United States
Environmental Protection
Agency
Region 8
1860 Lincoln Street
Denver, Colorado 80295
EPA-908/I-78-005
FEBRUARY I979
FINAL
FURTHER STUDIES OF
REGIONAL DIFFUSION
MODELING IN THE
NORTHERN GREAT PLAINS
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EPA-908/1-78-005
Final Report
FURTHER STUDIES OF REGIONAL DIFFUSION MODELING
IN THE NORTHERN GREAT PLAINS
by
Mei-Kao Liu
Michael Wojcik
Systems Applications, Incorporated
950 Northgate Drive
San Rafael, California 94903
Contract No. 68-01-3591
EF78-88R - EF79-40
March 1979
Prepared for
Donald Henderson
Project Officer
Environmental Protection Agency
Region VIII
1860 Lincoln Street
Denver, Colorado 80295
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DISCLAIMER
This report has been reviewed by the U.S. Environmental Protection
Agency, Region VIII, and approved for publication. Mention of trade
names or commercial products does not constitute endorsement or recom-
mendation for use.
This document is available to the public through the National
Technical Information Service, Springfield, Virginia 22151.
11
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ABSTRACT
This report describes the continuation of a project devoted to the
assessment of air quality impacts on a regional scale. In the previous
study, a Regional Air Pollution Model was developed and a series of
numerical experiments were carried out to test the sensitivity of the
model (Liu and Durran, 1977). The sensitivity studies showed that wind
distribution and horizontal eddy diffusivities in the mixed layer are
critical meteorological parameters.
Further work on improving the processing of meteorological data for
the Regional A1r Pollution Model indicated that the geostrophic wind
relationship provides the most appropriate basis for calculating the wind
field in the mixed layer. Implementing this relationship required con-
struction of the geopotential height field. The best method tested for
constructing this height field is a bicubic spline fit of geopotential
height data. For the horizontal eddy diffusivities, a parameterization
scheme first proposed by Smagorinsky (1963) was selected after an extensive
literature review. In that scheme the horizontal d1ffus1v1ty is assumed
to be proportional to the magnitude of velocity deformation.
The Regional Air Pollution Model was then exercised for the Northern
Great Plains using the new methodology for processing meteorological data.
The simulation Impacts of SO2 emissions from existing and proposed energy
developments were compared with the results from earlier work. Although
the conclusions of the original report concerning maximum concentrations
remain essentially unaltered, significant change was observed 1n the con-
figurations of the computed concentration isopleth. The weak-wind spring
scenario still produced the highest S02 and sulfate concentrations. For
estimated 1986 SOg emissions, three-hour-average SOg concentrations were
as high as 100 yg m"3 near large point sources but rarely exceeded
111
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_3
8 yg m 100 kilometers downwind. The sensitivity of calculated sulfate
concentrations to SOg-to-sulfate conversion rates was also tested in
the present study. A low conversion rate (0.3 percent per hour) generated
negligible sulfate concentrations even for the worst case. However, a
1 percent per hour conversion rate produced moderate sulfate buildup, with
_3
concentrations reaching 6 yg m , a level that has been considered as
marginal in causing visibility reduction (Trijonis and Yuan, 1978; Charlson,
Waggoner, and Thielke, 1979).
iv
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CONTENTS
DISCLAIMER ii
ABSTRACT i i i
LIST OF ILLUSTRATIONS vi
LIST OF TABLES xii
I INTRODUCTION 1
II SUMMARY AND CONCLUSIONS 3
III A REVIEW OF MESOSCALE TRANSPORT AND DIFFUSION 5
A. Review of Pertinent Studies 5
B. Parameterization of Horizontal Eddy Diffusivity 12
IV CHARACTERIZATION OF MESOSCALE TRANSPORT AND DIFFUSION .... 14
A. Bilinear Interpolation 15
B. Fitting of the Poisson Equation 17
C. Bicubic Spline Fit 27
V SENSITIVITY OF THE TRANSPORT AND DIFFUSION
CHARACTERIZATION SCHEME 35
VI ANALYSIS OF THE RESULTS 49
A. Analysis of the Effect of the New
Characterization Scheme 62
B. Air Quality Analysis 63
1. Spring Scenario 63
2. Winter Scenario 63
3. Summer Scenario 66
C. Sensitivity Study of the SO2/SO4
Conversion Rate 66
APPENDIX: SIMULATION RESULTS 72
REFERENCES 110
v
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ILLUSTRATIONS
1 Energy Spectrum for Atmospheric Flows 6
2 Empirical Relationship for Horizontal Plume
Spread on the Mesoscale 8
3 The Development of Clusters Initially of the Form ABCDEF
at Each Level to Clusters A'B'C'D'E'F' 18 Hours Later .... 11
4 850-mb Weather Map for 1700 MST on 30 January 1976 16
5 Bilinearly Interpolated Geopotential Height Field (m) . . . . 18
6 Zonal Wind Field Generated from Bilinearly Interpolated
Geopotential Height Data {m sec"'} 19
7 Meridional Wind Field Generated from Bilinearlv
Interpolated Geopotential Height Data (m sec-1) 20
8 Geopotential Height Field (m) Based on the Solution
of the Laplace Equation After 25 Iterations 22
9 Geopotential Height Field (m) Based on the Solution
of the Laplace Equation After 125 Iterations 23
10 Geopotential Height Field (m) Based on the Solution
of the Laplace Equation After 150 Iterations 24
U Zonal Wind Field (m sec'1) Generated from Geopotential
Heights Based on the Solution of the Laplace
Equation After 150 Iterations 25
12 Meridional Wind Field (m sec-1) Generated from
GeoDOtential Heights Based on the Solution of the
Laplace Equation After 150 Iterations 26
13 Geopotential Height Field (m) Based on the Solution of the
Poisson Equation with Prescribed Forcing Functions 28
14 Bicubic Spline Fit of Geopotential Height Data (m) 31
15 Zonal Wind Field (m sec"1) Generated by a Bicubic
Spline Fit of Geopotential Height Data 32
16 Meridional Wind Field (m sec"1) Generated by a Bicubic
Spline Fit of Geopotential Height Data 33
v1
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17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
34
36
37
38
39
40
41
42
43
44
45
46
47
50
51
52
53
54
55
Wind Vectors Generated by a Bicubic Spline Fit
of Geopotential Height Data
850-mb Weather Map for 500 MST on 27 January 1976
850-mb Weather Map for 1700 MST on 28 January 1976
850-mb Weather Map for 500 MST on 30 January 1976
Bicubic Spline Fit of Geopotential Height Data (m) for
500 MST on 27 January 1976
Bicubic Spline Fit of Geopotential Height Data (m) for
1700 MST on 28 January 1976
Bicubic Spline Fit of Geopotential Height Data (m) for
500 MST on 30 January 1976
Wind Vectors Generated by a Bicubic Spline Fit of Geopo-
tential Height Data for 500 MST on 27 January 1976
The Computed Horizontal Eddy Diffusivlty (in 104 m2 sec"1)
for 500 MST on 27 January 1976
Wind Vectors Generated by a Bicubic Spline Fit of Geopo-
tential Height Data for 1700 MST on 28 January 1976
4 2 -1.
The Computed Horizontal Eddy Diffusivity (in 10 m sec )
for 1700 MST on 28 January 1976
Wind Vectors Generated by a Bicubic Spline Fit of Geopo-
tential Height Data for 500 MST on 30 January 1976
The Computed Horizontal Eddy Diffusivlty (in 10* sec"^)
for 500 MST on 30 January 1976
Wind Vectors Generated by a Bicubic Spline Fit of
Geopotential Height Data for 1700 MST on 4 April 1976 . . . .
Wind Vectors Generated by a Bicubic Spline Fit of
Geopotential Height Data for 1700 MST on 5 April 1976 . . . .
Wind Vectors Generated by a Bicubic Spline Fit of
Geopotential Height Data for 1700 MST on 6 April 1976 . . . .
Wind Vectors Generated by a Bicubic Spline Fit of
Geopotential Height Data for 500 MST on 9 July 1975
Wind Vectors Generated by a Bicubic Spline Fit of
Geopotential Height Data for 500 MST on 10 July 1975 , . . . .
Wind Vectors Generated by a Bicubic Spline Fit of
Geopotential Height Data for 500 MST oft 11 July 1975
vf1
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36
37
38
39
40
41
42
43
44
45
46
47
48
49
A-l
A-2
A-3
A-4
56
57
58
59
60
61
64
64
65
67
67
68
69
71
74
75
76
77
Comparison of SO2 Concentration Fields (yg m ) for
Case 1: 500 to 800 MST on 5 April 1976
-3
Comparison of SO? Concentration Fields (yg m ) for
Case 1: 1700 to 2000 MST on 5 April 1976
-3
Comparison of SO2 Concentration Fields (yg m ) for
Case 1: 800 to 1100 MST on 6 April 1976
_3
Comparison of SO2 Concentration Fields (yg m ) for
Case 2: 500 to 800 MST on 5 April 1976
-3
Comparison of SO2 Concentration Fields (yg m ) for
Case 2: 1700 to 2000 MST on 5 April 1976
• 3
Comparison of SO2 Concentration Fields (yg m ) for
Case 2: 800 to 1100 MST on 6 April 1976
-3
SO2 Concentration Fields (yg m ) for Case 5 (Revised
Scheme): 1700 to 2000 MST on 27 January 1976 . . .
-3
SO2 Concentration Fields (yg m ) for Case 5 (Revised
Scrieme): 2000 to 2300 MST on 28 January 1976 . . .
-3
SO2 Concentration Fields (yg m ) for Case 5 (Revised
Scheme): 1400 to 1700 MST on 29 January 1976 . . .
SO2 Concentration Fields (yg m"3) for Case 6 (Revised
Scheme): 200 to 500 MST on 10 July 1975
SO? Concentration Fields (yg m" ) for Case 6 (Revised
Scheme): 500 to 800 MST on 11 July 1975
SO2 Concentration Fields (yg nf3) for Case 6 (Revised
Scheme): 1400 to 1700 MST on 11 July 1975
Concentration Fields (yg nf3) for Case 3 (Revised
Scheme): 800 to 1100 MST on 6 April 1976
O
Concentration Fields (yg m ) for Case 4 (Revised
Scheme): 800 to 1100 MST on 6 April 1976
S02 and SO4 Concentrations for Case 1:
1700 to 2000 MST on 4 April 1976
SO? and SO4 Concentrations for Case 1:
200 to 500 MST on 5 April 1976
SO2 and SO4 Concentrations for Case 1:
1100 to 1400 MST on 5 April 1976
SO2 and SO4 Concentrations for Case 1:
2000 to 2300 MST on 5 April 1976
vHi
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A-5 SO2 and SO4 Concentrations for Case 1
500 to 800 MST on 6 April 1976 . . .
