def __init__(self, emissions=None, time_step=1, intervals=10):
"""BEAMCarbon init
Args:
:param emissions: Array of annual emissions in GtC, beginning
in 2005
:type emissions: list
:param time_step: Time between emissions values in years
:type time_step: float
:param intervals: Number of times to calculate BEAM carbon
per timestep
:type intervals: int
"""
self._temperature_dependent = True
self._intervals = intervals
self._time_step = time_step
self.temperature = DICETemperature(self.time_step, self.intervals, 0)
if emissions is not None and type(emissions) in [list, np.ndarray]:
self.emissions = emissions
else:
self.emissions = np.zeros(1)
self._k_1 = 8e-7
self._k_2 = 4.53e-10
self._k_h = 1.23e3
self._A = None
self._B = None
self._Alk = 767.
self._initial_carbon = np.array([808.9, 725., 35641.])
self._carbon_mass = None
self._linear_temperature = False
def linear_temperature(self, value):
if value:
self.temperature = LinearTemperature(self.time_step,
self.intervals, self.n)
else:
self.temperature = DICETemperature(self.time_step, self.intervals,
self.n)
self._linear_temperature = value
def linear_temperature(self, value):
if value:
self.temperature = LinearTemperature(self.time_step,
self.intervals, self.n)
else:
self.temperature = DICETemperature(self.time_step,
self.intervals, self.n)
self._linear_temperature = value
def __init__(self, emissions=None, time_step=1, intervals=10):
"""BEAMCarbon init
Args:
:param emissions: Array of annual emissions in GtC, beginning
in 2005
:type emissions: list
:param time_step: Time between emissions values in years
:type time_step: float
:param intervals: Number of times to calculate BEAM carbon
per timestep
:type intervals: int
"""
self._temperature_dependent = True
self._intervals = intervals
self._time_step = time_step
self.temperature = DICETemperature(self.time_step, self.intervals, 0)
if emissions is not None and type(emissions) in [list, np.ndarray]:
self.emissions = emissions
else:
self.emissions = np.zeros(1)
self._k_1 = 8e-7
self._k_2 = 4.53e-10
self._k_h = 1.23e3
self._A = None
self._B = None
self._Alk = 767.
self._initial_carbon = np.array([808.9, 725., 35641.])
self._carbon_mass = None
self._linear_temperature = False
class BEAMCarbon(object):
"""Class for computing BEAM carbon cycle from emissions input.
"""
def __init__(self, emissions=None, time_step=1, intervals=10):
"""BEAMCarbon init
Args:
:param emissions: Array of annual emissions in GtC, beginning
in 2005
:type emissions: list
:param time_step: Time between emissions values in years
:type time_step: float
:param intervals: Number of times to calculate BEAM carbon
per timestep
:type intervals: int
"""
self._temperature_dependent = True
self._intervals = intervals
self._time_step = time_step
self.temperature = DICETemperature(self.time_step, self.intervals, 0)
if emissions is not None and type(emissions) in [list, np.ndarray]:
self.emissions = emissions
else:
self.emissions = np.zeros(1)
self._k_1 = 8e-7
self._k_2 = 4.53e-10
self._k_h = 1.23e3
self._A = None
self._B = None
self._Alk = 767.
self._initial_carbon = np.array([808.9, 725., 35641.])
self._carbon_mass = None
self._linear_temperature = False
@property
def initial_carbon(self):
"""Values for initial carbon in atmosphere, upper and lower oceans
in GtC. Default values are from 2005.
"""
return self._initial_carbon
@initial_carbon.setter
def initial_carbon(self, value):
self._initial_carbon = value
@property
def carbon_mass(self):
if self._carbon_mass is None:
self._carbon_mass = self.initial_carbon.copy()
return self._carbon_mass
@carbon_mass.setter
def carbon_mass(self, value):
self._carbon_mass = value
@property
def transfer_matrix(self):
"""3 by 3 matrix of transfer coefficients for carbon cycle.
