def get_minmax(data, deg=2):
"""
returns the interpolated extremum and position (in fractions of frames)
:args:
data (iterable): data to be fitted with a <deg> degree polynomial
deg (int): degree of polynomial to fit
:returns:
val, pos: a tuple of floats indicating the position
"""
x = arange(len(data))
p = polyfit(x, data, deg)
d = (arange(len(p))[::-1] * p)[:-1]
r = roots(d)
cnt = 0
idx = None
for nr, rx in enumerate(r):
if isreal(r):
idx = nr
cnt +=1
if cnt > 1:
raise ValueError("Too many real roots found." +
"Reduce order of polynomial!")
x0 = r[nr].real
return x0, polyval(p, x0)
def get_minmax(data, deg=2):
"""
returns the interpolated extremum and position (in fractions of frames)
:args:
data (iterable): data to be fitted with a <deg> degree polynomial
deg (int): degree of polynomial to fit
:returns:
val, pos: a tuple of floats indicating the position
"""
x = arange(len(data))
p = polyfit(x, data, deg)
d = (arange(len(p))[::-1] * p)[:-1]
r = roots(d)
cnt = 0
idx = None
for nr, rx in enumerate(r):
if isreal(r):
idx = nr
cnt += 1
if cnt > 1:
raise ValueError("Too many real roots found." +
"Reduce order of polynomial!")
x0 = r[nr].real
return x0, polyval(p, x0)
def find_solid_p(rho):
sigma=1.
p=pl.arange(10,20,0.01 )
v0=sigma**3/pl.sqrt(2)
v=1./rho
y=(p*sigma**3)**-1
coeffs=pl.zeros(7)
coeffs[0]=19328.09
coeffs[1]=-2609.26
coeffs[2]=141.6000
coeffs[3]=11.56350
coeffs[4]=-1.807846
coeffs[5]=3
coeffs[6]=-v+v0
def find_real_positive(roots):
for root in roots:
if root.imag==0 and root.real>0:
return root.real
# print coeffs
roots=1./pl.roots(coeffs)
# f=3-1.807846*y+11.56350*y**2+141.6000*y**3-2609.260*y**4+19328.09*y**5-(v-v0)/y
# # print pl.polyval(coeffs,1./p)
# polynomial= pl.poly1d(coeffs)
P=find_real_positive(roots)
return P
def Cretaceous_cc(
y, t0, cl_sens, deep_grad, PG, change_out, F_outgass, W_plus_1, F_carbw,
CWF, CO2_dep, Te, n, coef_for_diss, beta, Ebas
): #inputs include DIC and ALK for ocean and pore space, time, and key parameters
global pK1, pK2, H_CO2, Pore_mod, k_d, k_w, k_c, k_o, Mp, ppCO2_o, Ea, Mo, ko1, ko2
# Perscribed evolution of ocean and pore-space calcium molality (Fig. S6):
Ca = 7.00658e-27 * abs(t0)**3 - 1.9847e-18 * (t0)**2 + 2.4016e-10 * (
t0) + 0.0100278
#ocean variables
s = 1.8e20 / Mo #Constant for ensuring mass conversation
[c, d] = pylab.roots([
y[1] / (10**-pK2 * 10**-pK1) * (1 + s / H_CO2),
(y[1] - y[0]) / (10**-pK2), (y[1] - 2 * y[0])
])
EM_H_o = numpy.max([c, d]) ## Evolving model ocean hydrogen molality
EM_pH_o = -pylab.log10(EM_H_o) ## Evolving model ocean pH
EM_co3_o = y[1] / (2 + EM_H_o /
(10**-pK2)) ## Evolving model ocean carbonate molality
EM_hco3_o = y[
1] - 2 * EM_co3_o ## Evolving model ocean bicarbonate molality
EM_co2aq_o = (EM_hco3_o * EM_H_o / (10**-pK1)
) ## Evolving model ocean aqueous CO2 molality
EM_ppCO2_o = EM_co2aq_o / H_CO2 ## Evolving model atmospheric pCO2
EM_Ca_o = Ca #Perscribed ocean Ca molality
#pore space variables
[c, d] = pylab.roots([
y[3] / (10**-pK2 * 10**-pK1), (y[3] - y[2]) / (10**-pK2),
(y[3] - 2 * y[2])
])
EM_H_p = numpy.max([c, d]) ## Evolving model pore space hydrogen molality
EM_pH_p = -pylab.log10(EM_H_p) ## Evolving model pore space pH
EM_co3_p = y[3] / (2 + EM_H_p / (10**-pK2)
) ## Evolving model pore space carbonate molality
EM_hco3_p = y[
3] - 2 * EM_co3_p ## Evolving model pore space bicarbonate molality
EM_co2aq_p = (EM_hco3_p * EM_H_p / (10**-pK1)
) ## Evolving model pore space aqueous CO2 molality
EM_ppCO2_p = EM_co2aq_p / H_CO2 ## Evolving model pore space pCO2 (unused)
EM_Ca_p = Ca #Percribed pore space Ca molality
# Perscribed evolution of continental shelf area (Fig. S5):
area = (.540e-23 * abs(t0)**3 - 3.072e-15 * abs(t0)**2 +
2.9997e-07 * abs(t0) + 16.089) / 16.089
# Apply climate model to calculate surface temperature (equation 5):
T_surface_diff = (cl_sens / numpy.log(2)) * numpy.log(
EM_ppCO2_o / ppCO2_o) - cl_sens * abs(t0) / (0.181e9 *
1.26) + PG * abs(t0) / 1e8
T_surface = T_surface_diff + 285
# Calculate pore space temperature (equation 11):
interc = 274.037 - deep_grad * 285
buffer_T = deep_grad * T_surface + interc
F_outg = F_outgass + change_out * F_outgass * (
abs(t0) / 1e8) #Outgassing as a function of time, equation 9
Relative_outgassing = F_outg / F_outgass #Relative outgassing
weatherability = weatherability_func(
abs(t0), W_plus_1) #Weatherability as a functino of time
#Calculate saturation state of ocean and pore space (equation 19):
EM_omega_o = EM_Ca_o * EM_co3_o / (Sol_prod(T_surface))
EM_omega_p = EM_Ca_p * EM_co3_p / (Sol_prod(buffer_T + Pore_mod))
# Carbonate weathering flux (equartion 7)
carb_weath = F_carbw * (1 + CWF * abs(t0) / 1e8) * (
EM_ppCO2_o / ppCO2_o)**(CO2_dep) * numpy.exp(
(T_surface_diff) / Te) * weatherability
# Ocean carbonate precipitation flux (equation 17)
Precip_ocean = ko1 * area * (EM_omega_o - 1)**n + ko2 * (
EM_omega_o**2.84) #shelf + pelagic
# Pore space carbonate precipitation flux (equation 18)
Precip_pore = k_c * (EM_omega_p - 1)**n
#seafloor dissolution flux (equation 12)
F_diss = k_d * 2.88 * 10**-14 * 10**(
-coef_for_diss * EM_pH_p) * Relative_outgassing**beta * numpy.exp(
