Grand OverviewGrand Overview

Environmental Problems are Environmental Problems are generally characterize by generally characterize by noisy and ambiguous data.noisy and ambiguous data.Understanding errors and Understanding errors and data reliability/bias is key to data reliability/bias is key to implementing good policyimplementing good policy

Goals of this CourseGoals of this Course

• To gain practice in how to frame a problemTo gain practice in how to frame a problem• To practice making toy models involving To practice making toy models involving

data organization and presentationdata organization and presentation• To understand the purpose of making a To understand the purpose of making a

modelmodel• To understand the limitations of modeling To understand the limitations of modeling

and that models differ mostly in the and that models differ mostly in the precision of predictions madeprecision of predictions made

• Provide you with a mini tool kit for analysisProvide you with a mini tool kit for analysis

Sequence for Sequence for Environmental Data Environmental Data

AnalysisAnalysis• Conceptualization of the problem Conceptualization of the problem

which data is most important to which data is most important to obtainobtain

• Methods and limitations of data Methods and limitations of data collection collection know your biases know your biases

• Presentation of Results => data Presentation of Results => data organization and reduction; data organization and reduction; data visualization; statistical analysisvisualization; statistical analysis

• Comparing different modelsComparing different models

Three Problems with Three Problems with Environmental DataEnvironmental Data

• Its usually very noisyIts usually very noisy• It is often unintentionally biased It is often unintentionally biased

because the wrong variables are because the wrong variables are being measured to address the being measured to address the problem in question.problem in question.

• A control sample is usually not A control sample is usually not available.available.

Some Tools

• Linear Regression predictive power lies in scatter

• Slope errors are important• Identify anomalous points by sigma

clipping (1-cycle)• Learn to use the regression tool in Excel

More Tools• Chi square test

• Understand how to determine your expected frequencies

• Two chi square statistic requires marginal sum calculations

• Chi square statistic used to accept or reject the null hypothesis (that the data is consistent with the model plus random fluctuations)

Estimation TechniquesEstimation Techniques

Extremely useful skill Extremely useful skill makes you makes you valuablevaluable

Devise an estimation plan Devise an estimation plan what factors what factors do you need to estimatedo you need to estimate

Scale from familiar examples when Scale from familiar examples when possiblepossible

Perform a reality check on your estimatePerform a reality check on your estimate

Global Warming IGlobal Warming I

Global Warming IIGlobal Warming II

Understand basics of “greenhouse effect”Understand basics of “greenhouse effect” Ice core data and lag time issueIce core data and lag time issueWhat are best indicators of global climate What are best indicators of global climate

changechangeWhy is global mean temperature a poor Why is global mean temperature a poor

proxyproxySpatial distribution of temperature Spatial distribution of temperature

changes is most revealingchanges is most revealing

Global Warming IIIGlobal Warming III

Why is methane such a potential problem?Why is methane such a potential problem?What are anthropogenic sources of What are anthropogenic sources of

methane emission and how can they be methane emission and how can they be curtailedcurtailed

What is the hydrate problem?What is the hydrate problem?What are some other smoking guns for What are some other smoking guns for

global warming/climate change?global warming/climate change?120 Tornadoes Touch down March 12, 120 Tornadoes Touch down March 12,

20062006

Trend Extrapolation TechniquesTrend Extrapolation Techniques

Statistical DistributionsStatistical Distributions

Why are they useful?Why are they useful?How to construct a frequency distribution How to construct a frequency distribution

and/or a histogram of events.and/or a histogram of events.Frequencies are probabilitiesFrequencies are probabilitiesHow the law of large numbers manifests How the law of large numbers manifests

itself itself central limit theorem; random central limit theorem; random walk; expectation valueswalk; expectation values

Comparing DistributionsComparing Distributions

• Why? to identify potential differences and environmental drivers

• KS test uses the entire distribution by comparing cumulative frequency distributions (cfd) more powerful than tests based on means and standard deviations (e.g. Z-test; t-test)

• KS test is excellent for testing observed distribution for normality (Excel: random number generator normal distribution)

Predator Prey RelationsPredator Prey Relations Non linear in nature Non linear in nature small changes in one small changes in one

part of the system can produce rapid part of the system can produce rapid population crashespopulation crashes

Density dependent time lags are important Density dependent time lags are important (what causes them?)(what causes them?)

