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Environmental Science

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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