How does latitude affect the air temperature at 8 km altitude where planes fly?

Question

Is the air temperature (at 8km) above the North or South poles colder than the same altitude above the equator? Why?

Ground level air temperature difference between coldest and warmest places on Earth can be >70C. As you get higher, the temperature drops, of course. Does it mean that near Arctic circle air temperature at let's say, 8km altitude still maintains approximately the same difference with the 8km altitude above equator as at the ground level? Or does it even out? Is it perhaps even possible to have air at some altitude significantly warmer than at ground level?

Answer 1

In the troposphere, air at altitude is colder than air at ground level. But surprisingly, air at altitude at the poles can be warmer than air at altitude at the equator. From the wiki article on troposphere (I added the bullet points):

The troposphere is heated from below by latent heat, longwave radiation, and sensible heat. Surplus heating and vertical expansion of the troposphere occurs in the tropics.

• At middle latitudes, tropospheric temperatures decrease from an average of 15 °C (59-degree Fahrenheit) at sea level to about −55 °C (-67-degree Fahrenheit) at the tropopause.
• At the poles, tropospheric temperature only decreases from an average of 0 °C (32-degree Fahrenheit) at sea level to about −45 °C (-49-degree Fahrenheit) at the tropopause.
• At the equator, tropospheric temperatures decrease from an average of 20 °C (68-degree Fahrenheit) at sea level to about −70 to −75 °C (-94 to -103-degree Fahrenheit) at the tropopause.

The troposphere is thinner at the poles and thicker at the equator. The average thickness of the tropical troposphere is roughly 7 kilometers greater than the average tropospheric thickness at the poles.

There is quite a bit of variation in the troposphere as a function of place on earth, and much effort has been put into creating a standardised atmosphere that can be used for practical purposes around the world. The ICAO standard atmosphere serves that purpose. It cannot account for local wind conditions and humidity.

I found a graph in an old paper format uni book on the atmosphere, depicting average conditions in two separate places on earth, Berlin and 40° latitude in North America. The graph shows that although the temperature lapse rate is very similar in both cases, there is a difference in temperature at a given height. The arrow gives the temperature difference at 8 km height, also transported to 0 m (less average difference) and to 10 km (more average difference).

Above is for average temperature at two different places on earth, at similar latitudes. I could not find any direct comparison between average temperature at altitude of the poles and the equator - the wiki article seems to indicate that average temperature at the poles is higher at high altitude, a surprising indicat

Answer 2

The temperature decreases at approximately 3.57 degree Fahrenheit per 1000', the adiabatic lapse rate, until hitting the tropopause, the boundary between the troposphere (lower altitudes) and the stratosphere. At that point the temps flatten out. The lapse rate is pretty constant everywhere, so yes, it should be colder at higher latitudes for the same altitude.

But...

The tropopause is at a higher altitude at lower latitudes, so you actually end up with cooler temps above the equator then above the poles for very high altitudes (17 km range).

Answer 3

The airplanes do not cruise at a certain altitude, but at a certain pressure level. That could be an irrelevant nitpick if the temperature did not directly affect the pressure as a function of altitude. But it does (through the hydrostatic equilibrium). In colder areas the air is heavier and flight levels are lower as can be seen in maps of geopotential height

At FL360 the pressure is 225 hPa and the altitude is around 36 thousand feet. The 300 hPa and 250 hPa will be quite typical flight levels for airliners (~FL300 and FL340). You can see the current map of altitudes and temperatures for these and other levels at http://weather.uwyo.edu/upperair/uamap.shtml

For example: http://weather.uwyo.edu/cgi-bin/uamap?REGION=nh&OUTPUT=gif&TYPE=an&LEVEL=300&date=2020-01-09&hour=0

The green numbers are temperatures, the blue numbers are altitudes. You can see that for the same flight level the aircraft is at 9600 m above North Africa or Florida and at 8400 m near the north pole in the current weather. In summer the air is warmer and the flight levels are higher as you can easily see by choosing a different date in the app. Also, the south-north gradient is weaker in summer - related to the strength of the polar vortex.

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Due to the air compressibility you can never have higher temperatures in the stratosphere than at the Earth surface. However, in certain sense, the air at higher levels IS actually warmer. The potential temperature is higher and if the air is brought to the surface pressure level, it will be indeed warmer. However, that costs mechanical energy (work).