How fast does snow melt?

[97 0]

Hello.

 

I'm interested to know about how fast snow melts. Like, if it's a sunny day about how many cm will be melted in 1 day?

 

Is anyone able to give me an idea?

[mattlucas 0]

Not too sure but rain melts snow faster than sun

[97 0]

Really? That is interesting. I suppose it is worse for the condition of snow as well...

[sava 0]

What about sunshowers?

[mattlucas 0]

sunflowers?

[sava 0]

?!?!

[muikabochi 208]

It can go real fast on a sunny warm day... maybe 20cm or so.

 

Not sure about rain but that just makes it all mushy and then very hard and icy later.

 

[snowboard 0]

What I don't get is that with all the mild weather we seem to have got since pretty much the beginning of February how much there is still hanging on. Pretty insane amounts must have fallen in those few weeks in Jan.

[97 0]

Thanks you. It's another school project thing. I'm trying to put something together on how fast snow arrives and then how fast it disappears. It's difficult to find data about the melting bit though!

[soubriquet 0]

You should be looking at latent heat of melting/vapourisation, as well as heat capacity for gasses and liquids. I can help you a little there if neccessary, but I'm busy today.

[97 0]

That sounds difficult soubriquet. But anything easy to understand you could write would be great!

[mattlucas 0]

 Quote:

Originally posted by 97:
That sounds difficult soubriquet. But anything easy to understand you could write would be great! I'll just copy and paste it into my report. Thanks.

[97 0]

My school report, yes! I'm not making any money out of it! If he can't help thats fine, I was just asking because he mentioned it!

 

Thanks

[mattlucas 0]

Plagerism is plagerism even if you arn't making any money off of it. While you won't get kicked out of high school for it. It's a bad habbit to take the easy road out.

 

You will get kicked out of University

[97 0]

Sorry!

[mattlucas 0]

Don't worry

I'm just razzing you a bit

[soubriquet 0]

97 I'm going to be busy all this week, but I'll see if I can manage a calculation on about Monday. Haven't done a heat calc since 1968, but the problem is quite easy.

 

I think it is a very interesting question, and I'm keen to know the answer, so I'm happy to do it. If you use it in your report, fine, but you have to acknowledge your sources. That's the ethical way.

[marnix 0]

just footnote it and you'll be fine. Patents etc don't have any value in the name of science as long as you correctly name your source.

 

Or at least rewrite it in a way that you understand it and can explain it to others.

[97 0]

Of course soubriquet, I always do that! Thank you.

[soubriquet 0]

97 asked "I'm interested to know about how fast snow melts. Like, if it's a sunny day about how many cm will be melted in 1 day?" I thought it an interesting question, and I am very surprised at what has shown up. Read on..

 

A little scratching around found a nice set of daily global solar exposure maps for Australia.

 

http://www.bom.gov.au/sat/archive_new/solar_radiation/2001/IDE3GS01.20010814.gif

 

This is the map for August 14th. Melbourne received about 14Mj of energy per m2.

 

Some easy physics here:

http://www.physchem.co.za/Heat/Latent.htm

 

The latent heat of fusion for water/ice is 334 kj per kg, meaning that it takes 334,000 joules of energy to melt 1 kilogram of ice. Therefore, If all the incoming energy was absorbed, 14Mj is enought to melt 42kg of ice and produce 42 litres of water.

 

Wet new snow has a density of about 0.2, so 42 litres of water makes 210 litres of snow. This equates to a metre square layer about 21cm thick. Spring snow density is around 0.5, which yields 8.4 cm of snow.

 

Not all the incoming radiation is absorbed though. Fresh snow has a high albedo (0.8), and about 80% of the incident (incoming) energy is reflected straight back. The figure for spring snow is about 0.7.

http://www.arcticice.org/albedos.htm

Therefore, the numbers start to look like this:

 

Fresh snow 21cm * 20% = 4.2cm

Spring snow 8.4cm * 30% = 2.5cm

 

So we now apply the test: is it reasonable for 2-4cm of snow to melt on a sunny day in mid-February? The answer has to be yes. Goody.

 

Now for rain.

If we assume 1cm of rain over 1m2, we have 10kg and therefore 10 litres. If the rain is at 10C, then cooling it to freezing point will yield

 

10 (kg) * 4.18 (kJ.kg-1. K-1)x 10 (º K) = 418 (kj)

 

of energy. Note the change in scale, this is kj, not Mj. Three orders of magnitude less.

 

If we calculate it through we find:

 

334 (kJ.kg-1) / 418 (kj) = 0.8 (kg)

 

The heat from 1cm of rain at 10ºC is only enough to melt out 0.8 litres of water. The rain cannot possibly be causing significant snowmelt. If the calculation is correct, then the model must be wrong, and it is.

