Types of Models Marti Blad PhD PE Handouts/supplemental stuff for workshop: Air pollution Dispersion Models; List of different models from epa’s scram site Marti Blad PhD PE

EPA Definitions Dispersion Models: Estimate pollutants at ground level receptors Photochemical Models: Estimate regional air quality, predicts chemical reactions Receptor Models: Estimate contribution of multiple sources to receptor location based on multiple measurements at receptor Screening Models: applied 1st , determines if further modeling needed Refined Models: req’d for SIP, NSR, and PSD Regulatory requirement for permits

Models = Representations or pictures Numerical algorithms Sets of equations need inputs Describe = quantify movement Simplified representation of complex system Box or Mass Balance Used to study & understand the complex Physical, chemical, and spatial, interactions

Types of Models Gaussian Plume Statistical & Stochastic Empirical Analytical approximation of dispersion more later Statistical & Stochastic Based on probability Recall regression is linear model Empirical Based on experimental or field data Actual numbers Physical (scale models) Flow visualization in wind tunnels, etc. Understanding which model will help to understand its limitations. What is the model based on.

Recall bell shaped curve Plume dispersion in lateral & horizontal planes characterized by a Gaussian distribution Normal Distribution Mu is median Sigma is spread

Gaussian-Based Dispersion Models Pollutant concentrations are calculated estimations at receptor Uncertainty of input data values Data quality, completeness Steady state assumption No change in source emissions over time Screen3 will be end of the week

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

Air Pollution Dispersion (cont.) This assumption allows us to calculate concentrations downwind of source using this equation where      c(x,y,z) = contaminant concentration at the specified coordinate [ML-3],       x = downwind distance [L],       y = crosswind distance [L],       z = vertical distance above ground [L],       Q = contaminant emission rate [MT-1],       sy = lateral dispersion coefficient function [L],       sz = vertical dispersion coefficient function [L],       u = wind velocity in downwind direction [L T-1],       H = effective stack height [L]. 

Gaussian model picture Predicted concentration map

The Gaussian Plume Model The shape of the curve = Bell shaped = Gaussian curve hence the model is called by that name. Now, we come to why did I have to torture you with bell shaped curves and Z numbers, probability and predictions etc. Remember the computer will do calculations but think about how to mathematically describe the movement of pollutant molecules, dancing,

Ways to think about math Gaussian = “normal” curve math Recall previous distribution picture Dispersion & diffusion dominates Eulerian Assumes uniform concentrations in box Assumes rapid vertical and horizontal mixing Plume in a grid Predicts species concentrations Multi day scenarios

Eulerian Air Quality Models Grid type models Model simulates the species concentrations in an array of fixed computational cells (Zion) AKA Plume in Grid Figure from http://irina.colorado.edu/lectures/Lec29.htm

Box idea: 1-D and 2-D Models

Dimensional Concept Variable is Time: t Variable is Time and height: t, y Variable is Time, height and length distance: t, x, y t, x, y, z

3-Dimensional Models Depth of boxes discussed under meteorology

Other choice: Lagrangian “Puffs” of pollutants Trajectory models Follow the particle Puff W2 W1 S.S. Plume

Lagrangian Air Quality Models From “INTERNATIONAL AIR QUALITY ADVISORY BOARD 1997-1999 PRIORITIES REPORT, the HYSPLIT Model” (http://www.ijc.org/boards/iaqab/pr9799/project.html)

Assumptions & limitations Physical conditions: Topography Locations: buildings, source, community, receptor Appropriate for the averaging time period Statistics & math Meteorology Stack or source emission data Pollutant emission data Plume rise, Stack or source specific data Location of source and receptors

EPA MODELS—Screening

EPA MODELS—Regulatory CALPUFF AERMOD

EPA Models—Other