def Es(T, method=None):
"""Computes saturated pressure in Pa given T in K, using the method:
1: Hyland-Wexler formulation, polynomial coeff (absolute norm)
2: Wexler formulation
3: Hyland-Wexler formulation, polynomial coeff (relative error norm)
4: classic Goff Gratch equation
5: 6.112*numpy.ma.exp(17.67*tempc/(tempc+243.5))
Default is method 1
Note: 1 and 2 use method 3 where T is not : 173.15 < T < 473.15
ref for 1, 2 and 3:
Piotr Flatau and al., Journal of Applied Met., Vol 31, Dec 1992 ( http://ams.allenpress.com/perlserv/?request=get-document&doi=10.1175%2F1520-0450(1992)031%3C1507%3APFTSVP%3E2.0.CO%3B2&ct=1 )
"""
if method is None:
method = 1
if method == 1:
## Put in C
x = T - 273.15
## Water vapor
c0 = 0.611220713E03
c1 = 0.443944344E02
c2 = 0.143195336E01
c3 = 0.263350515E-01
c4 = 0.310636053E-03
c5 = 0.185218710E-05
c6 = 0.103440324E-07
c7 = -0.468258100E-10
c8 = 0.466533033E-13
eswat = c0 + x * (c1 + x * (c2 + x * (c3 + x * (c4 + x *
(c5 + x *
(c6 + x *
(c7 + x * c8)))))))
## ice
c0 = .611153246E03
c1 = .503261230E02
c2 = .188595709E01
c3 = .422115970E-01
c4 = .620376691E-03
c5 = .616082536E-05
c6 = .405172828E-07
c7 = .161492905E-09
c8 = .297886454E-12
esice = c0 + x * (c1 + x * (c2 + x * (c3 + x * (c4 + x *
(c5 + x *
(c6 + x *
(c7 + x * c8)))))))
## Combine
es = MV2.where(MV2.less(T, 273.15), esice, eswat)
## Overwrite values outside valid range with method 2
mn, mx = genutil.minmax(T)
if mn < 173.16 or mx > 473.15:
es2 = Es(T, method=2)
es = MV2.where(MV2.less(T, 173.16), es2, es)
es = MV2.where(MV2.greater(T, 473.15), es2, es)
elif method == 2:
# over water
g0 = -0.29912729E4
g1 = -0.60170128E4
g2 = 0.1887643854E2
g3 = -0.28354721E-1
g4 = 0.17838301E-4
g5 = -0.84150417E-9
g6 = 0.44412543E-12
g7 = 0.2858487E1
# over ice
k0 = -0.58653696e4
k1 = 0.2224103300E2
k2 = 0.13749042E-1
k3 = -0.34031775E-4
k4 = 0.26967687E-7
k5 = 0.6918651
esice = (k0 + (k1 + k5 * MV2.log(T) +
(k2 + (k3 + k4 * T) * T) * T) * T) / T # over ice
eswat = (g0 + (g1 + (g2 + g7 * MV2.log(T) +
(g3 + (g4 + (g5 + g6 * T) * T) * T) * T) * T) *
T) / T**2 # over water
es = MV2.where(MV2.less(T, 273.15), esice, eswat)
es = MV2.exp(es)
elif method == 3:
## Put in C
x = T - 273.15
## Water vapor
c0 = 0.611213476E03
c1 = 0.444007856E02
c2 = 0.143064234E01
c3 = 0.264461437E-01
c4 = 0.305930558E-03
c5 = 0.196237241E-05
c6 = 0.892344772E-08
c7 = -0.373208410E-10
c8 = 0.209339997E-13
eswat = c0 + x * (c1 + x * (c2 + x * (c3 + x * (c4 + x *
(c5 + x *
(c6 + x *
(c7 + x * c8)))))))
## ice
c0 = .611123516E03
c1 = .503109514E02
c2 = .1888369801E01
c3 = .420547422E-01
c4 = .614396778E-03
c5 = .602780717E-05
c6 = .387940929E-07
c7 = .149436277E-09
c8 = .262655803E-12
esice = c0 + x * (c1 + x * (c2 + x * (c3 + x * (c4 + x *
(c5 + x *
(c6 + x *
(c7 + x * c8)))))))
## Combine
es = MV2.where(MV2.less(T, 273.15), esice, eswat)
## Overwrite values outside valid range with method 2
mn, mx = genutil.minmax(T)
if mn < 173.16 or mx > 473.15:
es2 = Es(T, method=2)
es = MV2.where(MV2.less(T, 173.16), es2, es)
es = MV2.where(MV2.greater(T, 473.15), es2, es)
elif method == 4:
est = 101324.6 #Pa
Ts = 373.16 / T
a = -7.90298
b = 5.02808
c = -1.3816E-7
d = 11.344
f = 8.1328E-3
h = -3.49149
maxexp = int(numpy.log10(numpy.finfo(numpy.float).max))
minexp = 1 - a
es = a * (Ts - 1.)
es = es + b * numpy.ma.log10(Ts)
A = d * (1. - Ts)
A = numpy.ma.masked_greater(A, maxexp)
A = numpy.ma.masked_less(A, minexp)
es = es + c * (numpy.ma.power(10, A) - 1.)
