APRIL 1985
A REGIONAL-SCALE (1000 KM) MODEL OF PHOTOCHEMICAL AIR POLLUTION
Part 3. Tests of the Numerical Algorithms
ATMOSPHERIC SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC 27711
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A REGIONAL-SCALE (1000 KM) MODEL OF PHOTOCHEMICAL AIR POLLUTION
Part 3. Tests of the Numerical Algorithms
Robert G. Lamb
Meteorology and Assessment Division
Atmospheric Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
Gerard F. Laniak
Program Resources, Inc.
Annapolis, Maryland 21401
ATMOSPHERIC SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC 27711
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NOTICE
The information in this document has been subject to
the United States Environmental Protection Agency's
peer and administrative review and has been approved
for publication as an EPA document. Mention of trade
names or commercial products does not constitute
endorsement or reconmendation for use.
ii
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PREFACE
This is the last in a series of reports describing the development of
the Environmental Protection Agency's Regional Oxidant Model (ROM). The
first report described the theoretical bases of the model, the second
developed a system design for the network of processors that drive the
model, and the present report describes a series of technical evaluations
of the model's governing equations. Our objective here is to demonstrate
that the numerical algorithms that constitute the model's predictive
equations are accurate analogies of the differential equations that describe
the physical and chemical processes that the model is intended to simulate.
We consider this to be a necessary condition for model validity. A sufficient
condition is that all components of the model jointly — the numerical
algorithms are but a single part -- compose a basis for predicting given
features of the species concentrations that are consistently within given
error limits of the values one would actually observe under the meteorological
and emissions conditions simulated. Demonstrating that a model satisfies
the sufficient conditions for validity generally requires comparison of
predictions with observations. At the present time preparations are underway
to subject the ROM to tests of this sort. In this study we make no
comparisons of model predictions with observations. Rather, our standard
for judging the model's performance are known, exact solutions of the
equations that describe the hypothetical situations that we treat.
This study is a part of the quality assurance program that we have
implemented to achieve and maintain the highest degree of accuracy and
credibility possible. We have found that in a modeling system as complex
iii
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as the ROM, the sources of error are so numerous that meaningful model
applications are impossible unless stringent, comprehensive measures are
taken to erradicate error in every part of the system. This is not to say
that we believe that errors can be eliminated entirely. We expect that
residual errors will always remain in much the same way that sources of
error exist even in instruments of the highest quality. In this context we
view our quality assurance procedures as an effort to increase the signal-
to-noise ratio of the ROM. We are convinced that without such efforts, the
ROM would never achieve the level of reliability necessary to qualify it
for a role in assisting the development of emissions control policies and
air quality management.
R. G. Lamb
April 1985
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ABSTRACT
The regional oxidant model is applied to a series of test problems
whose exact solutions are known. The predicted concentrations are compared
with the true values to obtain a measure of the accuracy of the numerical
algorithms that comprise the model's governing equations. Some of the
problems test only the model's chemical kinetics algorithm, others test the
kinetics and transport/diffusion algorithms jointly, and one tests all
three of the models basic algorithms together — kinetics, transport/diffusion,
and vertical fluxes.
It is found that the kinetics algorithm produces exact solutions of
the chemical rate equations over the full range of species concentrations
that are likely to be encountered in applications. A modified version of
the algorithm yields concentrations that are within ± 5% of the correct
values in 1/2 to 1/3 the computer time needed for exact solutions.
In simulations of the advection of clouds of chemically reactive
compounds, the kinetics and transport algorithms jointly reproduce the correct
shapes and motions of clouds and they predict the peak peak concentration
in the cloud to within 10% of the true value over 48-hour simulation times.
In applications to continuous finite line sources in steady, spatially
variable flows, the combined algorithms, produced plumes with negligible
pseudo diffusion. In the case of ozone, the predicted plume centerline
concentration was within 5% of the true value in a plume five grid cells
wide and within 15% of the correct value in a plume two grid cells in width.
Corresponding errors in the CO concentrations were about 50% larger. In
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general, it was found that ozone is among the species simulated best while
compounds such as nitrous and nitric acid, alkyl nitrate and related nitrogen
containing species are simulated poorest. The predicted concentrations of
free radical species are of intermediate accuracy. Evidence was also found
that errors in plume concentration can be amplified when a plume crosses a
second source. The zone of enhanced error tends to be confined to the
vicinity of the second source. The accuracies of the simulated concentrations
have added significance in that the model employs a numerical transport-diffu-
sion scheme that does not maintain positive definite concentration. Negative
concentrations are simply clamped.
VI
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CONTENTS
Preface iii
Abstract v
Figures . . viii
Tables xxiv
Acknowledgment xxv
1. Introduction and Summary 1
2. Case 1A: Chemistry Without Transport or Sources 13
3. Case 2A: Chemistry with Transport 57
Case 2B: Chemistry with transport and vertical mixing ... 71
4. Case 3A: Chemistry With Transport and Continous Sources ... 127
References 264
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FIGURES
Number Page
1-1 Schematic illustration of the regional model and the
network of processors that supply it information 5
2-1 Temporal variations in the magnitudes of the photolytic
rate constants kj, k; and k23 used in both reactor
simulations 1A.L and 1A.R (and in all other experiments
presented in this report) 17
2-2(a) Results of NO concentration in batch reactor simulations
1A.L (top) and 1A.R (bottom) 22
2-2(b) Same as 2-2(a) but for N02. Case 1A.1 (top), 1A.R (bottom). . 23
2-2(c) Results for ozone in batch reactor simulations 1A.L (top)
and 1A.R (bottom) 24
2-2(d) Results for olefin in batch reactor simulations 1A.L (top)
and 1A.R (bottom) 25
2-2(e) Results for paraffin in batch reactor simulations 1A.L (top)
and 1A.R (bottom) 26
2-2(f) Results for aldehyde in batch reactor simulations 1A.L (top)
and 1A.R (bottom) 27
2-2(g) Results for aromatic in batch reactor simulations 1A.L (top)
and 1A.R (bottom) 28
2-2(h) Results for CO in batch reactor simulations 1A.L (top)
and 1A.R (bottom) 29
2-2(i) Results for nitrous acid in batch reactor simulations
1A.L (top) and 1A.R (bottom) 30
2-2(j) Results for nitric acid in batch reactor simulations
1A.L (top) and 1A.R (bottom) 31
2-2(k) Results for PAN in batch reactor simulations 1A.L (top)
and 1A.R (bottom) 32
2-2(1) Results for alkyl nitrate in batch reactor simulations
1A.L (top) and 1A.R (bottom) 33
2-2(m) Results for hydrogen peroxide in batch reactor simulations
1A.L (top) and 1A.R (bottom) 34
2-2(n) Results for atomic oxygen in batch reactor simulations
1A.L (top) and 1A.R (bottom) 35
viii
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Number Page
2-2(o) Results for nitrate in batch reactor simulations
1A.L (top) and 1A.R (bottom) 36
2-2(p) Results for hydroxyl radical in batch reactor simulations
1A.L (top) and 1A.R (bottom) 37
2-2(q) Results for pernitric acid in batch reactor simulations
1A.L (top) and 1A.R (bottom) 38
2-2(r) Results for hydroperoxyl radical in batch reactor simulations
1A.L (top) and 1A.R (bottom) 39
2-2(s) Results for alkoxyl radical in batch reactor simulations
1A.L (top) and 1A.R (bottom) 40
2-2(t) Results for alkylperoxyl radical in batch reactor simulations
1A.L (top) and 1A.R (bottom) 41
2-2(u) Results for alkoxy radical in batch reactor simulations
1A.L (top) and 1A.R (bottom) 42
2-2(v) Results for peroxyacyl radical in batch reactor simulations
1A.L (top) and 1A.R (bottom) 43
2-2(w) Results for peroxy radical in batch reactor simulations
1A.L (top) and 1A.R (bottom) 44
2-3(a) Results of NO concentration in batch reactor simulations
1A.L and 1A.R using a value of .01 for the control
parameter \ in the numerical algorithm. (Results shown
in Fig. 2-2(a) use \ =.001.) 45
2-3(b) Results of N02 concentration in batch reactor simulations
1A.L and 1A.R using a value of .01 for the control
parameter \ in the numerical algorithm. (Results shown
in Fig. 2-2(a) use X =.001.) 46
2-3(c) Results of 03 concentration in batch reactor simulations
1A.L and 1A.R using a value of .01 for the control
parameter \ in the numerical algorithm. (Results shown
in Fig. 2-2(a) use \ =.001.) 47
2-3(d) Results of aldehyde concentration in batch reactor
simulations 1A.L and 1A.R using a value of .01 for the
control parameter \ in the numerical algorithm. (Results
shown in Fig. 2-2(a) use \ =.001.) 48
2-3(e) Results of PAN concentration in batch reactor simulations
1A.L and 1A.R using a value of .01 for the control
parameter \ in the numerical algorithm. (Results shown
in Fig. 2-2(a) use \ =.001.) 49
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Number Page
2-3(f) Results of alkylperoxyl concentration in batch reactor
simulations 1A.L and 1A.R using a value of .01 for the
control parameter X in the numerical algorithm. (Results
shown in Fig. 2-2(a) use X =.001.) 50
2-4(a) Results of NO concentration in the batch reactor simulations
1A.L and 1A.R obtained with the modified numerical algorithm
that varies the parameter x temporally to effect maximum
speed and minimum error 51
2-4(b) Results of NOg concentration in the batch reactor simulations
1A.L and 1A.R obtained with the modified numerical algorithm
that varies the parameter \ temporally to effect maximum
speed and minimum error 52
2-4(c) Results of 03 concentration in the batch reactor simulations
1A.L and 1A.R obtained with the modified numerical algorithm
that varies the parameter x temporally to effect maximum
speed and minimum error 53
2-4(d) Results of aldehyde concentration in the batch reactor
simulations 1A.L and 1A.R obtained with the modified
numerical algorithm that varies the parameter \ temporally
to effect maximum speed and minimum error
54
2-4(e) Results of PAN concentration in the batch reactor simula-
tions 1A.L and 1A.R obtained with the modified numerical
algorithm that varies the parameter X temporally to effect
maximum speed and minimum error 55
2-4(f) Results of alkylperoxyl concentration in the batch reactor
simulations 1A.L and 1A.R obtained with the modified numerical
algorithm that varies the parameter X temporally to effect
maximum speed and minimum error 56
3-1 Initial concentration distribution ca(I,J,t0) in the cloud
simulated in Case 2A for species a = carbon monoxide. Also
shown is ca(I,J,t0 + 48 hr) 61
3-2 Comparison of simulations by 3 differencing schemes of the
advection of an ellipsoidal cloud in a rotating flow.
Panels a-d display different cross-sections of the cloud
(indicated by the upper right corner of each panel) after
one complete rotation of the cloud, 100 time steps in the
case of schemes 0 and S, 150 steps in the case of Z.
Notation: Q (circles) = transport algorithm used in the
ROM; S (x) = transport scheme of Mahrer and Pielke
(1978); Z = transport scheme of Zalesak (1979) 63
3-2 Continued 64
3-2 Continued 65
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Number
3-2
3-3(a)
3-3(a)
3-3(a)
3-3(a)
3-3(a)
3-3(a)
3-3(b)
3-3(b)
3-3(b)
3-3(b)
3-3(b)
3-3(c)
3-3(c)
3-3(c)
3-3(c)
3-3(c)
3-3(c)
3-3(c)
1
Concluded
Initial concentration of CO in cross-sections of the cloud
simulated in experiment 2A. Diagrams in the upper right
corner of each panel indicate the location of the cross-
section within the cloud. The curves labeled "chemistry"
represent the true solution
Continued. Travel time = 4 hours
Continued. Travel time = 8 hours
Continued. Travel time = 16 hours
Concluded. Travel time = 48 hours
Initial concentration of NO in cross-sections of the cloud
simulated in experiment 2A. Diagrams in the upper right
corner of each panel indicate the location of the cross-
section within the cloud. The curves labeled "chemistry"
represent the true solution
Continued. Travel time = 4 hours
Continued. Travel time = 8 hours
Continued. Travel time = 12 hours
Concluded. Travel time = 16 hours
Initial concentration of ozone in cross-sections of the cloud
simulated in experiment 2A. Diagrams in the upper right
corner of each panel indicate the location of the cross-
section within the cloud. The curves labeled "chemistry"
represent the true solution
Continued. Travel time = 2 hours
Continued. Travel time = 16 hours
Continued. Travel time = 24 hours
Continued. Travel time = 36 hours
Concluded. Travel time = 48 hours
Page
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74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
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Number Page
3-3(d) Initial concentration of N0£ in cross-sections of the cloud
simulated in experiment 2A. Diagrams in the upper right
corner of each panel indicate the location of the cross-
section within the cloud. The curves labeled "chemistry"
represent the true solution ..... 92
3-3(d) Continued. Travel time = 2 hours. . 93
3-3(d) Continued. Travel time = 4 hours 94
3-3(d) Continued. Travel time = 12 hours 95
3-3(d) Concluded. Travel time = 24 hours 96
3-3(e) Initial concentration of olefin in cross-sections of the
cloud simulated in experiment 2A. Diagrams in the upper
right corner of each panel indicate the location of the
cross-section within the cloud. The curves labeled
"chemistry" represent the true solution 97
3-3(e) Continued. Travel time = 4 hours , 98
3-3(e) Continued. Travel time = 8 hours. Insert in upper
panel is magnified plot of major axis cross-section 99
3-3(e) Concluded. Travel time - 12 hours. Insert in lower panel
is magnified plot of minor axis cross-section 100
3-4 Initial CO concentration in clouds 2B.L and 2B.R. Arcing lines
labeled E, M, and C are 48-hour trajectories of points originating
at the edge, midpoint, and center, respectively, of each cloud . . 101
3-5 Initial cross-section of ozone concentration in cloud 2B'.R.
Diagrams in the upper right corner of each panel show the
location of the cross-section in the cloud. Curves labeled
"chemistry" represent the true solution 102
3-5 Continued. Travel time = 4 hours (Case 2B.R) 103
3-5 Continued. Travel time = 12 hours. Vertical mixing between
layers 1 and 2 begins at this instant. (Case 2B.R) 104
3-5 Continued. Travel time = 16 hours, 4 hours after mixing
(Case 2B.R) 105
3-5 Continued. Travel time = 24 hours (Case 2B.R) 106
3-5 Continued. Travel time = 36 hours 107
3-5 Concluded. Travel time = 48 hours, 36 hours after1 mixing
(Case 2B.R) 108
xii
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Number Page
3-8(b) Time histories of NO following the edge point of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution ....................... 122
3-8(c) Time histories of ozone following the edge point of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution ....................... 123
3-8(d) Time histories of N0£ following the edge point of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution ....................... 124
3-8(e) Time histories of olefin following the edge point of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution ....................... 125
3-8(f) Time histories of PAN following the edge point of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution ....................... 126
4-1 Locations and relative strengths of 4 line sources (b, c, e,
and f) simulated in experiment 3A. Flow speed
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Number , Page
4-6(b) Same as 4-6(a) except travel time = 13 hours 152
4-6(c) Same as 4-6(a) except travel time = 25 hours 153
4-6(d) Same as 4-6(a) except travel time = 34 hours 154
4-6(e) Same as 4-6(a) except travel time = 44 hours 155
4-6(f) Same as 4-6(a) except travel time = 52 hours 156
4-7(a) Comparison of predicted (solid curve) and true (dashed)
N02 concentrations in experiment 3A along the cross-section
indicated in the insert. (Travel time = 7 hrs from sources
b, c and e) , 157
4-7(b) Same as 4-7(a) except travel time = 13 hours 158
4-7(c) Same as 4-7(a) except travel time = 25 hours 159
4-7(d) Same as 4-7(a) except travel time = 44 hours . 160
4-7(e) Same as 4-7(a) except travel time = 52 hours 161
4-8(a) Comparison of predicted (solid curve) and true (dashed)
olefin concentrations in experiment 3A along the cross-section
indicated in the insert. (Travel time = 7 hrs from sources
b, c and e) 162
4-8(b) Same as Figure 4-8(a) except travel time = 13 hours 163
4-8(c) Same as Figure 4-8(a) except travel time = 44 hours 164
4-8(d) Same as Figure 4-8(a) except travel time = 52 hours 165
4-9(a) Comparison of predicted (solid curve) and true (dashed)
PAN concentrations in experiment 3A along the cross-section
indicated in the insert. (Travel time = 7 hrs from sources
b, c and e) 166
4-9(b) Same as 4-9(a) except travel time * 13 hours 167
4-9(c) Same as Figure 4-9(a) except travel time = 25 hours,.
Insert shows magnified plot of the predicted and true PAN
concentration distributions 168
4-9(d) Same as Figure 4-9(a) except travel time = 34 hours.
Insert shows magnified plot of the predicted and true PAN
concentration distributions 169
4-9(e) Same as Figure 4-9(a) except travel time = 44 hours.
