phase.
The first phase (September 16-27, 1980) comprised 10 experiments
(performed mostly at night) to check out and refine the field program and to
gain operational and logistical experience. The objectives of this phase
were: (1) to practice techniques for generating and photographing oil-fog
plumes and (2) to practice procedures for choosing plume release locations,
release heights, and sampler locations on CCB in order to "capture"
different flow regimes or different aspects of plume-hill behavior.
*Short-term ambient air quality standards and increments for S02 and
particulates are expressed as maximum 3—hour or 24—hour averages, but the
ability to estimate 1-hour averages successfully is a necessary first step
toward models for the longer averaging times.
-------
If
The second phase (October 16-November 12, 1980) comprised 18 multihour
experiments conducted in the late evening, night, or early morning hours
during primarily stable flow conditions. The experimental program
concentrated on measurements of ground-level tracer gas (SF6 and CF^r)
concentrations on the butte as well as lidar sections through the plume and
an intensive set of fixed and mobile meteorological measurements and
photographic documentation. Most experiments lasted eight hours with tracer
gas releases during at least five or six hours.
When the project was begun in June 1980, the experimental approach and
methods for such a small hill study appeared promising but were untested.
Looking back, we may conclude that the CCB experiment was largely successful
and fulfilled its basic goal: creating an extensive, well-documented archive
of reliable meteorological, plume trajectory, and tracer concentration data
to illuminate the physics of plume transport and diffusion in the presence
of such a hill under stable nocturnal flow conditions. This unique data
archive will provide—more effectively than any previous data base—an
empirical foundation for developing models of stable plume impingement on
three-dimensional, nearly axisymmetric hills.
The data base compiled at CCB includes the following important
components:
• Source information: emission rates, locations, and heights of
SF,, CFoBr, and oil-fog releases.
• Meteorological information: descriptions of the undisturbed
mesoscale valley flow in the vicinity of CCB as well as
information on flow and dispersion on and over CCB itself.
• Hill surface tracer gas concentrations: data from more than
14,000 individual bag samples collected over the 18 days of
experiments from as many as 80 sampler locations in a given
experiment•
• Lidar data: sections across the plume characterizing the plume
trajectory and plume spread upwind of CCB.
• Photographic data: still photographs taken from fixed locations
on and around CCB, aerial photographs taken from an aircraft
flying overhead, and (occasional) 16 mm movies and videotapes.
-------
The problems that developed during the field program were caused mainly
by insufficient lead time to procure and successfully install all needed
equipment, data communication outages or instrument failures in the
real-time monitoring network, and failures in gas sampler collection or
processing. Immediately after the field program ended, a substantial effort
was undertaken to edit, validate, and assess the reliability of all
meteorological and tracer gas data. Although more remains to be done, the
result to date is an excellent data base for model development.
The major objectives of the model analyses are to develop and evaluate
the performance of new models against the observational data at CCB and to
compare their performance to the following current complex terrain
dispersion models:
e the EPA Valley model worst-case screening algorithm, widely used
in regulatory practice to screen elevated sources in complex
terrain;
« COMPLEX I and COMPLEX II, two new proposed complex terrain
screening models issued by EPA for public testing and evaluation;
and
• PFM, a potential flow model for turbulent dispersion of plumes in
the presence of simple terrain features.
For these comparisons, 45 case study hours were selected from the 18 field
experiment days. (The PFM model comparisons were made with about half of
these case study hours.)
We have begun to formulate and test new modeling approaches suggested
by the experimental evidence studied to date. One new model (called the
Impingement model) is used to simulate grounds-level concentrations in
strongly stable flows in which plumes go horizontally around the side of
CCB; another new model (called the Neutral model) simulates slightly stable
or neutral flows in which plumes rise over CCB. It must be emphasized,
though, that these new models—which thus far represent only a modest level
of effort—are tentative first steps toward the goal of practical, reliable
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complex terrain models. They are not the desired end results and are in no
way identified for routine application at this time.
All models were evaluated by comparing 1-hour average observed
concentrations with 1-hour average predicted concentrations. The
descriptive statistical measures used were chosen according to the
recommendations of a recent American Meteorological Society workshop (Fox
1981). These were supplemented with special statistical measures to
describe the mean and peak concentration ratios that were quite useful for
summarizing comparative model performance.
The early results are encouraging: the two provisional models appear to
simulate maximum concentrations and spatial concentration patterns more
realistically than the screening models. Much of the data base remains to
be analyzed, however. In the future, better model results may be
achieved—when, for example, all of the lidar data collected at CCB have
been analyzed, or the existing photographic and meteorological data archives
have been more fully used, in conjunction with fluid modeling experiments,
to extend the data base for developing and validating complex terrain plume
models.
1.2 Basic Concepts of Plume Dispersion in Stable Flows
Throughout this report, two basic concepts are used to characterize the
flow around a hill—the Froude number and the dividing streamline height.
Important dynamic features of flow around an isolated hill are characterized
by the hill Froude number (Fr), defined by
Fr
U/Nh
(1)
where U is the uniform wind speed of the flow approaching the hill, N is the
Brunt-Vaisala frequency, and h is the height of the hill. The stability of
the flow is described in terms of the Brunt-Vaisala frequency, N, which can
be written as
' 6
-------
N =
(2)
where 36/3z is the stable potential temperature gradient (assumed to be
uniform over the height of the hill), g is the acceleration caused by
gravity, and T is the average temperature.
In physical terms, the hill Froude number is the ratio of the inertia
of the flow to the buoyancy force that suppresses motion in the vertical.
Another physical interpretation of Fr can be obtained by recasting
Equation 1 in terms of the density gradient and squaring both sides:
Fr2 =
PIT
gh2(-3p/8z)
(3)
2
Here, Fr is the ratio of the kinetic energy of the fluid to the potential
energy gained by the fluid as it rises through the stable density gradient
to the top of the hill.
A hill Froude number less than unity implies that a fluid parcel at the
bottom of the hill will not have sufficient kinetic energy to rise to the
top of the hill and thus will be forced to go around it. A hill Froude
number of unity or greater implies that the fluid parcel can rise to the
top. These concepts can be refined by introducing the dividing streamline
height, H . , defined by the following integral formula (Snyder 1980a):
- g
crit
(h-.) (If
(4)
where U is evaluated at z = ^crit and (3p/3z) is the local
density gradient. The left-hand side of Equation 4 is the kinetic
energy of a fluid parcel at this critical height, and the right-hand
side is the potential energy gained by the fluid parcel rising through
the height h-H . . The equality in Equation 4 implies that
-------
is the height at which the fluid has just enough kinetic energy to
ascend the hill. If the wind speed increases with height, fluid
parcels originating below H are forced to either stagnate on the
hill or flow horizontally around it.
For a constant wind and density gradient, Equation 4 reduces to
H
crit
(5)
Note that H . embodies the physics of the hill Froude number, but in a
more flexible manner: it also accounts for nonuniform temperature and
velocity profiles. For Fr+0, Hh, suggesting that most of the flow
goes around the hill. When Fr*!, H • t~*"0, implying that most of the fluid
goes over the hill. Under these conditions, the flow pattern away from the
surface on the windward side of the hill can be modeled to a first
approximation as inviscid potential flow (Hunt et al. 1979).
When Fr is close to zero, the flow around a three-dimensional obstacle
such as CCB is essentially horizontal (Drazin 1961). Plumes embedded in
such a flow field will not be significantly displaced upward as they
disperse around the hill. Hunt et al. (1979) show that, given certain
limiting assumptions, this problem of plume impingement can be reduced to
that of two-dimensional diffusion of a line source around a cylinder. The
axis of the cylinder is parallel to the z-axis, and the cylinder has the
same cross section as the hill at the height of release z . Figure 1
shows plume behavior under such conditions. When the hill Froude number is
greater than unity, the flow (and hence a plume embedded in the flow) will
go over the top of the hill.
-------
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-------
SECTION 2
OVERVIEW OF COMPLEX TERRAIN FIELD STUDY
2.1 Geographic and Meteorological Setting
Cinder Cone Butte, Idaho, the site selected for the flow visualization
and tracer experiments, is an isolated hill in the Snake River Basin,
located about 30 miles south-southeast of Boise and 15 miles northwest of
Mountain Home Air Force Base (AFB) (see Figure 2). This site was selected
for the following reasons: (1) the butte is the dominant terrain feature
for many miles; (2) fairly simple meteorological conditions prevail during
the fall months; (3) the area is easily accessible and has available
electric power and telephone lines; (4) the Bureau of Land Management (which
manages the Bruno Resource Area in which CCB is located) was willing to
grant permission for use of the butte; and (5) the local farmers were
willing to lend or rent their facilities and land for the experiments.
Cinder Cone Butte is a two-peaked, roughly axisymmetrical hill about
100 meters (m) high. Its nearly circular base is about 1 kilometer (km) in
diameter (Figure 3). Figure 4 presents side views of the butte from the
north, northeast, and east; Figures 5 and 6 are aerial views* from the south
and southeast. Typical side slopes of the upper j?art of the butte are about
25°. A road paved with cinder provides access to the peaks. Numerous roads
around the hill provided access for the sampling crews and equipment;
several roads were constructed as part of the project. The butte could be
easily reached from Boise via Interstate 80.
Meteorological measurements taken at Mountain Home AFB provide
information on the wind speed and direction for the fall months. Figure 7
shows two wind roses—one for all stability conditions, the other for stable
conditions only—derived from September weather observations. During stable
*The two figures show elevated and ground-level smoke released on
October 24, 1980 at sunrise.
10
-------
•i "»t J««iKy
t: ?i"'i • 'X ;"'v • #''ifwv3*'^.'
IliSli;: iSSSliSMttttl
\,: -•• /- V. j-; -i-Srvd!.,^
" M:--\-f-1 .'
Figure 2. Topographic map of Cinder Cone Butte region.
11
-------
Elevation in feet above MSL
Contour intervals are 20 feet.
Figure 3. Topography of Cinder Cone Butte.
12
-------
sC^&'^V ^ v'H^f* -*
*-/>"'. - ,*^ «^ \ •-
1*&*•*•* **•• ^ >-
K^s»'S»J.»\ sis.
Cinder Cone Butte looking south
Cinder Cone Butte looking southwest
Cinder Cone Butte looking west
Figure 4. Side views of Cinder Cone Butte.
13
-------
•p
M-l
CD
oa
-------
tn
cd
o
in
o
+J
oa
(D
rt
o
i—I
OS
•H
0)
•H
PL,
15
-------
CO
en
vO
C7>
LO
CD LL,
•P E
co
H.5
O oj
•Si
4->
O -P
0) nj
•H t/)
-d -H
C •(->
rt rt
0
•P -H
•H
-------
conditions, which generally occur at night, the most frequent wind
directions are east, east-southeast, and west-northwest. Table 1 lists the
prevailing wind direction and frequency for every odd hour of the day as
derived from Mountain Home AFB data for October. The data illustrate the
prevailing up-valley flow (approximately 300°) during the day and
down-valley flow (approximately 110°) after midnight. Although the basin
circulation appears to occur regularly, it is quite variable about the most
frequent wind directions, as may be noted from the wind rose. Evidently,
the up-valley flow, most frequently from the west-northwest, can also come
from the northwest or west (even occasionally from the north). The
down-valley flow can come east-southeast and southeast as well as the most
frequent easterly direction shown in the wind rose for stable conditions.
Additional climatological data are available from the National Reactor
Testing Station (NRTS) at Idaho Falls, located about 300 km away in the
Snake River Basin (Yanskey et al. 1966). This information was assumed to be
generally representative of CCB as both sites are in the basin, although the
valley axis is northeast-southwest at NRTS and northwest-southeast at CCB.
The wind and temperature profiles were also assumed to be similar enough for
use in designing the experiments. Vertical temperature profile data suggest
the occurrence of. inversion conditions more than half the time during the
fall, and strong inversions (>3.7°C/100 m) occur approximately 20% of the
time (Yanskey et al. 1966). Typical positive temperature gradients and
light wind speeds suggest that Froude numbers are frequently less than 1.0
and occasionally as low as 0.2. For example, wind speeds at 75 m are less
than 2 meters per second (m/sec) about 20% of the time (Yanskey et al.
1966). If light winds are well correlated with inversion conditions,
Fr < 0.5 should occur about 20% of the time.
2.2 Fluid Modeling of Expected Flow Regimes
During the summer of 1980, three series of towing tank experiments at
. the EPA Fluid Modeling Facility (FMF) were conducted by William Snyder to
provide input to the design of the CCB field experiment. The first series
of experiments was made to assess the perturbations to the mesoscale basin
circulation caused by the presence of CCB. The question specifically
17
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TABLE 1. PREVAILING WIND DIRECTION AND FREQUENCY AT MOUNTAIN HOME AFB
(OCTOBER 1964-1970)
Hour
(MST)
U100
0300
0500
0700
0900
1100
1300
1500
1700
1900
2100
2300
Wind Direction
(degrees)
110
100
100
120
110
120
140
320
310
300
290, 310, 320
300
Average Speed
(knots )
5.4
4.0
4.'9
'3sce«3!«nQ
"*™"/ • y
7.8
10.7
7.5
12.1
10.2
4.8
6.0
6.8
Frequency
(%)
6.5
10.6
14.3
12.0
16.6
13.4
11.1
10.6
14.7
10.6
6.0
6.0
Note: Direction and frequency determined from all weather conditions.
18
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addressed was where to site a 150 m tower relative to CCB so that, given the ,
range of prevailing southeasterly or northwesterly wind directions expected
during strongly stable stratification, the flow fields at the proposed tower
site would not be appreciably perturbed by the hill.
For this series of tows in the FMF stratified towing tank, a model of
CCB was constructed at a scale of 1:1536 (with contours derived from
enlargements of USGS maps) and mounted so as to be easily rotated to change
the wind direction (Snyder I980b). Twenty-six tows were made for varied
Froude numbers and wind directions. Rakes of tubes emitted a dyed solution
for flow visualization. Vertical rakes were used to obtain centerplane
streamline patterns and semiquantitative information on vertical velocity
profiles (with pulsed releases). Horizontal rakes were used to obtain
horizontal streamline patterns at different elevations and information on
the horizontal velocity profiles (again, with pulsed releases). From the
limited number of wind directions (110°, 120°, 300°) and Froude numbers
investigated (Fr = 0.2, 0.4, 0.6) it was estimated that at the proposed
150 m tower site (2 km, 357° relative to hill center), the perturbations in
the flow field were negligible and that the streamline patterns appeared
independent of wind direction except quite close to the hill surface.
A second series of eleven tow tank experiments was made in the FMF
stratified towing tank to (1) guide the design of the smoke and tracer
experiments for the CCB ;field program, (2) preselect possible tracer gas
sampler and camera.locations, and (3) choose different sampling strategies
to account for the variation in wind flows (Bass 1980). The experiments
were run using a second model of CCB constructed to a scale of 1:640 and
contoured at 20-foot (3/8-inch) intervals. As before, rakes of tubes
emitted a dyed solution for flow visualization.
Each tow was filmed from the side with the camera moving with the tow
carriage, and from directly below the tow path with the camera held fixed at
two or three stationary points pointed upward at the (inverted) model hill.
The movie films were viewed with an analyst projector, and the plume
patterns were sketched independently by two analysts who used a plan map of
CCB identical to the model. The two sketches were then reconciled and
smoothed to define the (apparent) envelope of each plume path.
19
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Figures 8 and 9 illustrate the composite estimates of the plume paths
and dispersion for two of the towing tank simulations. Figure 8 illustrates
the simulation for a wind direction of 110°, Fr = 0.4, and releases equal to
0.25, 0.5, 0.75, and 1.25 of the hill height. Similarly, Figure 9
illustrates flows from 300°, Fr = 0.4, and releases equal to 0.125, 0.25,
0.375, 0.5, 0.75, and 1.25 of the hill height. The results corroborate the
suggestions of Hunt and Snyder (1980) that air parcels below H the
crit'
dividing streamline height, tend to impinge upon and pass around the sides
of the hill and that air parcels above_the dividing streamline height tend
to go over the hill. Note in Figure 8 the uphill-downhill extent of the
lowest plume as it impinges in the east "draw" and is swept around the side
of CCB; note also that the plumes emitted at one-half and three-quarters
hill height (h > Hcrit) are carried over the hill crest with negligible
spread before growing on the lee side of the hill.
The qualitative results of the second series of towing tank experiments
are summarized as follows:
• Locally, CCB perturbs the general mesoscale wind flow in the Snake
River Basin.
• A parcel of air below the dividing streamline height may impinge
on the upwind side of the butte if directed along a stagnation
streamline and may tend to flow around the butte.
• A plume released just above H . may produce a maximum
ground-level concentration on the upwind side as it passes over
the top.
• A plume released substantially above H . may occasionally
produce a maximum ground-level .concentration on the lee side of
the hill.
• A parcel of air traveling in a direction off the stagnation
streamline will tend to pass around CCB without significant impact.
The final series of tow tank experiments conducted to guide the field
program design was undertaken to establish more adequately the validity of
the general integral expression for the height of the dividing streamline in
stably stratified flow (see Section 1.2). Twelve tows of the 1:640 scale
20
-------
Figure 8. Composite estimates of plume paths based on towing tank
simulations: wind direction 110°, Fr = 0.4.
21
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270
75, 1.25
wwxfmsmmsxtf
~"-~-. !
t&satiXAfi&SBlRii* i;****<^e*fc;esiwdtt*."j
180
:r^^
Figure 9. Composite estimates of plume paths based on towing tank
simulations: wind direction 300°, Fr = 0.4.
22
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model were made under different combinations of density profiles, towing
speeds, and source heights (Snyder 1980a), with effective Brunt-Vaisala
frequencies (0.86, 0.089 rad sec ) very close to those expected at CCB
under stable nighttime conditions. A vertical rake of three tubes emitted
neutrally buoyant colored dyes. For each set of three source heights, the
general formula (see Equation 4) was integrated numerically using the
measured density profile and towing speed, and the resulting plume path
predictions were compared to the observed plume trajectories.
Overall, the agreement was excellent. The validity of the general
integral formula (Equation 4) for predicting the height of the dividing
streamline as a function of wind speed was demonstrated for a wide range of
stable density profiles. It was therefore recommended that the integral
formula be used as an operational, real-time decision-making tool during the
field study.
2.3 Experimental Design of Field Study
The basic program goal required the measurement of data that, together
with information obtained from fluid modeling experiments and recent
theoretical work, will be used to develop improved mathematical simulations
of plume dispersion and impingement from elevated sources in complex
terrain. The basic experimental design involved: (1) meteorological
measurements, (2) the emission of tracer gases and a visible plume,
(3) quantitative measurements of tracer gas concentrations, and
(4) photographic documentation of plume behavior. The variability of the
wind flow about the most frequent directions of both up-valley and
down-valley flows required that smoke and tracer sources be highly mobile.
The regularity of the basin circulation required sampler placement to
capture the prevailing west-northwest and east-southeast winds.
The expected perturbations of the air flow by the hill implied the
following requirements:
deployment of samplers to capture plume impacts near the
stagnation streamline, as plumes go around the side or up and over
CCB;
23
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• the need for real—time meteorological measurements and feedback in
order to locate the source azimuth and choose a source height
(e.g., release above or below H r-t)5
• meteorological measurements of the unperturbed flow as well as
measurements to characterize dispersion on the hill;
• visible elevated and ground-level plumes to capture qualitatively
the different classes of plume-terrain interaction; and
• sufficient vertical resolution of meteorological measurements to
calculate H .. and Fr.
crit
All of these features were included in the experimental design.
The first field study of the EPA program was conducted at CCB from
September through November 1980. The field study encompassed two distinct
phases. Phase I ran from September 16 to September 27, 1980 and included a
total of 10 experiments. The purpose of this preliminary phase was to gain
experience working at the CCB site and photograph various smoke releases for
flow visualization. Phase II, the major experimental phase, ran from
October 16 to November 12, 1980. Eighteen experiments were run with SF
as a tracer, in addition to the smoke plume releases. In nine of these
experiments, CF_Br was simultaneously used as a tracer gas.
2.3.1 Fixed Meteorological Network
ERT assembled at CCB a meteorological monitoring network to
characterize the unobstructed approach flow and to analyze the wind field as
it encountered the hill. A series of meteorological towers (a 150 m tower
located approximately 2 km north of CCB, and a 30 m tower and four 10 m
towers located on the hill) documented the local meteorology. The locations
of the towers (A, B, C, D, E, and F)* are shown in Figure 10, and the direct
measurements and derived parameters at each tower level are given in Table 2.
*0ne other F460 cup-and-vane wind set was on a 10 m mast adjacent to the
office trailers at Simco Road (ERT Command Post), but its output was
recorded only on strip charts (see Figure 10).
24
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25
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TABLE 2. TOWER INSTRUMENTATION AND MEASURES
Site
Tower A
Level 0 (1 m)
I.i-Vtfl I (2 n)
I.evi-I J (1(1 m)
Instruments*
Pyranomecer
Net radiometer
Triaxiat props
Uup & vane
KTU
Triaxial props
Cup & vaiu*
Itl'U
Ka.sl Iu»aiJ llii-rmiscor
Insolation
Net radiation
U, V, W, IX, tY, 12
UX, VX
T
U, V, W, IX, IY, IZ
UX, VX, U, a',,
4T
T, a.r
Cup & vane UX, VX
KTU AT
Kast bc'ad tlit-rmistor T, 0^
Derived Measures"1"
WS, WD
iSP, DR
WS, WD
SP, UK
T
Love I
Level
Levc 1
1,1-Vf I
Ll'V<;l
J
5
b
7
a
do
(bU
(SO
(100
llj<)
m)
m)
n.)
in)
m)
KT1)
Rl'U
RTD
Triaxial props
RID
KTD
Triaxial props
T
U, V, W, IX, IY, li.
4T
T
U, V, W, IX, IY, IZ
AT
T
U, V, W, IX, IY, IZ
WS ,
f
WS,
T
WS,
WD
WD
WD
SP, DR
r
Towr B
JO m
Towers C, D, E, F
2 a
10 m
Triaxial props
KTU
Triaxial props
Ctip & vane
K'I'D
Triaxial props
Cup tt vane
RID
Triaxial props
RTD
Triaxial props
Cup & vane
RTD
U, V, W, IX, IY, IZ
T
U, V, W, IX, IY, IZ
UX, VX
AT
U, V, W, IX, IY, IZ
UX, VX
AT
U, V, W, IX, IY, IZ
T
U, V, W, IX, IY, IZ
UX, VX
WS, WD
WS, WD
SP, DR
T
WS, WU
SP, DR
T
WS, WD
WS, WD
SP, DR
T
*A11 temperature sensors were mounted in aspirated radiation shields; an RTD is a
Resistance Thermometric Device.
**"Dlrect" measures are those calculated by the data station microprocessors from the
outputs of Che Instrument translators. The turbulence data (IX, IY, IZ, 09,
OT) were calculated for both 5-min and 1-hr data periods. All direct measures
were updated once per minute by the data stations. UX and VX are the westerly and
southerly components of the wind calculated from the cup and vane outputs at the 4 Hz
saapling frequency.
"Derived" measures are those calculated by the data collector computer from the
5-stn averages provided by the data stations. These derived measures comprise 5-min
average values of the measures Indicated as well as 1-hr averages of all direct and
derived measures except the turbulence data, 1-hr averages of which were calculated by
the data stations.
26
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The 150 m tower was instrumented at eight levels to characterize the
approach flow for the experiments. This tower had an unobstructed view of
the wind for almost all wind directions. The 30 m tower, mounted on the
southern peak of CCB, was instrumented at 2, 10, and 30 m. The four 10 m
towers were located in the northeast, southeast, southwest, and northwest
quadrants of the hill, each tower at a height approximately 65 m above the
plain.
2.3.2 Photography Program
A primary objective of the CCB experiment was to document
photographically the behavior of the plume' as it encountered the hill. This
objective was achieved only in part, because most of the experiments were
conducted during hours of darkness, and lighting of the smoke plume was a
problem. During both Phase I and Phase II, several photographic media were
used, including black-and-white as well as color still photographs (35 mm),
motion-picture film (16 mm), and videotape.
Five 35 mm cameras were operated simultaneously during the field
experiments. Locations were chosen on the basis of the climatological data,
the towing tank results, and previous experience with the aid of a
professional photographer. Cameras were operated manually at the desired
exposure. Exposure times at night were generally 3-5 minutes. Each camera
operator was in continuous contact with the lead photographer to synchronize
shots. Figure 11 shows the preselected camera locations.
When lighting allowed, a 16 mm motion picture camera was used in a
time—lapse mode. This camera, operated by a professional photographer, was
generally located at the top of CCB looking toward the plume. The videotape
camera was a valuable management tool, especially during debriefing and
planning sessions, for near—real-time review of visual experimental evidence.
Lighting of the plume proved to be extremely difficult. Under clear
conditions and a full moon, no lighting was required. For other conditions,
a carbon arc lamp was invaluable. The arc lamp was generally placed
approximately 2 miles away so that the light beam and the plume were nearly
perpendicular. The lamp was put in an automatic sweep mode that passed
along the plume at 30—second intervals.
27
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Aerial photographs were taken with a still 35 mm camera from a
single-engine airplane flying as slowly as safety allowed. ASA 400
black-and-white film was normally used at night, and ASA 64 color film was
used when sufficient sunlight was available. The plane flew at a range of
heights between 250 and 1,500 feet above the local basin level.
Light-gathering power at night was increased by a "Starscope" borrowed from
the Army, but the images obtained were not very satisfactory. In the later
experiments, aerial photographs were attempted only when there was
sufficient natural light.
2.3.3 Tracer Release, Sampling, and Analysis
Tracer Release System
Two tracer gases, SF, and CF^Br, were released at different heights
from the boom of a mobile crane. The mobility of the release system
resulted in a high number of successful hours per test (normally six or
seven hours out of eight) in which significant tracer concentrations were
recorded on the hill. In only one experiment (Test 212) were the wind
patterns so variable that it was not possible to align the release system
upwind of the hill.
The SF^ and CF^Br tracer gases were stored in individual compressed
gas cylinders kept at ground level; flexible Tygon tubing, approximately
100 m long, led from the gas cylinders to different release heights on the
crane boom. For the first nine experiments (Cases 201-209), the tracer
release tube was attached to the smoke generator platform at the smoke
release height but from 0.5 m to 1m away, horizontally. For the last nine
experiments (Cases 210-218), the tracer release tube was on a separate
pulley system independent of the smoke generator platform and about 1 m
away, horizontally, from the smoke release. The gas flow was monitored by
separate rotameters on the SFg and CF3Br cylinders, and the weight loss
of each cylinder was monitored by a separate electronic digital scale.
Because of the difficulty in calibrating rotameters with 100 m of
tubing attached, the rotameters were used simply to monitor a constant flow
rate of tracer; the weight loss of the cylinders (as recorded by the digital
29
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scales) was used to determine the emission rate of each tracer. The scales
could be read accurately only to the nearest 0.05 Ib, hoyever, and because
the SF, flow rate was initially as low as 0.06 g/sec (0.5 Ib/hr), the
possible uncertainty in the hourly emission rate determination could be up
to 10%. This problem was alleviated in the later experiments by increasing
the SF flow rate to about 0.18 g/sec (1.5 Ib/hr), thus reducing the
emission rate uncertainty to about 3%. Table 3 presents the average tracer
release rates in each experiment; release rates ranged from 0.06 g/sec to
0.20 g/sec for SF, and from 0.86 g/sec to 0.98 g/sec for CF-jBr.*
Tracer Sampling System
Tracer sampling was accomplished by means of approximately
90 individual battery-operated samplers capable of either 10-minute or
1-hour sequential operation. Each sampler contained 12 individual pumps,
each of which intermittently** filled a Tedlar bag over the time period of
interest. Thus, each sampler could take sequential 1-hour samples over a
12-hour period or sequential 10-minute samples over a 2-hour period.
Normally, 1-liter bags were used for both hourly and 10-minute samples.
Except for samples taken from reflection masts (described below), all
samples were taken at 1 m above ground level.
Figure 12 shows the locations of the 70 fixed samplers and also the
10 movable samplers that were placed on either the northwest or southeast
side of the hill, depending on the prevailing wind direction. Of these
80 samplers, typically 60 were used for 1-hour average samples and 20 were
used for 10-minute average samples. Another 10 samplers were used for
reflection masts, for background ambient air samples, and for co-located
samplers.
*In analysis by electron-capture gas chromatography,,CF3Br is about
20 times less sensitive than SFg.
**For a 1-hour average sample, a pump sampled intermittently for
about 1 second every 15 seconds.
30
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TABLE 3. SF6 AND CF-jBr RELEASE RATES (g/sec)
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
SF6 Average
Release Rate
0.09
0.08
0.08
0.09
0.09
0.06
0.16
0.19
0.16
0.17
0.17
0.16
0.20
0. 17
0.20
0.18
0.16
0. 15
Average
Release Rate
0.97
0.97
0.97
0.96
0.94
0.96
0.96
0.98
0.86
31
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The design of a reflection mast is shown in Figure 13. Air samples
were drawn in from 3 m and 6 m (in addition to the normal 1 m height) and
also at an uphill site equal in elevation to the 6 m height. The purpose of
this sampling strategy was to determine if tracer concentrations would
"reflect" off the surface as predicted by some dispersion models. Four of
these reflection masts were used during Cases 203-218. Normally, the 3 m
height was sampled on only one of the reflection masts; the other masts were
sampled at 6 m and 1 m, in addition to the uphill site-
Background air was sampled during each experiment by at least one
sampler upwind of the tracer release point. At two locations during each
test, an extra sampler was placed next to the normal sampler and set to
sample at the same time. These co-located samplers were used to assess the
variability in the sampling technique; the results from the co-located
samplers are discussed in Section 3.2.
The mechanical reliability of the samplers was relatively poor, with a
typical pump breakdown rate of about 20% during each test. During the
earlier experiments, the mechanical breakdown problems, when combined with
sampler crew mistakes in setting the sampler times, resulted in fairly low
data capture for some of the experiments. However, as the sampler crew
gained experience, the data capture during the later experiments was limited
mainly by mechanical problems.
The design of the sampling system proved to be a good compromise
between total flexibility of the system and personnel endurance. For
example, it was not possible to operate many more 10-minute samplers because
bags had to be manually changed by the sampler crew every two hours for each
10-minute sampler. The utility of the reflection mast system cannot be
properly assessed at present because a more detailed study of the results is
necessary.
Tracer Analysis System
The analysis of the bag samples by electron-capture gas chromatography
was accomplished in the NAWC laboratory in Boise. Six gas chromatographs
were used to analyze for the SFg tracer; however, because of problems in
obtaining adequate column packing material, only one of the chromatographs
33
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could analyze for the CF-Br tracer as well as SFg. The detection limit
of the chromatographs was about 5 parts per trillon (ppt) for SF,. and
about 100 ppt for CF3Br.
A chromatogram showing a good separation of the tracer gases using a
5A molecular sieve column is illustrated in Figure 14. The SF and
CF»Br* elute before the large oxygen peak, with a total analysis time of
about 4 minutes per sample. The SF areas were calculated by an
electronic digital integrator (the area under the peaks is directly
proportional to concentration). With six chromatographs and an average of
4 minutes per sample, a total of 90 samples per hour could be analyzed.
For quality assurance, about 5% of the samples were analyzed twice on
different gas chromatographs. The results of these recounts are discussed
in Section 3.2. Most analyzed bags were then flushed two times with
nitrogen and returned to the field. The exceptions were bags that contained
high tracer concentrations (>1 part per billion (ppb) SF,;
>10 ppb CF Br). These bags were discarded to prevent any possible
contamination caused by tracer desorption from the bag walls. Figure 15
illustrates the flow of procedures followed in bag sampling and analysis.
Calibrations were performed on each gas chromatograph at the start and
finish of each analysis day. Nine calibration gases, ranging from about
10 ppt to 40 ppb SF, and from about 200 ppt to 800 ppb CF^Br, were used
to calibrate each chromatograph in the early experiments. The calibration
points were reduced to seven (10 ppt to 10 ppb SFg) in later experiments
because no SFg tracer concentration greater than 10 ppb was ever detected
in the field studies. A check with one calibration gas (usually
100 ppt SF, ) was performed every four hours on every chromatograph; if
this span check showed a greater than 5% difference from the last
calibration, that chromatograph was completely recalibrated with all of the
calibration gases.
Figure 16 presents the procedures followed to obtain tracer gas
concentrations as a function of time and location. The data sheets from
each field sampler location that contained times and bag numbers were
transferred to the laboratory in Boise along with the bags, and the analysis
*0n the remaining five columns, the CFgBr peak could not be separated from
the oxygen peak.
35
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Field
Samplers
GC Analysis
1
High
Concentrations
Recounts
Bag Flushing
Figure 15. Bag sampling and analysis procedures.
37
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Field
Sampler
Data Sheets
QA
GC Analysis
i
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Raw
Data Entry
Recounts
Computer
}
Concentrations
GC Calibrations
i r
Calibration
Data Entry
Figure 16. Procedures to obtain tracer gas concentrations.
38
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information (date, time, and integrator area) was then written on the same
data sheet. These data were then entered into the ERT data base during the
field study from a console at the Boise laboratory.
Calibration data for each chromatograph were also entered separately
into the ERT data base. At first, a cubic spline interpolation was used to
fit a continuous curve to the calibration points. However, this cubic
spline technique resulted in too many degrees of freedom for some
calibration curves and produced inaccurate results for high concentrations,
as shown in Figure 17. Another function was selected to provide a better
fit to the calibration data:
y = ax (1 - e-b/X),
(6)
where y is the area or peak height and x is the concentration.,. This
function is based on the response of the electron-capture detector.at low
and high concentrations (Maggs et al. 1971) and fits the calibration data
quite well, as shown in Figure 17. Tracer concentrations of SF, and
CF3Br were then calculated by computer from a linear interpolation in time
between the two closest calibrations before and after the analysis time of
each sample.
In view of the huge number of tracer samples and the operation of the
gas chromatographs for 16 hours per day, the tracer analysis system worked
quite well. All samples were analyzed within 48 hours of sample
collection. The main deficiency was that only one chromatograph could
analyze both SF& and CF3Br. The only major instrument problem occurred
during the early experiments when it was difficult to obtain reproducible
results from three of the chromatographs. These chromatographs were
subsequently replaced, and the analysis proceeded quite smoothly
thereafter. The preliminary recount statistics, as discussed in
Section 3.2, showed good reproducibility of the tracer analysis system.
2.3.4 Lidar Measurements
Under funding through an EPA/NOAA Interagency Agreement, the NOAA Wave
Propagation Laboratory (WPL) operated a lidar to measure the back scattering
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of the oil-fog plume. The basic purpose of the lidar measurements was to
determine plume dimensions and to locate the plume centerline before it
reached the hill. A sampling protocol was developed so that WPL took
regularly scheduled measurements at three locations upwind of CCB. The
lidar proved to be also useful for operations management. The WPL crew
frequently provided sketches of the plume (see Figure 18), providing nearly
real-time feedback of plume location.
2.3.5 Other Measurements
To obtain katabatic wind information, cup-and-vane wind sensors and
temperature sensors were arranged at about 1 m above the axis of the east
draw at five locations separated by about 50 m. Three hot-wire anemometers
were located in a vertical array in the draw near the base of the butte.
These instruments were set out to, quantify the flow character as a function
of height on the hill and longitudinal position down the east draw. A field
of orange and white fluorescent streamers was constructed and located across
the bottom of both the east and northwest draws to qualitatively assess the
depth and extent of downhill flows. The cup-and-vane sets and temperature
sensors were connected to a tape recorder and the hot-wire anemometers to a
chart recorder.
To define the plume before it interacted with the hill, nephelometer
measurements of b were taken by instruments suspended from a crane
SO 3. L
that was driven across the plume path. A 10 m tower with three
nephelometers was located near the top of the east draw on CCB. Also, one
nephelometer was located at the top of each peak of the butte and one at
Tower D.
Supplementing the measurements from the six main meteorological towers
were various sounding devices operated by NAWC and WPL (see Figure 10).
NAWC operated a tethersonde from the more upwind of two locations about
1.3 km from the center of the butte. These sites were therefore usually '
within 700 m of the primary release point. An ascent-descent sequence
yielding profiles of temperature, pressure, and wind speed and direction was
normally performed once an hour (or more frequently) to heights at least
200 m above the local terrain.
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When this tethered balloon system was not available because wind speeds
were too high to allow tethersonde operation, the supplementary profiles
were obtained from minisonde flights. (The minisonde profiles were less
frequent than the tethersonde profiles.) Wind profiles were also derived
from pilot balloons (pibals) released approximately once an hour. The pilot
balloon flights were tracked by two theodolites for 10 minutes, if possible,
and the balloons rose at approximately 200 m/min; thus, many of the pibal
profiles extended as high as 2,000 m above the surface. (The azimuth and
elevation angles taken during the balloon flights have not as yet been
transformed by NAWC into heights and wind speed and direction profiles.)
WPL operated its frequency-modulated, continuous-wave (FM/CW) radar
from a point south of the butte as well as two monostatic acoustic radars,
one to the east and one to the west of the butte, to provide information on
the atmospheric boundary layer in the vicinity of the butte. Information
from these instruments has not yet been received by ERT.
