Why do we have snow on the top of mountains even though the distance from the sun is shorter?

-K Bryant

Search the internet or your fluid mechanics book for the change of atmospheric temperature and pressure as a function of altitude then check the steam tables. Solar energy exchange does not depend on the distance.

"Solar energy exchange does not depend on the distance"

it does depend on the distance! But not in the range of earth diameter...

Ralf I am sure you are familiar with the Stefan Boltzmann Equation. Please correct my knowledge and tell me what other equations are you referring to.

besides equations, our common sense tell us that you are right when refering to earth distances but get close to the sun and after get completely burned you will understand what Ralf was talking about.

Unfortuanetly for you "someone", science of heat transfer is well established in the area of Radiation Heat Transfer, so if you want to add to my knowledge you are wellcom other wise street talk is not my speciality

Ralf Schmidt wrote: ""Solar energy exchange does not depend on the distance"

it does depend on the distance! But not in the range of earth diameter... "

---------- The distance effect will apply in terms of the View Factor used to compute the net radiation exchange between sun & earth - based on the centreline distance between disks.

The height of mountains in relation to this centreline distance is negligible. Thus, Ahmed's direct use of the Stefan Boltzmann equation, with appropriate View Factor would be a reasonable assumption.

In any multi-mode heat-transfer problem, the various forms of heat-transfer will have different influence on the problem at hand. In the case of snow on the mountains, the radiation component would be approximately constant, whilst the convective component would most certainly be influenced by the change in air properties with height.

Lack of cloud cover could play a role in adjusting the absorptance/emittance of the atmospheric water vapour, thus influencing the incoming radiation effect slightly, with altitude.

diaw...

Diaw

How are you doing, hope every thing is ok.

That is right, the view factor, that is the key word, now the view factor calculations (very tedious for sure) depends on the cosine of the angle.

Now tell me "Ralf Schmidt" and "someone", what is the effect of a mountain height (the highest we know about, the Everest is just few thousands meters) compared to the Earth diameter, and the distance between Sun and Earth (Few billion meters) on calculating the cosine of the angle (using the best available computing machine)

The original query was about the formation of snow at the summit of a mountain on this planet Earth, and as I explained in my first posting it is the effect of atmospheric temperatures and pressures being effected by the altitude not by the lack or reduction in solar energy exchange.

Speaking of mountain height, here's an analogy... The earth circles the sun in an elliptical path. The earth is 0.3% closer to the sun during the winter in the Northern Hemisphere, than the summer. 0.3% of the distance from the sun to the earth is way taller than that of the highest mountain. Yet, its butt cold here in Wisconsin.

Hey Ahmed,

Maybe I am wrong, but there seems to be some venom in your posting to "someone" and Ralf Schmidt.

As far as I can tell, Ralf was correct in saying what he did, distance does matter, there are just other effects that are more important in the range of the earths diameter. You shouldn't attack anyone, particularly not someone who isn't saying anything wrong!

Diaw is the only person that injected some rigour into his argument in this thread and for that he should be thanked.

Hi!

I didn't expect, that my posting results in a large discussion. Now, I have two things to say:

First to the "street talk": In my opinion, street talk reflects reality. And it is the task of any scientist, if physicist or engineer, to explain reality and not vice versa. So, if the equations do not explain what we observe, ether observation is wrong or the equations are wrong or not complete. And if observation is wrong, science has to explain why!

Second: The sun emits radiance energy. So, the energy is divided on the surface of a sphere, that is made from the distance to the sun. It will result in 1.37 kW/m2 hitting the earth.

By the way, different than normally used, the sun light beams are NOT parallel!!! Of course, they are in the range of earth diameter!

Ralf

Ralf_Schmidt wrote: Second: The sun emits radiance energy. So, the energy is divided on the surface of a sphere, that is made from the distance to the sun. It will result in 1.37 kW/m2 hitting the earth.

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A few points regarding radiation:

(1) A suitable view factor needs to be considered which basically determines the fraction of radiation energy emitted from the sun that is intercepted by the Earth.

(2) Water-vapour in the Earth's atmosphere will absorb & scatter some of this 'intercepted' radiation arriving from the sun. This results in some energy reduction.

(3) A view then has to be taken on how much of the remaining radiation energy is actually absorbed by the Earth's surface - the rest is reflected & re-emitted. The emissivity of snow is around 0.82 - 0.90, soil 0.93 - 0.96, ice 0.95 - 0.98. Absorptivity of snow - fresh, fine particle 0.13, snow, ice granules 0.33. Absorptivity/emission ratio 0.16 / 0.37 respectively. So, snow absorbs far less radiation energy than it emits.

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It would be useful to perform an energy balance on a surface located at the top of the mountain & compute the radiation absorbed & the convective heat-transfer to/from the surface. I'm not sure that conduction back down into the rock surface should be neglected. It may be that the convective & conduction heat-transfers far outweigh the radiation effect.

What would the convection component come from? Winds blow rather strongly up mountainsides.

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So, there will always be a few components in the multi-mode heat-transfer problem. The best would be to perform an energy balance for each component & to determine the relative strengths of each.