diff --git a/flux_subs.py b/flux_subs.py
index 780de7339a48de26f084e205373c0c394859b07c..e59dd282a35056df45fcd4c033a3d356781c6394 100755
--- a/flux_subs.py
+++ b/flux_subs.py
@@ -8,107 +8,9 @@ kappa = 0.4 # NOTE: 0.41
# ---------------------------------------------------------------------
-def charnock_C35(wind, u10n, usr, seastate, waveage, wcp, sigH, lat):
- """ Calculates Charnock number following Edson et al. 2013 based on
- C35 matlab code (coare35vn.m)
-
- Parameters
- ----------
- wind : float
- wind speed (m/s)
- u10n : float
- neutral 10m wind speed (m/s)
- usr : float
- friction velocity (m/s)
- seastate : bool
- 0 or 1
- waveage : bool
- 0 or 1
- wcp : float
- phase speed of dominant waves (m/s)
- sigH : float
- significant wave height (m)
- lat : float
- latitude (deg)
-
- Returns
- -------
- ac : float
- Charnock number
- """
- 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):
- """ Calculates exchange coefficients following Edson et al. 2013 based on
- C35 matlab code (coare35vn.m)
-
- Parameters
- ----------
- u10n : float
- neutral 10m wind speed (m/s)
- wind : float
- wind speed (m/s)
- charn : float
- Charnock number
- monob : float
- Monin-Obukhov stability length
- Ta : float
- air temperature (K)
- hh_in : float
- input sensor's height (m)
- lat : float
- latitude (deg)
-
- Returns
- -------
- zo : float
- surface roughness (m)
- cdhf : float
- drag coefficient
- cthf : float
- heat exchange coefficient
- cqhf : float
- moisture exchange coefficient
- """
- 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="S80"):
+def cdn_calc(u10n, Ta, Tp, lat, meth="S80"):
""" Calculates neutral drag coefficient
-
+
Parameters
----------
u10n : float
@@ -117,39 +19,40 @@ def cdn_calc(u10n, Ta, Tp, method="S80"):
air temperature (K)
Tp : float
wave period
- method : str
-
+ meth : str
+
Returns
-------
cdn : float
"""
- if (method == "S80"):
+ if (meth == "S80"):
cdn = np.where(u10n <= 3, (0.61+0.567/u10n)*0.001,
(0.61+0.063*u10n)*0.001)
- elif (method == "LP82"):
+ elif (meth == "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 == "S88" or method == "UA" or method == "ERA5"):
- cdn = cdn_from_roughness(u10n, Ta, None, method)
- elif (method == "YT96"):
+ elif (meth == "S88" or meth == "UA" or meth == "ERA5" or meth == "C30" or
+ meth == "C35" or meth == "C40"):
+ cdn = cdn_from_roughness(u10n, Ta, None, lat, meth)
+ elif (meth == "YT96"):
# for u<3 same as S80
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"):
+ elif (meth == "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)
+ print("unknown method cdn: "+meth)
return cdn
# ---------------------------------------------------------------------
-def cdn_from_roughness(u10n, Ta, Tp, method="S88"):
+def cdn_from_roughness(u10n, Ta, Tp, lat, meth="S88"):
""" Calculates neutral drag coefficient from roughness length
-
+
Parameters
----------
u10n : float
@@ -158,42 +61,59 @@ def cdn_from_roughness(u10n, Ta, Tp, method="S88"):
air temperature (K)
Tp : float
wave period
- method : str
-
+ meth : str
+
Returns
-------
cdn : float
"""
- g, tol = 9.812, 0.000001
+ g, tol = gc(lat, None), 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)
usr = np.sqrt(cdn*u10n**2)
- if (method == "S88"):
+ if (meth == "S88"):
# .....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 == "UA"):
+ elif (meth == "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"):
+ elif (meth == "C30"):
+ a = 0.011*np.ones(Ta.shape)
