Dispersion Modeling

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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

Documents

Dispersion Modeling