1. Dr. Martin T. Auer MTU Department of Civil & Environmental Engineering CE5504 Surface Water Quality Modeling Lab 5. One-Dimensional Models Thermal Stratification, Vertical Mass Transport and Interactions with Trophic State

2. Temperature and the Density of Water 1.0000 0.9995 0.9990 0.9985 0.9980 0.9975 0.9970 0.9965 0.9960 0.9955 0.9950 Density (g∙cm 3 ) 0 5 10 15 20 25 30 Temperature (°C) Maximum Density 3.94 °C

3. Thermal Stratification spring summer Temperature (°C)

4. Thermal Stratification

5. Seasonality in Stratification and Mixing  = °C

6. Dollar Bay - Temperature 0 1 2 3 4 5 6 7 8 Depth (m) 0 5 10 15 20 Temperature (°C) 0 1 2 3 4 5 6 7 8 Depth (m) M A M J J A S O N D

7. Productivity and Oxygen

8. Trophic State and Oxygen Profiles Oligotrophic Lake Eutrophic Lake Temperature (°C)

9. Dollar Bay - Temperature 0 1 2 3 4 5 6 7 8 0 5 10 15 20 Temperature (°C) 0 1 2 3 4 5 6 7 8 Depth (m) M A M J J A S O N D

10. Dollar Bay – Dissolved Oxygen Depth (m) 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 Dissolved Oxygen (mg∙L -1 ) M A M J J A S O N D

11. Onondaga Lake – Dissolved Oxygen

12. Oneida Lake – Dissolved Oxygen

13. Lake Erie – Dissolved Oxygen

14. Gulf of Mexico – Dissolved Oxygen

15. 8 Lake Superior – 4/28/00 Completely-Mixed Lake

16. 8 8 Lake Superior – 8/25/00 Vertical Resolution - Stratification

17. Advection and Diffusion

18. Diffusion

19. Scales of Diffusion

20. Mathematics of Diffusion I

21. Fick’s 1 st Law X-direction E C Mathematics of Diffusion II

22. l Mathematics of Diffusion III

23. Mathematics of Diffusion IV

24. E, turbulent diffusion coefficient, m 2 /d E’, bulk diffusion coefficient, m 3 /d Mathematics of Diffusion V

25. Vertical Mass Transport

26. Application to Vertical Mass Transport turbulent diffusion coefficient thermocline heat transfer coefficient

27. Calculation of the Thermocline Heat Transfer Coefficient Epilimnion Heat Balance change in heat tributary heat in discharge heat out surface heat flux thermocline heat exchange

28. Calculation of the Thermocline Heat Transfer Coefficient Hypolimnion Heat Balance change in heat thermocline heat exchange assumes no direct heating of hypolimnion or sediments upper mixed layer (~epilimnion) lower mixed layer (~hypolimnion) thermoclinev t ∙A s

29. Calculation of the Thermocline Heat Transfer Coefficient Canceling the  and C p terms, dividing by V h and expanding … And defining … Yields … uml lml

30. Calculation of the Thermocline Heat Transfer Coefficient and re-arranging, yields … Which, for T h at the beginning of the calculation = Th i, yields … further re-arranging, yields … where a plot of t s versus term yields 1/v t as the slope term

31. Application to Dollar Bay

32. Dollar Bay - Temperature 0 1 2 3 4 5 6 7 8 0 5 10 15 20 Temperature (°C) 0 1 2 3 4 5 6 7 8 Depth (m) M A M J J A S O N D

33. Dollar Bay – Dissolved Oxygen Depth (m) 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 Dissolved Oxygen (mg∙L -1 ) M A M J J A S O N D

34. For diffusion calculation, need to choose an interval where T epi is stable and T hyp is warming. Dollar Bay – Temperature Calculations Hypolimnion temperature mass balance.

35. Sediment oxygen demand reflects the diffusion of oxygen into the sediment to meet the metabolic needs of microorganisms participating in the aerobic decomposition of organic matter. SOD is also exerted through the aerobic oxidation of reduced species byproducts of anaerobic respiration. The mass balance, for SOD alone is … Sediment Oxygen Demand uml lml

36. For the SOD calculation, we need to choose the interval of oxygen depletion. Dollar Bay – Oxygen Calculations (the question of the cones)

37. Time-Variable vt Values for Onondaga Lake (Doerr et al. 1996)