&EPA
United a*ts
Environmental Protection
Agency
AERMOD: DESCRIPTION OF
MODEL FORMULATION
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EPA-454/R-03-004
September 2004
AERMOD:
DESCRIPTION OF
MODEL FORMULATION
By:
Alan J. Cimorelli, U. S. Environmental Protection Agency, Region 3
Steven G. Perry1, Atmospheric Sciences Modeling Division/Air Resources
Laboratory/NOAA, MD-80, USEPA
Akula Venkatram, College of Engineering, University of California at Riverside
Jeffrey C. Weil, Cooperative Institute for Research in Environmental Sciences,
University of Colorado
Robert J. Paine, ENSR Corporation
Robert B. Wilson, U. S. Environmental Protection Agency, Region 10
Russell F. Lee, Charlotte, NC 28269
Warren D. Peters, U.S. Environmental Protection Agency, OAQPS
Roger W. Erode, MACTEC Federal Programs, Inc. Durham, NC, 27709
James O. Paumier MACTEC Federal Programs, Inc. Durham, NC, 27709
U.S. Environmental Protection Agency
Office of Air Quality Planning and Standards
Emissions Monitoring and Analysis Division
Research Triangle Park, North Carolina
lOn assignment to the Atmospheric Research and Exposure Assessment Laboratory, U.
S. Environmental Protection Agency.
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Disclaimer
This report has been reviewed by the Office of Air Qualtiy Planning and Standards, U.S.
Environmental Protection Agency, and has been approved for publication. Mention of trade
names or commercial products does not constitute endorsement or recommendation for use.
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Acknowledgments
This project was made possible through the continued support of Mr. Joe Tikvart, of EPA's
Office of Air Quality Planning and Standards (OAQPS), and Mr. Frank Schiermeier, of NOAA's
Atmospheric Sciences Modeling Division. The authors are particularly grateful to Dr. Gary
Briggs, and Mr. John Irwin, of NOAA's Atmospheric Sciences Modeling Division, for their
thorough and constructive review of an earlier version of this document. Finally, we would like
to thank the many scientists who participated in peer reviews and beta testing.
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Table of Contents
1 Introduction 8
1.1 Background 8
1.2 The AERMIC Focus: A Replacement for the ISC 3 Model 9
1.3 Model Development Process 10
1.4 Purpose of Document 11
2 Model Overview 12
3 Meteorological Preprocessor (AERMET) 15
3.1 Energy Balance in the PBL 15
3.1.1 NET RADIATION 16
3.1.2 TRANSITION BETWEEN THE CBL AND SBL 16
3.2 Derived Parameters in the CBL 17
3.2.1 FRICTION VELOCITY (w.) & MONIN OBUKHOV LENGTH (Z) IN THE CBL
17
3.2.2 CONVECTIVE VELOCITY SCALE (w.) 18
3.3 Derived Parameters in the SBL 19
3.3.1 FRICTION VELOCITY (w.) IN THE SBL 19
3.3.2 SENSIBLE HEAT FLUX (H) IN THE SBL 21
3.3.3 MONIN OBUKHOV LENGTH (Z) IN THE SBL 21
3.4 MixingHeight 21
3.4.1 CONVECTIVE MIXING HEIGHT (zw) 22
3.4.2 MECHANICAL MIXING HEIGHT (zj 22
4 Vertical Structure of the PBL - AERMOD's Meteorological Interface 24
4.1 General Profiling Equations 24
4.1.1 WIND SPEED PROFILING 24
4.1.2 WIND DIRECTION PROFILES 27
4.1.3 PROFILES OF THE POTENTIAL TEMPERATURE GRADIENT 27
4.1.4 POTENTIAL TEMPERATURE PROFILING 29
4.1.5 VERTICAL TURBULENCE CALCULATED 30
4.1.6 LATERAL TURBULENCE CALCULATED BY THE INTERFACE 33
4.2 Vertical Inhomogeneity in the Boundary Layer as Treated by the INTERFACE ... 36
5 The AMS/EPA Regulatory Model AERMOD 40
5.1 General Structure of AERMOD Including Terrain 41
5.2 Concentration Predictions in the CBL 45
5.2.1 DIRECT SOURCE CONTRIBUTION TO CONCENTRATION
CALCULATIONS IN THE CBL 52
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5.2.2 INDIRECT SOURCE CONTRIBUTION TO CONCENTRATION
CALCULATIONS IN THE CBL 53
5.2.3 PENETRATED SOURCE CONTRIBUTION TO CONCENTRATION
CALCULATIONS IN THE CBL 54
5.3 Concentrations in the SBL 54
5.4 Treatment of Lateral Plume Meander 55
5.5 Estimation of Dispersion Coefficients 57
5.5.1 DISPERSION FROM AMBIENT TURBULENCE 58
5.5.2 BUOYANCY INDUCED DISPERSION (BID) COMPONENT OF oy AND oz
62
5.5.3 TREATMENT OF BUILDING DOWNWASH 62
5.6 Plume Rise Calculations in AERMOD 63
5.6.1 PLUME RISE IN THE CBL 63
5.6.2 PLUME RISE IN THE SBL 64
5.7 Source Characterization 66
5.8 Adjustments for the Urban Boundary Layer 66
6 List of Symbols 70
7 APPENDIX: Input / Output Needs and Data Usage 75
7.1 AERMETInput Data Needs 75
7.1.1 METEOROLOGY 75
7.1.2 DIRECTIONALLY AND/OR MONTHLY VARYING SURFACE
CHARACTERISTICS 75
7.1.3 OTHER 75
7.1.4 OPTIONAL 76
7.2 Selection and Use of Measured Winds, Temperature and Turbulence in AERMET
76
7.2.1 THRESHOLD WIND SPEED 76
7.2.2 REFERENCE TEMPERATURE AND HEIGHT 76
7.2.3 REFERENCE WIND SPEED AND HEIGHT 76
7.2.4 CALCULATING THE POTENTIAL TEMPERATURE GRADIENT ABOVE
THE MIXING HEIGHT FROM SOUNDING DATA 76
7.2.5 MEASURED TURBULENCE 77
7.2.6 DATA SUBSTITUTION FOR MISSING ON-SITE DATA 77
7.3 Information Passed by AERMET to AERMOD 77
7.4 Restrictions on the Growth of PEL Height 77
7.5 Initializing the Mechanical Mixing Height Smoothing Procedure 77
7.6 Determining The Mixing Height When the Sounding Is Too Shallow 78
7.7 Input Data Needs for AERMAP 78
7.8 Information Passed by AERMAP to AERMOD 78
7.9 Wind Speed & Turbulence Limits Used in Model Calculations 78
7.10 Using Profiles for Interpolating Between Observations 79
7.11 Using Measured Mixing Heights 81
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References 82
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1 Introduction
1.1 Background
In 1991, the American Meteorological Society (AMS) and the U.S. Environmental Protection
Agency (EPA) initiated a formal collaboration with the designed goal of introducing current
planetary boundary layer (PEL) concepts into regulatory dispersion models. A working group
(AMS/EPA Regulatory Model Improvement Committee, AERMIC) comprised of AMS and
EPA scientists was formed for this collaborative effort.
In most air quality applications one is concerned with dispersion in the PEL, the turbulent air
layer next to the earth's surface that is controlled by the surface heating and friction and the
overlying stratification. The PEL typically ranges from a few hundred meters in depth at night to
1-2 km during the day. Major developments in understanding the PEL began in the 1970's
through numerical modeling, field observations, and laboratory simulations; see Wyngaard
(1988) for a summary. For the convective boundary layer (CBL), a milestone was Deardorff s
(1972) numerical simulations which revealed the CBL's vertical structure and important
turbulence scales. Major insights into dispersion followed from laboratory experiments,
numerical simulations, and field observations (e.g., see Briggs (1988), Lamb (1982),and Weil
(1988a) for reviews). For the stable boundary layer (SBL), advancements occurred more slowly.
However, a sound theoretical/experimental framework for surface layer dispersion and
approaches for elevated sources emerged by the mid 1980's (e.g., see Briggs (1988) and
Venkatram (1988)).
During the mid 1980's, researchers began to apply this information to simple dispersion
models for applications. This consisted of eddy-diffusion techniques for surface releases,
statistical theory and PEL scaling for dispersion parameter estimation, a new probability density
function (pdf) approach for the CBL, simple techniques for obtaining meteorological variables
(e.g., surface heat flux) needed for turbulence parameterizations, etc. Much of this work was
reviewed and promoted in workshops (Weil 1985), revised texts (Pasquill and Smith 1983), and
in short courses and monographs (Nieuwstadt and van Dop 1982; Venkatram and Wyngaard
1988). By the mid 1980's, new applied dispersion models based on this technology had been
developed including PPSP (Weil and Brower 1984), OML (Berkowicz et al. 1986), HPDM
(Hanna and Paine 1989), TUPOS (Turner et al. 1986), CTDMPLUS (Perry et al. 1989); later,
ADMS developed in the United Kingdom (see Carruthers et al. (1992)) was added as well as
SCIPUFF (Sykes et al. 1996). AERMIC members were involved in the development of three of
these models - PPSP, CTDMPLUS and HPDM.
By the mid-to-late 1980's, a substantial scientific base on the PEL and new dispersion
approaches existed for revamping regulatory dispersion models, but this did not occur. In a
review of existing or proposed regulatory models developed prior to 1984, Smith (1984) reported
that the techniques were many years behind the state-of-the-art and yielded predictions that did
not agree well with observations. Similar findings were reported by Hayes and Moore (1986),
who summarized 15 model evaluation studies. The need for a comprehensive overhaul of EPA's
basic regulatory models was clearly recognized. This need, including a summary of background
information and recommendations, was the focus of an AMS/EPA Workshop on Updating
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Applied Diffusion Models held 24-27 January 1984 in Clearwater, Florida (see Weil (1985) and
other review papers in the November 1985 issue of the Journal of Climate and Applied
Meteorology.
In February 1991, the U.S. EPA in conjunction with the AMS held a workshop for state and
EPA regional meteorologists on the parameterization of PEL turbulence and state-of-the-art
dispersion modeling. One of the outcomes of the workshop was the formation of AERMIC. As
noted above, the expressed purpose of the AERMIC activity was to build upon the earlier model
developments and to provide a state-of-the-art dispersion model for regulatory applications. The
early efforts of the AERMIC group are described by Weil (1992). In going through the design
process and in considering the nature of present regulatory models, AERMIC's goal expanded
from its early form. In addition to improved parameterization of PEL turbulence, other problems
such as plume interaction with terrain, surface releases, building downwash and urban
dispersion were recognized as needing attention.
The new model developed by AERMIC is aimed at short-range dispersion from stationary
industrial sources, the same scenario handled by the EPA Industrial Source Complex Model,
ISC3 (U.S.Environmental Protection Agency 1995). This work clearly has benefitted from the
model development activities of the!980's especially in the parameterization of mean winds and
PEL turbulence, dispersion in the CBL, and the treatment of plume/terrain interactions.
Techniques used in the new model for PEL parameterizations and CBL dispersion are similar to
those used in earlier models. Turbulence characterization in the CBL adopts "convective
scaling" as suggested by Deardorff (1972) as is included in most of the models mentioned above
(e.g., PPSP, OML, and HPDM). Algorithms used in these earlier models were considered along
with variants and improvements to them. In addition, the developers of OML met with
AERMIC to discuss their experiences. Thus, much credit for the AERMIC model development
is to be given to the pioneering efforts of the 1980s.
1.2 The AERMIC Focus: A Replacement for the ISC3 Model
AERMIC's initial focus has been on the regulatory models that are designed for estimating
near-field impacts from a variety of industrial source types. EPA's regulatory platform for
near-field modeling, during the past 25 years has, with few exceptions, remained fundamentally
unchanged. During this period, ISC3 was the workhorse regulatory model (used in the
construction of most State Implementation Plans, new source permits, risk assessments and
exposure analysis for toxic air pollutants) with code structure that is conducive to change.
Therefore, AERMIC selected the EPA's ISC3 Model for a major overhaul. AERMIC's
objective was to develop a complete replacement for ISC3 by: 1) adopting ISC3's input/output
computer architecture; 2) updating, where practical, antiquated ISC3 model algorithms with
newly developed or current state-of-the-art modeling techniques; and 3) insuring that the source
and atmospheric processes presently modeled by ISC3 will continue to be handled by the
AERMIC Model (AERMOD), albeit in an improved manner.
The AERMOD modeling system consists of two pre-processors and the dispersion model.
The AERMIC meteorological preprocessor (AERMET) provides AERMOD with the
meteorological information it needs to characterize the PEL. The AERMIC terrain
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pre-processor (AERMAP) both characterizes the terrain, and generates receptor grids for the
dispersion model (AERMOD).
AERMET uses meteorological data and surface characteristics to calculate boundary layer
parameters (e.g. mixing height, friction velocity, etc.) needed by AERMOD. This data, whether
measured off-site or on-site, must be representative of the meteorology in the modeling domain.
AERMAP uses gridded terrain data for the modeling area to calculate a representative
terrain-influence height associated with each receptor location. The gridded data is supplied to
AERMAP in the format of the Digital Elevation Model (DEM) data (USGS 1994). The terrain
preprocessor can also be used to compute elevations for both discrete receptors and receptor
grids.
In developing AERMOD, AERMIC adopted design criteria to yield a model with desirable
regulatory attributes. It was felt that the model should: 1) provide reasonable concentration
estimates under a wide variety of conditions with minimal discontinuities; 2) be user friendly and
require reasonable input data and computer resources as is the case with the ISC3 model; 3)
capture the essential physical processes while remaining fundamentally simple; and, 4)
accommodate modifications with ease as the science evolves.
Relative to ISC3, AERMOD currently contains new or improved algorithms for: 1)
dispersion in both the convective and stable boundary layers; 2) plume rise and buoyancy; 3)
plume penetration into elevated inversions; 4) computation of vertical profiles of wind,
turbulence, and temperature; 5) the urban nighttime boundary layer; 6) the treatment of receptors
on all types of terrain from the surface up to and above the plume height; 7) the treatment of
building wake effects; 8) an improved approach for characterizing the fundamental boundary
layer parameters; and 9) the treatment of plume meander.
1.3 Model Development Process
A seven step model development process, followed by AERMIC, resulted in the promulgation
of a regulatory replacement for the ISC3 model, AERMOD. The process followed is as follows:
1) initial model formulation; 2) developmental evaluation; 3) internal peer review and beta
testing; 4) revised model formulation; 5) performance evaluation and sensitivity testing; 6)
external peer review; and 7) submission to EPA's Office of Air Quality Planning and Standards
(OAQPS) for consideration as a regulatory model.
The initial formulations of AERMOD are summarized in Perry et al. (1994) and Cimorelli
et al. (1996). Once formulated, the model was tested (developmental evaluation) against a
variety of field measurements in order to identify areas needing improvement. The
developmental evaluation provided a basis for selecting formulation options.
This developmental evaluation was conducted using five data bases. Three consisted of
event-based tracer releases, while the other two each contain up to a full year of continuous SO2
measurements. These data bases cover elevated and surface releases, complex and simple
terrain, and rural and urban boundary layers. A description of the early developmental
evaluation is presented in Lee et al. (1995) and in a later report by Lee et al. (1998).
Additionally, a comprehensive peer review (U.S. Environmental Protection Agency 2002) was
conducted. Many revisions to the original formulation have resulted from this evaluation and
comments received during the peer review, beta testing, and the public forum at EPA's Sixth
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Conference on Air Quality Modeling (in 1995). Lee et al. (1998) describe the developmental
evaluation repeated with the current model (i.e., revisions based on the developmental evaluation
and peer review).
In addition, AERMOD underwent a comprehensive performance evaluation (Erode 2002)
designed to assess how well AERMOD's concentration estimates compare against a variety of
independent data bases and to assess the adequacy of the model for use in regulatory decision
making. That is, how well does the model predict concentrations at the high end of the
concentration distribution? AERMOD was evaluated against five independent data bases (two in
simple terrain and three in complex terrain), each containing one full year of continuous SO2
measurements. Additionally, AERMOD's performance was compared against the performance
of four other applied, regulatory models: ISC3 (U.S.Environmental Protection Agency 1995),
CTDMPLUS (Perry 1992), RTDM (Paine and Egan 1987) and HPDM (Hanna and Paine 1989;
Hanna and Chang 1993). The performance of these models against AERMOD has been
compared using the procedures in EPA's "Protocol for Determining the Best Performing Model"
(U.S. Environmental Protection Agency 1992).
