 #jsDisabledContent { display:none; } My Account |  Register |  Help Flag as Inappropriate This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate?          Excessive Violence          Sexual Content          Political / Social Email this Article Email Address:

# Goff-Gratch equation

Article Id: WHEBN0021751531
Reproduction Date:

 Title: Goff-Gratch equation Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Goff-Gratch equation

The Goff–Gratch equation is one (arguably the first reliable) amongst many equations that have been proposed to estimate the saturation water vapor pressure at a given temperature.

Another similar equation based on more recent data is the Arden Buck equation.

## Historical note

This equation is named after the authors of the original scientific article who described how to calculate the saturation water vapor pressure above a flat free water surface as a function of temperature (Goff and Gratch, 1946). Goff (1957) later revised his formula, and the latter was recommended for use by the World Meteorological Organization in 1988, with further corrections in 2000.

## Equations

The original Goff–Gratch (1946) equation reads as follows:

 $\log\ e^*\ =$ $-7.90298\left(T_\mathrm\left\{st\right\}/T-1\right)\ +\ 5.02808\ \log\left(T_\mathrm\left\{st\right\}/T\right)$ $-\ 1.3816\times10^\left\{-7\right\}\left(10^\left\{11.344\left(1-T/T_\mathrm\left\{st\right\}\right)\right\}-1\right)$ $+\ 8.1328\times10^\left\{-3\right\}\left(10^\left\{-3.49149\left(T_\mathrm\left\{st\right\}/T-1\right)\right\}-1\right)\ +\ \log\ e^*_\mathrm\left\{st\right\}$

where:

log refers to the logarithm in base 10
e* is the saturation water vapor pressure (hPa)
T is the absolute air temperature in kelvins
Tst is the steam-point (i.e. boiling point at 1 atm.) temperature (373.15 K)
e*st is e* at the steam-point pressure (1 atm = 1013.25 hPa)

Similarly, the equation for the saturation water vapor pressure over ice is:

 $\log\ e^*_i\ =$ $-9.09718\left(T_0/T-1\right)\ -\ 3.56654\ \log\left(T_0/T\right)$ $+\ 0.876793\left(1-T/T_0\right) +\ \log\ e^*_\left\{i0\right\}$

where:

log stands for the logarithm in base 10
e*i is the saturation water vapor pressure over ice (hPa)
T is the air temperature (K)
T0 is the ice-point (triple point) temperature (273.16 K)
e*i0 is e* at the ice-point pressure (6.1173 hPa)