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BFM50_rate_eqns.py
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BFM50_rate_eqns.py
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from __future__ import division, print_function
import numpy
import json
from scipy.integrate import solve_ivp
import matplotlib.pyplot as plt
from matplotlib.backends.backend_pdf import PdfPages
from Functions.seasonal_cycling_functions import get_wind, get_salinity, get_sunlight, get_temperature, calculate_density
from Functions.phyto import phyto_eqns
from Functions.bacteria import bacteria_eqns
from Functions.predation import get_mesozoo_predation_terms, get_microzoo_predation_terms
from Functions.micro import microzoo_eqns
from Functions.meso import mesozoo_eqns
from Functions.pel_chem import pel_chem_eqns
from Functions.oxygen import calculate_oxygen_reaeration
from Functions.co2_flux_functions import calculate_co2_flux
from Functions.other_functions import insw_vector, get_concentration_ratio
# Names of species in the system
species_names = ['O2o', 'N1p', 'N3n', 'N4n', 'O4n', 'N5s', 'N6r', 'B1c', 'B1n', 'B1p',
'P1c', 'P1n', 'P1p', 'P1l', 'P1s', 'P2c', 'P2n', 'P2p', 'P2l',
'P3c', 'P3n', 'P3p', 'P3l', 'P4c', 'P4n', 'P4p', 'P4l',
'Z3c', 'Z3n', 'Z3p', 'Z4c', 'Z4n', 'Z4p', 'Z5c', 'Z5n', 'Z5p',
'Z6c', 'Z6n', 'Z6p', 'R1c', 'R1n', 'R1p', 'R2c', 'R3c', 'R6c',
'R6n', 'R6p', 'R6s', 'O3c', 'O3h']
def bfm50_rate_eqns(time, conc, seasonal_cycle=True):
""" Calculates the change in concentration for the 50 state variables
NOTE: iron dynamics are not included, this is to compare to the standalone pelagic system
"""
#--------------------------------------------------------------------------
# import parameters from json file
with open("bfm50_parameters.json", "r") as read_parameters:
parameters = json.load(read_parameters)
constant_parameters = parameters["constants"]
environmental_parameters = parameters["environmental_parameters"]
bacteria_parameters = parameters["bacteria_parameters"]
phyto1_prameters = parameters["phyto1_parameters"]
phyto2_prameters = parameters["phyto2_parameters"]
phyto3_prameters = parameters["phyto3_parameters"]
phyto4_prameters = parameters["phyto4_parameters"]
mesozoo3_parameters = parameters["mesozoo3_parameters"]
mesozoo4_parameters = parameters["mesozoo4_parameters"]
microzoo5_parameters = parameters["microzoo5_parameters"]
microzoo6_parameters = parameters["microzoo6_parameters"]
zoo_availability_parameters = parameters["zoo_availability_parameters"]
pel_chem_parameters = parameters["pel_chem_parameters"]
co2_flux_parameters = parameters["co2_flux_parameters"]
oxygen_reaeration_parameters = parameters["oxygen_reaeration_parameters"]
#--------------------------------------------------------------------------
# Seasonal wind, temp, salinity, and radiation values
if seasonal_cycle:
t = time
# Wind
w_win = environmental_parameters["w_win"] # Winter wind speed
w_sum = environmental_parameters["w_sum"] # Summer wind speed
wind = get_wind(t,w_win,w_sum) # Yearly wind cylce
# Temperature
t_win = environmental_parameters["t_win"] # Winter temp value
t_sum = environmental_parameters["t_sum"] # Summer temp value
tde = environmental_parameters["tde"] # Sinusoidal temperature daily excursion degC
temper = get_temperature(t,t_win,t_sum, tde) # Yearly temp cycle
# Salinity
s_win = environmental_parameters["s_win"] # Winter salinity value
s_sum = environmental_parameters["s_sum"] # Summer salinity value
salt = get_salinity(t,s_win,s_sum) # Yearly salinity cycle
# Short wave irradiance flux (W/m^2)
qs_win = environmental_parameters["qs_win"] # Winter irradiance value