-Ebas / (8.314 * (buffer_T + Pore_mod)))
#continental silicate weathering flux (equation 2)
F_silic = k_w * weatherability * (EM_ppCO2_o /
ppCO2_o)**CO2_dep * numpy.exp(
(T_surface_diff) / Te)
return [
Ca, EM_H_o, EM_pH_o, EM_co3_o, EM_hco3_o, EM_co2aq_o, EM_ppCO2_o,
EM_Ca_o, EM_H_p, EM_pH_p, EM_co3_p, EM_hco3_p, EM_co2aq_p, EM_ppCO2_p,
EM_Ca_p, area, T_surface, T_surface_diff, buffer_T, EM_omega_o,
EM_omega_p, Relative_outgassing, weatherability, F_outg, carb_weath,
Precip_ocean, Precip_pore, F_diss, F_silic
]
def forward_model(W, F_outgass, n, CO2_dep, Te, mod_sea, alt_frac, Mp_frac,
W_plus_1, cl_sens, change_out, F_carbw, frac_pel, CWF,
deep_grad, coef_for_diss, beta, Ebas, PG):
#import pdb
#pdb.set_trace()
# Make carbon chemistry constants and other parameters global variables:
global pK1, pK2, H_CO2, Pore_mod, k_d, k_w, k_c, k_o, Mp, ppCO2_o, Ea, Mo, ko1, ko2
# Constants for carbon chemisty
T = 18 + 273 #Temperature held constant for the purposes of calculating equilibrium constants (see manuscript)
pK1 = 17.788 - .073104 * T - .0051087 * 35 + 1.1463 * 10**-4 * T**2
pK2 = 20.919 - .064209 * T - .011887 * 35 + 8.7313 * 10**-5 * T**2
H_CO2 = pylab.exp(
9345.17 / T - 167.8108 + 23.3585 * pylab.log(T) +
(.023517 - 2.3656 * 10**-4 * T + 4.7036 * 10**-7 * T**2) * 35)
Mo = 1.35e21 #Mass of ocean (kg)
W = Mo / W #convert timescale of circulation (yr) to water flux through pore space (kg/yr)
Mp = Mp_frac * Mo #Calculate mass of ocean in pore space
partition = mod_sea / F_outgass #seafloor precipitation as a fraction of total carbon sink (used to initialize)
############################################################################
## Compute initial conditions (i.e. fluxes and ocean chemistry for modern carbon cycle):
F_diss0 = alt_frac * partition * F_outgass # Modern seafloor dissolution flux in pore space
F_silic0 = (1 - partition) * F_outgass + (
1 - alt_frac
) * partition * F_outgass #Modern continental silicaet weathering
Precip_pore0 = partition * F_outgass # Modern carbonate precipitation in pore-space
### Initial conditions for modern atmosphere and ocean
pH_o = 8.2 #pH of modern ocean
ppCO2_o = .000280 #preindustrial pCO2 (ppm)
CO2_aq_o = H_CO2 * ppCO2_o #modern ocean aqueous pCO2 molality
hco3_o = (10**-pK1) * CO2_aq_o / (10**-pH_o
) #modern ocean bicarbonate molality
co3_o = (10**-pK2) * hco3_o / (10**-pH_o
) # modern ocean carbonate molality
DIC_o = co3_o + hco3_o + CO2_aq_o #modern ocean dissolved inorganic carbon
ALK_o = 2 * co3_o + hco3_o # modern ocean alkalinity
Ca_o = 0.0100278 # modern oceanic calcium molality (mol/kg)
salt = ALK_o - 2 * Ca_o ## set salt to ensure ALK is consistent with Ca
T_surface_diff = 0
T_surface = T_surface_diff + 285 # Modern average surface temperature (K)
interc = 274.037 - deep_grad * 285 # Calculate intercept for surface vs. deep ocean temperature relationship
buffer_T = deep_grad * T_surface + interc # Calculate modern deep ocean temperature (K)
Pore_mod = 9.0 # Constant difference between deep ocean temperature and pore space temperature (K)
## Use these constants and steady state assumption to calculate remaining initial conditions:
b1 = 2 * F_diss0 + W * ALK_o - 2 * W * DIC_o
b2 = 2 * F_silic0 - W * ALK_o - 2 * F_outgass + 2 * W * DIC_o
a1 = W
a2 = -2 * W
a3 = -W
a4 = 2 * W
# Solving system of equations for pore space properties
DIC_p = DIC_o - Precip_pore0 / W #Modern dissolved inorganic carbon in pore space
ALK_p = (b1 - a2 * DIC_p) / a1 #Modern alkalinity in pore space
Precip_ocean0 = (F_outgass + F_carbw
) - (DIC_o - DIC_p) * W #Carbonate precipitation in ocean
if DIC_p < 0:
print("WARNING: NO PHYSIAL STEADY STATE EXISTS! DIC is negative")
#Solve quadratic ignoring H in ALK but including CO2aq
[vv, xx] = pylab.roots([
ALK_p / (10**-pK1 * 10**-pK2), (ALK_p - DIC_p) / (10**-pK2),
ALK_p - 2 * DIC_p
])
H_p = numpy.max([vv, xx]) # Modern hydrogen molality in pore space
pH_p = -pylab.log10(H_p) # Modern pH of pore space
#Find remaining carbon chemistry from equilibrium conditions:
CO2aq_p = DIC_p / ((10**-pK1) * (10**-pK2) / H_p**2 + 10**-pK1 / H_p + 1
) # Modern aqueous CO2 in pore space
co3_p = ALK_p - DIC_p - H_p + CO2aq_p # Modern carbonate alkalinity in pore space
hco3_p = co3_p * 10**-pH_p / (
10**-pK2) #Modern bicarbonate alkalinity in pore space (not used)
Ca_p = 0.5 * (ALK_p - salt) #Modern calcium molality in pore space
omega_p = Ca_p * co3_p / Sol_prod(
buffer_T + Pore_mod) #Modern saturation state pore space
omega_o = Ca_o * co3_o / Sol_prod(
T_surface) #Modern saturatino state of ocean
## All initital conditions have been calculated
############################################################################
############ Calculate proportionality constants ###########################
# Given modern precipitation fluxes and saturation states, calculate proportionality constants
k_c = Precip_pore0 / (omega_p - 1)**n
k_o = Precip_ocean0 / (omega_o - 1)**n
## Partition ocean carbonate sink into shelf precipitation and carbonate precipitation
ko1 = (1 - frac_pel) * Precip_ocean0 / (omega_o -
1)**n #Modern shelf precipitation