A-6 SGo and SO4 Concentrations for Case 1
1400 to 1700 MST on 6 April 1976 . .
A-7 S0o and SO4 Concentrations for Case 2
1700 to 2000 MST on 4 April 1976 . .
A-8 SO2 and SO4 Concentrations for Case 2
200 to 500 MST on 5 April 1976 . . .
A-9 SO2 and SO4 Concentrations for Case 2:
1100 to 1400 MST on 5 April 1976 82
A-10 SO2 and SO4 Concentrations for Case 2:
2000 to 2300 MST on 5 April 1976 83
A-ll SO2 and SO4 Concentrations for Case 2:
500 to 800 MST on 6 April 1976 84
A-12 SO2 and SO4 Concentrations for Case 2:
1400 to 1700 MST on 6 April 1976 85
A-13 SO2 and SO4 Concentrations for Case 3:
1700 to 2000 MST on 4 April 1976 86
A-14 SO2 and SO4 Concentrations for Case 3:
200 to 500 MST on 5 April 1976 87
A-15 SO2 and SO4 Concentrations for Case 3:
1100 to 1400 MST on 5 April 1976 88
A-16 SO2 and SO4 Concentrations for Case 3:
2000 to 2300 MST on 5 April 1976 89
A-17 SO2 and SO4 Concentrations for Case 3:
500 to 800 MST on 6 April 1976 90
A-18 SO2 and SO4 Concentrations for Case 3:
1400 to 1700 MST on 6 April 1976 91
A-19 SO2 and SO4 Concentrations for Case 4:
1700 to 2000 MST on 4 April 1976 92
A-20 SO2 and SO4 Concentrations for Case 4:
200 to 500 MST on 5 April 1976 93
A-21 SO2 and SO4 Concentrations for Case 4:
1100 to 1400 MST on 5 April 1976 94
A-22 SO2 and SO4 Concentrations for Case 4:
2000 to 2300 MST on 5 April 1976 95
1x
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A-23 SO2 and SO4 Concentrations for Case 4:
500 to 800 MST on 6 April 1976 * . ™
A-24 SO2 and SO4 Concentrations for Case 4:
1400 to 1700 MST on 6 April 1976 9'
A-25 SO? and SO4 Concentrations for Case 5:
1700 to 2000 MST on 27 January 1976 98
A-26 SO? and SO4 Concentrations for Case 5:
200 to 500 MST on 28 January 1976 99
A-27 SO? and SO4 Concentrations for Case 5:
1100 to 1400 MST on 28 January 1976 100
A-28 SO2 and SO4 Concentrations for Case 5:
2000 to 2300 MST on 28 January 1976 101
A-29 SO2 and SO4 Concentrations for Case 5:
500 to 800 MST on 29 January 1976 . .
A-30 SO2 and SO4 Concentrations for Case 5:
1400 to 1700 MST on 29 January 1976 .
A-31 SO2 and SO4 Concentrations for Case 6:
1700 to 2000 MST on 9 July 1975 . . .
A-32 SO? and SO4 Concentrations for Case 6:
200 to 500 MST on 10 July 1975 ...
A-33 SO2 and SO4 Concentrations for Case 6:
1100 to 1400 MST on 10 July 1975 . .
A-34 SO2 and SO4 Concentrations for Case 6:
2000 to 2300 MST on 10 July 1975 . .
102
103
104
105
106
107
A-35 SO2 and SO4 Concentrations for Case 6:
500 to 800 MST on 11 July 1975 108
A-36 S02 and SO4 Concentrations for Case 6:
1400 to 1700 MST on 11 July 1975 109
x
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TABLES
1 850-mb Geopotential Height Data for 1700 MST
on 30 January 1976 17
2 List of the Computer Simulations 49
x1
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I INTRODUCTION
In a previous study, under Contract 68-01-3591 with the U.S. Environ-
mental Protection Agency (EPA), a Regional Air Pollution Model was
developed to simulate the effect of emissions from major point sources
on air quality over long distances (Liu and Durran, 1977). This model
was subsequently applied to the Northern Great Plains to assess the regional
impact of existing and proposed energy developments in that area. A series
of numerical experiments were also carried out to test the sensitivity of
the model. It was found that the wind field and horizontal eddy diffusiv-
ities in the mixed layer are not only two of the most critical parameters
in the model, but also the most difficult to characterize quantitatively.
A decision was thus made to extend the scope of work to include an investi-
gation of the best method for characterizing the wind field and diffusivities
in the mixed layer.
In the Regional Air Pollution Model, provisions have also been made to
treat the first-order reaction between SOg and sulfate. When an estimated
0.3 percent per hour conversion rate for SOg to sulfate was used, the pre-
dicted sulfate concentrations were found to be on the order of a few
micrograms per cubic meter—-not significantly above the background levels.
Recent studies, however, appear to indicate that sulfate concentrations on
the order of 10 yg m"3 may significantly affect visibility (Trijonis and Yuan,
1978; Charlson, Waggoner, and Thielke, 1979). Thus, a set of calculations
using a realistic but higher value for the rate of conversion of SO2 to
sulfate was in order.
This report delineates the work completed under the extension of this
contract. Chapter II presents a brief summary and the conclusions drawn
from this study. Chapter III reviews previous studies on mesoscale hori-
zontal eddy diffuslvity, and Chapter IV describes a methodology for charac-
terizing the mesoscale transport and diffusion. Chapter V discusses the
1
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sensitivity of the Regional Air Pollution Model predictions to the pro-
posed methodology. Finally, Chapter VI analyzes the air quality impact
predicted on the basis of the new set of model calculations.
2
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II SUMMARY AND CONCLUSIONS
In this study, methods for characterizing wind flow and horizontal
diffusion in mesoscale air quality modeling were examined. After a
review of pertinent theoretical and observational studies, the geostrophic
wind and a scheme first proposed by Smagorinsky (1963) for horizontal
eddy diffusivities were selected. A bicubic spline fit was used to
interpolate the geopotential height data needed for implementation of this
scheme. This method was used to compute the wind fields and horizontal
diffusivities for the three time periods studied in the previous efforts,
and the Regional Air Pollution Model was subsequently exercised using the
new meteorological data.
The shapes of the new concentration isopleths for both SOg and sulfate
differ considerably from those of the original simulation. The differences
are due primarily to the implementation of a smooth geostrophic wind field
in the mixing layer instead of the straightforward interpolation of the
wind in the previous study. The new prescription for horizontal diffusivity
and more realistic mixing heights also account for some of the differences
observed.
Despite these differences, however, the original conclusions remain
essentially unaltered. A scenario representative of the winter, character-
ized by low mixing depths and high winds, still produced the lowest concen-
trations. The mixing depths for the summer scenario are approximately
twice as high as in the spring scenario, combined with considerably weaker
winds, leading to moderate levels of pollutant concentrations. According
to the computer simulations, the spring scenario, characterized by low
winds and medium mixing depths, represents the worst case of the three
scenarios for regional impact. Maximum three-hour SO, concentrations for
-3
this case were found to be on the order of 100 yg m using the 1986 emissions.
3
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Assuming a 1 percent per hour S09-to-sulfate conversion rate, the maximum
-3
computed sulfate concentrations are 6 yg m , a level that has been con-
sidered as marginal in affecting visibility degradation.
4
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Ill A REVIEW OF MESOSCALE TRANSPORT AND DIFFUSION
To select and adapt an appropriate scheme for characterizing meso-
scale atmospheric motions and diffusion, the study team first reviewed
the pertinent theoretical and observational studies. This review is
summarized below, followed by a description of the scheme selected for
the present project.
A. REVIEW OF PERTINENT STUDIES
As shown in Figure 1, which presents the characteristics of the energy
spectrum, atmospheric motion covers a wide spectrum of phenomena, ranging
from the smallest scales associated with viscous dissipation to planetary
waves. The transport and dispersion of pollutants thus strongly depends
on its length scale in relation to the scales of turbulent motion or the
eddy size. Eddies much larger than the pollutant scale will transport it
as a whole, whereas eddies of the same size will deform it through wind
shear across the cloud, and eddies smaller than the cloud will disperse
it. The turbulent energy is primarily concentrated in large-scale air
motion. As a pollutant cloud disperses, its size increases, and therefore,
the turbulent motion that is of the same scale increases in energy. The
manner in which a cloud of pollutants interacts with eddies of equal and
different scale greatly affects the value of the horizontal eddy diffusivity.
Randerson (1972) analyzed the dispersion of a single nuclear debris
cloud and plotted its horizontal width ay as a function of travel time t.
He then calculated the horizontal eddy diffusivity, K^, according to the
simple formula discussed by Taylor (1921):
2
o..
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MACROSCALE
UPPER AIRFLOWS
SURFACE MEASUREMENTS
MICROSCALE
\ MESOSCALE
Time (hours)
i i 1 . L
106 105 104 103
Diffusivity, (m^ sec"^)
Sources: Murgatroyd (1969) for upper airflows.
van der Hoven (1957) for surface measurements.
FIGURE 1. ENERGY SPECTRUM FOR ATMOSPHERIC FLOWS
6
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Randerson's results are representative of observed mesoscale values
presented in a survey by Bauer (1973). Together with an upper and lower
bound proposed by Hage et al. (1966), the results of Randerson's observa-
tions are presented in Figure 2. All of the observational studies surveyed
found three distinct stages of dispersion. For travel times less than 1
hour and greater than 10 to 12 hours, was approximately constant. Dif-
fusion accelerated during the intermediate travel time, which is the range
of interest in regional-scale studies. Horizontal diffusivity was found
to vary from 10^ to 10^ m^ sec"^ with As Figure 2 suggests,
Kh can vary by a factor of 10 from Randerson's values at a given travel time.
