class FirnDensitySpin:
def __init__(self, configName):
'''
Sets up the initial spatial grid, time grid, accumulation rate, age, density, mass, stress, and temperature of the model run
:param configName: name of json config file containing model configurations
'''
# load in json config file and parses the user inputs to a dictionary
with open(configName, "r") as f:
jsonString = f.read()
self.c = json.loads(jsonString)
# create directory to store results
if os.path.exists(self.c['resultsFolder']):
rmtree(self.c['resultsFolder'])
os.makedirs(self.c['resultsFolder'])
# read in initial temperatures and accumulation rates
input_temp, input_year_temp = read_temp(self.c['InputFileNameTemp'])
input_bdot, input_year_bdot = read_bdot(self.c['InputFileNamebdot'])
# load in model parameters
self.bdot0 = input_bdot[0]
self.temp0 = input_temp[0]
gridLen, dx, dt, t, stp, Ts, T_mean, bdotSec, rhos0 = self.define_parameters()
# set up model grid
gridheight = np.linspace(c['H'], c['HbaseSpin'], gridLen)
self.z = self.c['H'] - gridHeight
self.dz = np.diff(self.z)
self.dz = np.append(self.dz, self.dz[-1])
# set up the initial age and density of the firn column using herron & langway analytic
THL = input_temp[0]
AHL = input_bdot[0]
self.age, self.rho = hl_analytic(self.c['rhos0'], self.z, THL, AHL)
# set up initial mass, stress, and mean accumulation rate
self.mass = self.rho * self.dz
self.sigma = self.mass * dx * GRAVITY
self.sigma = self.sigma.cumsum(axis = 0)
self.mass_sum = self.mass.cumsum(axis = 0)
self.bdot_mean = np.concatenate(([self.mass_sum[0] / (RHO_I * S_PER_YEAR)], self.mass_sum[1:] / (self.age[1:] * RHO_I / t)))
# set up initial temperature grid as well as a class to handle heat/isotope diffusion
init_Tz = input_temp[0] * np.ones(gridLen)
self.diffu = Diffusion(self.z, stp, gridLen, init_Tz)
# set up initial grain growth (if specified in config file)
if self.c['physGrain']:
if self.c['calcGrainSize']:
r02 = -2.42e-9 * (self.c['Ts0']) + 9.46e-7
self.r2 = r02 * np.ones(gridLen)
else:
self.r2 = np.linspace(self.c['r2s0'], (6 * self.c['r2s0']), gridLen)
def time_evolve(self):
'''
Evolve the spatial grid, time grid, accumulation rate, age, density, mass, stress, and temperature through time
based on the user specified number of timesteps in the model run. Updates the firn density using a user specified
'''
# load in model parameters
dx, dt, t, stp, Ts, T_mean, bdotSec, rhos0 = self.define_parameters()
steps = 1 / t
if not self.c['physGrain']:
r2_time = None
for iter in xrange(stp):
# getting the right physics for firn density based on user input
physics = {
'HLdynamic', HLdynamic,
'HLSigfus', HLSigfus,
'Barnola1991', Barnola1991,
'Li2004', Li2004,
'Li2011', Li2011,
'Ligtenberg2011', Ligtenberg2011,
'Arthern2010S', Arthern2010S,
'Simonsen2013', Simonsen2013,
'Morris2013', MorrisHL2013,
'Helsen2008', Helsen2008,
'Arthern2010T', Arthern2010T,
'Spencer2001', Spencer2001,
'Goujon2003', Goujon2003,
}
parameters = {
'HLdynamic', [steps, gridLen, bdotSec, self.diffu.Tz, self.rho],
'HLSigfus', [steps, gridLen, bdotSec, self.diffu.Tz, self.rho, sigma],
'Barnola1991', [steps, gridLen, bdotSec, self.diffu.Tz, self.rho, sigma],
'Li2004', [steps, gridLen, bdotSec, T_mean, self.rho],
