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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
DISCLAIMER
Publication of this report does not signify that the contents
necessarily reflect the views and policies of the U.S. Environmental
Protection Agency, nor does mention of trade names or commercial
products constitute endorsement or recommendation for use.
111
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS vii
LIST OF TABLES ix
1. INTRODUCTION 1-1
1.1 Background 1-1
1.2 The MESOSCALE Grid Model (MESOGRID) 1-2
1.3 Integrated Mesoscale Modeling System 1-3
1.4 Organization of the Report 1-3
2. MESOGRID Technical Discussion 2-1
2.1 Model Formulation 2-1
2.2 The Grid System 2-2
2.3 Specification of Model Inputs 2-2
2.4 Solution of the Advection-Diffusion Equations 2-4
2.4.1 Horizontal Advection 2-6
2.4.2 Vertical Diffusion 2-10
2.4.3 Calculation of Spatially Variable K Profiles 2-11
£>
2.4.4 Numerical Stability Criteria 2-14
2.5 Boundary Conditions 2-19
2.6 Conversion of Sulfur Dioxide to Sulfate 2-19
2.7 Dry Deposition of Sulfur Dioxide and Sulfate 2-20
2.8 Plume Rise 2-21
2.9 The MESOGRID Computer Program 2-22
3. MESOGRID User Instructions 3-1
3.1 General 3-1
3.2 Description of Card-Image Input 3-1
3.3 Other Input Considerations 3-7
3.3.1 Meteorological Considerations and
MESOPAC Input 3-7
3.3.2 Array Size Considerations 3-8
3.4 MESOGRID Model Output 3-8
3.4.1 Line Printer Output 3-8
3.4.2 Direct Access Disk Output 3-9
3.5 Execution Time and Core Requirements 3-11
4. TEST CASE FOR MESOGRID 4-1
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
TABLE OF CONTENTS (Continued)
REFERENCES
APPENDIX A
APPENDIX B
APPENDIX C
ABSTRACT
TEST CASE MESOPAC INPUT AND OUTPUT
TEST CASE MESOGRID OUTPUT
TEST CASE NAMELIST FILE
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
LIST OF ILLUSTRATIONS
Figure Page
1-1 Integrated Modeling System 1-4
2-1 A Schematic Representation of the MESOGRID
Cartesian Coordinate System 2-3
2-2 Vertical Structure of the MESOGRID Computation
Grid Assuming Default Values 2-5
2-3 Scale Parameters for the Advection of a Rectangular
Block of Uniformly Mixed Material 2-9
2-4 MESOGRID Flow Chart 2-23
4-1 MESOGRID Test Case Parameter and Emission Source
Inventory Input 4-2
4-2 Test Case Library File (MESOFILE) 4-3
4-3 MESOGRID 24-Hour Average SO Concentration Calcomp
Plot, 16 June, 1978 (from MESOFILE) 4-4
4-4 MESOGRID 24-Hour Average SO Concentration Line
Printer Plot, 16 June, 1978 (from MESOFILE} 4-5
4-5 Bulk Statistical Comparison of MESOPLUME to
MESOGRID, 16 June, 1&78 (from MESOFILE) 4-6
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ENVIRONMENTAL RESEARCH* TECHNOLOGY INC
LIST OF TABLES
Table Page
2-1 Inverse Monin-Obukhov Length L (m ) as a
Function of PGT Stability Class, for Roughness
Length z =25 cm (After Colder 1972) 2-12
2-2 Stability-Dependent Expressions for K in the
Surface Layer and 8K
32 S
z
2-15
2-3 Maximum Values of U and K p, K? _ Vs. Time Step
At for Nominal Model Parameters ' 2-17
2-4 Determining When MESOGRID Will Modify K Profiles 2-18
21
3-1 Logical Unit File Structure 3-10
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
1. INTRODUCTION
1.1 Background
In response to a growing national commitment to the use of
indigenous coal reserves to meet energy generation demands, several
regions of the country will experience greatly expanded use of coal and
oil shale resources for steam electric power plants and other coal-based
energy resource development. But, as mandated by federal National
Ambient Air Quality Standards, and by the PSD major source review pro-
cedures, additional coal-based energy resource development (ERD) will
only be permitted where consistent with the maintenance of human health,
welfare, and environmental quality. Accordingly, the siting and genera-
tion capacity of such ERD facilities may be constrained by their poten-
tial impacts on regional ambient air quality.
Various plans have been proposed for regional development of
multiple major new facilities, and suitable model simulation tools are
needed to assess the impacts of different energy development scenarios
on regional-scale air quality.
To meet this need in the public interest, the National Oceanic and
Atmospheric Administration (NOAA) has sponsored a study by Environmental
Research § Technology, Inc. (ERT) to develop, evaluate, and exercise a
number of alternative approaches to regional-scale ambient air quality
modeling. A major objective of this study is to provide a suite of air
quality simulation models that are both technically sound and computa-
tionally practical for assessing regional-scale impacts of energy
development scenarios.
As described in the companion report, Volume 1 (Bass et al. 1979),
three different air quality transport-diffusion models have been
developed, implemented and compared for simulation of point-source plume
dispersion on the mesoscale [e.g., dispersion at ranges of 100 to
1,000 kilometers (km)]. The models are optimized for regional-scale
impacts; ambient air concentrations calculated in the near field of
sources, that is, less than 100 km, are not realistic.* Both worst-case
and average dispersion situations are treated, with meteorological
inputs constructed from rawinsonde data that is readily available for
the region. The models are computationally practical for simulating the
impact of multiple point sources over periods of several days to several
weeks, and are easy to use for a variety of decision-making and regulatory
applications. Finally, these models are intended to serve as flexible
testbeds for further research, development and simulation tasks.
''Subsequently, the MESOPUFF model has been augmented to provide realistic
near-field impacts (see the companion report, Volume 3).
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
The three new models are, respectively:
• MESOPLUME, a mesoscale variable-trajectory Gaussian "plume-
segment" model (Benkley and Bass 1979a), adapted by ERT from
the plume segment approach taken in the STRAW model (Hales et
al. 1977),
• MESOPUFF, a mesoscale variable-trajectory Gaussian "puff"
superposition model (Benkley and Bass 1979b), adapted by ERT
from the puff approach taken in the MESODIF model (Start and
Wendell 1974); and
• MESOGRID, a mesoscale numerical grid model, adapted from the
method of moments approach taken in the SULFA3D model (Egan et
al. 1976).
This report, the fourth in a series entitled "Development of
Mesoscale Air Quality Simulation Models", describes the MESOGRID model
in technical detail; illustrates its application; and provides a User's
Guide to the model. However, to obtain a fuller understanding of the
model's capabilities, limitations and recommended usage, the user should
be familiar with the relevant materials contained in the following
related reports:
• the companion report (Volume 1) describing the extensive
series of comparison and model sensitivity analyses performed
with these models (Bass et al. 1979);
• the companion report describing the specially designed MESOSCALE
meteorological preprocessor program, MESOPAC (Benkley and
Bass, 1979c);
• the companion report (Volume 5) describing the specially
designed model postprocessing and analysis system, MESOFILE
(Scire et al. 1979) .
1.2 The MESOSCALE Grid Model (MESOGRID)
MESOGRID is a hybrid Lagrangian-Eulerian advection-diffusion model
for simulating the mass conservation equation. It is based on the Egan-
Mahoney method of moments (Egan and Mahoney 1972) and has been adapted
from the SULFA3D model originally developed by Rao (Egan et al. 1976).
The model accounts for horizontal advective transport and vertical eddy
diffusion, but no horizontal diffusion is included. At each time step,
pollutant mass is advected and diffused in a Lagrangian sense; immedi-
ately afterwards, a mass decomposition to a stationary Eulerian grid is
performed. The numerical method conserves the zeroth, first, and second
moments of the pollutant mass distribution; this method minimizes
pseudodiffusive errors associated with conventional finite-difference
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approximations. Note that, as is true of any Eulerian grid model, the
MESOGRID model will not conserve pollutant mass exactly in a divergent
wind field. MESOGRID accommodates multiple sources and includes modules
for plume rise, fumigation, linear conversion of sulfur dioxide (S02) to
sulfate (SOij), and dry deposition of SC>2 and SO^.
1.3 Integrated Mesoscale Modeling System
The MESOGRID model has been incorporated as a fully-independent
element within an efficient, easy to use integrated mesoscale modeling
system, depicted in Figure 1-1, comprising meteorological preprocessing,
mesoscale transport-diffusion, and post-processing components. The
standardization of model input/output functions in this system facil-
itates, for example, the easy combination of results from two or more
model runs, or the direct and cost-effective comparison of simulations
performed with two or more different models (see, for example, Bass et
al. 1979). The meteorology preprocessor MESOPAC drives identically any
of the three mesoscale transport-diffusion models. Each of these models
in turn identically communicates its results to the MESOFILE postprocess-
ing system responsible for file management, display, and statistical
analysis of all model output fields.
