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Basically you are making the air colder like that, not so much the snow. Ofcourse really cold air will eventually affect the snow but to a lesser extent than what the snow can do to itself be giving off radiation.
I think we're still dealing with a disconnect.
Im not at all saying that convective cooling is cooling the snow, but cooling the "T infinity" to where the snow is radiating its energy. The greater that delta T between the air\atmosphere and snow surface, the larger the radiative cooling effects....especially since we're dealing with FOURTH order temperatures in KELVIN. A 10 degree change in ambient\surrounding\"T infinity" temperature will increase your radiative cooling potential by ~90%. (ie almost double within this temp range)
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Side note: no idea about your part of the world but if we get strong cold wind, it usually brings clouds and humidity with it, it doesn’t just show up to make a nice overnight freeze. We often get a very warm wind, which eats away the snow so maybe I just associate wind with warm weather and sucky snow.
apparently youve never been to colorado ;)
Wind is the norm, even when its bluebird or not a cloud in the sky at night.
You do make a good point and it is something I think we should all think about when we see high winds, especially if its overcast and was especially warm\humid during the day.
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Stefan boltzmann law: s x e x T^4 (your formula in edit 2 should have different values e for Ta and Ts). This gives the emitted radiation of a body in Watt per m^2 of surface area. How many molecules of air would you need to get enough surface area to make a big difference in the net flux of radiation on the surface? Don't forget the particles emit in every direction, not just towards the ground.
its true the emissivities will be different, but im not wanting to get too nitpicky and solve anything with any accuracy right now, I just want to understand whats going on. Emmissivities for snow seem to be anywhere from .85 to almost unity, whereas air can range from .75 to unity depending on moisture content. Im willing to bet\argue that for typical colorado conditions with weather and snow, we could remove the emissivity factor completely and still get a semi accurate answer.
Im not following you at all when you ask about air molecules. Calculating radiative flux has nothing to do with surface area. Quite simply, it only has to do with your delta T.
Sure the air molecules radiate in every direction, but for our discussion its very reasonable to explain and assume that everything is radiating in one direction. From Snow, up to air, through the atmosphere, and finally to space.
If you know each steady state temp, you can plug and chug each scenario to find out what each interfaces radiative flux is, but we're only concerned with snow, since thats what we ski on and need to be stable.
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What amount of radiation the surface emits does not depend on the difference in temperature with the surroundings. The snow will send out radiation regardless of what is around it (be it rocks, trees, “air particles”). On angled slopes, under trees or clouds it may well also receive radiation from these sources, significantly changing the net flux of radiation and potentially preventing freezes.
This is my first 100% disagreement.
I dont know where you got that fact, but radiation is goverened by one thing and pretty much one thing only.
The temperature difference of the surface of the object and whatever the object is radiating its energy into.
In our scenario, snow surface vs sky temp.
I also just found a very very similar example in my heat xfer book, and they calculate it this same way Im describing. Worthy of mentioning is that theyre assuming 2 different numbers for the "Air Temp" and "Sky Temp".
Im not really sure where theyre drawing a distinction between what temperature you use for calculating radiative fluxes. Interesting. Maybe you have a text that specializes in this or have some insight or can ask a prof?
Id be interested to know where this distinction is drawn, since it might just be that its not the nearsurface air temp I should be thinkign about, but moreso the "Sky Temp", whatever and whereever that is.
Ive also been working this with the assumption that the air is colder than the snow.
Which brings me to another question which I think I know the answer to, but will ask it anyway cause its not making sense completely.
If the air is warmer than the snow, and both are above freezing on a clear night, will the snow radiate off enough energy to actually drop in temperature?