Initial Application of the Adaptive Grid Air Pollution Model
M. Talat Odman* and Maudood N. Khan
Georgia Institute of Technology
School of Civil & Environmental Engineering
Atlanta, GA 30332-0512
Ravi K. Srivastava
U.S. Environmental Protection Agency
National Risk Management Research Laboratory
Research Triangle Park, NC 27711
D. Scott McRae
North Carolina Slate University
Department of Mechanical and Aerospace Engineering
Raleigh, NC 27695-7910
Prepared for presentation at the 25Ul NATG/CCMS International Technical
Meeting on Air Pollution Modeling and Its Application, Louvain-la-Neuve,
Belgium, October 15-19. 2001
ABSTRACT
We have developed an adaptive grid algorithm for use in air pollution models. This
algorithm reduces the errors related to insufficient grid resolution by automatically
refining the grid scales in regions of high interest. Meanwhile, the grid scales are
coarsened in other parts of the domain that arc of lesser interest. This ensures a near-
optimal use of available computational resources at all times during the simulation. The
movement of the grid is controlled by a weight function formed as a linear combination
of errors in various pollutant species. The user defines which species should be included
in the weight function calculation.
At the Millennium (24th) International Technical Meeting (ITM), we discussed our
evaluation of the algorithm in model problems involving plumes and puffs with
simplified dispersion and chemistry and concluded that it could improve accuracy. Since
then, we incorporated the algorithm into an operational air pollution model. We
developed an emission processor that maps point, area, and mobile sources onto the non-
uniform grid cells after every adaptive grid movement. We also developed a
* Presenting author
1

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M. T. ODMAN etal
meteorological processor that can map the output of a uniform grid meteorological model
at a very fine scale onto the adapting grid. The ideal solution would be to have a
meteorological model that runs in parallel to the air pollution model and operates on the
same grid.
In this paper, after a brief description of the adaptive grid model, we discuss its
performance in an initial application to an ozone episode that occurred in the Tennessee
Valley during July 1995. A mesoscale model at 4-km resolution over the region provided
the meteorological inputs. We compare the estimated ozone levels to the observations
from the Acrometric Information Retrieval System (AIRS) network for a verification of
the model. The same episode was also simulated by a fixed grid model whose results and
run time statistics are compared to the adaptive grid model for an initial evaluation of
accuracy and efficiency. Finally, we outline how the model can be improved in the
future.
1. INTRODUCTION
Grid size (or resolution), when inadequate, can be an important source of uncertainty
for air quality model (AQM) simulations. Coarse grids used because of computational
limitations may artificially diffuse the emissions, leading to significant errors in the
concentrations of pollutant species, especially those that are formed via non-linear
chemical reactions. Further, coarse grids may result in large numerical errors. To address
this issue, multiscale modeling and grid nesting techniques have been developed (Odman
and Russell, 1991; Odman et al., 1997). These techniques use finer grids in areas that are
presumed to be of interest (e.g., cities) and coarser grids elsewhere (e.g., rural locations).
Limitations include loss in accuracy due to grid interface problems and inability to adjust
to dynamic changes in resolution requirements. Adaptive grids arc not subject to such
limitations and do not require a priori knowledge of where to place finer grids. Using
grid clustering or grid enrichment techniques, they automatically allocate fine resolution
to areas of interest. They are thus able to capture the physical and chemical processes that
occur in the atmosphere much more efficiently than their fixed grid counterparts.
The adaptive grid methodology used here is based on the Dynamic Solution
Adaptive Grid Algorithm (DSAGA) of Benson and McRae (1991), which was later
extended for use in air quality modeling by Srivastava et al. (2000). It employs a
structured grid with a constant number of grid nodes. The modeling domain is partitioned
into N x M quadrilateral grid cells. The grid nodes are repositioned in a two-
dimensional space throughout the simulation according to a weight function which
represents the resolution requirements. The area of the grid cells changes due to grid node
movements, but the connectivity of the grid nodes remains the same. Further, since the
number of grid nodes is fixed, refinement of grid scales in some regions is accompanied
by coarsening in other regions where the weight function has smaller values. This results
in optimal use of computational resources and yields a continuous multiscale grid where
the scales change gradually. Unlike nested grids there are no grid interfaces; therefore,
numerical problems related to the discontinuity of grid scales are avoided.
The adaptive grid algorithm was applied to problems with increasing complexity and
relevance to air quality modeling. Starting with pure advection tests (Srivastava et al.,

