Dispersion Modeling A Brief Introduction A Brief Introduction Image from Univ. of Waterloo Environmental Sciences Marti Blad

2 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

3 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

4 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

5 Diffusion & dispersion

6 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

7 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

8 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.

9 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

10 Recall Data Distribution  Linear: y = mx + b  Equation of a line  Polynomial: y = x 2 + 3x  Curved lines  Draw shape  Poisson; exponential, saturation  In natural populations  Draw shapes  Gaussian (Bell or Normal Curve)

11 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 Area =.05 on each side is 

13 Different Sigma: watch scale

14 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.

15 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 hh h H x y   h = plume rise h = stack height H = effective stack height H = h +  h C(x,y,z) Downwind at (x,y,z)? Gaussian Dispersion

Gaussian Dispersion Concentration Solution

18 Gaussian Plume Dispersion  One approach: assume each individual plume behaves in Gaussian manner  Results in concentration profile with bell-shaped curve

19 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

20 Graphic Gaussian Dispersion  Gaussian behavior extends in 3 dimensions

21 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

22 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

23 Computer Model Structure INPUT DATA: Operator experience METEROLOGY EMISSIONS RECEPTORS Model Output: Estimates of Concentrations at Receptors Model does calculations

24 Models allow multiple mechanisms Models describe this situation mathematically

25 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

26 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 27

28 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

29 Buoyancy =Plume rise

30 Different Stack Scenarios

31 Conceptual Effect of Buildings

Spatial Relationships 32

33 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

34 Screen3: Area Source 1 st  Emission rate  Area  Longest side, shortest side  Release height  Terrain  Simple Flat  Reflection and absorption  Distances  Discrete vs automated  Receptor height