<p>When trying to calculate the adiabatic lapse rate of moist air based on known values of basic thermodynamic properties of the constituents (ice, water, vapor,...) I came to the following question:</p>
<p>Lapse rate of moist air is less as compared to dry air because of the latent head released during condensation of water-vapor.</p>
<p>Now, below 0°C  there is no liquid phase in equilibrium, therefore instead of the latent heat of evaporation <span class="math-container">$L_{ev}$</span> of liquid I used the value for sublimation <span class="math-container">$L_{sub}$</span>. However, of course <span class="math-container">$L_{sub} &gt; L_{ev}$</span>, so according to my calculations the lapse rate must have a discontinuity at 0°C (see graph, where the dotted line is the dry lapse rate).</p>
<p>This discontinuity is not in accordance with observation - so where is my fault? What happens in rising air that this effect is not visible?
<a href="https://i.sstatic.net/Z2n6h.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Z2n6h.png" alt="enter image description here" /></a></p>

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2023-04-28T21:41:38.250Z
The fallacy is: Water becomes ice below 0°C. In the atmosphere water will often be "supercooled". It might be worth checking the "Bergeron-Findeisen process". A nice resource is: Physics and Dynamics of Clouds and Precipitation by Pao K. Wang.
Joscha Fregin
<meteorology><atmosphere><atmosphere-modelling><clouds><water-vapour>
Why atmospheric temperature lapse rate doesn't have a discontinuity at 0°C when ice is formed?
MichaelW
# Why atmospheric temperature lapse rate doesn't have a discontinuity at 0°C when ice is formed?

(Asked by: username_0 on 2023-04-28)

When trying to calculate the adiabatic lapse rate of moist air based on known values of basic thermodynamic properties of the constituents (ice, water, vapor,...) I came to the following question:

Lapse rate of moist air is less as compared to dry air because of the latent head released during condensation of water-vapor.

Now, below 0°C there is no liquid phase in equilibrium, therefore instead of the latent heat of evaporation $L\_{ev}$ of liquid I used the value for sublimation $L\_{sub}$. However, of course $L\_{sub} > L\_{ev}$, so according to my calculations the lapse rate must have a discontinuity at 0°C (see graph, where the dotted line is the dry lapse rate).

This discontinuity is not in accordance with observation - so where is my fault? What happens in rising air that this effect is not visible?
[![enter image description here](https://i.sstatic.net/Z2n6h.png)](https://i.sstatic.net/Z2n6h.png)

**Tags:** meteorology, atmosphere, atmosphere-modelling, clouds, water-vapour

> **Comments:**
> **username_1**: The fallacy is: Water becomes ice below 0°C. In the atmosphere water will often be "supercooled". It might be worth checking the "Bergeron-Findeisen process". A nice resource is: Physics and Dynamics of Clouds and Precipitation by Pao K. Wang.  

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## 0 answers

