DispersionModeling MLD

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Dispersion Modeling

A Brief Introduction

Image from Univ. of Waterloo Environmental Sciences

Mark Daniels, M.S., E.I.T.

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Introduction

Why use dispersion models?Many different types of modelsLimitations & assumptionsMath and science behind modelsTransport phenomenaComputers do Math for youGaussian dispersion modelsScreen3 model information

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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 guidelinesCompliance and regulatory

Evaluate AP control strategiesLook for change after implementation

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Types of Models

Gaussian PlumeMathematical approximation of dispersion

Numerical Grid ModelsTransport & diffusional flow fields

StoichasticStatistical or probability based

EmpiricalBased on experimental or field data

PhysicalFlow visualization in wind tunnels, scale mod

els,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 scalesSteady state conditions?

Understand limitationsMathematics-different typesChemistry-reactive or non-reactiveMeteorology-Climatology

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Momentum, Heat & Mass Transport

AdvectionMovement by flow (wind)

ConvectionMovement by heat

Heat island

RadiationDiffusion

Movement from high to low concentrationDispersionTortuous path, spreading out because goes aroundobstacles

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Diffusion & dispersion

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Transport of Air PollutionPlumes tell story

Ambient vs DALR

Models predict airpollutionconcentrationsInput knowledge ofsources and

meteorologyChemical reactionsmay need to beaddressed

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Models allow multiple mechanisms

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Buoyancy =Plume rise

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z

D h

h

H

x

y

D h = plume rise

h = stack heightH = effective stack

heightH = h + D h

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 z

y 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 areestimationsUncertainty of input data values

approximations used in the mathematicsintrinsic variability of dispersion process

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Simple GaussianModel Assumptions

Continuous constant pollutant emissionsConservation of mass in atmosphere

No reactions occurring between pollutants

When pollutants hit ground: reflected, or absorbedSteady-state meteorological conditions

Short term assumption

Concentration profiles are represented byGaussian distribution —bell curve shape

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Gaussian Plume DispersionOne 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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Gaussian Plume

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Graphic Gaussian DispersionGaussian behavior extends in 3 dimensions

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What is a Dispersion Model?

Repetitious solution of dispersion equationsComputer solves over and over againCompare and contrast different conditions

Based on principles of transportComplex mathematical equationsPreviously 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

METEROLOGY EMISSIONS RECEPTORS

Model Output: Estimates ofConcentrations at Receptors

Model does calculations

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Screen 3 modelUnderstand spatial and temporal relationshipsOne hour concentration estimates

Caveat in program

MeteorologySource type and specific information

Point, flare, area and volume

Receptor distanceDiscrete vs automated

Receptor height

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Meteorological Inputs

Actual pattern of dispersion depends onatmospheric conditions prevailing duringthe release

Appropriate meteorological conditionsWind rose

Speed and direction

Stability classMixing Height

Appropriate time period

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Point SourceSource emission data

Pollutant emission dataRate or emission factors

Stack or source specific dataTemperature in stack

Velocity out of stack

Building dimensionsBuilding location

Release HeightTerrain

More complex scenarios

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Different Stack Scenarios

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Model Inputs Effect Outputs

Height of plume rise calculatedMomentum and buoyancyCan significantly alter dispersion & location of

downwind maximum ground-level concentrationEffects of nearby buildings estimated

Downwash wake effectsCan significantly alter dispersion & location ofdownwind max. ground-level concentration

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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 SourceEmission rate

AreaLongest side, shortest sideRelease height

TerrainSimple FlatReflection and absorption

DistancesDiscrete vs automated

Receptor height

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ReviewTransport Phenomena

Meteorology and climatology Add convection, pressure changes

Gaussian = even spreading directionsHighest along axisNot as scary as sounds

Input data quality critical to model quality

Screen 3 limitation for reactive chemicalsNo reactions assumed to create or destroy

Create picture for Screen3 word problems