import numpy as np import logging """ Calculate the saturation vapor pressure Example: Calculate the vapor pressure over liquid water using the WMO formula temp = FINDGEN(100) - 100. P = VaporPressure(temp, 'liquid', 'WMO') For temperatures above 0 deg C the vapor pressure over liquid water is calculated. The optional parameter 'liquid' changes the calculation to vapor pressure over liquid water over the entire temperature range. The formula to be used can be selected with the appropriate keyword The current default fomulas are Hyland and Wexler for liquid and Goff Gratch for ice. Parameters ---------- temp : float Temperature in [deg C] phase : str 'liquid' : Calculate vapor pressure over liqiud water or 'ice' : Calculate vapor pressure over ice meth : str formula to be used MartiMauersberger : vaporpressure formula from Marti Mauersberger MagnusTetens : vaporpressure formula from Magnus Tetens GoffGratch : vaporpressure formula from Goff Gratch Buck_original : vaporpressure formula from Buck (original) Buck_manual : vaporpressure formula from the Buck manual CIMO : vaporpressure formula recommended by CIMO Vaisala : vaporpressure formula from Vaisala WMO_Goff : vaporpressure formula from WMO, which should have been Goff WMO2000 : vaporpressure formula from WMO (2000) containing a typo Wexler : vaporpressure formula from Wexler (1976) Sonntag : vaporpressure formula from Sonntag (1994) Bolton : vaporpressure formula from Bolton (1980) HylandWexler : vaporpressure formula from Hyland and Wexler (1983) IAPWS : vaporpressure formula from IAPWS (2002) Preining : vaporpressure formula from Preining (2002) MurphyKoop : vaporpressure formula from Murphy and Koop (2005) Returns ------- P : float Saturation vapor pressure in [hPa] Author ------ Holger Voemel NCAR / EOL PO BOX 3000 Boulder, CO 80303 USA Ported to Python and modified by S. Biri COPYRIGHT --------- Copyright (c) 2015, Holger Voemel """ def VaporPressure(temp, P, phase, meth): logging.basicConfig(filename='VaporPressure.log', format='%(asctime)s %(message)s',level=logging.info) Psat = np.zeros(temp.size)*np.nan if (np.nanmin(temp) > 200): # if Ta in Kelvin convert to Celsius temp = temp-273.16 T = np.copy(temp)+273.16 # Most formulas use T in [K] # Formulas using [C] use the variable temp # Default uses Hyland and Wexler over liquid. While this may not be # the best formula, it is consistent with what Vaisala uses in their # system # Calculate saturation pressure over liquid water if (phase == 'liquid'): if (meth == 'HylandWexler' or meth == ''): logging.info("Source Hyland, R. W. and A. Wexler, Formulations \ for the Thermodynamic Properties of the saturated \ Phases of H2O from 173.15K to 473.15K, \ ASHRAE Trans, 89(2A), 500-519, 1983.") Psat = np.exp(-0.58002206e4/T+0.13914993e1-0.48640239e-1*T + 0.41764768e-4*np.power(T, 2) - 0.14452093e-7*np.power(T, 3) + 0.65459673e1*np.log(T))/100 if (meth == 'Hardy'): logging.info("Source Hardy, B., 1998, ITS-90 Formulations \ for Vapor Pressure, Frostpoint Temperature, \ Dewpoint Temperature, and Enhancement Factors \ in the Range -100 to +100°C, The Proceedings of \ the Third International Symposium on Humidity & \ Moisture, London, England") Psat = np.exp(-2.8365744e3/np.power(T, 2)-6.028076559e3/T + 1.954263612e1-2.737830188e-2*T + 1.6261698e-5*np.power(T, 2) + 7.0229056e-10*np.power(T, 3) - 1.8680009e-13*np.power(T, 4) + 2.7150305*np.log(T))/100 if (meth == 'Preining'): logging.info("Source : Vehkamaeki, H., M. Kulmala, I. Napari, \ K. E. J. Lehtinen, C.Timmreck, M. Noppel, and \ A. Laaksonen (2002), J. Geophys. Res., 107, \ doi:10.1029/2002JD002184.") Psat = np.exp(-7235.424651/T+77.34491296+5.7113e-3*T - 8.2*np.log(T))/100 if (meth == 'Wexler'): logging.info("Wexler, A., Vapor Pressure Formulation for Water \ in Range 0 to 100 C. A Revision, Journal of Research \ of the National Bureau of Standards - A. Physics and \ Chemistry, September - December 1976, Vol. 80A, \ Nos.5 and 6, 775-785") Psat = np.exp(-0.29912729e4*np.power(T, -2) - 0.60170128e4*np.power(T, -1) + 0.1887643854e2-0.28354721e-1*T + 0.17838301e-4*np.power(T, 2) - 0.84150417e-9*np.power(T, 3) + 0.44412543e-12*np.power(T, 4) + # This line was corrected from '-' to '+' following the original citation. (HV 20140819). The change makes only negligible difference 2.858487*np.log(T))/100 if ((meth == 'GoffGratch') or (meth == 'MartiMauersberger')): # logging.info("Marti and Mauersberger don't have a vapor pressure \ # curve over liquid. Using Goff Gratch instead; \ # Goff Gratch formulation Source : Smithsonian \ # Meteorological Tables, 5th edition, p. 350, 1984 \ # From original source: Goff & Gratch (1946), p. 107) \ # Goff Gratch formulation; Source : Smithsonian \ # Meteorological Tables, 5th edition, p. 350, 1984 \ # From original source: Goff and Gratch (1946), p. 107") Ts = 373.16 # steam point temperature in K ews = 1013.246 # saturation pressure at steam point temperature Psat = np.power(10, -7.90298*(Ts/T-1)+5.02808*np.log10(Ts/T) - 1.3816e-7*(np.power(10, 11.344*(1-T/Ts))-1) + 8.1328e-3*(np.power(10, -3.49149*(Ts/T-1))-1) + np.log10(ews)) if (meth == 'CIMO'): logging.info("Source: Annex 4B, Guide to Meteorological \ Instruments and Methods of Observation, \ WMO Publication No 8, 7th edition, Geneva, 2008. \ (CIMO Guide)") Psat = (6.112*np.exp(17.62*temp/(243.12+temp)) * (1.0016+3.15e-6*P-0.074/P)) if (meth == 'MagnusTetens'): logging.info("Source: Murray, F. W., On the computation of \ saturation vapor pressure, J. Appl. Meteorol., \ 6, 203-204, 1967.") Psat = np.power(10, 7.5*(temp)/(temp+237.5)+0.7858) # Murray quotes this as the original formula and Psat = 6.1078*np.exp(17.269388*temp/(temp+237.3)) # this as the mathematical aquivalent in the form of base e. if (meth == 'Buck'): logging.info("Bucks vapor pressure formulation based on \ Tetens formula. Source: Buck, A. L., \ New equations for computing vapor pressure and \ enhancement factor, J. Appl. Meteorol., 20, \ 1527-1532, 1981.") Psat = (6.1121*np.exp(17.502*temp/(240.97+temp)) * (1.0007+(3.46e-6*P))) if (meth == 'Buck2'): logging.info("Bucks vapor pressure formulation based on \ Tetens formula. Source: Buck Research, \ Model CR-1A Hygrometer Operating Manual, Sep 2001") Psat = (6.1121*np.exp((18.678-(temp)/234.5)*(temp)/(257.14+temp)) * (1+1e-4*(7.2+P*(0.0320)+5.9e-6*np.power(T, 2)))) if (meth == 'WMO'): logging.info("Intended WMO formulation, originally published by \ Goff (1957) incorrectly referenced by WMO technical \ regulations, WMO-NO 49, Vol I, General \ Meteorological Standards and Recommended Practices, \ App. A, Corrigendum Aug 2000. and incorrectly \ referenced by WMO technical regulations, \ WMO-NO 49, Vol I, General Meteorological Standards \ and Recommended Practices, App. A, 1988.") Ts = 273.16 # triple point temperature in K Psat = np.power(10, 10.79574*(1-Ts/T)-5.028*np.log10(T/Ts) + 1.50475e-4*(1-np.power(10, -8.2969*(T/Ts-1))) + 0.42873e-3*(np.power(10, -4.76955*(1-Ts/T))-1) + 0.78614) if (meth == 'WMO2000'): logging.info("WMO formulation, which is very similar to Goff \ Gratch. Source : WMO technical regulations, \ WMO-NO 49, Vol I, General Meteorological Standards \ and Recommended Practices, App. A, \ Corrigendum Aug 2000.") Ts = 273.16 # triple point temperature in K Psat = np.power(10, 10.79574*(1-Ts/T)-5.028*np.log10(T/Ts) + 1.50475e-4*(1-np.power(10, -8.2969*(T/Ts-1))) + 0.42873e-3*(np.power(10, -4.76955*(1.