"""
return np.array([
-self.k_a,
self.k_a * self.A * self.B,
0,
self.k_a,
-(self.k_a * self.A * self.B) - self.k_d,
self.k_d / self.delta,
0,
self.k_d,
-self.k_d / self.delta,
]).reshape((
3,
3,
))
@property
def emissions(self):
"""Array of emissions values in GtC per year.
"""
return self._emissions
@emissions.setter
def emissions(self, value):
self._emissions = value
self.temperature.n = self.n
@property
def time_step(self):
"""Size of time steps in emissions array.
"""
return self._time_step
@time_step.setter
def time_step(self, value):
self._time_step = value
self.temperature.time_step = self.time_step
@property
def n(self):
return len(self.emissions)
@property
def intervals(self):
"""Number of intervals in each time step.
"""
return self._intervals
@intervals.setter
def intervals(self, value):
self._intervals = value
self.temperature.periods = self.intervals
@property
def k_a(self):
"""Time constant k_{a} (used for building transfer matrix).
"""
return .2
@property
def k_d(self):
"""Time constant k_{d} (used for building transfer matrix).
"""
return .05
@property
def delta(self):
"""Ratio of lower ocean to upper ocean (used for building transfer
matrix).
"""
return 50.
@property
def k_h(self):
"""CO2 solubility.
"""
if self._k_h is None:
self._k_h = self.get_kh(self.temperature.initial_temp[1])
return self._k_h
@k_h.setter
def k_h(self, value):
self._k_h = value
@property
def k_1(self):
"""First dissociation constant.
"""
if self._k_1 is None:
self._k_1 = self.get_k1(self.temperature.initial_temp[1])
return self._k_1
@k_1.setter
def k_1(self, value):
self._k_1 = value
@property
def k_2(self):
"""Second dissociation constant.
"""
if self._k_2 is None:
self._k_2 = self.get_k2(self.temperature.initial_temp[1])
return self._k_2
@k_2.setter
def k_2(self, value):
self._k_2 = value
@property
def AM(self):
"""Moles in the atmosphere.
"""
return 1.77e20
@property
def OM(self):
"""Moles in the ocean.
"""
return 7.8e22
@property
def Alk(self):
"""Alkalinity in GtC.
"""
return self._Alk
@Alk.setter
def Alk(self, value):
self._Alk = value
@property
def A(self):
"""Ratio of mass of CO2 in atmospheric to upper ocean dissolved CO2.
"""
if self._A is None:
if self.temperature_dependent:
self.k_h = self.get_kh(self.temperature.initial_temp[1])
self._A = self.get_A()
return self._A
@A.setter
def A(self, value):
self._A = value
@property
def B(self):
"""Ratio of dissolved CO2 to total oceanic carbon.
"""
if self._B is None:
self.temp_calibrate(self.temperature.initial_temp[1])
self._B = self.get_B(self.get_H(self.initial_carbon[1]))
return self._B
@B.setter
def B(self, value):
self._B = value
@property
def salinity(self):
"""Salinity in g / kg of seawater.
"""
return 35.
@property
def temperature_dependent(self):
"""Switch for calculating temperature-dependent parameters k_1,
k_2, and k_h.
"""
return self._temperature_dependent
@property
def linear_temperature(self):
return self._linear_temperature
@linear_temperature.setter
def linear_temperature(self, value):
if value:
self.temperature = LinearTemperature(self.time_step,
self.intervals, self.n)
else:
self.temperature = DICETemperature(self.time_step, self.intervals,
self.n)
self._linear_temperature = value
@temperature_dependent.setter
def temperature_dependent(self, value):
if type(value) is bool:
self._temperature_dependent = value
else:
raise TypeError(
'BEAMCarbon.temperature_dependent must be True or False.')
def temp_calibrate(self, to):
"""Recalibrate temperature-dependent parameters k_1, k_2, and k_h.
