Lecture 4: Models

Question 1

Model Jargon test: simulation, sensitivity analysis, optimization, simulation/gaming. What do each of these words indicate about the motivation to model (4)? What are other reasons to model (5)?

Answer 1

predict effects > simulation
system function > sensitivity analysis
alternatives > optimization
behavior > gaming

forecast, source apportionment, economy, complexity, required use

Question 2

Common model applications (3 and 2 notes)

Answer 2

complex trade-offs, policy decisions, compromises. ]

important to determine non-inferior solutions / production possibility frontier

models provide a way to make a rational choice

Question 3

What are boundaries in the modeling context? What boundaries need to be considered?

Answer 3

def: the delineation of processes included or excluded from the model

boundary of problem environment: determined by needs and constraints

boundary of model environment: what takes place in model (geographic scale, temporal scale, media pathways)

Question 4

Def mass balance modeling and some key terms (8)

Answer 4

def: mass accounting of chemical transport and fate of contaminants in various media compartments

source, pathway (route), sink, load/input/flux, control volume, reactions, steady state, conservative/inert

Question 5

What are the 5 key elements of a Mass Balance model? Most important thing?

Answer 5

Clearly defined control volume, inputs and outputs, transport characteristics, kinetics, recognition of assumptions

Make sure units match!

Question 6

Model 1: Dilution Model. What are the assumptions?

Answer 6

uniform mixing, infinite accuracy, contaminant is conservative

Question 7

Model 2: BOD Model. assumptions?

Answer 7

first order decay of contaminant, constant river velocity, uniform river geometry

Question 8

Model 3: Chemical Fate and Transport in 3 directions. just describe

Answer 8

control volume is fixed in space, fluid moves through it, and control volume properties change

Question 9

Model 4: Multimedia Fate and Transport.

Answer 9

shows major environmental compartments, travel along major pathways,

fugacity type model, equilibrium partitioning at steady state

Question 10

Model 5: Growth Model,

Answer 10

growth rate and death rate, you can solve with numerical integration, or calculus with assumptions and boundary conditions,

Question 11

Model 6: FSCCR

Answer 11

reactor volume is constant, balanced inflow and outflow. pollutant is conservative.

application: indoor air quality bioaerosol model and air exchange rate. problem separates into total concern, initial conditions, incoming air

Question 12

Model 7: FSNCCR

Answer 12

similar to FSCCR but material is allowed to degrade. the concept of retention time (how long the particle spends i the reactor, or V/Q). Compare the results here to the FSCCR example: what is the same, what is different?

Question 13

Governing Equations

Answer 13

differential equations representing a mass balance in a control volume. The solution requires initial conditions and boundary conditions, and analytical solutions require constant coefficients / parameters

Question 14

Describe the Model Development process, overview and 6 step process

Answer 14

System analysis , model development, model, model evaluation, decision making

1) define objectives 2) outcome variables 3) develop conceptual model or flow sheet (mechanisms, parameters, constraints) 4) implement 5) verify 6) check feasibility

Question 15

What does it mean for a model to be not feasible?

Answer 15

no solution, or no realistic solution can be obtained, meaning that the model is formulated incorrectly (constraints or problems boundaries are too restrictive or tight)

Question 16

What does the model formulation process look like for statistical or empirical models?

Answer 16

1) determine a structure based on prior understanding 2) estimate numerical values for parameters
2) estimate parameters
3) test validity
+ revise and iterate

Question 17

Define systems in the model formulation context.

Answer 17

A collection of components that are connected by some type of interaction to achieve a purpose (flows of mass, energy, etc)

Question 18

Define unit operation and some characteristics

Answer 18

unit operation: a physical chemical or biological treatment process (typically one step in a process). Allows simple models to be linked to create complex systems. applies to black box processes,

unit operations must conserve: mass, stoichiometry, equilibrium, kinetics, energy

Question 19

What are the 2 general rules to developing adequate models?

Answer 19

Need expert - modeling must be done by someone who understands the science
Need relevant data - the model must be able to be calibrate and analyzed

Question 20

List some common questions that come up with modeling

Answer 20

What makes a good model (i.e., constitution)? formulation? selection? calibration? accuracy? errors? result interpretation? sensitivity? assumptions?

Question 21

What makes a good model?

Answer 21

high explanatory power - validated with real data,
mechanistically consistent,
as simple as possible

Question 22

5 types of lower-level model errors

Answer 22

round-off error, truncation error, coding errors, input data errors, parameterization errors (GIGO), structural errors,

Question 23

Higher level model errors

Answer 23

variable selection, structure, calibration, validation, extrapolation, cross-level

Question 24

How do you select the best model?

Answer 24

find simplest model which is adequate, easiest to validate, provides required outputs, incorporates necessary features

Question 25

What is the biggest responsibility of a model user

Answer 25

understand the underlying assumptions and uncertainties

include a discussion of certainty and prediction confidence, discussion of errors

Question 26

define verification, calibration, evaluation, validation, validity

Answer 26

verify - ensure it works as intended,
calibrate - process of finding suitable parameters
evaluate - comparison of model results with data
validation - formal recognition of a model
validity - ability of a model to predict outcomes with accuracy enough to be used in decision making

Question 27

What is a margin of safety?

Answer 27

factor of 2, it should not be used because it is very costly

Question 28

Define variability and uncertainty

Answer 28

variability - true heterogeneity in the population

uncertainty - represents lack of knowledge

Question 29

What does the NRC say about model evaluation

Answer 29

It should continue throughout the life of the model, not just stop at release, to ensure that the model is not being used for purposes that they were not designed for

Question 30

What does the NRC say about model development

Answer 30

model developers should strive to make simple is best models, findings are that often too many unnecessary variables are included

Question 31

Common model deficiencies (6)

Answer 31

including irrelevant variables, excluding important variables, incorrect structure, calibration, inadequate validation, incorrect use,