Yes, water has some unusual properties near to freezing density wise.
However it makes not one whit of difference regarding the analysis!
A surface cooled near a warmer surface by radiating energy though it into space.
The atmosphere has a substantial heating effect on the Earth and the 2nd law of Thermodynamics rules the process all the way. If you treat heat like some sort of caloric fluid, yes you won't understand a thing. The caloric model will work for basic analysis, like central heating but will fail when dealing with determination of a planets temperature with an atmosphere.
Here are some figures. Take note of the very large percentage figures attributed to radiation. =================================================
Earth Heat Gains short-wave radiation from the sun...............34.7% long-wave radiation from the atmosphere.........65.3%
Earth Heat Losses Long-wave radiation to the atmosphere...........75.5% Long-wave radiation to space.................... 4.1% Evaporation from oceans/lakes/land..............15.6% Convection and conduction to atmosphere......... 4.8%
Atmospheric Heat Gains Short-wave radiation from the sun...............11.9% Heat to atmosphere from condensation............14.4% Heat to atmosphere from convection/conduction... 4.4% Long-wave radiation from earth..................69.4%
Atmospheric Heat Losses Long-wave radiation Radiated to Space...........40.0% Long-wave radiation radiated to earth...........60.0%
These values derived from graphs and charts from the textbook "Meterorology Today," (4th Ed.) by C. Donald Ahrens.
This is a greatly simplified summary of the radiation balance. Each of the above factors involve other effects, such as albedo, solar angle, selective absorption of radiation by atmospheric gases such as carbon dioxide, ozone, water vapor, et.al., scattering and reflection of solar radiation, etc.
You can see some interesting observations from the above data though. One suprise may be that the earth receives almost twice as much heat from the atmosphere as it does from the sun. But the sun only shines on a given point on the earth half the time, while the atmosphere radiates continuously.
The earth receives about one-third of its heat directly from the sun, but less than 5 percent of the heat from the earth is radiated back to space or >about the same amount that is involved in conduction and convection in the atmosphere
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