def heatDiff(self,iii):
'''
Heat diffusion function
:param z:
:param dz:
:param Ts:
:param rho:
:returns self.Tz:
:returns self.T10m:
thermal diffusivity: alpha = K_firn / (rho*c_firn)
'''
nz_P = len(self.z)
nz_fv = nz_P - 2
nt = 1
z_edges_vec1 = self.z[0:-1] + np.diff(self.z) / 2
z_edges_vec = np.concatenate(([self.z[0]], z_edges_vec1, [self.z[-1]]))
z_P_vec = self.z
phi_s = self.Tz[0]
phi_0 = self.Tz
K_ice = 9.828 * np.exp(-0.0057 * phi_0) # thermal conductivity, Cuffey and Paterson, eq. 9.2 (Yen 1981)
c_firn = 152.5 + 7.122 * phi_0 # specific heat, Cuffey and Paterson, eq. 9.1 (page 400)
# c_firn = CP_I # If you prefer a constant specific heat.
K_firn = firnConductivity(self,iii,K_ice) # thermal conductivity
if self.c['MELT']:
try:
if self.c['LWCheat']=='lowK':
K_firn[self.LWC>0]=K_firn[self.LWC>0]/1.e4
except:
pass
Gamma_P = K_firn
tot_rho = self.rho
c_vol = self.rho * c_firn
self.Tz = transient_solve_TR(z_edges_vec, z_P_vec, nt, self.dt[iii], Gamma_P, phi_0, nz_P, nz_fv, phi_s, tot_rho, c_vol)
self.T10m = self.Tz[np.where(self.z>=10.0)[0][0]]
if self.c['MELT']:
if self.c['LWCheat']=='effectiveT':
pass
elif np.any(self.Tz>273.15):
print('WARNING: TEMPERATURE EXCEEDS MELTING TEMPERATURE')
print('Maximum temperature was:',np.max(self.Tz),' at layers:',np.where(self.Tz == np.max(self.Tz)))
print('WARM TEMPERATURES HAVE BEEN SET TO 273.15; MODEL RUN IS CONTINUING')
self.Tz[self.Tz>=273.15]=273.15
return self.Tz, self.T10m
def heatDiff(self, iii):
'''
Heat diffusion function
:param z:
:param dz:
:param Ts:
:param rho:
:returns self.Tz:
:returns self.T10m:
'''
nz_P = len(self.z)
nz_fv = nz_P - 2
nt = 1
z_edges_vec = self.z[1:-2] + self.dz[2:-1] / 2
z_edges_vec = np.concatenate(([self.z[0]], z_edges_vec, [self.z[-1]]))
z_P_vec = self.z
# phi_s = self.Ts[iii]
phi_s = self.Tz[0]
phi_0 = self.Tz
# K_ice = 9.828 * np.exp(-0.0057 * phi_0)
# K_firn = K_ice * (self.rho / 1000) ** (2 - 0.5 * (self.rho / 1000))
K_firn = 0.021 + 2.5 * (self.rho / 1000.)**2
c_firn = 152.5 + 7.122 * phi_0
Gamma_P = K_firn / (c_firn * self.rho)
self.Tz = transient_solve_TR(z_edges_vec, z_P_vec, nt, self.dt, Gamma_P,
phi_0, nz_P, nz_fv, phi_s)
self.Tz = np.concatenate(([self.Ts[iii]], self.Tz[:-1]))
fT10m = interpolate.interp1d(self.z, self.Tz) # temp at 10m depth
self.T10m = fT10m(10)
return self.Tz, self.T10m
def isoDiff(self,iii):
'''
Isotope diffusion function
:param iter:
:param z:
:param dz:
:param rho:
:param iso:
:returns self.phi_t:
'''
nz_P = len(self.z) # number of nodes in z
nz_fv = nz_P - 2 # number of finite volumes in z
nt = 1 # number of time steps
# z_edges_vec = self.z[1:-2] + self.dz[2:-1] / 2 # uniform edge spacing of volume edges
# z_edges_vec = np.concatenate(([self.z[0]], z_edges_vec, [self.z[-1]]))
# z_P_vec = self.z
z_edges_vec1 = self.z[0:-1] + np.diff(self.z) / 2