2.3.6 Data Base Management
To house the enormous amount of data that was collected, ERT utilized a
Data Base Management System (DBMS) that was designed for efficient handling
of data at all levels of input, validation, reduction, processing, and
archiving. A Data General Nova minicomputer was located on-site to serve as
the prime data collector. This minicomputer provided maintenance
information, automatic calibration support, automatic screening of status
and value, hourly system summary reports, and data communications in
addition to data collection. An on-site hardcopy output printer and three
CRT terminals gave scientists direct access to the meteorological data in
real time. Data were permanently archived as both 5-minute and 1-hour
averages.
Figure 19 illustrates the configuration of the data collector system
and the ERT central data processing system. Measurements taken at the 150 m
tower were initially processed and averaged at a transponding data station,
telemetered to a shelter at the top of CCB, and transmitted to the data
collector. Similarly, meteorological data collected from instruments
located on the butte were first processed at the data stations there and
43
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then transmitted to the data collector located at the field headquarters.
Data were displayed in real time at the data collector for analysis and
operations management purposes. Data were transmitted to the ERT office in
Fort Collins, Colorado, and sent to the ERT central computer in Concord,
Massachusetts, via a dedicated telephone line. A computer terminal was
available at the NAWC Boise laboratory to allow entry of the SF, and
CF-jBr data into the data base. In addition to data analysis efforts at
CCB, meteorological data were analyzed at the ERT central data processing
facilities, and selected analysis results were sent back to the field
headquarters for use during the experiment. Table 4 lists examples of the
analysis programs used during the experiment.
2.4 Field Study Results
2.4.1 Summary of Field Data
When the project began in June 1980, the experimental methods to be
used in the small hill study were untested and unproven. We can now
conclude that the CCB dispersion experiment was successful. Extensive data
sets of meteorological conditions and ground-level tracer gas concentrations
have been assembled which will permit the development of models of plume
interaction with three-dimensional, approximately axisymmetric hills in
stable flows. Problems in the field occurred primarily because of
insufficient lead time, communications failure in the real—time
meteorological monitoring system, and tracer gas sampler failure. However,
the end result is an excellent data base for model development purposes.
A summary of the total number of tracer data samples analyzed for each
case (both 1-hour and 10-minute samples) is presented in Table 5. More
detailed data summaries presenting hour-by-hour data capture for each case
are tabulated in Appendix A. Table 5 shows a total of over 14,000 data
points for the 18 cases, or roughly 800 tracer samples analyzed per case.
Overall, 33% of the samples were 1-hour averages and 67% were 10-minute
averages. Two tracers (SF, and CF-Br) were released at different
D _5
heights in nine of the experiments (Cases 208, 210-211, and 213-218). The
45
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TABLE 4. SAMPLE ANALYSIS PROGRAMS AVAILABLE ONSITE
GRAD
Tabulates local temperature, potential temperature gradient,
gradient Richardson number, Froude number, and square of Brunt-Vaisala
frequency as a function of height for a specified tower and time.
TOWR
Tabulates U, V wind components, mean wind, and wind shear
profiles as a function of height for a specified tower and time.
FDIF
Computes the gradient Richardson number, square of Brunt-Vaisala
frequency, potential temperature gradient, and Froude number in finite
difference form as a function of selected heights for Z;L and Z2
for a specified tower and time.
SURF
Computes the Bulk Richardson number, Monin-Obuhkov length,
surface friction velocity, surface heat flux, and surface temperature
scale as a function of roughness height (ZQ), Z^ and Z2 for a
specified tower and time.
ZJD
Computes the roughness height from data from the 150 m tower for
a specified time. Heights used are 40, 10, and 2 m.
HCRIT
Calculates the dividing streamline height using data collected at
all eight levels of Tower A or from data collected at the other five
(B-F) towers.
46
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TABLE 5. SUMMARY OF TRACER DATA ANALYZED
Case
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
TOTAL
Number of 1-hr
Average Samples
SF6 CFsBr
73
169
79
222
225
228
150
173 64
240
251 109
291 149
86
216 62
233 61
278 64
368 98
339 95
382 74
Number of 10-min
Average Samples
CFBr
4,003
776
292
404
440
507
422
446
469
461
368
471
596
202
352
478
567
693
664
713
8,545
89
81
93
194
341
167
88
169
1,365
Total
365
573
519
729
647
619
841
608
608
920
1,117
288 "
723
966
1,250
1,326
1,186
1,338
14,689
47
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CF,Br data account for only 15% of the total because only one of the six
chromatographs could analyze for CF~Br.
It should be noted that Table 5 presents only the number of samples
that were analyzed. In most experiments, a number of presumably valid
samples were never analyzed because of assumed zero tracer concentrations
(e.g., the plume missed the hill for one or two hours). Figure 20 shows the
total number of samples analyzed for each case. The severe drop in number
for Case 212 was not caused by system failures but rather by a decision to
analyze only a few samples; the variable wind patterns during this
experiment made it impossible to align the release system upwind of the hill.
These are some of the specific achievements of the CCB experiment:
• Demonstration that the small-hill design concepts successfully
generated new knowledge of stable plume dispersion around an
isolated, three-dimensional, roughly axisymmetric hill.
• Assembly of a meteorological data base that adequately
characterizes the wind and temperature fields around CCB.
• Assembly of a SF and CF Br tracer concentration data base
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that will assist in the development of sound models of stable
plume impact on elevated terrain.
• Design, implementation, and operation of a data base management
system that generated useful real-time feedback for field
operations management and that subsequently will allow users to
combine the source, meteorological, and tracer concentration data
in a variety of useful formats to aid in developing models.
• Demonstration of the utility of a photographic record of plume
behavior in understanding the physics of flows.
• Corroboration of the utility of fluid modeling experiments in
understanding flows and dispersion in complex terrain and in
designing the CCB experiment.
• Demonstration of the utility of the lidar measurements—both in
managing operations and in providing information on plume behavior
upwind of CCB.
48
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• Confirmation in part that the concept of a dividing streamline
usefully describes flows around isolated, three-dimensional hills.*
Because we have not yet examined the nephelometer data, FM/CW radar
measurements, sampling mast SF, data, acoustic sounder data, and katabatic
wind measurements,** we cannot assess their usefulness for model development
at this time. Most of the 35 mm pictures (especially the nighttime aerial
photographs) provided little information and the formal fixed-location
photography program was too inflexible from a scientific viewpoint. Many of
the most valuable pictures were taken from arbitrary vantage points by
interested scientists free to change viewing position in order to best
capture the plume dynamics.
2.4.2 Example Results from Specific Experiments
To illustrate some of the experimental results, the remainder of this
section will describe four case study hours:
Case 206 (10/24/80)
Case 211 (10/31/80)
Case 210 (10/30/80)
Case 205 (10/23/80)
0500-0600
0400-0500
0200-0300
0400-0500
Case 206 represents a situation in which the plume remained basically
horizontal but quite unsteady throughout the hour. Case 211 illustrates an
*During the field experiments Hcrit appeared to distinguish instantaneous
plume behavior reasonably well for averaging times short enough that •
Hcrit remained approximately constant; however, fluctuations primarily
in wind speed rendered the 1-hour average Hcr£t value less useful in
determining hourly-averaged maximum ground-level concentrations.
**Much of the information was lost when the katabatic wind sensors,
recorders, and tapes were stolen near the end of the experiment.
+A11 times are in Mountain Standard Time (MST).
50
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experiment with the emission of both SF. and CF0Br. The smoke and
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CF3Br were released at an elevation above the dividing streamline height;
SFg was emitted below it. Case 210 is an example of a situation in which
the higher concentrations occurred on the lee side of CCB. Case 205 is the
hour used to illustrate the model evaluations described in the next two
sections.
Case 206 (0500-0600)
The morning of October 24, 1980 exemplifies a situation with light
east-southeasterly (126°) drainage winds down the Snake River Basin. The
source crane was located about 595 m from the hill center at an orientation
of 123.5°. The hourly average wind direction and speed (estimated for the
source height) were 126° and 2.0 m/sec, respectively. The SF^ was
6
released 35 m above the local ground elevation. H . was estimated as
crit
40 m. On the average, therefore, the SFg was emitted at a level slightly
below the dividing streamline height, suggesting flow around and toward the
north side of CCB during most of the hour (the average wind direction being
more southerly than the source orientation).
Figure 21 shows the observed SFg concentrations for the hour 0500 -
0600. All concentration labels are placed so that the lower left-hand
corner of the right-most digit lies at the sample location. Height contours
are presented at 10 m intervals, beginning with the 5 m height contour. The
zero height coincides with 945 m (3,100 ft) above sea level. The grid marks
radial distance increments of 100 m and angular increments of 22.5°. (The
numbers in parentheses represent averages of 10-minute average
concentrations; the number of 10-minute averages used to construct the value
is the subscript listed at the right. All other values in the figure are
hourly average concentrations.*)
Hcrit values calculated from the archived 5-minute meteorological
data range from 29 m to 45 m. Local Fr (calculated at 35 m) ranged from 0.3
to 0.8, and the wind direction varied from 81° to 157°. Most of the plume
*Subscripts greater than 6 indicate sampling mast results, which are
averaged over all heights sampled (1, 3, and 6m). A subscript of 2 can
also indicate two co-located, hourly averaged samples.
51
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CASE 206 HR 6 SF6
Figure 21. Observed SFg concentrations (ppt) for Case 206, 0500-0600.
Source: r = 595 m, 6 = 123.5°, relative height = 29.5 ra,
Q = 0.06 g/sec.
52
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material could be expected to be transported toward or along the north side
of the butte, at elevations close to the release height. With the changing
Hcrit an<* w:i-n^ direction, some SF, could be transported through the draw
and up the north peak. The hill concentration pattern confirms the
transport pattern suggested by the meteorological observations. The higher
concentrations (879, 957, and 687 ppt) were measured north of the mean
incident wind trajectory at contour heights of between 30 m and 45 m. (Note
that a contour height of zero lies approximately 5 m above the local terrain
at the release location.) High concentrations were also measured further up
in the draw (730 ppt) and on the north peak (606 and 438 ppt), and also
towards the base of the draw (1,248 ppt).
Figure 22 is a photograph (5-minute exposure) of the plume taken from
the north peak (camera location 0-15) at 0505. The photograph shows the
plume bending toward the north and staying at an elevation below the top of
the butte. Figure 23, a photograph (1-minute exposure) of the experimental
setting taken from the northeast three minutes later (0508), shows a
continuous plume going up the north peak and some plume material going
around the north side (indicative of the observed concentration pattern).
Two photographs, Figures 24 and 25, taken near the middle of the hour—at
0530 and 0540—from the north peak, show the initial plume trajectory toward
the butte with subsequent deflection toward the north side. These two
photographs suggest substantial crosswind plume diffusion and indicate that
the plume path stayed below the top of CCB. Figure 26, shot from the
southeast (camera location 0-11) at 0546, shows plume material moving up the
draw toward the north peak (but below its top) and around to the north.
Case 206 is a good example of plume transport and diffusion when the
release height is near or below the dividing streamline height during most
of the hour. Most plume material went toward and around the north side of
the butte, although the plume path varied with changes in meteorological
conditions.
Case 211 (0400-0500)
Halloween morning 1980 also experienced an east-southeasterly (119°)
drainage flow. During the experiment the source crane was located about
1,156 m from the hill center at an orientation of 120.5°. SF, was
6
53
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released at a local height of 20 m; smoke and CF«Br were released at
58 m. The average dividing streamline height was 28 m. The Tower A wind
direction near the height of the SF, source varied from 88° to 165°
(5-minute averages) during the hour; the direction near the height of the
smoke plume was steadier, ranging from 115° to. 142°.
Figures 27 and 28 show plots of the SF and CF.,Br concentration,
respectively. The low-level release is below Hcrit and the resulting
SF, plume spread all over the hill, with the maximum hourly concentration
(2,936 ppt) above the relative release height (i.e., approximately 30 m
elevation on CCB compared with a release height of 11 m relative to the 0 m
elevation contour). High concentrations were measured throughout an area
generally between the 15 m and 35 m contour lines extending from the
measured value of 2,936 ppt to values around 1,300 ppt on the northeast
slope. SF, concentrations above 1,000 ppt were measured in the draw on
both the windward and lee sides of CCB. The smoke and CF^Br plume are
transported over the hill, producing essentially zero CF^Br concentrations
on the hill surface. (The two nonzero values are near the detectable limit
of CF Br.)
Figure 29 shows a photograph of the smoke plume looking from the
southwest of 0414. The plume apparently goes up and over CCB with virtually
no ground-level impact. As shown in Figure 30 (0435), the plume stays
elevated as it is transported over the lee side of CCB.
Case 211 is a good example of plume transport and diffusion when the
SF, was released below the average dividing streamline height. The SF
plume apparently impinged on the hill at levels near and 10-20 m above the
relative release height and subsequently spread over and around the hill.
The case also shows the difference between releases below and above the
dividing streamline. SF released below H produced significant
ground-level concentrations almost everywhere on CCB whereas the CF^Br
plume, which was emitted well above H , went up and over the hill and
produced virtually no ground-level concentrations.
59
-------
CftSE 211 HR S SF6
Figure 27. Observed SF6 concentrations (ppt) for Case 211, 0400-0500.
Source: r = 1156 m, 9 = 120.5°, relative height = 11.1 m,
Q = 0.18 g/sec.
60
-------
CASE 811 HR 5 CF3BR
Figure 28. Observed CF3Br concentrations (ppt) for Case 211, 0400-0500.
Source: r = 1156 m, Q = 120.5°, relative height = 49.1 m,
Q = 1.02 g/sec.
61
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Case 210 (0200-0300)
Both SF, and CF0Br were emitted during this period of stable
o J
easterly down-valley winds. The SF, and oil-fog were released at 57 m;
CFoBr was emitted at 30 m above the surface. The release crane
orientation was 114° with an average wind direction of 110° at 5.5 m/sec
(estimated for the SF, release height). The wind measured at the 40 m
level of Tower A varied from 82° to 132°. The average Hcrifc was 30 m.
As expected, the CF-Br was transported around the sides (principally
the north side) of CCB (see Figure 31), and the SF& generally went up and
over the hill (see Figure 32). Evidently there was sufficient turbulence in
the lee of CCB to diffuse the SF, to ground level, thereby producing the
highest concentrations on the northwest lee side. Figure 33 shows the plume
going up and over the north peak at 0209. Figure 34, which was taken later
in the experiment at 0535, illustrates a plume trajectory typical of
Case 210.
Case 205 (0400-0500)
This case is presented because it was used to illustrate the model
evaluation techniques in Sections 4 and 5. It is representative of a
near-neutral, east-southeast (118°) flow with a wind speed of 6.0 m/sec at
the SF, local release height of 50 m. The release crane was located at an
orientation of 120.5° at a distance of 1,156 m from the center of CCB.
Figure 35 presents the sampled ground-level SF^ concentrations.
Values are relatively low; the maximum occurs well below the relative height
of the release (41 m). The observed variability of wind direction and
concentrations suggest that the plume covers almost the entire hill during
the hour.
64
-------
• 9
CASE 210 HR 3 CF3BR
Figure 31. Observed CF3Br concentrations (ppt) for Case 210, 0200-0300
Source: r = 1085 m, 6 = 114.0°, relative height = 22 8 m
Q = 0.95 g/sec. '
65
-------
CASE 210 HR 3 SF6
Figure 32. Observed SFe concentrations (ppt) for Case 210, 0200-0300.
Source: r = 1085 m, 9 = 114.0°, relative height = 49.8 m,
Q = 0.16 g/sec.
66
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CASE 205 HR 5 SF6
Figure 35. Observed SF6 concentrations (ppt) for Case 205, 0400-0500.
Source: r = 1156 m, 6 = 120.5°, relative height = 41.1 m,
Q = 0.09 g/sec.
69
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SECTION 3
QUALITY ASSURANCE PROGRAM
A comprehensive program plan provided quality assurance procedures
relating to all aspects of the meteorological and tracer measurements taken
during the field experiments. This section presents a summary of the
procedures followed during the field study, external audits, data validation
procedures, and a preliminary estimate of data quality.
All meteorological instrument calibration data have not yet been
received from WSSI, nor have the preformance experiments been performed with
sample wind instruments in a wind tunnel. Similarly, the results of some of
the tests and experiments relating to tracer gas measurements have not yet
been received by ERT from NAWC. These missing data and experiments include
the following:
• sample degradation with time in the Tedlar sample bags after the
bags were filled with known gases from the calibration cylinders
(some data on sample degradation of actual experimental samples,
however, are reported here);
• performance tests of the sequential bag samplers in an
environmental chamber prior to the tracer experiments;
• experiments with flushing the sample bags with nitrogen to clean
them of tracer gas in order to establish an effective procedure
for cleaning the bags for reuse in the field experiments; and
• chromatograms from bags exposed to large dosages of particulates
from orange smoke candles and smoke generators.
A final quality assurance program report will be produced when the full
complement of inputs has been assembled and analyzed.
70
-------
In general, the meteorological data are of excellent quality. Problems
with UVW propeller transmitters seizing, propellers breaking, and
communications failure between the data collector and the data stations
resulted in a loss of about 18% to 20% of real-time meteorological data
during the experiments. (Final data-capture statistics are not yet
available.) This estimate of data loss is by measure, not by instrument;
the failure of one U or V propeller transmitter results in the loss of all
six of the measures that use its input. Pibal, tethersonde, and minisonde
data may be used to fill in gaps in the definition of the flow approaching
the hill, should a measurement from Tower A be missing or intermediate
measurements be required.
The audit of the gas chromatographs by TRC indicates excellent accuracy
of the tracer data. All gas chromatograph responses were within +8% of the
designated concentrations specified by the supplier of the audit gases.
Nineteen of the 25 gas chromatograph audit points were within the +5%
accuracy range of concentrations specified by the supplier for the audit
cylinders.
Preliminary precision information of the tracer measurements is
presented in Section 3.2. In general, the precision statistics were very
good for both the SF and CF^Br tracers.
3.1 Meteorological Data
3.1.1 Quality Assurance of Meteorological Data
The basic quality assurance program for meteorological data comprised
the following procedures with appropriate documentation:
* performance and calibration checks of the DS-00 microprocessor
data stations prior to start-up;
a mechanical checks and calibrations of all instruments at
installation and before the tracer experiments;
e calibration checks (and, if necessary, recalibrations) of
replacement instruments during the course of the field, program;
71
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• two independent audits of instrument accuracy and data system
performance;
• calibration checks at system takedown; and
• real-time automated screening by the data collector computer for
values out of range.
Although all of these procedures were implemented, some of the documentation
has not yet been received by ERT.
The major quality assurance problems with the meteorological data were
the result of unforeseen difficulties with equipment. The triaxial
propeller (UVW) sensors, of which 48 were deployed in the network,
occasionally became unresponsive. Sometimes they would stop turning almost
completely, in x^hich case the fault was easy to identify. More frequently,
however, the failure was more subtle—a slight "stiffening" of the
instrument. This could be identified only by the low ratio of crosswind
intensity of turbulence (IY) to downwind intensity of turbulence (IX) if a U
or V transmitter failed, or by changes in the relative values of U or V
components with respect to an adjacent cup-and-vane wind set in similar flow
conditions but separated by one hour or more. When a U or V propeller
failed, it affected the values of WS, WD, IX, IY, and IZ.* If a W propeller
failed, it affected only IZ. The data have been flagged accordingly.
The second piece of equipment that failed to perform well was the
unshielded cable used for transmission of data between the shelters (located
on the butte and at Tower A) and the data collector computer (in the
operations trailer at Simco Road). Although ERT had specified shielded
cable for this purpose, it could not be obtained from vendors in time for
system start-up. These failures necessitated an unplanned requirement for
detailed value-by-value examination of the measurements taken during the
experiments.
*Measure codes are listed in Table 2; hourly average measures have the
same code as the 5-minute measures with a "1" suffix added.
72
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3.1.2 External Audits
Two independent audits of the real-time meteorological instruments and
data system were performed during the first week of November 1980. TRC,
under contract to ERT, audited the wind and temperature systems at every
level of the six towers using conventional techniques including Haake
temperature baths and synchronous motors. Meteorology Research, Inc.
(MRI), represented by Thomas J. Lockhart and under contract to EPA, audited
an easily accessible subset of temperature and UVW propellor systems using
techniques devised by Mr. Lockhart. TRC audited the instruments'
performance by checking the voltage output of the translator cards. The
calibration of the data stations was audited separately by imposing a
fixed, constant voltage on the inputs to the microprocessors for 10 minutes
or more and checking the 5-minute averages archived in the data system
against the measure values corresponding to the voltage applied. MRI's
audit checked the 5-minute averages received by the data collector directly
against the audit values. Cup-and-vane wind sets (Climatronics F460) and
the orientation of the wind instruments were checked only by TRC.
The results of the audits are shown in Tables 6 through 14. The data
for the temperature systems (Table 6) indicate that the errors found in
TRC's audit are often of opposite sign from those found in MRI's audit.
The largest error found by MRI, +0.40°C (at 2 m on Tower B near the ice
point), corresponds to -0.15°C in TRC's audit. Conversely, the largest
error found by TRC in a system also audited by MRI was -0.16°C (near the
ice point at 2 m on Tower A), for which MRI reported an error of +0.12°C.
The TRC audit results of the nine resistance thermometric device (RTD)
temperature systems indicate that the maximum measurement error was 0.20°C
in magnitude. The errors at six of the 18 audit points lay within the
resolution of the data system. The problem with the auditing of the
fast-response bead thermistors at 10 m and 150 m on Tower A has been traced
to an error in the color-coding of the wiring diagram supplied by
Climatronics. This error was corrected in the actual wiring of the sensors
but not on the diagrams in the system documentation left in the shelter.
Consequently, the wrong wires were jumpered during the audit. This error
73
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TABLE 6. AUDIT RESULTS: CLIMATRONICS TEMPERATURE SYSTEM
A
A
A
Level
(meters)
20
60
100
10
150
Audit Temp.
Error
Response-Audit
TRC
29.39
0.38
29.39
0.38
29.39
0.38
29.39
0.38
29.39
0.38
29.39
0.38
MR!
32.54
0.65
15.89
32.54
0.65
15.89
TRC
0.08
-0.16
0.10
-0.12
0.13
-0.11
0.10
-0.11
-8.75*
-8.59*
-8.64*
-8.49*
MRI
-0.08
0.12
0.04
0.09
-0.14
0.10
B
30.06
-0.01
35.41
1.16
19.68
0.07
-0.15
-0.16
0.40
0.02
30.06
-0.01
0.05
-0.15
D
30.06
0.02
0.07
-0.13
30.06
-0.01
33.15
3.20
18.60
0.07
-0.13
-0.14
0.00
0.04
30.06
0.02
0.20
-0.07
*The fast-response bead thermistors were audited incorrectly because
of an error in the manufacturer's wiring diagram that had been
corrected in the instruments' wiring but not in the diagrams kept in
the shelter at Tower A.
74
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TABLE 7. AUDIT RESULTS: CLIMATRONICS DELTA TEMPERATURE SYSTEM
Tower
A
A
Level
(meters)
10
40
Bath Temp.
Error
Response-Audit
(bc)
TRC
29.4
0.4
29.4
0.4
MRI
32.54
0.65
15.89
0.00
0.65
15.89
TRC
0.032
0.024
0.032
0.012
MRI
0.08
0.16
0.06
. 0.00
-0.09
0.06
A
80
150
10
30
10
10
10
29.4
0.4
29.4
0.4
29.6 35.41
-0.01 1.16
19.68
29.6
-0.01
29.6
-0.01
29.6
0.02
29.6 33.15
-0.01 3.20
18.60
Not working
0.092
0.076
0.044 -0
0.000 0
0
-0.044
-0.008
-0.012
-0.004
0.048
-0.012
. -0.084 -0
-0.080 0
0
-
.02
.32
.00
-
-
-
.13
.06
.06
10
29.6
0.02
-0.056
-0.120
75
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TABLE 9. AUDIT RESULTS: F460 WIND SPEED SYSTEM
Tower
Level
(meters)
Audit Speed
(m/sec)
Error
Respons e-Aud i t
(m/sec)
2
LO
150
8,6-9
8.69
8.69
0.16
0.16
0.15
B
10
30
8.69
8.69
0.15
0.26
10
8.69
-0.16
10
8.69
-0.14
10
8.69
-0.13
F
10
8.69
-0.15
78
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79
-------
TABLE 11. AUDIT RESULTS: CLIMATRONICS F460 WIND DIRECTION LINEARITY TEST
Tower
Level
(meters)
Audit
Direction
(degrees)
356
86
176
266
Response
(degrees)
356
85
177
266
Error
Response-Audit
(degrees)
0
-1
1
0
10
357
87
177
267
357
87
179
268
0
0
2
1
150
359
89
179
269
359
88
179
270
10
356
86
176
266
356
88
178
266
0
2
2
0
30
359
89
179
269
359
90
180
270
C.
10
349
79
169
259
349
82
170
260
0
3
1
1
10
360
90
180
270
360
90
182
271
0
0
2
1
10
359
89
179
269
359
91
182
270
10
364
94'
184
274
364
93
184
272
80
-------
TABLE 12. AUDIT RESULTS: ORIENTATION OF V PROPELLOR CROSSARM
Tower
Level
Error Relative to True North
2
10
30
80
150
1°42' West
2°47' East
2°47' East
8°14' East
6°47' East
2
10
30
2°54' East
1°28' East
2°54! East
2
10
1°58' East
2°22' East
D
2
10
56' East
14' East
E
2
10
12' West
19' East
2
10
1°56' East
1°56' East
81
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TABLE 14. AUDIT RESULTS: LANDMARK AND NORTH
STAKE ORIENTATION ERRORS
Landmark Orientation Errors
Tower
A
A
B
C
D
E
F
Audit Audit ERT
Landmark Measurement Measurement
Tower B 177°3' 177°
Tower C 173°22' 173°24'
Tower A 358°46' 357°
Tower A 353°50' 353°24'
None done
Center of Butte^ 279°43' 279°48'
Tower A, 18' 1°
NORTH STAKE ORIENTATION ERRORS
Tower North Stake Error
Error
-3'
2'
-!•«••
-26'
5'
42'
2°43!
1°36'
47'
D
83
-------
was discovered and duplicated by WSSI technicians after the instruments had
been returned to Fort Collins. When properly wired and audited, the bead
thermistors gave satisfactory responses. Because these probes were used
only to calculate cr , however, their actual accuracy is not of primary
concern.
The results of the auditing of the RTD AT systems are shown in
Table 7. (TRC reported the 80 m AT to be "not functioning," but the data
from Case 213, which began at midnight after the audit, show the 80 m AT
do be working satisfactorily. In any case, there are no audit data for
this instrument.) Twelve of the 18 good audits points taken by TRC on the
AT systems lay, within the performance goal of 0.05°C; ten of the points
lay within the PSD guideline criterion of 0.003°C error per meter of
vertical separation; and 14 of the points lay within the union of the two
goals, that is, the larger of 0.05°C or 0.003°C/m. The only points outside
this criterion were the 2-to-10 m AT'S on Towers E and F.
Again, the TRC results were not generally duplicated by the MRI
audit. Eight AT audit points, two on each of four different systems,
were done at comparable temperatures by both MRI and TRC. Of these, three
of MRI's results showed errors of opposite sign to those in the TRC
results, one showed no error where TRC had found one, and the largest error
(4O.32°C) found by MRI corresponds to an error-free point in TRC's audit.
TRC audited the 48 Climatronics UVW propellers by coupling the
propeller shafts to a synchronous motor running at 1,800 rpm (equivalent to
8.81 m/sec wind speed), checking the voltage response of the translator
cards, and converting it to meters per second. The propellers were spun in
both positive and negative directions. The voltage output of the systems
was also checked x?hen the shafts were held stationary. The UVW audit data
are shown in Table 8. An accurate but intermittent response was measured
from the 150 m U component when it was spun in the negative (easterly)
direction. Large negative errors were found in the V and W components at
2 m on Tower E when spun in the positive directions (southerly and upward,
respectively); these errors were -0.62 m/sec for V and -5.72 m/sec for W.
Other than these anomalous readings, the largest error for any of the
propeller instruments was 0.19 m/sec at Tower C's 2 m V component when spun
negatively.
84
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According to Climatronics' technical staff, the calibration of a W€-ll
propeller sensor and translator is practically linear from the bottom of
the signal range at maximum negative speed (-25 m/sec or 0 volts) across
the zero speed point (2.5 volts) to maximum positive speed (+25 m/sec or
5 volts.) Consequently, if a large error occurs at a positive speed of
8.8 m/sec and a small error at a negative speed of -8.8 m/sec, there should
be a substantial error near zero approximately equal to the mean of the
errors at +8.8 and -8.8 m/sec. This was not the case for the audit data
from the V and W transmitters at 2 m on Tower E. Furthermore, an error of
-5.72 m/sec such as that indicated by TRC for the 2 m W prop on Tower E
would be apparent in the data collected as either strongly negative W's or
very large IZ's when the propeller changed its direction of rotation.
Neither of these discrepancies appears in the data, however.
MRI examined a small sample of the UVW instruments at the 2 and 10 m
levels of Towers A and B and the 2 and 10 m levels of Tower E, which ERT's
quality assurance officer requested that MRI examine after TRC's anomalous
results. MRI spun the propellor shafts with a small motor that gave a low
equivalent wind speed of about 0.15 m/sec, which is close to the instrument
threshold. The MRI audit did not find the anomaly in the 2 m W component
of Tower E when it was spun in the negative direction, the error being
+0.04 m/sec at an imposed speed of -0.15 m/sec, but it did turn up an even
more extreme anomaly of -15.51 m/sec in the V component when it Was spun at
-0.16 m/sec. This error was due to a communication problem in which the
request for this measure value from the data collector was received by the
data station DS-00 as requested for the along-wind intensity of turbulence,
which was returned to the data collector in integer form and interpreted as
a V-component value. Other than the Tower E 2 m errors, the largest error
found by MRI when spinning the transmitters at low speed was -0.12 m/sec at
the 2 m U-component of the 150 m tower. This instrument had given a
positive error of 0.09 m/sec when spun at -8.81 m/sec by TRC.
Both MRI and TRC checked the instrument output when the UVW shafts
were held stationary. Of the 15 transmitters checked by both at this zero
wind-speed point, four of the errors were of opposite sign in the two
audits; these four errors were also associated with the largest differences
85
-------
In voltage response of the translator cards, the largest such difference
being 0.012 volts, or 0.25% of the instrument range of 5 volts. The
largest zero offset found by TRC among these 15 instruments was 0.12 m/sec
for the 10 m U on Tower B, for which MR! found an offset of 0.07 m/sec; the
largest zero offset found by MRI (checking the system all the way through
to the data archive) was 0.12 m/sec in the 2 m U-component on Tower E, for
which TRC found an offset of 0.08 m/sec.
TRC's audit of the nine F460 wind speed systems (see Table 9) showed a
maximum error of 0.26 m/sec at a cup speed corresponding to approximately
8.7 m/sec. The maximum misalignment of the F460 wind vanes with respect to
ERT's landmarks (see Table 10) was 2° except for the 2 m level of the 150 m
tower, which was mounted on a steel post about 4 m southwest of the tower
to keep it somewhat removed from the disruptive effects of the junction
box, tower elevator, and structural reinforcements of the tower's bottom
end. The boom at this level could be rotated fairly easily by any
passerby. The maximum nonlinearity of the F460 vane outputs was 3° (see
Table 11). TRC's calculations of the errors in ERT's directions to
landmarks and north stakes are tabulated in Table 12, and the total errors
of the F460 wind vanes are shown in Table 13. The maximum total error was
estimated to be 7° to 9° at the 2 m level of Tower A. All other vane
systems were judged to be accurate to within approximately 3°.
The orientation of the UVW systems was audited by TRC by checking the
axis of the V-component transmitter with respect to true north (see
Table 14). The 80 m and 150 m systems at Tower A were oriented
approximately 8° and 7° east of true north, respectively; these
misalignments were clear to an observer looking up the tower from the
ground. The 16 other UVWs were judged to be aligned within 3° of true
north.
Finally, the vertical orientation of the W propellers and the
cup-and-vane transmitters was checked by TRC by sighting with a transit
from two directions approximately 90° apart. The results of this test were
not quantified, but the audit report states that the worst misalignment was
less than 2°.
86
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3.1.3 Data Validation Procedures
No changes have been made to the values of the measurements in the
data base in response to the results of the audits for several reasons.
First, the audits are not generally consistent with each other, so that it
is not clear what to do to improve the accuracy of most of the data.
Second, the calibration history of all the instrumentation has not been
systematically studied for consistency. Third, for those instruments for
which an error was demonstrated in an audit, is discernible in the data,
and was perhaps even visible to the naked eye (such as the misorientation
of the 80 and 150 m UVW sets), it may not be prudent to make adjustments"
until more information is available.
The direct measures from misaligned propellor sets, for example, are
the U and V components and the downwind and crosswind intensities of
turbulence IX and IY. On the premise that the wind speeds determined from
U and V are independent of wind direction, adjustments could be made to the
wind directions and new U and V components resolved. The magnitude of wind
speed is dependent upon the wind direction because of the propellorfs
non-cosine response to the wind stack angle. Errors introduced in U and V,
and therefore wind speed and wind direction, by this deviation from cosine
response have not yet been examined in detail. When more conclusive
information is available, data derived from propellers can be corrected for
instrument response, and adjustments for misalignments can then be made.
Data taken during 17 of the 18 tracer experiments of Phase II are
being validated according to the procedures described below. (Data from
Case 212 have not yet been validated because the tracer plumes never hit
the hill.) The 5-minute average data were the basic measurements received
by the data collector. All hourly averages except the turbulence
intensities and standard deviations of wind direction and temperature were
calculated by the data collector from the 5-minute data. Therefore, the
major validation effort was directed to the 5-minute data.
The communications problems resulting from the unshielded cable caused
two major types of errors. The first type was a miscommunication from a
data station to the data collector which was not always picked up by the
87
-------
parity checking on the transmission. Such an error resulted in a value
that looked peculiar in the time series of values for the measure
affected. From the redundant wind measurements (both cup-and-vane and UW
propellers), errors of this type could be fairly easily verified for wind
speed and direction except at the 40 and 80 m levels of Tower A, where the
propellers were alone and vertically separated by 30 m or more from the
nearest source of data for comparison. Because of the strong thermal
layering during many experiments, it was often not feasible to verify a
communications "hit" by comparison at these levels, and the determination
that a value was suspect or in error depended entirely on whether it was
unreasonable or out of place in the time series. Calculated temperatures
at 10 m and 150 m could be validated by comparison with the values from the
fast-response thermistors at these sites. Temperatures and temperature
differences at other heights on Tower A were validated by comparison with
the temperatures above and below the height being validated.
Fortunately, few errors of communication from the data stations to the
data collector resulted in measure values that were in the range of
possible values. Most were recognized as faulty by the data collector and
identified as missing by an "M" flag.
A far more common problem of communication occurred in the data
requests from the data collector to the data stations. A request for a
wind component might be received as a request for a temperature, and the
temperature would therefore be returned to the data collector, which would
put it into the data base as the wind value. All measure values were
transmitted to the data collector as integers (called "counts") between 0
and 1,023 inclusively. The data collector converted them to proper
engineering units by interpolation in the range of the measure. A
temperature transmitted in error as a wind component would therefore not
appear in the data base as the value of the temperature that was sent but
rather as the value of the wind component appropriate to the number of
counts corresponding to the temperature. Consequently one could look
through all the data for the 5-minute scan in which the suspect value
occurred for another measure value that had the same associated counts. If
such a measure was found, the suspect value was regarded as bad.
88
-------
Typically, the same error in transmission of data requests to the data
stations occurred more than once during the course of an experiment, and
this recurrence confirmed the fault. The data collector sometimes
recognized that an error of this sort had occurred and flagged the measure
value in the subsequent scan with an "M." The data base therefore
contained good values flagged "M" as well as bad values with no error flag.
To expedite the time-consuming error check through all the
measurements taken during the experiments, the 5-minute data were retrieved
from the data base in time-series files for each experiment. In general,
each of these files included all the 5-minute measures for one measurement
height on a tower; there are 19 files per experiment in this "edit"
format. The program quality assurance officer drew up a series of
guidelines for editing these files and a set of data flags for identifying
the quality of the data. The flags are the following:
(blank): Both the editor and the data system concur that the
value is valid.
"M" (missing): Both the editor and the data system concur that the
value is invalid.
"U" (unavailable): The value is unavailable because of data
collector or data station failure.
"B" (bad): The editor believes the value is invalid but the data
system did not catch the error; this flag is therefore associated
either with instrument malfunction or communications problems.
"R" (restored): The editor believes the value is valid, although
the data system had flagged it "M."
"C" (calculated): The editor calculated a derived measure (WD, WS,
SP, DR, TC), usually from "R" values.
"S" (suspect): The editor believes the data are somewhat in error
but cannot confirm either an instrument malfunction or
communications failure.
