Lecture 4: Models Flashcards
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)?
predict effects > simulation
system function > sensitivity analysis
alternatives > optimization
behavior > gaming
forecast, source apportionment, economy, complexity, required use
Common model applications (3 and 2 notes)
complex trade-offs, policy decisions, compromises. ]
important to determine non-inferior solutions / production possibility frontier
models provide a way to make a rational choice
What are boundaries in the modeling context? What boundaries need to be considered?
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)
Def mass balance modeling and some key terms (8)
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
What are the 5 key elements of a Mass Balance model? Most important thing?
Clearly defined control volume, inputs and outputs, transport characteristics, kinetics, recognition of assumptions
Make sure units match!
Model 1: Dilution Model. What are the assumptions?
uniform mixing, infinite accuracy, contaminant is conservative
Model 2: BOD Model. assumptions?
first order decay of contaminant, constant river velocity, uniform river geometry
Model 3: Chemical Fate and Transport in 3 directions. just describe
control volume is fixed in space, fluid moves through it, and control volume properties change
Model 4: Multimedia Fate and Transport.
shows major environmental compartments, travel along major pathways,
fugacity type model, equilibrium partitioning at steady state
Model 5: Growth Model,
growth rate and death rate, you can solve with numerical integration, or calculus with assumptions and boundary conditions,
Model 6: FSCCR
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
Model 7: FSNCCR
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?
Governing Equations
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
Describe the Model Development process, overview and 6 step process
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
What does it mean for a model to be not feasible?
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)
What does the model formulation process look like for statistical or empirical models?
1) determine a structure based on prior understanding 2) estimate numerical values for parameters
2) estimate parameters
3) test validity
+ revise and iterate
Define systems in the model formulation context.
A collection of components that are connected by some type of interaction to achieve a purpose (flows of mass, energy, etc)
Define unit operation and some characteristics
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
What are the 2 general rules to developing adequate models?
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
List some common questions that come up with modeling
What makes a good model (i.e., constitution)? formulation? selection? calibration? accuracy? errors? result interpretation? sensitivity? assumptions?
What makes a good model?
high explanatory power - validated with real data,
mechanistically consistent,
as simple as possible
5 types of lower-level model errors
round-off error, truncation error, coding errors, input data errors, parameterization errors (GIGO), structural errors,
Higher level model errors
variable selection, structure, calibration, validation, extrapolation, cross-level
How do you select the best model?
find simplest model which is adequate, easiest to validate, provides required outputs, incorporates necessary features