z_edges_vec = np.concatenate(([self.z[0]], z_edges_vec1, [self.z[-1]]))
z_P_vec = self.z
### Node positions
phi_s = self.del_z[0] # isotope value at surface
phi_0 = self.del_z # initial isotope profile
### Define diffusivity for each isotopic species
### Establish values needed for diffusivity calculation
m = 0.018 # kg/mol; molar mass of water
pz = 3.454 * np.power(10, 12) * np.exp(-6133 / self.Tz) # Pa; saturation vapor pressure over ice
alpha_18_z = 0.9722 * np.exp(11.839 / self.Tz) # fractionation factor for 18_O
# alpha_18_z = np.exp(11.839/Tz-28.224*np.power(10,-3)) # alternate formulation from Eric's python code
alpha_D_z = 0.9098 * np.exp(16288 / np.power(self.Tz, 2)) # fractionation factor for D
Po = 1.0 # reference pressure in atm
P = 1.0
### Set diffusivity in air (units of m^2/s)
# Da = 2.1 * np.power(10.0, -5.) * np.power(self.Tz / 273.15, 1.94) * (Po / P)
Da = 2.1 * 1.0e-5 * (self.Tz / 273.15)**1.94 * (Po / P)
Da_18 = Da / 1.0285 # account for fractionation factor for 18_O, fixed Johnsen typo
Da_D = Da / 1.0251 # account for fractionation factor for D, fixed Johnsen typo
### Calculate tortuosity
invtau = np.zeros(int(len(self.dz)))
b = 0.25 # Tortuosity parameter
invtau[self.rho < RHO_I / np.sqrt(b)] = 1.0 - (b * (self.rho[self.rho < RHO_I / np.sqrt(b)] / RHO_I)) ** 2
invtau[self.rho >= RHO_I / np.sqrt(b)] = 0.0
### Set diffusivity for each isotope
if self.c['iso'] == '18':
D = m * pz * invtau * Da_18 * (1 / self.rho - 1 / RHO_I) / (R * self.Tz * alpha_18_z)
D = D + 1.5e-15
self.del_z = transient_solve_TR(z_edges_vec, z_P_vec, nt, self.dt, D, phi_0, nz_P, nz_fv, phi_s, self.rho)
elif self.c['iso'] == 'D':
D = m * pz * invtau * Da_D * (1 / self.rho - 1 / RHO_I) / (R * self.Tz * alpha_D_z)
D[D<=0.0] = 1.0e-20
self.del_z = transient_solve_TR(z_edges_vec, z_P_vec, nt, self.dt, D, phi_0, nz_P, nz_fv, phi_s, self.rho)
elif self.c['iso'] == 'NoDiffusion':
pass
### Solve for vertical isotope profile at this time step i
self.del_z = np.concatenate(([self.del_s[iii]], self.del_z[:-1]))
return self.del_z
def heatDiff(self,iii):
'''
Heat diffusion function
:param z:
:param dz:
:param Ts:
:param rho:
:returns self.Tz:
:returns self.T10m:
# thermal diffusivity: alpha = K_firn / (rho*c_firn)
'''
nz_P = len(self.z)
nz_fv = nz_P - 2
nt = 1
# z_edges_vec = self.z[1:-2] + self.dz[2:-1] / 2
# z_edges_vec = np.concatenate(([self.z[0]], z_edges_vec, [self.z[-1]]))
# z_P_vec = self.z
z_edges_vec1 = self.z[0:-1] + np.diff(self.z) / 2
z_edges_vec = np.concatenate(([self.z[0]], z_edges_vec1, [self.z[-1]]))
z_P_vec = self.z
phi_s = self.Tz[0]
phi_0 = self.Tz
K_ice = 9.828 * np.exp(-0.0057 * phi_0) # thermal conductivity, Cuffey and Paterson, eq. 9.2 (Yen 1981)
# c_firn = 152.5 + 7.122 * phi_0 # specific heat, Cuffey and Paterson, eq. 9.1 (page 400)
c_firn = CP_I # If you prefer a constant specific heat.
