def fn(m):
""" Our objective function, takes an ndarray m that contains depths removed
during each glaciation as a fraction of con['dz_max'].
"""
if SAVE_CONCENTRATION_DATA:
global concs
global indep_errs
raw_dz = m * (con['max_dz'] - con['min_dz']) + con['min_dz']
dz = np.ones(con['n_gl']) * raw_dz[-1]
dz[0:con['n_exact_depths']] = raw_dz[0:-1]
conc = sim.multiglaciate(dz,
con['t_gl'],
con['t_int'],
con['t_postgl'],
con['sample_depths'],
con['nuclide'],
p,
n_gl=con['n_gl'],
postgl_shielding=con['postgl_shielding'])
error = chi2(conc, con['C_meas'], con['C_meas_err'])
print "Chi**2:", error
if SAVE_CONCENTRATION_DATA:
concs.append(conc)
indep_errs.append(error)
return error
def fn(m):
""" Our objective function, takes an ndarray m that contains depths removed
during each glaciation as a fraction of con['dz_max'].
"""
if SAVE_CONCENTRATION_DATA:
global concs
dz = m * (con['max_dz'] - con['min_dz']) + con['min_dz']
conc = sim.multiglaciate(dz, con['t_gl'], con['t_int'], con['t_postgl'],
con['sample_depths'], con['nuclide'], p, n_gl=con['n_gl'])
if SAVE_CONCENTRATION_DATA:
concs.append(conc)
error = chi2(conc, conc_meas, sigma)
print "Chi**2:", error
return error
def fn(m):
""" Our objective function, takes an ndarray m that contains depths removed
during each glaciation as a fraction of con['dz_max'].
"""
if SAVE_CONCENTRATION_DATA:
global concs
dz = m * (con['max_dz'] - con['min_dz']) + con['min_dz']
conc = sim.multiglaciate(dz, con['t_gl'], con['t_int'], con['t_postgl'],
con['sample_depths'], con['nuclide'], p, n_gl=con['n_gl'],
postgl_shielding=con['postgl_shielding'])
if SAVE_CONCENTRATION_DATA:
concs.append(conc)
error = chi2(conc, con['C_meas'], con['sigma'])
print "Chi**2:", error
return error
def fn(m):
""" Our objective function, takes an ndarray m that contains depths removed
during each glaciation as a fraction of con['dz_max'].
"""
if SAVE_CONCENTRATION_DATA:
global concs
global indep_errs
raw_dz = m * (con['max_dz'] - con['min_dz']) + con['min_dz']
dz = np.ones(con['n_gl']) * raw_dz[-1]
dz[0:con['n_exact_depths']] = raw_dz[0:-1]
conc = sim.multiglaciate(dz, con['t_gl'], con['t_int'], con['t_postgl'],
con['sample_depths'], con['nuclide'], p, n_gl=con['n_gl'],
postgl_shielding=con['postgl_shielding'])
error = chi2(conc, con['C_meas'], con['C_meas_err'])
print "Chi**2:", error
if SAVE_CONCENTRATION_DATA:
concs.append(conc)
indep_errs.append(error)
return error
plt.xlabel("$^{10}$Be Concentration (atoms / g)")
plt.ylabel("Depth (m)")
plt.title("Synthetic and Perturbed $^{10}$Be Concentration Profiles")
plt.show()
figname = "perturbed_conc"
plt.savefig(figname + ".svg")
plt.savefig(figname + ".png")
# concentration profile with best fit
best_conc_fig = plt.figure(5)
best_conc_ax = best_conc_fig.add_subplot(111)
plt.semilogx(conc_true, z_m, "*-", label="Target")
plt.errorbar(conc_meas, z_m, xerr=conc_meas_err, fmt=".", ecolor="k", label="Target + Error")
min_misfit = min(misfits)
best_m = ms[misfits == min_misfit].T * 100.0 * con["rho"]
best_conc = sim.multiglaciate(
best_m, con["t_gl"], con["t_int"], con["t_postgl"], con["sample_depths"], con["nuclide"], p, n_gl=con["n_gl"]
