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Why there is always cold at high altitudes. e.g. at peak of mountains. Also as we go high from sea level, temperature starts decreasing. Why is it?

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Variation of temperature with altitude is more complicated than your question states. –  RedGrittyBrick Oct 16 '12 at 20:39

5 Answers 5

up vote 6 down vote accepted

I'd like to add to the answers already given. Indeed, the atmosphere is transparent to shortwave radiation from the Sun, but absorbs a lot of the longwave radiation from the Earth; that's why we have the greenhouse effect, that's why the Earths has a liveable climate and that's part of the reason why we have the lapse rate we observe. But why is it colder at the Tibetan plateau, which is a large, flat area at roughly 4 km elevation? Aren't we equally close to the local surface there as when we are at sea level?

Let's assume the Tibetan plateau receives the same intensity of solar radiation as lower areas at the same latitude. In reality, it probably receives more due to the dry climate. Then it should heat up more, shouldn't it? But it doesn't. The system Earth-Atmosphere can be considered to be in a local Radiative-Convective Equilibrium (see the diagram from Kevin Trenberth below). This means that the energy flows "in" and "out" cancel out by energy transport due to radiation and convection. In other words: what goes in, must go out (this is not really true locally, because there are large-scale flow patterns known as wind). Now, the Earth surface emits radiation according to its temperature with $P = \epsilon \sigma T^4$. Some of this radiation is aborbed by greenhouse gases (or clouds) in the atmosphere: water vapour, carbon dioxide, methane, and others. Then the atmosphere heats up, and again radiates according to $P = \epsilon \sigma T^4$; part of this radiation goes into space, and part goes back to the surface. The greenhouse gases keep the surface of the Earth warm like a blanket.

Now at the Tibetan plateau, the atmosphere is much less dense, because the elevation is so high. Therefore, radiation emitted by the surface is not absorbed much, but mostly exits straight into space. This means that the surface cools down. To return to the blanket analogy: Tibet has a much thinner blanket than lower elevations do.

Now I have made a number of severe simplifications, because in reality it depensd on day/night, on clouds, on atmospheric flow such as wind, on humidity, and on other factors. But whereas the explanation given by others explains why it gets colder higher up in the free atmosphere, I think it doesn't really explain why it is colder at the Tibetan plateau.

enter image description here

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A sub-question: why is the blanket Thinner on the Tibetan plateau? Gravity? Wolfram Alpha says (bit.ly/VuX0qn) that the gravity on sea level is 9.83 vs. 9.818 on this plateau, not much difference there. –  duality_ Oct 27 '12 at 13:26
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@duality_ I think that deserves to be its own question, but in short: due to its fluid nature, the atmosphere is roughly homogeneously distributed over the geoid. Therefore, the higher above the geoid an observer is, the less atmosphere (less blanket) there is above the observer. The local gravitational acceleration is of secondary importance only. –  gerrit Oct 27 '12 at 13:30
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So it kind of spilled from the plateau down to the lowlands, like a liquid would? I think I understand now. –  duality_ Oct 27 '12 at 13:32
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@duality_ I think that analogy is correct. –  gerrit Oct 27 '12 at 13:33

Gravity pulls air down closer towards lower altitudes. For this reason the atmospheric pressure is higher at lower altitudes. This higher pressure further results in a higher temperature as first described by Gay-Lussac's Law (Pressure is Proportional to temperature).

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As long as we don't go much higher (we stick ourselves within the troposphere), the lower regions in the atmosphere can be roughly approximated as a bulk of ideal gas (that's the standard atmosphere we use in our aerodynamics course), so that we can treat it using the ideal gas law ($PV\propto T$). As we go higher and higher, the atmospheric pressure decreases, causing the temperature to drop (since they're directly proportional).

This table shows the variation of pressure with altitude in psi.

Variation

For more info, see Lapse Rate in Wikipedia.

As an average, the International Civil Aviation Organization defines an international standard atmosphere with a temperature lapse rate of 6.49 °C/1,000 m (3.56 °F or 1.98 °C/1,000 ft) from sea level to 11 kilometres (36,000 ft). From 11 to 20 kilometres (36,000 to 66,000 ft), the constant temperature is −56.5 °C, which is the lowest assumed temperature in the ISA.

As Mark said, the water vapor content in the air also plays a major role. Different lapse rates have to be considered for change in humidity. Even a slight variation might significantly affect the lapse rates.

A natural question should've come by now, "Why does the pressure decrease then?"