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ADAPTIVE GRID AIR QUALITY MODEL
3
2000), it was applied to reactive flows (Srivastava et al., 2001a) and to the simulation of a
power-plant plume (Srivastava et al., 2001b). In all these applications, the adaptive grid
solution was more accurate than a fixed, uniform grid solution obtained by using the
same number of grid nodes. To achieve the same level of accuracy with the fixed uniform
grid required significantly more computational resources than the adaptive grid solution.
In this paper, we describe how the adaptive grid algorithm was implemented in an urban-
to-regional scale AQM. After a brief discussion of model components, we report
preliminary results from the first application of the adaptive grid AQM.
2. METHODOLOGY
An adaptive grid AQM simulation has two fundamental steps: a grid adaptation step,
that is responsible for repositioning of grid nodes according to the grid resolution
requirements, and a solution step, that simulates the physical and chemical processes that
occur in the atmosphere. The solution (i.e., concentration fields) remains unchanged
during the adaptation step, and the weight function clusters the grid nodes in regions
where finer resolution grids are required. In preparation for the solution step, the fields of
meteorological inputs and emissions must be mapped onto the new grid locations. This
task is also considered part of the adaptation step and is undertaken by efficient search
and intersection algorithms. During the solution step, the grid nodes remain fixed while
the solution is advanced in time. Ideally, the adaptation step should be repeated after each
solution step owing to the change in resolution requirements. However, since the
mapping of meteorological and emissions data is computationally expensive, we have
chosen to apply the adaptation step less frequently. Whereas, the solution is advanced in
time by 1 hour in several time steps, the adaptation step is performed once every hour. In
order to ensure numerical stability, we require that the Courant number be smaller than
unity while determining the time step of the solution. The rest of this section consists of a
more detailed description of the adaptation and solution steps.
2.1. Adaptation Step
The key to adaptation is a weight function that determines where grid nodes need to
be clustered for a more accurate solution. Such a weight function, w, can be built from a
linear combination of the errors in the concentrations of various chemical species:
w=c2>„V2c„	(1)
fl
where V2, the Laplacian, represents the error in cr, the computed value of the
concentration of species n. The chemical mechanisms used in AQMs usually have a large
number of species. Due to non-homogeneous distribution of emissions and disparate
residence times, each ¦ species may have very different resolution requirements.
Determining an such that pollutant concentrations (e.g., ozone) can be estimated most
accurately is a current research topic. Here, all an are set to zero, except the one for
nitric oxide (NO). Further, the grid adaptation is restricted to the horizontal plane, and the

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M. T. ODMAN f.tal
same grid structure, which is determined by the surface layer NO concentrations, is used
for all vertical layers. This, combined with the requirement that the Courant number
should be less than unity, may result in very small solution time steps because of high
wind speeds aloft. Adaptation in the vertical direction is possible but significantly more
complicated.
The grid nodes are repositioned by using the weight function. The new position of
the grid node /, P"" , is calculated as;
pr = i^h/t^	(2)
i-1	/ (=1
where Pk, k = 1,...,4 , are the original positions of the centroids of the four cells that
share the grid node /, and trt is the weight function value associated with each cell.
Once the grid nodes are repositioned, ecll-averaged species concentrations must be
recomputed for the adapted grid cells. Holding the concentration field fixed and moving
the grid is numerically equivalent to simulating the advection process on a fixed grid.
Therefore, we use a high-order accurate and monotonic advection scheme known as the
pieccwise parabolic method (Collcla and Woodward, 1984) to interpolate concentrations
from the old to the new grid locations.
The calculation of the weight function, the movement of the grid nodes, and the
interpolation of species concentration from the old to the new grid locations are three
distinct tasks of an iterative process. The process continues until the maximum grid node
movement is less than a preset tolerance. A very small tolerance may lead to a large
number of iterations. On the other hand, a large tolerance may not ensure adequate
resolution of the solution field. Currently, we stop iterating when, for any grid node, the
movement is less than 5% of the minimum distance between the node in question and the
four nodes to which it is connected.
After the grid nodes are repositioned, emissions and meteorological data must be
processed to generate the necessary inputs for the solution step. Note that, unlike the
practice with fixed grid AQMs. this processing could not be performed prior to the
simulation because there is no a priori knowledge of where the nodes would be located at
any given time. In case of meteorological data, an ideal solution would be to run a
meteorological model (MM), which can operate on the same adaptive grid, in parallel
with the AQM. This would ensure dynamic consistency of meteorological inputs, but
such a MM is currently nonexistent. Therefore, hourly meteorological data are obtained
from a high-resolution, fixed-grid MM simulation and interpolated onto the adaptive grid.
For mass conservation, as a minimum requirement, the vertical wind components are
readjusted later during the solution step as described in Odman and Russell (2000).
The processing of emission data is computationally expensive, requiring
identification of various emission sources in the adapted grid cells. Here, we treat all
emission sources in two categories: point and area sources. For simplicity, the mobile
sources have been included in the area-source category, but treating them as line sources

