"""Mass-balance models"""
# Built ins
# External libs
import numpy as np
import pandas as pd
import netCDF4
from scipy.interpolate import interp1d
from scipy import optimize as optimization
# Locals
import oggm.cfg as cfg
from oggm.cfg import SEC_IN_YEAR, SEC_IN_MONTH
from oggm.utils import (SuperclassMeta, lazy_property, floatyear_to_date,
date_to_floatyear, monthly_timeseries)
[docs]class MassBalanceModel(object, metaclass=SuperclassMeta):
"""Common logic for the mass balance models.
All mass-balance models should implement this interface.
"""
[docs] def __init__(self):
""" Initialize."""
self._temp_bias = 0
self.valid_bounds = None
@property
def temp_bias(self):
"""Temperature bias to add to the original series."""
return self._temp_bias
@temp_bias.setter
def temp_bias(self, value):
"""Temperature bias to add to the original series."""
self._temp_bias = value
[docs] def get_monthly_mb(self, heights, year=None):
"""Monthly mass-balance at given altitude(s) for a moment in time.
Units: [m s-1], or meters of ice per second
Note: `year` is optional because some simpler models have no time
component.
Parameters
----------
heights: ndarray
the atitudes at which the mass-balance will be computed
year: float, optional
the time (in the "hydrological floating year" convention)
Returns
-------
the mass-balance (same dim as `heights`) (units: [m s-1])
"""
raise NotImplementedError()
[docs] def get_annual_mb(self, heights, year=None):
"""Like `self.get_monthly_mb()`, but for annual MB.
For some simpler mass-balance models ``get_monthly_mb()` and
`get_annual_mb()`` can be equivalent.
Units: [m s-1], or meters of ice per second
Note: `year` is optional because some simpler models have no time
component.
Parameters
----------
heights: ndarray
the atitudes at which the mass-balance will be computed
year: float, optional
the time (in the "floating year" convention)
Returns
-------
the mass-balance (same dim as `heights`) (units: [m s-1])
"""
raise NotImplementedError()
[docs] def get_specific_mb(self, heights, widths, year=None):
"""Specific mb for this year and a specific glacier geometry.
Units: [mm w.e. yr-1], or millimeter water equivalent per year
Parameters
----------
heights: ndarray
the atitudes at which the mass-balance will be computed
widths: ndarray
the widths of the flowline (necessary for the weighted average)
year: float, optional
the time (in the "hydrological floating year" convention)
Returns
-------
the specific mass-balance (units: mm w.e. yr-1)
"""
if len(np.atleast_1d(year)) > 1:
out = [self.get_specific_mb(heights, widths, year=yr)
for yr in year]
return np.asarray(out)
mbs = self.get_annual_mb(heights, year=year) * SEC_IN_YEAR * cfg.RHO
return np.average(mbs, weights=widths)
def get_ela(self, year=None):
"""Compute the equilibrium line altitude for this year
Parameters
----------
year: float, optional
the time (in the "hydrological floating year" convention)
Returns
-------
the equilibrium line altitude (ELA, units: m)
"""
if len(np.atleast_1d(year)) > 1:
return np.asarray([self.get_ela(year=yr) for yr in year])
if self.valid_bounds is None:
raise ValueError('attribute `valid_bounds` needs to be '
'set for the ELA computation.')
# Check for invalid ELAs
b0, b1 = self.valid_bounds
if (np.any(~np.isfinite(self.get_annual_mb([b0, b1], year=year))) or
(self.get_annual_mb([b0], year=year)[0] > 0) or
(self.get_annual_mb([b1], year=year)[0] < 0)):
return np.NaN
def to_minimize(x):
o = self.get_annual_mb([x], year=year)[0] * SEC_IN_YEAR * cfg.RHO
return o
return optimization.brentq(to_minimize, *self.valid_bounds, xtol=0.1)
[docs]class LinearMassBalance(MassBalanceModel):
"""Constant mass-balance as a linear function of altitude.
The "temperature bias" doesn't makes much sense in this context, but we
implemented a simple empirical rule: + 1K -> ELA + 150 m
"""
[docs] def __init__(self, ela_h, grad=3., max_mb=None):
""" Initialize.