qs_sum = environmental_parameters["qs_sum"] # Summer irradiance value
qs = get_sunlight(t,qs_win,qs_sum) # Yearly irradiance cycle
else:
wind = environmental_parameters["w_win"]
temper = environmental_parameters["t_win"]
salt = environmental_parameters["s_win"]
qs = environmental_parameters["qs_win"]
#--------------------------------------------------------------------------
# State variables
o2o = conc[0] # Dissolved oxygen (mg O_2 m^-3)
n1p = conc[1] # Phosphate (mmol P m^-3)
n3n = conc[2] # Nitrate (mmol N m^-3)
n4n = conc[3] # Ammonium (mmol N m^-3)
o4n = conc[4] # Nitrogen sink (mmol N m^-3)
n5s = conc[5] # Silicate (mmol Si m^-3)
n6r = conc[6] # Reduction equivalents (mmol S m^-3)
b1c = conc[7] # Pelagic bacteria carbon (mg C m^-3)
b1n = conc[8] # Pelagic bacteria nitrogen (mmol N m^-3)
b1p = conc[9] # Pelagic bacteria phosphate (mmol P m^-3)
p1c = conc[10] # Diatoms carbon (mg C m^-3)
p1n = conc[11] # Diatoms nitrogen (mmol N m^-3)
p1p = conc[12] # Diatoms phosphate (mmol P m^-3)
p1l = conc[13] # Diatoms chlorophyll (mg Chl-a m^-3)
p1s = conc[14] # Diatoms silicate (mmol Si m^-3)
p2c = conc[15] # NanoFlagellates carbon (mg C m^-3)
p2n = conc[16] # NanoFlagellates nitrogen (mmol N m^-3)
p2p = conc[17] # NanoFlagellates phosphate (mmol P m^-3)
p2l = conc[18] # NanoFlagellates chlorophyll (mg Chl-a m^-3)
p3c = conc[19] # Picophytoplankton carbon (mg C m^-3)
p3n = conc[20] # Picophytoplankton nitrogen (mmol N m^-3)
p3p = conc[21] # Picophytoplankton phosphate (mmol P m^-3)
p3l = conc[22] # Picophytoplankton chlorophyll (mg Chl-a m^-3)
p4c = conc[23] # Large phytoplankton carbon (mg C m^-3)
p4n = conc[24] # Large phytoplankton nitrogen (mmol N m^-3)
p4p = conc[25] # Large phytoplankton phosphate (mmol P m^-3)
p4l = conc[26] # Large phytoplankton chlorophyll (mg Chl-a m^-3)
z3c = conc[27] # Carnivorous mesozooplankton carbon (mg C m^-3)
z3n = conc[28] # Carnivorous mesozooplankton nitrogen (mmol N m^-3)
z3p = conc[29] # Carnivorous mesozooplankton phosphate (mmol P m^-3)
z4c = conc[30] # Omnivorous mesozooplankton carbon (mg C m^-3)
z4n = conc[31] # Omnivorous mesozooplankton nitrogen (mmol N m^-3)
z4p = conc[32] # Omnivorous mesozooplankton phosphate (mmol P m^-3)
z5c = conc[33] # Microzooplankton carbon (mg C m^-3)
z5n = conc[34] # Microzooplankton nitrogen (mmol N m^-3)
z5p = conc[35] # Microzooplankton phosphate (mmol P m^-3)
z6c = conc[36] # Heterotrophic flagellates carbon (mg C m^-3)
z6n = conc[37] # Heterotrophic flagellates nitrogen (mmol N m^-3)
z6p = conc[38] # Heterotrophic flagellates phosphate (mmol P m^-3)
r1c = conc[39] # Labile dissolved organic carbon (mg C m^-3)
r1n = conc[40] # Labile dissolved organic nitrogen (mmol N m^-3)
r1p = conc[41] # Labile dissolved organic phosphate (mmol P m^-3)
r2c = conc[42] # Semi-labile dissolved organic carbon (mg C m^-3)
r3c = conc[43] # Semi-refractory Dissolved Organic Carbon (mg C m^-3)
r6c = conc[44] # Particulate organic carbon (mg C m^-3)
r6n = conc[45] # Particulate organic nitrogen (mmol N m^-3)
r6p = conc[46] # Particulate organic phosphate (mmol P m^-3)
r6s = conc[47] # Particulate organic silicate (mmol Si m^-3)
o3c = conc[48] # Dissolved inorganic carbon(mg C m^-3)
o3h = conc[49] # Total alkalinity (mmol Eq m^-3)
#--------------------------------------------------------------------------
# concentration ratios
p1n_p1c = get_concentration_ratio(p1n, p1c, constant_parameters["p_small"])
p1p_p1c = get_concentration_ratio(p1p, p1c, constant_parameters["p_small"])
p1l_p1c = get_concentration_ratio(p1l, p1c, constant_parameters["p_small"])
