Dr. Martin T. Auer MTU Department of Civil & Environmental Engineering ENVE5504 Surface Water Quality Modeling Lab 4. One-Dimensional Models Vertical Mass Transport in Dollar Bay, Michigan

8 8 Lake Superior – 8/25/00 Vertical Resolution: Lake Superior

Temperature and the Density of Water Density (g∙cm 3 ) Temperature (°C) Maximum Density 3.94 °C

Thermal Stratification spring summer Temperature (°C)

Thermal Stratification

Seasonality in Stratification and Mixing  = °C

Dollar Bay - Temperature Depth (m) Temperature (°C) Depth (m) M A M J J A S O N D

Productivity and Oxygen

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

Dollar Bay - Temperature Temperature (°C) Depth (m) M A M J J A S O N D

Dollar Bay – Dissolved Oxygen Depth (m) Dissolved Oxygen (mg∙L -1 ) M A M J J A S O N D

Onondaga Lake – Dissolved Oxygen

Oneida Lake – Dissolved Oxygen

Lake Erie – Dissolved Oxygen

Gulf of Mexico – Dissolved Oxygen

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

Vertical Mass Transport

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

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

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

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

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

Application to Dollar Bay

Dollar Bay - Temperature Temperature (°C) Depth (m) M A M J J A S O N D

Dollar Bay – Dissolved Oxygen Depth (m) Dissolved Oxygen (mg∙L -1 ) M A M J J A S O N D

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

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

For the SOD calculation, we need to choose the interval of oxygen depletion. Dollar Bay – Oxygen Calculations

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