# ERA5 Single Level - Calculate relative humidity

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

• You can refer to this question for more detail Commented Oct 12, 2023 at 13:45

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

$$$$e_s(T_d) = 6.1078 \exp\left({\frac{17.1 \cdot T_d}{235 + T_d}}\right) \text{hPa},$$$$ where $$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.

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 $$$$e (T_d) = 6.1078 \exp\left({\frac{17.1 \cdot T_d}{235 + T_d}}\right) \text{hPa}$$$$ and $$$$e_s (T) = 6.1078 \exp\left({\frac{17.1 \cdot T}{235 + T}}\right) \text{hPa}.$$$$ Finally calculate $$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 (see p188 of the document which is unfortunately not available anymore without registration).

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

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

• 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. Commented Nov 14, 2022 at 14:21
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Commented Nov 14, 2022 at 14:29

You can refer to this question for more detail. I calculated RH by using ERA5-land t2m and d2m. I think the result was ok.