# Read geopotential height data using the xarray module. The file contains
# December-February averages of geopotential height at 500 hPa for the
# European/Atlantic domain (80W-40E, 20-90N).
filename = example_data_path('hgt_djf.nc')
z_djf = xr.open_dataset(filename)['z']
# Compute anomalies by removing the time-mean.
z_djf = z_djf - z_djf.mean(dim='time')
# Create an EOF solver to do the EOF analysis. Square-root of cosine of
# latitude weights are applied before the computation of EOFs.
coslat = np.cos(np.deg2rad(z_djf.coords['latitude'].values)).clip(0., 1.)
wgts = np.sqrt(coslat)[..., np.newaxis]
solver = Eof(z_djf, weights=wgts)
# Retrieve the leading EOF, expressed as the covariance between the leading PC
# time series and the input SLP anomalies at each grid point.
eof1 = solver.eofsAsCovariance(neofs=1)
# Plot the leading EOF expressed as covariance in the European/Atlantic domain.
clevs = np.linspace(-75, 75, 11)
proj = ccrs.Orthographic(central_longitude=-20, central_latitude=60)
ax = plt.axes(projection=proj)
ax.coastlines()
ax.set_global()
eof1[0, 0].plot.contourf(ax=ax, levels=clevs, cmap=plt.cm.RdBu_r,
transform=ccrs.PlateCarree(), add_colorbar=False)
ax.set_title('EOF1 expressed as covariance', fontsize=16)
plt.show()
import xarray as xr
from eofs.xarray import Eof
from eofs.examples import example_data_path
# Read SST anomalies using the xarray module. The file contains November-March
# averages of SST anomaly in the central and northern Pacific.
filename = example_data_path('sst_ndjfm_anom.nc')
sst = xr.open_dataset(filename)['sst']
# Create an EOF solver to do the EOF analysis. Square-root of cosine of
# latitude weights are applied before the computation of EOFs.
coslat = np.cos(np.deg2rad(sst.coords['latitude'].values))
wgts = np.sqrt(coslat)[..., np.newaxis]
solver = Eof(sst, weights=wgts)
# Retrieve the leading EOF, expressed as the correlation between the leading
# PC time series and the input SST anomalies at each grid point, and the
# leading PC time series itself.
eof1 = solver.eofsAsCorrelation(neofs=1)
pc1 = solver.pcs(npcs=1, pcscaling=1)
# Plot the leading EOF expressed as correlation in the Pacific domain.
clevs = np.linspace(-1, 1, 11)
ax = plt.axes(projection=ccrs.PlateCarree(central_longitude=190))
fill = eof1[0].plot.contourf(ax=ax, levels=clevs, cmap=plt.cm.RdBu_r,
add_colorbar=False, transform=ccrs.PlateCarree())
ax.add_feature(cfeature.LAND, facecolor='w', edgecolor='k')
cb = plt.colorbar(fill, orientation='horizontal')
cb.set_label('correlation coefficient', fontsize=12)
def compute_relative_entropy(
initialized,
control,
anomaly_data=False,
neofs=None,
curv=True,
nlead=None,
nmember_control=10,
):
"""
Compute relative entropy.
Calculates EOFs from anomalies. Projects fields on EOFs to receive
pseudo-Principle Components per init and lead year. Calculate
relative entropy based on _relative_entropy_formula.
Args:
initialized (xr.Dataset): anomaly ensemble data with dimensions
lead, member, time and
spatial [lon (x), lat(y)].
DPLE or PM_ds
control (xr.Dataset): anomaly control distribution with
non-spatial dimensions:
spatial [lon (x), lat(y)].
- LENS: member, time
- PM_control: time
anomaly_data (bool): Input data is anomaly alread. Default: False.
neofs (int): number of EOFs to use.
