1 ADDENDUM

AERMOD: Model Formulation Document

Introduction

This Addendum to the AERMOD Model Formulation Document (MFD) (Cimorelli, et al. , 2002) provides a n 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 NO x to NO 2 first introduced in version 04300 of
AERMOD , and an a dditional 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

o n the description in Hanrahan (1999 a ) 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 de termines the conversion rate for NO x to NO 2 based on a calculation of
the NO x moles emitted into the plume, and the amount of O 3 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

- aver aged 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 d ispersion 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 dispersi on 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 effect s 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 defining2 relative dispersion, the relati ve dispersion coefficients are calculated based on the radial distance from source to receptor. Weil (1996 and 1998) assumes relative dispersion ( σ r ) to be isotropic,
so that F rx = F ry = F rz = F r . The relative dispersion ( σ r ) due to the combined effects of buoyancy

induced turbulence ( σ rb ) and ambient turbulence ( σ ra ) is parameterize d as follows:

3 / 1 3 3 ) (

ra rb r σ σ σ + = (1)

The buoyancy

- induced dispersion term, F rb , is calculated in AERMOD as

2 4

. 0 h

rb ∆

= σ (2)

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

Lr ra T t a t a
/ 1 2 2 / 3 2 / 1
1

+ = ε σ ( 3 )

where a 1 is a constant (= 0.57), a 2 = 0.62 a 1 , t is the plume travel time ( = x / U ) , and T Lr is a Lagrangian time scale for rel ative dispersion defined as

w i

r Lr z a T

σ 1 = ( 4 )

where a r 1 = 0.46, z i is the mixing height, and σ w 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 σ w 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 2.15 F z ), following the procedure used in AERMOD to calculate effective values. Using the effective values of σ w , AERMOD calculates effective values of the turbulence dissipation rate, g

.

S ince 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 complet e the plume
volume calculation.3 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 coefficient s for purposes of calculating the plume volume, as follows: 

# ( ) 3 / 1 3
0 3 3 σ σ σ σ + + = ra rb r ( 6 )

where F 0 is the initial dispersion coefficient of the volume source calculated as 0 0 z y σ σ based

on the initial lateral ( F y 0 ) and vertical ( F z 0 ) dime nsions 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 laterall y 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 NO x 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 coefficient s 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 cen terline, n z , 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 n z , corresponding to 80 percent of the area under the normal curve. The plume volume calculations for AERMOD are based on a value of n z = 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
minim um 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 n z = 1.282 and a minimum dispersion coe fficient 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 e ffective 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.4 Treatment of Penetrated Plumes

For unstable conditions with partial or full plume penetration above the mixing height, z i , 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 contributi ng 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 concentrat ion 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 con centration 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 rela tive 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 applica ble 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 conditio ns, but uses the “standard” total dispersion coefficients incorporated in AERMOD to define the plume volume during stable conditions.5 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 a mbient 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
PVMRM 2 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 AER MOD 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 st raight

- line, steady

state 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 AER M ET 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 th e 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 non

DFAULT/BETA options, requiring the user to also s pecify 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 increa ses 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 the6 FASTALL approach to replicate the ce nterline 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 measuremen ts. 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 short

term NO 2 concentrations,” J. Air Pollut. Control Assoc.

, 29 (8), 812

- 817.

Hanrahan, P.L., 1999 a . “The plume volume molar ratio method for determining NO 2 /NO x ratios in modeling. Part I: Methodolo gy,” J. Air & Waste Manage. Assoc.

, 49 , 1324

- 1331.

Hanrahan, P.L., 1999b. “The plume volume molar ratio method for determining NO 2 /NO x ratios in modeling. Part II: Evaluation Studies,” J. Air & Waste Manage. Assoc.

, 49 , 1332

- 1338.

Luhar, A.K. , and K. N . Rayne r, 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 doc ument 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 9 th Joint Conference on7 Applications of Air Pollution Meteorology , Ame rican 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.