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ADAPTIVE GRID AIR QUALITY MODEL
S
Figure 1. Intersection of an adapting grid cell with the area-source emissions grid.
would yield better resolution. For the point sources, the grid cell containing the
location of each stack must be identified. The search may be quite expensive if there are
thousands of stacks in the modeling domain. However, assuming that the cell containing
the stack before adaptation would still be in close proximity of the stack after adaptation,
the search can be localized. The localization of the search provides significant savings
over more general, global searches. As for the area sources, they are first mapped onto a
uniform high-resolution emissions grid using geographic information systems. This is
done in order to avoid higher computational costs associated with processing of
emissions from highly irregular geometric shapes presented by highways and counties.
Around each adaptive grid cell there is a box of emissions grid cells Et,i = l,...,/i, as
illustrated in Figure 1. Once each Ei is identified, then their polygonal intersections with
the adaptive grid cell are determined. Finally, the areas of these polygons, Sn are
multiplied by the emission fluxes of £(and summed over n to yield the total mass emitted
into the adaptive grid cell. This process is performed for all adaptive grid cells.
The final step in preparation for the solution step is reestablishing a uniform grid for
easy computation of the solution. This requires computation of a transformation from the
(x,y)space where the grid is non-uniform to the (£,?]) space where the grid would be
uniform. The calculation of the Jacobian of the transformation and other necessary
metrics (i.e., d^/dx,d^/dy,drj/dx,dt]/dy ) concludes the adaptation step.
2.2. Solution Step
The atmospheric diffusion equation in the (%,rj,a) space can be written as:
3c„ ^
^(Jc„) ( 3(-/vx) t 3(iv"e„) | d{jvacJ | d
dt dg	dt]	da

JKm ¦

9 T}
JKm
dr]
da
JK°
dc
n
3a
(3)
= JR„ + JS.

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6
M. T. ODMAN etal
where c„, Rn, and S„ are the concentration, chemical reaction, and emission terms of
species n, respectively, and a is a terrain-following vertical coordinate. J is the Jacobian
of the coordinate transformation:
/=_L *l'
m2 da
d£, dn d£, dr) 1
where in is the scale factor of a conformal map projection in the horizontal. The
components of the wind vector in £ and T] directions are v( and v" :
- m—^u +
dv
(5)
,, dr] dr]
v =in—U + in—-V
d.x	dy
where U and V are real horizontal wind velocities rotated in the map's coordinate
directions. The turbulent diffusivity tensor is assumed to be diagonal, and its elements are
K" , K'm , and KCT'T. Element Kcan be expressed in terms of vertical diffusivity
K™ as:
Ka" =
da
K::.	(6)
The expressions for v" (the wind component in the a direction), K"" , and Knn
are omitted here due to space limitations. Since the grid is uniform in the (£,??) space,
solution algorithms can be taken directly from existing AQMs. We use those described
by Odman and Ingram (1996).
3. MODEL VERIFICATION
The adaptive grid AQM is being verified by simulating ozone air quality in the
Tennessee Valley region for the July 7-17, 1995, period. Meteorological data from a
4x4 km resolution simulation with the Regional Atmospheric Modeling System
(RAMS) are being used. The emissions inputs for the region were developed from the
Southern Appalachian Mountains Initiative (SAMI) inventory. There are over 9000 point
sources in this domain including some of the largest power plants in the U.S.A. The area
sources were mapped onto a 4x4 km emissions grid. The AQM grid consists of 112 by
64 cells, initially at 8x8 km resolution. In the vertical, there are 20 unequally spaced
layers extending from the surface to 5340 m. Starting with 32 m, the thickness of each
layer increases with altitude.
Figure 2 shows the grid at 7:00 a.m. EST on July 7. Since the adaptation step is
performed once an hour, the grid shown will not change until 8:00 a.m. EST. Note
that the grid size is reduced to few hundred meters around large point sources. With

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ADAPTIVE GRID AIR QUALITY MODEL
7
wind speeds larger than 10 m/s aloft, the solution time step can drop below 1 minute to
keep the Courant number less than unity. Because of this, the simulation is progressing at
the speed of about 2 hours of CPU time per simulation hour on a SUN Blade workstation
(Model 1000) with a 750 MHz Ultra SPARC III processor.
Figure 2. The grid used from 7:00 to 8:00 a.m. EST during the simulation of July 7, 1995.
35
30
25
20
15
10
5
0
ppb
35
30
25
20
15
10
ppb
Figure 3, NO concentrations at 7:00 a.m. EST on July 7, 1995. from adaptive grid (top) and 4x4 km fixed grid
(bottom) AQM simulations.

