Urban Airshed Model: Algorithms

The Urban Airshed Model, like most photochemical grid models, is based on the numerical solution of a system of partial differential equations (PDEs) that are collectively known as the atmospheric diffusion euqations or the species continuity equations. All of the physical and chemical processes in the atmosphere that affect pollution -- emissions, transport, diffusion, chemical reactions , and pollutant deposition -- are described in these equations.

UAM, again like many photochemical grid models, is used to study photochemical air quality, the air quality that is determined by concentrations of ozone as compared with ambient (background) ozone levels. As has been described in various other readings in the OS411 series, the primary influencing factors for photochemical air quality are:

  • the spatial and temporal distribution of anthropogenic and biogenic NOx and VOCs
  • the composition of the emitted NOx and VOCs
  • the spatial and temporal variations in the wind fields
  • the dynamics of the planetary boundary level (PBL) including stability and mixing levels
  • the chemical reactions as described by the Carbon Bond-IV mechanism
  • the diurnal variations of solar radiation and temperature
  • the loss of ozone and ozone precursors by dry deposition
  • the ambient background of VOCs, NOx, and other species at the immediate outside of the boundary of the study region and above the study region

The atmospheric diffusion equation is shown below:

Graphic of atmospheric diffusion
Some observations on the treatment of the physical and chemical processes in UAM. Probably the most important consideration in this model (and others) is the representation of the atmospheric chemistry processes, as characterized by the Carbon Bond-IV mechanism. This mechanism contains 35 different species as represented by 86 chemical reactions. One of the problems with CB-IV is the fact that many of the equations are vastly different with regard to time scales. For example, one reaction mechanism has reaction times in fractions of a second, while another mechanism has a time scale of hours. This difference (resulting in differential equations that are known as "stiff") makes the computation quite difficult and time consuming. Specialized numerical methods, such as the Crank-Nicholson algorithm are used to try to speed up the calculations. This results in some error to the calculations.

Three other process algorithms are important in the UAM:

  1. Advective pollution transport: as shown in the equation above, we calculate the concentrations of pollutants as a function of both horizontal (U= easterly winds, V=northly winds) and vertical (W=upward winds) wind components, or wind "fields." This is done for each of the 4 to 6 vertical layers in the UAM model (horizontal resolution is typically about 2-5 km, layers extend up to the upper regions of the PBL, about 2 km above the surface). Simply put, the winds control how the different emissions are mixed, advected (transported) downwind, and diluted. The air quality modeler needs to accurately describe the three-dimensional wind variations, usually in hourly time steps.
  2. Turbulent diffusion: dispersion of the pollutants is proportional to the concentration gradient of the pollutants, that is, pollutants flow from areas of high concentration to areas of low concentration. The eddy diffusivity coefficients for both horizontal (KH) and vertical (KV) are approximated in UAM, since exact measurements of these values is difficult.
  3. Surface removal process: dry deposition and other processes work to remove many primary and secondary pollutants from the system. For example, dry deposition occurs as a two-step process: the transfer of pollutants through the atmosphere to the surface and then the uptake of the pollutants by vegetation and other materials at the surface. Some of these calculations are based on theoretical estimates while others are based on experimental data.
Quick Quiz: Why is the Crank-Nicholson algorithm used in UAM?
to improve the accuracy of the calculations
to speed up the complex calculations
to better simulate advective pollution transport calculations
all of the above

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