Insert shows magnified plot of the predicted and true PAN
concentration distributions 170
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Number Page
4-9(f) Same as Figure 4-9(a) except travel time = 52 hours 171
4-10(a) Comparison of predicted (dash-dot) and true NO concentration
(solid curve) along a Lagrangian trajectory that passes
through the center of source e, experiment 3A 172
4-10(b) Comparison of predicted (dash-dot) and true N02 concentration
(solid curve) along a Lagrangian trajectory that passes
through the center of source e, experiment 3A 173
4-10(c) Comparison of predicted (dash-dot) and true ozone concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source e, experiment 3A 174
4-10(d) Comparison of predicted (dash-dot) and true olefin concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source e, experiment 3A 175
4-10(e) Comparison of predicted (dash-dot) and true paraffin
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A. . . 176
4-10(f) Comparison of predicted (dash-dot) and true aldehyde
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A. . . 177
4-10(g) Comparison of predicted (dash-dot) and true aromatic
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A. . . 178
4-10(h) Comparison of predicted (dash-dot) and true carbon monoxide
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A. . . 179
4-10(i) Comparison of predicted (dash-dot) and true nitrous acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A. . . 180
4-10(j) Comparison of predicted (dash-dot) and true nitric acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A. . . 181
4-10(k) Comparison of predicted (dash-dot) and true PAN
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A. . . 182
4-10(1) Comparison of predicted (dash-dot) and true alkyl nitrate
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A. . . 183
4-10(m) Comparison of predicted (dash-dot) and true hydrogen
peroxide concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source e,
experiment 3A 184
xvi
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Number , Page
4-10(n) Comparison of predicted (dash-dot) and true atomic
oxygen concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source e,
experiment 3A 185
4-10(o) Comparison of predicted (dash-dot) and true nitrate concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source e, experiment 3A ..... 186
4-10(p) Comparison of predicted (dash-dot) and true hydroxyl concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source e, experiment 3A 187
4-10(q) Comparison of predicted (dash-dot) and true hydroperoxyl
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A. . . 188
4-10(r) Comparison of predicted (dash-dot) and true pernitric acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A. . . 189
4-10(s) Comparison of predicted (dash-dot) and true alkoxyl radical
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A. . . 190
4-10(t) Comparison of predicted (dash-dot) and true alkylperoxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source e,
experiment 3A 191
4-10(u) Comparison of predicted (dash-dot) and true alkoxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source e,
experiment 3A 192
4-10(v) Comparison of predicted (dash-dot) and true peroxyacyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source e,
experiment 3A 193
4-10(w) Comparison of predicted (dash-dot) and true peroxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source e,
experiment 3A 194
4-ll(a) Comparison of predicted (dash-dot) and true NO concentration
(solid curve) along a Lagrangian trajectory that passes through
the outer most grid cell of source e, experiment 3A 195
4-ll(b) Comparison of predicted (dash-dot) and true N02 concentration
(solid curve) along a Lagrangian trajectory that passes through
the outer most grid cell of source e, experiment 3A 196
xvii
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Number Page^
4-ll(c) Comparison of predicted (dash-dot) and true ozone concentration
(solid curve) along a Lagrangian trajectory that passes through
the outer most grid cell of source e, experiment 3A. ...... 197
4-ll(d) Comparison of predicted (dash-dot) and true olefin concentra-
tion (solid curve) along a Lagrangian trajectory that passes
through the outer most grid cell of source e, experiment 3A. . . 198
4-ll(e) Comparison of predicted (dash-dot) and true paraffin concen-
tration (solid curve) along a Lagrangian trajectory that passes
through the outer most grid cell of source e, experiment 3A. . . 199
4-ll(f) Comparison of predicted (dash-dot) and true aldehyde concen-
tration (solid curve) along a Lagrangian trajectory that passes
through the outer most grfd cell of source e, experiment 3A. . . 200
4-11(g) Comparison of predicted (dash-dot) and true aromatic concen-
tration (solid curve) along a Lagrangian trajectory that passes
through the outer most grid cell of source e, experiment 3A. . . 201
4-ll(h) Comparison of predicted (dash-dot) and true carbon monoxide
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A 202
4-ll(i) Comparison of predicted (dash-dot) and true nitrous acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A 203
4-ll(j) Comparison of predicted (dash-dot) and'true nitric acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A 204
4-ll(k) Comparison of predicted (dash-dot) and true PAN concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the outer most grid cell of source e,
experiment 3A 205
4-11(1) Comparison of predicted (dash-dot) and true alkyl nitrate
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A 206
4-ll(m) Comparison of predicted (dash-dot) and true hydrogen peroxide
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A 207
xvm
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Number , Page
4-ll(n) Comparison of predicted (dash-dot) and true oxygen atom
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A 208
4-ll(p) Comparison of predicted (dash-dot) and true nitrate
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A 209
4-ll(p) Comparison of predicted (dash-dot) and true hydroxyl
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A 210
4-11(q) Comparison of predicted (dash-dot) and true hydroperoxyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the outer most grid cell of
source e, experiment 3A 211
4-ll(r) Comparison of predicted (dash-dot) and true pernitric
acid concentration (solid curve) along a Lagrangian
trajectory that passes through the outer most grid cell of
source e, experiment 3A 212
4-ll(s) Comparison of predicted (dash-dot) and true alkoxyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the outer most grid cell of
source e, experiment 3A 213
4-ll(t) Comparison of predicted (dash-dot) and true alkylperoxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the outer most grid cell of
source e, experiment 3A 214
4-ll(u) Comparison of predicted (dash-dot) and true alkoxy radical
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A 215
4-ll(v) Comparison of predicted (dash-dot) and true peroxyacyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the outer most grid cell
of source e, experiment 3A 216
4-ll(w) Comparison of predicted (dash-dot) and true peroxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the outer most grid cell
of source e, experiment 3A 217
4-12(a) Comparison of predicted (dash-dot) and true NO concentration
(solid curve) along a Lagrangian trajectory that passes
through the center of source c, experiment 3A 218
xix
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Number Page
4-12(b) Comparison of predicted (dash-dot) and true N0£ concentration
(solid curve) along a Lagrangian trajectory that passes
through the center of source c, experiment 3A. .... ..... 219
4-12(c) Comparison of predicted (dash-dot) and true ozone concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source c, experiment 3A ...... 220
4-12(d) Comparison of predicted (dash-dot) and true olefin concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source c, experiment 3A ...... 221
4-12(e) Comparison of predicted (dash-dot) and true paraffin concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source c, experiment 3A ...... 222
4-12(f) Comparison of predicted (dash-dot) and true aldehyde concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source c, experiment 3A ...... 223
4-12(g) Comparison of predicted (dash-dot) and true aromatic concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source c, experiment 3A ...... 224
4-12(h) Comparison of predicted (dash-dot) and true carbon monoxide
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A. . . . 225
4-12(i) Comparison of predicted (dash-dot) and true nitrous acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A. . . . 226
4-12(j) Comparison of predicted (dash-dot) and true nitric acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A. . . . 227
4-12(k) Comparison of predicted (dash-dot) and true PAN concen-
tration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A. . . . 228
4-12(1) Comparison of predicted (dash-dot) and true alkyl nitrate
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A. . . . 229
4-12(m) Comparison of predicted (dash-dot) and true hydrogen peroxide
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A. . . . 230
4~12(n) Comparison of predicted (dash-dot) and true atomic oxygen
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A. . . . 231
xx
-------
Number Page
4-12(o) Comparison of predicted (dash-dot) and true nitrate
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A. . . . 232
4-12(p) Comparison of predicted (dash-dot) and true hydroxyl radical
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A. . . . 233
4-12(q) Comparison of predicted (dash-dot) and true hydroperoxyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source c,
experiment 3A 234
4-12(r) Comparison of predicted (dash-dot) and true pernitric
acid concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source c,
experiment 3A 235
4-12(s) Comparison of predicted (dash-dot) and true alkoxyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source c,
experiment 3A 236
4-12(t) Comparison of predicted (dash-dot) and true alkylperoxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source c,
experiment 3A 237
4-12(u) Comparison of predicted (dash-dot) and true alkoxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source c,
experiment 3A 238
4-12(v) Comparison of predicted (dash-dot) and peroxyacyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source c,
experiment 3A. . 239
4-12(w) Comparison of predicted (dash-dot) and peroxy radical
concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source c,
experiment 3A 240
4-13(a) Comparison of predicted (dash-dot) and true NO concentration
(solid curve) along a Lagrangian trajectory that passes
through the inner edge of source b, experiment 3A 241
4-13(b) Comparison of predicted (dash-dot) and true N02 concentration
(solid curve) along a Lagrangian trajectory that passes
through the inner edge of source b, experiment 3A 242
xxi
-------
Number Page
4-13(c) Comparison of predicted (dash-dot) and true ozone concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A . . . . 243
4-13(d) Comparison of predicted (dash-dot) and true olefin concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A . . . . 244
4-13(e) Comparison of predicted (dash-dot) and true paraffin concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A . . . . 245
4-13(f) Comparison of predicted (dash-dot) and true aldehyde concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A . . . . 246
4-13(g) Comparison of predicted (dash-dot) and true aromatic concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A . . . . 247
4-13(h) Comparison of predicted (dash-dot) and true carbon monoxide
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A. . 248
4-13(i) Comparison of predicted (dash-dot) and true nitrous acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A. . 249
4-13(j) Comparison of predicted (dash-dot) and true nitric acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A. . 250
4-13(k) Comparison of predicted (dash-dot) and true PAN concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A . . . . 251
4-13(1) Comparison of predicted (dash-dot) and true alky! nitrate
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A. . 252
4-13(m) Comparison of predicted (dash-dot) and true hydrogen peroxide
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A. . 253
4-13(n) Comparison of predicted (dash-dot) and true atomic oxygen
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A. . 254
4-13(o) Comparison of predicted (dash-dot) and true nitrate concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A . . . . 255
xxn
-------
Number Page
4-13(p) Comparison of predicted (dash-dot) and true hydroxyl radical
concentration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A . . . . 256
4-13(q) Comparison of predicted (dash-dot) and true hydroperoxyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the inner edge of source b,
experiment 3A „ 257
4-13(r) Comparison of predicted (dash-dot) and true pernitric acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A. . 258
4-13(s) Comparison of predicted (dash-dot) and true alkoxyl radical
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A. . 259
4-13(t) Comparison of predicted (dash-dot) and true alkylperoxyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the inner edge of source b,
experiment 3A 260
4-13(u) Comparison of predicted (dash-dot) and true alkoxy radical
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A. . 261
4-13(v) Comparison of predicted (dash-dot) and true peroxyacyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the inner edge of source b,
experiment 3A 262
4-13(w) Comparison of predicted (dash-dot) and true peroxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the inner edge of source b,
experiment 3A 263
xxm
-------
TABLES
Number
1-1 Chemical reactions included in the Demerjian/Schere
mechanism and the rate constants assumed for each .... 8
1-2 Summary of the conditions simulated in each of the five
groups of experiments performed in this report to test
the accuracies of the regional oxidant model's numerical
algorithm. In all experiments, the photolytic rate
constants undergo the temporal variations shown in
Figure 2-1 10
1-3 Summary of the results of each of the model tests
described in Table 1-2 11
2-1 Initial concentrations of each chemical species in
the batch reactor simulations 1A.L and 1A.R 16
2-2 Summary of the computer CPU times (VAX 11/780) required
by the ROM and Gear algorithms to perform the 48-hour
simulations for studies 1A.L and 1A.R 18
2-3 Comparison of computer times (VAX 11/780) required
by the variable FRAX and Gear algorithms to perform
the 48-hour batch reactor simulations for studies
1A.L and 1A.R 21
4-1 Base emission rates of species used for line sources
in experiment 3A. The emission rates of individual
source cells are fractions (1/3, 1/2, 2/3 or 1) or
the values shown here (see Figure 4-1) 132
xxiv
-------
ACKNOWLEDGMENTS
The authors are indebted to Ms. Barbara Hinton for her incomparable
workmanship and patience in typing the manuscript.
xxv
-------
SECTION 1
Introduction and Summary
Air pollution simulation models are not considered to be ready for formal
applications until after they have been "validated". Although the term
"validation" is not well defined, the validation process is generally taken
to mean the establishment of a quantitative measure of the inherent error
in a model. Here the distinction is drawn between the component of error
that is attributable to errors in the input data and the component that is
due to deficiencies in the "physics" and mathematical algorithms that
constitute the model itself. Ascertaining the extent to which a model's
poor performance is attributable to its own internal weaknesses is a task
that is plagued by several formidable problems.
One of these problems is that the measured concentrations that are used
as the standard for judging the model's accuracy contain errors whose
magnitudes are known only approximately. A second problem is that grid
models predict averages of concentration over large volumes of space —
volumes of the order of 100 km^ — whereas the measured concentrations
represent samples taken virtually at single points in space. A third, and
perhaps the most significant, problem is the limitation on predictability.
As we discussed in Sections 6 and 7 of Part 1 and in Section 10 of Part 2,
not even a perfect model working with error-free data could predict the
concentration that one would measure at a given site at a given time.
Models can predict probabilities of given concentration values and expected
-------
concentration levels but not the concentration itself. This limitation
arises from the character of atmospheric motion, and its magnitude is
determined in part by the type and density of meteorological data that are
used to prescribe the flow field in the model.
At the present time there does not exist a rational procedure for
model validation that takes all these sources of uncertainty into account.
Consequently, we will focus our immediate efforts on demonstrating that the
Regional Oxidant Model (ROM) satisfies certain necessary (but not sufficient)
conditions for validity. To understand what these necessary conditions
are, think of the model as being composed of three parts: physics, numerical
algorithms, and hypotheses.
The physics describe the chemical reactions, deposition, transport by
the wind, and all other relevant physical processes. The physics are
described mathematically by a set of differential equations whose solutions
constitute the model's predictions. Since closed form solutions of the
differential equations are not known, discrete analogues of these equations
must be constructed that are amenable to computer solution.
Solutions of the discrete equations are produced by the model 's
numerical algorithms. If these algorithms are not properly chosen or are
ill-conditioned, the solutions they yield can differ significantly from the
corresponding solution of the differential equations that they are supposed
to represent.
Finally, the model hypotheses include the mathematical descriptions of
physical processes whose spatial and temporal scales are smaller than the
-------
resolvable scales of the discrete analogue of the corresponding differential
equations, such as turbulent transport and concentration fluctuations.
They also include the hypotheses concerning the probabilities of the individual
members of the ensemble of flow fields (see part 1, Chapters 6 and 7; and
Part 2, Section 10). Let us digress for a moment on this last item since
it may be unfamiliar to the reader.
In all long range transport models developed before now, i.e., models
that treat the fate of species beyond distances of the order of 100 km from
the source, the "ensemble" of flow fields contained only a single member,
namely the wind field derived from a given set of data using some pre-selected
objective analysis or interpolation routine. We showed in Parts 1 and 2 of
this report that a given set of discrete meteorological data do not uniquely
specify the wind field. Rather, they define a set of fields each of which
is a possible description of the flow that existed during the time the
observations were made. We have adopted the position in our regional model
that the proper way to approach modeling under these circumstances is to
assign probabilities to each member of the set of possible flows -- the
probability values reflecting additional empirical, historical or other
information available about the winds in the given area — and to compute
the concentrations that the given set of sources would produce in each of
the flow fields that comprise the set of most probable flows. Assigning
quantitative probabilities to each of the possible flows requires a hypothesis
since no theoretical principle is available for this purpose. From this
viewpoint, we see that the conventional modeling approach has adopted the
tacit hypothesis that all of the possible flows have zero probability
except one, namely that given by the chosen objective analysis routine.
-------
Let us say that a model is "valid" if it produces concentration
predictions that are consistently within some given error limits of the
actual concentration that one would observe under the conditions simulated.
Under this definition necessary conditions for model validity are that each
of its three components individually satisfy specific accuracy criteria.
(Strictly speaking, arbitrarily large errors in one component could be
tolerated if sufficiently large errors of a compensating form existed in
another part. However, since the three model components that we have
defined are inherently distinct, this situation will not occur in general.
Thus, for all practical purposes we can assume that each component must
meet certain accuracy standards as a necessary condition for overall model
validity.)
The purpose of this report is to demonstrate the accuracy of only the
numerical alogorithms in the regional oxidant model. In a future study we
plan to present a rational procedure for model verification that will allow
us to assess the performance of the model overall.
To test the numerical algorithms we will apply the model to a series
of rather elementary problems whose exact solutions are known, and compare
the model's predictions in each case with the true values. Figure 1-1,
which is taken from Part 2, Section 1, will help give a clearer picture of
the specific part of the regional model that we will be examining. The box
labeled CORE represents the set of numerical algorithms that approximate
the differential equations on which the regional model is based. In Part
1, Section 9, we split the governing differential equations into three
distinct parts and we developed numerical algorithms for handling each part
4
-------
li
Ul
oc
o
o
Q.
z
TOPOGRAPHY
DATA
EMISSIONS
DATA
UPPER AtR
MET
DATA
T I
SURFACE
MET
DATA
SATELLITE
CLOUD COVER
DATA
LAND USE
DATA
SURFACE AIR
MONITORING
DATA
Figure 1-1.
Schematic illustration of the regional model and the
network of processors that supply it information.
-------
separately. One algorithm treats the advection and horizontal diffusion
processes, one algorithm handles the chemistry, and the third approximates
deposition and all other physical processes that affect vertical material
fluxes. In this report we will assess the accuracies of these three
algorithms both separately and jointly. The objective is to show that the
numerical portion of the regional model satisfies the necessary condition
for overall model validity.
In order to perform the desired tests, it is necessary first to adopt
a specific chemical mechanism for the model. This is actually a part of
the physics which, for flexibility purposes, we relegated to the external
module labeled CHEM in Figure 1-1. Any mechanism can be used as long as it
is structured in a way that is compatible with the interface that links the
module CHEM with the basic module CORE (see Part 2, Section 1). For testing
purposes we will employ the 23 species/36 reaction mechanism developed by
Demerjian and Schere (1979). Details of this scheme are given in Table 1-1.
One of our interests is to determine whether the accuracy of the algorithm
that handles the chemical kinetics portion of the model equation varies
greatly from species to species.
The test simulations are performed by assigning to each of the parameters
in the model input file (MIF) (see Figure 1-1) values characteristic of the
particular situation that we want to analyze. For example, to perform
tests of the transport and chemistry algorithms jointly, we assign values
to the members of the MIF that will prevent vertical fluxes of material
and that describe the flow fields and source emissions in each layer as we
want them. All together, five case studies are conducted to test various
-------
aspects of the model's numerical algorithms. The conditions simulated in
each of the studies is summarized in Table 1-2, and a brief summary of the
findings is presented in Table 1-3 (detailed discussions are provided in
the remainder of this report).
-------
Table 1-1. Chemical reactions included in the Demerjian/Schere
mechanism and the rate constants assumed for each.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
N02
0 + 02 + M
03 + NO
03 + N02
N03 + NO
N03 + N02 + H20
HONO
HO + NO
H02 + N02
H02 + NO
H02 + N02 + M
HOON02
HO + HONO
HO + N02 + M
HO + NO + M
H02 + 03
HO + 03
H02 + H02
OLEF + 0
OLEF + 03
OLEF + HO
PARAF -t- HO
ALD
Reaction
hv
-y NO + 0
-»• 03 + M
-y N02 + 02
-y NO-, + 09
o c.
-y 2N02
-y 2HONO
hv
-y HO + NO
(02)
H02 + C02
-y HONO + 02
-y HO + N02
> HOON02 + M
* H02 + N02
->• N02 + H20
+ HON02 + M
* HONO + M
-> HO + 202
-y H02 -t- 02
> H202 + 02
-y R02 + ALD + H02
-y R02 + ALD + H02
-y R02 + ALD
-y R02
hv
-y 0.5R02 + 1.5H02 H
Rate Constant*
(units3)
variable
2.3 x lO'5 c
2.7 x lO'1
4.8 x 10'2
3.0 x 104
3.4 x ID'3 c
variabled
4.1 x 102
4.4
1.2 x 104
1.5 x 10~3 c
3.3
9.8 x 103
1.5 x 10"2 c
7.4 x 10-3 c
3.0
1.0 x 102
3.7 x 103
5.1 x 103
1.4 x 10'2
3.1 x 104
5.0 x 103
i- l.OCO variabled
-------
Table 1-1, continued
Reaction
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
ALD
R02
RO
R102 J
RO H
R02
R102
AROM
R202
R20
R2°2
R102
+ HO
+ NO
+ °2
H N02
K N02
+ 03
+ NO
PAN
+ HO
+ NO
+ o2
+ 03
+ 03
Rate Constant
(units3)
-»• 0.3R102 + 0.7H02 + 0.7CO 1.4 x
> RO +
-» ALD
-»• PAN
* RONO
->• RO +
(02)
* R02
-»• R102
> R202
* R20
-» ALD
+ R20
* R02
N02
+ H02
2
202
+ N02
+ N02
+ 2ALD + CO
+ N02
+ H02 + 2CO
+ 202
+ 202
1.1 x
9.0 x
8.9 x
1.0 x
2.0
4.0 x
1.4 x
2.3 x
1.1 x
8.9 x
2.0
2.0
104
104
10-1
103
102
103
10-1 b
104
104
10-1
* Values of rate constants that vary by temperature are evaluated here for
298°K and 1 atm pressure.
a Rate constant units are ppm"l min'l unless otherwise noted.
b Units of rate constant are min~l.
c Units of rate constant are ppm'2 min~l.
^ Photolysis rate constants are based on data compiled by Demerjian, Schere
and Peterson (1980) and vary as a function of solar zenith angle. (See text)
Species definitions:
RN03 Alkyl Nitrate
H02 Hydroperoxyl Radical
H04N Pernitric Acid
RO Alkoxyl Radical
R02 Alkylperoxy Radical
R20 Alkoxy Radical
R102 Peroxyacyl Radical
R202 Peroxy Radical
-------
Table 1-2.
3A
Summary of the conditions simulated in each of the five
groups of experiments performed in this report to test
the accuracies of the regional oxidant model 's numerical
algorithm. In all experiments, the photolytic rate constants
undergo the temporal variations shown in Figure 2-1.
Case
1A.L
1A.R
IB
2A
28. L
2B.R
Horiz.
transport
No
No
No
Yes
Yes
Yes
Horiz.
diffusion
No
No
No
No
No
No
Vert.
diffusion
No
No
Yes**
No
Yes
Yes
Initial
concentrations*
Lean
Rich
Rich
Lean, elliptical
cloud
Lean, elliptical
cloud
Rich, elliptical
Sources
No
No
No
No
No
No
Remarks
Initial cloi
shown in Fii
Flow field .
initial cloi
shown in Fi>
Yes
No
No
cloud
Clean
Yes Sources and
flow field are
shown in Fig.
* "lean" and "rich" concentrations are defined in Table 2-1. "Clean" indicates
negligible concentrations of all species.
** In this experiment clean fluid is mixed with the contents of the simulated
batch reactor to approximate the vertical diffusion process.
10
-------
Table 1-3. Summary of the results of each of the model tests described
in Table 1-2.
Case Algorithms Tested
Results
1A
Chemical kinetics
IB
2A
Chemical kinetics
and vertical flux
jointly
Transport and chemical
kinetics jointly
2B
Transport, chemical
kinetics and vertical
flux jointly
Model predictions identical to true solutions
for all 23 species over a 48-hour simulation.
A modified version of the chemical kinetics
algorithm, called the variable FRAX algorithm,
which is designed for increased execution speed
yields concentrations that are within 5% of
the true values for all species over the
48-hour simulation.
Error levels same as in 1A.
Percentage errors in simulated peak concentra-
tion in advected clouds:
Species
Travel time (hrs)
CO
NO
03
N02
Olefin
4
-10
nil
-7
nil
-8
8
-10
+2
-7
nil
-8
16
-12
nil
-8
nil
-18
24
-13
-
-8
nil
36
-15
_
T
_
48
-15
-
-6
""
Notes: Negative value indicates model under-
estimates true value; - indicates species
concentration negligible.
Percentage errors in simulated peak concentra-
tion in advected clouds:
Species
Travel time (hrs)
CO
NO
03
N02*
Olefin
4
-8
nil
-
nil
-7
8
-9
+8
-9
nil
-7
16
-8
+2
-8
nil
-
24
-8
-
-9
nil
-
36
-8
nil
-4
nil
-
48
-8
_
nil
nil
-
* No2 underestimated by 10% at hour 8 when
extreme NOX and HC concentrations simulated
(see Figure 3-6(d)).
Notes: Negative error indicates underprediction;
- indicates concentration negligible.
11
-------
Table 1-3. Continued.
Case Algorithms Tested
Results
3A Chemical kinetics and Percentage errors in predicted center! ine
inhomogeneous transport concentration of
jointly (equations with various
continuous sources)
Species
CO
03
N02
Olefin
PAN
widths.
Travel
(hrs
7
34
52
13
25
34
7
12
18
3
7
12
7
13
20
plumes from
time
) units
5
-7
-12
-14
-4
-3
-4
-5
nil
nil
-4
nil
nil
-5
-10
-4
sources of
Source
=gri d
3
-17
-18
not
-13
-9
-6
-15
-14
nil
-12
-10
nil
-8
-23
-10
Width
cell dimens
2
-22
-25
available
-14
-11
-12
-15
-20
nil
-12
-15
-20
-6
-21
-12
Same as above but with
compound sources
Note: Negative error signifies underpre-
diction.
Percentage errors in predicted peak con-
centration following passage of a plume
from a source over a second source.
(First plume is three grid cells wide and
crosses second source after a travel time
of 40 hrs.)
