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e_eq_water_gg

PURPOSE ^

E_EQ_WATER_GG Equilibrium water vapor pressure over ice

SYNOPSIS ^

function [es] = e_eq_water_gg(T)

DESCRIPTION ^

 E_EQ_WATER_GG  Equilibrium water vapor pressure over ice

 Calculate the equilibrium water vapor pressure over a plane surface
 of ice according to http://en.wikipedia.org/wiki/Goff-Gratch_equation
 The formula (T in K, Ei in hPa):

 The original Goff–Gratch (1946) equation reads as follows:
  
 Log10(ew) = -7.90298 (Tst/T-1)
             + 5.02808 Log10(Tst/T) 
             - 1.3816 10-7 (1011.344 (1-T/Tst)  -1) 
             + 8.1328 10-3 (10-3.49149 (Tst/T-1)  -1) 
             + Log10(e_st)     
    
 where:
 Log10 refers to the logarithm in base 10
 ew is the saturation water vapor pressure (hPa)
 T is the absolute air temperature in kelvins
 Tst is the steam-point (i.e. boiling point at 1 atm.) temperature (373.16 K)
 e_st is ew at the steam-point pressure (1 atm = 1013.25 hPa)

 References:
 http://en.wikipedia.org/wiki/Goff-Gratch_equation
 Goff, J. A., and S. Gratch (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.
 Murphy, D. M. and Koop, T. (2005): Review of the vapour pressures of ice
 and supercooled water for atmospheric applications, Quarterly Journal of the 
 Royal Meteorological Society 131(608): 1539–1565. doi:10.1256/qj.04.94

 FORMAT   e = e_eq_water_gg(T)

 OUT       e = Equilibrium water vapor pressure over water in [Pa].
 IN       T = Temperature in [K].

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

DOWNLOAD ^

e_eq_water_gg.m

SOURCE CODE ^

0001 % E_EQ_WATER_GG  Equilibrium water vapor pressure over ice
0002 %
0003 % Calculate the equilibrium water vapor pressure over a plane surface
0004 % of ice according to http://en.wikipedia.org/wiki/Goff-Gratch_equation
0005 % The formula (T in K, Ei in hPa):
0006 %
0007 % The original Goff–Gratch (1946) equation reads as follows:
0008 %
0009 % Log10(ew) = -7.90298 (Tst/T-1)
0010 %             + 5.02808 Log10(Tst/T)
0011 %             - 1.3816 10-7 (1011.344 (1-T/Tst)  -1)
0012 %             + 8.1328 10-3 (10-3.49149 (Tst/T-1)  -1)
0013 %             + Log10(e_st)
0014 %
0015 % where:
0016 % Log10 refers to the logarithm in base 10
0017 % ew is the saturation water vapor pressure (hPa)
0018 % T is the absolute air temperature in kelvins
0019 % Tst is the steam-point (i.e. boiling point at 1 atm.) temperature (373.16 K)
0020 % e_st is ew at the steam-point pressure (1 atm = 1013.25 hPa)
0021 %
0022 % References:
0023 % http://en.wikipedia.org/wiki/Goff-Gratch_equation
0024 % Goff, J. A., and S. Gratch (1946) Low-pressure properties of water from −160
0025 % to 212 °F, in Transactions of the American Society of Heating and Ventilating
0026 % Engineers, pp 95–122, presented at the 52nd annual meeting of the American
0027 % Society of Heating and Ventilating Engineers, New York, 1946.
0028 % Goff, J. A. (1957) Saturation pressure of water on the new Kelvin temperature scale,
0029 % Transactions of the American Society of Heating and Ventilating Engineers, pp
0030 % 347–354, presented at the semi-annual meeting of the American Society of Heating
0031 % and Ventilating Engineers, Murray Bay, Que. Canada.
0032 % World Meteorological Organization (1988) General meteorological standards and
0033 % recommended practices, Appendix A, WMO Technical Regulations, WMO-No. 49.
0034 % World Meteorological Organization (2000) General meteorological standards and
0035 % recommended practices, Appendix A, WMO Technical Regulations, WMO-No. 49, corrigendum.
0036 % Murphy, D. M. and Koop, T. (2005): Review of the vapour pressures of ice
0037 % and supercooled water for atmospheric applications, Quarterly Journal of the
0038 % Royal Meteorological Society 131(608): 1539–1565. doi:10.1256/qj.04.94
0039 %
0040 % FORMAT   e = e_eq_water_gg(T)
0041 %
0042 % OUT       e = Equilibrium water vapor pressure over water in [Pa].
0043 % IN       T = Temperature in [K].
0044 
0045 % 2010-08-18 Created by Marston Johnston
0046 
0047 function [es] = e_eq_water_gg(T)
0048 
0049 if any(T <= 0), error('Temperatures must be greater than 0K!!'); end
0050 
0051 Tst  = 373.16;  % K
0052 est = 1013.25; % hPa
0053 a = -7.90298;
0054 b = 5.02808;
0055 c = -1.3816*10^(-7);
0056 d = 11.344;
0057 f = 8.1328*10^(-3);
0058 h = -3.49149;
0059 
0060 % Gives the log of saturation vapor pressure over water in hPa
0061 Z = a*((Tst./T)-1) + b*log10(Tst./T) + c*((10.^(d*(1-(T/Tst))))-1) + f*((10.^(h*((Tst./T)-1)))-1);
0062 es = (est*10.^Z)*1e2; % convert to Pa

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