### Conductivity. Choose your favorite! ###
# References are provided at the end of this script.
# alpha_DAVIDCS_m2s = 18.3 / S_PER_YEAR # special for work Max was doing for David Clemens-Sewell
# K_firn = alpha_DAVIDCS_m2s * self.rho * c_firn
# K_firn[self.z>=20.0] = K_ice[self.z>=20.0] * (self.rho[self.z>=20.0]/RHO_I) ** (2 - 0.5 * (self.rho[self.z>=20.0]/RHO_I)) # Schwander 1997, eq. A11
# K_firn = K_ice * (self.rho/RHO_I) ** (2 - 0.5 * (self.rho/RHO_I)) # Schwander 1997, eq. A11
# K_firn = 2.22362 * (self.rho / 1000)**1.885 # Yen 1981, eq 34 w/ fixed K_ice (original)
# K_firn = K_ice * (self.rho / 1000)**1.885 # Yen 1981, modified for variable K_ice
# K_firn = 0.021 + 2.5 * (self.rho/1000.)**2 # Anderson (1976)
# K_firn = 0.0688 * np.exp(0.0088*phi_0 + 4.6682*self.rho) # Yen 1981, eq. 35.
# K_firn = 0.138 - 1.01*(self.rho/1000) + 3.233*(self.rho/1000)**2 # Sturm, 1997.; rho < 0.6
# K_firn = 2.1e-2 + 4.2e-4 * self.rho + 2.2e-9 * (self.rho)**3 # Van Dusen 1929 (via C&P)
K_firn = (2 * K_ice * self.rho) / (3*RHO_I - self.rho) # Schwerdtfeger (via C&P)
# K_firn = 3.e-6 * self.rho**2 - 1.06e-5 * self.rho + 0.024 # Riche and Schneebeli 2013 eq. 10
# k_firn = 0.0784 + 2.697 * (self.rho/1000.)**2 # Jiawen 1991 eq. 3
Gamma_P = K_firn # (new)
# Gamma_P = K_firn / (c_firn) # old)
tot_rho = self.rho
c_vol = self.rho * c_firn
# print('c_vol',c_vol)
self.Tz = transient_solve_TR(z_edges_vec, z_P_vec, nt, self.dt, Gamma_P, phi_0, nz_P, nz_fv, phi_s, tot_rho, c_vol)
fT10m = interpolate.interp1d(self.z, self.Tz) # temp at 10m depth
self.T10m = fT10m(10)
if np.any(self.Tz>273.17):
print('WARNING: TEMPERATURE EXCEEDS MELTING TEMPERATURE')
print('Maximal temperature was:',np.max(self.Tz),' at layers:',np.where(self.Tz == np.max(self.Tz)))
print('WARM TEMPERATURES HAVE BEEN SET TO 273.15; MODEL RUN IS CONTINUING')
self.Tz[self.Tz>=273.15]=273.15
return self.Tz, self.T10m
def isoDiff(self, IsoParams, iii):
'''
Isotope diffusion function
:param iter:
:param z:
:param dz:
:param rho:
:param iso:
:returns self.phi_t:
'''
for k, v in list(IsoParams.items()):
setattr(self, k, v)
nz_P = len(self.z) # number of nodes in z
nz_fv = nz_P - 2 # number of finite volumes in z
nt = 1 # number of time steps
# z_edges_vec = self.z[1:-2] + self.dz[2:-1] / 2 # uniform edge spacing of volume edges
# z_edges_vec = np.concatenate(([self.z[0]], z_edges_vec, [self.z[-1]]))
# z_P_vec = self.z
z_edges_vec1 = self.z[0:-1] + np.diff(self.z) / 2
z_edges_vec = np.concatenate(([self.z[0]], z_edges_vec1, [self.z[-1]]))
z_P_vec = self.z
### Node positions
phi_s = self.del_z[0] # isotope value at surface
# phi_s = self.del_z[1] # isotope value at surface
# if iii==0:
# print('Caution! line 121, isotopeDiffusion.py')
phi_0 = self.del_z # initial isotope profile
### Define diffusivity for each isotopic species
### Establish values needed for diffusivity calculation
m = 0.018 # kg/mol; molar mass of water
pz = 3.454e12 * np.exp(
-6133 / self.Tz) # Pa; saturation vapor pressure over ice
alpha_18_z = 0.9722 * np.exp(
11.839 / self.Tz) # fractionation factor for 18_O
# alpha_18_z = np.exp(11.839/Tz-28.224*np.power(10,-3)) # alternate formulation from Eric's python code
alpha_D_z = 0.9098 * np.exp(16288 /
(self.Tz**2)) # fractionation factor for D
Po = 1.0 # reference pressure in atm
# P = 1.0
P = self.c[
'site_pressure'] / 1013.25 # Pressure at WAIS from Christo's thesis.