Species Travel time from error (%)
second source (hrs)
CO
4
8
-28
-26
4
8
-11
-11
See Section 4 for further details.
12
-------
SECTION 2
Case 1A: Chemistry Without Transport or Sources
In this test we simulate the concentrations of 23 chemical species in
a batch reactor over a 48 hour period. The objective is to evaluate the
performance of the algorithm that we developed in Part 1, Section 9, for
solving the chemical kinetics portion of the regional model's governing
equations.
The chemical kinetics are described by a system of nonlinear, ordinary
differential equations of the form
aYa I i
— = Z Z k ,, Y Y (2-1)
at 1-1 j-i a1J 1 J
where YCC denotes the concentration of species a ; I is the total number of
species present; and ka-jj is the rate constant of the reaction that
involves production of species a from species i and j, or destruction of
species a through its decomposition or its interaction with another species.
Eq. 2-1 describes concentrations in a chemical reactor where transport and
diffusion processes are insignificant. Hence, it is identical in form to
the chemical kinetics portion of the regional model equations (cf Part 1,
Eq. 9-24). Our interest here is in determining how well the solutions of
the numerical analogue of (2-1) that we formulated in Part 1, Section 9 for
use in the regional model compare with the exact solutions of (2-1).
Although the analytic forms of these solutions are not known, we can obtain
virtually exact approximations of them for any values of t using the numerical
technique developed originally by Gear (1971). In the test problems that
13
-------
we consider here, we will regard the the approximate solutions of (2-1)
derived from the Gear routine to be the exact solutions, and it is against
these results that we will assess the accuracy of the solution algorithm
that we use in the regional model.
At this point one might wonder why we bothered to develop a new technique
for solving (2-1) when an accurate method already exists. The answer is
that the Gear technique requires too much computer time and memory to make
it practicable in the regional model, or any model of multicell dimensions.
We have found in preliminary tests of the regional model that the computer
time required to solve the chemical kinetics portion of the governing
equations is 20 to 50 times larger than that required to solve the transport,
diffusion and vertical mixing portions of the equations combined. This was
a surprising finding, especially since the transport terms are represented
by a 5-th order differencing scheme which requires considerably more computer
time than conventional lower order approximations. Thus, the overall
efficiency of the regional model code is determined nearly exclusively by
the efficiency of the chemical kinetics solver, rather than the numerical
schemes used for the transport and diffusion processes.
If the Gear method were used to handle the chemical kinetics portion
of the regional model 's equations, which encompass some 7500 grid cells,
a 24 hour simulation would require about 1 week of CPU time on a VAX 11/780
computer. Using the numerical algorithm that we developed for handling the
kinetics (i.e., Eq. 2-1), the same simulation would require 10-50 hours of
CPU time depending on the accuracy one requires. Our scheme was developed
under the constraint of achieving maximum efficiency. Our task now is to
determine how much accuracy we have sacrificed for computational speed.
14
-------
As we noted earlier, out tests consist of two, 48-hour batch reactor
simulations. In one test which we shall call case 1A.L, the reactor is
initialized with a "lean" mix of NOX and hydrocarbons that produces ozone
concentrations near the current national air quality standard, namely 120
ppb, after one simulated day. This particular test will give an indication
of how well the numerical algorithm can be expected to perform in "typical"
simulations.
The second test, Case 1A.R, begins with a "rich" mixture of NOX and
hydrocarbons that produces ozone levels of the order of 550 ppb — a value
more than double the highest hourly ozone concentrations normally observed
in the Northeastern United States. The performance of the algorithm in
this extreme situation will give an indication of whether the accuracy of
the algorithm is sensitive to variations in the species concentrations.
The initial concentration values used for each of the 23 species in
cases 1A.1 and 1A.R are listed in Table 2-1. In both cases the simulated
reactor is irradiated with sunlight. The amplitude of the radiation varies
in a diurnal manner such that the three photolytic rate coefficients k]_, kj
and k23 acquire the magnitudes shown graphically in Figure 2-1. Note that
the initial instant t = 0 in the reactor corresponds to midnight in the time
frame of the sunlight variations.
Results of the two test simulations 1A.L and 1A.R are plotted in Figure
2-2a,...w on pages 22 through 44. The curves labeled "chemistry" represent
the solutions generated by our numerical algorithm and those labeled "Gear"
are the solutions produced by the Gear routine, which we regard as the
exact solutions. The results show that the solutions of chemical kinetics
15
-------
Table 2-1. Initial concentrations of each chemical species in the
batch reactor simulations 1A.L and 1A.R.
Species
NO
N02
°3
OLE
PAR
ALD
ARO
CO
HN02
HN03
PAN
RN03
H202
0
N03
HO
H02
H04N
RO
R02
R20
R102
R202
(Rich Mixture)
Case 1A.R
(PPM)
0.119
3.91 x ID"2
1.0 x 10-14
7.80 x lO-2
9.39 x lO-2
9.71 x 10-2
3.01 x 10-2
1.62
1.0 x 10~14
1.0 x ID"14
1.0 x 10-1*
9.42 x 10-13
1.0 x 10~6
1.0 x lO"12
1.0 x 10"14
8.09 x 10-!3
1.0 x 10"14
1.52 x 10~13
1.0 x 10-12
1.0 x 10-14
1.0 x 10-12
2.21 x 10-13
4.05 x 10~13
16
(Lean Mixture)
Case 1A.L
(PPM)
2.66 x 10-5
7.69 x 10'3
7.64 x 10"2
1.56 x 10-3
9.37 x 10-3
1.06 x 10-2
7.80 x 10-4
3.33 x 10-1
6.60 x 10'5
3.62 x ID'2
3.01 x 10-4
4.40 x lO'5
5.53 x 10'5
1.57 x 10-13
8.84 x lO'5
7.24 x 10-9
9.27 x 10-6
1.76 x 10-4
3.42 x 10-9
1.74 x 10-5
5.16 x 10-11
2.23 x 10-6
5.97 x lO'7
-------
8 10 12 14 IS 18 20 22
HOUR
Figure 2-1.
Temporal variations in the magnitudes of the photolytic
rate constants ki, ky and kgs used in both reactor
simulations 1A.L and 1A.R (and in all other experiments
presented in this report).
17
-------
equations (2-1) given by the ROM. (regional oxidant model) algorithm are
virtually identical to the exact solutions for all 23 species, over the
entire 48-hour duration of the simulation, in both test cases 1A.L and 1A.R.
We conducted a third test, IB, in which the contents of the simulated
reactor in case 1A.R were instantaneously mixed with an equal volume of
clean air at hour 12. Shocking the system in this way would reveal whether
the accuracy of the chemistry algorithm is sensitive to the action of
external agents, such as turbulent mixing; and it would drive the species
concentration into a third regime, intermediate between that of cases 1A.L
and 1A.R, which would reveal further information on the sensitivity of the
algorithm's accuracy to species concentrations. The results of this test
were also identical to the corresponding solutions derived from the Gear
routine. (For brevity we will not display the results of this test.)
We conclude from the three batch reactor tests that the algorithm that
we developed to handle the chemical kinetics portion of the regional oxidant
model is highly accurate over the entire range of pollutant concentrations
of concern to us in applied studies. Moreover, its accuracy is unaffected
by external agents such as turbulent mixing, source emissions or other
processes that alter species concentrations. Our tests also showed that
computationally the algorithm is quite efficient. The computer times
required for each of the tests are summarized in Table 2-2.
Table 2-2. Summary of the computer CPU times (VAX 11/780) required
by the ROM and Gear algorithms to perform the 48-hour
simulations for studies 1A.L and 1A.R.
Case
Algorithm
ROM
Gear
1A.L
59.6 (sec)
355.6
1A.R
129.1
409.2
18
-------
One reason that the Gear times are so large is that at the beginning
of each simulated period this routine computes initial estimates of time
derivatives of various orders for each species. In the regional model the
period of each chemistry simulation is only 5 minutes between reinitializa-
tions, because vertical exchange processes must be allowed to operate on the
concentrations in each of the model's three layers at least this often.
Therefore, in the ROM environment, the Gear routine's initialization require-
ments create a large computational overhead.
One might argue that the level of precision exhibited by the ROM chemistry
algorithm is unnecessarily high because errors exist in both the physics
and hypotheses portions of the model and in all the input data. In view of
this it would be practicable to sacrifice some of the algorithm's accuracy
for a further increase in computation speed. This trade-off can be achieved
easily by increasing the parameter x that controls the algorithm's integration
time step size (see page 192 of Part 1). In the batch reactor simulations
1A.L and 1A.R performed above, \ had the value 0.001. If we increase it by
a factor of 10 to \ =0.01, the execution time requirements drop from 59.6 sec
to 35.4 sec for case 1A.L, and from 129.1 to 43 sec for case 1A.R. The
accuracy penalty that is paid for this increase in speed can be seen in
Figure 2.3a-f, pages 45-50, where we have plotted a few of the best and a few
of the worst results obtained for both cases 1A.L and 1A.R using x = .01. In
the case of 1A.L, which represents concentrations typical of those that we
would encounter in actual applications, the errors in the predicted concentra-
tions are no larger than 10% for any of the 23 species. In fact for most of
the species, including all those not shown, the largest error is only a few
19
-------
percent over the entire 48-hour simulations. However, as the bottom panels
of Figure 2-3 reveal, performance in Case 1A.R is significantly poorer. In
the case of ozone, the predicted concentration is over 50% too high on the
second day of the simulation and for some of the other species, such as
shown in Figure 2-3f, the errors are still larger. Although Case 1A.R
represents conditions much more severe than any that we are likely to
encounter in applications, the magnitude of the errors revealed in this case
show an enhanced sensitivity of the numerical algorithm's accuracy to
species concentration when the control parameter \ has the value .01.
Therefore, in order to realize a high speed algorithm that would not
systematically generate larger errrors in regions where concentrations are
high, one of our colleagues, Kenneth Schere, developed a modified version
of the kinetics algorithm in which the parameter \ has a nominal value of
.01 but switches to the smaller value .001 wherever the magnitude of the
local time rate of change of NO concentration exceeds a given value: 0.5%
sec'*. It turns out that the temporal behavior of NO is a good indicator
of conditions in which the accuracy of the algorithm is critical. We call
this modified algorithm the variable FRAX or variable \ algorithm. Figures
2-4(a)-(f), pages 51-56, show results of new model runs for cases 1A.L and
1A.R for the same species plotted in Figure 2-3(a)-(f). The results are
greatly improved and are considered by us to be of sufficiently high quality
to justify use of the variable FRAX algorithm in all applications of the
regional oxidant model (ROM). (All results presented in this report utilize
the \ =.001 version.) Table 2-3 compares the computer time requirements of
the Gear and the variable FRAX algorithms for the two, 48-hour simulations,
Case 1A.L and 1A.R.
20
-------
Table 2-3. Comparison of computer times (VAX 11/780) required by the
variable FRAX and Gear algorithms to perform the 48-hour
batch reactor simulations for studies 1A.L and 1A.R.
Algorithm
ROM (variable FRAX)
Gear
1A.L
40.1
355.6
Case
(sec)
1A.R
98.0
409.2
In conclusion, the tests that we have presented here show that the
algorithm that we use in the regional model to solve the chemical kinetics
portion of the governing equations produces solutions with negligible errors
in a computation time only 1/3 to 1/6 that required by the highly accurate
Gear method. And it provides solutions with accuracies commensurate with
the error levels in other parts of the model and in the input data in a
computation time 1/10 that required by the Gear routine.
21
-------
HEM : 001
IA.L
4 8 12 16 20 2+ 4 B 12 16 20 24
CHEM :001
GEAR
IA.R
16 20
DAY 1
12
DAY 2
16
20
24
TIME (HOUR OF DAY)
Figure 2-2(a).
Results of NO concentration in batch reactor
simulations IA.L (top) and IA.R (bottom).
22
-------
CHOI : 001
GEAR
IA.L
8 12 18 20 24
TIME (HOUR OF DAY)
Figure 2-2(b). Same as 2-2(a) but for N02. Case IA.L (top),
1A.R (bottom).
23
-------
o
X
Q. -
Q_
UJ
O
z
a
o
CHEM :001
GEAR
IA.L
4 8 12 16 20 24 4 8 12 16 20 24
IA.R
8 12 18 20 24
12 16 20 24
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-2(c).
Results for ozone in batch reactor simulations IA.L (top)
and IA.R (bottom).
24
-------
CHEM : 001
GEAR
IA.L
TIME (HOUR OF DAY)
Figure 2-2(d).
Results for olefin in batch reactor simulations IA.L (top)
and 1A.R (bottom).
25
-------
CHOI : 001
IA.L
4 8 12 16 20 24 4 3 12 16
TIME (HOUR OF DAY)
Figure 2-2(e).
Results for paraffin in batch reactor simulations IA.L (top)
and 1A.R (bottom).
26
-------
CM
O
Q. -
Q.
g
§ 1
UJ
O
Z
O
O
^ 2|
O
X
Q_
CL
O
UJ
o
-z.
o
o
CHEU : 001
GEAR
IA.L
12 16
20
: 001
IA.R
• ' ' ' ' ' ' ' ' '
8 12 16 20
DAY 1
24
• i • ' • • •
TIME (HOUR OF DAY)
12 16 20 24
12 16 20 24
DAY 2
Figure 2-2(f). Results for aldehyde in batch reactor simulations IA.L (top)
and IA.R (bottom).
27
-------
CHEW.: 001
GEAR
IA.L
8 12 16 20 24
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-2(g).
Results for aromatic in batch reactor simulations IA.L (top)
and 1A.R (bottom).
28
-------
o
X f
8:
tr
LU
o
I'
o
o
CHEM : 001
GEAR
IA.L
CL
Q_
O
!<
UJ
O
Z
O
o
o
o
12
16
20
24
8 12 16 20 24
CHEM :
IA.R
16
DAY 1
12
DAY 2
20
24
TIME (HOUR OF DAY)
Figure 2-2(h).
Results for CO in batch reactor simulations IA.L (top)
and IA.R (bottom).
29
-------
CHEM : 001
GEAR
IA.L
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-2(1).
Results for nitrous acid in batch reactor simulations
IA.L (top) and 1A.R (bottom).
30
-------
CM
o
X
O 3E-
Ld 2E-
O
-z.
o
o
o
z
X
IA.L
O
v—
X
Q_
Q_
LJ
o
z:
o
o
ro
O
^.
X
8 12
CHEU :001
GEAR
24
12 18
IA.R
i i i i f 1^1 i t t i
20
8 12 16 20 24
DAY 1
12 ~Te 20 ~ST
DAY 2
TIME (HOUR OF DAY)
Figure 2-2(j).
Results for nitric acid in batch reactor simulations
IA.L (top) and IA.R (bottom).
31
-------
CM
o
Q_
Q.
o 3r
fe
o:
LU
o
a
o
<
Q_
1-
CHEM : 001
GEAR
IA.L
24
3 12 16 20 24
IA.R
12
DAY 1
16
20
24
12
DAY 2
16
TIME (HOUR OF DAY)
20
24
Figure 2-2(k). Results for PAN in batch reactor simulations IA.L (top)
and IA.R (bottom).
32
-------
O
X
CL
Q- t
CHEM : 001
-S&W
IA.L
2-
iLi
O
z
O
O
rO
O
z
tr
(O
O
X
CL
a.
o
tr *:
UJ
o
•ZL
O
o
rO
O
nf.' • ...i..•.. i i. 11 11 • 11 111 • 11 111111.1 111 111 i • 111 • 1111 111
u 4 8 12 16 20 24 4 8 12 16 20 24
01
IA.R
4 8 12 16 20 24 4 8 \2 16 20 24
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-2(1).
Results for alkyl nitrate in batch reactor simulations
IA.L (top) and IA.R (bottom).
33
-------
10r-
IA.L
IS 20 24 4 8 12 15 20 24
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-2(m). Results for hydrogen peroxide in batch reactor simulations
IA.L (top) and 1A.R (bottom).
34
-------
o
CHEW : 001
GEAR
IA.L
TIME (HOUR OF DAY)
Figure 2-2(n).
Results for atomic oxygen in batch reactor simulations
IA.L (top) and 1A.R (bottom).
35
-------
IA.L
16 20 24 4 3 12 16 20 24
8 12 16 20 24 4 8 12 16 20 24
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-2(o).
Results for nitrate in batch reactor simulations
IA.L (top) and 1A.R (bottom).
36
-------
IA.L
a 12 16 20 24
12 18 20 24
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-2(p).
Results for hydroxyl radical in batch reactor simulations
IA.L (top) and 1A.R (bottom).
37
-------
o
X
Q_
Q.
o
£
I
Ld
O
z:
o
o
o
X
8: ^
O
fe
DC.
Ld
o ,t
O
a
o
X
CHEM : 001
GEAR
8 12 16 20
CHEM : 001
GEAR
IA.L
'.••'•.. i ... i .. , i
8 12 " 16 20 24
IA.R
8 12 16 20 2+ 4 8 12 16
PAY 1
DAY 2
24
TIME (HOUR OF DAY)
Figure 2-2(q).
Results for pernltric acid in batch reactor simulations
IA.L (top) and IA.R (bottom).
38
-------
IA.L
DAY 1
8 12 16 20 24
DAY 2
TIME (HOUR OF DAY)
Figure 2-2(r).
Results for hydroperoxyl radical in batch reactor simulations
IA.L (top) and 1A.R (bottom).
39
-------
o
X
O
LU
O
O
CHEH : 001
GEAR
IA.L
* 3 12 16 20 24 4 8 12 16 20
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-2(s).
Results for alkoxyl radical in batch reactor simulations
IA.L (top) and 1A.R (bottom).
40
-------
CHEM : 001
GEAR
1A.L
1 • I 1 1 1 I 1 I 1. I 1 I I I. 1 I I I • I I I I 1 1 I I I I I I 1 I I I
* 8 12 16 20 24- 4 g 12
4 8 12 16 20 24 4 8 12 16 20 2+
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-2(t).
Results for alkylperoxyl radical in batch reactor simulations
1A.L (top) and 1A.R (bottom).
41
-------
r: 6
o
x
Q_
0.
O
5-
4-
CHEM : 001
GEAR
IA.L
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-2(u).
Results for alkoxy radical in batch reactor simulations
IA.L (top) and 1A.R (bottom).
42
-------
IA.L
8 12 16 20 24
O
T—
X
Q_
Q_
O
CHEM : 001
GEAR
IA.R
20 24-
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-2(v).
Results for peroxyacyl radical in batch reactor simulations
IA.L (top) and IA.R (bottom).
43
-------
O
X
Q_
Q_
CHEW :001
GEAR
1A.L
DAY 1
DAY 2
24
TIME (HOUR OF DAY)
Figure 2-2(w).
Results for peroxy radical in batch reactor simulations
1A.L (top) and 1A.R (bottom).
44
-------
O
X
a.
a.
z:
cr
LU
O
'Z.
O
O
1-
CHEM :01
GEAR
IA.L
(RELAXED
4 8 12 IB 20 24 4 8 12 16 20 24
IA.R
(RELAXED
1 1 1 I t 1 •
12
DAY 1
16
12
IS 20
DAY 2
TIME (HOUR OF DAY)
Figure 2-3(a).
Results of NO concentration in batch reactor simulations
IA.L and IA.R using a value of .01 for the control
parameter \ in the numerical algorithm. (Results shown
in Fig. 2-2(a) use X =.001.)
-------
CHEM : Ot
GEAR
1A.L
(RELAXED
CONCEN
ro d
1 '
C^ 2
O
><
Q.
QL
t\
x__
4 8 12 16 20 24
' CHEM : 01
GEAR
-
LU
O
z
o
o
c\i
O
12 16 20
IA.R
(RELAXED
12
DAY 1
16 20
12
DAY 2
16
24-
TIME (HOUR OF DAY)
Figure 2-3(b).
Results of N02 concentration in batch reactor simulations
1A.L and IA.R using a value of .01 for the control
parameter \ in the numerical algorithm. (Results shown
in Fig. 2-2(a) use \ =.001.)
46
-------
_ 2f-
O
Q_
CL
o •
o:
UJ
o
2
O
O
CHOI :Q1
GEAR
IA.L
(RELAXED A)
I , . i I i . . I . . i i i i . I f . , I , , . I , , . I
12
18
20 24 4 8 12 16 20 24
IA.R
(RELAXED
24
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-3(c). Results of 63 concentration in batch reactor simulations
IA.L and IA.R using a value of ,01 for the control
parameter X in the numerical algorithm. (Results shown
in Fig. 2-2(a) use \ =.001.)
47
-------
CM
o
X
Q_
0.
< 1
o:
LJ
o
z
o
o
CHEW :01
GEAR
IA.L
CRELAXED A)
1 1 I I 1 1 '
4 8 12 16 20 24 4 8 12 16 20 24
IA.R
(RELAXED A)
4 I 12 16 20 24 4 8 12 16 20 24
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-3(d).
Results of aldehyde concentration in batch reactor
simulations IA.L and IA.R using a value of .01 for the
control parameter \ in the numerical algorithm. (Results
shown in Fig. 2-2(a) use \ =.001.)
48
-------
O
X
Q_
Q.
UJ
O
-z.
O
O
CHEW : 01
GEAR
IA.L
(RELAXED
8 12 16 20 24
3 12 18 20 24
IA.R
(RELAXED
24
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-3(e).
