import numpy as np
import math
""" Conversion factor for [:math:`^\\circ` C] to [:math:`^\\circ` K] """
CtoK = 273.16 # 273.15
""" von Karman's constant """
kappa = 0.4 # NOTE: 0.41
def charnock_C35(wind,u10n,usr,seastate,waveage,wcp,sigH,lat):
g=gc(lat,None)
a1, a2=0.0017, -0.0050
charnC=np.where(u10n>19,a1*19+a2,a1*u10n+a2)
A, B=0.114, 0.622 #wave-age dependent coefficients
Ad, Bd=0.091, 2.0 #Sea-state/wave-age dependent coefficients
charnW=A*(usr/wcp)**B
zoS=sigH*Ad*(usr/wcp)**Bd
charnS=(zoS*g)/usr**2
charn=np.where(wind>10,0.011+(wind-10)/(18-10)*(0.018-0.011),np.where(wind>18,0.018,0.011*np.ones(np.shape(wind))))
if waveage:
if seastate:
charn=charnS
else:
charn=charnW
else:
charn=charnC
ac = np.zeros((len(wind),3))
ac[:,0] = charn
ac[:,1] = charnS
ac[:,2] = charnW
return ac
def cd_C35(u10n,wind,usr,charn,monob,Ta,hh_in,lat):
g=gc(lat,None)
zo=charn*usr**2/g+0.11*visc_air(Ta)/usr # surface roughness
rr=zo*usr/visc_air(Ta)
zoq=np.where(5.8e-5/rr**0.72>1.6e-4,1.6e-4,5.8e-5/rr**0.72) # These thermal roughness lengths give Stanton and
zot=zoq # Dalton numbers that closely approximate COARE 3.0
cdhf=kappa/(np.log(hh_in[0]/zo)-psiu_26(hh_in[0]/monob))
cthf=kappa/(np.log(hh_in[1]/zot)-psit_26(hh_in[1]/monob))
cqhf=kappa/(np.log(hh_in[2]/zoq)-psit_26(hh_in[2]/monob))
return zo,cdhf, cthf, cqhf
def cdn_calc(u10n,Ta,Tp,method="Smith80"):
if (method == "Smith80"):
cdn = np.where(u10n <=3,(0.61+0.567/u10n)*0.001,(0.61+0.063*u10n)*0.001)
elif (method == "LP82"):
cdn = np.where((u10n < 11) & (u10n>=4),1.2*0.001,np.where((u10n<=25) & (u10n>=11),(0.49+0.065*u10n)*0.001,1.14*0.001))
elif (method == "Smith88" or method == "COARE3.0" or method == "COARE4.0"):
cdn = cdn_from_roughness(u10n,Ta,None, method)
elif (method == "HEXOS"):
cdn = (0.5+0.091*u10n)*0.001 #Smith et al. 1991 #(0.27 + 0.116*u10n)*0.001 Smith et al. 1992
elif (method == "HEXOSwave"):
cdn=cdn_from_roughness(u10n,Ta,Tp, method)
elif (method == "YT96"):
cdn = np.where((u10n<6) & (u10n>=3),(0.29 + 3.1/u10n + 7.7/u10n**2)*0.001,np.where((u10n<=26) & (u10n>=6),(0.60 + 0.070*u10n)*0.001,(0.61+0.567/u10n)*0.001)) # for u<3 same as Smith80
elif (method == "LY04"):
cdn = np.where(u10n>=0.5,(0.142 + (2.7/u10n) + (u10n/13.09))*0.001,np.nan)
else:
print("unknown method cdn: "+method)
return cdn
#---------------------------------------------------------------------
def cdn_from_roughness(u10n,Ta,Tp,method="Smith88"):
g,tol = 9.812, 0.000001
cdn,ustar = np.zeros(np.asarray(u10n).shape),np.zeros(np.asarray(u10n).shape)
cdnn = (0.61 + 0.063 * u10n) * 0.001
zo,zc,zs=np.zeros(np.asarray(u10n).shape),np.zeros(np.asarray(u10n).shape),np.zeros(np.asarray(u10n).shape)
for it in range(5):
cdn = np.copy(cdnn)
ustar = np.sqrt(cdn*u10n**2)
if (method == "Smith88"):
zc = 0.011*ustar**2/g #.....Charnock roughness length (equn 4 in Smith 88)
zs = 0.11*visc_air(Ta)/ustar #.....smooth surface roughness length (equn 6 in Smith 88)
zo = zc + zs #.....equns 7 & 8 in Smith 88 to calculate new CDN
elif (method == "COARE3.0"):
zc = 0.011 + (u10n-10)/(18-10)*(0.018-0.011)
zc=np.where(u10n<10,0.011,np.where(u10n>18,0.018,zc))
zs = 0.11 * visc_air(Ta)/ ustar
zo = zc*ustar*ustar/g + zs
elif (method == "HEXOSwave"):
if (np.all(Tp==None) or np.nansum(Tp)==0):
Tp = 0.729*u10n # Taylor and Yelland 2001
cp_wave = g*Tp/2/np.pi # use input wave period
zo = 0.48*ustar**3/g/cp_wave # Smith et al. 1992
else:
print("unknown method for cdn_from_roughness "+method)
cdnn = (kappa/np.log(10/zo))**2
cdn=np.where(np.abs(cdnn-cdn) < tol, cdnn,np.nan)