ko2 = frac_pel * Precip_ocean0 / (omega_o**2.84
) #Modern pelagic precipitation
# Calculate remaining proportionality constants
k_d = F_diss0 / (2.88 * 10**-14 * 10**(-coef_for_diss * pH_p) *
numpy.exp(-Ebas / (8.314 * (buffer_T + Pore_mod))))
k_w = F_silic0
##### all proportionality constants have been calculated ###################
time = numpy.linspace(
0, 1e8,
100) # Time array for outputs, 100 timesteps between 0 and 100 Ma
#print ('IC new',DIC_o+1.8e20/Mo*ppCO2_o,ALK_o,DIC_p,ALK_p)
# Given initial conditions, unknown parameters, and system of ODEs (below), solve for time evolution of DIC and ALK of ocean and pore space:
[out, mes] = scipy.integrate.odeint(
system_of_equations,
[DIC_o + 1.8e20 / Mo * ppCO2_o, ALK_o, DIC_p, ALK_p],
time,
args=(W, F_outgass, n, CO2_dep, Te, mod_sea, alt_frac, Mp_frac,
W_plus_1, cl_sens, change_out, F_carbw, CWF, deep_grad,
coef_for_diss, beta, Ebas, PG),
full_output=1)
# Create empty arrays for storing model outputs
pH_array_o = 0 * time # pH of ocean
CO2_array_o = 0 * time # pCO2 of ocean
pH_array_p = 0 * time # pH of pore space
CO2_array_p = 0 * time # pCO2 pore space
Ca_array_o = 0 * time # Ca molality ocean
Ca_array_p = 0 * time # Ca molality pore space
CO3_array_o = 0 * time # Carbonate molality ocean
CO3_array_p = 0 * time # Carbonate molality pore space
HCO3_array_o = 0 * time # Bicarbonate molaity ocean
HCO3_array_p = 0 * time # Bicarbonate molality pore space
omega_o = 0 * time # Saturation state ocean
omega_p = 0 * time # Saturation state pore space
Tsurf_array = 0 * time # Surface temperature
Tdeep_array = 0 * time # Pore space temperature
Fd_array = 0 * time # Seafloor dissolution flux
Fs_array = 0 * time # Continental silicate weathering flux
Precip_ocean_array = 0 * time # Carbonate precipitaion ocean flux
Precip_pore_array = 0 * time # Carbonate precipitation pore space flux
volc_array = 0 * time # Volcanic outgassing flux
carbw_ar = 0 * time # Carbonate weathering flux
co2_aq_o = 0 * time # aqueous CO2 ocean molality
co2_aq_p = 0 * time # aqueous CO2 pore space molality
### Step through time, and fill output arrays with solution calculated above
for i in range(0, len(time)):
# Given time evolution of DIC and ALK for ocean and pore space, calculate time evolution for other carbon cycle variables (fluxes and equilibrium chemistry):
[
Ca, EM_H_o, EM_pH_o, EM_co3_o, EM_hco3_o, EM_co2aq_o, EM_ppCO2_o,
EM_Ca_o, EM_H_p, EM_pH_p, EM_co3_p, EM_hco3_p, EM_co2aq_p,
EM_ppCO2_p, EM_Ca_p, area, T_surface, T_surface_diff, buffer_T,
EM_omega_o, EM_omega_p, Relative_outgassing, weatherability,
F_outg, carb_weath, Precip_ocean, Precip_pore, F_diss, F_silic
] = Cretaceous_cc([out[i, 0], out[i, 1], out[i, 2], out[i, 3]],
time[i], cl_sens, deep_grad, PG, change_out,
F_outgass, W_plus_1, F_carbw, CWF, CO2_dep, Te, n,
coef_for_diss, beta, Ebas)
array_of_outputs = [
EM_pH_o, EM_co3_o, EM_hco3_o, EM_co2aq_o, EM_ppCO2_o, EM_Ca_o,
EM_omega_o, T_surface, buffer_T, F_diss, F_silic, Precip_ocean,
Precip_pore, EM_omega_p, carb_weath, EM_co3_p, EM_hco3_p,
EM_co2aq_p, EM_pH_p, EM_Ca_p, EM_co2aq_p
]
# Fill output array with appropriate model outputs:
co2_aq_o[i] = array_of_outputs[3]
pH_array_o[i] = array_of_outputs[0]
CO2_array_o[i] = array_of_outputs[4]
co2_aq_p[i] = array_of_outputs[17]
pH_array_p[i] = array_of_outputs[18]
CO2_array_p[i] = array_of_outputs[20]
Ca_array_o[i] = array_of_outputs[5]
Ca_array_p[i] = array_of_outputs[19]
CO3_array_o[i] = array_of_outputs[1]
CO3_array_p[i] = array_of_outputs[15]
HCO3_array_o[i] = array_of_outputs[2]
HCO3_array_p[i] = array_of_outputs[16]
omega_o[i] = array_of_outputs[6]
omega_p[i] = array_of_outputs[13]
carbw_ar[i] = array_of_outputs[14]
Tsurf_array[i] = array_of_outputs[7]
Tdeep_array[i] = array_of_outputs[8]
Fd_array[i] = array_of_outputs[9]
Fs_array[i] = array_of_outputs[10]
Precip_ocean_array[i] = array_of_outputs[11]
Precip_pore_array[i] = array_of_outputs[12]
volc_array[i] = F_outgass + change_out * F_outgass * (time[i] / 1e8)
############################################################################
#### Checking for mass balance
############################################################################
#max_el=numpy.size(time)-1
#tstep=numpy.max(time)/max_el #duration of timestep
#sources=numpy.sum(volc_array[2:]+carbw_ar[2:])*tstep
#sinks=numpy.sum(Precip_ocean_array[2:]+Precip_pore_array[2:])*tstep
#flux_bal=sources-sinks
#res_change=1.8e20*(CO2_array_o[max_el]-CO2_array_o[2])+Mo*(HCO3_array_o[max_el]+CO3_array_o[max_el]+co2_aq_o[max_el]-co2_aq_o[2]-CO3_array_o[2]-HCO3_array_o[2])+Mp*(HCO3_array_p[max_el]+CO3_array_p[max_el]+co2_aq_p[max_el]-co2_aq_p[2]-CO3_array_p[2]-HCO3_array_p[2])
#res_change2=(out[max_el,0]-out[2,0])*Mo+(out[max_el,2]-out[2,2])*Mp
#print flux_bal,res_change,res_change2,Mo*(HCO3_array_o[max_el]+CO3_array_o[max_el]+co2_aq_o[max_el]-co2_aq_o[2]-CO3_array_o[2]-HCO3_array_o[2])+Mp*(HCO3_array_p[max_el]+CO3_array_p[max_el]+co2_aq_p[max_el]-co2_aq_p[2]-CO3_array_p[2]-HCO3_array_p[2])
#imbalance=(flux_bal-res_change)/(out[max_el,0]*Mo)
#print imbalance
imbalance = 0 ## Comment out if wish to calculate mass imbalance
