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。

方程式

原始的戈夫-格雷奇方程式(1946) 如下:

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

其中:

log 是以10為底的對數

e^* 水的飽和蒸汽壓(hPa)

T是以開爾文表示的絕對溫度（K）

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：

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

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)

參考文獻

• 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）.