## Introduction

Major developments in an improved understanding of the planetary boundary layer (PBL) began in the 1970s (Wyngaard 1988). One milestone involved numerical simulations by Deardorff (1972), revealing the convective boundary layer’s (CBL’s) vertical structure and important turbulence scales. Insights into dispersion followed from laboratory experiments, numerical simulations, and field observations (Briggs 1988; Lamb 1982; Weil 1988a). 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 existed by the mid-1980s (Briggs 1988; Venkatram 1988).

During the 1980s, researchers began to apply this information to applied dispersion models. These included eddy-diffusion techniques for surface releases, statistical theory and PBL scaling for dispersion parameter estimation, and a new probability density function (PDF) approach for the CBL. 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- to late 1980s, new applied dispersion models had been developed, including the Power Plant Siting Program (PPSP) model (Weil and Brower 1984), Second-Order Closure Integrated Puff (SCIPUFF) (Sykes et al. 1996), Operationelle Meteorologiske Luftkvalitetsmodeller (OML) (Berkowicz et al. 1986), Hybrid Plume Dispersion Model (HPDM) (Hanna and Paine 1989), Multiple Source Dispersion Algorithm Using On-Site Turbulence Data (TUPOS) (Turner et al. 1986), and the Complex Terrain Dispersion Model Plus Algorithms for Unstable Situations (CTDMPLUS) (Perry et al. 1989); later, the Advanced Dispersion Modeling System (ADMS), developed in the United Kingdom (Carruthers et al. 1994), was added as well.

In February 1991, the U.S. Environmental Protection Agency (EPA) in conjunction with the American Meteorological Society (AMS) formed the AMS and EPA Regulatory Model (AERMOD) Improvement Committee (AERMIC), with the purpose of incorporating scientific advances from the 1970s and 1980s into a state-of-the-art dispersion model for regulatory applications. AERMIC’s early efforts are described by Weil (1992). To improved PBL parameterizations, other concerns such as plume interaction with terrain, surface releases, building downwash, and urban dispersion were addressed. These efforts resulted in AERMOD. AERMOD is aimed at the same scenarios currently handled by EPA’s Industrial Source Complex Short-Term model (ISCST3) (U.S. Environmental Protection Agency 1995). The early formulations of AERMOD are summarized in Perry et al. (1994) and Cimorelli et al. (1996). An extensive discussion of the current models’ formulations appears in Cimorelli et al. (2003).

AERMOD, a steady-state dispersion model, includes the effects on dispersion from vertical variations in the PBL. In the SBL the concentration distribution is Gaussian, both vertically and horizontally, as is the horizontal distribution in the CBL. However, the CBL’s vertical concentration distribution is described with a bi-Gaussian PDF, as demonstrated by Willis and Deardorff (1981). Buoyant plume mass that penetrates the elevated stable layer is tracked by AERMOD and allowed to reenter the mixed layer at some distance downwind.

For flow in complex terrain, AERMOD incorporates the concept of a dividing streamline (Snyder et al. 1985), and the plume is modeled as a combination of terrain-following and terrain-impacting states. The model considers the influence of building wakes and it enhances vertical turbulence to account for the “convective like” boundary layer found in nighttime urban areas.

This paper describes 1) algorithms for estimating PBL parameters, 2) algorithms for developing vertical meteorological profiles, 3) an approach for handling PBL inhomogeneity, 4) the approach used to establish the influence of terrain, 5) the general structure of the dispersion model, 6) the dispersion algorithms, 7) the building downwash algorithms, and 8) treatment of the urban boundary layer. Perry et al. (2005, hereinafter Part II) discusses the performance evaluation of AERMOD against 17 experimental databases.

## Meteorological preprocessor (AERMET)

The growth and structure of the PBL 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, albedo, and available surface moisture. As with models like HPDM (Hanna and Paine 1989; Hanna and Chang 1993) and CTDMPLUS (Perry 1992), AERMOD utilizes surface and mixed-layer scaling to characterize the structure of the PBL. AERMOD’s meteorological preprocessor (AERMET) requires, as input, surface characteristics, cloud cover, a morning upper-air temperature sounding, and one near-surface measurement of wind speed, wind direction, and temperature. With this, the model computes the friction velocity, Monin–Obukhov length, convective velocity scale, temperature scale, mixing height, and surface heat flux. In a manner similar to models like CTDMPLUS and HPDM these scaling parameters are used to construct vertical profiles of wind speed, lateral and vertical turbulence, potential temperature gradient, and potential temperature. Extensive independent evaluations of these scaling parameters and vertical profiles have not been performed for urban and complex terrain situations other than those accomplished in the many references sited. However, evaluations of the overall model have shown that these parameterizations lead to estimates of plume concentration that compare well with a wide variety of field observations (Part II).

### Derived parameters in the CBL

During convective conditions, AERMET characterizes the state of the PBL by first estimating the sensible heat flux (*H*) with a simple energy balance approach (Oke 1978), then the friction velocity (*u*∗) and the Monin–Obukhov length (*L*). With these parameters AERMET can estimate the mixing height (*z _{i}*) and the convective velocity scale (

*w*∗).

*u*∗ (Panofsky and Dutton 1984) is

*k*is the von Kármán constant,

*u*

_{ref}is the wind speed at reference height,

*z*

_{ref}is the lowest surface layer measurement height for wind,

*z*

_{0}is the roughness length, and Ψ

_{m}is defined by Panofsky and Dutton (1984) for the CBL and by van Ulden and Holtslag (1985) for the SBL. Note that braces are used throughout this paper to denote the functional form of variables. Assuming neutral conditions,

*u*∗ and

*L*are initialized using Eq. (1) and

*L*is defined as follows (Wyngaard 1988):

*g*is the acceleration of gravity,

*c*is the specific heat at constant pressure,

_{p}*ρ*is the density, and

*T*

_{ref}is the ambient temperature (K) that is representative of the surface layer. Final values for

*u*∗ and

*L*are found by iterating Eqs. (1) and (2) until convergence. The convective velocity scale (

*w*∗) is estimated from (Deardorff 1970)

*z*

_{ic}is the convective mixing height.

