Crop coefficient

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.

$\gamma ={\frac {\left(c_{p}\right)_{air}*P}{\lambda _{v}*MW_{ratio}}}$

$\gamma =$ 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.

T_dew = the dewpoint temperature at which water condenses.

T_wet = the temperature of a wet thermometer bulb from which water can evaporate to air.

T_dry = the temperature of a dry thermometer bulb in air.

See also

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References

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