"""
self.k_1 = self.get_k1(to)
self.k_2 = self.get_k2(to)
self.k_h = self.get_kh(to)
self.A = self.get_A()
def get_B(self, h):
"""Calculate B (Ratio of dissolved CO2 to total oceanic carbon),
given H (the concentration of hydrogen ions)
:param h: H, concentration of hydrogen ions [H+] (the (pH) of seawater)
:type h: float
:return: B, ratio of dissolved CO2 to total oceanic carbon
:rtype: float
"""
return 1 / (1 + self.k_1 / h + self.k_1 * self.k_2 / h**2)
def get_A(self):
"""Calculate A based on temperature-dependent changes in k_h
:return: A
:rtype: float
"""
return self.k_h * self.AM / (self.OM / (self.delta + 1))
def get_H(self, mass_upper):
"""Solve for H+, the concentration of hydrogen ions
(the (pH) of seawater).
:param mass_upper: Carbon mass in ocenas in GtC
:type mass_upper: float
:return: H
:rtype: float
"""
p0 = 1
p1 = (self.k_1 - mass_upper * self.k_1 / self.Alk)
p2 = (1 - 2 * mass_upper / self.Alk) * self.k_1 * self.k_2
return max(np.roots([p0, p1, p2]))
def get_kh(self, temp_ocean):
"""Calculate temperature dependent k_h
:param temp_ocean: ocean temperature (C)
:type temp_ocean: float
:return: k_h
:rtype: float
"""
t = 283.15 + temp_ocean
k0 = np.exp(9345.17 / t - 60.2409 + 23.3585 * np.log(t / 100.) +
self.salinity * (.023517 - .00023656 * t + .0047036 *
(t / 100.)**2))
kh = 1 / (k0 * 1.027) * 55.57
self.A = kh * self.AM / (self.OM / (self.delta + 1.))
return kh
def get_pk1(self, t):
return (-13.721 + 0.031334 * t + 3235.76 / t +
1.3e-5 * self.salinity * t - 0.1031 * self.salinity**0.5)
def get_pk2(self, t):
return (5371.96 + 1.671221 * t + 0.22913 * self.salinity +
18.3802 * np.log10(self.salinity)) - (
128375.28 / t + 2194.30 * np.log10(t) +
8.0944e-4 * self.salinity * t + 5617.11 *
np.log10(self.salinity) / t) + 2.136 * self.salinity / t
def get_k1(self, temp_ocean):
"""Calculate temperature dependent k_1
:param temp_ocean: ocean temperature (C)
:type temp_ocean: float
:return: k_1
:rtype: float
"""
return 10**-self.get_pk1(283.15 + temp_ocean)
def get_k2(self, temp_ocean):
"""Calculate temperature dependent k_2
:param temp_ocean: ocean temperature (C)
:type temp_ocean: float
:return: k_2
:rtype: float
"""
return 10**-self.get_pk2(283.15 + temp_ocean)
def run(self):
N = self.n * self.intervals
self.carbon_mass = self.initial_carbon.copy()
total_carbon = 0
emissions = np.zeros(3)
temp_atmosphere, temp_ocean = self.temperature.initial_temp
output = np.tile(
np.concatenate((
self.initial_carbon,
self.temperature.initial_temp,
np.array(
[self.transfer_matrix[0][1], self.transfer_matrix[1][1]]),
np.zeros(3),
)).reshape((10, 1)).copy(), (self.n + 1, ))
output = pd.DataFrame(
output,
index=[
'mass_atmosphere', 'mass_upper', 'mass_lower',
'temp_atmosphere', 'temp_ocean', 'phi12', 'phi22',
'cumulative', 'A', 'B'
],
columns=np.arange(self.n + 1) * self.time_step,
)
for i in range(N):
_i = int(floor(i / self.intervals)) # time_step
if i % self.intervals == 0 and self.temperature_dependent:
self.temp_calibrate(temp_ocean)
h = self.get_H(self.carbon_mass[1])
self.B = self.get_B(h)
emissions[0] = self.emissions[_i] * self.time_step / self.intervals
total_carbon += emissions[0]
self.carbon_mass += (
(self.transfer_matrix * self._time_step *
np.divide(self.carbon_mass, self.intervals)).sum(axis=1) +
emissions)