p1s_p1c = get_concentration_ratio(p1s, p1c, constant_parameters["p_small"])
p2n_p2c = get_concentration_ratio(p2n, p2c, constant_parameters["p_small"])
p2p_p2c = get_concentration_ratio(p2p, p2c, constant_parameters["p_small"])
p2l_p2c = get_concentration_ratio(p2l, p2c, constant_parameters["p_small"])
p3n_p3c = get_concentration_ratio(p3n, p3c, constant_parameters["p_small"])
p3p_p3c = get_concentration_ratio(p3p, p3c, constant_parameters["p_small"])
p3l_p3c = get_concentration_ratio(p3l, p3c, constant_parameters["p_small"])
p4n_p4c = get_concentration_ratio(p4n, p4c, constant_parameters["p_small"])
p4p_p4c = get_concentration_ratio(p4p, p4c, constant_parameters["p_small"])
p4l_p4c = get_concentration_ratio(p4l, p4c, constant_parameters["p_small"])
bp_bc = get_concentration_ratio(b1p, b1c, constant_parameters["p_small"])
bn_bc = get_concentration_ratio(b1n, b1c, constant_parameters["p_small"])
z3n_z3c = get_concentration_ratio(z3n, z3c, constant_parameters["p_small"])
z3p_z3c = get_concentration_ratio(z3p, z3c, constant_parameters["p_small"])
z4n_z4c = get_concentration_ratio(z4n, z4c, constant_parameters["p_small"])
z4p_z4c = get_concentration_ratio(z4p, z4c, constant_parameters["p_small"])
z5n_z5c = get_concentration_ratio(z5n, z5c, constant_parameters["p_small"])
z5p_z5c = get_concentration_ratio(z5p, z5c, constant_parameters["p_small"])
z6n_z6c = get_concentration_ratio(z6n, z6c, constant_parameters["p_small"])
z6p_z6c = get_concentration_ratio(z6p, z6c, constant_parameters["p_small"])
r1p_r1c = get_concentration_ratio(r1p, r1c, constant_parameters["p_small"])
r6p_r6c = get_concentration_ratio(r6p, r6c, constant_parameters["p_small"])
r1n_r1c = get_concentration_ratio(r1n, r1c, constant_parameters["p_small"])
r6n_r6c = get_concentration_ratio(r6n, r6c, constant_parameters["p_small"])
#--------------------------------------------------------------------------
#---------------------- Phytoplankton Equations ---------------------------
#--------------------------------------------------------------------------
# P1: Diatoms terms
(dP1cdt_gpp_o3c, dP1cdt_rsp_o3c, dP1cdt_lys_r1c, dP1cdt_lys_r6c, dP1cdt_exu_r2c, dP1ndt_upt_n3n, dP1ndt_upt_n4n,
extra_n1, dP1ndt_lys_r1n, dP1ndt_lys_r6n, dP1pdt_upt_n1p, dP1pdt_upt_r1p, dP1pdt_lys_r1p, dP1pdt_lys_r6p,
dP1ldt_syn, dP1sdt_upt_n5s, dP1sdt_lys_r6s) = phyto_eqns(conc, phyto1_prameters, environmental_parameters, constant_parameters, 1, p1c, p1n, p1p, p1l, qs, temper, time)
# P2: Flagellates terms
(dP2cdt_gpp_o3c, dP2cdt_rsp_o3c, dP2cdt_lys_r1c, dP2cdt_lys_r6c, dP2cdt_exu_r2c, dP2ndt_upt_n3n, dP2ndt_upt_n4n,
extra_n2, dP2ndt_lys_r1n, dP2ndt_lys_r6n, dP2pdt_upt_n1p, dP2pdt_upt_r1p, dP2pdt_lys_r1p, dP2pdt_lys_r6p,
dP2ldt_syn, dP2sdt_upt_n5s, dP2sdt_lys_r6s) = phyto_eqns(conc, phyto2_prameters, environmental_parameters, constant_parameters, 2, p2c, p2n, p2p, p2l, qs, temper, time)
# P3: PicoPhytoplankton terms
(dP3cdt_gpp_o3c, dP3cdt_rsp_o3c, dP3cdt_lys_r1c, dP3cdt_lys_r6c, dP3cdt_exu_r2c, dP3ndt_upt_n3n, dP3ndt_upt_n4n,
extra_n3, dP3ndt_lys_r1n, dP3ndt_lys_r6n, dP3pdt_upt_n1p, dP3pdt_upt_r1p, dP3pdt_lys_r1p, dP3pdt_lys_r6p,
dP3ldt_syn, dP3sdt_upt_n5s, dP3sdt_lys_r6s) = phyto_eqns(conc, phyto3_prameters, environmental_parameters, constant_parameters, 3, p3c, p3n, p3p, p3l, qs, temper, time)
# P4: Large Phytoplankton terms
(dP4cdt_gpp_o3c, dP4cdt_rsp_o3c, dP4cdt_lys_r1c, dP4cdt_lys_r6c, dP4cdt_exu_r2c, dP4ndt_upt_n3n, dP4ndt_upt_n4n,
extra_n4, dP4ndt_lys_r1n, dP4ndt_lys_r6n, dP4pdt_upt_n1p, dP4pdt_upt_r1p, dP4pdt_lys_r1p, dP4pdt_lys_r6p,
dP4ldt_syn, dP4sdt_upt_n5s, dP4sdt_lys_r6s) = phyto_eqns(conc, phyto4_prameters, environmental_parameters, constant_parameters, 4, p4c, p4n, p4p, p4l, qs, temper, time)
