<p>Dew point temperature is the temperature where saturation water vapor pressure <span class="math-container">$e_s$</span> is reached. If we use an empirical formula for the saturation water vapor pressure, like the Magnus formula given by</p>
<p><span class="math-container">\begin{equation}
e_s(T_d) = 6.1078 \exp\left({\frac{17.1 \cdot T_d}{235 + T_d}}\right) \text{hPa},
\end{equation}</span>
where <span class="math-container">$T_d$</span> is the dew point temperature (Caution: <span class="math-container">$T_d$</span> needs to be in degrees Celsius and note that <span class="math-container">$e_s$</span> is given in hPa), we can find the water vapor pressure <span class="math-container">$e$</span>. The formula is based on <a href="https://doi.org/10.1007/3-540-35017-9" rel="nofollow noreferrer">this book by Kraus</a>.</p>
<p>Relative humidity is just given by <span class="math-container">$RH = e/e_s$</span>. Now we can calculate the relative based on the following variables:</p>
<ol>
<li><span class="math-container">$T$</span> [°C] (ambient Temperature)</li>
<li><span class="math-container">$T_d$</span> [°C] (dew point temperature)</li>
</ol>
<p>Now set
<span class="math-container">\begin{equation}
e (T_d) = 6.1078 \exp\left({\frac{17.1 \cdot T_d}{235 + T_d}}\right) \text{hPa}
\end{equation}</span>
and
<span class="math-container">\begin{equation}
e_s (T) = 6.1078 \exp\left({\frac{17.1 \cdot T}{235 + T}}\right) \text{hPa}.
\end{equation}</span>
Finally calculate <span class="math-container">$RH = e/e_s$</span>.</p>
<p>Note that the Magnus formula is based on the integrated Clausius-Clapeyron equation. The factor 6.1078 hPa is a reference level water vapor pressure (at 273.15 K, assuming a constant specific heat capacity).</p>
<p>One more word of caution. The WMO has given some guidelines on how to calculate certain variables. If I'm not mistaken you can find them <a href="https://community.wmo.int/activity-areas/imop/wmo-no_8" rel="nofollow noreferrer">here</a> (see p188 of the document which is unfortunately not available anymore without registration).</p>

CC BY-SA 4.0
2022-08-15T14:25:57.920Z
2022-11-17T14:29:44.570Z
2022-11-17T14:29:44.570Z
Joscha Fregin
<p>Here you can find an explanation to calculate the surface relative humidity:</p>
<p><a href="https://confluence.ecmwf.int/pages/viewpage.action?pageId=171411214" rel="nofollow noreferrer">https://confluence.ecmwf.int/pages/viewpage.action?pageId=171411214</a></p>

CC BY-SA 4.0
2022-11-14T14:21:02.263Z
Welcome. Could you please edit your answer to include some of the information from this website? Link-only answers are discouraged as links tend to rot.
Jean-Marie Prival
CC BY-SA 4.0
2022-11-14T14:29:51.990Z
As it’s currently written, your answer is unclear. Please [edit] to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers [in the help center](/help/how-to-answer).
Community
CC BY-SA 4.0
2022-11-14T13:43:30.640Z
2022-11-14T13:43:30.640Z
canelo
<p>You can refer to <a href="https://earthscience.stackexchange.com/questions/16570/how-to-calculate-relative-humidity-from-temperature-dew-point-and-pressure?newreg=86cf2a3bb5bb47c5afd5fcaccfea796a">this question</a> for more detail. I calculated RH by using ERA5-land t2m and d2m. I think the result was ok.</p>

CC BY-SA 4.0
2023-10-12T13:46:14.047Z
2023-10-12T13:46:14.047Z
qingsong
<p>for ERA5 hourly data on single level relative humidity can not be downloaded. However, dewpoint temperature is given and in the description it is stated that &quot;combined with temperature and pressure, it can be used to calculate the relative humidity&quot;. After some research I only found formulas that take temperature but not pressure into account. Could you maybe help me how I calculate relative humidity taking all the variables temperature, dewpoint temperature and surface pressure into account?
Thank you so much in advance</p>