A = h * (Ts - 1.)
A = numpy.ma.masked_greater(A, maxexp)
A = numpy.ma.masked_less(A, minexp)
es = es + f * (numpy.ma.power(10, A) - 1.)
es = est * numpy.ma.power(10, es)
elif method == 5:
tempc = T - 273.15
es = 611.2 * numpy.ma.exp(17.67 * tempc / (tempc + 243.5))
return es
def logLinearInterpolation(A,
P,
levels=[
100000, 92500, 85000, 70000, 60000, 50000,
40000, 30000, 25000, 20000, 15000, 10000, 7000,
5000, 3000, 2000, 1000
],
status=None):
"""
Log-linear interpolation
to convert a field from sigma levels to pressure levels
Value below surface are masked
Input
A : array on sigma levels
P : pressure field from TOP (level 0) to BOTTOM (last level)
levels : pressure levels to interplate to (same units as P), default levels are:[100000, 92500, 85000, 70000, 60000, 50000, 40000, 30000, 25000, 20000, 15000, 10000, 7000, 5000, 3000, 2000, 1000]
P and levels must have same units
Output
array on pressure levels (levels)
Examples:
A=logLinearInterpolation(A,P),levels=[100000, 92500, 85000, 70000, 60000, 50000, 40000, 30000, 25000, 20000, 15000, 10000, 7000, 5000, 3000, 2000, 1000])
"""
try:
nlev = len(levels) # Number of pressure levels
except:
nlev = 1 # if only one level len(levels) would breaks
levels = [
levels,
]
order = A.getOrder()
A = A(order='z...')
P = P(order='z...')
sh = list(P.shape)
nsigma = sh[0] #number of sigma levels
sh[0] = nlev
t = MV2.zeros(sh, typecode=MV2.float32)
sh2 = P[0].shape
prev = -1
for ilev in range(nlev): # loop through pressure levels
if status is not None:
prev = genutil.statusbar(ilev, nlev - 1., prev)
lev = levels[ilev] # get value for the level
Pabv = MV2.ones(sh2, MV2.float)
Aabv = -1 * Pabv # Array on sigma level Above
Abel = -1 * Pabv # Array on sigma level Below
Pbel = -1 * Pabv # Pressure on sigma level Below
Pabv = -1 * Pabv # Pressure on sigma level Above
Peq = MV2.masked_equal(Pabv, -1) # Area where Pressure == levels
for i in range(1, nsigma): # loop from second sigma level to last one
a = MV2.greater_equal(
P[i], lev) # Where is the pressure greater than lev
b = MV2.less_equal(P[i - 1],
lev) # Where is the pressure less than lev
# Now looks if the pressure level is in between the 2 sigma levels
# If yes, sets Pabv, Pbel and Aabv, Abel
a = MV2.logical_and(a, b)
Pabv = MV2.where(a, P[i], Pabv) # Pressure on sigma level Above
Aabv = MV2.where(a, A[i], Aabv) # Array on sigma level Above
Pbel = MV2.where(a, P[i - 1],
Pbel) # Pressure on sigma level Below
Abel = MV2.where(a, A[i - 1], Abel) # Array on sigma level Below
Peq = MV2.where(MV2.equal(P[i], lev), A[i], Peq)
val = MV2.masked_where(
MV2.equal(Pbel, -1),
numpy.ones(Pbel.shape) *
lev) # set to missing value if no data below lev if there is
tl = MV2.log(val / Pbel) / MV2.log(
Pabv / Pbel) * (Aabv - Abel) + Abel # Interpolation
if ((Peq.mask is None) or (Peq.mask is MV2.nomask)):
tl = Peq
else:
tl = MV2.where(1 - Peq.mask, Peq, tl)
t[ilev] = tl.astype(MV2.float32)
ax = A.getAxisList()
autobnds = cdms2.getAutoBounds()
cdms2.setAutoBounds('off')
lvl = cdms2.createAxis(MV2.array(levels).filled())
cdms2.setAutoBounds(autobnds)
try:
lvl.units = P.units
except:
pass
lvl.id = 'plev'
try:
t.units = P.units
except:
pass
ax[0] = lvl
t.setAxisList(ax)
t.id = A.id
for att in A.listattributes():
setattr(t, att, getattr(A, att))
return t(order=order)
def logLinearInterpolation(A,P,levels=[100000, 92500, 85000, 70000, 60000, 50000, 40000, 30000, 25000, 20000, 15000, 10000, 7000, 5000, 3000, 2000, 1000],status=None):
"""
Log-linear interpolation
to convert a field from sigma levels to pressure levels
Value below surface are masked
Input
A : array on sigma levels
P : pressure field from TOP (level 0) to BOTTOM (last level)
levels : pressure levels to interplate to (same units as P), default levels are:[100000, 92500, 85000, 70000, 60000, 50000, 40000, 30000, 25000, 20000, 15000, 10000, 7000, 5000, 3000, 2000, 1000]
P and levels must have same units
Output
array on pressure levels (levels)
Examples:
A=logLinearInterpolation(A,P),levels=[100000, 92500, 85000, 70000, 60000, 50000, 40000, 30000, 25000, 20000, 15000, 10000, 7000, 5000, 3000, 2000, 1000])
"""
try:
nlev=len(levels) # Number of pressure levels
except:
nlev=1 # if only one level len(levels) would breaks
levels=[levels,]
order=A.getOrder()
A=A(order='z...')