#--------------------------------------------------------------------------
#------------------------- Bacteria Equations -----------------------------
#--------------------------------------------------------------------------
(dBcdt_lys_r1c, dBcdt_lys_r1n, dBcdt_lys_r1p, dBcdt_lys_r6c, dBcdt_lys_r6n, dBcdt_lys_r6p,
dBcdt_upt_r1c, dBcdt_upt_r6c, dBpdt_upt_rel_n1p, dBndt_upt_rel_n4n, dBcdt_upt_r2c, dBcdt_upt_r3c,
dBcdt_rel_r2c, dBcdt_rel_r3c, dBcdt_rsp_o3c, flPTN6r, f_B_O, f_B_n, f_B_p) = bacteria_eqns(conc, bacteria_parameters, constant_parameters, environmental_parameters, temper)
#--------------------------------------------------------------------------
#----------------------- Zooplankton Equations ----------------------------
#--------------------------------------------------------------------------
# Mesozooplankton predation terms
dZ3cdt_prd, dZ4cdt_prd, ic3, in3, ip3, ic4, in4, ip4 = get_mesozoo_predation_terms(conc, mesozoo3_parameters, mesozoo4_parameters, zoo_availability_parameters, environmental_parameters, constant_parameters, temper)
# Microzooplankton predation terms
dZ5cdt_prd, dZ6cdt_prd, ic5, in5, ip5, ic6, in6, ip6 = get_microzoo_predation_terms(conc, microzoo5_parameters, microzoo6_parameters, zoo_availability_parameters, environmental_parameters, constant_parameters, temper)
# Z3: Carnivorous Mesozooplankton terms
(dZ3cdt_rel_r1c, dZ3cdt_rel_r6c, dZ3cdt_rsp_o3c, dZ3ndt_rel_r1n, dZ3ndt_rel_r6n, dZ3pdt_rel_r1p, dZ3pdt_rel_r6p,
dZ3pdt_rel_n1p, dZ3ndt_rel_n4n) = mesozoo_eqns(conc, mesozoo3_parameters, constant_parameters, environmental_parameters, z3c, z3n, z3p, ic3, in3, ip3, temper)
# Z4: Omnivorous Mesozooplankton terms
(dZ4cdt_rel_r1c, dZ4cdt_rel_r6c, dZ4cdt_rsp_o3c, dZ4ndt_rel_r1n, dZ4ndt_rel_r6n, dZ4pdt_rel_r1p, dZ4pdt_rel_r6p,
dZ4pdt_rel_n1p, dZ4ndt_rel_n4n) = mesozoo_eqns(conc, mesozoo4_parameters, constant_parameters, environmental_parameters, z4c, z4n, z4p, ic4, in4, ip4, temper)
# Z5: Microzooplankton terms
(dZ5cdt_rel_r1c, dZ5cdt_rel_r6c, dZ5cdt_rsp_o3c, dZ5ndt_rel_r1n, dZ5ndt_rel_r6n, dZ5pdt_rel_r1p, dZ5pdt_rel_r6p,
dZ5pdt_rel_n1p, dZ5ndt_rel_n4n) = microzoo_eqns(conc, microzoo5_parameters, constant_parameters, environmental_parameters, z5c, z5n, z5p, ic5, in5, ip5, temper)
# Z6: Heterotrophic Nanoflagellates terms
(dZ6cdt_rel_r1c, dZ6cdt_rel_r6c, dZ6cdt_rsp_o3c, dZ6ndt_rel_r1n, dZ6ndt_rel_r6n, dZ6pdt_rel_r1p, dZ6pdt_rel_r6p,
dZ6pdt_rel_n1p, dZ6ndt_rel_n4n) = microzoo_eqns(conc, microzoo6_parameters, constant_parameters, environmental_parameters, z6c, z6n, z6p, ic6, in6, ip6, temper)
#--------------------------------------------------------------------------
#------------------------ Non-living components ---------------------------
#--------------------------------------------------------------------------
(dn4ndt_nit_n3n, dn3ndt_denit, dn6rdt_reox, dr6sdt_rmn_n5s) = pel_chem_eqns(pel_chem_parameters, environmental_parameters, constant_parameters, temper, conc, flPTN6r)
#---------------------- Oxygen airation by wind ---------------------------
dOdt_wind = calculate_oxygen_reaeration(oxygen_reaeration_parameters, environmental_parameters, constant_parameters, conc, temper, salt, wind)
#------------------------------- CO_2 Flux --------------------------------
do3cdt_air_sea_flux = calculate_co2_flux(co2_flux_parameters, environmental_parameters, constant_parameters, conc, temper, wind, salt)
#--------------------------------------------------------------------------
#----------------------------- Rate Equations -----------------------------
