Types of Models

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– 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.

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

C(x,y,z) Downwind at (x,y,z) ?

Gaussian Dispersion

Dh

hH

z

x

y

¤ Dh = plume rise

h = stack height

H = effective stack heightH = h + Dh

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

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The Gaussian Plume Model

• The shape of the curve = Bell shaped = Gaussian curve hence the model is called by that name.

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

Figure from http://irina.colorado.edu/lectures/Lec29.htm AKA Plume in Grid

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

W1

W2

S.S. Plume

Puff

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

COMPLEX1

RVD2

SHORTZ

VISCREENCTSCREEN

LONGZ

VALLEY

RTDM32

CTSCREEN

TSCREEN

SCREEN3

EPA MODELS—Regulatory

ISC3

UAM

CTDMPLUS BLP

CALINE3

CDM2

OCD

RAM

EKMA

MPTER

CAL3QHC

CRSTER

CALPUFF

AERMOD

EPA Models—Other

CMB7

MOBILE5 DEGADIS

COMPDEP

RPM-IV

MESOPUFF

SDM

TOXST

PLUVUE2

FDM