Dr. Martin T. Auer MTU Department of Civil & Environmental Engineering

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

2. Temperature and the Density of Water 1.0000 0.9995 0.9990 Maximum Density 3.94 °C 0.9985 0.9980 Density (g∙cm3) 0.9975 0.9970 0.9965 0.9960 0.9955 0.9950 0 5 10 15 20 25 30 Temperature (°C)

3. Thermal Stratification spring summer Temperature (°C)

4. Thermal Stratification

5. Seasonality in Stratification and Mixing  = °C

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

7. Productivity and Oxygen

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

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

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

11. Onondaga Lake – Dissolved Oxygen

12. Oneida Lake – Dissolved Oxygen

13. Lake Erie – Dissolved Oxygen

14. Gulf of Mexico – Dissolved Oxygen

15. Lake Superior – 4/28/00 8 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. X-direction Mathematics of Diffusion II Fick’s 1st Law E C

22. Mathematics of Diffusion III l

23. Mathematics of Diffusion IV

24. Mathematics of Diffusion V E, turbulent diffusion coefficient, m2/d E’, bulk diffusion coefficient, m3/d

25. Vertical Mass Transport

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

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

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

29. uml lml Calculation of the Thermocline Heat Transfer Coefficient Canceling the  and Cp terms, dividing by Vh and expanding … And defining … Yields …

30. Calculation of the Thermocline Heat Transfer Coefficient Which, for Th at the beginning of the calculation = Thi, yields … and re-arranging, yields … further re-arranging, yields … where a plot of ts versus term yields 1/vt as the slope term

31. Application to Dollar Bay

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

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

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

35. uml lml Sediment Oxygen Demand 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 …

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

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