*z*

_{ic}is calculated with a simple one-dimensional energy balance model (Carson 1973), as modified by Weil and Brower (1983). In addition, a mechanical mixing height (

*z*

_{im}) is estimated from an empirically based expression (Venkatram 1980) as

^{3/2}m

^{−1/2}).

For CBL dispersion calculations, the mixing height (*z _{i}*) is defined as the larger of

*z*

_{im}and

*z*

_{ic}.

*Derived parameters in the SBL*

*θ*∗), which sets the “level” of the temperature fluctuations in the surface layer, varies little during the night,

*u*∗ can be determined from

*θ*∗ = 0.09(1 − 0.5

*n*

^{2}) is taken from van Ulden and Holtslag (1985), where

*n*is the fractional cloud cover and the constant 0.09 has units of kelvins.

*β*= 5, the solution for

_{m}*u*∗ is found by substituting Eq. (6) into Eq. (7) (Hanna and Chang 1993; Perry 1992).

Having computed *u*∗ and *θ*∗, AERMET calculates the surface heat flux from Eq. (5). Last, because there is, by definition, no convective component in the SBL, the total mixing depth *z _{i}* is computed as the time-smoothed (Cimorelli et al. 2003) mechanical mixing depth

*z*

_{im}[Eq. (4)].

## Vertical structure of the PBL

AERMOD estimates meteorological profiles using both measurements and similarity parameterizations [i.e., AERMOD uses the shape of the similarity profiles to interpolate between adjacent vertical measurements (Cimorelli et al. 2003)]. AERMOD’s concentration formulations consider the effects from vertical variations in wind, temperature, and turbulence. These profiles are represented by equivalent (effective) values constructed by averaging over the layer through which plume material travels directly from the source to receptor (Cimorelli et al. 2003). The effective parameters are denoted by a tilde throughout the document (e.g., effective wind speed is denoted by *ũ*).

*Wind speed and direction*

*z*

_{0}represents an approximate height of roughness elements below which the profile is assumed to be linear.

Wind direction is assumed to be constant with height both above the highest and below the lowest measurement and to vary linearly between measurements.

*Potential temperature gradient*

In the CBL ∂*θ*/∂*z* is taken to be zero, in the stable interfacial layer it is estimated from the morning temperature sounding, and it is assumed to equal 0.005 K m^{−1} above, as suggested by Hanna and Chang (1991). Measurements (e.g., Clarke et al. 1971) of profiles throughout the day lend support to this approach.

*θ*/∂

*z*is estimated from Dyer (1974) and Panofsky and Dutton (1984) as

*z*

_{mx}= 100 m,

*z*= max(

_{iθ}*z*

_{im}, 100 m), and the constant 0.44 is taken from measurements (Andre and Mahrt 1982). Last, AERMOD limits ∂

*θ*/∂

*z*to a minimum of 0.002 K m

^{−1}(Paine and Kendall 1993).

### Vertical turbulence

*σ*

_{wm}∝

*u*∗) and a convective (

*σ*

_{wc}∝

*w*∗) component, with the total vertical turbulence (

*σ*

^{2}

_{wT}) given by

*σ*

_{wT}=

*σ*

_{wm}. These forms are similar to one introduced by Panofsky et al. (1977) and are included in other dispersion models (e.g., Berkowicz et al. 1986; Hanna and Paine 1989; and Weil 1988a).

*σ*

^{2}

_{wc}) of the total variance is calculated as

*σ*

^{2}

_{wc}to smoothly decay to zero well above

*z*

_{ic}.

*σ*

_{wm}) is assumed to consist of contributions from the current boundary layer (

*σ*

_{wml}) and residual turbulence from the previous day’s boundary layer (

*σ*

_{wmr}), such that

*σ*

_{wml}, following Brost et al. (1982), is

*σ*

_{wml}= 1.3

*u*∗ at

*z*= 0 is consistent with Panofsky et al. (1977). In the absence of measurements above

*z*,

_{i}*σ*

_{wmr}is taken from (Briggs 1973) to be 0.02

*u*{

*z*}.

_{i}### Lateral turbulence

*σ*

_{υm}) and a convective (

*σ*

_{υc}) portion, such that

^{−1}is assumed for

*σ*above

_{υc}*z*.

_{i}*σ*

^{2}

_{υm}varies linearly with height between its value at the surface and an assumed residual value at

*z*

_{im}as is suggested by field observations (e.g., Brost et al. 1982). The value of

*σ*

^{2}

_{υm}at

*z*

_{im}is assumed to persist at higher levels. The profile for lateral mechanical turbulence is calculated as

*σ*

^{2}

_{υm}{

*z*

_{im}} = min(

*σ*

^{2}

_{υo}, 0.25 m

^{2}s

^{−2}) and

*σ*

^{2}

_{υo}is equal to 3.6

*u*

^{2}∗ (Panofsky and Dutton 1984; Izumi 1971; Hicks 1985). In the SBL the turbulence is exclusively mechanical (

*σ*

_{υm}).

## General form of the AERMOD dispersion model with terrain

AERMOD simulates a plume, in elevated terrain, as a weighted sum of concentrations from two limiting states: a horizontal plume (terrain impacting) and a terrain-following plume. Each plume state is weighted using the concepts of the critical dividing streamline and a receptor-specific terrain height scale (*h _{c}*) (Venkatram et al. 2001; Cimorelli et al. 2003).