Results of PAN concentration in batch reactor simulations
IA.L and IA.R using a value of .01 for the control
parameter \ in the numerical algorithm. (Results shown
in Fig. 2-2(a) use \ =.001.)
49
-------
CHEM : 01
GEAR
IA.L
(RELAXED
CHEM : 01
GEAR
IA.R
(RELAXED
TIME (HOUR OF DAY)
Figure 2-3(f).
Results of alkylperoxyl concentration in batch reactor
simulations IA.L and IA.R using a value of .01 for the
control parameter x in the numerical algorithm. (Results
shown in Fig. 2-2(a) use X =.001.)
50
-------
IA.L
(VARIABLE
-pi , , | , . , i , . , I , , ,\i , , , i , , , I , ,X"TT, i I , . , 77>^l ...I,
4 8 12 16 20 24 4 3 12 16 20 24
_ 2|
O
Q_
CL
CHEMISTRY
GEAR
IA.R
(VARIABLE A)
12
DAY 1
12
DAY 2
TIME (HOUR OF DAY)
Figure 2-4(a).
Results of NO concentration
IA.L and IA.R obtained with
that varies the parameter \
speed and minimum error.
in the batch reactor simulations
the modified numerical algorithm
temporally to effect maximum
51
-------
CHDdlSTBY
G8W
IA.L
(VARIABLE A)
Q_
Q_
12 16
20
CHEMISTRY
GEAR
IA.R
(VARIABLE A)
24
DAY 1
12
DAY 2
24
TIME (HOUR OF DAY)
Figure 2-4(b).
Results of N02 concentration in the batch reactor simulations
IA.L and 1A.R obtained with the modified numerical algorithm
that varies the parameter \ temporally to effect maximum
speed and minimum error.
52
-------
O
X
o. _
a.
o
CHEM1STOY
GEAR
IA.L
(VARIABLE A)
IA.R
(VARIABLE A)
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-4(c).
Results of 03 concentration in the batch reactor simulations
IA.L and IA.R obtained with the modified numerical algorithm
that varies the parameter \ temporally to effect maximum
speed and minimum error.
53
-------
CM
O
X
Q_
D_
2r-
LU
O
z
O
O
CHEMISTRY
GEAR
IA.L
(VARIABLE A)
8 12
16
20
24
9 12 18 20
24
IA.R
(VARIABLE
r-iLl 1 1 1 I I I I I
12
DAY 1
20
24
12
DAY 2
18
24
TIME (HOUR OF DAY)
Figure 2-4(d).
Results of aldehyde concentration in the batch reactor
simulations IA.L and IA.R obtained with the modified
numerical algorithm that varies the parameter X temporally
to effect maximum speed and minimum error.
54
-------
CHEMISTRY
GEAR
IA.L
(VARIABLE A)
IA.R
(VARIABLE A)
12
DAY 1
12
DAY 2
TIME (HOUR OF DAY)
Figure 2-4(e).
Results of PAN concentration in the batch reactor simula-
tions IA.L and IA.R obtained with the modified numerical
algorithm that varies the parameter x temporally to effect
maximum speed and minimum error.
55
-------
m
O
Q.
D_
Ld
O
O
CN
O
an
CHEMISTRY
GEAR
IA.L
(VARIABLE
i , , , i , , , i , , i i , , , i , , , I , , , ! , , , i , , , i , , , i , , , i rr~,
8 12 16 20 24
S 12 16 20 24
IA.R
(VARIABLE
3 12 16 20 2+
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 2-4(f).
Results of alkylperoxyl concentration in the batch reactor
simulations IA.L and IA.R obtained with the modified numerical
algorithm that varies the parameter \ temporally to effect
maximum speed and minimum error.
56
-------
SECTION 3
Case 2A: Chemistry with transport
In the previous experiments, 1A.L and 1A.R, we examined the performance
of the algorithm that solves only the chemical kinetics portion of the
regional model equations. In experiment 2A we will advance one step in
complexity and look at how the algorithm that handles the kinetics and the
algorithm that handles the transport perform when they are coupled together.
In particular, we will consider a combined transport/chemistry problem
characterized by
Sca 3ca dca I I
— + u ... + v — * z z kaijcicj (3'1)
&t dx e>y i=l j=l
where (u, v) is the horizontal wind described by given functions u(x,y,t)
and v(x,y,t) of space and time. Eq. 3-1 is the form that the regional
model's equations acquire when the horizontal eddy diffusivity K^ and the
flux parameters that link the three layers of the model vertically are set
to zero.
The exact solutions of (3-1) can be expressed in terms of the solutions
of Eq. 2-1, which we evaluated numerically in the previous experiment, by
performing the following transformations of the space coordinates (x,y):
t
5 = x - x0 - / utx'.y'.t'Jdt1 = x - x0(t) (3-2)
to
t
n = y - y0 - J v(x',y',tl)dtl = y - y0(t) (3-3)
to
57
-------
where (x0,y0) is an arbitrary point and (x',y') is the the point (x,y) where
(£»n) = (o»o) at time t1. That is, x' = x0(t'), y' = y0(t'); and
(XQ> yo) is the origin in (x,y) space of the (S.n) coordinate system.
Making use of the chain rule of differentiation, namely
at at at at as at an
a as a an a ,
- = - - + - - (3-5)
ax ax as ax an
a as a an a
ay ay as ay an
We can express (3-1) in the form
— + (— -i- u — + v —) — + (— + u — + v —) — =
at at ax ay as at ax ay an
I I
2 2 ka1jcjcj (3-7)
i=l j=l
After evaluating the derivatives of S and n that appear in this equation
(using 3-1 and 3-3), we get
aca
[. u(x0,y0,t) + u(5 + x0, n + y0, t)] —
at a^
(3-8)
aca
- v(x0,y0,t) + v(i + x0, n + y0»t)] — =
I I
E
1=1
.I,kaijcicj
where the concentrations are evaluated at (z, + x0, n + y0) in (x,y) space.
58
-------
We see at once from (3-8) that at the origin of the ( £, n) coordinate
system, which is the moving point (x0 (t), y0(t)) in (x,y) space, the
solution of (3-1) is just the solution of the batch reactor equation (2-1)
that we considered earlier. This equivalence would not exist were the
horizontal diffusivity KH nonzero.
Thus, along any fluid particle trajectory, i.e., along any space-time
path [x0(t), y0(t),t] described by (3-2,3) for given initial point (x0,y0),
we can obtain the solution of (3-1) with the same precision that we
found solutions of (2-1) in the previous experiments. And we can compare
these solutions with those given by the transport/chemistry portion of the
regional model along the same paths to assess the joint accuracy of the
algorithms used in the model to describe these two processes.
The problem that we will consider in this experiment is that of an
ellipsoidal-shaped cloud of chemical species transported by a stationary
flow field whose velocity components (u,v) at any point (x,y) are given by
u = (y - y0)w (3-9a)
v = -(x - x0)w (3-9b)
where
-------
significant sources of error that are not activated unless the transported
field, in this case the species concentrations, deviates from forms that
possess axial symmetry. We want to excite all possible sources of error in
the transport algorithm so that we can see whether the disturbances that
these sources "create are amplified by the kinetics. Since we found in the
first experiment that the errors generated by the kinetics algorithm are
negligible when \ = 0.001, we will use this value in the present experiments.
It follows that any errors that arise in the joint simulation of transport
and chemistry have their origin in the transport algorithm. One of our
main interests here is to see whether the chemical kinetics amplify errors
generated by the transport algorithm and if so whether the coupling between
the kinetics and transport processes provides enough positive feedback for
errors to grow unboundedly.
The initial concentration of species a (= 1,...23) at grid point (I,J)
in the test cloud will be taken to be
ca(I,J,t0) = f(I,J)Ca(t0) (3-10)
where Ca(t0) is the concentration of species a at the center of the cloud
at the initial instant t0, and f is a fraction such that 0 < f < 1. The cloud
center concentrations Ca are the "lean mixture" values listed in Table 2.1,
page 16. Figure 3-1 shows the initial concentration distribution of CO in
the cloud at the initial instant t0. In this experiment the flow field remains
steady and the cloud is transported for a simulated period of 48 hours.
During this time there is no vertical mixing and the photolytic rate constants
vary in the diurnal manner shown in Figure 2-1, page 17. Figure 3-1 also
shows the simulated distribution of CO in the cloud at the end of the
60
-------
SIMULATED CO
IN CLOUD 2A
AT IMS HOURS
CO IN CLOUD
2A AT T» O
Figure 3-1.
Initial concentration distribution ca(I,J,t0) in the cloud
simulated in Case 2A for species a = carbon monoxide. Also
shown is ca(I,J,t0 + 48 hr).
61
-------
48-hour period. The relative positions and orientations of the cloud
at the beginning and end of the simulated period give an indication of the
speed and vorticity in the flow.
In the limited space of this report it is not practical to describe
the complete spatial and temporal structure of the simulated concentrations
of all 23 species. Therefore, in the present experiment we will focus on
the spatial variations in the concentration error field and in the next
experiments, 2B, where we add vertical mixing to the list "of processes that
we simulate, we will focus on the temporal variations.
Spatial features are seen clearest in plots of the concentrations
taken at points along cross-sections of the cloud. Figure 3-2 is an example
taken from part 1, Section 9. Shown there are numerical solutions of Eq.
3-1 for the case of a single, chemically inert species (ka-jj = 0) in a
rotating flow field of the form (3-9). The circles in Fig. 3-2 represent
the solutions obtained along the cross-section indicated in the upper
righthand corner of the figure at time t = t0 + 100 At using the biquintic
(Q) transport algorithm that we use in the regional model. The triangles
and crosses in the figure represent the corresponding solutions given by the
schemes of Zalesak (1979) (I) and Mahrer and Pielke (1978) (S), respectively,
The exact solution is represented by the straight, solid lines.
One reason for presenting this figure is to illustrate the two types
of errors in the transport algorithm that are of primary concern to us in
applications to chemically reactive species. The first is the distortion
error that is most pronounced in the solutions derived from the I and S
62
-------
r
AX
Figure 3-2.
Comparison of simulations by 3 differencing schemes of the
advection of an ellipsoidal cloud in a rotating flow. Panels a-d
display different cross-sections of the cloud (indicated by
the upper right corner of each panel) after one complete
rotation of the cloud, 100 time steps in the case of schemes
Q and S, 150 steps in the case of Z. Notation: Q (circles)
= transport algorithm used in the ROM; S (x) = transport
scheme of Mahrer and Pielke (1978); Z(A) = transport
scheme of Zalesak (1979).
63
-------
r
1.04- x EXACT
Figure 3-2. Continued.
64
-------
d
Figure 3-2. Continued.
65
-------
^.o• -
r
.8- -
.6--
*••••*••..
'•*.
EXACT
Q
Figure 3-2. Concluded.
66
-------
schemes. Since the chemical reactions are nonlinear, errors in the amplitudes
and phases of the concentration distributions can result in large errors
in the simulated chemical reaction rates. The second type of error is
negative concentrations. Both the Q and S algorithms generate errors of
this type, but the Z scheme was specifically designed to eliminate them.
Obviously, negative concentrations are inadmissable in the kinetics algorithm
because they would transform decay processes into mechanisms of chemical
production, and vice-versa. In the regional model we avoid this problem
simply by setting any negative concentrations produced by the transport
scheme to zero before they enter the kinetics algorithm. Negative
concentrations are not generated when the background concentration is larger
than the amplitude of the "undershoot" created by the transport scheme at
the edges of plumes where gradients are large. For this reason, negative
concentrations are a problem primarily with the radicals and other species-
whose background levels are normally very small. The test simulations that
we are about to present will show whether our simple procedure for handling
negative concentrations causes adverse effects.
Figure 3-3(a)-(e), pages 74-100, shows the simulated concentrations of
five principal species along the major and minor axes of the ellipsoidal
cloud at various instants during the 48-hour period. As Figure 3-1 indicates,
the cloud is transported in a direction that is about 30 degrees askew of
the minor axis. This orientation remains constant throughout the simulation
because the cloud rotates about its center at the same angular speed that it
moves around the center of the flow vortex. (The distribution of vorticity
in the flow field defined by 3-9 causes this.)
67
-------
Recall from the analyses presented at the beginning of this section
that under the conditions simulated in this problem, the true concentration
at any point in the cloud at any time t can be derived from the batch
reactor equations (2-1) treated in the previous section. For example, the
concentrations ca(xi,ti) of any species a at a given point xi in the cloud
r*i /NJ
at time t = tj is the solution of (2-1) initialized with concentrations
ca(x0,t0). Here t0 represents the initial instant in the cloud simulation
«%/
and x0 is the point on the back trajectory through xj that designates the
/>* cw
position at time t0 of the fluid parcel that is found at xj, at time t. Thus
i***
cross-sections of the true concentration in a cloud can be constructed by
solving (2-1) for each point in the cross-section. This was the procedure
used to derive the profiles of true concentration, labeled "chemistry" in
Figures 3-3 through 3-5.
Looking first at the series of CO concentration cross-sections shown
in Figure 3-3(a), pages 74-79, we see that the transport algorithm preserves
the symmetry of the cloud with a very high degree of fidelity. The only
distortions are smoothings of the cloud's sharp peak and edges. Within the
first four hours of travel, the peak concentration in the cloud drops
quickly to a value IQ% lower than the true value. However, during the
remainder of the 48-hour travel period, the error in the predicted peak
concentration grows at an average rate of only 2.5% per day. At the end of
the two day simulation, the peak concentration in the cloud is about 15%
low, which is well within the level of accuracy that we expect of the data
that are used as inputs during model applications.
68
-------
At the edges of the cloud the transport algorithm causes the
simulated concentrations to undershoot the background values by an amount
that is proportional to the concentration gradient at the cloud edge. This
is evident in the fact that the undershoot along the cloud's minor axis is
somewhat larger than that along the major axis. The worse values are only
a few percent of the cloud's center concentration. An important aspect of
the cloud edge error is that neither its amplitude nor its spatial extent
increases with time. It is also noteworthy that the error is symmetrically
distributed about the cloud.
The corresponding cross-sections of NO concentration are displayed in
Figure 3-3(b), pages 80-84. To facilitate comparison of the relative
errors from one travel time to another, we have used the same scale for the
ordinate of each of the NO concentration plots. The sequence of NO concen-
tration profiles shown in Figure 3-3(b) illustrates some of the unusual
phenomena created by the nonlinear chemical processes that are possible
sources of serious errors in the transport simulation. We see first that
following the initial hour 0000, day 215, the NO concentrations decrease
until at hour 0400, day 215, the peak concentration has fallen to a value
only one quarter its original value. By 0800, day 215, which is 2 hours
after sunrise, the NO concentrations have increased abruptly to levels ten
times the initial ones; and the distribution of concentration within the
cloud has changed from its initial pyramid form to a tooth-shaped pattern
with a concentration deficit at the center of the cloud and a ridge of high
concentrations surrounding the center. The Figure shows that the transport
algorithm captures the true shape of the cloud quite well. The largest
error is at the cloud center where the model overpredicts the true concen-
tration by about 10%.
69
-------
From the standpoint of the transport algorithm, the most significant
aspects of the change in the cloud's shape is the intensification of
concentration gradients around the cloud's edge. We saw earlier that the
magnitude of the concentration undershoot just outside the cloud is
proportional to the concentration gradient at the cloud's edge. It is not
surprising then that the errors in the simulated NO concentrations just
outside the cloud are larger than those produced in the simulation of CO.
Figure 3-3(b), page 82, shows that at hour 0800, day 215, the NO undershoot
attains a maximum amplitude, coinciding with the time of peak NO concentrations
inside the cloud. At this point the undershoot is about 15% the peak value
in the cloud. An interesting aspect of the error field surrounding the
cloud is the apparent absence of chemical change. The plots shown in
Figure 3-3(b) for hours 1200 and 1600, day 215 (pages 83 and 84), indicate
that the magnitude of the NO undershoot remains virtually unchanged for 8 '
hours or longer following its generation even though NO levels within the
cloud are declining during this entire period. By hour 1600, the undershoot
is as large as the amplitude of the cloud itself. However, in absolute
terms the magnitude of the undershoot is only of the order of 10~5 ppm NO,
a value much too low to have significant effects on the chemistry overall.
This conclusion is supported by the results of the ozone simulation
shown in Figure 3-3(c), pages 85-91. Throughout the simulated 48-hour
period, the model reproduces the ozone concentration with a precision
greater than about 95% over the body of the cloud. Subsequent to hour
0800, day 215, when the simulated NO achieves the largest undershoot at the
cloud's edges, Figure 3-3(c) shows that the ozone cloud base begins to
70
-------
broaden until by the end of the 48-hour period it is about 1 grid cell
wider than it started out. This is apparently a direct consequence of the
underestimated NO concentrations around the cloud's base; because the
chemical reaction NO + 03 ->• NOg + Og causes an inverse relationship between
the concentrations of NO and 03. In any event, the fractional error in the
simulated 03 levels at the cloud base are much smaller than those that we
found in NO.
Figures 3-3(d), pages 92-96, and 3-3(e), pages 97-100, show the simulated
N02 and olefin concentration distributions, respectively. Both of these
species are nearly completely consumed by chemical reactions well before
the end of the 48-hour simulation. During the time they are present, the
model reproduces their concentration distributions with the same level of
precision that it handled the other three species that we just discussed.
In the last two pages of Figure 3-3(e), which show the olefin concentration
results, we have added inserts that bring out details in the cloud cross-
sections when concentration has fallen to very low values. The results
show that the model's accuracy remains high throughout the period of declining
concentration.
Case 2B: Chemistry with transport and vertical mixing
In this experiment we extend the range of testing by adding vertical
turbulent mixing to transport and chemistry. The conditions here are the
same as in experiment 2A, except that rather than being confined to layer 1
for the duration of the 2-day simulation, the pollutant cloud is allowed to
mix virtually instantaneously with clean air in layer 2 above. This is
71
-------
done at hour 12 of the first day by abruptly changing the value of the rms
vertical turbulent velocity on the interface between layers 1 and 2 from
zero to a large value. Since layer 2 is 1000 m deep and layer 1 is only
300 m thick, mixing causes a reduction of the concentrations of all species
by about three-fourths.
Two elliptical clouds of the form treated in experiment 2A are considered
here. Their initial locations and subsequent trajectories are illustrated
in Figure 3-4, page 101. The initial concentration distribution in each cloud
has the form (3-10) (see page 57), with one cloud, which we shall refer to
as 2B.L, having the "lean" mix of Ca(t0) values at its center (see
Table 2.1, page 14); and the other cloud, 2B.R, having the "rich" mix of
Ca(t0) values listed in Table 2.1.
Cross-sections of the predicted ozone concentration in cloud 2B.R are-
shown at selected travel times in Figure 3-5, pages 102-108, in the same
format that we used in Figure 3-3. Simulated concentrations of CO, NO, 03,
N02, olefin, and PAN in clouds 2B.L and 2B.R are shown in Figure 3-6, 7 and
8 (pages 109-126) in the form of time histories following three different
points in each cloud. One point is the cloud center, one is midway between
the center and the edge, and the third point an outermost grid point.
These points and their resultant trajectories are illustrated in Figure
3-4 (page 101). The concentrations plotted in Figure 3-6, 7 and 8 were
obtained by interpolating the model output at points along each trajectory.
And the true solutions, labeled "chemistry" in the Figures, are the solutions
of the batch reactor equations (2-1) initialized with the cloud species
concentrations at the starting point of each trajectory.
72
-------
The quality of the model's performance in experiment 2B is not
significantly different from that found in experiment 2A.
We conclude from these combined tests of the transport, chemistry and
vertical mixing algorithms that the solutions of the combined transport and
chemistry equation (3-1) produced by the model are good facsimiles of the
true solutions over the range of species concentration values that we are
likely to encounter in actual problems. Among the species CO, 03, NO, N0£
and olefin, the largest error in the simulated concentration within the
cloud was found for CO. In this case the peak concentration was underestimated
by about 15%. For the other species the largest errors were between 5 and
10%. No evidence was found of adverse effects arising from the undershooting
of concentration outside the edges of clouds, which is a characteristic of
the algorithm used to treat the advection terms in the governing equations.
The principal effect was a slight broadening of the simulated ozone cloud.
Although our conclusions apply strictly to the rather limited conditions
that we have considered here, these tests nevertheless constitute essential
necessary conditions for model validity. Considering the quality of the
model performance shown and the invariance of this quality over the range
of conditions that we considered, we are confident that the model can handle
generalized flow fields, diffusion, vertical mixing and species concentrations
with comparable accuracy. One aspect that we have not yet treated is the
ability of the model to simulate continuous, discrete sources of pollutants.
We consider this in the next section.
73
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 000000
CHEMISTRY
NEROS
CO
CONCENTRATION
(PPM X101 )
HOD 1190 1100 14dO 1000 1100 1730 1130 1MB
I I I I I I I I I I I I 1 I I I
10:12 10:13 10:1+ 10:15 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:23 10:24 10:25 10:26 10:27 10:28
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(a).
Initial concentration of CO in cross-sections of the cloud
simulated in experiment 2A. Diagrams in the upper right
corner of each panel indicate the location of the cross-
section within the cloud. The curves labeled "chemistry"
represent the true solution.