The observational studies indicated that horizontal diffusivity
varies greatly and exhibits a definite scale dependence. However,
the rate of diffusion is not explained entirely by its scale dependence;
there is also variability in at a given travel time, indicating
that atmospheric conditions play an important part in diffusion.
Diffusion can also be studied by analyzing the trajectory of
hypothetical particles in a given flow field. Either a series of
particles can be released from a fixed point at set time intervals, or
a cluster of particles can be released at the same time. The second
approach is most similar to pollutant dispersion. Statistical analysis
of particle velocities and separation distances can reveal the char-
acteristics of large-scale diffusion. The Lagrangian reference frame
of trajectory studies is the center of mass of the particle. Mesoscale
models divide the region of interest into cells and then examine dis-
persion with respect to the cell from a Eulerian reference frame.
How applicable are Lagrangian studies to Eulerian models? In a
comparison of Lagrangian and Eulerian statistics, Kao and Bullock (1964)
analyzed the dispersion of the endpoints of particles initiated at regu-
lar intervals at a fixed point at the 500 mb-level. The velocity fluc-
tuations with time with respect to the center of mass along each tra-
jectory were computed. The fluctuations along one trajectory were con-
nected with those of the others to form a long time series. The same
statistical analysis was carried out at a fixed point, and the Lagrangian
7
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• DEBRIS CLOUD DATA
o CSANADY MODEL
PREDICTIONS
MEAN CURVE AND BOUNDS
(HAGE ET AL., 1966)
DOMAIN OF INTEREST
TO THIS STUDY
(RANDERSON,
1972)
/
/
02 10 mln jq3 1.0 hr 10 hr 1Q5 3 days
Time (sec)
Source: Randerson (1972).
FIGURE 2. EMPIRICAL RELATIONSHIP FOR HORIZONTAL PLUME
SPREAD ON THE MESOSCALE
8
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and Eulerian energy spectra were then computed and were found to have
identical statistics. As in Figure 1, turbulent energy was concentrated
in large-scale motions, with the Eulerian energy peak at a slightly larger
scale. The ratio of Lagrangian to Eulerian time scales was comparable.
Although the study was carried out for the mid-troposphere, motions at
all levels are interconnected and similar. Thus, the results indicate
that characteristics of diffusivity found in Lagrangian studies are appli-
cable to Eulerian models.
Kao (1968) examined the statistical theory of particle dispersion.
Working with a cluster of particles, he derived the equations governing
the motion of particles relative to their center of mass, since this
relative motion determines how particles disperse. He then related mean
square relative separation to travel time and derived relations for large
and small time. In the initial stage, diffusion is affected by turbulent
motions of all scales. At larger travel times, dispersion of particles
is primarily affected by turbulent motions of similar scales. Diffusion
becomes constant at large times.
Using one year of data, Kao and Gain (1968) plotted the trajectories
of a cluster of particles for travel times of 196 hours. The clusters
were all released from the same point at three levels: 200, 500, and
850 mb. The power spectra and mean square separation distance for the
zonal and meridional components were obtained, and yearly and seasonal
results were analyzed. Only the 850-mb results are discussed here. The
energy was found to be concentrated in the large-scale eddies with a
greater maximum in the zonal component. The rate of dispersion increased
with the size of the particle cluster, indicating that eddies of the
same size as the cluster have the greatest impact on their dispersion.
A seasonal variability in mean square separation distance showed that
separation was greatest in the winter and smallest in the summer. The
zonal component of mean square separation distance was found to be
twice the meridional component.
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Murgatroyd (1969) conducted an experiment on the dispersion of
a cluster of particles of various sizes at the 300-, 700-, and 900-nrt>
levels over an 18-hour period. The initial sizes and shapes of the
various clusters, as well as their shapes 18 hours later, are shown in
Figure 3. The clusters ranged in size from 100 to 1600 km in diameter.
At the 900-mb level, deformation was the predominant means of dispersion
for clusters of all sizes. Deformation, which is caused by eddies
of the same scales as the cluster, increases with cluster size. Eddies
of the same scale increase in energy with size. Murgatroyd derived a
simple relation between relative cluster separation and deformation assum-
ing that the velocity field was predominantly deformed. Using his results
for cluster separation, he was able to reproduce the deformation field of
the 900-mb level.
Kao and Henderson (1970) examined the importance of the shape of
the wind field and dispersion at the 500-mb level. Clusters of
particles were released at various positions in the wind field during
the summer and winter. The shape of the wind field was found to influence
diffusion strongly. Horizontal diffusivity was greatest near the jet
stream, where shear was the strongest. Dispersion was the weakest
near the center of a high, where the flow is weak and uniform. The
zonal horizontal diffusivity was at times an order of magnitude greater
than meridional diffusivity.
In summary, observations indicate that diffusion is strongly scale
dependent; horizontal eddy diffusivity increases with the scale of interest
in the horizontal direction. A review of observational data also reveals
that horizontal diffusivity can vary by an order of magnitude at a given
3 5
length scale; on a regional scale 1t ranges in value from 10 to 10
m2 sec"^. Further studies show that the shape of the flow field greatly
affects horizontal diffusivity and that diffusion 1s greater under strong
shear conditions.
10
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r^v
500mbar wf 9f~7_ 44iir.~
549 J^j||P*'^
/ 700mbar • _» nnn .
726^*^^^ { \ fiJZ
717 V<::-v7^ 936
^^C*7I2 I _ 894
Source: Murgatroyd (1969).
FIGURE 3. THE DEVELOPMENT OF CLUSTERS INITIALLY OF THE FORM ABCDEF AT EACH LEVEL
TO CLUSTERS A'B'C'D'E'F' 18 HOURS LATER
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B. PARAMETERIZATION OF HORIZONTAL EDDY DIFFUSIVITY
Horizontal diffusivlty predominantly depends on the length of scale
and the strength of the shear of the wind flow. Although zonal diffusion
is greater than meridional diffusion, diffusivity can be correlated with
travel time or with length scale. Both approaches have been attempted.
For example, by parameterizing cloud width as a function of an initial
width and travel time, Walton (1973) was able to reproduce Randerson's
data. This approach would have to be developed further to include
the effect of wind shear. In contrast, Murgatroyd related cloud width
directly to deformation, and he obtained good results. Smagorinsky (1963)
parameterized horizontal diffusivity in terms of deformation in his
general circulation model.
Statistical theory shows that after the initial stage, horizontal
diffusion is affected most by eddies of the same scale. Turbulent
energy, as revealed in statistical studies, is concentrated in large-
scale motion. Combining the two results, we can conclude that the
increase in horizontal diffusion with scale is due to the increase in
turbulent energy with scale and that deformation is the primary form
of diffusion.
Murgatroyd's work further exemplifies the importance of deforma-
tion beyond the initial diffusion stage. Therefore, the shape of the
flow field, and in particular the amount of shear present, must be
considered in determining horizontal diffusivity. In general, zonal
shear 1s greater than meridional shear» and zonal diffusion 1s greater
than meridional diffusion.
The observational and statistical studies summarized above show
that the horizontal eddy diffusivity KH 1s scale and shear dependent.
To evaluate realistically, one must take both of these effects Into
account. The theoretical framework of the present Investigation is based
on a treatise on numerical simulation of the atmospheric circulation by
Smagorinsky (1963), who showed that nonlinear lateral diffusion can be
12
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formulated on the basis of the Heisenberg (1948) similarity theory for
turbulence in the equilibrium range. If this theory is applicable to
the scale of interest to the present study, the following formula for
the horizontal eddy diffusivity coefficient can be derived (assuming that
density variations can be ignored):
where A is the grid spacing and |Def| is the magnitude of the velocity
deformation,
The empirical coefficient, a « 0.28, in this scheme was estimated from
global-scale modeling studies.
In this study, this parameterization was applied to the Great Plains
region and tested under various flow pattern conditions, adjusting the
scheme for this application as necessary. The horizontal diffusion
algorithm described above was then incorporated in the Regional Air Pol-
lution Model.
Kh - | • (aA)2 • |Def |
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IV CHARACTERIZATION OF MESOSCALE TRANSPORT AND DIFFUSION
To evaluate horizontal eddy diffusivity using the parameterization
scheme suggested in the previous chapter, one must have a realistically
smooth and continuous wind velocity field. Since only a limited number
of data points are available, the generation of winds for all cells in
a 120 x 100 grid model requires some form of interpolation. If the
interpolation scheme allows discontinuities to exist in the field, sub-
sequent discrepancies in the values of horizontal diffusivity will result.
In air quality modeling studies, wind data are normally collected and
used to interpolate a wind field. But since the horizontal component of
the wind is a two-dimensional vector, it is difficult to find an inter-
polation scheme that generates a field that 1s satisfactorily smooth.
However, the components of the wind can be calculated from the gradient of
geopotentlal height, Z, on a constant pressure surface using the geostrophic
wind relationship:
where g is the gravitational constant and f 1s the Coriolls parameter.
Geopotentlal height fields are readily available from weather maps pub-
lished by the National Weather Service.
Geopotentlal height 1s a scalar quantity. Therefore, 1n working with such
height data, one needs to smooth only one field Instead of the two components
of the wind. Assuming that one can find a method that generates a smooth
and continuous geopotentlal height field, the wind field resulting from the
14
-------
geostrophic relations should also be smooth and continuous. The geopotential
height interpolation techniques examined in this study are described below.
As shown in Figure 4, the test case used to study geopotential height
interpolation methods consists of an 850-mb pressure contour map over a
portion of the Northern Great Plains, with all of the calculated values
for 1700 MST on 30 January 1976. This choice was based primarily on the
convenience of available data for that example. The origin of the coordi-
nates is in the lower left corner of the grid. The first contour on the
left side of the grid has a geopotential height value of 1560 m, and geo-
potential height decreases toward the upper right-hand corner, where the
contour line with the smallest value, 1380 m, is located. The dashed lines
show the constant temperature contours. The geopotential height values
extracted manually from the map and their location on the grid are shown
in Table 1. From the 42 data points, a geopotential height field of
12,000 points was generated.
A. BILINEAR INTERPOLATION
The simplest interpolation scheme that can be used is bilinear inter-
polation. Values at each grid point were found by linearly interpolating
a value for the point from data points in both the east-west and north-
south directions and then equally weighing the resulting values to obtain
a single solution. As shown in Figure 5, the resultant 850-nrfb height
field exhibits a general shape similar to that 1r» Figure 4. The effect
of linear fitting between data points is also quite visible.
