def waveletTransform(self):
# Wavelet transform:
self.wave, self.period, self.scale, self.coi = \
wavelet(self.data, self.cadence, self.pad, self.dj, self.s0, self.j1, self.mother)
if len(self.time) != len(self.coi):
self.coi = self.coi[1:]
self.power = (np.abs(self.wave))**2 # compute wavelet power spectrum
# Significance levels: (variance=1 for the normalized data)
signif = wave_signif(([1.0]), dt=self.cadence, sigtest=0, scale=self.scale, \
lag1=self.lag1, mother=self.mother, siglvl = self.siglvl)
self.sig95 = signif[:, np.newaxis].dot(np.ones(
self.n)[np.newaxis, :]) # expand signif --> (J+1)x(N) array
self.sig95 = self.power / self.sig95 # where ratio > 1, power is significant
return
sst = sst / np.std(sst, ddof=1)
n = len(sst)
dt = 0.01
# time = np.arange(len(sst)) * dt + 1871.0 # construct time array
time = wl_fall_time # construct time array
xlim = ([min(time), max(time)]) # plotting range
pad = 1 # pad the time series with zeroes (recommended)
dj = 0.25 # this will do 4 sub-octaves per octave
s0 = 2 * dt # this says start at a scale of 6 months
j1 = 7 / dj # this says do 7 powers-of-two with dj sub-octaves each
lag1 = 0.72 # lag-1 autocorrelation for red noise background
print("lag1 = ", lag1)
mother = 'MORLET'
# Wavelet transform:
wave, period, scale, coi = wavelet(sst, dt, pad, dj, s0, j1,
mother)
power = (np.abs(wave))**2 # compute wavelet power spectrum
global_ws = (np.sum(power, axis=1) / n
) # time-average over all times
# Significance levels:
signif = wave_signif(([variance]),
dt=dt,
sigtest=0,
scale=scale,
lag1=lag1,
mother=mother)
sig95 = signif[:, np.newaxis].dot(np.ones(n)[
np.newaxis, :]) # expand signif --> (J+1)x(N) array
sig95 = power / sig95 # where ratio > 1, power is significant
# "http://paos.colorado.edu/research/wavelets/plot/" variance = np.std(sst1, ddof=1) ** 2 sst = (sst1 - np.mean(sst1)) / np.std(sst1, ddof=1) n = len(sst) dt = time[1] - time[0] time = np.arange(len(sst)) * dt + 28800.0 # construct time array xlim = ([28800.0 , 36600.0]) # plotting range pad = 1 # pad the time series with zeroes (recommended) dj = 0.25 # this will do 4 sub-octaves per octave s0 = 2 * dt # this says start at a scale of 6 months j1 = 7 / dj # this says do 7 powers-of-two with dj sub-octaves each lag1 = 0.72 # lag-1 autocorrelation for red noise background mother = 'PAUL' # 'PAUL' # Wavelet transform: wave, period, scale, coi = wavelet(sst, dt, pad, dj, s0, j1, mother) power = (np.abs(wave)) ** 2 # compute wavelet power spectrum # Significance levels: (variance=1 for the normalized SST) signif = wave_signif(([1.0]), dt=dt, sigtest=0, scale=scale, lag1=lag1, mother=mother) sig95 = signif[:, np.newaxis].dot(np.ones(n)[np.newaxis, :]) # expand signif --> (J+1)x(N) array sig95 = power / sig95 # where ratio > 1, power is significant # Global wavelet spectrum & significance levels: global_ws = variance * (np.sum(power, axis=1) / n) # time-average over all times dof = n - scale # the -scale corrects for padding at edges global_signif = wave_signif(variance, dt=dt, scale=scale, sigtest=1, lag1=lag1, dof=dof, mother=mother) # Scale-average between El Nino periods of 2--8 years avg = np.logical_and(scale >= 2, scale < 8) Cdelta = 0.776 # this is for the MORLET wavelet
#------------ LOMB-SCARGLE APPROACH ----------------
pers, pows = lombscargle(time,
data,
err,
Pmin=s0,
Pmax=np.max(time) - np.min(time))
plot_lcper(time, data, pers, pows, lctype=lctype)
peakpows_LS = peakutils.indexes(pows, thres=0.2, min_dist=10)
peakpers_LS = pers[peakpows_LS]
#------------ WAVELET TRANSFORM ----------------
# wave, period, scale, coi = wavelet(data, dt, pad, dj, s0, j1, mother='MORLET')
wave, period, scale, coi = wavelet(data,
dt,
pad,
dj=0.05,
mother=mother,
param=6)
