def varying_salinity():
salinities = [35, 40, 45]
pH_fixed = 8.2
temp_fixed = 15+273
fig, (Xp_ax, Xc_ax) = plt.subplots(1,2)
for sal in salinities:
print("sal = ", sal)
tol = 10e-15
n = 100
Nmax = 10**(n+10)
sensitivity_model = SENSITIVTY_ANALYSIS_MODEL(temp_fixed, sal, pH_fixed)
t0_s, T_end_s = 0, 0.999
z0_s = np.array([0, 10**(-n)])
t_s, y_s = ODE_solver(z0_s, t0_s, T_end_s, sensitivity_model, Nmax, tol)
r_TBT_c = r_TBT_advanced(temp_fixed, pH_fixed, sal)
tf_c = t_f(r_TBT_c)
X_p = np.zeros(len(t_s))
X_c = np.zeros(len(t_s))
for i in range(len(t_s)):
X_p[i] = y_s[i][0]
X_c[i] = y_s[i][1]
Xp_ax.plot(t_s*tf_c, X_p, label=salinity_label(sal))
Xc_ax.plot(t_s*tf_c, X_c, label=salinity_label(sal))
Xp_ax.set(xlabel=x_label_day, ylabel=conversion_label)
Xc_ax.set(xlabel=x_label_day, ylabel=conversion_label)
Xp_ax.set_title(Xp_label)
Xc_ax.set_title(Xc_label)
Xp_ax.legend(loc="lower right")
Xc_ax.legend(loc="lower right")
Xp_ax.grid(True)
Xc_ax.grid(True)
fig.suptitle("With constant T = " + str(temp_fixed-273) + "$^o$C and pH = " + str(pH_fixed))
plt.show()
def varying_temperature():
temperature = [10+273, 15+273, 20+273, 25+273]
pH_fixed = 8.2
sal_fixed = 35.1
fig, (Xp_ax, Xc_ax) = plt.subplots(1,2)
for temp in temperature:
tol = 10e-15
n = 100
Nmax = 10**(n+30)
sensitivity_model = SENSITIVTY_ANALYSIS_MODEL(temp, sal_fixed, pH_fixed)
t0_s, T_end_s = 0, 0.999
z0_s = np.array([0, 10**(-n)])
t_s, y_s = ODE_solver(z0_s, t0_s, T_end_s, sensitivity_model, Nmax, tol)
r_TBT_c = r_TBT_advanced(temp, pH_fixed, sal_fixed)
tf_c = t_f(r_TBT_c)
X_p = np.zeros(len(t_s))
X_c = np.zeros(len(t_s))
for i in range(len(t_s)):
X_p[i] = y_s[i][0]
X_c[i] = y_s[i][1]
Xp_ax.plot(t_s*tf_c, X_p, label=temp_label(temp))
Xc_ax.plot(t_s*tf_c, X_c, label=temp_label(temp))
Xp_ax.set(xlabel=x_label_day, ylabel=conversion_label)
Xc_ax.set(xlabel=x_label_day, ylabel=conversion_label)
Xp_ax.set_title(Xp_label)
Xc_ax.set_title(Xc_label)
Xp_ax.legend(loc="lower right")
Xc_ax.legend(loc="lower right")
Xp_ax.grid(True)
Xc_ax.grid(True)
fig.suptitle("With constant salinity = " + str(sal_fixed) + " g salt/kg seawater and pH = " + str(pH_fixed))
plt.show()
def varying_pH():
pHs = [7.5, 8, 8.5]
temp_fixed = 15+273
sal_fixed = 35.1
fig, (Xp_ax, Xc_ax) = plt.subplots(1,2)
for pH_v in pHs:
tol = 10e-15
n = 100
Nmax = 10**(n+50)
sensitivity_model = SENSITIVTY_ANALYSIS_MODEL(temp_fixed, sal_fixed, pH_v)
t0_s, T_end_s = 0, 0.999
z0_s = np.array([0, 10**(-n)])
t_s, y_s = ODE_solver(z0_s, t0_s, T_end_s, sensitivity_model, Nmax, tol)
