Goff–Gratch equation

The Goff–Gratch equation is one (arguably the first reliable in history) amongst many experimental correlations 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). According to the Smithsonian Meteorological Tables, the formula was adopted in Resolution 164 of the Twelfth Conference of Directors of the International Meteorological Organization (Washington, 1947). 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.^{[citation needed]}

The Guide to Meteorological Instruments and Methods of Observation a.k.a. CIMO-Guide (WMO-No. 8) contains the much simpler Magnus formula (p.197). For temperatures below ‑45 °C for liquid water or ‑65 °C for ice, the CIMO-Guide recommends formulations from Sonntag (1990,1994).

Experimental correlation

The original Goff–Gratch (1945) experimental correlation reads as follows:

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

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:

${\displaystyle \log \ e_{i}^{*}\ =}$	${\displaystyle -9.09718(T_{0}/T-1)\ -\ 3.56654\ \log(T_{0}/T)}$
	${\displaystyle +\ 0.876793(1-T/T_{0})+\ \log \ e_{i0}^{*}}$

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)

See also

• Vapour pressure of water
• Antoine equation
• Arden Buck equation
• Tetens equation
• Lee–Kesler method

References

External links

• Vömel, Holger (2016). "Saturation vapor pressure formulations". Boulder CO: Earth Observing Laboratory, National Center for Atmospheric Research.
• Murphy, D.M.; 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): 1539–65. Bibcode:2005QJRMS.131.1539M. doi:10.1256/qj.04.94. S2CID 122365938.