'Li2011', [steps, gridLen, bdotSec, self.bdot_mean, self.c['bdot_type'], self.diffu.Tz, T_mean, self.rho],
'Ligtenberg2011', [steps, gridLen, bdotSec, self.bdot_mean, self.c['bdot_type'], self.diffu.Tz, T_mean, self.rho],
'Arthern2010S', [steps, gridLen, bdotSec, self.bdot_mean, self.c['bdot_type'], self.diffu.Tz, T_mean, self.rho],
'Simonsen2013', [steps, gridLen, bdotSec, self.bdot_mean, self.c['bdot_type'], self.diffu.Tz, T_mean, self.rho],
'Morris2013', [steps, gridLen, self.diffu.Tz, dt, self.rho, True, iter],
'Helsen2008', [steps, bdotSec, self.c['bdot_type'], self.bdot_mean, self.diffu.Tz, Ts, self.rho],
'Arthern2010T', [gridLen, self.diffu.Tz, self.rho, self.sigma, self.r2, self.c['physGrain']],
'Spencer2001', [],
'Goujon2003', [],
}
try:
drho_dt = physics[self.c['physRho']](parameters[self.c['physRho']])
except KeyError:
default()
# update density and age of firn
self.age = np.concatenate(([0], self.age[:-1])) + dt
self.rho = self.rho + dt * drho_dt
self.rho = np.concatenate(([rhos0[iter]], self.rho[:-1]))
# update temperature grid and isotope grid if user specifies
if self.c['heatDiff']:
self.diffu.heatDiff(self.z, self.dz, Ts, self.rho)
if self.c['heatDiff']:
self.diffu.isoDiff(iter, self.z, self.dz, self.rho, self.c['iso'])
# update model grid
dzNew = bdotSec[iter] * RHO_I / rhos0[iter] * S_PER_YEAR
self.dz = self.mass / self.rho * dx
self.dz = np.concatenate(([dzNew], self.dz[:-1]))
self.z = self.dz.cumsum(axis = 0)
self.z = np.concatenate(([0], self.z[:-1]))
# update mass, stress, and mean accumulation rate
massNew = bdotSec[iter] * S_PER_YEAR * RHO_I
self.mass = np.concatenate(([massNew], self.mass[:-1]))
self.sigma = self.mass * dx * GRAVITY
self.sigma = self.sigma.cumsum(axis = 0)
self.mass_sum = self.mass.cumsum(axis = 0)
self.bdot_mean = np.concatenate(([self.mass_sum[0] / (RHO_I * S_PER_YEAR)], self.mass_sum[1:] * t / (self.age[1:] * RHO_I)))
# update grain radius
if self.c['physGrain']:
self.r2 = grainGrowth(self.diffu.Tz, Ts, iter, dt)
# write results at the end of the time evolution
if (iter == (stp - 1)):
rho_time = np.concatenate(([t * iter + 1], self.rho))
Tz_time = np.concatenate(([t * iter + 1], self.diffu.Tz))
age_time = np.concatenate(([t * iter + 1], self.age))
z_time = np.concatenate(([t * iter + 1], self.z))
if self.c['physGrain']:
r2_time = np.concatenate(([t * iter + 1], self.r2))
write_spin(self.c['resultsFolder'], self.c['physGrain'], rho_time, Tz_time, age_time, z_time, r2_time)
def define_parameters(self):
'''
Return the parameters used in the model, for the initialization as well as the time evolution
:returns gridLen: size of grid used in the model run
(unit: number of boxes, type: int)
:returns dx: vector of width of each box, used for stress calculations
(unit: ???, type: array of ints)
:returns dt: number of seconds per time step
(unit: seconds, type: float)
:returns t: number of years per time step
(unit: years, type: float)
:returns stp: total number of steps in the model run
(unit: number of steps, type: int)
:returns T_mean: interpolated temperature vector based on the model time and the initial user temperature data
(unit: ???, type: array of floats)