Default: initialized.member.size.
curv (bool): if curvilinear grids disables EOF weights.
nlead (int): number of timesteps calculated.
nmember_control (int): number of members created from
bootstrapping from control
Returns:
rel_ent (xr.Dataset): relative entropy
"""
if Eof is None:
raise ImportError("eofs is not installed; see"
"https://ajdawson.github.io/eofs/latest/index.html")
# Defaults
if neofs is None:
neofs = initialized.member.size
if nlead is None:
nlead = initialized.lead.size
# case if you submit control with dim time and member, LENS case
if "member" in control.dims:
control_uninitialized = _bootstrap_dim(
control,
initialized.lead.size,
dim="init",
dim_label=list(initialized.init.values),
)
# case if you only submit control with dim time, PM case
else:
control_uninitialized = xr.concat(
[
_bootstrap_dim(
control,
initialized.lead.size,
dim="member",
dim_label=np.arange(nmember_control),
) for _ in range(initialized.init.size)
],
dim="init",
)
control_uninitialized["init"] = initialized.init.values
# initialized and control_uninitialized are allowed to have different
# dims as I need more members to sample my control distr. properly
if set(initialized.dims) != set(control_uninitialized.dims):
warnings.warn(
"Warning: initialized and control_uninitialized have different coords."
)
# print(initialized, control_uninitialized)
# convert to xr.Data.Array
if isinstance(control_uninitialized, xr.Dataset):
control_uninitialized = control_uninitialized.to_array().squeeze()
if isinstance(initialized, xr.Dataset):
initialized = initialized.to_array().squeeze()
# detrend
non_spatial_dims = set(control_uninitialized.dims).intersection(
["init", "member"])
non_spatial_dims = list(non_spatial_dims)
if not anomaly_data: # if ds, control are raw values
anom_x = initialized - control_uninitialized.mean(non_spatial_dims)
anom_b = control_uninitialized - control_uninitialized.mean(
non_spatial_dims)
else: # leave as is when already anomalies
anom_x = initialized
anom_b = control_uninitialized
# prepare for EOF
if curv: # if curvilinear lon(x,y), lat(x,y) data inputs
wgts = None
else: # assumes there is 'lat' in coords
coslat = np.cos(np.deg2rad(anom_x.coords["lat"].values))
wgts = np.sqrt(coslat)[..., np.newaxis]
# EOF requires xr.dataArray
if isinstance(control, xr.Dataset):
control = control.to_array().squeeze()
if "member" in control.dims: # LENS
# stack member and init into time dim, make time first
non_spatial_control_dims = list(
set(control.dims).intersection(["time", "member"]))
transpose_dims = list(control.dims)
transpose_dims.remove("member")
transpose_dims.remove("time")
dims = tuple(["time"] + transpose_dims)
base_to_calc_eofs = (control.stack(
new=tuple(non_spatial_control_dims)).rename({
"new": "time"
}).set_index({
"time": "time"
}).transpose(*dims))
else:
# PM_control
base_to_calc_eofs = control
solver = Eof(base_to_calc_eofs, weights=wgts)
re_leadtime_list = []
leads = initialized.lead.values[:nlead]
inits = initialized.init.values
# DoTo: parallelize this double loop
for init in inits: # loop over inits
rl, sl, dl = ([] for _ in range(3)) # lists to store results in
for lead in leads: # loop over lead time
# P_b base distribution # eofs require time
pc_b = solver.projectField(
anom_b.sel(init=init, lead=lead).drop_vars("lead").rename(
{"member": "time"}),
neofs=neofs,