*C*{

_{T}*x*} is the total concentration,

_{r}, y_{r}, z_{r}*C*{

_{c,s}*x*} is the contribution from the horizontal plume (subscripts

_{r}, y_{r}, z_{r}*c*and

*s*refer to convective and stable conditions, respectively),

*C*{

_{c,s}*x*} is the contribution from the terrain-following plume,

_{r}, y_{r}, z_{p}*f*is the weighting factor, {

*x*} is the receptor coordinate,

_{r}, y_{r}, z_{r}*z*(=

_{p}*z*−

_{r}*z*) is the receptor height above local ground, and

_{t}*z*is the local terrain height. Figure 1 illustrates the relationship between the actual plume and AERMOD’s characterization of it.

_{t}The weighting of the two plume states depends on the amount of mass residing in each state. This mass partitioning is based on the relationship between the critical dividing streamline height (*H _{c}*) (Sheppard 1956; Snyder et al. 1985) and the vertical concentration distribution at a receptor. Complex terrain in often characterized by a number of irregularly shaped hills. Venkatram et al. (2001) first proposed the idea that

*H*could be calculated using a receptor-specific height scale (

_{c}*h*) that represents the height of a single isolated hill, which would act to affect the flow at the receptor in a manner similar to the real terrain. In this way, the participating of the plume mass into the two states is receptor specific. For a receptor at elevation

_{c}*z*and an effective plume height of

_{t}*h*, the height of the terrain-following state, at that receptor, is

_{e}*z*+

_{t}*h*. For streamlines to reach the terrain-following height the actual terrain that influences the flow at the receptor must extend up to or above this height; in this case,

_{e}*h*=

_{c}*z*+

_{t}*h*. If the actual terrain is less than

_{e}*z*+

_{t}*h*then

_{e}*h*is set to the actual terrain height that causes the maximum vertical displacement of the plume above the receptor. Therefore, for any receptor,

_{c}*h*is defined as the minimum of the highest actual terrain and the terrain-following height at that receptor. The dividing streamline height is computed using the same integral formula found in CTDMPLUS (Perry 1992), with

_{c}*h*substituted for hill height.

_{c}*H*(i.e.,

_{c}*φ*) is computed as

_{p}*H*= 0 and

_{c}*φ*= 0.

_{p}As described by Venkatram et al. (2001), the plume-state weighting factor *f* is given by *f* = 0.5(1 + *φ _{p}*). When the plume is entirely below

*H*(

_{c}*φ*= 1.0 and

_{p}*f*= 1.0) the concentration is determined by the horizontal plume only. When the plume is entirely above the critical dividing streamline height or when the atmosphere is convective,

*φ*= 0 and

_{p}*f*= 0.5. That is, during convective conditions the concentration at an elevated receptor is the average of the contributions from the two states. As plumes above

*H*encounter terrain and are deflected vertically, there is also a tendency for plume material to approach the terrain surface and to spread out around the sides of the terrain. To simulate this, concentration estimates always contain a component from the horizontal state. Evaluation of the model against field observations supports this assumption (Part II). Therefore, under no conditions is the plume allowed to completely approach the terrain-following state. For flat terrain, the contributions from the two states are equal in value and are equally weighted.

_{c}## AERMOD concentration predictions in the SBL

*L*> 0), AERMOD estimates concentrations from

*z*

_{ieff}is the effective mechanical mixing height,

*σ*

_{zs}is the total vertical dispersion,

*h*

_{es}is the plume height (Weil 1988b; Cimorelli et al. 2003), and

*F*is the lateral distribution functions.

_{y}Above the mechanical mixing layer turbulence is expected to be small. AERMOD is designed with an effective mixing lid *z*_{ieff} that retards but does not prevent plume material from spreading into this region of low turbulence. When the plume is below *z*_{im} but its “upper edge” (plume height plus 2.15*σ*_{zs}) reaches *z*_{im}, *z*_{ieff} is allowed to increase, maintaining its position relative to the plume.

*p*= 0.5,

*ũ*is the wind speed,

*σ̃*

_{υ}is lateral turbulence velocity [Eq. (15)], and

*T*

_{Ly}is the Lagrangian integral time scale. Application of Eq. (22) in a preliminary version of AERMOD yielded poor comparisons with data from the Prairie Grass Experiment (Barad 1958); the lateral spread was not well matched. In response, the lateral dispersion expression was reformulated to better fit the data.

*T*

_{Ly}is written as

*l*/

*σ̃*

_{υ}, where

*l*is a lateral turbulent length scale. This allows Eq. (22) to be written in terms of the nondimensional downwind distance

*X*and a nondimensional height scale

*δ*:

*X*=

*σ̃*

_{υ}

*x*/

*ũz*, and

_{i}*δ*=

*z*/

_{i}*l*.

Using a subset of stable and convective cases from the Prairie Grass Experiment, Eq. (23) (based on Taylor 1921) produced the best *σ _{y}* comparisons with

*δ*and

*p*set equal to 78, and 0.3, respectively. In an independent comparison with the full dataset (Fig. 2), Eq. (23) was found to fall within this widely scattered data, yet it tended toward the lower end of the distribution of measured dispersion. More important, good agreement between AERMOD concentration predictions and Prairie Grass observations was found (Part II).

*σ*

_{zs}) is assumed to be composed of contributions from an elevated (

*σ*

_{zes}) and near-surface (

*σ*

_{zgs}) component. Lacking a strong physical justification otherwise, for

*h*

_{es}

*< z*, a simple linear interpolation between the two components is assumed. That is,

_{i}*h*

_{es}is the plume height, and for

*h*

_{es}≥

*z*,

_{i}*σ*

_{zs}is set equal to

*σ*

_{zes}.