+ a = np.where(u10n > 10, 0.011+(u10n-10)/(18-10)*(0.018-0.011),
+ np.where(u10n > 18, 0.018, a))
+ zo = a*np.power(usr, 2)/g+0.11*visc_air(Ta)/usr
+ elif (meth == "C35"):
+ a = 0.011*np.ones(Ta.shape)
+ a = np.where(u10n > 18, 0.0017*19-0.0050,
+ np.where((u10n > 7) & (u10n <= 18),
+ 0.0017*u10n-0.0050, a))
+# 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))))
+ zo = 0.11*visc_air(Ta)/usr+a*np.power(usr, 2)/g
+ elif (meth == "C40"):
+ a = 0.011*np.ones(Ta.shape)
+ a = np.where(u10n > 22, 0.0016*22-0.0035, 0.0016*u10n-0.0035)
+ zo = a*np.power(usr, 2)/g+0.11*visc_air(Ta)/usr # surface roughness
+ elif (meth == "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 "+meth)
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="S80"):
+def ctcqn_calc(zol, cdn, u10n, zo, Ta, meth="S80"):
""" Calculates neutral heat and moisture exchange coefficients
-
+
Parameters
----------
zol : float
@@ -206,8 +126,8 @@ def ctcqn_calc(zol, cdn, u10n, zo, Ta, method="S80"):
surface roughness (m)
Ta : float
air temperature (K)
- method : str
-
+ meth : str
+
Returns
-------
ctn : float
@@ -215,27 +135,57 @@ def ctcqn_calc(zol, cdn, u10n, zo, Ta, method="S80"):
cqn : float
neutral moisture exchange coefficient
"""
- if (method == "S80" or method == "S88" or method == "YT96"):
+ if (meth == "S80" or meth == "S88" or meth == "YT96"):
cqn = np.ones(Ta.shape)*1.20*0.001 # from S88
ctn = np.ones(Ta.shape)*1.00*0.001
- elif (method == "LP82"):
+ elif (meth == "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 == "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
+ elif (meth == "LY04"):
+ cqn = 34.6*0.001*np.sqrt(cdn)
+ ctn = np.where(zol <= 0, 32.7*0.001*np.sqrt(cdn), 18*0.001*np.sqrt(cdn))
+ elif (meth == "UA"):
+ usr = np.sqrt(cdn*np.power(u10n, 2))
# Zeng et al. 1998 (25)
- zoq = zo*np.exp(-(2.67*np.power(usr*zo/visc_air(Ta), 1/4)-2.57))
+ re=usr*zo/visc_air(Ta)
+ zoq = zo/np.exp(2.67*np.power(re, 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"):
+ elif (meth == "C30"):
+ usr = np.sqrt(cdn*np.power(u10n, 2))
+ rr = zo*usr/visc_air(Ta)
+ zoq = np.where(5e-5/np.power(rr, 0.6) > 1.15e-4, 1.15e-4,
+ 5e-5/np.power(rr, 0.6)) # moisture roughness
+ zot=zoq # temperature roughness
+ cqn = kappa**2/np.log(10/zo)/np.log(10/zoq)
+ ctn = kappa**2/np.log(10/zo)/np.log(10/zot)
+ elif (meth == "C35"):
+ usr = np.sqrt(cdn*np.power(u10n, 2))
+ rr = zo*usr/visc_air(Ta)
+ zoq = np.where(5.8e-5/np.power(rr, 0.72) > 1.6e-4, 1.6e-4,
+ 5.8e-5/np.power(rr, 0.72)) # moisture roughness
+ zot=zoq # temperature roughness
+ cqn = kappa**2/np.log(10/zo)/np.log(10/zoq)
+ ctn = kappa**2/np.log(10/zo)/np.log(10/zot)
+ elif (meth == "C40"):
+ usr = np.sqrt(cdn*np.power(u10n, 2))
+ rr = zo*usr/visc_air(Ta)
+ zot = np.where(1.0e-4/np.power(rr, 0.55) > 2.4e-4/np.power(rr, 1.2),
+ 2.4e-4/np.power(rr, 1.2),
+ 1.0e-4/np.power(rr, 0.55)) # temperature roughness
+ zoq = np.where(2.0e-5/np.power(rr,0.22) > 1.1e-4/np.power(rr,0.9),
+ 1.1e-4/np.power(rr,0.9), 2.0e-5/np.power(rr,0.22))
+ # moisture roughness determined by the CLIMODE, GASEX and CBLAST data
+# zoq = np.where(5e-5/np.power(rr, 0.6) > 1.15e-4, 1.15e-4,
+# 5e-5/np.power(rr, 0.6)) # moisture roughness as in C30
+ cqn = kappa**2/np.log(10/zo)/np.log(10/zoq)
+ ctn = kappa**2/np.log(10/zo)/np.log(10/zot)
+ elif (meth == "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
@@ -243,14 +193,14 @@ def ctcqn_calc(zol, cdn, u10n, zo, Ta, method="S80"):
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)