On 21 April 2000 EPA proposed2 that AERMOD be adopted as a replacement to ISC3 in
appendix A of the Guideline on Air Quality Models (Code of Federal Regulations 1997). As
such, upon final action, AERMOD would become EPA's preferred regulatory model for both
simple and complex terrain. Furthermore, on 19 May 2000 EPA announced3 its intention to hold
the Seventh Conference on Air Quality Modeling on 28-29 June 2000. The purpose of this
conference was to receive comments on the April, 2000 proposal. At the Seventh Conference,
results of the performance evaluation and peer review were presented and public comments were
received. Based on these comments AERMOD was revised to incorporate the PRIME
algorithms for building downwash, to remove the dependency on modeling domain in
AERMOD's complex terrain formulation, and a variety of other less significant issues. A
description of the fully revised model is presented here and in Cimorelli et al. (2004) and Perry
et al. (2003). Performance of the final version of AERMOD is documented in Perry et al. (2003)
and Erode (2002).
1.4 Purpose of Document
The purpose of this document is to provide a comprehensive, detailed description of the
technical formulation of AERMOD and its preprocessors. This document is intended to provide
many of the details that are not included in the published journal articles (Cimorelli et al. 2004;
Perry et al. 2003).
This document does not include information related to model performance. As mentioned
above, a description of the performance of the model that is described in this document can be
found in Perry et al. (2003) and Erode (2002).
240CFRPart51 pages 21506-21546
3Federal Register on May 19, 2000 (Volume 65, Number 98)
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2 Model Overview
This section provides a general overview of the most important features of AERMOD.
With the exception of treating pollutant deposition, AERMOD serves as a complete replacement
for ISC3. However, it is the intention of AERMIC to incorporate both dry and wet particle and
gaseous deposition as well as source or plume depletion. Once this is accomplished this report
will be revised to include a description of the deposition formulation. Thus, the AERMOD
model described here is applicable to rural and urban areas, flat and complex terrain, surface and
elevated releases, and multiple sources (including, point, area and volume sources). Every effort
has been made to avoid model formulation discontinuities wherein large changes in calculated
concentrations result from small changes in input parameters.
AERMOD is a steady-state plume model. In the stable boundary layer (SBL), it assumes
the concentration distribution to be Gaussian in both the vertical and horizontal. In the
convective boundary layer (CBL), the horizontal distribution is also assumed to be Gaussian, but
the vertical distribution is described with a bi-Gaussian probability density function (pdf). This
behavior of the concentration distributions in the CBL was demonstrated by Willis and Deardorff
(1981) and Briggs (1993). Additionally, in the CBL, AERMOD treats "plume lofting," whereby
a portion of plume mass, released from a buoyant source, rises to and remains near the top of the
boundary layer before becoming mixed into the CBL. AERMOD also tracks any plume mass
that penetrates into the elevated stable layer, and then allows it to re-enter the boundary layer
when and if appropriate. For sources in both the CBL and the SBL AERMOD treats the
enhancement of lateral dispersion resulting from plume meander.
Using a relatively simple approach, AERMOD incorporates current concepts about flow
and dispersion in complex terrain. Where appropriate the plume is modeled as either impacting
and/or following the terrain. This approach has been designed to be physically realistic and
simple to implement while avoiding the need to distinguish among simple, intermediate and
complex terrain, as required by other regulatory models. As a result, AERMOD removes the
need for defining complex terrain regimes. All terrain is handled in a consistent and continuous
manner while considering the dividing streamline concept (Snyder et al. 1985) in stably-
stratified conditions.
One of the major improvements that AERMOD brings to applied dispersion modeling is its
ability to characterize the PEL through both surface and mixed layer scaling. AERMOD
constructs vertical profiles of required meteorological variables based on measurements and
extrapolations of those measurements using similarity (scaling) relationships. Vertical profiles of
wind speed, wind direction, turbulence, temperature, and temperature gradient are estimated
using all available meteorological observations. AERMOD is designed to run with a minimum
of observed meteorological parameters. As a replacement for the ISC3 model, AERMOD can
operate using data of a type that is readily available from National Weather Service (NWS)
stations. AERMOD requires only a single surface measurement of wind speed (measured
between 7 z0 and 100m - where z0 is the surface roughness height), wind direction and ambient
temperature. Like ISC3, AERMOD also needs observed cloud cover. However, if cloud cover
is not available (e.g. from an on-site monitoring program) two vertical measurements of
temperature (typically at 2 and 10 meters), and a measurement of solar radiation can be
substituted. A full morning upper air sounding (RAWINSONDE) is required in order to
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calculate the convective mixing height throughout the day. Surface characteristics (surface
roughness, Bowen ratio, and albedo) are also needed in order to construct similarity profiles of
the relevant PEL parameters.
Unlike existing regulatory models, AERMOD accounts for the vertical inhomogeneity of
the PEL in its dispersion calculations. This is accomplished by "averaging" the parameters of
the actual PEL into "effective" parameters of an equivalent homogeneous PEL.
Figure 2 shows the flow and processing of information in AERMOD. The modeling
system consists of one main program (AERMOD) and two pre-processors (AERMET and
AERMAP). The major purpose of AERMET is to calculate boundary layer parameters for use
by AERMOD. The meteorological INTERFACE, internal to AERMOD, uses these parameters
to generate profiles of the needed meteorological variables. In addition, AERMET passes all
meteorological observations to AERMOD.
MODELING
SYSTEM STRUCTURE
(INPUT)
"--__
N
W
S
~~~os
N 1
T
1 E
AERMET
• Generates PBL Para.
• Passes Measured
Profiles
p
A
S
S
1
O
B
P
B
S L
INTERFACE
p
A
R
A
M
• Similarity Relationships
• Interpolated Profiles
(INPUT)
^"~— -T—
I
AERMAP
Generates Terrain
and Receptor Data
X
Y
AERMOD p
u, turb, di/dz Concentration
*" Computations
Figure 2: Data flow in the AERMOD modeling system
Surface characteristics in the form of albedo, surface roughness and Bowen ratio, plus
standard meteorological observations (wind speed, wind direction, temperature, and cloud
cover), are input to AERMET. AERMET then calculates the PBL parameters: friction velocity
(u*\ Monin-Obukhov length (L), convective velocity scale (w,), temperature scale (ft), mixing
height (z,), and surface heat flux (H) These parameters are then passed to the INTERFACE
(which is within AERMOD) where similarity expressions (in conjunction with measurements)
are used to calculate vertical profiles of wind speed (w), lateral and vertical turbulent fluctuations
(ov, aw), potential temperature gradient (dd/dz), and potential temperature (6).
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The AERMIC terrain pre-processor AERMAP uses gridded terrain data to calculate a
representative terrain-influence height (/7C), also referred to as the terrain height scale. The
terrain height scale hc, which is uniquely defined for each receptor location, is used to calculate
the dividing streamline height. The gridded data needed by AERMAP is selected from Digital
Elevation Model (DEM) data. AERMAP is also used to create receptor grids. The elevation for
each specified receptor is automatically assigned through AERMAP. For each receptor,
AERMAP passes the following information to AERMOD: the receptor's location (xr, yr), its
height above mean sea level (zr), and the receptor specific terrain height scale (hc).
A comprehensive description of the basic formulation of the AERMOD dispersion model
including the INTERFACE, AERMET, and AERMAP is presented in this document. Included
are: 1) a complete description of the AERMET algorithms that provide quantitative hourly PEL
parameters; 2) the general form of the concentration equation with adjustments for terrain; 3)
plume rise and dispersion algorithms appropriate for both the convective and stable boundary
layers; 4) handling of boundary layer inhomogeneity; 5) algorithms for developing vertical
profiles of the necessary meteorological parameters; 6) a treatment of the nighttime urban
boundary layer; 7) treatment of building downwash (incorporation of PRIME); and 8)
enhancement of lateral dispersion due to plume meander. The model described here represents
the 04300 versions of AERMOD, AERMET and AERMAP. In addition, all of the symbols used
for the many parameters and variables that are referred to in this document are defined, with
their appropriate units, in the section titled "List of Symbols."
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3 Meteorological Preprocessor (AERMET)
The basic purpose of AERMET is to use meteorological measurements, representative of
the modeling domain, to compute certain boundary layer parameters used to estimate profiles of
wind, turbulence and temperature. These profiles are estimated by the AERMOD interface
which is described in Section 4.
While the structure of AERMET is based upon an existing regulatory model preprocessor,
the Meteorological Processor for Regulatory Models (MPRM) (Irwin et al. 1988) the actual
processing of the meteorological data is similar to that done for the CTDMPLUS (Perry 1992)
and HPDM (Hanna and Paine 1989; Hanna and Chang 1993) models. 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 surface roughness, reflectivity
(albedo), and the availability of surface moisture. The surface parameters provided by AERMET
are the Monin-Obukhov Length (Z), surface friction velocity (w*), surface roughness length (z0),
surface heat flux (H), and the convective scaling velocity (w*). AERMET also provides
estimates of the convective and mechanical mixed layer heights, zic and zim, respectively.
AERMET defines the stability of the PEL by the sign ofH (convective for H > 0 and stable for
H < 0 ). Although AERMOD is capable of estimating meteorological profiles with data from as
little as one measurement height, it will use as much data as the user can provide for defining the
vertical structure of the boundary layer. In addition to PEL parameters, AERMET passes all
measurements of wind, temperature, and turbulence in a form AERMOD needs.
3.1 Energy Balance in the PEL
The fluxes of heat and momentum drive the growth and structure of the PEL. To properly
characterize the PEL, one first needs a good estimate of the surface sensible heat flux (H) which
depends on the net radiation (Rn) and surface characteristics such as the available surface
moisture (described in the form of the Bowen ratio (BJ). In the CBL, a simple energy balance
approach, as in Oke (1978), is used to derive the expression, used in AERMET, to calculate the
sensible heat flux, H. We begin with the following simple characterization of the energy balance
in the PEL:
H+AE+G=Rn (1)
where H is the sensible heat flux, AE is the latent heat flux, G is the soil heat flux, and Rn is the
net radiation. To arrive at an estimate ofH simple parameterizations are made for the soil and
latent heat flux terms; that is, G = 0.1 Rn, and /I E = ff/B0 , respectively. Substituting these
expressions into eq. (1) the expression for surface heat flux becomes,
0.9 R
(2)
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3.1.1 NET RADIATION
If measured values for Rn are not available, the net radiation is estimated from the
insolation and the thermal radiation balance at the ground following the method of Holtslag and
vanUlden(1983)as
(l-
where c, = 5.3 IxlO'13 W m'2 K'6, c2 = 60 W m'2, c3 = 0.12, aSB is the Stefm Boltzman Constant
(5.67xlO"8 Wm"2K"4), Tre/is the ambient air temperature at the reference height for temperature
and Rn is the net radiation. The albedo is calculated as r{ + b) , where
a = -0.1 , b = -0.5(l - r')2, and r' = r{
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reaches approximately 13°; for overcast conditions crit from an
estimate of cloud cover rather than the actual observations themselves. In eq. (5) the cloud cover
(n) is replaced with an equivalent cloud cover (neq) that is calculated from eq. (4) such that
(l-R/R0 / v/"
n — \ ' °.
'0.75)
3.2 Derived Parameters in the CBL
In this section the methods used by AERMET to calculate the PEL parameters in the
convective boundary layer are discussed. AERMET first estimates the sensible heat flux (H),
then calculates the friction velocity (z/») and the Monin Obukhov Length (L). With H, u*. and Z,
AERMET can then estimate the height of the mixed layer and the convective velocity scale (vc«).
3.2.1 FRICTION VELOCITY (w.) & MONIN OBUKHOV LENGTH (L) IN THE CBL
In the CBL, AERMET computes the surface friction velocity, w*, and the Monin-Obukhov
length, Z, using the value ofH estimated from eq. (2). Since the friction velocity and the Monin
Obukhov length depend on each other, an iterative method, similar to that used in CTDMPLUS
(Perry 1992), is used. AERMOD initializes w*, and L by assuming neutral conditions (i.e., L=°°).
The final estimate of w* and L is made once convergence is reached through iterative
calculations (i.e., there is less than a 1% change between successive iterations). The expression
for w* (e.g., Panofsky and Button (1984)) is
where k is the von Karman constant (= 0.4), wre/is the wind speed at reference height, zre/is the
reference measurement height for wind in the surface layer, and z0 is the roughness length. The
stability terms (^m's) in eq. (6) are computed as follows:
(7)
- 2tan- H- ,2
where// = (l- 16zre//z)14 and ju0 = (l- 16z0/z)
The initial step in the iteration is to solve eq. (6) for z/» assuming that i/rm = 0 (neutral limit)
and setting u = uref. Having an initial estimate of w», L is calculated from the following
definition (eg. see Wyngaard (1988)):
17
-------
where g is the acceleration of gravity, cp is the specific heat of air at constant pressure, p is the
density of air, and Trefis the ambient temperature representative of the surface layer. Then w* and
L are iteratively recalculated using eqs. (6), (7) and (8) until the value of L changes by less than
1%.
The reference heights for wind speed and temperature that are used in determining the
friction velocity and Monin-Obukhov length are optimally chosen to be representative of the
surface layer in which the similarity theory has been formulated and tested with experimental
data. Typically, a 10 m height for winds and a temperature within the range of 2 to 10 m is
chosen. However, for excessively rough sites (such as urban areas with z0 can be in excess of 1
m), AERMET has a safeguard to accept wind speed reference data that range vertically between
7 z0 and 100 m. Below 7 z0 (roughly, the height of obstacles or vegetation), measurements are
unlikely to be representative of the general area. A similar restriction for temperature
measurements is imposed, except that temperature measurements as low as z0 are permitted.
Above 100 m, the wind and temperature measurements are likely to be above the surface layer,
especially during stable conditions. Therefore, AERMET imposes an upper limit of 100 meters
for reference wind speed and temperature measurements for the purpose of computing the
similarity theory friction velocity and Monin-Obukhov length each hour. Of course, other US
EPA guidance for acceptable meteorological siting should be consulted in addition to keeping
the AERMET restrictions in mind.
3.2.2 CONVECTIVE VELOCITY SCALE (w.)
AERMOD utilizes the convective velocity scale to characterize the convective portion of
the turbulence in the CBL. Field observations, laboratory experiments, and numerical modeling
studies show that the large turbulent eddies in the CBL have velocities proportional to the
convective velocity scale (w ,) (Wyngaard 1988). Thus in order to estimate turbulence in the
CBL, an estimate of w* is needed. AERMET calculates the convective velocity scale from its
definition as:
\ V3
pref
where zic is the convective mixing height (see Section 3.4).
18
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3.3 Derived Parameters in the SBL
In this section the parameters used to characterize the SBL are discussed along with their
estimation methods. During stable conditions the energy budget term associated with the ground
heating component is highly site-specific. During the day, this component is only about 10% of
the total net radiation, while at night, its value is comparable to that of the net radiation (Oke
1978). Therefore, errors in the ground heating term can generally be tolerated during the
daytime, but not at night. To avoid using a nocturnal energy balance approach that relies upon
an accurate estimate of ground heating, AERMIC has adopted a much simpler semi-empirical
approach for computing w* and L.
3.3.1 FRICTION VELOCITY (w.) IN THE SBL
The computation of w» depends on the empirical observation that the temperature scale, <9»,
defined as
0, = - Hjpcpu, (io)
varies little during the night. Following the logic of Venkatram (1980) we combine the
definition of L eq. (8) with eq. (10) to express the Monin-Obukhov length in the SBL as
ul (11)
From (Panofsky and Dutton 1984) the wind speed profile in stable conditions takes the form
Z I fimZref
u =
In— +
zj L
o
(12)
where flm = 5 and zre/is the wind speed reference measurement height. Substituting eq. (11) into
eq. (12) and defining the drag coefficient, CD, as k \n(zref jz\ (Garratt 1992), results in
u 1 ft 2 f g0*
— =7^+ 1 2 • (13)
u, CD Tref u,
Multiplying eq. (13) by CD u*2 and rearranging yields a quadratic of the form
* + CD u2o = 0, (14)
where u20 = /3m zrefg9f/Tref . As is used in HPDM (Hanna and Chang 1993) and CTDMPLUS
(Perry 1992) this quadratic has a solution of the form
19
-------
M* =
CDuref
- 1 +
(15)
Equation (15) produces real-valued solutions only when the wind speed is greater than or equal
[-11/2
^PmzrefgO*/TrefCD\ . For the wind speed less than the critical value, z/»
and ft are parameterized using the following linear expression:
u, = u*{u = ucr} (u/ucr) for u < ucr
0* = 9* (u/ucr) for u < ucr
These expressions approximate the z/» verses ft dependence found by van Ulden and Holtslag
(1983).
