1. David Schneider Memorial University, St. John’s, Canada Scale, Scope, and Power Laws in Environmental Science. Part II. Environmental Science 6000 17 September 2009

2. Scale –Dependence: examples and definition application (student examples) Space-Time Diagrams examples group projects in class Calculation across scales examples with background examples (worked in groups) Summary Scale, Scope, and Power Laws in Environmental Science

3. Scope of Phenomena, Impacts, and Action Examples –Coral Reefs –H1N1 –meHg in fish

4. Quantitative Definition of Scope – The Scope of Phenomena Lake depths El Niño return times Body Mass

5. Surveyor’s chain Meter Stick Satellite Image Definition of Scope – The Scope of Instruments

6. Multiscale Analysis is Accomplished by Systematically Changing the Scope spatial temporal mass Method of changing scopeApplications

7. Graphical Expression of Scope: Space – Time Diagrams Scope (a ratio) is the vertical or horizontal distance in space-time diagrams cmm km 1000 km minute hour day week month year decade

8. The first space-time diagrams in ecology come from Steele (1978) Conceptual Instrumental Displaying Scope: Space-Time Diagrams

9. Displaying Change in Scope: Space-Time Diagrams Diagrams showing spatial and temporal scope have become increasingly common.

10. Space-Time Diagrams: The Problem of Scale Environmental scientists collect data from limited areas, at small spatial scales. cmm km hour day week month year The questions they address extend over large areas, at the scale of populations and ecosystems.

11. Scope Diagrams: Statistical Scale-up

12. -more insightful literature reviews -workshop setting (what are you talking about?) -operationally defined science -derive one power law from another -test predictions Utility of the Concept of Scope

13. Case Study – Manukau monitoring Utility of the Concept of Scope in a Workshop Setting Conceptual Diagram Instrumental Diagram

14. Utility of the Concept of Scope in a Workshop Setting data harboursample month hour minute decade year week day model a. Data vs. model flat site plot b. Embedded experiment minute Spatial Scale day week year decade hour month X X cm 10 km1000 km100 mm Increase extent of experiment ? Increase resolution of model ? Develop embedded model ? Develop power law ?

15. Summary - Scope Diagrams Characterization of: –Scale of phenomena –Scale of natural processes –Scale of human impact –Scale of current information –Scale of feasible research activity Comparison Research planning

16. Scale, Scope, and Power Laws in Environmental Biology Group project: Working in groups of 4 (or 3 is possible), construct a conceptual scope diagram. Then construct an instrumental scope diagram.