Published in Air & Waste Manage. Assoc: Schichtel, B.A.; Husar, R.B. J. of Air & Waste
Manage. Assoc. 1996, 47, 331-343.
REGIONAL SIMULATION OF ATMOSPHERIC POLLUTANTS
WITH THE CAPITA MONTE CARLO MODEL
by
Bret A. Schichtel and Rudolf B. Husar
Center for Air Pollution and Trend Analysis (CAPITA)
Campus Box 1124
Washington University
St. Louis, MO 63130
September 25, 1995
ABSTRACT
A Monte Carlo model for the simulation of regional scale transport, transformation, and dry and
wet removal is presented. The model was newly re-designed in a modular framework, separating
the emissions, transport and kinetics calculations. The transport module employs a quantized
Monte Carlo technique for the simulation of atmospheric boundary layer physics. Kinetic
processes are simulated using rate equations where the rate coefficients are dependent upon
meteorological variables, and thus vary in space and time. The rate coefficient equations are
determined via a tuning process in which simulated values are compared to observed
measurements. Results from simulations of SO2 and SO42 over the eastern US are presented for
1992. Comparisons of simulated daily SO42 concentrations to observations had r2 = 0.35 - 0.83
depending on season and location, while for weekly SO42 wet deposition rates r2 = 0.5 - 0.95.
The utility of the model to investigate the source receptor relationship is demonstrated by
explicitly examining the role of emission rates, transport, and kinetic processes in the attribution
of sulfur dioxide and sulfate at a receptor in Massachusetts during the summer of 1992.
1
INTRODUCTION
During the 1970’s, air quality measurements demonstrated that pollutant emissions could
be transported over large distances, significantly influencing distant receptor concentrations. The
realization of regional scale transport of pollutants led to numerous air quality networks, models,
and large scale field studies to relate the contributions from near as well as distant sources to
receptor concentrations, i.e. to quantify the source receptor relationship. Many of the initial
studies focused on sulfur oxides, and were designed to attain better understandings of the
physical/chemical processes governing regional scale transport. For example, in Europe, the
OECD established the Long Range Transport of Air Pollutants (LRTAP) program in 1972 (1),
and in the US, the Sulfate Regional Experiment (SURE) was conducted (2), along with numerous
plume studies.
Associated with these studies were the development of models. The initial models tended
to be simple, using aggregated and parameterized meteorology and rate coefficients to simulate
the physical/chemical processes responsible for regional transport. These included trajectory
models (3, 4), statistical models (5, 6), as well as simple diffusion and box models (7, 8). As the
understanding of the atmospheric processes increased, these types of models were generalized to
include processes such as non-linear chemistry and atmospheric diffusion (9, 10).
During the 1980’s, with the concern over acid rain, substantial effort was devoted to the
development of elaborate Eulerian models, such as the Regional Acid Deposition Model
(RADM) (11) and the Acid Deposition and Oxidant Model (ADOM) (12). These models attempt
to simulate atmospheric processes, such as in-cloud oxidation, with great detail. However, the
data and computer resource needs have restricted their use to research activities with runs limited
in time and space. Also, it is difficult to separate the contributions from the various
2
physical/chemical processes involved in the source receptor relationship (13). As a result these
models tend to be operated in a “black box” approach.
In this paper, an IBM-PC based Monte Carlo model for the simulation of regional scale
transport, transformation, and removal of atmospheric pollutants is presented. This model is an
extension of the CAPITA Monte Carlo model developed in the 1980’s (9, 14). The model is
“data driven,” and was designed to take advantage of multiple meteorological, emission,
concentration, and deposition databases that are available from various data suppliers. Beyond
the calculation of ambient concentrations and deposition fluxes, the model was designed to be
used as a diagnostic tool for the investigation and quantification of the physical/chemical
processes governing the source receptor relationship, as well as for the estimation of unknown
emission fields given ambient concentration data.
The paper presents the simulation methodology, along with the underlying physical and
chemical processes. The suitability of the model for regional scale simulation is shown through
the simulation of sulfate and the total sulfate wet deposition over the Eastern US. Also, the
utility of the model to investigate the source receptor relation is demonstrated by examining the
role of emission rates, transport, and kinetic processes in the attribution of sulfur dioxide and
sulfate at a receptor in Massachusetts.
METHODOLOGY
Monte Carlo Approach
In the Monte Carlo approach to air pollution simulation, individual quanta or particles are
subjected to the same physical and chemical processes and events in the computer as in the
physical world. It can be thought of as a direct simulation of atmospheric pollutants. This
3
approach contrasts with more customary numerical simulations in that it does not require explicit
conservation equations and their solution as the basis for the simulation.
The Monte Carlo approach to the simulation of atmospheric pollutants has the following
key characteristics. First, each emitted quantum contains a fixed quantity of mass of various
pollutants based on the source's emission rate. Individual quanta are then subjected to transport,
transformation, and removal processes. Mass conservation is maintained at the quantum level by
accounting for the mass that has been chemically transformed and physically removed as an
assembly of quanta travel through three dimensional space (Figure 1). An airmass is depicted as
an ensemble of multiple quanta. The dispersion is represented by the spread of the quanta arising
from the integration of the equations of motion, where horizontal and vertical mixing are based
on mean and random wind components. This approach can be considered to be a Lagrangian
simulation since the trajectories and the fate of individual quanta are followed. In the limit of
infinite quanta, this approach results in a stochastic solution of the dispersion equation, yielding
results equivalent to an Eulerian solution to the governing equations.
In the Monte Carlo approach, the simulation of the meteorological dispersion of
pollutants proceeds independently from the nature and chemistry of the pollutants. This is based
upon the assumption that meteorology is not significantly influenced by trace constituents in the
atmosphere; however, it is understood that kinetic processes are dependent upon the pollutant
transport. Consequently, the calculation of the dispersion of the pollutants can proceed
independently from the calculation of kinetic processes. This allows for the separate
examination of the influence of the transport and kinetics processes upon receptor
concentrations.
4
Monte Carlo simulations of atmospheric processes were developed in the 1970’s (15, 16).
However, this technique lost favor in the 1980’s as other approaches were pursued. Due to the
multiple benefits of this modeling approach, it regained popularity during the 1990’s for
mescoscale simulations (17, 18, 19), and is believed to offer considerable improvements over
conventional Gaussain-plume models (20). The use of the Monte Carlo technique for regional
scale simulations has received less attention with little development since the initial studies were
conducted by Patterson et al. (14) and Husar (9).
