Goff–Gratch equation

The Goff–Gratch equation is one (arguably the first reliable in history) amongst many experimental correlation 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.

Experimental correlation

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

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

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

T_st 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 correlation for the saturation water vapor pressure over ice is:

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

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. doi:10.1256/qj.04.94

Goff–Gratch equation

Historical note

Experimental correlation

References

External links

See also