# Arden Buck equation

The Arden Buck equations are a group of empirical correlations that relate the saturation vapor pressure to temperature for moist air. The curve fits have been optimized for more accuracy than the Goff–Gratch equation in the range −80 to 50 °C (−112 to 122 °F).[1]

A set of several equations were developed, each of which is applicable in a different situation.

## Formula

The equations suggested by Buck (1996) (which are modifications of the equations in Buck (1981)) are:

${\displaystyle P_{\mathrm {s} }\left(T\right)=6.1121\exp \left(\left(18.678-{\frac {T}{234.5}}\right)\left({\frac {T}{257.14+T}}\right)\right)}$, over liquid water, T > 0 °C

${\displaystyle P_{\mathrm {s} }\left(T\right)=6.1115\exp \left(\left(23.036-{\frac {T}{333.7}}\right)\left({\frac {T}{279.82+T}}\right)\right)}$, over ice, T < 0 °C

where:

• Ps(T) is the saturation vapor pressure in hPa
• exp(x) is the exponential function
• T is the air temperature in degrees Celsius