Grand Overview

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

2. Goals of this Course • To gain practice in how to frame a problem • To practice making toy models involving data organization and presentation • To understand the purpose of making a model • To understand the limitations of modeling and that models differ mostly in the precision of predictions made • Provide you with a mini tool kit for analysis

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

4. Three Problems with Environmental Data • Its usually very noisy • 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.

5. 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

6. 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)

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

8. Global Warming I

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

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

11. Trend Extrapolation Techniques

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

13. 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)

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

15. Human Population Projections • What assumptions are used? • 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? • What role does increased life expectancy have?  changing population pyramids

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

17. Applied Ecology • Know what the terms mean and understand what an iterative solution is:

18. 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?

19. Techniques for Dealing with Noisy Data • Boxcar smoothing (moving average) • Exponential smoothing • Gaussian Kernel Smoothing

20. The Data Rules • Always, always ALWAYS plot your data • 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!

21. More Data Rules • Always compute the level of significance when comparing two distributions • Always know your measuring errors. If you don't them 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.

22. The Biggest Rules • 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. • Frame all environmental problems objectively and seek reliable data to resolve conflicts and make policy