AirWare User Manual
AERMOD: A Dispersion Model
for Industrial Source Applications
This documentation is extracted from Perry et al. (1998).
Algorithms for the Stable Boundary Layer
The form of the AERMOD concentration
expression (C(x,y,z) in eq. 1) that is appropriate for stable conditions
(L > 0) in flat terrain (and is similar to that of ISC2) is
the Gaussian expression:
where
and
In equations 1517, plume dilution and plume spread are
calculated using effective boundary layer variables (see section on
inhomogeneous boundary layer), h_{p} is the plume height,
s _{v} and
s _{w} are discussed below,
and h_{a} is the level where vertical mixing is
limited (= MAX(h_{p},h)) where h is the stable (mechanical)
mixed layer height. h_{p} is equal to the stack height plus
plume rise (D h), where plume rise
is given by Weil^{0} as
where x is downwind distance, N is the BruntVaisala frequency,
given by
and q is potential temperature.
Wind speed, u, and N are evaluated at stack height (subject to change after
development evaluation). The plume buoyancy flux, F_{b}, and
momentum flux, F_{m}, (given by Weil^{0})
are functions of stack parameters and ambient temperature.
Equation (18) applies while the plume is rising.
Weil^{0} defines the distance,
x_{max}, to final rise.
The plume dispersion parameters,
s _{y} and s
_{z}, are given by the familiar formulas:
and
where t is plume travel time (x/U) and T_{Lz}
is the Lagrangian integral time scale given by
Venkatram^{0}.
Note that the values of
s _{v}, s
_{w},
U, and T_{Lz} used in equations (20) and (21) are effective values
representative of the layer over which the plume is diffusing (see section on
inhomogeneity).
Inhomogeneity in the Boundary Layer
The algorithms in AERMOD function under the assumption that the
atmospheric boundary layer is vertically homogeneous (single values of
meteorological variables or parameters represent the layer).
Therefore, we designed a method to "convert" the inhomogeneous
values (as measured or estimated) into equivalent (representative) homogeneous
values. The approach basically interpolates (with downwind distance) between
two observations of plume behavior: 1) near the source, plume dispersion is
dominated by meteorological variables near the release point;
2) when the plume later disperses through the depth of the mixed layer,
it is reasonable to assume that plume behavior is governed by meteorological
variables averaged through the layer.
We will denote these two states for a generic meteorological
variable, a (z),
as a (h_{p}) for the value of the
variable at release height (near the source) and
for the value of the variable averaged through the layer from
the surface to h_{a}. h_{a},
the averaging height, is the maximum of the plume height,
h_{p}, and the mixed layer height, z_{i}
or h. To interpolate between a
(h_{p})
and , AERMOD uses the following expression to find the "effective" value:
where x is downwind distance, is the arithematic average
between u(h_{p}) and , and _{Lz} is the
arithematic average of T_{Lz}(h_{p}) and _{Lz}.
The appropriate formulations for T_{Lz} in
stable^{0} and
convective^{0} conditions are used for this
averaging. Equation (23) approaches the required limits of
a (h_{p}) and as x approaches
zero and a large value, respectively.
When h_{p} is less than the mixing height,
the relevant plume mixing is through that layer so the variables are averaged
through the layer. When the plume is above the mixed layer, the variables are
averaged through the mixed layer and into the layer above
(up to h_{p}) where there is relatively little turbulence.
In AERMOD, plumes that are in the elevated stable layer are allowed to disperse
downwards and become entrained into the mixed layer.
In these cases, near the source, the rate of spread is controlled by the small
value of turbulence at the source height.
AERMOD uses equation (23) to calculate the appropriate effective values of
wind speed, s _{v},
and s _{w} as needed throughout the
computations.
Meteorological Interface
Within AERMOD are routines that are designed to interface
between the information provided by the meteorological preprocessor (see
following section on AERMET) and the meteorological data needed by the model.
Specifically, the interface routines take the computed (by AERMET) boundary
layer parameters, the measured meteorological data, and other sitespecific
information to compute vertical profiles of:
 wind direction,
 wind speed,
 temperature,
 vertical potential temperature gradient,
 vertical turbulence, s _{w}, and
 6) horizontal turbulence, s _{v}.