The zonal, u, and meridional, v, velocity components were computed
using this height field, and the results shown 1n Figures 6 and 7 were
obtained. Although the winds obtained generally have the proper direction
and magnitude, sharp discontinuities appear near data points, and the
contour lines have a physically unrealistic rectangular shape owing to
the nature of bilinear interpolation. Thus, this technique was not
suitable for the present project.
15
-------
FIGURE 4. 850-mb WEATHER HAP FOR 1700 MST OH 30 JANUARY 1976
-------
TABLE 1. 850-mb GEOPOTENTIAL HEIGHT DATA FOR 1700 MST
ON 30 JANUARY 1976
X
1
20
40
60
80
100
120
1
1565
1545
1520
1490
1465
1440
1435
20
1580
1560
1530
1495
1465
1440
1430
40
1585
1565
1535
1500
1460
1435
1420
60
1580
1560
1530
1485
1455
1430
1410
80
1575
1545
1515
1475
1440
1410
1395
100
1560
1530
1490
1450
1410
1385
1370
B. FITTING OF THE POISSON EQUATION
Next, a method first developed by Harris, Thomasell, and Welsh (1966)
to analyze ocean temperatures was tested. That method requires the grid
values to satisfy Poisson's equation:
v2Z(i,j) = F(1,j)
where Z is the interpolated grid value and F is a forcing function defining
the shape of the field. The data points are taken to be interval boundary
conditions.
To implement this scheme, the study team first used the bilinearly
interpolated geopotential height field to generate the initial field. With
the data points fixed, the geopotential height field Z was required to
satisfy the Laplace equation:
v2Z(1,j) = 0
17
-------
inntiiiHHMHtlnHHn
iinliiinniijniHn
iiliiiiniiiliiiiiiin
i> 11 ni 1111
1410
1560
1530
1500
IK*:
1470
8-:
1440
FIGURE 5. BILINEARLY INTERPOLATED GEQPOTENTIAL
HEIGHT FIELD (m)
18
-------
iniinnniinm.mi..i..i.i.||pft
FIGURE 6. ZONAL WIND FIELD GENERATED FROM BILINEARLY INTERPOLATED
GEOPOTENTIAL HEIGHT DATA (m seH)
19
-------
TTTTH
TTTTT
IIHIMllllHIHJMIIIIIIIIll
mil i ilimin i|
:¦«
-\e
-15
*"
-2t
U
-12
iiiiimiiiMiii.it fiiiimiiiiiiiiim
-I1 |
FIGURE 7. MERIDIONAL MIND FIELD GENERATED FROM BILINEARLY INTERPOLATED
GEOPOTENTIAL HEIGHT DATA (m sec-1)
20
-------
Then a simultaneous relaxation procedure was invoked in which the finite
difference form of the second derivative at each nonboundary grid point
was used with the residual to compute a new value:
v2Z(i,j) = Z(i, j+1) + Z(i,j-1) + Z(i+l,j) + Z(i-lJ) - 4Z(i,j) ;
then
R(i,j) = v2Z(i,j) ,
and for iteration n,
Zn{i,j) = Zn_7 (i ,j) + <*Rn(i J)
where a must be less than 0.5 for convergence.
The mapping of the geopotential height field based on the solution
to the Laplace equation is plotted in Figures 8, 9, and 10 after 25,
125, and 150 iterations, respectively. Physically, the solution to
the Laplace equation can be viewed as an elastic tent tightly stretched
over poles (the data points), forming a smooth field with discontinuities
at these points. The contour lines exhibited in Figure 8, 9, and 10
are smoother than those of the bilinearly interpolated field in Figure 5,
except for the discontinuities around the data points. The resulting
wind field is displayed in Figures 11 and 12, which clearly show the
imposed constraint of keeping the data points fixed. Although the over-
all features of the wind field are physically more realistic, discontin-
uities around the data points still severely distort the velocity
fields in Figures 11 and 12.
The second step of the procedure is generation of a forcing function
that will allow modification of the shape of the tent and will thus,
in effect, smooth the field around the data points. Using the solution
of the Laplace equation found in the first step to generate the forcing
21
-------
itlllllllllil
IlllllllfllllllllWIIIIIIIIllltlllllllllllllllllJlllllllllllll
miimunnm
1410
I-
1560
1530
«-
1500
1470
1440
:.n^i«.iiiiiff»<|«»»i«m|i«»m»»i|tnnniiiiiliiiinininiiiiiiii»Atn|niiiii«.|iiin..nj<.i«iinitiiiin.ii
FIGURE 8. GE0P0TENTIAL HEIGHT FIELD (m) BASED ON THE SOLUTION OF THE
LAPLACE EQUATION AFTER 25 ITERATIONS
22
-------
iiiihiiiiii iiiii diiHiiiiilniMiiiiliiiii 111 Willi ihiiTiiiiiihimiiiih iiIjih MinhiiiiiiiihniiHijhuuini
V \ \ \ \ \ \13(B ¦
1560
1410
1530
1500
1470
: "8
1440
pinrf.ii^nmi.i.j^«ntm.j J |iif iji
FIGURE 9. GE0P0TENTIAL HEIGHT FIELD (m) BASED ON THE SOLUTION OF
THE LAPLACE EQUATION AFTER 125 ITERATIONS
23
-------
mmufniMiiiy niimifiiiiiiiiiTi
miimiJiiinni
iiii ii mini nijjii im iini 11 ii nliiii mjjiiMii im
\ X ^SJ380 j
1560
«¦
1530
[1500
1470
: *8
#" j
r«
1440
FIGURE 10. GEOPOTENTIAL HEIGHT FIELD (m) BASED ON THE SOLUTION OF
THE LAPLACE EQUATION AFTER 150 ITERATIONS
24
-------
to » to to k w n to to too no
I-:
8"f
po
:¦*
¦¦¦"¦*[' r
too
FIGURE 11. ZONAL WIND FIELD (m sec"1) GENERATED FROM GEOPOTENTIAL
HEIGHTS BASED ON THE SOLUTION OF THE LAPLACE EQUATION
AFTER 150 ITERATIONS
25
-------
o too tit
Ttl IT ill I If 1111 ll 111II11 It
iHiiiiiiliiMirnf&i ?fiiimiii*fiiiiiimTiiiiiiiiiTiiiiiiiiiTiiiiii
-IB
00
-12
""
100
FIGURE 12. MERIDIONAL WIND FIELD (m sec'1) GENERATED FROM
GEOPOTENTIAL HEIGHTS BASED ON THE SOLUTION OF THE
LAPLACE EQUATION AFTER 150 ITERATIONS
26
-------
function, the study team computed the Laplace values around the data points
and specified that the forcing function be zero elsewhere. The geopotential
height fields for this case are shown in Figure 13. Apparently, the forcing
functions were not strong enough to eliminate the discontinuities.
Consideration of the general shape of the geopotential height field and
the resultant geostrophic wind field may provide some insight into the
problem. The geopotential heights, which are on the order of 1500 m, vary
only on the order of 100 m, approximately 7 percent, over a distance of
10^ km. The resultant geostrophic wind can thus be estimated as:
which is within the expected range of variations in wind speed. This
result implies that accurately computing the wind field would then require
determination of 1 m in geopotential height over a distance of 10 km.
This value is only approximately 0.1 percent of the mean value for the
geopotential height, and it is within the margin of error of the data
points.
C. BICUBIC SPLINE FIT
The monotonic and small-amplitude characteristics of the geopotential
height field that caused a problem in the Poisson solver algorithm render
the geopotential height field ideal for a bicubic spline fit. Thus, an
algorithm available at the Computer Center at Lawrence Berkeley Laboratory
was used to test the feasibility of a spline fit.
Mathematically, the spline function is a piecewise cubic (third
degree) polynomial passing through all data points and having continuous
first and second derivatives. The spline can be viewed as a set of
27
-------
ii>i)iiiliinfiiiyiniiiiiilrMwii»yniii)»3°niiiniiTiii>iiH)lifniiiiiIiniM»iTiim>iMlmMuii(i
iiihuii
SL380 •
8-:
1410
1560
g-:
l1530
11500
r:
[1470
r*
[UUIIIII|lllllllll|ll/lllllHIIIHHIIlHlllllH|IHIllHI|ll.ll..,twflllllll|l
It n *0 « M M ft to H 100 no * 10
FIGURE 13. GEOPOTENTIAL HEIGHT FIELD (m) BASED ON THE SOLUTION OF THE
POISSON EQUATION WITH PRESCRIBED FORCING FUNCTIONS
28
-------
cubic equations, one equation for each interval between successive
data points. The coefficients of the cubic equations are such that
at any data point the equation for the left interval will yield the
same values for the first and second derivatives, respectively, as
will the equation for the right interval.
Given a set of N data points for which the coordinates (X^.Y^.) and
second derivatives (M^) are known for every point (i = 1, 2, 3, ..., N),
the interpolating spline function S(x) is defined as:
i 3 i (x - xi'3
x> = T ~ XT" + 6 M1+l Xi+1 -
6 Xi+1
X,,, - x
+ [Yi " I Mi(Xi+l " Xi)2] xj+] - Xi
x - X,
[Yi+1 " 6 Mi+l(Xi+l ' Xi)2] X.+1 - X.
where i is such that X^ < x < X^+^. The first and second derivatives
are:
... . »1 <*H1 " x>* . "itl *
S (X) = - T *1tl - X, 2 X1+1 -X,
s"w - H1 (fe
Many compact and efficient algorithms are available for evaluating
the coefficients (DeBoor, 1962).
Vi -v
xi+i
rr4'"i ->W'xui - *1>
- X
X,I + Mi+1
x - Xi
xi+l " Xi;
29
-------
Specifying only the 42 data points, the study team produced the field
shown in Figure 14. Since the gradients and shape appeared promising,
zonal and meridional velocity components were calculated, as shown in
Figures 15 and 16. With the exception of slightly erratic behavior at the
boundaries, the field seems smooth. The computed wind vectors are pre-
sented in Figure 17, in which the lengths of the arrows are proportional
to speed.