return cdnn
#---------------------------------------------------------------------
def ctcqn_calc(zol, cdn, u10n, zo,Ta, method="Smith80"):
l = np.shape(u10n)
if (method == "Smith80" or method == "Smith88" or method == "YT96"):
cqn = np.ones(l)*1.20*0.001 # from Smith88, no value given by S80 or YT80
ctn = np.ones(l)*1.00*0.001
elif (method == "LP82"):
cqn = np.where((zol <= 0) & (u10n>4) & (u10n<14),1.15*0.001,np.nan)
ctn = np.where((zol <= 0) & (u10n>4) & (u10n<25), 1.13*0.001, 0.66*0.001)
elif (method == "HEXOS" or method == "HEXOSwave"):
cqn = np.where((u10n<=23) & (u10n>=3),1.1*0.001,np.nan)
ctn = np.where((u10n<=18) & (u10n>=3),1.1*0.001,np.nan)
elif (method == "COARE3.0" or method == "COARE4.0"):
ustar = (cdn * u10n**2)**0.5
rr = zo*ustar/visc_air(Ta)
zoq = 5.5e-5/rr**0.6
zoq[zoq>1.15e-4] = 1.15e-4
zot = zoq
cqn = kappa**2/np.log(10/zo)/np.log(10/zoq)
ctn = kappa**2/np.log(10/zo)/np.log(10/zot)
elif (method == "LY04"):
cqn = 34.6*0.001*cdn**0.5
ctn = np.where(zol <= 0, 32.7*0.001*cdn**0.5, 18*0.001*cdn**0.5)
else:
print("unknown method ctcqn: "+method)
return ctn, cqn
#---------------------------------------------------------------------
def cd_calc(cdn, height, ref_ht, psim):
cd = cdn*np.power(1+np.sqrt(cdn)*np.power(kappa,-1)*(np.log(height/ref_ht)-psim),-2)
return cd
#---------------------------------------------------------------------
def ctcq_calc(cdn, cd, ctn, cqn, h_t, h_q, ref_ht, psit, psiq):
ct = ctn*(cd/cdn)**0.5/(1+ctn*((np.log(h_t/ref_ht)-psit)/(kappa*cdn**0.5)))
cq = cqn*(cd/cdn)**0.5/(1+cqn*((np.log(h_q/ref_ht)-psiq)/(kappa*cdn**0.5)))
return ct, cq
#---------------------------------------------------------------------
def psim_calc(zol, method="Smith80"):
coeffs = get_stabco(method)
alpha, beta, gamma = coeffs[0], coeffs[1], coeffs[2]
if (method == "COARE3.0" or method == "COARE4.0"):
psim = np.where(zol<0,psim_conv_coare3(zol,alpha,beta,gamma),psim_stab_coare3(zol,alpha,beta,gamma))
else:
psim = np.where(zol<0,psim_conv(zol,alpha,beta,gamma),psim_stab(zol,alpha,beta,gamma))
return psim
#---------------------------------------------------------------------
def psit_calc(zol, method="Smith80"):
coeffs = get_stabco(method)
alpha, beta, gamma = coeffs[0], coeffs[1], coeffs[2]
if (method == "COARE3.0" or method == "COARE4.0"):
psit = np.where(zol<0,psi_conv_coare3(zol,alpha,beta,gamma),psi_stab_coare3(zol,alpha,beta,gamma))
else:
psit = np.where(zol<0,psi_conv(zol,alpha,beta,gamma),psi_stab(zol,alpha,beta,gamma))
return psit
#---------------------------------------------------------------------
def get_stabco(method="Smith80"):
if (method == "Smith80" or method == "Smith88" or method == "LY04"):
# Smith 1980, from Dyer (1974)
alpha, beta, gamma = 16, 0.25, 5
elif (method == "LP82"):
alpha, beta, gamma = 16, 0.25, 7
elif (method == "HEXOS" or method == "HEXOSwave"):
alpha, beta, gamma = 16, 0.25, 8
elif (method == "YT96"):
alpha, beta, gamma = 20, 0.25, 5
elif (method == "COARE3.0" or method == "COARE4.0"):
# use separate subroutine
alpha, beta, gamma = 15, 1/3, 5 # not sure about gamma=34.15
#alpha <- NA #beta <- NA
else:
print("unknown method stabco: "+method)
coeffs = np.zeros(3)
coeffs[0] = alpha
coeffs[1] = beta
coeffs[2] = gamma
return coeffs
#---------------------------------------------------------------------
#======================================================================
def psi_conv_coare3(zol,alpha,beta,gamma):
x = (1-alpha*zol)**0.5 # Kansas unstable
psik = 2*np.log((1+x)/2.)