Data Flow
The independence of transport from chemical processes allowed for the separate
development of a meteorological module, for the calculation of pollutant dispersions, and a
kinetic module, for the calculation of pollutant concentrations and deposition rates. The flow of
raw meteorological, emission, chemical, etc. data through the meteorological and kinetic
modules is presented in Figure 2. The meteorological module transforms meteorological data
into a Lagrangian airmass history database, by computing the transport of conservative species
through three dimensional space. The first step in the processing of the meteorological data,
involves converting raw data from a random spatial distribution to a grid. Various institutions
convert meteorological state variables collected by the National Weather Service to a gridded
format using primitive equation models. Currently, we use data derived from the National
Meteorological Centers Nested Grid Model, NGM, (21, 22) and Colorado State University’s
Regional Atmospheric Modeling System, RAMS (23). The meteorological database is then
converted into Lagrangian airmass histories by the Eulerian/Lagrangian transformer. Along each
particle’s calculated trajectory, the particle’s positions and meteorological variables, such as
temperature, humidity, precipitation, etc., are saved. The resulting Lagrangian database, can be
5
either source oriented, simulating emissions forward in time from sources to receptors, or
receptor oriented, simulating the transport of airmasses backwards in time.
The kinetic module combines a source oriented Lagrangian airmass history database with
other data, such as emissions and surface meteorological data, for the calculation of the kinetic
processes. This is accomplished by first assigning species mass weights to the quantum when it
is released from the source. The weighting is dependent on each source’s emission rate. Kinetic
rate equations are then integrated along each quantum’s trajectory, accounting for the
transformation and removal of the pollutants with time. This creates additional Lagrangian
variables containing species mass weights. Receptor concentration fields can then be created
from the resulting database by defining a receptor volume and summing the species mass for all
quanta located in the volume. Deposition fields can also be created in a similar manner, but only
a receptor area needs to be defined. The concentration and deposition fields can be created
during the processing in the kinetic module, or as a post processor on the resulting kinetic
Lagrangian variables.
Normally, during the Eulerian to Lagrangian transformation only three dimensional
variables like humidity are stored along with the particles position. Within the kinetic module,
quanta airmass histories can be enriched with two dimensional Eulerian variables, such as
precipitation and cloud cover, required for the kinetic calculations. The data used to enrich the
airmass histories can be located in multiple databases. However, each database must use the
same Eulerian grid and time step. This is a flexible and efficient method allowing for the
inclusion or removal of meteorological variables and data sources for the calculation of kinetic
processes.
6
TRANSPORT AND KINETIC PROCESSES FOR REGIONAL SCALE SIMULATIONS
In a simulation of atmospheric transmission of a pollutant from its source to receptor, the
temporal and spatial scale of the simulation must match the atmospheric residence time and
transport distance of the pollutant. In this paper, we are interested in synoptic/regional scale
pollutants. Consequently, the scales of interest are on the order of 5000 - 10000 km in space, and
between 1 and 10 days in time. However, the understanding of the regional scale phenomena lies
in the proper simulation of the smaller scale processes that comprise the synoptic picture.
Regional Scale Transport
Regional scale dispersion is the result of the coupling of advective and random processes
in the atmosphere. The random processes are caused by the stochastic nature of turbulence in the
atmospheric boundary layer (ABL). The ABL experiences diurnal (Figure 3) and seasonal cycles
driven by the solar radiation. During the daytime, the ABL is unstable and well mixed. This is a
result of strong heating of the surface from solar radiation which produces temperature gradients
in the lower layers of the atmosphere. The temperature gradients produce discrete convective
elements called thermals. These are buoyant parcels of air 50-1000 m in diameter which develop
above a surface that is considerably warmer than the overlying air. The vertical turbulent
structure of the ABL then becomes organized in a pattern of updraughts and downdraughts. (24).
This mixing process is efficient enough that generally the potential temperature, relative
humidity, and pollutant concentrations of the thermals are conserved (25). Pollutants emitted
within the ABL quickly lose their identity and become part of the well mixed layer, extending up
to heights of several kilometers. The time scale associated with the vertical mixing ranges from
30 minutes to several hours during afternoon conditions (26, 27).
7
In the late afternoon, the surface heating is reduced and the ground temperature becomes
nearly equal to the overlying atmosphere. At this point, there is no upward heat flux to sustain
the convective thermals and the boundary layer collapses, resulting in the bulk of the former
daytime boundary layer becoming stable and stratified. The lack of vertical exchange confines
the movement of air parcels to shallow layers roughly parallel to the ground surface. The
pollutants that were part of the daytime mixing layer are now transported in horizontal layers
with varying wind directions and speeds. Unlike the daytime conditions, the nocturnal transport
within the former mixed layer will exhibit substantial veer and shear, the top layers heading in
directions and at speeds that may be markedly different from the movement of the bottom layer
(28, 29). It is this repeated process of vertical mixing followed by vertical wind veer which is
essentially responsible for regional dispersion.
During the evening hours, the vertical extent of the nocturnal mixing height is only on the
order of hundreds of meters. An important feature of the nocturnal surface based mixing layer is
that it generally coexists with a cooled surface. Thus, the mixing process has to overcome the
damping imposed by a stable stratified surface layer. These processes usually create a sharp
impermeable interface between the former mixed layer and the surface based nocturnal mixing
layer.
The interaction of a plume with the mixing layer is presented in Figure 3. As shown,
emissions from a source in the nocturnal mixing layer are trapped in that shallow layer, resulting
in high concentrations for a given emission rate. The pollutants confined to the surface layer are
mixed to and exposed to the absorbing ground surfaces and to the chemical mix of that surface
layer. Thus, dry deposition and potential chemical reactions significantly influence the fate of
8
these pollutants. Emissions from a plume emitting above the mixing height or those left from the
previous day’s mixing are confined to a relatively shallow layer, de-coupled from the ground.
Matter remaining above the surface layer overnight is not depleted by dry deposition, and
chemical reactions occur with species mixed during the previous day and those emitted directly
into the stratified atmosphere. During the morning hours, the mixing height begins to grow due
to solar heating, diluting the pollutant concentrations within the mixing layer and entraining
pollutants that were above the nocturnal layer.