Since the bicubic spline fit appears to be the most suitable inter-
polation technique for the present study, it was used to generate the wind
field from geopotential heights in the Regional Air Quality Model.
30
-------
IP n 10 « (0 (0 W W M I#
iminrliiiiiHiiJiniiiiiiliiiiiiiiiiiimiiiiliiiiiiliiliimiiiiliiiiiiiimiiniiiiliiiiiiiiili
380
:-8
8-:
1560
1410
:-8
,1530
1500
•s
1470
1440
FIGURE 14. BICUBIC SPLINE FIT OF GEOPOTENTIAL HEIGHT DATA (m)
31
-------
:-8
»¦:
*¦:
¦5
It":
R-:
: "8
*"""1
FIGURE 15. ZONAL WIND FIELD (m sec"1) GENERATED BY A
BICUBIC SPLINE FIT OF GEOPOTENTIAL HEIGHT DATA
32
-------
: -18 J
) W N 100 110
imniriijiiiiiiiuiiiniMiliiiMiiiifndiiiii
:-8
8-E
-21
8-1>
8*
:-8
-15
:S
R-:
: "8
-12
S-:
: -12 \ \
, ^ III ml I [ |IHI«III^IIIIIIIII|I
10 20 10 40
¦ mji.,Vin^n ^iil/iiii^if.iiiiii|
rHllflll(lll
FIGURE 16. MERIDIONAL WIND FIELD (m sec"1) GENERATED BY A BICUBIC
SPLINE FIT OF GEOPOTENTIAL HEIGHT DATA
33
-------
k^N\\ \
\
\ \
\ \ \
v V \ W\\\\\
* v * x > > > \ \ \ \
\ v M
* 1 l /
100 ISO
0 45 90 nph
mil .
0 20 40 ¦ sec'1
x 10 km
FIGURE 17. WIND VECTORS GENERATED BY A BICUBIC SPLINE
FIT OF GEOPOTENTIAL HEIGHT DATA
34
-------
V SENSITIVITY OF THE TRANSPORT AND
DIFFUSION CHARACTERIZATION SCHEME
To test the sensitivity of the transport and diffusion characterization
scheme described in the previous chapter, the study team recomputed the wind
field and the diffusivity field for the three time periods studied under the
original contract. The pertinent 850-mb weather maps were used in this
exercise. As shown in Figures 18, 19, and 20, in the grid representing the
Great Plains region overlaid on the maps, each cell contains 400 cells of
the Regional Model. The geopotential height fields generated from the
42 data points extracted using the appropriate weather map and a bicubic
spline fit are displayed in Figures 21, 22, and 23. Comparison of the
interpolated height field contour lines with the weather maps shows that
the spline fit scheme works equally well for three different types of wind
flow patterns.
Figures 24 through 29 present sets of wind fields and horizontal eddy
diffusivity fields, in which the former are represented graphically, and
the latter (Kw) are represented by contour lines with values of 0.1 x 10^
2 -1 42 1 42 -1
m sec , 0.5 x 10 m sec , and 1 x 10 m sec . In the original Regional
Model, a constant value of 1 x 10^ m2 sec"1 was used for K^. The velocity
diagrams show that the three days studied have interesting and differing
flow patterns.
For 27 January 1976, as shown in Figure 24, the curvature of the
flow changes from top to bottom on the left side of the figure. Flow on
the right side is weak and uniform. The effect of this change in curva-
ture on the resulting value of KR is shown in Figure 25. On the left side
of the Great Plains region, horizontal diffusion is uniformly large, but
Kh decreases by an order of magnitude on the right side of the region.
35
-------
u£inzo
4
5
IVl: H63
i.-iH0H97
S^SOB
=TO32r
E
-------
CO
*-4
6^3
\iHr3'"
St
£
N
*
FIGURE 19. 850-mb WEATHER MAP FOR 1700 MST ON 28 JANUARY 1976
-------
N
i
9
asax
P
%
1?„55H
X
f
«i537
— t'ki
I 12c524
113.521 X°B
13 JH5
[
!6'805M Ns
FIGURE 20. 850-mb WEATHER MAP FOR 500 MST ON 30 JANUARY 1976
-------
30
30
100
110
80
90
N OAtfflTA
1410
o.
e>
O)
1440
m
-------
20
10
30
50
40
60
100
70
80
90
110
NCNTRNfl
N DAK0TR
1350
at
at
1380
1410
o.
1440
£ DfMITR
o
CD
MTMING
»
ID
\1500
n
•3530
N
1560
no xl 0 km
so
20
40
50
100
BO
90
60
70
FIGURE 22. BICUBIC SPLINE FIT OF GEOPOTENTIAL HEIGHT DATA (m)
FOR 1700 MST ON 28 JANUARY 1976
-------
20
10
30
40
50
100
no
60
60
90
ct
1410
o.
as
CO
1440
o
CD
NY0N1NG
tn
in
1470
o.
m
1500
1530
20
30
50
80
90
100
70
60
FIGURE 23. BICUBIC SPLINE FIT OF GEOPOTENTIAL HEIGHT DATA (m)
FOR 500 MST ON 30 JANUARY 1976
-------
-e»
rv>
' 1 I 1 V U ' JL' 'll'Jj li-'jL-' ir' 'J ' 1 ' ' ' '
iToflRSTir
m
nEbrrskr
10 km
0 45 90 mph
1 l I l I
0 20 40 m sec
-1
FIGURE 24. WIND VECTORS GENERATED BY A BICUBIC SPLINE FIT OF GEOPDTENTIAL
HEIGHT DATA FOR 500 MST ON 27 JANUARY 1976
-------
60
TO
110
eo
100
90
90
DHKITft
o>
-------
SO 70 BO 90 too
It I I I I I I I I i I I I I > I I I I > I I I
lllllllllllllll
^'T\ \ \ \ \ \ \ \
\
\
\
\
\
^ \ \ \
90 100
0 45 90
1 i i i i
0 20 40 m sec
FIGURE 26. WIND VECTORS GENERATED BY A BICUBIC SPLINE FIT OF GEOPOTENTIAL
HEIGHT DATA FOR 1700 MST ON 28 JANUARY 1976
-------
40
50
60
110
SO
100
90
nXntrnr
O.
O)
0>
0.5
OB
CO
NT0HIN6
o
in
ID
(SI
CM
0.5
o.
40
50
too
30
60
70
so
20
60
FIGURE 27. THE COMPUTED HORIZONTAL EDDY DIFFUSIVITY (IN TO4 m2 sec"1)
FOR 1700 MST ON 28 JANUARY 1976
-------
to 20 30
I I I I 1 1 I I I f I I I I f I
40
r-H
TT
SO
rf-r
BO 70 80
I f I I I I I I I I I I I
90
H-i
too
r-H-
rr
Nk
8-
^ \ \ ^
1
\
V
\
\
J
\
\
\
\
I
\
\
V,
\
I
I
\
\
\
\
V
\
\
\
\
\
x
\
\
\
•*
\
\
V
X
X
\ \ ^ ^
\ H ^
\ \ H
* DflMT* * * + t t I t
\ H ^
^ ^ ^ \ \1 \
^ ^ ^ N \ \\\
^ > N \ \ \
. .O
CD
^ \ W^
V \ \ \ ^ ^ *
\ \ \ \ \ ^ >¦
\ \ \ \ \ \ ^
\ \ \ \ \ \ \
\ \ \ \ \ \ N.
\ \ \ \ \ \ ^
\ \ \ \ \ \ N*
04-\ \ \»\ \ \ ^
^ \ \ \ \ \ ^
1 i\l i\ 1 \| i\ 1
10 20 30
»
-s Dfl*0TfW ^ ^ \ \ ^ \C\
^ * * v
* k v v \ \
' ' « ^
> ^ V V \
' ^ *
\
\
\
\
\
k iMYatfUK*
^fc. V V
NEBRASKA
\ X * *
100 110 x 10 km
0 45 90 mph
1 1 l I I .
0 20 40 m sec"
FIGURE 28. WIND VECTORS GENERATED BY A BICUBIC SPLINE FIT OF GEOPOTENTIAL
HEIGHT DATA FOR 500 MST ON 30 JANUARY 1976
-------
20
90
40
50
110
100
SO
*0
.o
o>
e»
.o
CD
O.
o
9 ORMTfl i
CD
O
in
M)
.O
-------
The 28 January 1976 example (Figures 26 arid 27) was chosen because
of the manner in which the flow increases from the lower left to the upper
right corner of the region. The flow is relatively weak and uniform on
the left side of the diagram. The shear caused by increasing wind speed
results in high values of horizontal diffusivity in the upper right portion
of the area.
The wind field for the final test case (30 January 1976), shown in
Figure 28, indicates that the flow is quite weak and diffuse near the
center of the region, resulting in a highly variable diffusion field.
Although flow is weak in the center, it is divergent, thereby causing the
maximum value of diffusion to be near the center of the region. Quite
near the diffusion maximum the weak field is more uniform, and a Ku
minimum occurs.
In adapting Smagorinsky's (1963) global-scale parameterization scheme
to the regional scale, the study team found it necessary to increase the
empirical coefficient, a. This change is in line with dimensional analysis
for the scale of interest to this study. Also, a lower bound of 103 m^ sec"^
was imposed on K^; when deformation is weak, other dominant turbulent pro-
cesses may take place that are responsible for the horizontal diffusivity
at this magnitude. In a study of horizontal diffusion, Gelinas and Walton
(1974) divided turbulent processes into two components. One of the terms,
derived from similarity theory, proves to be a lower bound; on the scale
of the present study, it is on the order of 103 m^ sec"^.
The field of horizontal eddy diffusivity in the three test cases is
realistic in both magnitude and range. Thus, the study team proceeded
to evaluate the effect of the diffusion algorithm on the Regional Air
Pollution Model.
48
-------
VI ANALYSIS OF THE RESULTS
To examine the effect of the new transport and diffusivity charac-
terization scheme on the model's predictions, the study team exercised
the Regional Air Pollution Model for the three meteorological patterns
discussed in the previous chapter using the 1976 and 1986 emissions
scenarios developed for the previous study under this contract. The
sensitivity of SO2 and SO^ concentrations to the SC^-to-SO^ conversion
rate were also studied. Table 2 lists the computer simulations performed
under the contract extension.