1.4 Organization of the Report
The remainder of this report is organized as follows: A detailed
technical description of the MESOGRID model is contained in Section 2;
specific user instructions are described in Section 3; a test case for
t;he MESOGRID model is presented in Section 4. A complete Fortran
listing of the MESOGRID model is appended to the document in microfiche
form.
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MESOSCALE
METEOROLOGY
MESOPAC
MESOSCALE
TRANSPORT-
DIFFUSION
MODELS
i
MESOPLUME
MESOPUFF
1
MESOGRID
ANALYSIS
MESOFILE
Figure 1-1 Integrated Modeling System
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2. MESOGRID TECHNICAL DISCUSSION
2.1 Model Formulation
The horizontal advection, vertical diffusion,_linear decay, and dry
deposition of sulfur dioxide (S02) and sulfate (S04) species on regional
scales are represented in MESOGRID by a discrete-level numerical repre-
sentation of the continuous equations describing the mass conservation
of the respective pollutant species:
9C
= -u
3x
-V
3y
3z
3C
z 3z
(2-1)
3C,
= -u
3C,
i
3x~
-v
3C,
37
3z
9C,
z 3z
+ yklCl -f2C2<5(z,H,Azk)
(2-2)
where
X'is the east-west horizontal coordinate (m);
y is the north-south horizontal coordinate (m);
z is the vertical coordinate (m);
t is the time (s);
C.. , C7 are the ambient_concentrations of sulfur dioxide (S02)
and sulfate (SOiJ respectively (g m~3);
Q, is the source emission rate of S02 fg m 2 s *) within a
vertical cell of height Az, (the SO^ emission rate is
assumed to be zero);
u(x>y)j v(x,y) are, respectively, the x and y components of horizontal
wind velocity (m s *);
K is the vertical eddy diffusivity (m2 s'1);
k1 is the rate (s *) of linear decay of S02 to SO^;
f , f? are the dry deposition rate functions (s *) of S02 and
SO^, respectively. Dry deposition is considered only
when the height z of a parcel of pollutant is below the
mixing height H; and
6(z,H,Az ) = 1 for z < H and k = 1; 6(z,H,Az. ) = 0 for z > H or k j
K — K
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
The set of equations used by MESOGRID invokes these important
assumptions:
• the advective wind field is two-dimensional (horizontal) only;
thus if the model is to conserve mass strictly, it must be
driven by a horizontally nondivergent wind field.
• horizontal diffusion is negligible compared to advective
transport.
The MESOGRID model solves the set of discretized advection-
diffiision equations on a three-dimensional grid with either two or three
vertical levels (as desired). The Egan-Mahoney (1972) method of moments
is used to minimize pseudodiffusive errors by conservation of the lower
order moments of the pollutant distribution. The grid cell resolution
is user-specifiable (to a maximum of 26x26x3 cells) . The horizontal
grid size is uniform; the vertical cell dimensions may vary between
levels. The choice of grid cell dimensions will reflect the following
considerations:
1) the overall size of the area to be modeled, and required
spatial resolution of concentration fields,
2) the advective and diffusive numerical stability criteria, and
3) the relative model execution costs as dictated by items 1 and
2 above.
2.2 The Grid System
MESOGRID is referenced to a simple Cartesian coordinate system for
easy interaction with a variety of input/output (I/O) routines, as well
as pre- and postprocessors. The MESOGRID grid cell system is illus-
trated in Figure 2-1. Each grid cell is denoted by an ordered triple of
indices (i,j,k) where i is the east-west (x-direction) index (i=l is the
westernmost cell), j is the north-south (y-direction) index (j=l is the
southernmost cell), and k is the vertical (z-direction) index (k=l is
the lowest level). For example, the center of the southwesternmost and
lowest grid cell (with indices 1,1,1) corresponds to the physical loca-
tion (x=0, y=0, z=Az1/2). All emission source data and meteorological
data input to the MESOGRID model are referenced to this grid system.
2.3 Specification of Model Inputs
The meteorological fields required to drive the MESOGRID model are
generated by the MESOPAC model (Benkley and Bass 1979c), a meteoro-
logical preprocessing package developed specifically for this purpose.
MESOPAC produces gridded hourly interpolated fields of:
• horizontal (u,v) wind components (m s"1),
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ENVIRONMENTAL RESEARCH S TECHNOLOGY INC
(i,j) *= indices identifying cell number in horizontal
t
Ay = Arf
t
(1,4)
3 +
(1,3)
2 +
(1,2)
1 +
(1,1)
0 *•
0
-*-Ax = Ad-»-
(2,4)
+
(2,3)
(2,2)
(2,1)
— — + — —
1
(3,3)
(3,2)
(3,1)
__.f. __
2
(4,2)
(4,1)
__^. ^_
3
«._
Figure 2-1 A Schematic Representation of the MESOGRID Cartesian Coordinate
System
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
• mixing depth (m), and
• Pasquill-Gifford-Turner (PGT) stability class.
Interaction of the MESOGRID model with the MESOPAC preprocessor is
straightforward-the coordinate system is identical in both models and
the grid point values of meteorological variables produced by MESOPAC
apply directly to the center of each MESOGRID cell. At present, the
horizontal wind components generated by MESOPAC are treated as invariant
with height, although the MESOGRID model itself can accommodate ver-
tically layered wind fields. The mixing depth and stability fields are
used by MESOGRID to determine eddy diffusivity (K ) vertical profiles
(see a detailed discussion in Section 2.4.3).
Emission source locations are user-specified through a three-
dimensional Cartesian coordinate system (x,y,z coordinates), and
MESOGRID assigns the appropriate (i,j,k) grid cell. For example (see
Figure 2-1), a source with x,y coordinates (0.6, 1.4) is assumed to fall
within a grid cell with horizontal indices (2,2). Acceptable ranges of
x and y are (-0.5 <_ x <_ imax -0.5) and (-0.5 <_ y <_ jmax -0.5) ; if x or y
values are specified beyond those limits, a MESOGRID run will terminate
with the error message SOURCE NOT IN GRID. Source locations are assigned
vertical indices (k) as illustrated in Figure 2-2. Thus, a source with
an effective release height, he = h + hp = 600 m, where hs is the stack
height and hp the plume rise (see Section 2.8), is assumed to fall
within the second (k=2) vertical layer.
Point source emissions Q(g s *) are assumed to be distributed
uniformly throughout a grid cell; an equivalent volume emission source
rate is defined by:
Q = - ^ (2-3)
where Q is the cell-averaged source emission rate (g m 3s *), Q is the
point-source emission rate (g s"1), Azj^ is the vertical depth (m) of the
k-th cell, and Ad is the size of a horizontal grid cell. As an example,
if Q =_ 103(g s'^^Az, = 103 m, and Ad = 4 x 104 m (typical values),
then Q = 6.25 x 10~10 (g m 3s"1).
2.4 Solution of the Advection-Dif fusion Equations
The tracer equations for each pollutant (Equations 2-1 and 2-2)
are solved in finite difference representations. The solution proceeds
in two sequential steps. In the first step, pollutant mass is advected
by the wind field. Immediately thereafter, in the second step, pollu-
tant mass is diffused in the vertical at a rate proportional to the
layer values of the K field. These computational steps are described
next.
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ENVIRONMENTAL RESEARCH S. TECHNOLOGY INC
Az3 = 2500 m
Az2 = 1000 m
1
Az, = 500 m
1
I
n = 3
i
i
n = 2
n = 1
—
—
, Height (m)
4000
2750
1500
1000
500
250
0
Figure 2-2 Vertical Structure of the MESOGRID Computation Grid Assuming
Default Values
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
2.4.1 Horizontal Advection
Conventional finite-difference approximations to the two advection
terms, u8C/9x and v9C/9y in Equations 2-1 and 2-2, produce truncation
errors; these errors can introduce spurious, pseudodiffusive effects in
the predicted concentration terms. This artificial diffusion by the
numerical scheme can be, in some instances, orders of magnitude larger
than that resulting from the real atmospheric mixing process. Various
special finite-differencing methods have been proposed for control of
numerical diffusion (e.g., SHASTA--see Boris and Book 1973). In the
present model, the approach adopted is a unique mixture of both Eulerian
and Lagrangian approaches, called the Method of Moments (Egan and
Mahoney 1972). This method substantially reduces the pseudodiffusion
associated with numerical advection term by using one or more statis-
tical moments of the concentration distribution within a grid element
scheme. This section describes this procedure in detail. To keep the
explanation as simple as possible, the discussion of horizontal advec-
tion will be initially limited to the description of advection in the
east-west direction only.