)
plt.semilogx(best_conc, z_m, "-", label="Best fit (chi2=%0.2f)" % min_misfit)
best_conc_ax.invert_yaxis()
plt.legend(loc="lower right")
plt.xlabel("$^{10}$Be Concentration (atoms / g)")
plt.ylabel("Depth (m)")
plt.title("$^{10}$Be Depth Profiles")
plt.show()
figname = "best_conc"
plt.savefig(figname + ".svg")
plt.savefig(figname + ".png")
# concentration profile with best fit
best_conc_fig = plt.figure(5)
best_conc_ax = best_conc_fig.add_subplot(111)
plt.semilogx(conc_true, z_m, '*-', label='Target')
plt.errorbar(conc_meas,
z_m,
xerr=conc_meas_err,
fmt='.',
ecolor='k',
label='Target + Error')
min_misfit = min(misfits)
best_m = ms[misfits == min_misfit].T * 100.0 * con['rho']
best_conc = sim.multiglaciate(best_m,
con['t_gl'],
con['t_int'],
con['t_postgl'],
con['sample_depths'],
con['nuclide'],
p,
n_gl=con['n_gl'])
plt.semilogx(best_conc, z_m, '-', label='Best fit (chi2=%0.2f)' % min_misfit)
best_conc_ax.invert_yaxis()
plt.legend(loc='lower right')
plt.xlabel('$^{10}$Be Concentration (atoms / g)')
plt.ylabel('Depth (m)')
plt.title('$^{10}$Be Depth Profiles')
plt.show()
figname = 'best_conc'
plt.savefig(figname + '.svg')
plt.savefig(figname + '.png')
C_steady = sim.steady_erosion(z, p_sp, mu['P_fast'], mu['P_neg'], eros_rate,
nuc, t, t_exp)
t_gl = 15000
t_int = 85000
t_cycle = t_gl + t_int
n_gl = int(np.floor(t_exp / t_cycle))
dz_scalar = eros_rate * t_cycle
dz = np.ones(n_gl) * dz_scalar
# interpolate a really awesome production rate function
max_possible_depth = n_gl * dz_scalar + z_max
npts = 500 # points to interpolate through
p = production.interpolate_P_tot(max_possible_depth, npts, alt, lat, nuc)
C_gl = sim.multiglaciate(dz, t_gl, t_int, 0, z, nuc, p, n_gl=n_gl)
t_mid_postgl = 15000 # yr
C_post15k = sim.simple_expose(z, t_mid_postgl, nuc, p)
fig_height = 6 # in.
fig_width = 5 # in.
fig = Figure(figsize=(fig_width, fig_height))
fig_dpi = 500
canvas = FigureCanvas(fig)
ax = fig.add_subplot(111)
# ax.set_title('Steady v.s. glacial erosion', fontsize=14)
ax.semilogx(C_steady, z_m, 'k--', label='Steady erosion')
leg = ax.legend(loc='lower right', prop=leg_prop)
ax.invert_yaxis()
leg_prop = matplotlib.font_manager.FontProperties(size=10)
ax.set_xlabel('[$^{10}$Be] (atoms/g)', fontsize=12)
plt.title('$^{10}$Be Depth Profile')
plt.show()
figname = 'measured_conc'
plt.savefig(figname + '.svg')
plt.savefig(figname + '.png')
# concentration profile with best fit
min_misfit = np.min(misfits)
best_m = ms_denorm[misfits == min_misfit][0]
many_depths = np.linspace(0, con['sample_depths'][-1], 200)
best_conc_manypts = sim.multiglaciate(best_m,
con['t_gl'],
con['t_int'],
con['t_postgl'],
many_depths,
con['nuclide'],
p,
n_gl=con['n_gl'],
postgl_shielding=con['postgl_shielding'])
many_depths_m = many_depths / 100 / con['rho']
plt.semilogx(best_conc_manypts,
many_depths_m,
'-b',
label='Best Fit (ChiSquared = %0.2f)' % min_misfit)
plt.legend(loc='lower right')
plt.show()
figname = 'best_conc'
plt.savefig(figname + '.svg')
plt.savefig(figname + '.png')
canvas.print_figure('const_hist.png', dpi=500)
fig_height = 5 # in.
fig_width = 3.5 # in.
