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 (zi) and the convective velocity scale (w∗).
For CBL dispersion calculations, the mixing height (zi) is defined as the larger of zim and zic.
Derived parameters in the SBL
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 zi is computed as the time-smoothed (Cimorelli et al. 2003) mechanical mixing depth zim [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
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.
Vertical turbulence
Lateral turbulence
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 (hc) (Venkatram et al. 2001; Cimorelli et al. 2003).
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 (Hc) (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 Hc could be calculated using a receptor-specific height scale (hc) 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 zt and an effective plume height of he, the height of the terrain-following state, at that receptor, is zt + he. 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, hc = zt + he. If the actual terrain is less than zt + he then hc is set to the actual terrain height that causes the maximum vertical displacement of the plume above the receptor. Therefore, for any receptor, hc 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 hc substituted for hill height.
As described by Venkatram et al. (2001), the plume-state weighting factor f is given by f = 0.5(1 + φp). When the plume is entirely below Hc (φp = 1.0 and 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, φp = 0 and 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 Hc 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.
AERMOD concentration predictions in the SBL
Above the mechanical mixing layer turbulence is expected to be small. AERMOD is designed with an effective mixing lid zieff that retards but does not prevent plume material from spreading into this region of low turbulence. When the plume is below zim but its “upper edge” (plume height plus 2.15σzs) reaches zim, zieff is allowed to increase, maintaining its position relative to the plume.
Using a subset of stable and convective cases from the Prairie Grass Experiment, Eq. (23) (based on Taylor 1921) produced the best σy 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).
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).
Direct source contribution to concentrations in the CBL
The lateral dispersion coefficient (σy), in the equation for Fy, is estimated using the same approach that is used for the SBL [Eqs. (22) and (23)].
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
Penetrated source contribution to concentration in the CBL
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 (Fy)—the coherent plume limit FyC (which assumes that the wind direction is distributed about a well-defined mean direction) and the random plume limit FyR (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.
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.
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 (Hu) and urban mixed-layer height (ziu).
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 ziu in Eq. (47), and the Indianapolis population of 700 000, the value of ziuo is computed to be 500 m. This is not inconsistent with measurements by Bornstein (1968) in New York, New York.
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.
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AERMOD two-state approach. The total concentration predicted by AERMOD is the weighted sum of the two extreme possible plume states: the horizontal plume state and the terrain-following state.
Citation: Journal of Applied Meteorology 44, 5; 10.1175/JAM2227.1
Lateral spread (σy) 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