:returns Ts: interpolated temperature vector based on the model time & the initial user temperature data
may have a seasonal signal imposed depending on number of years per time step (< 1)
(unit: ???, type: array of floats)
:returns bdotSec: accumulation rate vector at each time step
(unit: ???, type: array of floats)
:returns rhos0: surface accumulate rate vector
(unit: ???, type: array of floats)
'''
gridLen = int((self.c['H'] - self.c['HbaseSpin']) / (self.bdot0 / self.c['stpsPerYearSpin']))
dx = np.ones(gridLen)
zz = np.min(z[self.rho > 850.0])
years = int(zz / self.bdot0)
stp = int(years * self.c['stpsPerYearSpin'])
dt = years * S_PER_YEAR / stp
t = 1.0 / self.c['stpsPerYearSpin']
if self.c['stpsPerYearSpin'] or (stp / years) >= 1.:
Ts = self.temp0 * np.ones(stp)
else:
TPeriod = self.c['yearSpin']
Ts = self.temp0 + self.c['TAmp'] * (np.cos(2 * np.pi * np.linspace(0, TPeriod, stp)) + 0.3 * np.cos(4 * np.pi * np.linspace(0, TPeriod, stp)))
T_mean = Ts
bdotSec0 = self.bdot0 / S_PER_YEAR / self.c['stpsPerYearSpin']
bdotSec = bdotSec0 * np.ones(stp)
rhos0 = self.c['rhos0'] * np.ones(stp)
return gridLen, dx, dt, t, stp, Ts, T_mean, bdotSec, rhos0
class FirnDensityNoSpin:
def __init__(self, configName):
'''
Sets up the initial spatial grid, time grid, accumulation rate, age, density, mass, stress, temperature, and diffusivity of the model run
:param configName: name of json config file containing model configurations
'''
# load in json config file and parses the user inputs to a dictionary
with open(configName, "r") as f:
jsonString = f.read()
self.c = json.loads(jsonString)
# read in initial depth, age, density, temperature
initDepth, initAge, initDensity, initTemp = read_init(self.c['resultsFolder'])
# set up the initial age and density of the firn column
self.age = initAge[1:]
self.rho = initDensity[1:]
# set up model grid
self.z = initDepth[1:]
self.dz = np.diff(self.z)
self.dz = np.append(self.dz, self.dz[-1])
# load in model parameters
gridLen, dx, dt, t, modeltime, years, stp, Ts, T_mean, bdot, bdotSec, rhos0, D_surf = self.define_parameters()
# set up the initial grid of diffusivity constant
self.Dcon = self.c['D_surf'] * np.ones(gridLen)
# set up vector of times data will be written
self.TWrite = modeltime[INTE::INTE]
# set up initial mass, stress, and mean accumulation rate
self.mass = self.rho * self.dz
self.sigma = self.mass * dx * GRAVITY
self.sigma = self.sigma.cumsum(axis = 0)
self.mass_sum = self.mass.cumsum(axis = 0)
self.bdot_mean = np.concatenate(([self.mass_sum[0] / (RHO_I * S_PER_YEAR)], self.mass_sum[1:] / (self.age[1:] * RHO_I / t)))
# set up class to handle heat/isotope diffusion using user provided data for initial temperature vector
self.diffu = Diffusion(self.z, stp, gridLen, initTemp[1:])
# set up initial values for density, temperature, age, depth, diffusivity, Clim??, and accumulation to write
rho_time = np.append(modeltime[0], self.rho)
Tz_time = np.append(modeltime[0], self.diffu.Tz)
age_time = np.append(modeltime[0], self.age)
z_time = np.append(modeltime[0], self.z)
D_time = np.append(modeltime[0], self.Dcon)
Clim_time = np.append(modeltime[0], [bdot[0], Ts[0]]) # not sure if bdot or bdotSec
bdot_time = np.append(modeltime[0], self.bdot_mean)
