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

Goals 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 data organization and presentationTo practice making toy models involving data organization and presentation To understand the purpose of making a modelTo understand the purpose of making a model To understand the limitations of modeling and that models differ mostly in the precision of predictions madeTo understand the limitations of modeling and that models differ mostly in the precision of predictions made Provide you with a mini tool kit for analysisProvide you with a mini tool kit for analysis

Sequence for Environmental Data Analysis Conceptualization of the problem  which data is most important to obtainConceptualization of the problem  which data is most important to obtain Methods and limitations of data collection  know you biasesMethods and limitations of data collection  know you biases Presentation of Results => data organization and reduction; data visualization; statistical analysisPresentation of Results => data organization and reduction; data visualization; statistical analysis Comparing different modelsComparing different models

Three Problems with Environmental Data Its usually very noisyIts usually very noisy It is often unintentionally biased because the wrong variables are being measured to address the problem in question.It is often unintentionally biased because the wrong variables are being measured to address the problem in question. A control sample is usually not available.A control sample is usually not 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 Least squares method used for best fit determination

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 Know how to compute it

Estimation Techniques Extremely useful skill  makes you valuable Extremely useful skill  makes you valuable Devise an estimation plan  what factors do you need to estimate Devise an estimation plan  what factors do you need to estimate Scale from familiar examples when possible Scale from familiar examples when possible Perform a reality check on your estimate Perform a reality check on your estimate

Global Warming I

Global Warming II Understand basics of “greenhouse effect” Understand basics of “greenhouse effect” Ice core data and lag time issue Ice core data and lag time issue What are best indicators of global climate change What are best indicators of global climate change Why is global mean temperature a poor proxy Why is global mean temperature a poor proxy Spatial distribution of temperature changes is most revealing Spatial distribution of temperature changes is most revealing

Global Warming III Why is methane such a potential problem? Why is methane such a potential problem? What are anthropogenic sources of methane emission and how can they be curtailed What are anthropogenic sources of methane emission and how can they be curtailed What is the hydrate problem? What is the hydrate problem? What are some other smoking guns for global warming/climate change? What are some other smoking guns for global warming/climate change? 120 Tornadoes Touch down March 12, Tornadoes Touch down March 12, 2006

Trend Extrapolation Techniques

Trend Estimation Exponential vs linear models Exponential vs linear models Exponential Exhaustion Timescales Exponential Exhaustion Timescales Why R doesn’t matter so much Why R doesn’t matter so much Why is exhaustion timescale driven mostly by the consumption rate, k Why is exhaustion timescale driven mostly by the consumption rate, k Exponential doubling times Exponential doubling times

The Importance of Trend Extrapolation

Statistical Distributions Why are they useful? Why are they useful? How to construct a frequency distribution and/or a histogram of events. How to construct a frequency distribution and/or a histogram of events. Frequencies are probabilities Frequencies are probabilities How the law of large numbers manifests itself  central limit theorem; random walk; expectation values How the law of large numbers manifests itself  central limit theorem; random walk; expectation values

Comparing 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 Relations Non linear in nature  small changes in one part of the system can produce rapid population crashes Non linear in nature  small changes in one part of the system can produce rapid population crashes Density dependent time lags are important Density dependent time lags are important “Equilibrium” is intrinsically unstable “Equilibrium” is intrinsically unstable Logistic growth curve makes use of carrying capacity concept, K Logistic growth curve makes use of carrying capacity concept, K Negative feedback occurs as you approach K Negative feedback occurs as you approach K R selected vs. K selected mammals R selected vs. K selected mammals

Human Population Projections What assumptions are used? What assumptions are used? Does human population growth respond to the carrying capacity concept? Does human population growth respond to the carrying capacity concept? World population growth rate is in continuous decline (but still positive)  will this continue indefinitely? World population growth rate is in continuous decline (but still positive)  will this continue indefinitely? What role does increased life expectancy have?  changing population pyramids What role does increased life expectancy have?  changing population pyramids

Non Normal Distributions Positive and Negative skewness  median value more relevant than mean Positive and Negative skewness  median value more relevant than mean Bi modal  sum of two normal distributions if the peaks are well separated Bi modal  sum of two normal distributions if the peaks are well separated Poisson Distribution for discrete arrival events  review this Poisson Distribution for discrete arrival events  review this Exponential Distribution for continuous arrival events Exponential Distribution for continuous arrival events

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

Applied Ecology II  Understand from the point of view of the framework (e.g. the equations) why stability is very hard to achieve  What role does finite reproductive age play?  What makes human growth special within this framework.  Understand concepts of equilibrium occupancy and demographic potential  Why is error assessment so important here?

Probabilistic Outcomes  Why is “natural selection” best described in this way?  What parameters determine the outcomes?  What are the differences between stabilization, directional, and disruptive forms of evolution?

Techniques for Dealing with Noisy Data Boxcar smoothing (moving average) Boxcar smoothing (moving average) Exponential smoothing Exponential smoothing Binning the data into two groups and comparing means via the Z-test (e.g. rainfall broken up into two distinct time periods) Binning the data into two groups and comparing means via the Z-test (e.g. rainfall broken up into two distinct time periods) Construction of a waveform and comparison of waveforms Construction of a waveform and comparison of waveforms

The Data Rules Always, always ALWAYS plot your data Always, always ALWAYS plot your data Never, never NEVER put data through some blackbox reduction routine without examining the data themselves Never, never NEVER put data through some blackbox reduction routine without examining the data themselves The average of some distribution is not very meaningful unless you also know the dispersion. Always calculate the dispersion and then know how to use it! The average of some distribution is not very meaningful unless you also know the dispersion. Always calculate the dispersion and then know how to use it!

More Data Rules Always compute the level of significance when comparing two distributions Always compute the level of significance when comparing two distributions Always know your measuring errors. If you don't then you are not doing science. Always know your measuring errors. If you don't then you are not doing science. Always calculate the dispersion in any correlative analysis. Remember that a correlation is only as good as the dispersion of points around the fitted line. Always calculate the dispersion in any correlative analysis. Remember that a correlation is only as good as the dispersion of points around the fitted line.

The Biggest Rules Always require someone to back up their "belief statements" with credible data. Always require someone to back up their "belief statements" with credible data. Change the world. Stop being a passive absorber of some one else's belief system. Change the world. Stop being a passive absorber of some one else's belief system. Frame all environmental problems objectively and seek reliable data to resolve conflicts and make policy Frame all environmental problems objectively and seek reliable data to resolve conflicts and make policy