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
]
def bacteria_eqns(conc, bacteria_parameters, constant_parameters,
environmental_parameters, temper):
""" Calculates the terms needed for the bacteria biological rate equations
Equations come from the BFM user manual
"""
# State variables
o2o = conc[0] # Dissolved oxygen (mg O_2 m^-3)
n1p = conc[1] # Phosphate (mmol P m^-3)
n4n = conc[3] # Ammonium (mmol N 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)
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)
# concentration ratios
bp_bc = get_concentration_ratio(b1p, b1c, constant_parameters["p_small"])
bn_bc = get_concentration_ratio(b1n, b1c, 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"])
# Temperature effect on pelagic bacteria
fTB = eTq_vector(temper, environmental_parameters["basetemp"],
environmental_parameters["q10b"])
# oxygen non-dimensional regulation factor[-]
# Oxygen environment: bacteria are both aerobic and anaerobic
f_B_O = max(constant_parameters["p_small"],
o2o)**3 / (max(constant_parameters["p_small"], o2o)**3 +
bacteria_parameters["h_B_O"]**3)
# external nutrient limitation
f_B_n = n4n / (n4n + bacteria_parameters["h_B_n"])
f_B_p = n1p / (n1p + bacteria_parameters["h_B_p"])
# Bacteria mortality (lysis) process [mg C m^-3 s^-1]
dBcdt_lys = (bacteria_parameters["d_0B"] * fTB +
bacteria_parameters["d_B_d"] * b1c) * b1c
dBcdt_lys_r1c = dBcdt_lys * constant_parameters["epsilon_c"]
dBcdt_lys_r1n = dBcdt_lys * bn_bc * constant_parameters["epsilon_n"]
dBcdt_lys_r1p = dBcdt_lys * bp_bc * constant_parameters["epsilon_p"]
dBcdt_lys_r6c = dBcdt_lys * (1.0 - constant_parameters["epsilon_c"])
dBcdt_lys_r6n = dBcdt_lys * bn_bc * (1.0 -
constant_parameters["epsilon_n"])
dBcdt_lys_r6p = dBcdt_lys * bp_bc * (1.0 -
constant_parameters["epsilon_p"])
# Substrate availability
if bacteria_parameters["bact_version"] == 1 or bacteria_parameters[
"bact_version"] == 2:
# nutrient limitation (intracellular)
nut_lim_n = min(1.0, max(0.0, bn_bc /
bacteria_parameters["n_B_opt"])) # Nitrogen
nut_lim_p = min(1.0, max(0.0, bp_bc /
bacteria_parameters["p_B_opt"])) # Phosphorus
f_B_n_P = min(nut_lim_n, nut_lim_p)
# Potential uptake by bacteria
potential_upt = f_B_n_P * fTB * bacteria_parameters["r_0B"] * b1c
# correction of substrate quality depending on nutrient content
f_r1_n_P = min(1.0, r1p_r1c / bacteria_parameters["p_B_opt"],
r1n_r1c / bacteria_parameters["n_B_opt"])
f_r6_n_P = min(1.0, r6p_r6c / bacteria_parameters["p_B_opt"],
r6n_r6c / bacteria_parameters["n_B_opt"])
else:
sys.exit(
'This code does not support this parameterization option, only bact_version=1'
)
# Calculate the realized substrate uptake rate depending on the type of detritus and quality
upt_R1c = (bacteria_parameters["v_B_r1"] * f_r1_n_P +
bacteria_parameters["v_0B_r1"] * (1.0 - f_r1_n_P)) * r1c
upt_R2c = bacteria_parameters["v_B_r2"] * r2c
upt_R3c = bacteria_parameters["v_B_r3"] * r3c
upt_R6c = bacteria_parameters["v_B_r6"] * f_r6_n_P * r6c
realized_upt = constant_parameters[
"p_small"] + upt_R1c + upt_R2c + upt_R3c + upt_R6c
# Actual uptake by bacteria
actual_upt = min(potential_upt, realized_upt)
# Carbon fluxes into bacteria
dBcdt_upt_r1c = actual_upt * upt_R1c / realized_upt
dBcdt_upt_r2c = actual_upt * upt_R2c / realized_upt
dBcdt_upt_r3c = actual_upt * upt_R3c / realized_upt
dBcdt_upt_r6c = actual_upt * upt_R6c / realized_upt
# Organic Nitrogen and Phosphrous uptake
dBcdt_upt_r1n = r1n_r1c * dBcdt_upt_r1c
dBcdt_upt_r6n = r6n_r6c * dBcdt_upt_r6c
dBcdt_upt_r1p = r1p_r1c * dBcdt_upt_r1c
dBcdt_upt_r6p = r6p_r6c * dBcdt_upt_r6c
# Bacteria respiration [mc C m^-3 s^-1]
dBcdt_rsp_o3c = (
bacteria_parameters["gamma_B_a"] + bacteria_parameters["gamma_B_O"] *
(1.0 - f_B_O)) * actual_upt + bacteria_parameters["b_B"] * b1c * fTB
# Fluxes from bacteria
if bacteria_parameters["bact_version"] == 1:
# There is no Carbon excretion
dBcdt_rel_r2c = 0.0
dBcdt_rel_r3c = 0.0
# Dissolved Nitrogen dynamics
dBndt_upt_rel_n4n = (bn_bc - bacteria_parameters["n_B_opt"]
) * b1c * bacteria_parameters["v_B_n"]
# Dissolved Phosphorus dynamics
dBpdt_upt_rel_n1p = (bp_bc - bacteria_parameters["p_B_opt"]
) * b1c * bacteria_parameters["v_B_p"]
# BACT2 parameterization
if bacteria_parameters["bact_version"] == 2:
print(
'This code does not support this parameterization option, only bact_version=1'
)
# BACT3 parameterization
if bacteria_parameters["bact_version"] == 3:
print(
'This code does not support this parameterization option, only bact_version=1'
)
# Term needed for denitrification flux (dn3ndt_denit) (from PelBac.F90 line 352)
flPTN6r = (1.0 - f_B_O) * dBcdt_rsp_o3c * constant_parameters[
