Data from: Differential cooling of a freshwater body below the temperature of maximum density

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.