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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X axis

Y a

xis

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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y

z H

z H

x y zy z y

z

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, , exp

exp

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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