TABLE 2. LIST OF THE COMPUTER SIMULATIONS
Case Meteorological Scenario
1 Spring, 4-7 April 1976
2 Spring, 4-7 April 1976
3 Spring, 4-7 April 1976
4 Spring, 4-7 April 1976
5 Winter, 27-31 January 1976
6 Summer, 9-11 July 1975
S02-to SO4
Emissions Conversion Rate
Scenario (percent per hour)
1976 0.3%
1986 0.3
1976 1.0
1986 1.0
1986 1.0
1986 1.0
Selected computed wind fields are shown In Figures 30 through 35.
Wind fields for the winter case were shown earlier in Figures 24, 26, and 28.
The resulting SOg concentration fields for Case 1 are compared with fields
from the original study in Figures 36 through 38. The concentration fields
are three-hour averages 27, 36, and 51 hours after the start of the simu-
lations, A comparison at the same time for Case 2 is given in Figures 39
through 41. The main difference between the original and new meteorological
data bases reflects the use of wind fields and horizontal diffusivities
49
-------
40
100
110
0)
o. _
00
o
in
CO
. .o
(M
no x 10 km
0 45 90 mph
eo
100
l I l I I
0 20 40 m sec"
FIGURE 30. WIND VECTORS GENERATED BY A BICUBIC SPLINE FIT OF GE0P0TENTIAL
HEIGHT DATA FOR 1700 MST ON 4 APRIL 1976
50
-------
110
100
90
o
o>
a
r~
OAKBT
S" •
.a
¦ -S
NEBRRSK
. .a
. .o
(M
\ \ \C0L^RflO9
no x 10 ki"
0 45 90 mph
100
80
20
Mill j
0 20 40 m sec"
FIGURE 31. WIND VECTORS GENERATED BY A BICUBIC SPLINE FIT OF GEOPOTENTIAL
HEIGHT DATA FOR 1700 MST ON 5 APRIL 1976
51
-------
100
110
fTfiNfi
©
N V
CO
o.
-------
4 ^ ^
UrAMINfr
NEBRHSKA
C0L^RRDfl
| 1 1 ' | ' 1 ' 1 | ' ' ' 1 | 1 1 ' 1 | ' ' 1 ' ) 1 1 ' ' 1 ' ' ' ] ' 1 1 ' | 1 1 ' 1 I ' ' ¦ ' ; ' ' 1 '
10 20 30 40 50 60 70 60 90 100 110 X 10 M1
0 45 90 mph
Mill
0 20 40 m sec
-1
FIGURE 33. WIND VECTORS GENERATED BY A BICUBIC SPLINE FIT OF GEOPOTENTIAL
HEIGHT DATA FOR 500 MST ON 9 JULY 1975
53
-------
50
60
70
100
30
90
110
20
80
10
CD
.O
CO
¦ .V ¦ H"
onaMMi ¦
100
0 45 90 mph
0 20 40 m sec
FIGURE 34. WIND VECTORS GENERATED BY A BICUBIC SPLINE FIT OF GEOPOTEHTIAL
HEIGHT DATA FOR 500 MST ON 10 JULY 1975
54
-------
110
100
! _o
a
m
8*
'• -8
8- -
no x 10' km
100
90
60
SO
40
20
0 45 90 mph
1 I M I
0 20 40 m sec
FIGURE 35. WIND VECTORS GENERATED BY A BICUBIC SPLINE FIT OF GEOPOTENTIAL
HEIGHT DATA FOR 500 MST ON 11 JULY 1976
55
-------
II l» M II W II 71 II
N MKOIft
• MftOTfl
.1 f '^f23
\
8 • *11
(a) Original Scheme
10 km
(b) Revised Scheme
FIGURE 36. COMPARISON OF S02 CONCENTRATION FIELDS (yg m~3) FOR
CASE 1: 500 TO 800 MST ON 5 APRIL 1976
56
-------
w
f 19
«•
M
• MKOfft
tfVOHtM
W H 71 91
(a) Original Scheme
Itt
•0
SO
SO
•0
70
>0
•0
'100
110
MNTMM
8
8
: *
* ¦
*:
MYtNINC
4 '«
x 10 In
100
110
(b) Revised Scheme
FIGURE 37. COMPARISON OF S02 CONCENTRATION FIELDS (yg m"3) FOR
CASE 1: 1700 TO 2000 MST ON 5 APRIL 1976
57
-------
I* II M II U «• tf
I I I I I I I I I I I I I I I I l I I l I I I
r\
vj.
UYOftl
(_/
6__.
-e >
¦ 1 1 M
Mm
M IM 111
• OMOIM
/v
U \
RMfMKA
.. ^Yf
111 ¦ ¦' i ¦ »y.'|. i j-11|.
Colombo
I* »• M «• (• M Ti •• M II* X 10 kin
(a) Original Scheme
« M to 70 to
I OMIT
Vn
to ao n> to w too 110 x 10 km
(b) Revised Scheme
FIGURE 38. COMPARISON OF S02 CONCENTRATION FIELDS (yg m~3) FOR
CASE 1: 800 TO 1100 MST ON 6 APRIL 1976
58
-------
w
M
¦ MKOT0
8
moni
8
20
!• SI M 79 ••
(a) Original Scheme
M
M
MMTAM H PftKfT*
t PAKSTt
10 20 SO «0 SO SO TO tOM 100 UO XlO fai
(b) Revised Scheme
FIGURE 39. COMPARISON OF S02 CONCENTRATION FIELDS (yg m"5) FOR
CASE 2: 500 TO 800 MST ON 5 APRIL 1976
59
-------
1ft It
«• II II 71 M
I f > i i I i i i r I * i i i I i i i H i ii' i I i i i f < > i * i I i t i i I i i i i I
MWTMfl N Mwom
IM 110
{ 7p .'l£;;A-
' 'LJ
\V:-' \
WW
« PMOT0
(CcS ^
21 ^\lO
7* •* •» i»« no x 10 km
(a) Original Scheme
MNTMA « OMSTA
10 20 SO 40 fO M TO MO §0 100 HO X 10 lOR
(b) Revised Scheme
FIGURE 40. COMPARISON OF SO? CONCENTRATION FIELDS (Mg m"'i) FOR
CASE 2: 1700 TO 2000 MST ON 5 APRIL 1976
60
-------
M
110
M
•#
M
M
"8
$ MKOTA
•¦8
•a
x 10 in
110
w
(a) Original Scheme
to
•0
to
•0
70
•0
•0
ISO
110
- s
- *
- *
- 8
• '8
* 10 In
20
10
«0
SO to 70 SO
(b) Revised Scheme
110
•0
too
FIGURE 41. COMPARISON OF SO? CONCENTRATION FIELDS (yg m"3) FOR
CASE 2: 800 TO 1100 MST ON 6 APRIL 1976
61
-------
computed by the new scheme and the measured mixing height data. In the
original simulations, the appropriate seasonally averaged mixing height
data were used for the three meteorological scenarios. Measured mixing
heights at 12-hour intervals for the period of time for each of the three
scenarios were obtained. These data were interpolated to three-hour
intervals. A constant value for horizontal diffusivity was used in the
original simulation, whereas the newly developed algorithm for determining
horizontal eddy diffusivity was used in the present study. Thus, in the new
simulations, horizontal diffusivity is variable in time and space. The wind
field in the mixed layer was also calculated, so that it now corresponds to
the geostrophic wind on the 850-mb weather maps. The reader is reminded that
meteorological scenarios are not climatologically representative of the given
seasons.
A. ANALYSIS OF THE EFFECT OF THE NEW CHARACTERIZATION SCHEME
It was found that dispersion of pollutants on the mesoscale is sensitive
to variation of the horizontal eddy diffusivity parameter. In particular,
decreasing the horizontal diffusivity decreased the size of the plumes
far downstream from the source. The horizontal diffusivity fields resulting
from the new characterization scheme for the spring scenario have values
¦j o -1 4 2-1
ranging from 5x10m sec <. <. 10 m sec . Since a constant value
of 104 m2 sec"^ was used for horizontal diffusivity in the original simu-
lations, the diffusivity field was not expected to change drastically the
dispersion of pollutants in the worst case, i.e., the spring scenario.
The wind fields constructed using the new characterization scheme differ,
however, considerably from those used in the original analysis. The effect
of the new wind field is illustrated in Figure 37, which shows a signif-
icantly greater buildup of S02 near the sources in North Dakota. The dif-
fusivity and mixing height have not varied enough to account for such a
change. Owing to the weak geopotential height gradient in that region, the
new mixing layer winds are weak, as shown in Figure 38. As a result, trans-
port of pollutants to downwind areas is quite limited, and it causes a con-
centration buildup in the North Dakota region. The computed maximum con-
centration in that region is more than double that in the original simulation.
62
-------
B. AIR QUALITY ANALYSIS
The following three subsections discuss the effect of the new scheme
for characterizing wind and diffusivity fields on the computed concentra-
tion distributions.
1. Spring Scenario
The effect of the 1986 emissions on air quality in the spring scenario
are presented in Figures 39 through 41. In general, pollutants are trans-
ported only a short distance in the southwest and northeast portions of
the modeling region in the new simulations, resulting in greater pollutant
buildup. They are transported a greater distance in the northwest to south-
east strip of the region, which permits better mixing and lower concentra-
tions of pollutants. In the northeast section, three-hour-average concen-
_3
trations exceed 8 yg m at distances on the order of 100 km downwind of
_3
the sources. Elsewhere, SOg concentrations are greater than 2 yg m , but
since the pollutants are evenly dispersed, concentrations rarely exceed
_3
4 pg m except near the source.
