1. David Schneider Memorial University, St. John’s, Canada Scale, Scope, and Power Laws in Environmental Science. Part I 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. “We can no longer… cling to the belief that the scale on which we view systems does not affect what we see.... J. Wiens 1999 p371 in Landscape Ecological Analysis. Berlin: Springer Verlag.

4. “bacteria are.. the dominant forms of life on earth. Our failure to grasp this … arises… as an effect of scale.” S. J. Gould. 1996. Life's Grandeur London: Jonathan Cape

5. “We should resist the temptation to find some problem that can be studied on a convenient scale… R.M. May. 1989. p 339 in Ecological Concepts: The Contribution of Ecology to an Understanding of the Natural World. Oxford: Blackwell

6. Examples –Coral Reefs Impact: –Local nutrients –Global acidification Action: –Nutrients –Acidification Scale-Dependence in Environmental Science Examples –Coral Reefs –H1N1 –meHg in fish

7. Examples –H1N1 (Swine Flu) Dynamics: R o = Reproductive Number = New/Infected Action –R o > 4 locally (depends on crowding) –R o < 1.4 in Mexico (public health response) Scale-Dependence in Environmental Biology

8. Examples –meHg in fish Dynamics: –Local discharge of industrial waste –Global source + local mobilization Action –Cease point discharge of industrial waste –Avoid fish from flooded reservoirs Scale-Dependence in Environmental Science

9. Examples –meHg in fish Dynamics: –Local discharge of industrial waste –Global source + local mobilization Action –Cease point discharge of industrial waste –Avoid fish from flooded reservoirs Scale-Dependence in Environmental Science

10. Latin: ScalaNorse: Skal According to the OED, the word “scale” has 15 distinct meanings, from two different roots. Definitions of “Scale”

11. Common Technical Definitions of Scale Type of measurement scale Cartographic scale Scale refers to the extent relative to the grain of a variable indexed by time or space Ecological scaling (Calder 1984) Scale is the distance before some quantity of interest changes. Multiscale analysis – changing the scope

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

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

14. -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

15. Summary Scale-Dependence applies to: –Physical, chemical, and biological phenomena –Dynamics that underlie these phenomena –Environmental impact of human activities –Any measurement program –Societal action (mitigation, monitoring, etc) ‘Scale has multiple definitions