74
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 040000
CHEMISTRY
NEROS
CO CONCENTRATION
(PPM X101 )
2A
I I I I I I I I II I I I I I
10:12 10:13 10:1+ 10:13 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:23 10:2+ 10:23 10:26 10:27 10:28
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(a). Continued. Travel time = 4 hours,
75
-------
TEST : CLOUD ADVECT10N TEST
DATE : 79215
HOUR : 080000
CHEMISTRY
HERDS
CO CONCENTRATION
(PPM X101 )
2A
i—i—i—i—i—i—i—i '—i—i—i—i 1—i r .
10:12 10:13 10:14 10:13 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:23 10:2+ 10:23 10:28 10:27 10:28
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(a). Continued. Travel time = 8 hours,
76
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 160000
CHEMISTRT
NEROS
CO CONCENTRATION
(PPM X101 )
2A
1000 nao ixao nao i4
-------
TEST : CLOUD ADVECTION TEST
DATE : 79216
HOUR : 120000
CHEMISTRY
NEROS
CO CONCENTRATION
(PPM X101 )
2A
II I I I _!.. .1.. !
I
. "I 1 1 1 1 1 1 1 1 1 1 1 1 T .
10:12 10:13 10:14 10:13 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:23 10:24 10:23 10:28 10:27 10:28
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(a). Continued. Travel time = 36 hours.
78
-------
TEST : CLOUD ADVECT10N TEST
DATE : 79217
HOUR : 000000
CHEMETRV
NEROS
CO CONCENTRATION
(PPM X101 )
2A
aatiaatafaaataataataanauaa'^p r~— •••« ana iaaa uoe uoo uao t«n nao 1*30 at
CHEMISTRY
NEROS
2A t
I I I I I I I I IT I I I I
10:12 10:13 10:14 10:13 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:23 10:24 10:25 10:28 10:27 10:28
CLOUD CELL LOCATION (ROWrCOLUMN)
Figure 3-3(a). Concluded. Travel time = 48 hours,
79
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 000000
CHEMismr
NEROS
NO CONCENTRATION
(P|M X104 )
1—
2A
MO
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 040000
NO CONCENTRATION
(PEM X104 )
CHEMISTRT
NEROS
BOD too too aea too
2f\
too 730 KK> MD 1000 \\aa not laao i«oo inao laoa trao i» i»
CHEMISTRY
NEROS
1-4-
2A ,
10:12 10:t3 1ttt4 10:13 1(KI6 10:17 10:18 10:18 1020 1021 1022 10:23 ia-2+ 10:23 1028 10:27 10:28
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(b). Continued. Travel time = 4 hours,
81
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 080000
CHEMISTRY
NEROS
NO CONCENTRATION
(PEM X104 )
rau tau »ai 1000 uao iiao -.x» iwo 1000 itao ma iiaa IMD xaa
l i iiiiii i r i i r r r
70:12 10:13 10:14 10:13 10:18 10:17 10:18 10:19 1020 1021 1CKZ2 1033 1024 1023 1026 1027 1028
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(b). Continued. Travel time = 8 hours,
82
-------
TEST : CLOUD ADVECT10N TEST
DATE : 79215
HOUR : 120000
NO CONCENTRATION
(P|M X104 )
CHEMISTRY
NEROS
1
cattiaBtaoaaotaotaoiaaTaatae**
\\o
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 160000
CHEMISTOlT
NEROS
NO CONCENTRATION
(PEM X104 )
1~
—1—1—I—I—1—I—
139 an aaa too too tag ran
2A
ing itao inn tag i«o woo i«ag i?ao ita itsa aaa
CHEMISTRY
NEROS
1
2A t
10:12 10:13 10:14 10:13 10:18 10:17 10:18 10:19 10:20 10:21 10:22 1023 1024 10:25 10:26 1027 1028
CLOUD CELL LOCATION (ROWrCOLUMN)
Figure 3-3(b). Concluded. Travel time = 16 hours.
84
-------
TEST : CLOUD ADVECT10N TEST
DATE : 79215
HOUR : 000000
CHEMISTWT
NEROS
02 CONCENTRATION
1
(PEM X101 )
t T"
14-
2A
aaa\aaaaaaaiaoiaa»aotatiaoiaa icon »ao 1100 ixn i«a tun i
CHEMlSTWr
NEROS
14-
I I 1 I" I I I I I I I ~ I ~ T 1 1 1 1
10:12 10:13 10:14 10:13 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10^3 10:24 10:25 10:26 1027 10:28
CLOUD CELL LOCATION (ROW-.COLUMN)
Figure 3-3(c).
Initial concentration of ozone in cross-sections of the cloud
simulated in experiment 2A. Diagrams in the upper right
corner of each panel indicate the location of the cross-
section within the cloud. The curves labeled "chemistry"
represent the true solution.
85
-------
TEST : CLOUD ADVECT10N TEST
DATE : 79215
HOUR : 020000
CHEMISTRY
NEROS
03 CONCENTRATION
(P|M X101 )
CHEM1STRT
NEROS
2A
I [ i i i I i
ioa lisa isao i«o loao ios» 1799 moo itao axao
1
2A ,
i i i r i i i i i i i i i i i i
10:12 10:13 10:14 10:13 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:23 10:24 10:23 10:26 10:27 10:28
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(c). Continued. Travel time = 2 hours.
86
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 120000
CHEMISTRT
NEROS
03 CONCENTRATION
X101 )
i i i ill
Moie»2ao«n««i«ao»aaTao«aowD 1000 iiao IBM 1*» 1*00 iua inoo irao iaao man 2000
CHEMISTRY1
NEROS
I I I Till! I T I I I I T
10:12 10:13 10:1+ 10:15 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:23 10:24 10:23 10:26 10:27 10:28
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(c). Continued. Travel time = 12 hours.
87
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 160000
CHEMISTRY
NEROS
03 CONCENTRATION
X101 )
2A
I I I ! I I
1009 11SB 1MO 1320 1400 1KB 1UO 1738 1K20 1MB 2K»
I I I I I I I I I I 1 I
10:12 10:13 10:1 + 10:1S 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:23 10:24- 10:25 10:26 10:27 10:28
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(c). Continued. Travel time = 16 hours.
88
-------
TEST : CLOUD ADVECTION TEST
DATE : 79216
HOUR : 000000
CHEMISTOY
NEROS
03 CONCENTRATION
(PBM X101 )
10:12 10:13 10:14 10:15 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:23 10:24 10:25 10:26 10:27 10:28
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(c). Continued. Travel time = 24 hours.
89
-------
TEST : CLOUD ADVECTION TEST
DATE : 79216
HOUR : 120000
03 CONCENTRATION
(P|M X101
CHEMISTRY
NEROS
1039 1130 1230 1300 \tOO 1KB 1MO IT-JO 1*20 1MO 2090
1 1
10:12 10:13 10:14 10:15 10:16 10:17 10:13 10:19 10:20 10:21 10:22 10:23 10:24 10:25 10:26 10:27 10:2S
CLOUD CELL LOCATION (ROWrCOLUMN)
Figure 3-3(c). Continued. Travel time = 36 hours.
90
-------
TEST : CLOUD ADVECT10N TEST
DATE : 79217
HOUR : 000000
CHEMISTRY
NEROS
03 CONCENTRATION
(P|M_X101
I I I I I I I ! I
1000 1100 iea 1*30 twa 1100 i«an traa 1000 iwo 2000
1 1 T~ I I I i I I ~" I 1 1 1 1 1
10:12 10:13 10:14 10:15 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:23 10:24 10:23 10:26 10:27 10:28
CLOUD CELL LOCATION (ROWrCOLUMN)
Figure 3-3(c). Concluded. Travel time = 48 hours.
91
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 000000
CHEMISTRT
NEROS
N02 CONCENTRATION
i i i i i i i i i r i i i i
10:12 10:13 10:1+ 10:13 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:2J 10:24 10:23 10:26 10:27 10:28
CLOUD CELL LOCATION (ROWrCOLUMN)
Figure 3-3(d). Initial concentration of N02 in cross-sections of the cloud
simulated in experiment 2A. Diagrams in the upper right
corner of each panel indicate the location of the cross-
section within the cloud. The curves labeled "chemistry"
represent the true solution.
92
-------
TEST : CLOUD ADVECT10N TEST
DATE : 79215
HOUR : 020000
CHEMISTRY
NEROS
N02 CONCENTRATION
)
10:12 10:13 10:14 10:13 10:16 10:17 10:18 10:18 10:20 10:21 10:22 10:23 10:2+ 10:23 10:28 10:27 10:28
CLOUD CELL LOCATION (ROWrCOLUMN)
Figure 3-3(d). Continued. Travel time = 2 hours.
93
-------
TEST : CLOUD ADVECT10N TEST
DATE : 79215
HOUR : 040000
N02 CONCENTRATION
(PEM X103 )
CHEMISTRY
NEROS
2A
iota nan iz» i3ao i«a ttoo iota iTao iiba IMO 2000
!1 "1 " i ! I I
10:12 10:13 10:14 10:15 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:23 10:2+ 10:23 10:26 10:27 10:28
CLOUD CELL LOCATION (ROWrCOLUMN)
Figure 3-3(d). Continued. Travel time = 4 hours.
94
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 12QOOO
CHEMISTRT
NEROS
N02 CONCENTRATION
(P|MX1Q3
2A
r r i T [ T i T r i r i i T i i ;
taotaotaoaaataaiatiaaraataoiao 1000 1100 izao ixa i«ao IBOO rat i«o 1100 IKH ma
CHEMISTRY
NEROS
6-h
2A i
4-t-
1-h
i r
10:12 10:13 10:14 10:15 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:23 10:24 10:23 10:26 10:27 10:28
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(d). Continued. Travel time = 12 hours.
95
-------
TEST : CLOUD ADVECTION TEST
DATE : 79216
HOUR : 000000
CHEMISTRT
NEROS
N02 CONCENTRATION
(P|M_X103 )
2A
CHEMISTRY
NEROS
2A *
T
41
'
I I i \ l ! I ! | j 1 1— I '.', , i
10:12 10:13 10:1+ 10:13 10:16 10:17 10:18 10:19 10:20 10:21 10:22 10:23 10:24 10:23 10:26 10:27 10-28
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(d). Concluded. Travel time = 24 hours.
96
-------
TEST
DATE
HOUR
CLOUD ADVECTION TEST
79215
000000
CHEMISTRY
NEROS
OLE
CONCENTRATION
(P|M XIO'1 )
2A
i—i—r
10:12 10:13 10:14 10:13 10:18 10:17 10:18 10:19 1020 1021 1022 1023 1024 10:23 1026 1027 1028
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(e).
Initial concentration of olefin in cross-sections of the
cloud simulated in experiment 2A. Diagrams in the upper
right corner of each panel indicate the location of the
cross-section within the cloud. The curves labeled
"chemistry" represent the true solution.
97
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 04QQOO
CHEMISTRT
NEROS
OLE CONCENTRATION
(P|M X103 )
2A
I I I 1 I I I I I I I I I 1^ II
10:12 10:13 10:14 10:15 10:18 10:17 10:18 10:19 1020 10:21 10^2 10:23 10^4 10-^3 1026 10^7 1028
CLOUD CELL LOCATION (ROWrCOLUMN)
Figure 3-3(e). Continued. Travel time = 4 hours.
98
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 080000
OLE CONCENTRATION
(P|MX104
OLE CONCENTRATION
(PEM X103 )
2A
CLOUD CELL LOCATION (ROW.-COLUMN) -j
1-1-
10:12 10:13 10:14 10:13 10:18 10:17 10:18 10:19 1030 10-21 10:22 10:23 10:24 10:23 10-28 10:27 10:28
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-3(e). Continued. Travel time = 8 hours. Insert in upper
panel is magnified plot of major axis cross-section,
99
-------
TEST : CLOUD ADVECTION TEST
DATE : 79215
HOUR : 120000
CHEMISTRY
NEROS
OLE CONCENTRATION
(P|M_X103 )
2A
OLE CONCENTRATION
(P|MX105 )
2A t
CLOUD CELL LOCATION (ROW:COLUMN)
, -j
1031 mi
CLOUD CELL LOCATION (ROWrCOLUMN)
Figure 3-3(e).
Concluded. Travel time = 12 hours. Insert in lower panel
is magnified plot of minor axis cross-section.
100
-------
2B.R
Figure 3-4.
Initial CO concentration in clouds 2B.L and 2B.R. Arcing lines
labeled E, M, and C are 48-hour trajectories of points originating
at the edge, midpoint, and center, respectively, of each cloud.
101
-------
TEST : DILUTION SIMULATION TEST
DATE : 79215
HOUR : 000000
03 CONCENTRATION
X101 )
CHEMISTRY
NEROS
i
2B.R
CHEMISTRY
NEROS
2B.R ,
1 I I 1 I I i I i i I I I . ,
9:22 9:23 9:24 9:25 9:26 9:27 9:28 9:29 9:10 9:31 9:32 9:33 9:34 9:35 9:36 9:37 9:38
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-5. Initial cross-section of ozone concentration in cloud 2B.R.
Diagrams in the upper right corner of each panel show the
location of the cross-section in the cloud. Curves labeled
"chemistry" represent the true solution.
102
-------
TEST : DILUTION SIMULATION TEST
DATE : 79215
HOUR : 040000
CHEMISTRY
NEROS
03 CONCENTRATION
X101 )
2B.R
2-4-
T I i T T I II Illllllil I
-MO -iao iaa tat «o wo ud MB rat mat tea 1000 mo luo iug man tuo iuo inia i«JO two
NEROS
2B.R ,
i I i i r i r r i i i i i
9:22 9:23 9:24 9:25 9:26 9:27 9:28 9:29 9:30 9:31 9:32 9:33 9:34 9:35 9:36 9:37 9:38
CLOUD CELL LOCATION (ROWrCOLUMN)
Figure 3-5. Continued. Travel time = 4 hours (Case 2B.R).
103
-------
TEST : DILUTION SIMULATION TEST
DATE : 79215
HOUR : 120000
03 CONCENTRATION
(P|M X101
CHEMISTRY
NEROS
-aa -wo t-jo lot *» wo wo tan rat taa MO itug HJO two tua
9:22 9:23 9:24 9:25 9:26 9:27 9:28 9:29 9:30 9:31 9:32 9:33 9:34 9:35 9:36 9:37 9:38
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-5.
Continued. Travel time = 12 hours. Vertical mixing between
layers 1 and 2 begins at this instant. (Case 2B.R).
104
-------
TEST : DILUTION SIMULATION TEST
DATE : 79215
HOUR : 160000
03 CONCENTRATION
(P|M X101 )
CHEMISTRY
NEROS
r i i i I
-MO -iso tan wo MB
CHEMISTW
NEROS
2B.R
III ! I I I I ! I I I I
uo Taa *jo MO ituo ttao mo IUD mx isuo itn irjo IKJO IK
EB.R
I 1 1 1 1 i 1 1 1 1 1 1 1 1 ! 1
9:22 9:23 9:24 9:25 9:26 9:27 9:28 9:29 9:30 9:31 9:32 9:33 9:34 9:35 9:36 9:37 9:38
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-5. Continued. Travel time = 16 hours, 4 hours after mixing
(Case 2B.R).
105
-------
TEST : DILUTION SIMULATION TEST
DATE -.79216
HOUR : 000000
03 CONCENTRATION
(PBM X101 )
CHEMISTRY
NEROS
2B.R
•on TOO auo wo ID-JO 1130 IZJQ uuio iwo iua mo inn iajo i»jo
CHEMISTRY
NEROS
2B.R i
. 1 i 1 i ! 1 1 1 T
9:22 9:23 9:24 9:25 9:26 9:27 9:28 9:29 9:30 9:31 9:32 9:33 9:34 9:35 9:36 9:37 9:38
CLOUD CELL LOCATION (ROWrCOLUMN)
Figure 3-5. Continued. Travel time = 24 hours (Case 28.R).
106
-------
TEST : DILUTION SIMULATION TEST
DATE : 79216
HOUR : 120000
03 CONCENTRATION
(P|MJX101 )
CHEMISTWT
NEROS
2B.R
toe too IB* uao its) ion i«a iuo iuo IT-JO IKH two
1 1 1 1 1 1 I I 1 1 1 1 1 1 1
9:22 9:23 9:24 9:25 9:26 9:27 9:28 9:29 9:30 9:31 9:32 9:33 9:34 9:35 9:36 9:37 9:38
CLOUD CELL LOCATION (ROW:COLUMN)
Figure 3-5. Continued. Travel time = 36 hours.
107
-------
TEST : DILUTION SIMULATION TEST
DATE : 79217
HOUR : 000000
03 CONCENTRATION
(P|M
M X10
CHEMISTRY
NEROS
2B.R
-tat -ma ijo £» Juo «o too «uo ran KB KB ioao mo i&jg iuo I«JD iajo iam true IK» HOD
CHEMISIHY
NEROS
6-T-
S-t-
2B.R ,
. 1 i i i 1 1 1 1 1 r
9:22 9:23 9:24 9:25 9:26 9:27 9:28 3:29 9:30 9:31 9:32 9:33 9:34 9:35 9:36 9:37 9:38
CLOUD CELL LOCATION (ROWrCOLUMN)
Figure 3-5. Concluded. Travel time = 48 hours, 36 hours after mixing
(Case 2B.R).
108
-------
~
-------
CHEMISTRY
ROM..
2B.L
T=0
8 12 16 20 24
8 12 18 20 24 48 12 i 6' ' '20' ' '24'
DAY 1
DAY 2
DAY
TIME (HOUR OF DAY)
Figure 3-6(b).
Time histories of NO concentration following the center of
cloud 2B.L, top, and cloud 2B.R, bottom. Curve labeled
"chemistry" represents the true solution.
110
-------
o
X
CL
CL
O
I'
UJ
a
z
o
o
T=0
CHEMISTRY
ROM
2B.L
12
16 20 24
12
16
20
24
12 15 20 24
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 3-6(c). Time histories of ozone concentration following the center
of cloud 2B.L, top, and cloud 2B.R, bottom. Curve labeled
"chemistry" represents the true solution.
Ill
-------
T=0
CHEMISTRY
ROM
2B.L
_ 2|
O
X
Q_
Q_
UJ
O
z:
O
O
CN
O
T=48hc
CHEMISTRY
ROM
2B.R
r=o
12
DAY 1
16
20
24
12
DAY 2
16
20
24
j DAY 2
TIME (HOUR OF DAY)
Figure 3-6(d).
Time histories of N0£ concentration following the center
of cloud 2B.L, top, and cloud 2B.R, bottom. Curve labeled
"chemistry" represents the true solution.
112
-------
O
X
CL
Q_
g
tc
LU
O
2
O
O
UJ
O
CHEMISTRY
ROM
2B.L
T=0
4 8 12 16 20 24 4 8 12 16
8r
CHEMISTRY
?(_ -i^^RQM
2B.R
T=48V>r
DAY 1
DAY 2
TIME (HOUR OF DAY)
T=4SKr
20 24
8 12 16 20 24 4 3 12 16 20 24
DAY
Figure 3-6(e). Time histories of olefin concentration following the center
of cloud 2B.L, top, and cloud 2B.R, bottom. Curve labeled
"chemistry" represents the true solution.
113
-------
O
X
Q.
Q-
o:
-z.
uu
O
z:
o
O
CHEMISTRy
ROM
2B.L
T=0
12 16 20 24
12 16 20 2+
O
V—
X
Q-
Q_ p
O 3
o:
z: 2i
LU ^
O .
§ r
o f
< r
Q_
2B.R
T=0
i i i i i i i i i i i i i i
4 8 12 16 20 24 4 S 12 16 20 24
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 3-6(f).
Time histories of PAN concentration following the
center of cloud 2B.L, top, and cloud 2B.R, bottom.
Curve labeled "chemistry" represents the true solution,
114
-------
O
X
T
CHEMISTRY
r
Q_ L
2B.L
Ld
O
-z.
O
o
o
o
XX
IE
Q_
~z.
o
r
r—
1 —
z:
LJ
O
O
0
0
i
1
L
1
i —
i
t-
t-
nlm i i » 1 < i ' 1 ' i ' 1
U 4 8 15
10r-
t CHEMISTga
9(. ROM/
I" — ^
8f
h
t
6~:
5r
4P-
h
3r
2r
F
1H-
p
(-»r ILI i ^ i 1 i i i
u 4 S 1
I DAI
*•
i i ^ 1 i i i 1 i i i 1 i i i I i i i 1 i i . i 1 i i i 1 i .1 i 1 i. i i 1 i _i
! 16 20 24 4 8 12 16 20 24
OD D T=48Kr
^^^^ /r^
[ \1*
\_^*^
iHii
T=0 lip
1 | | 1 1 1 1 ' 1 i 1 1 1 ! 1 | ! 1 | | I 1 | | 1 1 1 ! 1 1 | i ! 1 ! [ J
2 16 20 24 4 8 12 16 20 24
' 1 i DAY 2 ,
TIME (HOUR OF DAY)
Figure 3-7(a).
Time histories of CO following the midpoint of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution.
115
-------
CHEMISTRY
ROM
2B.L
8 12 16 20 24
2B.R
T=0
T*48
3 12 16 20 24
T=0
8 12 16 20 24 ~4 " 3 '""12 16 20 24~
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 3-7(b).
Time histories of NO following the midpoint of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution.