-Ts/T))-1) + 0.78614) if (meth == 'Sonntag'): logging.info("Source: Sonntag, D., Advancements in the field of \ hygrometry, Meteorol. Z., N. F., 3, 51-66, 1994.") Psat = np.exp(-6096.9385*np.power(T, -1)+16.635794 - 2.711193e-2*T+1.673952e-5*np.power(T, 2) + 2.433502*np.log(T))#*(1.0016+P*3.15e-6-0.074/P) if (meth == 'Bolton'): logging.info("Source: Bolton, D., The computation of equivalent \ potential temperature, Monthly Weather Report, 108, \ 1046-1053, 1980. equation (10)") Psat = 6.112*np.exp(17.67*temp/(temp+243.5)) if (meth == 'IAPWS'): logging.info("Source: Wagner W. and A. Pruss (2002), The IAPWS \ formulation 1995 for the thermodynamic properties \ of ordinary water substance for general and \ scientific use, J. Phys. Chem. Ref. Data, 31(2), \ 387-535. This is the 'official' formulation from \ the International Association for the Properties of \ Water and Steam The valid range of this formulation \ is 273.16 <= T <= 647.096 K and is based on the \ ITS90 temperature scale.") Tc = 647.096 # K : Temperature at the critical point Pc = 22.064e4 # hPa : Vapor pressure at the critical point nu = (1-T/Tc) a1, a2, a3 = -7.85951783, 1.84408259, -11.7866497 a4, a5, a6 = 22.6807411, -15.9618719, 1.80122502 Psat = (Pc*np.exp(Tc/T*(a1*nu+a2*np.power(nu, 1.5) + a3*np.power(nu, 3)+a4*np.power(nu, 3.5) + a5*np.power(nu, 4)+ a6*np.power(nu, 7.5)))) if (meth == 'MurphyKoop'): logging.info("Source : Murphy and Koop, Review of the vapour \ pressure of ice and supercooled water for \ atmospheric applications, Q. J. R. Meteorol. \ Soc (2005), 131, pp. 1539-1565.") Psat = np.exp(54.842763-6763.22/T-4.210*np.log(T)+0.000367*T + np.tanh(0.0415*(T-218.8))*(53.878-1331.22/T - 9.44523*np.log(T)+0.014025*T))/100 # Calculate saturation pressure over ice ---------------------------------- elif (phase == 'ice'): logging.info("Default uses Goff Gratch over ice. There is little \ ambiguity in the ice saturation curve. Goff Gratch \ is widely used.") if (meth == 'MartiMauersberger'): logging.info("Source : Marti, J. and K Mauersberger, A survey and \ new measurements of ice vapor pressure at \ temperatures between 170 and 250 K, GRL 20, \ 363-366, 1993.") Psat = np.power(10, -2663.5/T+12.537)/100 if (meth == 'HylandWexler'): logging.info("Source Hyland, R. W. and A. Wexler, Formulations \ for the Thermodynamic Properties of the saturated \ Phases of H2O from 173.15K to 473.15K, ASHRAE Trans,\ 89(2A), 500-519, 1983.") Psat = np.exp(-0.56745359e4/T+0.63925247e1-0.96778430e-2*T + 0.62215701e-6*np.power(T, 2) + 0.20747825e-8*np.power(T, 3) - 0.9484024e-12*np.power(T, 4) + 0.41635019e1*np.log(T))/100 if (meth == 'Wexler'): logging.info("Wexler, A., Vapor pressure formulation for ice, \ Journal of Research of the National Bureau of \ Standards-A. 81A, 5-20, 1977.") Psat = np.exp(-0.58653696e4*np.power(T, -1)+0.22241033e2 + 0.13749042e-1*T-0.34031775e-4*np.power(T, 2) + 0.26967687e-7*np.power(T, 3) + 0.6918651*np.log(T))/100 if (meth == 'Hardy'): logging.info("Source Hardy, B., 1998, ITS-90 Formulations for \ Vapor Pressure, Frostpoint Temperature, Dewpoint \ Temperature, and Enhancement Factors in the Range \ -100 to +100°C, The Proceedings of the Third \ International Symposium on Humidity & Moisture, \ London, England. These