Transport Simulation. The simulation of the regional transport in the Monte Carlo
models is conducted by moving inertialess particles in the Eulerian frame according to the
equation:
x t  t   x t    u x, t   u x, t . t
(1)
where x (=x,y,z) represents the particle position vector, and u (= u, v, w ) and u’ (=u’,v’,w’),
represent the time-averaged and fluctuating components of the flow field respectively. The
application of equation (1) results in the transport and dispersion of the particles. The basic
meteorological information required for this consists of the mean wind field u, v, w and the
fluctuating components u’,v’,w’ at all times over the whole model domain.
The mean wind field is generated from meteorological models, such as the National
Meteorological Center’s synoptic scale model (21, 22) and Colorado State University’s Regional
Atmospheric Modeling System (RAMS) (23). The random component of the velocity field
occurs at a resolution smaller than the meteorological model grids used to generate wind fields.
Consequently, the fluctuating components are calculated from the available meteorological
variables and treated as a sub-grid phenomena.
9
Vertical Diffusion. The above discussion, identified two key inputs for the simulation of
vertical diffusion within the planetary boundary layer. First, an upper boundary or "lid" exists up
to which convective mixing occurs, and second, the vertical daytime mixing occurs rather
rapidly. In Monte Carlo simulations, the rapid daytime vertical mixing is implemented by
changing the height of a particle at each 2-hour time step. Due to the rapid mixing, it is assumed
that the particle height at each time step is independent of the height during the previous step,
and is chosen according to a uniform probability distribution within the mixing layer. The
exception is that material which has been previously transported above the local mixing height is
subjected only to the mean wind vector.
A graphical illustration of the implementation of the above processes is presented by the
three trajectories in Figure 3. The intense vertical mixing within the mixing layer is indicated by
the crossing of the trajectory lines. The stable layers, during nocturnal hours, are illustrated in
the lines of near constant height for each quantum.
Horizontal Diffusion. A common approach for the calculation of the horizontal
diffusion is based upon the Prandtl mixing length model. This allows for the parameterization of
the diffusion by an effective eddy diffusion coefficient K . The diffusion process is implemented
as a random walk displacement of radius 2Kt for each time step in the model. The value of
the diffusion coefficient is a geographical function of the time of day and season. Values of K
ranging between 102 m2/s in stable conditions and 106 m2/s during intense convective activity
have been used in the past (14, 30). It is recognized that using an eddy diffusion coefficient to
represent horizontal diffusion is a crude approximation. However, it will be shown below that
horizontal diffusion has a small effect on regional dispersion.
10
Examples of Monte Carlo Simulations. The dispersion of a puff of emissions from a
source in western Tennessee is illustrated in Figure 4. This figure was created by simulating the
release of pollutants from a source using 25 particles. The position of the particles were plotted
every two hours after their initial release at twelve in the afternoon and tracked for three days.
The left hand picture contains the trajectories and height history of the particles when no
horizontal diffusion was imposed, i.e. K = 0 m2/s. The right hand figure contains the trajectories
and height history when a diffusion coefficient of K = 104 m2/s was employed for both day and
night.
The initial six hours of transport from the source took place within the mixing layer. The
wind velocity was relatively constant throughout the mixing layer, so the horizontal spreading of
the plume was due to the turbulence. After approximately six hours of transport, the puff was in
southern Illinois. At this point, the mixing layer had collapsed and the trajectories were
transported in separate de-coupled layers with varying wind velocities producing horizontal
spreading. This is seen in the left hand part of Figure 4 where the lateral spreading of the puff
was due solely to wind veer. After approximately one day of travel, the airmass parcels were
over the northwestern part of Ohio. At this point, it divided into a surface airmass heading
towards New Jersey and Connecticut, and an upper air airmass heading towards Maine. The
bifurcated plume continued to spread laterally, and after three days of transport the puff had a
width of over 600 km encompassing most of New England and a height over three kilometers. It
is evident that the large lateral spreading of the plume after three days of travel was primarily due
to the wind veer rather than the horizontal eddy diffusion.
11
The simulation of airmass transport in the lowest few kilometers of the atmosphere is
presented in Figure 5. This figure displays the position of particles on 01/16/1992 noon
Greenwich mean time (GMT) which were released at some previous time from multiple sources
uniformly distributed over the western US. In this sense, it is a flow visualization “experiment.”
The Eulerian to Lagrangian transformation was conducted using meteorological data generated
by RAMS. A nested grid was employed where a grid of 60 km was used over the western US
and a 24 km grid over Southern California and the Colorado Plateau (31).
A prominent characteristic of the western US is the complex terrain consisting of multiple
large valleys and mountain peaks. Also, during January there is little solar input resulting in
maximum daily mixing heights of approximately 600 m, as estimated from the RAMS data. The
combination of complex terrain and poor vertical mixing resulted in the uneven spatial
concentrations of particles displayed in Figure 5. The clumping of particles is due to the constant
emission of particles into poorly ventilated areas. This is particularly noticeable in the Southwest
where there are accumulations of particles in the San Joaquin Valley, Death Valley, and the
Colorado River Valley. The poor vertical mixing also forces particles to travel around features,
such as the Sierra Mountains. During the summer season, there is significantly more vertical
mixing and horizontal dispersion resulting in more uniform particle patterns over the western
US.
Chemical Transformation and Removal Kinetics
In the Monte Carlo model, a semi-empirical approach is employed for the simulation of
pollutant transformation and dry and wet deposition. The approach is deterministic in that rate
equations are used for the calculation of kinetic processes applied to each quantum. At a
quantum’s release, it is assigned a species mass weight based upon the source's emission rate.
12
Mass conservation is maintained at the quantum level by accounting for the mass that has been
transformed and removed. The kinetic rate coefficients are dependent upon the chemical,
meteorological, and geological environment of the quanta. Consequently, these coefficients vary
with space and time creating variable transformation and removal rates.
The simulation of the kinetic processes is empirical, in the sense that the rate coefficient
relationships are determined through a fitting process matching simulated to observed
concentration and deposition fields. The main thrust of this approach is to make maximum use
of existing meteorological, emission, receptor, etc. data in conjunction with a physical-chemical
model to derive the best set of rate coefficient equations. This approach assumes that the correct
pollutant transport and emission rates are known. It is hypothesized that given sufficient quality
and quantity of data, it would be possible to identify a unique set of rate parameters, thereby
simulating the physical/chemical processes.