89
-------
"L" (at limit): The measure is at the upper limit of its range and
the "true" value exceeds that shown. The instrument ranges were
not themselves exceeded during the experiments, and this flag is
necessary only for the turbulence data (IX, IY, IZ, SD) in very
light and variable winds.
No data have been estimated and inserted into the data base.
The program quality assurance officer personally conducted a final
quality check on all of the real-time meteorological values before they
were released to the EPA. In this final editing, he tried to maintain a
balance between the premise that all data are potentially valid and the
premise that no data are above suspicion. Consequently, if no instrument
failure or communications error could be verified, a value was regarded as
valid unless it appeared to be unreasonable with respect to comparable
values adjoining it in time or space. This is generally not a difficult
judgment to make, but in some situations a value may look peculiar but not
completely unreasonable and might indicate a significant phenomenon. Such
data were left unflagged if they were not misleading or were flagged "S" if
they were sufficiently removed from the general trend to substantially
influence an hourly average.
The different characteristics of propellor wind sets and cup-and-vane
systems are well demonstrated in the CCB data. In general, the vector
resultant wind speed from propellers was less than the vector resultant
wind speed from a cup-and-vane set at the same location. The ratio of WS
to SP decreases from 0.8 to 0.9 in high-speed, smooth flows down to 0.5 or
less in light and variable winds. In near-calm conditions, the props were
observed to be more responsive to gentle puffs than the vanes, so that a
5-minute wind direction and wind speed resolved from the props might be
175° at 0.2 m/sec whereas the corresponding cup-and-vane direction and
speed might be 245° at 0.5 m/sec. Both these pairs of wind measurements
might appear in the data without any error flag because there was no
indication of instrument malfunction or communications error. The
differences between the measurements are thus attributable to the
differences in the instruments.
90
-------
Similarly, the response of propellor sensors is somewhat
direction-dependent. Often the difference between WD and DR. at a site
changed markedly when WD passed through a cardinal direction such as 0°,
45°, 90°, or 135°. Again, the measures were both retained as valid in the
data base. The users of the data should be aware of these instrumental
characteristics. To invalidate the data from the propellers would require
that WS, WD, IX, IY, and IZ all be flagged "B" or "S." Such a requirement
would decrease the utility of the data enormously.
The differences between the speeds and directions from the two kinds
of instruments show quite general consistency with the differences
anticipated as a result of the departure from the cosine response curve.
Furthermore, the horizontal intensities of turbulence IX and IY tend to
become more nearly equal when the average angle of attack of the wind is
approximately equal on both propellers (i.e., directions near 45°, 135°,
225°, 315°), whereas IX tends to exceed IY when the average angles of
attack are substantially different (i.e., directions near 0°, 90°, 180°,
270°). This consistency suggests that the quality of the UVW data might
significantly improve if corrections were applied similar to those
described by Horst (1973), which were derived from comparisons of propellor'
data and sonic anemometer data. ERT has been unable to find any similar
comparative analysis of data for the,Climatronlcs system.
The procedures for data validation were based on common sense,
comparison between neighboring sensors, searching for measures whose
contemporaneous values were associated with the same "counts" as a suspect
measure, reports of malfunctions in the field logs by the instrument
technicians and others, and by a learned feeling for how instruments track
one another when they are working correctly. Examples of an as—taken file
and its edited version are given in Figures 36 and 37.
When editing and flagging of the 5-minute data were completed,
hour-averages of the direct measures other than the turbulence measures
were calculated by computer from the 5-minute values; hour-averages of the
derived measures were in turn calculated from these. A set of
classification criteria and data quality flags has been established for the
hour—averages; it is shown in Table 15.
91
-------
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5 5O3
5. SO3
3 816
3 66O
5 894
6 O51
5 582
-30 OOOM
5 816
3, 73S
5 582
311?
3.347
3. 66O
-30, OOOM
3. 347
-3O OOOM
3 503
3. 3O3
3 874
4. 643
4 BOO
3 112
-30 OOOM
4,878
5, 034
4, 721
4 330
4, 096
-30. OOOM
-3O OOOM
3, 783
3 703
3 348
3 939
9 115
B. 920
7, 076
8 9OO
8 275
-5 OOOU
3 OOOM
4 87 3D
-5 OOOM
8. B42R
8.685
-5 OOOM
B 93?
-5. OOOM
9 326
O. O73
9. 7BO
9. 9375
-5. OOOM
B26Q
1, 147R
-5, OOOM
-5. OOOM
8 8P2
-5. OOOM
B 177
-5. OOOM
O, 621
4 6380
0 171
1 168
1 283
O 953
O 582
O 894
5 244B
0 62 1
O. 347
O 362
O Ob4
9 171
-2. 3228
-S. OOOM
-5. 000(1
-3. OOOM
-3, QOOM
8 8O3
-3. OOOM
-3. OOOM
4 286
4 638
-5. OOOM
3. 915
4 286
-5. OOOM
-5 OOOM
4 380
-5. OOOM
7, 317
7 9O3
7 884
5, 264
5. OOOM
f 927
9, B09
9. 9O7C
9, 377
7. OQ6
. OOOU
OOOM
5 528 D
OOOM
9. 194C
S. 558
OOOM
, OOOM
B. 617
8. 48O
8. 793C
B. 96BC
. OOOM
-1. 96OD
8. 598C
. OOOM
, OOOM
7. 131
. OOOM
6. 753
OOOM
6 349
445D
6 681
7, 053
7. 24B
7 072C
7 O14C
7 170
OOOM
6 193
3 84OC
3 743C
5 626
5 137
.OOOM
. OOOM
, OOOM
. OOOM
. OOOM
y. BTIC-
6, 173
. OOOM
. OOOM
OOOM
3. 567
5 917C
. OOOM
5. 352
5. 645C
. OOOM
OOOM
4 218
. OOOM
3. 827
4 O22
4. 081
4, 257
4. 277
OOOM
4 35SC
7. 96 L
9. B83
-30. OOOM
-30 OOOM
9 413
-3O OOOU
-30 OOOM
-30 OOOM
-3O OOOM
-30. OOOM
7. 1O1
-3O OOOM
7, 1O1
-30. OOOM
8.866
B. 788
8 710
8. 71O
8, 7BB
8. 553
8. 162
-30 OOOM
-3O OOOM
7 380
-30. OOOM
6. 52O
6. 578
B, 240
-30 OOOM
8. 162
7. 537
-3O. OOOM
7 537
6 833
6. 031
3 738
5 582
-3O OOOM
-3O OOOM
5, 503
3. 660
3. 738
-3O OOOM
-30 OOOM
-30. OOOM
6.285
6, 32O
6. 833
-30. OOOM
6. 676
-30. OOOM
5 773
5.973
-30. OOOM
4. 800
4 365
-3O. OOOM
4 O18
4. O96
4. 096
-30. OOOM
4. 643
-3O. OOOM
9, 643
9.213
9. 154
9 252
8 744
-5. OOOU
9. 154
8, 627
8. 757
9, 096
9. 389
9. 467
9. 897
10. 406
7,995
8.959
10, 875
11 364
1 1 . 97O
12. 028
14. 668
14. 629
11 403
11. 383
11. SS9
11,731
14. 157
13. 727
13, 725
4. 482B
13. 045
12. 713
12. 361
12. 322
1 1 . 657
11. 012
1O, 714
11. IBB
1O. 152
9. 663
10. 758
1O. 523
9.877
1O. 152
1O. 982
10. 073
9,800
B. 683
7. 736
3. 91 SB
6. 867
6. 730
5. 987
6. 574
8.627
5, 362
5. 186
3.440
6. 476
7. 903
B. 4.7O
8. 333R
8. 548
6. 496
6. 32O
10. 454C
10, 103C
9, 763C
7. 751
9, 553
OOOU
9 340
7. 2B2
9 457
9 438
9. 262C
9. 106
9. 535C
9. 477
7 086
B. 988C
9, 027
B, 871
7. 027
9, 477C
11, 491
11. 139
9. 712C
1O. 161
10. 239
10, 553C
9, BBS
9 926C
1O, 200
, 28BB
f, 164
8, 910
B. 793
8. 597
7, 933
6. 384
6. 307C
6 369
5. 723
5. 626
6,017
6. 251
6. 231
6. 349
6. 344
6. 740C
7. 170C
7. 151
7. 952C
, OOOM
7. 463C
8. 069C
a. one
7, 170
8. OtlC
9. 785
6. 486C
5. 606.
5 156
4 394
4 335
4. 511
4 433
OOOM
4, 374 C
5. 137
5. 508
5. 802
Figure 37. Example of an edited data file.
93
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TABLE 15. CLASSIFICATION CRITERIA AND DATA QUALITY FLAGS FOR
HOUR-AVERAGES PRODUCED FROM 5-MINUTE DATA
Definitions:
• Invalid 5-minute data are those flagged either M (Missing),
B (Bad), or U (Unavailable).
• Valid 5-minute data are those flagged either " " (Good),
C (Calculated) or R (Restored).
• Doubtful 5-minute data are those flagged either S (Suspect)
or L (at Limit).
MB - Number of missing and bad 5-minute values
U =• Number of unavailable values
GCR - Number of good, calculated, or restored values
SL = Number of suspect or at-limit values
Cases
I. MB + U - 12
1) U < MB
2) U >. MB
II. 6 < MB + U < 12
1) U < MB Hr-avg
2) U > MB Hr-avg
III. MB + U < 6
Hr-avg = -999.0; Flag = M
Hr-avg = -999.0; Flag = U
lyalid + jdoubtful.
GCR + SL
Same
; Flag = M
; Flag = U
1) GCR > 10 Hr-avg
2) 7 < GCR Hr-avg
GCR
-; Flag
valid . .
• GCR ; Flag - I (Incomplete)
invalid + doubtful
GCR + SL :
3) GCR < 6 and SL - 1 Hr-avg
4) GCR < 6 and SL > 1
yvalid + doubtful
1) S > L 1 Hr-avg - ^ GCR + SL ;
-; Flag
2) S < L
Hr-avg
Same
; Flag = L
94
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3.2 Tracer Data
3.2.1 Quality Assurance Procedures During Field Study
Strict quality assurance procedures were followed during every phase
of the tracer sampling and analysis field program. These procedures
included:
• multipoint calibrations of every gas chromatograph at the start
and finish of each analysis day;
• span checks every four hours on every gas chromatograph;
• recounts (samples analyzed twice on different gas chromatographs)
on 5% of the total samples;
® background air samples upwind of the tracer release in every
experiment;
« pairs of co—located samplers set up at two locations in every
experiment;
e testing of sample degradation with time in the sample bags up to
42 hours;
a an independent audit on the accuracy of the SF analysis system.
Each of these quality assurance procedures is discussed below in more
detail.
Calibrations were performed on each gas chromatograph at the start and
finish of each analysis day. However, because a typical analysis day was
16 hours long, a span check with one calibration gas (usually 100 ppt
SFg) was performed every four hours on every chromatograph to check any
response drift with time. If the span check showed a greater than 5%
difference from the most recent calibration, that.chromatograph was
completely recalibrated with all of the calibration gases. On the average,
one extra calibration during the analysis day was performed for each
chromatograph because of failure to pass a span check.
95
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Roughly 5% of the samples analyzed in each test were analyzed again,
usually on a different gas chromatograph.* The results of these recounts
are summarized in Table 16. The results are segregated into low and high
SF, and CF0Br concentrations because of the higher imprecision inherent
6 3
in concentrations near the lower detection limit. The recount statistics
on the higher SF, and CFJBr concentrations were very good, with 89% of
the SF, recounts greater than 50 ppt within +15%, and 95% of the CF~Br
6 ->
recounts greater than 1,000 ppt within +10%. The CF3Br recount
"statistics were somewhat better than the SF, recounts, possibly because
all CF,Br samples were analyzed on one gas chromatograph.
Background air samples taken upwind of the tracer release system
consistently recorded zero concentrations for both SF, and CFJBr.
Therefore, contamination from sources other than the release was not a
problem. Perhaps the best documentation of the lack of background air
contamination was Case 212, in which the tracer plume missed the hill for
the entire 8-hour experiment. No concentrations higher than 5 ppt SF,
(the detection limit of the gas chromatographs) were recorded during this
8-hour experiment, indicating no background contamination nor any residual
contamination in the sampler or the sample bags from previous experiments.
At two locations during each experiment, two samplers were placed side
by side and set to sample air during the same time periods. These
co-located samplers were used to assess the variability in the sampling
technique. The results are shown in Table 17. Because of random sampler
failure, the co-located data capture was relatively poor. The co-located
statistics were somewhat poorer than the recount statistics, with only 50%
of the SF- co-located samples (greater than 50 ppt) within +15%. One
o
reason for this relatively poor comparison may have been the intermittent
pump sampling; because the samplers took in air for only one second every
15 seconds, they were not sampling the same air parcels because the
samplers were driven by separate timers.
*A11 CF3Br analyses were done on gas chromatograph No. 8, the AID
instrument, since this was the only one that could separate SF5 and
CF^Br. Hence, all recounts for CF3Br were also done on this gas chroma-
tograph.
96
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TABLE 16. RECOUNT STATISTICS
Percent
Difference
0-5
5-10
10-15
15-20
20-25
25-30
>30
No. SI
<50 ppt
221
26
28
13
11
15
57
?5 Samples
>50 ppt
140
65
42
16
5
5
4
No. CF3Br Samples
Total
371
111
jjlOQO ppt
11
9
2
2
0
1
1
26
>1000 ppt
17
2
0
1
0
0
0
20
TABLE 17. CO-LOCATED SAMPLER STATISTICS
Percent
D if ference
0-5
5-10
10-15
15-20
20-25
25-30
>30
No. SF6
£50 ppt
28
0
0
1
0
1
17
Samples
>50 ppt
3
3
3
1
1
1
6
No. CFjBr Samples
Total
47
18
£1000 ppt
7
1
1
0
1
0
3
13
>1000 ppt
0
0
0
0
2
0
0
97
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During most experiments, all samples were analyzed within 24 hours;
the longest time period between sampling and analysis for any experiment was
48 hours. A test was made to determine if any sample degradation took place
in the Tedlar bags by analysing five test samples immediately and at various
times up to 42 hours later. The results are shown in Table 18. As shown,
no sample degradation was apparent for any of the samples; the concentration
variability was well within that demonstrated by the recounts.
3.2.2 External Audits _=,.^..,
Under subcontract to ERT, Edmund J. Burke, manager of quality assurance
at TRC Environmental Consultants, supervised an independent performance
audit of the four chromatographs that were operational in the Boise
laboratory on the audit day. The results, shown in Table 19, indicate that
15 of the 20 audit samples were within the +5% limit of accuracy given by
the supplier (+3% for Gas 3), and all samples were within +8%.
Because the calibration gases used by NAWC and the audit gases used by
TRC were all supplied by Scott-Marrin, Inc., of Riverside, California, the
audit gases were subsequently analyzed by C. Ray Dickson at the NOAA Air
Resources Laboratory (ARL) in Idaho Falls to check the concentrations (and
hence the calibrations of the GCs in Boise) against standards other than
Scott-Marrin's. The results of these replicated analyses are also listed in
Table 19. If the results for Gas 5 are disregarded because the
concentration was outside the range of calibration of the ARL system, the
mean analysis for each of the other four audit gases was within 6% of the
concentration indicated by Scott-Marrin.
3.2.3 Data Validation Procedures
As discussed in Section 2.3, all sampler and analysis data were entered
into the ERT computer during the field study, and concentrations were then
calculated on the basis of the two closest calibrations before and after the
analysis time. Because of the time constraints during the experiment, it
was not possible to double check the data entry process during the field
study. All tracer data files were therefore validated after the field
experiment was over.
98
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TABLE 18. SAMPLE DEGRADATION TEST
Sample
1
2
3
4 '
5
Time in
Bag (hr)
0
6
11
18
42
0
6
11
18
42
0
6
11
18
42
0
6
11
18
42
0
6
11
18
42
SF6 (ppt)
11
9
13
15
9
23
21
22
22
21
24
21
24
24
22
45
46
51
47
48
68
67
66
72
66
(ppt)
490
510
480
420
450
2,970
3,030
3,250
3,090
3,130
5,530
5,550
5,670
5,520
5,630
6,270
6,330
6,340
6,400
6,500
4,100
4,110
4,160
4,110
4,100
99
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TABLE 19. RESULTS OF ANALYSES OF TRC'S SF, AUDIT GASES
o
(concentrations in ppt)
SFft Audit Gases
Concentration Analysis
Supplier's Analysis*
GC No. (Make)
5 (S3)
6 (S3)
7 (S3)
7 (S3)**
8 (AID)
Avg/Std Dev
ARL/NOAA Analysis
Std Dev (No. of pts)
Percent Differences
GC 5 - Supplier
GC 6 - Supplier
GC 7 - Supplier
GC 8 - Supplier
Average
GC 5 - ARL
GC 6 - ARL
GC 7 - ARL
GC 8 - ARL
Average
ARL - Supplier
Gas 1
99
105
101
96
96
99
100/3.8
95
2.5(22)
6.1
2.0
-3.0
0.0
1.3
10.5
6.3
1.1
4.2
5.5
-4.0
Gas 2
247
260
244
241
234
264
252/11.4
235
2.6(19)
5.3
-1.2
-2.4
6.9
2.2
10.6
3.8
2.6
12.3
7.3
-4.9
Gas 3
505
518
483
465
471
510
494/24.5
484
5.1(19)
2.6
-4.4
-7.9
1.0
-2.2
7.0
-0.2
-3.9
5.4
2.1
-4.2
Gas 4
1,000
1,000
954
958
950
989
975/22.7
1,060
11.6(10)
0.0
-4.6
-4.2
-1.1
-2.5
-5.7
-10.0
-9.6
-6.7
-8.0
6.0
Gas 5
10,300
10,100
10,400
10,500
10,300
10,700
10,400/250
7,990+
15.6(10)
. -1.9
1.0
1.9
3.9
1.2
__+
—
—
—
—
—
Mean Absolute Percent Differences
NAWC GCs - Supplier 3
NAWC GCs - ARL 6
ARL - Supplier 4
.1%
.2%
.8%
Avg
Avg
NAWC GCs
NAWC GCs
- Supplier
- ARL
1.7%
5.6%
*Gas supplier certified Gas 3 to +3%, other gases to ^5
**This audit of GC 7 was done with audit gases first injected into Tedlar
sampler bags and then into the GC; results were not used in the remainder
of this table.
4-ARL's GC was not calibrated for SFg concentraitons as high as Gas 5 and
gave a low response.
100
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The entire tracer data base (over 14,000 data points) was methodically
checked line-by-line against the original data sheets. This validation
process revealed numerous simple data entry errors, primarily in the sampler
on-off times, which were relatively easy to correct. Other discrepancies,
such as uncertain sampler locations, were resolved using best judgment.
Questionable data that could not be resolved satisfactorily (such as unknown
sampler times) were deleted from the data base. Questionable tracer
concentrations, which conceivably could be resolved by reviewing the
original recorder strip charts and integrator tapes, were indicated by a "Q"
in the tracer data files. These questionable data consisted mainly of
recounts and co—located samples that differed by more than +30%, in addition
to other probable errors in transcription from the integrator tapes to the
data sheets.
The systematic line-by-line check of the original data sheets was
complemented by a number of computer tests on the data base. These quality
assurance computer checks included:
A printout of any sampler on-off times outside the time window of
the experiment and any times indicating other than 10-minute or
hourly averages. In many of the tracer tests, some samples were
actually taken after the experiment had concluded; these data have
been kept in the tracer data base for possible use in following
the tracer decay with time after the release was stopped.
A printout of all tracer data indicating the same location and
on—off times. This check revealed a number of duplicate and
erroneous entries, as well as the correct co—located sampler data.
A comparison of all recount data (bags that were analyzed twice on
a different gas chromatograph). The recounts are tabulated in the
data base by the fictitious "75Z" sampler location.
A printout of all SF concentrations higher than 1,000 ppt and
all CF_Br concentrations higher than 10,000 ppt. These high
tracer concentrations were then checked again for accuracy against
the original data sheets.
A printout of any sampler locations other than those used in the
field experiments.
101
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All obvious discrepancies found by the computer checks were corrected. The
data sheet verification and computer checking validation procedures
necessitated corrections in roughly 10% of the total number of data points.
i
The tracer data files now contain four different alphabetic codes for
each sample:
• G - good sample
• B - bad sample (a bag half-full or less but which could still be
analyzed)
• R — recount
• Q — questionable concentration (generally, recounts and
co-located samples that differed by more than + 30%)
It may be possible to resolve the questionable concentrations by reviewing
the original recorder strip charts and integrator tapes. In the evaluation
and testing of the various air quality models in Sections 4 and 5, only
those tracer concentrations considered good were used in the analyses.
102
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SECTION 4
AIR QUALITY MODELS EVALUATED
4.1 Introduction
One key objective for this phase of the program was to evaluate
existing complex terrain models against the CCB field data. The performance
of the Valley model is of special interest because it is the only complex
terrain screening model recommended for regulatory use by the EPA.
Comparisons of Valley estimates of the peak hourly concentrations with
observed peak hourly concentrations not only test the model's ability to
estimate the peak tracer concentration during the field study but also offer
references of model performance against which to evaluate other complex
terrain models. Other models chosen with the concurrence of the EPA Project
Officer for evaluation against the CCB observations were COMPLEX I,
COMPLEX II, and PFM. Two new experimental algorithms—one for flow over the
crest of the hill (Neutral model), the other for stable flow around the hill
(Impingement model)—were developed in this phase of the program.
None of these more refined models has been validated or accepted for
regulatory use. COMPLEX I and COMPLEX II have been.issued by EPA only for
public testing and evaluation. PFM may be made available soon (for the same
purpose) as a modeling system (called COMPLEX/PFM) similar to the COMPLEX
models. The two new experimental models are very preliminary, contain many
partly tested algorithms, and have no regulatory status. The following
subsections briefly describe each model and its application to the CCB data.
103
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4.2 Valley Model
4.2.1 Description
The Valley model (Burt 1977) is recommended by EPA for screening
analyses in support of regulatory decisions (Budney 1977). Valley is
designed to provide an estimate of the maximum 24-hour pollutant
concentration expected to occur on elevated terrain near a point source of
air pollution in any one-year period. This concentration is computed with a
steady-state, univariate Gaussian plume dispersion equation, modified to
provide a uniform crosswind distribution over a 22.5° sector, using assumed
worst-case meteorology.
The model assumes that the plume travels toward nearby terrain with no
vertical deflection until the centerline of the plume comes to within 10 m
of the local terrain surface. (Thereafter, the centerline is deflected to
maintain a stand-off distance of 10 m from the terrain surface.) The plume
is considered to impinge upon the terrain at points where terrain height
equals the plume height, and the impingement point used in the calculation
of maximum plume impact is the nearest such topographic point as viewed from
the source, independent of hourly wind direction.
Worst-case meteorology is that combination of wind speed and
Pasquill-Gifford (PG) dispersion stability class leading to the highest
concentration at the impingement point. For most large sources of air
pollution, a stack-top wind speed of 2.5 m/sec and PG stability class F are
recommended for the vertical growth of the plume under inversion conditions
at night when plume impingement is most likely.
The model estimate is implied to be a 1-hour average concentration.
The 24-hour average concentration is estimated by dividing this 1-hour
average concentration by four, on the premise that the plume may affect a
specific point for no more than six hours in any 24-hour period.
It should be stressed that because neither the tracer source release
heights, crane locations, nor meteorology were equivalently "persistent"
from hour to hour during the actual experiment, the CCB data base is not
appropriate for testing the Valley model as it is used in regulatory
applications. (The CCB field experiment was not intended specifically to
104
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validate or invalidate the Valley model but rather to assemble a data base
that will support the development and refinement of progressively better
modeling approaches for plume interactions with complex terrain.)
4.2.2 Application Procedures
The longest steady averaging period for tracer releases and
concentrations in the CCB field study was four hours. Most steady averaging
periods were between one and two hours. Consequently, only 1—hour Valley
estimates were compared with maximum observed hourly tracer concentrations.
Release crane positions during the experiments ranged from a distance
of 538 m to a distance of 1,452 m from the center of the hill. The local
release heights of the nonbuoyant tracer gas varied from 15 m to 60 m. The
distance to the nearest point of impingement was obtained from a contour map
of the hill for each hour of the 45 case hours modeled. (Section 5.1 lists
those experiment case hours included in the model evaluation.) These
distances ranged from 213 m to 867 m. In each instance, the difference
between the local elevation at the crane position and the zero height
contour on the hill was taken into account to maintain the level plume
geometry of the model. The local elevation at each release location was
interpolated from the nearest survey points and the shape of the local hill
contours.
Concentration estimates scaled by the emission rate were computed by:
(7)
which is derived from Equation 2-1 of the Valley User's Guide (Burt 1977).
3
C is in units of Vg/m , and Q is in units of g/sec.
The standard deviation of the vertical pollutant distribution (cr )
z
is calculated from:
a = 0.362 x °"55 - 2.7
z
(8)
105
-------
The constants in this equation are taken from Table 2-1 of the Valley User's
Guide. They are applicable for PG stability class F over a range of x
between 100 and 1,000 m, which includes all of the impingement distances
developed for the 45 test case hours.
The wind speed was set to 2.5 m/sec, and the stand-off distance (H) was
fixed at 10 m to be consistent with the regulatory applications of Valley.
However, because the 10 m value is not based on any theoretical analysis, it
may not be an appropriate scale for the narrow plume configuration of the
tracer experiments (compared to plume sizes encountered with large pollutant
sources). Therefore, parallel computations are also presented for the
centerline (i.e., center of the plume) concentration at the impingement
point, not including a surface reflection contribution.
4.3 COMPLEX I and COMPLEX II Models
4.3.1 Description
COMPLEX 1 and COMPLEX II are sequential complex terrain models designed
to estimate 1-hour, 3-hour, 24-hour, and annual pollutant concentrations
resulting from emissions from many point sources. Concentrations are
estimated at many receptors using hour-by-hour meteorological data.
Several terrain treatment options (formulated by the Complex Terrain
Team at the February 1980 Chicago Workshop on Air Quality Models) are
available in the COMPLEX models. The standard option for PG stability
classes E and F simulates the plume behavior contained in the Valley model.
This was the option selected for comparison with the CCB field data. (The
COMPLEX models also contain a buoyancy-induced dispersion option, but this
feature was not used in this modeling because the tracer releases are not
buoyant.)
COMPLEX I is a univariate Gaussian plume model with 22.5° sector
averaging in the horizontal. It uses the PG stability class system.
COMPLEX II differs from COMPLEX I only in its representation of crosswind
plume spread. Whereas COMPLEX I assumes a 22.5° horizontal sector
averaging, COMPLEX II assumes the familiar crosswind Gaussian profile. (In
all other respects, the two models are identical.)
106
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COMPLEX I is essentially an extension of the direct-impingement Valley
model to hourly averaged wind speed, wind direction, and stability class
instead of the assumed worst-case meteorology; and COMPLEX II merely
replaces Valley's 22.5° horizontal sector averaging with a Gaussian
crosswind profile. For neutral or unstable conditions, COMPLEX I and
COMPLEX II permit different (nonimpingement) terrain assumptions. For
stability classes A through D, the terrain treatment allows the plume
centerline to rise over terrain features but at a height less than its
initial height over flat terrain. Its actual height at any point is
computed from its initial height,^ the local terrain height, and a, plume path
coefficient.
4.3.2 Application Procedures
With the concurrence of the EPA Project Officer, it was decided that
for efficiency, the evaluations of COMPLEX I and COMPLEX II with the CCB
data base would actually be carried out by embedding the essential
computational algorithms of these two models within a flexible,
research-oriented computer code. The COMPLEX algorithms are invoked by
selecting specific options for plume path coefficients, dispersion
parameters, sector averaging, and surface reflection treatment. The
flexibility inherent in this code structure will allow the testing of
various permutations of the COMPLEX modeling assumptions in future analyses.
In addition, because this modeling system was developed by ERT
specifically for the CCB field experiment, it can access any portion of the
CCB data archive. It retrieves such information as the locations,
elevations, and validated concentrations of all samples recorded, hourly
average winds, and other field data for a given hour. The predictive
segment of the code is set up for real-time application via an interactive
terminal. It also allows a wide choice of user input and data override
options, control over postprocessing, data archiving and file management,
and statistical and graphical displays.
Input data for the models consist of hourly average wind speed and
direction, source location, source height, stability class, receptor
location, and receptor height. Receptor information is provided for all
107
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potential (93) sampling locations. Although the samplers were designed to
measure tracer concentrations no closer to the surface than 1 m, no receptor
height offset was used in the modeling because the overall model resolution
is no more accurate than 1 m. Source locations are input to the nearest
meter and nearest 0.5 degree (polar coordinates referenced to the center of
the hill). Release heights relative to the zero height contour on the hill
are input to the nearest 0.1 m. Average wind speed is input to the nearest
0.5 m/sec, and the wind direction is input to the nearest whole degree.
Data used in the modeling are summarized^in Section 5.2.
Stability classes used in the modeling required special treatment. No
attempt was made before the fact to select only the one PG stability class
that is most appropriate for a given hour. Instead, both models were run
three times for each hour, assuming (in turn) stability classes D, E, and
F. Thus, for each hour of observational data, six model predictions were
generated—three for COMPLEX 1, three for COMPLEX II—with the following
rationale.
The PG stability classification scheme, in conjunction with the PG
dispersion coefficients, is strictly applicable only to near-surface
releases; its use to characterize dispersion of plumes at elevations of 30 m
to 40 m in a very stable, layered flow is less justified. It was therefore
prudent to run COMPLEX I and COMPLEX II with the same range of stability
classes for all of the case hours and compare observed and predicted
concentrations for each hour to judge whether the PG classification scheme
was appropriate.
We made no attempt to compare COMPLEX I and COMPLEX II to the CCB data
in terms of 3-hour or 24-hour averages because the source position or
release height was often changed during a field experiment. The CCB field
experiment does not provide a basis for evaluating the multiple-hour
(running average) performance of these models; only the 1-hour averages may
be legitimately compared.
108
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4.4 Potential Flow Model (PFM)
4.4.1 Description
The PFM was developed and refined by ERT under EPA Contract 68-02-2759
(Isaacs et al. 1980; Bass et al. 1981; Strimaitis et al. 1981). Grounded in
both empirical evidence and theoretical arguments, PFM takes as its starting
point the fact that as air flows over and around terrain features, an
embedded plume will experience regions of acceleration and distortion along
its trajectory. For flow situations in which vertical density gradients are
unimportant and surface boundary layer effects can be ignored, inviscid
potential flow theory provides an analytical tool for approximating velocity
fields, streamline trajectories, and plume deformation in the presence of
simple, isolated terrain features.
The model calculations of terrain-modified plume dispersion
coefficients and surface concentrations are based largely on work by Hunt
and Mulhearn (1973) and Hunt and Snyder (1978) on the theory of turbulent,
Gaussian-like plumes embedded within potential flow fields. Strimaitis
et al. (1981) describe additional modifications made to incorporate more
general isolated terrain features. They present a method for incorporating
PFM computations within the framework of sequential complex terrain models
(such as COMPLEX).
PFM has recently undergone final revisions allowing it to operate
within the framework of the COMPLEX models—specifically, a version called
COMPLEX/PFM (Strimaitis et al. 1981). The version of PFM used in
comparisons against the CCB field data is fully equivalent to the PFM
algorithm in COMPLEX/PFM. However, more data analysis is required in
running PFM separately, as some required input data are computed within
COMPLEX/PFM.
The PFM code is used to generate a potential flow streamline that
defines the path of a plume in neutral flow about an isolated hill or ridge
(modeled as either an ellipsoid or a bluff). The code then alters the path
and velocity along the path to approximate changes introduced by
stratification as measured by the hill Froude number. Line integrals from
the source then determine cumulative distortions in the plume sigmas.
109
-------
Output from PFM includes a file containing the coordinates of the plume
trajectory and a file containing modification factors (for Cf , O ,
y z
plume elevation, and centerline concentration) that connect flat terrain
values to values consistent with the computed flow field.
Other subroutines within COMPLEX/PFM use this information in computing
concentrations at all receptors. A postprocessor performs this function in
a similar way here. The postprocessor evaluates plume-receptor geometry,
computes modified plume o and O values based on Turner workbook
coefficients (although other functions may be substituted easily), and uses
the hourly emission rate and wind speed to calculate the field of
concentration estimates in a format consistent with the requirements of the
statistical analysis software.
4.4.2 Application Procedures
PFM requires the following information:
• hill shape: along-wind and crosswind aspect ratios,
• effective hill height,
• distance from source to hill center,
• effective source height,
• wind angle (zero degrees takes the plume over the hill center),
• effective Froude number, and ;
• downwind receptor resolution. J
The CCB-specific postprocessor requires the following information:
local source height,
absolute hill height,
height of the critical dividing streamline (H ^f
actual wind speed and direction,
emission rate,
PG stability class, and
sampler positions and heights.
110
-------
Although some of these quantities are needed to run other models (wind
speed, direction, source height and location, and emission rates are
presented in Section 5.2), several are specific to the PFM computations.
These are highlighted below:
Hill Height and Shape - CCB is taken to be an axisymmetric ellipsoid.
The aspect ratios are therefore equal and are derived by dividing the mean
radius of the hill at the 40 m contour by the total hill height (the 40 m
contour is about halfway up the hill). The highest labeled contour on the
hill is 95 m on the south peak; the highest contour that virtually spans the
saddle between the peaks is 85 m. The 90 m contour, which spans much of
both peaks, is taken to represent the top of the hill for modeling
purposes. The base of the hill is taken to be the -5 m contour height.
(The contour heights on the hill are referenced to the 945 m (3,100 ft)
height contour above sea level.) Thus, the total hill height is taken as
95 m. The average radius at the 40 m height contour is 244 m, which gives a
hill aspect ratio of 2.6.
H . - The concept of the dividing streamline height was presented
in Section 1.2. H . values are computed with a hill height of 95 m for
each case hour.
Effective Source and Hill Heights - The potential flow is assumed to
take place only above a surface defined by the effective value of Hcrit>
as shown in Figure 38. The region below H is considered "dead"
insofar as interaction with the plume is concerned. The hill height is just
that portion of the hill above H —that is (in cross-section), the arc
AB. The model approximates this upper portion of the hill with an
equivalent ellipsoid of the same semimajor axes b and c used to define the
entire hill shape. (The dashed curve represents this equivalent ellipsoid,
exaggerated for illustration.) Similarly, the effective source height is
the local source height minus H . (This definition implies that the
dividing streamline of the flow is assumed to follow the small undulations
of the terrain up to the base of the hill.) If any release heights lie
below H , no PFM computation is performed. This does not mean that the
crit'
111 .
-------
Q.
CD
o>
ui
-------
CQ
3
O
c
O
O
co
.c
ro
ID-
CQ
.:=:• ro
X «
£. DC
CO
(0
OC
s
3:
in
CD
GC
CO
o
2
O)
'5
CD
CC
IB
§
o
\ I
1 ro
\ 9
I
,2
m
O
O
a>
CQ
C_)
n)
CD CH
•H
fi CD
(/) O
i-l CD
CD M
CD
m o
O PH
g.H
• H 13
4-> C
rt rt
3 bfl
r-H -H
r-l
-------
plume will impinge somewhere on the hill; it means only that the flow is
likely to move around the hill with more horizontal than vertical deflection
and that PFM in its present configuration is not applicable. Within the
COMPLEX/PFM system,- a COMPLEX I computation would be performed under these
circumstances.
Effective Froude Number - The Froude number (Fr) used with PFM is a
bulk Froude number defined over the layer extending from H ..to 150 m
~"~~~~*" cri t
(the top measurement level on Tower A). It is assumed that H . caps a
surface layer of large AT so that above H the temperature gradients
vary slowly; hence, a simple bulk value will suffice for the Froude number.
One Froude number is computed for each hour.
Receptor Resolution - PFM is run for receptors spaced evenly along the
trajectory from the source to ,a point near the downwind base of CCB. The
resolution varies from 25 m to 36 m along the direction from the source
through the center of the hill. The end receptor is located 600 m beyond
the hill center. Once the PFM computations are made, the postprocessor
converts the plume trajectory and the plume deformation factors to a field
of tracer concentrations for various choices of stability class.
Following a rationale such as that used to run the COMPLEX models with
different stability classes, the PFM model was run for each hour with
stability classes D and E to form two estimates at each receptor for each
hour. (Class F computations have not been made, as the class D and E
comparisons are thought to form an adequate base for comparing the relative
performance of PFM with the other models.)
4.5 New Experimental Models
4.5.1 Overview
This section describes initial progress in the development of new
models to explain 1—hour average concentration patterns observed on CCB
during the field study conducted in the fall of 1980. It must be emphasized
114
-------
that these models are preliminary and subject to change as this study
proceeds.
A complicated plume dispersion problem such as that presented by CCB
involves a large number of physical processes that together constitute the
relevant physical system. It is desirable to identify a small number of
essential variables that may control the behavior of the system. One way of
doing this is to construct a simple model with empirical parameterization of
important effects.* Testing this type of model against observations can
lead to an understanding of the relative importance of the controlling
physical variables. This approach to modeling, adopted to guide new model
development, relies heavily on the analysis of concentration observations.
