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Mathematical Modeling of Photochemical Air Pollution


McRae, Gregory John (1981) Mathematical Modeling of Photochemical Air Pollution. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/n8p7-f149.


Air pollution is an environmental problem that is both pervasive and difficult to control. An important element of any rational control approach is a reliable means for evaluating the air quality impact of alternative abatement measures. This work presents such a capability, in the form of a mathematical description of the production and transport of photochemical oxidants within an urban airshed. The combined influences of advection, turbulent diffusion, chemical reaction, emissions and surface removal processes are all incorporated into a series of models that are based on the species continuity equations. A delineation of the essential assumptions underlying the formulation of a three-dimensional, a Lagrangian trajectory, a vertically integrated and single cell air quality model is presented. Since each model employs common components and input data the simpler forms can be used for rapid screening calculations and the more complex ones for detailed evaluations.

The flow fields, needed for species transport, are constructed using inverse distance weighted polynomial interpolation techniques that map routine monitoring data onto a regular computational mesh. Variational analysis procedures are then employed to adjust the field so that mass is conserved. Initial concentration and mixing height distributions can be established with the same interpolation algorithms.

Subgrid scale turbulent transport is characterized by a gradient diffusion hypothesis. Similarity solutions are used to model the surface layer fluxes. Above this layer different treatments of turbulent diffusivity are required to account for variations in atmospheric stability. Convective velocity scaling is utilized to develop eddy diffusivities for unstable conditions. The predicted mixing times are in accord with results obtained during sulfur hexafluoride (SF6) tracer experiments. Conventional models are employed for neutral and stable conditions.

A new formulation for gaseous deposition fluxes is presented that provides a means for estimating removal rates as a function of atmospheric stability. The model satisfactorily reproduces measured deposition velocities for reactive materials. In addition it is shown how computational cell size influences the representation of surface removal.

Chemical interactions between twenty nine chemical species are described by a 52 step kinetic mechanism. The atmospheric hydrocarbon chemistry is modeled by the reactions of six lumped classes: alkanes, ethylene, other olefins, aromatics, formaldehyde and other aldehydes; a grouping that enables representation of a wide range of smog chamber experiments and atmospheric conditions. Chemical lumping minimizes the number of species while maintaining a high degree of detail for the inorganic reactions. Variations in rate data, stoichiometric coefficients and initial conditions have been studied using the Fourier Amplitude Sensitivity Test.

The wide variation in time scales, non-linearity of the chemistry and differences in transport processes complicates selection of numerical algorithms. Operator splitting techniques are used to decompose the governing equation into elemental steps of transport and chemistry. Each transport operator is further split into advective and diffusive components so that linear finite element and compact finite difference schemes can be applied to their best advantage. Because most of the computer time is consumed by the chemical kinetics those species that could be accurately described by pseudo-steady state approximations were identified reducing the number of species, described by differential equations, to 15.

While the mathematical formulation of the complete system contains no regional or area specific information, performance evaluation studies were carried out using data measured in the South Coast Air Basin of Southern California. Detailed emissions and meteorological information were assembled for the period 26-28 June 1974. A comparison between predictions and observed air quality, during multi-day periods, indicates that the model can satisfactorily describe urban scale atmospheric concentration dynamics.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Environmental Engineering Science
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Environmental Science and Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Seinfeld, John H.
Thesis Committee:
  • Brooks, Norman H. (chair)
  • Kreiss, Heinz-Otto
  • Shair, Fredrick H.
  • Holmes, John R.
  • Seinfeld, John H.
Defense Date:4 May 1981
Funding AgencyGrant Number
California Air Resources BoardA5-046-87
California Air Resources BoardA7-187-30
Department of Energy (DOE)EY-76-G-03-1035
Record Number:CaltechETD:etd-05042006-134537
Persistent URL:
Related URLs:
URLURL TypeDescription;2DOIArticle adapted for Chapter 3.2;2DOIArticle adapted for Chapter 3.7 adapted for Chapter 12.3 adapted for Chapter 12.5
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1609
Deposited By: Imported from ETD-db
Deposited On:23 May 2006
Last Modified:16 Apr 2021 22:17

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