############################################################################
# Return selected outputs to Main_code.py for plotting
return [
out[:, 0], out[:, 1], out[:, 2], out[:,
3], time, pH_array_o, CO2_array_o,
pH_array_p, CO2_array_p, Ca_array_o, Ca_array_p, CO3_array_o,
CO3_array_p, HCO3_array_o, HCO3_array_p, omega_o, omega_p, Tsurf_array,
Tdeep_array, Fd_array, Fs_array, Precip_ocean_array, Precip_pore_array
], imbalance
def soln(mchirp): return pylab.roots([1., 0., -mchirp**(5./3), -1])[0]**3
def carbon_cycle(y, t0, Bio_f, ppCO2_00, n, climp, tdep_weath, F_meta_mod,
F_out_mantle_mod, pH_00, lfrac, R_carb_00, del_carb0, F_carbw,
R_mantle_00, F_sub_mod, coef_for_diss, beta, n_out, mm,
growth_timing, new_add_Ca, Ebas, e1, protero_O2, del_org0, e2,
j1, j2, j3, org_weath_mod0, thermo_weath, multplic,
Mantle_temp_mod):
Ca_cofactor = new_add_Ca / 5000.0 * (
(1 - abs(t0) / (4.5e9))**-0.5 - 1) #Redundant
global pK1, pK2, H_CO2, salt, Pore_mod, T_surface0, ALK_o, ALK_p, Ca_p, Ca_o, Rcrust0, Rorg0, k_meta0_carb, k_meta0_org, k_sub0_carb, k_sub0_org, F_orgB0, imply_forg0, org_weath0, carb_minus_org, carb_minus_AO
global landf_vary, lum_vary, salt0, k_w, k_c, k_o, k_r, Mp, ppCO2_o, Mo, ko1, ko2, k_meta0, k_sub0, k_mantle0, k_sub_arc0
global mantle_mod, Rcrust_mod, Rorg_mod, F_meta_mod_carb, F_meta_mod_org
global F_sub_mod_carb, F_sub_mod_org, ppCO2_mod, deep_grad
s = 1.8e20 / Mo
[c, d] = pylab.roots([
y[1] / (10**-pK2 * 10**-pK1) * (1 + s / H_CO2),
(y[1] - y[0]) / (10**-pK2), (y[1] - 2 * y[0])
])
EE_H_o = numpy.max([c, d])
EE_pH_o = -pylab.log10(EE_H_o)
EE_co3_o = y[1] / (2 + EE_H_o / (10**-pK2))
EE_hco3_o = y[1] - 2 * EE_co3_o
EE_co2aq_o = (EE_hco3_o * EE_H_o / (10**-pK1))
EE_ppCO2_o = EE_co2aq_o / H_CO2
EE_Ca_o = Ca_o + 0.5 * (y[1] - ALK_o) + Ca_cofactor
#pore space
EE_H_p = EE_H_o
EE_pH_p = EE_pH_o
EE_co3_p = EE_co3_o
EE_hco3_p = EE_hco3_o
EE_co2aq_p = EE_co2aq_o
EE_ppCO2_p = EE_ppCO2_o
EE_Ca_p = EE_Ca_o
bio_now = 1 - 1 / (1 / (1 - Bio_f) + numpy.exp(-5 * (abs(t0) - 1e9) / 1e9))
bio_Archean = 1 - 1 / (1 /
(1 - Bio_f) + numpy.exp(-5 *
(abs(4.1e9) - 1e9) / 1e9))
biology_modern = 1 - 1 / (1 /
(1 - Bio_f) + numpy.exp(-5 *
(abs(0.0) - 1e9) / 1e9))
biology = bio_now / bio_Archean
biology_mod = biology_modern / bio_Archean
Q0 = (1 - abs(4.1e9) / (4.5e9))**-n_out
Q = (1 - abs(t0) / (4.5e9))**-n_out
spread = Q**beta
Mantle_temp = Mantle_temp_mod * (Q)**0.1
Ccrit = (3.125e-3 * 80.0 + 835.5 - 285.0) / (Mantle_temp - 285.0)
carb_eff_modifier = numpy.min([1.0, (Ccrit - 0.3) / (0.6 - 0.3)])
if carb_eff_modifier < 0.0:
carb_eff_modifier = 0.0
F_out_mantle = F_out_mantle_mod * (Q**mm) * (y[5] / mantle_mod)
F_meta_carb = F_meta_mod_carb * (Q**mm) * (y[4] / Rcrust_mod)
F_meta_org = F_meta_mod_org * (Q**mm) * (y[6] / Rorg_mod)
F_meta = F_meta_carb + F_meta_org
F_sub_carb = F_sub_mod_carb * (Q**beta) * (y[4] / Rcrust_mod)
F_sub_org = F_sub_mod_org * (Q**beta) * (y[6] / Rorg_mod)
F_sub = F_sub_carb + F_sub_org
F_sub_arc = F_sub_carb * (1 - carb_eff_modifier) + F_sub_org * e1
F_outg = F_out_mantle + F_meta + F_sub_arc
#isotopes
del_sub = (F_sub_carb * y[8] + F_sub_org * y[7]) / F_sub_arc
del_arc_volc = (F_sub_carb * (1 - carb_eff_modifier) * y[8] +
e1 * F_sub_org * y[7]) / F_sub_arc
del_meta_volc = (F_meta_carb * y[8] + F_meta_org * y[7]) / F_meta
del_crust = (y[4] * y[8] + y[6] * y[7]) / (y[4] + y[6])
del_out = (F_out_mantle * y[9] + F_meta_carb * y[8] + F_meta_org * y[7] +
F_sub_carb * (1 - carb_eff_modifier) * y[8] +
(e1) * F_sub_org * y[7]) / F_outg
carb_minus_org = 0
carb_minus_AO = 0
if abs(t0) < 4.0e9:
carb_minus_org = 28.0
carb_minus_AO = 2
del_carb_precip = y[10] + carb_minus_AO
del_org_buried = del_carb_precip - carb_minus_org
if landf_vary == "y":
land = lf(t0, lfrac, growth_timing)
land_mod = lf(0, lfrac, growth_timing)
else:
land = 1
land_mod = 1
if lum_vary == "y":
L_over_Lo = 1 / (1 + 0.4 * (abs(t0) / 4.6e9))
T_surface = clim_fun(EE_ppCO2_o, L_over_Lo)
else:
L_over_Lo = 1 / (1 + 0.4 * (abs(4.1e9) / 4.6e9))
T_surface = clim_fun(EE_ppCO2_o, L_over_Lo)
T_surface_mod = clim_fun(ppCO2_mod, 1 / (1 + 0.4 * (abs(0) / 4.6e9)))
T_surface_diff_mod = T_surface - T_surface_mod
T_surface_diff = T_surface - T_surface0
interc = 274.037 - deep_grad * 285.44411576277344
buffer_T = deep_grad * T_surface + interc
buffer_Ti = numpy.max([deep_grad * T_surface + interc, 271.15])
buffer_T = numpy.min([buffer_Ti, T_surface])
EE_omega_o = EE_Ca_o * EE_co3_o / (Sol_prod(T_surface))
EE_omega_p = EE_Ca_p * EE_co3_p / (Sol_prod(buffer_T + Pore_mod))
#ocean carbonate sink
Carb_sink = ko1 * (land / land_mod) * (EE_omega_o)**n + ko2 * (EE_omega_o**
2.84)
Precip_ocean = Carb_sink
Precip_pore = k_c * (EE_omega_p)**n
# Carbonate weathering flux
carb_weath = (y[4] / Rcrust_mod) * F_carbw * (biology / biology_mod) * (
EE_ppCO2_o / ppCO2_mod)**(climp) * numpy.exp(
(T_surface_diff_mod) / tdep_weath) * (land / land_mod)
F_diss = k_r * (2.88 * 10**-14 * 10**(-coef_for_diss * EE_pH_p) *
numpy.exp(-Ebas / (8.314 *
(buffer_T + Pore_mod)))) * spread
F_silic = k_w * (biology / biology_mod) * (land / land_mod) * (
EE_ppCO2_o / ppCO2_mod)**climp * numpy.exp(