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8
M. T. ODMAN etai.
PPb
1105
90
75
60
sf.
- 45
30
15
0
Figure 4, Ozone concentrations at 5:00 p.m. EST on July 7, 1995, from the adaptive grid AQM simulation.
The surface layer NO concentrations at 7:00 a.m. EST that were used in generating
the grid in Figure 2 are shown in Figure 3 (top frame). Also shown are the NO
concentrations at the same hour from a 4x4 km resolution fixed grid AQM simulation
(bottom frame). The adaptive grid captures the NO gradients near source areas with a
level of detail that is far superior to the fixed grid even though the latter used 4 times
more grid nodes. Note that some large power plant stacks, such as Cumberland, are
emitting above the stable boundary layer at this hour. Since their plumes do not affect the
surface layer NO concentrations, no grid clustering is observed in Figure 2 around such
stacks. During daytime hours, as such plumes mix down and start affecting the surface
layer NO concentrations, grid nodes are clustered around them, along with other sources.
Figure 4 shows the ozone (0;) concentrations obtained from the adaptive grid AQM
simulation at 5:00 p.m. EST on July 7, 1995. Since this is only the first day of the
simulation, the 03 concentrations are probably still sensitive to the uniform initial
conditions (35 ppb everywhere). However, the observed level of variability in the field
and the captured detail in the gradients are encouraging. Once this simulation is finished,
03 fields will be compared to those obtained from fixed grid AQM simulation at 4x4
and 8x8 km resolutions using the same inputs and solution algorithms. To complete the
verification, all simulated 03 fields will be compared to observations from routine
monitoring network as well as intensive field studies conducted in the region during this
episode.
4. CONCLUSION
An adaptive grid, urban-to-regional scale AQM has been developed. A simulation
with this model evolves as a sequence of adaptation and solution steps. During the
adaptation step, the solution (i.e., concentration fields) is frozen in time. A weight
function that can detect the error in the solution is used to move the nodes of a structured
grid. Iterative movement of the grid nodes continues until the solution error is reduced
sufficiently. During the solution step, the grid is held fixed and the solution is advanced

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ADAPTIVE GRID AIR QUALITY MODEL
9
in time. However, before this can be done, the meteorological and emissions inputs must
be mapped onto the adapted grid. For meteorological inputs, data are interpolated from a
very-high-resolution mesoscale model simulation. For emissions, efficient search and
intersection algorithms were developed to ensure proper allocation of point and area
sources to the cells of the adapted grid. Using coordinate transformations, the non-
uniform grid can be mapped into a space where it becomes uniform. The atmospheric
diffusion equation in this new space has been derived. Since the form of the equation is
very similar to forms in existing AQMs and the grid is uniform, numerical algorithms
developed for fixed uniform grid AQMs can be used to advance the solution.
To verify the model, the July 7-17, 1995, ozone episode in the Tennessee Valley is
being simulated. So far, the grid is adapting to dynamic changes in the NO fields as
expected. Nodes are clustered around major emission sources with grid resolutions
around 200 m. The NO and 03 fields show gradients with a level of detail that is likely
unprecedented for a regional simulation of this scale. However, the simulation is
progressing slowly due to very short solution time steps. This will probably necessitate
changes in solution algorithms such as using an implicit advection scheme that is not
subject to the Courant stability limit. Adaptation criteria are also being developed that
would consider the errors not only in NO but in other species as well, especially those
involved in important 03 formation reactions.
5. ACKNOWLEDGEMENTS
This research is supported by U.S. Environmental Protection Agency Grant No. R
827028-01-0. We thank Steve Mueller of the Tennessee Valley Authority for providing
the meteorological data.
6. REFERENCES
Benson, R. A., and McRae, D. S., 1991, A Solution adaptive mesh algorithm for dynamic/static refinement of
two and three-dimensional grids, in: Proceedings of the Third International Conference on Numerical
Grid Generation in Computational Field Simulations, Barcelona, Spain, p. 185.
Collela, P., and Woodward, P. R., 1984, The piecewise parabolic method (PPM) for gas-dynamical simulations,
J. Comput. Phys. 54:174.
Odman, M. T„ and Russell, A.G., 1991, A multiscale finite element pollutant transport scheme for urban and
regional modeling, Atmos. Environ. 25A: 2385.
Odman, M. T., and Ingram, €., 1996, Multiscale Air Quality Simulation Platform (MAQSIP): Source Code
Documentation and Validation, MCNC Technical Report ENV-96TR002, Research Triangle Park, North
Carolina, pp. 11-32.
Odman, M. T„ Mathur, R., Alapaty, K., Srivastava, R. K., McRac, D. S , and Yamartino, R. J., 1997, Nested
and adaptive grids for multiscale air quality modeling, in: Next Generation Environmental Models and
Computational Methods, G. Dclic, and M. F. Wheeler, eds., SIAM, Philadelphia, pp. 59-68.
Odman, M. T, Russell, A. G., 2000. Mass conservative coupling of non-hydrostatic meteorological models
with air quality models, in: Air Pollution Modeling and Us Application Xlll, S.-E.Gryning, and E.
Batchvarova, eds., Kluwer Academic/Plenum Publishers, New York, pp. 651-660.
Srivastava, R. K., McRae, D. S., and Odman, M. T„ 2000, An adaptive grid algorithm for air quality modeling;
J. Comput. Phys. 165: 437.
Srivastava, R. K., McRae, D. S., and Odman, M. T,, 2001(a), Simulation of a reacting pollutant puff using an
adaptive grid algorithm, J. Geophys. Res., in press.
Srivastava, R. K » McRae, D. S , and Odman, M. T., 2001(b), Simulation of dispersion of a power plant plume
using an adaptive grid algorithm, Atmos. Environ., in press.