Because the air molecules here at lower altitudes experience the weight ($mg$) of the molecules above them, thereby a net compressive force is produced. Though the force is very small (of the order of $10^{-25}$ or something) for an individual molecule, considering as a whole (a few kilometers depth and width), the net weight is big! As altitude increases, the downward force also decreases due to the decreased density of the molecules.

And, (as Chris & John say), as we go to the upper atmosphere, the temperature starts increasing with altitude, as air gets heated up directly by sun's radiation!

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What about the number density of molecules that decreases with height? –  Prathyush Oct 16 '12 at 15:07
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"Directly related" isn't very good for the description of pressure and temperature in the atmosphere. First, I would imagine that modeling the ideal gas as expanding adiabatically as it rises gives a slightly better estimate than isovolumetric. Also, there are some more complicated effects such as water vapor concentrations that matter quite a bit, as I remember. –  Mark Eichenlaub Oct 16 '12 at 15:20
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No I am taking about n/V. Which is inversely related to temperature. Perhaps It is not a significant effect. ps: A molecule weights much less then nano Kgs, remember 1 Gram weight = 10^23 molecules. We would be crushed to death if each molecule weighted nano Kilos. –  Prathyush Oct 16 '12 at 15:27
    
It would be useful to see if its significant. Even a one percentage change will correspond to a couple of degrees change in Temperature. –  Prathyush Oct 16 '12 at 15:49
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@CrazyBuddy Mark is right. While you do have the rough qualitative idea, the troposphere is very well approximated as isentropic due to convection. A full thermodynamic treatment allows for things such as temperature increasing with height in the stratosphere and thermosphere. –  Chris White Oct 16 '12 at 22:42

Crazy Buddy is quite correct that it's because gas expands and cools as it rises, but there is more to it than that.

For something to be be heated it must either absorb EM radiation, or it must be heated by some hot object it's in contact with. Air doesn't absorb light so it can't be directly heated by sunlight. Instead the sunlight passes through the air and heats the ground, and the ground heats the air.

The expansion comes in because the hot air that is heated by the ground rises. However as it rises it's volume increases and therefore it's temperature decreases. So the decrease in temperature with height is indeed due to expansion, but this is only the case because air is heated from below by the ground.

If air absorbed light directly it would heat up independantly of the ground and we would not see the same temperature variation with height. In fact exactly this effect happens in the stratosphere. In the upper reaches of the stratosphere ozone molecules absorb ultraviolet light and heat up, and in the stratosphere temperature increases with height instead of decreasing.

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+1 for mentioning the primary source of heat and Ozone in the Stratosphere. Certainly if there were no Sun we'd still have a temperature gradient due to changes in pressure, but that's not the biggest factor on Earth. –  ghoppe Oct 16 '12 at 18:30
    
In places of high altitude too we have ground to heat up the air then why its still cold. It is ( as @CrazyBuddy pointed out) just because of low pressure ? –  user10001 Oct 16 '12 at 19:17
    
@John Rennie : thank you very much for your answer. –  android developer Oct 17 '12 at 6:54
    
@John Rennie: Why then the temperature of different places can not become the same because they are in contact and can exchange heat? –  richard Nov 19 '13 at 14:56
    
@richard: do you mean different heights, or different areas e.g. different countries? –  John Rennie Nov 19 '13 at 15:21

This is a very old question, but none of the answers fully address the question. I'll frame my answer in terms of answers to a series of questions:

  • How much does temperature vary with altitude?
  • Why does pressure vary with altitude?
  • Why does temperature vary with altitude?
  • What about the second law of thermodynamics?
  • Why is the Tibetan Plateau so cold so warm?

How much does temperature vary with altitude?
The answer is quite a bit. The following graph that depicts average behaviors of temperature as a function of altitude:


Image courtesy of Nick Strobel at www.astronomynotes.com.

Starting at the surface, temperature tends to drop linearly with altitude within the troposphere, reverses direction at the tropopause and increases with altitude in the stratosphere, reverses direction again at the stratopause and decreases and in the mesosphere, and finally once again reverses direction at the mesopause and increases in the thermosphere. The above graph gives brief explanations for those regions where temperature increases with increasing altitude. It also gives a hint as to why temperature decreases in the troposphere, greenhouse and convection. The rest of this answer focuses on those tropospheric temperature variations.

Why does pressure vary with altitude?
The atmospheric pressure gradient is one of the key drivers of the tropospheric temperature gradient. Before one can understand why temperature varies with altitude, it's important to understand why pressure varies with altitude. At any altitude, the atmospheric pressure must more or less bear the weight of the air above that altitude. Mathematically, this can be expressed as the hydrostatic equilibrium condition $dp/dz = -\rho g$, where $p$, $\rho$, and $g$ are the pressure, density, and gravitational acceleration at altitude $z$. This would mean an exponential decay in pressure if temperature was constant. The decay is faster than exponential in regions where temperature decreases with altitude but slower than exponential in regions where temperature increases with altitude.