*σ̃*

_{wT}is the vertical turbulence due to mechanical mixing [Eq. (11)].

*T*

_{Lzs}=

*l*/

*σ̃*

_{wT}(Venkatram et al. 1984) and interpolating

*l*(1/

*l*= 1/

*l*+ 1/

_{n}*l*) between its neutral (

_{s}*l*= 0.36

_{n}*h*

_{es}) and stable (

*l*= 0.27

_{s}*σ̃*

_{wT}/

*N*) limits allows Eq. (25) to be rewritten as

*N*is the Brunt–Väisälä frequency, that is, the frequency of the particle oscillation about its equilibrium position.

*h*is the stable plume rise above stack top (Cimorelli et al. 2003). Total dispersion is calculated by adding

*σ*, in quadrature, to

_{b}*σ*and also to

_{y}*σ*

_{zs}(Pasquill and Smith 1983).

## AERMOD concentration predictions in the CBL

Unlike the SBL, in the CBL (i.e., convective and neutral stratifications when *L* < 0), the vertical velocity (*w*) distribution is positively skewed and results in a non-Gaussian vertical concentration distribution (Weil et al. 1997; Lamb 1982) and a general descent of the plume centerline for an elevated nonbuoyant source (Lamb 1982; Weil 1988a). The vertical spread in concentration is modeled using a bi-Gaussian distribution, a good approximation to laboratory convection tank data (Baerentsen and Berkowicz 1984). In contrast, the lateral concentration distribution assumes a Gaussian shape, consistent with the lateral velocity distribution (Lamb 1982).

*z*and all subsequent reflections at

_{i}*z*= 0 and

*z*of this indirect mass. A plume-rise component is added to delay the downward dispersion of the indirect source material from the CBL top; this mimics the tendency of buoyant plumes to remain temporarily near

_{i}*z*and resist downward mixing. Additionally, a “penetrated” source (above the CBL top) is included to account for material that initially penetrates the elevated inversion while allowing for it to subsequently reentrain into the growing CBL. The fraction

_{i}*f*of the source material that does not penetrate is

_{p}*h*=

_{h}*z*−

_{i}*h*, and

_{s}*h*

_{eq}is the equilibrium plume rise in a stable environment (Weil et al. 1997).

*C*) in the CBL is found by summing the contribution from the three sources. For the horizontal plume state,

_{c}*C*,

_{d}*C*, and

_{r}*C*are the contributions from the direct, indirect, and penetrated sources, respectively. This three-plume concept is shown schematically in Fig. 3. Similarly, the concentration for the terrain-following state has the form of Eq. (30), but with

_{p}*z*replaced by

_{r}*z*.

_{p}*Direct source contribution to concentrations in the CBL*

*Ψ*

_{dj}=

*h*+ Δ

_{s}*h*+

_{d}*w*

*/*

_{j}x*ũ*is the plume height,

*ũ*is the effective wind speed,

*F*[Eq. (21)] is the lateral distribution function, and Δ

_{y}*h*is the plume rise (Briggs 1984). With

_{d}*z*=

*z*and

_{r}*z*, Eq. (31) estimates concentrations for the horizontal or terrain-following plume, respectively. The subscript

_{p}*j*is equal to 1 for updrafts and 2 for downdrafts with

*λ*defined as the weighting coefficient for each distribution. Equation (31) uses an image plume to handle ground reflections by assuming a source at

_{j}*z*= −

*h*. All subsequent reflections are handled by sources at

_{s}*z*= 2

*z*+

_{i}*h*, −2

_{s}*z*−

_{i}*h*, 4

_{s}*z*+

_{i}*h*, −4

_{s}*z*−

_{i}*h*, and so on.

_{s}The lateral dispersion coefficient (*σ _{y}*), in the equation for

*F*, is estimated using the same approach that is used for the SBL [Eqs. (22) and (23)].

_{y}*σ*

_{zj}) is composed of an elevated (

*σ*

_{zej}) and surface (

*σ*

_{zg}) portion, such that

*σ*

_{wj}is the standard deviation of the updraft (

*j*= 1) and downdraft (

*j*= 2) distributions of vertical wind speed. The coefficient

*α*= min(0.6 + 4Ψ

_{b}_{dj}/

*z*, 1.0) is designed to be 1.0 above the surface layer (

_{i}*ψ*

_{dj}≥ 0.1

*z*) and match Venkatram’s (1992) result for a surface source in neutral conditions. For the surface component,

_{i}*b*= 0.5. Above the surface layer,

_{c}*σ*

_{zg}is set to zero, while for a surface release, Eq. (34) reduces to the form suggested by Venkatram (1992) for vertical dispersion in the unstable surface layer, that is,

*σ*

_{zg}∝ (

*u*∗/

*ũ*)

^{2}

*x*

^{2}/|

*L*|. The constant

*b*was chosen to provide good agreement between the modeled and observed concentrations for the Prairie Grass Experiment data.

_{c}Total lateral and vertical dispersion, for all CBL plumes, are enhanced by plume buoyancy effects in the same manner as described for the SBL [Eq. (28)].

*Indirect source contribution to concentrations in the CBL*

*σ*

_{zj}and

*F*are the same as defined for the direct source, the plume height

_{y}*ψ*

_{rj}=

*ψ*

_{dj}− Δ

*h*, and Δ

_{i}*h*, which delays vertical mixing to account for residual buoyancy in the plume at the top of the boundary layer, is given by

_{i}*r*and

_{y}*r*are the plume half-widths in the lateral and vertical directions,

_{z}*u*is the wind speed used for plume rise, and

_{p}*α*= 1.4 (see Weil et al. 1997).