116
-------
T=0
2B.L
T*48
, t , , , i i i , i , , i. i i , , i , ..... i , , , i , , i i , , , i , , , i , , , f . , , i , ,
4 8 12 16 20 2+ 4 3 12 16 20 24
o t
X
£f
H
It
§ t.
o r
z '-
O f-
O r
ro i-
O P
r,tL_
CHEMISTOY
ROM
2B.R
T«48W
0
T-0
•V^ 'a' ' ','2' ' ','s1 ' '2V— -2V—V—i—^'2—iV ' '2'0' ' "iV"
DAV 1-
DAY 2
TIME (HOUR OF DAY)
Figure 3-7(c).
Time histories of ozone following the midpoint of cloud 28. L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution.
117
-------
CHEMISTRY
ROM
T=0
2B.L
T*48
8 12 16 20 24
TIME (HOUR OF DAY)
Figure 3-7(d).
Time histories of N02 following the midpoint of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution.
118
-------
O ft CHEMISTO*
X 7h\ "CM
T=0
2B.L
T*48
8 12 16 20 24
8 12 16 20 2+
DAY 2
TIME (HOUR OF DAY)
Figure 3-7(e).
Time histories of olefin following the midpoint of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution.
119
-------
T=0
2B.L
T>48
3 12 16 20 24
TIME (HOUR OF DAY)
Figure 3-7(f).
Time histories of PAN following the midpoint of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution.
120
-------
T=0
0 t
X 7h
CHEMISTRY
UJ Sf-
O L
z: r
O £-
o -
ROM
2B.L
O
O
0L
-* «r
O r CHEMISTRY
X f ROM
^> —
a. 3h._ ^_
' i , -~
v~
Z h
-
"8" 12 16 '20 "" 24." 4 3 12 16 20 2T"
2B.R
T=0
Ld i-
" r
O
O
-
r\\ i i L 1 i :
i
8 '2 '6 20 24
DAY 1
i . I
- 3 <2 '6 20 2i
D^Y 2
Figure 3-8(a).
Time histories of CO following the edge point of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution.
121
-------
T=0
2B.L
1 I 1 I I 1 ! I U^Tl I , , , I ! , .-I ,
TIME (HOUR OF DAY)
Figure 3-8(b).
Time histories of NO following the edge point of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution.
122
-------
X
\JA
r\ r^> i
2B.L
O 3r
% i
£ E
5f
o E
z: L-
o •-
0 1E-
h
rO H
o
T=0
8 12 16 20 24
Figure 3-8(c).
Time histories of ozone following the edge point of cloud 28.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution.
123
-------
1*5
o
CHEMiSTOY
ROM
T=0
2B.L
T*48hr
8 12 16 20 24
Ol ... I ... I ... IT
U 4 8 12
16 20
DAY 1
3 12 16 20 24
DAY_2 - DAY 3
"!ME (HOUR Qr DAY)
Figure 3-8(d).
Time histories of N02 following the edge point of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution.
124
-------
T=0
X
O
2B.L
X
I I 1 I | | I | | TM |. . | I 1 I I I ' I I I I I I. I ' I I ! ' i I I I I ' I • I I I I I ' I I I I
4 8 12 16 20 24 4 8 12 16 20 24
CHEMISTRY
2B.R
c?
\
_,V
4 3 12 '6 20 24
DAY 1 ;
3 '2 16 2D 24
DAY 2 , DAY
TIME (HOUR OF DAY)
Figure 3-8(e).
Time histories of olefin following the edge point of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution.
125
-------
O
X
CHEMISTRY
ROM
T=0
2B.L
h
r
+ 8 12 16 20 24 4 a 12 16 20 24
2B.R
T=0
DAY 5
Figure 3-8(f).
Time histories of PAN following the edge point of cloud 2B.L,
top, and 2B.R, bottom. Curves labeled "chemistry" represents
the true solution.
126
-------
SECTION 4
Case 3A: Chemistry with transport and continuous sources
The earlier experiments 1A, 2A and 2B investigated the ability of the
transport and chemistry algorithms to handle the homogeneous forms of their
differential equation counterparts. That is, situations in which pollutant
species concentrations change only as a consequence of chemical reaction,
horizontal transport or vertical mixing, but not source emissions. Since
the primary role of the regional model is to assess the changes in air
quality that would accompany given changes in the strengths of anthropogenic
sources, it is essential that the model possess the ability to simulate
accurately the fate of species released at arbitrary sites and times within
the model domain. This is the feature we will examine in experiment 3A.
One might assume that since our model can simulate isolated clouds
well, it could automatically handle the sequences of puffs that compose the
plumes produced by continuous sources. But this is not necessarily the
case. In independent studies Schere (1984) and Yarmartino (1984) found
that when applied to a continuous source in a uniform flow, the Zalasak
(1979) scheme discussed earlier produced a sequence of large clouds rather
than a continuous plume. The cause of this error is not certain but it is
likely due to the mechanism built into the scheme that prevents concentrations
from becoming negative. - -
As we noted earlier, our transport algorithm can generate negative
concentration; but when this happens we merely reset the values to zero.
127
-------
It has been argued that this procedure is unacceptable because it leads to
a violation of mass conservation in the simulated species. In our case the
the deviations in total mass are typically no larger than a few percent.
Indeed, we found no evidence in experiments 2A and 28 that the total mass
error is large enough to create significant errors in predicted 03, NO or
any of the other principal pollutants. In experiment 3A, we will consider
this matter further.
The generation of negative concentrations is associated with truncation
error in the transport algorithm. We saw in experiments 2A and 2B that the
magnitude of this error is proportional to the spatial gradients in
concentrations. Since the grid size of the ROM is about 18 km, there are
a number of sites in the grid network where one cell contains an entire
small city or source complex while surrounding cells contain few if any
sources. These situations create maximal spatial concentration gradients .
and hence maximal truncation error. Of particular concern to us are
situations in which neighboring, isolated sources produce parallel plumes.
It is conceivable that the truncations error in these instances could cause
enough lateral exchange of species between plumes that the chemistry
simulation would be adversely affected. We will investigate this matter
in experiment 3A.
Another possible source of error that we want to examine is the method
used to handle the outflow boundaries of the model domain. Although the
differential equation that describes advection does not permit the imposition
of restrictions at outflow boundaries, the discrete equation that we use to
model the differential equation requires such values. Therefore, unless the
outflow conditions on the discrete equation, i.e., the transport algorithm,
128
-------
are properly chosen, the solutions produced by the model will not be accurate
facsimiles of the advection process. In experiment 3A we will examine
situations where plumes pass through the lateral boundaries of the domain.
A final question of interest is the rate at which errors grow in the
simulated plume with travel time — vis-a-vis model applications to multiday-
long distance transport — and the compounding of error that might result
as a plume encounters a new source after traveling for a day or more.
To summarize, our objectives in experiment 3A are:
(1) To examine the ability of the transport algorithm to simulate simple
continuous source plumes over multi-day travel periods;
(2) To examine the effects of truncation error on the simulation of parallel
plumes from isolated sources;
(3) To determine the rate of error growth in plumes with travel time and any
compounding of error upon interaction of a plume with distant sources;
(4) To investigate error levels at outflow boundaries;
(5) To assess the impact of errors caused by the clamping of negative
concentrations in the transport algorithm.
The experiment that we have devised to attain all these objectives is
as follows. A collection of four "line" sources of various widths,
illustrated in Figure 4-1, emit hydrocarbons and NOX steadily into a flow
field identical to that employed in experiments 2A and 2B, namely a fluid
in solid body rotation of angular speed oo = 0.02 radians/time step (= 30 min).
In physical terms, this represents a wind speed of about 7 km/hr at the
center of the line source nearest the center of the flow vortex, i.e.,
source e (see Figure 4-1); and a speed of about 18 km/hr at the outermost
129
-------
b
c
jf
i/a
i/a
SOU RCE
STRENGTHS
(SEE TABLE 4-1 )
CO
DOMAIN
BOUNDARY
Figure 4-1.
Locations and relative strengths of 4 line sources (b, c, e,
and f) simulated in experiment 3A. Flow speed u = .02 radian
per time step.
130
-------
source b. The emission rate of each grid cell that composes a source is
the product of the fraction shown in Figure 4-1 beside that cell and the
base emission rates given in Table 4-1, page 132. The latter represent the
highest actual emissions observed in the geographical area covered by the
regional model. Specifically, they were taken from the emissions inventory
at a cell in the vicinity of New York City.
The experiment simulates a 58-hour period during which solar radiation
varies in the diurnal fashion implicit in the rate constants plotted in
Figure 2-1, page 17. During the entire simulation, pollutants are confined
to layer 1 which has a constant, uniform depth of 300 meters in this experiment,
The emissions and meteorological conditions simulated in this experiment
have deliberately been made extreme so that error sources in the model will
be stimulated as strongly as is ever likely during actual applications.
Consequently, the error levels exhibited in this test should provide a good
measure of the upper bound that we could expect in actual applications.
The rationale for the sizes and locations of the sources shown in
Figure 4-1 that are used in experiment 3A is as follows. First, sources b,
c, and e are positioned so that in the rotating flow field their plumes
will move parallel to each other with a distance of about 3 grid cells
separating each plume. The widths of these sources have been made different
(2, 3, and 5 grid cells widths, respectively) so that we can measure the
sensitivity of the model's accuracy to the widths of the sources simulated.
Plumes b, c, and e will also allow us to infer the extent of lateral
exchange of species among plumes due to truncation error effects.
131
-------
Table 4-1. Base emission rates of species used for line sources
in experiment 3A. The emission rates of individual
source cells are fractions (1/3, 1/2, 2/3, or 1) of
the values shown here (see Figure 4-1).
Species Emission rate (ppm » m * sec"l)
NO 4.91 • ID"3
N02 3.56 . 10"4
Olefin 1.53 • 10~3
Paraffin ^ 3.21 • 10~3
Aldehyde 2.52 . 1(H
Aromatic 5.65 • 10'4
CO 5.55 • lO-2
132
-------
Source f has been positioned so that the edges of the plumes generated
by sources c and e will pass over the edges of source f after a travel time
of about 40 hours. With this configuration of sources we will be able to
measure the extent to which errors in the simulation of plume edges are
compounded when plumes impact new sources after prolonged periods of travel.
Finally, source b, the narrowest of the four sources, is positioned so that
its plume will encounter no additional sources and will pass through the
southern boundary of the model domain after a travel time of about 48 hours.
The behavior of this plume will provide information not only on the magnitude
of errors at outflow boundaries but also on the rate of growth of total
error under the most severe conditions of lateral concentration gradients
that we are likely to encounter in actual applied studies.
The actual plumes produced by the four sources are shown in Figure 4-2,
which is a plot of the contours of CO concentration at the end of the 58-hour
simulation. Although CO is not chemically inert, variations in its
concentration due to chemical processes are small enough that CO can be
regarded as a conservative chemical tracer for our present purposes. From
this viewpoint we note several qualitative aspects of the model performance
evident in Figure 4-2.
The first is that lateral spread of the plumes due to truncation error
in the transport algorithm is nil inasmuch as the concentration contours of
plumes b, c, and e form nearly perfect, concentric circles, as one would
expect in the source/flow configuration (Figure 4-1) simulated here." (Keep
in mind that in experiment 3A the horizontal diffusivity KH is zero.) A
second point is that the peak value of concentration in each plume is well
133
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Figure 4-2. Isopleths of CO concentration (units = ppm) at the end of the
58-hour period simulated in experiment 3A. Letters b, c, e
and f refer to the sources shown in Figure 4-1.
134
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preserved, as is evident in plume b. Third, at the lower boundary where
plume b exits the model domain and where plume c touches the boundary,
there are no aberrations in the concentration isopleths that would signal
errors generated by the outflow boundary conditions in the transport
algorithm. Finally, the isopleths show that the simulated plumes are
continuous rather than disjointed, as Schere and Yamartino found in
applications of the Zalesak transport scheme to continuous sources.
In order to obtain quantitative estimates of the model's performance,
we will examine the predicted concentrations of each of the 23 species
along both cross-sections of the plumes normal to the air flow and along
Lagrangian trajectories within each plume. The cross-sections reveal
spatial variations in accuracy at a given time while the plots of concen-
tration following a Lagrangian trajectory show error behavior as a function
of travel time from a source. Figure 4-3 is a schematic representation of
the simulated plumes (shown in Figure 4-2) that illustrates some of the
cross-sections and trajectories that we will consider. We will use Figure
4-3 as an insert in all subsequent concentration plots to identify the
cross-section or trajectory to which the concentrations apply.
One point to keep in mind in interpreting the concentration fields is
that due to photochemical reactions, many of the species undergo marked
temporal variations that are synchronized with time-of-day. One consequence
of this is that concentration isopleths of most reactive species do not
exhibit orderly plume patterns like the CO distribution shown in Figure 4-2.
An example of a temporally varying species is ozone. Figure 4-4, page 137,
shows isopleths of ozone at the same hour as the CO isopleths shown in
135
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LAGRANGIAN
TRAJECTORY
CROSS-SECTION
DOMAIN
BOUNDARY
Figure 4-3.
Schematic representation of the continuous plumes generated
by sources b, c, e and f in experiment 3A. Examples are shown
of a cross-section and a Lagrangian trajectory.
136
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Figure 4-4. Isopleths of ozone concentration at the last hour, 0930 day 3,
of the line source simulation experiment 3A.
137
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Figure 4-2. Since this particular plot is for hour 0930, which is only 3
1/2 hours after sunrise, ozone has not yet been generated from the fresh
precursor emissions of sources b, c, e and f. As a result the ozone
contours give the illusion that all these sources have been displaced about
45 degrees clockwise, i.e., downwind, from their actual locations. Because
of this complexity in the behavior of the species concentrations, a variety
of spatial and temporal cross-sections are required to form a comprehensive
picture of the model's performance. In the remainder of this section we
will present and discuss an assortment of results obtained in experiment 3A
that will allow us to formulate conclusive statements regarding each of the
modeling questions raised earlier.
We begin with a sequence of four cross-section plots of CO shown in
Figure 4-5(a)-(d), pages 147-150. The profiles labeled chemistry represent
the true concentrations. They were obtained in the manner described in
Section 3 to generate the cross-sections shown in Figures 3-3 through 3-5.
The only difference is that in the present instance, equation (2-1) contains
an inhomogeneous term that represents source emissions. Sections a and b of
Figure 4-5 show cuts through plumes b, c and e at 7 hours and 34 hours
travel time, respectively. Comparing these two plots we see a slight
increase in error in the predicted peak concentration in each plume with
travel time. The figure also indicates that the error is inversely propor-
tional to the plume width, as we saw earlier. According to Figure 4-5(b),
at the 34-hour point, the model underestimates the peak concentration in
plume e (five cells wide) by 10%; by 18% in the case of plume c (three
cells wide); and it underestimates the peak in plume b (two cells wide) by
about 23%. The cross-sections shown in Figures 4-5(a), (b) confirm the
138
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observation that we made earlier in connection with the CO isopleths in
Figure 4-2 that there is not an appreciable widening of any of the plumes
beyond a few hours travel distance from a source. At 52 hours distance,
Figure 4-5(d) shows that the plumes from sources c and e have merged with
that from source f to form a single, double-peaked plume. As one can see
from the symbols along the abscissa of Figure 4-5 that designate the source
locations, the left-hand peak in the plume shown in Figure 4-5(d), i.e.,
the peak closest to the flow vortex center, is composed only of material
from source e. The model underestimates this peak by about 13%, which is
consistent with the error growth rate that we found earlier in plume e.
However, the right-hand peak in the plume in Figure 4-5(d) is made up of
material from both sources c and f; and it is underestimated by about 25%,
which is larger than either a 3-cell (source c) or 6-cell (source f) source
plume would produce at this point. The cause of this enhanced error is not
clear. As we shall see shortly, it is not apparent in the concentration
profiles of other species.
Figures 4-6(a)-(f), pages 151-156, show corresponding cross-sections of
ozone at a number of travel distances. The first four sections of this
figure, (a)(d), show that up until the point where the plumes first encounter
source f, the model actually simulates the ozone plumes more accurately
than the CO. The maximum error is an underestimate of about 10% in plume
b. The error in the predicted widths of the plumes is comparable to that
found with CO. Figures 4-6(e) and (f) show that after the plumes pass
source f, the ozone concentrations at the edges of both plumes c and e drop
markedly, due to reaction with NO emissions from source f. In fact, the
background ozone that fills the space between plumes c and e before they
139
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impact source f is completely erradicated at the 44-hour travel point
(Figure 4-6(e)), which is only a short distance downwind of source f. The
error level in the simulated ozone at this point is an underestimate of
peak values by about 10%. At the 52-hour travel point, Figure 4-6(f), the
spatial variation of ozone has acquired a rather complex shape which is
simulated by the model to within about 15% of the true values. However,
the model significantly overestimates the rate at which ozone is replenished
along the center-line of plume f. This error is undoubtedly due to errors
in the simulated NO and N02 concentrations in this region, rather than to
erronous lateral diffusion of ozone.
The error level in the predicted N02 concentrations can be seen in
Figures 4-7(a)-(e), pages 157-161. The first 3 sections of the figure,
(a)-(c), show that the peak N02 concentration is underestimated by only a
few percent in plume e and by about 15% in the narrowest plume, b. The
fractional error appears to grow as the NOg concentrations decrease toward
zero. Figure 4-7(d) indicates that just downwind of source f, the predicted
N02 concentration is too large by nearly a factor of two. Since this error
is grossly different than that apparent in Figure 4-7(a) at a comparable
distance downwind of sources b, c, and e, the large error in the f plume
must be due primarily to errors in species that are coupled to N02 chemically,
According to Figure 4-7(e), the error in the predicted N02 concentration
decreases rather rapidly with distance from source f.
Cross-sections of the predicted and true olefin concentrations are
displayed in Figures 4-8(a)-(d). The first two of these indicate an error
level comparable to or lower than that we have seen in any of the species
considered thus far. Downwind of source f, Figure 4-8(c) and (d) show an
140
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enhanced, asymmetrical error distribution that varies from a slight
overprediction on the left side of the plume to and underprediction on the
other side. The latter error has the larger magnitude, varying from about
15% to 40%. This is the second species in which we have seen a significant
deterioration of model accuracy following the merger of two plumes.
The final species that we will examine in cross-section is the highly
reactive compound PAN. Figures 4-9(a)-(f), pages 166-171, reveal an error
pattern in this species similar to that seen in CO: 10% to 15% underestimate
of peak concentration in plume b, c and e prior to intercepting source f,
and a somewhat larger error downwind of source f. In Figures 4-9(c)-(e) we
have added magnified plots of the concentration cross-sections to show the
fractional error in the predicted PAN levels when the concentration is very
low. Except for the left hand side of plume c, where concentration is
underpredicted by about 50%, the relative errors within the plumes are
comparable to that found in Figures 4-9(a) and (b) at higher concentrations.
At low concentrations, the fractional error is much larger in the areas
between plumes because in these zones the weak fluxes of material generated
by truncation error quickly produce concentration levels that are comparable
to the ambient values.
In summary, the cross-sections of species concentration give evidence
of some compounding of error when plumes from one source cross other
sources downwind. The magnitude of the error amplification appears to be
species dependent. Of the species we considered, ozone and CO showed the
least increase in error while N02 showed the largest change. In the latter
case the error increased from a 10% underprediction prior to plume merger
141
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to a 100% overprediction immediately following plume combination. The zone
of largest error is confined to a small area right around the second source.
In the next set of concentration plots we will look further at this phenomenon
of error amplification.
The first of four sequences of concentration profiles along Lagrangian
trajectories is presented in Figure 4-10, pages 172-194. Sections (a)-(w)
of this figure compare the predicted and true concentrations of each of the
23 simulated species along a 57-hour trajectory that passes through the
center of source e. This particular trajectory passes through the grid
cell adjacent to the left edge of source f approximately 40 hours downwind
of source e. Figures 4-10(a) and (b) show that the predicted NO and N02
concentrations are within about 10% of the true value during the time that
the concentration levels are significant, namely during the first 24 hours
of travel. Figure 4-10(c) indicates that the predicted ozone concentration
is within 5% of the true value during the first 44 hours, but departs from
the correct level by about 10% beyond that point. This slight increase in
the error level is undoubtedly due to interaction of plume e with the plume
from source f.
Figures 4-10(d)-(g), pages 175-178, indicate that all four hydrocarbon
species are simulated with accuracies better than 10% over the entire 57
hour travel period. The paraffin concentration profile in Figure 4-10(e)
contains a rather noticeable perturbation at about the 44 hour point (i.e.,
day 2, hour 20) where the trajectory passes source f. The fact that this
error fluctuation is quite localized supports the conclusion drawn earlier
in our analysis of the concentration cross-sections, that the compounding
142
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of error upon the interception of a plume with another source is a localized
phenomenon, at least for species like hydrocarbons, NOX, PAN and others that
are active in the photochemical process.