### Set diffusivity in air (units of m^2/s)
Da = 2.11e-5 * (self.Tz / 273.15)**1.94 * (Po / P)
### Calculate tortuosity
invtau = np.zeros(int(len(self.dz)))
b = 1.3 # Tortuosity parameter (Johnsen 2000)
invtau[self.rho < RHO_I / np.sqrt(b)] = 1.0 - (
b * (self.rho[self.rho < RHO_I / np.sqrt(b)] / RHO_I)**2)
# b = 0.25 # Tortuosity parameter (Emma's value), effective b = 0.0625 (taken outside of squared term)
# invtau[self.rho < RHO_I / np.sqrt(b)] = 1.0 - (b * (self.rho[self.rho < RHO_I / np.sqrt(b)] / RHO_I))**2 #Emma
invtau[self.rho >= RHO_I / np.sqrt(b)] = 0.0
### Set diffusivity for each isotope
c_vol = np.ones_like(
self.rho) # Just a filler here to make the diffusion work.
if ((self.isotope == '18') or (self.isotope == 'd18O')):
Da_18 = Da / 1.0285 # account for fractionation factor for 18_O, fixed Johnsen typo
D = m * pz * invtau * Da_18 * (1 / self.rho - 1 / RHO_I) / (
R * self.Tz * alpha_18_z)
D = D + 1.5e-15 # Emma added - not sure why? prevent negative?
self.del_z = transient_solve_TR(z_edges_vec, z_P_vec, nt, self.dt,
D, phi_0, nz_P, nz_fv, phi_s,
self.rho, c_vol)
elif ((self.isotope == 'D') or (self.isotope == 'dD')):
Da_D = Da / 1.0251 # account for fractionation factor for D, fixed Johnsen typo
D = m * pz * invtau * Da_D * (1 / self.rho - 1 / RHO_I) / (
R * self.Tz * alpha_D_z)
D[D <= 0.0] = 1.0e-20
self.del_z = transient_solve_TR(z_edges_vec, z_P_vec, nt, self.dt,
D, phi_0, nz_P, nz_fv, phi_s,
self.rho, c_vol)
elif ((self.isotope == 'NoDiffusion') or (self.isotope == 'ND')):
D = np.zeros_like(self.z)
dsig2_dt = 2 * (-1 * self.drho_dt / self.rho) * self.iso_sig2_z + 2 * D
self.iso_sig2_z = self.iso_sig2_z + dsig2_dt * self.dt
# Advect profile down
if self.bdot > 0.0:
self.del_z = np.concatenate(([self.del_s[iii]], self.del_z[:-1]))
self.iso_sig2_z = np.concatenate(
([self.iso_sig2_s[iii]], self.iso_sig2_z[:-1]))
else:
pass
# self.del_z[0] = self.del_z[1]
# print('Caution!!! You are altering the upper isotope value! Line 173, isotopeDiffusion.py')
return self.del_z, self.iso_sig2_z
def firn_air_diffusion(self, AirParams, iii):
'''
Solve the diffusion equation.