In order to calculate w* from eq. (15) an estimate of ft is needed. If representative cloud
cover observations are available the temperature scale in the SBL is taken from the empirical
form of van Ulden and Holtslag (1985) as:
0. = 0.09(l -0.5«2), (16)
where n is the fractional cloud cover. However, if cloud cover measurements are not available
AERMET can estimate ft from measurements of temperature at two levels and wind speed at
one level. This technique, know as the Bulk Richardson approach, starts with the similarity
expression for potential temperature (Panofsky and Button 1984), that is,
9, ( z z]
00 = ^- In—+/?- (17)
where flm ~ 5 and k (= 0.4) is the von Karman constant. Applying eq. (17) to the two levels of
temperature measurements and rearranging terms yields
L
(18)
Since both u*. (eq. (12)) and ft(eq. (18)) depend onZ, andL (eq. (11)) in turn depends on z/*
and ft, an iterative approach is needed to estimate w*. w* and ft are found by first assuming an
initial value for L and iterating among the expressions for w», ft(eq. (18)) andL (eq. (11)) until
convergence is reached. The expression used for w*, in the iteration, is taken from (Holtslag
20
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1984) and depends on atmospheric stability. For situations in which Z/L < 0.5 ut is estimated
using eq. (12), otherwise (for more stable cases) w* is calculated as follows:
ku
M* = T
z z 4.25
In 4- 7 In 4.
111 + / 111 + / \
0.5 A,
(\ 2 o
z/ L] ^
(19)
3.3.2 SENSIBLE HEAT FLUX (H) IN THE SBL
Having computed w* and ft for stable conditions, AERMET calculates the surface heat flux
from eq. (10) as
H=-pcpu,0*. (20)
AERMET limits the amount of heat that can be lost by the underlying surface to 64 W m"2. This
value is based on a restriction that Hanna (1986) placed on the product of ft and z/». That is, for
typical conditions Hanna found that
\9,u,\ = 0.05ms~1K. (21)
L Jmax v '
When the heat flux, calculated from eq. (20), is such that ft w* > 0.05 m s"1 K, AERMET
recalculates w* by substituting 0.05/w* into eq. (15) for ft (u0 in eq. (15) is a function of ft ).
3.3.3 MONIN OBUKHOV LENGTH (L) IN THE SBL
Using the sensible heat flux of eq.(20) and z/* from eq. (15), the Monin-Obukhov Length, for
the SBL is calculated from eq. (8).
3.4 Mixing Height
The mixing height (z,) in the CBL depends on both mechanical and convective processes and
is assumed to be the larger of a mechanical mixing height (zim) and a convective mixing height
(z!C). Whereas, in the SBL, the mixing height results exclusively from mechanical (or shear
induced) turbulence and therefore is identically equal to zim. The same expression for calculating
zim is used in both the CBL and the SBL. The following two sections describe the procedures
used to estimate zic and zim, respectively.
21
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3.4.1 CONVECTIVE MIXING HEIGHT (zlc)
The height of the CBL is needed to estimate the profiles of important PEL variables and to
calculate pollutant concentrations. If measurements of the convective boundary layer height are
available they are selected and used by the model. If measurements are not available, zic is
calculated with a simple one-dimensional energy balance model (Carson 1973) as modified by
Weil and Brower (1983). This model uses the early morning potential temperature sounding
(prior to sunrise), and the time varying surface heat flux to calculate the time evolution of the
convective boundary layer as
zw9{zw}- 9{z}dz= (1+ 2A)\dt', (22)
0 0 PCp
where 6 is the potential temperature, A is set equal to 0.2 from Deardorff (1980), and t is the
hour after sunrise. Weil and Brower found good agreement between predictions and
observations of zic, using this approach.
3.4.2 MECHANICAL MIXING HEIGHT (zj
In the early morning when the convective mixed layer is small, the full depth of the PEL may
be controlled by mechanical turbulence. AERMET estimates the heights of the PEL during
convective conditions as the maximum of the estimated (or measured if available) convective
boundary layer height (zic) and the estimated (or measured) mechanical mixing height.
AERMET uses this procedure to insure that in the early morning, when zic is very small but
considerable mechanical mixing may exist, the height of the PEL is not underestimated. When
measurements of the mechanical mixed layer are not available, zim is calculated by assuming that
it approaches the equilibrium height given by Zilitinkevich (1972) as
u,L
(23)
where zie is the equilibrium mechanical mixing height and/is the Coriolis parameter.
Venkatram (1980) has shown that, in mid-latitudes, eq. (23) can be empirically represented
as
zie = 2300 uT , (24)
where zie (calculated from eq. (24)) is the unsmoothed mechanical mixed layer height. When
measurements of the mechanical mixed layer height are available they are used in lieu of zie.
To avoid estimating sudden and unrealistic drops in the depth of the shear-induced, turbulent
layer, the time evolution of the mechanical mixed layer height (whether measured or estimated)
is computed by relaxing the solution toward the equilibrium value appropriate for the current
hour. Following the approach of Venkatram (1982)
22
-------
im _ \ ie im) (25)
dt T '
The time scale, T , governs the rate of change in height of the layer and is taken to be
proportional to the ratio of the turbulent mixed layer depth and the surface friction velocity (i.e. r
= zim / PTu^. AERMOD uses a constant /Rvalue of 2. For example, if w* is of order 0.2 m s"1,
and zim is of order 500 m, the time scale is of the order of 1250 s which is related to the time it
takes for the mechanical mixed layer height to approach its equilibrium value. Notice that when
zim < zie, the mechanical mixed layer height increases to approach its current equilibrium value;
conversely, when zim > zie, the mechanical mixed layer height decreases towards its equilibrium
value.
Because the friction velocity changes with time, the current smoothed value ofzim{t+A.t} is
obtained by numerically integrating eq. (25) such that
z^{t + A?}fl-e(~A//r)l (26)
ie
where zim{t} is the previous hour's smoothed value. For computing the time scale in eq. (26), zim
is taken from the previous hour's estimate and u* from the current hour. In this way, the time
scale (and thus relaxation time) will be short if the equilibrium mixing height grows rapidly but
will be long if it decreases rapidly.
Although eqs. (24) and (26) are designed for application in the SBL, they are used in the
CBL to ensure a proper estimate of the PEL height during the short transitional period at the
beginning of the day when mechanical turbulence generally dominates. The procedure, used by
AERMET, guarantees the use of the convective mixing height once adequate convection has
been established even though the mechanical mixing height is calculated during all convective
conditions. Since AERMET uses eq. (26) to estimate the height of the mixed layer in the SBL,
discontinuities in zt from night to day are avoided.
In AERMOD, the mixing height z;, has an expanded role in comparison to how it is used in
ISC3. In AERMOD the mixing height is used as an elevated reflecting/penetrating surface, an
important scaling height, and enters in the w* determination found in eq. (9). The mixing height
zt for the convective and stable boundary layers is therefore defined as follows:
z, = MAx[zlc- zm] for L < 0 (CBL)
z, = z,m forL<0(SBL)
Since algorithms used for profiling differ in the SBL and CBL, the stability of the PEL must
be determined. For this purpose the sign of L is used by AERMET; if Z < 0 then the PEL is
considered to be convective (CBL) otherwise it is stable (SBL).
23
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4 Vertical Structure of the PEL - AERMOD's Meteorological Interface
The AERMOD interface, a set of routines within AERMOD, uses similarity relationships
with the boundary layer parameters, the measured meteorological data, and other site-specific
information provided by AERMET to compute vertical profiles of: 1) wind direction, 2) wind
speed, 3) temperature, 4) vertical potential temperature gradient, 5) vertical turbulence (ow) and
6) lateral turbulence (ov).
For any one of these six variables (or parameters), the interface (in constructing the profile)
compares each height at which a meteorological variable must be calculated with the heights at
which observations were made and if it is below the lowest measurement or above the highest
measurement (or in some cases data is available at only one height), the interface computes an
appropriate value from selected PEL similarity profiling relationships. If data are available both
above and below a given height, an interpolation is performed which is based on both the
measured data and the shape of the computed profile (see Section 7.10). Thus the approach used
for profiling, simultaneously takes advantage of the information contained in both the
measurements and similarity parameterizations. As will be discussed, at least one level of
measured wind speed, wind direction, and temperature is required. However, turbulence profiles
can be parameterized without any direct turbulence measurements.
The following sections provide a comprehensive description of AERMOD's profiling
equations and how these estimated profiles are used to extract pertinent layer-averaged
meteorology for AERMOD's transport and dispersion calculations. Also, example profiles (one
typical of the CBL and one typical of the SBL) for the various parameters have been constructed
for illustration. The CBL case assumes that zt = 1000 m, L = -10 m and z0 = 0.1 m (i.e., z0 =
O.OOOlz, and L = - O.Olz,). The SBL case assumes that z,• = 100 m, L = 10 m and z0 = 0.1 m (i.e.,
z0= 0.00 lz,and L = O.I z,).
4.1 General Profiling Equations
4.1.1 WIND SPEED PROFILING
The AERMOD profile equation for wind speed, has the familiar logarithmic form:
u= u{lz0]
lz
u =
u*.
~k
u= u{z]
for z < lz
z,
(28)
At least one wind speed measurement, that is representative of the surface layer, is required
for each simulation with AERMOD. Since the logarithmic form does not adequately describe
the profile below the height of obstacles or vegetation, eq.(28) allows for a linear decrease in
wind speed from its value at Iz0.
24
-------
For the CBL, the i/fm 's are evaluated using eq.(7) with zref replaced by z, and during stable
conditions they are calculated from van Ulden & Holtslag (1985) as
1- exp[ - 0.29 —
/ j
l-exp|-0.29-?-
(29)
For small z/L («1) and with a series expansion of the exponential term, the first equation in (29)
reduces to the form given in eq. (12), i.e., y/m = - fim z/L with flm = 5. However, for large
z/L (>1) and heights as great as 200 m in the SBL, the ifrm given by eq. (29) is found to fit wind
observations much better than the i/fm given by eq.(12) (van Ulden and Holtslag 1985). Using the
example case parameter values Figure 3 and Figure 4 were constructed to illustrate the form of
the wind profiles used by AERMOD in the layers above and below Iz0.
25
-------
6 -
4 -
2 -
0.0010 -
8
6
4 -
2 -
0.0001
7z -SBL— — — -*—
_ -, 7z - CBL
Wind Speed
CBL
- — SBL
i • r
o.o i.o 2.0
\ • \
3.0 4.0
u/u *
\
5.0 6.0 7.0
Figure 3: Wind speed profile, for both the CBL and SBL, in the region below 7Z0
26
-------
1.6 -i
1.4 -
1.2 -
1.0 -
^ 0.8 -
N
0.6 -
0.4 -
0.2 -
0 0
z .
-y
Wind Speed 1
— — SBL
v y
1 _
'
'
s
s
^
^
i 1 i 1 i 1 i 1 i 1 i 1
0.0 10.0 20.0 30.0 40.0 50.0 60.0
u/u „
Figure 4 Wind speed profile, for both the CBL and SBL, in the region above 7Z0.
4.1.2 WIND DIRECTION PROFILES
For both the CBL & SBL wind direction is assumed to be constant with height both above
the highest and below the lowest measurements. For intermediate heights, AERMOD linearly
interpolates between measurements. At least one wind direction measurement is required for
each AERMOD simulation.
4.1.3 PROFILES OF THE POTENTIAL TEMPERATURE GRADIENT
Above the relatively shallow superadiabatic surface layer, the potential temperature gradient
in the well mixed CBL is taken to be zero. The gradient in the stable interfacial layer just above
the mixed layer is taken from the morning temperature sounding. This gradient is an important
factor in determining the potential for buoyant plume penetration into and above that layer.
27
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Above the interfacial layer, the gradient is typically constant and slightly stable. Although the
interfacial layer depth varies with time, for the purposes of determining the strength of the stable
stratification aloft, AERMET uses a fixed layer of 500 m to insure that a sufficient layer of the
morning sounding is sampled. A 500 m layer is also used by the CTDMPLUS model (Perry
1992) for this same calculation. This avoids strong gradients (unrealistic kinks) often present in
these data. For a typical mixed layer depth of 1000 m an interfacial layer depth of 500 m is
consistent with that indicated by Deardorff (1979). A constant value of 0.005 K m"1 above the
interfacial layer is used as suggested by Hanna and Chang (1991). Using the morning sounding
to compute the interfacial temperature gradient assumes that as the mixed layer grows
throughout the day, the temperature profile in the layer above zt changes little from that of the
morning sounding. Of course, this assumes that there is neither significant subsidence nor cold
or warm air advection occurring in that layer. Field measurements (e.g. Clarke et al. (1971)) of
observed profiles throughout the day lend support to this approach. These data point out the
relative invariance of upper level temperature profiles even during periods of intense surface
heating.
Below 100 m, in the SBL, AERMOD uses the definition of the potential temperature
gradient suggested by Dyer (1974) as well as Panofsky and Button (1984). That is,
dB 9,
for z < 2m
(30)
1+5^ for 2m
-------
data. If no measurements of dd/dz are available, in that height range, then ft is calculated by
combining eqs. (8) and (20). ft is not used in the CBL.
Figure 5 shows the inverse height dependency of dd/dz in the SBL. To create this curve we
assumed that: Zim=100 m; and therefore, Zig =100 m; L=10 m; w*=.124, which is consistent with
a mixing height of 100 m; Tref = 293 K; and therefore based on eq. (11) ft = 0.115 K. These
parameter values were chosen to represent a strongly stable boundary layer. Below 2 m dd/dz is
persisted downward from its value of 0.228 K m"1 at 2m. Above 100 m dd/dz is allowed to decay
exponentially with height.
N
150
125
100 —\
75 —
50 —
25 —
0
0.000
0.200
d 6/dz (° K/m)
0.400
Figure 5: Profile of potential temperature gradient for the SBL.
4.1.4 POTENTIAL TEMPERATURE PROFILING
For use in plume rise calculations, AERMOD develops the vertical profile of potential
temperature from its estimate of the temperature gradient profile First the model computes the
potential temperature at the reference height for temperature (i.e., zrre/) as
/-\ f rri , O msl ^ '
29
-------
where zmsl = zref + zbase and zbase is the user specified elevation for the base of the temperature
profile (i.e., meteorological tower). Then for both the CBL and SBL the potential temperature is
calculated as follows:
dQ
0{z+ Az}= 6>{z} + —Az (33)
GZ
where — is the average potential temperature gradient over the layer Az. Note that for z <
Gl
zTref, Az is negative.
4.1.5 VERTICAL TURBULENCE CALCULATED
In the CBL, the vertical velocity variance or turbulence (o2wj) is profiled using an expression
based on a mechanical or neutral stability limit (awm ^ w») and a strongly convective limit (awc ^
w»). The total vertical turbulence is given as:
(J 2T = (J 2 + (J 2 (34)
wT we wm ^ '
This form is similar to one introduced by Panofsky et al. (1977) and included in other dispersion
models (e.g., Berkowicz et al. (1986), Hanna and Paine (1989), and Weil (1988a)).
The convective portion (o2wc) of the total variance is calculated as:
^1 = 1-6— -w.2 for z zic
where the expression for z < 0.1 zic is the free convection limit (Panofsky et al. 1977), for
0. \zt < z < zic is the mixed-layer value (Hicks 1985), and for z > zic is a parameterization to
connect the mixed layer a2wc to the assumed near-zero value well above the CBL. An example
profile of convective vertical turbulence described in eq. (35) is presented in Figure 6.
30
-------
N
1.6 -i
1.4 -
1.2 -
1.0
0.8
0.6
0.4
0.0 0.1 0.2 0.3 0.4 0.5 0.6
a ._„ /w .
Figure 6: Convective portion of the vertical turbulence in the CBL.
The mechanical turbulence (owm) is assumed to consist of a contribution from the boundary
layer (&wml) and from a "residual layer" (&wmr) above the boundary layer (z > z;) such that,
wm wml wmr'
(36)
This is done to satisfy the assumed decoupling between the turbulence aloft (z > z,) and that at
the surface in the CBL shear layer, and to maintain a continuous variation of o2wm with z near z =
The expression for awml following the form of Brost et al. (1982) is
~=I*HI--J
wml = o.o
(37)
for z > zi
where the owml =1.3M* at z = 0 is consistent with Panofsky et al. (1977).
