The Air Pollution Simulation

The Air Pollution Simulation is a demonstration of how gridMathematica can be applied to a complex issue that presents the real-world challenges of serious modeling, and illustrates how Mathematica can provide precise solutions to large-scale problems.

The model simulates the distribution and diffusion of pollution in the atmosphere, accounting for the impacts of wind, solar radiation, and the chemical reactions between pollutants. It is an example of high-level research intended to examine, among other things, the net effect of pollution controls within a region and the most cost-effective strategy for reducing the concentration of pollutants.

The Air Pollution Simulation draws on many disparate data sources in different formats, requires multidisciplinary analysis to combine chemical interactions and wind interactions, and is computationally intensive beyond the scope of single-threaded computation. The solution makes extensive use of Mathematica's Import functionality, differential-equation solvers, visualization capabilities, and dynamic interactivity, and of gridMathematica's integration with grid systems.

Data Integration: Providing a Robust Environment for Efficient Computation through Innovative Technology
The Air Pollution Simulation combines data from a wide variety of primary sources. This is possible through Mathematica's data sources, which provide a unified framework for importing and accessing data. The ability to synthesize data from different locations and in different forms to solve a real-world problem is a key Mathematica capability.

In this case, the following sources were used:

• U.S. Environmental Protection Agency (EPA)
  Average pollutant concentrations for each Illinois county
• National Oceanic and Atmospheric Administration (NOAA) National Weather Service (NWS) Aviation Weather Center
  Upper atmospheric wind speed and direction
• College of DuPage Next Generation Weather Lab (COD NexLab)
  Illinois surface wind speed, wind direction, air temperature, and air pressure
• U.S. Geological Survey (USGS) National Atlas
  Illinois surface elevation and water features
• NASA Shuttle Radar Topography Mission (SRTM)
  Elevation data

Mesh Generation: Using Visualization for Computation
The chemical and wind field models in the Air Pollution Simulation are solved on an unstructured, refined 3D mesh. Each of the 2D layers is generated with Mathematica's DensityPlot function by extracting the mesh used to create the graphic. The 2D layers are combined to make the final 3D solution mesh. This approach draws on Mathematica's ability to plot arbitrary mathematical functions, allowing adaptive, refined meshes uniquely optimized for a particular problem.

Dynamic Graphics: Bringing Data to Life with Mathematica
The cloud that represents the pollutant concentrations in the example is rendered using a spherical collection of translucent points for each point on the solution mesh. The size and density of the collection at each point is dependent on the pollutant concentration at that point, computed by the chemistry and wind models. Using Mathematica's dynamic computing capabilities, the cloud is automatically re-rendered continuously, triggered as the equations evolve. As a result, after the initial visualization is created, no extra work is required to change the visualization as the simulation progresses.

Parallelism: High-Performance Computing Is Highly Productive with gridMathematica
The Air Pollution Simulation is parallelized using the Partition function, splitting the mesh into blocks, as many as there are computing processors, with overlapping boundaries. The chemistry and wind models are solved individually on each sub-mesh. The exchanges of new pollution concentrations along the boundaries are implemented in high-level gridMathematica functions, dramatically simplifying a very complex parallel operation.

Chemical Modeling: Solving Complicated Systems with the World's Best Collection of Algorithms
The chemical model simulates the reactions of 31 chemicals, including ozone, hydrocarbons, carbon dioxide, nitrogen oxides, and particulate matter. The chemical reactions are modeled in a general way, where the concentrations of any individual chemical are dependent on the concentrations of the others and the temperature of the surrounding environment. This is implemented as a system of differential equations, solved with the Mathematica function NDSolve.

Wind Modeling: Strengthening a Solution with Added Data Capacity
The wind model is constructed from data originating from two sources. The atmospheric wind, from 3000 feet up, was obtained from the NWS aviation weather services. Data from the surface wind was sourced from COD NexRad center, since that provided a higher degree of granularity. The merged wind field is approximated each point on the 3D mesh using the Mathematica function Interpolation.

Wind affects pollutant concentrations by dispersing the pollutants throughout the air. This dispersion is modeled using a finite element method and solved with the Mathematica function LinearSolve.

GIS: Accurately Representing the World Around Us
The Illinois landscape in the background of the air pollution example is an actual 3D representation of the elevation data, although as Illinois is quite flat, this is not readily apparent. The land is colored using the Mathematica function ReliefPlot, with the rivers, lakes, and adjacent states overlaid.

The wind field and pollution sources are geolocated against the landscape to ensure an accurate representation of the pollutant concentrations.

Other Uses of the Technology in This Simulation
The same few lines of code used to create the Air Pollution Simulation can readily be modified for use in epidemiology, porous media tracking, biological agent diffusion, climatology, combustion engine simulations, and urban sprawl studies, among many others.