CC BY-SA 4.0
2023-10-12T13:45:19.993Z
You can refer to [this question](https://earthscience.stackexchange.com/questions/16570/how-to-calculate-relative-humidity-from-temperature-dew-point-and-pressure?newreg=86cf2a3bb5bb47c5afd5fcaccfea796a) for more detail
qingsong
<climate><humidity><reanalysis><era><pressure>
ERA5 Single Level - Calculate relative humidity
Anna Wenning
# ERA5 Single Level - Calculate relative humidity

(Asked by: username_0 on 2022-08-12)

for ERA5 hourly data on single level relative humidity can not be downloaded. However, dewpoint temperature is given and in the description it is stated that "combined with temperature and pressure, it can be used to calculate the relative humidity". After some research I only found formulas that take temperature but not pressure into account. Could you maybe help me how I calculate relative humidity taking all the variables temperature, dewpoint temperature and surface pressure into account?
Thank you so much in advance

**Tags:** climate, humidity, reanalysis, era, pressure

> **Comments:**
> **username_1**: You can refer to [this question](https://earthscience.stackexchange.com/questions/16570/how-to-calculate-relative-humidity-from-temperature-dew-point-and-pressure?newreg=86cf2a3bb5bb47c5afd5fcaccfea796a) for more detail  

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## 3 answers

### Answer by username_2 on 2022-08-15. Score: 3

Dew point temperature is the temperature where saturation water vapor pressure $e\_s$ is reached. If we use an empirical formula for the saturation water vapor pressure, like the Magnus formula given by

\begin{equation}
e\_s(T\_d) = 6.1078 \exp\left({\frac{17.1 \cdot T\_d}{235 + T\_d}}\right) \text{hPa},
\end{equation}
where $T\_d$ is the dew point temperature (Caution: $T\_d$ needs to be in degrees Celsius and note that $e\_s$ is given in hPa), we can find the water vapor pressure $e$. The formula is based on [this book by Kraus](https://doi.org/10.1007/3-540-35017-9).

Relative humidity is just given by $RH = e/e\_s$. Now we can calculate the relative based on the following variables:

1. $T$ [°C] (ambient Temperature)
2. $T\_d$ [°C] (dew point temperature)

Now set
\begin{equation}
e (T\_d) = 6.1078 \exp\left({\frac{17.1 \cdot T\_d}{235 + T\_d}}\right) \text{hPa}
\end{equation}
and
\begin{equation}
e\_s (T) = 6.1078 \exp\left({\frac{17.1 \cdot T}{235 + T}}\right) \text{hPa}.
\end{equation}
Finally calculate $RH = e/e\_s$.

Note that the Magnus formula is based on the integrated Clausius-Clapeyron equation. The factor 6.1078 hPa is a reference level water vapor pressure (at 273.15 K, assuming a constant specific heat capacity).

One more word of caution. The WMO has given some guidelines on how to calculate certain variables. If I'm not mistaken you can find them [here](https://community.wmo.int/activity-areas/imop/wmo-no_8) (see p188 of the document which is unfortunately not available anymore without registration).


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### Answer by username_3 on 2022-11-14. Score: 0

Here you can find an explanation to calculate the surface relative humidity:

<https://confluence.ecmwf.int/pages/viewpage.action?pageId=171411214>

> **Comments:**
> **username_4**: Welcome. Could you please edit your answer to include some of the information from this website? Link-only answers are discouraged as links tend to rot.  
> **username_5**: As it’s currently written, your answer is unclear. Please [edit] to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers [in the help center](/help/how-to-answer).  

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### Answer by username_1 on 2023-10-12. Score: 0

You can refer to [this question](https://earthscience.stackexchange.com/questions/16570/how-to-calculate-relative-humidity-from-temperature-dew-point-and-pressure?newreg=86cf2a3bb5bb47c5afd5fcaccfea796a) for more detail. I calculated RH by using ERA5-land t2m and d2m. I think the result was ok.


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