1. Environmental Modeling Steven I. Gordon Ohio Supercomputer Center sgordon@osc.edu June, 2004

2. Environmental Models Offer Many Options Many models –Atmospheric processes –Hydrologic processes –Ecological systems –Natural hazards –Many interactions Many scales –Local habitats –Regional – mesoscale –Global

3. Problems in Instruction Modeling complex, dynamic systems Changes occur both spatially and temporally Quality of data to confirm model validity often questionable High degrees of uncertainty Many different processes cross disciplinary boundaries –Challenge for students with varying background –Challenge for faculty trying to apply to instruction

4. Mixed Approaches Models based on physical theory –Fluid dynamics –Mechanics –Biochemistry Models based on statistical and empirical estimates –Used to simplify the complex dynamic systems –Based on abstractions that do not always apply

5. Many Places Many Parameters Requirements for data describing initial conditions at each place in the model –Amount of data required dependent on model scale –Data acquisition difficult –Increasing availability of spatial data from public sources Most models embed many parameter choices –Values found under different circumstances –Calculated based on different principles Choices can make model use decisions dizzying

6. Basic Model Components State variables describing status as different places at time zero Flow over time and space of matter, energy, organisms Transformation of physical, chemical, or biological characteristics over time

7. Alternative Representations What governs the movement from one place to another? How does movement vary with changes in environmental conditions? How is this change represented (steady steady, stochastically, statistically)? How will space be represented – implicitly, one, two or three dimensions?

8. First Example – Dissolved Oxygen in a Stream Measure of health – ability to support diverse ecosystem Basic relationship –Inversely related to temperature –Range between 0 and 14 ppm (mg/l)

9. Conceptual model Organic waste (BOD) decomposed by bacteria that use oxygen –DO=f(1/BOD) Two processes –Deoxygenation –Reaeration

10. Graphical Representation of Point Discharge and DO

11. Basic Equations Where D = dissolved oxygen deficit over time L = concentration of organic matter requiring decomposition k1= coefficient of deoxygenation k2 = coefficient of reaeration

12. Stella Model Example

13. Excel Engineering Version Qual2K Based on EPA code for DO called Qual2E http://www.epa.gov/athens/wwqtsc/html/qual2 k.htmlhttp://www.epa.gov/athens/wwqtsc/html/qual2 k.html Example run

14. Complexity of the Model Choose which aspects to focus on Leave the rest as a “black box” Create an exercise that focuses on variables of interest –E.G. BOD load; sensitivity to reaeration parameter and temperature

15. Simple Point Source/Receptor Model

18. Gaussian Plume Model Dispersion in downwind direction proportional to wind speed (x) Dispersion in y and z direction normally distributed along the plume center line Mean concentration and dispersion vary with stability class in known empirical quantity

19. Equation

20. Where: C (x,y,z) = concentration of pollutant in 3 dimensions given steady state emission X = horizontal distance from source in direction of wind vector and along plume centerline Y= horizontal distance perpendicular to and measured from the plume center line Z= vertical distance from ground to plume center line Q= mass rate of production of pollutant over time

21. Where: Ū = mean wind speed in the x direction H = effective height of plume

22. Equation Emission dispersed as statistical dispersion in 3 directions Dispersion in cross-wind and vertical dimension

23. Empirically Solve for Coefficients

24. Solving the Equation Probability distribution of different wind speed, direction, stability class occurrence Solve the model for each condition Weight the answer by the frequency of each condition

25. Stability Wind Rose

26. Excel Version of the Model

27. The Climatological Dispersion Model

28. Alternative Approaches Find a simple version of a model to run in Stella or a spreadsheet Have students add to the simple model by taking advantage of the documentation/discussion in more complex models Run a more complex model but vary only a few variables most relevant to the class topics

29. Create and Test a Set of Exercises Regardless of approach – need to carefully prepare instructions that include: –Readings on the model basis –Step-by-step instructions –Realistic scenarios –Clear list of expected exercise outcomes –Opportunities for feedback

30. Sources of Information See attached sheet with web links to a variety of modeling and data sites