戈夫-格雷奇方程式

戈夫-格雷奇方程式（英語：Goff-Gratch equation）可以在給定溫度的情況下用來確定水的飽和蒸汽壓。另一個類似的方程是Arden Buck方程式。

歷史

戈夫-格雷奇方程式是以它的兩個作者戈夫（Goff）和格雷奇（Gratch）命名，他們在文章裡介紹了在某個溫度下，如何計算平靜的水面上水的飽和蒸汽壓。戈夫在1957年修訂了這個方程，1988年戈夫-格雷奇方程式被世界氣象組織所推薦，2000年又進行了進一步修正。

原始的戈夫-格雷奇方程式(1946) 如下:

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

其中:

log 是以10為底的對數

T_st是沸點溫度(373.15 K)

e^*_st 是沸點壓力(1 atm = 1013.25 hPa)

在冰面上方，水的飽和蒸汽壓可簡化為：

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

其中:

log 是以10為底的對數

e^*_i 在冰面上方水的飽和蒸汽壓(hPa)

T 是空氣溫度(K)

T₀ 是冰點溫度(273.16 K)

e^*_i0 是冰點壓力(6.1173 hPa)

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.
WMO Guide To Meteorological Instruments and Methods of Observation (the CIMO Guide). 2014 [2023-04-04]. WMO-No. 8. （原始內容存檔於2021-04-27）.
Murphy, D.M.; Koop, T. Review of the vapour pressures of ice and supercooled water for atmospheric applications. Quarterly Journal of the Royal Meteorological Society. 2005, 131 (608): 1539–65 [2023-04-04]. Bibcode:2005QJRMS.131.1539M. doi:10.1256/qj.04.94. （原始內容存檔於2020-08-18）.