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Dispersion Modeling
A Brief Introduction
smoke stacks image from Univ. of Waterloo Environmental Sciences
Marti Blad, Ph.D., P.E.
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Introduction
Many different types of models
Limitations & assumptions
Math and science behind models
Transport phenomena
Computers do Math for you
Gaussian dispersion models
Screen3 model information Why use mathematical models
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Types of Models
Gaussian Plume
Mathematical approximation of dispersion
Numerical Grid Models
Transport & diffusional flow fields
Stoichastic
Statistical or probability based
Empirical Based on experimental or field data
Physical
Flow visualization in wind tunnels, scale models,etc
.
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Limitations & Assumptions
Useful tools: right model for your needs
Allows quantification of air quality problem
Space different distances, scale
Time
different time scales Steady state conditions?
Understand limitations
Mathematics-different types
Chemistry-reactive or non-reactive
Meteorology-Climatology
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Momentum, Heat & Mass Transport
Advection Movement by flow (wind)
Convection
Movement by heat
Heat island
Radiation
Diffusion
Movement from high to low concentration Molecule Dance
Dispersion
Tortuous path, spreading out because goes around
obstacles
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Diffusion & dispersion
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Transport of Air Pollution
Plumes tell story Ambient vs DALR
Models predict air
pollutionconcentrations
Input knowledge ofsources and
meteorology Chemical reactions
may need to beaddressed
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Models allow multiple mechanisms
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Buoyancy =Plume rise
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z
Dh
h
H
x
y
Dh = plume rise
h = stack height
H = effective stack
heightH = h + Dh
C(x,y,z) Downwind at (x,y,z)?
Gaussian Dispersion
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Gaussian DispersionConcentration Solution
C
Q
u
y
z H
z H
x y zy z y
z
z
, , exp
exp
exp
2 2
2
2
2
2
2
2
2
2
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The Gaussian Plume Model
The mathematicalshape of the curveis similar to that of
Gaussian curvehence the model iscalled by thatname.
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Gaussian-BasedDispersion Models
Plume dispersion in lateral & horizontal planescharacterized by a Gaussian distribution
Picture
Pollutant concentrations predicted areestimations
Uncertainty of input data values
approximations used in the mathematics intrinsic variability of dispersion process
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Simple GaussianModel Assumptions
Continuous constant pollutant emissions
Conservation of mass in atmosphere
No reactions occurring between pollutants
When pollutants hit ground: reflected, or absorbed
Steady-state meteorological conditions
Short term assumption
Concentration profiles are represented byGaussian distributionbell curve shape
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Gaussian Plume Dispersion
One approach: assume each individual plume behavesin Gaussian manner
Results in concentration profile with bell-shaped curve
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Is this clear?
Time averaged concentration profiles aboutplume centerline
Recall limitations
Normal Distribution is used to describe randomprocesses
Recall bell shaped curves in 3-D
Maximum concentration occurs at the center ofthe plume
See up coming model pictures
Dispersion is in 3 directions
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Graphic Gaussian Dispersion
Gaussian behavior extends in 3 dimensions
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What is a Dispersion Model?
Repetitious solution of dispersion equations
Computer solves over and over again
Compare and contrast different conditions
Based on principles of transport Complex mathematical equations
Previously discussed meteorological conditions
Computer-aided simulation of atmosphere basedon inputs
Best models need good quality and site specific data
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Computer Model Structure
INPUT DATA: Operator experience
METEROLOGYEMISSIONS
RECEPTORS
Model Output: Estimates ofConcentrations at Receptors
Model does calculations
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Screen 3 model
Understand spatial and temporal relationships One hour concentration estimates
Caveat in program
Meteorology
Source type and specific information
Point, flare, area and volume
Receptor distance
Discrete vs automated
Receptor height
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Meteorological Inputs
Actual pattern of dispersion depends onatmospheric conditions prevailing duringthe release
Appropriate meteorological conditions
Wind rose
Speed and direction
Stability class
Mixing Height
Appropriate time period
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Point Source Source emission data
Pollutant emission data
Rate or emission factors
Stack or source specific data
Temperature in stack
Velocity out of stack
Building dimensions
Building location
Release Height
Terrain
More complex scenarios
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Different stack scenarios
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Model inputs effect outputs
Height of plume rise calculated
Momentum and buoyancy
Can significantly alter dispersion & location of
downwind maximum ground-level concentration Effects of nearby buildings estimated
Downwash wake effects
Can significantly alter dispersion & location of
downwind max. ground-level concentration
C t l ff t f
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Conceptual effect ofbuildings
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Spatial relationships
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Gaussian Plume
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Screen3 Area Source
Emission rate Area
Longest side, shortest side
Release height
Terrain
Simple Flat
Reflection and absorption
Distances Discrete vs automated
Receptor height
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Why Use Dispersion Models?
Predict impact from proposed and/or existingdevelopment
NSR- new source review
PSD- prevention of significant deterioration Assess air quality monitoring data
Monitor location
Assess air quality standards or guidelines
Compliance and regulatory
Evaluate AP control strategies
Look for change after implementation
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Why Use Dispersion Models?
Evaluate receptor
exposure
Monitoring network
design Review data
Peak locations
Spatial patterns
Model Verification
image from collection of Pittsburgh Photographic Library, Carnegie Library of Pittsburgh
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Review
Transport Phenomena Meteorology and climatology
Add convection, pressure changes
Gaussian = even spreading directions
Highest along axis
Not as scary as sounds
Input data quality critical to model quality
Screen 3 limitation for reactive chemicals No reactions assumed to create or destroy
Create picture for Screen3 word problems