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The permanent snow line in the Alps is around 10,000 ft (3,000 m) elevation. This was further confirmed by a passenger flight I took late June where the screen showed 0°C (freeze point) around 10,000 ft north of NYC (and therefore, in summer above a temperate region).

However, temperature is said to fall 6.5°C each 1000 m. In Central and Western Europe, temperatures reach up to 40°C each summer. If we assume 35°C for a mid-summer day at sea level, the temperature should be 9°C at 4000 m (13,100 ft) and 2.5°C at 5000 m (16,400 ft). So according to that formula, the permanent snow line should be well above all Alps (the highest is Mont Blanc around 4810 m) as all snow should have molten on a warm summer day. If we assume 26°C at sea level, 0°C should be reached at 4000 m according to the above formula. Yet, many considerably lower Alps are covered by snow year-round, as low as ~3,000 m.

Did I miss something? Is the snow high up in the Alps just too robust to melt away even if temperatures are considerably above freeze point? Or can't one apply the above formula for temperate regions / mid-latitudes of Earth (as obviously was indicated in the airplane too)?

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There are a couple of issues that you need to add to your picture.

First, the temperature varies over time so it is not constant at a certain elevation throughout e.g. the summer.

Second, snow will melt from the energy provided to the snow pack. This energy is not exclusively expressed as temperature. The energy fluxes that reach the ground and can provide energy for melt include

  • Long wave radiation (infra red)
  • Short wave radiation (visible light)
  • Sensible heat (heat content of the air convected towards the surface due to turbulence)
  • Latent heat (Air moisture advected to the surface through turbulence; a phase change from gas to liguid during condensation expells heat)
  • Energy contained in rain drops, i.e. the temperature of the rain water, falling on the surface

The radiation will in part be reflected so not all incoming radiation will be available for melting. A new fresh snow surface can reflect as much as 90% of the incoming radiation, we say the snow has an albedo of 0.9 where 1 is 100% reflection and 0 is no reflection at all. Snow surface commonly have lower albedo since there may be dust and other particles that can accumulate and lower the albedo making the snow pack absorb more radiation thereby allowing more energy to contribute to melting. Wet snow also lowers the albedo, particularly for long wave radiation.

A melting snow surface will always be at the melting point, essentially zero but particularly the radiation components will contribute energy to cause melting at subzero temperatures. It is common to experience wet snow with a thin frozen crust in spring when incoming radiation is high but air temperature may be below zero. The radiation causes subsurface melt while the cold air keeps the crust frozen.

When snow covers rocky ground some radiation will heat rocks that protrude the cover and help snow to melt in the proximity of such rocks. If the snow cover is thin the ground may be heated from absorbing the radiation and cause melting at the base of the snow pack. Radiation can penetrate about a meter of snow (depends on density) so when the snow pack is a few dm or so a fair portion of radiation will reach the ground beneath the snow pack.

Bare paches of ground will absorb more radiation that the snow cover surrounding the patches and become heat islands in the general snow cover. The air above these patches will warm up due to the warm ground and in the presence of wind provide warm air for melting in the near surroundings.

So, in conclusion, there are several processes we need to consider when trying to understand the snow line, one is the heat balance and the other is the micro-climate that result from surfaces having different albedo. Therefore the snow line elevation will move up in elevation during the melt season due to the cumulative effect of what has been discussed above.

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  • $\begingroup$ You describe examples of why snow might melt even at temperatures below freezing point. That adds to the puzzle why there is snow at altitudes far below the freezing point, i.e. with temperatures far above the freezing point. $\endgroup$
    – user29677
    Commented Sep 21, 2023 at 17:54
  • $\begingroup$ When you say temperatures, you need to consider what temperature you consider. Is it annual average temperature? Is it the temperature at some point in time? Since temperature varies over time, snow can accumualte during periods when the temperature is lower, this can be seasonal or just short-term fluctuations. The snow will of course melt when temperatures increase again. So it is difficult to see your point without information about the climatology of the specific site. $\endgroup$ Commented Sep 21, 2023 at 20:07
  • $\begingroup$ Well, if sea level temperatures are higher than 30°C for say an entire day sometime in the summer, the freeze point (0°) should be well above 4000 m. Shouldn't much snow at altitudes lower than 4000 m melt soon? It's not like temperature would change so drastically in the following days that sea level temperatures would become spring- /fall-like. Unless it suddenly becomes overcast and perhaps rains at sea level, but mountain summits like Mont Blanc are likely to be above many rain (at those altitudes snow?) clouds often. I wonder if there are images of any ~3,500 m Alp without any snow on it. $\endgroup$
    – user29677
    Commented Sep 22, 2023 at 6:24
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    $\begingroup$ @Hannes: though there are some misunderstandings in your question (one can't compare atmospheric conditions near a megacity to those at mountain ranges), the snowline in parts of the alps these days is 500-1000m higher than the long term average that may be found on wikipedia etc. dlr.de/eoc/en/desktopdefault.aspx/tabid-18823/30125_read-83952 and agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2019gl085742 But it is dynamic process with regional differences. $\endgroup$
    – user29219
    Commented Sep 22, 2023 at 7:25

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