_{h}*Penetrated source contribution to concentration in the CBL*

*F*is the same as defined for the SBL and

_{y}*z*

_{ieff}is the height of the upper reflecting surface in a stable layer (see section 6). The penetrated plume height

*h*

_{ep}=

*h*+ Δ

_{s}*h*

_{eq}for (

*f*0), while for partial penetration

_{p}=*h*

_{ep}= (

*h*+

_{s}*z*/2) + 0.75Δ

_{i}*h*

_{eq}. The vertical dispersion coefficient (

*σ*

_{zp}) contains only a stable elevated component, Eq. (26), because this source is decoupled from the surface. However, for the penetrated source, Eq. (26) is applied with

*N*set to zero because it must pass into or through the well-mixed CBL prior to reaching ground-level receptors.

## Treatment of lateral plume meander

Plume meander is the slow lateral back-and-forth shifting of the plume in response to nondispersing lateral eddies that are larger than the plume. For time-averaged concentrations, meander has the effect of increasing the lateral spread of the actual plume’s distribution. Meander is treated by interpolating the concentrations that result from two limits of the horizontal distribution function (*F _{y}*)—the coherent plume limit

*F*

_{yC}(which assumes that the wind direction is distributed about a well-defined mean direction) and the random plume limit

*F*

_{yR}(which assumes that the plume has equal probability of moving in any direction). The estimated concentration is a weighted sum of the concentrations from these two limits, where the weighting is proportional to the horizontal energy in each of these state.

*F*

_{yC}has the familiar Gaussian form

*F*

_{yR}is written as

*x*is the straight line distance from the source to the receptor.

_{r}*C*) is determined as a weighted sum of the coherent (

_{c,s}*C*

_{Ch}) and random (

*C*) plume concentrations as

_{R}*C*

_{Ch}is computed from Eq. (20) in the SBL and from Eq. (30) in the CBL, with the lateral terms replaced by Eq. (38). Similarly,

*C*is computed with the lateral terms replaced by Eq. (39). The weighting factor is the ratio of the random component of the horizontal wind energy (

_{R}*σ*

^{2}

*) to the total horizontal wind energy (*

_{r}*σ*

^{2}

*).*

_{h}*ū*, and random components

*σ*and

_{u}*σ*. Thus, a measure of the total horizontal wind “energy” can be represented as

_{υ}*u*

*ũ*

^{2}− 2

*σ̃*

^{2}

_{υ})

^{1/2}. The random component is initially 2

*σ̃*

^{2}

_{υ}and becomes equal to

*σ*

^{2}

*at large travel times when the mean wind is uncorrelated, as is seen in the following expression for*

_{h}*σ*

^{2}

*:*

_{r}*T*is an autocorrelation time scale that is set to 24 h for uncorrelated winds (Brett and Tuller 1991).

_{r}## Building downwash

AERMOD incorporates the Plume Rise Model Enhancements (PRIME) algorithms to handle plumes that are affected by building wakes. A detailed description of PRIME’s formulation is found in Schulman et al. (2000). Conceptually, PRIME partitions plume mass between a cavity and wake region according to boundaries that are specified by the lateral and vertical separation streamlines. Dispersion of the mass that is initially captured within the cavity is based on building geometry and is assumed to be uniformly mixed. Beyond the cavity region, this mass is emitted into the wake where it is combined with uncaptured plume mass and dispersed at an enhanced rate (beyond ambient dispersion). In the wake, turbulence smoothly decays with distance, achieving ambient levels in the far field. Plume rise 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, and velocity deficit.

*C*

_{total}) is calculated as follows:

*C*

_{prime}is the concentration that is estimated using the PRIME algorithms with AERMOD-derived meteorological inputs and

*C*

_{AERMOD}is the concentration that is estimated using AERMOD without building effects. The weighting parameter

*γ*is designed such that the contribution from the PRIME calculation decreases exponentially with vertical, lateral, and downwind distance from the wake boundaries. That is,

*x*is the distance from the upwind edge of the building to the receptor,

*y*is the crosswind distance from the building centerline to the receptor,

*z*is the receptor height above ground,

*σ*

_{xg}is the longitudinal dimension of the wake,

*σ*

_{yg}is the distance from the building centerline to lateral edge of the wake, and

*σ*

_{zg}is the height of the wake at the receptor location, as specified in Schulman et al. (2000).

## Dispersion characterization in the urban boundary layer

Although urban surface characteristics influence the boundary layer parameters at all times, the thermal effects of the urban area on the structure of the boundary layer is largest at night and relatively absent during the day (Oke 1998). In built-up areas a weak “convective like” boundary layer forms during nighttime hours when stable rural air flows onto a warmer urban surface. AERMOD accounts for this by enhancing the vertical turbulence beyond that found in the nighttime rural boundary layer. A representative convective velocity scale is defined from the urban heat flux (*H _{u}*) and urban mixed-layer height (

*z*

_{iu}).

*H*is calculated from

_{u}*α*as the “bulk” transfer coefficient. Because the urban–rural temperature difference Δ

*T*has a maximum value on the order of 10°C, and with light winds

_{u−r}*u*∗ on the order of 0.1 m s

^{−1},

*α*should have a maximum value on the order of 0.1 in the city center. Assuming a linear variation of

*α*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 of approximately 0.03. This value of

*α*yields very good concentration comparisons between AERMOD and the Indianapolis, Indiana, data (Part II). Here, Δ

*T*, used to estimate

_{u−r}*H*, is empirically based on data from Oke (1973, 1982) for a number of Canadian cities with populations from 1000 to 2 000 000. These data were collected during conditions of clear skies, low winds, and low humidities, and represent periods of expected maximum urban effect. An empirical fit to these data yields

_{u}*T*

_{max}= 12°C,

*P*= 2 000 000, and

_{o}*P*is the population of the modeling domain.

