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Abstract

We propose a simplified model for the time rate of change of average basin temperature for a freshwater lake which has two connected basins: a shallow littoral zone of depth D1, and a deeper main basin of depth D2. This system is cooled below the temperature of maximum density (Tmd) with a constant and uniform outgoing surface heat flux, Ho. The differential cooling that is established via this setup gives rise to an exchange flow between the two basins, which we approximate as a time-dependent heat flux controlled by the strength of the time-dependent density difference between the two basins. Our model is a coupled system of two ordinary differential equations, which allows for a process-based investigation into the importance of exchange on the timing of ice-onset for a lake with a shallow littoral zone. While basin geometry plays a role in the overall timing of ice-onset for the system, it is the relative strength of Ho to the exchange flow-related heat flux due to the density anomaly of fresh water, ρ*, which dictates the behaviour of the cooling system. We show that at sufficiently large values of the heat flux ratio, Φ, the difference in timing of ice onset between the littoral zone and main basin becomes insensitive to the initial conditions in the lake. We use data from Base Mine Lake, Canada, to both verify our model assumptions and evaluate the predictions made by our simple model.

Temperature data used in this study and included in this dataset were collected using RBR SoloT temperature loggers (0.002 °C accuracy) located at the Southwest platform (P3) mooring at Base Mine Lake (57° 1' N, 111° 37' W in Alberta, Canada). We have excluded the temperature measurements made at 9 m depth from the dataset here, as these measurements were made in the mud at the bottom of the lake, and thus not used in the present study. Hourly average wind speeds shown in the corresponding manuscript were measured at 3.3 m above the lake surface at the central platform (P1) at Base Mine Lake. For further information on data collection and processing, please refer to Tedford et al (2019).

The Excel spreadsheet of lake coverage observations was generated by Karin Huang in 2017. The observations for 'Status' in this spreadsheet were analysed to identify ice onset times used in the corresponding manuscript. Images corresponding with the before and after times of observed ice-onset in both the littoral zone and main basin are included as validation of the observations made and recorded by Karin. 

Tedford, T., Halferdahl, G., Pieters, R., and Lawrence, G. A. (2019): Temporal variations in turbidity in an oil sands pit lake. Environmental Fluid Mechanics 19: 457-473. https://doi.org/10.1007/s10652-018-9632-6</p>