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ADDENDUM

AERMOD: Model Formulation Document

Introduction

This Addendum to the AERMOD Model Formulation Document (MFD) (Cimorelli, et 

al., 2002) provides an update to the technical description of the AERMOD modeling system 

regarding modifications to the model formulation that are not reflected in the original AERMOD 

MFD. This includes the implementation of the Plume Volume Molar Ratio Method (PVMRM) 

option for modeling the conversion of NOx to NO2 first introduced in version 04300 of 

AERMOD, and an additional option referred to as PVMRM2, first introduced in version 15181 

of AERMOD. In addition, the non-DEFAULT/BETA ADJ_U* option in AERMET and the 

non-DEFAULT/BETA LowWind3 option in AERMOD are also described.

Plume Volume Molar Ratio Method (PVMRM)

Hanrahan (1999a) provides a technical description of the PVMRM algorithm. Hanrahan 

also implemented and evaluated the PVMRM algorithm as a post-processor for the ISCST3 

model (Hanrahan, 1999b). The design and implementation of PVMRM in AERMOD is based 

on the description in Hanrahan (1999a) and the ISCST3 post-processor code. However, the 

implementation was adapted for the AERMOD dispersion algorithms, as described below.

Definition of Plume Volume for PVMRM

Total vs. Relative Dispersion

The PVMRM determines the conversion rate for NOx to NO2 based on a calculation of 

the NOx moles emitted into the plume, and the amount of O3 moles contained within the volume 

of the plume between the source and receptor. The dispersion algorithms in AERMOD and other 

steady-state plume models are based on the use of total dispersion coefficients, which are 

formulated to represent the time-averaged spread of the plume. A more appropriate definition of 

the volume of the plume for purposes of determining the ozone moles available for conversion of 

NOx is based on the instantaneous volume of the plume, which is represented by the use of 

relative dispersion coefficients, (Cole and Summerhays, 1979; Bange, 1991). The 

implementation of PVMRM in AERMOD is based on the use of relative dispersion coefficients 

to calculate the plume volume. Weil (1996 and 1998) has defined formulas for relative 

dispersion that are consistent with the AERMOD treatment of dispersion, and which can be 

calculated using meteorological parameters available within AERMOD. 

Calculation of Relative Dispersion Coefficients

The formula for relative dispersion combines the effects of buoyancy-induced turbulence, 

which should dominate close to the source, and ambient turbulence, which begins to dominate 

further downwind. Since the travel time from the source to the receptor is important for defining 
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relative dispersion, the relative dispersion coefficients are calculated based on the radial distance 

from source to receptor. Weil (1996 and 1998) assumes relative dispersion (σr) to be isotropic, 

so that Frx = Fry = Frz = Fr. The relative dispersion (σr) due to the combined effects of buoyancyinduced turbulence (σrb) and ambient turbulence (σra) is parameterized as follows:

3 3 1/ 3 ( ) σ r = σ rb +σ ra (1)

The buoyancy-induced dispersion term, Frb, is calculated in AERMOD as 

2

0.4 h

rb

∆

σ = (2)

where )h is the plume rise. Relative dispersion due to ambient turbulence, Fra, is parameterized 

by 

Lr

ra a t T

a t

1 / 2

1/ 2 3/ 2

1

+ = ε

σ (3)

where a1 is a constant (= 0.57), a2 = 0.62 a1, t is the plume travel time (= x/U), and TLr is a 

Lagrangian time scale for relative dispersion defined as

w

i

Lr r

z T a

σ = 1 (4)

where ar1 = 0.46, zi is the mixing height, and σw is the vertical turbulence parameter. The 

turbulence dissipation rate, g, is calculated as follows, based on Weil (1996): 

Lr

w

T

b 2 σ

ε = (5)

where b is a constant (= 0.78).

The values of wind speed (U) and σw used in Equations 3 through 5 are the effective 

values, calculated as averages across the layer from the plume centroid height to the receptor 

height (up to 2.15Fz), following the procedure used in AERMOD to calculate effective values. 