*z*

_{iu}

*∝ P*

^{1/4}, such that

*z*

_{iuo}is the boundary layer height corresponding to

*P*.

_{o}Hanna and Chang (1991) report lidar measurements from the Indianapolis tracer study for nocturnal conditions. While the mixing heights at night range from 100 to 500 m, they were generally around 400 m during clear, calm conditions. Using 400 m for *z*_{iu} in Eq. (47), and the Indianapolis population of 700 000, the value of *z*_{iuo} is computed to be 500 m. This is not inconsistent with measurements by Bornstein (1968) in New York, New York.

*z*

_{iu}and

*H*into the definitional equation for

_{u}*w*∗ (Deardorff 1970), such that

## Summary

This paper presents a comprehensive description of the AERMOD dispersion model formulations, including AERMOD’s characterization of the boundary layer, the representative terrain used to influence flow, and the specification of model dispersion algorithms for both convective and stable conditions in urban and rural areas. A notable strength of AREMOD’s formulations, particularly in the characterization of the boundary layer, lies in its reliance on previously successful modeling approaches that have been established in the literature, coupled with the developers’ efforts to avoid major discontinuities that are often found in atmospheric dispersion models. The performance of this model has been evaluated, with results documented in Part II.

## Acknowledgments

The authors recognize the significant contributions of Mr. James Paumier of Pacific Environmental Services, Inc., in developing the AERMET preprocessor. This project was made possible through the continued support of Mr. Joe Tikvart, formally of EPA’s Office of Air Quality Planning and Standards (OAQPS), and Mr. Frank Schiermeier, formerly of NOAA’s Atmospheric Sciences Modeling Division. We thank the many scientists who participated in peer reviews and beta testing, especially Dr. Steven Hanna, Dr. Gary Briggs, and Mr. John Irwin. This paper has been reviewed in accordance with the U.S. Environmental Protection Agency’s peer review and administrative review policies for approval for presentation and publication. Mention of trade names or commercial products does not constitute endorsement or recommendation for use.

## REFERENCES

Andre, J. C. and L. Mahrt. 1982. The nocturnal surface inversion and influence of clean-air radiative cooling.

*J. Atmos. Sci.*39:864–878.Baerentsen, J. H. and R. Berkowicz. 1984. Monte Carlo simulation of plume dispersion in the convective boundary layer.

*Atmos. Environ.*18:701–712.Barad, M. L. 1958. Project Prairie Grass, A field program in diffusion. Vols. I and II, Geophysical Research Papers No. 59, Air Force Cambridge Research Center, AFCRC-TR-58-235, 439 pp.

Berkowicz, R., J. R. Olesen, and U. Torp. 1986. The Danish Gaussian air pollution model (OLM): Description, test and sensitivity analysis, in view of regulatory applications.

*Air Pollution Modeling and Its Application*, V. C. De Wispelaire, F. A. Schiermeier, and N. V. Gillani, Eds., Plemum, 453–481.Bornstein, R. D. 1968. Observations of urban heat island effects in New York city.

*J. Appl. Meteor.*7:575–582.Brett, A. C. and S. E. Tuller. 1991. Autocorrelation of hourly wind speed observations.

*J. Appl. Meteor.*30:823–833.Briggs, G. A. 1973. Diffusion estimation for small emissions. Air Resources Atmospheric Turbulence and Diffusion Laboratory, Environmental Research Laboratory, NOAA, 1973 Annual Rep. ATDL-79, 59 pp.

Briggs, G. A. 1984. Plume rise and buoyancy effects.

*Atmospheric Science and Power Production*, D. Randerson, Ed., U.S. Department of Energy, 327–366.Briggs, G. A. 1988. Analysis of diffusion field experiments.

*Lectures on Air Pollution Modeling*, A. Venkatram and J. C. Wyngaard, Eds., Amer. Meteor. Soc., 63–117.Brost, R. A., J. C. Wyngaard, and D. H. Lenschow. 1982. Marine stratocumulus layers. Part II: Turbulence budgets.

*J. Atmos. Sci.*39:818–836.Businger, J. A. 1973. Turbulent transfer in the atmospheric surface layer.

*Workshop on Micrometeorology*, D. A. Haugen, Ed., Amer. Meteor. Soc., 67–100.Carruthers, D. J. Coauthors 1994. UK-ADMS: A new approach to modelling dispersion in the Earth’s atmospheric boundary layer.

*J. Wind Eng. Indust. Aerodyn.*52:139–153.Carson, D. J. 1973. The development of a dry inversion-capped convectively unstable boundary layer.

*Quart. J. Roy. Meteor. Soc.*99:450–467.Caughey, S. J. and S. G. Palmer. 1979. Some aspects of turbulence structure through the depth of the convective boundary layer.

*Quart. J. Roy. Meteor. Soc.*105:811–827.Cimorelli, A. J., S. G. Perry, R. F. Lee, R. J. Paine, A. Venkatram, J. C. Weil, and R. B. Wilson. 1996. Current progress in the AERMIC model development program. Preprints,

*89th Annual Meeting Air and Waste Management Association*, Pittsburgh, PA, Air and Waste Management Association, 1–27.Cimorelli, A. J., S. G. Perry, A. Venkatram, J. C. Weil, R. J. Paine, R. B. Wilson, R. F. Lee, and W. D. Peters. 2003. AERMOD description of model formulation. U.S. Environmental Protection Agency, EPA Rep. 454/R-03-002d, 85 pp.

