# relative humidity derivations

1. relative humidity from H2O partial pressure

   symbol | description | unit | variable name
   --- | --- | --- | ---
   \(e_{w}\) | saturated water vapor pressure | \(Pa\) |
   \(p_{H_{2}O}\) | partial pressure of H2O | \(Pa\) | H2O_partial_pressure {:}
   \(T\) | temperature | \(K\) | temperature {:}
   \(\phi\) | relative humidity | \(\frac{Pa}{Pa}\) | relative_humidity {:}

   The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

   \begin{eqnarray} e_{w} & = & 610.94e^{\frac{17.625(T-273.15)}{(T-273.15)+243.04}} \\ \phi & = & \frac{p_{H_{2}O}}{e_{w}} \end{eqnarray}