y = (1-34.15*zol)**beta
psic = 1.5*np.log((1+y+y*y)/3.)-(3)**0.5*np.arctan((1+2*y)/
(3)**0.5)+4*np.arctan(1)/(3)**0.5
f = zol*zol/(1.+zol*zol)
psit = (1-f)*psik+f*psic
return psit
#======================================================================
def psi_stab_coare3(zol,alpha,beta,gamma): #Stable
c = np.where(0.35*zol > 50, 50, 0.35*zol) #Stable
psit = -((1+2*zol/3)**1.5+0.6667*(zol-14.28)/np.exp(c)+8.525)
return psit
#======================================================================
def psi_conv(zol,alpha,beta,gamma):
xtmp = (1 - alpha*zol)**beta
psit = 2*np.log((1+xtmp**2)*0.5)
return psit
#======================================================================
def psi_stab(zol,alpha,beta,gamma):
psit = -gamma*zol
return psit
#======================================================================
def psim_conv_coare3(zol,alpha,beta,gamma):
x = (1-15*zol)**0.25 #Kansas unstable
psik = 2*np.log((1+x)/2)+np.log((1+x*x)/2)-2*np.arctan(x)+2*np.arctan(1)
y = (1-10.15*zol)**0.3333 #Convective
psic = 1.5*np.log((1+y+y*y)/3.)-np.sqrt(3)*np.arctan((1+2*y)/np.sqrt(3))+4.*np.arctan(1)/np.sqrt(3)
f = zol*zol/(1+zol*zol)
psim = (1-f)*psik+f*psic
return psim
#======================================================================
def psim_stab_coare3(zol,alpha,beta,gamma):
c = np.where(0.35*zol > 50, 50, 0.35*zol) #Stable
psim = -((1+1*zol)**1.0+0.6667*(zol-14.28)/np.exp(-c)+8.525)
return psim
#======================================================================
def psim_conv(zol,alpha,beta,gamma):
xtmp = (1 - alpha*zol)**beta
psim = 2*np.log((1+xtmp)*0.5)+np.log((1+xtmp**2)*0.5)-2*np.arctan(xtmp)+np.pi/2
return psim
#======================================================================
def psim_stab(zol,alpha,beta,gamma):
psim = -gamma*zol
return psim
#======================================================================
#---------------------------------------------------------------------
def get_skin(sst,qsea,rho,jcool,Rl,Rs,Rnl,cp,lv,usr,tsr,qsr,lat):
# coded following Saunders (1967) with lambda = 6
g=gc(lat,None)
if ( np.nanmin(sst) > 200 ): # if Ta in Kelvin convert to Celsius
sst = sst-273.16
#************ cool skin constants *******
rhow, cpw, visw, tcw = 1022, 4000, 1e-6, 0.6 # density of water, specific heat capacity of water, water viscosity, thermal conductivity of water
Al = 2.1e-5*(sst+3.2)**0.79
be = 0.026
bigc = 16*g*cpw*(rhow*visw)**3/(tcw*tcw*rho*rho)
wetc = 0.622*lv*qsea/(287.1*(sst+273.16)**2)
Rns = 0.945*Rs # albedo correction
hsb=-rho*cp*usr*tsr
hlb=-rho*lv*usr*qsr
qout=Rnl+hsb+hlb
tkt = 0.001*np.ones(np.shape(sst))
dels=Rns*(0.065+11*tkt-6.6e-5/tkt*(1-np.exp(-tkt/8.0e-4)))
qcol=qout-dels
alq=Al*qcol+be*hlb*cpw/lv
xlamx=np.where(alq>0,6/(1+(bigc*alq/usr**4)**0.75)**0.333,6)
tkt=xlamx*visw/(np.sqrt(rho/rhow)*usr) #np.nanmin(0.01, xlamx*visw/(np.sqrt(rhoa/rhow)*usr))
tkt=np.where(alq>0,np.where(tkt > 0.01, 0.01,tkt),tkt)
dter=qcol*tkt/tcw
dqer=wetc*dter
return dter, dqer
#---------------------------------------------------------------------
def get_gust(Ta,usr,tsrv,zi,lat):
