def lowess_homemade_kern(x, y, w, a1, kernel='Exp'):
"""
#inspired by: https://xavierbourretsicotte.github.io/loess.html
homebaked lowess with variogram kernel + heteroscedasticity of observations with error
:param x:x
:param y:y
:param w: heteroscedastic weights (inverse of variance)
:param a1: range of the kernel (in variogram terms)
:param kernel: kernel function
:return:
"""
n = len(x)
yest = np.zeros(n)
err_yest = np.zeros(n)
if kernel == 'Gau':
kernel_fun = kernel_gaussian
elif kernel == 'Exp':
kernel_fun = kernel_exp
elif kernel == 'Exc':
kernel_fun = kernel_exclass
else:
print('Kernel not recognized.')
sys.exit()
W = np.array([kernel_fun(x, x[i], a1) * w for i in range(n)]).T
X = np.array([x for i in range(n)]).T
Y = np.array([y for i in range(n)]).T
beta1, beta0, _, Yl, Yu = ft.wls_matrix(X, Y, W, conf_interv=0.68)
for i in range(n):
yest[i] = beta1[i] * x[i] + beta0[i]
err_yest[i] = (Yu[i, i] - Yl[i, i]) / 2
return yest, err_yest
# new_err_vals[i] = np.nanmean(err_vals[ind])
# data_vals = new_data_vals
# time_vals = new_time_vals
# err_vals = new_err_vals
# good_vals = np.isfinite(data_vals)
# here we need to change the 0 for the x axis, in case we are using a linear kernel
ax = fig.add_subplot(grid[6:12,5:])
ax.text(0.025, 0.95, 'd', transform=ax.transAxes,
fontsize=16, fontweight='bold', va='top', ha='left')
while (n_out > 0 or final_fit==0) and num_finite >= 2:
beta1, beta0, incert_slope, _, _ = ft.wls_matrix(time_vals[good_vals], data_vals[good_vals],
1. / err_vals[good_vals], conf_slope=0.99)
# standardized dispersion from linearity
res_stdized = np.sqrt(np.mean(
(data_vals[good_vals] - (beta0 + beta1 * time_vals[good_vals])) ** 2 / err_vals[good_vals]))
res = np.sqrt(np.mean((data_vals[good_vals] - (beta0 + beta1 * time_vals[good_vals])) ** 2))
if perc_nonlin[min(niter, len(perc_nonlin) - 1)] == 0:
opt_var = 0
else:
opt_var = (res / res_stdized ** 2) ** 2 * 100. / (5 * perc_nonlin[min(niter, len(perc_nonlin) - 1)])
k1 = PairwiseKernel(1, metric='linear') + PairwiseKernel(1, metric='linear') * C(opt_var) * RQ(10, 3) # linear kernel
k2 = C(30) * ESS(length_scale=1, periodicity=1) # periodic kernel
k3 = C(50) * RBF(0.75)
kernel = k1 + k2 + k3
def bin_valid_df_by_vals(df,
bins,
bins_val,
list_var=['dh', 'zsc'],
ls_dvardt=True,
weight_ib=1. / 40,
return_ls=False):
mid_bin, med, std, dvardt, dvardt_2std, ns_ics, ns_ib = ([]
for i in range(7))
for i in range(len(bins) - 1):
ind = np.logical_and(bins_val >= bins[i], bins_val < bins[i + 1])
df_ind = df[ind]
nics = np.count_nonzero(df_ind.sensor == 'ICS')
nib = np.count_nonzero(df_ind.sensor == 'IB')
ns_ics.append(nics)
ns_ib.append(nib)
mid_bin.append(bins[i] + 0.5 * (bins[i + 1] - bins[i]))
sub_med = []
sub_std = []
sub_dvardt = []
sub_dvardt_2std = []
sub_mu = []
sub_w = []
sub_t = []
for var in list_var:
if weight_ib is not None:
if nics != 0 or nib != 0:
sub_med.append(
np.nansum(
(np.nanmedian(
df_ind[df_ind.sensor == 'ICS'][var]) * nics,
np.nanmedian(df_ind[df_ind.sensor == 'IB'][var]) *
nib * weight_ib)) / (nics + nib * weight_ib))
sub_std.append(
np.nansum(
(nmad(df_ind[df_ind.sensor == 'ICS'][var]) * nics,
nmad(df_ind[df_ind.sensor == 'IB'][var]) * nib *
weight_ib)) / (nics + nib * weight_ib))
else:
sub_med.append(np.nan)
sub_std.append(np.nan)
else:
sub_med.append(np.nanmedian(df_ind[var]))
sub_std.append(nmad(df_ind[var].values))
if ls_dvardt:
list_t = sorted(list(set(list(df_ind.t.values))))
ftime_delta = np.array([
(np.datetime64(t) -
np.datetime64('{}-01-01'.format(int(2000)))).astype(int) /