For any one of these six variables (or parameters),
the interface (in constructing the profile) takes each height above ground
and if it is below the lowest measurement or above the highest measurement
(or in some cases there is no data at all), the interface computes an
appropriate value from selected profile relationships based on boundary
layer parameterizations that are adjusted to the nearest data point, if any.
If data are available both above and below a given height, an interpolation
(based on both the measured data and the shape of the computed profile) is
performed.
This overall profiling approach simultaneously takes advantage of the
information contained in both the measurements and parameterizations.
As will be discussed, at least one level of measured wind speed, wind
direction, and temperature is needed for the model to function.
Turbulence can be parameterized without any direct turbulence
measurements.
Wind Direction
At least one wind direction measurement is required for each simulation
(hour) with AERMOD. Three methods are currently being considered for
computing the wind direction change with height.
The first is given by van Ulden and Holtslag^{0}
as an exponential turning with height:
where WD(z) is the angle change from the
surface wind direction, WD(h) is the angle change at h,
and d_{1} and d_{2} are empirical constants
equal to 1.58 and 1.0, respectively
(NOTE: in convective conditions, z_{i} is substituted for h
in equation 24). Van Ulden and Holtslag
tabulated WD(h) as a function of MoninObukhov length, L.
AERMOD interpolates between these values.
A second wind direction profiling method under consideration
is that of Tennekes^{0} (currently implemented in
CTDMPLUS) where the turning of the wind within the mixed layer is computed as
a function of friction velocity (u_{*}), h, L,
roughness length (z_{o}), and the Coriolis parameter.
In either of methods one and two, the wind direction above the mixed layer
is set equal to that at the top of the layer.
The third option being considered for AERMOD is to have no wind direction
oturning with height.
Wind Speed.
At least one wind speed measurement is required for each simulation with
AERMOD.
As suggested by van Ulden and Holtslag^{0},
the AERMOD profile equation for wind speed is:
where k is the von Karman constant, d is
the displacement height, z_{o} is the roughness length,
and y _{m} is a correction to the
wind profile for stability other than neutral.
Temperature Gradient
.
This section deals with the determination of vertical profiles of
potential temperature gradient (dq /dz)
from which AERMOD can also construct ambient temperature profiles.
At least one air temperature measurement is required for each
simulation with AERMOD.
In unstable conditions (L < 0),
dq /dz is assumed to be zero from near
the surface up to the top of the mixed layer,
at z_{i}.
Above z_{i}, dq /dz
is assumed constant at 0.005 ° K/m.
In stable conditions (L > 0), AERMOD uses two
profiling equations, one very near the surface and another above.
Near the surface (below the lowest measurement of
dq /dz or below 10 meters if no
measurements) AERMOD uses an expression of
Businger^{0} et al.
where q _{*},
the temperature scale, is a simple function of cloud
cover^{0} (and is computed by AERMET).
If one or more observations of dq /dz exist,
then the value at the lowest level is used with eq. (26) to determine
a value for q _{*}.
Above the highest measurement level (or 10 meters with no measurements),
AERMOD scales dq /dz with an expression
by Stull^{0}
where a is constant of 0.44. AERMOD uses the
higher of eq. (27) and 0.002 ° K/m,
wherever eq. (27) applies.
Turbulence in Convective Conditions.
For L < 0, the profile of s _{v}
is assumed constant from the surface to z_{i}.
In the absence of measurements, s _{v}
is calculated from^{0}
where w_{*} is the convective
scaling velocity. If observations of s
_{v}
are available, then AERMOD persists the value at the lowest level down
to the surface and persists the value at the highest level in the mixed
layer up to z_{i}. Between z_{i} and
1.2z_{i}, s _{v} is
linearly decreased to 0.5 of its value at z_{i}.
In the absence of measurements, the profile
of s _{w} is given
by^{0}
These formulations are complimented by any observations
of s _{w} and the profile is adjusted
as discussed earlier. As with s _{v},
s _{w} is linearly interpolated
between z_{i} and 1.2z_{i} except that
s _{w} reduces to 0.1 of its value
at z_{i}.
Turbulence in Stable Conditions
.