"omega_c"] * constant_parameters["omega_r"]
return (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)
def microzoo_eqns(conc, microzoo_parameters, constant_parameters,
environmental_parameters, zc, zn, zp, i_c, i_n, i_p, temp):
""" Calculates the micorzooplankton (Z5 & Z6) terms needed for the zooplankton biological rate equations
Equations come from the BFM user manual and the fortran code MicroZoo.F90
"""
# Dissolved oxygen concentration (mg O_2 m^-3)
o2o = conc[0]
# Concentration ratios
zn_zc = get_concentration_ratio(zn, zc, constant_parameters["p_small"])
zp_zc = get_concentration_ratio(zp, zc, constant_parameters["p_small"])
# Temperature regulating factor
fTZ = eTq_vector(temp, environmental_parameters["basetemp"],
environmental_parameters["q10z"])
# Oxygen dependent regulation factor
fZO = min(1.0, (o2o / (o2o + microzoo_parameters["z_o2o"])))
#---------------------- Microzooplankton Respiration ----------------------
# Zooplankton total repiration rate (eqn. 2.4.8, and matches fortran code)
rrac = i_c * (1.0 - microzoo_parameters["etaZ"] -
microzoo_parameters["betaZ"])
rrsc = microzoo_parameters["bZ"] * fTZ * zc
dZcdt_rsp_o3c = rrac + rrsc
#------------- Microzooplankton mortality and activity excretion ----------
# From fortran code MesoZoo.F90 lines 327-331
rdc = ((1.0 - fZO) * microzoo_parameters["d_ZO"] +
microzoo_parameters["d_Z"]) * zc
reac = i_c * (1.0 -
microzoo_parameters["etaZ"]) * microzoo_parameters["betaZ"]
rric = reac + rdc
dZcdt_rel_r1c = rric * constant_parameters["epsilon_c"]
dZcdt_rel_r6c = rric * (1.0 - constant_parameters["epsilon_c"])
#------------------- Microzooplankton nutrient dynamics -------------------
# Organic Nitrogen dynamics (from fortran code) [mmol N m^-3 s^-1]
rrin = i_n * microzoo_parameters["betaZ"] + rdc * zn_zc
dZndt_rel_r1n = rrin * constant_parameters["epsilon_n"]
dZndt_rel_r6n = rrin - dZndt_rel_r1n
# Organic Phosphorus dynamics (from fortran code) [mmol P m^-3 s^-1]
rrip = i_p * microzoo_parameters["betaZ"] + rdc * zp_zc
dZpdt_rel_r1p = rrip * constant_parameters["epsilon_p"]
dZpdt_rel_r6p = rrip - dZpdt_rel_r1p
#--------------- Microzooplankton Dissolved nutrient dynamics -------------
# Equations from fortran code (MicroZoo.F90 line 368-371)
runc = max(0.0, i_c * (1.0 - microzoo_parameters["betaZ"]) - rrac)
runn = max(0.0, i_n * (1.0 - microzoo_parameters["betaZ"]) + rrsc * zn_zc)
runp = max(0.0, i_p * (1.0 - microzoo_parameters["betaZ"]) + rrsc * zp_zc)
dZpdt_rel_n1p = max(
0.0, runp / (constant_parameters["p_small"] + runc) -
microzoo_parameters["p_Zopt"]) * runc
dZndt_rel_n4n = max(
0.0, runn / (constant_parameters["p_small"] + runc) -
microzoo_parameters["n_Zopt"]) * runc
return dZcdt_rel_r1c, dZcdt_rel_r6c, dZcdt_rsp_o3c, dZndt_rel_r1n, dZndt_rel_r6n, dZpdt_rel_r1p, dZpdt_rel_r6p, dZpdt_rel_n1p, dZndt_rel_n4n
def mesozoo_eqns(conc, mesozoo_parameters, constant_parameters,
environmental_parameters, zc, zn, zp, i_c, i_n, i_p, temp):
""" Calculates the mesozooplankton (Z3 & Z4) terms needed for the zooplankton biological rate equations
Equations come from the BFM user manual and the fortran code MesoZoo.F90
"""
# Dissolved oxygen concentration (mg O_2 m^-3)
o2o = conc[0] # Dissolved oxygen (mg O_2 m^-3)
# Concentration ratios
zn_zc = get_concentration_ratio(zn, zc, constant_parameters["p_small"])
zp_zc = get_concentration_ratio(zp, zc, constant_parameters["p_small"])
# Temperature regulating factor
fTZ = eTq_vector(temp, environmental_parameters["basetemp"],
environmental_parameters["q10z"])
# Oxygen dependent regulation factor
fZO = (max(constant_parameters["p_small"], o2o)**
3) / (max(constant_parameters["p_small"], o2o)**3 +
mesozoo_parameters["z_o2o"]**3)
# energy cost of ingestion
prI = 1.0 - mesozoo_parameters["etaZ"] - mesozoo_parameters["betaZ"]
# Zooplankton total repiration rate (from 'MesoZoo.F90' line 343)
dZcdt_rsp_o3c = prI * i_c + mesozoo_parameters["bZ"] * fTZ * zc
# Specific rates of low oxygen mortality and Density dependent mortality
# from fortran code MesoZoo.F90 lines 343-344
rdo_c = mesozoo_parameters["d_Zdns"] * (1.0 - fZO) * fTZ * zc
rd_c = mesozoo_parameters["d_Z"] * zc**mesozoo_parameters["gammaZ"]
# Total egestion including pellet production (from MesoZoo.F90 line 359 - 361)
dZcdt_rel_r6c = mesozoo_parameters["betaZ"] * i_c + rdo_c + rd_c
dZndt_rel_r6n = mesozoo_parameters["betaZ"] * i_n + zn_zc * (rdo_c + rd_c)
dZpdt_rel_r6p = mesozoo_parameters["betaZ"] * i_p + zp_zc * (rdo_c + rd_c)
# Check the assimilation rate for Carbon, Nitrogen and Phosphorus
# compute P:C and N:C ratios in the assimilation rate
# from MesoZoo.F90 lines 371-375
ru_c = mesozoo_parameters["etaZ"] * i_c