Two preliminary models are proposed. One model, the Impingement model,
corresponds to low Froude-number flows in which the plume remains horizontal
as it flows around the hill. The other model, the Neutral model,
corresponds to moderate or large Froude-number flows and allows the plume to
go over the top of the hill. The simplicity of these models is deliberate;
it will encourage applications in situations for which input information for
the model is minimal.
4.5.2 Impingement Model for Low Froude Number Flows
This preliminary model development effort focused on 1-hour average
concentrations and meteorology to parallel the regulatory use
of existing models. Visual plume observations made during the field study
indicate that when the flow was stably stratified, there was often
considerable meander of the horizontal wind. Moreover, horizontal turbulent
intensities averaged over an hour were typically around 20% of the mean
vector average wind speed. Under these circumstances, it is not physically
realistic to assume that the mean flow can be separated from much smaller
scale turbulence. This assumption of separability is central to the
theories of Hunt and others (see, for example, Hunt and Mulhearn 1973). To
be consistent with observations, a distribution of streamlines about a
*This approach to modeling should be contrasted to that which relies on
prior assumptions about the relevant physics of the problem in order to
assemble the model by combining detailed mechanistic submodels.
115
-------
"mean" streamline corresponding to the hourly average wind is postulated.
Next, the concentration at a receptor is determined by the probability (the
fraction of time) that the wind blows in the direction of the streamline
that passes close to the receptor.
Figure 39 is a schematic of the physical situation being considered.
The figure shows that the stagnation streamline is the.only one that hugs
the hill. If the dispersion caused by small-scale motion (turbulence) is
small compared to the horizontal meandering of the instantaneous plume, the
hill concentration is determined by the probability that the wind blows
along the stagnation streamline. For a hill with a circular cross section,
the maximum concentration will occur at stagnation point A. The
instantaneous concentration C. at A can be written as
Q/(/2ifu a 6 d)
s z s
(9)
where 6 is the instantaneous angular spread (in radians) of the plume
s
and d is the distance of the source to the receptor. The mass per unit
length of the plume is Q/u where Q is the emission rate and ug is the
mean wind speed at the source. We can compute u if we assume that the
flow around the obstacle is described by potential theory. Then,
dw
dz
; z = x + iy
(10)
where w is the complex velocity potential with the argument z given by
w
(11)
and U is the mean wind speed far upwind of the hill (Milne-Thompson 1968)
It is assumed that the concentration distribution is Gaussian in the
vertical.
116
-------
Instantaneous Streamline
Stagnation Streamline
Figure 39. Geometry used in formulating Impingement model for low
Froude number flows.
117
-------
The maximum hourly averaged concentrations, C at A, can be written
as
c - c. r
max i J
(12)
where P(0)d6 is the probability that the wind blows in the interval
(6 - d8/2, 6 + d6/2) during the hour. By assumption, a0>>es and
Equation 12 can be written as
max
P(0,)0
id s
(13)
where OQ is the hourly average standard deviation of the horizontal
wind direction and 0, is the angle between the stagnation streamline and
d
U.
With Equation 9, Equation 13 becomes
max /2Tr u O d
r s z
(14)
The distribution of P(6d) is assumed to be Gaussian, so that Equation 14
can be written as
max
2JTu O crfld
S Z **
exp
(15)
Note that in Equation 15, 0 , is used instead of the angular difference
between u and the direction of the stagnation streamline. This is
s
because P(0,) is determined by the upstream flow field rather than the
d
distorted flow close to the obstacle. In order to use Equation 15, a
formulation for Cf is needed; the suggested expression for a is
z z
presented in Section 4.5.4.
118
-------
4.5.3 Neutral Model For Moderate to High Froude-Number Flows
Figure 40 is a schematic of a plume embedded in a neutral flow (that
is, a flow that can be considered to be a potential flow based upon the hill
Froude number). For convenience, an axisymmetric flow is considered. The
lower figure shows, in cross section, the plume heading towards the hill.
As the plume goes over the hill, it is distorted in the vertical and
horizontal directions and its height (the height of the plume centerline
above the hill surface) varies with the distance along the plume. These
effects must be parameterized in-a dispersion model. Based on the model of
Egan (1975), the following formulation for the concentration on the hill
surface is proposed:
C(x,y) =
2Q
(2TTuCf CT ) D D
v y z'f y z
exp -
•
h2
2 -
r
I? / 22
z zf
exp
(By)2
2 2
y yf
(16)
where the subscript f denotes values in the absence of the hill
(e.g., CJ is the unperturbed horizontal plume spread, and CT is
the plume spread perturbed .by the hill). The other terms in Equation 16
are defined as follows:
T| = n /z
o r
(See Figure 40)
D = a /a • D = a /a
y y yf z z zf
(17)
(18)
(19)
In Equation 18, ^ is the stream function. The factor C is the ratio of
the streamline spacing at the position of the source to that at a given
distance. It accounts for the vertical deformation of the plume. The
justification for using local stream function gradients to account for the
vertical distortion of cr relies on the fact that O is relatively
Z "
small when the flow is stably stratified (that is, when 90/3z is large).
119
-------
bfl
0) (1)
I"?
§2
CD PU
w C
O
O -H
f-i
d> ,^3
e +->
O -H
120
-------
Because of horizontal meandering of the wind, the same assumption
cannot be made to estimate the horizontal distortion factor fi. To
estimate J3 we use the fact that in axisymmetric flow the angle 4> (see
Figure 40) remains a constant along a streamline. We next assume that
horizontal plume distortion is uncoupled from turbulent plume spread and
occurs after the plume has spread because of turbulence. In other words,
the segment AB (in Figure 40), which would describe the plume spread at a
downwind distance x from the source in the absence of the hill, becomes the
plume segment CD at the same downwind distance in the presence of the hill.
In effect, the point ?„ maps onto the point P-j^ on the "flat terrain"
plume. For a plume directed towards the center of the hill, simple geometry
shows that B> = z /z.* As a first approximation, it is also assumed that
D = D = 1.0.
y z
A hill factor, f,, can be defined as:
(20)
Using potential flow theory, Egan (1975) shows that for two-dimensional
flow, fjVL. On the other hand, ffa is usually smaller than unity for
three-dimensional flows. The minimum value is close to 1/2. In
the absence of detailed flow computations, a simple formulation that
interpolates between these two values is suggested:
fh = l-z/2zr; z<
(21)
=1/2
When the receptor is not located on elevated terrain (z = 0), f^ =1.0 as
expected. (Note that Equation 21 does not allow fh to be smaller than
1/2.)
*When the plume direction is not along the radius of the hill, the
expression for B is slightly less straightforward, although the
concept behind its derivation is still very simple.
121
-------
4.5.4 Dispersion Parameters
Dispersion in stable flows is far from being fully understood, ;although
some progress has been made in modeling the behavior of surface releases
(see Van Ulden 1978). At the present time, the analysis of lidar data
collected during the small hill experiment is not complete. Because of this
lack of adequate theory and data, the suggested expressions for sigmas
should be considered very tentative.
The horizontal meandering of the wind suggests that CT can be
expressed as
= crX
(22)
where CFg is measured at source height. This equation has not yet been
fully tested.
For elevated releases in the stable boundary layer, the vertical length
scale of turbulence, & , can be expressed as
JL ^ a /N
w w
(23)
where CT is the standard deviation of vertical velocity fluctuations and
w
N is the Brunt—Vaisala frequency. The Lagrangian integral timescale, tn,
should be on the order of 1/N. A typical value of N measured at source
height during the CCB experiment is 0.05 s , which translates to a t,,
of about 20 s. With a typical wind speed of 5 ms , it is expected that
d will approach the large travel time behavior beyond 200 m from the
z
source. Because the source receptor distance was usually more than 400 m,
the following equation is tentatively proposed for cr :
Z
w
u¥
(24)
where all of the variables in Equation 24 refer to source height.
122
-------
A preliminary test of Equation 24 for O has been made using lidar
data from 15 case hours. In the course of reducing the raw lidar data, the
Wave Propagation Laboratory (WPL) has computed standard deviations of the
inferred smoke plume density. These values apply to the nearly
instantaneous distribution of oil fog material in one of several sampling
planes. Sampling planes lie along rays originating at the lidar location.
Therefore, calculated o values usually apply to a plane that is not a
z
perpendicular slice through the plume.
An estimate of 1-hour plume sigmas is obtained from these lidar data by
assuming that the effective 1-hour sigma is a combination of the average
instantaneous sigma and the standard deviation of the positions of the
instantaneous centroid of the distribution. For example, during hour 2 of
Case 202, the plume was sampled five times in a plane approximately 210 m
downwind of the source. The mean instantaneous sigma () was
Z
8.6 m. This average is formed as follows:
N
= (I l a2)172
z VN 1=1 i'
(25)
The standard deviation of the height of the centroid (OH) using N - 1
weighting is 0.9 m. An effective 1-hour O is formed according to
Z
ze
>2 +
'I
(26)
Using the data from Case 202, hour 2, az& = 8.6 m.
All 1-hour estimates of plume sigmas .formed in this way from the lidar
should be viewed as crude estimates only. Many planes are sampled no more
than three times in an hour, and these may be grouped in the first half-hour
during some hours. The results are presented mainly to see if the distance
function proposed in Equation 24 is a reasonable description of plume
development upwind of the hill and if the magnitudes of the predicted sigmas
are comparable to the observed values.
123
-------
Table 20 summarizes the results of the sigma comparisons. In the
table, "R" is the approximate distance of the sampling plane from the center
of the hill. Any distances less than 300 m are likely to be close enough to
the hill to produce significant distortion in the instantaneous plume.
"Calculated O " is the value of cr computed from Equation 24.
z z
Undoubtedly, interpolating measured intensities of turbulence to the release
height contributes to the imprecision of the estimate.
There is generally good agreement between the lidar-derived a
z
values and those calculated using Equation 24 in 12 of the 15 case hours
analyzed. The mean percentage error (absolute value of the difference
divided by lidar-derived cr ), assuming all of the error is contained in
Z
the predicted O values, is 22% with a standard deviation of 17%.
Agreement was much poorer for the remaining three case hours. The
worst comparison is with Case 209, hour 8.
one-third the size of the lidar cr
The calculated O is about
z
Calculated cr for the other two
z z
hours differ from the lidar sigmas by about a factor of two (100% error).
Figure 41 'summarizes the behavior of the lidar-derived cr as a
z
function of downwind distance. Distance is scaled by the length scale u/N,
and CT is scaled by the vertical length scale of turbulence in the
Z
Stable boundary layer, CTW/N. Although scatter is certainly evident,
there appears to be a significant growth of cr with distance. The curve
of CT values calculated with Equation 24 is also displayed in the
Z
figure. Its square root growth assumption appears to be reasonable.
Case 209, hour 8, is plotted separately in Figure 41. It is the case
hour with the worst correpondence between lidar observations and predicted
values. Four of the five sampling planes show nearly equal plume spread.
This hour, which has the lowest value of cr /N, may represent a case in
which the density stratification inhibits continued plume growth with
distance.
PG Cf values are also compared with the lidar observations in
Z
Table 20. In seven of the 15 case hours, the best stability class (based on
0" alone) is class F; class E appears best in three of the hours. If
Z
the same hours are classified by the Turner scheme, 13 hours are classified
class F, one hour class E, and one hour class D. These latter two
designations agree with those inferred from the lidar observations.
124
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TABLE 20.
COMPARISON OF a DERIVED FROM LIDAR OBSERVATIONS WITH PREDICTED
uz
Case Hour
202 1
202 2
204 1
204 8
205 4
205 5
205 6
206 4
206 6
209 1
209 3
209 8
210 3
211 1
211 4
Downwind
Distance
200
520
210
480
225
450
660
130
360
580
555
780
865
350
555
785
350
545
690
800
215
425
225
215
385
485
350
195
95
190
295
510
605
200
295
565
785
210
385
470
445
645
885
R
820
500
810
535
810
585
375
830
600
380
600
375
290
805
600
370
805
610
465
355
380
170
370
775
600
505
640
795
905
810
705
490
395
885
790
520
302
790
615
530
710
510
270
No. of
Lidar
Scans
3
4
5
6
2
3
3
2
1
1
3
3
2
1
3
2
1
3
2
1
5
4
3
3
2
9
2
2
2
2
3
4
3
1
4
5
10
2
2
7
3
3
9
Lidar Derived Calculated
<°,> SH 2ze °z
7.8 2.5 8.2 15.0
12.9
8.6
11.0
3.8
3.4
5.1
7.4
20.3
, 16.6
8.2
7.4
6.9
3.2
8.1
8.8
4.8
6.6
5.8
5.5
3.2
5.2
7.9
8.1
11-2
8.9
7.5
7.4
8.2
9.2
8.6
8.0
6.9
4.3
3.9
6.5
7.2
9.9
8.7
10.6
4.2
5.6
5.9
7.9
0.9
3.2
1.8
2.6
6.3
3.5
-
-
2.6
1.1
8.7
-
4.6
2.6
-
0.8
3.5
-
0.8
4.1
5.8
3.0
8.6
11.9
1.2
7.4
5.0
5.0
7.5
6.6
2.2
-
1.0
1.8
4.2
0.8
0.6
8.2
6.1
3.1
9.0
15.1
. 8.6
11.4
4.2
4.3
8.1
8.2
(20.3)
(16.6)
8.6
7.5
11.1
(3.2)
9.3
9.2
(4.8)
6.6
6.8
(5.5)
3.3
6.6
9.8
8.6
14.1
14.9
7.6
10.5
9.6
10.5
11.4
10.4
7.2
(4.3)
4.0
6.7
8.3
9.9
8.7
13.4
7.4
6.4
10.8
24.2
9.0
13.5
4.1
5.8
7.0
7.5
12.5
15.8
7.7
9.1
9.6
9.2
11.5
13.7
5.6
7.0
7.9
8.5
4.4
6.2
10.9
10.1
13.5
-6.6
5.6
4.2
1.7
2.4
3.0
3.9
4.3
2.3
2.7
3.8
4.5
8.7
11.8
13.0
14.0
16.9
19.8
OW/N
18.6
18.6
7.6
7.6
1.2
1.2
1.2
2.1
2.1
2.1
2.6
2.6
2.6
3.7
3.7
3.7
2.2
2.2
2.2
2.2
2.0
2.0
3.7
6.7
6.7
1.2
1.2
1.2
0.6
0.6
0.6
0.6
0.6
1.3
1.3
1.3
1.3
1.9
1.9
1.9
2.8
2.8
2.8
Pasquill-Gif f ord
g,(D) o,(E) o,(F)
8.5 6.2 4.1
18.9
8.9
17.7
9.4
16.8
22.9
5.8
14.0
20.6
19.9
26.2
28.5
13.7
19.9
26.4
13.7
19.6
23.8
26.8
9.1
16.0
9.4
9.1
14.8
17.9
13.7
8.3
4.4
8.1
11.9
18.6
21.4
8.5
11.9
20.2
26.4
8.9
14.8
17.4
16.6
22.5
29.0
13.2
6.5
12.4
6.9
11.8
15.8
4.4
10.0
14.3
13.9
17.9
19.4
9.8
13.9
18.0
9.8
13.7'
16.3
18.3
6.6
11.3
6.9
6.6
10.5
12.5
9.8
6.1
3^4
6.0
8.6
13.0
14.8
6.2
8.6
14.0
18.0
6.5
10.5
12.2
11.7
15.5
19.7
8.7
4.3
8.1
4.5
7.7
10.4
2.9
6.5
9.4
9.1
11.8
12.6
6'. 3
9.1
11.8
6.3
9.0
10.8
12.0
6.8
7.4
4.5
4.3
6.8
8.2
6.3
4.0
2~.T
3.9
5.6
8.5
9.7
4.1
5.6
9.2
11.8
4.3
6.8
8.0
7.7
10.3
12.8
125
-------
0 O
(3 cti
0) O
PM
0) LO
0)
W)
126
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4.5.5 Application Procedures
The Neutral model was run in much the same way as the COMPLEX models.
The relationship between the source and the receptors on the hill is the
same. However, several additional meteorological variables are needed:
N (Brunt-Vaisala frequency) and IX, IY, and IZ (turbulence intensities).
N is calculated at release height from the local temperature gradient. The
intensities of turbulence are linearly interpolated to the release height.
Section 5.2 summarizes these data.
The Impingement model computes a maximum concentration on the hill
rather than an entire concentration field. This maximum occurs at the
theoretical stagnation point for a wind flow directed from the source to the
hill center. The location of this point is approximated in the following
way.
An average radius for each height contour between 10 m and 60 m is
obtained from a map of the hill. The contours are evaluated for each 10 m
height change. Averages are computed from actual north-south and east-west
dimensions. These radii are then fit with a function of the form
R = A H
.B
(27)
where H is the height in meters above the zero height contour, and the
constants A and B are then found to be 970 and -0.38, respectively. This
function is now included in the modeling system so that the Impingement
model operates from the same input file used to run the Neutral model.
127
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SECTION 5
MODEL PERFORMANCE USING CINDER CONE BUTTE FIELD DATA
5.1 Case Hours Selected for Model Evaluations
To select case hours for model evaluation, all 120 hours of experimental
data for Cases 201-215 were examined.* In 21 of these hours, no SFg had
been released. From the remaining 99 hours, 54 were identified as having
reasonably good SF,. sampling data (i.e., more than trace amounts of SF,
were measured at many samplers on the hill). These 54 hours are distributed
among Cases 201, 202, 204-211, and 213-215. Some of the hours removed will
be analyzed at a later date, as they are still considered useful in the model
development and evaluation tasks.
The final number of case hours selected for model evaluation in this
report was reduced to 45 by removing Cases 207, 208, 213, and 215 from
consideration at this time because quality assurance evaluations of the
meteorological data had not been completed. The final selection of 45
representative hours was made among Cases 201-202, 204-206, 209-211, and 214.
Each of the models was evaluated using these 45 case hours except PFM,
which was applied only for hours in which the release height exceeded the
critical dividing streamline height (Hcrit;) by at least 5 m. The choice of
a 5 m margin of error in H . was included to ensure that the model would
be applied in cases where the plume was higher than the theoretical dividing
streamline height. A total of 23 of the 45 hours were selected for the PFM
evaluation. The 45 case hours chosen for the evaluations are described in
more detail in Section 5.2.5.
*Case hour data for Cases 216—218 were not yet fully reduced to be
included in the comparisons made in this report.
128
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5.2 Data Preparation
5.2.1 Tracer Release Data
Release logs maintained during the field experiment at CCB contain
information on the release crane position, the time and duration of tracer
releases, the change in weight of the tracer container as the material is
released, and the height of the tracer release above the local surface. When
used in conjunction with survey data, this information defines the location
of the release point in the hill polar coordinate system (r, 6, z) and the
tracer emission rate.
The emission rate was computed directly from the weight change entries
for the tracer gas cylinders. The weight of the cylinders was recorded
several times during each hour and whenever the tracer was started or
stopped. Emission rates were computed for each hour and tabulated to the
nearest 0.01 g/sec for modeling. Over the course of the experiment,
characteristic SF& emission rates varied from 0.06 g/sec to 0.20 g/sec.
Release positions were denoted by distances from known markers along the
major roads. Primary markers were surveyed for position as well as height
with respect to the zero height of the hill coordinate system (945 m [3,100
feet] above sea level). Secondary markers were set out by the tracer release
crew and were not surveyed; the positions of these secondary markers were
plotted on the survey map of the hill. Release locations were described by
the distance and direction to the nearest marker. The coordinates of these
release points were then measured directly on the map and recorded to the
nearest meter from the hill center and to the nearest 0.1°. The angular
coordinate was later rounded to the nearest 0.5° for input to the models.
The local elevation of the release point was not directly measured but
rather interpolated from the elevations of the closest primary markers and
the general shape of the height contours. In most cases, bracketing primary
markers existed and the height at an intermediate point could be linearly
interpolated. When there was only one primary marker near the release point,
the shape of the nearest height contours was used as a guide. The local
elevation was recorded to the nearest 0.1 m when warranted by the proximity
129
-------
of the primary markers. Otherwise, the elevation was recorded to the nearest
0.5 m.
Release height above the local surface was measured by a calibrated rope
hanging from the release system (see Section 2.3.3). This height was
reported to the nearest meter on the release logs.
5.2.2 Wind Data
Wind speeds and directions derived primarily from Tower A data (the
150 m tower north, of the hill) were used in the modeling to represent
conditions at the release point. Meteorology at the release height was
assumed to be equivalent to the meteorology at Tower A for the same height
above the local surface. If this height corresponded to a measurement level
on the tower, the measurements were used directly; if the release height fell
between two instrumented levels, a linear interpolation was used to estimate
the meteorology at the release height.
At times, additional guidance was needed from photographs, tracer
concentration maps, tethersonde data, and data from the instrumented 30 m
tower on top of CCB (Tower B). This need arose in cases in which one of the
propeller anemometers at the 40 m level of Tower A had seized up or when
there was considerable directional wind shear between the instrumented
levels. When one propeller malfunctioned at 40 m, the wind at that level was
usually reconstructed from the good wind component at 40 m and the mean wind
speeds at the adjacent levels (10 m and 80 m). A reasonable interpolation of
wind speed at 40 m could usually be corroborated by the derived wind
direction (consistent with the good wind component and the inferred mean wind
speed) and other supporting evidence (photos, SFg, and maps). This was not
always possible, however; therefore, the inferred wind speed at 40 m was
computed to be consistent with the most reasonable wind direction in these
cases.
For modeling purposes, wind speeds were rounded to the nearest 0.5 m/sec
although they are probably less certain in many cases. Wind directions were
rounded to the nearest 1.0° but the accuracy may be more like ±2°.
Subjective choices, where they were made, were based mainly on 1-hour average
data. Later analyses of the 5-minute average meteorology may
130 ,
-------
suggest alternate methods for inferring reasonable wind data for the release
height. v
Another source of uncertainty in wind data was the problem of
interpreting the 1-hour vector-averaged wind data taken from the propeller
anemometers. The response of a propeller is less sensitive at large attack
angles. This loss of sensitivity could be responsible for some
underestimation of wind speed or for several degrees of error in wind
direction, the error magnitudes depending upon both speed and direction.
Data used in the modeling have not yet been modified for this effect;
moreover, 1-hour vector averages themselves are usually-an underestimation of
actual wind speeds during the hour. A complete analysis of model sensitivity
to possible underestimation of the wind speed has not been made.*
5.2.3 Turbulence Intensities
The 1-hour intensities of turbulence were measured at 2, 10, 40, 80, and
150 m on Tower A. Linear interpolation was used when the release height did
not coincide with one of these instrumented levels.
Some horizontal turbulence intensity data were not available because of
a seizing propeller anemometer at 40 m. In such cases, the interpolation was
carried out across the 10 m to 80 m interval. The vertical turbulence
intensity at 40 m could be corrected in these instances because the vertical
propeller data were good, but the mean horizontal wind was underestimated.
The correction factor was approximately the ratio of the speed from the good
horizontal wind component to the inferred wind speed (see Section 5.2.2).
5.2.4 Dividing Streamline Height (Hcrlt)
Computation of H . is based on wind speed and temperature data from
Tower A and the height of CCB. The effective height of CCB is taken to be
*Concentrations from models like COMPLEX, which use the wind speed
only for dilution, are inversely proportional to changes in the wind
speed.
131
-------
95 m (base at -5 m; "top" at the 90 m contour). The computation of H ..
was made from 1-hour averaged data.
Where valid 1-hour average data were available on Tower A, H . was
computed from the data base directly. In cases where one 40 m wind component
malfunctioned, however, the computation made use of the inferred wind speed
calculated for that height (see Section 5.2.2).
5.2.5 Summary of Model Input Data
All of the data used as input to the models evaluated in this report are
listed in Table 21. The time and date of each of the 45 test case hours is
followed by the SFg emission rate (Q), the relative release height above
the hill zero contour (not the base of the hill), the local release height,
the local height of the critical dividing streamline (H ^(.)j the release
location, the hourly average wind speed and direction, the turbulence
intensities (IX, IY, IZ), the Brunt-Vaisala frequency (N), and the bulk
Froude number (Fr) of the flow above H . . See Figure 38b for a depiction
of the relationship between H .,., release heights, and the hill coordinate
system.
5.3 Model Evaluation Methods
The statistical evaluation measures adopted for this report follow the
recommendations of the Woods Hole Workshop on Dispersion Model Performance
(Fox 1981). Of the broad set of difference measures suggested in the
Workshop report, a subset was judged appropriate for the observed and modeled
concentration data sets. We routinely calculated and tabulated the following
difference measures:
the average of the absolute residuals, IC -C I (the "absolute
the average of the residuals, C -C (called "the bias" in the
Workshop report);
the average of
gross error");
2
the variance of the residual, cr (C -C.) (the "noise"); and
o p 2
the variance of the absolute residual, CT |C -C |.
o p
132
-------
co
o
CO
O
O
<*i t*S evj e*i «M
Q
i
erf
o
Q
W
H
U
w
co
CO
erf
1
w
CO
g
H
s
M
^1 sssspgssi§sissisillllss§ssslppslsgl|illiii
Q y
u ^ ,
3 g.
0) B
> fl) ^
*r-l y 4J
•w t-< jr
« 3 M
!-* O *H
£ m x
4 CQ CD O U1
§000000000000000001
__ 000000 000000000001
\o IA \o o^ o
CM
w
133
-------
In addition, because it is sometimes asserted that observed
concentrations are lognormally distributed, the following relative difference
measures, although not expressly recommended in the Workshop, were routinely
calculated as well:
the arithmetic and geometric means of the ratio (C /C ) (for
nonzero observed concentrations) and
the corresponding variances.
Data pairings also follow the priority recommendations of the Workshop.
For each data hour, the 1-hour average observed and modeled concentrations
are paired as follows :
• The peak observed concentration is paired with the concurrent
modeled concentration at the same location.
• The peak observed concentration is paired with the concurrent peak
modeled concentration independent of location.
• All observed concentrations are paired with the concurrent modeled
concentrations at the same locations.
Next, to examine and compare their respective distribution functions,
the concurrent observed concentrations, modeled concentrations, residuals,
and absolute residuals are routinely sorted into frequency histograms so as
to emphasize any gross biases or asymmetries in the distributions.
In accord with the Workshop recommendations for graphical displays,
concurrent sets of observed and modeled concentrations were also compared in
scatterplots of C versus C . Scatterplots of C /C versus the ratio
p o p o
of release height to critical dividing streamline height (z /H . ) were
IT CIL It
also generated. These were done to flag any systematic or clear— cut
differences in how the models performed in the limiting cases of stable
(impingement— type) flow (z «H . ) or neutral flow (z »H )
i
The form of the scatterplots was chosen to emphasize model relative
performance — for example, to show how many of the 1— hour average model
predictions fall within a factor of 2 (or more) of the observed
concentrations .
134
-------
Table 22 summarizes the descriptive statistics (including graphical
displays) used for this report. In this table, "paired concentrations" means
sets of 1-hour average observations for the same case hour. The nomenclature
for "peak values" follows the Workshop report:
C (1 ,t ) = peak value observed at time t and location
o n n n
1 .
n
C (1 ,t ) = the corresponding modeled value for the same time
period at the location of observed peak value.
C (l..t ) = the peak modeled value for the time t ,
P J' n' n
irrespective of location.
Finally, in order to compare the overall relative performance of the
different models, statistics for each individual case hour were aggregated
and summarized for the ensemble of 45 case study hours. Evaluating and
interpreting overall model performance on the basis of these statistics
requires a clear understanding of the relationship between modeled and
observed concentrations. This relationship is described below.
Time-averaged concentrations at a single point are governed by complex
phenomena with wide ranges of space and time scales. Models characteris-
tically use parametric descriptions of many of these phenomena in order to
simplify or reduce the input information and number of computations
required. Such simplifications introduce many sources of uncertainty and,
therefore, model estimates will usually not agree precisely with observed
concentrations.
These differences between modeled and observed concentrations result
both from the input data and from the model formulation. Any discrete set of
model input data is necessarily an incomplete description of the actual flow
field. Many Gaussian plume models in use today characterize the flow field
by hourly averages of wind speed and direction measured at one point. This
information is insufficient to resolve the detailed spatial and temporal
structures of the flow field. Any number of different flow fields may be
described by the same average data, and each distinct realization of the flow
field may produce a different observed concentration at a particular point.
The incomplete model inputs, therefore, lead to an infinite set of possible
135
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TABLE 22. DESCRIPTIVE STATISTICS AND ASSOCIATED ANALYSES
Paired Scatter- Tabular
Concentrations Means Variances Distributions plots Data
X
X
X
X
Peak Values
X
vs. C
X
C -C
o p
X
X
X
X
C -C
o p
X
X
X
vs. C
X
C /C
P
X
X
vs. C
X
Co(1n> tn)
C (1 , t )
p n n
X
X
X
X
lCo(1n> V-
Cp(1n>
X
X
Co(1n> tn)
C (1., t )
P J n
X
X
X
X
lCo(1n> V-
'.'
X
X
X
C (1 , t )
on n
X
vs. Zr/Hcrit X
vs. C
136
-------
observed concentrations for each set of input data; or, in other words, the
input data set itself describes an ensemble of possible observed
concentrations .
The Venn diagram in Figure 42 illustrates the ensembles of observed
concentrations corresponding to two distinct input data sets. Each input
data set contains the same variables, but their values are different in the
two sets. In principle, if many more events are observed for the same two
sets of input data, more concentration measurements will be associated with
one or the other of these two data sets. Eventually, an ensemble of possible
observed concentrations might be described for each set of input data
values. Ensembles associated with different input data sets may overlap, and
the range of each ensemble will depend, among other things, upon how fully
the input data describes the wind flow's influence on measured concentrations.
If the input data and concentration measurements contain no measurement
errors, then for a particular input data set the difference between modeled
and observed concentrations will depend upon the standard deviation of the
distribution of possible observed concentrations within the ensemble, and the
difference between the mean of the ensemble and the model estimate. A highly
accurate model may closely estimate the mean of the ensemble, and may
incorporate enough information so that the standard deviation of the
distribution is a small fraction of the mean concentration in the ensemble.
A less accurate model that incorporates less input data might also
closely reproduce all ensemble means but with larger standard deviation. The
performance of these two models will differ because the second model will be
estimating the means of ensembles with broader distributions of possible
observed concentrations.
Figure 43 illustrates the difference between the two models. Denote the
less accurate model as model A, with input data set A, and ensemble standard
deviation O . Model B is the more accurate model. Suppose an observed
A.
concentration, C , lies in the region in which the two ensembles overlap.
Model A's estimate of the ensemble mean concentration, C., might not be
useful if o is large compared to the range of C over all data sets .
A O
Model B's estimate of the ensemble mean concentration, that is, C,
provides a more useful estimate of C because d is smaller.
137
-------
A Single
Observed Concentration
Corresponding to
Inputs I
Set of Possible Observed
Concentrations Associated
with Inputs I
A Single
Observed Concentration
Corresponding to Inputs II
Set of Possible Observed
Concentrations Associated
with Inputs II
Figure 42. Relationship between model inputs, single concentration
observations, and the set of possible concentrations
associated with model inputs.
it
§
138
-------
to
1-1
cd CD
6 -d
•H o
4-> 6
to
(D CD
s
O
CD O
•P
cd
0)
CD
O
td ^
f-i pa
•p o
C -d O
CD fi
O cd p!
C cd
O < CD
*"Cl fH CD
<1> CD r-H
^ o "6
CD B CD
CO CO
f> 6 C
O O CD
fi ^n CD
C -P
C O
CD -H CD
CD -P +->
!3 cd nj
-------
This way of looking at the relationship between model estimates and
observed concentrations suggests that the performance of a model is
ultimately limited by the amount of input information available. A good
model will extract and correctly interpret this information so that the
residual between modeled and observed concentrations is reduced to a random
variable. The observed concentration should actually be treated as a random
variable (Papoulis 1965) because it embodies everything that is "unknown" in
the model. If two or more models use the same input information, then a
comparison of residuals for each model will show which model is most
successful in interpreting the input data. Similarly, a comparison of
residuals for models that are formulated in nearly the same way, but that use
different input information, will show the value of incorporating more
information. The costs of providing more input data and the unavoidable
measurement errors are likely to constrain the benefits of more complicated,
data-intensive models. Careful analyses of residuals should help in defining
the technical benefits associated with increased modeling costs.
We will now recast in mathematical terms the approach to model
comparison.
Observed Concentration
Inputs to an air quality model constitute only part of the information
required to explain concentrations. If the set of model inputs (the "known"
variables) are denoted by x.. , the concentration C at a specific location
can be expressed as
(28)
where f(x , x~) is some function of known variables (the set x^), and
unknown variables (the set x2). Because the set x2 can take any values
for given x,, the concentration C can also assume any of a broad range of
values. Therefore, the model inputs x^ define an infinitely large ensemble
of concentrations.
140
-------
An observed concentration C (x..) belonging to this ensemble can be
written as the sum of the mean of the ensemble and a random variable £:
(29)
= 0. In Equation 29, the angle brackets denote an
ensemble average obtained by keeping x.. fixed. Therefore, the ensemble
mean is independent of x». If C ,is the average over the ensemble of
concentrations defined by the x.. , then = C (x, ) .
1 o 1 2. pi
The Modeled Concentration
Equation 29 may be rewritten as:
.» X2> " W
(30)
In this equation only x., is known, so the best a model can do is estimate
C (x ). Because x_ is unknown, we expect any single observation
corresponding to x to deviate from the ideal model prediction C (x,).
2 2 p
The magnitude of this deviation is determined by <£ > = O .
Because £ is a random variable, x should be chosen so that O
is as small as possible. Also, in order to use a model it is necessary to
know how cr varies with x . This means that an air quality model
should ideally consist of a submodel for C as well as a submodel for the
stochastic term £. While physical principles can help in constructing the
model for C , we have to rely on trial-and-error empirical methods to infer
O£. To simplify the modeling of e, it is convenient to choose the
model inputs x1 (and the model itself) so that £ is not a function of the
inputs x1 . Equation 30 can then be written as
Co *
£(X2)
(31)
Equation 31 then represents the "ideal" relationship between model calcula-
tion and observation. As described by Box, Hunter, and Hunter (1978), such a
141
-------
model produces e's that have zero mean and constant variance (independent
of x,), and are distributed independently of one another. The characteris-
tics of an adequate model can then be described in terms of the residual
£ 3 C -C . With a series of observations and calculations we can
o p
calculate the following statistics:
e « —
(32)
- F>
(33)
Then, for an adequate model, e should be near zero (i.e., the model should
be accurate) and Cf should be small (i.e., the model should be precise).
Model Improvement
The previous discussion shows that a model can be improved by reducing
0_. This process is equivalent to expanding x, to include as much of
£ J_
X2 as possible. If x, included all of x™, a model could in principle
calculate the observed concentration C precisely. Because this is
impossible in practice, the observed concentration must be treated as a
random variable. The formulation of an improved model is subject to several
limitations. The uncertainty associated with formulating a model to
incorporate added information can lead to errors. Also, inevitable errors in
model inputs may degrade the utility of increasing the complexity of a model.
A Method to Test Models
The previous discussion provides the framework for a method to test
s. We have seen that for
have the following properties:
models. We have seen that for an adequate model, the residuals (C -C )
142
-------
• e - 0,
• CJ should be small, and
• e should be unrelated to C or x,.
The first step in examining a model is to plot e against C or x .
The plot should show a band-like structure in which e is uncorrelated with C .
Also £ should be randomly distributed about zero. This visual examination
provides an easy check on residual behavior. It also indicates the range of C
over which the model can be used. Clearly, one would like to have as large a
range of C as possible in which the model behavior is acceptable.
To use the statistics of e, it is desirable to transform C and C
so that £ is normally distributed. This knowledge of the distribution of
£ allows us to estimate confidence intervals for the model prediction.
This procedure is illustrated in Appendix C.
i
The relationship between the transformed observation C and the
transformed prediction C can be written as
C + e
P
(34)
where e is normally distributed with zero mean and variance
-------
Figure 44. The relative performance of different models.
144
-------
For the transformation C = In C, it is convenient to plot the
logarithmic mean m against the logarithmic standard deviation s , where
° " , 8
m and s are defined as follows:
g g
m
exp
exp In (Co/Cp)
(36)
s = exp (a ) = exp a(ln(C /C ))
g e op
(37)
When plotted on double log paper, m and s figures are equivalent to e
O &
and cr£ figures. This labeling allows one to interpret model performance
in terms of multiplicative factors. For example, an m of 0.5 implies a
o
tendency to overestimate by factor of 2.
5.4 Sample Case Study Results - Case 205, Hour 5
This section provides a representative case study to illustrate the
kinds of analyses available for use in evaluating model performance on an
hour-by-hour basis. Spatial characteristics of calculated.and observed
concentration fields must be used if we want to know why one model may
estimate the highest observed concentrations better than another. This
sample case study hour (Case 205, hour 5) has already been described in
Section 2.4.2. The following discussion presents a synopsis of the meteoro-
logical conditions and the observed distribution of 1-hour average SFfi
concentrations.
