def __call__(self, t, z):
zp = z[0]
zc = z[1]
lc = zc * L_F
lp = zp * L_F
r_TBT = r_TBT_advanced(self.T(t), self.pH(t), self.salinity(t))
r_Cu2O = r_Cu2O_advanced(self.T(t), self.pH(t), self.salinity(t), lc,
lp)
dzpdt = tf_average * (M_unit * r_TBT) / (L_F * M_TBT * rho_p * V_p)
dzcdt = tf_average * (M_Cu2O * r_Cu2O) / (2 * V_c * rho_c * L_F)
return np.array([dzpdt, dzcdt])
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()
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()