# interpolate a production function
max_possible_depth = con['n_gl'] * con['max_dz'] + con['bottom_depth']
p = production.interpolate_P_tot(max_possible_depth,
npts=con['n_prod_interp_pts'], alt=con['alt'],
lat=con['lat'], n=con['nuclide'])
# make target concentration graph
z_target = np.linspace(0, con['bottom_depth'])
C_target = sim.multiglaciate(con['dz'], con['t_gl'], con['t_int'],
con['t_postgl'], z_target, con['nuclide'], p,
con['n_gl'],
postgl_shielding=con['postgl_shielding'])
conc_fig = Figure(figsize=(fig_width, fig_height))
conc_canvas = FigureCanvas(conc_fig)
ax = conc_fig.add_subplot(111)
ax.set_title('Target Concentration Profile', fontsize=12)
ax.semilogx(C_target, z_target / con['rho'] / 100)
ax.invert_yaxis()
ax.set_xlabel('[$^{10}$Be] (atoms/g)', fontsize=10)
ax.set_ylabel('Depth (m)', fontsize=10)
conc_fig.subplots_adjust(left=0.15, top=0.95)
conc_canvas.print_figure('target_conc.png', dpi=500)
C_true = sim.multiglaciate(con['dz'], con['t_gl'], con['t_int'],
con['t_postgl'], con['sample_depths'],
max_possible_depth = con['n_gl'] * con['max_dz'] + con['bottom_depth']
# if production file exists already
p = production.interpolate_P_tot(max_possible_depth,
npts=con['interp_pts'],
alt=con['alt'],
lat=con['lat'],
n=con['nuclide'])
# calculate the true concentration profile (w/ many points, not sample depths)
z_true_manypts = np.linspace(0, con['bottom_depth'], 200)
C_true_manypts = sim.multiglaciate(con['dz'],
con['t_gl'],
con['t_int'],
con['t_postgl'],
z_true_manypts,
con['nuclide'],
p,
con['n_gl'],
postgl_shielding=con['postgl_shielding'])
## make the true concentration graph
#true_conc_fig = plt.figure()
#ax = true_conc_fig.add_subplot(111)
#ax.title('True Concentration Profile')
#plt.semilogx(C_true_manypts, z_true_manypts / con['rho'] / 100, lw=2)
#ax.invert_yaxis()
#plt.xlabel(r'[$^{10}$Be] (atoms/g)')
#plt.ylabel('Depth (m)')
##ax.tick_params(labelsize=6)
##plt.setp(true_conc_ax.get_xticklabels(), rotation='horizontal')
max_possible_depth = con['n_gl'] * con['max_dz'] + con['bottom_depth']
npts = 500 # points to interpolate through
zs = np.unique(np.logspace(0, np.log2(max_possible_depth + 1), npts, base=2)) - 1
prod_rates = production.P_tot(zs, con['alt'], con['lat'], con['nuclide'])
#p = interp1d(zs, prod_rates, kind=3)
# interp1d used as above gives crazy negative dives around z = 82000, do not
# want that! UnivariateSpline seems to work much much better
p = UnivariateSpline(zs, prod_rates, k=3, s=0)
util.pickle(p, 'production_rate.dat')
# get data for plotting a depth vs time curve, meters and years
t_true, z_true = sim.glacial_depth_v_time(con['t_gl'], con['t_int'], con['t_postgl'],
con['dz_true_m'], n_gl=con['n_gl'])
conc_true = sim.multiglaciate(dz_true, con['t_gl'], con['t_int'],
con['t_postgl'], con['sample_depths'],
con['nuclide'], p, con['n_gl'])
sigma_true = con['nuclide'].measurement_error(conc_true)
conc_meas = np.random.normal(loc=conc_true, scale=sigma_true)
# we need a way to measure error between models
def chi2(a, b, sigma):
""" Chi squared of two vectors """
return (((a - b) / sigma)**2).sum()
# degrees of freedom in our problem
dof = dz_true.size
print 'Degrees of freedom =', dof
sigma = con['nuclide'].measurement_error(conc_meas)
perm_err = chi2(conc_meas, conc_true, sigma)
canvas.print_figure('const_hist.png', dpi=500)
fig_height = 5 # in.