Case 205, hour 5 was an hour with persistent southeast winds averaging
6.0 m/sec at the release height. The flow regime was observed to be neutral
(flow up the east draw and over the top of CCB) with respect to plume
behavior, although the Turner scheme for estimating dispersion stability
class indicated that class F was appropriate for this hour (1.3 m/sec hourly
average wind speed at 10 m). The local release height was 50 m, and the
computed dividing streamline height was 25 m. The observed 1-hour SF,-
o
concentration distribution for this hour, shown in Figure 45, confirms the
considerable spatial extent to which the plume contacted the surface of CCB,
although concentrations are relatively low.
145
-------
Figure 45. Observed SF6 concentrations (ppt) for Case 205, 0400-0500.
Source: r = 1156 m, 0 = 120.5°, effective height = 41.1 ra,
Q = 0.09 g/sec.
146
-------
The model evaluation products for this case hour are presented for
COMPLEX I and II, PFM, and the Neutral model only. Estimates from Valley and
the Impingement models are deferred until Section 5.5, as these models
produce an estimate of the maximum concentration only.
5.4.1 COMPLEX I and COMPLEX II
The first step in the model evaluation is a quantitative comparison of
the distribution of measured and calculated concentrations. The 1-hour
average ground-level SF concentrations calculated by COMPLEX I and COMPLEX
II for stability classes D, E, and F, respectively, are shown in Figures 46
through 51. (For stability class D, COMPLEX I and COMPLEX II use plume path
coefficient = 0.5; for stability classes E and F, both models use plume path
coefficient =0.) The calculated concentrations are given as parts per
trillion (ppt). The model calculations were made at each of the 93 possible
sample locations shown earlier in Figure 12.
Only in the COMPLEX II runs for E and F stability is the peak
concentration (385 ppt, observed at the base of the southeast draw) equaled
or exceeded elsewhere on the hill. Qualitatively, though,' the spatial
distribution pattern shown in the COMPLEX II runs is too narrow in the
crosswind direction (compared to the observed concentrations).
If the peak concentration at the base of the hill is ignored for the
moment*, then COMPLEX II estimates using stability class D dispersion
coefficients show a better agreement with the observations. It nonetheless
appears that the calculations across the top of the hill and out to the sides
would improve further if the model plume were broader.
The COMPLEX I results, by comparison, show a horizontal spread that
appears too large, especially with respect to the concentrations on the south
side of the hill. Nonetheless, if we focus on the higher concentrations near
*These locally large concentrations at the base of the hill were
observed on several occasions during the experiments; they are
tentatively attributed to downslope flows driven by horse—shoe
vortices or drainage. None of the models addresses this effect, but
the model statistics reflect these large measured concentrations
nonetheless.
147
-------
Figure 46. Complex I: calculated SFe concentrations (ppt) for Case
205, Hour 5, Stability Class D.
148
-------
38."
Figure 47. Complex I: calculated SFg concentrations (ppt) for Case
205,, Hour 5, Stability Class E.
149
-------
Figure 48. Complex I: calculated SFg concentrations (ppt) for Case
205, Hour 5, Stability Class F.
150
-------
80.
Figure 49. Complex II: calculated SFg concentrations (ppt)
205, Hour 5, Stability Class D.
Case
151
-------
Figure 50. Complex II: calculated SFg concentrations (ppt) for Case
205, Hour 5, Stability Class E.
152
-------
3S.
Figure 51. Complex II: calculated SFg concentrations
205, Hour 5, Stability Class F.
for Case
153
-------
the top of the hill, COMPLEX I with class E dispersion coefficients does a
fair job of estimating those concentrations.
A better quantitative idea of the performance of each of the models is
obtained by looking at scatterplots of modeled versus observed
concentrations. In Figures 52, 53, and 54, the solid triangles indicate
COMPLEX II results and the open squares indicate COMPLEX I results. For
potential regulatory application, of course, the chief interest is to gauge
how extensively and consistently the models may overestimate or underestimate
concentrations, especially the highest observed concentrations. Scatterplots
are extremely helpful in identifying such gross tendencies. As shown in the
second of these scatterplots, for example, the COMPLEX I model run with E
stability tends to overestimate the lower observed concentrations (C <
80 ppt) but to underestimate the higher concentrations. By comparison, the
COMPLEX II model both overestimates and underestimates the lower observed
concentrations by much wider margins than COMPLEX I. COMPLEX II
underestimates the peak observed concentration but overestimates the second
highest, in each case by substantial margins.
Tables 23 through 25 display frequency histograms for the observed
concentrations, for the concentrations modeled with COMPLEX I and COMPLEX II,
and for the residuals. (As before, the model calculations are shown
successively for stability classes D, E, and F.) For example, as Table 24
for class E shows, the COMPLEX I results span a narrow range similar to the
observed concentrations; whereas the COMPLEX II results are broadly
distributed. From the histograms of the residuals, it can readily be seen
that the COMPLEX II paired results are on average skewed slightly toward
overestimation; that the COMPLEX I results are skewed (very weakly) toward
overestimation; and that for either model most of the residuals are less than
160 ppt.
The next level of analysis uses the descriptive statistics calculated
from all paired concentrations for the case study hour. Tables 26 through 31
show these calculations for the six previous combinations of model and
stability class. The column "ID" refers to individual sampler locations
shown previously in Figure 12. (For this data hour, a total of 31 valid,
nonzero, full-hour average SF,- concentration samples was obtained.) The
other table entries are self-explanatory.
154
-------
PREDICTED
540.0-
480.8-
4S0.0-
360.0-
300.0-
340.0-
180.0-
130.0-
60.0-
60.0 180.0 180.0 240.0 300.0 36«.0 480.0 480.0 540.0
LEGEND
a COMPLEX I
A COMPLEX II
OBSERVED (PPT)
Figure 52. Complex I and II: calculated SP^ concentrations versus
observed SFg concentrations for Case 205, Hour 5,
Stability Class D.
155
-------
PREDICTED CPPT)
480.0-
430.0-
366.0-
360.0-
340.0-
180.0-
120.0-
60.8-
LEGEND
OBSERVED (PPT)
COMPLEX
COMPLEX
Figure 53. Complex I and II: calculated SF6 concentrations versus
observed SF6 concentrations for Case 205, Hour 5,
Stability Class E.
156
-------
PREDICTED (PPT)
1080.0-
960.0-
840.0-
730.0-
600.0-
480.0-
360.0-
340.0-
150.0-
180.0 a40.0 360.0 480.0 600.0 720.0 840.0 960.0 1080.0
LEGEND
n COMPLEX I
* COMPLEX II
OBSERVED (PPT)
Figure 54. Complex I and II: calculated SFg concentrations versus
observed SFg concentrations for Case 205, Hour 5,
Stability Class F.
157
-------
TABLE 23. FREQUENCY DISTRIBUTIONS OF SF6 CONCENTRATIONS (ppt)
FOR COMPLEX I AND II MODELS
(CASE 205, HOUR 5, STABILITY CLASS D)
CLASS INTERVAL
OBSERVED
COMPLEX I
COMPLEX II
0.
5.
10.
60.
HO.
160.
210.
260.
310.
360.
5.
10.
60.
110.
160.
210.
260.
310.
360.
410.
0
O
6
14
7
2
1
0
0
1
6
O
3
17
6
0
0
0
0
0
8
4
2
5
5
5
2
0
0
0
#»##»**#*##*********************************************************************
##»»#*»*#«#****#**#**»*************#********************************************
RESIDUALS (CO-CP)
CLASS INTERVAL COMPLEX I COMPLEX II
ABSOLUTE RESIDUALS !CO-CP!
CLASS INTERVAL COMPLEX I COMPLEX II
-400.
-32O.
-240.
-160.
-SO.
0.
SO.
160.
24O.
320.
-320.
-240.
-160.
-BO.
O.
80.
160.
240.
320.
400.
O
0
0
0
12
13
5
0
1
0
O
0
0
1
10
16
3
O
1
0
0.
4O.
80.
120.
160.
200.
240.
2BO.
320.
360.
40.
SO.
120.
160.
200.
240.
280.
320.
360.
400.
IS
7
3
2
O
O
0
1
0
0
9
17
4
0
0
O
1
0
O
0
if*******************************************************************************
158
-------
TABLE 24. FREQUENCY DISTRIBUTIONS OF SF6 CONCENTRATIONS (ppt)
FOR COMPLEX I AND II MODELS
(CASE 205, HOUR 5, STABILITY CLASS E)
CLASS INTERVAL
OBSERVED
COMPLEX I
COMPLEX II
0. -
5. -
1O. -
90. -
170. -
250. -
330. -
41O. -
490. -
570. -
5.
10.
90.
170.
250.
330.
410.
490.
570.
65O.
o
o
IS
9
3
O
1
0
0
0
6
O
3
14
8
0
0
0
0
0
12
1
5
3
2
4
0
3
O
1
RESIDUALS (CO-CP)
CLASS INTERVAL COMPLEX I COMPLEX II
ABSOLUTE RESIDUALS !CO-CP!
CLASS INTERVAL COMPLEX I COMPLEX II
-400.
-320.
-240.
-16O.
-80.
O.
80.
160.
240.
320.
-32O.
-240.
-160.
-80.
0.
80.
160.
240.
320.
400.
O
0
0
6
14
7
3
0
0
1
1
3
3
2
4
11
6
0
1
0
0.
40.
80.
12O.
160.
200.
240.
280.
320.
360.
40.
80.
120.
16O.
200.
24O.
280.
320.
36O.
400.
9
12
7
2
0
O
O
0
1
0
2
13
7
1
3
O
2
2
0
1
159
-------
TABLE 25. FREQUENCY DISTRIBUTIONS OF SF6 CONCENTRATIONS (ppt)
FOR COMPLEX I AND II MODELS
(CASE 205, HOUR 5, STABILITY CLASS F)
****»»##»#*##**####**#**#**##«•****#*#**********•*********************************
CLASS INTERVAL
OBSERVED
COMPLEX I
COMPLEX II
0.
5.
10.
160.
31O.
460.
610.
760.
910.
1060.
5.
1O.
160.
310.
460.
610.
760.
910.
1060.
1210.
0
O
27
3
1
0
0
0
0
0
6
1
4
20
0
0
0
0
0
0
16
2
3
1
5
2
0
1
0
1
»*#»**#***##**##*»#*»*****»*********#******«•*#**********#**************«•********
RESIDUALS (CO-CP)
CLASS INTERVAL COMPLEX I COMPLEX II
ABSOLUTE RESIDUALS !CO-CP!
CLASS INTERVAL COMPLEX I COMPLEX II
-10OO.
-BOO.
-600.
-400.
-200.
0.
200.
400.
60O.
BOO.
-BOO.
-600.
-400.
-200.
0.
200.
400.
600.
BOO.
1000.
O
O
O
1
19
10
1
O
0
0
1
1
0
6
3
19
1
0
0
O
0.
1OO.
200.
300.
400.
500.
6OO.
7OO.
800.
900.
100.
200.
300.
400.
500.
600.
700.
800.
900.
1000.
17
12
1
1
0
0
O
O
0
0
18
4
3
4
0
0
O
1
0
1
**##*#*#***»***#**#**«•#********************************************************
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166
-------
To determine which of these six model/stability class combinations best
matches the observed concentrations during Case 205, hour 5, the respective
statistics shown at the bottom of each table should be compared. Table 32
lists these for side-by-side comparisons. If all criteria were given equal
weight, the descriptive statistics would seem to suggest that of these six
choices of model and stability class, the COMPLEX I model with E stability is
preferred (note that the maximum is estimated better by two other choices):
e the mean modeled value agrees most closely with the mean observed
value and is somewhat larger (slightly conservative),
a the mean residual error is smallest (least bias),
e the standard deviation of the residual error is not much larger
than the standard deviation of the observed concentrations, and
e the standard deviation of the modeled concentrations is only
marginally greater than that of the observed concentrations.
5.4.2 PFM
A similar set of plots, tables, and figures is presented below for the
PFM simulation of Case 205, hour 5. Stability classes D and E were both used
in running PFM so that comparisons could be made with the best-performing
versions of the COMPLEX computations.
The 1-hour average ground-level SF& concentrations calculated by PFM
are shown in Figures 55 and 56. The distribution of modeled concentrations
is qualitatively similar to that calculated by the COMPLEX II model for the
same stability classes because they use similar horizontal distribution
functions. The magnitudes, however, are different.
PFM with stability class E produces concentrations in excess of the
observed maximum but tends to overestimate all of the concentrations on the
central part of the hill. If the observed maximum (located at the base of
the windward side of the hill) is ignored, PFM with stability class D does
better; still, there appears to be too little plume spread to match the
observations.
167
-------
TABLE 32. SUMMARY STATISTICS FOR COMPLEX I AND COMPLEX II
(Case 205, Hour 5)
Number of Points
max (C0)
max (C )
o p
-
max |CQ -Cp|
'Co - V
-------
Figure 55. PFM: calculated SF6 concentrations for Case 205, Hour 5,
Stability Class D.
169
-------
85.
Figure 56. PFM: calculated SFg concentrations for Case 205, Hour 5,
Stability Class E.
170
-------
Scatterplots of modeled versus observed concentrations presented in
Figures 57 and 58 show evident similarities with the scatterplots for
COMPLEX II with stability classes D and E. Many low concentrations away from
the hill center are underestimated, and most of the concentrations above
60 ppt are overestimated (especially for stability class E). Frequency
distributions presented in Tables 33 and 34 show that although many
similarities between PFM and COMPLEX II concentrations exist, PFM tends to
produce higher concentrations. This tendency increases the range in the
distribution of residuals.
Finally, paired concentrations and a summary table of the PFM statistics
for this case hour are presented in Tables 35 through 37. The stability
class for which PFM performs better (on the basis of summary statistics)
appears to be class D, even though the mean statistics and the peak
concentration show a tendency toward underestimation. A comparison of PFM
and COMPLEX summary statistics shows that PFM performs as well as any of the
COMPLEX models for the case hour.
5.4.3 New Experimental Models
Figure 59 displays the distribution of concentrations calculated by the
Neutral model (see Section 4.5.3) for Case 205, hour 5. Concentrations are
presented only at those samplers with good SF, data. The spread of
concentrations over the hill appears to be reproduced fairly well, but most
concentrations are underestimated.
These features are evident in the scatterplot of modeled versus observed
concentrations as well (see Figure 60). The lower concentra- tions are just
as likely to be either over- or underestimated, but few concentrations are
calculated to be less than 5 ppt. The higher concentrations (>120 ppt) are
underestimated.
Frequency distributions (see Table 38) and the statistics of paired
concentrations (see Tables 39 and 40) reinforce this description. Modeled
concentrations populate lower class intervals, and the distribution of
residuals is biased toward underestimation. One half of the calculations lie
within 40 ppt of the corresponding observations. The mean of all
calculations is slightly greater than half the mean of all observed
171
-------
PREDICTED (PPT)
540.0-
480.0-
420.0-
360.0-
300.0-
240.0-
180.0-
130.©-
60.0-
60.0 180.0 180.0 240.0 300.0 360.0 4S0.0 480.0 540.0
OBSERVED (PPT)
Figure 57. PFM: calculated SFg concentrations versus observed SFg
concentrations for Case 205, Hour 5, Stability Class D.
172
-------
PREDICTED
-------
TABLE 33. FREQUENCY DISTRIBUTIONS OF SFg CONCENTRATIONS (ppt)
FOR PFM (CASE 205, HOUR 5, STABILITY CLASS D)
CLASS INTERVAL.
OBSERVED
PFM
0.
5.
1O.
6O.
HO.
160.
210.
260.
310.
360.
5.
10.
60.
110.
160.
210.
260.
31O.
360.
410.
0
0
6
14
7
2
1
0
0
1
7
3
4
5
5
2
3
1
1
0
RESIDUALS (CO-CP)
CLASS INTERVAL PFM
ABSOLUTE RESIDUALS !CO-CP!
CLASS INTERVAL PFM
-300.
-240.
-ISO.
-12O.
-60.
0.
60.
120.
ISO.
24O.
-240.
-180.
-120.
-60.
0.
60.
120.
ISO.
240.
3OO.
0
0
2
5
5
e
10
o
i
o
o.
30.
60.
90.
120.
150.
ISO.
210.
240.
270.
30.
60.
90.
120.
150.
180.
210.
240.
270.
300.
5
8
12
3
2
O
0
1
0
0
174
-------
TABLE 34. FREQUENCY DISTRIBUTIONS OF SF6 CONCENTRATIONS (ppt)
FOR PFM (CASE 205, HOUR 5, STABILITY CLASS E)
CLASS INTERVAL
OBSERVED
PFM
0.
5.
10.
80.
ISO.
220.
29O.
36O.
43O.
500.
5.
10.
80.
150.
22O.
290.
360.
43O.
50O.
57O.
0
O
12
13
4
1
0
1
0
0
13
1
5
1
3
5
0
1
1
1
RESIDUALS
CLASS INTERVAL PFM
ABSOLUTE RESIDUALS ICO-CP!
CLASS INTERVAL PFM
-400.
-320.
-240.
-16O.
-SO.
0.
80.
16O.
240.
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177
-------
TABLE 37. SUMMARY STATISTICS FOR PFM
(Case 205, Hour 5)
OBSERVED
PFM
Stability Class
D E
Number of Points
a(co)
max (C )
C
P
o(Cp)
max (C )
a
-------
Figure 59. Neutral model: calculated SF6 concentrations (ppt) for Case
205, Hour 5.
179
-------
PREDICTED (PPT)
543.0"
486.0-
420.0-
360.0-
300.0-
240.0-
180.0-
130.0-
60.0-
60.0 120.0 180.0 240.0 300.0 360.0 430.0 480.0 540.0
OBSERUED (PPT)
Figure 60. Neutral model: calculated SF^ concentrations versus
observed SF6 concentrations for Case 205, Hour 5.
180
-------
TABLE 38. FREQUENCY DISTRIBUTIONS OF SFg CONCENTRATIONS (ppt)
FOR NEUTRAL MODEL (CASE 205, HOUR 5)
CLASS INTERVAL
OBSERVED NEUTRAL MODEL
0.
5.
10.
60.
110.
160.'
21O.
260.
310.
360.
5.
10.
60.
110.
16O.
210.
26O.
310.
360.
410.
0
0
6
14
7
2
1
0
0
1
2
2
11
14
2
0
0
O
0
0
RESIDUALS (CO-CP)
CLASS INTERVAL NEUTRAL
ABSOLUTE RESIDUALS !CO-CP!
CLASS INTERVAL NEUTRAL
-400.
-320.
-240.
-16O.
-80.
0.
BO.
160.
240.
320.
-320.
-240.
-160.
-80.
0.
80.
160.
240.
320.
400.
0
0
0
O
7
20
2
1
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1
0. -
40. -
80. -
12O. -
160. -
200. -
24O. -
280. -
32O. -
36O. -
4O.
SO.
120.
160.
200.
240.
2SO.
320.
36O.
400.
16
11
2
0
1
0
0
0
0
1
181
-------
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182
-------
TABLE 40. SUMMARY STATISTICS FOR NEUTRAL FLOW MODEL
(Case 205, Hour 5)
OBSERVED
NEUTRAL MODEL
Number of Points
a(co)
max (CQ)
r
p
a(Cp)
max ( C )
C -C
o p
max C -C
_ p ... p.
|Co - Cp'
a(|co -cpl)
31
110
69
385
62
38
115
49
73
378
55
68
Note:
SF, concentrations are in ppt.
D
183
-------
concentrations, and the maximum calculated concentration is about one-third
of the maximum observed.
5.5 Summary of Model Performance
5.5.1 Model Performance Statistics
Valley
Valley model estimates of the maximum 1-hour average tracer
concentrations (scaled by the emission rate) are presented in Table 41 for
each of the 45 case hours. The concentrations are scaled by the emission
rate to facilitate comparisons. Also included are the associated centerline
concentrations (zero stand-off distance, no surface reflection), observed
concentrations, and ratios of the hourly calculated to observed
concentrations.
The Valley estimates of C/Q depend only on the distance from the source
to the nearest possible point of impingement. With Valley, predicted C/Q
values* range from 53 to 105. The maximum possible C/Q from the Valley model
occurs at a distance of 366 m. This value is about 107, so the calculated
value of 105 is virtually the greatest C/Q possible from Valley.
Valley appreciably underestimated peak observed concentrations in the
four test case hours with the highest observed scaled peak concentrations
(C/Q), and estimated the fifth and sixth highest scaled peak concentrations
to within 1%. All peak concentrations in the remaining 39 case hours were
overestimated by Valley. Of the four hours in which Valley underestimated
observed concentrations, one was a nonimpingement case in that the plume was
released above the critical dividing streamline. This case hour occurred in
the early morning as the sun was rising, and the release was very close to
the hill (213-m); so the class F dispersion rate for O^ apparently
underestimated the size of the plume. Wind speeds for the other three
-3
-3
*Units of 10 sec m ; 1 yg/m = 167.5 ppt for
184
-------
TABLE 41. SUMMARY C/Q STATISTICS FOR VALLEY AND
CENTERLINE VALLEY CALCULATIONS
Exp.
201
201
201
301
20 1
202
202
2O2
2O2
202
202
204
204
204
204
204
2O4
205
205
205
206
206
206
2O6
206
209
209
209
209
209
210
210
210
210
210
211
211
211
211
211
211
214
214
214
214
Case
Hour
1
2
4
3
6
1
2
3
4
5
6
1
2
5
6
7
S
4
5
6
4
5
6
7
S
1
2
3
7
3
3
4
6
7
S
1
2
3
4
5
6
3
4
7
8
Max Co
32. 2
25. 1
IS. 6
34. 6
18. 7
18. 0
33. 6
67. 2
81. 6
49. 2
11. 8
14. 5
11. 3
4. 8
17. 6
9. 6
16. 1
15. 4
25. 5
15. 5
56. 7
41. 2
124. 2
92. 8
154. 6
3. 8
5. 0
5. 6
7. 6
20. 3
11. 5
4. 6
4. 4
8. 1
17. 9
11. 5
6. 4
3. 9
33. 0
97. 4
53. 1
77. 6
54. 4
119. 1
31. 7
Max Cp
79. 5
79. 5
86. 2
86. 2
86. 2
68. 2
68. 2
81. 4
81. 4
76. 7
71. 9
6B. 9
6S. 9
SI. 3
81. 3
81. 3
81. 3
56. 5
54. 8
60. 9
92. 2
92. 2
92. 2
92. 2
92. 2
7S. 6
75. 6
75. 6
60. 8
60. S
55. 3
55. 3
58. 1
58. 1
64. 1
69. 6
69. 6
69. 6
62. 6
62. 6
62. 6
105. 1
93. 4
53. 4
7O. 1
Max Cp/
Max Co
2. 47
3. 17
4. 63
2. 49
4. 61
3. 79
2. 03
1. 21
1. 00
1. 56
6. 09
4. 75
6. 10
16. 94
4. 62
8. 47
5. 05
3. 67
2. 15
3. 93
1. 63
2. 24
O. 74
0. 99
0. 6O
19. 89
15. 12
13. 50
8. 00
3. 00
4. 31
12. 02 •
13. 20
7. 17
3. 58
6. 05
1O. 83
17. 85
1. 9O
O. 64
1. IS
1. 35
1. 72
0. 45
2. 21
Max CL
67. 5
67. 5
78. 5
78. 5
78. 5
52. 4
52. 4
70. 3
70. 3
63. 4
57. 0
53. 2
53. 2
70. 3
70. 3
70. 3
70. 3
39. 9
38. 2
44. 3
279. 0
279. 0
279. 0
279. 0
279. 0
61. 8
61. 8
61. 3
44. 2
44. 2
38. 7
38. 7
41. 5
41. 5
47. S
54. 2
54. 2
54. 2
46. 2
46. 2
46. 2
139. 7
93. 7
454. 5
376. 4
Max CL/
Max Co
2. 10
2. 69
4. 22
2. 27
4. 2O
2. 91
1. 56
1. 05
. 36
1. 29
4. 83
3. 67
4. 71
14. 64
3. 99
7. 32
4. 37
2. 59
1. SO
2. 86
4. 92
6. 77
2. 25
3. 01
1. 81
16. 27
12. 36
11. 04
5. 82
2. 18
3. 37
8. 42
9. 43
5. 13
2. 67
4. 71
S. 46
13. 89
1. 4O
. 48
. 87
1. SO
1. 72
3. 82
11. 8S
185
-------
hours were between 2 and 2.5 m/sec (Case 206, hours 5 and 8; Case 211,
hour 5). In fact, the highest observed C/Q of 155 occurred with a wind speed
of 2.5 m/sec and PG class F (Case 206, hour 8).
One possible cause of Valley's failure to estimate the highest observed
hourly SFg concentrations at CCB may be related to the assumed 10 m "miss
distance." Although this distance may be appropriate for large pollutant
sources in complex terrain where plume QZ values are considerably larger
than 10 m, it may be too large for the scale of the experiment at CCB.
Reducing the miss distance to 8.4m would be sufficient to reproduce the
maximum observed C/Q ratio in Case 206, hours 6 and 8. However, it would not
be sufficient to reproduce the maximum concentration of 97 ppt observed in
Case 211, hour 5. If the average wind speed for this hour were used
(2.0 m/sec instead of 2.5 m/sec), then a C/Q in excess of 97 would be
produced with a miss distance of 6.5 m. The use of a lower wind speed as
well as a smaller miss distance at CCB may be justified again by the scale of
the experiment: tracer plumes are much closer to the ground, much closer to
terrain, and much narrower than typical plumes from large sources.
Figures 61 and 62 are scatterplots of modeled to observed concentration
ratios versus modeled concentrations for both Valley and Valley centerline
SF, concentrations. It is seen that about one-third of the 45 observed
6
concentrations are within a factor of 2 of the hourly Valley calculations,
whereas about one-fourth are within a factor of 2 of the Valley centerline
calculations. (Note that in these scatterplots some data points fell on top
of one another within the resolution of the plotter, and some values fell
below the bottom of the plot when modeled values were very small. Therefore,
the number of points distinguishable on the plots may not be as large as the
number of sample points in the data set plotted.)
COMPLEX I and COMPLEX II
A complete set of statistical and graphical analyses of COMPLEX model
calculations, like those illustrated for the example case study hour, was
assembled for each of the 45 case hours. (The complete set of analyses is
available from the EPA Project Office upon request.) Most of the key
statistical results are summarized in Tables 42 and 43. The asterisks that
186
-------
C(PRED)xCCOBS)
100.0-
50.0-
30.fi-
le.9-
5.0-
2.0'
i.e-
.5
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C(Um.lEV)/C(OBS) US. C/0
PEftK CONCENTRrtTIONS
®
1.0 10.0 20.0 50.0 100.0 800.0 506.6 1000.0
C(PRED>/0
Figure 61. Variation of modeled-to-observed ratios of maximum hourly
concentrations with modeled concentrations calculated by
Valley. Circles identify the five highest observed SF6
concentrations CC/Q).
187
-------
C(UAU.EV-CENTERLINE>/CCOBS> US. C(UAUEV-CENTERUNE>/0
PEAK CONCENTRATIONS
C(PRED)'CCOBS)
160.0-
50.0-
20.0-
10.0-
5.0-
2.0-
1.0-
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i.e
®
@
200.0 500.0 1000.0
C(PRED>'0
Figure 62. Variation of modeled-to-observed ratios of maximum hourly
SFg concentrations with modeled concentrations calculated
by Valley (centerline). Circles identify the five highest
observed SF^ concentrations (C/Q).
188
-------
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189
-------
CO
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•-t n v o « -» -* •* N -« -4 ^- o in o ch -* ~* -H m n -< «r « ni ci nl o «r *^ *-•-H on n t n *• n -o -o
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-------
appear in Table 42 denote the stability class for each case hour according to
the Turner scheme for nighttime stability using the observed 10 m wind speed
(assuming no cloud cover, which generally agreed with net radiometer
measurements). For a given case hour, the appropriate stability class is
signaled by an asterisk in one of the three C columns. For example, at
the entries for Case 205, hour 5, the asterisk appears in the C column
corresponding to stability class F; for this hour, class F stability was the
most appropriate choice according to the Turner scheme because the mean 10 m
wind speed was 1.3 m/s and clear skies prevailed.
Figures 63 through 70 are scatterplots of modeled maximum-to-observed
maximum concentration ratios versus modeled maximum concentrations. These
concentrations have been scaled by the emission rate (Q) to facilitate
comparisons from one case hour to the next. About one-half of the points lie
in the range 0.5 < C /C < 2 (at least in the COMPLEX I results), and
- p o —
the other half lie significantly above this range (indicating
overestimation). As the stability class changes from D to F, both COMPLEX I
and COMPLEX II tend to overestimate more. Figures 66 and 70 illustrate the
performance of COMPLEX I and COMPLEX II when the stability class is selected
be the Turner scheme. These figures show that COMPLEX I would be preferable
to COMPLEX II for use at CCB.
Each of these scatterplots may be interpreted as a plot of the residual
between the modeled and observed concentration versus the modeled
concentration, if the observed concentration is assumed to be lognormally
distributed about the modeled concentration (see Section 5.3). An excellent
model should produce a scatterplot with the residuals tightly clustered about
zero (C /C =1) for all C , and the scatter about zero should be equal
throughout the range of C .
" Figures 63 through 70 show that the residuals based on maximum
concentrations (for all variants of the COMPLEX models tested) do not exhibit
these characteristics. The scatter is large at all C , and the mean
increases with C .
191
-------
C US. C(COHPLEX I)/0
PEAK CONCENTRATIONS
®
1 1 1 1 ~1 I
i.e 10.0 20.e 50.0 100.0 200.0 500.0 1000.0
CCPREDVQ
Figure 63. Variation of modeled-to-observed ratios of maximum hourly SF(,
concentrations with modeled concentrations calculated by
Complex I (Stability Class D). Circles identify the five
highest observed SF6 concentrations (C/Q).
192
-------
C(PRED)/C(OBS)
50.0-
30.0-
10.0-
5.0-
2.0-
1.0-
.5
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C(COMPLEX I)/C(OBS) US. CCCOHPLEX I )/Q
PErtK CONCENTRATIONS
®
®
®
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1.0 10.0 20.0 50.0 100.0 290.e 500,0 1000.0
C
-------
CCPREDVCCOBS)
ioa.0-
50.0-
20.0-
10.0-
5.0-
3.0
1.0-
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l.C
CCCOMPtEX I)XC(OBS) US. CCCONPLEX IJ/0
PEAK CONCENTRATIONS
1 1
10.e se.0
50.0 100.0 800.0 500.0 1000.0
Figure 65. Variation of modeled-to-observed ratios of maximum hourly
concentrations with modeled concentrations calculated by
Complex I (Stability Class F). Circles identify the five
highest observed SF6 concentrations (C/Q).
194
-------
CJCOHPLEX I)/CCOBS> US. C(COHPLEX IJ/O
PEAK CONCEMTRftTIONS
C
100.9-
50.0-
30.0-
10.0-
5.0-
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Figure 66.
10.0 59.
50.0 100.0 S00.0 506.9 1000.0
CCPREDJ/0
Variation of modeled-to-observed ratios of maximum hourly
concentrations with modeled concentrations calculated by
Complex I (appropriate stability class - Turner scheme).
Circles identify the five highest observed SF6 concentrations (C/Q)
195
-------
CCCOMPLEX II)xC(OBS) US. CCCOMPLEX ID/Q
PEAK CONCENTRATIONS
C(PRED)/CCOBS)
iee.0-
se.a-
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.1
®
1.0 10.8 30.0 50.0 100.0 300.0 500.0 1000.0
C(PRED)/Q
Figure 67. Variation of modeled-to-observed ratios of maximum hourly SF6
concentrations with modeled concentrations calculated by
Complex II (Stability Class D). Circles identify the five
highest observed SF^ concentrations (C/Q).
196
-------
CCPRED)XC(OBS)
100.0-
50.0-
ee.0-
10.0-
5.0-
a.0-
1.0-
.5-
.5-
.1
1.0
C
-------
CCCOflPLEX II)/C/CCOBS>
se.e-
ae.e-
ie.8-
5.0-
a.e
i.e-
.5
.a-
.1
i.e
1 1
ie.e 20.0
—i 1 1—
50.0 100.8 H00.0
500.0 1000.0
C(PRED)/Q
Figure 69.
Variation of modeled-to-observed ratios of maximum hourly SFg
concentrations with modeled concentrations calculated by
Complex II (Stability Class F). Circles identify the five
highest observed SF6 concentrations (C/Q).
198
-------
C(COMPLEX II)/C(OBS) US. C(COMPLEX ID/Q
PEAK CONCENTRATIONS
C(PRED)/C
se.e-
aa.e-
s.e-
2.0
i.e-
.5-
.2-
.1
1.0 ie. e ae.e se.o lee.e aee.e see.e
C(PRED)/G
Figure 70. Variation of modeled-to-observed ratios of maximum hourly SF6
concentrations with modeled concentrations calculated by
Complex II (appropriate stability class - Turner scheme).
Circles identify the five highest observed SF6
concentrations (C/Q).
199
-------
PFM
The analysis of PFM model calculations followed the same procedures used
in preparing results from the COMPLEX models. Differences in tabular data
summaries arise only from the fewer case hours used and the fewer stability
classes tested.
Table 44 summarizes PFM model performance statistics for the 23 hours in
which the SFg release height exceeded Hcrit by 5 m or more. All
concentrations have again been scaled by the emission rate. Figures 71
and 72 present scatterplots of peak calculated concentration ratios. The
distribution of data in these figures shows some tendency toward
overestimation, and this overestimation increases in going from class D to
class E dispersion rates. However, in comparing the PFM scatterplots with
the COMPLEX model scatterplots, there appears to be less of a trend toward
increasing the magnitude of the residuals with Cp. This is apparently more
a function of the case hours selected than the model. The relationship
between model performance and data classification by H will be
discussed further in Section 5.5.2.
Impingement Model
Impingement model calculations are similar to those of Valley—a maximum
concentration is calculated for each hour. Unlike Valley, however, the
Impingement model simulates the maximum concentrations using actual
meteorological conditions observed during a particular hour. The Impingement
model should better account for the hour-to-hour variability in the observed
maximum concentrations because it uses dispersion parameters calculated from
observed turbulence intensities (see Section 4.5.4). Table 45 summarizes the
analysis of the calculated concentrations (scaled by the emission rate) for
each of the 45 hours.
Two consecutive case hours (Case 209, hours 7 and 8) show conspicuously
large overestimates, apparently because of differences in the o^
calculated by the model and the GZ estimated from lidar data (see
Section 4.5.4). In particular, for Case 209, hour 8, the proposed equation
for O seriously underestimates the size of the a derived for this
z z
200
-------
CO
a
a
t-t
|
u
o
LU
en
a. o
J U
X X
m m
jj jj
a> <-
ui 3
rn o
o I
N <* • -o o i -o -o -a *-> o- « -ci -H I o «* • «j-
*-< ft n-i -< -< in cu •? *•< ru
-c o- cri
-i ri
CM ru
o- ci ri -< OD s ri •*• N N s oi ri od o ri -o ni -d i -o rJ o
^ n "< — i -< ^ «
OD o •* -6 oa "S- in iri N in
a -o ri « in o t> o- o o o o o T *t
OOOOOOOOOOOOOOOO-i-irtrtrt«-i
oi oi ro CM rj rii ni rj r
-------
CCPRED1/CCOBS)
iw.e-
59.6-
ae.e-
5.0-
s.e
i.e-
.5-
.a-
.1
i.e
C(PFM)/C(OBS) US. CCPFID'O
PEftK CONCENTRATIONS
®
®
A
A A
®
ae.e
— i
59. t>
1
1
100.0 380.
1
500.0 1000.0
C(PRED)/Q
Figure 71. Variation of modeled-to-observed ratios of maximum hourly
concentrations with modeled concentrations calculated by PFM
(Stability Class D). Circles identify the five highest
observed SF6 concentrations (C/Q).
202
-------
C(PFN)/C/C
100.0-
S0.e-
20.0-
10.0-
5.0-
3.0-
1.0-
.5
.1
1.0
Figure 72.
A ®
@
—i 1—
10.0 20.9
, 1 1 1
50.0 100.0 200.0 500.0 1000.0
CtPREDJ/'Q
Variation of modeled-to-observed ratios of maximum hourly
concentrations with modeled concentrations calculated by PFM
(Stability Class E). Circles identify the five highest
observed SF6 concentrations (C/Q).
203
-------
TABLE 45.
