Introduction to Modeling – Part I

Sarah Kelly

ITEP

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Why Model? To answer questions:

If a source emitting 250 tons/year of PM2.5 is built 5 miles to the west of my reservation, how will it effect the air we breathe?

What if the same source is built on my reservation? Or 10 miles to the north? What if it emits 500 tons/year of PM2.5 ?

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Why Model? (cont.) To answer questions (cont.)

How much CO is being emitted into the air because of truck traffic on my reservation?

What kind of air toxics are being emitted by the fuel storage facility on my reservation How much air toxics are being emitted? Once toxics are emitted, where do they go? Where should I locate air toxics monitors?

Where is the regional haze on my reservation coming from?

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Why Model? (cont.)

To Predict Future Need to “calibrate” with reality Check against data collected in field

To Interpret Study system and/or organize field data Does not require calibration, but “reality

checks” are always useful

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What is a Model?

Any approximation of a field situation Physical model

Laboratory experiment simulating how pollutants travel or react with each other (example: wind tunnel experiment)

Statistical model Study data you have, use statistics to make

predictions or interpret field situation

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What is a Model? (cont.)

Empirical model Derived from information gained from

observations or experiments Mathematical model

Simulates field situation indirectly using equations

Workshop focuses on mathematical and empirical models

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What is a Model? (cont.) Mathematical models have

Governing equation – represents physical processes occurring in system

Boundary equations (conditions) Initial conditions (for time-dependent

problems)

X = Q * K * V * D * exp[-0.5 * (y/ Φy)2 ] /

(2 * Β* us * Φy * Φz)

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What is a Model? (cont.) Two ways to solve mathematical models

Analytical Solved using algebra or other math techniques Good where underlying assumptions are simple

Numerical Solved using complex approximation techniques Good where field situation is complex

Both can be solved using computer programs

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What is a Computer Model? Set of commands used to solve

mathematical or empirical model on computer Computer programs are generic – written

once Model is designed each time you enter a set

of boundary and initial conditions, and site- specific values, into computer program

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Computer Models Commercial modeling programs

Make it easier for users to communicate with computer code and enter data

Often have graphical interfaces Ease data entry Eases visualization of modeling results

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Computer Models (cont.) Graphics packages – Picture instead of

number grid

5 10 50 10 105 11 21 11 65 8 10 8 45 6 6 4 25 3 3 2 1

40-50

30-40

20-30

10-20

0-10

PM10 Concentrations

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Computer Model – Dangers Modern modeling programs and graphics

packages are easy to use, produce impressive pictures and graphs

Model only as good as site-specific data, initial and boundary conditions you enter

Garbage IN = Garbage OUT

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What type of model should you use? Step One: Establish your purpose!

Make predictions? Interpret and better understand what’s going on?

What do you want to learn? What questions do you want to answer?

Is modeling the best way to answer your questions?

THEN: What type of model should you use?

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Models – Two Opinions Models are worthless

Too expensive to run, require too much data Real world too complex to be modeled Models can never be proven “correct”

Models are essential for complex analyses Combines human judgment with computer power Provide framework for analyzing large data sets Good way to make informed analysis or prediction