ru_n = (mesozoo_parameters["etaZ"] + prI) * i_n
ru_p = (mesozoo_parameters["etaZ"] + prI) * i_p
pu_e_n = ru_n / (constant_parameters["p_small"] + ru_c)
pu_e_p = ru_p / (constant_parameters["p_small"] + ru_c)
# Eliminate the excess of the non-limiting constituent
# Determine whether C, P or N is the limiting element and assign the value to variable limiting_nutrient
# from MesoZoo.F90 lines
limiting_nutrient = 'carbon'
temp_p = pu_e_p / (zp_zc + constant_parameters["p_small"])
temp_n = pu_e_n / (zn_zc + constant_parameters["p_small"])
if temp_p < temp_n or abs(temp_p -
temp_n) < constant_parameters["p_small"]:
if pu_e_p < zp_zc:
limiting_nutrient = 'phosphorus'
else:
if pu_e_n < zn_zc:
limiting_nutrient = 'nitrogen'
# Compute the correction terms depending on the limiting constituent
if limiting_nutrient == 'carbon':
q_Zc = 0.0
q_Zp = max(0.0, (1.0 - mesozoo_parameters["betaZ"]) * i_p -
mesozoo_parameters["p_Zopt"] * ru_c)
q_Zn = max(0.0, (1.0 - mesozoo_parameters["betaZ"]) * i_n -
mesozoo_parameters["n_Zopt"] * ru_c)
elif limiting_nutrient == 'phosphorus':
q_Zp = 0.0
q_Zc = max(
0.0, ru_c - (1.0 - mesozoo_parameters["betaZ"]) * i_p /
mesozoo_parameters["p_Zopt"])
q_Zn = max(0.0, (1.0 - mesozoo_parameters["betaZ"]) * i_n -
mesozoo_parameters["n_Zopt"] * (ru_c - q_Zc))
elif limiting_nutrient == 'nitrogen':
q_Zn = 0.0
q_Zc = max(
0.0, ru_c - (1.0 - mesozoo_parameters["betaZ"]) * i_n /
mesozoo_parameters["n_Zopt"])
q_Zp = max(0.0, (1.0 - mesozoo_parameters["betaZ"]) * i_p -
mesozoo_parameters["p_Zopt"] * (ru_c - q_Zc))
# Nutrient remineralization basal metabolism + excess of non-limiting nutrients
dZpdt_rel_n1p = mesozoo_parameters["bZ"] * fZO * fTZ * zp + q_Zp
dZndt_rel_n4n = mesozoo_parameters["bZ"] * fZO * fTZ * zn + q_Zn
# Fluxes to particulate organic matter
# Add the correction term for organic carbon release based on the limiting constituent
dZcdt_rel_r6c += q_Zc
# mesozooplankton are assumed to have no dissolved products
dZcdt_rel_r1c = 0.0
dZndt_rel_r1n = 0.0
dZpdt_rel_r1p = 0.0
return dZcdt_rel_r1c, dZcdt_rel_r6c, dZcdt_rsp_o3c, dZndt_rel_r1n, dZndt_rel_r6n, dZpdt_rel_r1p, dZpdt_rel_r6p, dZpdt_rel_n1p, dZndt_rel_n4n
def get_mesozoo_predation_terms(conc, mesozoo3_parameters, mesozoo4_parameters,
zoo_availability_parameters,
environmental_parameters, constant_parameters,
temp):
""" Calculates the predation terms for mesozooplankton """
# Species concentrations
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)
# concentration ratios
conc_ratio_n = {
"p1": get_concentration_ratio(p1n, p1c,
constant_parameters["p_small"]),
"p2": get_concentration_ratio(p2n, p2c,
constant_parameters["p_small"]),
"p3": get_concentration_ratio(p3n, p3c,
constant_parameters["p_small"]),
"p4": get_concentration_ratio(p4n, p4c,
constant_parameters["p_small"]),
"z3": get_concentration_ratio(z3n, z3c,
constant_parameters["p_small"]),
"z4": get_concentration_ratio(z4n, z4c,
constant_parameters["p_small"]),
"z5": get_concentration_ratio(z5n, z5c,
constant_parameters["p_small"]),
"z6": get_concentration_ratio(z6n, z6c, constant_parameters["p_small"])
}
conc_ratio_p = {
"p1": get_concentration_ratio(p1p, p1c,
constant_parameters["p_small"]),
"p2": get_concentration_ratio(p2p, p2c,
constant_parameters["p_small"]),
"p3": get_concentration_ratio(p3p, p3c,
constant_parameters["p_small"]),
"p4": get_concentration_ratio(p4p, p4c,
constant_parameters["p_small"]),
"z3": get_concentration_ratio(z3p, z3c,
constant_parameters["p_small"]),
"z4": get_concentration_ratio(z4p, z4c,
constant_parameters["p_small"]),
"z5": get_concentration_ratio(z5p, z5c,
constant_parameters["p_small"]),
"z6": get_concentration_ratio(z6p, z6c, constant_parameters["p_small"])
}
# Zooplankton temperature regulating factor
fTZ = eTq_vector(temp, environmental_parameters["basetemp"],
environmental_parameters["q10z"])
# Calculate total potential food given the non-dim prey availability
# There is no parameter for capture efficiency in mesozooplankton
# From MesoZoo.F90 lines 247-259
# Phytoplankton LFG: Food availability of prey Phytoplankton for predator Z3 and Z4
available_phyto_c3 = (zoo_availability_parameters["del_z3p1"] * p1c) + (
zoo_availability_parameters["del_z3p2"] *
p2c) + (zoo_availability_parameters["del_z3p3"] *
p3c) + (zoo_availability_parameters["del_z3p4"] * p4c)
available_phyto_c4 = (zoo_availability_parameters["del_z4p1"] * p1c) + (
zoo_availability_parameters["del_z4p2"] *
p2c) + (zoo_availability_parameters["del_z4p3"] *
p3c) + (zoo_availability_parameters["del_z4p4"] * p4c)