Clarke, R. H., A. J. Dyer, R. R. Brook, D. G. Reid, and A. J. Troop. 1971. The Wangara experiment: Boundary layer data. Division of Meteorological Physics CSIRO Tech. Rep. 19, 358 pp.

Deardorff, J. W. 1970. Convective velocity and temperature scales for the unstable boundary layer for Rayleigh convection.

*J. Atmos. Sci.*27:1211–1213.Deardorff, J. W. 1972. Numerical investigation of neutral and unstable planetary boundary layers.

*J. Atmos. Sci.*29:91–115.Dyer, A. J. 1974. A review of flux-profile relationships.

*Bound.-Layer Meteor.*7:363–372.Hanna, S. R. 1983. Lateral turbulence intensity and plume meandering during stable conditions.

*J. Appl. Meteor.*22:1424–1430.Hanna, S. R. and R. J. Paine. 1989. Hybrid Plume Dispersion Model (HPDM) development and evaluation.

*J. Appl. Meteor.*28:206–224.Hanna, S. R. and J. S. Chang. 1991. Analysis of urban boundary layer data. Vol. III, Modification of the Hybrid Plume Dispersion Model (HPDM) for Urban Conditions and Its Evaluation Using the Indianapolis Data Set, Electric Power Research Institute Project RP-02736-1, 131 pp.

Hanna, S. R. and J. S. Chang. 1993. Hybrid Plume Dispersion Model (HPDM), improvements and testing at three field sites.

*Atmos. Environ.*27A:1491–1508.Hicks, B. B. 1985. Behavior of turbulent statistics in the convective boundary layer.

*J. Climate Appl. Meteor.*24:607–614.Izumi, Y. 1971. Kansas 1968 Field Program data report. Air Force Cambridge Research Laboratory, No. 379, AFCRL-72-0041, 79 pp.

Kaimal, J. C., J. C. Wyngaard, D. A. Haugen, O. R. Cote, Y. Izumi, S. J. Caughey, and C. J. Readings. 1976. Turbulence structure in the convective boundary layer.

*J. Atmos. Sci.*33:2152–2169.Lamb, R. G. 1982. Diffusion in the convective boundary layer.

*Atmospheric Turbulence and Air Pollution Modelling*, F. T. M. Nieuwstadt and H. van Dop, Eds., Reidel, 159–229.Nieuwstadt, F. T. M. and H. van Dop. 1982.

*Atmospheric Turbulence and Air Pollution Modelling*. Reidel, 358 pp.Oke, T. R. 1973. City size and the urban heat island.

*Atmos. Environ.*7:769–779.Oke, T. R. 1978.

*Boundary Layer Climates*. John Wiley and Sons, 372 pp.Oke, T. R. 1982. The energetic basis of the urban heat island.

*Quart. J. Roy. Meteor. Soc.*108:1–24.Oke, T. R. 1998. An algorithmic scheme to estimate hourly heat island magnitude. Preprints,

*Second Urban Environment Symp.*, Albuquerque, NM, Amer. Meteor. Soc., 80–83.Paine, R. J. and S. B. Kendall. 1993. Comparison of observed profiles of winds, temperature, and turbulence with theoretical results. Preprints,

*Joint Conf. of the American Meteorological Society and Air and Waste Management Association Specialty Conf.: The Role of Meteorology in Managing the Environment in the 90s*, Scottsdale, AZ, Air and Waste Management Association, Publication VIP-29, 395–413.Panofsky, H. A. and J. A. Dutton. 1984.

*Atmospheric Turbulence: Models and Methods for Engineering Applications*. John Wiley and Sons, 417 pp.Panofsky, H. A., H. Tennekes, D. H. Lenschow, and J. C. Wyngaard. 1977. The characteristics of turbulent velocity components in the surface layer under convective conditions.

*Bound.-Layer Meteor.*11:355–361.Pasquill, F. 1976. Atmospheric dispersion parameters in Gaussian plume modeling—Part III: Possible requirements for change in the Turner’s Workbook values. U.S. Environmental Protection Agency Rep. EPA-600/4-76-030B, 53 pp.

Pasquill, F. and F. R. Smith. 1983.

*Atmospheric Diffusion*. John Wiley and Sons, 440 pp.Perry, S. G. 1992. CTDMPLUS: A dispersion model for sources in complex topography. Part I: Technical formulations.

*J. Appl. Meteor.*31:633–645.Perry, S. G. Coauthors 1989. Model description and user instructions. Vol. 1, User’s Guide to the Complex Terrain Dispersion Model Plus Algorithms for Unstable Situations (CTDMPLUS), U.S. Environmental Protection Agency Rep. EPA/600/8-89/041, 196 pp.

Perry, S. G., A. J. Cimorelli, R. F. Lee, R. J. Paine, A. Venkatram, J. C. Weil, and R. B. Wilson. 1994. AERMOD: A dispersion model for industrial source applications. Preprints,

*87th Annual Meeting of the Air and Waste Management Association*, Pittsburgh, PA, Air and Waste Management Association, Publication 94-TA2.3.04, 16 pp.Perry, S. G., A. J. Cimorelli, J. C. Weil, A. Venkatram, R. J. Paine, R. B. Wilson, R. F. Lee, and W. D. Peters. 2005. AERMOD: A dispersion model for industrial source applications. Part II: Model performance against seventeen field-study databases.

*J. Appl. Meteor.*44:694–708.Readings, C. J., D. A. Haugen, and J. C. Kaimal. 1974. The 1973 Minnesota atmospheric boundary layer experiment.

*Weather*29:309–312.Schulman, L. L., D. G. Strimaitis, and J. S. Scire. 2000. Development and evaluation of the PRIME plume rise and building downwash model.

*J. Air Waste Manage. Assoc.*50:378–390.Sheppard, P. A. 1956. Airflow over mountains.