P=P(order='z...')
sh=list(P.shape)
nsigma=sh[0] #number of sigma levels
sh[0]=nlev
t=MV2.zeros(sh,typecode=MV2.float32)
sh2=P[0].shape
prev=-1
for ilev in range(nlev): # loop through pressure levels
if status is not None:
prev=genutil.statusbar(ilev,nlev-1.,prev)
lev=levels[ilev] # get value for the level
Pabv=MV2.ones(sh2,MV2.float)
Aabv=-1*Pabv # Array on sigma level Above
Abel=-1*Pabv # Array on sigma level Below
Pbel=-1*Pabv # Pressure on sigma level Below
Pabv=-1*Pabv # Pressure on sigma level Above
Peq=MV2.masked_equal(Pabv,-1) # Area where Pressure == levels
for i in range(1,nsigma): # loop from second sigma level to last one
a=MV2.greater_equal(P[i], lev) # Where is the pressure greater than lev
b= MV2.less_equal(P[i-1],lev) # Where is the pressure less than lev
# Now looks if the pressure level is in between the 2 sigma levels
# If yes, sets Pabv, Pbel and Aabv, Abel
a=MV2.logical_and(a,b)
Pabv=MV2.where(a,P[i],Pabv) # Pressure on sigma level Above
Aabv=MV2.where(a,A[i],Aabv) # Array on sigma level Above
Pbel=MV2.where(a,P[i-1],Pbel) # Pressure on sigma level Below
Abel=MV2.where(a,A[i-1],Abel) # Array on sigma level Below
Peq= MV2.where(MV2.equal(P[i],lev),A[i],Peq)
val=MV2.masked_where(MV2.equal(Pbel,-1),numpy.ones(Pbel.shape)*lev) # set to missing value if no data below lev if there is
tl=MV2.log(val/Pbel)/MV2.log(Pabv/Pbel)*(Aabv-Abel)+Abel # Interpolation
if ((Peq.mask is None) or (Peq.mask is MV2.nomask)):
tl=Peq
else:
tl=MV2.where(1-Peq.mask,Peq,tl)
t[ilev]=tl.astype(MV2.float32)
ax=A.getAxisList()
autobnds=cdms2.getAutoBounds()
cdms2.setAutoBounds('off')
lvl=cdms2.createAxis(MV2.array(levels).filled())
cdms2.setAutoBounds(autobnds)
try:
lvl.units=P.units
except:
pass
lvl.id='plev'
try:
t.units=P.units
except:
pass
ax[0]=lvl
t.setAxisList(ax)
t.id=A.id
for att in A.listattributes():
setattr(t,att,getattr(A,att))
return t(order=order)
def Es(T, method=None):
"""Computes saturated pressure in Pa given T in K, using the method:
1: Hyland-Wexler formulation, polynomial coeff (absolute norm)
2: Wexler formulation
3: Hyland-Wexler formulation, polynomial coeff (relative error norm)
4: classic Goff Gratch equation
5: 6.112*numpy.ma.exp(17.67*tempc/(tempc+243.5))
Default is method 1
Note: 1 and 2 use method 3 where T is not : 173.15 < T < 473.15
ref for 1, 2 and 3:
Piotr Flatau and al., Journal of Applied Met., Vol 31, Dec 1992
( http://ams.allenpress.com/perlserv/?request=get-document&\
doi=10.1175%2F1520-0450(1992)031%3C1507%3APFTSVP%3E2.0.CO%3B2&ct=1 )
"""
if method is None:
method = 1
if method == 1:
# Put in C
x = T - 273.15
# Water vapor
c0 = 0.611220713e03
c1 = 0.443944344e02
c2 = 0.143195336e01
c3 = 0.263350515e-01
c4 = 0.310636053e-03
c5 = 0.185218710e-05
c6 = 0.103440324e-07
c7 = -0.468258100e-10
c8 = 0.466533033e-13