2. Winter Scenario
The winter scenario results after 12, 39, and 57 hours of simulation
using 1986 emissions are presented in Figures 42 through 44. The mixing
heights are approximately one-half their spring values during this winter
simulation. In general, the horizontal diffusivity varies over an order of
3 4 2 -1
magnitude ranging from 1 x 10 to I x 10 m sec . The mixing layer winds
vary over twice the range of their spring counterparts, reaching maximum
speeds close to 30 m sec"^. The increase in wind speed is the dominant
factor in creating the difference between the spring and winter SOg concen-
tration fields. After 12 hours, pollutants have traveled up to 500 km from
_3
their sources, and concentrations of 8 ug m occur 300 km from point sources
in North Dakota. Note that because of the increased wind speeds the computed
SOg concentrations on 29 January 1976 are significantly lower compared with
63
-------
•0
90
•0
to
100
IJO
r
I
*0
00
x 10 ton
•o
oo
100
110
FIGURE 42. S02 CONCENTRATION FIELDS (yg nf3) FOR CASE 5 (REVISED
SCHEME): 1700 TO 2000 MST ON 27 JANUARY 1976
10
to
K
00
100
no
I 0HKIT0
' %
[Off]
• -8
¦ s
40
100
110
FIGURE 43. S02 CONCENTRATION FIELDS (yg m ) FOR CASE 5 (REVISED
SCHEME): 2000 TO 2300 MST ON 28 JANUARY 1976
64
-------
110
100
•0
•0
•0
10
«0
>0
« *8
r
ITU
; -8
¦ -8
« 8
z— -2
X 10 in
110
too
•0
•0
40
SO
M
SO
FIGURE 44. S02 CONCENTRATION FIELDS (yg m'3) FOR CASE 5 (REVISED
SCHEME): 1400 TO 1700 MST ON 29 JANUARY 1976
65
-------
those on 27 January 1976 and 28 January 1976. After 57 hours of transport
_ "3
and diffusion, S02 concentrations are greater than 4 pg m in only a
small area.
3. Summer Scenario
The summer scenario results in Figures 45 through 47 show that SO^
concentrations in that season can reach the spring levels under the proper
meteorological conditions. The summer season characteristically has the
greatest mixing heights (approximately twice the spring heights) because
of the increased surface heating. The mixing heights for the summer
scenario are generally above the seasonal average values in the northwest
portion of the Great Plains region. Consequently, the summer mixing heights
tend to prevent pollution buildup in this area. The diffusivities, however,
are slightly lower than the corresponding spring values because of more
uniform wind fields. The winds are generally moderate and greater than
the spring winds in the eastern half of the region. In the western half
of the region, the winds are weak. Unlike the winter winds, the summer
mixing layer winds can favor poor transport and therefore high pollu-
tant concentrations. The SOg three-hour-average concentrations as a
result of the wind field were uniform in the eastern portion of the
region and were equal to their spring scenario counterparts in the
western portion of the region. Again, because of the increase in wind speeds,
-3
pollutant concentrations remained below 4 yg m through most of the region
after 57 hours of simulation.
C. SENSITIVITY STUDY OF THE S02/S04 CONVERSION RATE
The concentrations of SOg and SO^ after 51 hours of simulation for
the spring scenario with a 1 percent SOg/SO^ conversion rate are shown
in Figures 48 and 49 for 1976 and 1986 emissions. When a 0.3 percent
conversion rate was used in the original model, the resulting SO^ values
were not much higher than background concentrations. As shown in Figure 48,
SO^ pollutant concentrations were generally on the order of 4 yg in"3 for
66
-------
to
160
110
N
• 8
- 8
' S
:
- ¦»
«- ••
x 10 kn
100
io
•D
110
40
90
70
FIGURE 45. S02 CONCENTRATION FIELDS (yg nf3) FOR CASE 6 (REVISED
SCHEME): 200 TO 500 MST ON 10 JULY 1975
no
100
«o
00
• OfttfTH
" t
s
BHIM6
110 x 10 In
•o
too
00
70
•0
ao
FIGURE 46. S02 CONCENTRATION FIELDS (yg m~3) FOR CASE 6 (REVISED
SCHEME): 500 TO 800 MST ON 11 JULY 1975
67
-------
v V1" " "
\ \ mmmn
1
1' 1 11111 1111111111,11.111 III 11111
II MKVTH I
\
S DMKVTR l> \ J
\ *\
' \ C~Vs\>Ns' ^ '"•""s
NEtylSftfl \
\ \ \ \ :
\ \ V
^ \ \ 1 .
u \ \ \
' 0^1 cftiKftoi (v Vv \ * n
^ C^\ ^\ \ 1 I
FIGURE 47. SO2 CONCENTRATION FIELDS (yg m"3) FOR CASE 6 (REVISED
SCHEME): 1400 TO 1700 MST ON 11 JULY 1975
68
-------
100
110
•0
•0
90
40
SO
70
to
g-
r.
x 10 ka
100
no
30
40
50
SO
70
•0
•0
(a) SOg Concentration Field
«0
100
110
so
80
70
to
90
40
x 10 kn
110
90
90
too
40
to
SO
(b) SO^ Concentration Field
FIGURE 48. CONCENTRATION FIELDS (yg m"3) FOR CASE 3 (REVISED SCHEME):
800 TO 1100 MST ON 6 APRIL 1976
69
-------
1976 emissions with the higher conversion rate. The effects of the
increased conversion rate are more noticeable in the 1986 emissions
_3
simulations; the SO. concentrations exceed 6 yg m in a small portion
. -3
of North Dakota, as shown in Figure 49, and are higher than 3 yg m
over most of the region. In weak circulations, such as that over North
Dakota in the spring scenario, SC^ conversion to SO^ is a significant
process if the conversion rate is on the order of 1 percent or more
because 200 km from the source 30 percent of the SOg has been converted
to S0^.
70
-------
so
•0
70
•0
to
>0
so
too
no
iai&
o
*
«¦
x 10 In
40 SO SO 70 00 90
S0o Concentration Field
10
to
too
no
so
to
70
to
to
40
100
no
to
90
*•
HEtXMKf)
SO
to
to
to
to
100
110
70
(b) SO^ Concentration Field
FIGURE 49. CONCENTRATION FIELDS (yg m"3) FOR CASE 4 (REVISED SCHEME):
800 TO 1100 MST ON 6 APRIL 1976
71
-------
Appendix
SIMULATION RESULTS
72
-------
Appendix
SIMULATION RESULTS
72
-------
40
•0
•0
•0
90
too
20
MNTMIA
M OMMTR
S DAKBTA
NEBRASKA
CILIRAOi
40
SO
•0
100
•0
90
(a) S02
70
90
100
9 0AK9TA
HT9M1NC
SO
•0
70
90
90
100
(b) S04
FIGURE A-l. S02 AND S04 CONCENTRATIONS FOR CASE 1:
1700 TO 2000 MST ON 4 APRIL 1976
74
-------
•0
100
H MMTA
« *
» WKITA
3
to
so
40
SO
•0
70
#0
•0
100
(a) S02
>0
•0
TO
40
10
•0
too
MONTANA
S MKfTII
MTfNINC
•0
to
•0
too
110
(b) S04
FIGURE A-2. S02 AND SO4 CONCENTRATIONS FOR CASE 1:
200 TO 500 MST ON 5 APRIL 1976
75
-------
I | ¦ I I | ' 1 1 1 I 1 1 1 1 I 1 1 1 1 I ' 1 1 1 I I ' I I I I I I | ! I I I | I ! I I | I II I
10 20 SO 40 SO (0 70 80 «0 100 I!0
(a) S02
SO
SO
BO
70
100
eo
90
MTtHINC
SO
•0
40
•0
•0
100
(b) S04
FIGURE A-3. S02 AND SO4 CONCENTRATIONS FOR CASE 1:
1100 TO 1400 MST ON 5 APRIL 1976
76
-------
110
100
•0
70
•0
•0
to
40
t s
•S
100
70
to
to
to
40
SO
(a) S02
too
110
to
to
40
*¦
NYtftING
ctLtmot
110
to
100
to
to
70
(b) S04
FIGURE A-4. S02 AND SO4 CONCENTRATIONS FOR CASE 1:
2000 TO 2300 MST ON 5 APRIL 1976
77
-------
70
•0
to
SO
40
too
90
40
SO
60
70
20
80
BO
100
(a) S02
50
30
40
60
80
too
20
N DRK0TA
S 0AK6TR
KTBHING
CW.MA08
60
60
60
60
100
20
(b) S04
FIGURE A-5. S02 AND SO4 CONCENTRATIONS FOR CASE 1:
500 TO 800 MST ON 6 APRIL 1976
78
-------
so
10
•0
to
100
•0
110
so
<0
TO
40
•0
•0
too
20
so
(a) S02
90
70
100
to
•0
HTtMIMC
20
70
•0
too
(b) S04
FICURE A-6. S02 AND SO4 CONCENTRATIONS FOR CASE 1:
1400 TO 1700 MST ON 6 APRIL 1976
79
-------
«D
SO
40
*0
too
110
* :
8
?¦
40
SO
J 00
no
(a) S02
90
40
SO
90
too
110
p
fr'
*'
CflHMI
to
40
SO
70
•0
SO
100
(b) S04
FIGURE A-7. SO2 AND SO4 CONCENTRATIONS FOR CASE 2:
1700 TO 2000 MST ON 4 APRIL 1976
80
-------
•0
70
100
no
40
10
>0
• 8
8
8- ¦
•o
100
no
•o
(a) SO.
10 jo so 40 SO §0 TO 00 tO 100 110
MtfTMR
\
* OftKITN \
*b=> \ !
• Mean /
] :
j NTMINC
! ^
s.
v
*
Ncomswi V/'-Ns!
» N
CMMOC
•
1 1 i 1 1 1 l » 1 * 1 1 1 1 1 1 i 1 > 1 PI ' ' ' 1 1 ' ' l 1 ' ¦ l ' 1 ' ' ' ' 1 1 ' 1 1*
(b) S04
FIGURE A-8. S02 AND SO4 CONCENTRATIONS FOR CASE 2:
200 TO 500 MST ON 5 APRIL 1976
81
-------
BTMIMG
(a) S02
NINTANfl
N MKITO \
C \!