Defining C as the average concentration within a grid element, the
forward-in-time, backward-in-space, finite-difference approximation to
the horizontal advection for a uniform wind field u > 0 (neglecting
diffusive, source, and sink terms) is
T+1 T T
C , = (1 - a) C , + aC . , (2-4)
m,k k J m,k m-l,k ^ '
where T denotes the T time step such that t = TAt, m and k denote the
m (i or jtn) horizontal and the k vertical grid elements, and
a = uAt/Ad, the ratio of the advection distance per unit time step to
the grid element dimension. The Courant advective criterion stability
requires that a <_ 1. After many time steps, the resulting horizontal
advection can be likened to advection with velocity u and upwind- .
downwind mixing with a pseudodiffusive coefficient of magnitude .
uAd(l - a)/2. A substantial reduction in this diffusive effect can be
achieved if the first and second moments of the material within a cell
are calculated after each time step and used to adjust the amount of
material advected downwind during the next time step. Specifically, the
procedure calculates the first and second moments of the concentration
distribution after material has been advected into and out of a grid
cell. These moments are then used to define a simple rectangular con-
centration distribution in the grid cell having the same amount of total
mass and identical first and second moments.
Suppose £m denotes the relative displacement of material within the
mth cell from the center of the cell, such that 5m ranges from -0.5 at
the left hand to +0.5 at the right-hand extreme boundary of a cell. The
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ENVIRONMENTAL RESEARCH 8 TECHNOLOGY INC
zeroth, first, and centered second moments of the grid cell concentra-
tion distributions, corresponding to the mean concentration, the center
of mass, and the scaled distribution variance are given by
0.5
C
m m m
-0.5
0.5
F = C(5 ) 5 d£ /C (2-5)
m j *• m m m m
-0.5
0.5
2 f 2
R = C(£ ) (C - F ) d£ /C
m J m m m m m
-0.5
For simple rectangular concentration distributions, these integrals
are readily evaluated by summation for each grid element in terms of the
material distributions of the portions remaining and newly advected in
after each successive time step. It may be seen that the nature of the
downwind transfer depends on the value of the "portioning" parameter,
P = (F + a + 0.5 R - 0.5)/R (2-6)
m *• m m •" m *• -*
For Pm <_ 0 none of the material is advected into the m+1 cell. If
Pm >_ 1 all of the material is advected into the downwind cell. For
1 > Pm > 0, an amount of material PmCm is advected to the downwind cell,
and (1 - Pm)Cm remains in the mth cell. Considering now the general
case for the mtn cell with inflow from the m-1 cell, outflow to the m-t-1
cell, and continuous source addition during the time step, the forward-
time computation procedure at grid element m can be represented as
C = C + C + 0 AT
m r a TII
T+1 T+1
C F = CF + C F +Q At(a/2)
m m rr a a xm ^
T+1 9 T+1 7 T+1 7
Cm CR }m = Cr[Rr + 12CFm ' V ] (2~7^
+ C [R2 + 12(FT+1 - F )2]
a1 a m a
7
12(F - a/2)Z],
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ENVIRONMENTAL RESEARCH 8 TECHNOLOGY INC
where subscripts r and a indicate quantities remaining and newly
advected in, respectively. This procedure completely eliminates pseudo-
diffusive effects for a simple rectangular concentration distribution.
Small diffusive errors will remain when more complicated distributions
are advected.
In the MESOGRID model, the scheme described above has been general-
ized to two-dimension horizontal advection. Figure 2-3 illustrates in
top view the advection of a block of material with a uniform concen-
tration distribution. In analogy to the one-dimensional advection
procedure, one may define [suppressing the horizontal grid element
subscripts (i,j)]
P. = (F- + a. + 0.5 R. - 0.5)/R.
i ^11 i " i
P. = (F. + a. + 0.5 R. - 0.5)/R.
J J J J J
(2-8)
Then (imagining a newly emitted parcel of material contained within one
grid cell), for the case illustrated in Figure 2-3, where 0 < P^,
P- < 1, the contribution to the new concentrations at each of the four
grid cells sharing the material after advection is
T+1 T
c! : . = c! . P. (1 - P.) ,
1+1, j i,j i r
T+l T
c. . . = c: . (i - P.)P.,
J '
T+l T
c! : . . = c! . P.P.,
'
(2_9)
T+l T
c: = c: . (i - P.)(I - P.) .
1,3 i,jv i^v j'
The rules for advection for P < 0 or P > 1 follow those derived for
one-dimensional advection, as do the expressions for calculating the
first and second moments. In general the moments are evaluated from the
concentration distributions advected into a cell from more than one
adjacent cell. The computation procedure determines which neighboring
cells contribute to the moment calculations and computes ECm, ECmFm,
EC R 2> and then the new values for each element:
m m
CT+1 = ZCm (2-10)
£C F
pT+1 _ m m .
F - - (2-11)
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
Vj
1 J .
J J
J J .
J J
j J .
J J
Vd
J J
J J
J J
J J .
J J
J J .
%
\
a
j J j J _
U J J J J
J J J J _
J J J J j
J J -J J -,
J J J J j
J J J J J
.^J J J J j
-J .-" J /I-
•Vj-'j- rx
j j j j j
j j j j j
j j j j j
Ij ij^ij i P
fWv;
\
y
j j j j .
j j j j j
j j j j .
j j j j j
j j j j ,
J J J vKJ
J J J Jr J
J J J/J J
jj j/TJ ,J ,J
irj ^ .-1 ,J .
c Vj7?
VDJJJJJ
j j j j j
j j j j j
j j j j j
xrtjrV
•::;
o o
°0«
0°0
00
°0°
0°0
O 0
° o °
0 O
0 0
'°iV
Si^
J J
J J
j J
J J
j J
J J
j j
J J
J J
j j
j J
J J
A "Y"*Y nte
ffW
:v:::v:sS::-'-:s:-'
O^^
x — ^
t
DC
oT
i + 2
Figure 2-3 Scale Parameters for the Advection of a Rectangular Block of
Uniformly Mixed Material
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ENVIRONMENTAL RESEARCH 8 TECHNOLOGY INC
+ 12
ZF 2 C
m m
„!+!
(2-12)
2.4.2 Vertical Diffusion
The vertical diffusion terms 8/8z (Kz9C/8z) in Equations 2-1 and
2-2 are simulated by a conventional forward-time, centered-difference
technique modified so that the vertical grid spacing can be variable.
(The MESOGRID model is easily modified to include more vertical levels
if computer resources and budgets permit.) In regions where parameters
or concentrations change rapidly with height, resolution and accuracy
can be improved with smaller vertical grid spacing. The vertical
diffusion calculation may be represented by
T+l
fk-l
where the horizontal subscript m is now suppressed, and
fk+l
'k-l
(2-13)
The diffusivities Kt, are calculated at the center of each grid
element, and Az^ denotes the depth of the kth grid element. The diffu
sive computational stability criterion requires that the y's are less
than 0.5. The first and second moments of the horizontal distribution
are maintained in the diffusive transfer by two additional equations:
TT
F +
k k
T T
Vl Cn-l Fn-l
/ C
T-l
k+l
(2-14)
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»T+1
T
- F
T+lV
k+l
k-l
k+1
- F
T+l
k+1
(2-15)
2.4.3 Calculation of Spatially Variable K " Profiles
MESOGRID computes spatially variable profiles of vertical eddy
diffusivity for use in the vertical dispersion algorithms. The scheme
uses the mixing depth, wind speed, and stability class information
provided by MESOPAC to compute Kz profiles in each of two altitude
regimes: (1) the surface layer of depth S = 0.1H and (2) the Ekman
layer extending from the top of the surface layer to the mixing height
H.
To develop the profiles of KZ in the boundary layer, it is assumed
that atmospheric pollutants diffuse in the same manner as heat. The
vertical eddy diffusivity in the surface boundary layer is then given
by:
0.35
z
Kh[L
(2-16)
where
a* is the friction velocity,
z is height above ground,
L is the Monin-Obukhov length,
J>, is the nondimensional potential temperature gradient,
fzl fz
By definition, 4>n h- equals 1 for neutral conditions -
.ce layer. For staole conditions ^
surface layer
'h L
- = 0 in the
1 + 4.7
(2-17aJ
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ENVIRONMENTAL RESEARCH S TECHNOLOGY INC
and for unstable conditions (z/L > 0)
r = l- 15 ' (2-17b)
Substitution of Equations (2-17a and 2-17b) into Equation (2-16) yields
for stable conditions
K = - — ; (2-18a)
Z 1 + 4.7 f
LJ
and for unstable conditions
K = 0.35u*z 1 - 15 f . (2-18b)
Z ( LJ
The value of u^ is taken to be 0.035 uf, where U£ is the "free stream"
wind velocity (Blackadar 1962). If the MESOPAC model is used to compute
wind fields, the winds may not be significantly less than the free
stream wind speeds as long as the reference level chosen to describe the
wind fields falls typically within the upper two-thirds of the boundary
layer.
