# Why is the troposphere 8km higher at the equator than the poles?

Fundamentals of atmospheric modeling show that the height of the tropopause depends on the location, notably the latitude, and that the troposphere is roughly 8km higher at the equator than the poles depending on the time of year.

First guess was that the temperature of the would impact its density (for example, here's the data for -50° and 50° c) - though this does not appear to show the cause of why is the troposphere 8km higher at the equator than the poles.

Why is the troposphere 8km higher at the equator than the poles?

• A significant part (but not all) of the answer to this question will be the same as the answers at Why is earth not a sphere? – naught101 May 1 '14 at 6:22
• It depends not only on location, but also on season and even on the weather. Might write down an answer if I find the time, unless somebody else does first. – gerrit May 1 '14 at 13:23
• I'm pretty certain the Coriolis force has nothing to do with tropopause height? Will edit my answer below when I'm in the same place as my lecture notes on this. – kaberett May 1 '14 at 13:50
• It is due to centrifugal force being greatest above the equator. – Douglas Cotton Nov 24 '16 at 4:27
• It is NOT due to the centrifugal force being greatest at the equator, though that adds 1, maybe 2%. It has to do with temperature. Warmer temperature = higher troposphere. More heat creates a greater vertical region of convection. The tropopause is at the relative equilibrium of temperature where it stops falling and begins to rise. – userLTK Oct 25 '17 at 5:07

To start with a definition, the tropopause is the boundary between troposphere and stratosphere; within the troposphere temperature decreases with increase in altitude (the temperature profile is dominated by radiative heat from the Earth's surface), whereas in the stratosphere temperature increases with altitude (the temperature profile is dominated by solar radiation).

Increases in troposphere temperature are associated with increase in tropopause height. Factors in play include the amount of water vapour being evaporated from equatorial seas; interannual variations in tropopause height can result from both local and large-scale driving forces. The tropopause responds to the average temperature of the entire underlying layer: this is higher at the equator and lower at the poles.

• Wow, this is wrong and it got accepted. Thermal expansion around a few Kelvin cannot account for a increase of the Tropopause by a factor of two. Do the math, it's the centrifugal force. – AtmosphericPrisonEscape Oct 24 '17 at 13:09
• @AtmosphericPrisonEscape it is thermal expansion. Use the hydrostatic equation over a layer with an average temperature, and you will find that it does explain MOST of the variability. There are some other influences, but the hydrostatic equation is sufficient on a large scale. – BarocliniCplusplus Oct 24 '17 at 15:56
• @Baro: Exactly. It gives you $H \sim T$ and T doesn't vary by a factor of 2. So it's NOT the temperature. – AtmosphericPrisonEscape Oct 24 '17 at 16:24
• This answer is correct, not wrong. This really should get cleared up cause we don't want two conflicting answers to a question (unless the question is genuinely unresolved). See this article here: www-das.uwyo.edu/~geerts/cwx/notes/chap01/tropo.html It says the highest Tropopause is over warm oceans and monsoons (water-vapor clearly plays a role). It also indicates that Temperature is a key factor. The tropopause rises and falls based on the seasons over the same location. – userLTK Oct 25 '17 at 5:14

In addition to the answer by @Kaberett lapse rate explains the height variation of the tropopause quite well. Lapse rate is a property of gravity and the ideal gas law and it has to be adjusted for circulation and condensation and the top-down heating from the sun, which is a small effect given a mostly transparent atmosphere. Lapse rate isn't perfect, but it's still good for an approximation.

Wikipedia summary

Shorter, Britannica summary

From the Britannica summary:

The lapse rate of nonrising air—commonly referred to as the normal, or environmental, lapse rate—is highly variable, being affected by radiation, convection, and condensation; it averages about 6.5 °C per kilometre (18.8 °F per mile) in the lower atmosphere (troposphere).

If we take that averaged 6.5°C per km, that explains pretty close to the surface temperature variation on the Earth at sea level. (Antarctica, being mostly more than a mile in elevation, you need to adjust the temperature -6.5°C per km in altitude for surface temperature). The troposphere being an average of 8 km higher at the equator, corresponds to 52°c variation using that -6.5 degree estimate, or about 32 degrees (equator) to minus 20 (pole), which is very much in the ballpark.

Also, as noted in the Wikipedia article

the dry adiabatic lapse rate is a constant 9.8 °C/km (5.38 °F per 1,000 ft, 3 °C/1,000 ft), the moist adiabatic lapse rate varies strongly with temperature. A typical value is around 5 °C/km

Moist air has a lower lapse rate, which explains why the troposphere is highest over warm equatorial Pacific and why it peaks over monsoons. - see this article.

It's the surface temperature and water vapor. That's the gist of it. The rotation of the Earth can't account for a troposphere that's twice as high over the equator. The rotation of the Earth (and if we want to get silly, also the Moon's atmospheric tidal bulges) both affect the troposphere some, but they are minor players.

Earth's atmosphere shouldn't bulge much more than it's body, about 1 part in 298, even if you multiply that by 4, and I think that's too aggressive a mathematical approach, but even so, that would be less than 1 part in 70 of atmospheric expansion over the equator due to the spin of the Earth. That's very far from the doubling that temperature explains.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7681004405021667, "perplexity": 913.9012913731402}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141729522.82/warc/CC-MAIN-20201203155433-20201203185433-00296.warc.gz"}