Even if the air reaches the freezing point or even a bit lower it takes some time for the water to cool down. And again if there is some sun then it will heat up the water first and it takes some time for this heat to be transferred to the air. So when you see weather getting freezing cold during the night and then a bit above during the day you typically do not see the lakes freezing.
For rivers or fast moving lakes it is even worse as the water will be constantly moving and therefore never have time to freeze. Cooling the water does not work as it will just get replaced by a bit hotter water. It is also very hard for ice crystals to grow in constantly moving water as it will only get broken up as soon as they form. So a river can actually be a few degrees bellow freezing, and the air above the river can be far bellow freezing.
Water accumulates great amount of heat energy compared to air it is in contact with and most other materials and takes a while to cool down. Unlike the soil, it also mixes and equalizes its temperature. When water has already cooled down to 0 degrees it needs to give up more heat to turn into a solid. Once some ice forms on the surface, it forms an isolating layer.
I can think of a couple of reasons. Firstly, both water and the ground are great at holding on to heat so even if the air temperature is below 0, that doesn’t mean the water is.
Secondly, *pure* water freezes at 0, but impurities can keep it liquid down to lower temperatures. This is the reason why we put salt/grit on the roads in Winter – the salt mixes with the water and stops it turning to ice so the roads don’t get slippy
Turning 0°C ice into 0°C liquid water needs the same amount of energy as then heating the water up to 80°C. The freezing/melting step involves the transfer of a large amount of heat so it takes a long time. Large bodies of water can eventually freeze but it takes a very long time if the surrounding temperatures are not far below freezing. Even apart from freezing and melting, water has one of the highest “specific heats” of any chemical so it strongly resists temperature changes.
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