diff --git a/flux_subs.py b/flux_subs.py
index 113d9c83d8abb079a2aed102803061a8c9aaa57d..adc074d198d3b319ac484458aa737e628575e9e5 100755
--- a/flux_subs.py
+++ b/flux_subs.py
@@ -1,163 +1,218 @@
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))))
+
+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
+ charn = charnS
else:
- charn=charnW
+ charn = charnW
else:
- charn=charnC
- ac = np.zeros((len(wind),3))
- ac[:,0] = charn
- ac[:,1] = charnS
- ac[:,2] = charnW
+ 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"):
+# ---------------------------------------------------------------------
+
+
+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)
+ # These thermal roughness lengths give Stanton and
+ zoq = np.where(5.8e-5/rr**0.72 > 1.6e-4, 1.6e-4, 5.8e-5/rr**0.72)
+ 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)
+ 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)
+ 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" or method == "UA" or method == "ERA5"):
+ 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
+ # Smith et al. 1991 #(0.27 + 0.116*u10n)*0.001 Smith et al. 1992
+ cdn = (0.5+0.091*u10n)*0.001
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
+ cdn = cdn_from_roughness(u10n, Ta, Tp, method)
+ elif (method == "YT96"):
+ # for u<3 same as Smith80
+ 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))
elif (method == "LY04"):
- cdn = np.where(u10n>=0.5,(0.142 + (2.7/u10n) + (u10n/13.09))*0.001,np.nan)
+ 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)
+# ---------------------------------------------------------------------
+
+
+def cdn_from_roughness(u10n, Ta, Tp, method="Smith88"):
+ g, tol = 9.812, 0.000001
+ cdn, usr = np.zeros(Ta.shape), np.zeros(Ta.shape)
+ cdnn = (0.61+0.063*u10n)*0.001
+ zo, zc, zs = np.zeros(Ta.shape), np.zeros(Ta.shape), np.zeros(Ta.shape)
for it in range(5):
cdn = np.copy(cdnn)
- ustar = np.sqrt(cdn*u10n**2)
+ usr = 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
+ # .....Charnock roughness length (equn 4 in Smith 88)
+ zc = 0.011*np.power(usr, 2)/g
+ # .....smooth surface roughness length (equn 6 in Smith 88)
+ zs = 0.11*visc_air(Ta)/usr
+ 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
+ zc = np.where(u10n < 10, 0.011, np.where(u10n > 18, 0.018, zc))
+ zs = 0.11*visc_air(Ta)/usr
+ zo = zc*np.power(usr, 2)/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
+ if ((Tp is 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*np.power(usr, 3)/g/cp_wave # Smith et al. 1992
+ elif (method == "UA"):
+ # valid for 0<u<18m/s # Zeng et al. 1998 (24)
+ zo = 0.013*np.power(usr, 2)/g+0.11*visc_air(Ta)/usr
+ elif (method == "ERA5"):
+ # eq. (3.26) p.40 over sea IFS Documentation cy46r1
+ zo = 0.11*visc_air(Ta)/usr+0.018*np.power(usr, 2)/g
else:
- print("unknown method for cdn_from_roughness "+method)
+ 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)
-
+ 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)
+
+def ctcqn_calc(zol, cdn, u10n, zo, Ta, method="Smith80"):
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
+ cqn = np.ones(Ta.shape)*1.20*0.001 # from Smith88
+ ctn = np.ones(Ta.shape)*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)
+ 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)
+ 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)
+ usr = (cdn*u10n**2)**0.5
+ rr = zo*usr/visc_air(Ta)
zoq = 5.5e-5/rr**0.6
- zoq[zoq>1.15e-4] = 1.15e-4
+ 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)
+ elif (method == "UA"):
+ usr = (cdn * u10n**2)**0.5
+ # Zeng et al. 1998 (25)
+ zoq = zo*np.exp(-(2.67*np.power(usr*zo/visc_air(Ta), 1/4)-2.57))
+ zot = zoq
+ cqn = np.where((u10n > 0.5) & (u10n < 18), np.power(kappa, 2) /
+ (np.log(10/zo)*np.log(10/zoq)), np.nan)
+ ctn = np.where((u10n > 0.5) & (u10n < 18), np.power(kappa, 2) /
+ (np.log(10/zo)*np.log(10/zoq)), np.nan)
+ elif (method == "ERA5"):
+ # eq. (3.26) p.40 over sea IFS Documentation cy46r1
+ usr = np.sqrt(cdn*np.power(u10n, 2))
+ zot = 0.40*visc_air(Ta)/usr
+ zoq = 0.62*visc_air(Ta)/usr
+ cqn = kappa**2/np.log(10/zo)/np.log(10/zoq)
+ ctn = kappa**2/np.log(10/zo)/np.log(10/zot)
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)
+ 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"):
+# ---------------------------------------------------------------------
+
+
+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))
+ psim = np.where(zol < 0, psim_conv_coare3(zol, alpha, beta, gamma),
+ psim_stab_coare3(zol, alpha, beta, gamma))
+ elif (method == "ERA5"):
+ psim = np.where(zol < 0, psim_conv(zol, alpha, beta, gamma),
+ psim_stab_era5(zol, alpha, beta, gamma))
else:
- psim = np.where(zol<0,psim_conv(zol,alpha,beta,gamma),psim_stab(zol,alpha,beta,gamma))
-
+ 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))
+ psit = np.where(zol < 0, psi_conv_coare3(zol, alpha, beta, gamma),
+ psi_stab_coare3(zol, alpha, beta, gamma))
+ elif (method == "ERA5"):
+ psit = np.where(zol < 0, psi_conv(zol, alpha, beta, gamma),
+ psi_stab_era5(zol, alpha, beta, gamma))
else:
- psit = np.where(zol<0,psi_conv(zol,alpha,beta,gamma),psi_stab(zol,alpha,beta,gamma))
-
+ 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
+ if (method == "Smith80" or method == "Smith88" or method == "LY04" or
+ method == "UA" or method == "ERA5"):
+ alpha, beta, gamma = 16, 0.25, 5 # Smith 1980, from Dyer (1974)
elif (method == "LP82"):
- alpha, beta, gamma = 16, 0.25, 7
+ alpha, beta, gamma = 16, 0.25, 7
elif (method == "HEXOS" or method == "HEXOSwave"):
alpha, beta, gamma = 16, 0.25, 8
elif (method == "YT96"):
@@ -165,157 +220,295 @@ def get_stabco(method="Smith80"):
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)
+ 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
+# ---------------------------------------------------------------------
+
+
+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
+ 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
+ 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_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)
+# ---------------------------------------------------------------------
+
+
+def psi_stab_era5(zol, alpha, beta, gamma):
+ # eq (3.22) p. 39 IFS Documentation cy46r1
+ a, b, c, d = 1, 2/3, 5, 0.35
+ psit = -b*(zol-c/d)*np.exp(-d*zol)-np.power(1+(2/3)*a*zol, 1.5)-(b*c)/d+1
return psit
-#======================================================================
-def psi_conv(zol,alpha,beta,gamma):
- xtmp = (1 - alpha*zol)**beta
- psit = 2*np.log((1+xtmp**2)*0.5)
+# ---------------------------------------------------------------------
+
+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
+# ---------------------------------------------------------------------
+
+
+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
+# ---------------------------------------------------------------------
+
+
+def psit_26(zet):
+ """
+ computes temperature structure function as in COARE3.5
+ """
+ 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 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)
+ 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
+# ---------------------------------------------------------------------
+
+
+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
+# ---------------------------------------------------------------------
+
+
+def psim_stab_era5(zol, alpha, beta, gamma):
+ # eq (3.22) p. 39 IFS Documentation cy46r1
+ a, b, c, d = 1, 2/3, 5, 0.35
+ psim = -b*(zol-c/d)*np.exp(-d*zol)-a*zol-(b*c)/d
+ 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
+# ---------------------------------------------------------------------
+
+
+def psim_stab(zol, alpha, beta, gamma):
+ psim = -gamma*zol
+ return psim
+# ---------------------------------------------------------------------
+
+
+def psiu_26(zet):
+ """
+ computes velocity structure function COARE3.5
+ """
+ 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 COARE3.5
+ """
+ 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 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
-#---------------------------------------------------------------------
+ # ************ cool skin constants *******
+ # density of water, specific heat capacity of water, water viscosity,
+ # thermal conductivity of water
+ rhow, cpw, visw, tcw = 1022, 4000, 1e-6, 0.6
+ 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)
+ 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(beta, 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, beta*np.power(Bf*zi, 1/3), 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]
+ 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]
+ 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
+ """
+ calculates saturation vapour pressure
+ 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):
+ 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 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, as in Haltiner and Martin p.24
+ """
+ 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)))
+ return qair
+# ------------------------------------------------------------------------------
+
+
+def bucksat(T, P):
+ """
+ computes saturation vapor pressure [mb] as in COARE3.5
+ 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] as in COARE3.5
+ 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] as in COARE3.5
+ 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 gc(lat, lon=None):
"""
computes gravity relative to latitude
inputs:
@@ -330,31 +523,20 @@ def gc(lat,lon=None):
c3 = 0.0000001262
c4 = 0.0000000007
if lon is not None:
- lon_m,lat_m = np.meshgrid(lon,lat)
+ 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))
+ 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
+ Computes the kinematic viscosity of dry air as a function of air temp.
following Andreas (1989), CRREL Report 89-11.
input:
Ta : air temperature [Celsius]
@@ -362,104 +544,7 @@ def visc_air(Ta):
visa : kinematic viscosity [m^2/s]
"""
Ta = np.asarray(Ta)
- if ( np.nanmin(Ta) > 200 ): # if Ta in Kelvin convert to Celsius
+ 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
\ No newline at end of file