+ print("unknown method ctcqn: "+meth)
return ctn, cqn
# ---------------------------------------------------------------------
def cd_calc(cdn, height, ref_ht, psim):
""" Calculates drag coefficient at reference height
-
+
Parameters
----------
cdn : float
@@ -261,7 +211,7 @@ def cd_calc(cdn, height, ref_ht, psim):
reference height (m)
psim : float
momentum stability function
-
+
Returns
-------
cd : float
@@ -274,7 +224,7 @@ def cd_calc(cdn, height, ref_ht, psim):
def ctcq_calc(cdn, cd, ctn, cqn, h_t, h_q, ref_ht, psit, psiq):
""" Calculates heat and moisture exchange coefficients at reference height
-
+
Parameters
----------
cdn : float
@@ -295,7 +245,7 @@ def ctcq_calc(cdn, cd, ctn, cqn, h_t, h_q, ref_ht, psit, psiq):
heat stability function
psiq : float
moisture stability function
-
+
Returns
-------
ct : float
@@ -307,24 +257,26 @@ def ctcq_calc(cdn, cd, ctn, cqn, h_t, h_q, ref_ht, psit, psiq):
# ---------------------------------------------------------------------
-def psim_calc(zol, method="S80"):
+def psim_calc(zol, meth="S80"):
""" Calculates momentum stability function
-
+
Parameters
----------
zol : float
height over MO length
- method : str
-
+ meth : str
+
Returns
-------
psim : float
"""
- coeffs = get_stabco(method)
+ coeffs = get_stabco(meth)
alpha, beta, gamma = coeffs[0], coeffs[1], coeffs[2]
- if (method == "ERA5"):
+ if (meth == "ERA5"):
psim = np.where(zol < 0, psim_conv(zol, alpha, beta, gamma),
psim_stab_era5(zol, alpha, beta, gamma))
+ elif (meth == "C30" or meth == "C35" or meth == "C40"):
+ psim = psiu_26(zol, meth)
else:
psim = np.where(zol < 0, psim_conv(zol, alpha, beta, gamma),
psim_stab(zol, alpha, beta, gamma))
@@ -332,24 +284,26 @@ def psim_calc(zol, method="S80"):
# ---------------------------------------------------------------------
-def psit_calc(zol, method="S80"):
+def psit_calc(zol, meth="S80"):
""" Calculates heat stability function
-
+
Parameters
----------
zol : float
height over MO length
- method : str
-
+ meth : str
+
Returns
-------
psit : float
"""
- coeffs = get_stabco(method)
+ coeffs = get_stabco(meth)
alpha, beta, gamma = coeffs[0], coeffs[1], coeffs[2]
- if (method == "ERA5"):
+ if (meth == "ERA5"):
psit = np.where(zol < 0, psi_conv(zol, alpha, beta, gamma),
psi_stab_era5(zol, alpha, beta, gamma))
+ elif (meth == "C30" or meth == "C35" or meth == "C40"):
+ psit = psit_26(zol)
else:
psit = np.where(zol < 0, psi_conv(zol, alpha, beta, gamma),
psi_stab(zol, alpha, beta, gamma))
@@ -357,26 +311,27 @@ def psit_calc(zol, method="S80"):
# ---------------------------------------------------------------------
-def get_stabco(method="S80"):
+def get_stabco(meth="S80"):
""" Gives the coefficients \\alpha, \\beta, \\gamma for stability functions
-
+
Parameters
----------
- method : str
-
+ meth : str
+
Returns
-------
coeffs : float
"""
- if (method == "S80" or method == "S88" or method == "LY04" or
- method == "UA" or method == "ERA5"):
+ if (meth == "S80" or meth == "S88" or meth == "LY04" or
+ meth == "UA" or meth == "ERA5" or meth == "C30" or meth == "C35" or
+ meth == "C40"):
alpha, beta, gamma = 16, 0.25, 5 # Smith 1980, from Dyer (1974)
- elif (method == "LP82"):
+ elif (meth == "LP82"):
alpha, beta, gamma = 16, 0.25, 7
- elif (method == "YT96"):
+ elif (meth == "YT96"):
alpha, beta, gamma = 20, 0.25, 5
else:
- print("unknown method stabco: "+method)
+ print("unknown method stabco: "+meth)
coeffs = np.zeros(3)
coeffs[0] = alpha
coeffs[1] = beta