31
-------
Above the mixing height awmr is set equal to the average of measured values in the residual
layer above zt. If measurements are not available, then owmr is taken as the default value of 0.02
u{z,}. The constant 0.02 is an assumed turbulence intensity /'z ( = owm/u) for the very stable
conditions presumed to exist above zt (Briggs 1973). Within the mixed layer the residual
turbulence (&wmr) is reduced linearly from its value at zt to zero at the surface. Figure 7 presents
the profile of the mechanical portion of the vertical turbulence in the CBL. The effect of
combining the residual and boundary layer mechanical turbulence (eq. (36)) can be seen in this
figure.
N
N
0.0
0.2
0.4
0.6
0.3
1.0
1.2
1.4
a /u
wra.
Figure 7: Mechanical portion of the vertical turbulence in the CBL
In the SBL the vertical turbulence contains only a mechanical portion which is given by eq. (36).
The use of the same o2wm expressions for the SBL and CBL is done to ensure continuity of
turbulence in the limit of neutral stability. Figure 8 illustrates AERMOD's assumed vertical
turbulence profile for the SBL. This is similar to the profile for the CBL except for a notable
increase in the value of owmr. Since values for owmr are based on the magnitude of the wind speed
32
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at Zj, the differences in the two figures stem from setting z0 = O.OOOlz, in the CBL example case
while for the SBL case zn = O.OOlz,,
N
N
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
1.4
/U
Figure 8: Profile of vertical turbulence in the SBL
4.1.6 LATERAL TURBULENCE CALCULATED BY THE INTERFACE
In the CBL the total lateral turbulence, a2vT, is computed as a combination of a mechanical
(crvm) and convective (<7VC) portions such that
< = °l +
-------
4.1.6.1 Mechanical Portion of the Lateral Turbulence
The variation with height of the mechanical portion of the lateral turbulence is bounded by
its value at the surface and an assumed residual value at the top of the mechanical mixed layer.
The variation between these two limits is assumed to be linear. Based on observations from
numerous field studies, Panofsky and Button (1984) report that, in purely mechanical turbulence,
the lateral variance near the surface has the form
av2 = Cu2 (39)
where the constant, C, ranges between 3 and 5. Based on an analysis of the Kansas data, Izumi
(1971) and Hicks (1985) support the form of eq. (39) with a value of 3.6 for C.
Between the surface and the top of the mechanically mixed layer, cfvm is assumed to vary
linearly as
.2
vm
im
Z Zim
(40)
\Zim]
where a2m {z.m} = MIN\a20, 025m2 s 2] and avo2, the surface value of the lateral turbulence, is
equal to 3.6 u2. This linear variation of o\m with z is consistent with field observations (e.g.,
Brost et al. (1982)). In the SBL the total lateral turbulence contains only a mechanical portion
and it is given by eq. (40).
Above the mixed layer, lateral turbulence is expected to maintain a modest residual level.
Hanna (1983) analyzed ambient measurements of lateral turbulence in stable conditions. He
found that even in the lightest wind conditions, the measurements of ovc were typically 0.5 m s"1,
but were observed to be as low as 0.2 m s"1. AERMOD adopts the lower limit of 0.2 m s"1 for ovc
in near-surface conditions, as discussed below, but uses the more typical value of 0.5 m s"1 for
the residual lateral turbulence above the mixed layer. Above the height of the CBL, the model
linearly decreases ov2 from ovc2{ zic} to 0.25 at 1.2 zic and holds ovc2 constant above 1.2zic.
However, if ov2{zic} < 0.25 m2 s"2, then ov2{zic} is persisted upward from zic. Furthermore, it
was found that a value of the order ov2 = 0.25 m2 s"2 provided consistently good model
performance (for plumes commonly above zim) during the developmental evaluation (Paine et al.
2001) supporting the presence of residual lateral turbulence in this layer.
Figure 9 shows how the vertical profile of lateral mechanical turbulence changes over a
range of mechanical mixing heights, and related friction velocities. The values of u*. used to
produce these curves are consistent with the relationship between zim and w» which is found in eq.
(24). For the SBL Figure 9 represents profiles of the total lateral turbulence. In the CBL these
curves depict only the mechanical portion of the total lateral variance. Note that for zim = 300 m
and 100 m the values ov2 are less than 0.25 m2 s"2. Therefore the profiles are constant with
height.
34
-------
1000 -q
-
900 -
~
™
800 -_
—
700 -_
600 -_
S/"-v
^ 500 ^
N
400 -_
300 ^
200 ^
100 -_
P.
0.
0
1 1 '
0.1
Affixing Heights
^^^^^^^m TOO
im
X = 200 m
im
— — — • Z = 300 m
im
— — — Z = 400 m
im
— — z = 500 m
' ^— ^— Z = 600 m
im
\ \ — ~ Zim = 70°m
\ \
1 . ^
1 \ \
\\ \ \
\ \ v \
* \ \
\ \ V
' v \ \
, \ \ N
\ \ \ \
, , , , , , , , 1 . | , , , | , , ,] , , , | . , , |
0.2 0.3 0.4 0.5 0.6 0.7 0.8
a2vm (m2/sec2)
Figure 9: Family of lateral mechanical turbulence profiles over a range of
mechanical mixing heights
4.1.6.2 Convective Portion of the Lateral Turbulence
The convective portion of the lateral turbulence within the mixed is constant and calculated
as:
= 0.35W
(41)
This constant value of cr^/w*2 = 0.35 is supported by the Minnesota data (Readings et al. 1974;
Kaimal et al. 1976) and by data collected at Ashchurch England (Caughey and Palmer 1979).
35
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2
For z > zic, the model linearly decreases ovc2 from ovc2{ zic} to 0.25 at 1.2 zic and holds
constant above 1.2 zic. However, if ovc2{zic } < .25 m2 s"2, then ovc2{zic} is persisted upward from
4.2 Vertical Inhomogeneity in the Boundary Layer as Treated by the INTERFACE
AERMOD is designed to treat the effects on dispersion from vertical variations in wind and
turbulence. Consideration of the vertical variation in meteorology is important for properly
modeling releases in layers with strong gradients, for capturing the effects of meteorology in
layers into which the plume may be vertically dispersing, and to provide a mechanism (in the
CBL) by which sources that are released into or penetrate into an elevated stable layer can
eventually re-enter the mixed layer. However, AERMOD is a steady-state plume model and
therefore can use only a single value of each meteorological parameter to represent the layer
through which these parameters are varying. Thus, the model "converts" the inhomogeneous
values into equivalent effective or homogeneous values. This technique is applied to w, ovr, awr,
dd/dz and the Lagrangian time scale. The effective parameters are denoted by a tilde throughout
the document (e.g., effective wind speed is denoted by u )•
Fundamental to this approach is the concept that the primary layer of importance, relative to
receptor concentration, is the one through which plume material travels directly from source to
receptor. Figure 10 presents a schematic illustration of the approach AERMOD uses to
determine these effective parameters (a is used to generically represent these parameters). The
effective parameters are determined by averaging their values over that portion of the layer that
contains plume material between the plume centroid height, Hp {x}, (a simplified surrogate for
the height of the plume's center of mass) and the receptor height (zr). In other words, the
averaging layer is determined by the vertical half-depth of the plume (defined as 2.15 az {xr}
where xr is the distance from source to receptor) but is bounded by Hp {xr} and zr. The values
used in the averaging process are taken from AERMOD's vertical profiles. This technique is
best illustrated with examples.
36
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INHOMOGENEITY
Hp(x)= Plume Centrald
Height (in the CBL)
Figure 10:AERMOD's Treatment of the Inhomogeneous Boundary Layer
Consider the two receptors depicted in Figure 10. Both receptors are located at the same
distance xr from the source but at different heights above ground, i.e., zrl and zr2. An example
profile of some parameter a is shown at the far left of the figure. The value of the effective
parameter used by AERMOD to represent transport and diffusion from source to receptor
depends on the location of the receptor. For receptor 1 the effective parameter value a\
(shown in the figure as aeffl) is determined by averaging the values of a {z} between Hp {xr} and
zrl. Therefore, the layer over which this average is taken is smaller than the plume's half-depth.
Whereas, «2 (shown in the figure as aeff2) is determined by averaging a {z} over the full layer
from Hp {xr} down through a depth of 2.15 az {xr} since the receptor is located below the defined
lower extent of the plume.
Since oz {xr}depends on the effective values of owT and u, the plume size is estimated by
first using the plume height values of owT {Hp } and u {Hp } to calculate oz {xr}. As illustrated in
Figure 10, oz {xr} is then used to determine the layer over which O"wT {xr } and u {xr} are
37
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calculated. Once the averaging layer for a given plume and receptor is established the effective
values, cc , are computed as simple averages:
1
a =
(42)
where hb and ht are the bottom and top, respectively, of the layer of importance such that:
if Hp{xr,yr}zr
MIN{[ Hp {xr ,yr}+ 2.15az {xsr}], zr}, // Hp {xr ,yr}zr
h =
(43)
For all plumes, both limits are bounded by either the zr or Hp. For both the direct and indirect
sources h^ in eq. (43) is not allowed to exceed zi and if hb > zi then a = a {z.} .
For plumes in stable conditions and for the penetrated source in the CBL, Hp is always set
equal to the plume centerline height \khs + hs j, where hs is the stack height corrected for stack
tip downwash and A.hs is the stable source plume rise. The stable source plume rise A.hs is
calculated from expressions found in Section 5.6.2.
In the CBL, the specification of Hp is somewhat more complicated. Because of limited
mixing in the CBL the center of mass of the plume will be the plume height close to the source
and the mid-point of the PEL at the distance where it becomes well mixed. Beyond final plume
rise, Hp is varied linearly between these limits.
Prior to plume stabilization, i.e., x < xf (distance to plume stabilization),
H = hs + hhd , where A.hd is the plume rise for the direct source (estimated from eq. (91)),
and A.hp (= hep - hs) is the plume rise for the penetrated source, where hep (penetrated source
plume height) is calculated from eq. (94).
The distance to plume stabilization, xf, is determined following Briggs (Briggs 1975; Briggs
1971)as
xf = 49F** for Fb<55
(44)
xf = \\9Fb/5 for Fb>55
where the buoyancy flux (Fb) is calculated from eq. (57).
For Fb = 0 the distance to final rise is calculated from the ISCST3 ((U.S.Environmental
Protection Agency 1995)) expression
(45)
38
-------
where up is the wind speed at source height, rs is the stack radius, and ws is the stack exit gas
velocity.
Beyond plume stabilization ( x>xf), Hp varies linearly between the stabilized plume height
(H{xf}) and the mid-point of the mixed layer (zt /2). This interpolation is performed over the
distance range xfto xm, where xm is the distance at which pollutants first become uniformity
mixed throughout the boundary layer.
The distance xm is taken to be the product of the average mixed layer wind speed and the
mixing time scale, z. /awT . That is,
(46)
where the averaging of u and awT are taken over the depth of the boundary layer.
For distances beyond xf, Hp is assumed to vary linearly between the plume's stabilized
height, H [xf }, and zt /2 such that:
z.
Hp = H{xf}+- H{xf} - - r (47)
Note that in the CBL, both the direct and indirect source will have the same a (effective
parameter) values. In eq. (43) oz is the average of the updraft oz and the downdraft a, , the
maximum value of ht is zt , and when hb>zi,a=a {z}.
As discussed previously, when multiple vertical measurements of wind direction are
available a profile is constructed by linearly interpolating between measurements and persisting
the highest and lowest measurements up and down, respectively. The approach taken for
selecting a transport wind direction from the profile is different from the above. The transport
wind direction is selected as the mid point of the range between stack height and the stabilized
plume height.
39
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5 The AMS/EPA Regulatory Model AERMOD
AERMOD is a steady-state plume model in that it assumes that concentrations at all
distances during a modeled hour are governed by the temporally averaged meteorology of the
hour. The steady state assumption yields useful results since the statistics of the concentration
distribution are of primary concern rather than specific concentrations at particular times and
locations. AERMOD has been designed to handle the computation of pollutant impacts in both
flat and complex terrain within the same modeling framework. In fact, with the AERMOD
structure, there is no need for the specification of terrain type (flat, simple, or complex) relative
to stack height since receptors at all elevations are handled with the same general methodology.
To define the form of the AERMOD concentration equations, it is necessary to simultaneously
discuss the handling of terrain.
In the stable boundary layer (SBL), the concentration distribution is assumed to be Gaussian
in both the vertical and horizontal. In the convective boundary layer (CBL), the horizontal
distribution is assumed to be Gaussian, but the vertical distribution is described with a bi-
Gaussian probability density function (pdf). This behavior of the concentration distributions in
the CBL was demonstrated by Willis and Deardorff (1981) and Briggs (1993). Additionally, in
the CBL, AERMOD treats "plume lofting," whereby a portion of plume mass, released from a
buoyant source, rises to and remains near the top of the boundary layer before becoming
vertically mixed throughout the CBL. The model also tracks any plume mass that penetrates into
an elevated stable layer, and then allows it to re-enter the boundary layer when and if
appropriate.
In urban areas, AERMOD accounts for the dispersive nature of the "convective-like"
boundary layer that forms during nighttime conditions by enhancing the turbulence over that
which is expected in the adjacent rural, stable boundary layer. The enhanced turbulence is the
result of the urban heat flux and associated mixed layer which are estimated from the urban-rural
temperature difference as suggested by Oke (1978; 1982).
In complex terrain, AERMOD incorporates the concept of the dividing streamline (Snyder
et al., 1985) for stably-stratified conditions. Where appropriate the plume is modeled as a
combination of two limiting cases: a horizontal plume (terrain impacting) and a terrain-following
(terrain responding) plume. That is, AERMOD handles the computation of pollutant impacts in
both flat and complex terrain within the same modeling framework. Generally, in stable flows, a
two-layer structure develops in which the lower layer remains horizontal while the upper layer
tends to rise over the terrain. The concept of a two-layer flow, distinguished at the dividing
streamline height (Hc), was first suggested by theoretical arguments of Sheppard (1956) and
demonstrated through laboratory experiments, particularly those of Snyder et al. (1985). In
neutral and unstable conditions Hc = 0.
A plume embedded in the flow below Hc tends to remain horizontal; it might go around the
hill or impact on it. A plume above Hc will ride over the hill. Associated with this is a tendency
for the plume to be depressed toward the terrain surface, for the flow to speed up, and for vertical
turbulent intensities to increase. These effects in the vertical structure of the flow are accounted
for in models such as the Complex Terrain Dispersion Model (CTDMPLUS) (Perry 1992).
However, because of the model complexity, input data demands for CTDMPLUS are
considerable. EPA policy (Code of Federal Regulations 1997) requires the collection of wind
40
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and turbulence data at plume height when applying CTDMPLUS in a regulatory application. As
previously stated, the model development goals for AERMOD include having methods that
capture the essential physics, provide plausible concentration estimates, and demand reasonable
model inputs while remaining as simple as possible. Therefore, AERMIC arrived at a terrain
formulation in AERMOD that considers vertical flow distortion effects in the plume, while
avoiding much of the complexity of the CTDMPLUS modeling approach. Lateral flow
channeling effects on the plume are not considered by AERMOD.
AERMOD captures the effect of flow above and below the dividing streamline by weighting
the plume concentration associated with two possible extreme states of the boundary layer
(horizontal plume and terrain-following). As is discussed below, the relative weighting of the
two states depends on: 1) the degree of atmospheric stability; 2) the wind speed; and 3) the
plume height relative to terrain. In stable conditions, the horizontal plume "dominates" and is
given greater weight while in neutral and unstable conditions, the plume traveling over the
terrain is more heavily weighted.
5.1 General Structure of AERMOD Including Terrain
In general, AERMOD models a plume as a combination of two limiting cases: a horizontal
plume (terrain impacting) and a terrain-following plume. Therefore, for all situations, the total
concentration, at a receptor, is bounded by the concentration predictions from these states. In
flat terrain the two states are equivalent. By incorporating the concept of the dividing
streamline height, in elevated terrain, AERMOD's total concentration is calculated as a weighted
sum of the concentrations associated with these two limiting cases or plume states(Venkatram et
al. 2001).
The AERMOD terrain pre-processor (AERMAP) uses gridded terrain data to calculate a
representative terrain-influence height (hc) for each receptor with which AERMOD computes
receptor specific Hc values. Through this approach, AERMOD handles the computation of
pollutant impacts in both flat and elevated terrain within the same modeling framework thereby
obviating the need to differentiate between the formulations for simple and complex terrain (as
required with previous regulatory models) .