# Mesozooplankton LFG
available_mesozoo_c3 = (zoo_availability_parameters["del_z3z3"] * z3c) + (
zoo_availability_parameters["del_z3z4"] * z4c)
available_mesozoo_c4 = (zoo_availability_parameters["del_z4z3"] * z3c) + (
zoo_availability_parameters["del_z4z4"] * z4c)
# Microzooplankton LFG
available_microzoo_c3 = (zoo_availability_parameters["del_z3z5"] * z5c) + (
zoo_availability_parameters["del_z3z6"] * z6c)
available_microzoo_c4 = (zoo_availability_parameters["del_z4z5"] * z5c) + (
zoo_availability_parameters["del_z4z6"] * z6c)
# sys.exit(available_microzoo_c4)
# Total potential food (from Meso.F90 'rumc')
f_c3 = available_phyto_c3 + available_mesozoo_c3 + available_microzoo_c3
f_c4 = available_phyto_c4 + available_mesozoo_c4 + available_microzoo_c4
# Calculate total food uptake rate (from Meso.F90 'rugc')
total_uptake_rate_z3 = fTZ * mesozoo3_parameters["r_Z0"] * (
mesozoo3_parameters["nu_z"] * f_c3 /
((mesozoo3_parameters["nu_z"] * f_c3) +
mesozoo3_parameters["r_Z0"])) * z3c
total_uptake_rate_z4 = fTZ * mesozoo4_parameters["r_Z0"] * (
mesozoo4_parameters["nu_z"] * f_c4 /
((mesozoo4_parameters["nu_z"] * f_c4) +
mesozoo4_parameters["r_Z0"])) * z4c
# Calculate specific uptake rate considering potentially available food (from Meso.F90 'sut')
specific_uptake_rate_z3 = total_uptake_rate_z3 / (
constant_parameters["p_small"] + f_c3)
specific_uptake_rate_z4 = total_uptake_rate_z4 / (
constant_parameters["p_small"] + f_c4)
# Total Gross Uptakes from every LFG
dZ3cdt_prd = {
"p1":
specific_uptake_rate_z3 * zoo_availability_parameters["del_z3p1"] *
p1c,
"p2":
specific_uptake_rate_z3 * zoo_availability_parameters["del_z3p2"] *
p2c,
"p3":
specific_uptake_rate_z3 * zoo_availability_parameters["del_z3p3"] *
p3c,
"p4":
specific_uptake_rate_z3 * zoo_availability_parameters["del_z3p4"] *
p4c,
"z3":
specific_uptake_rate_z3 * zoo_availability_parameters["del_z3z3"] *
z3c,
"z4":
specific_uptake_rate_z3 * zoo_availability_parameters["del_z3z4"] *
z4c,
"z5":
specific_uptake_rate_z3 * zoo_availability_parameters["del_z3z5"] *
z5c,
"z6":
specific_uptake_rate_z3 * zoo_availability_parameters["del_z3z6"] * z6c
}
dZ4cdt_prd = {
"p1":
specific_uptake_rate_z4 * zoo_availability_parameters["del_z4p1"] *
p1c,
"p2":
specific_uptake_rate_z4 * zoo_availability_parameters["del_z4p2"] *
p2c,
"p3":
specific_uptake_rate_z4 * zoo_availability_parameters["del_z4p3"] *
p3c,
"p4":
specific_uptake_rate_z4 * zoo_availability_parameters["del_z4p4"] *
p4c,
"z3":
specific_uptake_rate_z4 * zoo_availability_parameters["del_z4z3"] *
z3c,
"z4":
specific_uptake_rate_z4 * zoo_availability_parameters["del_z4z4"] *
z4c,
"z5":
specific_uptake_rate_z4 * zoo_availability_parameters["del_z4z5"] *
z5c,
"z6":
specific_uptake_rate_z4 * zoo_availability_parameters["del_z4z6"] * z6c
}
# Total ingestion rate
ic3 = 0.0
in3 = 0.0
ip3 = 0.0
for key in dZ3cdt_prd:
ic3 += dZ3cdt_prd[key]
in3 += dZ3cdt_prd[key] * conc_ratio_n[key]
ip3 += dZ3cdt_prd[key] * conc_ratio_p[key]
ic4 = 0.0
in4 = 0.0
ip4 = 0.0
for key in dZ4cdt_prd:
ic4 += dZ4cdt_prd[key]
in4 += dZ4cdt_prd[key] * conc_ratio_n[key]
ip4 += dZ4cdt_prd[key] * conc_ratio_p[key]
return dZ3cdt_prd, dZ4cdt_prd, ic3, in3, ip3, ic4, in4, ip4
def get_microzoo_predation_terms(conc, microzoo5_parameters,
microzoo6_parameters,
zoo_availability_parameters,
environmental_parameters, constant_parameters,
temp):
""" Calculates the predation terms for microzooplankton """
# Species concentrations
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)
# concentration ratios
conc_ratio_n = {
"b1": get_concentration_ratio(b1n, b1c,
constant_parameters["p_small"]),
"p1": get_concentration_ratio(p1n, p1c,
constant_parameters["p_small"]),
"p2": get_concentration_ratio(p2n, p2c,
constant_parameters["p_small"]),
"p3": get_concentration_ratio(p3n, p3c,
constant_parameters["p_small"]),
"p4": get_concentration_ratio(p4n, p4c,
constant_parameters["p_small"]),
"z5": get_concentration_ratio(z5n, z5c,
constant_parameters["p_small"]),
"z6": get_concentration_ratio(z6n, z6c, constant_parameters["p_small"])
}
conc_ratio_p = {
"b1": get_concentration_ratio(b1p, b1c,
constant_parameters["p_small"]),
"p1": get_concentration_ratio(p1p, p1c,
constant_parameters["p_small"]),
"p2": get_concentration_ratio(p2p, p2c,
constant_parameters["p_small"]),
"p3": get_concentration_ratio(p3p, p3c,
constant_parameters["p_small"]),
"p4": get_concentration_ratio(p4p, p4c,
constant_parameters["p_small"]),
"z5": get_concentration_ratio(z5p, z5c,
constant_parameters["p_small"]),
"z6": get_concentration_ratio(z6p, z6c, constant_parameters["p_small"])
}
# Zooplankton temperature regulating factor
fTZ = eTq_vector(temp, environmental_parameters["basetemp"],
