<p>There's some kind of explanation about the units under the picture. The formula is based off the <a href="https://energyeducation.ca/encyclopedia/Temperature_of_the_Earth#cite_note-RE1-3" rel="noreferrer">average temperature in degrees Celsius (measured over the entire year, and the entire Earth)</a>, which is 15.04 at sea level, and the temperature decreases by 0.00649 degrees every meter above sea level (the average <a href="https://www.britannica.com/science/normal-lapse-rate" rel="noreferrer">lapse rate</a>). The formula is 'valid' until 11 kilometers, where the troposphere ends.</p>
<p>It's just a model of the average temperature; of course, at the poles it will be colder and at the equator it will be warmer. The lapse rate also varies, while the average of 6.5 °C per kilometer is quite well-known, it can vary between 9.8 °C when it's dry and about 5 °C when it's moist; see <a href="https://en.wikipedia.org/wiki/Lapse_rate#Mathematics_of_the_adiabatic_lapse_rate" rel="noreferrer">Wikipedia</a> for the derivation of these rates.</p>

CC BY-SA 4.0
2020-10-24T18:25:40.273Z
what if I want to give the equation my own temperature?  For example, simulate a hotter day or colder, will the change of (15.04)  to other temperature fix this? Or should I also add something like dry air coefficient?
mad.redhead
CC BY-SA 4.0
2020-10-24T18:30:01.080Z
On average, yes. The 6.5 degrees decrease in temperature per kilometer altitude is quite well-known. But it does depend on the humidity.
Glorfindel
CC BY-SA 4.0
2020-10-24T18:43:37.423Z
But there is no humidity coef in the equation. Is there any alternative options to calculate atmospheric pressure?
mad.redhead
CC BY-SA 4.0
2020-10-25T10:49:36.157Z
I've added some more information about how lapse rates vary with humidity; I doubt I know much more about the subject than you do. If you now have a question about *pressure*, it's probably better to ask a new question.
Glorfindel
CC BY-SA 4.0
2020-10-25T14:40:42.807Z
The local lapse rate can even be negative (temperature increases locally with increasing altitude), as happens with inversion layers.
David Hammen
CC BY-SA 4.0
2020-10-25T20:00:43.557Z
@mad.redhead If you want to account for humidity you'll need to distinguish between the dry adiabatic lapse rate when relative humidity is less than 100% and the moist adiabatic lapse rate when relative humidity is 100%. That said, the atmosphere is only approximately adiabatic. How much the troposphere locally deviates from adiabatic (convective available potential energy) is one of the key indicators of whether bad weather is on the way.
David Hammen
CC BY-SA 4.0
2020-10-26T10:06:07.007Z
@mad.redhead If you need anything precise, the approximation by this equation may be insufficient for your needs.  In the real world, all kinds of profiles including inversions and unstable distributions are possible, which is why we use radiosondes and remote sensing techniques to measure profiles of T and q worldwide multiple times per day.  The average lapse rate is just good enough for a rough approximation, but nothing more.
gerrit
CC BY-SA 4.0
2020-10-26T10:11:08.423Z
@gerrit, yeah, found out recently about other more complicated and accurate equations.
mad.redhead
CC BY-SA 4.0
2020-10-24T18:20:52.853Z
2020-10-25T10:47:55.970Z
2020-10-25T10:47:55.970Z
Glorfindel
<p><a href="https://www.grc.nasa.gov/WWW/K-12/airplane/atmosmet.html" rel="nofollow noreferrer">NASA's page about Earth atmosphere models</a> gives a weird equation about temperature change in different atmospheric layers. One of the formulas looks like this:</p>
<p><a href="https://i.sstatic.net/71Ioj.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/71Ioj.png" alt="" /></a></p>
<p>Can someone explain to me what this means?</p>

CC BY-SA 4.0
2020-10-25T14:59:36.157Z
I just thought that these are two different equations
mad.redhead
CC BY-SA 4.0
2020-10-25T15:14:02.107Z
I'm not sure I understand. They are indeed two different equations. One is for temperature vs altitude. The other is for pressure vs temperature. Every equation is described in the above link, with the associated units.
Eric Duminil
CC BY-SA 4.0
2020-10-26T10:15:24.480Z
sorry, I guess my question was really dumb and incorrect. But I just couldnt stand the fact that T = 15.04 + 0.00649*h is that simple formula to calculate temperature with altitude.
mad.redhead
CC BY-SA 4.0
2020-10-26T16:54:27.090Z
Your question wasn't dumb nor incorrect. In order to save time, you could have mentioned what you understand and what not, but that's about it. It's always better to ask when something's not clear.
Eric Duminil
<atmosphere><atmosphere-modelling><barometric-pressure>
Temperature change in Earth atmosphere models?
mad.redhead
# Temperature change in Earth atmosphere models?