if (i + 1) % self.intervals == 0:
emissions[0] = self.emissions[_i] * self.time_step
total_carbon += emissions[0]
ta = temp_atmosphere
temp_atmosphere = self.temperature.temp_atmosphere(
index=_i,
temp_atmosphere=ta,
temp_ocean=temp_ocean,
mass_atmosphere=self.carbon_mass[0],
carbon=total_carbon,
initial_carbon=self.initial_carbon,
phi11=self.transfer_matrix[0][0],
phi21=self.transfer_matrix[1][0])
temp_ocean = self.temperature.temp_ocean(ta, temp_ocean)
output.iloc[:, _i + 1] = (np.concatenate(
(self.carbon_mass.copy(),
np.array([temp_atmosphere, temp_ocean]),
np.array([
self.transfer_matrix[0][1],
self.transfer_matrix[1][1], total_carbon, self.A,
self.B
]))))
return output
class BEAMCarbon(object):
"""Class for computing BEAM carbon cycle from emissions input.
"""
def __init__(self, emissions=None, time_step=1, intervals=10):
"""BEAMCarbon init
Args:
:param emissions: Array of annual emissions in GtC, beginning
in 2005
:type emissions: list
:param time_step: Time between emissions values in years
:type time_step: float
:param intervals: Number of times to calculate BEAM carbon
per timestep
:type intervals: int
"""
self._temperature_dependent = True
self._intervals = intervals
self._time_step = time_step
self.temperature = DICETemperature(self.time_step, self.intervals, 0)
if emissions is not None and type(emissions) in [list, np.ndarray]:
self.emissions = emissions
else:
self.emissions = np.zeros(1)
self._k_1 = 8e-7
self._k_2 = 4.53e-10
self._k_h = 1.23e3
self._A = None
self._B = None
self._Alk = 767.
self._initial_carbon = np.array([808.9, 725., 35641.])
self._carbon_mass = None
self._linear_temperature = False
@property
def initial_carbon(self):
"""Values for initial carbon in atmosphere, upper and lower oceans
in GtC. Default values are from 2005.
"""
return self._initial_carbon
@initial_carbon.setter
def initial_carbon(self, value):
self._initial_carbon = value
@property
def carbon_mass(self):
if self._carbon_mass is None:
self._carbon_mass = self.initial_carbon.copy()
return self._carbon_mass
@carbon_mass.setter
def carbon_mass(self, value):
self._carbon_mass = value
@property
def transfer_matrix(self):
"""3 by 3 matrix of transfer coefficients for carbon cycle.
"""
return np.array([
-self.k_a, self.k_a * self.A * self.B, 0,
self.k_a, -(self.k_a * self.A * self.B) - self.k_d,
self.k_d / self.delta,
0, self.k_d, -self.k_d / self.delta,
]).reshape((3, 3,))
@property
def emissions(self):
"""Array of emissions values in GtC per year.
"""
return self._emissions
@emissions.setter
def emissions(self, value):
self._emissions = value
self.temperature.n = self.n
@property
def time_step(self):
"""Size of time steps in emissions array.
"""
return self._time_step
@time_step.setter
def time_step(self, value):
self._time_step = value
self.temperature.time_step = self.time_step
@property
def n(self):
return len(self.emissions)
@property
def intervals(self):
"""Number of intervals in each time step.
"""
return self._intervals
@intervals.setter
def intervals(self, value):
self._intervals = value
self.temperature.periods = self.intervals
@property
def k_a(self):
"""Time constant k_{a} (used for building transfer matrix).
"""
return .2
@property
def k_d(self):
"""Time constant k_{d} (used for building transfer matrix).