coefficients are updated to \ ITS90 based on the work by Bob Hardy at Thunder \ Scientific: http://www.thunderscientific.com/\ tech_info/reflibrary/its90formulas.pdf \ The difference to the older ITS68 coefficients used \ by Wexler is academic.") Psat = np.exp(-0.58666426e4*np.power(T, -1)+0.2232870244e2 + 0.139387003e-1*T-0.34262402e-4*np.power(T, 2) + 0.27040955e-7*np.power(T, 3) + 0.67063522e-1*np.log(T))/100 if (meth == 'GoffGratch' or meth == '' or meth == 'IAPWS'): logging.info("IAPWS does not provide a vapor pressure formulation \ over ice use Goff Gratch instead.\ Source : Smithsonian Meteorological Tables, \ 5th edition, p. 350, 1984") ei0 = 6.1071 # mbar T0 = 273.16 # triple point in K Psat = np.power(10, -9.09718*(T0/T-1)-3.56654*np.log10(T0/T) + 0.876793*(1-T/T0)+np.log10(ei0)) if (meth == 'MagnusTetens'): logging.info("Source: Murray, F. W., On the computation of \ saturation vapor pressure, J. Appl. Meteorol., 6, \ 203-204, 1967.") Psat = np.power(10, 9.5*temp/(265.5+temp)+0.7858) # Murray quotes this as the original formula and Psat = 6.1078*np.exp(21.8745584*(T-273.16)/(T-7.66)) # this as the mathematical aquivalent in the form of base e. if (meth == 'Buck'): logging.info("Bucks vapor pressure formulation based on Tetens \ formula. Source: Buck, A. L., New equations for \ computing vapor pressure and enhancement factor, \ J. Appl. Meteorol., 20, 1527-1532, 1981.") Psat = (6.1115*np.exp(22.452*temp/(272.55+temp)) * (1.0003+(4.18e-6*P))) if (meth == 'Buck2'): logging.info("Bucks vapor pressure formulation based on Tetens \ formula. Source: Buck Research, Model CR-1A \ Hygrometer Operating Manual, Sep 2001") Psat = (6.1115*np.exp((23.036-temp/333.7)*temp/(279.82+temp)) * (1+1e-4*(2.2+P*(0.0383+6.4e-6*np.power(T, 2))))) if (meth == 'CIMO'): logging.info("Source: Annex 4B, Guide to Meteorological \ Instruments and Methods of Observation, \ WMO Publication No 8, 7th edition, Geneva, 2008. \ (CIMO Guide)") Psat = (6.112*np.exp(22.46*temp/(272.62+temp)) * (1.0016+3.15e-6*P-0.074/P)) if (meth == 'WMO' or meth == 'WMO2000'): logging.info("There is no typo issue in the WMO formulations for \ ice. WMO formulation, which is very similar to Goff \ Gratch. Source : WMO technical regulations, \ WMO-NO 49, Vol I, General Meteorological Standards \ and Recommended Practices, Aug 2000, App. A.") T0 = 273.16 # triple point temperature in K Psat = np.power(10, -9.09685*(T0/T-1)-3.56654*np.log10(T0/T) + 0.87682*(1-T/T0)+0.78614) if (meth == 'Sonntag'): logging.info("Source: Sonntag, D., Advancements in the field of \ hygrometry, Meteorol. Z., N. F., 3, 51-66, 1994.") Psat = np.exp(-6024.5282*np.power(T, -1)+24.721994+1.0613868e-2*T - 1.3198825e-5*np.power(T, 2)-0.49382577*np.log(T)) if (meth == 'MurphyKoop'): logging.info("Source : Murphy and Koop, Review of the vapour \ pressure of ice and supercooled water for \ atmospheric applications, Q. J. R. Meteorol. Soc \ (2005), 131, pp. 1539-1565.") Psat = np.exp(9.550426-5723.265/T+3.53068*np.log(T) - 0.00728332*T)/100 s = np.where(temp > 0) if (s.size[0] >= 1): logging.info("Independent of the formula used for ice, use \ Hyland Wexler (water) for temperatures above freezing\ (see above). Source Hyland, R. W. and A. Wexler, \ Formulations for the Thermodynamic Properties of the \ saturated Phases of H2O from 173.15K to 473.15K, \ ASHRAE Trans, 89(2A), 500-519, 1983.") Psat_w = np.exp(-0.58002206e4/T+0.13914993e1-0.48640239e-1*T + 0.41764768e-4*np.power(T, 2) - 0.14452093e-7*np.power(T, 3) + 0.65459673e1*np.log(T))/100 Psat[s] = Psat_w[s] return Psat