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1、There is a large number of saturation vapor pressure equations used to calculate the pressure of water vapor over a surface of liquid water or ice. This is a brief overview of the most important equations used. Several useful reviews of the existing vapor pressure curves are listed in the references
2、. Please note the updated discussion of the WMO formulation.1) Vapor Pressure over liquid water below 0C Goff Gratch equation(Smithsonian Tables, 1984, after Goff and Gratch, 1946):Log10 p = -7.9029810 w(373.16/7-1)1+ 5.02808 Log10(373.16/7- 1.3816 10-7(1011.344 (1-77373.16) -1) + 8.1328 10-3 (10-3.
3、49149 (373.16/7-1) -1) + Log10(1013.246) with T in K and pw in hPa WMO(Goff, 1957):Log10 p = 10.7957410 w(1-273.16/7)2-5.02800 Log10(77273.16) + 1.50475 10-4(1 -1 0(-8.2969*(刀273.16-1)+ 0.42873 10-3 (10(+4.76955*(1-273.16/“)-1)+ 0.78614 with T in K and pw in hPa (Note: WMO based its recommendation o
4、n a paper by Goff (1957), which is shown here. The recommendation published by WMO (1988) has several typographical errors and cannot be used. A corrigendum (WMO, 2000) shows the term +0.42873 10-3(10(-4.76955*(1-273.16/-1) in the fourth line compared to the original publication by Goff (1957). Note
5、 the different sign of the exponent. The earlier 1984 edition shows the correct formula.) Hyland and Wexler(Hyland and Wexler, 1983):Log pw = -0.58002206 104 /T 3+ 0.13914993 101-0.48640239 10-1 T + 0.41764768 10-4 72 -0.14452093 10-7 73 + 0.65459673 101 Log(7) with T in K and pw in Pa Buck(Buck Res
6、earch Manual (1996); updated equation from Buck, A. L., New equations for computing vapor pressure and enhancement factor, J. Appl. Meteorol., 20, 1527-1532, 1981) pw = 6.1121 e(18.678 -1/234.5) t/(257.14 + t)19964pw = 6.1121 e17.502 t/ (240.97 + t)19815with t in C andpw in hPa Sonntag(Sonntag, 1994
7、)Log pw = -6096.9385 /T + 16.635794-2.711193 10-2 * T+ 1.673952 10-5 * T2 + 2.433502 * Log(T with T in K and pw in hPa Magnus Teten(Murray, 1967)Log10 pw = 7.5 t / (t+237.3) +0.78587with t in C and pw in hPa Bolton(Bolton, 1980)pw = 6112 e17-67 *t /(t+243.5)8with t in C and pw in hPaAt low temperatu
8、res most of these are based on theoretical studies and only a small number are based on actual measurements of the vapor pressure. The Goff Gratch equation 1 for the vapor pressure over liquid water covers a region of -50C to 102D Gibbins 1990. This work is generally considered the reference equatio
9、n but other equations are in use in the meteorological community Ellio tt and Gaffen, 1993. There is a very limited number of measurements of the vapor pressure of water over supercooled liquid water at temperatures below C. Detwiler 1983 claims some indirect evidence to support the extrapolation of
10、 the Goff-Gratch equation down to temperatures of -60C. However, this currently remains an open issue.The Hyland and Wexler formulation is used by Vaisala and is very similar to the formula by Sonntag (6). The Magnus Teten formulation 7 is widely used in Meteorology and appeals for its simplicity.Th
11、e comparison for the liquid saturation vapor pressure equations 2-8 with the Goff-Gratch equation 1 in figure 1, shows that uncertainties at low temperatures become increasingly large and reach the measurement uncertainty claimed by some RH sensors. At -60C the deviations range from -6% to +3% and a
12、t -70C the deviations range from -9% to +6%. For RH values reported in the low and mid troposphere the influence of the saturation vapor pressure formula used is small and only significant for climatological studies Ellio tt and Gaffen 1993.The WMO recommended formula is a derivative of the Goff-Gra
13、tch equation, originally published by Goff (1957). The differences between Goff (1957) and Goff-Gratch (1946) are less than 1% over the entire temperature range. The formulation published by WMO (1988) cannot be used due to several typographical errors. The corrected formulation WMO (2000) still dif
14、fers in the sign of one exponent compared to Goff (1957). This incorrect formulation is in closer agreement with the Hyland and Wexler formulation; however, it is to be assumed that Goff (1957) was to be recommended.The study by Fukuta and Gramada 2003 shows direct measurements of the vapor pressure
15、 over liquid water down to -38C. Their result indicates that at the lowest temperatures the measured vapor pressure may be as much as 10% lower than the value given by the Smithsonian Tables 1, and as shown in figure 1 lower as any other vapor pressure formulation.It is important to note that in the upper troposphere, water vapor measurements reported in the WMO convention as relative humidity with respect to liquid water depend critically on the saturation vapor pressure equation that was used to calculate the RH value.一駛fJeEMQceEQiucaQ-25-100-90-80-70-60-50-40-
