# Psychrometric constant

The psychrometric constant $\gamma$ relates the partial pressure of water in air to the air temperature. This lets one interpolate actual vapor pressure from paired dry and wet thermometer bulb temperature readings.[1]

$\gamma =\frac{ \left( c_p \right)_{air} * P }{ \lambda_v * MW_{ratio} }$
$\gamma =$ psychrometric constant [kPa °C-1],
P = atmospheric pressure [kPa],
$\lambda_v =$ latent heat of water vaporization, 2.45 [MJ kg-1],
$c_p =$ specific heat of air at constant pressure, [MJ kg-1 °C-1],
$MW_{ratio} =$ ratio molecular weight of water vapor/dry air = 0.622.

Both $\lambda_v$ and $MW_{ratio}$ are constants.
Since atmospheric pressure, P, depends upon altitude, so does $\gamma$.
At higher altitude water evaporates and boils at lower temperature.

Although $\left( c_p \right)_{H_2 O}$ is constant, varied air composition results in varied $\left( c_p \right)_{air}$.

Thus on average, at a given location or altitude, the psychrometric constant is approximately constant. Still, it is worth remembering that weather impacts both atmospheric pressure and composition.

## vapor pressure estimation

Saturated vapor pressure, $e_s = e \left[ T_{wet}\right]$
Actual vapor pressure, $e_a = e_s - \gamma * \left( T_{dry} - T_{wet} \right)$

here e[T] is vapor pressure as a function of temperature, T.
Tdew = the dewpoint temperature at which water condenses.
Twet = the temperature of a wet thermometer bulb from which water can evaporate to air.
Tdry = the temperature of a dry thermometer bulb in air.