@@ -386,16 +341,16 @@ def get_stabco(method="S80"):
def psi_stab_era5(zol, alpha, beta, gamma):
- """ Calculates heat stability function for stable conditions
+ """ Calculates heat stability function for stable conditions
for method ERA5
-
+
Parameters
----------
zol : float
height over MO length
alpha, beta, gamma : float
constants given by get_stabco
-
+
Returns
-------
psit : float
@@ -406,16 +361,43 @@ def psi_stab_era5(zol, alpha, beta, gamma):
return psit
# ---------------------------------------------------------------------
+
+def psit_26(zol):
+ """ Computes temperature structure function as in C35
+
+ Parameters
+ ----------
+ zol : float
+ height over MO length
+
+ Returns
+ -------
+ psi : float
+ """
+ b, d = 2/3, 0.35
+ dzol = np.where(d*zol > 50, 50, d*zol) # stable
+ psi = -((1+b*zol)**1.5+b*(zol-14.28)*np.exp(-dzol)+8.525)
+ psi = np.where(zol < 0, (1-(np.power(zol, 2)/(1+np.power(zol, 2))))*2 *
+ np.log((1+np.sqrt(1-15*zol))/2)+(np.power(zol, 2) /
+ (1+np.power(zol, 2))) *
+ (1.5*np.log((1+np.power(1-34.15*zol, 1/3) +
+ np.power(1-34.15*zol, 2/3))/3) -
+ np.sqrt(3)*np.arctan((1+2*np.power(1-34.15*zol, 1/3)) /
+ np.sqrt(3))+4*np.arctan(1)/np.sqrt(3)), psi)
+ return psi
+# ---------------------------------------------------------------------
+
+
def psi_conv(zol, alpha, beta, gamma):
""" Calculates heat stability function for unstable conditions
-
+
Parameters
----------
zol : float
height over MO length
alpha, beta, gamma : float
constants given by get_stabco
-
+
Returns
-------
psit : float
@@ -428,14 +410,14 @@ def psi_conv(zol, alpha, beta, gamma):
def psi_stab(zol, alpha, beta, gamma):
""" Calculates heat stability function for stable conditions
-
+
Parameters
----------
zol : float
height over MO length
alpha, beta, gamma : float
constants given by get_stabco
-
+
Returns
-------
psit : float
@@ -445,43 +427,17 @@ def psi_stab(zol, alpha, beta, gamma):
# ---------------------------------------------------------------------
-def psit_26(zol):
- """ Computes temperature structure function as in C35
-
- Parameters
- ----------
- zol : float
- height over MO length
-
- Returns
- -------
- psi : float
- """
- dzol = np.where(0.35*zol > 50, 50, 0.35*zol) # stable
- psi = -((1+0.6667*zol)**1.5+0.6667*(zol-14.28)*np.exp(-dzol)+8.525)
- k = np.where(zol < 0) # unstable
- x = (1-15*zol[k])**0.5
- psik = 2*np.log((1+x)/2)
- x = (1-34.15*zol[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 = zol[k]**2/(1+zol[k]**2)
- psi[k] = (1-f)*psik+f*psic
- return psi
-# ---------------------------------------------------------------------
-
-
def psim_stab_era5(zol, alpha, beta, gamma):
- """ Calculates momentum stability function for stable conditions
+ """ Calculates momentum stability function for stable conditions
for method ERA5
-
+
Parameters
----------
zol : float
height over MO length
alpha, beta, gamma : float
constants given by get_stabco
-
+
Returns
-------
psim : float
@@ -495,14 +451,14 @@ def psim_stab_era5(zol, alpha, beta, gamma):
def psim_conv(zol, alpha, beta, gamma):
""" Calculates momentum stability function for unstable conditions
-
+
Parameters
----------
zol : float
height over MO length
alpha, beta, gamma : float
constants given by get_stabco
-
+
Returns
-------
psim : float
@@ -516,14 +472,14 @@ def psim_conv(zol, alpha, beta, gamma):
def psim_stab(zol, alpha, beta, gamma):
""" Calculates momentum stability function for stable conditions
-
+
Parameters
----------
zol : float