. MMT« / :
7 HTIHIRG
NCMM4U) X,/—v (
^ \ ^
a I
Cj CSLMMOf Jt
(b) so4
FIGURE A-9. S02 AND SO4 CONCENTRATIONS FOR CASE 2:
1100 TO 1400 MST ON 5 APRIL 1976
82
-------
to
N
100
¦ MKfTft
<8
8
• n
to
00
20
>0
to
10
•0
too
no
(a) S02
20
90
to
•0
•0
•0
100
MONTOUR
« MMf*
HTOHING
* '
00
00
too
110
(b) S04
FIGURE A-10. S02 AND SO4 CONCENTRATIONS FOR CASE 2:
2000 TO 2300 MST ON 5 APRIL 1976
83
-------
no
to
100
•0
\\
IKfTR
R
no
100
20
(a) S02
ao
40
100
no
•o
HTIMIHC
100
110
(b) S04
FIGURE A-ll. SO2 AND SO4 CONCENTRATIONS FOR CASE 2:
500 TO 800 MST ON 6 APRIL 1976
84
-------
no
70
too
so
•0
90
N MKVTI
8
no
70
•0
•0
SO
40
20
(b) S04
FIGURE A-12. S02 AND SO4 CONCENTRATIONS FOR CASE 2;
1400 TO 1700 MST ON 6 APRIL 1976
85
-------
•0
TO
00
*0
100
110
40
90
*0
¦ MKtTft
S DAKOTA
CfLflRROI
no
60
100
60
20
(a) S02
no
100
NY6NING
SO
60
70
•0
•0
100
20
(b) S04
FIGURE A-13. SO2 AND S04 CONCENTRATIONS FOR CASE 3:
1700 TO 2000 MST ON 4 APRIL 1976
86
-------
•0
100
>10
•0
so
« MK0TA
MMTI
S MKfTfl
110
100
to
SO
so
40
20
(a) S02
100
110
•0
70
SO
40
20 SO
1 -U H T
HTMIMO
110
100
SO
(h) S04
FIGURE A-14. S02 AND SO4 CONCENTRATIONS FOR CASE 3:
200 TO 500 MST ON 5 APRIL 1976
87
-------
70
to
•0
•0
•0
110
M
100
20
M ONK0TR
r-
so
40
$0
20
lie
100
(a) S02
20
40
•0
100
no
N ORKSTR
C0LMIMM
20
to
•0
70
•0
100
110
(b) S04
FIGURE A-15. SO2 AND SO4 CONCENTRATIONS FOR CASE 3:
1100 TO 1400 MST ON 5 APRIL 1976
88
-------
too
110
•0
TO
SO
SO
•0
to
CSLfftWM
•0
too
no
70
•0
BO
40
SO
SO
20
(a) S02
100
110
70
SO
SO
HINTANA
S OflKSTft
MTSMIH6
SO
too
uo
40
SO
SO
(b) S04
FIGURE A-16. SO2 AND S04 CONCENTRATIONS FOR CASE 3:
2000 TO 2300 MST ON 5 APRIL 1976
89
-------
, j ^MINC
(a) S02
too
110
* J
3 OMUTfi
/¦S
CfLMMM
SO
•0
110
70
•0
•0
100
M
(b) S04
FIGURE A-17. S02 AND S04 CONCENTRATIONS FOR CASE 3:
500 TO 800 MST ON 6 APRIL 1976
90
-------
to
10
00
to
100
no
S
8-
*' ¦
' S
\«*
40
too
110
(a) S02
•P
•0
100
no
NINTIWR
S OftKCTlh
•0
100
no
(b) S04
FIGURE A-18. SO? AND S04 CONCENTRATIONS FOR CASE 3:
1400 TO 1700 MST ON 6 APRIL 1976
91
-------
' *€
ft l-
1 MKCTft I
8 DMC8TR / \
//
Mi^.M
MCMflSKR sj[
^ ^ NfiT"
(a) S02
100
90
80
»0
70
80
80
40
too
no
(b) S04
FIGURE A-19. SO2 AND SO4 CONCENTRATIONS FOR CASE 4
1700 TO 2000 MST ON 4 APRIL 1976
92
-------
*?
to
so
TO
•0
M
too
110
• MKtm
*¦
IMC
MCMRSKf)
€0
SO
to
TO
•0
•0
(a) S02
SO
so
to
too
110
• '9
so
i'io
so
TO
•0
100
(b) S04
FIGURE A-20. SO2 AND SO4 CONCENTRATIONS FOR CASE 4:
200 TO 500 MST ON 5 APRIL 1976
93
-------
70
•0
•0
40
•0
too
110
to
•8
8\
* u
9¦
n-
so
40
20
70
UO
00
100
(a) S02
40
20
SO
•0
70
100
110
•0
MNTftM
8' '
,> £
S OAKSTft
; *8
•8
8* •
R-
so
too
110
(b) S04
FIGURE A-21. SO2 AND SO4 CONCENTRATIONS FOR CASE 4:
1100 TO 1400 MST ON 5 APRIL 1976
94
-------
110
90
too
40
jmrmm
' 8
8 f
: '2
HMI
¦#
8- ¦
i:o
«o
so
•0
70
too
10
90
SO,
70
•0
•0
too
110
t OMC0TJI
• ?
-t
to
70
no
(b) S04
FIGURE A-22. S02 AND SO4 CONCENTRATIONS FOR CASE 4:
2000 TO 2300 MST ON 5 APRIL 1976
95
-------
70
•0
100
110
X >
70
100
110
(a) S02
KWMKl)
(b) S04
FIGURE A-23. S02 AND S04 CONCENTRATIONS FOR CASE 4:
500 TO 800 MST ON 6 APRIL 1976
96
-------
10 *0 SO 40 SO M 70 tO M 100 110
« 0*KiT»
I I I | I I I ¦ | I'I ' ' I " ' ' I ¦ ' I » I I ' ' t I ' ' »l |'< I » H ' I I ' I ' ' ' ' I ' ' ' ¦ I * ' ' '
io to m «b w to to so to too i:o
(b) S04
FIGURE A-24. SO? AND S04 CONCENTRATIONS FOR CASE 4:
1400 TO 1700 MST ON 6 APRIL 1976
97
-------
TO
100
110
20
S OMIITA
X *
CtLI
80
110
20
00
00
00
too
(a) S02
20
40
60
100
00
110
MTM1M6
COLORADO
100
no
(b) S04
FIGURE A-25. SO2 AND SO4 CONCENTRATIONS FOR CASE 5:
1700 TO 2000 MST ON 27 JANUARY 1976
98
-------
M
40
SO
•0
too
>10
9 DAKOTA
9 ¦
to
•0
•0
100
110
(b) S04
FIGURE A-26. SO2 AND SO4 CONCENTRATIONS FOR CASE 5:
200 TO 500 MST ON 28 JANUARY 1976
99
-------
•0
100
no
so
¦ OMUTN
MWTMM
\\
\\
Vxv
90
40
20
SO
eo
100
uo
(a) S02
SO
100
60
TO
•0
110
RINTMM
*'
CILMAM
SO
•0
M
•0
100
•0
(b) S04
FIGURE A-27. SO? AND S04 CONCENTRATIONS FOR CASE 5:
1100 TO 1400 MST ON 28 JANUARY 1976
100
-------
z
r •
•e
n\
' s
••s
20
so
«0
to
•0
•0
to
100
no
(a) S02
•0
70
100
«0
•0
to
so
N DWltTft
a
8
HTtHINC
too
110
to
w
40
(b) S04
FIGURE A-28. SO2 AND SO4 CONCENTRATIONS FOR CASE 5
2000 TO 2300 MST ON 28 JANUARY 1976
101
-------
TO
•0
100
110
•0
40
*0
s-
uo
90
100
SO
40
20
50
60
(a) S02
100
no
60
HTtNING
8"
"8
* '
60
too
no
(b) S04
FIGURE A-29. S02 AND SO4 CONCENTRATIONS FOR CASE 5:
500 TO 800 MST ON 29 JANUARY 1976
102
-------
to
TO
90
40
to
to
110
100
¦ MIMTft
8
ft- *
v\>.
• *
*•
to
to
100
110
20
•0
to
20
to
to
to
100
110
HTM INS
110
to
to
too
70
(b) S04
FIGURE A-30, SO? AND S04 CONCENTRATIONS FOR CASE 5:
1400 TO 1700 MST ON 29 JANUARY 1976
103
-------
MNTMM
! VN> ^
N OMUTR \
s omtfTD \ /
) :
HTiMINO
¦Ox
x ^
: '1X r-s
NCBRMKR (
Sn1*. 'IV X^i\ ^v.e«L«R0». (" U)\
>vcg) ^
10 <0 so 40 to to 70 to 90 100 J10
(a) S02
40
60
•0
100
110
t"
8-
• 8
MYINIKG
O
*¦¦
Si
100
no
(b) S04
FIGURE A-31. SO2 AND SO4 CONCENTRATIONS FOR CASE 6
1700 TO 2000 MST ON 9 JULY 1975
104
-------
(a) S02
100
so
40
10
70
•0
•0
110
•0
MNTRNft
M MK1TII
HTfHINC
SO
•0
70
M
100
•0
no
(b) S04
FIGURE A-32. SO? AND S04 CONCENTRATIONS FOR CASE 6:
200 TO 500 MST ON 10 JULY 1975
105
-------
BO
•0
SO
110
100
S MMTR
s
8'«.
* R
-•v. -^5
¦ i" i
40 SO SO 70
20
SO
100
no
eo
so
(a) S02
40
SO
tio
90
SO
SO
SO
100
70
•8
\ HTSN1MC
8* •
100
110
so
(b) S04
FIGURE A-33. S02 AND SO4 CONCENTRATIONS FOR CASE 6:
1100 TO 1400 MST ON 10 JULY 1975
106
-------
no
rftMlNC
too
70
•0
•0
110
so to
(a) SO.
40
too
110
to
•0
to
3
• *
ISO
100
•0
00
so so
(b) SO,
40
so
FIGURE A-34. S02 AND SO4 CONCENTRATIONS FOR CASE 6:
2000 TO 2300 MST ON 10 JULY 1975
107
-------
70
!00
110
'•MUG
40
SO
so
•0
20
70
•0
100
110
(a) S02
90
20
80
SO
•0
90
too
110
8
«¦
40
70
100
(b) S04
FIGURE A-35. S02 AND SO4 CONCENTRATIONS FOR CASE 6:
500 TO 800 MST ON 11 JULY 1975
108
-------
to
•0
100
110
TO
to
to
8- -
8
I
HTMIH6
8
100
lto
70
to
to
<0
BO
to
to
40
(a) S02
too
lto
to
to
70
to
SO
40
20
i OftXtT*
MONTANA
8-
-8
•8
8
¦8
•8
uo
to
100
to
to
(b) S04
FIGURE A-36. S02 AND SO4 CONCENTRATIONS FOR CASE 6:
1400 TO 1700 MST ON 11 JULY 1975
109
-------
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Ill
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