*Quart. J. Roy. Meteor. Soc.*82:528–529.Snyder, W. H., R. S. Thompson, R. E. Eskridge, R. E. Lawson, I. P. Castro, J. T. Lee, J. C. R. Hunt, and Y. Ogawa. 1985. The structure of the strongly stratified flow over hills: Dividing streamline concept.

*J. Fluid Mech.*152:249–288.Stull, R. B. 1983. A heat flux history length scale for the nocturnal boundary layer.

*Tellus*35A:219–230.Sykes, R. I., D. S. Henn, and S. F. Parker. 1996. SCIPUFF—A generalized hazard dispersion model. Preprints,

*Ninth Joint Conf. on Applications of Air Pollution Meteorology with AWMA*, Atlanta, GA, Amer. Meteor. Soc., 184–188.Taylor, G. I. 1921. Diffusion by continuous movements.

*Proc. London Math. Soc. Ser.*2:20,. 196–211.Turner, D. B., T. Chico, and J. Catalano. 1986. TUPOS—A multiple source Gaussian dispersion algorithm using on-site turbulence data. U.S. Environmental Protection Agency Rep. EPA/600/8-86/010, 39 pp.

U.S. Environmental Protection Agency 1995. User instructions. Vol. 1, User’s Guide for the Industrial Source Complex (ISC3) Dispersion Models (revised), Environmental Protection Agency Rep. EPA-454/b-95-003a, 390 pp.

van Ulden, A. P. and A. A. M. Holtslag. 1985. Estimation of atmospheric boundary layer parameters for diffusion applications.

*J. Climate Appl. Meteor.*24:1196–1207.Venkatram, A. 1978. Estimating the convective velocity scale for diffusion applications.

*Bound.-Layer Meteor.*15:447–452.Venkatram, A. 1980. Estimating the Monin-Obukhov length in the stable boundary layer for dispersion calculations.

*Bound.-Layer Meteor.*19:481–485.Venkatram, A. 1988. Dispersion in the stable boundary layer.

*Lectures on Air Pollution Modeling*, A. Venkatram and J. C. Wyngaard, Eds., Amer. Meteor. Soc., 229–265.Venkatram, A. 1992. Vertical dispersion of ground-level releases in the surface boundary layer.

*Atmos. Environ.*26A:947–949.Venkatram, A. and J. C. Wyngaard. 1988.

*Lectures on Air Pollution Modeling*. Amer. Meteor. Soc., 390 pp.Venkatram, A., D. G. Strimaitis, and D. Dicristofaro. 1984. A semiemperical model to estimate vertical dispersion of elevated releases in the stable boundary layer.

*Atmos. Environ.*18:923–928.Venkatram, A. Coauthors 2001. A complex terrain dispersion model for regulatory applications.

*Atmos. Environ.*35:4211–4221.Weil, J. C. 1985. Updating applied diffusion models.

*J. Climate Appl. Meteor.*24:1111–1130.Weil, J. C. 1988a. Dispersion in the convective boundary layer.

*Lectures on Air Pollution Modeling*, A. Venkatram and J. C. Wyngaard, Eds., Amer. Meteor. Soc., 167–227.Weil, J. C. 1988b. Plume rise.

*Lectures in Air Pollution Modeling*, A. Venkatram and J. C. Wyngaard, Eds., Amer. Meteor. Soc., 119–162.Weil, J. C. 1992. Updating the ISC model through AERMIC. Preprints,

*85th Annual Meeting of Air and Waste Management Association*, Pittsburgh, PA, Air and Waste Management Association, Publication 92-100.11, 14 pp.Weil, J. C. and R. P. Brower. 1983. Estimating convective boundary layer parameters for diffusion applications. Maryland Power Plant Siting Program, Maryland Department of Natural Resources Rep. PPSP-MD-48, 45 pp.

Weil, J. C. and R. P. Brower. 1984. An updated gaussian plume model for tall stacks.

*J. Air Pollut. Control Assoc.*34:818–827.Weil, J. C., L. A. Corio, and R. P. Brower. 1997. A PDF dispersion model for buoyant plumes in the convective boundary layer.

*J. Appl. Meteor.*36:982–1003.Willis, G. E. and J. W. Deardorff. 1981. A laboratory study of dispersion in the middle of the convectively mixed layer.

*Atmos. Environ.*15:109–117.Wyngaard, J. C. 1988. Structure of the PBL.

*Lectures on Air Pollution Modeling*, A. Venkatram and J. C. Wyngaard, Eds., Amer. Meteor. Soc., 9–57.

Lateral spread (*σ** _{y}*) as a function of nondimensional distance (

*X*). The data are taken from the Prairie Grass Experiment (Barad 1958).

Citation: Journal of Applied Meteorology 44, 5; 10.1175/JAM2227.1

Lateral spread (*σ** _{y}*) as a function of nondimensional distance (

*X*). The data are taken from the Prairie Grass Experiment (Barad 1958).

Citation: Journal of Applied Meteorology 44, 5; 10.1175/JAM2227.1

Lateral spread (*σ** _{y}*) as a function of nondimensional distance (

*X*). The data are taken from the Prairie Grass Experiment (Barad 1958).

Citation: Journal of Applied Meteorology 44, 5; 10.1175/JAM2227.1

AERMOD’s three-plume treatment of the CBL.

Citation: Journal of Applied Meteorology 44, 5; 10.1175/JAM2227.1

AERMOD’s three-plume treatment of the CBL.

Citation: Journal of Applied Meteorology 44, 5; 10.1175/JAM2227.1

AERMOD’s three-plume treatment of the CBL.

Citation: Journal of Applied Meteorology 44, 5; 10.1175/JAM2227.1