r_TBT_c = r_TBT_advanced(temp_fixed, pH_v, sal_fixed)
tf_c = t_f(r_TBT_c)
X_p = np.zeros(len(t_s))
X_c = np.zeros(len(t_s))
for i in range(len(t_s)):
X_p[i] = y_s[i][0]
X_c[i] = y_s[i][1]
Xp_ax.plot(t_s*tf_c, X_p, label=pH_label(pH_v))
Xc_ax.plot(t_s*tf_c, X_c, label=pH_label(pH_v))
Xp_ax.set(xlabel=x_label_day, ylabel=conversion_label)
Xc_ax.set(xlabel=x_label_day, ylabel=conversion_label)
Xp_ax.set_title(Xp_label)
Xc_ax.set_title(Xc_label)
Xp_ax.legend(loc="lower right")
Xc_ax.legend(loc="lower right")
Xp_ax.grid(True)
Xc_ax.grid(True)
fig.suptitle("With constant T = " + str(temp_fixed-273) + "$^o$C and salinity = " + str(sal_fixed) + " g salt/kg seawater")
plt.show()
# Run method tol = 10e-20 n = 100 Nmax = 10**(n + 10) ### FIRST 400 days, Bueno Aires coastline ### model_400 = ADVANCED_MODEL(p_400_temp, p_400_sal, p_400_pH) t0_400, T_end_400 = 0, 400 l0_400 = np.array([0, 10**(-n)]) t_400, y_400 = ODE_solver(l0_400, t0_400, T_end_400, model_400, Nmax, tol) ### 20 DAYS VOYAGE ### model_20 = ADVANCED_MODEL(p_20_temp, p_20_sal, p_20_pH) t0_20, T_end_20 = 0, 19.9 l0_20 = np.array([y_400[-1][0], y_400[-1][1]]) t_20, y_20 = ODE_solver(l0_20, t0_20, T_end_20, model_20, Nmax, tol) ### 400 + 20 days modeling t_1 = t_400[:] y_1 = y_400[:] t_2 = t_20[:] + 400
return np.array([dzpdt, dzcdt])
# Run method
tol = 10e-10
n = 100
Nmax = 10**(n + 15)
idealized_route_model = IDEALIZED_ROUTE(p_i_temp, p_i_sal, p_i_pH)
t0_s, T_end_s = 0, 0.999
z0_s = np.array([0, 10**(-n)])
t_s, y_s = ODE_solver(z0_s, t0_s, T_end_s, idealized_route_model, Nmax, tol)
def plot_conversion_idealized():
plt.plot(t_s, y_s)
plt.plot([0.375, 0.375], [0, 0.7], '--', color="black")
plt.plot([0.500, 0.500], [0, 0.7], '--', color="black")
plt.plot([0.625, 0.625], [0, 0.7], '--', color="black")
plt.plot([0.750, 0.750], [0, 0.7], '--', color="black")
plt.plot([0.875, 0.875], [0, 0.7], '--', color="black")
plt.legend(conversion_legend)
plt.grid(True)
plt.ylim(0, 0.75)
plt.xlabel(tau_label)
plt.ylabel(conversion_label)
def __call__(self, t, z):
dzp_dt = 1
dzc_dt = (M_TBT * M_Cu2O) / M_unit * (rho_p * V_p * D_CuCl) / (
r_TBT * 2 * V_c * rho_c) * C_CuCl_s / (z[1] * L_F - z[0] * L_F)
return np.array([dzp_dt, dzc_dt])
model = MODEL()
# Run method
tol = 1.0e-15 # Tolerance in adaptive method
n = 100
Nmax = 10**(n + 25)
### FIRST, solve from tau = 0 to an upper limit
t0_0, T_0 = 0, 0.925
z0_0 = np.array([0, 10**(-n)])
ts_0, ys_0 = ODE_solver(z0_0, t0_0, T_0, model, Nmax, tol)
## SECOND, solve from tau = limit to tau = 1
t0_1, T_1 = ts_0[-1], 1
