饱和蒸汽压计算方法.docx

1、饱和蒸汽压计算方法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 r

2、eferences. 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 pw = -7.90298 (373.16/T-1) 1 + 5.02808 Log10(373.16/T) - 1.3816 10-7 (1011.344 (1-T/373.16) -1) + 8.1

3、328 10-3 (10-3.49149 (373.16/T-1) -1) + Log10(1013.246) with T in K and pw in hPa WMO (Goff, 1957): Log10 pw = 10.79574 (1-273.16/T) 2 - 5.02800 Log10(T/273.16) + 1.50475 10-4 (1 - 10(-8.2969*(T/273.16-1) + 0.42873 10-3 (10(+4.76955*(1-273.16/T) - 1) + 0.78614 with T in K and pw in hPa (Note: WMO ba

4、sed its recommendation on 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/T) - 1) in the fourth line compared to the original pub

5、lication by Goff (1957). Note 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 T2 - 0.14452093 10-7 T3 + 0.65459673 101 Log(T) wi

6、th T in K and pw in Pa Buck (Buck Research 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 - t / 234.5) t / (257.14 + t) 1996 4 pw = 6.1121 e17.502 t / (240.97 + t) 1981

7、 5 with t in C and pw in hPa Sonntag (Sonntag, 1994) Log pw = -6096.9385 / T 6 + 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) + 0.7858 7 with t in C and pw in hPa Bolton (Bolton, 1980) pw = 6

8、.112 e17.67 * t / (t+243.5) 8 with t in C and pw in hPaAt low temperatures 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 102

9、C Gibbins 1990. This work is generally considered the reference equation but other equations are in use in the meteorological community Elliott 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. Detwi

10、ler 1983 claims some indirect evidence to support the extrapolation of 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 formul

11、ation 7 is widely used in Meteorology and appeals for its simplicity. The 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 claime

12、d by some RH sensors. At -60C the deviations range from -6% to +3% and at -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 Elliott and

13、Gaffen 1993. The WMO recommended formula is a derivative of the Goff-Gratch 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 seve

14、ral typographical errors. The corrected formulation WMO (2000) still differs 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 b

15、y Fukuta and Gramada 2003 shows direct measurements of the vapor pressure 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

16、 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.

17、 Figure 1: Comparison of equations 2-8 with the Goff Gratch equation 1 for the saturation pressure of water vapor over liquid water. The measurements by Fukuta et al. 2003 are shown as well. (*)WMO (2000) is also shown. This is based on Goff (1957) with the different sign of one exponent, likely due

18、 to a typographical error. 2) Vapor Pressure over ice Goff Gratch equation (Smithsonian Tables, 1984): Log10 pi = -9.09718 (273.16/T - 1) 9 - 3.56654 Log10(273.16/ T) + 0.876793 (1 - T/ 273.16) + Log10(6.1071) with T in K and pi in hPa Hyland and Wexler (Hyland and Wexler, 1983.): Log pi = -0.567453

19、59 104 / T 10 + 0.63925247 101 - 0.96778430 10-2 T + 0.62215701 10-6 T2 + 0.20747825 10-8 T3 - 0.94840240 10-12 T4 + 0.41635019 101 Log(T) with T in K and pi in Pa Magnus Teten (Murray, 1967) Log10 pi = 9.5 t / (t+265.5) + 0.7858 11 with t in C and pi in hPa Buck (Buck Research Manual (1996); update

20、d equation from Buck, A. L., New equations for computing vapor pressure and enhancement factor, J. Appl. Meteorol., 20, 1527-1532, 1981) pi = 6.1115 e(23.036 - t / 333.7) t / (279.82 + t) 1996 12 pi = 6.1115 e22.452 t / (272.55+t) 1981 13 with t in C and pi in hPa Marti Mauersberger (Marti, J. and K

21、 Mauersberger, A survey and new measurements of ice vapor pressure at temperatures between 170 and 250 K, GRL 20, 363-366, 1993) Log10 pi = -2663.5 / T + 12.537 14 with T in K and pi in PaThe Goff Gratch equation 9 for the vapor pressure over ice cover a region of -100C to 0C. It is generally consid

22、ered the reference equation; however, other equations have also been widely used. The equations discussed here are mostly of interest for frost-point measurements using chilled mirror hygrometers, since these instruments directly measure the temperature at which a frost layer and the overlying vapor

23、 are in equilibrium. In meteorological practice, relative humidity is given over liquid water (see section 1) and care needs to be taken to consider this difference. Buck Research, which manufactures frost-point hygrometers, uses the Buck formulations in their instruments. These formulations include

24、 an enhancement factor, which corrects for the differences between pure vapor and moist air. This enhancement factor is a weak function of temperature and pressure and corrects about 0.5% at sea level. For the current discussion it has been omitted. The Marti Mauersberger equation is the only equati

25、on based on direct measurements of the vapor pressure down to temperatures of 170 K. The comparison of equations 2-6 with the Goff Gratch equation (figure 2) shows, that with the exception of the Magnus Teten formula, the deviations in the typical meteorological range of -100C to 0C are less than 2.

26、5%, and smaller than typical instrumental errors of frost-point hygrometers of 5-10%. Not shown is the WMO recommended equation for vapor pressure over ice, since it is nearly identical with the Goff-Gratch equation 9. Figure 2: Comparison of equations 10-14 with the Goff Gratch equation 9 for the s

27、aturation pressure of water vapor over ice. 3) ReferencesBolton, D., The computation of equivalent potential temperature, Monthly Weather Review, 108, 1046-1053, 1980. equation (10). Buck, A. L., New equations for computing vapor pressure and enhancement factor, J. Appl. Meteorol., 20, 1527-1532, 19

28、81. Buck Research Manuals, 1996 Detwiler, A., Extrapolation of the Goff-Gratch formula for vapor pressure over liquid water at temperatures below 0C, J. Appl. Meteorol., 22, 503, 1983. Elliott, W. P. and D. J. Gaffen, On the utility of radiosonde humidity archives for climate studies, Bull. Am. Meteorol. Soc., 72, 1507-1520, 1991. Elliott, W. P. and D. J. Gaffen, Effects of conversion algorithms on reported upper air dewpoint depressions, Bull. Am. Meteorol. Soc., 74, 1323-1325, 1993. Fukuta, N. and C. M. Gramada, Vapor pressure measurement of supercooled water, J.