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# Goff-Gratch equation

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 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)

## References

• Goff, J. A., and S. Gratch (1946) Low-pressure properties of water from −160 to 212 °F, in Transactions of the American Society of Heating and Ventilating Engineers, pp 95–122, presented at the 52nd annual meeting of the American Society of Heating and Ventilating Engineers, New York, 1946.
• Goff, J. A. (1957) Saturation pressure of water on the new Kelvin temperature scale, Transactions of the American Society of Heating and Ventilating Engineers, pp 347–354, presented at the semi-annual meeting of the American Society of Heating and Ventilating Engineers, Murray Bay, Que. Canada.
• World Meteorological Organization (1988) General meteorological standards and recommended practices, Appendix A, WMO Technical Regulations, WMO-No. 49.
• World Meteorological Organization (2000) General meteorological standards and recommended practices, Appendix A, WMO Technical Regulations, WMO-No. 49, corrigendum.
• Murphy, D. M. and Koop, T. (2005): Review of the vapour pressures of ice and supercooled water for atmospheric applications, Quarterly Journal of the Royal Meteorological Society 131(608): 1539–1565. 10.1256/qj.04.94