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}