1. David Schneider Memorial University, St. John’s, Canada Scale, Scope, and Power Laws in Environmental Science. Part III. 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. Euclidean Scaling Relates One Scope to Another Respiration scales as Euclidean Area in Spherical Animals Scaling Relations Power Law Some algebra

4. Euclidean Scaling Relates One Scope to Another Supply scales as delivery volume in a structured network Scaling Relations Power Law Some algebra

5. Euclidean Scaling Relates One Scope to Another Respiration scales as Euclidean Area in Spherical Animals

6. Euclidean Scaling Relates One Scope to Another Respiration scales as Euclidean Area in Spherical Animals

7. Species number scales as Area Power Law Allometric Scaling Relates One Scope to Another

8. Fractal Scaling Relates a Count to Unit Size Steps along a coastline scale as step Length Df 50 km Steps 200 km Steps Detail increases rapidly with increasing resolution along a complex coastline The exponent D f quantifies the rate of change in detail

9. Power Laws in Biology Have Limited Spatial Scopes Literature search that excluded body size allometry and species- area relations Nearly 200 found, but only 60 usable Annual rate of publication increased exponentially. Where spatial scope could be determined it was limited, usually less than 10 3.

10. Predicting Hydro Impact on Fish 1 2 4 1 4 16 64 Yield = kg / ha MEI = ppm / m 8 a We are scaling one ratio to another Ryder’s Morphoedaphic Index is used to predict change in catch due to reservoir flooding Completely empirical scaling

11. Predicting Hydro Impact on Fish Dimensional analysis showed that the MEI formula was driven by an artifact. Dimensional analysis  1 Water Clarity  (ppm) 050100150200250 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 b    Lake Geometry

12. Predicting Hydro Impact on Fish Dimensional analysis showed that the MEI formula was driven by an artifact. 0.0000.0050.0100.0150.0200.0250.0300.035 10 3 4 5 6 7 c    Lake Geometry Total Catch (kg) 050100150200250 10 3 4 5 6 7 d Total Catch (kg)    Water Clarity

13. Predicting Hydro Impact on Fish Improved formula: Process is flux across the surface

14. Predicting Impact of Oil Spills Test the prediction, via trained observers coordinated to emergency response. Spill Size (Tonnes) 10 1 2 3 4 5 6 Carcasses 10 1 2 3 4 5 CarcassesTonnes CIto   313 0223 95%00240423... Data from A.Burger (1993) 1000 barrel spill Predicted Count: 520 to 1760 carcasses

15. Power Laws: Phenomena, Impacts, and Action Examples –Coral Reefs –H1N1 –meHg in fish Coral reefs Dynamics:Growth vs Loss via nutrification Scale from lab measurements to lagoon Action:Reduce nutrient input into lagoon

16. Power Laws: Phenomena, Impacts, and Action Examples –Coral Reefs –H1N1 –meHg in fish H1N1 (Swine Flu) Dynamics: Ro = Reproductive Number = New/Infected ActionRo > 4 locally (depends on crowding) Ro < 1.4 in Mexico (public health response)

17. Power Laws: Phenomena, Impacts, and Action Examples –Coral Reefs –H1N1 –meHg in fish meHg in fish Dynamics: Hg  to meHg in anoxic environments Action reduce local input (Minimata disease) avoid mobilizing global input (Canada reservoirs)

18. Summary – Power Laws Phenomena, Impacts, Action Comparison of cases at different scales Calculate predicted effects: –From local to larger scale –From larger scale to local Research planning Calculate impacts Science based action

19. Scale, Scope, and Power Laws in Environmental Biology Group project: In groups of 2 or at most 3, work through the problem sets provided.