#--------------------------------------------------------------------------
# Dissolved oxygen [mmol O_2 m^-3 s^-1]
do2o_dt = (constant_parameters["omega_c"]*((dP1cdt_gpp_o3c - dP1cdt_rsp_o3c) + (dP2cdt_gpp_o3c - dP2cdt_rsp_o3c) + (dP3cdt_gpp_o3c - dP3cdt_rsp_o3c) + (dP4cdt_gpp_o3c - dP4cdt_rsp_o3c)) -
constant_parameters["omega_c"]*f_B_O*dBcdt_rsp_o3c -
constant_parameters["omega_c"]*(dZ3cdt_rsp_o3c + dZ4cdt_rsp_o3c + dZ5cdt_rsp_o3c + dZ6cdt_rsp_o3c) -
constant_parameters["omega_n"]*dn4ndt_nit_n3n -
(1.0/constant_parameters["omega_r"])*dn6rdt_reox) + dOdt_wind
# Dissolved inorganic nutrient equations
dn1p_dt = - (dP1pdt_upt_n1p + dP2pdt_upt_n1p + dP3pdt_upt_n1p + dP4pdt_upt_n1p) + (dBpdt_upt_rel_n1p*insw_vector(dBpdt_upt_rel_n1p)) - ((-1)*f_B_p*dBpdt_upt_rel_n1p*insw_vector(-dBpdt_upt_rel_n1p)) + (dZ3pdt_rel_n1p + dZ4pdt_rel_n1p + dZ5pdt_rel_n1p + dZ6pdt_rel_n1p)
dn3n_dt = - (dP1ndt_upt_n3n + dP2ndt_upt_n3n + dP3ndt_upt_n3n + dP4ndt_upt_n3n) + dn4ndt_nit_n3n - dn3ndt_denit
dn4n_dt = - (dP1ndt_upt_n4n + dP2ndt_upt_n4n + dP3ndt_upt_n4n + dP4ndt_upt_n4n) + (dBndt_upt_rel_n4n*insw_vector(dBndt_upt_rel_n4n)) - ((-1)*f_B_n*dBndt_upt_rel_n4n*insw_vector(-dBndt_upt_rel_n4n)) + (dZ3ndt_rel_n4n + dZ4ndt_rel_n4n + dZ5ndt_rel_n4n + dZ6ndt_rel_n4n) - dn4ndt_nit_n3n
do4n_dt = dn3ndt_denit
dn5s_dt = - dP1sdt_upt_n5s + dr6sdt_rmn_n5s
# Reduction equivalents
dn6r_dt = constant_parameters["omega_r"]*constant_parameters["omega_c"]*(1.0 - f_B_O)*dBcdt_rsp_o3c - constant_parameters["omega_r"]*constant_parameters["omega_dn"]*dn3ndt_denit*insw_vector(-(o2o - n6r)/constant_parameters["omega_r"]) - dn6rdt_reox
# Bacterioplankton
db1c_dt = dBcdt_upt_r1c + dBcdt_upt_r6c - dBcdt_rsp_o3c - dBcdt_lys_r1c - dBcdt_lys_r6c - (dZ5cdt_prd["b1"] + dZ6cdt_prd["b1"])
db1n_dt = - dBcdt_lys_r1n - dBcdt_lys_r6n + (r1n_r1c*dBcdt_upt_r1c) + (r6n_r6c*dBcdt_upt_r6c) - (dBndt_upt_rel_n4n*insw_vector(dBndt_upt_rel_n4n)) + ((-1)*f_B_n*dBndt_upt_rel_n4n*insw_vector(-dBndt_upt_rel_n4n)) - (bn_bc*(dZ5cdt_prd["b1"] + dZ6cdt_prd["b1"]))
db1p_dt = (r1p_r1c*dBcdt_upt_r1c) + (r6p_r6c*dBcdt_upt_r6c) - (dBpdt_upt_rel_n1p*insw_vector(dBpdt_upt_rel_n1p)) + ((-1)*f_B_p*dBpdt_upt_rel_n1p*insw_vector(-dBpdt_upt_rel_n1p)) - dBcdt_lys_r1p - dBcdt_lys_r6p - (bp_bc*(dZ5cdt_prd["b1"] + dZ6cdt_prd["b1"]))
# Phytoplankton
dp1c_dt = dP1cdt_gpp_o3c - dP1cdt_exu_r2c - dP1cdt_rsp_o3c - dP1cdt_lys_r1c - dP1cdt_lys_r6c - dZ3cdt_prd["p1"] - dZ4cdt_prd["p1"] - dZ5cdt_prd["p1"] - dZ6cdt_prd["p1"]
dp1n_dt = dP1ndt_upt_n3n + dP1ndt_upt_n4n - extra_n1 - dP1ndt_lys_r1n - dP1ndt_lys_r6n - (p1n_p1c*(dZ3cdt_prd["p1"] + dZ4cdt_prd["p1"] + dZ5cdt_prd["p1"] + dZ6cdt_prd["p1"]))
dp1p_dt = dP1pdt_upt_n1p - dP1pdt_upt_r1p - dP1pdt_lys_r1p - dP1pdt_lys_r6p - (p1p_p1c*(dZ3cdt_prd["p1"] + dZ4cdt_prd["p1"] + dZ5cdt_prd["p1"] + dZ6cdt_prd["p1"]))
dp1l_dt = dP1ldt_syn - (p1l_p1c*(dZ3cdt_prd["p1"] + dZ4cdt_prd["p1"] + dZ5cdt_prd["p1"] + dZ6cdt_prd["p1"]))
dp1s_dt = dP1sdt_upt_n5s - dP1sdt_lys_r6s - (p1s_p1c*(dZ3cdt_prd["p1"] + dZ4cdt_prd["p1"] + dZ5cdt_prd["p1"] + dZ6cdt_prd["p1"]))
dp2c_dt = dP2cdt_gpp_o3c - dP2cdt_exu_r2c - dP2cdt_rsp_o3c - dP2cdt_lys_r1c - dP2cdt_lys_r6c - dZ3cdt_prd["p2"] - dZ4cdt_prd["p2"] - dZ5cdt_prd["p2"] - dZ6cdt_prd["p2"]
dp2n_dt = dP2ndt_upt_n3n + dP2ndt_upt_n4n - extra_n2 - dP2ndt_lys_r1n - dP2ndt_lys_r6n - (p2n_p2c*(dZ3cdt_prd["p2"] + dZ4cdt_prd["p2"] + dZ5cdt_prd["p2"] + dZ6cdt_prd["p2"]))
dp2p_dt = dP2pdt_upt_n1p - dP2pdt_upt_r1p - dP2pdt_lys_r1p - dP2pdt_lys_r6p - (p2p_p2c*(dZ3cdt_prd["p2"] + dZ4cdt_prd["p2"] + dZ5cdt_prd["p2"] + dZ6cdt_prd["p2"]))
dp2l_dt = dP2ldt_syn - (p2l_p2c*(dZ3cdt_prd["p2"] + dZ4cdt_prd["p2"] + dZ5cdt_prd["p2"] + dZ6cdt_prd["p2"]))