The profile of CO concentration shown in Figure 4-10(h), page 179,
provides evidence that the error compounding phenomenon is associated with
the concentration undershoot phenomenon that we discussed earlier in our
analysis of experiments 2A and 2B. In particular, between hours 18 and 21
of day 2, which is the period that the Lagrangian trajectory through the
center of source e passes the edge of source f, Figure 4-10(h) shows a
slight negative perturbation in the predicted CO concentration. The fact
that the concentration "recovers" to its proper level downstream of source
f suggests that the undershoot zone has the character of a standing wave
that is locked to the source. As each air parcel that composes a plume
enters the undershoot standing wave that surrounds an isolated source, the
concentrations of all species in that parcel are disturbed from their
equilibrium values. The altered chemical reactions that this imbalance
excites gives rise in the case of some species to new concentrations that
are more erroneous than those that entered the undershoot wave. Most of
the evidence we have seen thus far suggests that downstream of the undershoot
zone, error levels tend to return to their lower, original values. Moreover,
ozone, which is the species of primary concern to us, is one of the species
that is least affected by the undershoot phenomenon.
These observations bring us back to the question of whether a'transport
algorithm that maintains positive definite concentrations, i.e., an algorithm
that does not generate the undershoot, would not be preferable in modeling
applications such as this. Two responses come to mind.
143
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First, the aberrations that are attributable to our transport algorithm
are localized and are not seriously large. As we have already noted, the
model's ability to simulate ozone is practically untarnished by the undershoot
phenomenon. A second point is that the methods used in transport schemes
to prevent negative concentrations may cause serious distortions in the spatial
distribution and propagation speed of material (see Figure 3-2, pages 63-66)
that are potential sources of major, widespread errors. The authors are
unaware of any study such as the present one in which a "positive definite"
transport algorithm has been applied to chemically reactive material.
Therefore, despite the fact that designers of both the NCAR and the Canadian
regional acid rain models have recently chosen transport schemes of the
positive definite type, there apparently is no quantitative evidence that
algorithms of this type are superior.
Continuing with our analysis of the Lagrangian profiles, we refer the
reader to Figure 4-10(i)-(w), pages 180-194, for plots of the remaining 23
species. Since there are no significant aspects of any of these species
other than the phenomena we have already discussed, we will not elaborate
on any of these results. We include them for completeness in our demonstra-
tion of the models overall simulation capability. One counter-intuitive
characteristic of the species profiles shown in these figures is that the
highly reactive free radicals appear to be predicted more accurately than
the less reactive compounds.
The second sequence of concentration profiles along a Lagrangian
trajectory is given in Figure 4-ll(a)-(w), pages 195-217. A major difference
between this trajectory and the one depicted in Figure 4-10 is that the
144
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former actually crosses source f whereas the one represented in Figure 4-11
only skirts it (see the inserts in Figure 4-11 for details). We find on
comparing each species plot in Figure 4-11 with its counterpart in Figure
4-10, that the accuracy of the concentration predictions along this trajectory
is generally comparable or better than that found along the former trajectory.
One possible explanation of this is that the trajectory represented in
Figure 4-10 passes through the center of source e; and as we have seen the
model is not able to maintain the full amplitude of narrow plumes. By
contrast, the trajectory represented in Figure 4-11 passes through the
outer edge of source e where both the concentration and the curvature of
its profile are smaller. The differences in the problems of simulating the
centerline of a narrow plume vs its edge is particularly evident in a
comparison of the alkyl nitrate concentration time profiles given in Figures
4-10(1) and 4-11(1), pages 183 and 206, respectively.
Plots of primary species, such as olefin, paraffin, and CO given in
Figure 4-ll(d), (e) and (h), respectively, indicate that the fractional
error in the predicted concentrations downwind of the second source (f) is
approximately the same as that downwind of the first source e. Species
such as 03, (Figure 4-ll(c)), nitric acid (4-ll(j)), alkyl nitrate (4-
11(1)), and a few others exhibit almost no sensitivity to source f, while
others such as PAN (4-ll(k)), nitrate (4-ll(o)), and hydroperoxyl radical
(4-ll(q)) show enhanced error levels immediately after crossing source f
that subside eventually to their former levels some distance downstream.
The final sequence of concentration profiles along Lagrangian trajec-
tories is given in Figures 4-12, pages 218-240 and 4-13, pages 241-263.
145
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The former describes conditions along a path that passes through the center of
source c and through the outer edge cell of source f. Figure 4-13 illustrates
concentrations within the plume from source b. The errors apparent in
these two sets of profiles follow the same pattern as those we have already
discussed. The principle difference is that the magnitudes of the errors
tend to increase as the width of the simulated plume decreases, which we
have already been led to expect. For example, we find from Figures 4-10h,
12h and 13h that the fractional error in the simulated center!ine CO concen-
trations in sources 5, 3 and 2 cells wide are 10%, 18%, and 24%, respectively,
The corresponding errors in ozone are considerably lower: 4%, 8% and 9%,
respectively. These are well within what we consider to be acceptable
limits. It is fortunate that ozone, which is the pollutant of primary
concern to us, is among the species simulated most accurately. In contrast,
the predicted concentrations of some of the nitrogen species such as nitrous
acid, nitric acid, alkyl nitrate and others are in error by as much as 50%
or more in places. We suspect that these differences in accuracy reflect
differences in the character of the chemical reactivity of each species.
We leave further analysis of the results shown in Figures 4-12 and 13
to the reader. A brief summary of the chief conclusions is given in Section
1.
146
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TEST : UNESOURCE EMISSION TEST
DATE : 79215
HOUR : 180000
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DISTANCE FROM VORTEX CENTER (100KM)
Figure 4-8(b). Same as Figure 4-8(a) except travel time = 13 hours
163
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CROSS-SECTION PLOT
TEST : UNESOURCE EMISSION TEST
DATE : 79217
HOUR : 010000
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DISTANCE FROM VORTEX CENTER (100KM)
Figure 4-8(c). Same as Figure 4-8(a) except travel time = 44 hours.
164
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CROSS-SECTION PLOT
TEST : UNESOURCE EMISSION TEST
DATE : 79217
HOUR : 090000
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DISTANCE FROM VORTEX CENTER (100KM)
Figure 4-8(d). Same as Figure 4-8(a) except travel time = 52 hours
165
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CROSS-SECTION PLOT
TEST : UNESOURCE EMISSION TEST
DATE : 79215
HOUR : 120000
-------
CROSS-SECTION PLOT
TEST : LINESOURCE EMISSION TEST
DATE : 79215
HOUR : 180000
-------
CROSS-SECTION PLOT
TEST : UNESOURCE EMISSION TEST
DATE : 79216
HOUR : 060000
0. 8 1.1 1.3 1.6 1.8 2.1 2.3 2.5 2.9 3.1 3. 4 3. 6 3. 5 4. 1 4. 4 4.6 4.9
DISTANCE FROM VORTEX CENTER (100KM)
Figure 4-9(c).
Same as Figure 4-9(a) except travel time = 25 hours.
Insert shows magnified plot of the predicted and true PAN
concentration distributions.
168
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CROSS-SECTION PLOT
TEST : LJNESOURCE EMISSION TEST
DATE : 79216
HOUR : 150000
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DISTANCE FROM VORTEX CENTER (100KM)
Figure 4-9(d).
Same as Figure 4-9(a) except travel time = 34 hours.
Insert shows magnified plot of the predicted and true PAN
concentration distributions.
169
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CROSS-SECTION PLOT
TEST : UNESOURCE EMISSION TEST
DATE : 79217
HOUR : 010000
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DISTANCE FROM VORTEX CENTER (100KM)
Figure 4-9(e).
Same as Figure 4-9(a) except travel time = 44 hours.
Insert shows magnified plot of the predicted and true PAN
concentration distributions.
170
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CROSS-SECTION PLOT
TEST : UNESOURCE EMISSION TEST
DATE : 79217
HOUR : 090000
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DISTANCE FROM VORTEX CENTER (100KM)
Figure 4-9(f). Same as Figure 4-9(a) except travel time = 52 hours
171
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.29 COLUMN - 35.47
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DAY 2
20
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DAY 3
8
TIME (HOUR OF DAY)
Figure 4-10(a).
Comparison of predicted (dash-dot) and true NO concentration
(solid curve) along a Lagrangian trajectory that passes
through the center of source e, experiment 3A.
172
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TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.25 COLUMN - 33.47
CHEMISTRY
ROM
S 12 16 20 24
DAY 1 |
8 12 16 20
DAY 2
24 4 8
I DAY 3
TIME (HOUR OF DAY)
Figure 4-10(b). Comparison of predicted (dash-dot) and true N02 concentration
(solid curve) along a Lagrangian trajectory that passes
through the center of source e, experiment 3A.
173
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LU
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UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.25 COLUMN - 35.47
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ROM
8
12
DAY 1
16 20 24-
8 12 16 20
DAY 2
24
8
I DAY 3
TIME (HOUR OF DAY)
Figure 4-10(c). Comparison of predicted (dash-dot) and true ozone concen
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source e, experiment 3A.
174
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UNESOURCE EMISSION SIMULATION TEST
INCTIAL LOCATION OF TRACK : ROW - 29.23 COLUMN - 35.47
CHEMISTRY
ROM
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8 12 16 20 24
DAY 1 |
8 12 18 20 24
8
DAY 2
I DAY 3
TIME (HOUR OF DAY)
Figure 4-10(d). Comparison of predicted (dash-dot) and true olefin concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source e, experiment 3A.
175
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.23 COLUMN - 35.47
,I ... I ... I ... I ... I ... I ... I ... I ...
8 12 18 20 24
DAY 1 |
8
12 16
DAY 2
20 24 4 8
I DAY 3
TIME (HOUR OF DAY)
Figure 4-10(e). Comparison of predicted (dash-dot) and true paraffin
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A.
176
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.25 COLUMN
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 4-10(f).
Comparison of predicted (dash-dot) and true aldehyde
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A.
177
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.23 COLUMN - 33.47
12 16 20 24
DAY 1
6 12 16 20 24
DAY 2
8
DAY 3
TIME (HOUR OF DAY)
Figure 4-10(g). Comparison of predicted (dash-dot) and true aromatic
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A,
178
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.25
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Figure 4-10(h).
Comparison of predicted (dash-dot) and true carbon monoxide
concentration (solid curve) along a lagrangian trajectory
that passes through the center of source e, experiment 3A.
179
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TIME TRACK PLOT
UNE50URCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.23 COLUMN - 35.47
JEMISTRY
12 16 20 24
r . . . i/. , t . . . t . \ i . .
8 12 18 20 24 4 8
DAY 2 , DAY 3
TIME (HOUR OF DAY)
Figure 4-10(i). Comparison of predicted (dash-dot) and true nitrous acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A.
180
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INfTlAL LOCATION OF TRACK : ROW - 2933
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12 16 20 24
DAY 1
8 12 18 20 24
DAY 2 i
8
DAY 3
TIME (HOUR OF DAY)
Figure 4-10(j).
Comparison of predicted (dash-dot) and true nitric acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A.
181
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TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.25 COLUMN - 39.47
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8 12 16 20 24
8 12 16 20
DAY 1
TIME (HOUR OF DAY)
Figure 4-10(k).
Comparison of predicted (dash-dot) and true PAN
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A.
182
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.25
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I
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 4-10(1).
Comparison of predicted (dash-dot) and true alkyl nitrate
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A.
183
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.25
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8 12 16 20 24
DAY 1 |
8 12 18 20 24
DAY 2
I DAY 3
TIME (HOUR OF DAY)
Figure 4-10(m).
Comparison of predicted (dash-dot) and true hydrogen
peroxide concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source e,
experiment 3A.
184
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.23 COLUMN - 35.47
12 16 20 24
DAY 1
8
12
DAY 2
16 20 24
4
DAY 3
8
TIME (HOUR OF DAY)
Figure 4-10(n).
Comparison of predicted (dash-dot) and true atomic
oxygen concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source e,
experiment 3A.
185
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TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.23 COLUMN - 33.47
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12 16 20 24
12 16 20 24
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 4-10(o).
Comparison of predicted (dash-dot) and true nitrate concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source e, experiment 3A.
186
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TIME TRACK PLOT
UNE50URCE EMISSION SIMULATION 1EST
INfTIAL LOCATION OF TRACK : ROW - 26.25 COLUMN - 35.47
S 12 16 20 24
DAY 1 I
8 12 18 20 24 4 8
DAY 2 i DAY 3
TIME (HOUR OF DAY)
Figure 4-10(p). Comparison of predicted (dash-dot) and true hydroxyl concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source e, experiment 3A.
187
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INfHAL LOCATION OF TRACK : ROW - 20.23 '
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.25 COLUMN - 35.47
8 12 16 20 24
DAY 1
DAY 2
20 24 4 8
I DAY 3
TIME (HOUR OF DAY)
Figure 4-10(r).
Comparison of predicted (dash-dot) and true pernitric acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A.
189
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INmAL LOCATION OF TRACK : ROW - 29.25 COLUMN - 35.47
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12 16 20 24
8
DAY 1
DAY 2
I DAY 3
TIME (HOUR OF DAY)
Figure 4-10(s).
Comparison of predicted (dash-dot) and true alkoxyl radical
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source e, experiment 3A.
190
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TIME TRACK PLOT
LJNE50URCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.25
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ROM
3 12 16 20 24
DAY 1
8 12 16 20 24
8
DAY 2
I DAY 3
TIME (HOUR OF DAY)
Figure 4-10(t). Comparison of predicted (dash-dot) and true alkylperoxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source e,
experiment 3A.
191
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.25 COLUMN - 35.47
CHEMISTRY
ROM
I ... I
8 12 16 20 24
DAY 1
8 12 16 20 24
DAY 2 i
DAY 3
TIME (HOUR OF DAY)
Figure 4-10(u). Comparison of predicted (dash-dot) and true alkoxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source e,
experiment 3A.
192
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.25 COLUMN - 30.47
ct:
8 12 16 20 24
DAY 1
8 12 18 20 24 4 8
DAY 2 | DAY 3
TIME (HOUR OF DAY)
Figure 4-10(v). Comparison of predicted (dash-dot) and true peroxyacyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source e,
experiment 3A.
193
-------
TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 29.25
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK I ROW - 31.91 COLUMN - 37.03
CHEMISTRY
S 12 16 20 24
A
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12 16 20 24 4 3
DAY 2 i DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(a). Comparison of predicted (dash-dot) and true NO concentration
(solid curve) along a Lagrangian trajectory that passes
through the outer most grid cell of source e, experiment 3A.
195
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW - 31.51
CHEMISTRY
ROM
12 18 20 24
DAY 1
3 12 16 20 24
DAY 2
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8
DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(b). Comparison of predicted (dash-dot) and true N02 concentration
(solid curve) along a Lagrangian trajectory that passes
through the outer most grid cell of source e, experiment 3A.
196
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW - 31.81
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8 12 16 20 24
DAY 1
8 12 18 20 24
DAY 2
8
DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(c).
Comparison of predicted (dash-dot) and true ozone concentration
(solid curve) along a Lagrangian trajectory that passes
through the outer most grid cell of source e, experiment 3A.
197
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TIME TRACK PLOT
UNE50URCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW - 31.61
CM
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a 12 16 20 24
DAY 2 ,
3
DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(d).
Comparison of predicted (dash-dot) and true olefin concentra^
tion (solid curve) along a Lagrangian trajectory that passes
through the outer most grid cell of source e, experiment 3A.
198
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW - 31.01
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DAY 1
j_
DAY 2
1
DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(e).
Comparison of predicted (dash-dot) and true paraffin concen-
tration (solid curve) along a Lagrangian trajectory that passes
through the outer most grid cell of source e, experiment 3A.
199
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW -
1. 8 1
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DAY 1 i
8 12 18 20 24
DAY 2
I DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(f). Comparison of predicted (dash-dot) and true aldehyde concen-
tration (solid curve) along a Lagrangian trajectory that passes
through the outer most grid cell of source e, experiment 3A.
200
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW - 31.81
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8 12 16 20 24 4 3 12 16
DAY 1 , DAY 2
20 24 4 8
i DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(g). Comparison of predicted (dash-dot) and true aromatic concen-
tration (solid curve) along a Lagrangian trajectory that passes
through the outer most grid cell of source e, experiment 3A.
201
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW - 3T.A1
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4 8 12 16 M 24 48 12 16 20 24 4 8
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(h).
Comparison of predicted (dash-dot) and true carbon monoxide
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A.
202
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TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION
INFITAL LOCATION OF TRACK : ROW -
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CHEMISTRY
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12 16 20 24
12 16 20 24
8
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(i).
Comparison of predicted (dash-dot) and true nitrous acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A.
203
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
IN/HAL LOCATION OF TRACK : ROW - JT.61 COLUMN
- 37 JOS
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8 12 18 20 24
DAY 1
8 12 16 20 24 4 8
DAY 2 i DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(j).
Comparison of predicted (dash-dot) and true nitric acid
concentration (solid curve) along a lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A.
204
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TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW - 31.C1
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CHEMISTRY
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a 12 16 20 24
DAY 1 ,
4 S 12 16
DAY 2
20
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I DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(k).
Comparison of predicted (dash-dot) and true PAN concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the outer most grid cell of source e,
experiment 3A.
205
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : .ROW - 31.81 COLUMN - 37.03
03
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12 16 20 24
12 18 20 24
8
DAY 1
DAY 2
I DAY 3
TIME (HOUR OF DAY)
Figure 4-11(1).
Comparison of predicted (dash-dot) and true alkyl nitrate
concentration (solid curve) along a tagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A.
206
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INITIAL LOCATION OF TRACK : ROW
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4 8 12 16 20 24 4 8 12 18 20 24 4 8
DAY 1 • DAY 2 , DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(n).
Comparison of predicted (dash-dot) and true oxygen atom
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A.
208
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TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW - 31.81 COLUMN
- 37.03
2r
O
X
Q. _
Q_
OH
z:
LU
O
Z
O
O
O
CHEMISTRY
ROM
ni i i iM-Vri i t ' i i t -»-
U 4 8 12
DAY 1
16 20 24
A
S 12 16 20 24
DAY 2 i
8
DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(o).
Comparison of predicted (dash-dot) and true nitrate
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A.
209
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW - 31.61
8 12 16 20 24
8 12 16 20 24
DAY 1
DAY 2
i DAY 3
TIME (HOUR OF DAY)
Figure 4-11(p).
Comparison of predicted (dash-dot) and true hydroxyl
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A.
210
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK ; ROW - 31.81
.I ... I ... I... I ... I ...
I i
a 12 16 20 24
DAY 1 i
12 18 20 24
8
DAY 2
I DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(q). Comparison of predicted (dash-dot) and true hydroperoxyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the outer most grid cell of
source e, experiment 3A.
211
-------
TIME TRACK PLOT
UNE50URCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW - Jf.SI
12 16 20 24
DAY 1
8 12 16 20 24 48
DAY 2 i DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(r).
Comparison of predicted (dash-dot) and true pernitric
acid concentration (solid curve) along a Lagrangian
trajectory that passes through the outer most grid cell
source e, experiment 3A.
of
212
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW - 31.91
O
P
LJ
O
z:
o
o
O 1
6r
5-
3b
2h
o 10
O
T- 9
X
2 8
^M
l»
«•
*Mir-tji0-mts
fTAII
I I I I I I I I I I I I I I I
a
12
DAY 1
16 20 24
12
DAY 2
16 20 24
DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(s).
Comparison of predicted (dash-dot) and true alkoxyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the outer most grid cell of
source e, experiment 3A.
213
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LJ
o
•z.
a
o
CM
o
tr
TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW - 31.61
O
X
Q_
CL
O 3
I I I I , I , , I I , I , , I I , , I , , 1 I , , ,
8 12 16 20 24
8 12 18 20 24
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(t). Comparison of predicted (dash-dot) and true alkylperoxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the outer most grid cell of
source e, experiment 3A.
214
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
INITIAL LOCATION OF TRACK : ROW - 4(1.61 COLUMN
O 2r~
O
X
Q_ _
Q.
h-
LJ
O
O
O
O
CN
a:
o
4 _
" '
CHEMISTRY
ROM
8 12 16 20 24 4 8 12 18 20 24 4 8
DAY 1 , DAY 2 , DAY 3
TIME (HOUR OF DAY)
Figure 4-11(u).
Comparison of predicted (dash-dot) and true alkoxy radical
concentration (solid curve) along a Lagrangian trajectory
that passes through the outer most grid cell of source e,
experiment 3A.
215
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION
INflTAL LOCATION OF TRACK : ROW - 31.01 COLUMN
37.03
10 •»
O
X
-
.
-
(*{ |Pl||"ILfV
rtnii
CL
CL
g
s
2-
UJ
z tf~
o
o
CN
O
4 S 12 16 20 24
DAY 1 ,
8 12 16 20 24 4 8
DAY 2 i DAY 3
TIME (HOUR OF DAY)
Figure 4-ll(v).
Comparison of predicted (dash-dot) and true peroxyacyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the outer most grid cell
of source e, experiment 3A.
216
-------
o:
Ld
o
z
o
o
(N
O
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 36.32 COLUMN
40.16
CHEMISTRY
ROM
I I I 1 1 1 t I 1 1 1
I Li II 1 1 t L...I I I
4 8 12 16 20 24 4 3 12 16 20 24 4
DAY 1
DAY 2
I DAY 5
TIME (HOUR OF DAY)
Figure 4-12(a).
Comparison of predicted (dash-dot) and true NO concentration
(solid curve) along a Lagrangian trajectory that passes
through the center of source c, experiment 3A.