Using the effective values of σw, AERMOD calculates effective values of the turbulence 

dissipation rate, g.

Since the relative dispersion coefficients are source- and meteorology-dependent in 

AERMOD, the model generates a table of relative dispersion coefficients as a function of 

distance for the dominant source for each receptor and each hour in order to complete the plume 

volume calculation. 
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Treatment of Volume and Area Sources

If the dominant source is a volume source, then the initial lateral and vertical dimensions 

of the volume source are included in the calculation of the relative dispersion coefficients for 

purposes of calculating the plume volume, as follows:

( )

1/ 3 3

0

3 3 σ r = σ rb +σ ra +σ (6)

where F0 is the initial dispersion coefficient of the volume source calculated as σ y0 σ z0 based 

on the initial lateral (Fy0) and vertical (Fz0) dimensions input by the user. If a volume source is 

included among the major contributing sources it is treated the same as a point source in defining 

the combined plume volume.

For application of PVMRM to area sources, the plume volume is extended laterally if 

necessary to include the projected width of the area source or sources that are included among 

the major contributing sources. The emissions from an area source are included in the 

calculation of the NOx moles emitted into the plume if the centroid of the area source is within 

the box defined by the alongwind and crosswind extent of major contributing sources. In 

addition, if an area source is the dominant source, then the relative dispersion coefficients are 

calculated based on the radial distance from the centroid of the area source to the receptor.

Defining Extent of Plume

Since relative dispersion coefficients are used to define the plume volume, the number of 

standard deviations from the plume centerline, nz, used in the calculation of plume volume was 

increased from the value used by Hanrahan (1999) for ISCST3. The ISCST3 postprocessor 

version used a value of 1.282 for nz, corresponding to 80 percent of the area under the normal 

curve. The plume volume calculations for AERMOD are based on a value of nz = 4.0, which 

corresponds to about 99.99 percent of the area under the normal curve. The minimum value of 

the dispersion coefficient was also reduced from the 15m minimum used with ISCST3 to a 

minimum of 5m for AERMOD in order to maintain approximately the same minimum plume 

volume in AERMOD as used for ISCST3. A minimum value of 4.8m in AERMOD would 

provide the same minimum plume volume as used by ISCST3 with nz = 1.282 and a minimum 

dispersion coefficient of 15m. 

Adaptation for AERMOD Terrain Algorithm

The vertical dimension of the plume volume is based on the relative dispersion 

coefficient for the dominant source and the range in plume heights for the major contributing 

sources. Since the effective plume heights differ for the terrain following and terrain responding 

components, the vertical dimension was modified to calculate the range of plume heights 

separately for both the terrain following and terrain responding components, and then use a 

weighted value for the vertical dimension based on the terrain (plume state) weighting factor, f, 

defined in Section 5.1 of the MFD.
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Treatment of Penetrated Plumes

For unstable conditions with partial or full plume penetration above the mixing height, zi, 

separate relative dispersion coefficients are calculated for the penetrated portion of the dominant 

plume. For cases with partial penetration for the dominant plume, AERMOD calculates two 

plume volumes, one based on relative dispersion coefficients for the direct source and another 

based on the relative dispersion coefficients for the penetrated source. Since AERMOD uses the 

same dispersion coefficients for the direct and indirect sources, separate values of relative 

dispersion coefficients for the indirect source are not needed. The effective plume volume used 

in the application of PVMRM is based on a weighted average of the direct and penetrated plume 

volumes using the plume penetration factor (PPF) for the dominant source. The model stores the 

plume centroid heights for both the direct and penetrated plumes for all sources at each receptor, 

and these are used to incorporate the effect of the major contributing sources on the volumes for 

the direct and penetrated plumes.