SUMMARY C/Q STATISTICS FOR IMPINGEMENT
MODEL CALCULATIONS
Observed
Case
EXR, Hour
20 1
20 1
201
20 1
201
2O2
202
202
2O2
2O2
202
204
204
204
204
204
204
205
2O5
205
206
2O6
206
206
2O6
2O9
209
2O9
209
209
210
21O
210
21O
21O
211
211
211
211
211
211
214
214
214
214
1
2
4
5
6
1
2
3
4
5
6
1
2
5
6
7
8
4
5
6
4
5
6
7
8
1
2
3
7
8
3
4
6
7
8
1
2
3
4
5
6
3
4
7
8
N
16
16
16
1O
11
26
32
28
24
24
21
37
36
3O
34
32
33
33
31
37
35
3O
28
33
7O
47
46
48
46
40
45
39
40
45
15
43
36
34
36
40
37
41
37
43
46
Co
13. 1
8. 3
6. 4
11. 2
7. 9
4. O
B. 4
8. 6
7. 8
5. 2
3. 1
1. 7
2. 0
1. 1
2. 1
2. 5
6. 6
5. 2
7. 3
5. 3
13. 6
5. 7
35. 4
21. 6
38. 6
. 4
. 9
2. 1
1. 6
3. 2
2. 4
1. 6
. 5
. 8
3. 3
4. 3
2. 3
. 5
8. 7
24. 6
12. 3
5. 0
16. 7
25. O
9. 0
rf(Co)
B. 4
8. 1
5. 6
10. 1
5. 7
4. 9
6. 8
16. 9
17. 8
11. 1
3. 2
2. 7
2. 9
1. 0
3. 4
2. 4
4. 3
4. 4
4. 6
3. 6
16. 1
9. 5
31. 5
25. 5
35. 3
. 6
1. 3
1. 3
2. 0
4. 9
2. 7
1. 3
1. 0
1. 5
5. 4
2. 8
1. 4
. 8
9. 2
23. 0
12. 2
14. 9
13. 8
31.7
8. 4
Max
32.
25.
IB.
34.
18.
18.
33.
67.
81.
49.
11.
14.
11.
4.
17.
9.
16.
15.
25.
15.
56.
41.
124.
92.
154.
3.
5.
5.
7.
On
2
1
6
6
7
O
6
2
6
2
B
5
3
8
6
6
1
4
5
5
7
2
2
8
6
8
0
6
6
20. 3
11. 5
4. 6
4. 4
8. 1
17
11
6
3
. 9
. 5
. 4
. 9
33. O
97
53
77
54
119
31
. 4
. 1
. 6
. 4
. 1
. 7
Max Cp
14.
41.
71.
126.
137.
9.
27.
41.
12.
1.
58.
50.
18.
23.
57.
23.
38.
26.
11.
22.
169.
89.
126.
47.
23.
22.
28.
8.
221.
2B1.
44.
14.
3.
B.
40.
14.
15.
9.
11.
22.
28.
24.
55.
128.
12.
1
8
4
5
8
9
4
8
1
6
6
6
5
2
1
O
4
6
O
4
1
9
3
4
7
4
7
1
7
1
2
4
1
7
5
2
6
1
3
6
1
2
0
5
8
Max
Max
1.
3.
3.
7.
4.
3.
1.
4.
3.
2.
2.
1.
1.
2.
2.
1.
5.
5.
1.
29.
13.
3.
3.
1.
2.
1.
2.
2.
1.
1.
Op/
Co
44
66
83
66
39
55
82
62
15
03
96
49
63
88
25
41
39
73
43
44
98
18
02
51
15
94
69
45
17
86
87
16
71
08
26
23
45
34
34
23
53
31
Ol
08
40
Co-Cp
IB. 0
-16. 7
-52. B
-91. 9
-119. 2
B. 1
6. 2
25. 3
69. 6
47. 6
-46. B
-36. 1
-7. 2
-18. 5
-39. 5
-13. 5
-22. 3
-11. 2
14. 6
-6. 9
-112. 3
-48. 6
-2. 1
45. 4
131. 0
-IB. 6
-23. 6
-2. 5
-214. 1
-260. 8
-32. B
-9. 9
1. 3
— . 6
-22. 6
-2. 7
-9. 2
-5. 2
21. 7
74. B
25. 0
53. 4
-. 6
-9. 5
19. 0
204
-------
hour from the lidar data. No other case hour showed so large a discrepancy.
If the turbulent plume spread during the preceding hour was also
underestimated to the same extent, then the consecutive hours of
overestimation are not surprising. (Hour 7 lidar data are currently
unavailable because only selected hours of lidar data have been processed to
date.) It is not known if the turbulence measurements, the temperature
measurements, or the functional form for a are responsible for these
z
discrepancies.
A scatterplot of the Impingement model calculated-to-observed
concentration ratios versus calculated concentrations (scaled by the emission
rate) is presented in Figure 73. It shows a general tendency for
overestimation of concentration peaks, although many observations are
underestimated. The scatter in the residuals is very large,
especially for the lower two-thirds of the data points (as ordered by Cp) .
Neutral Model
Neutral model calculations are summarized and the overall statistics are
presented in Table 46. A scatterplot of calculated-to-observed concentration
ratios versus calculated concentrations is presented in Figure 74.
The Neutral model calculations underestimated the concentrations
observed during the two case hours singled out above (Case 209, hours 7
and 8). A third hour (Case 202, hour 6) stands out because the model
predicted no SF, anywhere on the hill. This clearly results from the
magnitude of the vertical intensity of turbulence (IZ) used to compute
0 . IZ for this hour was extremely small compared to all other hours
z
tested. Although the magnitude of IZ is unusual, the variation of IZ and IW
throughout the hour (5-minute averages) indicates that the propellor
anemometer was probably not seizing.
The scatterplot for the Neutral model shows a wide variability in model
performance, with cases of overestimation and underestimation of the hourly
maximum concentration. However, no strong increase in the residual with Cp
is evident. The Neutral model may thus have a mean residual close to zero,
but it is far from being a good model for estimating maximum hourly
205
-------
CUrtPINGEMENT P10DEL)/C(OBS> US. CariPINCErtENT HODEU/0
PEAK CONCENTRATIONS
C(PRED)/C(OBS>
iee.e-
50.8-
ae.e-
ie.0-
5.0-
E.e
i.e-
.5
.2-
.1
i.e
Figure 73.
10.0 28.0 50.0 100.0 200.0 500.0 1000.0
CCPRED)/0
Variation of modeled-to-observed ratios of maximum hourly SF
concentrations with modeled concentrations calculated by the
Impingement model. Circles identify the five highest
observed SF6 concentrations (C/Q).
206
-------
TABLE 46. SUMMARY C/Q STATISTICS FOR NEUTRAL
MODEL CALCULATIONS
Observed
Exp.
2O1
20 1
201
201
201
202
202
202
2O2
202
202
20-1
2O4
204
204
204
204
2O5
205
205
206
206
206
2O6
206
209
209
2O9
209
2O9
21O
210
210
210
210
211
211
211
211
211
211
214
214
214
214
Case
Hour
1
2
4
5
6
1
2
3
4
5
6
1
2
5
6
7
8
4
5
6
4
5
6
7
B
1
3
3
7
B
3
4
6
7
B
1
2
3
4
5
6
3
4
7
3
N
16
16
16
10
11
26
32
28
24
24
21
37
36
3O
34
32
33
33
31
37
35
30
23
33
70
47
46
48
46
40
45
39
40
45
15
43
36
34
36
4O
37
41
37
43
46
Co
13. 1
8. 3
6. 4
11.2
7. 9
4. O
B. 4
8. 6
7. B
5. 2
3. 1
1. 7
2. O
1. 1
2. 1
2. 5
6. 6
5. 2
7. 3
5. 3
13. 6
5. 7
35. 4
21. 6
38. 6
. 4
. 9
2. 1
1. 6
3. 2
2. 4
1. 6
. 5
. 8
3. 3
4. 3
2. 3
. 5
B. 7
24. 6
12. 3
5. O
16. 7
25. 0
9. 0
ff(Co)
B. 4
B. 1
5. 6
1O. 1
5. 7
4. 9
6. B
16. 9
17. B
11. 1
3. 2
2. 7
2. 9
1. O
3. 4
2. 4
4. 3
4. 4
4. 6
3. 6
16. 1
9. 5
31. 5
25. 5
35. 3
. 6
1. 3
1. 3
2. 0
4. 9
2. 7
1. 3
1. O
1. 5
5. 4
2. 8
1. 4
. S
9. 2
23. 0
12. 2
14. 9
13. 8
31. 7
8. 4
Max Co
32. 2
25. 1
18. 6
34. 6
18. 7
18. 0
33. 6
67. 2
81. 6
49. 2
11.8
14. 5
11. 3
4. B
17. 6
9. 6
16. 1
15. 4
25. 5
15. 5
56, 7
41. 2
124. 2
92. B
154. 6
3. B
5. 0
5. 6
7. 6
20. 3
11. 5
4. 6
4. 4
B. 1
17. 9
11.5
6. 4
3. 9
33. O
97. 4
53. 1
77. 6
54. 4
119. 1
31. 7
Cp
12. 4
1O. 0
22. 0
17. 0
2. 4
6. 4
4. 9
22.2
11. 5
4. 9
. O
20. 6
B. 7
21. 0
30. 9
2O. 4
33. 0
8. 7
4. 1
12. 7
6. 4
1O. 2
42. 6
17. 9
11.4
13. 6
9. 7
2. 9
. 5
1. 3
1. O
2. 9
. 7
3. B
8. 2
11. 1
13. 3
6. 6
1O. 5
19. O
21. 5
11.9
25. 7
29. 9
7. 1
(T
-------
CCNEUTRAL riODEL)/C(OBS> US. CtNEUTRAL flODEL >/0
PEAK CONCENTRATIONS
C/-C(01S)
100.0-
se.0-
20.0-
10.0-
5.0-
a.0
1.0-
.5
.2-
.1
1.0
Figure 74.
* 9
®
10.0 20.0 50.0 100.0 200.0 500.0 1000.0
C(PRED)/0
Variation of modeled-to-observed ratios of maximum hourly SFg
concentrations with modeled concentrations calculated by the
Neutral model. Circles identify the five highest observed
concentrations (C/Q).
208
-------
concentrations at CCB because of the scatter in the residuals and because it
underestimates the highest observations.
5.5.2 Performance Evaluation
Overall model error statistics for Valley, COMPLEX I, COMPLEX II, PFM,
and the new experimental models have been assembled in Table 47 for the
following measures related to e and cr£:
e m , s : lognormal statistics (geometric mean and geometric
gp1
o
standard deviation) of the residual errors in maximum computed and
maximum observed concentrations.
Max C - Max C , O(Max C - Max C ): statistics of the
o p o p
residuals in maximum computed and maximum observed concentrations.
C -C , CJ(C -C ): statistics of the residuals in computed
o p' o p'
and observed concentrations paired by sampling location.
The first two sets of statistics summarize the errors in estimating 1-hour
maximum concentrations, regardless of location, over the hours included in
this analysis. The third set summarizes the mean errors in estimating
observed concentrations at all sampling points. Plots of £ versus cre
based on the data in Table 47 are displayed in Figures 75 through 77.
Not all model statistics summarized in Table 47 are based on 45 case
hours. The geometric statistics include only those hours with maximum
estimated concentrations greater than zero. Several models produced an
estimate of zero for one hour, and so the geometric statistics for these are
based on 44 hours. Furthermore, PFM was run for only those 23 hours in which
the release height exceeded the calculated dividing streamline height by 5 m.
Table 47 also contains statistics for a "hybrid" model made up of
Neutral and Impingement model estimates. Neutral model results are taken for
those 23 cases where the release height exceeds ^clc±t by 5 m or more and
the Impingement model results are taken for the remaining 22 hours. However,
geometric statistics for this Neutral-Impingement combination model are based
on only 44 case hours because one of the 23 Neutral model estimates is zero.
209
-------
TABLE 47. SUMMARY OF ANALYSIS OF C/Q RESIDUALS - ALL CASE HOURS
Model
Valley
Valley
COMPLEX
COMPLEX
COMPLEX
COMPLEX
(CD
I D
I E
I F
I T*
N
45
45
45
45
45
45
i
0
0
0
0
0
0
.29
.28
.66
.40
.37
.39
s
2
2
3
3
3
3
g
.64
.27
.10
.09
.18
.37
Max C -Max
-38
-64
-11
-37
-36
-37
C
.9
.9
.5
.8
.1
.6
COMPLEX II D
COMPLEX II E
COMPLEX II F
COMPLEX II T*
45
45
44
44
0.41
0.23
0.13
0.16
3.16
3.87
3.29
3.85
PFM** D
PFM** E
Neutral
Impingement
23
23
44
45
0.68 2.43
0.52 2.49
0.97 2.81
0.72 3.56
-40.9
-109.9
-178.9
-165.3
-11.7
-29.4
6.5
-15.5
o(Hax Co - Max C )
33.2
80.0
43.4
52.6
53.2
55.9
60.8
113.3
158.4
162.8
32.0
46.3
31.1
65.0
C -C
o(C -C )
-12.0
-20.2
-24.8
-24.0
-9.3
-17.3
-23.7
-23.2
-1.4
-2.2
-4.6
18.9
24.5
25.1
25.5
26.0
45.5
68.5
67.2
16.6
22.1
12.1
Neucral-
ImpingemRnt
Combinacion
44
0.76
3.14
-10.0
62.9
Note: Estimated concentrations for one case hour were zero according to COMPLEX II (Class F,T), Neutral
and the Neutral-Impingement combination models. Consequently, geometric statistics were computed
over 44 case hours for these models, instead of over 45 case hours, as in the other statistics.
*The Turner objective scheme is used to determine the hourly stability class.
**PFM was run for case-hours in which H ^ Hcrit + 5 m.
210
-------
On the basis of the lognormal statistics, the Neutral model best
estimates the highest observed_concentration each hour (in the sense that it
r\ __ f\ O
gives the smallest values of £ = e + cr£). It shows a slight bias toward
overestimation (m = 0.97). The Neutral-Impingement hybrid, the Impingement
O
model, and COMPLEX I (class D)'follow closely in performance with mean biases
of 0.66 to 0.76. These are the only models in the test group that, on
average over at least 44 test cases, estimate the highest observed
concentration to within a factor of 2. A second group of models has a bias
factor of about 0.4. This group includes COMPLEX I (class E, F, and
appropriate stability class), and COMPLEX II (class D).
Model ranking mostly depends on the magnitude of m (e) because s
o &
(or cr£) shows less variability among the models. The models that show
the largest biases are in increasing order: the Valley model, mg = 0.29;
Valley centerline, m = 0.28; COMPLEX II (class E), mg = 0.23; COMPLEX II
(appropriate stability class), m = 0.16; and finally COMPLEX II (class F),
O
m = 0.13.
g
The relative performance of COMPLEX I and COMPLEX II indicates that
1-hour average calculated maximum concentrations at CCB are overestimated by
greater margins when:
e 22.5° sector averaging is not used, and
e stable plume configuration is used.
The best combination includes 22.5° sector averaging and a 0.5 plume path
coefficient (COMPLEX I, class D), but it is not clear if best performance is
due primarily to the difference between class E and class D dispersion
coefficients or to the difference in plume trajectory assumptions (partial
lift rather than impingement). For example, it is possible that the use of
class E plume spread coefficients in combination with the 0.5 path
coefficient might yield m value closer to unity, but this has not been
&
explored.
A similar picture of relative model performance emerges if the
(untransformed) concentration errors are assumed to be normally distributed.
Mean residuals and standard deviations of the residuals between calculated
and observed maximum concentrations are plotted in Figure 76. The models
with the smallest mean residuals are Neutral, Neutral/Impingement, COMPLEX I
211
-------
8.0'
7.0-
6.0-
s.e-
mg
3.6-
a.e-
1.0-
.7
COMPLEX II (Class F)
* COMPLEX II
(Appropriate Stability Class)
COMPLEX II (Class E)
Valley (Centerline) A
Valley
^COMPLEX I (Class F)
COMPLEX I (Class E) ^ * COMPLEX I (Appropriate Stability
COMPLEX II Class'
(Class D)
A COMPLEX I (Class D)
A Impingement
* Neutral/Impingement
Neutral
.7
1.0
2.0
3.0
-4.6 5.0 6.0 7.0 8.0 18.
Figure 75. Relative performance of models tested with 45 case hours
of data from CCB with model performance based on ratios of
maximum calculated and observed hourly SFg concentrations.
Note: mg and s.g are the geometric mean and geometric standard deviation
of the ratio Co/Cp.
212
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flax Co - Hex Cp
i Neutral
COMPLEX I (Class D).
-38.8-
Valleys
Neutral/Impingement
* Impingement
COMPLEX I (Class F)
£ A COMPLEX I (Appropriate Stability Class)
A COMPLEX II (Class D)
COMPLEX I (Class E)
-se.e-
Valley (Centerline)
COMPLEX II (Class E)
-iae.0-
-159.e-
COMPLEX II (Appropriate Stability Class) t
COMPLEX II (Class F) .
-189. .9
—r—
69.e
"T
isa.'s
Co - Res Cp)
Figure 76.
Relative performance of models tested with 45 case hours of
data from CCB with model performance based on residuals of
maximum calculated and observed hourly SF6 concentrations.
213
-------
-S.0-
• Neutral
> COMPLEX II (Class D)
* COMPLEX I (Class D)
-15.9-
* COMPLEX II (Class E)
-ae.e-
> COMPLEX I (Class E)
COMPLEX II (Appropriate Stability Class)
-as.e-
A COMPLEX I (Appropriate Stability Class)
* COMPLEX I (Class F)
'COMPLEX II
(Class F)
49.9
69.9
99.9
alCo - Cp)
Figure 77.
Relative performance of models tested with 45 case hours of
data at CCB with model performance based on residuals of
calculated and observed hourly SFg concentrations at all
samplers.
214
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(class D), and Impingement. (The Neutral model underestimates maximum
concentrations on the average, but it still exhibits the best performance in
terms of e2. The next best model is COMPLEX I (class D).) Those with
the largest mean residuals are Valley centerline and COMPLEX II (stable
classes). Valley, COMPLEX I (stable classes), and COMPLEX II (class D) are
grouped not far from the relatively better models.
A different relative ordering is foundjvhen paired residuals from all
2
sampling points are evaluated in terms of e (see Figure 77). The
Neutral model is again nearest to a zero mean residual. COMPLEX II (class D)
now ranks ahead of COMPLEX I (class D), COMPLEX II (class E) is virtually
tied with COMPLEX I (class E), and COMPLEX II (class F) is poorer than
COMPLEX I (class F). The Valley and Impingement model results are not
presented because they estimate only the maximum concentration.
The relative performances of COMPLEX I and COMPLEX II become clearer
when added importance is attached to the standard deviation of the residuals
(a ). COMPLEX I results show uniformly smaller CT£ values than do
COMPLEX II results. Therefore, the mean residuals for COMPLEX II are
probably closer to zero than the corresponding COMPLEX I residuals because
underestimates and overestimates tend to balance. This interpretation is
consistent with the fact that COMPLEX I is a sector-averaged model, whereas
COMPLEX II is a narrow plume model.
PFM performance was not included in the foregoing comparisons because it
was run for only 23 of the 45 test cases. Instead, PFM is separately
compared against the Neutral model and against the COMPLEX models for those
23 case hours during which the release height was equal to or greater than
H plus 5 m. Table 48 presents the residual statistics for this
crit
comparison and these results are displayed in Figures 78 to 80.
PFM ranks about the same as COMPLEX II (class D) and COMPLEX I (stable
classes) in estimating the maximum concentrations, both with and without the
log transformation. Its bias (m ) is 0.68. The only models with a bias
closer to unity are Neutral (m = 1.03) and COMPLEX I, class D (mg = 1.10).
Point-by-point residual analysis (see Figure 80) shows PFM (class D) to have
2
the smallest mean residual, but its mean square error (£ ) is not as
small as that for the Neutral model.
215
-------
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216
-------
is.e
8.6
7.9
6.0-
5.0-
4.0-
3.0-
mg
a.e-
1.0H
COMPLEX II (Class F)
COMPLEX II
(Appropriate Stability Class)
COMPLEX II (Class E)
* PFM (Class E)
COMPLEX I (Class F) * COMPLEX I (Class E)
COMPLEX II (Class D) A ^ * COMPLEX I (Appropriate Stability Class)
* PFM (Class D)
Neutral
* COMPLEX I (Class D)
.7
.7 1.0 a.e 3.0 4.6 s.e e.e 7.0 8.0
Note: rrig and sg are the geometric standard deviation of the ratio Co/Cp.
Figure 78. Relative performance of models tested with 23 hours case
hours (release height > Hcr^t) of data at CCB with model
performance based on ratios of maximum calculated and
observed hourly SF^ concentrations.
217
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n«x Co - n«x
10.8
-ie.0-
-30.0-
-50.0-
-70.0-
-90.0-
A Neutral
COMPLEX I (Class F)
* COMPLEX I (Class D)
PFM (Class D)
A COMPLEX I (Appropriate Stability Class)
*• COMPLEX II (Class D)
* COMPLEX I (Class E)
. PFM (Class E)
COMPLEX II (Class E)
^ COMPLEX II
(Appropriate Stability Class)
i COMPLEX II
(Class F)
-ne.0
.0
30.0
40.0
60.0
80.0
Hcrit) of data at CCB with model performance
based on residuals of maximum calculated and observed
hourly SF, concentrations.
218
-------
Co -
-3.©-
-e.e-
-9.0-
-15.8-
-18.0-
Neutral
PFM (Class D)
A PFM (Class E)
* COMPLEX II (Class D)
COMPLEX II (Class E)
COMPLEX I (Class D)
COMPLEX II
(Appropriate Stability Class)
A COMPLEX II (Class F)
COMPLEX I
(Appropriate Stabil ity Class) •
A COMPLEX I (Class E)
COMPLEX I (Class F)
ae.e
30.0
- Cp)
Figure 80. Relative performance of models tested with 23 case hours
(release height > Hcrit) of data at CCB with model performance
based on residuals of calculated and observed hourly SFg
concentrations at all samplers.
219
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Figures 78 through 80 also show that the models perform better on the
subset of case hours during which the release was above Hcrit than they do
on the entire 45-hour set. For example, only the COMPLEX II (stable)
computations overestimate maximum observed concentrations by more than a
factor of 2. Furthermore, the COMPLEX II estimates provide a marginally
better description of the overall distribution of concentrations than the
COMPLEX I estimates. This suggests that the flow was generally steadier when
the release was above Hcrit, and, consequently, that nonsector-averaged
models tend to do as well or better than sector-averaged models in describing
plume spread over 1-hour periods for this class of flow. This is best
demonstrated with PG class D dispersion rates.
Model performance may also be addressed by quantifying the uncertainty
in model estimates in terms of confidence intervals computed from the error
statistics (mean and standard deviation). One approach to computing
confidence intervals is described in Appendix C.
The evaluations of model performance presented above show that there is
clearly room for improving the reliability of Gaussian models intended for
use in complex terrain settings. ERT's plans for further development of
models with data from the experiments at CCB are presented in the next
section.
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SECTION 6
CONCLUSIONS AND EECOMMENDATIONS FOR
FURTHER ANALYSIS AND DEVELOPMENT
6.1 Accomplishments in Overview
The Cinder Cone Butte study, the initial field study in EPA's continuing
program to develop and validate reliable dispersion models for applications
in complex terrain, has achieved its stated objectives (Holzworth 1980) of
providing both a set of visual observations of smoke plumes interacting with
an isolated terrain feature in generally stably stratified flows and a
detailed data base of meteorological and tracer measurements with which to
develop appropriate models for these interactions.
The field program has verified the basic concepts of the experimental
design. The flexibility provided by the release of gaseous and visible
tracers from mobile cranes allowed experiments to be run cost-effectively
under various meteorological conditions. The study has also demonstrated the
value of a meteorological data-handling system that collects, processes, and
displays information to guide the experiments in real time.
Moreover, the CCB study has confirmed the utility and effectiveness of
scaled physical modeling within the overall program. The general features of
the flows visualized at CCB replicated the flows produced at the Fluid
Modeling Facility, thereby verifying that to a very useful extent, the
essential physics of stably stratified flows over complex terrain features
can be reduced to the laboratory scale in order to examine particular flow
conditions and to guide experimental design.
For example, during the design of the CCB field study, information
derived from experiments in the FMF's stably stratified water tank was
valuable in siting the 150 m tower outside the perturbing influences of the
butte. Pictures of dye streaklines in tank experiments were the primary
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basis for choosing the array of sampler locations on CCB and for relocating
some samplers in response to meteorological forecasts. In addition, a series
of quantitative laboratory experiments provided important support for the
Hunt-Snyder critical streamline height, which in turn was the basis for
positioning the heights of tracer releases in response to computed Froude
numbers during the field experiments.
Laboratory modeling of case hours from the CCB experiments is continuing
at the FMF to aid in the interpretation of the field observations. The
detailed fluid modeling study of one case hour is reported in Appendix B.
This study shows the influence on hourly averaged concentrations of the use
of sequential 5-minute flow data instead of hourly averaged flow data.
Before any general conclusions may be deduced, however, additional data from
both physical and mathematical models should be obtained for other case
hours, and results of sequential simulations should be compared with hourly
averaged results as well as with field data. Although laboratory fluid
modeling cannot simulate the real world exactly (because of differences in
scales and intensity of turbulence, differences in wind and temperature
profiles, and lack of meander in the laboratory flows, as well as for other
reasons), it is nonetheless a valuable adjunct to field experiments; as
Holzworth (1980) states, "by allowing the controlled variation of independent
variables, laboratory experiments will provide deeper insight and
understanding of the fundamental physics."
The CCB field program has provided a detailed, reliable data archive
with which to evaluate the accuracy of the present generation of complex
terrain models as well as to develop more reliable models. The data archive
includes the following:
• meteorological measurements,
• observations of the patterns of tracer concentrations on the butte,
• lidar-derived plume sections, and
• photographic evidence.
The edited data archive is unique in its detailed and reliable
documentation of stable flow and dispersion near an isolated hill. Moreover,
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in addition to its quantitative content, this data base also has important
qualitative value: many of the photographs clearly demonstrate that plumes
interact with elevated terrain features in a complicated variety of ways
under stable flow conditions and that the simple impingement description used
in some current dispersion models may not be in accord with the behavior of
plumes.
Substantial progress has also been made in developing improved
dispersion models for projecting ground-level concentrations on complex
terrain from elevated point sources in stably stratified flows. We have
developed new statistical techniques for evaluating the performance of air
quality models and have applied these techniques to current complex terrain
models. Preliminary new models have been constructed that incorporate some
on-site turbulence data and only the simplest sort of field observations
that is, the two distinct regimes of plumes released above or below the
dividing streamline height. Even these first attempts at more physically
realistic models show better performance than current models. The
evaluations of the performance of these preliminary models point to the need
for further development of complex terrain models of known reliability and
demonstrated applicability for regulatory use.
Of course, the results of these evaluations cannot be simply applied to
other sites with different scales, such as power plants near mountains, or to
different sorts of terrain elements, such as bluffs, ridges, or mesas where
the potential for blocking of the flow is greater and where the dividing
streamline height is related to the flow characteristics in a different way.
The data base of the CCB field study cannot be used to address all these
problems directly—nor was the experiment intended to address them. Other
field experiments must be designed and performed for these purposes, as the
EPA's program has recognized.
We have only begun to exploit the data gathered at CCB, however. We
anticipate that because of the good quality of the meteorological and tracer
measurements, these data contain valuable information on the characteristics
of the flow over the butte and on the effects of both 5-minute and 1-hour
turbulence on the observed patterns of tracer gases. This information will
lead to an improved understanding of transport and diffusion around the
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butte—which will, in turn, point the way to better models of these
processes. The remainder of this report summarizes comparative performance
evaluations of the several models tested (Section 6.2) and presents
recommendations for further analysis of CCB data and further model
development with this data base (Section 6.3).
6.2 Comparative Model Performance Evaluations
Valley, COMPLEX I, COMPLEX II, and PFM computations of 1-hour average
SF, concentrations were compared with measured SF- concentrations from as
b o
many as 45 experiment case hours in the CCB data archive. Two new
experimental models were also evaluated with the same data. This evaluation
serves to document how well each of these models performed with the CCB data,
in both an absolute and a relative sense.
The Valley model is a screening algorithm intended for estimating the
highest expected 24-hour average concentration of pollutants released from
large point sources in complex terrain. It is based upon a univariate
Gaussian plume formula incorporating 22.5° horizontal sector averaging and
postulated worst—case meteorology leading to stable impingement situations.
The comparison of Valley with CCB SF tracer concentrations only tests how
well the model simulates 1—hour average concentration estimates at CCB, not
the way the Valley model is used in regulatory practice for estimating
24—hour average concentrations by persisting the assumed worst—case
meteorology for six hours.
In 39 of the 45 test case hours, the concentration maximums were
overestimated by Valley, and in four of the case hours, maximum
concentrations were appreciably underestimated. The mean ratio (over all
45 hours) of the Valley model estimate to the observed concentration is 5.3
and the geometric mean ratio is 3.4.
The four cases in which Valley underestimated peak observed values may
be "explainable" by the scale of the CCB experiment. The Valley model and
its assumed worst-case meteorological conditions are supposed to apply to
real sources in complex terrain, where source heights and transport distances
are generally much larger than the source-terrain geometry of the CCB
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- But during the experiments, wind speeds at release heights were
frequently less than 2.5 in/sec, and as the plume approached the impingement
point, CT was at times significantly smaller than the 10 m plume
2
centerline stand-off distance assumed by the model. This phenomenon is
associated, of course, with the small scale of the CCB experiment. For most
regulatory applications of the Valley model, cr is large by comparison to
z
the 10 m stand-off distance, and therefore the model concentration estimates
usually correspond closely to maximum plume centerline values.
Unlike Valley, COMPLEX I, COMPLEX II, and PFM are sequential air quality
models. These models are intended to produce 1-hour concentration estimates
using on-site meteorology. COMPLEX I and COMPLEX II were tested with
45 experiment case hours, and PFM was tested with 23 of these hours in which
the SF, tracer was released at least 5 m above the critical dividing
6
streamline height. The 1-hour average meteorology used to drive these models
was estimated for the tracer release height. No "tuning" of the model inputs
was done to improve the performance of these models.
COMPLEX I was found to overestimate in the mean when peak observed
concentrations were compared to peak modeled concentrations (regardless of
location) and when the hourly stability class was derived from the Turner
scheme. The mean of the ratios of the peak modeled to peak observed
concentrations is 5.3 and the geometric mean is 2.6, both nearly the same as
Valley.
COMPLEX II was also found to overestimate maximum observed
concentrations when the hourly stability class was derived from the Turner
scheme. The mean of the ratios of peak concentrations is 14.4, and the
geometric mean is 6.3. Therefore, COMPLEX I, with the constant sector
averaging to simulate crosswind diffusion, appears to do a better job of
estimating the magnitude of peak hourly concentrations at CCB than COMPLEX II.
Additional evaluations of the COMPLEX models were made by fixing the
stability class for all test hours. Each model was run x^ith stability
classes D, E, and F in turn. Note that both COMPLEX I and COMPLEX II include
the following default values for plume path coefficients as functions of
stability class. For stability class D the plume path coefficient is 0.5.
For stability classes E and F, the plume path coefficients is 0.0, and full
225
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surface reflection (doubling of concentrations) is assumed. The COMPLEX I
and COMPLEX II model runs were made with these default values.
Both models overestimated peak concentrations on the average but the
bias toward overestimation decreased as the stability class was changed from
F to D. However, the scatter in the data (as characterized by the standard
deviation of the residual CT(C -C )) was not significantly affected.
These models performed better, however, on the subset of hours in which
the tracer was released above the dividing streamline height of the flow.
The overall bias toward overestimation was reduced, and the scatter in the
data was also reduced, although it remained large. Again, COMPLEX I
performed better than COMPLEX II.
PFM was compared with COMPLEX I and COMPLEX II using Turner a and
a values for PG stability classes D and E on the same subset of hours.
z
PFM appears to offer some improvement over COMPLEX II, particularly for
stability class E (when COMPLEX II adopts the Valley model stable impingement
plume path). PFM does not appear to offer improvement over COMPLEX I.
Two new experimental models were also tested and compared with COMPLEX I
and COMPLEX II. The Neutral model is similar to COMPLEX II (class D). Like
COMPLEX II, it uses a 0.5 plume path coefficient for neutral stability, but
unlike COMPLEX II, it uses on-site turbulence intensities to calculate
dispersion coefficients. The Impingement model also uses on-site turbulence
data. It estimates the maximum 1-hour concentration for a plume that
impinges upon the terrain and then passes around the sides of the terrain
feature.
The Neutral model performs better than the other models evaluated in
terms of mean bias and offers an improvement in terms of the standard
deviation of residuals over all the data, but no improvement in the standard
deviation of the residuals of peak concentrations.
A hybrid model that combines the Neutral model (for cases in which the
tracer is released above the critical dividing streamline) and the
Impingement model (for cases in which the tracer is released below) was
disappointing—both the bias and standard deviation of the residuals
increased over those obtained when the Neutral model alone was used for all
hours.
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It appears that the use of oil-site turbulence data does, to some extent,
improve model performance at CCB and that the use of horizontal sector
averaging over 22.5° (in lieu of turbulence data) to describe effective
crossplume spread over an hour is more helpful than the use of the CF
inferred from the Turner surface stability class. For this data base,
however, none of the models tested to date yielded precise estimates.
6.3 Recommendations for Further Research
Although the CCB f i,eld program" has provided good visual and quantitative
data on the interactions of stable plumes with an isolated hill, much remains
to be done to achieve the goal of practical, easily comprehensible, and
reliable dispersion models applicable to stable flows in complex terrain and
transferable to other sites. This section describes the research and
development we plan to perform with the data already obtained from the CCB
experiments. We expect that substantial progress toward the program's goal
will result from these efforts.
The key to successful modeling of observed tracer concentrations at CCB
lies in relating the meteorological data to the observed behavior of the
visible plume. Over the course of the field program, smoke plumes exhibited
a wide range of shapes, dimensions, and trajectories as they passed near the
hill.
A dominant feature of plume trajectories at CCB is the sensitivity of
plume path in the horizontal to small changes in wind direction or source
position. As the stability of the atmosphere increased and the mean wind
speed decreased, the plume rested on one side of the hill or the other but
spent very little time in between. During experiment hours in which the mean
wind was directed toward the center of the hill, the plume generally swept
quickly across the hill, coming to rest on alternate sides of the hill in
turn. This behavior is consistent with the notion of flow beneath the
critical dividing streamline.
For periods of weaker thermal stratification or greater wind speed at
source height, horizontal trajectories were steadier and the plumes rose over
part of CCB for significant periods during some hours. At times, in passing
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over the crest of the hill, plumes appeared to shrink in vertical extent, and
gave at least the visual impression they were not in contact with the
surface. This behavior is consistent with the notion of flow above the
critical dividing streamline.
Often, however, the distinction between these two conceptual
descriptions was not well defined in the visual appearance of the plumes.
The appearance of the plumes varied from hour to hour and quite often varied
a great deal during the course of one hour. Sometimes the plume was very
wide and flat; at other times, it was a well-collimated "pencil beam"; and
undulations, waves, and even spiraling pulsations were occasionally
observed. For initially narrow plumes, some increase in spread upwind of the
hill was often noted if the plume was transported toward the center of the
hill, but no such spread was seen if the plume curved around the side. This
suggests that the hill influenced at least locally the upwind flow field and
turbulence levels.
The model comparison and evaluation studies described in this report
underscore the importance of these qualitative plume features. Models that
employed unaltered PG a and cr values did least well because
horizontal meander over time scales of 10 minutes to an hour often produced
plume spread much larger than that described by the stable (class E and F)
a curves. Horizontal sector averaging improved model performance, but a
y
fixed sector width is not applicable to all stable-flow plume phenomena or to
all source-terrain geometries. A model that uses on-site turbulence data to
estimate plume size performed better than similar models that use PG sigmas
with or without sector averaging. Yet although on-site turbulence data
contain information about plume spread and meander, the use of such data also
introduces new sources of uncertainty into the modeled concentration
estimates. Systematic errors in meteorological instrumentation, for example,
produce errors in modeled a estimates. It is therefore essential to
correct the data for documented deficiencies in order to take fuller
advantage of the data's ability to characterize observed plume behavior.
The development of mathematical models incorporating the effects of
these phenomena will require further analysis of the CCB data base. This
analysis will involve refinements of the data base, identification and
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formulation of model components for describing important transport and
dispersion phenomena, testing and evaluation of new model formulations, and
continued improvement arid refinement of these formulations.
Refinement of the Meteorological Data
Refining the meteorological data will include adjusting wind and
turbulence data to account for non-cosirie response characteristics of the
propeller anemometers. The knowledge and use of these kinds of adjustments
is especially important for evaluating model performance.
As noted earlier, the values of mean wind derived at CCB from,the
propeller anemometers often disagreed with corresponding values derived from
the cup-and-vane anemometers. Where the source of the discrepancy is
obvious—misalignment of the instrument on the tower or a seized propeller,
for example—the anemometer data can be corrected (or deleted) on the basis
of the information at hand. But other sources of discrepancy arise from
differences in the way the two kinds of systems respond to winds at various
angles of incidence, differences in the way they react to the same levels of
turbulence intensity, or for kindred reasons. In a few cases, the
discrepancies in mean wind speed may be so large that winds derived from
propeller systems could imply H >H, whereas winds from cups could :
imply Hcrit
-------
Identification and Testing of Model Components
Aided by observational evidence, we will continue to develop and test
model components such as flow-field, turbulent diffusion, boundary-layer, and
wake components. These components will individually undergo sensitivity
tests, refinements, and calibrations until their theoretical formulations are
as consistent as possible with the observations. The tests will serve to
define acceptable ranges for parameters and to permit a structured tuning of
the complete model with observed tracer concentrations. (Tuned models will
be evaluated with a data set separate from that used to adjust model
parameters.)