Why does temperature vary with altitude?
The above graph supplies two reasons: convection and the greenhouse effect. A parcel of air warmed by the surface will start rising when the parcel's temperature exceeds that of the surrounding air. This rising parcel of air will cool adiabatically as it rises. Assuming that (1) atmosphere is balanced hydrostatically, (2) the rising parcel acts as an ideal gas, and (3) the rising parcel is more or less isolated thermally, the parcel's temperature will drop linearly with increased altitude. The rate at which this cooling occurs is dry adiabatic lapse rate. The parcel will keep rising so long as the temperature of the parcel remains higher than that of the surrounding air. The relative humidity within the parcel will rise as the parcel continues to rise. Water will start condensing once the parcel cools to the dew point. This condensation provides heat to the rising parcel. This isn't enough to completely counteract the cooling due to rising. The lapse rate falls to a new value, the moist adiabatic lapse rate. Once again, the parcel continues to rise so long as the parcel's temperature stays above that of the surrounding air.

There are two more important lapse rates, the atmospheric lapse rate and the environmental lapse rate. The adiabatic lapse rates are dictated solely by the gas laws and the hydrostatic balance of the atmosphere. The atmospheric lapse rate is the rate at which temperature actually drops with increasing atmosphere. This may or may not be linear, and it may or may not be in line with the adiabatic lapse rates. If the atmosphere cools more quickly with altitude than do rising parcels of air, those parcels will rise to the top of the troposphere. The temperature inversion at the tropopause forms a very strong barrier to rising parcels of air. The rising parcels will stop rising within the troposphere if the atmospheric lapse rate is less than adiabatic. Finally, the environmental lapse rate is the observed average value of the atmospheric lapse rate, with the average taken over time and worldwide. This is the profile plotted in the graph above.

This convection-driven heat transfer is one of the two key mechanisms by which heat is transferred from the bottom of the atmosphere to higher levels. The other mechanism is the greenhouse effect. While our atmosphere is more or less transparent at visible wavelengths, it is more or less opaque in the thermal infrared. Water vapor, carbon dioxide, and methane are the key greenhouse gases that cause this greenhouse warming. Just as we use blankets in winter to keep us warm at night, those greenhouse gases act as a blanket to slow the transfer of thermal radiation from the sunlight-warmed surface to the blackness of space. Convection dominates over radiative heat transfer if convection is possible. The greenhouse gases and the radiative heat transfer that results is what makes the conditions right for convection to occur.

What about the second law of thermodynamics?
A uniform temperature atmosphere would maximize the atmosphere's entropy. Any deviation represents a departure from that maximal entropy. The existence of a lapse rate seems to fly in the face of the second law of thermodynamics. Energy can drive and does drive departures from thermal equilibrium. My air conditioner and refrigerator take advantage of this. My air conditioner and refrigerator do not violate the second law of thermodynamics. Neither does the atmosphere.

The greenhouse gases set up conditions in the atmosphere that make an adiabatic lapse rate be a local maximum in entropy. Convection moves the atmosphere toward that local maximum. Finally, sunlight provides the energy that drives convection. The existence of a lapse rate does not violate the second law of thermodynamics.

Why is the Tibetan Plateau so cold so warm?
One of the answers uses the Tibetan Plateau to explain the lapse rate. There's one problem with this: The temperature difference between places on the Tibetan Plateau and locations at sea level at the same altitude is much smaller than that suggested by the lapse rate. Lhasa, for example, at an altitude of 3490 meters has a mean year-round high of 15.8 °C and a mean low of 1.5 °C. The environmental lapse rate of 6.5 K/km suggests that Lhasa should be significantly cooler than that. The highest timberlines in the northern hemisphere are at the southern edges of the Tibetan Plateau. The Tibetan Plateau is rather warm given it's high altitude. The lapse rate explains why the Tibetan Plateau should be cool, and it is. By why is it so warm?

The answer is because the plateau is so very high. Free air at that altitude is heated rather indirectly from the ground far below. Intervening air steals much of the rising warmth. The lapse rate is in full swing. The plateau is heated directly by the high elevation land. The solar flux is higher than at sea level because of the plateau's great altitude. The plateau is in fact a major heat source for the upper atmosphere. A large number of scientific articles have been published on this subject since the 1950s.

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