If the Monin-Obukhov length L is assigned a value dependent on the
PGT stability class estimated by MESOPAC, the surface layer Kz profiles
become stability-dependent as well. Table 2-1 depicts values of L l as
a function of PGT stability class for a typical roughness length z =25 cm,
as suggested by Colder (1972). °
TABLE 2-1
INVERSE MONIN-OBUKHOV LENGTH L'^nf1) AS A FUNCTION OF
PGT STABILITY CLASS, FOR ROUGHNESS
LENGTH z = 25 cm (AFTER COLDER 1972)
PGT Stability Class
A B C D E F
L"1 -0.11 -0.05 -0.01 - 0.01 0.05
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
To develop the KZ profiles in the Ekman layer, MESOGRID uses an
interpolation method suggested by O'Brien (1970) to determine diffu-
sivities between the top of the surface layer (S) and the top of the
mixed layer (H). Taking into account the physical requirement that the
first derivative of Kz be continuous with height in the Ekman layer,
O'Brien formulated the second-order equation
(z - H)
(H -
3K
z
3z
s)2
+ 2
S
rs T <•
Ks "
H - S
(z - S)
(2-19)
where
3K
z is the height at which K is to be determined
Li
H is the height of the mixed layer (from MESOPAC)
S is the height of the surface layer
_ is the value of K at the top of the surface layer (from
Equation 2-16)
is the derivative of K evaluated at S.
z
Here, it is assumed that Kz approaches zero at the top of the mixed
layer. Three stability-dependent equations for 3Kz/3zL are formulated
by differentiating Equation 2-16 and evaluating at height S:
For unstable conditions
3K
3z
= 0.35u_
for neutral conditions
1 - 22.5 f-
1 - 15 f-
-1/2
(2-20a)
= 0.35U,
(2-20b)
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
and for stable conditions
9K
= 0.35U,
1 + 4.7
(2-20c)
Table 2-2 contains formulations for surface-layer K (Equation 2-16)
and 3K2/9z|s (Equation 2-20J appropriate to each PGT stability
class, using the stability-dependent values of L l from Table 2-1.
Equations 2-16 through 2-20 are used by MESOGRID to calculate
values of Kz at the mean height z^ of each vertical grid element when-
ever the meteorological data is updated by MESOPAC. Because of the way
the MESOGRID model characterizes vertical diffusion the mixing depth, H
cannot be used directly as the depth through which pollutants diffuse in
the vertical. However, the effect of a mixing lid can be simulated
approximately--MESOGRID sets Kz in a grid cell essentially to zero if
the mean grid cell lies above the mixing height. Referring to the
example in Figure 2-2, if the mixing depth H lies between 1,000 and
2,750 meters, Kz is set to zero in the uppermost layer but is left
unchanged in the two lower layers. But because diffusive transfer of
mass by two contiguous vertical grid cells is made proportional to the
average of the Kz values for each cell (Equation 2-13), without further
modification of the Kz profiles, mass transfer would take place between
Levels 2 and 3 even though Level 3 lies entirely above the mixing depth.
MESOGRID will correct partially for this behavior; the average of Kz for
Levels 2 and 3 will be set equal to zero if 1,000 <_H < 1,500 m, but
will be unchanged if 1,500 <_ H < 2,750 m. ~~
2.4.4 Numerical Stability Criteria
As described before, computational stability of the computational
scheme is ensured only if:
uAt
(2-21)
and
< 0.5
(2-22)
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
TABLE 2-2
STABILITY-DEPENDENT EXPRESSIONS FOR K IN THE
z
SURFACE LAYER AND 8K
3z
PGT
Stability
K (surface layer)
3K
0.35u.z(l + 1.65 z)
1/2
0.35u.(l + 2.48 S)(l + 1.65 S)
-1/2
0.35u.z(l + 0.75 z
1/2
0.35u.(1 + 1.13 S)(l + 0.75 S)
-1/2
0.35u.z(l + 0.15 z)
1/2
0.35u*(l + 0.23 S)(l + 0.15 S)
0.35Uj
0.35u^z(l + 0.05 z)
-1
0.35u.(l + 0.05 S)'
+ 0.23 z)
-1
0.35u.(l + 0.23 S)'
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
Equation (2-21), the advective stability criterion (Courant condition)
means that a parcel of mass must not be advected, in either horizontal
direction, through a distance greater than one grid space Ad within a
time step At. Equation (2-22) means that the effective vertical diffu-
sion velocity (K^ + K]c+^)/(Az]< + Az^+i) cannot be such that a parcel is
displaced vertically (by diffusion) more than a distance Az, /2 within
At. k
Given the maximum values of u and Kz at the beginning of each hour,
MESOGRID calculates the maximum time step allowed by the more stringent
of these stability criteria, except that the actual time steps used by
MESOGRID are constrained to be even fractions of one hour; thus the
possible choices for At are 5, 6, 7.5, 10, 15, 20, 30, and 60 minutes.
Note that, notwithstanding the above, MESOGRID does not currently allow
selection of a time step shorter than 5 minutes.
Table 2-3 lists the maximum values wind velocity u and KZ values
(expressed as averages between adjacent levels, e.g., K-^ 5 = (Kj + K2)/2,
for the nominal choices (Ad = 40,000 m, AZ} = 500 m, Az2'= 1,000 m, and
Az3 = 2,500 m). Under stable conditions, the advective criterion will
normally dominate, whereas for unstable conditions (resulting in computed
Kz values up to 103 in test simulations), the vertical diffusion stability
criterion may dominate. Specific choices of horizontal and vertical
grid cell dimensions can yield stability criteria significantly dif-
ferent from those of the hypothetical example. For instance, if the
desired near-ground vertical resolution dictates choice of a small Az
value, the maximum time step may be determined by the diffusion criteria,
whatever the stability class.
In the MESOGRID model simulations performed by Bass et al. (1979),
it was often found that for unstable conditions, KZ would be so large
that the time steps necessary to ensure computational stability were
smaller than the minimum value deemed reasonable for regional-scale
transport (At = 5 minutes). Because such small time steps result in
very expensive computing costs, a method, explained next, has been
provided to give the user a degree of control over the diffusion-
specified time step by systematically decreasing very large values of
KZ. Such a procedure may be justifiable if the MESOGRID model is used
for regional-scale simulations (as distinct from near-source impacts).
Because, in a grid model, the magnitude of Kz values determines the
rapidity with which vertical mixing will occur by diffusion—as long as
the reduced Kz values lead to uniform vertical mixing within travel
distances that are small compared to the regional transport scales of
interest, the effect on regional-scale concentration patterns should be
minimal (unless ground-level removal processes are of dominant importance)
The approach taken here forces the model to reduce large values of
Kz to within a range consistent with both the advective stability time
step Ata (Equation 2-21) and a user-specified "requested" time step Atr.
There are six distinct cases delineated in Table 2-4 for modification or
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
TABLE 2-3
MAXIMUM VALUES OF u AND I
1.5' K2.5 VS'
TIME STEP At FOR NOMINAL MODEL PARAMETERS
Model Time
Step
At (min)
5
15
30
60
Assumptions :
Advective
Stability
Criterion
u(m s"1)
135
45
22
11
Ad = 40,01
Az. = 51
K, , (m2 s'1)
1.5
Diffusive
Stability
Criterion
K
2.5
(m2 s"1)
Az,
Az.
625
208
104
52
2916
972
486
293
500 m
1,000 m
2,500 m
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
TABLE 2-4
DETERMINING WHEN MESOGRID WILL MODIFY K PROFILES
z
Case Number Possible Time Step Orderings Modify K ?
1 At < At, < At No
a — d — r
2 At < At < At, MO
a — r — d 1NO
3 At < At < At, MO
r — a — d 1NO
4 At < At, < At No
r — d — a
5 At, < At < At Yes, in accordance
d r ~ a with At
r
6 At, < At < At Yes, in accordance
d a r with At
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
nonmodification of KZ; these six cases are the six possible orderings
of Atr, Ata and the diffusive stability time step Atj (Equation 2-22) by
increasing magnitude. No modification of Kz is required in Cases 1, 2,
and 3, because the advective stability criterion is at least as stringent
as the diffusive stability criterion, thus the model selects a time step
shorter than that required by the largest KZ values. In Case 4, the
diffusive stability criteria is more stringent than the advective
stability criteria, but no Kz modification is necessary because Atr
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ENVIRONMENTAU RESEARCH & TECHNOLOGY INC
AQn(S02) = k: Qn(S02) At
AQn(SO~) = -1.5 kl Qn(S02)
At
(2-23a)
(2-23b)
where Q [802) is the mass of SC>2 at the beginning of the nth time step,
and ki (s"1) is the conversion rate constant. MESOGRID uses the nominal
value ki = -5.56 x 10~6, as suggested by Hales et al . (1977), unless
otherwise specified by the user.