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TECHNICAL REPORT DATA
NRMRL-RTP-P-637 (Please read Instructions on the reverse before completing)
1. REPORT NO 2.
EPA/600/A-01/096
3. RECIPIENTS ACCESSION NO.
4 TITLE AND SUBTITLE
Initial Application of the Adaptive Grid Air
Pollution Model
5. REPORT DATE
6. PERFORMING ORGANIZATION CODE
7.authors M.x.odnan and M.N.Khan (GA Tech), R.K.Srivas-
tava (EPA), and D.S.McRae (NC State)
8. PERFORMING ORGANIZATION REPORT NO
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Georgia Inst, of Technology NC State University
School of Civil and Environ- Dept. of Mechanical and
mental Engineering Aerospace Engineering
Atlanta, GA 30332 Raleigh, NC 27695
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO,
EPA Grant R827028-01-0
(GA Tech)
12. SPONSORING AGENCY NAME AND ADDRESS
U. S. EPA, Office of Research and Development
Air Pollution Prevention and Control Division
Research Triangle Park, North Carolina 27711
13. TYPE OF REPORT AND PERIOD COVERED
Published paper; 1-8/01
14. SPONSORING AGENCY CODE
EPA/600/13
15 supplementary notes ^PPCD project officer is Ravi K. Srivastava, Mail Drop 65, 919/511-
3444. Presented at 25th NATO/CCMS Int. Technical Conf., Air Pollution Modeling and Its
Application. Louvain-la-Neuve. Belgium. 10/15-19*/200i.
16.abstract ¦phe paper discusses an adaptive-grid algorithm used in air pollution models.
The algorithm reduces errors related to insufficient grid resolution by automatically
refining the grid scales in regions of high interest. Meanwhile the grid scales are
coarsened in other parts of the domain that are of lesser interest. This ensures a near-
optimal use of available computational resources at all times during the simulation.
The movement of the grid is controlled by a weight function formed as a linear combina-
tion of errors in various pollutant species. The user defines which species should be
included in the weight-function calculation. After a brief description of the adaptive-
grid model, the paper discusses its performance in an initial application to an ozone
episode that occurred in the Tennessee Valley during July 1995. A mesoscale model at 4-
km resolution over the region provided the meteorological inputs. The estimated ozone
levels are compared to the observations from the Aerometric Information Retrieval Sys-
tem (AIRS) network for verification of the model. The same episode was also simulated
by a fixed-grid model whose results and run-time statistics are compared to the adap-
tive-grid model for an initial evaluation of accuracy and efficiency. Finally, the
paper outlines how the model can be improved.
17 KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Air Pollution
Mathematical Models
Adaptive Systems
Meteorological Data
Ozone
Nitrogen Oxide (NO)
Adaptive Grid Model
13B
12A
14G
04B
07B
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19. SECURITY CLASS (This Report)
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