The general concentration equation, which applies in stable or convective conditions is
given by
CT{xr,yr,zr} = f-Cc/,xr,yr,zr}+(l-f)Cc,s{xr,yr,zp} (48)
where CT{xr,yr,zr} is the total concentration, Ccs{xr,yr,zr} is the contribution from the
horizontal plume state (subscripts c and s refer to convective and stable conditions, respectively),
Ccs{xr,yr,zp} is the contribution from terrain-following state, / is the plume state weighting
function, {xr ,yr,zr} is the coordinate representation of a receptor (with zr defined relative to
stack base elevation), zp = zr - z, is the height of a receptor above local ground, and zt is the
terrain height at a receptor. Note that in flat terrain, zt - 0 , zp-zr, and the concentration
(eq. (48)) reduces to the form for a single horizontal plume. It is important to note that for any
41
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concentration calculation all heights (z) are referenced to stack base elevation. Figure 11
illustrates the relationship between the actual plume and AERMOD's characterization of it.
Actual Plume
Reflecting Surface
X
Receptor
Horizontal
Plume
State
Terrain
Responding
Plume State
Figure 11: AERMOD Two State Approach. The total concentration predicted by
AERMOD is the weighted sum of the two extreme possible plume states.
The formulation of the weighting factor requires the computation of Hc. Using the receptor
specific terrain height scale (hc) from AERMAP, Hc is calculated from the same algorithms
found in CTDMPLUS as:
rtc
l/2-u2{Hc}= \N2(hc-z)dz.
(49)
where u {Hc} is the wind speed at height Hc, and TV =
is the Brunt-Vaisala frequency.
The height scale, hc, characterizes the height of the surrounding terrain that most dominates the
flow in the vicinity of the receptor.
The weighting between the two states of the plume depends on the relationship between Hc
and the vertical concentration distribution at the receptor location. Assuming that the wind
42
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speed increases with height, Hc can be thought of as the level in the stable atmosphere where the
flow has sufficient kinetic energy to overcome the stratification and rise to the height of the
terrain. However, in determining the amount of plume material in the terrain-following state at a
receptor, it is only important to know the lowest height in the flow where the kinetic energy is
sufficient for a streamline to just maintain its height above the surface, i.e. terrain-following.
Whether it will be deflected further and reach the top of some specified hill is not important for
determining the amount of plume material in the terrain-following state for this receptor.
Venkatram et al. (2001) first proposed the idea that for real terrain, often characterized by a
number of irregularly-shaped hills, Hc should be defined in relation to a terrain-following height
at each receptor location. This is in contrast to the more classical definition where Hc is defined
in relation to the top of a single representative hill upon which may reside many receptor
locations.
In the AERMOD approach, plume height, receptor elevation, and Hc will determine how
much plume material resides in each plume state. For a receptor at elevation zt and an effective
plume at height he the height that the streamlines must reach to be in the terrain-following state is
zt+he . Therefore the terrain height of importance, /zc, in determining Hc is simply equal to this
local terrain-following height. Any actual terrain above hc= zt + he is of no consequence to the
concentration at the receptor. This receptor and plume dependent approach to computing Hc
assumes that there is sufficient terrain affecting the flow near the receptor to vertically force the
streamlines to the terrain-following level. If the actual surrounding terrain does not reach the
height of the terrain-following state, hc is calculated from the highest actual terrain height in the
vicinity of the receptor. Therefore, for any receptor, hc is defined as the minimum of the highest
actual terrain and the local terrain-following height. Given /zc, the dividing streamline height is
computed with the same integral formula found in the CTDMPLUS model.
The fraction of the plume mass below Hc (i.e., ^,) is computed as:
Cs{xr,yr,zr}dz
P
J0 Cs{xr,yr,zr}dz
where Cs{xr,yr,zr} is the concentration in the absence of the hill for stable conditions. In
convective conditions, Hc = 0 and (p p = 0.
As described by Venkatram et al. (2001), the plume state weighting factor/is given by
/ = 0.5(l +
-------
following state. For flat terrain, the contributions from the two states are equal, and are equally
weighted.
Figure 12 illustrates how the weighting factor is constructed and its relationship to the
estimate of concentration as a weighted sum of two limiting plume states.
Clot - f CHOHZ + (1-f) ^Ten-Res
Dividing
Streamline
Mass Above Hc
- 5fl
. J \ 1
Weightin8
•Horizontal Plume
Terrain Responding
Plume
Figure 12: Treatment of Terrain in AERMOD. Construction of the weighting factor used in
calculating total concentration.
The general form of the expressions for concentration in each term of eq. (48) for both the
CBL and the SBL can be written as follows:
,y,z} = (Qlu)py{y;x}P2{z;x},
(51)
where Q is the source emission rate, u is the effective wind speed, andpy andpz are probability
density functions (pdf) which describe the lateral and vertical concentration distributions,
respectively. AERMOD assumes a traditional Gaussian pdf for both the lateral and vertical
distributions in the SBL and for the lateral distribution in the CBL. The CBL's vertical
distribution of plume material reflects the distinctly non-Gaussian nature of the vertical velocity
44
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distribution in convectively mixed layers. The specific form for the concentration distribution in
the CBL is found in eq. (54) which uses the notation Cc {xr, yr, zr}. Similarly, in the SBL, the
concentration takes the form of eq. (67) and used the notation Cs {x^ yr zr}.
AERMOD simulates five different plume types depending on the atmospheric stability and
on the location in and above the boundary layer: 1) direct, 2) indirect, 3) penetrated, 4) injected
and 5) stable. All of these plumes will be discussed, in detail, throughout the remainder of this
document. During stable conditions, plumes are modeled with the familiar horizontal and
vertical Gaussian formulations. During convective conditions (L
-------
downdrafts, the ensemble average has a general downward trend. Since downdrafts are more
prevalent the average velocity of the downdrafts is correspondingly weaker than the average
updraft velocity to insure that mass is conserved. In AERMOD, a skewed vertical velocity pdf is
modeled using a bi-Gaussian distribution, which has been shown to be a good approximation to
laboratory convection tank data (Baerentsen and Berkowicz 1984). In contrast to the vertical
component, the lateral velocity pdf is approximately Gaussian (Lamb 1982), and this pdf and the
resulting concentration distribution, F are assumed to be Gaussian.
Instantaneous Plume
Ensemble - Averaged Plume
Zi
Figure 13: Instantaneous and corresponding ensemble-averaged plume in the CBL
In addition to the non-Gaussian Fz, AERMOD has the following features. For buoyant
releases, there is no "final" plume rise assumed. Instead, the plume or particle trajectories are
determined by the addition of a distance-dependent plume rise and the random vertical
displacement caused by the vertical distribution of w. Ground level concentrations first appear
when the negative or downdraft velocities are sufficiently large to overcome the plume rise
velocity and carry plume sections to the surface. The direct transport of plume material to the
46
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ground is treated by the "direct" source located at the stack. That is, the direct source treats that
portion of the plume's mass to first reach the ground, and all subsequent reflections of the mass at
z = zi and 0 (where zi is the mixed layer height in the CBL (Cimorelli et al., 2004). For plume
segments or particles initially rising in updrafts, an "indirect" or modified-image source is
included (above the mixed layer) to address the initial quasi-reflect! on of plume material at z = zt,
i.e., for material that does not penetrate the elevated inversion. This source is labeled "indirect"
because it is not a true image source (i.e., as is found in models such as ISC) - the plume is not
perfectly reflected about zt. Thus, the indirect source treats that portion of the plume's mass that
first reaches zt and all subsequent reflections of that particular mass at z = 0 and zt, For the
indirect source, a plume rise (A/7,) is added to delay the downward dispersion of material from the
CBL top (see Figure 14); this mimics the plume's lofting behavior, i.e., the tendency of buoyant
plumes to remain temporarily near zt and resist downward mixing. For non-buoyant sources the
indirect source reduces to the first image source (as found in ISCST3) resulting from the first
reflection at z = zt. Additionally, a "penetrated" source or plume (above the CBL top) is included
to account for material that initially penetrates the elevated inversion but is subsequently
reentrained by and disperses in the growing CBL.
Reflection if
From Buoyancy Non-Buoyant v
Figure 14: AERMOD's Three Plume Treatment of the CBL
47
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In line with the above concepts there are three main mathematical sources that contribute to
the modeled concentration field: 1) the direct source (at the stack), 2) the indirect source, and 3)
the penetrated source. The strength of the direct source isfpQ, where Q is the source emission
rate and^, is the calculated fraction of the plume mass trapped in the CBL (0
-------
plume buoyancy (vbuoy\ and 3) the mean updraft (w;) or downdraft (w2) velocity. The mean
height of each trajectory zcl or zc2, can be found by averaging eq. (53). These parcel (or
particle) height distributions are thus related to concentration and are characterized by ozl (=
owlx/u) and oz2 (= aw2x/u), the standard deviations of the two concentration distributions
comprising the bi-Gaussian form as derived in Weil et al. (1997).
Up-draft Plume
Down-draft
Plume
y
~ f (awl)
Figure 15: AERMOD's pdf approach for plume dispersion in the CBL.
AERMOD approximates the skewed distribution by superimposing two
Gaussian distributions, the updraft and downdraft distributions.
Figure 16 compares the bi-Gaussian pdf with the Gaussian form, which is symmetric about
w = 0. As can be seen, for the negative and positive tails of the distributions, the bi-Gaussian pdf
is biased towards smaller and largerpw values, respectively, than the Gaussian. In addition, for
the bi-Gaussian forms, approximately 60% of the area under the/?w curve is on the negative side
of the w axis and approximately 40% on the positive side. This is consistent with the results of
numerical simulations and field observations (Lamb 1982; Weil 1988a).
49
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0.6
0.4 -
0.2 -
-4
-2
0
w
cr,.
Figure 16: Probability density functon of the vertical velocity. While the Gaussian
curve is unskewed the bi-Gaussian curve has a skewness of S= 1.
In the pdf approach used here (Weil et al. 1997), there are, as mentioned in the previous
section, three primary sources that contribute to the modeled concentration field: 1) the "direct"
or real source at the stack, 2) an "indirect" source that the model locates above the CBL top to
account for the slow downward dispersion of buoyant plumes that "loft" or remain near, but
below, Zj, and 3) a "penetrated source" that contains the portion of plume material that has
penetrated into the stable layer above zt. The direct source describes the dispersion of plume
material that reaches the ground directly from the source via downdrafts. The indirect source is
included to treat the first interaction of the "updraft" plume with the elevated inversion - that is,
for plume sections that initially rise to the CBL top in updrafts and return to the ground via
downdrafts. Image sources are added to treat the subsequent plume interactions with the ground
and inversion and to satisfy the zero-flux conditions atz = 0 and at z = zt. This source plays the
same role as the first image source above zt in the standard Gaussian model, but differs in the
treatment of plume buoyancy. For the indirect source, a modified reflection approach is adopted
in which the vertical velocity is reflected at z = zt, but an "indirect" source plume rise A/7, is added
to delay the downward dispersion of plume material from the CBL top. This is intended to mimic
the lofting behavior. The penetrated source is included to account for material that initially
penetrates the elevated inversion but subsequently can reenter the CBL via turbulent mixing of
50
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the plume and eventual reentrainment into the CBL. Figure 14 illustrates this three plume
approach; a fundamental feature of AERMOD's convective model. In AERMOD, the total
concentration (Cc) in the CBL is found by summing the contribution from the three sources. For
the horizontal plume state, the Cc is given by
Cc{Xr>yr>Zr}= CAXr,yr,Zr}+Cr{Xr,yr,Zr}+Cp{Xr,yr,Zr}, (54)
where Cd, Cn and Cp are the contributions from the direct, indirect and penetrated sources,
respectively. The total concentration for the terrain-following state has the form of eq. (54) but
with zr replaced by zp.
The fraction^ of the source material that remains trapped in the CBL is found from
A/7,
A/T
if A/7, < 0.5A/7eg
if A/7, > 1.5A/7eg
if 0.5AA < A/7, < L5AA .
(55)
eq
where A/zA = zt - hs, and A/z is the equilibrium plume rise in a stable environment. The A/7,
has the form Berkowicz et al. (1986)
•eq
(56)
where: Ps = Fb /uN^khl is the penetration parameter, and the stack buoyancy flux (Fb), and
Brunt-Vaisala frequency (Nh) are given respectively by
T,
(57)
and
g dO
0{z,}
(58)
Here, u is the wind speed at stack height; g is the gravitational acceleration; ws, rs, and Ts are the
stack exit velocity, radius, and temperature, respectively; and 6is the ambient potential
temperature. The Nh in eq. (58) is based on the potential temperature gradient in the elevated
stable layer, provided by AERMET, capping the CBL. In general this layer is within zt and zt +
500m.
51
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5.2.1 DIRECT SOURCE CONTRIBUTION TO CONCENTRATION CALCULATIONS IN
THECBL
Following Weil et al. (1997), the concentration due to the direct plume is given by:
f I \2\ ( I \2\
Ca{xr,yr,z} =
where
Of,
j=l m=0 & zj
exp
= h
+ exp
2a:
,(59)
(60)
u is the wind speed at stack top, Fy I = . exp~r\ I is the lateral distribution function with
meander (discussed in Section 5.4), Wj = a} w* (a,, is defined below in eq.(62), A/z^is the direct
source plume rise calculated from eq. (91), and z = zr and zp in the horizontal and terrain-
following states, respectively. Here, Tdj and ozj are the effective source height and vertical
dispersion parameter corresponding to each of the two distributions in eq. (53). The subscript y is
equal to 1 for updrafts and 2 for downdrafts. The lateral and vertical dispersion parameters (oy and
azj), resulting from the combined effects of ambient, buoyancy-induced, and building-induced
turbulence are calculated as discussed in Sections 5.5.1.1 and 5.5.1.2 respectively. Here, ozj (with
j = 1 or 2) is the vertical dispersion parameter corresponding to each of the Gaussian distributions
used in the bi-Gaussian pdf, (see Section 5.5.1.2) and Ap the weighting coefficient for each
distribution in eq.(53), is calculated from Weil et al. (1997) as
W,
a,
a2 - al
(61)
where
(62)
52
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Recall that 0.\z,
for Hp{x}<0.lz,
(63)
where,
\+R2
f3= l+R2
S = -W = Skewness factor,
(64)
and R is assumed to be 2.0 (Weil et al., 1997). Likewise, the term wj x/u in eq. (60) follows
from the Fz derivation and the Wj appearing in the bi-Gaussian form (see discussion of eq. (53)) .
The lateral dispersion parameter (ay,) is calculated from eq. (75) (Weil et al., 1997).
In eq. (59), an image plume is used to satisfy the no-flux condition at the ground, i.e., an
image plume from a source at z = -hs, which results in the exponential terms containing z + Vd]o
the right-hand side of eq. (59). This image source results in a positive flux of material at z = zt,
and additional image sources are introduced at z = 2 z,• + hs, -2 zi - hs, 4zf + hs, -4zf - hs, etc. to
satisfy all the subsequent no-flux conditions occurring at z = 0 and zt.
5.2.2 INDIRECT SOURCE CONTRIBUTION TO CONCENTRATION CALCULATIONS
IN THE CBL
The concentration due to the indirect source is calculated from:
C,{x,,yr,z} =
Of,
2 oo
j=l m=\ '
exp
(z+Vrj -2mz^
2
-------
5.2.3 PENETRATED SOURCE CONTRIBUTION TO CONCENTRATION
CALCULATIONS IN THE CBL
For the penetrated source the concentration expression has a Gaussian form in both the
vertical and lateral directions. The concentration due to this source is given by:
/ / \2\ ( I \1\
Cp{xr,yr,z} =
Q(l~ff)
;
U(7
zp
exp
(z- hep + 2mzjeff)
2(7
zp
exp
2(7
zp
(66)
where zieffis the height of the upper reflecting surface in a stable layer (see Section 5.3) and z is
either zr for the horizontal plume state or zp for the terrain-following state. The vertical dispersion
parameters (ozp) are calculated as described in Section 5.5.1.2.
The penetrated plume height, hep, is taken as the height of the plume centroid above the
mixed layer and is calculated from eq. (94).
5.:
Concentrations in the SBL
For stable conditions, the AERMOD concentration expression (Cs in eq. (48)) has the
Gaussian form, and is similar to that used in many other steady-state plume models (e.g., HPDM
(Hanna and Paine 1989)). The Cs is given by
C,{xr,yr,z} =
Q
exp
\z-h- 2mz,.
2(7,
+ exp
\z+ h + 2mz,
)2
2(7,
,(67)
where zieffis the effective mechanical mixed layer height, ozs is the total vertical dispersion in the
SBL (see discussion in Section 5.5), and hes is the plume height (i.e., stack height plus the plume
rise - see Section 5.6.2).