It should be noted that the conversion of S02 to SO^ represented by
Equation 2-23 is (1) made independent of the vertical or horizontal
distribution of 862 within a plume, and (2) independent of whether a
plume lies above or below the mixing height.
When Equation 2-23 is applied to an individual grid cell after the
advection calculation and prior_to the diffusion calculation, the changes
in concentrations of S02 and SOi^ resulting from linear conversion are:
AC(S02)
n
C(S02) At
(2-24a)
AC(SCf) = -1.5
Cn(S02) At
(2-24b)
where, for example, Cn(S02) is the grid cell concentration of S02 at
time step n, following the horizontal advection operation.
2.7 Dry Deposition of Sulfur Dioxide and Sulfate
n
The changes of mass AQ (g) of each pollutant at time step n
resulting from dry deposition are given by:
AQn(S02) = -
(2-25a)
AQn(SO=)
(2-25b)
where Qn(S02) and Qn(S(\) are the total masses of S02 and SO^, respectively,
in a vertical column at the beginning of time step n (Qfj is the mass in
the lowest_cell) ; vd(S02) and vd(SO^) are the deposition velocities of
S02 and S(\ respectively; and Azi is the vertical depth of the lowest
grid layer. MESOGRID uses vd(S02) = 0.01 (m s'1) and vd(SCQ =
'
0.001 (m s'1), 'the nominal values of Hales et al .
wise specified by the user.
(1977), unless other-
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ENVIRONMENTALRESEARCH&TECHNOIOGYINC
There is an important difference in the way mass is depleted by
MESOGRID as compared to the plume and puff models; although the amounts
of SC>2 and SO^ removed by dry deposition are the same in each model for
vertically uniform distributions, MESOGRID depletes mass in only the
lowest of its vertical layers rather than throughout the entire mixing
depth (as do the other models). However, since MESOGRID exercises the
dry deposition algorithm before the vertical diffusion algorithm, mass
loss in a cell in the lowest grid layer is redistributed through cells
in the upper layers (as long as they are below the mixing lid). There-
fore, if the effective "diffusion velocity" (see Section 2.4.4) is
large, the dry deposition algorithm in MESOGRID yields equivalent
results as the algorithm in the other models.
2.8 Plume Rise
The effective emission height hg of each point source is computed
as he = h + hp, where hs is the stack height (m) and hp is the plume
rise (m). The plume rise equations used by the MESOGRID model are those
described by Briggs (1975) for equilibrium (final) plume rise.
For unstable and neutral conditions with h1 <_ H (i.e., the plume does
not rise into an elevated stable layer)
h = h' = 1.6 F 1/3 (3.5 x*)2/3 u"1; (2-26a)
For unstable and neutral conditions with h' > H (i.e., the plume penetrates
into an elevated stable layer)
•5 1 1 1/3
h = MIN{h', (zr + 18.75 F u^ S ) } (2-26b)
for stable conditions when u > 1.37 m s~
hp = 2.6 F S -u -; (2-26c)
for stable conditions when u < 1.37 m s~
h = 5.0 F 1/4 S 3/8; (2-26d)
where:
4 _3
F = buoyancy flux (m s )
x* = 34.49 F°'4 for F > 55
= 14.0 F°'625 for F <_ 55
S = (g/T)(39/9z)
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
-2
g = 9.8 m s
T = 290°K
z = 0.0137°K m"1
H = mixing depth (m)
z = H - h (m)
-1
u = wind speed (m s )
u- = MAX {u, 1.37}
m
2.9 THE MESOGRID Computer Program
MESOGRID is a highly modular computer program which shares with
MESOPUFF and MESOPLUME standardized input/output features and, where
possible, identical program modules. The computer program flow chart
(Figure 2-4) outlines the order of execution of the individual modules
described at length in the 'MESOGRID Technical Discussion'.
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ENVIRONMENTAL RESEARCH B. TECHNOLOGY INC
I
Initialize input parameters
(Subroutines INPARM,BLOCK DATA)
Initialize direct access files
(Subroutine FILMAN)
Initialize S02 and 804
background concentrations
KOUIMT1=0, NTIMEX=0
I
Update hour, day, year
(Subroutine KALEND)
I
Update meteorology
(Subroutine READER)
I
Calculate KZ
(Subroutine KSUBZ)
Determine time step DT
(Subroutines DIFFDT,MODKZ)
Determine grid location of sources
(Subroutines SOURCE,PRISE)
NTIMEX=NTIMEX+DT
Yes
MOD (NTIMEX, 3600)=0?
KOUNT1=KOUNT1+1
Calculate boundary conditions
(Subroutines EWBND,NSBND)
Advection calculation
(Subroutine POLLUT)
Add source and removal terms (POLLUT)
Diffusion calculation (POLLUT)
MOD (KOUNT1, IAVG)=0?
Yes
If (MOD (KOUNT1,IPRINF))=0,
output fields to line printer
(Subroutines WRITER,RANGE,DISP,PAGE)
If (MOD (KOUNT1,ISAVEF))=0,
output fields to direct access files
(Subroutine PUTOUT)
MET DATA UPDATE?
Figure 2-4 MESOGRID Flow Chart
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3. MESOGRID USER INSTRUCTIONS
3.1 General
A MESOGRID model simulation requires the following two input data
sets:
• meteorological fields from MESOPAC (unformatted disk or tape
input via logical unit 2) and
• model simulation control parameters and emission source
inventory (cards or card-image disk input via logical unit 5)
A complete description of model simulation control parameter and emission
source inventory input is contained in Section 3.2. For most convenient
operation, MESOGRID should interface with the output of the MESOPAC
meteorological preprocessor (see Section 3.3).
Concentration array output of a MESOGRID simulation can be routed
to either (or both) of the following:
• line printer (logical unit 6) and
• direct-access disk storage system (logical units 13, 15, 21,
22, 23, and 24).
Both optional output media are discussed in detail in Section 3.4. The
direct access storage system allows for automatic storage, cataloguing,
and easy retrieval of all output data files from MESOGRID and its sister
regional-scale models MESOPUFF and MESOPLUME. Availability of on-line
direct-access disk storage enables the user to invoke the powerful
MESOFILE file-management system, designed especially for interface with
the regional-scale models. The MESOFILE system has file management
components that produce, for each run for which output has been requested
for disposal to disk, a record of the date of the run, the run charac-
teristics, the disk file locations of all the concentration data output,
and the values of all the input parameters for the run. The MESOFILE
program allows this information to be retrieved for all the previous
runs made on a particular set of disk files. The MESOGRID program
contains a file management subroutine (FILMAN) which determines without
further user input the proper locations for all of the various MESOGRID
disk output files. MESOFILE can then be used for flexible time averag-
ing of any set of fields, summation of different model simulations,
statistical comparison of model results, and graphical contour display.
3.2 Description of Card-Image Input
This section provides a detailed description of all the card-image
input requirements of the MESOGRID model, model simulation control
parameters, and emission inventory. The input package has been designed
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ENVIRONMENTAL HESEARCH & TECHNOLOGY INC
for use in common by all three mesoscale models (MESOPLUME, MESOPUFF,
and MESOGRID) especially to facilitate intermodel comparison tests. The
common input subroutine (INPARM) reads in all model simulation control
parameters in Fortran NAMELIST format so that input parameters common to
all three models can be included in standardized NAMELIST blocks. A few
model-specific NAMELIST sets, however, are required because of certain
features peculiar to each model algorithm. There are thirteen NAMELIST
blocks included within the INPARM subroutine package, as follows:
(1) MODEL, (2) CONTR, (3) GRID, (4) SIGMA, (5) METD, (6) PUFF1, (7) PUFF2,
(8) PLUM1, (9) PLUM2, (10) GRIDY, (11) REMOV, (12) OUTPT, and (13) SOURC.
NAMELIST blocks SIGMA, PUFF1, PUFF2, PLLIM1, and PLUM2 are not used by
MESOGRID and must be omitted from the input data runstream.
The remainder of this section provides detailed descriptions of the
parameters in each NAMELIST set.* These NAMELIST sets are to be included
in the input run stream in the identical sequence described above.
