Dispersion Modeling
A Brief Introduction
Image from Univ. of Waterloo Environmental Sciences
Marti Blad
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Transport of Air Pollution Plumes tell story
Ambient vs DALR Models predict air
pollution concentrations
Input knowledge of sources and meteorology
Chemical reactions may need to be addressed
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Outline
Transport phenomena review
Why use dispersion models?
Many different types of models
Limitations & assumptions
Math & science behind models
Gaussian dispersion models
Screen3 model information
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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 Dispersion
Tortuous path, spreading out because goes around obstacles
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Diffusion & dispersion
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Why Use Dispersion Models?
Predict impact from proposed and/or existing development 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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Types of Models
Gaussian Plume Mathematical approximation of dispersion
Numerical Grid Models Transport & diffusional flow fields
Stochastic 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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Recall Data Distribution
Linear: y = mx + b Equation of a line
Polynomial: y = x2 + 3x Curved lines Draw shape
Poisson; exponential, saturation In natural populations Draw shapes
Gaussian (Bell or Normal Curve)
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Normal Distribution Gaussian Distribution
Normal or Bell shaped curve Assumes measurement varies randomly Commonly characteristic of data error
Mean= Average = center of “bell” Mu = μ
Std. Dev. = variation from average Precision or spread Sigma = σ
Skew = bias Describes curve or point(s) Equipment calibration
Normal Curve Sample Mean = 20, Std Dev = 5
90% Shaded curve means 90% confident a sample value falls between 14 and 26
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Area = .05 on each side is
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Different Sigma: watch scale
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The Gaussian Plume Model
The mathematical shape of the curve is similar to that of Gaussian curve hence the model is called by that name.
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Gaussian-Based Dispersion Models
Plume dispersion in lateral & horizontal planes characterized by a Gaussian distribution Picture
Pollutant concentrations predicted are estimations
Uncertainty of input data values approximations used in the mathematics intrinsic variability of dispersion process
z
Dh
hH
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
Gaussian Dispersion Concentration Solution
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Gaussian Plume Dispersion
One approach: assume each individual plume behaves in Gaussian manner Results in concentration profile with bell-shaped curve
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Is this clear?
Time averaged concentration profiles about plume centerline Recall limitations
Normal Distribution is used to describe random processes Recall bell shaped curves in 3-D
Maximum concentration occurs at the center of the 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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Simple Gaussian Model 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 by
Gaussian distribution—bell curve shape
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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 based on inputs Best models need good quality and site
specific data
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Computer Model Structure
INPUT DATA: Operator experience
METEROLOGY EMISSIONS RECEPTORS
Model Output: Estimates of Concentrations at Receptors
Model does calculations
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Models allow multiple mechanisms
Models describe this situation mathematically
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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 on atmospheric conditions prevailing during the release
Appropriate meteorological conditions Wind rose
Speed and direction Stability class Mixing Height Appropriate time period
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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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
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Buoyancy =Plume rise
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Different Stack Scenarios
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Conceptual Effect of Buildings
Spatial Relationships
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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
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Screen3: Area Source 1st
Emission rate Area
Longest side, shortest side Release height
Terrain Simple Flat Reflection and absorption
Distances Discrete vs automated
Receptor height