365.2422 for t in list_t
])
mu = []
w = []
for val_t in list_t:
ind_t = df_ind.t.values == val_t
df_ind_t = df_ind[ind_t]
nics_t = np.count_nonzero(df_ind_t.sensor == 'ICS')
nib_t = np.count_nonzero(df_ind_t.sensor == 'IB')
if np.count_nonzero(ind_t) > 20:
med_t = np.nansum(
(np.nanmedian(
df_ind_t[df_ind_t.sensor == 'ICS'][var]) *
nics_t,
np.nanmedian(
df_ind_t[df_ind_t.sensor == 'IB'][var]) *
nib_t * weight_ib)) / (nics_t + nib_t * weight_ib)
mu.append(med_t)
std_t = np.nansum(
(nmad(df_ind_t[df_ind_t.sensor == 'ICS'][var]) *
nics_t,
nmad(df_ind_t[df_ind_t.sensor == 'IB'][var]) *
nib_t * weight_ib)) / (nics_t + nib_t * weight_ib)
w.append(std_t / np.sqrt(nics_t + nib_t * weight_ib))
else:
mu.append(np.nan)
w.append(np.nan)
mu = np.array(mu)
w = np.array(w)
if np.count_nonzero(~np.isnan(mu)) > 5:
# reg = LinearRegression().fit(ftime_delta[~np.isnan(mu)].reshape(-1, 1),
# mu[~np.isnan(mu)].reshape(-1, 1))
beta1, _, incert_slope, _, _ = ft.wls_matrix(
ftime_delta[~np.isnan(mu)],
mu[~np.isnan(mu)],
1. / w[~np.isnan(mu)]**2,
conf_slope=0.95)
# fig = plt.figure()
# plt.scatter(ftime_delta,mu_dh,color='red')
# plt.plot(np.arange(0,10,0.1),reg.predict(np.arange(0,10,0.1).reshape(-1,1)),color='black',label=reg)
# plt.ylim([-20,20])
# plt.text(5,0,str(reg.coef_[0]))
# plt.legend()
# coef = reg.coef_[0][0]
coef = beta1
sub_dvardt.append(coef)
sub_dvardt_2std.append(incert_slope)
else:
sub_dvardt.append(np.nan)
sub_dvardt_2std.append(np.nan)
sub_mu.append(mu)
sub_w.append(w)
sub_t.append(ftime_delta)
med.append(sub_med)
std.append(sub_std)
dvardt.append(sub_dvardt)
dvardt_2std.append(sub_dvardt_2std)
df_out = pd.DataFrame()
df_out = df_out.assign(mid_bin=mid_bin, ns_ics=ns_ics, ns_ib=ns_ib)
for var in list_var:
df_out['med_' + var] = list(zip(*med))[list_var.index(var)]
df_out['nmad_' + var] = list(zip(*std))[list_var.index(var)]
if ls_dvardt:
df_out['d' + var + '_dt'] = list(zip(*dvardt))[list_var.index(var)]
df_out['d' + var + '_dt_2std'] = list(
zip(*dvardt_2std))[list_var.index(var)]
if return_ls and ls_dvardt:
df_ls = pd.DataFrame()
for var in list_var:
# print(len(sub_mu))
df_ls['mu_' + var] = sub_mu[list_var.index(var)]
df_ls['w_' + var] = sub_w[list_var.index(var)]
df_ls['t_' + var] = sub_t[list_var.index(var)]
return df_out, df_ls
else:
return df_out
'2000-01-01_2020-01-01'].err_dmdt.values[0]) +
' Gt yr-1')
print('Glacier mass loss totalled ' + '{:.3f}'.format(glac_trend) + ' ± ' +
'{:.3f}'.format(2 * glac_trend_err) + ' mm of sea-level rise')
contr_trend = -glac_trend / gmsl_trend * 100
contr_trend_err = -glac_trend / gmsl_trend * np.sqrt(
(gmsl_trend_err / gmsl_trend)**2 + (glac_trend_err / glac_trend)**2) * 100
print('Glacier contribution to SLR is ' + '{:.2f}'.format(contr_trend) +
' % ± ' + '{:.2f}'.format(2 * contr_trend_err) + ' %')
#GLACIER ACCELERATION
beta1_t, beta0, incert_slope, _, _ = ft.wls_matrix(
x=np.arange(0, 16, 5),
y=df_g.dhdt.values[:-1],
w=1 / df_g.err_dhdt.values[:-1]**2)
print('Global thinning acceleration is ' + '{:.5f}'.format(beta1_t) + ' ± ' +
'{:.5f}'.format(2 * incert_slope) + ' m yr-2')
beta1, beta0, incert_slope, _, _ = ft.wls_matrix(x=np.array([0, 5, 10, 15]),
y=df_np.dhdt.values[:-1],
w=1 /
df_np.err_dhdt.values[:-1]**2)
print('Global excl. GRL and ANT thinning acceleration is ' +
'{:.5f}'.format(beta1) + ' ± ' + '{:.5f}'.format(2 * incert_slope) +
' m yr-2')
beta1_g, beta0, incert_slope_g, _, _ = ft.wls_matrix(
x=np.arange(0, 16, 5),
y=df_g.dmdt.values[:-1],
w=1 / df_g.err_dmdt.values[:-1]**2)