For L > 0, the vertical profile of s
_{v} is given by^{0
}
where
The vertical profile of
s _{w} in stable conditions has the same
form as equations (31) and (32) with the substitution of
s _{wo} for
s _{vo} and with
If observations of
s _{v} or
s _{w} are available,
they are used to adjust the profiles as discussed above.
AERMOD PREPROCESSORS
AERMOD has two data preprocessors that prepare
meteorological data (onsite and offsite), terrain information,
and receptor information for input to AERMOD.
The meteorological preprocessor is named AERMET; the
terrain/receptor preprocessor is yet unnamed.
AERMOD's Meteorological Preprocessor (AERMET)
As is the case with AERMOD, its meteorological preprocessor,
AERMET, is based upon an existing regulatory model structure, that of
the Meteorological Processor for Regulatory
Models^{0}(MPRM).
AERMET is discussed by Weil^{0}.
Its overall treatment of the processing of meteorological data is similar
to that done for the CTDMPLUS^{0}
and HPDM^{0} models.
The important surface parameters provided by AERMET are the MoninObukhov
Length, L, surface friction velocity, u_{*},
surface roughness length, z_{o}, surface heat flux,
H, and the convective scaling velocity, w_{*}.
AERMET also provides estimates of the convective and mechanical mixed
layer heights, z_{i} and h.
In addition, AERMET passes through any measurements of wind, temperature,
and turbulence (provided to it) in a form AERMOD expects.
The growth and structure of the atmospheric boundary layer is
driven by the fluxes of heat and momentum which in turn depend upon surface
effects.
The depth of this layer and the dispersion of pollutants within it are
influenced on a local scale by surface characteristics, such as the roughness
of the underlying surface, the reflectivity (albedo), and the availability
of surface moisture.
For ISC2, default assumptions for these characteristics are built into
the RAMMET/MPRM preprocessors, reflecting "open country" vegetation
cover (a mixture of grassland with occasional forest).
For AERMET, the user can specify monthly variations of
three surface characteristics for up to 12 upwind direction sectors.
These include:

the albedo, which is the fraction of radiation reflected by the surface;

the Bowen ratio (B_{o}), which is the ratio of the sensible
heat flux to the evaporation heat flux; and
 the surface roughness length, z_{o}, which is the
height above the ground at which the mean horizontal wind velocity
is theoretically zero (z_{o} is also thought of as the average
height of the surface roughness elements).
The user will be guided by lookup tables (in the AERMET user's guide)
of typical values for these three variables for a variety of
seasons and land use types.
Besides the specification of surface characteristics, AERMOD
accepts meteorological data from the following sources:
 standard hourly National Weather Service (NWS) surface data
(winds, temperature, cloud cover, etc.) from the most representative site;
 2) twicedaily soundings of winds, temperature, and dew point from
the most representative NWS upper air station; and
 3) onsite wind, temperature, turbulence, pressure, and
radiation measurements.
Determination of the representativeness of data will vary with modeling
situation (e.g. complex terrain applications may require onsite measurements).
Unstable Conditions
.
When the net radiation is positive for a given hour (net radiation is
either measured or estimated as a function of cloud cover, solar angle,
albedo, and surface temperature), an energy balance technique is used to
determine the sensible heat flux, H, as
where R_{n} is the net radiation,
and B_{o} is the Bowen ratio. Eq. (35) assumes that the
soil heat flux is 10% of the net radiation.
With this estimate of H, AERMET computes the surface
friction velocity, u_{*}, and MoninObukhov length with an
iterative approach (since each are functions of each other) similar to
that of CTDMPLUS^{0}.
Friction velocity is found from eq. (25) and MoninObukhov length from eq. (6),
described in previous sections.
AERMOD initializes u_{*} assuming neutral conditions,
calculates L, then proceeds with subsequent estimates
of u_{*} and L until convergence (less than 1% change).
The boundary layer height (z_{i}) for the
CBL is calculated with a simple onedimensional energy balance
model^{0,0} using the early morning potential
temperature sounding (prior to radiation sunrise) and the surface heat flux
as a function of time.
This model applies to an arbitrary temperature distribution which is
obtained with early morning radiosonde soundings.
Good agreement between predictions and observations of z_{i}
have been found^{0}.
Stable Conditions
.
