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].

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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