SO2 - SO42 Simulation Over the Eastern US. Recently, a project was undertaken for the
retuning of the Monte Carlo model for the simulation of the SO2 - SO42 system over the Eastern
US during 1992. The following will present the resulting rate coefficient equations and some of
the resultant simulated SO42 concentrations and wet deposition rates. The process by which the
rate coefficient relationships were developed and their justification is given in Schichtel (32).
The rate of change of a quantum’s SO2 mass can be expressed as:
d ( SO2 )
 ( k t 2  k d 2  k w 2 ) SO2
dt
(2)
where k t 2 , k d 2 , and k w2 are the oxidation, dry deposition, and wet deposition rate coefficients of
SO2 respectively. Similarly, the rate of change of the SO42 mass can be expressed as:
13
d ( SO42  )
 k t 2 SO2  ( k d 4  k w4 ) SO42 
dt
(3)
where k d 4 and k w4 are the dry and wet deposition rate coefficients of SO42 respectively. It was
assumed that all SO2 and SO42 mass arose from the simulated sources only, thus, background
SO2 and SO42 were neglected.
The tuning process was conducted using the meteorological data generated from the
National Weather Service’s Nested Grid Model (21, 22). The data were available on a
stereographic grid with approximately 180 km size. Using the NGM data, a Lagrangian database
was created by releasing particles from the center of each meteorological grid cell, east of
Colorado. Approximately 350 sources were simulated in this manner. The three dimensional
location of each particle, along with the specific humidity and temperature, were deposited in the
Lagrangian database every two hours. Each particle was tracked for seven days, or until it was
transported past the edge of the meteorological grid.
The NGM data contained a precipitation field. However, it was found that the
precipitation field did not compare well with measured data. Deviations in the seasonal
precipitation rates up to a factor of two were found depending on the season and location (32).
The NGM precipitation field was replaced by hourly measured precipitation data from the US
Control COOP Hourly Precipitation database (33). This was accomplished by averaging the
precipitation rates over a two hour period, and spatially interpolating the data to the same grid
used by the NGM meteorological data. The resulting database was then suitable for input into
the kinetic module. A similar process was used for the creation of gridded total cloud cover data
from hourly data in the National Solar Radiation Database (34).
14
Emissions were obtained from the 1985 NAPAP inventory (35). The original data were
provided as point and area emissions on a 20 km grid. The data were transformed to the
meteorological grid by summing all point and area emissions together for all emission grid cells
which fell into the same meteorological grid cell. No attempt had been made to account for
variations in 1992 emission from those in 1985.
The observed data utilized for the tuning process consisted of ambient fine sulfur aerosol
concentrations from the IMPROVE (36) and the NESCAUM (37) monitoring networks, airport
visibility data (38), ambient SO2 concentrations from the AIRS database (39), and total SO42 wet
deposition data from the National Atmospheric Deposition Program/National Trends Network
(40).
The final relations derived for the rate coefficients are:
k t 2 = 0.001 + SR (0.02 + 0.05 SH/SHmax + 0.1*PF)
(4)
SR = (1-.65TS)GSR
k d 2 = Vd / H
(5)
(6)
Vd = .22 + 2 * SR
k d 4 = k d 2 /10
(7)
(8)
k w2 = Ws2/H * P = Sqr(40000 / (SO2CC + 2)) * P
(9)
k w4 = Ws4/H * P = 250 * P
(10)
where SR = ground level solar radiation [kW/m2]
TS = total cloud cover
GSR = ground level solar radiation in the absence of clouds [kW/m2]
SH = specific humidity [kg Water/kg Air]
PF = precipitation flag, i.e. PF = 1 if it rains PF = 0 otherwise
Vd = deposition velocity [cm/s]
H = mixing height [m]
Ws2, Ws4 = washout ratios for SO2 and SO42 respectively
SO2CC = SO2 column concentration [mg/m2]
P = precipitation rate [m/hr]
15
To illustrate how the meteorological variables affect the kinetic rate coefficients, a
quantum was released from St. Louis on July 15 at 10:00 GMT, and tracked for four days.
Figure 6 presents the quantum’s trajectory, and six of the airmass history variables necessary for
the calculation of the rate coefficients. The resulting rate coefficients and a corresponding sulfur
budget are presented in Figure 7. As shown, the quantum was released, and remained, below the
mixing height for the initial fourteen hours. Thus, it was exposed to the ground and a SO2 dry
depositions rate of approximately 5%/hr occurred. This resulted in about 38% of the SO2 to be
dry deposited. During this time, the solar input cycled from 0 to 0.6 back to 0 kW/m2 producing
transformation rates from 0.1 %/hr to 3 %/hr. This caused approximately 12% of the SO2 to be
transformed to SO42 . With the end of the solar input, the mixing layer collapsed and the quanta
was above the mixing height. These conditions resulted in no deposition of the SO2 and little
transformation. During the beginning of the second day, the ground level solar flux increased
and the quantum encountered a light precipitating airmass. The precipitation caused total
removal rates of the SO2 to be as high as 12%/hr removing 60% of the remaining SO2 mass over
the next 12 hours. The precipitation also washed out a significant fraction of the SO42 .
However, the enhanced transformation rates during precipitation, caused the overall SO42 mass to
increase to 20% of the total sulfur. After this period the precipitation increased, and after two
days of travel, nearly all of the SO2 and SO42 mass of the quantum had been dry and wet
deposited.
Simulated SO42 concentrations. Using the above rate equations, the Monte Carlo
model was run for all of 1992, generating 24-hour concentration and deposition fields over the
Eastern US. The surface concentrations were calculated for receptor volumes defined by the
16
meteorological grid cell and the mixing height. Figure 8, presents the average simulated SO42
concentration fields during the periods January - March, quarter 1, and July -September, quarter
3. Also, plotted for comparison are “observed” SO42 isopleth maps generated from the fusion of
IMPROVE and NESCAUM SO42 data and airport visibility data (41). During quarter 1, the
observed SO42 is nearly uniform over the east with a concentration of about 3 g/m3. The
simulated concentrations have more spatial variability then the observed, but reproduce the
general spatial pattern and magnitudes. The simulation deviates from the observed the greatest in
a belt from eastern Ohio to the Chesapeake Bay, with simulated concentrations greater than 5
g/m3 compared to about 3 g/m3 for the observed SO42 .