Parameters
----------
ela_h: float
Equilibrium line altitude (units: [m])
grad: float
Mass-balance gradient (unit: [mm w.e. yr-1 m-1])
max_mb: float
Cap the mass balance to a certain value (unit: [mm w.e. yr-1])
"""
super(LinearMassBalance, self).__init__()
self.valid_bounds = [-1e4, 2e4] # in m
self.orig_ela_h = ela_h
self.ela_h = ela_h
self.grad = grad
self.max_mb = max_mb
@MassBalanceModel.temp_bias.setter
def temp_bias(self, value):
"""Temperature bias to change the ELA."""
self.ela_h = self.orig_ela_h + value * 150
self._temp_bias = value
def get_monthly_mb(self, heights, year=None):
mb = (np.asarray(heights) - self.ela_h) * self.grad
if self.max_mb is not None:
mb = mb.clip(None, self.max_mb)
return mb / SEC_IN_YEAR / cfg.RHO
def get_annual_mb(self, heights, year=None):
return self.get_monthly_mb(heights, year=year)
[docs]class PastMassBalance(MassBalanceModel):
"""Mass balance during the climate data period."""
[docs] def __init__(self, gdir, mu_star=None, bias=None, prcp_fac=None,
filename='climate_monthly', input_filesuffix=''):
"""Initialize.
Parameters
----------
gdir : GlacierDirectory
the glacier directory
mu_star : float, optional
set to the alternative value of mustar you want to use
(the default is to use the calibrated value)
bias : float, optional
set to the alternative value of the calibration bias [mm we yr-1]
you want to use (the default is to use the calibrated value)
Note that this bias is *substracted* from the computed MB. Indeed:
BIAS = MODEL_MB - REFERENCE_MB.
prcp_fac : float, optional
set to the alternative value of the precipitation factor
you want to use (the default is to use the calibrated value)
filename : str, optional
set to a different BASENAME if you want to use alternative climate
data.
input_filesuffix : str
the file suffix of the input climate file
"""
super(PastMassBalance, self).__init__()
self.valid_bounds = [-1e4, 2e4] # in m
if mu_star is None:
df = pd.read_csv(gdir.get_filepath('local_mustar'))
mu_star = df['mu_star'][0]
if bias is None:
if cfg.PARAMS['use_bias_for_run']:
df = pd.read_csv(gdir.get_filepath('local_mustar'))
bias = df['bias'][0]
else:
bias = 0.
if prcp_fac is None:
df = pd.read_csv(gdir.get_filepath('local_mustar'))
prcp_fac = df['prcp_fac'][0]
self.mu_star = mu_star
self.bias = bias
# Parameters
self.t_solid = cfg.PARAMS['temp_all_solid']
self.t_liq = cfg.PARAMS['temp_all_liq']
self.t_melt = cfg.PARAMS['temp_melt']
# Public attrs
self.temp_bias = 0.
# Read file
fpath = gdir.get_filepath(filename, filesuffix=input_filesuffix)
with netCDF4.Dataset(fpath, mode='r') as nc:
# time
time = nc.variables['time']
time = netCDF4.num2date(time[:], time.units)
ny, r = divmod(len(time), 12)
if r != 0:
raise ValueError('Climate data should be N full years')
# This is where we switch to hydro float year format
# Last year gives the tone of the hydro year
self.years = np.repeat(np.arange(time[-1].year-ny+1,
time[-1].year+1), 12)
self.months = np.tile(np.arange(1, 13), ny)
# Read timeseries
self.temp = nc.variables['temp'][:]
self.prcp = nc.variables['prcp'][:] * prcp_fac
self.grad = nc.variables['grad'][:]
self.ref_hgt = nc.ref_hgt
def get_monthly_climate(self, heights, year=None):
"""Monthly climate information at given heights.
Note that prcp is corrected with the precipitation factor.
