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
z

Dh = plume rise
h = stack height
Dh
H = effective stack
height
H = h + Dh
H
h
x
C(x,y,z) Downwind at (x,y,z) ?
y
Air Pollution Dispersion (cont.)
• This assumption allows us to calculate
concentrations downwind of source using this
equation
where
c(x,y,z) = contaminant concentration at the specified coordinate [ML3],
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.
11
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
Figure from http://irina.colorado.edu/lectures/Lec29.htm
AKA Plume in Grid
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
Puff
W2
W1
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
CTSCREEN
COMPLEX1
LONGZ
RTDM32
SCREEN3
RVD2
CTSCREEN
VISCREEN
TSCREEN
SHORTZ
VALLEY
EPA MODELS—Regulatory
MPTER
ISC3
OCD
CALPUFF
EKMA
CRSTER
UAM
CALINE3
AERMOD
CDM2
CAL3QHC
RAM
CTDMPLUS
BLP
EPA Models—Other
MESOPUFF
TOXST
COMPDEP
FDM
CMB7
PLUVUE2
RPM-IV
SDM
MOBILE5
DEGADIS