The simulation during quarter 3, also reproduces the general spatial pattern and
magnitudes of the observations. The highest observed concentrations are from southern
Pennsylvania and north Virginia to western Kentucky and Tennessee ranging from 6 to greater
than 7 g/m3. The simulated SO42 has a similar high concentration band, however, it is pushed
slightly to the north and west of the observed SO42 band. The concentrations for both the
observed and simulated SO42 progressively decrease in all direction from the high concentration
band producing similar concentrations over New England (~ 3 g/m3), the South (~5 g/m3), and
into the Mid west (2 - 5 g/m3).
The daily averaged simulated SO42 are seasonally compared to observations in
correlation plots (Figure 10). Due to the coarse meteorological grid used, it is unreasonable to
expect the model to simulate concentrations at a single receptor. Therefore, these comparisons
were conducted by averaging the model results and the NESCAUM/IMPROVE observations
over a New England and East Central spatial domains as defined in Figure 9. The simulated
17
SO42 in New England compares well with the observations, with squared correlation coefficients
varying between 0.56 during quarter 3 and 0.83 during quarter 2. The data points are centered
around the one to one line, except for quarter 1 where the model simulation tends to
underestimate the observed SO42 concentrations.
The correlation plots in the East Central domain have squared correlation coefficients
varying between 0.35 during quarter 1 to 0.61 during quarter 3 with r2 = 0.59 for the entire year.
The simulation reproduced the average observed concentrations for quarters 1 and 4, but tended
to underestimate them the rest of the year.
Simulated Total SO42 Wet Deposition Rates. The average simulated and observed total
SO42 wet deposition rates for quarters 1 and 3 are presented in Figure 11. The observed
deposition rates during quarter 1 range between 0.6 and 1.8 g/m2/yr with the largest depositions
occurring in a band from New York around the Carolinas and into the deep South. The
simulation reproduces this pattern, but tends to underestimate the deposition rates along the coast
and at the model domain boundaries. For example, the simulated deposition rates in Florida are
about 0.3 g/m2/yr compared to 1 g/m2/yr for the observations.
During quarter 3, the model results properly simulate the high deposition rates south of
Lake Erie and Ontario, where they exceed 4.2 g/m2/yr, and the decreasing deposition gradient
extending from this region. However, like quarter 1, the simulation underestimates the
deposition rates along the east coast, Florida, and the western part of the model domain between
a factor of 1.5 and 2.
Comparisons of the simulated total SO42 wet deposition rates to observed rates in New
England and East Central for weekly data are presented in Figure 12. This figure was created
18
using the spatial domains defined in Figure 9. The seasonal squared correlation’s for New
England show high correlation ranging from 0.5 to 0.94 with an overall squared correlation of
0.79 for the year. The simulated deposition rates underestimated the observed by about 25%
over the year, 1.71 g/m2/yr compared to 2.15 g/m2/yr for the observed rates. In the East Central
domain, the seasonal squared correlation varied between 0.71 and 0.89 with a yearly correlation
of 0.83. The yearly average deposition rates were 2 and 2.2 g/m2/yr for the simulated and
observed data respectively.
SOURCE RECEPTOR RELATIONSHIP
The source receptor relationship defines the attribution of a receptor’s concentration to
specific sources and/or source types. The Monte Carlo model was designed to be used as a
diagnostic tool for the investigation and quantification of the source receptor relationship. This
tool is based upon the fact, that in the Monte Carlo approach physical/chemical processes are
simulated as discrete events. Thus, the influence of each process on the source receptor
relationship can be analyzed separately.
It can be shown, that from the Lagrangian formulation of the dispersion equation (42, 43)
the source receptor relationship can be defined as:
mRijkl  Tijkl mE jl = ( Pt Pk )ijkl mE jl
where i
j
k
l
mRijkl
(11)
identifies the receptor volume
identifies the source volume
identifies the receptor time
identifies the source release time (k - l= pollutant age)
the mass within the receptor volume i at time k due to emissions from source j
released at time l
the mass released from source j at time l
mE jl
Tijkl the transfer matrix, the relative fraction of mass released from the source volume j
19
Pt
Pk
at time l that impacts the receptor volume i at time k
the transit probability
the kinetic probability
This equation states that the pollutant mass at a receptor i and time k, due to emissions from
source j released at time l, is proportional to the mass released at the source j at time l, where the
proportionality constant is the element of the transfer matrix Tijkl. The physical interpretation of a
transfer matrix element is that it represents the fraction of matter emitted from a source that
reaches the receptor in the chemical form of interest. The total mass contribution to a receptor
volume from a source can be found by simply summing over the source release time l.
Each element of the transfer matrix can be decomposed into a transit probability, Pt and a
kinetic probability Pk. Pt defines the transport of the emissions, and can be thought of as the
probability of a conservative species being transported from the source to the receptor. Pk
defines the kinetic processes of the emitted pollutant mass. Pk for a primary species, such as SO2,
is the probability that the pollutant mass will not be transformed or removed before being
transported to the receptor, while for a secondary species, Pk is the probability that the pollutant
mass will be transformed and not removed before being transported to the receptor. For
example, Pk for SO42- is the probability that a quantum's initial SO2 mass is transformed to SO42and the resulting SO42- mass is not removed before being transported to the receptor. For a
conservative species, Pk is unity.
The source receptor relationship is presented graphically in Figure 13. The maps in this
figure represent the three components of the source receptor relationship, mE, Pt, and Pk, and the
resulting average source contributions to the SO2 and SO42 column concentrations at a receptor
located in Massachusetts during quarter 3, 1992. The source grid is overlaid each map. The
emission rate map shows that the highest values are over the Ohio River Valley where they can
20
exceed 106 tons/yr. In the transit probability map, there is a decreasing probability of source
impact with distance from the receptor. For example, sources in Michigan are about 7 times less
likely to impact the Massachusetts receptor then the source located in Vermont. There is also a
higher likelihood of emissions impacting the Massachusetts receptor from sources to the west
and south than from the north. The SO2 kinetic probability map also displays an inverse
relationship with distance. Sources in the vicinity of the receptor have Pk higher than 50% while
in the Ohio River Valley the Pk is approximately 20%. The inverse relation with distance is
expected since SO2 is a reactive primary species, and the residence time is roughly proportional
to transport distance. The SO2 source attribution map shows that the concentration is dominated
by contributions from nearby sources. The Massachusetts and Connecticut source grids supply
over 35% of the SO2 mass. The large contributions from these sources are the result of their
relatively high transit and kinetic probabilities. However, the high emissions in the Ohio River
Valley lead to this area contributing almost 25% of the mass.