(Asked by: username_0 on 2020-10-24)

[NASA's page about Earth atmosphere models](https://www.grc.nasa.gov/WWW/K-12/airplane/atmosmet.html) gives a weird equation about temperature change in different atmospheric layers. One of the formulas looks like this:

[![](https://i.sstatic.net/71Ioj.png)](https://i.sstatic.net/71Ioj.png)

Can someone explain to me what this means?

**Tags:** atmosphere, atmosphere-modelling, barometric-pressure

> **Comments:**
> **username_0**: I just thought that these are two different equations  
> **username_1**: I'm not sure I understand. They are indeed two different equations. One is for temperature vs altitude. The other is for pressure vs temperature. Every equation is described in the above link, with the associated units.  
> **username_0**: sorry, I guess my question was really dumb and incorrect. But I just couldnt stand the fact that T = 15.04 + 0.00649*h is that simple formula to calculate temperature with altitude.  
> **username_1**: Your question wasn't dumb nor incorrect. In order to save time, you could have mentioned what you understand and what not, but that's about it. It's always better to ask when something's not clear.  

---

## 1 answers

### Answer by username_2 on 2020-10-24. Score: 11 | Accepted answer

There's some kind of explanation about the units under the picture. The formula is based off the [average temperature in degrees Celsius (measured over the entire year, and the entire Earth)](https://energyeducation.ca/encyclopedia/Temperature_of_the_Earth#cite_note-RE1-3), which is 15.04 at sea level, and the temperature decreases by 0.00649 degrees every meter above sea level (the average [lapse rate](https://www.britannica.com/science/normal-lapse-rate)). The formula is 'valid' until 11 kilometers, where the troposphere ends.

It's just a model of the average temperature; of course, at the poles it will be colder and at the equator it will be warmer. The lapse rate also varies, while the average of 6.5 °C per kilometer is quite well-known, it can vary between 9.8 °C when it's dry and about 5 °C when it's moist; see [Wikipedia](https://en.wikipedia.org/wiki/Lapse_rate#Mathematics_of_the_adiabatic_lapse_rate) for the derivation of these rates.

> **Comments:**
> **username_0**: what if I want to give the equation my own temperature?  For example, simulate a hotter day or colder, will the change of (15.04)  to other temperature fix this? Or should I also add something like dry air coefficient?  
> **username_2**: On average, yes. The 6.5 degrees decrease in temperature per kilometer altitude is quite well-known. But it does depend on the humidity.  
> **username_0**: But there is no humidity coef in the equation. Is there any alternative options to calculate atmospheric pressure?  
> **username_2**: I've added some more information about how lapse rates vary with humidity; I doubt I know much more about the subject than you do. If you now have a question about *pressure*, it's probably better to ask a new question.  
> **username_3**: The local lapse rate can even be negative (temperature increases locally with increasing altitude), as happens with inversion layers.  
> **username_3**: @username_0 If you want to account for humidity you'll need to distinguish between the dry adiabatic lapse rate when relative humidity is less than 100% and the moist adiabatic lapse rate when relative humidity is 100%. That said, the atmosphere is only approximately adiabatic. How much the troposphere locally deviates from adiabatic (convective available potential energy) is one of the key indicators of whether bad weather is on the way.  
> **username_4**: @username_0 If you need anything precise, the approximation by this equation may be insufficient for your needs.  In the real world, all kinds of profiles including inversions and unstable distributions are possible, which is why we use radiosondes and remote sensing techniques to measure profiles of T and q worldwide multiple times per day.  The average lapse rate is just good enough for a rough approximation, but nothing more.  
> **username_0**: @username_4, yeah, found out recently about other more complicated and accurate equations.  

---