eswat = c0 + x * (c1 + x * (c2 + x * (c3 + x * (c4 + x * (c5 + x * (c6 + x * (c7 + x * c8)))))))
# ice
c0 = 0.611153246e03
c1 = 0.503261230e02
c2 = 0.188595709e01
c3 = 0.422115970e-01
c4 = 0.620376691e-03
c5 = 0.616082536e-05
c6 = 0.405172828e-07
c7 = 0.161492905e-09
c8 = 0.297886454e-12
esice = c0 + x * (c1 + x * (c2 + x * (c3 + x * (c4 + x * (c5 + x * (c6 + x * (c7 + x * c8)))))))
# Combine
es = MV2.where(MV2.less(T, 273.15), esice, eswat)
# Overwrite values outside valid range with method 2
mn, mx = genutil.minmax(T)
if mn < 173.16 or mx > 473.15:
es2 = Es(T, method=2)
es = MV2.where(MV2.less(T, 173.16), es2, es)
es = MV2.where(MV2.greater(T, 473.15), es2, es)
elif method == 2:
# over water
g0 = -0.29912729e4
g1 = -0.60170128e4
g2 = 0.1887643854e2
g3 = -0.28354721e-1
g4 = 0.17838301e-4
g5 = -0.84150417e-9
g6 = 0.44412543e-12
g7 = 0.2858487e1
# over ice
k0 = -0.58653696e4
k1 = 0.2224103300e2
k2 = 0.13749042e-1
k3 = -0.34031775e-4
k4 = 0.26967687e-7
k5 = 0.6918651
esice = (k0 + (k1 + k5 * MV2.log(T) + (k2 + (k3 + k4 * T) * T) * T) * T) / T # over ice
eswat = (
g0 + (g1 + (g2 + g7 * MV2.log(T) + (g3 + (g4 + (g5 + g6 * T) * T) * T) * T) * T) * T
) / T ** 2 # over water
es = MV2.where(MV2.less(T, 273.15), esice, eswat)
es = MV2.exp(es)
elif method == 3:
# Put in C
x = T - 273.15
# Water vapor
c0 = 0.611213476e03
c1 = 0.444007856e02
c2 = 0.143064234e01
c3 = 0.264461437e-01
c4 = 0.305930558e-03
c5 = 0.196237241e-05
c6 = 0.892344772e-08
c7 = -0.373208410e-10
c8 = 0.209339997e-13
eswat = c0 + x * (c1 + x * (c2 + x * (c3 + x * (c4 + x * (c5 + x * (c6 + x * (c7 + x * c8)))))))
# ice
c0 = 0.611123516e03
c1 = 0.503109514e02
c2 = 0.1888369801e01
c3 = 0.420547422e-01
c4 = 0.614396778e-03
c5 = 0.602780717e-05
c6 = 0.387940929e-07
c7 = 0.149436277e-09
c8 = 0.262655803e-12
esice = c0 + x * (c1 + x * (c2 + x * (c3 + x * (c4 + x * (c5 + x * (c6 + x * (c7 + x * c8)))))))
# Combine
es = MV2.where(MV2.less(T, 273.15), esice, eswat)
# Overwrite values outside valid range with method 2
mn, mx = genutil.minmax(T)
if mn < 173.16 or mx > 473.15:
es2 = Es(T, method=2)
es = MV2.where(MV2.less(T, 173.16), es2, es)
es = MV2.where(MV2.greater(T, 473.15), es2, es)
elif method == 4:
est = 101324.6 # Pa
Ts = 373.16 / T
a = -7.90298
b = 5.02808
c = -1.3816e-7
d = 11.344
f = 8.1328e-3
h = -3.49149
maxexp = int(numpy.log10(numpy.finfo(numpy.float).max))
minexp = 1 - a
es = a * (Ts - 1.0)
es = es + b * numpy.ma.log10(Ts)
A = d * (1.0 - Ts)
A = numpy.ma.masked_greater(A, maxexp)
A = numpy.ma.masked_less(A, minexp)
es = es + c * (numpy.ma.power(10, A) - 1.0)
A = h * (Ts - 1.0)
A = numpy.ma.masked_greater(A, maxexp)
A = numpy.ma.masked_less(A, minexp)
es = es + f * (numpy.ma.power(10, A) - 1.0)
es = est * numpy.ma.power(10, es)
elif method == 5:
tempc = T - 273.15
es = 611.2 * numpy.ma.exp(17.67 * tempc / (tempc + 243.5))
return es