eofscaling=0,
weighted=False,
).rename({"time": "lead"})
mu_b = pc_b.mean("lead")
sigma_b = xr.DataArray(np.cov(pc_b.T))
# P_x init distribution
pc_x = solver.projectField(
anom_x.sel(init=init, lead=lead).drop_vars("lead").rename(
{"member": "time"}),
neofs=neofs,
eofscaling=0,
weighted=False,
).rename({"time": "lead"})
mu_x = pc_x.mean("lead")
sigma_x = xr.DataArray(np.cov(pc_x.T))
r, d, s = _relative_entropy_formula(sigma_b, sigma_x, mu_x, mu_b,
neofs)
rl.append(r)
sl.append(s)
dl.append(d)
re_leadtime_list.append(
xr.Dataset({
"R": ("lead", rl),
"S": ("lead", sl),
"D": ("lead", dl)
}))
re = xr.concat(re_leadtime_list, dim="init").assign(init=inits, lead=leads)
return re
def main(args):
#environmental constants
if platform.system() == 'Windows':
in_dir='../examples/'
out_dir='../regressors/'
reg_dir='../regressors/'#${in_dir}'regresory_2013/'
nc_gen=True
pdf_gen=False
plus = ''
else:
n_samples = int(os.environ['n_samples'])
in_dir = os.environ['in_dir']
#out_dir = os.environ['out_dir']
reg_dir = os.environ['reg_dir']
pdf_gen = os.environ['pdf_gen']
nc_gen = os.environ['nc_gen']
what_re = args.what_re
vari = args.vari
i_year = args.i_year
s_year = args.s_year
e_year = args.e_year
in_file_name = args.in_file_name
if args.verbose:
print('dataset: ', what_re)
print('variable: ', vari)
print('initial year of dataset: ', i_year)
print('initial year of analysis: ', s_year)
print('end year of analysis: ', e_year)
print('input filename: ', in_file_name)
print('data opening')
in_netcdf = in_dir + in_file_name
print(in_netcdf)
ds = xr.open_dataset(in_netcdf)
#print(ds)
lat_name = fce.get_coords_name(ds, 'latitude')
lat = ds.coords[lat_name]
nlat = lat.shape[0]
lev_name = fce.get_coords_name(ds, 'pressure')
if ds.coords[lev_name].attrs['units'] == 'Pa':
lev = ds.coords[lev_name]/100.
ds[lev_name] = lev
else:
lev = ds.coords[lev_name]
n = ds.coords['time'].shape[0]
#it may happen that the field is 3D (longitude is missing)
try:
lon_name = fce.get_coords_name(ds, 'longitude')
lon = ds.coords[lon_name]
nlon = lon.shape[0]
except:
nlon = 1
#print nlat, nlev, n, nlon
#zonal mean
if nlon != 1:
uwnd = ds[vari].mean(lon_name)
else:
uwnd = ds[vari]
#equatorial average and level selection
sel_dict = {lev_name: fce.coord_Between(lev,10,50), lat_name: fce.coord_Between(lat,-10,10)}
zm_u = uwnd.sel(**sel_dict).mean(lat_name)
#period selection
times = pd.date_range(str(s_year)+'-01-01', str(e_year)+'-12-31', name='time', freq = 'M')
zm_u_sel = zm_u.sel(time = times, method='ffill') #nearest
#remove seasonality
climatology = zm_u_sel.groupby('time.month').mean('time')
anomalies = zm_u_sel.groupby('time.month') - climatology
#print anomalies
#sys.exit()
#additional constants
npca = 30
norm=2 #5
norms=3 #5
what_sp = '' # what solar proxy?
print("regressors' openning")
global reg#, reg_names, nr
reg, reg_names, history = fce.configuration_ccmi(what_re, what_sp, norm, 'no_qbo' , i_year, s_year, e_year, reg_dir)
nr = reg.shape[1]
#print(anomalies)
#extracting of other variability by MLR
stacked = anomalies.stack(allpoints = [lev_name])
stacked = stacked.reset_coords(drop=True)
resids = stacked.groupby('allpoints').apply(xr_regression)
resids = resids.rename({'dim_0': 'time'})
resids['time'] = times
#EOF analysis
solver = Eof(resids.T, weights=None)
#sys.exit()
#coslat = np.cos(np.deg2rad(lat)).clip(0.,1.)