NAMELIST TITLE--MODEL
MODEL defines which model is to be run. Initialize LGRID = .TRUE.
for a MESOGRID run.
Parameter
LPLUME
LPUFF
LGRID
LOGICAL
LOGICAL
Definition
If .TRUE., MESOPLUME is
to be run
If .TRUE., MESOPUFF is
to be run
If .TRUE., MESOGRID is
to be run
Default
.FALSE.
.FALSE.
.FALSE.
NAMELIST TITLE--CONTR
CONTR initializes computational control variables.
Parameter Type Definition
DTIME REAL
Default
Length of the basic or 'requested1 1.0
time step (hours)
NADVTS
INTEGER
Length of the simulation (hours)
24
*The description of certain parameters that were retained from an earlier
version of the model but not otherwise used or that were included only
to perform various model sensitivity tests, are omitted from this
discussion--these parameters would not be activated by the average
user. However, for a complete list of possible input parameters, the
interested reader should consult the documentation included as comment
cards directly in subroutine INPARM.
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
Parameter
MTFREQ
Type
INTEGER
IAVG
INTEGER
Definition
Interval between wind, mixing
depth, and stability
fields updates (hours)--
must be equal to or an eveji
multiple of the MESOPAC
time step 'ISTEP' (hours)
Number of hours over which
output concentration arrays
are to be averaged
Default
1
24
NAMELIST TITLE —GRID
GRID initializes parameters defining the two major grids: meteoro-
logical and basic computational. The basic computational grid must
be a subset of the meteorological grid and also must have the same
grid spacing. Currently, the maximum allowable size of the
basic computational is 26 by 26 horizontal grid indices.
Parameter
Definition
Default
IELMET
JELMET
DELTMT
IASTAR
IASTOP
JASTAR
JASTOP
INTEGER
INTEGER
REAL
INTEGER
INTEGER
INTEGER
INTEGER
Number of elements in the x- 26
direction of the meteorological
grid—must be the same as 'IMAX'
used by MESOPAC (must be <_ 40) .
Number of elements in the y- 26
direction of the meteorological
grid- -must be the same as 'JMAX1
used by MESOPAC (must be <_ 40) .
Basic computational grid spacing 40,000.
(meters) --must be equal to the
grid spacing, DX, used by the
MESOPAC meteorological grid.
Element number of the meteoro- 1
logical grid where the basic
computational grid starts
(x-direction) .
Element number of the meteoro- 26
logical grid where the basic
computational grid stops
(x-direction) .
Element number of the meteoro- 1
logical grid where the basic
computational grid starts
(y-direction) .
Element number of the meteoro- 26
logical grid where the basic
computational grid stops
(y-direction) .
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
NAMELIST TITLE—METD
METD initializes parameters that identify the input meteorological
data base.
Parameter
Type
Definition
Default
METSRT
INTEGER
METCOD
INTEGER
Year (2 digits), Julian day 7700101
(3 digits), and hour (2 digits)
in the MESOPAC output data file
at which the MESOPLUME run
begins.
4-digit serial number to 1001
identify the meteorological
data used (previously assigned
by the user to the MESOPAC
simulation run that generated
the input meteorology fields).
NAMELIST TITLE—GRIDY
For MESOGRID only, GRIDY initializes computational parameters.
Parameter
Definition
Default
INVL
CZ(4)
INTEGER
REAL
NOSPEC
CREFLT
INTEGER
REAL
Number of vertical layers in the 3
3-dimensional grid (must be either
2 or 3).
Height of the grid lines (m). 0..500.,
'CZ(1)'=0; 'CZ(2)' = height of 1500.,4000.
the top of the lowest layer;
?CZ(3)' = height of the top of
the second layer; *CZ(4) '= height
of the top of the third layer (if
necessary).
Number of species modeled (1 = SO 2
only is modeled, 2 = SO and S0~
are modeled).
Reflection coefficient at the top 1
of the highest layer. (1.0 = com-
plete reflection, 0.0 = complete
absorption).
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ENVIRONMENTAL RESEARCH S TECHNOLOGY INC
Parameter
Definition
Default
LBACK
LOGICAL
CBOUND (A,B,C) REAL
BACK2
REAL
BACK4 REAL
NPTS INTEGER
NPKZ
INTEGER
24*0.
If .TRUE., background values .FALSE,
for SCL and S0~ are to be read
in.
This is the boundary value con-
centration array (yg m 3) (A is
incremented the fastest, C is
incremented the slowest). A=l,2
for S02 and SOi^, respectively;
8=1,2,3,4 for the west, north,
east, and south grid boundaries,
respectively; C = 1,2,3 for the
1st, 2nd, and 3rd grid level,
respectively.
Background value for S02
(ug m~3)--at every grid
cell--This is applied only at
the very first time step of the
run. For a continuous background,
set, 'CBOUND1 elements equal to
'BACK2' and 'BACK41 values.
Background value for SO^ (pg m~3)
at every grid cell.
If 'LPRINT' = .TRUE, (see Namelist 9999.
OUTPT), the rate (hours) for
output of a variety of grid and
source information (2 pages per
basic time step) .
0.
If 'LPRINT' = .TRUE., the rate
of KZ array output (2-6 pages
depending on number of levels
and size of grid).
9999.
NAMELIST TITLE—REMOV
REMOV assigns values to the removal rate parameters.
Parameter
Type
Definition
Default
LDCAY
LOGICAL
If .TRUE.^ exponential decay of
S02 to SO^ is simulated; If
.FALSE., no decay is simulated.
.TRUE.
3-5
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
Parameter
EXTNCT
LDEPOT
Type
REAL
LOGICAL
DEPVEL(2) REAL ARRAY
Definition
If 'LDCAY' is .TRUE., conversion
rate of S02 to SO^ (negative,
for loss of S02).
If .TRUE, dry deposition is
simulated for both species.
If .FALSE., dry deposition is
not simulated for either specie.
If 'LDEPOT' is .TRUE., 'DEPVEL(l)'
and, *DEPVEL(2)' are deposition
velocities (m s"1) for SO? and
respectively.
Default
-5.56x10 6
.TRUE.
(.01,.001)
NAMELIST TITLE—OUTPT
OUTPT initializes the output control parameters.
Parameter
Definition
Default
LPRINT
IPRINF
LSAVE
ISAVEF
LOGICAL
INTEGER
LOGICAL
INTEGER
Is .TRUE, if line printer out- .TRUE.
put of gridded concentration
arrays is desired.
If 'LPRINT' is .TRUE., specifies 24
the rate (hours) of gridded con-
centration array output (to line
printer) Must be_ equal to^ or an_
even multiple of_ ' IAVG' (see
NAMELIST CONTR)T
If .TRUE., concentration arrays .FALSE,
are to be saved on disk or tape.
If 'LSAVE' is .TRUE., the rate 24
(hours) of concentration array
output to tape or disk. Must be_
an even multiple of 'IAVG' (see
NAMELIST CONTR).
NAMELIST TITLE —SOURC
SOURC assigns values to the parameters associated with source
characteristics.
Parameter
NSOURC
INTEGER
Definition
Default
Number of sources (up to 50).
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ENVIRONMENTAL RESEARCH S, TECHNOLOGY INC
The following formatted (non-NAMELISTED) input follows the NAMELISTED
input described above: For each source (there are a total of 'NSOURC'
sources) one formatted card of stack parameters must be included.
STACK PARAMETERS (1 card per source)
Columns Format Parameter
Definition
1-10 F10.2 STAKHT Stack height (m) above ground
11-20 F10.2 XXSTAK x-coordinate of source (meteorological
grid units)
21-30 F10.2 YYSTAK y-coordinate of source (meteorological
grid units)
31-40 F10.2 EMISS(l) Emission rate (g s"1) for S02
41-50 F10.2 EMISS(2) Emission rate (g s'1) for S(T
4-3
51-60 F10.2 BFLUX Buoyancy flux (m s ) for plume rise
3.3 Other Input Considerations
3.3.1 Meteorological Considerations and MESOPAC Input
The meteorological input for the MESOGRID model is specified as a
time sequence of spatially variable, gridded fields of horizontal (u,v)
wind components, mixing depth, and PGT stability class. These fields
are generated and written to off-line storage (disk or tape) by the
MESOPAC* Meteorological Preprocessing Program (see Benkley and Bass
1979c). As mentioned in Section 3.1, MESOGRID retrieves the meteoro-
logical data set from logical unit 2.
Direct compatibility of MESOGRID input with MESOPAC output is
ensured if the successive runs of MESOPAC and MESOGRID jointly satisfy
the following constraints on respective run parameters.
• The four-digit serial number 'METCOD' used to identify the
meteorological data sets requested by MESOGRID must match the
'METCOD' assigned when MESOPAC created and tagged its output
meteorological data set.