The kinetic probability map for SO42 presents a very different picture then seen for the
SO2 . SO42 is a secondary species, and it takes time before a significant fraction of the SO2 in an
airmass can be transformed to SO42 . This leads to kinetic probabilities that at first increase and
then decrease with distance from the receptor. As shown, the Pk is about 2 to 5% for sources
close to the receptor. This increases to almost 10% in western Pennsylvania and Northern
Virginia, and again decreases to 2-5% in Illinois and Missouri. The SO42 source attribution map
shows that the nearby sources contribute less than 10% of the SO42 mass to the receptor while
the Ohio River Valley contributes nearly 30%.
21
SUMMARY AND DISCUSSION
A redesigned and re-calibrated Monte Carlo model for the simulation of regional scale
transport, transformation, and removal of atmospheric pollutants was presented. The model was
developed in a modular fashion, separating the calculation of the pollutant transport from the
kinetics. The pre-computed transport data could then be used for the calculation of kinetic
processes. This procedure was based upon the assumption that pollutant species do not influence
meteorology to a significant degree. Transport calculations were conducted using 3-D gridded
mean wind fields, and simulating horizontal and vertical diffusion. The kinetic processes were
calculated through kinetic rate equations, where the rate coefficients were based upon space and
time dependent environmental variables.
The model was used to simulate the SO2 - SO42 system over the Eastern US during 1992.
Comparisons, of simulated seasonal SO42 concentrations to observations, showed that the model
was able to reproduce the spatial patterns and magnitudes. Comparisons, performed with daily
observations, showed that the model adequately simulated SO42 concentrations in New England
with seasonal r2 = 0.56 - 0.83. In the East Central US, the seasonal r2 = 0.35 - 0.61.
Comparisons of simulated total SO42 wet deposition rates to observed rates also showed strong
agreement. Correlations of the weekly data in both New England and the East Central had
seasonal r2 = 0.5 - 0.94.
A possible explanation, for the better correlations of the SO42 concentrations to
observations in New England than the East Central domain, is that New England may be more
dominated by regional scale phenomena than the East Central domain. There are few large sulfur
emitting sources in the New England region. High and low concentrations of SO42 will tend to
22
correspond to the transport of SO2 and SO42 from high and low emitting regions. The East
Central domain, on the other hand, has large sources within and around the domain. Also, the
Great Smoky Mountains are at the eastern edge of the domain. This is a complex situation, and
the proper simulation of the SO42 concentrations is more likely to be dependent upon mesoscale
transport and kinetics processes than in New England.
The Monte Carlo model was designed in such a manner as to allow for the investigation
and quantification of the physical/chemical processes in the source receptor relationship. This
was demonstrated by examining the role of source emissions, pollutant transport, and kinetics
processes responsible for the source contributions of SO2 and SO42 to a Massachusetts receptor
site during the quarter 3, 1992. It was found that the SO2 concentrations were highly influenced
by nearby sources, such as those in Connecticut and Vermont. This was a result of the inverse
relationship of the transit and kinetic probabilities with distance in the source receptor
relationship. The high emissions in the Ohio River Valley also lead to significant contributions
to the Massachusetts receptor concentration. The SO42 concentrations were dominated by
emissions from more distant sources, particularly from the Ohio River Valley. This was due to
the fact, that the concentrations of secondary species in a plume first increase and then decrease
with time. Consequently, emissions from distant sources generally have less of a likelihood of
impacting the receptor, but when they do, a higher fraction of the emissions is in the form of
secondary pollutants than is the case with emissions from nearby sources.
Acknowledgment. Although the research described in this article has been funded in part by the
U.S. Environmental Protection Agency under cooperative agreement CR 823756 and CR
818969, it has not been subjected to the Agency's peer and administrative review and therefore
23
may not necessarily reflect the views of the Agency, and no official endorsement should be
inferred. The information in this document has also been funded in part by Colorado State
University Subcontract G-2887-4.
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13. Middleton P.; J. S. Chang; J.C. Del Conal; H. Geiss; J. M. Rosinkski. Atmos. Environ. 1988, 22, 1195-1208.
14. Patterson, D.E.; R.B. Husar; W.E. Wilson; L.F. Smith. J. Appl. Meteor. 1981, 20, 404-420.
15. Hall, C.D. Quart. J. Roy. Meteor. Soc. 1975, 101, 235-244.
16. Alsmiller, F.S.; Alsmiller R.G.; H.W. Bertini; C.L. Begovich. J. Appl. Meteor. 1979, 18, 17-26.
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18. Wiel, J.C. Atmos. Environ. 1994, 28, 3433-3448.
19. Luhar, A.K.; Rao, K.S. Atmos. Environ. 1994, 28, 3417-3431.
20. National Research Council. Science and Judgment in Risk Assessment. National Academy Press: Washington
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21. Hoke J.E.; N.A. Phillips; G.J. DiMego; J.J. Tuccillo; J.G. Sela. Wea. and Forecasting 1989, 4, 323-334.
22. Rolph G.D. National Climatic Data Center Report, 1992; TD-6140.
23. Pielke, R.A.; W.R. Cotton; R.L. Walko; C.J. Tremback; W.A. Lyons; L.D. Grasso; M.E. Nicholls; M.D. Moran;
D.A. Ewlsey; T.J. Lee; J.H. Copeland. Meteorol. Atmos. Phys. 1992, 49, 69-91.
24. Lenschow, D.H.; Stephens, P.L. Boundary layer Meteor. 1980, 19, 509 - 532.
25. Willis, G.E.; Deardorff, J.W. J. Atmos. Sci. 1974, 31, 1297-1307.
26. Gillani, N.V. Atmos. Environ. 1978, 12, 569-588.
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27. Gryning S.E., A.A.M. Holtslag, J.S. Irwin, and B. Sivertsen. Atmos. Environ. 1987, 21, 79-89.
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30. Munn, R.E.; Bolin B. Atmos. Environ. 1971, 5, 363-402.