Above the mechanical mixed layer height, zim (eq. (26)), the turbulence level is generally
expected to be small and thus supports little vertical mixing of the plume. AERMOD is designed
(in the SBL) with an effective mixing lid, zieffi that retards but does not prevent plume material
from spreading into the region above the estimated mechanical mixed layer. When the final
plume height is well below zim, the plume does not interact with zim. When the plume is below zim
yet the "upper edge" (plume height plus 2.15 azs) of the stabilized plume reaches zim, the effective
mixing lid is allowed to increase and remain at a level near the upper edge of the plume. In this
way, AERMOD allows the plume to disperse downwards, but where the turbulence aloft is low,
vertical plume growth is limited by an effective reflecting surface that is folding back only the
extreme tail of the vertical plume distribution. There is no strong concentration doubling effect as
occurs with reflections from an assumed hard lid. Downward dispersion is primarily a factor of
aw averaged from the receptor to the plume height. If the plume height is above the mixed layer
height, the calculation of the effective aw will include regions in which aw is likely to be small.
This, in effect, retards plume growth by an amount dependent upon how much of the plume is
54
-------
above zim. Therefore, whether the plume is above or below zim, the region of low turbulence above
zim will have an appropriate effect on the concentration distribution within the mixing layer.
When the plume buoyancy carries the rising plume into the relatively non-turbulent layer
above zim, the reflecting surface is still placed at 2.15 ozs above the effective plume height because
there will be plume spread due to plume buoyancy and downward mixing is still important.
Therefore, in the SBL, plume material is assumed to reflect off an elevated surface which is
defined as:
z,eff = MAX\(hes + 2.\5azs{hes}' zj]. (68)
where ozs in eq. (68) is determined from equations found in Section 5.5.1.2 with owT and u
evaluated at hes; not as an effective parameter. It is important to note that zieff depends on
downwind distance since ozs is distance dependent. In fact, as eq. (68) suggests, this effective
reflecting surface is only folding back the extreme tail of the upward distribution. Also, if the
height of the receptor zr > z^then the effective reflecting surface is not considered. This
approach is also implemented for the penetrated source. For the penetrated and injected sources
zjeff is calculated using eq. (68) with ozs and hes replaced by ozp and //^respectively.
5.4 Treatment of Lateral Plume Meander
In AERMOD we include the effect that lower-frequency, non-diffusing eddies (i.e., meander)
have on plume concentration. Meander (or the slow lateral back and forth shifting of the plume)
decreases the likelihood of seeing a coherent plume after long travel times. This effect on plume
concentration could best be modeled with a particle trajectory model, since these models estimate
the concentration at a receptor by counting the number of times a particle is seen in the receptor
volume. However, as a simple steady state model, AERMOD is not capable of producing such
information. AERMOD accounts for meander by interpolating between two concentration limits:
the coherent plume limit (which assumes that the wind direction is distributed about a well-
defined mean direction with variations due solely to lateral turbulence) and the random plume
limit, (which assumes an equal probability of any wind direction).
For the coherent plume, the horizontal distribution function (FyC) has the familiar Gaussian
form:
F „-•
where oy is the lateral dispersion parameter (see Section 5.5). For the random plume limit, the
wind direction (and plume material) is uniformly distributed through an angle of 2n. Therefore,
the horizontal distribution function FyR takes the simple form:
<70>
55
-------
where xris radial distance to the receptor. Although the form of the vertical distribution function
remains unchanged for the two plumes, its magnitude is based on downwind distance for the
coherent plume and radial distance for the random plume.
Once the two concentration limits (Cch - coherent plume; CR - random plume) have been
calculated, the total concentration for stable or convective conditions (Ccx) is determined by
interpolation. Interpolation between the coherent and random plume concentrations is
accomplished by assuming that the total horizontal "energy" is distributed between the wind's
mean and turbulent components. That is,
Cc,, = Cch (l - a] /a2) + CR (a2 /a2 ) (71)
where ah2 is a measure of the total horizontal wind energy and o2 is a measure of the random
component of the wind energy. Therefore, the ratio o2lo^ is an indicator of the importance of the
random component and can therefore be used to weight the two concentrations as done in eq.
(71)
The horizontal wind is composed of a mean component u , and random components ou and
ov. Thus, a measure of the total horizontal wind "energy" (given that the alongwind and
crosswind fluctuations are assumed equal i.e., ou = <7V), can be represented as
ah2 = 2av2 + u2 (72)
where u = (u2 - 25;2)1'2 . The random energy component is initially 2<7V2 and becomes equal to o2 at
large travel times from the source when information on the mean wind at the source becomes
irrelevant to the predictions of the plume's position. The evolution of the random component of
the horizontal wind energy can be expressed as
a2 = 2a2 + u2l- exp (73)
where Tr is a time scale (= 24 hrs) at which mean wind information at the source is no longer
correlated with the location of plume material at a downwind receptor. Analyses involving
autocorrelation of wind statistics (Brett and Tuller 1991) suggest that after a period of
approximately one complete diurnal cycle, plume transport is "randomized." Equation (73)
shows that at small travel times, o-2 = 2<7V2, while at large times (or distances) a2 = 25;2 + u2 ,
which is the total horizontal kinetic energy (ah2) of the fluid. Therefore, the relative contributions
of the coherent and random horizontal distribution functions (eq. (71)) are based on the fraction of
random energy contained in the system (i.e.,o-r2/o-h2 ).
The application of eq. (71) is relatively straight forward in the SBL. Since concentrations in
the SBL are represented as a single plume, Cs can be calculated directly from eq. (71). By
contrast for convective conditions the situation is complicated by the inclusion of plume
penetration. Since a2 depends on the effective parameters (eq. (73)), the concentration weighting
factors found in eq. (71) will be different for the non-penetrated and penetrated plumes of the
-------
CBL. This is handled by combining the penetrated and non-penetrated weighting factors
and Or/°h NP) mto a single effective factor (<7//<7/ CBL). That is,
CBL
(74)
NP
where ^ (see eq. (55)) is the fraction of the source material that remains trapped in the CBL.
Using eq.(74), concentrations in the CBL (Cc) are calculated from eq. (71) with (or2lo^} replaced
by (ar2l°h\cBi)-
5.5 Estimation of Dispersion Coefficients
The overall standard deviations (oyz) of the lateral and vertical concentration distributions
are a combination of the dispersion (represented by oya, oza) resulting from ambient turbulence,
and dispersion (<76) from turbulence induced by plume buoyancy. Building induced dispersion is
not included here since a separate approach (see Section 5.5.3) is taken for situations in which
building wake effects contribute to the total dispersion. Dispersion induced by ambient
turbulence is known to vary significantly with height, having its strongest variation near the
earth's surface. Unlike present regulatory models, AERMOD has been designed to account for
the effect of variations of turbulence with height on dispersion through its use of "effective
parameters" (see Section 4.2), which are denoted by an overscript tilde, e.g., ffwT .
AERMOD treats vertical dispersion from ambient turbulence (aza) as a combination of a
specific treatment for surface dispersion and the more traditional approach based on Taylor
(1921) for elevated dispersion. Using this approach good agreement with observations was
achieved in the SBL. However, the results in the CBL indicated that the treatment of lateral
dispersion near the surface was problematic. This problem was corrected through the
development of an empirical relationship for oya near the surface using the full (CBL and SBL)
Prairie Grass data set. A description of the resulting formulations for oya & oza is presented in the
next section.
The approach used to combine the above contributions to dispersion assumes that the effects
are independent of one another. Thus, the total dispersion coefficients, for situations that do not
include building downwash effects, are calculated from the following general expression (Pasquill
and Smith 1983):
(75)
where the subscripts y and z are deleted from ob because oyb is assumed equal to ozb. With the
exception of the CBL's penetrated source the form of eq. (75) applies to all source dispersion in
both the CBL and SBL such that oyiZ becomes oySjZS and oyjStZj and oyajZa becomes 0yaSjZas and oyajSjZaj
for the SBL and CBL, respectively. For the penetrated source, the total dispersion is assumed to
include ambient and buoyancy induced turbulence only; building wakes are assumed to have little
influence. For the injected source, the total dispersion is calculated as if the source were in the
SBL.
57
-------
A comment on notation: eq. (75) applies for both lateral and vertical dispersion in the SBL
and CBL. In references to the SBL, oz appears as ozs in the dispersion equation; oza appears as
ozas. In reference to the CBL, oz appears as ozj for the dispersion expression applicable to the
direct and indirect sources and oza appears as oaj; for the penetrated source oz appears as ozp in the
dispersion expression.
5.5.1 DISPERSION FROM AMBIENT TURBULENCE
5.5.1.1 Lateral Dispersion from Ambient Turbulence
In general terms, the ambient component of the lateral dispersion is based upon Taylor (1921)
such that:
a x
v
27V
Lyj
P (76)
where/? = 0.5, u is the wind speed, ov is the root-mean-square lateral turbulence velocity, and TLy
is the Lagrangian integral time for the lateral turbulence. Application of eq. (76) in a preliminary
version of AERMOD yielded poor concentration estimates in comparison to those found in the
Prairie Grass field experiments (Barad 1958). Specifically, the lateral spread was not well
matched. Therefore, the lateral dispersion expression was reformulated to allow for an empirical
fit to the Prairie Grass data.
Using an approach similar to that of Venkatram et al. (1984) TLy is found to be l/ov where / is
an appropriate length scale for lateral turbulence. Equation (76) can be written in terms of the
non-dimensional downwind distance X and a non-dimensional height scale «as:
aX)
(77>
where x(= avxluz^ is the non-dimensional distance with u and ov given by effective parameters,
where a = zt //, and zt is the mixed layer height.
Based on a preliminary comparison of oya (eq. (77)) with selected stable and convective cases
from the Prairie Grass experiment (Barad 1958) a was found equal to 78 and/? equal to 0.3. As
such, a is treated as a fitting parameter. In later comparisons against the full Prairie Grass data
set (Figure 17), eq. (77) tended towards the lower envelope of this widely scattered data (i.e.,
lateral dispersion estimates are on the lower end of the distribution of measurements). However,
the preliminary values of a (= 78) and/? (= 0.3) produced good agreement between AERMOD
concentration predictions and observations (Erode 2002). Therefore, these preliminary values
were retained in AERMOD, and eq. (77) applies for the calculation of oya for all plumes in both
the SBL and CBL.
58
-------
Prairie Grass Data
1/(1+78X)03
0.001
0.01 0.1
X=avxr/uzj
10
Figure 17: Lateral spread (oy) as a function of non-dimensional distance
(X). The data is taken from the Prairie Grass experiment (Barad
1958).
The ambient component of the lateral dispersion for the penetrated source, i.e. a source which
has been released below zt, but penetrates above, is calculated using eq. (77) with hes set equal to
hep (the height of the penetrated source). However, for the injected source, i.e. source released
above zt, no substitution is needed since these sources are modeled as a stable source.
To account for the increase in the turbulence length scale and hence the Lagrangian time scale
with release heights greater than that at Prairie Grass, a is scaled as follows:
(78)
59
-------
where ZPG = 0.46 m (Prairie Grass release height), andzmax = MAX\z;zPG\. To insure that «does
not become unrealistically large for surface releases, z is not allowed below ZPG (i.e., 0.46 m). In
the SBL, z = hes; in the CBL z = hs; for penetrated sources, z = hep. . As a becomes small for
large release heights, oya would tend to grow linearly with downwind distance.
5.5.1.2 Vertical Dispersion from Ambient Turbulence
For sources in the SBL (and for sources in the CBL that are emitted directly into the stable
layer above the mixed layer), the ambient portion of the vertical dispersion (azas) is composed of
an elevated (&zes) and near-surface (&zgs) component. For hes < zt simple interpolation provides a
smooth transition between the two components.
(79)
For hes > zi azas is set equal to azes. The expressions for calculating hes are found in Section 5.6.2.
It should be noted, for sources in the SBL, that ozas is the specific form of the ambient portion of
the vertical dispersion (i.e., oza in eq. (75)).
In the SBL, the elevated portion of the vertical dispersion follows the form of eq. (76):
1/2
(80)
where owT is the vertical turbulence due to the mechanical mixing (Cimorelli et al., 2004).
As with the lateral component, the Lagrangian time scale (TLzs) for the vertical turbulence can
be written in the form (Venkatram et al. 1984)
TLZS = 4- (81)
The length scale / is an interpolation between the limiting length scales for neutral conditions,
/„ = 036hes , and stable conditions ls = 0.27
1 1 1
l-T+r <82>
where ln = 036hes and ls = 0.27
-------
°zes =
036h
(83)
Finally, to complete the description of eq. (79), the surface portion of vertical dispersion (crzgs)
in the SBL, is calculated from Venkatram (1992) as
-1/3
For the direct and indirect sources in the CBL, the ambient portion of the vertical dispersion
(oza of eq. (75)) is denoted as ozaj (j = 1, 2) to distinguish between updrafts and downdrafts. ozaj is
composed of an elevated (azej) and surface (azg) portion and is given by
°laj = °le] + °zg> (85)
where the elevated portion (azej) is obtained from Weil et al. (1997)as
a = „ ^k^ (86)
"J b u ' ^ '
where owj is a parameter in the bi-Gaussian pdf (eq.(53)).
The expression ab = MinW.6+ 4Hp/zt, l.OJ is designed to be 1.0 above the surface layer
(Hp > 0.1 z;) and to otherwise match Venkatram's (1992) result for vertical dispersion from a
surface source in a neutral boundary layer.
For the CBL, the vertical dispersion from a source within the surface layer (Hp{x] < 0.1 z,) is
parameterized by
-™(Hp/}}-(u*/rf-(x2/\L\} <87>
where bc = 0.5, u*. is the friction velocity, and L is the Monin-Obukhov length; above the surface
layer (Hp> O.lz;), ozg is assumed to equal zero. In the limit of a surface release (Hp = 0), the
parameterization of eq. (87) follows the form suggested by Venkatram (1992) for vertical
dispersion in the unstable surface layer; i.e., crz K (ut/u}2 x2/\L\. The parameterization is designed
to: 1) agree with Venkatram's result in the limit of a surface release, 2) provide good agreement
between the modeled and observed concentrations from the Prairie Grass experiment (Paine et al.,
2001), and 3) decrease with source height in the surface layer and ultimately vanish for above the
61
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surface layer. The constant bc was chosen to satisfy the second design requirement. In the limit
of a neutral boundary layer ozg is equal to zero.
The total vertical dispersion for the penetrated source ozp (= oz in eq. (75)) is a combination of
both ambient and buoyancy effects. The ambient portion of the vertical dispersion for the
penetrated source contains only an elevated component ozes (= azss) since it is assumed to be
decoupled from the ground surface by its location above zt and therefore unaffected by the
underlying surface. The ambient vertical dispersion for the penetrated source is computed as the
elevated portion of a stable source (ozes of eq. (83) ) with N = 0 and with no contribution from the
surface component. The Brunt-Vaisala frequency, N, is set to zero because the penetrated plume
passes through the well mixed layer (where N =0) prior to dispersing to receptors within the
mixed layer.
5.5.2 BUOYANCY INDUCED DISPERSION (BID) COMPONENT OF oy AND oz
For all plumes, the buoyancy induced dispersion (BID) is calculated following Pasquill
(Pasquill 1976) and Weil (1988b) as
0.4A/7
' (88)
where A/7 is the plume rise appropriate for each of the plume types (direct, indirect, penetrated,
and stable plumes). The direct source plume rise is calculated from eq. (91), stable plume rise
(A/7, ) is calculated from eq. (95) and the plume rise for the penetrated source t^hp = hep - hs
(where hepis calculated from eq. (94)).
5.5.3 TREATMENT OF BUILDING DOWNWASH
AERMOD incorporates the Plume Rise Model Enhancements (PRIME) (Schulman et al.
2000) algorithms for estimating enhanced plume growth and restricted plume rise for plumes
affected by building wakes(U.S.Environmental Protection Agency 1995). PRIME partitions
plume mass between a cavity recirculation region and a dispersion enhanced wake region based
upon the fraction of plume mass that is calculated to intercept the cavity boundaries. These
boundaries are established from estimates of the locations of the lateral and vertical separation
streamlines. Dispersion of the recirculated cavity mass is based on building geometry and is
assumed to be uniformly mixed in the vertical. At the boundary of the cavity region, cavity mass
is emitted into the wake region. Here, it is combined with plume mass that was not captured by
the cavity and dispersed at an enhanced rate based on source location, release height and building
geometry. The enhancement of turbulence within the wake decays gradually with distance,
allowing for a smooth transition to ambient levels of turbulence in the far-field. A probability
density function model and an eddy diffusivity model (Weil 1996) are used for dispersion
estimates in the near-wake and far-wake regions, respectively. Plume rise, for sources influenced
by a building, is estimated using a numerical model that includes effects from streamline
deflection near the building, vertical wind speed shear, enhanced dilution from the turbulent wake
62
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and velocity deficit. In general, these building induced effects act to restrict the rise that the
plume would have in the absence of the building.