Returns
-------
(temp, tempformelt, prcp, prcpsol)
"""
y, m = floatyear_to_date(year)
pok = np.where((self.years == y) & (self.months == m))[0][0]
# Read timeseries
itemp = self.temp[pok] + self.temp_bias
iprcp = self.prcp[pok]
igrad = self.grad[pok]
# For each height pixel:
# Compute temp and tempformelt (temperature above melting threshold)
npix = len(heights)
temp = np.ones(npix) * itemp + igrad * (heights - self.ref_hgt)
tempformelt = temp - self.t_melt
tempformelt[:] = np.clip(tempformelt, 0, tempformelt.max())
# Compute solid precipitation from total precipitation
prcp = np.ones(npix) * iprcp
fac = 1 - (temp - self.t_solid) / (self.t_liq - self.t_solid)
prcpsol = prcp * np.clip(fac, 0, 1)
return temp, tempformelt, prcp, prcpsol
def get_monthly_mb(self, heights, year=None):
_, tmelt, _, prcpsol = self.get_monthly_climate(heights, year=year)
y, m = floatyear_to_date(year)
mb_month = prcpsol - self.mu_star * tmelt
mb_month -= self.bias * SEC_IN_MONTH / SEC_IN_YEAR
return mb_month / SEC_IN_MONTH / cfg.RHO
def get_annual_mb(self, heights, year=None):
year = np.floor(year)
pok = np.where(self.years == year)[0]
if len(pok) < 1:
raise ValueError('Year {} not in record'.format(int(year)))
# Read timeseries
itemp = self.temp[pok] + self.temp_bias
iprcp = self.prcp[pok]
igrad = self.grad[pok]
# For each height pixel:
# Compute temp and tempformelt (temperature above melting threshold)
heights = np.asarray(heights)
npix = len(heights)
grad_temp = np.atleast_2d(igrad).repeat(npix, 0)
grad_temp *= (heights.repeat(12).reshape(grad_temp.shape) -
self.ref_hgt)
temp2d = np.atleast_2d(itemp).repeat(npix, 0) + grad_temp
temp2dformelt = temp2d - self.t_melt
temp2dformelt[:] = np.clip(temp2dformelt, 0, temp2dformelt.max())
# Compute solid precipitation from total precipitation
prcpsol = np.atleast_2d(iprcp).repeat(npix, 0)
fac = 1 - (temp2d - self.t_solid) / (self.t_liq - self.t_solid)
fac = np.clip(fac, 0, 1)
prcpsol *= fac
mb_annual = np.sum(prcpsol - self.mu_star * temp2dformelt, axis=1)
return (mb_annual - self.bias) / SEC_IN_YEAR / cfg.RHO
[docs]class ConstantMassBalance(MassBalanceModel):
"""Constant mass-balance during a chosen period.
This is useful for equilibrium experiments.
"""
[docs] def __init__(self, gdir, mu_star=None, bias=None, prcp_fac=None,
y0=None, halfsize=15, filename='climate_monthly',
input_filesuffix=''):
"""Initialize
Parameters
----------
gdir : GlacierDirectory
the glacier directory
mu_star : float, optional
set to the alternative value of mustar you want to use
(the default is to use the calibrated value)
bias : float, optional
set to the alternative value of the annual bias [mm we yr-1]
you want to use (the default is to use the calibrated value)
prcp_fac : float, optional
set to the alternative value of the precipitation factor
you want to use (the default is to use the calibrated value)
y0 : int, optional, default: tstar
the year at the center of the period of interest. The default
is to use tstar as center.
halfsize : int, optional
the half-size of the time window (window size = 2 * halfsize + 1)
filename : str, optional
set to a different BASENAME if you want to use alternative climate
data.
input_filesuffix : str
the file suffix of the input climate file
"""
super(ConstantMassBalance, self).__init__()
self.mbmod = PastMassBalance(gdir, mu_star=mu_star, bias=bias,
prcp_fac=prcp_fac, filename=filename,
input_filesuffix=input_filesuffix)
if y0 is None:
df = pd.read_csv(gdir.get_filepath('local_mustar'))
y0 = df['t_star'][0]
# This is a quick'n dirty optimisation
try:
fls = gdir.read_pickle('model_flowlines')
h = []
for fl in fls:
# We use bed because of overdeepenings
h = np.append(h, fl.bed_h)
h = np.append(h, fl.surface_h)
zminmax = np.round([np.min(h)-50, np.max(h)+2000])
except FileNotFoundError:
# in case we don't have them
with netCDF4.Dataset(gdir.get_filepath('gridded_data')) as nc:
zminmax = [nc.min_h_dem-250, nc.max_h_dem+1500]
self.hbins = np.arange(*zminmax, step=10)
self.valid_bounds = self.hbins[[0, -1]]
self.y0 = y0
self.halfsize = halfsize
self.years = np.arange(y0-halfsize, y0+halfsize+1)
@MassBalanceModel.temp_bias.setter
def temp_bias(self, value):
"""Temperature bias to add to the original series."""
for attr_name in ['_lazy_interp_yr', '_lazy_interp_m']:
if hasattr(self, attr_name):
delattr(self, attr_name)
self.mbmod.temp_bias = value
self._temp_bias = value
@lazy_property
def interp_yr(self):
# annual MB
mb_on_h = self.hbins*0.
for yr in self.years:
mb_on_h += self.mbmod.get_annual_mb(self.hbins, year=yr)
return interp1d(self.hbins, mb_on_h / len(self.years))
@lazy_property
def interp_m(self):
# monthly MB
months = np.arange(12)+1
interp_m = []
for m in months:
mb_on_h = self.hbins*0.
for yr in self.years:
yr = date_to_floatyear(yr, m)
mb_on_h += self.mbmod.get_monthly_mb(self.hbins, year=yr)
interp_m.append(interp1d(self.hbins, mb_on_h / len(self.years)))
return interp_m
def get_climate(self, heights, year=None):
"""Average climate information at given heights.