Calls solver.py
'''
for k, v in list(AirParams.items()):
setattr(self, k, v)
nz_P = len(self.z)
nz_fv = nz_P - 2
nt = 1
z_edges1 = self.z[0:-1] + np.diff(self.z) / 2
z_edges = np.concatenate(([self.z[0]], z_edges1, [self.z[-1]]))
z_P_vec = self.z
# if (iii>100 and iii<110):
# print('z_P',z_P_vec[0:5])
# print('len p', len(z_P_vec))
# print('edges',z_edges[0:5])
# print('len edges',len(z_edges))
# input('enter')
# phi_s = self.Ts[iii]
phi_s = self.Gz[0]
phi_0 = self.Gz
# K_ice = 9.828 * np.exp(-0.0057 * phi_0)
# K_firn = K_ice * (self.rho / 1000) ** (2 - 0.5 * (self.rho / 1000))
self.rho_co, self.por_co, self.por_tot, self.por_cl, self.por_op, self.bcoRho, self.LIDRho = self.porosity(
)
# self.air_pressure_old = np.copy(self.air_pressure)
porosity_old = (RHO_I - self.rho_old) / RHO_I
por_co1 = 1 - self.rho_co / RHO_I # Porosity at close-off
alpha = 0.37 # constant determined in Goujon
por_cl1 = np.zeros_like(porosity_old)
por_cl1[porosity_old > 0] = alpha * porosity_old[porosity_old > 0] * (
porosity_old[porosity_old > 0] / por_co1)**(-7.6)
ind = por_cl1 > porosity_old
por_cl1[ind] = porosity_old[ind]
por_op_old = porosity_old - por_cl1 # Open Porosity
self.air_volume_old = por_op_old * self.dz_old
# self.air_volume_old = np.copy(self.air_volume)
self.air_volume = self.por_op * self.dz
volfrac = self.air_volume_old / self.air_volume
# volfrac = np.concatenate(([volfrac[0]],volfrac))
self.air_pressure = (self.p_a * np.exp(
M_AIR * GRAVITY * self.z / (R * self.Tz))) * volfrac - (
self.p_a * np.exp(M_AIR * GRAVITY * self.z / (R * self.Tz))
) # assume air pressure is atmos in entire column
self.pressure_grad = np.gradient(self.air_pressure, self.z)
self.z_co = min(self.z[self.rho >= (
self.bcoRho)]) #close-off depth; bcoRho is mean close off density
# self.z_co = min(self.z[self.rho>=(self.rho_co)]) #close-off depth; bcoRho is close off density
# self.z_co = self.z[np.where(self.rho>=self.rho_co)[0][0]] #close-off depth; bcoRho is close off density
self.LID = min(self.z[self.rho >= (
self.LIDRho)]) #lock in depth; LIDRho is lock-in density
# print(self.LID)
self.bdot_t = self.bdot[iii]
self.diffu, self.d_eddy = self.diffusivity()
# ij = np.where(self.diffu<=1e-20)[0][0]
# print('Diffu zero',self.z[ij])
airdict = {
'd_eddy': self.d_eddy,
'por_op': self.por_op,
'Tz': self.Tz,
'deltaM': self.deltaM,
'omega': self.omega,
'dz': self.dz,
'rho': self.rho,
'gravity': self.cg['gravity'],
'thermal': self.cg['thermal'],
'air_pressure': self.air_pressure,
'pressure_grad': self.pressure_grad,
'z': self.z,
'dt': self.dt,
'z_co': self.z_co,
'p_a': self.p_a,
'por_tot': self.por_tot,
'por_cl': self.por_cl,
'w_firn': self.w_firn,
'advection_type': self.cg['advection_type'],
'iii': iii,
'gaschoice': self.gaschoice
}
msk = np.where(self.z > self.z_co)[0][0]
c_vol = np.ones_like(
self.rho) # Just a filler here to make the diffusion work.