dp3c_dt = dP3cdt_gpp_o3c - dP3cdt_exu_r2c - dP3cdt_rsp_o3c - dP3cdt_lys_r1c - dP3cdt_lys_r6c - dZ3cdt_prd["p3"] - dZ4cdt_prd["p3"] - dZ5cdt_prd["p3"] - dZ6cdt_prd["p3"]
dp3n_dt = dP3ndt_upt_n3n + dP3ndt_upt_n4n - extra_n3 - dP3ndt_lys_r1n - dP3ndt_lys_r6n - (p3n_p3c*(dZ3cdt_prd["p3"] + dZ4cdt_prd["p3"] + dZ5cdt_prd["p3"] + dZ6cdt_prd["p3"]))
dp3p_dt = dP3pdt_upt_n1p - dP3pdt_upt_r1p - dP3pdt_lys_r1p - dP3pdt_lys_r6p - (p3p_p3c*(dZ3cdt_prd["p3"] + dZ4cdt_prd["p3"] + dZ5cdt_prd["p3"] + dZ6cdt_prd["p3"]))
dp3l_dt = dP3ldt_syn - (p3l_p3c*(dZ3cdt_prd["p3"] + dZ4cdt_prd["p3"] + dZ5cdt_prd["p3"] + dZ6cdt_prd["p3"]))
dp4c_dt = dP4cdt_gpp_o3c - dP4cdt_exu_r2c - dP4cdt_rsp_o3c - dP4cdt_lys_r1c - dP4cdt_lys_r6c - dZ3cdt_prd["p4"] - dZ4cdt_prd["p4"] - dZ5cdt_prd["p4"] - dZ6cdt_prd["p4"]
dp4n_dt = dP4ndt_upt_n3n + dP4ndt_upt_n4n - extra_n4 - dP4ndt_lys_r1n - dP4ndt_lys_r6n - (p4n_p4c*(dZ3cdt_prd["p4"] + dZ4cdt_prd["p4"] + dZ5cdt_prd["p4"] + dZ6cdt_prd["p4"]))
dp4p_dt = dP4pdt_upt_n1p - dP4pdt_upt_r1p - dP4pdt_lys_r1p - dP4pdt_lys_r6p - (p4p_p4c*(dZ3cdt_prd["p4"] + dZ4cdt_prd["p4"] + dZ5cdt_prd["p4"] + dZ6cdt_prd["p4"]))
dp4l_dt = dP4ldt_syn - (p4l_p4c*(dZ3cdt_prd["p4"] + dZ4cdt_prd["p4"] + dZ5cdt_prd["p4"] + dZ6cdt_prd["p4"]))
# mesozooplankton
dz3c_dt = dZ3cdt_prd["p1"] + dZ3cdt_prd["p2"] + dZ3cdt_prd["p3"] + dZ3cdt_prd["p4"] + dZ3cdt_prd["z4"] + dZ3cdt_prd["z5"] + dZ3cdt_prd["z6"] - dZ4cdt_prd["z3"] - dZ3cdt_rel_r1c - dZ3cdt_rel_r6c - dZ3cdt_rsp_o3c
dz3n_dt = p1n_p1c*dZ3cdt_prd["p1"] + p2n_p2c*dZ3cdt_prd["p2"] + p3n_p3c*dZ3cdt_prd["p3"] + p4n_p4c*dZ3cdt_prd["p4"] + z4n_z4c*dZ3cdt_prd["z4"] + z5n_z5c*dZ3cdt_prd["z5"] + z6n_z6c*dZ3cdt_prd["z6"] - z3n_z3c*dZ4cdt_prd["z3"] - dZ3ndt_rel_r1n - dZ3ndt_rel_r6n - dZ3ndt_rel_n4n
dz3p_dt = p1p_p1c*dZ3cdt_prd["p1"] + p2p_p2c*dZ3cdt_prd["p2"] + p3p_p3c*dZ3cdt_prd["p3"] + p4p_p4c*dZ3cdt_prd["p4"] + z4p_z4c*dZ3cdt_prd["z4"] + z5p_z5c*dZ3cdt_prd["z5"] + z6p_z6c*dZ3cdt_prd["z6"] - z3p_z3c*dZ4cdt_prd["z3"] - dZ3pdt_rel_r1p - dZ3pdt_rel_r6p - dZ3pdt_rel_n1p
dz4c_dt = dZ4cdt_prd["p1"] + dZ4cdt_prd["p2"] + dZ4cdt_prd["p3"] + dZ4cdt_prd["p4"] + dZ4cdt_prd["z3"] + dZ4cdt_prd["z5"] + dZ4cdt_prd["z6"] - dZ3cdt_prd["z4"] - dZ4cdt_rel_r1c - dZ4cdt_rel_r6c - dZ4cdt_rsp_o3c
dz4n_dt = p1n_p1c*dZ4cdt_prd["p1"] + p2n_p2c*dZ4cdt_prd["p2"] + p3n_p3c*dZ4cdt_prd["p3"] + p4n_p4c*dZ4cdt_prd["p4"] + z3n_z3c*dZ4cdt_prd["z3"] + z5n_z5c*dZ4cdt_prd["z5"] + z6n_z6c*dZ4cdt_prd["z6"] - z4n_z4c*dZ3cdt_prd["z4"] - dZ4ndt_rel_r1n - dZ4ndt_rel_r6n - dZ4ndt_rel_n4n
dz4p_dt = p1p_p1c*dZ4cdt_prd["p1"] + p2p_p2c*dZ4cdt_prd["p2"] + p3p_p3c*dZ4cdt_prd["p3"] + p4p_p4c*dZ4cdt_prd["p4"] + z3p_z3c*dZ4cdt_prd["z3"] + z5p_z5c*dZ4cdt_prd["z5"] + z6p_z6c*dZ4cdt_prd["z6"] - z4p_z4c*dZ3cdt_prd["z4"] - dZ4pdt_rel_r1p - dZ4pdt_rel_r6p - dZ4pdt_rel_n1p
# microzooplankton
dz5c_dt = dZ5cdt_prd["b1"] + dZ5cdt_prd["p1"] + dZ5cdt_prd["p2"] + dZ5cdt_prd["p3"] + dZ5cdt_prd["p4"] + dZ5cdt_prd["z6"] - dZ3cdt_prd["z5"] - dZ4cdt_prd["z5"] - dZ6cdt_prd["z5"] - dZ5cdt_rel_r1c - dZ5cdt_rel_r6c - dZ5cdt_rsp_o3c
dz5n_dt = bn_bc*dZ5cdt_prd["b1"] + p1n_p1c*dZ5cdt_prd["p1"] + p2n_p2c*dZ5cdt_prd["p2"] + p3n_p3c*dZ5cdt_prd["p3"] + p4n_p4c*dZ5cdt_prd["p4"] + z6n_z6c*dZ5cdt_prd["z6"] - z5n_z5c*dZ3cdt_prd["z5"] - z5n_z5c*dZ4cdt_prd["z5"] - z5n_z5c*dZ6cdt_prd["z5"] - dZ5ndt_rel_r1n - dZ5ndt_rel_r6n - dZ5ndt_rel_n4n
dz5p_dt = bp_bc*dZ5cdt_prd["b1"] + p1p_p1c*dZ5cdt_prd["p1"] + p2p_p2c*dZ5cdt_prd["p2"] + p3p_p3c*dZ5cdt_prd["p3"] + p4p_p4c*dZ5cdt_prd["p4"] + z6p_z6c*dZ5cdt_prd["z6"] - z5p_z5c*dZ3cdt_prd["z5"] - z5p_z5c*dZ4cdt_prd["z5"] - z5p_z5c*dZ6cdt_prd["z5"] - dZ5pdt_rel_r1p - dZ5pdt_rel_r6p - dZ5pdt_rel_n1p
