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Environmental Science

ENVSCI 301

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Spring

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EnvSci 310 11/1/2013 3:34:00 PM
Lecture 4: introduction to models and modeling
Models:
Representation of a system, copies of mimics something,
simplification, reproduces the parts that are interested in
How much you know or how much you understand
o i.e. stock market, a lot of data but no understanding, =>
statistical modeling
o i.e. planetary motion, high understanding => prediction
modelling
o i.e. understanding conceptually but hard to get data on,
kauri trees (need it over long period of time) => past
modeling but difficult to predict
o quantitative statement of a scientific hypothesis
model state: predictive
model process: process of what is happening
Non-linear: some changes cause no response and some cause a huge
response, hard to predict
Conceptual model; story or picture, easier to understand than words, i.e.
flow chart
Hardware model; rescaled model of a system, issue is scaling – will they
behave the same way?
Mathematical models; take advantage of the absolute truths and formats
that are in maths
Empirical model; observation based, don’t worry about process, start with
data and build a model from there
Simulation models; virtually recreate a system in a computer
Understand model, map it back to real system and so on; surrogative
reasoning
Lets us generalize
Collect a lot of data, and figure out what they tell us
Fourth model; there is no relationship Lecture 5: introduction to Models and Modeling part II
Scale:
Grain: resolution, how big the pixel is, how large the quadrate is,
how often you take the data
Extent: total area encompassed by the study
What we see is driven by the scales we based experiments on
Environmental studies: fine grained and small extent or visa
versa
Empiricism vs. Mechanism:
Empirical; observation, doesn’t say why things happen, doesn’t
explain causality, predictions
Mechanistic: what response will occur and why (looking at
processes)
How complicated to make the models
Detailed vs. simple
How fast does it grow and what is its carrying capacity
Sex and age
Types and Uses of Math Models 11/1/2013 3:34:00 PM
Lecture 8
Use of Maths
1. To expose, make us think about assumptions
2. Learn new things, provide testable consequences, new insights
that are testable
Theoretical models
Designed for generality, not for specificity
Fishery scientists
Don’t need data for these models
Need to make predictions that are testable and strong =>
falsifiable
Key divide in types of mathematical models:
Analytical vs. deterministic
Deterministic Models
Perfectly fixed, predict into future and back into past
Simplistic view
Stochastic Models
Probabilities
Sequences are different, they share similarities
Calculus = mathematics of change Model Analysis 11/1/2013 3:34:00 PM
Week 5: Lecture 13
Uncertainty
Epistemic: uncertainty in known facts
Linguistic: uncertainty in the ways in which we convey information
(convey science to others)
Any system we deal with in time and space varies and we can’t change
that
Can’t ignore it, have to address uncertainty
Lecture 14: Guesstimation 11/1/2013 3:34:00 PM
Week 7
Statistical or empirical modeling: spatio-temporal data
Modeling spatio-temporal data: some preliminaries
Time: indefinite continues progress of existence and events in the past,
present and future regarded as a whole
Time is a human construct
Part of a measuring system used for:
Sequence events
Compare the durations of events and intervals between them
Quantify rates of change
Space: unlimited of incalculably great (boundless) three dimensional
realm or expanse in which all material objects are located and all events
occur and have relative position and direction
Is space and entity, relationship or a conceptual framework?
o In exam: what does this mean
Space vs. Time
Time is one dimensional and ordered (can only ever move
forward from past to present, passing continuously i.e. time
three always happens after time two)
Space is multidimensional and has no natural ordering (random,
three dimensional, describe a cloud in 3D space and spin axis
and still describe, put an artificial thing on space)
Space and time give common domains => interrelations of things
Have to consider both simultaneously because this is reality
Uncertainty
World in uncertain: stochastic variability
Empirical modeling is the science of uncertainty (coherent
approach to handle sources of uncertainty) It is most often expressed mathematically as variability in a
measured signal. Lack of reproduction of the same value if you
measure it repeatedly
Total variability: can partition (decompose) variability into
components (variability due to factors A, B, C etc)
Data have error due to
o Measurement: way we measure, larger error = unvaluable
o Manipulation: e.g. chop off a significant digit
o Archiving: save it and put it into databases
o Aggregation: i.e. taking averages from different parts into
one
Models that are
Scientifically meaningful
Predict well
Conceptually simple
Are preferred
Balance between simplicity and adequacy (goldilocks principle of
modeling)
Lecture 3: Empirical modeling of temporal data
Stationarity: mean hasn’t changed and variance hasn’t changed i.e.
process causing it has not changed over time
Predict well for one year, but harder to predict the value as lag time
increases
Correlogram: cyclical variation: oscillating over time
No partial autocorrelation 11/1/2013 3:34:00 PM
Week 9 lecture 2
Markov Chain: mathematical system that describes changes from one
state to a fixed number of other possible states (including the original)
Different probabilities for changing state or remaining in the
same one: state transition probabilities
Spatio temporal resolution: determines how much info about behavior can
be extracted from geospatial lifeline. Models in Air Quality Science and Mgmt

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