environmental_parameters["q10z"])
# Capture efficiencies
capture_efficiencies_z5 = {
"b1": b1c / (b1c + microzoo5_parameters["mu_z"]),
"p1": p1c / (p1c + microzoo5_parameters["mu_z"]),
"p2": p2c / (p2c + microzoo5_parameters["mu_z"]),
"p3": p3c / (p3c + microzoo5_parameters["mu_z"]),
"p4": p4c / (p4c + microzoo5_parameters["mu_z"]),
"z5": z5c / (z5c + microzoo5_parameters["mu_z"]),
"z6": z6c / (z6c + microzoo5_parameters["mu_z"])
}
capture_efficiencies_z6 = {
"b1": b1c / (b1c + microzoo6_parameters["mu_z"]),
"p1": p1c / (p1c + microzoo6_parameters["mu_z"]),
"p2": p2c / (p2c + microzoo6_parameters["mu_z"]),
"p3": p3c / (p3c + microzoo6_parameters["mu_z"]),
"p4": p4c / (p4c + microzoo6_parameters["mu_z"]),
"z5": z5c / (z5c + microzoo6_parameters["mu_z"]),
"z6": z6c / (z6c + microzoo6_parameters["mu_z"])
}
# Calculate total potential food given the non-dim prey availability and capture efficiency
# From MicroZoo.F90 lines 209-237
# Bacteria LFG: Food availability of prey Bacteria for predator Z5 and Z6
available_bact_c5 = zoo_availability_parameters[
"del_z5b1"] * b1c * capture_efficiencies_z5["b1"]
available_bact_n5 = zoo_availability_parameters[
"del_z5b1"] * b1c * capture_efficiencies_z5["b1"] * conc_ratio_n["b1"]
available_bact_p5 = zoo_availability_parameters[
"del_z5b1"] * b1c * capture_efficiencies_z5["b1"] * conc_ratio_p["b1"]
available_bact_c6 = zoo_availability_parameters[
"del_z6b1"] * b1c * capture_efficiencies_z6["b1"]
available_bact_n6 = zoo_availability_parameters[
"del_z6b1"] * b1c * capture_efficiencies_z6["b1"] * conc_ratio_n["b1"]
available_bact_p6 = zoo_availability_parameters[
"del_z6b1"] * b1c * capture_efficiencies_z6["b1"] * conc_ratio_p["b1"]
# Phytoplankton LFG: Food availability of prey Phytoplankton for predator Z5 and Z6
available_phyto_c5 = ((zoo_availability_parameters["del_z5p1"] * p1c *
capture_efficiencies_z5["p1"]) +
(zoo_availability_parameters["del_z3p2"] * p2c *
capture_efficiencies_z5["p2"]) +
(zoo_availability_parameters["del_z3p3"] * p3c *
capture_efficiencies_z5["p3"]) +
(zoo_availability_parameters["del_z3p4"] * p4c *
capture_efficiencies_z5["p4"]))
available_phyto_n5 = (
(zoo_availability_parameters["del_z5p1"] * p1c *
capture_efficiencies_z5["p1"] * conc_ratio_n["p1"]) +
(zoo_availability_parameters["del_z3p2"] * p2c *
capture_efficiencies_z5["p2"] * conc_ratio_n["p2"]) +
(zoo_availability_parameters["del_z3p3"] * p3c *
capture_efficiencies_z5["p3"] * conc_ratio_n["p3"]) +
(zoo_availability_parameters["del_z3p4"] * p4c *
capture_efficiencies_z5["p4"] * conc_ratio_n["p4"]))
available_phyto_p5 = (
(zoo_availability_parameters["del_z5p1"] * p1c *
capture_efficiencies_z5["p1"] * conc_ratio_p["p1"]) +
(zoo_availability_parameters["del_z3p2"] * p2c *
capture_efficiencies_z5["p2"] * conc_ratio_p["p2"]) +
(zoo_availability_parameters["del_z3p3"] * p3c *
capture_efficiencies_z5["p3"] * conc_ratio_p["p3"]) +
(zoo_availability_parameters["del_z3p4"] * p4c *
capture_efficiencies_z5["p4"] * conc_ratio_p["p4"]))
available_phyto_c6 = ((zoo_availability_parameters["del_z6p1"] * p1c *
capture_efficiencies_z6["p1"]) +
(zoo_availability_parameters["del_z6p2"] * p2c *
capture_efficiencies_z6["p2"]) +
(zoo_availability_parameters["del_z6p3"] * p3c *
capture_efficiencies_z6["p3"]) +
(zoo_availability_parameters["del_z6p4"] * p4c *
capture_efficiencies_z6["p4"]))
available_phyto_n6 = (
(zoo_availability_parameters["del_z6p1"] * p1c *
capture_efficiencies_z6["p1"] * conc_ratio_n["p1"]) +
(zoo_availability_parameters["del_z6p2"] * p2c *
capture_efficiencies_z6["p2"] * conc_ratio_n["p2"]) +
(zoo_availability_parameters["del_z6p3"] * p3c *
capture_efficiencies_z6["p3"] * conc_ratio_n["p3"]) +
(zoo_availability_parameters["del_z6p4"] * p4c *
capture_efficiencies_z6["p4"] * conc_ratio_n["p4"]))
available_phyto_p6 = (
(zoo_availability_parameters["del_z6p1"] * p1c *
capture_efficiencies_z6["p1"] * conc_ratio_p["p1"]) +
(zoo_availability_parameters["del_z6p2"] * p2c *
capture_efficiencies_z6["p2"] * conc_ratio_p["p2"]) +
(zoo_availability_parameters["del_z6p3"] * p3c *
capture_efficiencies_z6["p3"] * conc_ratio_p["p3"]) +
(zoo_availability_parameters["del_z6p4"] * p4c *
capture_efficiencies_z6["p4"] * conc_ratio_p["p4"]))
# Phytoplankton LFG: Food availability of prey Microzooplankton for predator Z5 and Z6
available_microzoo_c5 = (zoo_availability_parameters["del_z5z5"] * z5c *
capture_efficiencies_z5["z5"]) + (
zoo_availability_parameters["del_z5z6"] *
z6c * capture_efficiencies_z5["z6"])
available_microzoo_n5 = (zoo_availability_parameters["del_z5z5"] * z5c *
