Types of models
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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

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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

  • 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

  • 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 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

  • Plume dispersion in lateral & horizontal planes characterized by a Gaussian distribution

  • Normal Distribution

    • Mu is median

    • Sigma is spread

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



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.)

  • 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

  • Predicted concentration map

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

  • 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

AKA Plume in Grid

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

Box idea: 1-D and 2-D Models

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

Depth of boxes discussed under meteorology

Other choice: Lagrangian

  • “Puffs” of pollutants

  • Trajectory models

  • Follow the particle




S.S. Plume

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

  • 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

EPA MODELS—Screening

EPA MODELS—Regulatory



EPA Models—Other

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