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 references. Please note the updated discussion of the WMO formulation.

1) Vapor Pressure over liquid water below 0°C

•Goff Gratch equation

(Smithsonian Tables, 1984, after Goff and Gratch, 1946):

Log10p w = -7.90298

(373.16/T-1) [1]

+ 5.02808 Log10(373.16/T)

- 1.3816 10-7 (1011.344 (1-T/373.16)-1)

+ 8.1328 10-3 (10-3.49149 (373.16/T-1) -1)

+ Log10(1013.246)

with T in [K] and p w in [hPa]

•WMO

(Goff, 1957):

Log10p w = 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 p w in [hPa]

(Note: WMO based 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

publication 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 p w = -0.58002206 104 /

T [3]

+ 0.13914993 101

- 0.48640239 10-1T

+ 0.41764768 10-4T2

- 0.14452093 10-7T3

+ 0.65459673 101 Log(T)

with T in [K] and p w 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) p w = 6.1121 e(18.678 - t / 234.5) t / (257.14 + t)[1996] [4]

p w = 6.1121 e17.502 t / (240.97 + t)[1981] [5]

with t in [°C] and p w in [hPa]

•Sonntag

(Sonntag, 1994)

Log p w = -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 p w in [hPa]

•Magnus Teten

(Murray, 1967)

Log10p w = 7.5 t / (t+237.3) +

0.7858 [7]

with t in [°C] and p w in [hPa]

•Bolton

(Bolton, 1980)

p w = 6.112 e17.67 * t /

(t+243.5)[8]

with t in [°C] and p w in [hPa]

At 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 -50°C to 102°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. Detwiler [1983] claims some indirect evidence to support the extrapolation of the Goff-Gratch equation down to temperatures of -60°C. 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.

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