power = (np.abs(wave))**2 # compute wavelet power spectrum
global_ws = (np.sum(power, axis=1) / n) # time-average over all times
# Significance levels:
signif = wave_signif(([variance]),
dt=dt,
sigtest=0,
scale=scale,
lag1=lag1,
mother=mother)
sig95 = signif[:, np.newaxis].dot(
np.ones(n)[np.newaxis, :]) # expand signif --> (J+1)x(N) array
sig95 = power / sig95 # where ratio > 1, power is significant
def plot_according_to_library(field):
cumulative_differences, interpolated_data = get_interpolated_data(field)
sst = interpolated_data
sst = sst - np.mean(sst)
variance = np.std(sst, ddof=1) ** 2
n = len(sst)
dt = 11
time = np.arange(len(sst)) * dt + 1 # construct time array
xlim = ([time[0], time[-1]]) # plotting range
pad = 1 # pad the time series with zeroes (recommended)
dj = 0.25 / 4 # this will do 4 sub-octaves per octave
s0 = 2 * dt # this says start at a scale of 6 months
j1 = 7 / dj # this says do 7 powers-of-two with dj sub-octaves each
lag1 = 0.72 # lag-1 autocorrelation for red noise background
mother = 'MORLET'
# Wavelet transform:
wave, period, scale, coi = wavelet(sst, dt, pad, dj, s0, j1, mother)
power = (np.abs(wave)) ** 2 # compute wavelet power spectrum
global_ws = (np.sum(power, axis=1) / n) # time-average over all times
# Significance levels:
signif = wave_signif(
(
[variance]
),
dt=dt,
sigtest=0, scale=scale,
lag1=lag1, mother=mother
)
sig95 = signif[:, np.newaxis].dot(
np.ones(n)[np.newaxis, :]
) # expand signif --> (J+1)x(N) array
sig95 = power / sig95 # where ratio > 1, power is significant
# Global wavelet spectrum & significance levels:
dof = n - scale # the -scale corrects for padding at edges
global_signif = wave_signif(
variance, dt=dt, scale=scale, sigtest=1,
lag1=lag1, dof=dof, mother=mother
)
fig = plt.figure(figsize=(9, 10))
gs = GridSpec(3, 4, hspace=0.4, wspace=0.75)
plt.subplots_adjust(
left=0.1, bottom=0.05,
right=0.9, top=0.95, wspace=0, hspace=0
)
plt.subplot(gs[0, 0:3])
plt.plot(time, sst, 'k')
plt.xlim(xlim[:])
plt.xlabel('Time (Seconds)')
plt.ylabel('{}'.format(snake_to_camel(field)))
plt.title('a) {} vs Time'.format(snake_to_camel(field)))
# --- Contour plot wavelet power spectrum
# plt3 = plt.subplot(3, 1, 2)
plt3 = plt.subplot(gs[1, 0:3])
levels = [0, 0.5, 1, 2, 4, 999]
CS = plt.contourf(
time, period, power, len(levels)
) # *** or use 'contour'
im = plt.contourf(
CS, levels=levels,
colors=['white', 'bisque', 'orange', 'orangered', 'darkred']
)
plt.xlabel('Time (Seconds)')
plt.ylabel('Period (Seconds)')
plt.title('b) Wavelet Power Spectrum (contours at 0.5,1,2,4\u00B0C$^2$)')
plt.xlim(xlim[:])
# 95# significance contour, levels at -99 (fake) and 1 (95# signif)
plt.contour(time, period, sig95, [-99, 1], colors='k')
# cone-of-influence, anything "below" is dubious
plt.plot(time, coi, 'k')
# format y-scale
plt3.set_yscale('log', basey=2, subsy=None)
plt.ylim([np.min(period), np.max(period)])
ax = plt.gca().yaxis
ax.set_major_formatter(ticker.ScalarFormatter())
plt3.ticklabel_format(axis='y', style='plain')
plt3.invert_yaxis()
# set up the size and location of the colorbar
# position = fig.add_axes([0.5, 0.36, 0.2, 0.01])
# plt.colorbar(
# im, cax=position, orientation='horizontal'
# ) # fraction=0.05, pad=0.5)
plt.subplots_adjust(right=0.7, top=0.9)
# --- Plot global wavelet spectrum
plt4 = plt.subplot(gs[1, -1])
plt.plot(global_ws, period)
plt.plot(global_signif, period, '--')
plt.xlabel('Power (\u00B0C$^2$)')
plt.title('c) Global Wavelet Spectrum')
plt.xlim([0, 1.25 * np.max(global_ws)])
# format y-scale
plt4.set_yscale('log', basey=2, subsy=None)
plt.ylim([np.min(period), np.max(period)])
ax = plt.gca().yaxis
ax.set_major_formatter(ticker.ScalarFormatter())
plt4.ticklabel_format(axis='y', style='plain')
plt4.invert_yaxis()
# fig.tight_layout()
plt.show()