31. Stocker, R.A.; M. Uliasz; R.A. Pielke. “Aerosol and Atmospheric Optics: Radiative Balance and Visual Air
Quality, Volume A.” In Proceedings of the International Specialty Conference, Snowbird, Utah, September
1994.
32. Schichtel, B.A. The retrieval of pollutant emission fields from ambient concentration precipitation chemistry
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33. National Center for Atmospheric Research (NCAR), DS505.0 NCDC TD3240, US Controled Hourly
precipitation, Daily 1948-Cont.
34. National Renewable Energy Laboratory (NREL). September 1992. User’s Manual: National Solar Radiation
Database (1961-1990), Volume 1.0. Distributed by National Climatic Data Center, Federal Building,
Asheville, NC 28801.
35. Irving, Patricia M. Acidic Deposition: State of Science and Technology, Vol. I, Report 1, (Emissions).
Government Printing Office: Washington, DC, 1991; 20402-9325.
36. Sisler J.F.; D. Huffman; D.A. Latimer; W.C. Malm; and M. Pitchford. Spatial and temporal patterns and the
chemical composition of the haze in the Unites States: An analysis of data from the IMPROVE network,
1988-1991. CIRA, CSU, Fort Collins, CO, 1993; #ISSN No. 0737-5352-26.
37. Poirot, R. L.; P. J. Galvin; N. Gordon; S. Quan; A.V. Arsdale; R.G. Flocchini. “Annual and seasonal fine
particle composition in the Northeast: second year results from the NESCAUM monitoring network.” In
the A&WMA conference, Vancouver, Canada, 1991; 91-49.1.
38. Husar R.B.; Elkins J.B.; Wilson W.E. “US visibility trends, 1960-1992, regional and national.” In the 87th
Annual Air & Waste Management Meeting, Cincinnati, OH, 1994.
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Resource Ecology Laboratory, Colorado State University, Fort Collins, CO, 1993.
41. Husar, R.B.; Husar, J.D. Fine particle maps derived from regional PM2.5 and visibility data. Final Report to
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42. Lamb, R.G.; Seinfeld, J.H. Environmental Science & Technology, 1973, 7, 253-261.
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1983; 83p4.
25
FIGURE CAPTIONS
Figure 1. A depiction of the Monte Carlo approach simulating the physical and chemical processes applied to
a quantum.
Figure 2. The Monte Carlo Model data flow chart.
Figure 3. The dynamics of the planetary boundary layer and of pollutants being emitting into this layer as
simulated by the CAPITA Monte Carlo Model. The mixing heights were taken from the NGM Eulerian
database (21, 22), averaged over the Southwest, during the summer of 1992.
Figure 4. Illustration of transport in the Monte Carlo simulation. The left figure displays the dispersion of a
puff over three days of travel without horizontal eddy diffusion and the height history of each particle in the
puff. The right figure is a similar puff, but an eddy diffusion coefficient of 10,000 m2/sec was used.
Figure 5. A snap shot of the simulation of the atmospheric flow over the western US, during January 16 at
noon GMT. The Lagrangian data were created from RAMS Meteorological data.
Figure 6. The variation of six airmass history variables for a quantum that was released from St. Louis on
July 15, 1992 at 10:00 GMT.
Figure 7. The variation of the kinetic rate coefficients along a quantum’s trajectory and the corresponding
quantum’s sulfur budget. The quantum was released from St. Louis on July 15, 1992 at 10:00 GMT.
2
Figure 8. The simulated SO4 concentration fields during quarters 1 and 3 1992, and the corresponding
2
“observed” SO4 isopleth maps generated from the fusion of IMPROVE and NESCAUM fine sulfur
measurements and airport visibility data.
2
Figure 9. The spatial domains used to average the simulated and observed SO4 concentrations and wet
deposition rates. The symbol  represents the IMPROVE and NESCAUM aerosol monitoring sites,  the
NADP wet deposition sites, and the center of receptor grid cells.

2
Figure 10. Comparison of the daily averaged simulated SO4 concentrations, during 1992, to the
NESCAUM/IMPROVE measurements over a New England and East Central domain, as defined in Figure 9.
2
Figure 11. The simulated total SO4 wet deposition rates during quarters 1 and 3 1992, and the
2
corresponding observed total SO4 wet deposition rates generated from the NADP observations.
2
Figure 12. Comparison of the simulated weekly total SO4 wet deposition rates, during 1992, to NADP
observations over a New England and East Central domain, as defined in Figure 9.
2
Figure 13. The source attribution of the SO2 and SO4 column concentrations at a receptor located in
Massachusetts. a) 1985 NAPAP Emission rates. b) Transit probabilities, Pt. c) SO2 kinetic probabilities, Pk.
2
2
d) SO2 source attribution map. e) SO4 kinetic probabilities, Pk. f) SO4 source attribution map. The X on
each map identifies the location of the Massachusetts receptor.
1
Figure 5. A snap shot of the simulation of the atmospheric flow over the western US, during January 16 at
noon GMT. The Lagrangian data were created from RAMS Meteorological data.
2
Figure 8. The simulated SO4 concentration fields during quarters 1 and 3 1992, and the corresponding
2
“observed” SO4 isopleth maps generated from the fusion of IMPROVE and NESCAUM fine sulfur
measurements and airport visibility data.
2
Figure 11. The simulated total SO4 wet deposition rates during quarters 1 and 3 1992, and the
2
corresponding observed total SO4 wet deposition rates generated from the NADP observations.
2
Figure 13. The source attribution of the SO2 and SO4 column concentrations at a receptor located in
Massachusetts. a) 1985 NAPAP Emission rates. b) Transit probabilities, Pt. c) SO2 kinetic probabilities, Pk.
2
2
d) SO2 source attribution map. e) SO4 kinetic probabilities, Pk. f) SO4 source attribution map. The X on
each map identifies the location of the Massachusetts receptor.
Figure 13. Continued
Figure 11. Continued
Figure 8. Continued
2
The Monte Carlo Approach
Quantum
Secondary Pollutant
Primary Pollutant
Deposited Primary
Deposited Secondary
Figure 1. A depiction of the Monte Carlo approach simulating the physical and chemical processes applied to
a quantum.
3
M e t e o r o lo g ic a l M o d u le
K in etic M o d u le
Emissions
Chemical
Surface Met.