capture_efficiencies_z5["z5"] * conc_ratio_n["z5"]
) + (zoo_availability_parameters["del_z5z6"] *
z6c * capture_efficiencies_z5["z6"] *
conc_ratio_n["z6"])
available_microzoo_p5 = (zoo_availability_parameters["del_z5z5"] * z5c *
capture_efficiencies_z5["z5"] * conc_ratio_p["z5"]
) + (zoo_availability_parameters["del_z5z6"] *
z6c * capture_efficiencies_z5["z6"] *
conc_ratio_p["z6"])
available_microzoo_c6 = (zoo_availability_parameters["del_z6z5"] * z5c *
capture_efficiencies_z6["z5"]) + (
zoo_availability_parameters["del_z6z6"] *
z6c * capture_efficiencies_z6["z6"])
available_microzoo_n6 = (
zoo_availability_parameters["del_z6z5"] * z5c *
capture_efficiencies_z6["z5"]**conc_ratio_n["z5"]) + (
zoo_availability_parameters["del_z6z6"] * z6c *
capture_efficiencies_z6["z6"]**conc_ratio_n["z6"])
available_microzoo_p6 = (
zoo_availability_parameters["del_z6z5"] * z5c *
capture_efficiencies_z6["z5"]**conc_ratio_p["z5"]) + (
zoo_availability_parameters["del_z6z6"] * z6c *
capture_efficiencies_z6["z6"]**conc_ratio_p["z6"])
# Total potential food (from MicroZoo.F90 'rumc', 'rumn', 'rump')
f_c5 = available_bact_c5 + available_phyto_c5 + available_microzoo_c5
f_n5 = available_bact_n5 + available_phyto_n5 + available_microzoo_n5
f_p5 = available_bact_p5 + available_phyto_p5 + available_microzoo_p5
f_c6 = available_bact_c6 + available_phyto_c6 + available_microzoo_c6
f_n6 = available_bact_n6 + available_phyto_n6 + available_microzoo_n6
f_p6 = available_bact_p6 + available_phyto_p6 + available_microzoo_p6
# Calculate total food uptake rate (from MicroZoo.F90 line 243 'rugc')
total_uptake_rate_z5 = fTZ * microzoo5_parameters["r_Z0"] * (
f_c5 / (f_c5 + microzoo5_parameters["h_Z_F"])) * z5c
total_uptake_rate_z6 = fTZ * microzoo6_parameters["r_Z0"] * (
f_c6 / (f_c6 + microzoo6_parameters["h_Z_F"])) * z6c
# Calculate specific uptake rate considering potentially available food (from MicroZoo.F90 line 244 'sut')
specific_uptake_rate_z5 = total_uptake_rate_z5 / (
f_c5 + constant_parameters["p_small"])
specific_uptake_rate_z6 = total_uptake_rate_z6 / (
f_c6 + constant_parameters["p_small"])
# Total Gross Uptakes from every LFG
dZ5cdt_prd = {
"b1":
specific_uptake_rate_z5 * zoo_availability_parameters["del_z5b1"] *
b1c * capture_efficiencies_z5["b1"],
"p1":
specific_uptake_rate_z5 * zoo_availability_parameters["del_z5p1"] *
p1c * capture_efficiencies_z5["p1"],
"p2":
specific_uptake_rate_z5 * zoo_availability_parameters["del_z5p2"] *
p2c * capture_efficiencies_z5["p2"],
"p3":
specific_uptake_rate_z5 * zoo_availability_parameters["del_z5p3"] *
p3c * capture_efficiencies_z5["p3"],
"p4":
specific_uptake_rate_z5 * zoo_availability_parameters["del_z5p4"] *
p4c * capture_efficiencies_z5["p4"],
"z5":
specific_uptake_rate_z5 * zoo_availability_parameters["del_z5z5"] *
z5c * capture_efficiencies_z5["z5"],
"z6":
specific_uptake_rate_z5 * zoo_availability_parameters["del_z5z6"] *
z6c * capture_efficiencies_z5["z6"]
}
dZ6cdt_prd = {
"b1":
specific_uptake_rate_z6 * zoo_availability_parameters["del_z6b1"] *
b1c * capture_efficiencies_z6["b1"],
"p1":
specific_uptake_rate_z6 * zoo_availability_parameters["del_z6p1"] *
p1c * capture_efficiencies_z6["p1"],
"p2":
specific_uptake_rate_z6 * zoo_availability_parameters["del_z6p2"] *
p2c * capture_efficiencies_z6["p2"],
"p3":
specific_uptake_rate_z6 * zoo_availability_parameters["del_z6p3"] *
p3c * capture_efficiencies_z6["p3"],
"p4":
specific_uptake_rate_z6 * zoo_availability_parameters["del_z6p4"] *
p4c * capture_efficiencies_z6["p4"],
"z5":
specific_uptake_rate_z6 * zoo_availability_parameters["del_z6z5"] *
z5c * capture_efficiencies_z6["z5"],
"z6":
specific_uptake_rate_z6 * zoo_availability_parameters["del_z6z6"] *
z6c * capture_efficiencies_z6["z6"]
}
# Total ingestion rate
ic5 = 0.0
in5 = 0.0
ip5 = 0.0
for key in dZ5cdt_prd:
ic5 += dZ5cdt_prd[key]
in5 += dZ5cdt_prd[key] * conc_ratio_n[key]
ip5 += dZ5cdt_prd[key] * conc_ratio_p[key]
ic6 = 0.0
in6 = 0.0
ip6 = 0.0
for key in dZ6cdt_prd:
ic6 += dZ6cdt_prd[key]
in6 += dZ6cdt_prd[key] * conc_ratio_n[key]
ip6 += dZ6cdt_prd[key] * conc_ratio_p[key]
return dZ5cdt_prd, dZ6cdt_prd, ic5, in5, ip5, ic6, in6, ip6
def phyto_eqns(conc, phyto_parameters, env_parameters, constant_parameters, group, pc, pn, pp, pl, qs, temp, time):
""" Calculates the terms needed for the phytoplnaktion biological rate equations
Equations come from the BFM user manual
"""
# Species concentrations
n1p = conc[1] # Phosphate (mmol P m^-3)
n3n = conc[2] # Nitrate (mmol N m^-3)
n4n = conc[3] # Ammonium (mmol N m^-3)
n5s = conc[5] # Silicate (mmol Si m^-3)
p1l = conc[13] # Diatoms chlorophyll (mg Chl-a m^-3)