z0_1 = ys_0[-1]
ts_1, ys_1 = ODE_solver(z0_1, t0_1, T_1, model, Nmax, tol)
## MERGE the two solutions
tau_simple = np.concatenate((ts_0, ts_1))
X_simple = np.concatenate((ys_0, ys_1))
def release_sensitivity():
temp_fixed = 15+273
sal_fixed = 35.1
pH_fixed = 8.2
fig, (T_ax, sal_ax, pH_ax) = plt.subplots(1,3)
temp_vary = [10+273, 15+273, 20+273, 25+273]
sal_vary = [35, 40, 45]
pH_vary = [7.5, 8, 8.5]
tol = 10e-15
n = 100
Nmax = 10**(n+30)
t0_s, T_end_s = 0, 0.999
z0_s = np.array([0, 10**(-n)])
for temp in temp_vary:
sensitivity_model = SENSITIVTY_ANALYSIS_MODEL(temp, sal_fixed, pH_fixed)
t_s, y_s = ODE_solver(z0_s, t0_s, T_end_s, sensitivity_model, Nmax, tol)
r_TBT_c = r_TBT_advanced(temp, pH_fixed, sal_fixed)
tf_c = t_f(r_TBT_c)
r_Cu = np.zeros(len(t_s))
for i in range(len(t_s)):
r_Cu[i] = r_Cu2O_advanced(temp, pH_fixed, sal_fixed, y_s[i][1]*L_F, y_s[i][0]*L_F) * M_Cu * 10**(-4)
T_ax.plot(t_s[:]*tf_c, r_Cu[:], label=temp_label(temp))
for sal in sal_vary:
sensitivity_model = SENSITIVTY_ANALYSIS_MODEL(temp_fixed, sal, pH_fixed)
t_s, y_s = ODE_solver(z0_s, t0_s, T_end_s, sensitivity_model, Nmax, tol)
r_TBT_c = r_TBT_advanced(temp_fixed, pH_fixed, sal)
tf_c = t_f(r_TBT_c)
r_Cu = np.zeros(len(t_s))
for i in range(len(t_s)):
r_Cu[i] = r_Cu2O_advanced(temp_fixed, pH_fixed, sal, y_s[i][1]*L_F, y_s[i][0]*L_F) * M_Cu * 10**(-4)
sal_ax.plot(t_s[:]*tf_c, r_Cu[:], label=salinity_label(sal))
for pH in pH_vary:
sensitivity_model = SENSITIVTY_ANALYSIS_MODEL(temp_fixed, sal_fixed, pH)
t_s, y_s = ODE_solver(z0_s, t0_s, T_end_s, sensitivity_model, Nmax, tol)
r_TBT_c = r_TBT_advanced(temp_fixed, pH, sal_fixed)
tf_c = t_f(r_TBT_c)
r_Cu = np.zeros(len(t_s))
for i in range(len(t_s)):
r_Cu[i] = r_Cu2O_advanced(temp_fixed, pH, sal_fixed, y_s[i][1]*L_F, y_s[i][0]*L_F) * M_Cu * 10**(-4)
pH_ax.plot(t_s[:]*tf_c, r_Cu[:], label=pH_label(pH))
y_lim_upper=20
T_ax.set(ylim = (0,y_lim_upper))
T_ax.legend()
T_ax.grid(True)
T_ax.set(xlabel=x_label_day, ylabel=release_Cu_label)
T_ax.set_title("Salinity = " + str(sal_fixed) + " g salt/kg saltwater and pH = " + str(pH_fixed))
sal_ax.set(ylim=(0, y_lim_upper))
sal_ax.legend()
sal_ax.grid(True)
sal_ax.set(xlabel=x_label_day)
sal_ax.set_title("T = " + str(temp_fixed-273) + " $^o$C and pH = " + str(pH_fixed))
pH_ax.set(ylim=(0, y_lim_upper))
pH_ax.legend()
pH_ax.grid(True)
pH_ax.set(xlabel=x_label_day)
pH_ax.set_title("T = " + str(temp_fixed-273) + " $^o$C and salinity = " + str(sal_fixed) + " g salt/kg saltwater")
plt.show()