218
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0
X
Q_
Q_
Z:
O
O
O
CM
O
TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 36J2 COLUMN
40.16
5-
Ld
-
CHEMISTRY
ROM.
1-
8 12 16 20 24 4 3 12 16
DAY 1 | DAY 2
20 24 4 3
i DAY 3
TIME (HOUR OF DAY)
Figure 4-12(b). Comparison of predicted (dash-dot) and true N02 concentration
(solid curve) along a Lagrangian trajectory that passes
through the center of source c, experiment 3A.
219
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INfTTAL LOCATION OF TRACK : ROW - 36 J2 COLUMN - 40.16
I 1 1 1 I I I 1 ! I 1 1 I 1 I I I I I
4 8 12 16 20 24 4 a 12 18 20 24 4 8
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 4-12(c). Comparison of predicted (dash-dot) and true ozone concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source c, experiment 3A.
220
-------
TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 36.32 COLUMN - 40.16
4 8 12 16 20 24 4 & 12 16
20 24 4 3
I DAY 5
TIME (HOUR OF DAY)
Figure 4-12(d).
Comparison of predicted (dash-dot) and true olefin concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source c, experiment 3A.
221
-------
TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 36,32 COLUMN - 40.16
CM
O
X
a.
o.
61-
5-
4-
g
|3P
f—
Z
O 2
O
CJ
a.
CHEM1STRY
ROM
V
I JJ i A II I I I II I II 1 1 L Ll i I 1 t I i L I L I 1 L I L 1 I 11 1 L I t I 1 I I 1
4 8 12 16 20 24 4 8 12 16 20 24 4 B
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 4-12(e).
Comparison of predicted (dash-dot) and true paraffin concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source c, experiment JA.
222
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW -
CM
O
X
Q_
O 3F-
CE
i—
Ld
o
o
o
<
4 3 ^2 16 20 24 4 3 12 16 20 24 4
DAY 1
DAY 2
I DAY 5
TIME (HOUR OF DAY)
Figure 4-l2(f).
Comparison of predicted (dash-dot) and true aldehyde concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source c, experiment 3A.
223
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 36.32 COLUMN
8 12 16 20 24
DAY 1
3 12 16
DAY 2
20 24 4 3
DAY 3
TIME (HOUR OF DAY)
Figure 4-12(g).
Comparison of predicted (dash-dot) and true aromatic concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the center of source c, experiment 3A.
224
-------
Q_
CL
-------
o
T—
X
CL
CL
LJ
O
z:
o
o
CN
O
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INfTlAL LOCATION OF TRACK : ROW -
4-
O 3F-
CHEMISTRY
ROM
8 12 16 20 24
DAY 1 i
3 12 16
DAY 2
20
24
DAY 3
TIME (HOUR OF DAY)
Figure 4-12(1)
Comparison of predicted (dash-dot) and true nitrous acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A.
226
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 36.
4 8 12 16 20 24 4 3 12 16 20 24 4 8
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 4-12(j).
Comparison of predicted (dash-dot) and true nitric acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A.
227
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - -36.32 COLUMN
40.16
I' J I
o
X «L
g
!<
LU
o
z:
o
o
<
CL
CHEMISTRY
ROM
! 1 1 I t 1 I
8 12 16 20 24
DAY 1 i
8 12 16 20 24
DAY 2 i
DAY 3
TIME (HOUR OF DAY)
Figure 4-12(k).
Comparison of predicted (dash-dot) and true PAN concen-
tration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A.
228
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW -
to
o
X
Q_
Q_
O
2r-
UJ
o
z:
o
o
ro
O
CHEMISTRY
ROM
1 I [ I I \^4T\ I L I I I I t I _1. t.. l_ 1 II t I I 1 I 1 I t 1 I I 1 I I 1 I I II 111 | | | 1 1 L I_ 1 I | | I I |
8 12 16 20 24-
DAY 1 ,
8 12 16 20 24
DAY 2 ,
DAY 3
TIME (HOUR OF DAY)
Figure 4-12(1). Comparison of predicted (dash-dot) and true alky! nitrate
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A.
229
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INmAL LOCATION OF TRACK : ROW -
CM
O
4r-
Q_
3-
I 2
z:
LU
O
O
O
CM
O
CM
X
CHEMISTRY
ROM
1-
4 3 12 16 20 24
DAY 1 i
8 12 16 20 24 4 8
DAY 2 i DAY 3
TIME (HOUR OF DAY)
Figure 4-12(m).
Comparison of predicted (dash-dot) and true hydrogen peroxide
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A.
230
-------
O
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 36.32 COLUMN - 40.16
O5
O
X
CL
S>
z:
o
t>
5
4
-
"
IM>
r>\ IPHI*VTPV
ROM
A
/\
/ \
4
12
DAY 1
16 20
24
12
DAY 2
16
20
24
DAY 3
TIME (HOUR OF DAY)
Figure 4-12(n).
Comparison of predicted (dash-dot) and true atomic oxygen
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A.
231
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INfTIAL LOCATION OF TRACK : ROW - 36.32 COLUMN
O
X
CL
CL
g
i
i—
z:
Ld
o
o
O
2-
CHEMISTRY
ROM
/
i I i i i I i i i I i i i r I I I I I ' • I iT*! i I i i i I i I i I i i
4- S 12 16 20 24 4 8 12 16 20 24 4 8
DAY 1 i DAY 2 | DAY 3
TIME (HOUR OF DAY)
Figure 4-12(o).
Comparison of predicted (dash-dot) and true nitrate
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A.
232
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 36.J2 COLUMN - 40.16
O
X
Q_
Q-
o:
Ld
O 1
o
o
o
X
CHEMISTRY
ROM
8 12 16 20 24
3 12 6 20 24
TIME (HOUR OF DAY)
Figure 4-12(p).
Comparison of predicted (dash-dot) and true hydroxyl radical
concentration (solid curve) along a Lagrangian trajectory
that passes through the center of source c, experiment 3A.
233
-------
TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 36.32 COLUMN - 40.16
2r-
O
X
Q_ _
Q_
O
I—
Z
LJ
O
IZ
O
O
O
X
CHEMISTRY
ROM
_!___!_ .XT^^.
8 12 16 20 24
DAY 1 |
3 12 16 20 24
DAY 2 ,
DAY 3
TIME (HOUR OF DAY)
Figure 4-12(q).
Comparison of predicted (dash-dot) and true hydroperoxyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source c,
experiment 3A.
234
-------
TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 36.32
3r-
O
X
Q_
Q_
O
21-
Lu
O
O
o
CHEMISTRY
ROM
8 12 16 20 24
TIME (HOUR OF DAY)
Figure 4-12(r).
Comparison of predicted (dash-dot) and true pernitric
acid concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source c,
experiment 3A.
235
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 36.32 COLUMN - 40.16
12 16 20 24
8 12 16 20 24
DAY 1
DAY 2
I DAY 5
TIME (HOUR OF DAY)
Figure 4-12(s).
Comparison of predicted (dash-dot) and true alkoxyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source c,
experiment 3A.
236
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INfTlAL LOCATION OF TRACK : ROW - 36.32
10r-
S 12 16 20 24-
DAY 1
8 12 16 20 24 4 8
DAY 2 | DAY 3
TIME (HOUR OF DAY)
Figure 4-12(t).
Comparison of predicted (dash-dot) and true alkylperoxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source c,
experiment 3A.
237
-------
Ld
O
~ZL
O
O
o
CM
LT
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 36.32 COLUMN - 40.16
o 2
O
X
CL
Q_
O
CHEMISTRY
ROM
4 a 1
2 16 20 24
DAY 1 ,
, , i , H^-m-i , , . i | , i , ; | I.-M i —-fn
4 8 12 16 20 24
DAY 2
4
8
DAY 3
TIME (HOUR OF DAY)
Figure 4-12(u).
Comparison of predicted (dash-dot) and true alkoxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source c,
experiment 3A.
238
-------
TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INmAL LOCATION OF TRACK : ROW - 36.32 COLUMN
40.16
5r-
O
X
Q_
Q_
O 3
LJ
O
Z
O
O
-------
TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW = 36.32
CO
O
X
Q-
CL
O
!<
LT
61-
5-
z:
UJ
i 2
O
O
CM 1
O
C\l
C£
3-
CHEMISTRY
ROM
8 12 16 20 24
8 12 16 20 24
DAY 1
DAY 2
DAY 3
1ME (HOUR OF DAY)
Figure 4-12(w).
Comparison of predicted (dash-dot) and peroxy radical
concentration (solid curve) along a Lagrangian
trajectory that passes through the center of source c,
experiment 3A.
240
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04 COLUMN
- 43.28
CHEMISTRY
.ROM
It j I j | 11 I | | 1 ..J_ I ! I 1 III! t I * I 1 I. I I I It 1
12 16 20 24
DAY 1
12 18
DAY 2
24
DAY 3
TIME (HOUR OF DAY)
Figure 4-13(a). Comparison of predicted (dash-dot) and true NO concentration
(solid curve) along a Lagrangian trajectory that passes
through the inner edge of source b, experiment 3A.
241
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04 COLUMN - 43.28
CM
O
X -
CL
Q.
~z.
Ld
O
~Z.
O
O
CN
O
i i I i i i i i i i I | i i I i
DAY 1
DAY 2
TIME (HOUR OF DAY)
Figure 4-13(b). Comparison of predicted (dash-dot) and true N0£ concentration
(solid curve) along a Lagrangian trajectory that passes
through the inner edge of source b, experiment 3A.
242
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INfTW. LOCATION OF TRACK : ROW - 41.04
O
X
Q- U
CL
CHEMISTRY
ROM
i i ! i i f I i i i I i i i I i i i 1 i i i I i i i ! i i i !
i j
3 12 16 20 24
DAY 1 .
3 12 Id
DAY 2
20 24
DAY 3
TIME (HOUR OF DAY)
Figure 4-13(c).
Comparison of predicted (dash-dot) and true ozone concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A.
243
-------
O
X
CL
CL
g
i
H-
LU
O
O
O
LU
O
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04 COLUMN - 43.28
2r-
CHEMISTRY
.ROM
QUO*
I
I
3 12 16 20 24
DAY 1 i
3 12 IS 20
DAY 2
24 4 3
i DAY 3
TIME (HOUR OF DAY)
Figure 4-13(d).
Comparison of predicted (dash-dot) and true olefin concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A.
244
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04 COLUMN - 43.28
N *
X
^
•z.
O
1 —
*••»
-
»
\ \
ruruicrpv
- POM\
N^
\
L
(
z: c
LJ r
o F
z F
o jt
0 1p
r
o: ^>
ni'i L
I
^ ~— ^^x^_
""\^^
'^\.
\
J
.•if i i | 1 i I i 1 i \ i 1 ( i | 1 i | i I [ i i [ i i i 1 i i i I i i i I i i i | \. \ | I i i
! I ! \ \ \ 1
4 8 12 16 20 24 4 3 12 18 20 24 4 3
DAY 1 i DAY 2 , DAY 3
TIME (HOUR OF DAY)
Figure 4-13(e). Comparison of predicted (dash-dot) and true paraffin concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A.
245
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
LOCATION OF TRACK : ROW -
Li_j.-i_i-t...-i i .1 i i i .1 i i i i in i i i i . i
4 3 12 16 20 24 4 3 t2 16 20 24 4 3
DAY 1
DAY 2
I DAY 5
TIME (HOUR OF DAY)
Figure 4-13(f).
Comparison of predicted (dash-dot) and true aldehyde concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A.
246
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04 COLUMN - 43.28
DAY 1
DAY 2
4 4
i DAY 3
TIME (HOUR OF DAY)
Figure 4-13(g).
Comparison of predicted (dash-dot) and true aromatic concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A.
247
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INfTlAL LOCATION OF TRACK : ROW - *
1 . . . I
I I 1 I I 1 1 I
I , , , 1
1 ! 1 | I I
4 8 12 18 20 24
DAY 1 ,
12 18 20 24
DAY 2 i
3
DAY 3
TiME (HOUR OF DAY)
Figure 4-13(h).
Comparison of predicted (dash-dot) and true carbon monoxide
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A
248
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
LOCATION OF TRACK : ROW - 41.04 COLUMN -
43.23
CHEMISTRY
ROM
DAY 1
12 18 20 24
DAY 2 !
DAY 3
TIME (HOUR OF DAY)
Figure 4-13(i). Comparison of predicted (dash-dot) and true nitrous acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A,
249
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.
CM
O
X
Q_
Q_
CHEMISTRY
ROM
cr
i—
Ld
O
z:
o
O
o
:z
X
12 18 20 24
DAY 1
12 16
DAY 2
2Q 24 4 3
DAY 3
TIME (HOUR OF DAY)
Figure 4-13(j).
Comparison of predicted (dash-dot) and true nitric acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A.
250
-------
TIME TRACK PLOT
UNESGURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04 COLUMN - 43.23
3 12 16 20 24
TIME (HOUR OF DAY)
Figure 4-13(k).
Comparison of predicted (dash-dot) and true PAN concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A.
251
-------
TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04
4 8 12 16 20 24 4 3 12 16 20 24 4 3
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 4-13(1).
Comparison of predicted (dash-dot) and true alkyl nitrate
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A
252
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04
O
X
CL
Q_
O
CHEMISTRY
ROM
3 12 18 20 24
DAY 1
DAY 2
20 24 4 3
! DAY 3
TIME (HOUR OF DAY)
Figure 4-13(m).
Comparison of predicted (dash-dot) and true hydrogen peroxide
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A.
253
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INfTlAL LOCATION OF TRACK : ROW - 4t.04 COLUMN - 43.28
05
O
X
<
IT
^ r
Ld -
O
1 '
o
' I I
12 18 20 24
DAY 1
3 12 18 20 24
DAY 2 ,
DAY 3
T!ME (HOUR OF DAY)
Figure 4-13(n). Comparison of predicted (dash-dot) and true atomic oxygen
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A.
254
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INfTlAL LOCATION OF TRACK : ROW - 41.04
O
X
a.
o_
ct:
z:
LJ
O
^
O
0
CHEMISTRY
ROM
n[ i i | i\ Ni i ! i i i !
U 4 8 U
I t 1 I I 1
II | | _j LI j j i 1 ! \ i lit t
12 16 20 24
DAY 1 i
4 3 12 18 20 24 4 3
DAY 2 i DAY 3
TIME (HOUR OF DAY)
Figure 4-13(o).
Comparison of predicted (dash-dot) and true nitrate concen-
tration (solid curve) along a Lagrangian trajectory that
passes through the inner edge of source b, experiment 3A.
255
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TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INfTIAL LOCATION OF TRACK : ROW - 41.04 COLUMN - 43.28
3 12 16 20 24
DAY 1
3 12 18
DAY 2
24 4 3
1 DAY 3
TIME (HOUR OF DAY)
Figure 4-13(p). Comparison of predicted (dash-dot) and true hydroxyl radical
concentration (solid curve) along a Lagrangian trajectory thai
passes through the inner edge of source b, experiment 3A.
256
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04 COLUMN - 43.28
«• 2
O
X
Q_
O
cr
UJ
o
2
O
O
£N
O
X
CHEMISTRY
ROM
4 3 12 18 20 24 4 S 12 16 20 24 4 B
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 4-13(q). Comparison of predicted (dash-dot) and true hydroperoxyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the inner edge of source b,
experiment 3A.
257
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TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04 COLUMN - 43.28
2r-
O
X
CL
Q_
LJ
O
z:
o
o
o
X
CHEMISTRY
ROM
DAY 1
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 4-13(r).
Comparison of predicted (dash-dot) and true pernitric acid
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A
258
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TIME TRACK PLOT
LJNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04 COLUMN
3 12 16 20 24-
3 12 16 20 24
TIME (HOUR OF DAY)
Figure 4-13(s).
Comparison of predicted (dash-dot) and true alkoxyl radical
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A.
259
-------
TIME TRACK PLOT
L'NESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04
7
lO
o
>< 6
CL
P-, 5
5*
tr
UJ
o
z
o
o
CN
O
CHEMISTRY
ROM
2h
Ib
t
QLu.
J^^1 I < 1 -L-
'I'll t 111 III I
a 12 16 20 24
I ' ' ' I ' i..i 1 i i i ! i i i I i i i 1 i i
4 3 12 16 20 24
1 I I ! I I
4 3
I
DAY 1
DAY 2
. DAY 3
TIME (HOUR OF DAY)
Figure 4-13(t).
Comparison of predicted (dash-dot) and true alkylperoxyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the inner edge of source b,
experiment 3A.
260
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04 COLUMN - 43.23
- 10
t — q
». - y
X
S 8
Q.
0-, 7
Z
O 6
5 5
cr °
s *
^3
8 .
—
XM 1^1 111. II IVJ
^
rjf«l/ \
KUM \
L / \
1 ft
^ I 1
1- \\
^ \
E \
\\
I Is-ft I I I I
I , , , I , ,> L, , j.j
3 12 16 20 24
DAY 1
3 12 16 20 24
DAY 2
DAY 3
TIME (HOUR OF DAY)
Figure 4-13(u).
Comparison of predicted (dash-dot) and true alkoxy radical
concentration (solid curve) along a Lagrangian trajectory
that passes through the inner edge of source b, experiment 3A.
261
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INITIAL LOCATION OF TRACK : ROW - 41.04
in
O
x I-
Q. _
Q_
O
o:
LJ
o
z:
o
o
CN
O
\\
L
CHEMISTRY
ROM
12 18 20 24-
DAY 1
12 16 20 24
DAY 2
! DAY 3
TIME (HOUR OF DAY)
Figure 4-13(v).
Comparison of predicted (dash-dot) and true peroxyacyl
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the inner edge of source b,
experiment 3A.
262
-------
TIME TRACK PLOT
UNESOURCE EMISSION SIMULATION TEST
INfTlAL LOCATION OF TRACK : ROW - 41.04 COLUMN - 43.25
o
X
Q_
CL
O
I-
Ld
O
•z.
O
o
CM
O
CN
LT
CHEMISTRY
ROM
12 16 20 24
DAY 1
DAY 2
20 24 4 3
DAY 3
TIME (HOUR OF DAY)
Figure 4-13(w). Comparison of predicted (dash-dot) and true peroxy
radical concentration (solid curve) along a Lagrangian
trajectory that passes through the inner edge of source b,
experiment 3A.
263
-------
REFERENCES
Demerjian, K. L. and K. L. Schere, (1979): "Applications of a Photochemical
Box Model for Ozone Air Quality in Houston, Texas. Proceedings, Ozone/
Oxidants: Interactions with the Total Environment II, Houston, TX, 14-17
Oct. 1979, APCA, Pittsburgh, Pa., pp. 329-352.
Demerjian, K. L., K. L. Schere, and J. T. Peterson, (1980): "Theoretical
estimates of actinic (spherically integrated) flux and photolytic rate
constants of atmospheric species in the lower troposphere." In Advances
In Environmental Science and Technology - Vol. 10, J. N. Pitts et al.,
eds., John Wiley and Sons, New York, pp. 369-459.
Gear, C. W., (1971): "The automatic integration of ordinary differential
equation". Communications of the ACM, Vol. 14, 176-179.
Lamb, R. G., (1983): "A Regional Scale (1000 km) Model of Photochemical Air
Pollution: Part 1. Theoretical Formulation". EPA-600/3-83-035. 237 pages.
Lamb, R. G., (1984): "A Regional Scale (1000 km) Model of Photochemical Air
Pollution: Part 2. Input processor network design". EPA-600/S3-84-085.
310 pages.
Mahrer, Y. and R. A. Pielke, (1978): "A Test of an Upstream Spline Interpolation
Technique for the Advection Terms in a Numerical Mesoscale Model".
Mon. Uea. Rev., Vol. 106, pp 818-830.
Schere, K. L., (1984): Private communication.
Yamartino, R. J., (1984): Private communication.
Zalesak, S., (1979): "Fully Multidimensional Flux-Corrected Transport Algorithms
for Fluids", J. Comp. Physics, 31: 335-362.
264
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
5. REPORT DATE
A REGIONAL-SCALE (1000 KM) MODEL OF PHOTOCHEMICAL AIR
POLLUTION Part 3. Tests of the Numerical Algorithms
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Robert G. Lamb and Gerard F. Laniak
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
10. PROGRAM ELEMENT NO.
CDWA1A/02-1335 FY"85
Same as Block 12
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
Atmospheric Sciences Research Laboratory—RTF, NC
Office of Research and Development
Environmental Protection Agency
Research Triangle Park, North Carolina 27711
13. TYPE OF REPORT AND PERIOD COVERED
In-house
14. SPONSORING AGENCY CODE
EPA/600/09
15. SUPPLEMENTARY NOTES
16. ABSTRACT
The Regional Oxidant Model (ROM) developed in two earlier reports is applied
to a series of hypothetical problems whose exact solutions are known. Comparisons
are made between the model's predictions and the known solutions to assess the
accuracies of the numerical algorithms that comprise the model's predictive
equations. It is found that in the case of ozone, the solutions of the numerical
algorithms on which the model is based are within 10 percent of the solutions of
the corresponding differential equations that describe the chemical and physical
processes that the model simulates. Extensive documentation is provided in the
report of the model's performance in simulating the concentrations of 23 chemical
species over a 48-hour period.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
21. NO. OF PAGES
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (R*v. 4-77) PREVIOUS EDITION is OBSOLETE
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