(T_surface_diff_mod) / tdep_weath)
aa = -0.5 * numpy.log10(protero_O2)
bb = 4.5 + 0.5 * numpy.log10(protero_O2)
cc = -4.5
pO2 = 10**(aa * numpy.tanh(-20 * (abs(t0) - 0.55e9) / 1e9) +
bb * numpy.tanh(-20 * (abs(t0) - 2.45e9) / 1e9) + cc)
org_weath = org_weath_mod0 * (y[6] / Rorg_mod) * (land / land_mod) * (
pO2)**0.30809 + thermo_weath * (y[6] / Rorg_mod
) ## This is running in retrieval
total_carb_inputs = (carb_weath + org_weath + F_outg)
if (abs(t0) > 4.0e9):
F_orgB = 0 * total_carb_inputs
if (abs(t0) < 4.0e9) and (abs(t0) > 3.9e9):
F_orgB = j1 * total_carb_inputs * (-abs(t0) + 4.0e9) / 0.1e9
if (abs(t0) < 3.9e9) and (abs(t0) > 2.5e9):
F_orgB = j1 * total_carb_inputs
if (abs(t0) < 2.5e9) and (abs(t0) > 2.4e9):
inbetween = (abs(t0) - 2.4e9) / 0.1e9
F_orgB = j1 * total_carb_inputs * inbetween + (
1 - inbetween) * j2 * j1 * total_carb_inputs
if (abs(t0) < 2.4e9) and (abs(t0) > 0.6e9):
F_orgB = j2 * j1 * total_carb_inputs
if (abs(t0) > 0.5e9) and (abs(t0) < 0.6e9):
inbetween = (abs(t0) - 0.5e9) / 0.1e9
F_orgB = j1 * j2 * total_carb_inputs * inbetween + (
1 - inbetween) * j3 * j2 * j1 * total_carb_inputs
if (abs(t0) < 0.5e9):
F_orgB = j3 * j2 * j1 * total_carb_inputs
if (abs(t0) > 4.0e9):
tempforg = 0
if (abs(t0) < 4.0e9) and (abs(t0) > 3.9e9):
tempforg = j1 * (-abs(t0) + 4.0e9) / 0.1e9
if (abs(t0) < 3.9e9) and (abs(t0) > 2.5e9):
tempforg = j1
if (abs(t0) < 2.5e9) and (abs(t0) > 2.4e9):
inbetween = (abs(t0) - 2.4e9) / 0.1e9
tempforg = j1 * inbetween + (1 - inbetween) * j2 * j1
if (abs(t0) < 2.4e9) and (abs(t0) > 0.6e9):
tempforg = j2 * j1
if (abs(t0) > 0.5e9) and (abs(t0) < 0.6e9):
inbetween = (abs(t0) - 0.5e9) / 0.1e9
tempforg = j1 * j2 * inbetween + (1 - inbetween) * j3 * j2 * j1
if (abs(t0) < 0.5e9):
tempforg = j3 * j2 * j1
current_volc = F_out_mantle_mod + F_meta_mod + F_sub_mod
multiplicative = 1 + multplic * abs(t0) / 4.1e9
O2_fast_sink = multiplicative * 2.4e12 * F_outg / current_volc
model_modern_forg = j1 * j2 * j3
reduced_early = (F_orgB + 5.15e12 * tempforg / model_modern_forg -
org_weath - O2_fast_sink)
del_inputs = (F_outg * del_out + org_weath * y[7] +
carb_weath * y[8]) / (F_outg + org_weath + carb_weath)
O2_source = F_orgB + 5.15e12 * (tempforg / model_modern_forg)
Kox = O2_source / O2_fast_sink
return [
EE_pH_o, EE_co3_o, EE_hco3_o, EE_co2aq_o, EE_ppCO2_o, EE_Ca_o,
EE_omega_o, T_surface, buffer_T, F_diss, F_silic, Precip_ocean,
Precip_pore, EE_omega_p, F_outg, carb_weath, EE_co3_p, EE_hco3_p,
EE_co2aq_p, EE_pH_p, EE_ppCO2_p, EE_Ca_p, EE_H_o, EE_H_p,
T_surface_diff, F_outg, F_meta, F_sub, F_out_mantle, F_meta_carb,
F_sub_carb, F_meta_org, F_sub_org, org_weath, F_orgB, del_org_buried,
del_carb_precip, del_crust, del_out, del_inputs, pO2, reduced_early,
F_sub_arc, del_arc_volc, del_meta_volc, del_sub, 1 - carb_eff_modifier,
Kox
]
def carbon_cycle(y, t0, W, F_outgass, n, climp, tdep_weath, mod_sea, alt_frac,
Mp_frac, lfrac, carb_exp, sed_thick, F_carbw, CWF, deep_grad,
coef_for_diss, beta, n_out, mm, growth_timing, new_add_Ca,
Ebas):
## Ca_cofactor is only important for the sensitivity tests where a wide range of Archean Ca abundances are imposed
Ca_cofactor = new_add_Ca / 1000.0 * numpy.exp(
t0 / 1e9 - 4) # perscribed ocean Ca molality evolution
global pK1, pK2, H_CO2, salt, Pore_mod, T_surface0, ALK_o, ALK_p, Ca_p, Ca_o, options_array
global landf_vary, lum_vary, salt0, k_w, k_c, k_o, k_r, Mp, ppCO2_o, Mo, ko1, ko2 #,Mg_fun,Ca_Tfun,coef_for_diss
#ocean variables
s = 1.8e20 / Mo #correction factor for mass balance (see manuscript)
#### Temperature loop ####
# This loop is necessary because the carbon chemistry equilibrium constants are temperatue dependent,
# but surface temperature is controlled by atmospheric pCO2, which is in turn modulated by
# the carbon chemistry of the ocean. Therefore, several iterations are required to ensure the temperature
# used to calculate equilibrium constants is the same as the surface climate. Sensitivity tests reveal
# that three iterations are sufficient for accurate (within 1 degree) convergence.
# Note that if Carbon_chem is set to 0 then the only a single iteration is executed and
# the carbon chemistry constants are assumed to be fixed. This is faster and only slightly less
# accurate than the full calculation.
## initial guesses for surface temperature and pore space, to be used to determine equilibrium carbon chemistry constants:
T_upd = 273 + 18 # initial guess for surface temperature
T_upd2 = 273 + 18 # initial guess for pore-space temperature
T_surface = 100.0 # Filler value (T_surface will be calcauled within the loop)
# Check to see if Carbon_chem is 0 or 1
if options_array[1] == 0:
max_temp_iter = 1 # run single iteration
else:
max_temp_iter = 3 # run 3 iterations
jk = 0
for jk in range(0, max_temp_iter):
## Calculate temperature-dependent carbon chemistry constants for the ocean:
[pK1, pK2, H_CO2] = equil_cont(T_upd)
# Calculate equilibrium carbon chemistry for the ocean:
[c, d] = pylab.roots([
y[1] / (10**-pK2 * 10**-pK1) * (1 + s / H_CO2),
(y[1] - y[0]) / (10**-pK2), (y[1] - 2 * y[0])
]) #equation S15
EE_H_o = numpy.max([c, d]) ## make sure get right root!