# set up initial grain growth (if specified in config file)
if self.c['physGrain']:
initr2 = np.genfromtxt(r2Path, delimiter = ',')
self.r2 = initr2
r20 = r2
r2_time = np.append(modeltime[0], self.r2)
else:
r2_time = None
# write initial values to the results folder
write_nospin(self.c['resultsFolder'], self.c['physGrain'], rho_time, Tz_time, age_time, z_time, D_time, Clim_time, bdot_time, r2_time)
# set up initial values for bubble close-off depth & age, lock-in zone depth & age, and depth integrated porosity
self.bcoAgeMartAll = []
self.bcoDepMartAll = []
self.bcoAge815All = []
self.bcoDep815All = []
self.LIZAgeAll = []
self.LIZDepAll = []
self.intPhiAll = []
update_BCO()
update_LIZ()
update_DIP()
def time_evolve(self):
'''
Evolve the spatial grid, time grid, accumulation rate, age, density, mass, stress, temperature, and diffusivity through time
based on the user specified number of timesteps in the model run. Updates the firn density using a user specified
'''
# load in model parameters
gridLen, dx, dt, t, modeltime, years, stp, Ts, T_mean, bdot, bdotSec, rhos0, D_surf = define_parameters()
steps = 1 / t
if not self.c['physGrain']:
r2_time = None
for iter in xrange(stp):
mtime = modeltime[iter]
# getting the right physics for firn density based on user input
physics = {
'HLdynamic', HLdynamic,
'HLSigfus', HLSigfus,
'Barnola1991', Barnola1991,
'Li2004', Li2004,
'Li2011', Li2011,
'Ligtenberg2011', Ligtenberg2011,
'Arthern2010S', Arthern2010S,
'Simonsen2013', Simonsen2013,
'Morris2013', MorrisHL2013,
'Helsen2008', Helsen2008,
'Arthern2010T', Arthern2010T,
'Spencer2001', Spencer2001,
'Goujon2003', Goujon2003,
}
parameters = {
'HLdynamic', [steps, gridLen, bdotSec, self.diffu.Tz, self.rho],
'HLSigfus', [steps, gridLen, bdotSec, self.diffu.Tz, self.rho, sigma],
'Barnola1991', [steps, gridLen, bdotSec, self.diffu.Tz, self.rho, sigma],
'Li2004', [steps, gridLen, bdotSec, T_mean, self.rho],
'Li2011', [steps, gridLen, bdotSec, self.bdot_mean, self.c['bdot_type'], self.diffu.Tz, T_mean, self.rho],
'Ligtenberg2011', [steps, gridLen, bdotSec, self.bdot_mean, self.c['bdot_type'], self.diffu.Tz, T_mean, self.rho],
'Arthern2010S', [steps, gridLen, bdotSec, self.bdot_mean, self.c['bdot_type'], self.diffu.Tz, T_mean, self.rho],
'Simonsen2013', [steps, gridLen, bdotSec, self.bdot_mean, self.c['bdot_type'], self.diffu.Tz, T_mean, self.rho],
'Morris2013', [steps, gridLen, self.diffu.Tz, dt, self.rho, True, iter],
'Helsen2008', [steps, bdotSec, self.c['bdot_type'], self.bdot_mean, self.diffu.Tz, Ts, self.rho],
'Arthern2010T', [gridLen, self.diffu.Tz, self.rho, self.sigma, self.r2, self.c['physGrain']],
'Spencer2001', [],
'Goujon2003', [],
}
try:
drho_dt = physics[self.c['physRho']](parameters[self.c['physRho']])
except KeyError:
default()
# update density and age of firn
self.age = np.concatenate(([0], self.age[:-1])) + dt
self.rho = self.rho + dt * drho_dt
self.rho = np.concatenate(([rhos0[iter]], self.rho[:-1]))
self.Dcon = np.concatenate(([D_surf[iter]], self.Dcon[:-1]))
# update temperature grid and isotope grid if user specifies
if self.c['heatDiff']:
self.diffu.heatDiff(self.z, self.dz, Ts, self.rho)
if self.c['heatDiff']:
self.diffu.isoDiff(iter, self.z, self.dz, self.rho, self.c['iso'])
# update model grid
dzNew = bdotSec[iter] * RHO_I / rhos0[iter] * S_PER_YEAR
self.dz = self.mass / self.rho * dx
self.dz = np.concatenate(([dzNew], self.dz[:-1]))
self.z = self.dz.cumsum(axis = 0)
self.z = np.concatenate(([0], self.z[:-1]))
# update mass, stress, and mean accumulation rate
massNew = bdotSec[iter] * S_PER_YEAR * RHO_I
self.mass = np.concatenate(([massNew], self.mass[:-1]))
self.sigma = self.mass * dx * GRAVITY
self.sigma = self.sigma.cumsum(axis = 0)
self.mass_sum = self.mass.cumsum(axis = 0)
self.bdot_mean = np.concatenate(([mass_sum[0] / (RHO_I * S_PER_YEAR)], self.mass_sum[1:] * t / (self.age[1:] * RHO_I)))
# update grain radius
if self.c['physGrain']:
self.r2 = grainGrowth(self.diffu.Tz, Ts, iter, dt)
# write results as often as specified in the init method
if [True for iter in self.TWrite if iter == mtime] == [True]:
rho_time = np.append(mtime, self.rho)
Tz_time = np.append(mtime, self.diffu.Tz)
age_time = np.append(mtime, self.age)
z_time = np.append(mtime, self.z)
Dcon_time = np.append(mtime, self.Dcon)
Clim_time = np.append(mtime, [bdot[iter], Ts[iter]])
bdot_time = np.append(mtime, self.bdot_mean)
if c['physGrain']:
r2_time = np.append(mtime, self.r2)
write_nospin(self.c['resultsFolder'], self.c['physGrain'], rho_time, Tz_time, age_time, z_time, D_time, Clim_time, bdot_time, r2_time)
update_BCO()
update_LIZ()
update_DIP()
# write BCO, LIZ, DIP at the end of the time evolution
write_nospin_BCO(self.c['resultsFolder'], self.bcoAgeMartAll, self.bcoDepMartAll, self.bcoAge815All, self.bcoDep815All)
write_nospin_LIZ(self.c['resultsFolder'], self.LIZAgeAll, self.LIZDepAll)
write_nospin_DIP(self.c['resultsFolder'], self.intPhiAll)
def define_parameters(self):
'''
Return the parameters used in the model, for the initialization as well as the time evolution
:returns gridLen: size of grid used in the model run
(unit: number of boxes, type: int)
:returns dx: vector of width of each box, used for stress calculations
(unit: ???, type: array of ints)
:returns dt: number of seconds per time step
(unit: seconds, type: float)
:returns t: number of years per time step
(unit: years, type: float)
:returns modeltime: linearly spaced time vector from indicated start year to indicated end year
(unit: years, type: array of floats)
:returns years: total number of years in the model run
(unit: years, type: float)
:returns stp: total number of steps in the model run
(unit: number of steps, type: int)
:returns T_mean: interpolated temperature vector based on the model time and the initial user temperature data
(unit: ???, type: array of floats)
:returns Ts: interpolated temperature vector based on the model time & the initial user temperature data
may have a seasonal signal imposed depending on number of years per time step (< 1)
(unit: ???, type: array of floats)
:returns bdot: bdot is meters of ice equivalent/year. multiply by 0.917 for W.E. or 917.0 for kg/year
(unit: ???, type: )
:returns bdotSec: accumulation rate vector at each time step
(unit: ???, type: array of floats)
:returns rhos0: surface accumulate rate vector
(unit: ???, type: array of floats)
:returns D_surf: diffusivity tracker
