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I am involved in developing a weather based application which needs to calculate relative humidity and display it. I grab other weather variables like temperature, precipitation, wind speed and direction from the weather site. Is it possible to calculate relative humidity using this data?

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No, this is not enough.

Relative humidity is defined as the water vapour partial pressure relative relative to the saturation water vapour pressure:

$$ \phi = {{e_w} \over {{e^*}_w}} $$

where ${e^*}_w$ is the equilibrium vapour pressure (which may be relative to either liquid water, or to ice), and $e_w$ is the partial pressure of water.

${e^*}_w$ can be calculated using the Clausius-Clapeyron relation, but to get $e_w$ you need some information on the water content. This information may come in many forms:

  • Water vapour mixing ratio (the number of water molecules per unit volume)
  • Specific humidity (the mass of water per unit volume)
  • Partial pressure of water vapour ($e_w$)
  • Dew point, which is the temperature at which $e_w = e^*_w$.

The one you are most likely to find on meteorology websites is the dew point temperature. Basically, if you have two of temperature, dew point temperature, and relative humidity, you can calculate the third. For example, see this University of Miami calculator.

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    $\begingroup$ +1 Dew point is the key. Moreover, it's value is in general much smoother in space than for instance temperatures, therefore you can try and get a value from another near meteostation if the one you're interested in doesn't provide it. $\endgroup$ – yo' Nov 3 '14 at 21:35

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