# Why does snow stay after a snowfall?

I have just experienced a snowfall and I am not so clear on how it works.

Three days after a short day of snowfall, and having 2 min | 17 max degrees Celsius, full sunny scarcely cloudy each day, there is still some snow persisting in shadow and dark places.

This is contrary to my intuition: I would've expected all the snow to have melted and disappeared after the first sunny day, or after the second. Yet we are on the third day and still some snowman heads are alive.

Is it because the snow contains salt? Or does the snow create low temperature air around itself? Or does the daily morning humidity turn the snow into ice blocks that are harder to melt and more solid to scatter sun rays?

• Consider that ice cubes don't instantly melt when you take them out of the freezer either. – Olin Lathrop Jul 20 '17 at 21:08

## 3 Answers

Just as a complement to Ziggurat's answer: you can try to estimate the time required for the sun to melt a certain quantity of snow by yourself.

• The energy required to melt a mass $m$ of snow is $$Q=L m$$ where $L$ is the latent heat of fusion. For ice, $L=334$ kJ/kg.

• The density of snow $\rho$ ranges from $100$ to $800$ kg/m$^3$

• Solar irradiance $I$ ranges from $150$ to $300$ W/m$^2$.
• The albedo of snow (percentage of reflected sunlight) $A$ ranges from $0.2$ for dirty snow to $0.9$ for freshly fallen snow.

If the surface exposed to sunlight is $S$, the absorbed energy in the time interval $\Delta t$ will be

$$E_{in}=(1-A) IS \Delta t$$

If $V$ is the snow volume, the energy required to melt it will be

$$E_{melt} =L \rho V$$

Equating these two expressions we get

$$\Delta t = \frac{L \rho V}{(1-A)IS}$$

Assuming $A=0.9$, $\rho=300$ kg/m$^3$ and $I=200$ W/m$^2$, we get, for a sheet of snow of surface $1$ m$^2$ and thickness $1$ cm, $\Delta t \simeq 5 \cdot 10^4$ s, i.e. $\simeq 14$ hours.

This is a very rough estimate that doesn't consider conduction processes. But anyway, you can see that even if we assume a pretty high irradiance we need a considerably long time to melt a modest quantity of snow. If the snow is in the shade, the value of $I$ will be less. Also, for snowmen, since we would be talking about compressed snow, the value of $\rho$ could be $2-2.5$ times larger.

For one thing, snow has a high albedo (it's very reflective) so it won't absorb much sunlight and warm up through that process. Thus, it will have to mainly heat up from convection, which isn't terribly efficient. Snow is a good insulator, so only the surface will be prone to melting. Also, the heat of fusion must be overcome in order to achieve the phase change. This answer isn't very well organized, but hopefully it conveys that there are many factors that work against the melting of snow.

• Add this to the fact that, especially later in the season, the ground is also often just as cold as the snow, so no melting occurs from the bottom either. This is also why it takes a day or two of snow for it to start piling up; at the beginning of winter, the ground is just too warm, and the snow immediately melts. Once enough snow melts, the ground is cool enough for snow to touch it without immediately melting. – probably_someone Jul 19 '17 at 3:13
• Wouldn't convection imply that the heated air by the sunlight would immediately start rising away from the snow, being replaced by the denser cold air? – JAD Jul 19 '17 at 7:46
• By convection you mean conduction by the snow material? Or advection of heat by air flow inside the porous snow mass? – Vladimir F Jul 19 '17 at 8:38
• @JarkoDubbeldam That's pretty much how natural convective flows are made, so it's somewhat implied. I dont think you would get a lot of flow from that process though. A lot of the convective heat transfer would come from the forced convection due to wind. – JMac Jul 19 '17 at 10:20
• @JarkoDubbeldam Yes, both of those would add to convective heat transfer. What I am saying is that the natural convection is not going to be that strong. Depending on the surface temperature of the snow, it may not even happen. If the ground is colder than the air, it will tend to stagnate, with the dense cold air hanging low. – JMac Jul 19 '17 at 10:35

There is some heat energy needed to melt snow, and it corresponds roughly to the energy needed to heat water by 80 degrees Celsius - this is quite a lot even compared to other substances, and so it takes few days of sunny weather for all snow to absorb the required energy from its surroundings.

Few notes to your sub-questions: 1) Melting the same mass of ice and snow requires the same energy, they do not differ chemically. Ice however absorbs more sunlight. 2) Yes, the air above snow in windless weather is colder and helps to insulate the snow from the warmer environment. This is particularly true in trenches and valleys. 3) No, snow usually does not contain any salt, but if it did, it would melt faster.

• Just a little note about when you say "it takes the same energy as heat up water by 80 degrees celsius". Although this may be true; it will be far easier to melt snow than it is to heat water to 80 degrees, due to the temperature gradient. It's fairly easy to heat something above 0 degrees celsius; but it's a lot harder to heat something above 80. Although the require the same energy, the exergy is different. – JMac Jul 19 '17 at 10:26