During stable conditions (negative net radiation) AERMET calculates the
friction velocity with a method of Venkatram^{0}
that is a counterpart to eq. (25) except that the stability corrections to
the wind profile are not specifically functions of L. The
energy balance approach is not used at night since the uncertainty in the
ground heating term can be as large as the sensible and latent heat fluxes.
Instead, the temperature scale^{0},
q _{*}, is used by Venkatram in
estimating u_{*}.
The temperature scale is given by
where N_{c} is the opaque cloud cover.
Once u_{*} and q _{*}
are computed, the surface heat flux is given by
where r is air density.
Finally, the MoninObukhov length is calculated from eq. (6) using
u_{*} and H.
The boundary layer height (h) is
calculated by AERMET in stable conditions with the diagnostic
expression^{0}
where f_{c} is the Coriolis
parameter.
The Terrain Preprocessor
The terrain preprocessor for AERMOD is designed to provide
the terrain information necessary to calculate the dividing streamline height,
H_{c}, appropriate for each receptor location. The processor
uses an objective method to estimate a "height scale", h_{c},
that is related to the terrain height in the vicinity of the receptor but
does not correspond to the height of a particular hill.
Instead, h_{c} can be thought of as the terrain height of the
surrounding terrain that will influence the flow in stable conditions.
Use of the height scale (instead of actual terrain feature height as in
CTDMPLUS) to calculate H_{c}, provides a reasonable and
objective method to calculate the weighting factor, f, in eq. (1).
In defining h_{c} for a given receptor,
all terrain elevations within the user defined modeling domain and the
distances of those elevations from the receptor are considered.
Therefore each receptor may have a unique height scale.
Consider a domain of interest, and a receptor at (x,y,z)
for which we need an associated terrain height scale.
The inherent assumption in this objective scheme is that 1)
the effect of surrounding terrain on the flow near the receptor
decreases with increasing distance and 2) the effect increases
with increasing elevation of that terrain.
In other words, the "effective elevation", h_{eff},
of surrounding terrain is a function of its actual elevation and
its distance from the receptor.
This is expressed quantitatively as:
where z_{t} is the terrain elevation
at (x_{t},y_{t}), r is the horizontal distance
from the receptor to the terrain such that:
f_{t}(r/r_{o}) is the functional
form of the distance weighting, and r_{o} represents the
radius of influence and is taken to be:
where h_{max} is the elevation of the highest
terrain in the modeling domain, and a is a constant set to 10.
The distance weighting function is currently specified as:
After evaluation (and with further experience)
we may find it appropriate to refine either r_{o}
or the distance weighting function.
For a given receptor, h_{eff} is calculated
for all terrain points within the modeling domain.
This is why it is imperative to have the terrain information already
digitized.
The height scale for receptor is then related to the maximum effective value.
Specifically, h_{c} is the actual terrain elevation at the
location with the maximum h_{eff}.
Quantitatively, the height scale is given as:
This calculation is repeated for each receptor location
requested by the user. The terrain preprocessor is designed to include a
receptor generator in which the user can specify receptor grids (polar,
rectangular, discrete), as is currently done in ISC2, and the
preprocessor will assign the appropriate terrain elevation to each receptor
and the calculate the height scale for each receptor.
This objective approach to terrain preprocessing is
designed for use with digitized terrain data such as the Digital Elevation
Model (DEM) data available from the U. S. Geological Survey.
As digitized data becomes more and more readily available, the AERMOD objective
approach will eliminate the subjectivity and inconsistency in terrain
specification.
In addition, it is very user friendly in that receptor and terrain
information can be provided to the dispersion model without extracting
detailed information from terrain maps.
AERMOD MODEL EVALUATION
A critical element of any model development effort is
the evaluation of the model algorithms with data from highgrade
measurement studies.
AERMIC is approaching model evaluation in two distinct phases:
1) model development evaluation where we are interested primarily in whether
the model is based on sound physical principles and yields good results for
the "right" reasons, and 2) an operational performance evaluation where the
focus is on how well the model predicts concentrations on the high end of the
distribution (which is important to regulatory decision making).
As the model coding is nearing completion (as of this writing),
AERMIC is beginning to undertake the model development evaluation (phase 1).
The are several reasons to perform a thorough developmental
evaluation rather than skipping directly to "how well does the model perform?"