fig_width = 3.5 # in.
# interpolate a production function
max_possible_depth = con['n_gl'] * con['max_dz'] + con['bottom_depth']
p = production.interpolate_P_tot(max_possible_depth,
npts=con['n_prod_interp_pts'], alt=con['alt'],
lat=con['lat'], n=con['nuclide'])
# make target concentration graph
z_target = np.linspace(0, con['bottom_depth'])
C_target = sim.multiglaciate(con['dz'], con['t_gl'], con['t_int'],
con['t_postgl'], z_target, con['nuclide'], p,
con['n_gl'],
postgl_shielding=con['postgl_shielding'])
conc_fig = Figure(figsize=(fig_width, fig_height))
conc_canvas = FigureCanvas(conc_fig)
ax = conc_fig.add_subplot(111)
ax.set_title('Target Concentration Profile', fontsize=12)
ax.semilogx(C_target, z_target / con['rho'] / 100)
ax.invert_yaxis()
ax.set_xlabel('[$^{10}$Be] (atoms/g)', fontsize=10)
ax.set_ylabel('Depth (m)', fontsize=10)
conc_fig.subplots_adjust(left=0.15, top=0.95)
conc_canvas.print_figure('target_conc.png', dpi=500)
C_true = sim.multiglaciate(con['dz'], con['t_gl'], con['t_int'],
con['t_postgl'], con['sample_depths'],
#plt.xlim(left=2)
#plt.ylim(bottom=75)
#plt.savefig('true_hist.png')
# interpolate a production function
max_possible_depth = con['n_gl'] * con['max_dz'] + con['bottom_depth']
# if production file exists already
p = production.interpolate_P_tot(max_possible_depth,
npts=con['interp_pts'], alt=con['alt'],
lat=con['lat'], n=con['nuclide'])
# calculate the true concentration profile (w/ many points, not sample depths)
z_true_manypts = np.linspace(0, con['bottom_depth'], 200)
C_true_manypts = sim.multiglaciate(con['dz'], con['t_gl'], con['t_int'],
con['t_postgl'], z_true_manypts, con['nuclide'], p,
con['n_gl'],
postgl_shielding=con['postgl_shielding'])
## make the true concentration graph
#true_conc_fig = plt.figure()
#ax = true_conc_fig.add_subplot(111)
#ax.title('True Concentration Profile')
#plt.semilogx(C_true_manypts, z_true_manypts / con['rho'] / 100, lw=2)
#ax.invert_yaxis()
#plt.xlabel(r'[$^{10}$Be] (atoms/g)')
#plt.ylabel('Depth (m)')
##ax.tick_params(labelsize=6)
##plt.setp(true_conc_ax.get_xticklabels(), rotation='horizontal')
##true_conc_fig.subplots_adjust(left=0.15, bottom=0.12, top=0.95)
#plt.savefig('true_conc.png')
mu = muon.P_mu_total(z, alt, nuc, full_data=True)
C_steady = sim.steady_erosion(z, p_sp, mu["P_fast"], mu["P_neg"], eros_rate, nuc, t, t_exp)
t_gl = 15000
t_int = 85000
t_cycle = t_gl + t_int
n_gl = int(np.floor(t_exp / t_cycle))
dz_scalar = eros_rate * t_cycle
dz = np.ones(n_gl) * dz_scalar
# interpolate a really awesome production rate function
max_possible_depth = n_gl * dz_scalar + z_max
npts = 500 # points to interpolate through
p = production.interpolate_P_tot(max_possible_depth, npts, alt, lat, nuc)
C_gl = sim.multiglaciate(dz, t_gl, t_int, 0, z, nuc, p, n_gl=n_gl)
t_mid_postgl = 15000 # yr
C_post15k = sim.simple_expose(z, t_mid_postgl, nuc, p)
fig_height = 6 # in.