(unit: ???, type: array of floats)
'''
gridLen = np.size(self.z)
dx = np.ones(gridLen)
input_temp, input_year_temp = read_temp(self.c['InputFileNameTemp'])
input_bdot, input_year_bdot = read_bdot(self.c['InputFileNamebdot'])
yr_start = max(input_year_temp[0], input_year_bdot[0])
yr_end = min(input_year_temp[-1], input_year_bdot[-1])
modeltime = np.linspace(yr_start, yr_end, stp + 1)
years = (yr_end - yr_start) * 1.0
stp = int(years * self.c['stpsPerYear'])
dt = years * S_PER_YEAR / stp
t = 1.0 / self.c['stpsPerYear']
TPeriod = years
Ts = np.interp(modeltime, input_year_temp, input_temp)
T_mean = Ts
if t < 1.0:
Ts = Ts + self.c['TAmp'] * (np.cos(2 * np.pi * np.linspace(0, TPeriod, stp + 1)) + 0.3 * np.cos(4 * np.pi * np.linspace(0, TPeriod, stp + 1)))
bdot = np.interp(modeltime, input_year_bdot, input_bdot)
bdotSec = bdot / S_PER_YEAR / (stp / years)
rhos0 = self.c['rhos0'] * np.ones(stp)
D_surf = self.c['D_surf'] * np.ones(stp)
return gridLen, dx, dt, t, modeltime, years, stp, Ts, T_mean, bdot, bdotSec, rhos0, D_surf
def update_BCO(self):
'''
Updates the bubble close-off depth and age based on the Martinerie criteria as well as through assuming the critical density is 815 kg/m^3
'''
bcoMartRho = 1 / (1 / (917.0) + self.diffu.T10m * 6.95E-7 - 4.3e-5) # Martinerie density at close off; see Buizert thesis (2011), Blunier & Schwander (2000), Goujon (2003)
bcoAgeMart = min(self.age[selfrho >= bcoMartRho]) / S_PER_YEAR # close-off age from Martinerie
bcoDepMart = min(selfz[selfrho >= (bcoMartRho)])
self.bcoAgeMartAll.append(bcoAgeMart) # age at the 815 density horizon
self.bcoDepMartAll.append(bcoDepMart) # this is the 815 close off depth
# bubble close-off age and depth assuming rho_crit = 815kg/m^3
bcoAge815 = min(self.age[self.rho >= (RHO_2)]) / S_PER_YEAR # close-off age where rho = 815 kg m^-3
bcoDep815 = min(self.z[self.rho >= (RHO_2)])
self.bcoAge815All.append(bcoAge815) # age at the 815 density horizon
self.bcoDep815All.append(bcoDep815) # this is the 815 close off depth
def update_LIZ(self):
'''
Updates the lock-in zone depth and age
'''
bcoMartRho = 1 / (1 / (917.0) + self.diffu.T10m * 6.95E-7 - 4.3e-5) # Martinerie density at close off; see Buizert thesis (2011), Blunier & Schwander (2000), Goujon (2003)
LIZMartRho = bcoMartRho - 14.0 # LIZ depth (Blunier and Schwander, 2000)
self.LIZAgeMart = min(self.age[self.rho > LIZMartRho]) / S_PER_YEAR # lock-in age
self.LIZDepMart = min(self.z[self.rho >= (LIZMartRho)]) # lock in depth
self.LIZAgeAll.append(LIZAgeMart)
self.LIZDepAll.append(LIZDepMart)
def update_DIP(self):
'''
Updates the depth-integrated porosity
'''
bcoMartRho = 1 / (1 / (917.0) + self.diffu.T10m * 6.95E-7 - 4.3e-5) # Martinerie density at close off; see Buizert thesis (2011), Blunier & Schwander (2000), Goujon (2003)
phi = 1 - self.rho / RHO_I # total porosity
phi[phi <= 0] = 1e-16
phiC = 1 - bcoMartRho / RHO_I; # porosity at close off
phiClosed = 0.37 * phi * (phi / phiC) ** -7.6 # Closed porosity, from Goujon. See Buizert thesis (eq. 2.3) as well
phiOpen = phi - phiClosed # open porosity
phiOpen[phiOpen <= 0] = 1.e-10 # don't want negative porosity.
intPhi = np.sum(phi * self.dz) # depth-integrated porosity
self.intPhiAll.append(intPhi)