Minimum Ozone Concentration for Stable Conditions

Hanrahan (1999a) applied a minimum ozone concentration of 40 ppb for stable 

conditions for implementation with ISCST3, due to the fact that surface measurements may be 

artificially low during nighttime stable conditions due to the formation of a stable vertical 

temperature gradient. Since the AERMOD model does not use Pasquill-Gifford (P-G) stability 

categories, this minimum ozone concentration was modified to use Monin-Obukhov length as 

the stability parameter. The AERMOD model first keeps track of the maximum ozone 

concentration over the previous 24 hours. If the Monin-Obukhov length is positive (i.e. stable), 

with a value of less than 50 meters (very stable), then the maximum ozone concentration over the 

previous 24 hours is used as the minimum value. If the Monin-Obukhov length is positive and 

the value is over 500 meters (nearly neutral), then no minimum ozone concentration is applied 

for that hour. If the Monin-Obukhov length is between 50 meter and 500 meters, then the 

minimum ozone concentration is determined by linear interpolation, i.e., the minimum value is 

calculated as O3MAX * (500 – L)/450, where O3MAX is the maximum ozone concentration 

over the previous 24 hours, and L is the Monin-Obukhov length in meters.

Plume Volume Molar Ratio Method - 2 (PVMRM2)

The PVMRM2 option included in version 15181 of AERMOD includes several 

modifications to the calculation of plume volume relative to the original PVMRM formulation. 

A summary of these changes is presented below:

1. The original PVMRM option utilizes the relative dispersion coefficients described 

above to define the plume volume. These relative dispersion coefficients are 

applicable to unstable/convective conditions, but are likely to overpredict the plume 

volume for stable conditions, resulting in overpredictions of NO2 concentrations. 

The PVMRM2 option uses these relative dispersion coefficients for 

unstable/convective conditions, but uses the “standard” total dispersion coefficients 

incorporated in AERMOD to define the plume volume during stable conditions.
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2. The original PVMRM option also used four (4) times the relative dispersion 

coefficients to define the plume volume, which accounts for more than 99.99% of the 

plume. Given the fact that the PVMRM option in AERMOD assumes full and 

instantaneous mixing of the NO and O3 within the plume, using such a large 

percentage of the plume volume may also introduce a bias to overpredict ambient 

concentrations of NO2. For unstable conditions, the PVMRM2 option uses 2.58 times 

the relative dispersion coefficients to define the plume volume during unstable 

conditions, which accounts for about 99% of the plume. For stable conditions, the 

PVMRM2 option uses 1.282 times the total dispersion coefficients to define the 

plume volume during stable conditions, consistent with the original approach 

proposed by Hanrahan (1999), which accounts for about 80 percent of the plume 

volume. However, since AERMOD incorporates a horizontal meander algorithm that 

increases lateral plume spread beyond that accounted for based on dispersion 

coefficients, the number of sigmas used to define the plume volume for stable 

conditions is adjusted to account for meander, i.e.,

NSUBZ = MIN( 2.15, 1.282 * (SYEFF/SY)

 where

SYEFF is the effective sigma-y value that replicates the plume centerline 

associated with meander, but based on a standard Gaussian plume 

calculation.

3. The PVMRM2 uses the downwind distance from source to receptor to calculate the 

plume volume and the moles of NOx contained in the plume, instead of the radial 

distance used in the original PVMRM option. Use of the downwind distance provides 

a more realistic estimate of NOx conversion consistent with a straight-line, steadystate plume model, such as AERMOD.

Additional details regarding the formulation of the PVMRM2 option in AERMOD, and 

preliminary model evaluation results are available in EPA (2015).

