import numpy as np
import sys
from util_subs import (CtoK)
def VaporPressure(temp, P, phase, meth):
"""
Calculate the saturation vapor pressure
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 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
Hardy : vaporpressure formula from Hardy (1998)
MagnusTetens : vaporpressure formula from Magnus Tetens
GoffGratch : vaporpressure formula from Goff Gratch
Buck : vaporpressure formula from Buck (1981)
Buck2 : vaporpressure formula from the Buck (2012)
WMO : vaporpressure formula from WMO (1988)
WMO2018 : vaporpressure formula from WMO (2018)
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
------
Ported to Python and modified by S. Biri from Holger Voemel's original
"""
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
# Calculate saturation pressure over liquid water
if (phase == 'liquid'):
if (meth == 'HylandWexler' or meth == ''):
"""
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'):
"""
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'):
"""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'):
"""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')):
"""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)
"""
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 == 'MagnusTetens'):
"""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'):
"""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'):
"""Bucks vapor pressure formulation based on Tetens formula.
Source: Buck Research, Model CR-1A Hygrometer Operating Manual,
May 2012"""
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'):
"""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) + # in eq. 13 is -4.76955; in aerobulk is like this
0.78614)
if (meth == 'WMO2018'):
"""WMO 2018 edition. Annex 4.B, eq. 4.B.1, 4.B.2, 4.B.5 """
Psat = 6.112*np.exp(17.62*temp/(243.12+temp))*(1.0016+3.15e-6*P -
0.074/P)
if (meth == 'Sonntag'):
"""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'):
"""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'):
"""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'):
"""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'):
"""Default uses Goff Gratch over ice. There is little ambiguity in the
ice saturation curve. Goff Gratch is widely used."""
if (meth == 'MartiMauersberger'):
"""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'):
"""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'):
"""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'):
"""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 """
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'):
"""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'):
"""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'):
"""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'):
"""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'):
"""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'):
"""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'):
"""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'):
"""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):
"""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
#-----------------------------------------------------------------------------
def qsat_sea(T, P, qmeth):
"""
computes surface saturation specific humidity [g/kg]
Parameters
----------
T : float
temperature ($^\\circ$\\,C)
P : float
pressure (mb)
qmeth : str
method to calculate vapor pressure
Returns
-------
qs : float
"""
T = np.asarray(T)
if (np.nanmin(T) > 200): # if Ta in Kelvin convert to Celsius
T = T-CtoK
ex = VaporPressure(T, P, 'liquid', qmeth)
es = 0.98*ex # reduction at sea surface
qs = 622*es/(P-0.378*es)
return qs
#-----------------------------------------------------------------------------
def qsat_air(T, P, rh, qmeth):
"""
computes saturation specific humidity [g/kg]
Parameters
----------
T : float
temperature ($^\circ$\,C)
P : float
pressure (mb)
rh : float
relative humidity (%)
qmeth : str
method to calculate vapor pressure
Returns
-------
q : float
em : float
"""
T = np.asarray(T)
if (np.nanmin(T) > 200): # if Ta in Kelvin convert to Celsius
T = T-CtoK
es = VaporPressure(T, P, 'liquid', qmeth)
em = 0.01*rh*es
q = 622*em/(P-0.378*em)
return q
#------------------------------------------------------------------------------
def get_hum(hum, T, sst, P, qmeth):
"""
Get specific humidity output
Parameters
----------
hum : array
humidity input switch 2x1 [x, values] default is relative humidity
x='rh' : relative humidity in %
x='q' : specific humidity (kg/kg)
x='Td' : dew point temperature (K)
T : float
air temperature in K
sst : float
sea surface temperature in K
P : float
air pressure at sea level in hPa
qmeth : str
method to calculate specific humidity from vapor pressure
Returns
-------
qair : float
specific humidity of air
qsea : float
specific humidity over sea surface
"""
if (hum[0] not in ['rh', 'q', 'Td']):
sys.exit("unknown humidity input")
qair, qsea = np.nan, np.nan
elif (hum[0] == 'rh'):
RH = hum[1]
if (np.all(RH < 1)):
sys.exit("input relative humidity units should be \%")
qair, qsea = np.nan, np.nan
# RH = np.where(RH > 100, np.nan, RH) # ensure RH <=100
qsea = qsat_sea(sst, P, qmeth)/1000 # surface water q (kg/kg)
qair = qsat_air(T, P, RH, qmeth)/1000 # q of air (kg/kg)
elif (hum[0] == 'q'):
qair = hum[1]
qsea = qsat_sea(sst, P, qmeth)/1000 # surface water q (kg/kg)
elif (hum[0] == 'Td'):
Td = hum[1] # dew point temperature (K)
Td = np.where(Td < 200, np.copy(Td)+CtoK, np.copy(Td))
T = np.where(T < 200, np.copy(T)+CtoK, np.copy(T))
esd = 611.21*np.exp(17.502*((Td-273.16)/(Td-32.19)))
es = 611.21*np.exp(17.502*((T-273.16)/(T-32.19)))
RH = 100*esd/es
# RH = np.where(RH > 100, np.nan, RH) # ensure RH <=100
qair = qsat_air(T, P, RH, qmeth)/1000 # q of air (kg/kg)
qsea = qsat_sea(sst, P, qmeth)/1000 # surface water q (kg/kg)
return qair, qsea
#------------------------------------------------------------------------------
def gamma(opt, sst, t, q, cp):
"""
Computes the adiabatic lapse-rate
Parameters
----------
opt : str
type of adiabatic lapse rate dry or "moist"
dry has options to be constant "dry_c", for dry air "dry", or
for unsaturated air with water vapor "dry_v"
sst : float
sea surface temperature [K]
t : float
air temperature [K]
q : float
specific humidity of air [kg/kg]
cp : float
specific capacity of air at constant Pressure [kJ/(kg*K)]
Returns
-------
gamma : float
lapse rate [K/m]
"""
if (np.nanmin(sst) < 200): # if sst in Celsius convert to Kelvin
sst = sst+CtoK
if (np.nanmin(t) < 200): # if sst in Celsius convert to Kelvin
t = t+CtoK
if (opt == "moist"):
t = np.maximum(t, 180)
q = np.maximum(q, 1e-6)
w = q/(1-q) # mixing ratio w = q/(1-q)
iRT = 1/(287.05*t)
# latent heat of vaporization of water as a function of temperature
lv = (2.501-0.00237*(sst-CtoK))*1e6
gamma = 9.8*(1+lv*w*iRT)/(1005+np.power(lv, 2)*w*(287.05/461.495) *
iRT/t)
elif (opt == "dry_c"):
gamma = 0.0098*np.ones(t.shape)
elif (opt == "dry"):
gamma = 9.81/cp
elif (opt == "dry_v"):
w = q/(1-q) # mixing ratio
f_v = 1-0.85*w #(1+w)/(1+w*)
gamma = f_v*9.81/cp
return gamma
#------------------------------------------------------------------------------