def epsilon_family(
limited_srm,
par_dict,
control_start_values,
times,
func_dict,
epsilons
):
z=Symbol('z')
eps=Symbol('eps')
u_z_exp=half_saturation(z,eps)
bm=BastinModel(limited_srm,u_z_exp,z)
fig=plt.figure()
ax1=fig.add_subplot(1,1,1)
ax1.set_title("control u for different values of epsilon")
for eps_val in epsilons:
par_dict[eps]=eps_val
bmr=BastinModelRun(
bm,
par_dict,
control_start_values,
times,
func_dict
)
phi_num=bmr.phi_num((z,))
soln=bmr.solve()
z_sol=soln[:,3]
pe('bm.u_expr',locals())
u=phi_num(z_sol)
ax1.plot(times,u)
ax1.legend(loc=3)
fig.savefig(my_func_name()+'.pdf')
def panel_two(bm, par_dict_v1, control_start_values, times, func_dict):
start_values=control_start_values[:-1]
bmr=BastinModelRun( bm, par_dict_v1, control_start_values, times, func_dict)
soln_controlled = bmr.solve()
tup=(bm.time_symbol,bm.z_sym)
phi_num=bmr.phi_num(tup)
z_vals=soln_controlled[:,3]
u_vals=phi_num(times,z_vals)
efl=bmr.external_input_flux_funcs()
f=efl[0]
values=f(times)
fig=plt.figure(figsize=(10,10))
#fig1.title('Total carbon'+title_suffs[version])
ax1=fig.add_subplot(2,1,1)
ax1.tick_params(axis='both', which='major', labelsize=12)
ax1.plot(times, u_vals,color='green',label='u')
ax1.set_ylabel('$u(t)$ (unitless)', fontsize=15)
#ax1.legend(loc=2)
ax1.set_title("(a)")
ax1.set_xlim(1900, 2500)
ax2=fig.add_subplot(2,1,2)
ax2.tick_params(axis='both', which='major', labelsize=12)
ax2.plot(times, values,color='blue' ,label='u d')
ax2.set_ylabel('Allowed carbon emissions (Pg C/yr)', fontsize=15)
ax2.set_xlabel('Time (yr)', fontsize=15)
ax2.set_ylim(ax1.get_ylim())
ax2.set_xlim(1900, 2500)
ax2.set_title("(b)")
fig.savefig(my_func_name()+'.pdf', bbox_inches='tight')
def panel_one(limited_srm,bm, par_dict_v1, control_start_values, times, func_dict):
start_values=control_start_values[:-1]
limited_smr = SmoothModelRun(limited_srm, par_dict_v1, start_values, times, func_dict)
bmr=BastinModelRun( bm, par_dict_v1, control_start_values, times, func_dict)
soln_uncontrolled = limited_smr.solve()
soln_controlled = bmr.solve()
fig=plt.figure(figsize=(10,10))
#fig1.title('Total carbon'+title_suffs[version])
ax1=fig.add_subplot(2,1,1)
ax1.tick_params(axis='both', which='major', labelsize=12)
ax1.plot(times, soln_uncontrolled[:,0],color='blue' ,label='Atmosphere')
ax1.plot(times, soln_uncontrolled[:,1],color='green',label='Terrestrial Biosphere')
ax1.plot(times, soln_uncontrolled[:,2],color='red' ,label='Surface ocean')
ax1.set_ylabel('Carbon stocks (Pg C)', fontsize=15)
ax1.legend(loc=2)
ax1.set_title("(a)")
ax1.set_xlim(1900, 2500)
ax2=fig.add_subplot(2,1,2)
ax2.tick_params(axis='both', which='major', labelsize=12)
ax2.plot(times, soln_controlled[:,0],color='blue' ,label='Atmosphere')
ax2.plot(times, soln_controlled[:,1],color='green',label='Terrestrial Biosphere')
ax2.plot(times, soln_controlled[:,2],color='red' ,label='Surface ocean')
ax2.set_ylabel('Carbon stocks (Pg C)', fontsize=15)
ax2.set_xlabel('Time (yr)', fontsize=15)
ax2.set_ylim(ax1.get_ylim())
ax2.set_xlim(1900, 2500)
ax2.set_title("(b)")
#limited_soln_uncontrolled
fig.savefig(my_func_name()+'.pdf', bbox_inches='tight')
def epsilon_family_2(limited_srm, par_dict, start_values, times, func_dict, zs,
epsilons):
z = Symbol('z')
eps = Symbol('eps')
z0 = Symbol('z0')
u_z_exp = half_saturation(z, eps)
bm = BastinModel(limited_srm, u_z_exp, z)
fig = plt.figure()
ax1 = fig.add_subplot(1, 1, 1)
ax1.set_title("control u for different values of epsilon")
for z0_val in zs:
for eps_val in epsilons:
control_start_values = np.array(list(start_values) + [z0_val])
par_dict[eps] = eps_val
par_dict[z0] = z0_val,
bmr = BastinModelRun(bm, par_dict, control_start_values, times,
func_dict)
phi_num = bmr.phi_num((z, ))
soln = bmr.solve()
z_sol = soln[:, 3]
pe('bm.u_expr', locals())
u = phi_num(z_sol)
ax1.plot(times,
u,
label="eps:" + str(eps_val) + ",z0=" + str(z0_val))
ax1.legend(loc=3)
fig.savefig(my_func_name() + '.pdf')
def deceleration_family(limited_srm, par_dict, start_values, times, func_dict,
zs, alphas):
z = Symbol('z')
z_max = Symbol('z_max')
alph = Symbol('alph')
u_z_exp = deceleration(z, z_max, alph)
bm = BastinModel(limited_srm, u_z_exp, z)
fig = plt.figure()
ax1 = fig.add_subplot(1, 1, 1)
ax1.set_title(
"control u with deceleration limiter for different values of alph")
for z_max_val in zs:
for alpha_val in alphas:
control_start_values = np.array(list(start_values) + [z_max_val])
par_dict[z_max] = z_max_val
par_dict[alph] = alpha_val
bmr = BastinModelRun(bm, par_dict, control_start_values, times,
func_dict)
phi_num = bmr.phi_num((z, ))
soln = bmr.solve()
z_sol = soln[:, 3]
pe('bm.u_expr', locals())
u = phi_num(z_sol)
ax1.plot(times,
u,
label="alph:" + str(alpha_val) + ",z_max=" +
str(z_max_val))
ax1.legend(loc=3)
fig.savefig(my_func_name() + '.pdf')
def cubic_family(
limited_srm,
par_dict,
start_values,
times,
func_dict,
zs
):
z=Symbol('z')
z_max=Symbol('z_max')
u_z_exp=cubic(z,z_max)
bm=BastinModel(limited_srm,u_z_exp,z)
fig=plt.figure()
ax1=fig.add_subplot(1,1,1)
#ax1.set_title("control u for different values of z_max")
for z_max_val in zs:
control_start_values=np.array(list(start_values)+[z_max_val])
par_dict[z_max]=z_max_val
bmr=BastinModelRun(
bm,
par_dict,
control_start_values,
times,
func_dict
)
phi_num=bmr.phi_num((z,))
soln=bmr.solve()
z_sol=soln[:,3]
pe('bm.u_expr',locals())
u=phi_num(z_sol)
ax1.plot(times,u,label="$z_{max}$="+str(z_max_val))
ax1.set_ylabel('$u(t)$ (unitless)')
ax1.set_xlabel('Time (years)')
ax1.legend(loc=3)
fig.savefig(my_func_name()+'.pdf')