6.2 Photochemical Air Pollution Modeling

The main objective of Photochemical Air Quality Simulation Models (PAQSMs) is to establish causal relations among emission levels, meteorological conditions and ambient air quality. These are numerical models that simulate the transport and chemical transformation of pollutants in the atmosphere. Air quality can be modeled via prognostic modeling, that is based on the fundamental physiochemical principles governing air pollution, and as via diagnostic modeling, that is statistical description of observed data.

These models have been applied to local scale (e.g., plume models), to urban and regional scales (e.g., airshed models). The applications of PAQSMs range from simulation of transport and transformation of chemicals over a few kilometers over few hours (local scale) to over a few thousand kilometers over a few weeks (regional scale).

In the application of PAQSMS, one of the main pollutants of concern is ozone, as mentioned in Chapter 5.2 and Appendix C. Ozone is a ``secondary pollutant'' formed through nonlinear chemical reactions between precursor species, oxides of nitrogen (NO$_x$) and volatile organic compounds (VOCs) that are emitted by a wide variety of both anthropogenic and natural (biogenic) emissions sources. Certain meteorological conditions can significantly enhance the ambient concentrations of ozone in specific locales, leading to substantial health risks [182,78]. The PAQSMs are employed to study the effectiveness of various alternative strategies for reductions in emissions with respect to reductions in ambient ozone levels.

6.2.1 Mathematical and Numerical Formulation of PAQSMs

Many PAQSMs are based on the fundamental description of atmospheric transport and chemical processes. The atmospheric diffusion equation, given by

 

$$\frac{\partial \left< c_{i} \right>}{\partial t} + \overline{u}_{... ...ght>,\ldots,\left<c_{N}\right>\right) + \mathit{S}_{i}\left(\mathbf{x},t\right)$$ (6.1)

is typically employed to describe the pollutant concentration in a selected control volume. This equation expresses the conservation of mass of each pollutant in a turbulent fluid in which chemical reactions occur. In the above equation, $\left<\,\cdot\,\right>$ represents the ensemble average, $c_{i}$ is the concentration, $\mathit{R}_{i}$ is the rate of formation of the $i$th species, $\mathit{K}_{jj}$ is the turbulent dispersion coefficient (obtained by approximating turbulent transport with a gradient diffusion scheme), and $\mathit{S}_{i}$ is the rate of emissions of the $i$th species into the control volume. The Einstein summation convention is used here with respect to the subscript $j$. A more detailed description of the atmospheric diffusion is given in Appendix C (Equation C.1).

The assumptions leading to the atmospheric diffusion equation above include: (a) first order closure approximation (i.e., turbulent fluxes are approximated by a gradient driven fluxes), (b) negligence of molecular diffusion compared to turbulent dispersion, (c) incompressibility of the atmosphere, and (d) approximation of ensemble average of reaction rates with the reaction rates for ensemble averages.

Air quality models can be broadly categorized into the following types:

Box models: These are the simplest of the numerical models for air quality modeling. The region to be modeled is treated as a single cell, or box, bounded by the ground at the bottom, and some upper limit to the mixing on the top, and the east-west and north-south boundaries on the sides. Here, the pollutant concentrations in a volume of air, a ``box'', are spatially homogeneous and instantaneously mixed. Under these conditions, the pollutant concentrations can be described by a balance among the rates they are transported in and out of the volume, their rates of emissions, and the rates at which pollutants react chemically or decay. Since these models lack spatial resolution, they cannot be used in situations where the meteorological or emissions patterns vary significantly across the modeling region.

Grid Models: Grid models employ a fixed Cartesian reference system and divide the modeling region into a two- or three-dimensional array of uniform grid cells. Horizontal dimensions of each cell usually measure on the order of kilometers, while vertical dimensions can vary from a few meters to a few hundred meters. One example of the grid models is the Urban Airshed Model (UAM), briefly described in Section 5.3 and in Appendix C.

Grid models as currently designed are generally not capable of resolving pollutant concentrations at the microscale - that is, at scales smaller than the size of a grid cell. Thus, important local effects, such as high pollutant concentrations in the immediate vicinity of point sources, tend to become obscured by the averaging of pollutant concentrations over the grid cell volume.

There are practical and theoretical limitations to the minimum grid cell size. Increasing the number of cells increases computing and data acquisition effort and costs. In addition, choice of a grid cell implies that the input data, such as the wind flows, turbulence, and emissions, are resolved to that scale. In practice, most applications employ grid cell sizes of a few kilometers. Further, the assumptions involved in the formulation of the atmospheric diffusion equation make it applicable for gird models with horizontal resolution coarser than 2 km[137].

These models are used to assess the effectiveness of emissions reductions at a urban/regional scale. In essence, considering the domain-wide effects of emissions reductions. As these models assume uniform conditions within each grid cell, all the local scale processes are lumped into one average quantity.

Trajectory Models: The trajectory models use a moving coordinate approach to describe pollutant transport. Here, the atmospheric diffusion equation is solved in an air parcel of interest, which is assumed to travel solely with the horizontal wind. These models give results only on the path of traversed by the air parcel described, and do not permit construction of the spatial and temporal variation of concentrations over the entire region. However, their utility is in the calculation of extreme concentrations that are typically found in the plumes from point sources.

Since the numerical grids used in grid models are considerably large in size (on the length scales of a few kilometers), an understanding of the ``sub-grid'' effects is important in order to assess local scale effects. In order to describe the sub-grid phenomena, with specific emphasis on establishing causal relationships between emissions from point sources (such as industrial stacks) and the pollutant concentrations in the neighborhood of the point sources, plume models are employed. Plume models are trajectory models that describe short term behavior of the plume of emissions from a point source. The typical time scales range from 1 hour to 24 hours, with length scales ranging from a few hundred meters to a few kilometers. Such detail cannot be achieved by increasing the resolution of grid-based models, since the model formulation of the grid-based models is not valid for finer resolutions (i.e., less than 2 km length scales). The formulation of the grid models and of the plume models is discussed extensively in the literature [80,181,144,78,223].