height over MO length
alpha, beta, gamma : float
constants given by get_stabco
-
+
Returns
-------
psim : float
@@ -533,41 +489,54 @@ def psim_stab(zol, alpha, beta, gamma):
# ---------------------------------------------------------------------
-def psiu_26(zol):
+def psiu_26(zol, meth):
""" Computes velocity structure function C35
-
+
Parameters
----------
zol : float
height over MO length
-
+
Returns
-------
psi : float
"""
- dzol = np.where(0.35*zol > 50, 50, 0.35*zol) # stable
- a, b, c, d = 0.7, 3/4, 5, 0.35
- psi = -(a*zol+b*(zol-c/d)*np.exp(-dzol)+b*c/d)
- k = np.where(zol < 0) # unstable
- x = (1-15*zol[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*zol[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 = zol[k]**2/(1+zol[k]**2)
- psi[k] = (1-f)*psik+f*psic
+ if (meth == "C30"):
+ dzol = np.where(0.35*zol > 50, 50, 0.35*zol) # stable
+ psi = -((1+zol)+0.6667*(zol-14.28)*np.exp(-dzol)+8.525)
+ k = np.where(zol < 0) # unstable
+ x = np.power(1-15*zol[k], 0.25)
+ psik = (2*np.log((1+x)/2)+np.log((1+np.power(x, 2))/2)-2*np.arctan(x) +
+ 2*np.arctan(1))
+ x = np.power(1-10.15*zol[k], 0.3333)
+ psic = (1.5*np.log((1+x+np.power(x, 2))/3)-np.sqrt(3) *
+ np.arctan((1+2*x)/np.sqrt(3))+4*np.arctan(1)/np.sqrt(3))
+ f = np.power(zol[k], 2)/(1+np.power(zol[k], 2))
+ psi[k] = (1-f)*psik+f*psic
+ elif (meth == "C35" or meth == "C40"):
+ dzol = np.where(0.35*zol > 50, 50, 0.35*zol) # stable
+ a, b, c, d = 0.7, 3/4, 5, 0.35
+ psi = -(a*zol+b*(zol-c/d)*np.exp(-dzol)+b*c/d)
+ k = np.where(zol < 0) # unstable
+ x = np.power(1-15*zol[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 = np.power(1-10.15*zol[k], 0.3333)
+ psic = (1.5*np.log((1+x+np.power(x, 2))/3)-np.sqrt(3) *
+ np.arctan((1+2*x)/np.sqrt(3))+4*np.arctan(1)/np.sqrt(3))
+ f = np.power(zol[k], 2)/(1+np.power(zol[k], 2))
+ psi[k] = (1-f)*psik+f*psic
return psi
# ------------------------------------------------------------------------------
def psiu_40(zol):
""" Computes velocity structure function C35
-
+
Parameters
----------
zol : float
height over MO length
-
+
Returns
-------
psi : float
@@ -587,9 +556,9 @@ def psiu_40(zol):
# ---------------------------------------------------------------------
-def get_skin(sst, qsea, rho, Rl, Rs, Rnl, cp, lv, usr, tsr, qsr, lat):
+def get_skin(sst, qsea, rho, Rl, Rs, Rnl, cp, lv, tkt, usr, tsr, qsr, lat):
""" Computes cool skin
-
+
Parameters
----------
sst : float
@@ -602,10 +571,14 @@ def get_skin(sst, qsea, rho, Rl, Rs, Rnl, cp, lv, usr, tsr, qsr, lat):
downward longwave radiation (W/m^2)
Rs : float
downward shortwave radiation (W/m^2)
+ Rnl : float
+ upwelling IR radiation (W/m^2)
cp : float
specific heat of air at constant pressure
lv : float
latent heat of vaporization
+ tkt : float
+ cool skin thickness
usr : float
friction velocity
tsr : float
@@ -614,12 +587,12 @@ def get_skin(sst, qsea, rho, Rl, Rs, Rnl, cp, lv, usr, tsr, qsr, lat):
star humidity
lat : float
latitude
-
+
Returns
-------
dter : float
- dqer : float
-
+ dqer : float
+
"""
# coded following Saunders (1967) with lambda = 6
g = gc(lat, None)
@@ -629,30 +602,31 @@ def get_skin(sst, qsea, rho, Rl, Rs, Rnl, cp, lv, usr, tsr, qsr, lat):
# 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
+ Al = 2.1e-5*np.power(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)
+ bigc = 16*g*cpw*np.power(rhow*visw, 3)/(np.power(tcw, 2)*np.power(rho, 2))
+ wetc = 0.622*lv*qsea/(287.1*np.power(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 = 6*np.ones(sst.shape)