Note that prcp is corrected with the precipitation factor.
Returns
-------
(temp, tempformelt, prcp, prcpsol)
"""
yrs = monthly_timeseries(self.years[0], self.years[-1],
include_last_year=True)
heights = np.atleast_1d(heights)
nh = len(heights)
shape = (len(yrs), nh)
temp = np.zeros(shape)
tempformelt = np.zeros(shape)
prcp = np.zeros(shape)
prcpsol = np.zeros(shape)
for i, yr in enumerate(yrs):
t, tm, p, ps = self.mbmod.get_monthly_climate(heights, year=yr)
temp[i, :] = t
tempformelt[i, :] = tm
prcp[i, :] = p
prcpsol[i, :] = ps
# Note that we do not weight for number of days per month - bad
return (np.mean(temp, axis=0),
np.mean(tempformelt, axis=0) * 12,
np.mean(prcp, axis=0) * 12,
np.mean(prcpsol, axis=0) * 12)
def get_monthly_mb(self, heights, year=None):
yr, m = floatyear_to_date(year)
return self.interp_m[m-1](heights)
def get_annual_mb(self, heights, year=None):
return self.interp_yr(heights)
[docs]class RandomMassBalance(MassBalanceModel):
"""Random shuffle of all MB years within a given time period.
This is useful for finding a possible past glacier state or for sensitivity
experiments.
Note that this is going to be sensitive to extreme years in certain
periods, but it is by far more physically reasonable than other
approaches based on gaussian assumptions.
"""
[docs] def __init__(self, gdir, mu_star=None, bias=None, prcp_fac=None,
y0=None, halfsize=15, seed=None, filename='climate_monthly',
input_filesuffix=''):
"""Initialize.
Parameters
----------
gdir : GlacierDirectory
the glacier directory
mu_star : float, optional
set to the alternative value of mustar you want to use
(the default is to use the calibrated value)
bias : float, optional
set to the alternative value of the calibration bias [mm we yr-1]
you want to use (the default is to use the calibrated value)
Note that this bias is *substracted* from the computed MB. Indeed:
BIAS = MODEL_MB - REFERENCE_MB.
prcp_fac : float, optional
set to the alternative value of the precipitation factor
you want to use (the default is to use the calibrated value)
y0 : int, optional, default: tstar
the year at the center of the period of interest. The default
is to use tstar as center.
halfsize : int, optional
the half-size of the time window (window size = 2 * halfsize + 1)
seed : int, optional
Random seed used to initialize the pseudo-random number generator.
filename : str, optional
set to a different BASENAME if you want to use alternative climate
data.
input_filesuffix : str
the file suffix of the input climate file
"""
super(RandomMassBalance, self).__init__()
self.valid_bounds = [-1e4, 2e4] # in m
self.mbmod = PastMassBalance(gdir, mu_star=mu_star, bias=bias,
prcp_fac=prcp_fac, filename=filename,
input_filesuffix=input_filesuffix)
if y0 is None:
df = pd.read_csv(gdir.get_filepath('local_mustar'))
y0 = df['t_star'][0]
# Climate period
self.years = np.arange(y0-halfsize, y0+halfsize+1)
self.yr_range = (y0-halfsize, y0+halfsize+1)
self.ny = len(self.years)
# RandomState
self.rng = np.random.RandomState(seed)
self._state_yr = dict()
@MassBalanceModel.temp_bias.setter
def temp_bias(self, value):
"""Temperature bias to add to the original series."""
self.mbmod.temp_bias = value
self._temp_bias = value
def get_state_yr(self, year=None):
"""For a given year, get the random year associated to it."""
year = int(year)
if year not in self._state_yr:
self._state_yr[year] = self.rng.randint(*self.yr_range)
return self._state_yr[year]
def get_monthly_mb(self, heights, year=None):
ryr, m = floatyear_to_date(year)
ryr = date_to_floatyear(self.get_state_yr(ryr), m)
return self.mbmod.get_monthly_mb(heights, year=ryr)
def get_annual_mb(self, heights, year=None):
ryr = self.get_state_yr(int(year))
return self.mbmod.get_annual_mb(heights, year=ryr)