<p>The formula you found comes from the <a href="https://en.wikipedia.org/wiki/Barometric_formula" rel="nofollow">barometric formula</a>. It assumes a hydrostatic atmosphere (no vertical accelerations), a constant temperature with height (or a mean temperature) and uses the <a href="https://en.wikipedia.org/wiki/Ideal_gas_law" rel="nofollow">ideal gas law</a>:</p>

<p>$$h= -\frac{RT}{g} \cdot \log \frac{p}{p_{sfc}}
$$
where h is height above ground, R is the ideal gas constant, T is the mean temperature, g is the gravitational constant, p is the pressure of the cloud top in your case and $p_{sfc}$ is <a href="https://en.wikipedia.org/wiki/Surface_pressure" rel="nofollow">surface pressure</a> (not reduced)</p>

<p>The first factor comes down to a value of $-8$km if $T \approx 273$ K. This value is also known as <a href="https://en.wikipedia.org/wiki/Scale_height" rel="nofollow">scale height</a>. $p_{sfc}$ is approx. 1013 hPa if you're at sea level.</p>

<p>So LOGS would most probably mean the natural logarithm.</p>

<p>I don't think there is a simple equation for the cloud top height from ground observations because e.g. how high a cumulus grows depends on the temperature of the surrounding air.</p>

<p>Cloud base height and cloud top height are two totally different things. The <a href="https://en.wikipedia.org/wiki/Lifted_condensation_level" rel="nofollow">cloud base height formula</a> does not depend on the on the upper air temperature. </p>

<p>Whether a thermal (which evolves into the cloud later on) reaches its cloud base or not, is not sure. As long as it's warmer than its surroundings, it rises. The same for the cloud: It rises up as long as it is warmer than its surroundings. You may know what's the temperature of the cloud at each height, but how cold the air at, say 15,000 ft is, varies a lot.</p>

CC BY-SA 3.0
2016-08-05T14:55:24.070Z
2016-08-05T17:29:41.393Z
2016-08-05T17:29:41.393Z
Lukas
<p>So, I'm trying to find the Height of the Top of a cloud from basic weather information (ie. temperature on the ground, altitude, pressure, humidity, dew point, etc.)</p>

<p>I'm looking for an equation that will give or at least estimate the cloud top. Doing some searching, I've found this equation:</p>

<blockquote>
  <p>The Cloud top height can be calculated by the formula<br>
           h [km] = -8 * LOGS (cloud_top_press [hPa]/1013).</p>
</blockquote>

<p><a href="http://www.brockmann-consult.de/CloudStructures/introduction.htm" rel="nofollow">From this site</a>. My question is, will this equation produce the height of a cloud and what does "LOGS" mean in this equation?</p>

CC BY-SA 3.0
2016-08-05T06:43:40.897Z
With 'basic weather information' you mean ground based measurements? Thus, pressure and humidity data are only available on ground level? 'Altitude' means the altitude of the ground above sea level? It is not possible to calculate the height of the cloud top from ground based data. The formula you posted is for calculating this height from satellite derived data (MERIS level 2 data => post-processes satellite data). I am not sure what the 'S' in 'LOGS' means.
daniel.heydebreck
CC BY-SA 3.0
2016-08-05T12:38:36.310Z
@daniel.neumann I am able to figure in altitude from gps coordinates. What I'm trying to avoid is that it seems it's possible to solve for this using some type of lasers which I don't have access to. Is there any way to figure the cloud top height without using satellite data? I know it's possible to do this with the cloud base.
Tom
CC BY-SA 3.0
2016-08-07T19:16:05.917Z
I have no experience in measuring cloud parameters. Radar or combined lidar + radar measurements seem to yield cloud top height data (what looking at some publication titles indicate ...).
daniel.heydebreck
CC BY-SA 4.0
2021-09-02T08:56:51.417Z
The best you could do is maybe use a promixate weather sounding, model, or climatology to estimate equilbrium level. But this only works some times, as many  clouds don't overcome convective inhibition (basically the energy needed to rise and cool enough to reach saturation, where it often then accelerates upward on its own merit) to realize the EL [= cumulus humilis/mediocris/congestus], and other clouds develop from non-surface based parcels\from mechanical forcing [most stratus, altocu, etc]. So the LCL and EL can estimate thunderstorm [cumulonimbus] base & top, but limited use overall
JeopardyTempest
<meteorology><clouds>
Calculate the Top of a Cloud
Tom
# Calculate the Top of a Cloud

(Asked by: username_0 on 2016-08-05)

So, I'm trying to find the Height of the Top of a cloud from basic weather information (ie. temperature on the ground, altitude, pressure, humidity, dew point, etc.)