EE_pH_o = -pylab.log10(EE_H_o) # equation S16
EE_co3_o = y[1] / (2 + EE_H_o / (10**-pK2))
EE_hco3_o = y[1] - 2 * EE_co3_o
EE_co2aq_o = (EE_hco3_o * EE_H_o / (10**-pK1)) # equation S13
EE_ppCO2_o = EE_co2aq_o / H_CO2 # equation S12
EE_Ca_o = Ca_o + 0.5 * (y[1] - ALK_o) + Ca_cofactor #equation S17
## Calculate temperature-dependent carbon chemistry constants for the pore space:
[pK1, pK2, H_CO2] = equil_cont(T_upd2)
# Calculate equilibrium carbon chemistry for the pore space:
[c, d] = pylab.roots([
y[3] / (10**-pK2 * 10**-pK1), (y[3] - y[2]) / (10**-pK2),
(y[3] - 2 * y[2])
]) # equation S15
EE_H_p = numpy.max([c, d]) ## make sure get right root!
EE_pH_p = -pylab.log10(EE_H_p) # equation S16
EE_co3_p = y[3] / (2 + EE_H_p / (10**-pK2))
EE_hco3_p = y[3] - 2 * EE_co3_p
EE_co2aq_p = (EE_hco3_p * EE_H_p / (10**-pK1)) #equation S14
EE_ppCO2_p = EE_co2aq_p / H_CO2 #equation S12
EE_Ca_p = Ca_p + 0.5 * (y[3] - ALK_p) + Ca_cofactor # equation S17
# Calculate biological modification of continental weathering using equation S7:
fb_EE = 1 / (1 - CWF)
biology_modifier = 1 - 1 / (fb_EE + numpy.exp(-10 *
(t0 - 0.6e9) / 1e9))
#biology_modifier=1.0
# Calculate internal heatflow, outgassing, and spreading rate using equations S8-10:
Q = (1 - t0 / (4.5e9))**-n_out
#Q=1.0
#Q=1-(1-n_out)*(t0/4e9)**2.0 # alternative for lowering outgassing
F_outg = F_outgass * Q**mm
#F_outg=F_outgass*Q # alternative for lowering outgassing
spread = Q
if landf_vary == "y":
land = lf(t0, lfrac, growth_timing)
else:
land = 1.0
if lum_vary == "y":
L_over_Lo = 1 / (
1 + 0.4 *
(t0 / 4.6e9)) # Evolution of solar luminosity from Gough 1981.
if options_array[
2] == 1: # Check to see if methane option is on. If yes, use methane climate models:
### Weighting functions for Phanerozoic, Proterozoic, and Archean methane climates (only used high methane tests)
### Smooth weighting functions are required because sudden temperature jumps break the model.
w0 = 1 - 1 / (1 + numpy.exp(-15 * (t0 / 1e9 - 0.541))
) # 1 in the Phanerozoic, 0 elsewhere
w1 = 1 / (1 + numpy.exp(-15 * (t0 / 1e9 - 0.541))) - 1 / (
1 + numpy.exp(-15 * (t0 / 1e9 - 2.5))
) # 1 in the Proterozoic, 0 elsewhere
w2 = 1 / (1 + numpy.exp(-15 * (t0 / 1e9 - 2.5))
) # 1 in the Archean, 0 elsewhere
arch_temp = clim_fun_highCH4(
EE_ppCO2_o,
L_over_Lo) ## Archean temperature with high methane
Protero_temp = clim_fun_lowCH4(
EE_ppCO2_o,
L_over_Lo) ## Proterozoic temperature with high methane
### Climate model for eleveated Proterozoic and Archean methane abundances:
T_surface = (w0 * clim_fun_CO2_only(EE_ppCO2_o, L_over_Lo) +
w1 * Protero_temp + w2 * arch_temp) / (w0 + w1 +
w2)
else: # methane option off -> use CO2 only climate model (nominal model)
T_surface = clim_fun_CO2_only(EE_ppCO2_o, L_over_Lo)
###T_surface=clim_fun_CO2_only(EE_ppCO2_o,L_over_Lo)+30.0 * (1/(1+numpy.exp(-15*(t0/1e9-2.5)))) ## for +30 K sensitivity test
else:
T_surface = clim_fun_CO2_only(
EE_ppCO2_o,
1.0) # For CO2-only, no evolution in solar luminosity
## Calculate deep ocean temperature
T_surface_diff = T_surface - T_surface0
interc = 274.037 - deep_grad * T_surface0 # intercept chosen to reproduce initial (modern) temperature
buffer_T = deep_grad * T_surface + interc
buffer_Ti = numpy.max([deep_grad * T_surface + interc,
271.15]) # ensures deep ocean is not frozen
buffer_T = numpy.min(
[buffer_Ti, T_surface]
) # This is deep ocean temperature (cannot be warmer than the surface)
## Calculate pore space temperature,
## accounting for effect of sediment thickness and heatflow
Pore_mod_dynamic = Pore_mod
sed_depth = 700 - 700 * (1 - sed_thick) * t0 / 4e9 # equation S5
Pore_mod_dynamic = Q * sed_depth / 77.7777777 ## Difference is 9 K for Q=1
T_pore_space = buffer_T + Pore_mod_dynamic
#T_pore_space=buffer_T+9.0 # sensitivity test constant temperature difference between pore space and deep ocean
T_upd = T_surface #update surface temperature for next iteration
T_upd2 = T_pore_space #update pore space temperature for next iteration
# Calculate saturation state of ocean and pore space (equation S18):
# combined activity coefficients for Ca and CO3. Assumed to be 1 except for Ca sensitiviy test where complexing is important
act_o = 1.0 #-7.89*EE_Ca_o**3+10.847*EE_Ca_o**2-5.2246*EE_Ca_o+1.0551 #from Aspen polynomial fit Fig. S20, or 1.0 for nominal case
act_p = 1.0 #-7.89*EE_Ca_p**3+10.847*EE_Ca_p**2-5.2246*EE_Ca_p+1.0551 #from Aspen polynomial fit Fig. S20, or 1.0 for nominal case
EE_omega_o = act_o * EE_Ca_o * EE_co3_o / (Sol_prod(T_surface)
) # saturation state ocean
EE_omega_p = act_p * EE_Ca_p * EE_co3_p / (Sol_prod(T_pore_space)
) # saturation state pore space
#Calculate carbonate sinks
Carb_sink = ko1 * land * (EE_omega_o - 1)**n + ko2 * (
EE_omega_o**2.84
) # ocean carbonate from equation S19, noting that ko2 is 0 in this version of the model
