def bootstrap_ssh(ssha, niter, tw, order, simlen=10000):
"""
Generate [niter] white and red noise maps,
then passes a low-pass filter through them
Parameters
----------
ssha : ARRAY[time x lat x lon]
SSH anomalies
niter : INT
# of white noise timeseries to generate
tw : INT
Low pass filter cutoff time window
order : INT
Order of the low-pass filter
simlen : INT, optional
Total length of generated wn timeseries (before truncation). The default is 10000.
Returns
-------
wnout : ARRAY [niter x time x lat x lon]
White Noise Maps
rnout : ARRAY [niter x time x lat x lon]
Red Noise Maps
ar1m : [lat x lon]
AR1 Coefficients
neffm : [lat x lon]
Effective DOF
"""
# Get Dimensions
ntime, nlat, nlon = ssha.shape
# Make land/ice mask
msk = ssha.copy()
msk = msk.sum(0)
msk[~np.isnan(msk)] = 1
# Calculate Stdev
aviso_std = ssha.std(0)
# Preallocate
wnout = np.zeros((niter, ntime, nlat, nlon)) * np.nan
rnout = np.zeros((niter, ntime, nlat, nlon)) * np.nan
# Loop for each interation
for it in tqdm(range(niter)):
# Create white noise timeseries
wn = np.random.normal(0, 1, (simlen, nlat5, nlon5))
wn *= msk[None, :, :]
# Create scaled form of timeseries
wnstd = wn.copy()
wnstd *= aviso_std[None, :, :]
# Get stddev and AR1 for red noise timeseries
rnstd, ar1m, neffm = slutil.return_ar1_model(ssha, simlen)
# Select the last n points (match sample size of aviso)
wnstd = wnstd[-ntime:, :, :]
rnstd = rnstd[-ntime:, :, :]
# Low Pass Filter The Timeseries
wnlp = slutil.lp_butter(wnstd, tw, order)
rnlp = slutil.lp_butter(rnstd, tw, order)
# Apply Save the results
wnout[it, ...] = wnlp
rnout[it, ...] = rnlp
return wnout, rnout, ar1m, neffm
# ----------------------
#%% Design Low Pass Filter
# ----------------------
# ---
# Apply LP Filter
# ---
# Filter Parameters and Additional plotting options
dt = 24 * 3600 * 30
M = 5
xtk = [1 / (10 * 12 * dt), 1 / (24 * dt), 1 / (12 * dt), 1 / (3 * dt), 1 / dt]
xtkl = ['decade', '2-yr', 'year', 'season', 'month']
order = 5
tw = 15 # filter size for time dim
sla_lp = slutil.lp_butter(ssha, tw, order)
#% Remove NaN points and Examine Low pass filter
slars = sla_lp.reshape(ntimer, nlat5 * nlon5)
# ---
# Locate points where values are all zero
# ---
tsum = slars.sum(0)
zero_pts = np.where(tsum == 0)[0]
ptmap = np.array(tsum == 0)
slars[:, zero_pts] = np.nan
ptmap = ptmap.reshape(nlat5, nlon5)
# Map removed points
fig, ax = plt.subplots(
1, 1, subplot_kw={'projection': ccrs.PlateCarree(central_longitude=0)})
maxar1 = np.nanmax(sshac[1, :, :]) # Find Maximum Autocorrelation
# ----------------------
#%% Design Low Pass Filter
# ----------------------
# ---
# Apply LP Filter
# ---
# Filter Parameters and Additional plotting options
dt = 24 * 3600 * 30
M = 5
xtk = [1 / (10 * 12 * dt), 1 / (24 * dt), 1 / (12 * dt), 1 / (3 * dt), 1 / dt]
xtkl = ['decade', '2-yr', 'year', 'season', 'month']
order = 5
tw = 15 # filter size for time dim
sla_lp = slutil.lp_butter(ssha, tw, order)
#% Remove NaN points and Examine Low pass filter
slars = sla_lp.reshape(ntimer, nlat5 * nlon5)
# ---
# Locate points where values are all zero
# ---
tsum = slars.sum(0)
zero_pts = np.where(tsum == 0)[0]
ptmap = np.array(tsum == 0)
slars[:, zero_pts] = np.nan
ptmap = ptmap.reshape(nlat5, nlon5)
# Map removed points
fig, ax = plt.subplots(
1, 1, subplot_kw={'projection': ccrs.PlateCarree(central_longitude=0)})