I'm looking for an equation that will give or at least estimate the cloud top. Doing some searching, I've found this equation:

> The Cloud top height can be calculated by the formula  
> h [km] = -8 \* LOGS (cloud\_top\_press [hPa]/1013).

[From this site](http://www.brockmann-consult.de/CloudStructures/introduction.htm). My question is, will this equation produce the height of a cloud and what does "LOGS" mean in this equation?

**Tags:** meteorology, clouds

> **Comments:**
> **username_1**: With 'basic weather information' you mean ground based measurements? Thus, pressure and humidity data are only available on ground level? 'Altitude' means the altitude of the ground above sea level? It is not possible to calculate the height of the cloud top from ground based data. The formula you posted is for calculating this height from satellite derived data (MERIS level 2 data => post-processes satellite data). I am not sure what the 'S' in 'LOGS' means.  
> **username_0**: @daniel.neumann I am able to figure in altitude from gps coordinates. What I'm trying to avoid is that it seems it's possible to solve for this using some type of lasers which I don't have access to. Is there any way to figure the cloud top height without using satellite data? I know it's possible to do this with the cloud base.  
> **username_1**: I have no experience in measuring cloud parameters. Radar or combined lidar + radar measurements seem to yield cloud top height data (what looking at some publication titles indicate ...).  
> **username_2**: The best you could do is maybe use a promixate weather sounding, model, or climatology to estimate equilbrium level. But this only works some times, as many  clouds don't overcome convective inhibition (basically the energy needed to rise and cool enough to reach saturation, where it often then accelerates upward on its own merit) to realize the EL [= cumulus humilis/mediocris/congestus], and other clouds develop from non-surface based parcels\from mechanical forcing [most stratus, altocu, etc]. So the LCL and EL can estimate thunderstorm [cumulonimbus] base & top, but limited use overall  

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## 1 answers

### Answer by username_3 on 2016-08-05. Score: 6 | Accepted answer

The formula you found comes from the [barometric formula](https://en.wikipedia.org/wiki/Barometric_formula). It assumes a hydrostatic atmosphere (no vertical accelerations), a constant temperature with height (or a mean temperature) and uses the [ideal gas law](https://en.wikipedia.org/wiki/Ideal_gas_law):

$$h= -\frac{RT}{g} \cdot \log \frac{p}{p\_{sfc}}
$$
where h is height above ground, R is the ideal gas constant, T is the mean temperature, g is the gravitational constant, p is the pressure of the cloud top in your case and $p\_{sfc}$ is [surface pressure](https://en.wikipedia.org/wiki/Surface_pressure) (not reduced)

The first factor comes down to a value of $-8$km if $T \approx 273$ K. This value is also known as [scale height](https://en.wikipedia.org/wiki/Scale_height). $p\_{sfc}$ is approx. 1013 hPa if you're at sea level.

So LOGS would most probably mean the natural logarithm.

I don't think there is a simple equation for the cloud top height from ground observations because e.g. how high a cumulus grows depends on the temperature of the surrounding air.

Cloud base height and cloud top height are two totally different things. The [cloud base height formula](https://en.wikipedia.org/wiki/Lifted_condensation_level) does not depend on the on the upper air temperature.

Whether a thermal (which evolves into the cloud later on) reaches its cloud base or not, is not sure. As long as it's warmer than its surroundings, it rises. The same for the cloud: It rises up as long as it is warmer than its surroundings. You may know what's the temperature of the cloud at each height, but how cold the air at, say 15,000 ft is, varies a lot.


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