PRIME was originally designed (Schulman et al., 2000) to enhance plume growth using
Pasquill Gifford (PG) dispersion (Pasquill 1961; Gifford 1961). AERMOD's estimate of plume
growth is based on dispersion parameters derived from profiles of turbulence (see Section 4), not
from radiation base turbulence surrogates as is done in the PG approach. A basic design tenet for
incorporating PRIME into AERMOD was to be as faithful as possible to the PRIME formulation
while ensuring that 1) AERMOD's ambient dispersion was used in place of PG dispersion and 2)
far beyond the wake region, where building influences should be insignificant, concentrations
approach the AERMOD estimate. Therefore, within the wake, PRIME algorithms are use
exclusively to calculate concentration with AERMOD-derived ambient turbulent intensities as
input. To insure a smooth transition between concentrations estimated by PRIME, within the
wake, and AERMOD estimates in the far field, concentrations beyond the wake are estimated as
the weighted sum of the two calculations. That is, beyond the wake the total concentration (Ctotaj)
is calculated as follows:
= yC +(\- v\C
/ ^Prime \ / / .
Total
-AERMOD
(89)
where Cprime is the concentration estimated using the PRIME algorithms with AERMOD-derived
meteorological inputs, CAERMOD is the concentration estimated using AERMOD without
considering building wake effects, and /the weighting parameter. The weighting parameter, 7, is
designed such that the contribution from the PRIME calculation decreases exponentially with
vertical, lateral and downwind distance from the wake. It is calculated as follows:
y = exp
2\
2a*
GXP
2\
GXP
7.\
(90)
where x is the downwind distance from the upwind edge of the building to the receptor, y is the
lateral (crosswind) distance from the building centerline to the receptor, z is the receptor height
above ground, oxg is longitudinal dimension of the wake, oyg is the distance from the building
centerline to lateral edge of the wake, and ozg is the height of the wake at the receptor location.
5.6 Plume Rise Calculations in AERMOD
5.6.1 PLUME RISE IN THE CBL
The plume rise for the direct source is given by the superposition of source momentum and
buoyancy effects following Briggs (1984).
63
-------
where Fm = \T/TsJw2srf is the stack momentum flux, Fb = gwsr2 (AT/T^ J is the stack buoyant
flux, rs is the stack radius corrected for stack tip downwash, and fi, (= 0.6) is an entrainment
parameter. It should be noted that up is the wind speed used for calculating plume rise. In the
CBL up is set equal to u{hs}.
As shown in Figure 14, the indirect plume, which is included to treat the no flux condition at
z = zh is modeled as a reflected version of the direct plume with an adjustment (A/z,) to the
reflected plume height to account for the delay in vertical mixing due to plume lofting at the top
of the boundary layer. That height adjustment is given by
X (92)
py
where ryand rzare the lofting plume half-widths in the lateral and vertical directions, up is the
wind speed used for plume rise, and ar = 1.4. The produce of cross-wind dimensions of the
assumed elliptical plume is calculated from Weil et al. (1997) as
(93)
where rh = J32 \zi - h\,p2 = 0.4, Ay = 2.3, and ae = 0.l (dimensionless entrainment parameter).
For a derivation and discussion of A/z, see Weil et al. (1997).
The height that the penetrated source achieves above zt is calculated as the equilibrium plume
rise in a stratified environment and is determined by the source buoyancy flux, the stable
stratification above zt, and the mean wind speed. In line with Weil et al. (1997), the penetrated
source plume height, hep, is taken as the centroid of plume material above the inversion. For
complete penetration (fp = 0} hep = hs+A.heq. However, for partial penetration (fp > 0), hep is
chosen as the average of the heights of the upper plume edge hs + 1.5 A.heq and zt, or
(94)
where A.heq is defined in eq. (56).
5.6.2 PLUME RISE IN THE SBL
Plume rise in the SBL is taken from Weil (1988b), which is modified by using an iterative
approach which is similar to that found in Perry et al. (1989). When a plume rises in an
atmosphere with a positive potential temperature gradient, plume buoyancy decreases because the
ambient potential temperature increases as the plume rises; thus, plume buoyancy with respect to
the surroundings decreases. To account for this, the plume rise equations have to be modified.
With this modification, AERMOD computes stable plume rise, &hs, from Weil et al. (1988b) as
64
-------
1/3
A/7 = 2.66
b
N Fm \N'x\ N'x
-sin + 1- cos
(95)
where N' = 0.77V with N given by eq. (58). TV and u are evaluated initially at stack height. Once
plume rise has been computed, subsequent plume rise estimates are made (iteratively until
convergence) by averaging the u and TV values at stack top with those at hs + A/^/2 . Equation (95)
is used for downwind distances that are less than the distance to final rise (xj). Beyond xfi A/z,
remains constant. The distance at which the stable plume reaches its maximum rise is given
by
UP t-w]
Xf = arctan ~~ — ' (96)
Upon substituting eq. (96) for x in eq. (95) the maximum final rise of the stable plume
&hs{xf} reduces to:
( F r
M,{X} = 2.66- . (97)
As with eq. (95), the velocity, up, and TV in eqs. (97) are evaluated initially at stack height and
then iteratively.
When the atmosphere is close to neutral, the Brunt Vaisala frequency, N, is close to zero, and
eq.(95) can predict an unrealistically large plume rise. Under, these circumstances, plume rise is
limited by atmospheric turbulence. This happens when the rate of plume rise under neutral
conditions is comparable to aw. Under these conditions, stable plume rise (eq. (97)) is limited by
the neutral rise calculated from Weil (1985) as
5 (98)
where the neutral length scale Ln = Fb (u ul\ .
As the wind speed approaches zero, eq. (95) again predicts unrealistic values. In these near-
calm conditions the stable plume rise (eq. (97)) is limited by the calm rise expression that is based
on the work of Morton et al. (1956) and Briggs (1969) such that,
4/71/4
= -- <">
Finally, the stable plume rise is limited by a calculation of the unstable rise (see Section
5.6.1).
65
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5.7 Source Characterization
AERMOD gives the user the ability to characterize a source as either a point, an area, or a
volume. AERMOD additionally has the capability of characterizing irregularly shaped area
sources.
Point sources are characterized exactly as in the ISC3 model (U.S.Environmental Protection
Agency 1995). The input to the model includes the location, elevation, emission rate, stack
height, stack gas temperature, stack gas exit velocity, and stack inside diameter. The temperature,
exit velocity, and diameter are required for plume rise calculations.
Similarly, volume sources require the same input as the ISC3 model. This includes the
location, elevation height (optional), height of release, emission rate, the initial lateral plume size
(oy) and initial vertical plume size (oz). AERMOD differs from ISC3 in the treatment of volume
sources only in how the initial plume size is implemented. Where ISC3 uses the virtual source
technique to account for initial plume size, AERMOD adds the square of the initial plume size to
the square of the ambient plume size:
°l = °2yl +
-------
1000 up to 2,000,000. These data represent the maximum urban effect for each city since they
were collected during ideal conditions of clear skies, low winds, and low humidities. An
empirical fit to the data yields the following relationship
Ar
max
0.11n[%J + 1.0|, (101)
where &Tmax = 12 °C, P0 = 2,000,000 (the city population associated with the maximum
temperature difference in Oke's data), and P is the population of the urban area being modeled.
Since the ambient nighttime temperature of an urban area is higher than its surrounding rural
area, an upward surface heat flux must exist in the urban area. It is assumed that this upward
surface heat flux is related to the urban-rural temperature difference through the following
relationship
Hu = apcpkTu_ru., (102)
where a is an empirical constant, pis the density of air, and cp is the specific heat at constant
pressure. This expression is analogous to the bulk transfer parameterization of heat flux over a
homogeneous surface (e.g., Businger (1973)),with a defined as the "bulk" transfer coefficient.
We chose a to ensure that the upward heat flux is consistent with maximum measured values of
the order of 0.1 m s"1 °C . Because kTu_r has a maximum value on the order of 10 °C, and w» is on
the order of 0.1 m s"1, a should have a maximum value on the order of 0.1. Although we assume
that a has a maximum (city center) value of about 0.1, AERMOD uses an effective value of a a
that is averaged over the entire urban area. Assuming a linear variation of a from 0 at the edge of
the urban area to about 0.1 at the center of the urban area results in an areal average equal to one-
third of that at the center (since the volume of cone is one-third of that of a right circular cylinder
of the same height). Therefore, AERMIC tested an area-averaged value of a equal to 0.03 against
the Indianapolis data. This choice for a is consistent with measured values of the upward heat
flux in Canadian cities reported by Oke (1973; 1982). The results of the developmental testing
indicated that this choice for a resulted in an adequate fit between observations and AERMOD-
predicted concentrations.
The mixing height in the nighttime urban boundary layer, ziu, is based on empirical evidence
presented in Oke (1973; 1982) that, in turn, suggests the following relationships:
zm * Rl/2 and R* Pl/\ (103)
where R is a measure of the city size and P is the population of the city. The first relationship is
based on the observed growth of the internal convective boundary layer next to shorelines
(Venkatram 1978). The second relationship implicitly assumes that population densities do not
vary substantially from city to city.
Equation (103) leads to the following equation for the nocturnal urban boundary layer height
due to convective effects alone:
^, ^ ^1/4
iuc h
67
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where ziuo is the boundary layer height corresponding to P0. Based on lidar measurements taken
in Indianapolis (1991), and estimates of ziu found by Bornstein (1968) in a study conducted in
New York city, ziuo is set to 400 m in AERMOD.
In addition, since effects from urban heating should not cause ziuto be less than the
mechanical mixing height, ziu is restricted from being less than zim. Therefore, the mixed layer
height for the nighttime urban boundary layer is computed as:
zm= MaX[zmc-zm\ (105)
Once the urban mixing height has been estimated, a surrogate convective velocity scale
(appropriate for the magnitude of convective turbulence present) is computed by substituting ziu
and Hu into the definitional equation for w*. (Deardorff 1970). That is,
/ \ 1/3
= SHU zluc
"
where wtu is the urban nighttime convective velocity scale and Tis the near-surface air
temperature.
Having estimated w*.u the turbulence in the nighttime urban can be enhanced using the
expressions found in Section 4.1.5. However, since for low level sources <7wrdepends primarily
on ut (see eqs. (34) and (35)) it is not possible to directly enhance owT for these sources using wtu.
Therefore, an effective friction velocity (u*eff) is developed as a surrogate for wtu in the lower
portion of urban PEL. We define w*e^as the friction velocity that is consistent with owm= owc atz
= Iz0. Assuming that z = Iz0 is always less 0. \ziuc, u*effis estimated by equating awc (eq. (35)) with
°wm (ecl- (37)) and solving for u*. Once w»^is found, the urban friction velocity for nighttime
conditions (w»H) is calculated as the maximum of w»^and w* (the rural and daytime urban friction
velocity).
Then using the enhanced velocity scales w»H and w*H, the nighttime convective portion of the
turbulence in the urban boundary layer is computed using the expressions turbulence found in
Section 4.1.5. That is, owc and owm are calculated from eqs. (35) and (37), respectively, with w»H
used in place of the daytime convective velocity scale (w») and w»H substituted for the rural w».
Furthermore, for consistency purposes, a urban nighttime Monin-Obukhov length is calculated
using eq. (8) with substitutions z/*H for w* andHu (eq. (102)) for//.
Finally, the total nighttime turbulence in the urban boundary layer is calculated as the sum (in
quadrature) of the convective and mechanical portions. With these enhanced levels, vertical
dispersion due to ambient turbulence (aza) in the urban boundary layer is calculated from eq. (83)
(the SBL formulation for oza ) with the urban PEL assumed to be neutral (i.e., N= 0). For the
lateral dispersion in the urban boundary layer, oya is calculated using the SBL formulation given
by eq. (76).
The potential temperature gradient in the night-time urban boundary layer is set equal to the
upwind rural profile (Section 4. 1 .3) for all heights above ziu, and is assumed to be equal to a small
positive value below zim i.e.,
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dz = 1(T5 for z < z.
/* 11 ,
d6/dz = rural value for z > ziu.
For plumes below ziu, the effective reflection surface is set equal to the height of the urban
boundary layer (i.e., zieff = ziu). Plumes that rise above ziu (hes > ziu) are modeled with a zieffthat is
calculated from eq. (68) with zim replaced by ziu. Plume rise in the urban stable boundary layer is
calculated from eqs. (95) - (99) with dd/dz, taken from eq.(107).
Use of this value for dd/dz provides an appropriate near-neutral plume rise formulation that is
expected within the nocturnal urban boundary layer. However, plume height in these conditions
is not allowed to exceed 1.25 ziu.
For daytime conditions (L < 0) in urban areas, AERMOD uses the same formulations as in
rural areas (i.e., no urban-related adjustments to boundary layer characteristics).
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6 List of Symbols
B0 Bowen ratio - ratio of the sensible to latent heat fluxes (dimensionless)
CAERMOD concentration estimated using AERMOD without considering building
wake effects (g m"3)
Cc,s{xr>yr>zr} concentration contribution from the horizontal plume state - convective and
stable (g m"3)
CCtS{xr,yr,zp} concentration contribution from the terrain-following plume state -
convective and stable (g m"3)
C^x^y^z,,} total concentration (CBL) (g m"3)
Cyr>zr} concentration contribution from the direct source (CBL) (g m"3)
Cp{xr,yr,zr} concentration contribution from the penetrated source (CBL) (g m"3)
Cr{xryrzr} concentration contribution from the indirect source (CBL) (g m"3)
Cs{xr,y,,zr} total concentration (SBL) (g m"3)
Cr{xr>y^zr} total concentration (CBL) (g m"3)
Cch concentration from the coherent plume used in meander calculations (gm"3)
CR concentration from the random plume used in meander calculations (g m"3)
CD neutral drag coefficient (cal g"1 "C"1)
Cprime concentration estimated using the PRIME algorithms with AERMOD-
derived meteorological inputs (g m"3)
cp specific heat at constant pressure (= 1004 J g"1 K"1)
Fb plume buoyancy flux (m4 s3)
Fy total horizontal distribution function - with meander (m"1)
FyC horizontal distribution function for a coherent plume (m"1)
FyR horizontal distribution function for a random plume (m"1)
FG flux of heat into the ground (W m"2)
Fm plume momentum flux (mV)
Fz total vertical distribution function (m"1)
/ plume state weighting function (dimensionless)
fp fraction of plume mass contained in CBL = (1 - penetration factor)
dimensionless)
g acceleration due to gravity (9.8 m s"2)
H sensible heat flux (W m"2)
Hc critical dividing streamline (m)
Hp plume centroid height (m)
Hu heat flux in the nighttime boundary layer (W m"2)
hc receptor specific terrain height scale (m)
hep penetrated source plume height above stack base (m)
hs stack height corrected for stack tip downwash (m)
A/7 general symbol for distance dependent plume rise (m)
A/ZJ plume rise for the direct source (m)
A/7e? equilibrium plume rise in a stable environment (m)
A/7A depth of the layer between z; and the stack top (m)
A/Zp plume rise for the penetrated source (m)
70
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A/7, plume rise for the indirect source (m)
A/7X plume rise for the stable source (m)
iz vertical turbulence intensity
k von Karman constant k = 0.4 (dimensionless)
/ length scale used in determining the Lagrangian time scale (m)
/„ neutral length scale - a component of / (m)
ls stable length scale - a component of / (m)
L Monin-Obukhov length (m)
N Brunt-Vaisala frequency (s"1)
Nh Brunt-Vaisala frequency above zt (s"1)
n cloud cover (fractional)
P population of urban area
py lateral probability density function
pz vertical probability density function
pw probability density function of the instantaneous vertical velocities
Q source emission rate (g/s)
R solar insolation (W m"2)
Rn net radiation (Wm"2)
R0 clear sky solar insolation (W m"2)
r() Albedo (solar elevation} (dimensionless)
r' noontime albedo (dimensionless)
rs stack radius - corrected for stack tip downwash (m)
ry lateral dimension of an elliptical plume
rz vertical dimension of an elliptical plume
S skewness factor (dimensionless)
T ambient temperature (K)
TLy lateral lagrangian time scale (sec)
TLzc vertical lagrangian time scale for the CBL (sec)
TLzs vertical lagrangian time scale for the SBL (sec)
Tr Time scale used in the meander algorithm (sec)
Tref ambient temperature - at reference temperature height (K)
Ts stack gas temperature (K)
Tu urban surface temperature (K)
t time (sec)
AT difference between stack gas and ambient temperature (K)
Ara_r urban-rural temperature difference (K)
u wind speed (m s"1)
ucr minimum speed for which the expression for w*, in the SBL, has a real
valued solution (m s"1)
u0 defined in eq. (14) and used in eq. (15).