if (np.max(Ta)<200): # convert to K if in Celsius
Ta=Ta+273.16
if np.isnan(zi):
zi = 600
g=gc(lat,None)
Bf=-g/Ta*usr*tsrv
ug=np.ones(np.shape(Ta))*0.2
ug=np.where(Bf>0,1.2*(Bf*zi)**0.333,0.2)
return ug
#---------------------------------------------------------------------
def get_heights(h):
hh=np.zeros(3)
if type(h) == float or type(h) == int:
hh[0], hh[1], hh[2] = h, h, h
elif len(h)==2:
hh[0], hh[1], hh[2] = h[0], h[1], h[1]
else:
hh[0], hh[1], hh[2] = h[0], h[1], h[2]
return hh
#---------------------------------------------------------------------
def svp_calc(T):
# t is in Kelvin
# svp in mb, pure water
if ( np.nanmin(T) < 200 ): # if T in Celsius convert to Kelvin
T = T+273.16
svp = np.where(np.isnan(T), np.nan,2.1718e08*np.exp(-4157/(T-33.91-0.16)))
return svp
#---------------------------------------------------------------------
def qsea_calc(sst,pres):
# sst in Kelvin
# pres in mb
# qsea in kg/kg
if ( np.nanmin(sst) < 200 ): # if sst in Celsius convert to Kelvin
sst = sst+273.16
ed = svp_calc(sst)
e = 0.98*ed
qsea = (0.622*e)/(pres-0.378*e)
qsea = np.where(~np.isnan(sst+pres),qsea,np.nan)
return qsea
#---------------------------------------------------------------------
def rh_calc(Ta,qair,pres):
if ( np.nanmin(Ta) < 200 ): # if sst in Celsius convert to Kelvin
Ta = Ta+273.16
e = np.where(np.isnan(Ta+qair+pres),np.nan,(qair*pres)/(0.62197+qair*0.378))
ed = np.where(np.isnan(e),np.nan,svp_calc(Ta))
rh = np.where(np.isnan(ed),np.nan,e/ed*100)
return rh
#---------------------------------------------------------------------
def q_calc(Ta,rh,pres):
# rh in %
# air in K, if not it will be converted to K
# pres in mb
# qair in kg/kg
if ( np.nanmin(Ta) < 200 ): # if sst in Celsius convert to Kelvin
Ta = Ta+273.15
e = np.where(np.isnan(Ta+rh+pres),np.nan,svp_calc(Ta)*rh*0.01)
qair = np.where(np.isnan(e),np.nan,((0.62197*e)/(pres-0.378*e))) # Haltiner and Martin p.24
return qair
#---------------------------------------------------------------------
def gc(lat,lon=None):
"""
computes gravity relative to latitude
inputs:
lat : latitudes in deg
lon : longitudes (optional)
output:
gc: gravity constant
"""
gamma = 9.7803267715
c1 = 0.0052790414
c2 = 0.0000232718
c3 = 0.0000001262
c4 = 0.0000000007
if lon is not None:
lon_m,lat_m = np.meshgrid(lon,lat)
else:
lat_m = lat
phi = lat_m*np.pi/180.
xx = np.sin(phi)
gc = gamma*(1+c1*np.power(xx,2)+c2*np.power(xx,4)+c3*np.power(xx,6)+c4*np.power(xx,8))
return gc
#---------------------------------------------------------------------
def PtoDepth(p,Lat):
"""
computes depth in m from pressure in db following
Saunders and Fofonoff (1976). Deep sea res.
"""
x=math.sin(math.radians(Lat))
x=x*x
# gravity variation with latitude (Anon, 1970)
gr = 9.780318 * (1 + (5.2788E-3 + 2.36E-5 * x) * x) + 1.092E-6 * p
d = (((-1.82E-15 * p + 2.279E-10) * p - 2.2512E-5) * p + 9.72659) * p;
depth = d/gr
return depth
#---------------------------------------------------------------------
def visc_air(Ta):
"""
Computes the kinematic viscosity of dry air as a function of air temperature
following Andreas (1989), CRREL Report 89-11.