dz6c_dt = dZ6cdt_prd["b1"] + dZ6cdt_prd["p1"] + dZ6cdt_prd["p2"] + dZ6cdt_prd["p3"] + dZ6cdt_prd["p4"] + dZ6cdt_prd["z5"] - dZ3cdt_prd["z6"] - dZ4cdt_prd["z6"] - dZ5cdt_prd["z6"] - dZ6cdt_rel_r1c - dZ6cdt_rel_r6c - dZ6cdt_rsp_o3c
dz6n_dt = bn_bc*dZ6cdt_prd["b1"] + p1n_p1c*dZ6cdt_prd["p1"] + p2n_p2c*dZ6cdt_prd["p2"] + p3n_p3c*dZ6cdt_prd["p3"] + p4n_p4c*dZ6cdt_prd["p4"] + z5n_z5c*dZ6cdt_prd["z5"] - z6n_z6c*dZ3cdt_prd["z6"] - z6n_z6c*dZ4cdt_prd["z6"] - z6n_z6c*dZ5cdt_prd["z6"] - dZ6ndt_rel_r1n - dZ6ndt_rel_r6n - dZ6ndt_rel_n4n
dz6p_dt = bp_bc*dZ6cdt_prd["b1"] + p1p_p1c*dZ6cdt_prd["p1"] + p2p_p2c*dZ6cdt_prd["p2"] + p3p_p3c*dZ6cdt_prd["p3"] + p4p_p4c*dZ6cdt_prd["p4"] + z5p_z5c*dZ6cdt_prd["z5"] - z6p_z6c*dZ3cdt_prd["z6"] - z6p_z6c*dZ4cdt_prd["z6"] - z6p_z6c*dZ5cdt_prd["z6"] - dZ6pdt_rel_r1p - dZ6pdt_rel_r6p - dZ6pdt_rel_n1p
# DOM
dr1c_dt = (dP1cdt_lys_r1c + dP2cdt_lys_r1c + dP3cdt_lys_r1c + dP4cdt_lys_r1c) + dBcdt_lys_r1c - dBcdt_upt_r1c + (dZ5cdt_rel_r1c + dZ6cdt_rel_r1c)
dr1n_dt = (dP1ndt_lys_r1n + dP2ndt_lys_r1n + dP3ndt_lys_r1n + dP4ndt_lys_r1n) + (extra_n1 + extra_n2 + extra_n3 + extra_n4) + dBcdt_lys_r1n - dBcdt_upt_r1c*r1n_r1c + (dZ5ndt_rel_r1n + dZ6ndt_rel_r1n)
dr1p_dt = (dP1pdt_lys_r1p + dP2pdt_lys_r1p + dP3pdt_lys_r1p + dP4pdt_lys_r1p) + (dP1pdt_upt_r1p + dP2pdt_upt_r1p + dP3pdt_upt_r1p + dP4pdt_upt_r1p) + dBcdt_lys_r1p - dBcdt_upt_r1c*r1p_r1c + (dZ5pdt_rel_r1p + dZ6pdt_rel_r1p)
dr2c_dt = (dP1cdt_exu_r2c + dP2cdt_exu_r2c + dP3cdt_exu_r2c + dP4cdt_exu_r2c) - dBcdt_upt_r2c + dBcdt_rel_r2c
dr3c_dt = dBcdt_rel_r3c - dBcdt_upt_r3c
# POM
dr6c_dt = (dP1cdt_lys_r6c + dP2cdt_lys_r6c + dP3cdt_lys_r6c + dP4cdt_lys_r6c) + dBcdt_lys_r6c - dBcdt_upt_r6c + (dZ3cdt_rel_r6c + dZ4cdt_rel_r6c + dZ5cdt_rel_r6c + dZ6cdt_rel_r6c)
dr6n_dt = (dP1ndt_lys_r6n + dP2ndt_lys_r6n + dP3ndt_lys_r6n + dP4ndt_lys_r6n) + dBcdt_lys_r6n - dBcdt_upt_r6c*r6n_r6c + (dZ3ndt_rel_r6n + dZ4ndt_rel_r6n + dZ5ndt_rel_r6n + dZ6ndt_rel_r6n)
dr6p_dt = (dP1pdt_lys_r6p + dP2pdt_lys_r6p + dP3pdt_lys_r6p + dP4pdt_lys_r6p) + dBcdt_lys_r6p - dBcdt_upt_r6c*r6p_r6c + (dZ3pdt_rel_r6p + dZ4pdt_rel_r6p + dZ5pdt_rel_r6p + dZ6pdt_rel_r6p)
dr6s_dt = dP1sdt_lys_r6s - dr6sdt_rmn_n5s + (p1s_p1c*(dZ3cdt_prd["p1"] + dZ4cdt_prd["p1"] + dZ5cdt_prd["p1"] + dZ6cdt_prd["p1"]))
# Dissolved inorganic carbon
do3c_dt = (-dP1cdt_gpp_o3c + dP1cdt_rsp_o3c) + (-dP2cdt_gpp_o3c + dP2cdt_rsp_o3c) + (-dP3cdt_gpp_o3c + dP3cdt_rsp_o3c) + (-dP4cdt_gpp_o3c + dP4cdt_rsp_o3c) + dBcdt_rsp_o3c + dZ3cdt_rsp_o3c + dZ4cdt_rsp_o3c + dZ5cdt_rsp_o3c + dZ6cdt_rsp_o3c + do3cdt_air_sea_flux
# Total alkalinity (from Alkalinity.F90)
if pel_chem_parameters["calc_alkalinity"] and o3c>0.0:
do3h_dt = -dn3n_dt + dn4n_dt
else:
do3h_dt = 0.0
return [do2o_dt, dn1p_dt, dn3n_dt, dn4n_dt, do4n_dt, dn5s_dt, dn6r_dt, db1c_dt, db1n_dt, db1p_dt,
dp1c_dt, dp1n_dt, dp1p_dt, dp1l_dt, dp1s_dt, dp2c_dt, dp2n_dt, dp2p_dt, dp2l_dt,
dp3c_dt, dp3n_dt, dp3p_dt, dp3l_dt, dp4c_dt, dp4n_dt, dp4p_dt, dp4l_dt, dz3c_dt, dz3n_dt, dz3p_dt,
dz4c_dt, dz4n_dt, dz4p_dt, dz5c_dt, dz5n_dt, dz5p_dt, dz6c_dt, dz6n_dt, dz6p_dt, dr1c_dt, dr1n_dt, dr1p_dt,
dr2c_dt, dr3c_dt, dr6c_dt, dr6n_dt, dr6p_dt, dr6s_dt, do3c_dt, do3h_dt]
if __name__ == '__main__':
# Names of species in the system
species_names = ['O2o', 'N1p', 'N3n', 'N4n', 'O4n', 'N5s', 'N6r', 'B1c', 'B1n', 'B1p',
'P1c', 'P1n', 'P1p', 'P1l', 'P1s', 'P2c', 'P2n', 'P2p', 'P2l',
'P3c', 'P3n', 'P3p', 'P3l', 'P4c', 'P4n', 'P4p', 'P4l',
'Z3c', 'Z3n', 'Z3p', 'Z4c', 'Z4n', 'Z4p', 'Z5c', 'Z5n', 'Z5p',
'Z6c', 'Z6n', 'Z6p', 'R1c', 'R1n', 'R1p', 'R2c', 'R3c', 'R6c',
'R6n', 'R6p', 'R6s', 'O3c', 'O3h']