self.Gz, w_p = transient_solve_TR(z_edges, z_P_vec, nt, self.dt,
self.diffu, phi_0, nz_P, nz_fv,
phi_s, self.rho, c_vol, airdict)
self.Gz = np.concatenate(([self.Gs[iii]], self.Gz[:-1]))
ind_LID = np.where(self.z >= self.LID)[0]
self.gas_age[self.gas_age >
0] = self.gas_age[self.gas_age > 0] + self.dt / S_PER_YEAR
self.gas_age = np.concatenate(([0], self.gas_age[:-1]))
self.gas_age[ind_LID[0]] = 15.0
ii2 = np.where((self.z > self.LID) & (self.gas_age == 0))[0]
self.gas_age[ii2] = 15
# print('diffu',self.diffu[0:10])
return self.Gz, self.diffu, w_p, self.gas_age
def isoDiff(self, iii):
'''
Isotope diffusion function
:param iter:
:param z:
:param dz:
:param rho:
:param iso:
:returns self.phi_t:
'''
nz_P = len(self.z) # number of nodes in z
nz_fv = nz_P - 2 # number of finite volumes in z
nt = 1 # number of time steps
# z_edges_vec = self.z[1:-2] + self.dz[2:-1] / 2 # uniform edge spacing of volume edges
# z_edges_vec = np.concatenate(([self.z[0]], z_edges_vec, [self.z[-1]]))
# z_P_vec = self.z
z_edges_vec1 = self.z[0:-1] + np.diff(self.z) / 2
z_edges_vec = np.concatenate(([self.z[0]], z_edges_vec1, [self.z[-1]]))
z_P_vec = self.z
### Node positions
phi_s = self.del_z[0] # isotope value at surface
phi_0 = self.del_z # initial isotope profile
### Define diffusivity for each isotopic species
### Establish values needed for diffusivity calculation
m = 0.018 # kg/mol; molar mass of water
pz = 3.454 * np.power(10, 12) * np.exp(
-6133 / self.Tz) # Pa; saturation vapor pressure over ice
alpha_18_z = 0.9722 * np.exp(
11.839 / self.Tz) # fractionation factor for 18_O
# alpha_18_z = np.exp(11.839/Tz-28.224*np.power(10,-3)) # alternate formulation from Eric's python code
alpha_D_z = 0.9098 * np.exp(
16288 / np.power(self.Tz, 2)) # fractionation factor for D
Po = 1.0 # reference pressure in atm
P = 1.0
### Set diffusivity in air (units of m^2/s)
# Da = 2.1 * np.power(10.0, -5.) * np.power(self.Tz / 273.15, 1.94) * (Po / P)
Da = 2.1 * 1.0e-5 * (self.Tz / 273.15)**1.94 * (Po / P)
Da_18 = Da / 1.0285 # account for fractionation factor for 18_O, fixed Johnsen typo
Da_D = Da / 1.0251 # account for fractionation factor for D, fixed Johnsen typo
### Calculate tortuosity
invtau = np.zeros(int(len(self.dz)))
b = 0.25 # Tortuosity parameter
invtau[self.rho < RHO_I / np.sqrt(b)] = 1.0 - (
b * (self.rho[self.rho < RHO_I / np.sqrt(b)] / RHO_I))**2
invtau[self.rho >= RHO_I / np.sqrt(b)] = 0.0
### Set diffusivity for each isotope
if self.c['iso'] == '18':
D = m * pz * invtau * Da_18 * (1 / self.rho -
1 / RHO_I) / (R * self.Tz * alpha_18_z)
D = D + 1.5e-15
self.del_z = transient_solve_TR(z_edges_vec, z_P_vec, nt, self.dt, D,
phi_0, nz_P, nz_fv, phi_s, self.rho)
elif self.c['iso'] == 'D':
D = m * pz * invtau * Da_D * (1 / self.rho -
1 / RHO_I) / (R * self.Tz * alpha_D_z)
D[D <= 0.0] = 1.0e-20
self.del_z = transient_solve_TR(z_edges_vec, z_P_vec, nt, self.dt, D,
phi_0, nz_P, nz_fv, phi_s, self.rho)
elif self.c['iso'] == 'NoDiffusion':
pass
### Solve for vertical isotope profile at this time step i
self.del_z = np.concatenate(([self.del_s[iii]], self.del_z[:-1]))
return self.del_z
def heatDiff(self, iii):
'''
Heat diffusion function
:param z:
:param dz:
:param Ts:
:param rho:
:returns self.Tz:
:returns self.T10m:
# thermal diffusivity: alpha = K_firn / (rho*c_firn)
'''
nz_P = len(self.z)
nz_fv = nz_P - 2
nt = 1
# z_edges_vec = self.z[1:-2] + self.dz[2:-1] / 2
# z_edges_vec = np.concatenate(([self.z[0]], z_edges_vec, [self.z[-1]]))
# z_P_vec = self.z
z_edges_vec1 = self.z[0:-1] + np.diff(self.z) / 2
z_edges_vec = np.concatenate(([self.z[0]], z_edges_vec1, [self.z[-1]]))
z_P_vec = self.z
phi_s = self.Tz[0]
phi_0 = self.Tz
K_ice = 9.828 * np.exp(
-0.0057 *
phi_0) # thermal conductivity, Cuffey and Paterson, eq. 9.2 (Yen 1981)
# c_firn = 152.5 + 7.122 * phi_0 # specific heat, Cuffey and Paterson, eq. 9.1 (page 400)
c_firn = CP_I # If you prefer a constant specific heat.
