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Types of Models. Marti Blad PhD PE. EPA Definitions. Dispersion Models : Estimate pollutants at ground level receptors Photochemical Models : Estimate regional air quality, predicts chemical reactions

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types of models
Types of Models

Marti Blad PhD PE

epa definitions
EPA Definitions
  • Dispersion Models: Estimate pollutants at ground level receptors
  • Photochemical Models: Estimate regional air quality, predicts chemical reactions
  • Receptor Models: Estimate contribution of multiple sources to receptor location based on multiple measurements at receptor
  • Screening Models: applied 1st , determines if further modeling needed
  • Refined Models: req’d for SIP, NSR, and PSD
    • Regulatory requirement for permits
models representations or pictures
Models = Representations or pictures
  • Numerical algorithms
    • Sets of equations need inputs
    • Describe = quantify movement
    • Simplified representation of complex system
    • Box or Mass Balance
  • Used to study & understand the complex
    • Physical, chemical, and spatial, interactions
types of models1
Types of Models
  • Gaussian Plume
    • Analytical approximation of dispersion
    • more later
  • Statistical & Stochastic
    • Based on probability
    • Recall regression is linear model
  • Empirical
    • Based on experimental or field data
    • Actual numbers
  • Physical (scale models)
    • Flow visualization in wind tunnels, etc.
recall bell shaped curve
Recall bell shaped curve
  • Plume dispersion in lateral & horizontal planes characterized by a Gaussian distribution
  • Normal Distribution
    • Mu is median
    • Sigma is spread
gaussian based dispersion models
Gaussian-Based Dispersion Models
  • Pollutant concentrations are calculated estimations at receptor
  • Uncertainty of input data values
    • Data quality, completeness
  • Steady state assumption
    • No change in source emissions over time
  • Screen3 will be end of the week
gaussian dispersion
Gaussian Dispersion



Dh = plume rise

h = stack height


H = effective stack


H = h + Dh




C(x,y,z) Downwind at (x,y,z) ?


air pollution dispersion cont
Air Pollution Dispersion (cont.)
  • This assumption allows us to calculate concentrations downwind of source using this equation


     c(x,y,z) = contaminant concentration at the specified coordinate [ML-3],       x = downwind distance [L],       y = crosswind distance [L],       z = vertical distance above ground [L],       Q = contaminant emission rate [MT-1],  sy = lateral dispersion coefficient function [L],  sz = vertical dispersion coefficient function [L],       u = wind velocity in downwind direction [L T-1],       H = effective stack height [L].

gaussian model picture
Gaussian model picture
  • Predicted concentration map
the gaussian plume model
The Gaussian Plume Model
  • The shape of the curve = Bell shaped = Gaussian curve hence the model is called by that name.
ways to think about math
Ways to think about math
  • Gaussian = “normal” curve math
    • Recall previous distribution picture
    • Dispersion & diffusion dominates
  • Eulerian
    • Assumes uniform concentrations in box
    • Assumes rapid vertical and horizontal mixing
    • Plume in a grid
    • Predicts species concentrations
    • Multi day scenarios
eulerian air quality models
Eulerian Air Quality Models

AKA Plume in Grid

Figure from http://irina.colorado.edu/lectures/Lec29.htm

dimensional concept
Dimensional Concept

Variable is Time: t

Variable is Time and height: t, y

Variable is Time, height and length distance:

t, x, y

t, x, y, z

3 dimensional models
3-Dimensional Models

Depth of boxes discussed under meteorology

other choice lagrangian
Other choice: Lagrangian
  • “Puffs” of pollutants
  • Trajectory models
  • Follow the particle




S.S. Plume

lagrangian air quality models
Lagrangian Air Quality Models

From “INTERNATIONAL AIR QUALITY ADVISORY BOARD 1997-1999 PRIORITIES REPORT, the HYSPLIT Model” (http://www.ijc.org/boards/iaqab/pr9799/project.html)

assumptions limitations
Assumptions & limitations
  • Physical conditions: Topography
    • Locations: buildings, source, community, receptor
    • Appropriate for the averaging time period
  • Statistics & math
  • Meteorology
  • Stack or source emission data
    • Pollutant emission data
    • Plume rise, Stack or source specific data
    • Location of source and receptors