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| The '''Goff–Gratch equation''' is one (arguably the first reliable) amongst many equations that have been proposed to estimate the [[Vapour pressure of water|saturation water vapor pressure]] at a given temperature.
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| Another similar equation based on more recent data is the [[Arden Buck equation]].
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| ==Historical note==
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| 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. {{Citation needed|date=October 2011}}
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| ==Equations==
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| The original Goff–Gratch (1946) equation reads as follows:
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| :{|
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| |<math>\log\ e^*\ = </math>
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| |<math>-7.90298(T_\mathrm{st}/T-1)\ +\ 5.02808\ \log(T_\mathrm{st}/T)</math>
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| |<math>-\ 1.3816\times10^{-7}(10^{11.344(1-T/T_\mathrm{st})}-1)</math>
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| |-
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| |<math>+\ 8.1328\times10^{-3}(10^{-3.49149(T_\mathrm{st}/T-1)}-1)\ +\ \log\ e^*_\mathrm{st}</math>
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| |}
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| where:
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| :log refers to the logarithm in base 10
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| :''e''<sup>*</sup> is the saturation water vapor pressure ([[Pascal (unit)|hPa]])
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| :''T'' is the [[absolute temperature|absolute air temperature]] in [[kelvin]]s | |
| :''T''<sub>st</sub> is the steam-point (i.e. [[boiling point]] at 1 atm.) temperature (373.15 K)
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| :''e''<sup>*</sup><sub>st</sub> is e<sup>*</sup> at the steam-point pressure (1 atm = 1013.25 hPa)
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| Similarly, the equation for the saturation water vapor pressure over ice is:
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| :{|
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| |<math>\log\ e^*_i\ = </math>
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| |<math>-9.09718(T_0/T-1)\ -\ 3.56654\ \log(T_0/T)</math>
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| |<math>+\ 0.876793(1-T/T_0) +\ \log\ e^*_{i0}</math>
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| |}
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| where:
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| :log stands for the logarithm in base 10
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| :''e''<sup>*</sup><sub>i</sub> is the saturation water vapor pressure over ice (hPa)
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| :''T'' is the air temperature (K) | |
| :''T''<sub>0</sub> is the ice-point ([[triple point]]) temperature (273.16 K) | |
| :''e''<sup>*</sup><sub>i0</sub> is e<sup>*</sup> at the ice-point pressure (6.1173 hPa) | |
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| ==References==
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| * 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.
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| * 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.
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| * World Meteorological Organization (1988) General meteorological standards and recommended practices, Appendix A, WMO Technical Regulations, WMO-No. 49.
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| * World Meteorological Organization (2000) General meteorological standards and recommended practices, Appendix A, WMO Technical Regulations, WMO-No. 49, corrigendum.
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| * 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}}
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| ==External links==
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| * http://cires.colorado.edu/~voemel/vp.html
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| * [http://www.phymetrix.com/Software.htm Free Windows Program, Moisture Units Conversion Calculator w/Goff-Gratch equation] - PhyMetrix
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| ==See also==
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| *[[Vapour pressure of water]]
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| *[[Antoine equation]]
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| *[[Arden Buck equation]]
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| {{DEFAULTSORT:Goff-Gratch equation}}
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| [[Category:Atmospheric thermodynamics]]
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