• The grid spacing 'DELTMT' used by MESOGRID must be identical
to the grid spacing 'DX' used by MESOPAC; of course, the
number of horizontal grid elements 'IELMET' and 'JELMET' used
to specify the met data array sizes in both models must be
identical.
*If desired, another meteorological preprocessing routine, if properly
designed, can be substituted to drive the MESOGRID model.
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ENVIRONMENTAL RESEARCH S TECHNOLOGY INC
• the geographical area covered by the MESOGRID basic computa-
tional grid must be identical to, or a subset of the area
covered by the MESOPAC meteorological grid.
• the chronological time period over which the MESOGRID simu-
lation run is performed must be a subset of the time period
used by MESOPAC to define the meteorological fields.
• the interval at which the meteorological fields are updated by
MESOGRID 'MTFREQ' (hours) must be equal to or an even
multiple of the time interval 'ISTEP' (hours) used by MESOPAC
to generate and output successive sets of meteorological
fields.
3.3.2 Array Size Considerations
Currently, MESOGRID allows for the basic computational grid to
be as large as 26 elements in each horizontal direction and 3 elements
in the vertical direction. Since most of the large arrays in MESOGRID
are related to the grid size, the size of the grid cannot be increased
without directly increasing the core required by MESOGRID. The user can
specify up to 50 sources; it would be trivial to increase the number of
sources, however, and this increase would not significantly increase
model storage needs.
3.4 MESOGRID Model Output
MESOGRID output can be specified in either (or both) of two media
depending on further user needs. The results can be output directly to
the line printer, and/or routed for storage on the direct-access disk
storage system for subsequent postprocessing. This section describes
the types of output data that can be routed through each system. In
most cases, the user may specify whether a certain type of output data
will be received.
3.4.1 Line Printer Output
The following is a complete list of the line printer output options
available from a MESOGRID simulation:
• a table that lists the values of all input parameters used in
the run (this output is always generated);
• arrays_of ground-level concentrations for S02 (always output)
and SO^ (output if 'NOSPEC' = 2) block averaged over time
intervals of 'IAVG' hours and output at intervals of 'IPRINF'
hours during the run (these fields are printed only if
'LPRINT1 = .TRUE.);
30
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ENVIRONMENTAL RESEARCH 8 TECHNOLOGY INC
• a table of information, output every 'NPTS' hours, describing
allowable advection and diffusion time steps, number of
gridded values of K that were adjusted based on the 'requested'
time step, and aggregate grid cell source data (this infor-
mation is provided only if 'LPRINT' = .TRUE.); and
• an array of Kz values for each level, output every 'NPKZ1
hours (these arrays are output only if 'LPRINT' = .TRUE.).
3.4.2 Direct Access Disk Output
Table 3-1 describes the logical unit file structure of the direct
access disk storage system expected by MESOGRID. (Model outputs are
only directed to direct access disk storage when 'LSAVE' = .TRUE.) As
indicated, six distinct direct access files are used, each with indepen-
dent size characteristics; these file characteristics are currently
frozen within the MESOGRID code itself via Fortran "Define File" state-
ments and may require specific modification for adaptation to the user's
host system.
Concentration Files 21 and 22 contain the S02 and SO^ concentration
fields for each output time step. An identifying header record iden-
tical to the format used for File 15 (see File 15 description below)
precedes the concentration fields. Files 21 and 22 can accommodate a
maximum of 1,800 records each; therefore, for example, the results of 10
independent model simulations, each of 179 hours duration with hourly
output, will fit exactly within the 1,800_records allotted. Note that
if only S02 is modeled ('NOSPEC' = 1), SO^ arrays output to File 22 will
contain all zeroes.
The library file (13) contains a single-record descriptor for each
model run; File 13 can accommodate a maximum of 25 independent model
runs. A hard copy printout of the library file produced by MESOFILE is
shown in Figure 4-2 in the next section.
The parameters defining each model simulation run are as follows:
INUMB - a model run number which is automatically assigned by the
direct access disk output subroutine.
DATFLD - The date of execution (day, month, and year) of the model
run [not the day (or days) simulated].
MODEL - The particular mesoscale dispersion model chosen from the
integrated modeling mesoscale system--in this case,
MESOGRID.
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ENVIRONMENTALRESEARCH&TECHNOLOGY INC
TABLE 3-1
LOGICAL UNIT FILE STRUCTURE
Device Logical
Unit Number
13
15
21
22
23
File Name
Library
NAMELIST
SCL Concentration
SO. Concentration
Run Number
Record Structure
25 records,
14 words/record
25 records,
800 words/record
1,800 records,
1,610 words/record
1,800 records,
1,610 words/record
1 record,
2 words
24
Pointer
1 record,
4 words
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
YR/DAY/HR - The year, Julian day, and hour on which the model
simulation begins (Note that the first gridded
concentration field is not output until 'ISAVEF'
hours subsequently.
NGRIDS - The total number of concentration arrays output for
each pollutant during the model simulation
('NGRIDS' = 'NADVTS'/'ISAVEF1 where 'NADVTS' is the
total number of time steps in the model simulation.)
IAVG - The concentration array averaging rate (hours).
ISAVEF - The concentration array direct-access disk output
rate (hours).
ISAFE - The direct access address of the duplicate File 15
record.
IBEGIN
I STOP
ICHECK
The direct access address of the first of the
'NGRIDS1 number of arrays output to File 21 for SO,, and
File 22 for S0~.
The direct access address of the last of the
'NGRIDS' number of arrays to File 21 for SO and
File 22 for S0~.
The run termination status indicator 'ICHECK1 = 1
indicates the model simulation terminated normally;
'ICHECK' = 0 indicates it terminated abnormally. In
the latter case, the results of this run must be
deleted from the file management system using the
program BACKUP01 (see Scire et al. 1979) before
another run is made.
NAMELIST File 15 contains a one-record detailed description of the
parameters used for each model run. Each record in File 15 contains:
(1) a duplicate of the corresponding FILE 13 record for the run and
(2) the NAMELIST parameters used to make the run (also output to the
line printer).
Finally, the Run Number and Pointer Files (23 and 24) preserve
information between runs necessary to maintain proper archival sequen-
cing of run outputs—they are invisible to the user.
3.5 Execution Time and Core Requirements
The run time required for a MESOGRID simulation is determined by
the number of time steps, the number of grid points, and various mete-
orological factors that control the time step At satisfying the hori-
zontal and vertical computational stability criteria (see Section 2.4.4)
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FNVIRONMENTAL RESEARCH A TECHNOLOGY INC
Note especially that MESOGRID execution time varies directly with the
number of grid points but is independent of the number of sources.
MESOGRID becomes cost-effective compared to the plume and puff models
only when large numbers of sources are to be included. The execution
time (on an IBM 370/158) of MESOGRID for the computational grid and
typical meteorological conditons used is described by:
*r •> N* n. ^^
t(sec) = — — - (3-1)
where N* is the total number of time steps (of duration At minutes) in
a MESOGRID simulation. Table 2-3 (see Section 2) listed the maximum
values of u and K consistent with various choices of At, assuming a
horizontal grid interval of 40 km and vertical layer thicknesses of 500,
1,000 and 2,500m. On the IBM 370/158 system, MESOGRID requires 380k
bytes of core storage.
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ENVIRONMENTAL RESEARCH 8 TECHNOLOGY INC
4. TEST CASE FOR MESOGRID
A test case is provided in this section to familiarize the user
with the operation of the MESOGRID model and to verify that the model is
running properly on his system. The test case included here is a 3-day
sequence of MESOGRID model output for the time period 0000 Greenwich
Mean Time (GMT} June 14, 1978 through 0000 GMT June 17, 1978 in the Four
Corners area of the southwestern United States [the first three days of
the five-day run sequence studied in detail by Bass et al. (1979}]. A
10-source partial emission inventory was selected from the full set of
energy-related major point sources of S02 in the Four Corners area. To
save on computational costs, SO^ is not modeled in the test case.
Figure 4-1 contains the run control parameters and emission source
inventory (input on logical unit 5} for this test case. Note that most
of the model input variables assume their default values. Appendix A
contains the entire input data set used by the MESOPAC preprocessor to
generate the meteorological fields that were subsequently read in by
MESOGRID (on logical unit 2). Appendix A also contains a very small
portion of the MESOPAC model output — included to aid the user in veri-
fying the full test case.