### Conductivity. Choose your favorite! ###
# References are provided at the end of this script.
# alpha_DAVIDCS_m2s = 18.3 / S_PER_YEAR
# K_firn = alpha_DAVIDCS_m2s * self.rho * c_firn
# K_firn[self.z>=20.0] = K_ice[self.z>=20.0] * (self.rho[self.z>=20.0]/RHO_I) ** (2 - 0.5 * (self.rho[self.z>=20.0]/RHO_I)) # Schwander 1997, eq. A11
# K_firn = K_ice * (self.rho/RHO_I) ** (2 - 0.5 * (self.rho/RHO_I)) # Schwander 1997, eq. A11
# K_firn = 2.22362 * (self.rho / 1000)**1.885 # Yen 1981, eq 34 w/ fixed K_ice (original)
K_firn = K_ice * (self.rho /
1000)**1.885 # Yen 1981, modified for variable K_ice
# K_firn = 0.021 + 2.5 * (self.rho/1000.)**2 # Anderson (1976)
# K_firn = 0.0688 * np.exp(0.0088*phi_0 + 4.6682*self.rho) # Yen 1981, eq. 35.
# K_firn = 0.138 - 1.01*(self.rho/1000) + 3.233*(self.rho/1000)**2 # Sturm, 1997.; rho < 0.6
# K_firn = 2.1e-2 + 4.2e-4 * self.rho + 2.2e-9 * (self.rho)**3 # Van Dusen 1929 (via C&P)
# K_firn = (2 * K_ice * self.rho) / (3*RHO_I - self.rho) # Schwerdtfeger (via C&P)
# K_firn = 3.e-6 * self.rho**2 - 1.06e-5 * self.rho + 0.024 # Riche and Schneebeli 2013 eq. 10
# k_firn = 0.0784 + 2.697 * (self.rho/1000.)**2 # Jiawen 1991 eq. 3
Gamma_P = K_firn # (new)
# print('K_firn',K_firn)
# Gamma_P = K_firn / (c_firn) # old)
tot_rho = self.rho
c_vol = self.rho * c_firn
# print('c_vol',c_vol)
self.Tz = transient_solve_TR(z_edges_vec, z_P_vec, nt, self.dt, Gamma_P,
phi_0, nz_P, nz_fv, phi_s, tot_rho, c_vol)
fT10m = interpolate.interp1d(self.z, self.Tz) # temp at 10m depth
self.T10m = fT10m(10)
if np.any(self.Tz > 273.17):
print('WARNING: TEMPERATURE EXCEEDS MELTING TEMPERATURE')
print('Maximal temperature was:', np.max(self.Tz), ' at layers:',
np.where(self.Tz == np.max(self.Tz)))
print(
'WARM TEMPERATURES HAVE BEEN SET TO 273.15; MODEL RUN IS CONTINUING'
)
self.Tz[self.Tz >= 273.15] = 273.15
return self.Tz, self.T10m
def firn_air_diffusion(self,AirParams,iii):
for k,v in list(AirParams.items()):
setattr(self,k,v)
nz_P = len(self.z)
nz_fv = nz_P - 2
nt = 1
z_edges1 = self.z[0:-1] + np.diff(self.z) / 2
z_edges = np.concatenate(([self.z[0]], z_edges1, [self.z[-1]]))
z_P_vec = self.z
# if (iii>100 and iii<110):
# print('z_P',z_P_vec[0:5])
# print('len p', len(z_P_vec))
# print('edges',z_edges[0:5])
# print('len edges',len(z_edges))
# input('enter')
# phi_s = self.Ts[iii]
phi_s = self.Gz[0]
phi_0 = self.Gz
# K_ice = 9.828 * np.exp(-0.0057 * phi_0)
# K_firn = K_ice * (self.rho / 1000) ** (2 - 0.5 * (self.rho / 1000))
self.rho_co, self.por_co, self.por_tot, self.por_cl, self.por_op, self.bcoRho, self.LIDRho = self.porosity()