Low Wind Options in AERMET and AERMOD

Non-DFAULT/BETA options have been incorporated in AERMET and AERMOD to 

address issues associated with model overpredictions under low-wind/stable conditions. The 

ADJ_U* option is available in AERMET by specifying ADJ_U* on the METHOD STABLEBL 

keyword in the Stage 3 AERMET input file. The LOWWIND option in AERMOD can be 

selected by including the LOWWIND1, LOWWIND2, or LOWWIND3 option on the CO 

MODELOPT keyword in AERMOD. The low wind options in AERMOD are nonDFAULT/BETA options, requiring the user to also specify the BETA option on the 

MODELOPT keyword and excluding the DFAULT option. The LOWWIND1 option increases 

the minimum value of sigma-v from the default of 0.2 to 0.5 m/s, and also eliminates the 

horizontal meander algorithm. The LOWWIND2 option increases the minimum value of sigma-v 

from 0.2 to 0.3 m/s, and retains the horizontal meander algorithm with an upper limit of 0.95. 

The LOWIND3 option increases the minimum value of sigma-v from 0.2 to 0.3 m/s, and uses the 
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FASTALL approach to replicate the centerline concentration accounting for horizontal meander, 

but utilizes an effective sigma-y and eliminates upwind dispersion.

The ADJ_U* option can be specified with or without the Bulk Richardson Number 

option in AERMET, which utilizes delta-T measurements. The Bulk Richardson Number option 

in AERMET is selected by specifying BULKRN on a separate METHOD STABLEBL keyword 

in the Stage 3 AERMET input file. The formulation for the ADJ_U* option without the 

BULKRN option is based on Equation 26 of Qian and Venkatram (2011). The formulation for 

the ADJ_U* option with the BULKRN option is based on Equations 22, 23, and 25 of Luhar and 

Rayner (2009), with a critical value of z/L of 0.7.

References

Bange, P., L. Jannsen, F. Nieuwstadt, H. Visser, and J. Erbrink, 1991. “Improvement of the 

modeling of daytime nitrogen oxidation in plumes by using instantaneous plume 

dispersion parameters,” Atmos. Environ., 25A (10), 2321-2328.

Cimorelli, A. J., S. G. Perry, A. Venkatram, J. C. Weil, R. J. Paine, R. B. Wilson, R. F. Lee, W. 

D. Peters, R. W. Brode, and J. O. Paumier, 2002: AERMOD: Description of Model 

Formulation (Version 02222). EPA 454/R-02-002d. U. S. Environmental Protection 

Agency, Research Triangle Park, NC.

Cole, H.S. and J.E. Summerhays, 1979. “A review of techniques available for estimating shortterm NO2 concentrations,” J. Air Pollut. Control Assoc., 29(8), 812-817.

Hanrahan, P.L., 1999a. “The plume volume molar ratio method for determining NO2/NOx ratios 

in modeling. Part I: Methodology,” J. Air & Waste Manage. Assoc., 49, 1324-1331.

Hanrahan, P.L., 1999b. “The plume volume molar ratio method for determining NO2/NOx ratios 

in modeling. Part II: Evaluation Studies,” J. Air & Waste Manage. Assoc., 49, 1332-

1338.

Luhar, A.K., and K. N. Rayner, 2009: “Methods to Estimate Surface Fluxes of Momentum and 

Heat from Routine Weather Observations for Dispersion Applications under Stable 

Stratification”, Boundary-Layer Meteorology, 132, 437–454.

Qian, W., and A. Venkatram, 2011: "Performance of Steady-State Dispersion Models Under 

Low Wind-Speed Conditions", Boundary Layer Meteorology, 138, 475-491. 

U.S. EPA, 2015. “Technical Support Document (TSD) for NO2-related AERMOD 

modifications.” EPA document EPA-454/B-15-004. July 2015.

Weil, J.C., B. Templeman, R. Banta, R. Weber, and W. Mitchell, 1996. “Dispersion model 

development for open burn/open detonation sources,” Preprints 9th Joint Conference on 
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Applications of Air Pollution Meteorology, American Meteorological Society, Boston, 

MA, 610-616.

Weil, J.C., 1998. The SERDP Open Burn/Open Detonation Dispersion Model (SOBODM), 

Volume IIa – Technical Description, and Volume IIb – Meteorological Inputs (DRAFT), 

CIRES, University of Colorado, Boulder, CO.