[sandworm101]

It is a simplified model. The obvious next question is why doesn't the entire lake freeze from the top down? Why does the ice not get progressively thicker every day? The next-level is to model the thermal insulation of the ice. Heat from beneath is insulated from the cold air above. With a constant supply of heat from below but a reduced heat transfer due to the ice/snow, along with reduced evaporation, it is theoretically possible for the depths of a lake to get warmer once frozen over.

https://en.wikipedia.org/wiki/Lake_stratification

[dev_tty01]

Here's a good article if you anyone wants to learn more. There is a lot going on down there.

https://seagrant.umn.edu/news-info/featured-stories/lake-riv...

[HPsquared]

That's a bit like the atmosphere.

At low altitudes, temperature reduces with height (in daytime the atmosphere is heated by contact with the hot surface of the earth (as the atmosphere itself doesn't really get heated by the sun). The hot air rises, and expands as it ascends (pressure reduces as you climb, less air pushing down from above) and therefore cools (adiabatic expansion). Therefore, in the troposphere at least, temperature reduces with altitude due to all this vertical air movement and heating from below.

This is contrasted with the stratosphere, where the temperature begins to rise with altitude again and therefore is very stable and stratified without much vertical air movement.

Somewhat different physics at play, but funny how there are similarities.