"""
return .05
@property
def delta(self):
"""Ratio of lower ocean to upper ocean (used for building transfer
matrix).
"""
return 50.
@property
def k_h(self):
"""CO2 solubility.
"""
if self._k_h is None:
self._k_h = self.get_kh(self.temperature.initial_temp[1])
return self._k_h
@k_h.setter
def k_h(self, value):
self._k_h = value
@property
def k_1(self):
"""First dissociation constant.
"""
if self._k_1 is None:
self._k_1 = self.get_k1(self.temperature.initial_temp[1])
return self._k_1
@k_1.setter
def k_1(self, value):
self._k_1 = value
@property
def k_2(self):
"""Second dissociation constant.
"""
if self._k_2 is None:
self._k_2 = self.get_k2(self.temperature.initial_temp[1])
return self._k_2
@k_2.setter
def k_2(self, value):
self._k_2 = value
@property
def AM(self):
"""Moles in the atmosphere.
"""
return 1.77e20
@property
def OM(self):
"""Moles in the ocean.
"""
return 7.8e22
@property
def Alk(self):
"""Alkalinity in GtC.
"""
return self._Alk
@Alk.setter
def Alk(self, value):
self._Alk = value
@property
def A(self):
"""Ratio of mass of CO2 in atmospheric to upper ocean dissolved CO2.
"""
if self._A is None:
if self.temperature_dependent:
self.k_h = self.get_kh(self.temperature.initial_temp[1])
self._A = self.get_A()
return self._A
@A.setter
def A(self, value):
self._A = value
@property
def B(self):
"""Ratio of dissolved CO2 to total oceanic carbon.
"""
if self._B is None:
self.temp_calibrate(self.temperature.initial_temp[1])
self._B = self.get_B(self.get_H(self.initial_carbon[1]))
return self._B
@B.setter
def B(self, value):
self._B = value
@property
def salinity(self):
"""Salinity in g / kg of seawater.
"""
return 35.
@property
def temperature_dependent(self):
"""Switch for calculating temperature-dependent parameters k_1,
k_2, and k_h.
"""
return self._temperature_dependent
@property
def linear_temperature(self):
return self._linear_temperature
@linear_temperature.setter
def linear_temperature(self, value):
if value:
self.temperature = LinearTemperature(self.time_step,
self.intervals, self.n)
else:
self.temperature = DICETemperature(self.time_step,
self.intervals, self.n)
self._linear_temperature = value
@temperature_dependent.setter
def temperature_dependent(self, value):
if type(value) is bool:
self._temperature_dependent = value
else:
raise TypeError('BEAMCarbon.temperature_dependent must be True or False.')
def temp_calibrate(self, to):
"""Recalibrate temperature-dependent parameters k_1, k_2, and k_h.
"""
self.k_1 = self.get_k1(to)
self.k_2 = self.get_k2(to)
self.k_h = self.get_kh(to)
self.A = self.get_A()
def get_B(self, h):
"""Calculate B (Ratio of dissolved CO2 to total oceanic carbon),
given H (the concentration of hydrogen ions)
:param h: H, concentration of hydrogen ions [H+] (the (pH) of seawater)
:type h: float
:return: B, ratio of dissolved CO2 to total oceanic carbon
:rtype: float
"""
return 1 / (1 + self.k_1 / h + self.k_1 * self.k_2 / h ** 2)
def get_A(self):
"""Calculate A based on temperature-dependent changes in k_h
:return: A
:rtype: float
"""
return self.k_h * self.AM / (self.OM / (self.delta + 1))
def get_H(self, mass_upper):
"""Solve for H+, the concentration of hydrogen ions
(the (pH) of seawater).