p1s = conc[14] # Diatoms silicate (mmol Si m^-3)
p2l = conc[18] # NanoFlagellates chlorophyll (mg Chl-a m^-3)
p3l = conc[22] # Picophytoplankton chlorophyll (mg Chl-a m^-3)
p4l = conc[26] # Large phytoplankton chlorophyll (mg Chl-a m^-3)
r6c = conc[44] # Particulate organic carbon (mg C m^-3)
# Concentration ratios (constituents quota in phytoplankton)
pn_pc = get_concentration_ratio(pn, pc, constant_parameters["p_small"])
pp_pc = get_concentration_ratio(pp, pc, constant_parameters["p_small"])
pl_pc = get_concentration_ratio(pl, pc, constant_parameters["p_small"])
#--------------------------------------------------------------------------
# Temperature response of Phytoplankton Include cut-off at low temperature if p_temp>0
et = eTq_vector(temp, env_parameters["basetemp"], env_parameters["q10z"])
fTP = max(0.0, et - phyto_parameters["p_temp"])
#--------------------------------------------------------------------------
# Nutrient limitations (intracellular and extracellular) fpplim is the
# combined non-dimensional factor limiting photosynthesis
# from Phyto.F90 lines 268-308
in1p = min(1.0, max(constant_parameters["p_small"], (pp_pc - phyto_parameters["phi_Pmin"])/(phyto_parameters["phi_Popt"] - phyto_parameters["phi_Pmin"])))
in1n = min(1.0, max(constant_parameters["p_small"], (pn_pc - phyto_parameters["phi_Nmin"])/(phyto_parameters["phi_Nopt"] - phyto_parameters["phi_Nmin"])))
if group == 1:
fpplim = min(1.0, n5s/(n5s + phyto_parameters["h_Ps"] + (phyto_parameters["rho_Ps"]*p1s)))
else:
fpplim = 1.0
#--------------------------------------------------------------------------
# multiple nutrient limitation, Liebig rule (from Phyto.F90 line ~318, iN)
multiple_nut_lim = min(in1p, in1n)
#--------------------------------------------------------------------------
# Total extinction coef (m^-1)
suspended_sediments = 0.0
# from CalcVerticalExtinction.F90 line 82
xEPS = env_parameters["p_eps0"] + env_parameters["p_epsESS"]*suspended_sediments + env_parameters["p_epsR6"]*r6c
# from CalcVerticalExtinction.F90 line 101 (ChlAttenFlag=1, ChlDynamicsFlag=2)
xEPS = xEPS + p1l + p2l*2 + p3l*3 + p4l*4
#--------------------------------------------------------------------------
# Light limitation with Chl dynamics
# irradiance (uE m^-2 s^-1) from Phyto.F90 lines 353-355
irradiance = qs*env_parameters["epsilon_PAR"]/constant_parameters["e2w"]
r = xEPS * env_parameters["del_z"]
r = irradiance/xEPS/env_parameters["del_z"]*(1.0 - numpy.exp(-r))
irr = max(constant_parameters["p_small"], r)
# Compute exponent E_PAR/E_K = alpha0/PBmax (part of eqn. 2.2.4)
exponent = pl_pc*phyto_parameters["alpha_chl"]/phyto_parameters["rP0"]*irr
# light limitation factor (from Phyto.f90 line 374, eiPPY)
light_lim = (1.0 - numpy.exp(-exponent))
#--------------------------------------------------------------------------
# total photosynthesis (from Phyto.F90 line ~380, sum)
photosynthesis = phyto_parameters["rP0"]*fTP*light_lim*fpplim
#--------------------------------------------------------------------------
# Lysis nad excretion
# nutr. -stress lysis (from Phyto.F90 lines ~385-387, sdo)
nut_stress_lysis = (phyto_parameters["h_Pnp"]/(multiple_nut_lim + phyto_parameters["h_Pnp"]))*phyto_parameters["d_P0"]
nut_stress_lysis += phyto_parameters["p_seo"]*pc/(pc + phyto_parameters["p_sheo"] + constant_parameters["p_small"])
# activity excretion (Phyto.F90 line 389)
activity_excretion = photosynthesis*phyto_parameters["betaP"]
# nutrient stress excretion from Phyto.F90 line 396
nut_stress_excretion = photosynthesis*(1.0 - phyto_parameters["betaP"])*(1.0 - multiple_nut_lim)
#--------------------------------------------------------------------------
# Apportioning over R1 and R6: Cell lysis generates both DOM and POM
pe_R6 = min(phyto_parameters["phi_Pmin"]/(pp_pc + constant_parameters["p_small"]), phyto_parameters["phi_Nmin"]/(pn_pc + constant_parameters["p_small"]))
pe_R6 = min(1.0, pe_R6)
rr6c = pe_R6*nut_stress_lysis*pc
rr1c = (1.0 - pe_R6)*nut_stress_lysis*pc
#--------------------------------------------------------------------------
# Respiration rate
# activity (from Phyto.F90 line 416)
activity_rsp = phyto_parameters["gammaP"]*(photosynthesis - activity_excretion - nut_stress_excretion)
# basal (from Phyto.F90 line 417)
basal_rsp = fTP*phyto_parameters["bP"]
# total (from Phyto.F90 line 418)
total_rsp = activity_rsp + basal_rsp
# total actual respiration
dPcdt_rsp_o3c = total_rsp*pc
#--------------------------------------------------------------------------
# Production, productivity and C flows
# Phytoplankton gross primary production [mg C m^-3 s^-1]
dPcdt_gpp_o3c = photosynthesis*pc