up wind speed that is used for plume rise (m s"1)
uref wind speed at reference height (m s"1)
uth wind speed instrument threshold - separate value for each data set (offsite
& onsite) (m s"1)
71
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M* surface friction velocity (m s"1)
w*eff effective surface friction velocity (w*^) - surrogate for w*H (m s"1)
M*U surface friction velocity for nighttime urban conditions (m s"1)
w random vertical velocity in the CBL (m s"1)
W. mean vertical velocity for the updraft (j = 1) and the downdraft (j = 2)
distributions (m-s"1)
ws stack exit gas velocity (m-s"1)
w* convective velocity scale (m-s"1)
w*H urban nighttime convective velocity scale (m-s"1)
X non-dimensional downwind distance (dimensionless)
xr downwind distance to a receptor (m)
xf distance to final plume rise (m) - eq. (44) for the CBL and eq. (96) for the
SBL
xm downwind distance at which plume material uniformly mixed throughout
the boundary layer (m)
(x^y^z^ receptor location
(xpypzt) terrain point location
zbase user specified elevation for the base of the temperature profile (i.e.,
meteorological tower)
zc total height of the plume in the CBL considering both plume rise and
effects from convective turbulence (m)
Zj mixing height (m): z; = MAX [zic; zim] in the CBL and z; = zim in the SBL
zic convective mixing height (m)
zie equilibrium height of stable boundary layer
zieff height of the reflecting surface in the SBL or in the stable layer above the
above the CBL (m)
zim mechanical mixing height (m)
ziu urban nighttime boundary layer mixing height (m)
ziuc urban nighttime boundary layer mixing height due to convective effects
alone (m)
Zmsl height of stack base above mean sea level (m)
z0 surface roughness length (m)
ZPG release height used in the Prairie Grass experiment (m)
zp receptor "flagpole" height - the height of a receptor above local terrain (m)
zr height of the receptor above local source base (m)
zref reference height for wind (m)
zTref reference height for temperature (m)
zt height of the terrain above mean sea level (m)
a General symbol used to represent the effective parameters in the treatment
of the inhomogeneous boundary layer. In the text the effective values of
the parameters u, aw, ov and TL are denoted by underscoring the character.
y parameter used to weight CAERMOD and CPrime in estimating concentrations
that are influenced by building downwash (dimensionless)
72
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6 potential temperature (K)
ft temperature scale (K)
Aj weighting coefficient for the updraft (j = 1) and downdraft (j = 2)
distributions of eqs. (53), (59) and (65)
p density of air (Kg m"3)
oh buoyancy induced dispersion for the direct & indirect sources (m)
<7/ total horizontal wind "energy" used in the meander algorithm (m2)
<7/ random "energy" component of the total horizontal wind "energy" used in
the meander algorithm (m2)
aSB Stephen Boltzman constant (5.67xlCT8 Wm'2K'4)
ou along-wind turbulence (m s"1)
av lateral turbulence (m s"1)
ovc convective portion of the lateral turbulence (m s"1)
ovo surface value of the lateral turbulence (m s"1)
ovm mechanical portion of the lateral turbulence (m s"1)
ovT total lateral turbulence (m s"1)
aw vertical turbulence (m s"1)
awc convective portion of the vertical turbulence (m s"1)
awm mechanical portion of the vertical turbulence (m s"1)
owml mechanical portion of the vertical turbulence generated in the PEL (m s"1)
awmr mechanical portion of the vertical turbulence above the PEL (residual)
(m s-1)
owT total vertical turbulence (m s"1)
oxg longitudinal dimension of the building wake (m)
oy total lateral dispersion for the direct & indirect sources (m)
oyazaj ambient turbulence induced dispersion for the direct & indirect sources
(m)
ozas ambient dispersion for the stable source (m)
oyg distance from the building centerline to lateral edge of the building wake
(m)
ayi lateral spread from combined effects of ambient turbulence and building
downwash (m)
ozp total dispersion for the penetrated source (m)
ozs total dispersion for the stable source (m)
ozaj ambient vertical dispersion for the updraft & downdrafts plumes (j = 1,2),
respectively, for both the direct & indirect sources (m)
ozej elevated portion of ozaj (m)
ozes elevated portion of ozas (m)
ozg height of the building wake at the receptor location (m)
ozj total vertical dispersion for the updrafts and downdrafts
(j=l,2 respectively), for both the direct and indirect sources
ozg surface portion of ozaj (m)
ozgs surface portion of ozas (m)
T time constant controlling the temporal interpolation ofzim (sec)
73
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$ solar elevation angle
(f)p fraction of plume mass below Hc (dimensionless)
¥dj total height of the direct source plume (i.e. release height + buoyancy +
convection) (m)
¥rj total height of the indirect source plume (m)
ifrm similarity function for momentum (stability correction) - eq. (7) for the
CBL and eq. (29) for the SBL (dimensionless)
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7 APPENDIX: Input / Output Needs and Data Usage
7.1 AERMETInput Data Needs
Besides defining surface characteristics, the user provides several files of hourly
meteorological data for processing by AERMET. At the present time AERMET is designed to
accept data from any for the following sources: 1) standard hourly National Weather Service
(NWS) data from the most representative site; 2) morning soundings of winds, temperature, and
dew point from the nearest NWS upper air station; and 3) on-site wind, temperature, turbulence,
pressure, and radiation measurements (if available).
The minimum measured and/or derived data needed to run the AERMOD modeling system
are as follows:
7.1.1 METEOROLOGY
wind speed (w); wind direction; cloud cover - opaque first then total («); ambient temperature
(t); morning sounding
Cloud cover is also used in dry deposition calculations in the AERMOD model. Therefore, if
cloud cover is missing and the Bulk Richardson Number Scheme is being used (see 3.3.1) then an
equivalent could cover is calculated as follows, based on van Ulden and Holtslag (van Ulden and
Holtslag 1985):
(1-0. /0.09V'5
n = (108)
eq \ 0.5 )
where ft, is the temperature scale as calculated from eq. (18).
7.1.2 DIRECTIONALLY AND/OR MONTHLY VARYING SURFACE CHARACTERISTICS
Noon time albedo (r'); Bowen ratio (50); roughness length (z0) - For AERMET, the user can
specify monthly variations of three surface characteristics for up to 12 upwind direction sectors.
These include: the albedo (r), which is the fraction of radiation reflected by the surface; the
Bowen ratio (B0), which is the ratio of the sensible heat flux to the evaporation heat flux; and the
surface roughness length (z0) , which is the height above the ground at which the horizontal wind
velocity is typically zero. The user will be guided by look-up tables (in the AERMET user's
guide) of typical values for these three variables for a variety of seasons and land use types. The
information presented in the user's guide is not be considered regulatory guidance. The user is
encouraged to research the literature to determine the most appropriate values for surface
characteristics, for a specific application.
7.1.3 OTHER
Latitude; longitude; time zone; wind speed instrument threshold for each data set (uth).
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7.1.4 OPTIONAL
Solar radiation; net radiation (/?„); profile of vertical turbulence (aw); profile of lateral
turbulence (<7V)
7.2 Selection and Use of Measured Winds, Temperature and Turbulence in AERMET
7.2.1 THRESHOLD WIND SPEED
The user is required to define a threshold wind speed (uth) for on-site data sets. Although the
current version of AERMOD cannot accept a separate uth for NWS data, a separate uth should be
selected for each on-site data set being used.
7.2.2 REFERENCE TEMPERATURE AND HEIGHT
The reference height for temperature (zrre/), and thus the reference temperature, is selected as
the lowest level of data which is available between z0 & 100 m.
7.2.3 REFERENCE WIND SPEED AND HEIGHT
The reference height for winds (zre/), and thus the reference wind speed (wre/), is selected as the
lowest level of data which is available between 7 z0 & 100m. Although the current version of
AERMOD cannot accept a separate zre/for offsite data, we believe that a separate zref should be
selected for each data set being used.
If no valid observation of the reference wind speed or direction exists between these limits
the hour is considered missing and a message is written to the AERMET message file. For the
wind speed to be valid its value must be greater than or equal to the threshold wind speed.
AERMOD processes hours of invalid wind speed, e.g. calms, in the same manner as ISC (EPA
calms policy).
All observed wind speeds in a measured profile that are less than uth are set to missing and are
therefore not used in the construction of the wind speed profile (profiling of winds is
accomplished in AERMOD).
7.2.4 CALCULATING THE POTENTIAL TEMPERATURE GRADIENT ABOVE THE
MIXING HEIGHT FROM SOUNDING DATA
AERMET calculates dd/dz for the layer above zt as follows:
If the sounding extends at least 500 m above zt the first 500 m above zt is used to
determine dd/dz above zt.
- If the sounding extends at least 250 m above zt (but not 500 m) then the available
sounding above zt is used to determine dd/dz above zt.
AERMET limits dd/dz above zi to a minimum of 0.005 K m"1.
If the sounding extends less than 250 m above zi then set dd/dz = 0.005 K m"1 (a default
value).
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7.2.5 MEASURED TURBULENCE
All measured turbulence values are passed to AERMOD if the hour is non-missing. This is
true even for those levels where the wind speed is below uth. Based on measurements with
research grade instruments, reasonable minimum turbulence levels in non-calm conditions for
vertical turbulence (aw ) and lateral turbulence (<7V) values are set by AERMOD to 0.02 m s"1 and
0.2 m s"1, respectively. Although these lower limits are applied to the measured values of the
turbulence the calculated profile values of ow & ov are not subjected to any lower limits. We do
not restrict these estimated profiles because it would bias the calculation of the effective values of
turbulence, which are averages through the layer between the receptor and the plume height, in
determining the dispersion of the plume. However, as discussed in Section 7.9 these limits are
applied to the effective values of turbulence and wind speed.
7.2.6 DATA SUBSTITUTION FOR MISSING ON-SITE DATA
If on-site data are missing for an hour, the hour is considered missing unless the user specifies
a substitute data set. AERMET does not default to NWS (or any other off site) data.
7.3 Information Passed by AERMET to AERMOD
The following information is passed from AERMET to AERMOD for each hour of the
meteorological data record.
- All observations of wind speed (u); wind direction; ambient temperature (T); lateral
turbulence (av); & vertical turbulence (aw) with their associated measurement heights.
Sensible heat flux (//), friction velocity (M*), Monin Obukhov length L, zim (for all hours),
zic & wt (for convective hours only), z0, r{
-------
7.6 Determining The Mixing Height When the Sounding Is Too Shallow
The left hand side of eq. (22) is determined from the morning temperature sounding and the
right hand side from the daytime history of surface heat flux. When the temperature sounding,
obtained from the NWS, does not reach a height which is greater than the convective mixing
height, we must assume a profile for the potential temperature gradient in order to estimate zic.
This is accomplished as follows:
Determine dd/dz in the top 500 m layer of the sounding. However, if part of the 500 m
layer is within the first 100 m of the PEL, the layer should be reduced (to a minimum
thickness of 250 m) to avoid using the portion of the sounding that is below 100 m. If the
above conditions can not be satisfied then zic is defined as missing.
- Extend the sounding by persisting dd/dz up and recomputing zic.
Provide warning messages which tell users
- the height of the actual sounding top,
- that dd/dz has been extrapolated above the sounding zic, and
that zic has been recomputed.
Allow the user to reject the "fixed-up" value for zic by defining it as missing.
7.7 Input Data Needs for AERMAP
The following data is required input for AERMAP
- DEM formatted terrain data ( xt, yp zt)
- Design of receptor grid; AERMAP accepts either polar, Cartesian or discrete receptors
7.8 Information Passed by AERMAP to AERMOD
AERMAP passes the following parameters to AERMOD: xr, yr, zr, zt, & the height scale (/zc)
for each receptor.
7.9 Wind Speed & Turbulence Limits Used in Model Calculations
When calculating the effective parameters limits are placed on the such that:
aw{z} = Max\aw{z}- 0.02 ms1}
r i (109)
av{z} = Max[(Tv{z}- 0.05u{h,}; 0.2 "
These limits are also applied when selecting the turbulence for plume rise calculations.
Dilution of the plume is determined by the wind that corresponds to the average over the
magnitudes of the wind vectors during a given time interval. But measurements only give the
vector averaged wind, which can be zero, even though the dilution wind is not zero. We can
estimate the dilution wind by assuming that the vector wind, uv, can be expressed as
uv = (u + u', v') (110)
78
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where u is the mean measured wind, and the primed quantities refer to the turbulent
fluctuations. The assumption being made is that uv = u . If we assume that the measured
velocity fluctuations correspond only to the angular variations of a constant vector, uv, we can
write from eq. (110) that
U2V = u2 + cl + cl. (Ill)
In this simple model, uv, is the dilution wind. If we take ou = om the dilution wind can be written
as
(112)
This formulation assures that the dilution wind is not zero as long as either u or ov is not zero.
Similarly, at the time of plume rise calculations, the effective turbulence and effective wind speed
will be recalculated using eqs. (109) & (112), where the turbulence and winds will be evaluated
at stack top .
7.10 Using Profiles for Interpolating Between Observations
When observations are available AERMOD uses the similarity profile functions to
interpolate adjacent measurements. Figure 18 illustrates how AERMOD' s INTERFACE uses the
expected shape of a meteorological profile to interpolate between observations.
79
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' Calculated Profile
Measured
Data Points
Modified Profile
Meteorological Variable
Figure 18: AERMOD's construction of a continuous meteorological profiles by
interpolating between observations.
For a gridded profile height between two observed profile heights, the observations are
interpolated to the gridded height while maintaining the shape of the similarity profile. This is
accomplished as follows:
1. the observations are linearly interpolated to the gridded profile height;
2. the similarity function is evaluated at the gridded profile height;
3. the similarity function is evaluated at the observed profile heights immediately above
and below the grid height and linearly interpolated to the grid height;
4. the ratio of the value obtained in 2. to the value obtained in 3. is applied to the value
obtained in 1.
For a gridded profile height above the highest observation, the procedure is modified slightly:
1. the observation at the highest observed profile height is extrapolated by persisting the
value upward;
2. the similarity function is evaluated at the grid height;
3. the similarity function is evaluated at the highest height in the observed profile;
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4. the ratio of the value obtained in 2. to the value obtained in 3. is applied to the value
obtained in 1.
A similar procedure for extrapolating to heights above the observed profile is applied to
heights below the lowest observed profile height.
7.11 Using Measured Mixing Heights
If measured mixing heights are available, then they are treated in the following manner: If
L>0 (SBL) the measured mixing height is defined as zie and it is treated the same as a calculated
mechanical mixing height (smoothed as explained in Section 3.4.2). If L<0 (CBL) the measured
mixing height is defined as zic, and zie is calculated from eq. (24), smoothed, then proceed as if
both zic and the smoothed zim had been calculated values.
If a user has "measured" mixing heights available (and chooses to use them), AERMET
defaults to substituting calculated mixing heights for missing measurements and a message is
written that a substitution has occurred. If the user elects to substitute calculations for missing
measurements, AERMET will print out a message to the message file for each hour that a
substitution has occurred.
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TECHNICAL REPORT DATA
(Please read Instructions on reverse before completing)
1. REPORT NO.
EPA-454/R-03-004
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
5. REORT DATE
AERMOD: Description of Model Formulation
September 2004
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
10. PROGRAM ELEMENT NO.
See below.
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency
Office of Air Quality Planning and Standards
Emissions Monitoring and Analysis Division
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final technical report. Supplement A
14. SPONSORING AGENCY CODE
EPA/200/04
15. SUPPLEMENTARY NOTES
16. ABSTRACT The purpose of this document is to provide a comprehensive, detailed description of the
technical formulation of AERMOD and its preprocessors - AERMAP and AERMET.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
AERMOD, FORMULATION, DESCRIPTION,
Air Pollution models
18. DISTRIBUTION STATEMENT
Release Unlimited
19. SECURITY CLASS (Report)
21. No of pages
20. SECURITY CLASS (Page) Unclassified
EPA Form 2220-1 (Rev. 4-77)
PREVIOUS EDITION IS OBSOLETE
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United States Office of Air Quality Planning and Standards Publication No. EPA-454/R-03-004
Environmental Protection Agency Emissions Monitoring and Analysis Division September 2004
Research Triangle Park, NC
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