Precip_ocean = Carb_sink ## Precipitaion of carbonate in ocean
Precip_pore = k_c * (EE_omega_p -
1)**n ## Precipitation of carbonate in pore space
# Carbonate weathering flux
carb_weath = F_carbw * biology_modifier * (EE_ppCO2_o / ppCO2_o)**(
carb_exp) * numpy.exp(
(T_surface_diff) / tdep_weath) * land # equation S2
### Dissolution of seafloor flux:
F_diss = k_r * 2.88 * 10**-14 * 10**(-coef_for_diss *
EE_pH_p) * spread**beta * numpy.exp(
-Ebas /
(8.314 *
(T_pore_space))) # equation S3
#F_diss=k_r*2.88*10**-14*10**(-coef_for_diss*8.57)*numpy.exp(-Ebas/(8.314*(283))) # sensitivity test holding dissolution artifically constant
#Continetnal silicate weathering flux
F_silic = k_w * biology_modifier * land * (
EE_ppCO2_o / ppCO2_o)**climp * numpy.exp(
(T_surface_diff) / tdep_weath) # equation 1
#return selected carbon cycle variables and fluxes
return [
EE_pH_o, EE_co3_o, EE_hco3_o, EE_co2aq_o, EE_ppCO2_o, EE_Ca_o,
EE_omega_o, T_surface, buffer_T, F_diss, F_silic, Precip_ocean,
Precip_pore, EE_omega_p, F_outg, carb_weath, EE_co3_p, EE_hco3_p,
EE_co2aq_p, EE_pH_p, EE_ppCO2_p, EE_Ca_p, EE_H_o, EE_H_p,
T_surface_diff, F_outg, spread, T_pore_space
] #T_pore_space
def Forward_Model(W, F_outgass, n, climp, tdep_weath, mod_sea, alt_frac,
Mp_frac, lfrac, carb_exp, sed_thick, F_carbw, fpel, CWF,
deep_grad, coef_for_diss, beta, n_out, mm, growth_timing,
new_add_Ca, Ebas):
# define global variables:
global pK1, pK2, H_CO2, salt, Pore_mod, T_surface0, Ca_p, Ca_o, options_array
global landf_vary, lum_vary, salt0, k_w, k_c, k_o, k_r, Mp, ppCO2_o, Mo, ko1, ko2, ALK_o, ALK_p
# load options defined in main_code_parallel.py:
options_array = numpy.load('options_array.npy')
# Initial (modern) ocean pH and atmospheric pCO2 (bar)
pH_o = 8.2
ppCO2_o = .000280
T = clim_fun_CO2_only(ppCO2_o, 1.0) # find initial (modern) temperature
# Calculate equilibrium constants for carbon chemistry:
[pK1, pK2, H_CO2] = equil_cont(T)
Mo = 1.35e21 # Mass of ocean (kg)
W = Mo / W # convert mixing time of ocean (yr) to mass flux (kg/yr)
Mp = Mp_frac * Mo # Mass of water in pore space
##############################################################
############ Compute other initial conditions ################
# First, we use the assumed values for modern seafloor carbonate precipitation, outgassing, and seafloor dissolution to carbonate precipitation ratio
# along with the carbon cycle steady state assumption to calculated the modern seafloor dissolution and continental silciate weathering
partition = mod_sea / F_outgass
F_diss0 = alt_frac * partition * F_outgass #initial seafloor dissolution flux i.e. dissolution = alt_frac*precip_seafloor
F_sil0 = (1 - partition) * F_outgass + (
1 - alt_frac
) * partition * F_outgass #initial continental silicate weathering flux
Fprecip_p = partition * F_outgass #initial pore space carbonate precipation flux (reduntant)
#vary solar luminosity? y or n (don't modify these options - better to change elsewhere).
lum_vary = "y"
landf_vary = "y"
### Initial conditions for modern atmosphere and ocean (equations S12 to S14)
CO2_aq_o = H_CO2 * ppCO2_o #aqueous dissolved CO2
hco3_o = (10**-pK1) * CO2_aq_o / (10**-pH_o) # aqueous bicarbonate
co3_o = (10**-pK2) * hco3_o / (10**-pH_o) #aqueous carbonate
DIC_o = co3_o + hco3_o + CO2_aq_o #dissolved inorganic carbon
ALK_o = 2 * co3_o + hco3_o #carbonate alkalinity
Ca_o = 0.0100278 # initial (modern) calcium molality
salt = ALK_o - 2 * Ca_o ## set salt to ensure ALK is consistent with Ca
salt0 = salt # initial (modern) salt
T_surface0 = clim_fun_CO2_only(ppCO2_o, 1.0)
interc = 274.037 - deep_grad * T_surface0
buffer_T = deep_grad * T_surface0 + interc #initial deep ocean temperature
Pore_mod = 9.0 #difference between pore space and deep ocean temperature for modern Earth
## Use these constants and steady state assumption to calculate remaining initial conditions:
b1 = 2 * F_diss0 + W * ALK_o - 2 * W * DIC_o
b2 = 2 * F_sil0 - W * ALK_o - 2 * F_outgass + 2 * W * DIC_o
a1 = W
a2 = -2 * W
a3 = -W
a4 = 2 * W
# Solving system of equations for pore space properties
DIC_p = DIC_o - Fprecip_p / W
ALK_p = (b1 - a2 * DIC_p) / a1
Fprecip_o = (F_outgass + F_carbw) - (DIC_o - DIC_p) * W
if DIC_p == 0:
print "WARNING: NO PHYSIAL STEADY STATE EXISTS! DIC is negative"
#Solve quadratic ignoring H in ALK but including CO2aq
[vv, xx] = pylab.roots([
ALK_p / (10**-pK1 * 10**-pK2), (ALK_p - DIC_p) / (10**-pK2),
ALK_p - 2 * DIC_p
]) #equation S15
H_p = numpy.max([vv, xx]) # take positive root
pH_p = -pylab.log10(H_p)
#Find remaining carbon chemistry from equilibrium conditions:
CO2aq_p = DIC_p / ((10**-pK1) * (10**-pK2) / H_p**2 + 10**-pK1 / H_p + 1)
co3_p = ALK_p - DIC_p - H_p + CO2aq_p ## only true for high pH, okay for fitting I think (actually should include CO2aq to get exact).