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)
+ tkt = np.where(alq > 0, xlamx*visw/(np.sqrt(rho/rhow)*usr),
+ np.where(xlamx*visw/(np.sqrt(rho/rhow)*usr) > 0.01, 0.01,
+ xlamx*visw/(np.sqrt(rho/rhow)*usr)))
dter = qcol*tkt/tcw
dqer = wetc*dter
- return dter, dqer
+ return dter, dqer, tkt
# ---------------------------------------------------------------------
def get_gust(beta, Ta, usr, tsrv, zi, lat):
""" Computes gustiness
-
+
Parameters
----------
beta : float
@@ -667,17 +641,15 @@ def get_gust(beta, Ta, usr, tsrv, zi, lat):
scale height of the boundary layer depth (m)
lat : float
latitude
-
+
Returns
-------
ug : float
"""
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
+ 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
@@ -686,12 +658,12 @@ def get_gust(beta, Ta, usr, tsrv, zi, lat):
def get_heights(h):
""" Reads input heights for velocity, temperature and humidity
-
+
Parameters
----------
h : float
input heights (m)
-
+
Returns
-------
hh : array
@@ -709,12 +681,12 @@ def get_heights(h):
def svp_calc(T):
""" Calculates saturation vapour pressure
-
+
Parameters
----------
T : float
temperature (K)
-
+
Returns
-------
svp : float
@@ -729,17 +701,17 @@ def svp_calc(T):
def qsea_calc(sst, pres):
""" Computes specific humidity of the sea surface air
-
+
Parameters
----------
sst : float
sea surface temperature (K)
pres : float
pressure (mb)
-
+
Returns
-------
- qsea : float
+ qsea : float
(kg/kg)
"""
if (np.nanmin(sst) < 200): # if sst in Celsius convert to Kelvin
@@ -754,7 +726,7 @@ def qsea_calc(sst, pres):
def q_calc(Ta, rh, pres):
""" Computes specific humidity following Haltiner and Martin p.24
-
+
Parameters
----------
Ta : float
@@ -763,7 +735,7 @@ def q_calc(Ta, rh, pres):
relative humidity (%)
pres : float
air pressure (mb)
-
+
Returns
-------
qair : float, (kg/kg)
@@ -778,14 +750,14 @@ def q_calc(Ta, rh, pres):
def bucksat(T, P):
""" Computes saturation vapor pressure (mb) as in C35
-
+
Parameters
----------
T : float
temperature ($^\\circ$\\,C)
P : float
pressure (mb)
-
+
Returns
-------
exx : float
@@ -800,14 +772,14 @@ def bucksat(T, P):
def qsat26sea(T, P):
""" Computes surface saturation specific humidity (g/kg) as in C35
-
+
Parameters
----------
T : float
temperature ($^\\circ$\\,C)
P : float
pressure (mb)
-
+
Returns
-------
qs : float
@@ -824,14 +796,14 @@ def qsat26sea(T, P):
def qsat26air(T, P, rh):
""" Computes saturation specific humidity (g/kg) as in C35
-
+
Parameters
----------
T : float
temperature ($^\circ$\,C)
P : float
pressure (mb)
-
+
Returns
-------
q : float
@@ -849,14 +821,14 @@ def qsat26air(T, P, rh):
def gc(lat, lon=None):
""" Computes gravity relative to latitude
-
+
Parameters
----------
lat : float
latitude ($^\circ$)
lon : float
longitude ($^\circ$, optional)
-
+
Returns
-------
gc : float
@@ -879,22 +851,23 @@ def gc(lat, lon=None):
# ---------------------------------------------------------------------
-def visc_air(Ta):
+def visc_air(T):
""" Computes the kinematic viscosity of dry air as a function of air temp.
following Andreas (1989), CRREL Report 89-11.
-
+
Parameters
----------
Ta : float
air temperature ($^\circ$\,C)
-
+
Returns
-------
visa : float
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)
+ T = np.asarray(T)
+ if (np.nanmin(T) > 200): # if Ta in Kelvin convert to Celsius
+ T = T-273.16
+ visa = 1.326e-5*(1+6.542e-3*T+8.301e-6*np.power(T, 2) -
+ 4.84e-9*np.power(T, 3))
return visa