Gridder
Gridder
Gridder
Raw 3-D
Meteorological Data
NGM
RAMS
Model
Gridded
Meteorological Data
Eulerian Lagrangian
Transformer
Transport and Kinetics
Kinetic
History
Airmass History
Data
Filter
Filter
Filter
Trajectory
Plume
Met. Transfer
Matrix
Gridder
Filter
Concentration
Grid
Tranfer Matrix
Figure 2. The CAPITA Monte Carlo Model data flow chart.
4
Figure 3. The dynamics of the planetary boundary layer and of pollutants being emitting into this layer as
simulated by the CAPITA Monte Carlo Model. The mixing heights were taken from the NGM Eulerian
database (21, 22), averaged over the Southwest, during the summer of 1992.
5
Figure 4. Illustration of transport in the Monte Carlo simulation. The left figure displays the dispersion of a
puff over three days of travel without horizontal eddy diffusion and the height history of each particle in the
puff. The right figure is a similar puff, but an eddy diffusion coefficient of 10,000 m2/sec was used.
6
Height (m)
Mixing Hgt
Quantum Hgt
1000
0
1
0.5
0
0
1.
With Clouds
No Clouds
1
2
3
Quantum Age (Days)
1
2
3
Quantum Age (Days)
0.2
Precipitation Rate
(cm/hr)
Scaled Specific Humidity
0
Ground Level
Solar Radiation (KW/m2)
2000
0.5
0.1
0.
0.
0
1
2
3
Quantum Age (Days)
0
1
2
3
Quantum Age (Days)
Figure 6. The variation of six airmass history variables for a quantum that was released from St. Louis on
July 15, 1992 at 10:00 GMT.
7
Rate Coefficients (% / hr)
40
30
SO4 Wet Deposition
SO2 Wet Deposition
20
SO2 Dry Deposition
10
SO2 Transformation
0
0
1
2
3
Quantum Age (days)
Sulfur Budget
Fractional Sulfur Mass
1
SO42-
Deposited SO42-
0.5
Deposited SO2
SO2
0
0
1
2
3
Quantum Age, Days
Figure 7. The variation of the kinetic rate coefficients along a quantum’s trajectory and the corresponding
quantum’s sulfur budget. The quantum was released from St. Louis on July 15, 1992 at 10:00 GMT.
8
2
Figure 9. The spatial domains used to average the simulated and observed SO4 concentrations and wet
deposition rates. The symbol  represents the IMPROVE and NESCAUM aerosol monitoring sites,  the
NADP wet deposition sites, and the center of receptor grid cells.

9
Q1
15
y = 1.61x - 1.69
2
R = 0.80
15
12
9
18
15
6
12
9
6
3
3
6
9 12
Observed
15
18
12
9
6
6
9 12
Observed
15
18
0
3
6
9 12
Observed
15
18
y = 1.18x - 0.48
2
R = 0.72
15
Simulation
15
3
Q4
18
y = 0.93x + 0.63
2
R = 0.56
6
0
0
Q3
18
9
3
0
0
YEAR
y = 1.03x - 0.18
R2 = 0.64
12
3
0
Simulation
Q2
y = 0.88x - 0.13
2
R = 0.83
18
Simulation
18
Simulation
Simulation
New England
Daily SO42- Concentrations, g/m3
12
9
6
3
3
0
0
0
3
6
9 12
Observed
15
18
0
3
6
9 12
Observed
15 18
Central East
Daily SO42- Concentrations, g/m3
Q1
9
6
0
6
3
6
9 12 15 18
Observed
12
9
6
3
3
6
9 12
Observed
15
18
0
3
6
9 12 15 18
Observed
y = 0.76x + 1.02
R2 = 0.40
15
Simulation
15
6
Q4
18
y = 0.84x - 0.36
R2 = 0.61
9
0
0
Q3
18
12
3
0
0
Simulation
9
3
3
y = 0.73x + 0.54
R2 = 0.59
15
12
12
YEAR
18
y = 0.80x - 0.17
R2 = 0.56
15
Simulation
Simulation
15
Q2
18
y = 0.69x + 0.51
R2 = 0.35
Simulation
18
12
9
6
3
0
0
0
3
6
9 12
Observed
15
18
0
3
6 9 12 15 18
Observed
2
Figure 10. Comparison of the daily averaged simulated SO4 concentrations, during 1992, to the
NESCAUM/IMPROVE measurements over a New England and East Central domain, as defined in Figure 9.
10
New England
Weekly Total SO42- Wet Deposition Rates, g/m2/yr
Q1
Q2
7
6
5
4
3
2
1
0
Simulation
0
1
2 3 4 5
Observation
6
7
Q3
7
6
5
4
3
2
1
0
0
y = 0.72x + 0.16
R2 = 0.79
1
2 3 4 5
Observation
6
7
6
7
0
1
2 3 4 5
Observation
6
7
6
7
Q4
7
6
5
4
3
2
1
0
y = 0.82x + 0.17
R2 = 0.82
Simulation
Simulation
y = 0.68x + 0.28
R2 = 0.68
YEAR
7
6
5
4
3
2
1
0
y = 0.80x - 0.07
R2 = 0.94
Simulation
y = 0.61x + 0.21
R2 = 0.50
Simulation
7
6
5
4
3
2
1
0
0
1
2 3 4 5
Observation
6
7
0
1
2 3 4 5
Observation
Central East
Weekly Total SO42- Wet Deposition Rates, g/m2/yr
Q1
7
6
5
4
3
2
1
0
Q2
7
6
5
4
3
2
1
0
0
1
2 3 4 5
Observation
6
7
Q3
7
6
5
4
3
2
1
0
1
2 3 4 5
Observation
6
7
6
7
0
1
2 3 4 5
Observation
Q4
y = 0.88x + 0.10
R2 = 0.89
Simulation
Simulation
y = 0.81x + 0.20
R2 = 0.83
Simulation
0
7
6
5
4
3
2
1
0
y = 0.67x + 0.65
R2 = 0.71
YEAR
7
6
5
4
3
2
1
0
y = 0.92x - 0.17
R2 = 0.84
Simulation
Simulation
y = 0.93x + 0.01
R2 = 0.86
0
1
2 3 4 5
Observation
6
7
0
1
2 3 4 5
Observation
2
Figure 12. Comparison of the simulated weekly total SO4 wet deposition rates, during 1992, to NADP
observations over a New England and East Central domain, as defined in Figure 9.
11