input:
Ta : air temperature [Celsius]
output
visa : kinematic viscosity [m^2/s]
"""
Ta = np.asarray(Ta)
if ( np.nanmin(Ta) > 200 ): # if Ta in Kelvin convert to Celsius
Ta = Ta-273.16
visa = 1.326e-5 * (1 + 6.542e-3*Ta + 8.301e-6*Ta**2 - 4.84e-9*Ta**3)
return visa
######
# functions from coare35vn.mat
######
#------------------------------------------------------------------------------
def psit_26(zet):
"""
computes temperature structure function
"""
dzet= np.where(0.35*zet > 50, 50, 0.35*zet) # stable
psi=-((1+0.6667*zet)**1.5+0.6667*(zet-14.28)*np.exp(-dzet)+8.525)
k=np.where(zet<0) # unstable
x=(1-15*zet[k])**0.5
psik=2*np.log((1+x)/2)
x=(1-34.15*zet[k])**0.3333
psic=1.5*np.log((1+x+x**2)/3)-np.sqrt(3)*np.arctan((1+2*x)/np.sqrt(3))+4*np.arctan(1)/np.sqrt(3)
f=zet[k]**2/(1+zet[k]**2)
psi[k]=(1-f)*psik+f*psic
return psi
#------------------------------------------------------------------------------
def psiu_26(zet):
"""
computes velocity structure function
"""
dzet=np.where(0.35*zet > 50, 50, 0.35*zet) # stable
a, b, c, d= 0.7, 3/4, 5, 0.35
psi=-(a*zet+b*(zet-c/d)*np.exp(-dzet)+b*c/d)
k=np.where(zet<0) # unstable
x=(1-15*zet[k])**0.25
psik=2*np.log((1+x)/2)+np.log((1+x**2)/2)-2*np.arctan(x)+2*np.arctan(1)
x=(1-10.15*zet[k])**0.3333
psic=1.5*np.log((1+x+x**2)/3)-np.sqrt(3)*np.arctan((1+2*x)/np.sqrt(3))+4*np.arctan(1)/np.sqrt(3)
f=zet[k]**2/(1+zet[k]**2)
psi[k]=(1-f)*psik+f*psic
return psi
#------------------------------------------------------------------------------
def psiu_40(zet):
"""
computes velocity structure function
"""
dzet=np.where(0.35*zet > 50, 50, 0.35*zet) # stable
a, b, c, d= 1, 3/4, 5, 0.35
psi=-(a*zet+b*(zet-c/d)*np.exp(-dzet)+b*c/d)
k=np.where(zet<0) # unstable
x=(1-18*zet[k])**0.25
psik=2*np.log((1+x)/2)+np.log((1+x**2)/2)-2*np.arctan(x)+2*np.arctan(1)
x=(1-10*zet[k])**0.3333
psic=1.5*np.log((1+x+x**2)/3)-np.sqrt(3)*np.arctan((1+2*x)/np.sqrt(3))+4*np.arctan(1)/np.sqrt(3)
f=zet[k]**2/(1+zet[k]**2)
psi[k]=(1-f)*psik+f*psic
return psi
#------------------------------------------------------------------------------
def bucksat(T,P):
"""
computes saturation vapor pressure [mb]
given T [degC] and P [mb]
"""
T = np.asarray(T)
if ( np.nanmin(T) > 200 ): # if Ta in Kelvin convert to Celsius
T = T-CtoK
exx=6.1121*np.exp(17.502*T/(T+240.97))*(1.0007+3.46e-6*P)
return exx
#------------------------------------------------------------------------------
def qsat26sea(T,P):
"""
computes surface saturation specific humidity [g/kg]
given T [degC] and P [mb]
"""
T = np.asarray(T)
if ( np.nanmin(T) > 200 ): # if Ta in Kelvin convert to Celsius
T = T-CtoK
ex=bucksat(T,P)
es=0.98*ex # reduction at sea surface
qs=622*es/(P-0.378*es)
return qs
#------------------------------------------------------------------------------
def qsat26air(T,P,rh):
"""
computes saturation specific humidity [g/kg]
given T [degC] and P [mb]
"""
T = np.asarray(T)
if ( np.nanmin(T) > 200 ): # if Ta in Kelvin convert to Celsius
T = T-CtoK
es=bucksat(T,P)
em=0.01*rh*es
q=622*em/(P-0.378*em)
return q,em
#------------------------------------------------------------------------------
def RHcalc(T,P,Q):
"""
computes relative humidity given T,P, & Q
"""
es=6.1121*np.exp(17.502*T/(T+240.97))*(1.0007+3.46e-6*P)
em=Q*P/(0.378*Q+0.622)
RHrf=100*em/es
return RHrf