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 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 .Buck 1981
A ...
.
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
The World Meteorological Organization (WMO) is a specialized agency of the United Nations responsible for promoting international cooperation on atmospheric science, climatology, hydrology and geophysics.
The WMO originated from the Inter ...
in 1988, with further corrections in 2000.
The current 2015 edition of the WMO Technical Regulations (WMO-No. 49) however states in Volume 1, Part III, Section 1.2.1, that any formula or constant given in the Guide to Meteorological Instruments and Methods of Observation a.k.a. CIMO-Guide (WMO-No. 8) shall be used, and this document only contains the much simpler Magnus formula (Annex 4.B. – Formulae for the computation of measures of humidity). Regarding the measurement of upper-air humidity, this publication also reads (in Section 12.5.1):
''The saturation with respect to water cannot be measured much below –50 °C, so manufacturers should use one of the following expressions for calculating saturation vapour pressure relative to water at the lowest temperatures – Wexler (1976, 1977),
reported by Flatau et al. (1992).,
Hyland and Wexler (1983) or Sonntag (1994) – and not the Goff-Gratch equation recommended in earlier WMO publications.''
Experimental correlation
The original Goff–Gratch (1945) experimental correlation reads as follows:
:
where:
:log refers to the logarithm in base 10
:''e''
* is the saturation water vapor pressure (
hPa)
:''T'' is the
absolute air temperature in
kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and ...
s
:''T''
st is the steam-point (i.e.
boiling point
The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.
The boiling point of a liquid varies depending upon the surrounding env ...
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:
:
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)
:''T''
0 is the ice-point (
triple point
In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium.. It is that temperature and pressure at which the ...
) temperature (273.16 K)
:''e''
*i0 is e
* at the ice-point pressure (6.1173 hPa)
See also
*
Vapour pressure of water
The vapour pressure of water is the pressure exerted by molecules of water vapor in gaseous form (whether pure or in a mixture with other gases such as air). The saturation vapour pressure is the pressure at which water vapour is in thermodynamic ...
*
Antoine equation
The Antoine equation is a class of semi-empirical correlations describing the relation between vapor pressure and temperature for pure substances. The Antoine equation is derived from the Clausius–Clapeyron relation. The equation was presented ...
*
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 .Buck 1981
A ...
*
Tetens equation The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice. It is named after its creator, O. Tetens who was an early German meteorologist. He published his equation in 1930,Tetens, O. 1930. Über e ...
*
Lee–Kesler method
The Lee–Kesler method
allows the estimation of the saturated vapor pressure at a given temperature for all components for which the critical pressure ''P''c, the critical temperature ''T''c, and the acentric factor ''ω'' are known.
Equation ...
References
* Goff, J. A., and Gratch, S. (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.
*
*
;Notes
External links
*
Free Windows Program, Moisture Units Conversion Calculator w/Goff-Gratch equation— PhyMetrix
{{DEFAULTSORT:Goff-Gratch equation
Atmospheric thermodynamics