Observational evidence will be assembled from a "learning" subset of the
CCB data to support additional case study analyses. The analyses done to
date have been performed largely without the benefit of correlative CCB
data—nephelometer, sonde, lidar, sampling mast concentrations, and
photographs—that could help in quantifying plume transport and diffusion
phenomena. The purpose of continuing case study analyses is to delineate
these phenomena as well as possible using all available information
(including cae hours of near-zero tracer concentrations), so that we can
understand the evolution of the measured 1-hour tracer concentration
distributions within the resolution of the 5-minute average meteorological
data and the 10-minute average tracer data in the CCB data base.
The 5-minute meteorological data base is essential to our understanding
of the CCB experiments. Many of the theoretical descriptions of plume
behavior near terrain are linked to notions about streamline patterns.
These, in turn, depend critically upon the spatial and temporal variability
in wind speed and wind direction. It has been shown, for example, that the
mean wind field used in the models exerts a critical influence on the
inferred flow regime (H < H lt, H > Hcrl(.) and especially on the
magnitudes and locations of the maximum concentrations. It is therefore
important to seek ways to infer the time-dependent structure of the flow
field from supporting short-term data.
One suggested approach to this task is to construct the streamlines at
CCB implied by the 10 m and 30 m potential temperature data on the butte,
230
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taking as a working assumption that streamlines are constrained to travel
along surfaces of constant potential temperature, at least during fairly
steady-state periods. The streamlines thus derived could be used to
determine from what elevations, in the approach flow over the plain, air
parcels over the butte appear to originate. (Leeward 10 m temperatures may
be contaminated by heat exchange with the butte surface, but this could be
checked by comparing windward and leeward temperatures.) These implied
streamlines could then be compared to estimates of one or more candidate flow
models.
The short-term data will prove' valuable in other ways as well. We have
not begun to explore the wealth of information that could be extracted from
time series of the mean wind and turbulence fields or from their
autocorrelations and cross-correlations in time and space. Spectral analyses
of these data may lead to a better understanding of stable boundary layer
processes, to new insight into the mechanics of plume meander and turbulent
growth at CCB, and to more successful algorithms for relating small-scale
turbulence to large-scale flow characteristics.
Supplementary data akin to those in the 5-minute and 10-minute average
data base will be obtained in simulated flows set up in EPA1s towing tank.
These data will help to refine, extend, arid test model components. For
example, to explore further the use of the CCB potential temperature data as
a quantitative indication of streamline patterns, it would also be worthwhile
to simulate these same flow situations in the towing tank in order to
ascertain how well the laboratory model describes the flow fields inferred
from the observed temperature fields. We recognize that it may be difficult
or impractical to set up in the towing tank the corresponding nonuniform
density gradient; however, if even an approximate correspondence in the
profile of N(z) can be established, the experiments could be very instructive.
Another example of such testing of model components is the analysis of
how plume deformation and plume growth effects combine during stable
impingement conditions. To help distinguish these effects, we suggest
performing a series of towing tank experiments to simulate case hours of
strongly stable plume impingement. The purpose of these runs would be to
observe and record the lateral and vertical growth of the plume as it
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approaches the butte in a nonturbulent flow—that is, to estimate the pattern
of plume growth resulting from flow distortion only. Where possible, the
plume dimensions estimated from the tank experiments could be compared with
the CCB photographs and lidar results. Because the tank flows would be
almost entirely nonturbulent, the (scaled) laboratory plume should be smaller
than the plume observed at CCB. If initial plume dimensions can be ignored
or readily accounted for, any relative differences found in the plume's
crosswind or vertical spread would measure the additional plume dispersion
caused by local small—scale turbulence or drainage winds.
The quantitative correspondence cannot be taken at face value because of
essential differences between flows in the laboratory model experiment and
the prototype flow at CCB—differences in surface boundary layer
characteristics, in hill roughness, in profiles of temperature (density) and
winds in the approach flow, in steadiness of the flow, and so forth. At
least qualitatively, however, any significant differences in plume dimensions
should suggest the relative magnitude of distortion and diffusion processes
at CCB under impingement conditions.
Evaluation of Models
Models formulated and adjusted by means of the learning data set must be
evaluated on a test data set. Individual case hours within this data set
should be studied in the same detail as is done for the learning set, so that
sufficient data are available to run the models and so that enough
familiarity with the data is obtained to gauge the expected imprecision in
model estimates.
Model performance will be primarily gauged by comparing estimated tracer
concentrations to observed concentrations. Where possible, we will test
individual model components to assess the adequacy of the components that
make up the model (as well as the adequacy of the model as a whole) and to
identify important deficiencies. Residuals between observed and modeled
variables will be analyzed in accordance with the methods presented in
Section 5. Efforts will also be made to include a broader range of
statistical tests consistent with recommendations of the AMS Workshop on
Dispersion Model Performance (Fox 1981).
232
-------
Improvement and Refinement of Model Formulations
Model formulation and testing is viewed as an iterative process. First
attempts, such as those described in Section 4, are made to investigate the
scope of the problem and to set a model performance mark to be exceeded by
more refined approaches. It is our intent to develop and evaluate a number
of models over the course of this project and to assemble a hierarchy of
modeling techniques, accuracies, and data needs.
The data needs are especially critical. For practical use in various
regulatory applications, complex terrain models will not always have
available as much research-grade meteorological data as that gathered at
CCB. The range of turbulence measurements available at CCB—for example, the
5-minute average and 1-hour average winds and turbulence intensities at
16 locations from the propeller anemometers—might represent a monitoring
program for a critical siting study planned well in advance of the model
application. However, the CCB data base may yield useful information for
estimating turbulence statistics (such as O or Cf ) or other
important features that govern flow (such as N(z)) entirely from surface and
low-level measurements. If such empirical formulae are found and understood
within a sound theoretical framework, perhaps they can be generalized for
testing in full-scale plume-terrain geometries under different meteorological
conditions. It is therefore suggested that such relationships in the CCB
data base be explored and their possible utility evaluated for routine
operational use in improved complex terrain models.
As an example of areas in which a hierarchy of modeling approaches may
be studied, consider two major elements of the transport and dispersion
process, plume transport or flow and plume diffusion or spread. Several
models evaluated in Section 5 use simple empirical terrain adjustments to the
plume height above the ground to siimilate flow distortion and use the
standard PG coefficient for plume spread. One of the new models also uses a
simple terrain adjustment but uses on-site turbulence data instead of the PG
sigmas to estimate plume spread. The new model therefore represents a step
in the hierarchy toward more refined models that require additional on-site
data.
233
-------
A hierarchy of approaches to the flow and diffusion, components of a
complex terrain air quality dispersion model is suggested below. We do not
want to imply, however, that the full hierarchy would have to be pursued to
develop an adequate complex terrain model.
• Flow Module Component
1) Empirical terrain adjustment: An empirical terrain correction
factor is incorporated into a straight-line Gaussian air quality
model. (The "half-height" correction is an example.)
2) Simple potential flow: The flow is assumed to be inviscid and
stratification is ignored. Potential flow theory is used to
calculate the flow around a terrain feature.
3) Stratification adjustment to potential flow: An empirical
adjustment is made to potential flow to ensure that streamline
deflections become more horizontal with increasing stratification.
For small stratification, the adjustment factor becomes inoperative.
4) Linearized inviscid flow: The flow is assumed to be inviscid, but
density stratification is included. The resulting momentum
equation may be solved if it is assumed that the hill is so small
that the boundary condition for vertical velocity may be applied at
the surface of the plain (z = 0) rather than at the hill's surface
(z - z(x,y)). In principle, this approximation allows the flow
field to be computed for arbitrary hill shapes.
5) Numerical solutions: In this approach, the momentum equation is
solved by numerical methods. Turbulence is modeled with any one of
the several approximations available.
• Dispersion Module Component
1) Sigma curves: Here, the plume spread is estimated with stability
classification schemes. It is also assumed that the hill does not
affect turbulence.
234
-------
2) Turbulence data: Again, turbulence is assumed to be unaffected by
the hill; however, the sigmas are estimated from measurements of
turbulence intensity.
3) Terrain-modified sigmas: Turbulence intensities over the hill are
modified by empirical factors based on simple theories (such as
rapid distortion theorjr) or from turbulence data from the tower on
the butte.
4) Turbulence models: Here, the evolution of turbulence is estimated
from models of turbulence. An example of this would be the k-e
model suggested by Launder and Spalding (1972).
235
-------
REFERENCES
Bass, A. 1980. Towing Tank Studies in Support of Field Experiments at
Cinder Cone Butte, Idaho. Phase II: Plume Behavior with Froude Number
and Incident Wind Direction. Environmental Research and Technology
Inc., Concord, MA.
Bass, A., D.G. Strimaitis, and B.A. Egan 1981. Potential Flow Model
for Gaussian Plume Interaction with Simple Terrain Features.
EPA-600/54-81-008. U.S. Environmental Protection Agency, Research
Triangle Park, NC.
Box, G.E.P., W.G. Hunter, and J.S. Hunter 1978. Statistics for
Experimenters: An Introduction to Design, Data Analysis, and Model
Building.New York:John Wiley & Sons.
Budney, L.J. 1977. Guidelines for Air Quality Maintenance Planning
and Analysis. Volume 10 (revised): Procedures for Evaluating Air
Quality Impact of New Stationary Sources. EPA-450/4-77-001 (OAQPS
No. 1.2-029R). U.S. Environmental Protection Agency, Research Triangle
Park, NC.
Burt, E.W. 1977. Valley Model User's Guide. EPA-450/2-77-018.
U.S. Environmental Protection Agency, Research Triangle Park, NC.
Csanady, G.T. 1973. Turbulent Diffusion in the Environment.
D. Reidel, Dordrecht-Holland.
Drazin, P.G. 1961.. On the Steady Flow of a Fluid of Variable Density
Past an Obstacle. Tellus 13: 239-251.
Egan, B.A. 1975. Turbulent Diffusion in Complex Terrain. Lectures on
Air Pollution and Environmental Impact Analyses. American
Meteorological Society, Boston, MA.
Fox, D.G. 1981. Judging Air Quality Model Performance. A Summary of
the AMS Workshop on Dispersion Model Performance, Woods Hole, MA,
September 1980. AMS Bulletin 62; 599-609.
Holzworth, G.C. 1980. The EPA Program for Dispersion Model
Development for Sources in Complex Terrain. Second Joint Conference on
Applications of Air Pollution Meteorology, New Orleans, LA. American
Meteorological Society, Boston, MA.
236
-------
Horst, T.W. 1973. Corrections for Response Errors in a Three-
Component Propeller Anemometer. J. Appl. Meteorol. 12; 716-725.
Hovind, E.L., M.W. Edelstein, and V.C. Sutherland 1979. Workshop on
Atmospheric Dispersion Models in Complex Terrain. EPA-600/9-79-041.
U.S. Environmental Protection Agency, Research Triangle Park, NC.
Hunt, J.C.R. and R.J. Mulhearn 1973. Turbulent Dispersion from
Sources near Two-Dimensional Obstacles. J. Fluid Mech. 61; 245-274.
Hunt, J.C.R. and J.S. Puttock, and W.H. Snyder 1979. Turbulent
Diffusion from a Point Source in Stratified and Neutral Flows around a
Three-Dimensional Hill (Part I - Diffusion Equation Analysis). Atmos.
Environ. 13: 1227-1239.
Hunt, J.C.R. and W.H. Snyder 1978. Flow Structure and Turbulent
Diffusion around a Three-Dimensional Hill. (Part II - Surface
Concentrations Due to Upstream Sources - unpublished manuscript).
Hunt, J.C.R. and W.H. Snyder 1980. Experiments on Stably and
Neutrally Stratified Flow over a Model Three-Dimensional Hill.
J. Fluid Mech. 96; 671-704.
Isaacs, R.G., A. Bass, and B.A. Egan 1979. Application of Potential
Flow Theory to a Gaussian Point Source Diffusion Model in Complex
Terrain. Fourth Symposium on Turbulence, Diffusion, and Air Pollution,
Reno, NV. American Meteorological Society, Boston, MA.
Izumi, Y., Barad, M.L. 1970. Wind Speeds as Measured by Cup and Sonic
Anemometers and Influenced by Tower Structure. J. Appl. Meteorol.
£: 851-6.
Launder, B.E. and D.B. Spaulding 1972. Lectures in Mathematical
Models of Turbulence. New York: Academic Press.
Maggs, R.J., P.L. Joynes, A.J. Davies, and J.E. Lovelock 1971. The
Electron-Capture Detector - A New Mode of Operation. Anal. Chem. 43;
1966-1971.
Milne-Thompson, L.M. 1968. Theoretical Hydrodynamics. New York: The
MacMillan Company.
Papoulis, A. 1965. Probability, Random Variables, and Stochastic
Processes. New York: McGraw Hill Book Company
Snyder, W.H. 1980a. Towing Tank Studies in Support of Field
Experiments at Cinder Cone Butte, Idaho. Phase III; Verification of
Formula for Prediction of Dividing Streamline Height. U.S.
Environmental Protection Agency, Research Triangle Park, NC.
237
-------
Snyder, W.H. 1980b. Towing Tank Studies in Support of Field
Experiments at Cinder Cone Butte, Idaho. Phase I: Influence of Hill on
Wind Field at the Meteorological Tower Site. U.S. Environmental
Protection Agency, Research Triangle Park, NC.
Strimaitis, D.G., J.S. Scire, and A. Bass 1981. COMPLEX/PFM. Air Quality
Model User's Guide. Final Draft Report, EPA Contract No. 68-02-2759.
Environmental Research & Technology, Inc., Concord, MA.
Van Ulden, A.P. 1978. Simple Estimates for Vertical Diffusion From
Sources near the Ground. Atmos. Environ. 12; 2125-2129.
Yanskey, G.R., E.H. Markee, Jr., and A.P. Richter 1966. Climatography
of the National Reactor Testing Station. Report IDO-12048.
U.S. Atomic Energy Commission.
238
-------
APPENDIX A
SUMMARY OF TRACER DATA ANALYZED FOR TESTS 201-218
239
-------
TABLE A-l. CASE 201 (10/16/80 - 1700-2500)
No. 1—Hour Ave Samples
No. 10-Min Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
Hour
1
2
3
4
5
6
7
8
TOTAL
SFg CF-^Br
11
11
3
13
8
11
10
6
73
TABLE A-2. CASE 202
No. 1-Hour Ave Samples
SF6 CF_3l£
14
19
24
23
23
22
24
20
169
SJ.6
70
82
39
54
31
14
2
0
292
(10/17/80 -
No. 10-Min
SF6
113
136
56
46
21
23
9
0
404
CFjjBr
1700-2500)
Ave Samples
CF3Br
•
Total
81
93
42
57
49
25
12
6
365
Total
127
155
80
69
44
45
33
20
573
240
-------
TABLE A-3. CASE 203 (10/20/80 - 0000-0800)
Hour
1
2
3
4
5
6
7
8
TOTAL
Hour
1
2
3
4
5
6
7
8
TOTAL
No. 1-Hour Ave Samples
SFg CF3Br
1
21
20
2
9
7
3
16
79
'TABLE A^. CASE 204
No. 1-Hour Ave Samples
SF6 CF3Br
32
33
12
26
29
28
32
30
222
No. 10-Min Ave Samples
57
67
49
29
55
64
49
70
440
(10/21/80 - 0000-0800)
No. 10-Min Ave Samples
SFfc CF3Br
53
66
47
61
51
72
74
83
507
Total
58
88
69
31
64
71
52
86
519
Total
85
99
59
87
80
100
106
113
729
241
-------
TABLE A-5. CASE 205 (10/23/80 - 0000-0800)
Hour
1
2
3
4
5
6
7
8
TOTAL
No. 1-Hour Ave Samples
SF6 CF3Br
20
12
29
31
33
35
33
32
225
No. 10-Min Ave Samples
SF6 CF3Br
6
11
41
78
69
70
69
78
422
Total
26
23
70
109
102
105
102
110
647
TABLE A-6. CASE 206 (10/24/80 - 0000-0800)
No. 1—Hour Ave Samples
No. 10-Min Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
SF6 CF3Br
1
33
34
34
30
29
31
36
228
SF6 CF3I
11
78
62
58
58
57
62
60
446
Jr Tota]
12
111
96
92
88
86
93
96
674
242
-------
TABLE A-7. CASE 207 (10/25/80 - 0000-0800)
No. 1-Hour Ave Samples
No. 10-Min Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
SF6
2
31
30
25
2
3
30
27
150
TABLE A-8
CF3Br
CASE 208
No. 1-Hour Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
SF6
15
15
28
33
4
35
3
40
173
CF3Br
2
2
11
15
1
17
0
16
64
SF.6
5
65
55
75
63
66
72
68
469
(10/27/80 -
No. 10-Min
Si6
63
72
69
73
38
60
19
67
461
GF3Br
1700-2500)
Ave Samples
CF3Br
6
14
16
21
15
28
14
29
143
Total
7
96
85
100
65
69
102
95
619
Total
86
103
124
142
58
140 •
36
152
841
243
-------
TABLE A-9. CASE 209 (10/28/80 - 1700-2500)
No. 1-Hour Ave Samples
No. 10-Min Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
SFfi CF3E
L n i- n — —* —
46
49
48
1
3
3
48
42
240
•T SFft CF-^Br
78
65
78
2
5
6
65
69
368
Total
124
114
126
3
8
9
113
111
608
TABLE A-10. CASE 210 (10/30/80 - 0000-0800)
No. 1-Hour Ave Samples
No. 10-Min Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
SF.6
39
31
42
35
3
43
43
15
251
CF3Br
9
15
22
15
1
22
19
6
109
SF6
73
83
60
74
23
84
65
9
471
CF3Br
11
17
15
13
0
15
16
2
89
TotaJ
132
146
139
137
27
164
143
32
920
244
-------
TABLE A-ll. CASE 211 (10/31/80 - 0000-0800)
No. 1-Hour Ave Samples
No. 10-Min Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
SF6
40
35
31
36
42
34
34
39
291
CF3Br
20'
18
17
19 -"
21
16
20
18
149
SF6
90
70
63
76
82
78
72
65
596
CEjBr
26
13
4
11
5
4
8
10
81
Total
176
136
115
142
150
132
134
132
1,117
TABLE A-12. CASE 212 (11/2/80 - 1700-2500)
No. 1-Hour Ave Samples
No. 10-Min Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
11
10
17
1
8
18
20
_JL
86
S£6 CF3*
37
34
25
0
3
42
53
8
202
5r Tota!
48
44
42
1
11
60
73
9
288
245
-------
TABLE A-13. CASE 213 (11/4/80 - 0000-0800)
No. 1-Hour Ave Samples
No. 10-Min Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
SF6
3
3
4
29
43
47
42
45
216
TABLE A- 14
CF-^Br
1
1
2
10
13
12
10
13
62
. CASE 214
No. 1-Hour Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
SF6
0
26
38
36
42
7
41
43
233
CFjBr
0
8
11
9
3
1
15
14
61
SF6
4
2
0
41
84
75
82
64
352
(11/5/80
CF^Br
0
0
0
27
28
9
15
14
93
- 0200-1000)
No. 10-Min Ave Samples
SF6
0
81
80
65
75
0
89
88
478
CF3Br
0
32
35
36
24
0
33
34
194
Total
8
6
6
107
168
143
149
136
723
Total
0
147
164
146
144
8
178
179
966
246
-------
TABLE A-15. CASE 215 (11/6/80 - 0000-0800)
No. 1-Hour Ave Samples
No. 10-Min Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
SF6
45
47
43
50
46
46
1
0
278
TABLE A-16.
CFjjBr
9
11
11
2
16
15
0
0
64
p A C T7 O 1 A
, V^r\Oi-j «£JLQ
No. 1-Hour Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
SF6
52
47
54
48
57
51
53
6
368
CF3Br
15
14
14
11
15
13
14
2
98
S£6
83
94
96
103
97
94
0
0
567
(11/9/80 -
CF^Br
75
56
53
0
80
77
0
0
341
0000-0800)
No. 10-Min Ave Samples
SFfi
94
97
89
92
103
107
105
0
693
CF3Br
16
14
30
28
34
26
19
0
167
Total
212
208
203
155
239
232
1
0
1,250
Total
177
172
187
179
209
197
191
14
1,326
247
-------
TABLE A-17. CASE 217 (11/10/80 - 0200-1000)
No. 1-Hour Ave Samples
No. 10-Min Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
SF6
50
50
52
1
48
45
49
44
339
TABLE A-18
CF3Br
8
10
8
0
15
15
21
18
95
. CASE 218
No. 1-Hour Ave Samples
Hour
1
2
3
4
5
6
7
8
TOTAL
SF6
50
45
44
50
49
44
51
49
382
CF3Br
6
12
7
8
13
7
9
12
74
SF6
96
95
89
5
97
97
102
83
664
(11/12/80
CFjBr
0
0
5
0
15
24
26
18
88
- 0200-1000)
Total
154
155
154
6
175
181
198
163
1,186
No. 10-Min Ave Samples
SF6
65
95
92
105
103
95
87
71
713
CF3Br
10
21
30
31
32
26
9
10
169
Total
131
173
173
194
197
172
156
142
1,338
248
-------
APPENDIX B
LABORATORY SIMULATION OF STABLE PLUME
DISPERSION OVER CINDER CONE BUTTE
249
-------
LABORATORY SIMULATION OF STABLE PLUME
DISPERSION OVER CINDER CONE BUTTE
Comparison with Field Data
by
William H. Snyder*
and
Robert E. Lawson, Jr.*
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
May 1981
*0n assignment from National Oceanic and Atmospheric Administration,
U.S. Department of Commerce.
250
-------
INTRODUCTION
The purpose of this series of experiments was to duplicate, in the labora-
tory, the field experiments performed by Environmental Research and Technology,
Inc. (ERT) at Cinder Cone Butte, Idaho. In particular, one hour (0500-0600)
of case 206 was modeled. As case 206 was representative of very stable atmo-
spheric conditions, the Fluid Modeling Facility towing tank was selected as
the proper facility for these experiments. Measurements made during the towing
tank experiments included ground level concentration, vertical distributions of
concentration at selected points, plume dispersion in the absence of the hill,
and visual observations of plume characteristics and trajectories. In the
following pages, the conduct of this study is described (not necessarily in
chronological order) along with some observations in regard to the correlation
of field and laboratory data.
251
-------
SUMMARY OF FIELD OBSERVATIONS
Meteorological Data
The field meteorological data has been summarized in a separate data report
(Cinder Cone Butte Meteorological Data, Lawson, March 1981), but there are seve-
ral points of interest which require further explanation. A considerable portion
of the meteorological data was missing due to failure of the instruments or data
collection system. At the 40 m-level (which is the level nearest the source
height), only the westerly component of wind speed was available. This was over-
come to some extent by assuming a wind direction of 122°. The southerly wind
component and hence the mean wind speed were then calculated. Since no informa-
tion was available to indicate the distribution of wind direction at this level,
the frequency distribution of wind directions at the source height was assumed
to be the same as that at the 80 m-level. Where temperature data was missing,
it was possible in some cases to interpolate between data for the previous
time period and data for the following time period in order to obtain a reason-
able estimate for the missing data point. The values of HC reported by ERT and
summarized in the above mentioned report were revised using the estimated wind
speeds at the 40 m-level and some interpolated temperatures. This resulted
in an increase in the average value of HC from about 34 m to about 41 m.
Figures 1 and 2 show the mean wind speed and temperature profiles for the one
hour period. Table 1 provides a listing of the newly computed values of HC for
each 5-minute period within the hour. Figure 3 shows the variation of wind
direction at the 80 m-level during the hour. Note the slight shift in wind
direction during the hour. The mean wind direction (derived from the mean
westerly and southerly wind speeds) is 122.3°. In Figure 4, an admittedly
crude attempt was made to determine the frequency distribution of wind direction.
As noted, this distribution is for the 80 m-level. Although the number of data
points used to form this distribution was small, the bimodality of the distri-
bution is apparent, with the main peak occurring around 121° and a secondary
one near 125.5°. Similar plots were produced for HC as shown in Figures 5 and
6. There appears to be no systematic trend in HC and the distribution shows a
single peak around 41 m.
252
-------
No analysis of the remaining meteorological tower data was attempted as
most of the data was reported as missing. The lower-level winds, as indicated
by the instruments at the 2 and 10 m elevations, appeared to be decoupled
from the upper level winds.
Concentration Data
Field concentration data for case 206 were acquired using sulfur hexa- ,
fluoride (SFg) as a tracer source, the concentrations being reported in parts
per trillion. The SFg was released at a rate of 0.063 grams/second from a
height of 35 m. The source was reportedly located at 122°/597 m from the hill
center but examination of photographs of the source and maps of the road on
which the source was known to be located indicated a more likely position to
be 124.6°/597 m. This alteration of the source coordinates was supported by
ERT.
As both the source height and meteorological tower data were referenced
to local ground level, these heights were adjusted to reference all measure-
ments to the base of the hill. Careful examination of the topographic maps
showed the met tower to be located at an elevation of 941 m (3087 ft), while
the source was located at an elevation of 939 m (3081 ft). The met tower was
thus 3.9 m and the source 5.8 m lower than the base of the hill. This then
means that the source height relative to the base of the hill was 29.2 ms and
all H values calculated from met tower data should be reduced by 3.9 m in
order to maintain comparability relative to the hill. Although the source
height used in the model is shown as 31 m, the 1.8 m difference was deemed
insignificant in relation to the errors in estimating elevations from the
topographic maps.
Figure 7 shows the one-hour average concentration distribution over the
hill. The wind direction indicated on this plot is from 122°. The distribu-
tion is seen to favor the northeast side of the hill with the axis of the
distribution on a southeast-northwest line. The maximum concentration is
located in the east draw near the 30 m elevation contour. There is a rather
tight concentration gradient along the southwest side of the distribution with
the tightest gradient being directly between the two peaks.
Although not plotted, there were several 10-minute average concentration
253
-------
samples available. These samples were used to form one-hour averages for com-
parison with the data plotted in Figure 7. The resulting one-hour averages
were in good agreement with data from the one-hour average samplers.
Sampler location 60X (FMF sample port 34) showed an anomalously low
value (15 ppt) and is believed to be in error.
Slides
Several 35 mm slides of the case 206 field experiments were available for
analysis. While it was not possible to obtain quantitative data from these
slides, several qualitative observations were made. The plume was initially
observed to split with a portion traveling around the north side of the hill
and the remainder traveling through the draw and over the hill. Approximately
half-way through the hour the plume trajectory was directly through the draw.
There was some evidence that the plume was being downwashed on the upwind side
of the hill. The slides indicate that the area of peak surface concentration
may have been at a somewhat greater elevation («\, 50 m contour) than indicated
by the concentration data. The fact that the plume was initially observed to
split around the north butte and later traveled directly through the draw is
in apparent contradiction to the reported 80 m wind directions. It should
be noted that the travel time from the source to the hill was on the order of
6 minutes and this must be taken into account when comparing observations with
met data.
The slides were also used to visually confirm the location and release
height of the source.
254
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EXPERIMENTAL DETAILS
Model Speci f i ca11ons
The model was constructed of acrylic plastic by a vacuum forming tech-
nique. The nominal model scale was 1:640; after fabrication, the model scale
was determined to be 1:647 horizontal and 1:694 vertical (model height =
14.4 cm). The model was mounted on a circular platform (1.7 m dia.) which
was inserted into a circular, recessed cutout in a 2.5 m square baseplate to
allow for rotation to various wind directions. The baseplate provided an
upstream fetch of about 0.7 m and a downstream fetch of about 0.2 m; its
width was 3 cm less than the width of the towing tank (2.5 m). Both baseplate
and model were covered with small gravel (average diameter on the order of
2 mm) in order to simulate surface roughness. The gravel size was chosen by
application of Jensen's criterion (Snyder, 1981),
om
op
n
With a prototype z ^ 5-8 cm, then z
where e is the grain size, e
U*z /v > 2.5. Assuming U^/U
* 0.07-0.12 mm, and since z
2-3 mm. To be aerodynamica'lly rough,
/30,
0.045, and a tow speed of 10 cm/sec, the
value of U*z /v is on the order of 0.5. In spite of this small value of
roughness Reynolds number., the boundary layer on the baseplate approaching
the hill was visually observed to be turbulent, albeit quite thin (^ 2 cm).
Under the strongly stratified flows, the surface flow on the hill itself was
not observed to be turbulent.
Sample ports were located on the model at the same locations as in the
field study although port identification numbers were altered for more efficient
data processing. The ports projected approximately 2 mm above the surface
255
-------
roughness, except for the mast mounted samplers, which were scaled in height
in proportion to their field counterparts. The ports were fabricated from
0.24 cm O.D. brass tubing with equal lengths of vinyl tubing leading from the
ports to the sampling system.
The source was simulated with a 0.32 cm I.D. brass tube with the upper
portion bent over such that the tracer dye was released parallel to the
approach flow.
The tracer dye was a mixture of concentrated blue food dye (Warner
Oenkinson No. 393), towing-tank water drawn through the stack, and small
amounts of either saturated salt water or alcohol. The diluent (salt water
or alcohol and towing-tank water) was mixed in such proportions that the
final mixture - 1 part concentrated dye with 10 parts diluent - was neutrally
buoyant. The emission rate of tracer dye was nominally 190 cc/min, the exact
rate being determined each tow.
0, 30, 60, and 90 m contour lines were added to the model to aid in
Visualization and photography. Index marks were placed around the periphery
to aid in aligning both source and model in relation to the desired wind
direction.
Stratification of Towin£ Tajik
The water channel was stratified using layers of salt water as described
by Hunt, et al_ (1978). Linear stratification was used to simulate the potential
temperature profile derived from Figure 2. The sharp gradient near the
surface was ignored as it translates to a layer of only 1.4 cm depth and
cannot, for practical reasons, be maintained in the water channel. This appears
justified because, as mentioned earlier, the surface winds in the field were
decoupled from the higher level winds.
As successive experiments lead to erosion of the density profile near
the surface, it was necessary after each two to three tows to siphon 3 to 6
centimeters of water from the surface layer and to add the same volume of
saturated salt water to the bottom. This had the effect of restoring the
original linear profile to the surface.
The dye tracer used as the effluent also discolored the water after two
to three tows; hence, in conjunction with the siphoning process, the water was
chlorinated to bleach out the residual dye. The chlorine treatment was followed
256
-------
by dechlorination with sodium thlosulfate to insure that tracer samples were not
also bleached out.
The density profile and water quality were checked each day prior to
initiating a series of tows. A typical density profile is shown as Figure 8.
Photography
Photographic records of each test were made using 35 mm cameras. One
camera was used to photograph a plan view of the model while a second was used
to record a side view. In addition to these still photos, 16 mm movies were
made of each tow. A polaroid-back Graflex camera was used to provide black-
and-white photos for immediate evaluation and comparison. A list of available
photographic records is seen in Table 2,
Colorimetric Technique for Concentration Measurements
The technique used for measuring concentrations is conceptually very
simple. Samples were withdrawn through the sample ports via a vacuum system
which deposited each port sample in a separate test tube. The contents of
each tube were then analyzed for concentration using a Brinkman PC-600 color-
imeter. The PC-600 utilizes a fiber-optic probe with fixed path length which
is simply dipped into the contents of each tube. The output of the instrument
is a voltage which is related to the opacity of the solution being tested. This
voltage is sampled by computer and converted to concentration in percent dye.
The conversion from voltage to'concentration utilizes a calibration curve
formed by recording the output voltage vs. concentration for 12 "standards"
which consist of accurately known dilutions of the same dye used for the tracer
source. A "Beer's Law" type of curve is then best-fit to the standards for
use in converting the voltage from the unknown sample into a dye concentration.
Although the instrument required some care in use, frequent checks of the
calibration showed excellent repeatability. A typical calibration curve is
shown in Figure 9.
257
-------
Procedure Followed
The sequence of events leading to a daily series of tows was as follows;
1. Measure density profile.
2. If density profile is not linear, then siphon from surface
to restore the profile and add an equal volume of brine
at the bottom of the channel to restore the original depth.
3. Withdraw a sufficient quantity of water through the stack
to mix the dye tracer. Mix the dye, diluent water, and
alcohol such that the effluent specific gravity is the
same as that.at the source height.
4. Use program IMPINGE to determine, from the density
profile, the tow speed appropriate to the desired HC.
5. Place one drop of sodium thiosulfate solution in each
sample test tube to insure that any residual chlorine
does not affect the sample concentration.
6. Check and/or adjust the source flow rate and the
sample flow rate. Check vacuum seals on sampling
device.
7. Check that all cameras and lights are ready - also
check alignment of stack vs. wind direction.
8. Set desired tow speed on carriage controller and
check timer used to monitor actual tow speed.
9. Initiate tow, monitoring source flow rate and sample
time during the tow - sampling is initiated only
after the starting transient has decayed and conditions
are stabilized.
10. After the tow, record all pertinent data immediately,
then remove the sample test tubes and proceed with
analysis of samples.
11. At the end of each day's experiments, or more frequently
if necessary, chlorinate the water to remove the residual
dye - this must be followed by dechlorination and a check
of the density profile.
A total of 41 tows was made. A summary list showing all tests conducted is
provided in Table 3 along with remarks on visual observations made after each
tow.
258
-------
Observations of Erratic
ti PUni
The only erratic behavior observed during the entire series of tests was
a tendency for the plume to be deflected slightly toward the north side of the
hill during the last 1/3 of the tow. This was not observed during the tests
with the flat baseplate9 rather some slight horizontal meandering of the plume
was observed. No tests were conducted to investigate this phenomenon as it
did not appear to be significantly affecting the concentration measurements.
Flat Baseplate Measurements
The last nine tows were conducted with the model hill removed and a flat
disk inserted in its place. The disk was coated with gravel of the same size
as that on the model and was equipped with a cross-rake of sampling ports.
The rake was mounted at three locations during the experiments , corresponding
to model distances of 48.5, 91 .4, and 134.2 cm and full-scale distances
of 314, 591, and 868 m downwind from the source. Samples were drawn from the
cross-rake using the vacuum sampling system and similarly analyzed for dye
concentration. The resulting measurements provided an indication of concentra-
tion in the absence of the hill and estimates of the vertical and horizontal
spread of the plume.
Conversion of Model Concentrations to Field Concentrations
Model concentrations were recorded in percent of dye by volume, these
values then being converted to nonditnenslonal form by, the. foil owing equation:
x = CUH2 s
Q
where x is the nondlmensional concentration, U is the tow speed, H is the
hill height, and Q is the effluent flow rate. These nonditnensional concentra-
tion values were then used to convert the model concentrations to their field
equivalents as follows:
xmodel = xfield 9
259
-------
so
and
Cf =
Field concentrations were reported in parts-per-trillion (ppt) of SFg which
has a density of 6.5 grams/liter at 20°C and 760 mm Hg. The height of the
hill, H-, was TOO m, and the wind speed at the source height was 1.3 m/s.
Making the substitutions,
C(ppt) =
(.063 gm/s)(l
12
ppt)x
(6.5 gm/A)(1.3 m/s)(100 m)2
= 746 X.
Thus, conversion of nondimensional model concentrations to equivalent field
concentrations in ppt is simply a matter of multiplying by 746. Note that
the conversion factor is inversely proportional to wind speed and, since the
wind speed data near the source height was missing, this value was estimated
from the wind profile as was previously discussed.
260
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PRESENTATION AND DISCUSSION OF RESULTS
Dispersion in the Absence pf_ the.
Nine tows were made to characterize plume dispersion in the absence of
the hill. During each tows lateral and vertical concentration profiles were
measured in one cross-section (one downwind distance). Tests were conducted
at three towing speeds, corresponding to H values of 24, 44 and 60 ms and
C»
lateral and vertical concentration profiles were measured at downwind distances
corresponding to 314, 591, and 868 m. Typical profiles are shown in Figures
10 and 11. These results (as well as the remainder of data to be presented) are
displayed in terms of full scale equivalents. "Best-fit" Gaussian profiles are
also displayed; it may be observed that the concentration distributions are
very close to Gaussian in shape.
Standard deviations of horizontal and vertical plume widths are shown in
Figure 12. As the average effluent flow speed was 40 cm/s, the effluent was
emitted as a turbulent jet; the jet was visually observed to expand rapidly
initially both in the vertical and horizontal directions. Horizontal growth
continued at a slower rate, but vertical growth approached zero, with a hint
of plume collapse (negative growth) further downwind. These qualitative
observations are substantiated by the growth curves displayed in Figure 12.
Neither horizontal nor vertical plume widths appear to be strongly affected by
the towing speed.
Figure 13 shows the variation of plume centerline concentration versus
downwind distance. Table 4 summarizes the plume statistics in the absence of
the hill.