:param mass_upper: Carbon mass in ocenas in GtC
:type mass_upper: float
:return: H
:rtype: float
"""
p0 = 1
p1 = (self.k_1 - mass_upper * self.k_1 / self.Alk)
p2 = (1 - 2 * mass_upper / self.Alk) * self.k_1 * self.k_2
return max(np.roots([p0, p1, p2]))
def get_kh(self, temp_ocean):
"""Calculate temperature dependent k_h
:param temp_ocean: ocean temperature (C)
:type temp_ocean: float
:return: k_h
:rtype: float
"""
t = 283.15 + temp_ocean
k0 = np.exp(
9345.17 / t - 60.2409 + 23.3585 * np.log(t / 100.) +
self.salinity * (
.023517 - .00023656 * t + .0047036 * (t / 100.) ** 2))
kh = 1 / (k0 * 1.027) * 55.57
self.A = kh * self.AM / (self.OM / (self.delta + 1.))
return kh
def get_pk1(self, t):
return (
-13.721 + 0.031334 * t + 3235.76 / t + 1.3e-5 * self.salinity * t -
0.1031 * self.salinity ** 0.5)
def get_pk2(self, t):
return (
5371.96 + 1.671221 * t + 0.22913 * self.salinity +
18.3802 * np.log10(self.salinity)) - (128375.28 / t +
2194.30 * np.log10(t) + 8.0944e-4 * self.salinity * t +
5617.11 * np.log10(self.salinity) / t) + 2.136 * self.salinity / t
def get_k1(self, temp_ocean):
"""Calculate temperature dependent k_1
:param temp_ocean: ocean temperature (C)
:type temp_ocean: float
:return: k_1
:rtype: float
"""
return 10 ** -self.get_pk1(283.15 + temp_ocean)
def get_k2(self, temp_ocean):
"""Calculate temperature dependent k_2
:param temp_ocean: ocean temperature (C)
:type temp_ocean: float
:return: k_2
:rtype: float
"""
return 10 ** -self.get_pk2(283.15 + temp_ocean)
def run(self):
N = self.n * self.intervals
self.carbon_mass = self.initial_carbon.copy()
total_carbon = 0
emissions = np.zeros(3)
temp_atmosphere, temp_ocean = self.temperature.initial_temp
output = np.tile(np.concatenate((
self.initial_carbon,
self.temperature.initial_temp,
np.array([
self.transfer_matrix[0][1], self.transfer_matrix[1][1]]),
np.zeros(3),
)).reshape((10, 1)).copy(), (self.n + 1, ))
output = pd.DataFrame(
output,
index=['mass_atmosphere', 'mass_upper', 'mass_lower',
'temp_atmosphere', 'temp_ocean', 'phi12', 'phi22',
'cumulative', 'A', 'B'],
columns=np.arange(self.n + 1) * self.time_step,
)
for i in xrange(N):
_i = int(floor(i / self.intervals)) # time_step
if i % self.intervals == 0 and self.temperature_dependent:
self.temp_calibrate(temp_ocean)
h = self.get_H(self.carbon_mass[1])
self.B = self.get_B(h)
emissions[0] = self.emissions[_i] * self.time_step / self.intervals
total_carbon += emissions[0]
self.carbon_mass += (
(self.transfer_matrix *
np.divide(self.carbon_mass, self.intervals)).sum(axis=1) +
emissions)
if (i + 1) % self.intervals == 0:
emissions[0] = self.emissions[_i] * self.time_step
total_carbon += emissions[0]
ta = temp_atmosphere
temp_atmosphere = self.temperature.temp_atmosphere(
index=_i, temp_atmosphere=ta,
temp_ocean=temp_ocean, mass_atmosphere=self.carbon_mass[0],
carbon=total_carbon, initial_carbon=self.initial_carbon,
phi11=self.transfer_matrix[0][0],
phi21=self.transfer_matrix[1][0])
temp_ocean = self.temperature.temp_ocean(
ta, temp_ocean)
output.iloc[:, _i + 1] = (
np.concatenate((self.carbon_mass.copy(),
np.array([temp_atmosphere, temp_ocean]),
np.array([self.transfer_matrix[0][1],
self.transfer_matrix[1][1],
total_carbon,
self.A, self.B]))))
return output