““Equilibrium” is intrinsically unstableEquilibrium” is intrinsically unstable Logistic growth curve makes use of carrying Logistic growth curve makes use of carrying

capacity concept, Kcapacity concept, K Negative feedback occurs as you approach Negative feedback occurs as you approach

KK R selected vs. K selected mammalsR selected vs. K selected mammals

Human Population ProjectionsHuman Population Projections

What assumptions are used?What assumptions are used?Does human population growth respond to Does human population growth respond to

the carrying capacity concept? the carrying capacity concept? World population growth rate is in World population growth rate is in

continuous decline (but still positive) continuous decline (but still positive) will will this continue indefinitely?this continue indefinitely?

What role does increased life expectancy What role does increased life expectancy have? have? changing population pyramids changing population pyramids

Non Normal DistributionsNon Normal Distributions

Positive and Negative skewness Positive and Negative skewness median value more relevant than meanmedian value more relevant than mean

Bi modal Bi modal sum of two normal sum of two normal distributions if the peaks are well distributions if the peaks are well separatedseparated

Poisson Distribution for discrete arrival Poisson Distribution for discrete arrival events events review this review this

Exponential Distribution for continuous Exponential Distribution for continuous arrival eventsarrival events

Applied EcologyApplied Ecology

Know what the terms mean and Know what the terms mean and understand what an iterative solution is:understand what an iterative solution is:

Applied Ecology IIApplied Ecology II

Understand from the point of view of the Understand from the point of view of the framework (e.g. the equations) why stability is framework (e.g. the equations) why stability is very hard to achievevery hard to achieve

What role does finite reproductive age play?What role does finite reproductive age play? What makes human growth special within this What makes human growth special within this

framework.framework. Understand concepts of equilibrium occupancy Understand concepts of equilibrium occupancy

and demographic potentialand demographic potential Why is error assessment so important here?Why is error assessment so important here?

Techniques for Dealing with Noisy Techniques for Dealing with Noisy DataData

Boxcar smoothing (moving average)Boxcar smoothing (moving average)Exponential smoothingExponential smoothingGaussian Kernel SmoothingGaussian Kernel Smoothing

The Data RulesThe Data Rules

Always, always ALWAYS plot your data Always, always ALWAYS plot your data Never, never NEVER put data through Never, never NEVER put data through

some blackbox reduction routine without some blackbox reduction routine without examining the data themselves examining the data themselves

The average of some distribution is not The average of some distribution is not very meaningful unless you also know very meaningful unless you also know the dispersion. Always calculate the the dispersion. Always calculate the dispersion and then know how to use it! dispersion and then know how to use it!

More Data RulesMore Data Rules

Always compute the level of significance Always compute the level of significance when comparing two distributions when comparing two distributions

Always know your measuring errors. If you Always know your measuring errors. If you don't them you are not doing science. don't them you are not doing science.

Always calculate the dispersion in any Always calculate the dispersion in any correlative analysis. Remember that a correlative analysis. Remember that a correlation is only as good as the correlation is only as good as the dispersion of points around the fitted line. dispersion of points around the fitted line.

The Biggest RulesThe Biggest Rules

Always require someone to back up Always require someone to back up their "belief statements" with credible their "belief statements" with credible data. data.

Change the world. Stop being a Change the world. Stop being a passive absorber of some one else's passive absorber of some one else's belief system.belief system.

Frame all environmental problems Frame all environmental problems objectively and seek reliable data to objectively and seek reliable data to resolve conflicts and make policyresolve conflicts and make policy