fig_width = 5 # in.
fig = Figure(figsize=(fig_width, fig_height))
fig_dpi = 500
canvas = FigureCanvas(fig)
ax = fig.add_subplot(111)
# ax.set_title('Steady v.s. glacial erosion', fontsize=14)
ax.semilogx(C_steady, z_m, "k--", label="Steady erosion")
leg = ax.legend(loc="lower right", prop=leg_prop)
ax.invert_yaxis()
leg_prop = matplotlib.font_manager.FontProperties(size=10)
ax.set_xlabel("[$^{10}$Be] (atoms/g)", fontsize=12)
markersize=8,
ecolor='k',
label='Measured')
conc_ax.invert_yaxis()
plt.legend(loc='lower right')
plt.xlabel('$^{10}$Be Concentration (atoms / g)')
plt.ylabel('Depth (m)')
plt.title('$^{10}$Be Depth Profile')
plt.show()
figname = 'measured_conc'
plt.savefig(figname + '.svg')
plt.savefig(figname + '.png')
# concentration profile with best fit
min_misfit = np.min(misfits)
best_m = ms_denorm[misfits == min_misfit][0]
many_depths = np.linspace(0, con['sample_depths'][-1], 200)
best_conc_manypts = sim.multiglaciate(best_m, con['t_gl'], con['t_int'],
con['t_postgl'], many_depths, con['nuclide'], p,
n_gl=con['n_gl'], postgl_shielding=con['postgl_shielding'])
many_depths_m = many_depths / 100 / con['rho']
plt.semilogx(best_conc_manypts, many_depths_m, '-b',
label='Best Fit (ChiSquared = %0.2f)' % min_misfit)
plt.legend(loc='lower right')
plt.show()
figname = 'best_conc'
plt.savefig(figname + '.svg')
plt.savefig(figname + '.png')
prod_rates = production.P_tot(zs, con['alt'], con['lat'], con['nuclide'])
#p = interp1d(zs, prod_rates, kind=3)
# interp1d used as above gives crazy negative dives around z = 82000, do not
# want that! UnivariateSpline seems to work much much better
p = UnivariateSpline(zs, prod_rates, k=3, s=0)
util.pickle(p, 'production_rate.dat')
# get data for plotting a depth vs time curve, meters and years
t_true, z_true = sim.glacial_depth_v_time(con['t_gl'],
con['t_int'],
con['t_postgl'],
con['dz_true_m'],
n_gl=con['n_gl'])
conc_true = sim.multiglaciate(dz_true, con['t_gl'], con['t_int'],
con['t_postgl'], con['sample_depths'],
con['nuclide'], p, con['n_gl'])
sigma_true = con['nuclide'].measurement_error(conc_true)
conc_meas = np.random.normal(loc=conc_true, scale=sigma_true)
# we need a way to measure error between models
def chi2(a, b, sigma):
""" Chi squared of two vectors """
return (((a - b) / sigma)**2).sum()
# degrees of freedom in our problem
dof = dz_true.size
print 'Degrees of freedom =', dof