The full set of line printer output for this MESOGRID test case is
included in Appendix B. Descriptions of the model output fields
assigned to the direct access disk storage system (as echoed in hard
copy form by the MESOFILE system) are shown in Figure 4-2 (the library
file) and in Appendix C (the NAMELIST file). In this example, the
results from the MESOGRID test case are stored together with the results
from the MESOPUFF and MESOPLUME test cases as discussed in the MESOPLUME
user's manual (Benkley and Bass 1979a) and the MESOPUFF user's manual
(Benkley and Bass 1979b). Appendix C also shows the NAMELIST file;
there, the library record NAMELIST input parameters and emission source
data are stored for future reference.
The MESOFILE postprocessing system (Scire et al. 1979) operates on
the direct access disk output files produced by MESOGRID, to produce
various forms of result analyses. Figure 4-3 illustrates one such
option—a Calcomp contour plot of the 24-hour average ground-level S02
concentration field for June 16, 1978 as obtained from the test case.
(Concentration isopleth values are not printed directly on the contour
plot, but the user can generate an equivalent line printer plot, as
illustrated in Figure 4-4, which does include the actual isopleth
values.) Figure 4-5 illustrates the bulk statistical descriptors
(described by Bass et al. 1979) used to compare, for example, two time
sequences of model result fields. In this example, the base case
24-hour average ground-level S02 concentration fields for June 16
computed by the MESOPLUME model are compared to those computed by the
MESOGRID model.
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ENVIRONMENTAL RESEARCH S TECHNOLOGY INC
&MUDEL LGRID=.TH'UE. SEND
fcCONTR NADVTSS72 SEND
fcGHID tEND
4METD METSRT=7816500,METCOD*1003 SEND
&GRIDY NOSPEC=1 SEND
ftREMOV IEND
&OUTPT LSAVEs.TRUE. 4EMD
4SOURC NSOURCslO &END
236.
152.
152.
152.
183.
229.
76.2
163.
175.
152.
,7
,5
a.e
23.4
17.2
23,
13,
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8.0
9.7
0.9
1.5
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13.1
19.5
15.2
8.U
4.1
2560.
343.8
633.4
488.
53.7
320.
146.9
1310.8
268.8
1011.
0
0
0
0
0
0
0
0
0
0
6397.
1503.
2847.
3353.
3016.
6222.
240.
3016.
1047.
11144.
Figure 4-1 MESOGRID Test Case Parameter and Emission Source
Inventory Input
4-2
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
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Day 167 MESOGRID
Figure 4-3 MESOGRID 24-Hour Average S02 Concentration Calcomp
Plot, 16 June, 1978 (from MESOFILE)
4-4
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
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ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
REFERENCES
Bass A., C. W. Benkley, J. S. Scire, and C. S. Morris. 1979. Develop-
ment of Mesoscale Air Quality Simulation Models Volume 1. Com-
parative Sensitivity Studies of Puff, Plume, and Grid Models for
Long-Distance Dispersion Modeling. EPA 600/7-79-XXX, Environmental
Protection Agency, Research Triangle Park, NC, 210 pp.
Benkley, C. W. and A. Bass. 1979a. Development of Mesoscale Air Quality
Simulation Models Volume 2. User's Guide to MESOPLLIME (Mesoscale
Plume Segment) Model. EPA 600/7-79-XXX, Environmental Protection
Agency, Research Triangle Park, NC, 141 pp.
Benkley, C. W. and A. Bass. 1979b. Development of Mesoscale Air
Quality Simulation Models Volume 3. User's Guide to MESOPUFF
(Mesoscale Puff) Model. EPA 600/7-79-XXX, Environmental Protection
Agency, Research Triangle Park, NC, 118 pp.
Benkley, C. W. and A. Bass. 1979c. Development of Mesoscale Air
Quality Simulation Models Volume 6. User's Guide to MESOPAC
(Mesoscale Meteorology Package). EPA 600/7-79-XXX, Environmental
Protection Agency, Research Triangle Park, NC, 85 pp.
Blackadar, A. K. 1962. The Vertical Distribution of Wind and Turbulent
Exchange in the Neutral Atmosphere. J. Geophys. Res. 67: 3095-
3102.
Boris, J. P., and D. L. Book. 1973. Flux-corrected Transport--!.
SHASTA, A Fluid Transport Algorithm That Works. Jour. Comp. Phys.
11:38-69.
Briggs, G. S. 1975. Plume Rise Predictions. Lectures on Air Pollution
and Environmental Impact Analyses. American Meteorological Society,
Boston, MA, p. 59-111.
Egan, B. A. and J. R. Mahoney. 1972. Numerical Modeling of Advection
and Diffusion of Urban Area Source Pollutants. J. Appl. Meteor.
11:312-322.
Egan, B. A., K. S. Rao, and A. Bass. 1976. A Three-Dimensional
Advective-Diffusive Model for Long Range Sulfate Transport and
Transformation. Seventh International Technical Meeting on Air
Pollution Modeling and its Application, Airlie, VA, September 7-10,
1976, p. 697-714.
Colder, P. 1972. Relations Among Stability Parameters in the Surface
Layer. Bound. Layer Meteor. 3:47-58.
Hales, J. M., D. C. Powell and T. D. Fox. 1977. STRAM-An Air Pollution
Model Incorporating Non-linear Chemistry, Variable Trajectories,
and Plume Segment Diffusion. EPA 450/3-77-012. Environmental
Protection Agency, Research Triangle Park, NC, 147 pp.
-------
ENVIRONMENTAL RESEARCH & TECHNOLOGY INC
REFERENCES (Continued)
O'Brien, J. J., 1970. A Note on the Vertical Structure of the Eddy
Exchange Coefficient in the Planetary Boundary Layer. J. Atmos.
Sci. 27:1213-1215.
Scire, J. S., J. E. Beebe, C. W. Benkley and A. Bass. 1979. Develop-
ment of Mesoscale Air Quality Simulation Models Volume 5. User's
Guide to the MESOFILE Postprocessing Package. EPA 600/7-79-XXX,
Environmental Protection Agency, Research Triangle Park, NC, 67 pp.
Start, G. E. and L. L. Wendell. 1974. Regional Effluent Dispersion
Calculations Considering Spatial and Temporal Meteorological Calcu-
lations. NOAA Tech. Memo. ERL-ARL-44, National Oceanic and
Atmospheric Administration, Washington, DC, 63 pp.
-------
APPENDIX A
TEST CASE MESOPAC INPUT AND OUTPUT
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APPENDIX B
TEST CASE MESOGRID OUTPUT
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-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1 REPORT NO
L:, PA-6 00/7-79-XXX
4. TITLE AND SUBTITLE
Development of Mesoscale Air Quality Simulation
Models. Volume 4. User's Guide to MESOGRID (Meso-
scale Grid) Model
6. PERFORMING ORGANIZATION CODE
3. RECIPIENT'S ACCESSION>NO.
5. REPORT DATE
September. 1979
7 AUIHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
Charles S. Morris, Carl W. Benkley, and Arthur Bass
9 PERFORMING ORGANIZATION NAME AND ADDRESS
linvi ronmental Research and Technology, Inc.
G96 Virginia Road
Concord, MA 01742
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
03-6-022-35254/NOAA Contract
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA-600/7
15. SUPPLEMENTARY NOTES
Performed under contract to the National Oceanic and Atmospheric Administration
16. ABSTRACT
MESOGRID is a regional-scale grid model, based on the Egan-Mahoney method of
moments, especially designed to simulate the air quality impacts of multiple
sources at long transport distances. It has been developed to answer the need
for a simple, computationally practical, easy to use and flexible mesoscale grid
model - suitable for decision-making and regulatory applications - particularly
at transport distances beyond the range of applicability of conventional straight-
line Gaussian plume models. MESOGRID explicitly includes vertical diffusion;
horizontal diffusion is included only through spatial and temporal variations in
mesoscale meteorology.
Highly user-oriented, MESOGRID provides a range of flexible options, and
its clean, modular structure permits further modifications with ease. It is
designed to be driven by user-specified meteorological scenarios, of arbitrary
duration, constructed by a suitable meteorological preprocessor model (e.g.,
MESOPAC). It outputs spatially-gridded concentration arrays averaged over
arbitrary time intervals of one hour or more, and is designed to be coupled
to a postprocessor model (e.g., MESOFILE) to provide additional graphical and
statistical analyses. Routines are provided for: plume rise; fumigation;
linear conversion of S0_ to SO.; and dry deposition of S0~ and SO..
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
*Air Pollution
*A1gorithms
*Atmospheric Models
b.IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
13B
12A
04A
18 DISTRIBUTION STATEMENT
Release to Public
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UNCLASSIFIED
21. NO. OF PAGES
118
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UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
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17. KEY WORDS AND DOCUMENT ANALYSIS
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(b) IDENTIFIERS AND OPEN-ENDED TERMS - Use identifiers for project names, code names, equipment designators, etc. Use open-
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