# Initial concentrations
c0 = [300.0, # O2o
1.0, # N1p
5.0, # N3n
1.0, # N4n
200.0, # O4n
8.0, # N5s
1.0, # N6r
1.0, # B1c
1.67e-2, # B1n
1.85e-3, # B1p
1.0, # P1c
1.26e-2, # P1n
7.86e-4, # P1p
2.50e-2, # P1l
1.00e-2, # P1s
1.0, # P2c
1.26e-2, # P2n
7.86e-4, # P2p
1.50e-2, # P2l
1.0, # P3c
1.26e-2, # P3n
7.86e-4, # P3p
2.00e-2, # P3l
1.0, # P4c
1.26e-2, # P4n
7.86e-4, # P4p
2.00e-2, # P4l
1.0, # Z3c
1.5e-2, # Z3n
1.67e-3, # Z3p
1.0, # Z4c
1.5e-2, # Z4n
1.67e-3, # Z4p
1.0, # Z5c
1.67e-2, # Z5n
1.85e-3, # Z5p
1.0, # Z6c
1.67e-2, # Z6n
1.85e-3, # Z6p
1.0, # R1c
1.26e-2, # R1n
7.862e-4, # R1p
0.1, # R2c
1.0, # R3c
1.0, # R6c
1.26e-2, # R6n
7.862e-4, # R6p
1.45e-2, # R6s
27060.0, # O3c
2660.0 # O3h
]
# Time span for integration
t_span = [0, 86400*365*10]
# Assign multiplier = 1, indicating all species are present
multiplier = numpy.ones(len(c0))
# Integrate
solution_full_model = solve_ivp(bfm50_rate_eqns, t_span, c0, method='RK23')
# -------------------------------- Plots --------------------------------------
# Plot style
plt.rc('font', family='serif', size=14)
plt.rc('xtick', labelsize=12)
plt.rc('ytick', labelsize=12)
plt.rc('axes', labelsize=12, linewidth=2)
species_names_units = ['Oxygen (mmol O$_2$/m$^3$)',
'Phosphate (mmol P/m$^3$)',
'Nitrate (mmol N/m$^3$)',
'Ammonium (mmol N/m$^3$)',
'Nitrogen sink (mmol N/m$^3$)',
'Silicate (mmol Si/m$^3$)',
'Reduction Equivalents (mmol S/m$^3$)',
'Pelagic Bacteria (mg C/m$^3$)',
'Pelagic Bacteria (mmol N/m$^3$)',
'Pelagic Bacteria (mmol P/m$^3$)',
'Diatoms (mg C/m$^3$)',
'Diatoms (mmol N/m$^3$)',
'Diatoms (mmol P/m$^3$)',
'Diatoms (mg Chl-a/m$^3$)',
'Diatoms (mmol Si/m$^3$)',
'Flagellates (mg C/m$^3$)',
'Flagellates (mmol N/m$^3$)',
'Flagellates (mmol P/m$^3$)',
'Flagellates (mg Chl-a/m$^3$)',
'PicoPhytoplankton (mg C/m$^3$)',
'PicoPhytoplankton (mmol N/m$^3$)',
'PicoPhytoplankton (mmol P/m$^3$)',
'PicoPhytoplankton (mg Chl-a/m$^3$)',
'Large Phytoplankton (mg C/m$^3$)',
'Large Phytoplankton (mmol N/m$^3$)',
'Large Phytoplankton (mmol P/m$^3$)',
'Large Phytoplankton (mg Chl-a/m$^3$)',
'Carnivorous Mesozooplankton (mg C/m$^3$)',
'Carnivorous Mesozooplankton (mmol N/m$^3$)',
'Carnivorous Mesozooplankton (mmol P/m$^3$)',
'Omnivorous Mesozooplankton (mg C/m$^3$)',
'Omnivorous Mesozooplankton (mmol N/m$^3$)',
'Omnivorous Mesozooplankton (mmol P/m$^3$)',
'Microzooplankton (mg C/m$^3$)',
'Microzooplankton (mmol N/m$^3$)',
'Microzooplankton (mmol P/m$^3$)',
'Heterotrophic Nanoflagellates (mg C/m$^3$)',
'Heterotrophic Nanoflagellates (mmol N/m$^3$)',
'Heterotrophic Nanoflagellates (mmol P/m$^3$)',
'Labile Dissolved Organic Carbon (mg C/m$^3$)',
'Labile Dissolved Organic Nitrogen (mmol N/m$^3$)',
'Labile Dissolved Organic Phosphate (mmol P/m$^3$)',
'Semi-labile Dissolved Organic Carbon (mg C/m$^3$)',
'Semi-refractory Dissolved Organic Carbon (mg C/m$^3$)',
'Particulate Organic Carbon (mg C/m$^3$)',
'Particulate Organic Nitrate (mmol N/m$^3$)',
'Particulate Organic Phosphate (mmol P/m$^3$)',
'Particulate Organic Silicate (mmol Si/m$^3$)',
'Dissolved Inorganic Carbon (mg C/m$^3$)',
'Total Alkalinity (mmol Eq/m$^3$)'
]
plt.close('all')
with PdfPages('BFM50_plot.pdf') as pdf:
for index,species in enumerate(species_names_units):
fig = plt.figure(index)
ax = fig.add_axes([0, 0, 1, 1])
ax.grid(linestyle='--')
ax.plot(solution_full_model.t/86400/365, solution_full_model.y[index])
ax.set_ylabel(species)
ax.set_xlabel('Time (year)')
ax.set_xlim(0,10)
if index == 4:
plt.ylim([199.9,200.1])
if index == 42:
plt.ylim([0.09,0.11])
pdf.savefig(fig, bbox_inches = "tight")
if index == 19 or index == 39 or index == 49:
plt.close('all')
plt.close('all')