Let us address the correspondence between these laboratory measurements
in the absence of the hill and the field plume behavior. The field plume was
generated by a thermal fogger suspended from a crane. Because of the rapid
mixing of the jet in the wake of the fogger, and because the fogger was free
to rotate about a vertical axis, ERT (Strimaitis, 1981) has estimated virtual
261
-------
plume widths of a * 2 m and a = 3 m. When the field plume was observed
"missing" the hill under strongly stable conditions, it was frequently described
as looking like a "piece of yarn", i.e., a long, reasonably straight plume with
slightly ruffled edges and near-zero growth. Hence, for short time periods
(*> 5 min), the plume dimensions may be very roughly estimated as az = 5 m and
a s 15 m. The laboratory values shown in Table 4 and Figure 12 are comparable
to these estimated, short-term field values.
On the other hand, plume meander, as was immediately apparent in the field,
was obviously lacking in the laboratory simulations. Also lacking were the low
frequency fluctuations in wind speed (or H ). Since adequate field measurements
\f
of plume dimensions and concentrations as functions of averaging time were un-
available at this time, it was not possible to draw firmer conclusions concern-
ing the relationship between laboratory and field measurements of plume behavior
in the absence of the hill. However, some elementary attempts at simulating
the fluctuating wind speed and direction in the presence of the hill were made
(see next section).
Concentration Patterns on the Butte
A total of 32 tows with the model of Cinder Cone Butte in place was made,
representing different source locations (by mistake), wind directions and wind
speeds. A summary of all tows is given in Table 3. A map of port numbers is
provided in Figure 14 for later reference and a cross-reference list to ERT
sampler locations is given in Table 5. In Figure 14, the precise port location
is the lower left corner of the dot matrix from which the number is configured.
The first 9 tows were preliminary in nature; only the highlights will be
described here.
Figure 15 shows top and side views of the plume diffusing over the hill
during Tow 8. The source height Hg was 31 m, the dividing streamline
height H was 38 m, and the wind direction was 122°. Under these conditions,
\f
the flow was observed to be limited in vertical travel such that the plume
passed around and between the two peaks, but did not surmount them.
Tows 1 and 2 were done approximately 2 hours apart under ostensibly
identical conditions for the purpose of testing repeatability. The two con-
centration distributions may be compared by examination of Figure 16. The
262
-------
one-digit numbers on these maps are relative concentrations (same scaling
factor on both maps). The decimal points associated with the numbers are
located at the sampler locations. Care should be exercised in reading the
maps, i.e., if the number is to the left of the decimal point, the relative
concentration is a whole number; if to the right, a fractional number. (These
numbers are truncated, not rounded.) Also, 100 samples were collected during
each tow. If no number appears at a port location, it is because a visual
inspection of the contents of the sample collection test tube revealed no
dye, and the sample was not analyzed, if the sample was analyzed and the
relative concentration was found to be less than 0.1, then a 0 appears on the
map (sampler location is at the bottom center of the zero).
Figure 17 compares the concentrations from the two tows on a scatter
diagram. Except for one obvious outlier (which is unexplained at this point),
concentrations generally match to within 10 to 2Q% of each other without any
obvious bias over the range from 0.02 Cmx to Cmx, and is considered excellent
repeatability. The obvious departures at the very low concentrations is most
likely due to slight secondary flows in the towing tank.
Tows 7 and 8 were also done for the purpose of testing repeatability,
but in this case, two high speed tows and a twenty-four hour delay occurred
between the two; the density profile was not restored by skimming as was
usual, so that the two profiles differed somewhat, as shown in Figure 18.
Note that the towing speeds differed between the two tows (see Table 3) such
that H was the same, according to Hunt's formula (Snyder, 1980):
\f
V
The scatter diagram for tows 7 and 8 is shown in Figure 19, where it may
be observed that the scatter is very much larger than in the previous compar-
ison. Variations between the two tows do not appear to have significant bias,
but are typically factors of 3 to 5 apart. The conclusion that may be drawn
from this test, then, is that the precise shape of the density profile is
quite important in determining the concentration distribution, i.e., a gross
characterization of the stability (such as by specifying HC alone) is clearly
263
-------
not sufficient.
Figure 20 shows a 3 x 6 matrix of concentration distributions, covering
all combinations of three wind directions (117°, 122°, and 127°) and six
values of HC (24, 31, 38, 44, 49 and 60 m). Concentration isopleths have
been drawn by eye so that the distributions can be more readily comprehended.
Several points are to be noted from this figure. First, at the wind direction
of 122°, as H increased from 24 to 60 m, the location of the maximum shifted
from the downwind side of the hill to the top and finally to the upwind side.
The crosswind width of the distributions increased as H increased, but the
value of the maximum concentration changed relatively little (less than a
factor of 2). At H = 60 m, the maximum surface concentration was located at
c
nearly the same elevation as the source. Second, changes of only ±5° in wind
direction had dramatic effects on the distributions, moving the locations of
the maximum concentrations from the north skirt of the hill at a wind direc-
tion of 127°, to the centerline at 122°, then to the south skirt at 117°.
Again, the values of the maximum concentrations changed relatively little with
changes in H and/or wind direction, although the values of the maximums
c
were noticeably less at 127°. Third, for centerline winds (122°), the shapes
of the distributions change substantially with changes in H , whereas for off-
C
axis winds (117° or 127°), the distributions are, for practical purposes, indep-
endent of H . Unfortunately, very few field samplers were located within the
areas of maximum concentration for the off-axis winds. During this hour, only
two samplers were working within the 1600 ppt SFg contour on the south side of
the hill. Finally, it is noteworthy that the maximum surface concentration was
1/2 to 2/3 of the plume centerline concentration in the absence of the hill
(cf., Figure 13).
A scatter diagram comparing concentration distributions measured in
three of these tows (11,12, and 13) with field distributions is presented in
Figure 21. There is one obviously suspicious field measurement point (port 34;
ERT sampler location 60X; see Figure 14 for sampler location and Figure 7 for
field concentration distribution). Ignoring that, it is generally apparent
that maximum model concentrations were much higher than maximum field concen-
trations (by factors of 3 to 10) and low model concentrations were much lower
than low field values; there were many ports on the model where zero-concen-
trations were observed, whereas in the field, all the samplers showed at least
a trace concentration. It is impossible, of course, to show these points
264
-------
properly on the logarithmic scatter diagram of Figure 21; they are Indicated, .
however, by the hand-drawn points on the bottom of the figure.
As mentioned earlier, low-frequency fluctuations in wind speed and
direction as observed in the field were obviously lacking in the towing tank.
This is almost certainly the explanation for the discrepancies between the
model and field data of Figure 21,, The previous series of 18 tows was done in
an attempt to determine whether a superposition of concentration patterns from
tows done at a series of discrete wind speeds (various H 's) and wind directions
C
could be used to simulate field conditions with continuous distributions of
wind speed and direction. As mentioned earlier, however* the 40 sn-level winds
were lacking, so that proper choices for particular wind speeds and directions
to simulate and superpose were difficult to make. The particular choices for
the previous series of tows (122° ±5° and 24 m < HC < 60 m) were made on an
ad hoc basis after studying the field photographs of plume behavior and
available meteorological data at other levels on the tower.
The first attempt at superposition is shown in Figure 22. It was con-
structed as the simple arithmetic average of the distributions from each of
the 18 tows. Figure 23S a scatter plot of resulting model concentrations
versus field concentrations, showed a marked improvement over the previous
single-tow comparisons. The highest model concentrations here are within a
factor of 2 of the highest field values. Whereas the low model concentrations
are still lower than the low field values, there were no zero-model-concentra-
tion values. The indication for improving the correspondence iss therefore,
an even larger series of towss although particular choices to be made for
other wind speeds and/or directions are not immediately obvious.
Three points on the scatter plot of Figure 23 deserve discussion. The
two points marked 49 and 61 (port numbers) were the only two operating field
samplers on the south side of the hill, and both of them indicated quite small
values of concentration. Evidently the choice of the 117° wind direction was
a poor one; it created the lobe of the concentration distribution around the
south side of the butte. In an attempt to improve the correspondence, the
6 tows at the 117° wind direction were eliminated from the superposition; this
process reduced model concentrations at these two points to only a factor of
2 higher than the observed field values. However, it increased nearly all
remaining concentrations by approximately 50%; such a simple solution is
265
-------
therefore not sufficient.
The point marked 31 on the scatter plot was located at the 25 m elevation,
i.e., 5 m lower than the source; it happens to be the location of the highest
concentration measured during this hour in the field. This may at first appear
anomalous. However, Hunt and Venkatram (private communication) have reported
similar observations during other very stable periods. Hunt has further pos-
tulated as a possible mechanism a vortex roll-up on the windward side of the
hill and has done some preliminary calculations showing that such vortex roll-
up is plausibly due to shear in the approach flow. Vortex roll-up was not
observed on the windward side of the CCB model, as shear in the approach flow
was absent. Such vortex roll-up has been observed in the towing tank, however,
on model hills of much steeper slope (Hunt and Snyder, 1980).
Other combinations and superpositions from this set of 18 tows were
attempted, but the superposition of the entire set (Figures 22 and 23) appeared
to yield the best results.
Five additional tows were made, 3 at 120° and 2 at 125.5°, so that super-
positions could be made on the basis of the probability distribution of HC and
the bimodal distribution of wind direction at the 80 m-level (Figures 6 and 4,
respectively). Various combinations of distributions including those from these
5 tows were made, using uniform as well as weighted averaging. None of these
superpositions were as successful as those shown in Figures 22 and 23.
Figures 24 and 25 show the variation of maximum surface concentration with
H and wind direction, respectively. No systematic variation of Cmx with HC
is observed, but there is a definite tendency for the maximum concentration to
peak around a wind direction of 120°. It is also to be noted that the maxi-
mum surface concentration at this wind direction is approximately equal to
the plume centerline concentration in the absence of the hill.
266
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CONCLUSIONS
1. Repeatability of the concentration distributions in the towing tank was
good. Under ostensibly identical conditions, concentrations can be matched
to within 10 to 20% upon successive tows.
2. Gross stability classifications are not sufficient for characterizing
concentration distributions. It appears that the detailed shape of the
density profile is quite important in determining concentrations on a point-
by-point basis. However, such a gross classification would appear to be
reasonable for predicting the values of maximums as well as ranges of values
of concentration (but not locations).
3. Surface concentration distributions around the hill are extremely sensi-
tive to changes in wind direction under stable conditions. In these exper-
iments, 24 m < H, < 60 m, the location of the maximum concentration shifted
c
through an angle of approximately 60° (looking from the source) with a shift
of only 10° in wind direction.
4. The value of the maximum surface concentration changed relatively little
with changes in wind direction or wind speed; over the entire range of
24 m £ H £ 60 m and 117° <_ e <_ 127°, the maximum changed by only a factor
of 3.5.
5. For "on-axis" wind directions (i.e., plume aimed directly toward hill
center), the location of the maximum surface concentration moved from the lee
side to the windward side as HC increased from 24 to 60 m. The value of the
maximum surface concentration changed by only a factor of 1.5 over this same
range of Hr.
v»
267
-------
6. For "off-axis" wind directions (on the order of ±5°), the locations and
values of the maximum surface concentrations are, for practical purposes,
Independent of HC.
7. Because of the absence of low frequency fluctuations In wind speed and
direction in the tank, the concentration distributions observed in the tank
were exceedingly narrow; maximum concentrations were 5 to 10 times larger than
those observed in the field.
8. An ad hoc attempt was made to simulate the low frequency wind fluctuations
by superposing concentration patterns from tows done at a series of discrete
wind speeds and wind directions. This attempt was moderately successful in
that 80% of the model concentrations were within a factor of 2.5 of the field
concentrations. The highest model concentrations were a factor of 2.5 larger
than field values. The points where the model showed concentrations lower
than field values were located on the extreme edges of the distributions,
indicating that tows at very slightly different wind directions could have
brought these points in-line.
9. The ad hoc attempt was made because of malfunctions in the measurement
system at the 40-m level (closest to plume elevation), so that a detailed
analysis of 80-m level winds was made. Additional tows were made on the basis
of the frequency distribution of wind directions at the 80-m level. Several
superpositions on this basis yielded results less satisfactory than did the
ad hoc attempt. Frequency distributions of wind speed and direction at. plume
elevation are evidently essential in order to improve performance of the model.
10. For "on-axis" winds in the model, maximum surface concentrations approached
those at the centerline of the plume in the absence of the hill, i.e., Cmx = aCQ,
where 0.5 <. a <.!. However, because of the extreme sensitivity of the location
of maximum concentration to wind direction, the plume is "smeared" broadly
across the hill surface as the wind direction changes by only a few degrees.
Hence, short term (-v5 min) in the field may be expected to approach CQ; larger
term averages H hr) may be expected to be reduced by factors of 5 to 10 (or
more depending, of course, on the magnitudes of au and OQ).
268
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REFERENCES
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.s v. 96,
pt. 4, p. 671-704.
Hunt, J.C.R., Snyders W.H., and Lawson, R.E. Jr., 1978: Flow Structure and
Turbulent Diffusion around a Three-Dimensional Hill: Fluid Modeling Study on
Effects of Stratification: Part I:-,Flow Structures Envir. Prot. Agcy. Rpt. No.
EPA 600/4-78-041, Res. Tri. Pk.9 NC.
Snydera W.H., 1980: Towing Tank Studies in Support of Field Experiments at
Cinder Cone Butte, Idaho; Phase III: Verification of Formula for Prediction
of Dividing Streamline Height, Rpt. to Envir. Res. & Tech., Aug. 29S 12p.
Snyder, W.H., 1981: Guideline for Fluid Modeling of Atmospheric Diffusion,
Envir. Prot. Agcy. Rpt. No. EPA-450/4-81-004, Res. Tri. Pk., NC, 200p.
Strimaitis, D.6., 1981: private communication.
269
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TABLE 1: VALUE OF HC DURING EACH 5-MINUTE PERIOD OF THE HOUR 0500-0600
TIME
(END)
FIVE-MINUTE
PERIOD NUMBER
Hc
(m)
0505
0510
0515
0520
0525
0530
0535
0540
0545
0550
0555
0600
1
2
3
4
5
6
7
8
9
10
11
12
40.
38.
42.
42,
40,
38,
38.8
40.
44.
40.
40.3
40.7
.2
.5
.3
Average HC = 40.8
m
= 1.7 m
Note: H was calculated assuming a hill height of 100 m.
These values are referenced to local ground level.
270
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TABLE 2. PHOTOGRAPHIC RECORDS AVAILABLE
TYPE OF RECORD
16 mm motion picture film
35 mm color prints
35 mm color prints
Polaroid b & w prints
LOCATION AND EXPERIMENTS RECORDED
all tows - plan view only
all tows - plan view
all tows - side view
tows 10-41 - plan view only
271
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TABLE 3. SCHEDULE OF TOWS
DENSITY
PROFILE I
source at 597 in/122' very
little dye reaching south
peak need to check field
repeat of tow Jl to check
adjusted source height to
correct for differences
In local around level
slight roll-up on windward
side of model - may be effect
source location changed to
ran two high speed tows fc
JCRH following this tow
repeatability check
effluent released 1sok1nat1cally. 41
97 4 source location moved to 597 ml 4
124.6', plume splits around
north butte
a little more dye getting
plume goes primarily
through (over?) the draw
very little dye through the
saddle - most splits around
iged wind direction to 127
... of plume goes around the
north butte - max * 30 m
contour
not very different from
previous tow
Klume doesn't go over hill -
plume very thin at top of
hill, not reaching top of
masts
no plume over the north peak
large wake with uniformly
low concentration
changed wind direction to 117
272
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TABLE 3. SCHEDULE OF TOWS (continued)
TOW I
DATE
1981
23
4/22
24
4/22
25
4/22
26
4/23
27
4/23
28
4/29
29
4/30
30
5/1
31
5/1
32
5/4
33
5/11
34
5/12
35
5/12
36
37
5/13
38
5/13
39
5/15
40
5/15
41
5/15
FILE * e
CCBRD . degrees
23 117
24 117
25 117
26 117
27 117
28 120
29 120
30 120
31 125.5
32 125.5
Sfci D
11 13 °
37 (z) 0
38 (y)
39 (z) 0
40 (y)
41 (z) 0
42 (y)
43 {z) 0
44 (y)
45 (z) 0
46 (y)
47 (z) 0
48 (y)
49 (z) 0
50 (y)
"s
ni
(cm)
(43S,
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
(4.5)
31
<4.5)
Hc
..<«)
60
(8.64)
24
(3.5)
38
(5.51)
44
(6.4)
49
(7.06)
38
(5.51)
31
(4.5)
31
(4.5)
38
(5.51)
31
(4.5)
24
(3.5)
60
(8.64)
44
(6.4)
24
(3.5)
60
(8.64)
44
(6.4)
24
(3.5) .
60
(8.64)
44
(6.4)
TOM
SPEED
cm/sec
8.49
14.13
11.85
11.33
10.31
12.87_
13.87
13.61
11.86
12.98
14.47
7.89
10.85
15.25
7.87
11.28
14.84
7.49
10.85
EFFLUENT
RATE
cc/n1n
191.9
194.7
193.4
193.7
194.6
194.5
195.1
200.0
195.2
192.6
194.5
198.1
198.2
196.8
196.4
195.9
192.8
194.7
192.5
SAMPLE
TIDE
sec
142.4
100.2
114.4
106.1
119.2
110.9
96.2
99.1
106.3
104.6
105.2
156.3
124.5
95.8
154.8
118.3
97.3
153.0
117.9
DENSITY
REMARKS PROFILE t
CCBRS.
plume goes around south side
of hill - large uniform wake
small portion of plume went
over top of Mil
very similar to tow #24 -
slight wisp over draw about
2/3 of way down the channel
mostly around south side -
but, about 2/3 of way down
the channel got some around
north side and draw
very similar to previous tow
some shift about 2/3 of way
down the channel
changed wind direction to 120*
plume splitting around both
peaks similar to higher HC
changed wind direction to
125.5°
plume spreads mostly around
north butte - occasionally
. goes over north butte - get
shift 2/3 of way down channel
model removed and flat base-
plate Installed with cross
rake 48.5 cm from source
observe no- shift of plums
centerllne during the tow
moved cross rake downstream
to 91.4 cm from source
toward end of tow» plume
centerllne wavers a bit
moved cross rake downstream
to 134.2 cm from source
toward end of tow, plume
centerllne wavers a bit
last tow for case 206
53
53
53
55
55
56
58
59
59
60
61
63
63
64
64
64
65
65
65
273
-------
TABLE 4. SUMMARY OF FLAT BASEPLATE MEASUREMENTS
X
(m)
313.8
313.8
313.8
591.4
591.4
591.4
868.3
868.3
868.3
Hc
(m)
24
44
60
24
44
60
24
44
60
°z
(m)
4.8
5.0
4.5
4.7
4.0
3.8
4.6
3.8
3.7
oy
(m)
' 7.3
8.7
9.4
11.7
13.4
13.7
11.2
13.7
14.5
Cz
max
(ppt)
25,350
21,026
15,658
19,758
17,894
14,912
21,996
17,074
14,688
cy
max
(ppt)
24,978
20,504
15,881
16,925
14,166
13,719
21,250
14,912
13,644
274
-------
TABLE 5. LOCATION OF SAMPLERS ON CINDER CONE BUTTE
FMF
PORT
i
2
3
4
5
6
7
9
10
11
12
13
15
16
17
IB
19
za
Zl
ZZ
Z3
24
23
Z6
Z7
ZB
23
38
31
32
33
34
35
36
37
38
39
4B
42
43
44
45
46
47
48
43
3B
51
32
33
34
33
36
37
38
33
6B
61
62
63
64
63
66
67
68
69
70
71
72
73
74
73.
76
77
78
79
80
81
82
83
84
83
86
87
88
89
90
31
52
93
94
95
?O
97
98
99
ERT
PORT
37.
37.
37.
37.
37.
37.
37.
37.
37.
37.
37.
37.
34.
31.
31.
31,
31.
31.
31.
Z9,
ZB,
ZB.
27,
Z6,
26,
Z6,
63,
62,
60.
6O,
68
60,
SO,
60.
60,
60.
60.
38,
38
57
57
37
57
57
56
56
56
33
33
55
35
33
34
33
33
39
39
33
39
39
39
33
39
39
33
43
45
43
4B
48
48
48
48
48
30
64
64
65
67
67
67
67
67
67
67
67
67
67
69
69
7B
7B
7D
72
72
73
73
74
01 083
0200E1
83000
84000
05808
85BBO
07083
B988B
1BB0B
11800
12000
20080
26380
10BBB
9000O
.9603O
.07000
.03003
,26000
,83003
.B4B0B
.Z6BBB
. 1 1O00
.03BBB
.03088
. 03B00
.06000
,03000
. B3B3B
. B3B3B
. 84038
.2ZOOO
.230BB
.24BBO
.23083
.26000
.81880
.82000
.08000
.B7OOO
. Z5000
.26880
.96080
. 13000
.30380
.03308
.04008
.85800
.B30BB
. 13B00
.96BBO
. Z6B0B
.90000
.04800
.03000
. 04BOB
.21088
.01000
.BZBBB
.03000
.03000
.07000
. 1Z000
. 17000
. 1B0B8
. Z3BBB
. 243B0
.07080
. 10383
. 1Z0BB
. BZ000
. 03338
.03838
. 07B3O
. 10000
.87830
.83BBO
. 10033
.03000
.01080
.B2BB0
. 84080
.83000
. B6BB3
. 13330
.23000
. 24000
.23000
.26000
.B700B
.26080
.88080
.26008
.rr'jrT
. 2^-yoFi
. ?4ODE3
. loono
. 118015
.830^3
** 74.84083
ANGLE
, DEC.
8.
8.
8.
B,
B,
3,
8,
8,
8,
8.
'6
8
8
38
32
S3
33
33
53
33
68
71
73
83
30
90
90
98
103
1ZD
1ZO
128
120
1ZO
1Z8
12B
1ZO
120
135
137
143
143
143
143
147
150
158
130
138
138
138
139
133
163
171
173
1B7
187
187
187
187
187
187
187
187
187
Z3Z
Z3Z
232
Z33
233
233
233
233
Z33
278
277
277
283
300
3BB
388
300
38B
388
300
300
380
3BB
315
313
3Z2
322
333
338
330
343
343
333
333
.88008
, 00800
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, OOOOO
, 83088
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. 88888
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.00000
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.00333
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. O8O30
. 00800
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51B.
449.
391.
3BS.
275.
2sn.
227.
177.
154.
I 7"? ,
lif.
193.
19.
1415,
146,
1S4,
200,
134,
107,
246,
187,
420
73
. 260
360
20B
142.
315
190
362
297
Z33
164
124
94
43
318
418
195
243
327
148
165
165
162
255
198
86
250
284
2O4
163
196
3B1
139
Z60
37
310
411
348
Z91
231
113
IBB
• 130
77
107
Z24
138
63
411
3Z7
Z5B
211
130
238
282
133
252
510
416
343
311
284
230
247
178
130
54
ZOO
3Z5
151
IBB
Z7C.
Z8S
21 1
1Z7
183
31B
197
R
m
08880
30008
00003
DB80I.1
8BBB0
08000
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00883
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. 300FI8
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. B8OOB
.03008
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.83308
. B8000
. 0B800
. 30800
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.30000
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. 33000
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.80008
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.00000
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. B0BBB
.BBBBB
.BB0BB
.B3BB8
.80808
.03888
.8BB8B
.83388
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.BBBBB
.BBBBB
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78.
62.
54.
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3B.
34.
31 ,
?4,
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16,
11
26
2
73
115
122
139
122
85
196
173
337
72
258
368
208
142
311
1B3
313
257
ZB3
142
107
81
37
44!
355
137
163
196
.84
99
33
88
127
3B
42
S3
76
76
33
78
77
21
31
-4
-62
-5B
-42
-35
-30
-14
-21
-18
-9
-a.4
-176
-124
-60
-396
-315
-249
-203
-144
-238
-279
-157
-243
-441
-368
-237
-269
-245
-133
-213
-154
-112
-46
-141
-2Z9
-92
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-124
-106
-73
-32
-Z7
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-Z4
X
m
.37845
.48886
.41681
.86541
.27269
,73333
. 59237
.63378
.43271
.37916
.2730-3
.86847
.64429
.08816
.84976
.93007
.7Z736
.39007
.43414
. 46463
. 38338
. 11826
. 44438
.06213
.08838
.08800
.08888
.9343B
.32571
.50034
. 28886
.51543
.02779
. 38686
. 486 1 7
.23839
.67173
. 06946
. 88587
.67863
.79282
.25346
.23873
.29873
.23871
.49866
.99895
.33355
.65815
.41852
.41832
. 1Z974
.23896
.98236
. 74343
. 68423
.50343
. 15722
.33141
.41317
.46618
.59118
.81584
.93784
.28154
.3B45Z
.31778
.31372
.38562
.83330
.93664
.83864
.Z0356
.81833
.88928
.80088
.83764
.81464
.41258
.66986
.26404
.84462
. 33200
.94348
. 18445
.90677
. 15144
. 5825 1
.76584
.41337
.80679
.36336
. 43035
. C44B6
. 75923
. B3334
.F!68 3 4
. 17461
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505.
444.
387.
305.
272.
247.
224.
175.
15J.
l?n .
ea.
131 .
is.
126.
89.
92.
128.
92.
64.
14B.
7B.
136.
13.
31.
-0.
-0.
-8.
-43.
-43.
-181.
-148.
-117.
-82.
-62.
-47.
-21.
-255.
-205.
-137.
-175.
-261.
-111.
-131.
-131.
-135.
-228.
-171.
-74.
-231 .
-183.
-183.
-154.
-182.
-238.
-137.
-258.
-36.
-3B6,
-407.
-345.
-288,
-243,
-114.
-178.
-143.
-76,
-65,
-137,
-97.
-15,
-186.
-84,
-66
-54
-38
0
34
19
65.
255,
208,
171
155
142
115
123
63,
65
27
141.
229
118
85
24?
?6'1
195
122
181
3(17
19^
y
m
B3671
63034
19479
00256
32T7B
567^ •*
7SBU5
27745
SB 128
81271
21172
12173
81589
43963
88633
67324
36265
67324
39482
84637
B5B33
73743
41 113
68313
08135
8B378
08033
B4081
1764B
00138
50122
5B097
00067
00331
00039
58818
00209
00163
68668
52583
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77545
77545
86517
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. 14631
. 14631
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.40576
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. 12883
. 14271
.65816
.88173
. 42533
.87438
.98651
.27334
.38435
.37038
.63043
.77264
.68863
.82130
.88267
.37834
.37332
.22526
.00542
.80441
.50363
.50330
.OB3B1
.00244
.50262
,80183
.08138
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. 18632
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.67301
. 42239
.63965
.53194
275
-------
150
3 li 5 6 7 8 9
HERN HIND SPEED (M/S)
Figure 1. Average Wind Speed Profile, 0500-0600.
276
-------
150
100 -
TEMPERHTURE .(DEC C]
Fiqure 2. Average Temperature Profile, 0500-0600
277
-------
130
125 --•
UJ
LU
cc
CD
UJ
a
o
t—>
h-
CJ
UJ
a:
a
a
115 -
110
FIVE-MINUTE PERIOD
Figure 3. Variation of 80 m Wind Direction During the Hour.
278
-------
CM
CM
Lf)
CM
"
B
f
-
1
1
\
\
\
I
1
1
1
I
t
i
\
-
\
\
\
j
i —
CO
CM
r—
CM
CM
OJ
r—
0
f-"
r~~
CO
©
O
OJ
o
c
o
•t~"
13
{/I
•i —
O
I
O)
OJ
I
CD
279
-------
o
25
15
FIVE-MINUTE PERIOD
0600
Figure 5. Variation of H During the Hour.
w
280
-------
I
I
I
I
\
IT)
o
oo
CM
*d-
o
o
en
oo
CO
oo
oo
q-
o
-Q
•r-
4J
to
•i—
Q
c:
O)
C3"
OJ
U_
VJO
I
O)
o
281
-------
Figure 7. One-Hour-Average SFg Concentrations from Field Data.
282
-------
110
100 -
90 -
UJ
1.05 1.1 1.15
SPECIFIC GRRVITY
1.2
Figure 8. Typical Density Profile in Towing Tank.
283
-------
o
t^t
H-
a:
tr
i_
2:
at
o
LU
>-
Q
.01 -
.001 -•
.0001
A Standards
— Best-fit Beer's Law
A .2 .3' .U .5 . S .7 .8 .9 1
VQLTPGE ",: ". :. ,," • '.: :
Figure 9. Colorimeter Calibration Curve
284
-------
100
90 -1
80 --
70 -•
60 -
50
140 -
30 --
20 -•
10 -•
5000
10000 15000 20000
CONCENTRflTION IPPT]
3000U
Figure 10. Vertical distributions of plumes over flat baseplate 48.5 cm
(314 m) downwind of source.
285
-------
30000
25000
20000
D_
a:
LU
CD
CJ
15000
10000 +
5000 -•
tM]
Figure 11. Horizontal distributions of plumes over flat baseplate
48.5 cm (314 m) downwind of source.
80
286
-------
20
is
a- 10 -•
tn
0 -
CENTER ! M I i M I Ml i i M M
OF
HILL
0 100 200 300 liOO 500 600 700 300 900 1000
Figure 12. Plume Widths in the Absence of the Hill
287
-------
3UUGO -
25COO --
Q-
O
i—t
h—
F ^0000 -f
U4
CJ
CJ
15000 -•
10000
0 100 200 300 100 500 600
X (M3
700 - SOO . 903 1000
Figure 13. Concentration vs. downwind distance in the absence of the hill
Open points from vertical distributions; closed points from
horizontal distributions.
288
-------
XV _-^-,;-..^-
EPF1
INDFR CONE FLUID
u J- IN V nnuir? MODELING
I [JHnlu SECTION
Figure 14. Sampling Port Location Map.
289
-------
Figure 15. Side and Top Views of Model during Tow 8.
290
-------
Figure 16. Concentration Distributions from Tows 1 (top) and 2 (bottom)
291
-------
100000
10000 -
D_
D_
OC
OC
(—
2
LLJ
O
2:
Q
O
OJ
IS
to
h-
1000
100
100
A
1000 10000
TOW 1 CONCENTRfl'TIQN tPPT)
100000
Figure 17. Scatter Diagram Showing Repeatability Between Successive Tows,
292
-------
o
LlJ
C3
J. iU -
1 n n -
8r! -
~> n
1
RTl
•rr
M-lTf
— — •
Eg..-
i
i.
.
,
1
i —
"3
T — — '
l
^]
=a
i — -
ITT
1.
.
15
. iM
1 —
tJ
_ — _,
-1
i
1
!
J
1
s
J
j
"
"I
i
1
1
— — • r
1.
SPECIFIC GRRVITT
Figure 18. Density Profiles for Tows 7 and 8.
293
-------
100000
10
10
100 1000 10000
TQH 7 CQNCEHTRflTIQN (PPT)
100000
Figure 19. Scatter Diagram Showing Effects of Change in Shape of Density Profile.
294
-------
TOW 24
24 m; 0 = 117°
TOW 22
31 m; 0 = 117°
TOW 25
Hc = 38 m; e » 117°
/
H. =
TOW 12
24 m; 0 « 122*
TOW 11
H = 31 m; 0 = 122°
c
TOW 10
H. = 38 m; 0 = 122C
TOW 18
Hc = 24 m; 0 = 127{
TOW 19
H = 31 m; 0 = 127°
C
TOW 17
38 m; 0 - 127°
Figure 20: Concentration Distributions Resulting from TOWS at
3 Wind Directions and 6 Values of H ; H = 31 m.
C S
295
-------
TOW
f-L « 44 m; e - 117'
- 49 m; 0 - 117C
23
= 60 m; e * 117'
H = 44 m; G = 122{
49 m; e « 122C
TOW 13
H, = 61 m; 0 - 122C
TOW 20
44 m; G - 127C
TOW 21
= 49 m; 6 = 127'
TOW 16
H = 60 m; 0 • 127e
Figure 20: (continued)
296
-------
10000 +<
Q_
D_
CL
tr
LLJ
o
2:
D
O
UJ
a
a
2:
1000 -•
! A 11
I""-- 'D 12
i O 13
100 -
100 9 1.000
FIELD CONCENTRflTION (PPTJ
10000
Figure 21. Scatter Diagram Comparing Concentration Distributions from
3 Individual Tows with Field Distributions.
297
-------
200M
Figure 22. Concentration Distribution from Superposition of 18 Tows.
298
-------
10000
Q_
Q_
cr
01
D
o
UJ
a
1000
100 - -
10
100 100D
FIELD CONCENTRRTIQN IPP'T)
10000
Figure 23. Scatter Diagram Comparing Superposition of
Concentration Distributions from 18 Tows with
Field Distributions.
299
-------
20000
Wind Direction
A117 degrees
I]120 degrees
O122 degrees
0 125.5 degrees
A127 degrees
Hr CM)
Figure 24. Variation of Maximum Concentration with H
300
-------
20000
15000
i—
Q_
Q-
CC
cc
t—
CJ
CD
O
X
CC
10000
sooo
A Hc=24m
D Hc=31tn
O Hc=38m
0 Hc=44m
120 125
WIND DIRECTION (DEGREES]
130
Figure 25. Variation of Maximum Concentration with Wind Direction.
301
-------
APPENDIX C
USE OF MODEL PERFORMANCE STATISTICS
The model tests discussed in Section 5 are based on the following
hypothesized relationship between an observation C and the corresponding
model estimate C :
e (x2)
(1)
where x, are known model inputs, and x« are unknown variables. Recall
that because x? is unknown, the estimate C can be associated with an
infinite ensemble of possible observations. This ensemble is in effect
described by the distribution of the residuals £.
To understand how the statistics of e can be used to link model
estimates with observations, the following questions might be asked:
1) Given a model estimate C , what is the probability that the
corresponding observation C will exceed a specified
concentration C ?
s
2) Given an estimate C , what fraction of corresponding
observations are expected to lie within a factor of 2 of the
modeled concentration?
To answer these questions assume that e is normally distributed with
zero mean. Then the sample variance of e is given by
1 N
J- v
N 1-1
-------
where N is the number of observations. It can be readily shown that
CC - C )/S follows a Student-t distribution with N degrees of
oi pi
freedom.*
To answer Question I, we construct the following t-statistic, t^
(C -
(3)
The probability Pr(t > t ) can be readily obtained from statistical
tables. For example, consider the standard deviation of the residuals
associated with log-transformed concentrations
S = In
1/2
(4a)
The log-transformation of concentrations allows us to restate Question 1
as: What is the probability that the observed concentration CQ will
exceed x times the predicted concentration C ? Let us take x = 2 and
s =2.5 for N = 45 so that t becomes
e r
ln(xC ) - In C
p p _ In 2
(4b)
In s
In 2.5
0.76
From tables, we find Pr (t>tr> - 26%.
This calculation immediately allows us to answer Question 2. Because
the t-distribution is symmetric, we expect 26% of the observations to be
less than one-half the estimated concentration and 26% to be greater than
twice the estimated concentration. Therefore, 48% of the observations are
expected to lie within a factor of 2 of the estimate.
*See Box, G.E.P., W.G. Hunter, and J.S. Hunter 1978. Statistics for Experi-
ments; An Introduction to Design, Data Analysis, and Model Building. New
York: John Wiley & Sons.
303
-------
We can also estimate confidence intervals for the model calculations.
Specifically, we can express the (1 - Y) confidence interval for the ratio
C /C as follows:
o p
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/3-82-036
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
EPA COMPLEX TERRAIN MODEL DEVELOPMENT
First Milestone Report - 1981
B. REPORT DATE
April 1982
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
T. F. Lavery, A. Bass, D. G. Strimaitis, A. Venkatram,
B. R. Greene. P. J. Drivas. and B. A. Eoan
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Research & Technology, Inc.
696 Virginia Road
Concord, Massachusetts 01742
10. PROGRAM ELEMENT NO.
CABN1D/01-0566 (FY-82)
11. CONTRACT/GRANT NO.
68-02-3421 .
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory - RTP, NC
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
13. TYPE OF REPORT AND PERIOD COVERED
Interim 6/80-12/81
14. SPONSORING AGENCY CODE
EPA/600/09
15. SUPPLEMENTARY NOTES
16. ABSTRACT
The U.S. Environmental Protection Agency is sponsoring the Complex Terrain
Model Development program, a multi-year integrated program to develop and validate
practical plume dispersion models of known reliability and accuracy for simulating
one-hour average ground-level concentrations downwind of elevated sources during
stable atmospheric conditions in complex terrain. The first major component of the
Complex Terrain Model Development program was a field study conducted during the
fall of 1980 at Cinder Cone Butte, a roughly axisymmetric, isolated 100-meter-tall
hill located in the broad Snake River Basin near Boise, Idaho. The field program
consisted of ten flow visualization experiments and eighteen multi-hour tracer gas
experiments conducted during stable flow conditions.
This report presents an overview of the Cinder Cone Butte field program and
the results of the modeling analyses completed through June 1, 1981. The objec-
tives of this phase of the modeling program were to begin the development of new
dispersion models using the Cinder Cone Butte data base and to compare their
performance with existing complex terrain dispersion models.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
13. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThisReport)
UNCLASSIFIED
21. NO. OF PAGES
327
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
305
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