The air pollution modeling (APM) area has developed substantially during the last 15-20 years mainly due to the advances in computer power and technology and also due to the advance in numerical techniques. Atmospheric models are used to assess the distribution of toxic pollutants which are often used in ecotoxicology and also the impact of air pollutants on human health. The development of comprehensive air quality models (AQMs) started in the late 1970s. The urban Airshed Model (UAM), followed by the Regional oxidant model (ROM) provided Eulerianbased models for ozone; the former for urban and the latter for regional scale. The Sulfur Transport and Emission Model (STEM) focused on regional and continental acid deposition modeling. The CMAQmodeling system is capable of processing great and diverse information from complicated emission mixtures and complex distribution of sources, to modeling the complexities of atmospheric process that transport and transform these mixtures in a dynamic environment that operates in a large range of timescales covering minutes to days to weeks. The European CHIMERE model was primarily developed for producing air quality forecasts at European level. An air quality modeling system consists of a meteorological model (offline or online coupled), an emissions model, and an AQM. The meteorological model calculates as a function of time the three-dimensional fields of wind, temperature, relative humidity, pressure, and in some cases, turbulent eddy diffusivity, clouds, and precipitation. The emissions model estimates the amount and chemical speciation of low-level (area sources) and elevated (point sources) primary pollutants based on process information (e.g., vehicle miles traveled) and day-specific meteorology (e.g., temperature). The output of the emissions and meteorological models is then input into the AQM, which calculates the concentrations and deposition rates of gases and aerosols as a function of space and time. There are various mathematical models that can be used to simulate meteorology and air quality at the mesoscale domain. Although mathematical models differ in their treatment of meteorology or air quality (e.g., considering feedback mechanisms), all three-dimensional models are based on a similar framework and consist of the same major components.
The main components of the AQMs are:
1. a transport and diffusion component that calculates the three-dimensional motion of gases and aerosols in a gridded model domain;
2. a gas-phase chemistry component that calculates the change in gaseous concentrations due to chemical transformations;
3. an aerosol component that calculates the size distribution and chemical composition of aerosols due to chemical and physical transformations;
4. a cloud/fog component that calculates the physical characteristics of clouds and fog based on information from the meteorological model (or from observation);
5. a cloud/fog chemistry component that calculates the change in chemical concentrations in clouds and fog;
6. a wet deposition component that calculates the rates of deposition due to precipitation (and, possibly, cloud impaction and fog settling) and the corresponding change in chemical concentrations;
7. a dry deposition component that calculates the rates of dry deposition for gases and aerosols and the corresponding changes in their concentrations.
The spatial distribution of meteorological and chemical variables is approximated by three-dimensional gridded systems. The meteorological and the AQMs may have different grid structures over the same domain and methods of the numerical discretization. The detailed modular formation varies from model to model. It is possible, however, to formulate a general modular framework that is common to most three-dimensional modeling systems. First, the spatial and temporal resolutions of the modeling system must be defined. For example, the meteorological model may use a system based on altitude (with respect to mean sea level), whereas the AQM may use a terrain-following coordinate system. The output of the meteorological model will need to be processed to provide meteorological fields that match the gridded system of the AQM. The emissions model uses a gridded spatial resolution that is consistent with that of the AQM-The spatial resolution does not need to be uniform throughout the domain. In the vertical direction, meteorological and AQMs typically, due to the importance of the boundary layer structure, use a finer resolution near ground level than aloft. In addition, nesting of domains with different horizontal resolutions may be performed to accommodate the need for fine spatial resolution (e.g., in the order of 1-5 km) in critical source or receptor areas without penalizing the computational cost over the entire domain (where a larger horizontal grid size of the order of 20 km would be used). The three-dimensional field of meteorological variables can be constructed by a diagnostic model that uses interpolation techniques to develop a three-dimensional field based on a discrete set of data or by a dynamic (or prognostic) model that solves the fundamental equations of mass, momentum, and energy to calculate the three-dimensional field of meteorological variables. Diagnostic meteorological models are used mostly for impact assessments and case-study simulations; however for prediction and forecasting air quality modeling the diagnostic approach is less promising.
The quality of the air pollution modeling/forecast and the Air Quality Information and Forecasting Systems (AQIFS) critically depend on:
1. the mapping of emissions,
2. the air pollution (APM) and chemical transport models
3. the meteorological fields over the considered areas.
The main problem in forecasting air quality is the prediction of episodes with high pollutant concentration in urban or complex geographical condition areas where most of the well-known methods and models, based on in situ meteorological measurements, fail to realistically produce the meteorological input fields for the urban air pollution (UAP) models. An additional challenge for contemporary AQ models lies in the fact that the legislation on AQ targets to new categories of information, like the likelihood of hotspot occurrence, or the number of exceedances within a year, that associate AQ forecasting capabilities with urban environment modeling demands, thus making the forecasting issue more complicated.
The governing atmospheric diffusion equation in the generalized coordinates where the turbulent flux terms are expressed with the eddy diffusion theory can be written as:
The terms in eqn  are summarized as follows:
1. time rate of change of pollutant concentration;
2. horizontal advection;
3. vertical advection;
4. horizontal eddy diffusion (diagonal term);
5. vertical eddy diffusion (diagonal term);
6. off-diagonal horizontal diffusion;
7. off-diagonal vertical diffusion;
8. production or loss from chemical reactions;
10. cloud mixing and aqueous-phase chemical production or loss;
11. aerosol process; and
12. plume-in-grid process where j is the trace species concentration in density units (e.g., kgm~3), J is the vertical Jacobian of the terrain-influenced coordinate £, m is the map scale factor, Vs is the vertical and horizontal wind components in the generalized coordinates, qi is the species mass mixing ratio, K is the diagonal component of the eddy diffusivity tensor in the generalized coordinates, p is the density of the air. The dry deposition process can be included in the vertical diffusion process as a flux boundary condition at the bottom of the model layer. The numerical solution of the eqn  is the basis of the so-called air quality dispersion model which is referred to in the present contribution.
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