Types of Models
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Types of Models
Marti Blad PhD PE
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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
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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
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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.
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Recall bell shaped curve
• Plume dispersion in lateral & horizontal planes characterized by a Gaussian distribution
• Normal Distribution– Mu is median– Sigma is spread
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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
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C(x,y,z) Downwind at (x,y,z) ?
Gaussian Dispersion
Dh
hH
z
x
y
¤ Dh = plume rise
h = stack height
H = effective stack heightH = h + Dh
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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 [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].
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Gaussian model picture
• Predicted concentration map
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11
The Gaussian Plume Model
• The shape of the curve = Bell shaped = Gaussian curve hence the model is called by that name.
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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
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Eulerian Air Quality Models
Figure from http://irina.colorado.edu/lectures/Lec29.htm AKA Plume in Grid
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Box idea: 1-D and 2-D Models
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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
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3-Dimensional Models
Depth of boxes discussed under meteorology
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Other choice: Lagrangian
• “Puffs” of pollutants • Trajectory models
• Follow the particle
W1
W2
S.S. Plume
Puff
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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)
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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
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EPA MODELS—Screening
COMPLEX1
RVD2
SHORTZ
VISCREENCTSCREEN
LONGZ
VALLEY
RTDM32
CTSCREEN
TSCREEN
SCREEN3
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EPA MODELS—Regulatory
ISC3
UAM
CTDMPLUS BLP
CALINE3
CDM2
OCD
RAM
EKMA
MPTER
CAL3QHC
CRSTER
CALPUFF
AERMOD
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EPA Models—Other
CMB7
MOBILE5 DEGADIS
COMPDEP
RPM-IV
MESOPUFF
SDM
TOXST
PLUVUE2
FDM