hco3_p = co3_p * 10**-pH_p / (
10**-pK2) #Modern bicarbonate alkalinity in pore space (not used)
Ca_p = 0.5 * (ALK_p - salt) #initial calcium molality in pore space
omega_p = Ca_p * co3_p / Sol_prod(
buffer_T + Pore_mod) # saturation state pore space
omega_o = Ca_o * co3_o / Sol_prod(T_surface0) # saturation state ocean
## All initital conditions have been calculated ############################
############################################################################
############ Calculate proportionality constants ###########################
# Given modern precipitation fluxes and saturation states, calculate proportionality constants
k_c = Fprecip_p / (omega_p - 1)**n
k_o = Fprecip_o / (omega_o - 1)**n
## Partition ocean carbonate sink into shelf precipitation and carbonate precipitation
frac_pel = fpel # no pelagic carbonates in this version of the code (i.e. default is fpel=0)
ko1 = (1 - frac_pel) * Fprecip_o / (omega_o - 1)**n
ko2 = frac_pel * Fprecip_o / (omega_o**2.84)
### remaining proportionality constants
k_r = F_diss0 / (2.88 * 10**-14 * 10**(-coef_for_diss * pH_p) * numpy.exp(
-Ebas / (8.314 * (buffer_T + Pore_mod)))) #for seafloor dissolution
k_w = F_sil0 # for continental silicate weathering
time = numpy.linspace(
0, 4e9, 100
) #define time array from 0 to 4 Ga in 100 time steps. Number of time steps can be increased for greater precision (takes longer)
# run ode solver with initial conditions defined above, and inputs from main_code_parallel.py. The ode solver will output the dissolved inorganic carbon and
# alkalinities of the ocean and pore space through time (all containted in 'out'). The diagnostic 'mes' is also returned
[out, mes] = scipy.integrate.odeint(
system_of_equations,
[DIC_o + 1.8e20 / Mo * ppCO2_o, ALK_o, DIC_p, ALK_p],
time,
args=(W, F_outgass, n, climp, tdep_weath, mod_sea, alt_frac, Mp_frac,
lfrac, carb_exp, sed_thick, F_carbw, CWF, deep_grad,
coef_for_diss, beta, n_out, mm, growth_timing, new_add_Ca, Ebas),
full_output=1)
# Given alkalinities and dissolved inorganic carbon, calculate time-evolution for other carbon cycle variables
# define empty arrays for variables of interest:
pH_array_o = 0 * time #ocean pH
CO2_array_o = 0 * time # atmospheric CO2
pH_array_p = 0 * time # pore space pH
CO2_array_p = 0 * time # pore space CO2
Ca_array_o = 0 * time # ocean calcium molality
Ca_array_p = 0 * time # pore space calcium molality
CO3_array_o = 0 * time # ocean carbonate molality
CO3_array_p = 0 * time # pore space carbonate molality
HCO3_array_o = 0 * time # ocean bicarbonate molality
HCO3_array_p = 0 * time # pore space bicarbonate molality
omega_o = 0 * time # saturation state ocean
omega_p = 0 * time # saturation state pore space
Tsurf_array = 0 * time # Surface temperature
Tdeep_array = 0 * time # Deep ocean temperature
Fd_array = 0 * time # Seafloor dissolution
Fs_array = 0 * time # Continental silciate weathering
Precip_ocean_array = 0 * time # ocean carbonate precipitation
Precip_pore_array = 0 * time # pore space carbonate precipitation
volc_array = 0 * time # volcanic outgassing
carbw_ar = 0 * time # Continental carbonate weathering
co2_aq_o = 0 * time # ocean aqueous CO2
co2_aq_p = 0 * time # pore space aqueous CO2
spread_ar = 0 * time # spreading rate relative to modern
T_pore_space_ar = 0 * time # pore space temperature
for i in range(0, len(time)):
# using ode solution (alkalinities and DIC abundances) and input parameters, fill array pl1 with other carbon cycle evolution variables
pl1 = carbon_cycle([out[i, 0], out[i, 1], out[i, 2], out[i, 3]],
time[i], W, F_outgass, n, climp, tdep_weath,
mod_sea, alt_frac, Mp_frac, lfrac, carb_exp,
sed_thick, F_carbw, CWF, deep_grad, coef_for_diss,
beta, n_out, mm, growth_timing, new_add_Ca,
Ebas) #ocean
# Fill in arrays define above
pH_array_o[i] = pl1[0]
co2_aq_o[i] = pl1[3]
CO2_array_o[i] = pl1[4]
pH_array_p[i] = pl1[19]
CO2_array_p[i] = pl1[20]
Ca_array_o[i] = pl1[5]
Ca_array_p[i] = pl1[21]
CO3_array_o[i] = pl1[1]
CO3_array_p[i] = pl1[16]
HCO3_array_o[i] = pl1[2]
HCO3_array_p[i] = pl1[17]
co2_aq_p[i] = pl1[18]
omega_o[i] = pl1[6]
omega_p[i] = pl1[13]
Tsurf_array[i] = pl1[7]
Tdeep_array[i] = pl1[8]
Fd_array[i] = pl1[9]
Fs_array[i] = pl1[10]
Precip_ocean_array[i] = pl1[11]
Precip_pore_array[i] = pl1[12]
carbw_ar[i] = pl1[15]
volc_array[i] = pl1[14]
spread_ar[i] = pl1[26]
T_pore_space_ar[i] = pl1[27]
max_el = numpy.size(time) - 1 #number of elements in time array
tstep = numpy.max(time) / max_el #time step (yrs) in time array
# calculate mass imbalance
flux_bal = numpy.sum(volc_array[2:] + carbw_ar[2:]) * tstep - numpy.sum(
Precip_ocean_array[2:] + Precip_pore_array[2:]
) * tstep # integral of carbon inputs minus outpus over all timesteps
res_change = 1.8e20 * (CO2_array_o[max_el] - CO2_array_o[2]) + Mo * (
HCO3_array_o[max_el] + CO3_array_o[max_el] + co2_aq_o[max_el] -
co2_aq_o[2] - CO3_array_o[2] - HCO3_array_o[2]
) + Mp * (
HCO3_array_p[max_el] + CO3_array_p[max_el] + co2_aq_p[max_el] -
co2_aq_p[2] - CO3_array_p[2] - HCO3_array_p[2]
) # final - initial carbon abundances (starting at second element to avoid transients)
res_change2 = (out[max_el, 0] - out[2, 0]) * Mo + (
out[max_el, 2] - out[2, 2]
) * Mp # alternative way of calculating final - initial carbon abundances
imbalance = (flux_bal - res_change) / (
out[max_el, 0] * Mo
) # difference between integrated flux balance and final-initial abundances (should be zero).
# return selected carbon cycle outputs to main_code_parallel.py
return [
out[:, 0], out[:, 1], out[:, 2], out[:, 3], time, pH_array_o,
CO2_array_o, pH_array_p, CO2_array_p, Ca_array_o, Ca_array_p,
CO3_array_o, CO3_array_p, HCO3_array_o, HCO3_array_p, omega_o, omega_p,
Tsurf_array, Tdeep_array, Fd_array, Fs_array, Precip_ocean_array,
Precip_pore_array, spread_ar, volc_array, T_pore_space_ar
], imbalance