# self.air_pressure_old = np.copy(self.air_pressure)
porosity_old = (RHO_I-self.rho_old)/RHO_I
por_co1 = 1 - self.rho_co/RHO_I # Porosity at close-off
alpha = 0.37 # constant determined in Goujon
por_cl1 = np.zeros_like(porosity_old)
por_cl1[porosity_old>0] = alpha*porosity_old[porosity_old>0]*(porosity_old[porosity_old>0]/por_co1)**(-7.6)
ind = por_cl1>porosity_old
por_cl1[ind] = porosity_old[ind]
por_op_old = porosity_old - por_cl1 # Open Porosity
self.air_volume_old = por_op_old * self.dz_old
# self.air_volume_old = np.copy(self.air_volume)
self.air_volume = self.por_op * self.dz
volfrac = self.air_volume_old / self.air_volume
# volfrac = np.concatenate(([volfrac[0]],volfrac))
self.air_pressure = (self.p_a*np.exp(M_AIR*GRAVITY*self.z/(R*self.Tz))) * volfrac - (self.p_a*np.exp(M_AIR*GRAVITY*self.z/(R*self.Tz))) # assume air pressure is atmos in entire column
self.pressure_grad = np.gradient(self.air_pressure,self.z)
self.z_co = min(self.z[self.rho>=(self.bcoRho)]) #close-off depth; bcoRho is mean close off density
# self.z_co = min(self.z[self.rho>=(self.rho_co)]) #close-off depth; bcoRho is close off density
# self.z_co = self.z[np.where(self.rho>=self.rho_co)[0][0]] #close-off depth; bcoRho is close off density
self.LID = min(self.z[self.rho>=(self.LIDRho)]) #lock in depth; LIDRho is lock-in density
print(self.LID)
self.bdot_t = self.bdot[iii]
self.diffu, self.d_eddy = self.diffusivity()
# ij = np.where(self.diffu<=1e-20)[0][0]
# print('Diffu zero',self.z[ij])
airdict = {
'd_eddy': self.d_eddy,
'por_op': self.por_op,
'Tz': self.Tz,
'deltaM': self.deltaM,
'omega': self.omega,
'dz': self.dz,
'rho': self.rho,
'gravity': self.cg['gravity'],
'thermal': self.cg['thermal'],
'air_pressure': self.air_pressure,
'pressure_grad': self.pressure_grad,
'z': self.z,
'dt': self.dt,
'z_co': self.z_co,
'p_a': self.p_a,
'por_tot': self.por_tot,
'por_cl': self.por_cl,
'w_firn': self.w_firn,
'advection_type': self.cg['advection_type'],
'iii': iii,
'gaschoice': self.gaschoice
}
msk = np.where(self.z>self.z_co)[0][0]
self.Gz, w_p = transient_solve_TR(z_edges, z_P_vec, nt, self.dt, self.diffu, phi_0, nz_P, nz_fv, phi_s, self.rho, airdict)
self.Gz = np.concatenate(([self.Gs[iii]], self.Gz[:-1]))
ind_LID = np.where(self.z>=self.LID)[0]
self.gas_age[self.gas_age>0] = self.gas_age[self.gas_age>0] + self.dt/S_PER_YEAR
self.gas_age = np.concatenate(([0], self.gas_age[:-1]))
self.gas_age[ind_LID[0]] = 15.0
ii2 = np.where((self.z>self.LID) & (self.gas_age==0))[0]
self.gas_age[ii2] = 15
# print('diffu',self.diffu[0:10])
return self.Gz, self.diffu, w_p, self.gas_age