Establishing that the model is based on good model physics greatly increases
a user's confidence in applying the model in situations (sources, terrain,
climatology) for which there is no existing evaluation data.
In addition, the developmental evaluation will also aid in flushing
out pathologies in the model algorithms.
AERMIC has gathered field (meteorological and
concentration) data from eight separate studies for the
phase 1 (developmental) evaluation of AERMOD and AERMET.
These include tracer studies of rural, flatterrain, surface releases,
rural, flatterrain, elevatedbuoyant releases, and urban, flatterrain,
elevated releases; and sulfur dioxide studies of rural, flatterrain,
elevated releases, and rural, complexterrain, elevated releases.
With this variety of data, we intend to challenge the AERMOD algorithms in as
many situations as our time will allow.
Following the lead of Weil
et al.^{0} and Hanna^{0}
,
the phase 1 analyses will focus on model residuals (predicted/observed)
as functions of key model parameters.
This will help to identify both systematic problems in model formulations
(signified by trends in the residuals with parameter variation) and
sensitivity to a particular parameter (signified by large variations in
residuals). Residual plots are done with a time and downwinddistance
(modified space) pairing of the data (using maximum predicted and
observed on a sampling arc for each time period).
Particularly for the fullyear sulfurdioxide data bases,
phase 1 will also include some statistical summaries of performance
measures (e.g. fractional bias, mean square error) as suggested by
Cox and Tikvart^{0} and also by
Hanna^{0}.
Correlation plots of predictions to observations of concentration
will also be helpful in comparing AERMOD to other models such as
ISC2 and CTDMPLUS. Finally, it is AERMIC's intention to share the
results of the phase one evaluation (as they exist at that time)
at both the conference this summer and in future publications about this
model.
Model Sensitivity
We can gain additional understanding of model
behavior by performing sensitivity analyses on AERMOD.
Two types of sensitivity analyses will be performed:
1) to determine the effects (on calculated concentrations) of incremental
changes in various input variables, and 2) to determine the effects of
extreme values of various input variables on concentrations.
The first type will be helpful both in defining the needed
accuracy for various input values and in identifying spurious
behavior of the model (determining model robustness).
The second type of analysis will be helpful in defining the
limits of applicability of the model.
FUTURE PLANS FOR AERMOD
The initial impetus for the development of AERMOD did
not come from a desire to develop a new stateofart model.
AERMOD was conceived from a growing sense that EPA's basic regulatory
modeling approach could be improved scientifically, without compromising the
important need for consistency.
As such, the success of AERMOD will be based as much on its regulatory
status as on its ability to successfully predict design concentrations.
If AERMOD is found to accurately estimate concentrations but does
not become a significant part of EPA's regulatory program, we would not
have accomplished our primary goal.
Consequently, AERMIC's plans for AERMOD go beyond model development and
testing.
We have planned activities that consider what is needed for both
regulatory promulgation and technology transfer.
Promulgation of a regulatory model, i.e.
achieving "Appendix A" guideline status^{0}, is a
long and arduous task.
In preparation for the rulemaking process, information will need to be
developed that identifies the proposed model and how it will affect existing
emission limits.
Also, the guidance needed for consistent implementation of the model,
must be available for public review. In support of these needs, AERMIC
has planned for the development of both meteorological guidance and the
comparisons of AERMOD with any existing regulatory model appropriate
for the same applications.
By using concepts such as similarity scaling and
nonGaussian pdf's, AERMOD represents a significant change in the
underlying science of regulatory models.
For those environmental engineers and scientists whose modeling experiences
have included only regulatory type analyses, the shift from ISC to AERMOD may
be substantial.
In anticipation of the need for training, we are developing a document, the
AERMOD Model Formulation Document(MFD) with this transition in mind.
The MFD will include not only a complete description of AERMOD, but also
a primer on boundary layer meteorology as it relates to this new model.
The MFD will also include explainations designed to make the link
between PG dispersion and the approach taken by AERMOD.
Also, we will be evaluating the need for other mechanisms (e.g. workshops)
of transferring this technology.
Finally, AERMIC anticipates that AERMOD will be presented to the
public as a regulatory proposal upon completion of model development, testing,
and evaluation.
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