 

We have ignored the gas phases. I'm not going through the maths because I found a very nice paper which does a much better job than I could.

 

http://earth.boisestate.edu/home/jmcnamar/seltopics/2006/marks.pdf

 

They have included air temp, wind speed and humidity in their model. They find:

 

"The relative magnitude of the energy balance terms, particularly the importance of the turbulent transfer terms during rain-on-snow shows how the combination of warm air temperatures, high winds and high humidities can cause significant condensation on the snow surface, providing adequate energy for rapid melting of the snow cover."

 

The heat which is driving the system is coming from water vapour condensing into rain. Heating the atmosphere causes it to expand, creating turbulent winds bringing humid air into contact with the snow. 1kg of condensation releases 2258kj into the snowpack whereas rainwater only supplies 4.18 (kJ.kg-1. K-1). So it seems that it is not the rain itself which causes the snowmelt, but the act of raining.

 

Water is such lovely stuff.

[scouser 4]

Blimey, stick that in your report 97!!

[mattlucas 0]

 Quote:

Originally posted by Toque:
Not too sure but rain melts snow faster than sun

Should have just listened to me

[97 0]

Thank you soubriquet! I think if I put that in my report they would think it was not me I will look at what you wrote and try to understand the ideas.

[soubriquet 0]

Ok, I'll re-organise it to make it a little less stream-of consciousness.

 

 

This is a heating curve for 1kg of water. Starting at -50ºC, we add heat, and the ice warms up (A). When it gets to 0ºC, it stops warming because the heat we are applying is being used to change state from solid to liquid (. Only when the ice is melted will the water heat up. At 100ºC we get a similar stop to warming and a further change of state, from liquid to vapour (D). The key here is that it takes much more energy to evaporate the water than to melt it. This is a physical reaction, so it is reversible. If we run it in reverse, we get the same amount of heat out at each step as we put in.

 

On a sunny February day in Hakuba we can expect about 14 Mega Joules of energy to land on every square metre of snow, but 80% of that energy is reflected back up, leaving 20% (2.8 MJ) to do heating.

 

2.8 (MJ) / 0.334 (MJ kg-1) = 8.4 (kg)

 

We can melt 8.4kg of ice.

 

The next day we have 10cm of rain (a lot) we get 100kg per m2. If the rain was at 10ºC (warm for February) and we cool the rain to OºC we can extract:

 

100 (kg) x 0.00418 (MJ.kg-1. ºC-1) x 10 (ºC) = 4.18 (MJ)

 

and

 

4.18 (MJ) / 0.334 (MJ.kg-1) = 12.5 (kg)

 

We can melt 12.5kg of ice.

 

(The numbers look a little different because I am using only MJ now, and I've upped the rainfall from 1 to 10cm).

 

We still have some solar radiation though, 2-3 MJ m-2. 20% of that gives about

 

0.5 (MJ) / 0.334 (MJ kg-1) = 1.5 (kg)

 

12.5kg + 1.5kg = 14kg

 

So, a heavy rain can melt about 60% more snow than a sunny day.

 

One litre of dew over an area of 1m2 equates to a 1mm film. If we can precipitate a litre of dew from the air directly to the snow surface:

 

1 (kg) x 2.26 (MJ.kg-1) = 2.26 (MJ)

 

and:

 

2.26 (MJ) / 0.334 (MJ kg-1) = 6.7 (kg)

 

1 litre of dew releases enough heat to melt 6.7kg of ice (step D on the cooling curve), whereas it takes 100 litres of rain to melt 14kg.

 

Converting from ice to snow thickness loss we have

 

. . Fresh snow (d 0.2). . . Spring snow (d 0.5)

 

Sun. . . 4.2cm . . . . .. . . . . 1.7cm

Rain . . 7 cm . . . . . . . . . . 2.8cm

Dew. . . 3.35cm . . . . . . . . . 1.34cm

 

So, whichever way we cut the numbers, 1mm of dew can melt the about same amount of snow as a sunny day, but you need about 6cm of rain water to do the same work. When we have rain, we have dew. The rain itself tells us that the air temperature is below the dew point, but we don't see the dew because it is raining.

 

A couple of other things. If the snow is fresh, then the rain will compact it and deflate the top surface of the snow (apparent melting). Also it will warm the snow if it is frozen, and it will increase the rate at which heat is conducted through the snow.

 

I hope this is clearer. It's not hard. There's no maths here, just arithmetic, so don't be frightened.

[fukdane 2]

Wow. Thats very interesting soubriquet.

You　sound like a scientist dude. (Are you?)