# specific loss terms (from Phyto.F90 line 428)
specific_loss_terms = activity_excretion + nut_stress_excretion + total_rsp + nut_stress_lysis
# All activity excretions are assigned to R1
# p_switchDOC=1 and P_netgrowth=FLASE: [mg C m^-3 s^-1]
rr1c += activity_excretion*pc + nut_stress_excretion*pc
dPcdt_exu_r2c = 0.0
# Phytoplankton DOM cell lysis- carbon lost to DOM [mg C m^-3 s^-1]
dPcdt_lys_r1c = rr1c
# Phytoplankton POM cell lysis- carbon lost to POM (eqn. 2.2.9) [mg C m^-3 s^-1]
dPcdt_lys_r6c = rr6c
#--------------------------------------------------------------------------
# Potential-Net primary production
# from Phyto.F90 line 455
sadap = fTP*phyto_parameters["rP0"]
# Net production (from Phyto.F90 line 457, 'run')
net_production = max(0.0, (photosynthesis - specific_loss_terms)*pc)
#--------------------------------------------------------------------------
# Nutrient Uptake: calculate maximum uptake of N, P based on affinity
cqun3 = phyto_parameters["h_Pn"]/(constant_parameters["p_small"] + phyto_parameters["h_Pn"] + n4n)
# max potential uptake of N3 (from Phyto.F90 'rumn3')
max_upt_n3n = phyto_parameters["a_N"]*n3n*pc*cqun3
# max potential uptake of N4 (from Phyto.F90 'rumn4')
max_upt_n4n = phyto_parameters["a_N"]*n4n*pc
# max potential uptake of DIN (from Phyto.F90 'rumn')
max_upt_DIN = max_upt_n3n + max_upt_n4n
# max pot. uptake of PO4 (from Phyto.F90 line 468)
rump = phyto_parameters["a_P"]*n1p*pc
#--------------------------------------------------------------------------
# Nutrient dynamics: NITROGEN
# Intracellular missing amount of N (from Phyto.F90)
misn = sadap*(phyto_parameters["phi_Nmax"]*pc - pn)
# N uptake based on net assimilat. C (from Phyto.F90)
rupn = phyto_parameters["phi_Nmax"]*net_production
# actual uptake of NI (from Phyto.F90, 'runn')
dPndt_upt = min(max_upt_DIN, rupn + misn)
# if nitrogen uptake rate is positive, then uptake is divided between coming from the nitrate and ammonium reservoir
# if nitrogen uptake is negative, all nitrogen goes to the DOM pool
upt_switch_n = insw_vector(dPndt_upt)
# actual uptake of N3n (from Phyto.F90, 'runn3')
dPndt_upt_n3n = upt_switch_n*dPndt_upt*max_upt_n3n/(constant_parameters["p_small"] + max_upt_DIN)
# actual uptake of N4n (from Phyto.F90, 'runn4')
dPndt_upt_n4n = upt_switch_n*dPndt_upt*max_upt_n4n/(constant_parameters["p_small"] + max_upt_DIN)
extra_n = -dPndt_upt*(1.0 - upt_switch_n)
#--------------------------------------------------------------------------
# Nutrient dynamics: PHOSPHORUS
# intracellular missing amount of P (from Phyto.F90 line 514)
misp = sadap*(phyto_parameters["phi_Pmax"]*pc-pp)
# P uptake based on C uptake (from Phyto.F90 line 517)
rupp = phyto_parameters["phi_Pmax"]*net_production
# Actual uptake
runp = min(rump, rupp + misp)
upt_switch_p = insw_vector(runp)
dPpdt_upt_n1p = runp*upt_switch_p
# is uptake is negative flux goes to DIP (R1P) pool
dPpdt_upt_r1p = -runp*(1.0 - upt_switch_p)
#--------------------------------------------------------------------------
# Excretion of N and P to PON and POP
dPndt_lys_r6n = pe_R6*nut_stress_lysis*pn
dPndt_lys_r1n = nut_stress_lysis*pn - dPndt_lys_r6n
dPpdt_lys_r6p = pe_R6*nut_stress_lysis*pp
dPpdt_lys_r1p = nut_stress_lysis*pp - dPpdt_lys_r6p
#--------------------------------------------------------------------------
# Nutrient dynamics: SILICATE
if group == 1:
# Gross uptake of silicate excluding respiratory costs (from Phyto.F90, 'runs')
dPsdt_upt_n5s = max(0.0, phyto_parameters["phi_Sopt"]*pc*(photosynthesis - basal_rsp))
# losses of Si (from Phyto.F90)
dPsdt_lys_r6s = nut_stress_lysis*p1s
else:
dPsdt_upt_n5s = 0.0
dPsdt_lys_r6s = 0.0
#--------------------------------------------------------------------------
# Chl-a synthesis and photoacclimation
if phyto_parameters["chl_switch"] == 1:
# dynamical chl:c ratio from Fortran code Phyto.F90
rho_chl = phyto_parameters["theta_chl0"]*min(1.0, phyto_parameters["rP0"]*light_lim*pc/(phyto_parameters["alpha_chl"]*(pl + constant_parameters["p_small"])*irr))
# Chlorophyll synthesis from Fortran code Phyto.F90, rate_chl
dPldt_syn = rho_chl*(photosynthesis - nut_stress_excretion - activity_excretion - activity_rsp)*pc - nut_stress_lysis*pl
else:
sys.exit("Warning: This code does not support other chl systhesis parameterizations")
#--------------------------------------------------------------------------
return (dPcdt_gpp_o3c, dPcdt_rsp_o3c, dPcdt_lys_r1c, dPcdt_lys_r6c, dPcdt_exu_r2c,
dPndt_upt_n3n, dPndt_upt_n4n, extra_n, dPndt_lys_r1n, dPndt_lys_r6n,
dPpdt_upt_n1p, dPpdt_upt_r1p, dPpdt_lys_r1p, dPpdt_lys_r6p,
dPldt_syn, dPsdt_upt_n5s, dPsdt_lys_r6s)