#wgts = np.sqrt(coslat)[np.newaxis,...]
for i in range(npca):
var_eofs = solver.varianceFraction(neigs=i)
#print var_eofs
if np.sum(var_eofs) > 0.95:
npca=i
total_variance = np.sum(var_eofs)
print(total_variance, ' % based on ', i, ' components')
break
var_eofs = solver.varianceFraction(neigs=npca)
pcs = solver.pcs(npcs=npca, pcscaling=1)
nte = solver.northTest(neigs=npca, vfscaled=True)
subdir = './'
if pdf_gen:
fig = plt.figure(figsize=(11,8))
ax1 = fig.add_subplot(111)
ax1.set_title(str(npca)+' PCAs cover '+str(np.round(total_variance*100, 2))+'% of total variance')
for i in xrange(npca):
#plotting
pcs[:,i].plot(linewidth = 2, ax = ax1, label = 'pca '+str(i+1))
ax1.set_xlabel('time [years]')
ax1.set_ylabel('QBO index')
ax1.set_title('')
ax1.legend(loc = 'best')
plt.savefig(reg_dir+'qbo_'+what_re+'_pcas.pdf', bbox_inches='tight')
plt.close(fig)
if nc_gen:
#save to netcdf
#print(pcs[:,0])
for i in range(npca):
pcs_ds = pcs[:,i].to_dataset(name = 'index')
pcs_ds.to_netcdf(reg_dir+r'qbo_'+what_re+'_pc'+str(i+1)+pripona_nc)
def eof_orca_latlon_box(run, var, modes, lon_bnds, lat_bnds, pathfile, plot,
time, eoftype):
if (var == 'temp'):
key = 'votemper'
key1 = "votemper"
elif (var == 'sal'):
key = 'vosaline'
key1 = "vosaline"
elif (var == 'MLD'):
key = 'somxl010'
key1 = "somxl010"
# read data
ds = xr.open_dataset(pathfile)
#ds["time_counter"] = ds['time_counter']+(np.datetime64('0002-01-01')-np.datetime64('0001-01-01'))
if time == 'comparison':
ds = ds.sel(time_counter=slice('1958-01-01', '2006-12-31'))
# cut box for EOF at surface
if var == 'MLD':
data = ds[key].sel(lon=slice(lon_bnds[0], lon_bnds[1]),
lat=slice(lat_bnds[0], lat_bnds[1]))
#data = cut_latlon_box(ds[key][:,:,:],ds.lon,ds.lat,
# lon_bnds,lat_bnds)
else:
data = ds[key][:, 0, :, :].sel(lon=slice(lon_bnds[0], lon_bnds[1]),
lat=slice(lat_bnds[0], lat_bnds[1]))
#data = cut_latlon_box(ds[key][:,0,:,:],ds.lon,ds.lat,
# lon_bnds,lat_bnds)
data = data.to_dataset()
# detrend data
data[key1] = (['time_counter', 'lat', 'lon'],
signal.detrend(data[key].fillna(0), axis=0, type='linear'))
#data=data.where(data!=0)
# remove seasonal cycle and drop unnecessary coordinates
if 'time_centered' in list(data.coords):
data = deseason_month(data).drop('month').drop(
'time_centered') # somehow pca doesn't work otherwise
else:
data = deseason_month(data).drop(
'month') # somehow pca doesn't work otherwise
# set 0 values back to nan
data = data.where(data != 0)
# EOF analysis
#Square-root of cosine of latitude weights are applied before the computation of EOFs.
coslat = np.cos(np.deg2rad(data['lat'].values))
coslat, _ = np.meshgrid(coslat, np.arange(0, len(data['lon'])))
wgts = np.sqrt(coslat)
solver = Eof(data[key], weights=wgts.transpose())
pcs = solver.pcs(npcs=modes, pcscaling=1)
if eoftype == 'correlation':
eof = solver.eofsAsCorrelation(neofs=modes)
elif eoftype == 'covariance':
eof = solver.eofsAsCovariance(neofs=modes)
else:
eof = solver.eofs(neofs=modes)
varfr = solver.varianceFraction(neigs=4)
print(varfr)
#----------- Plotting --------------------
plt.close("all")
if plot == 1:
for i in np.arange(0, modes):
fig = plt.figure(figsize=(8, 2))
ax1 = fig.add_axes([0.1, 0.1, 0.3, 0.9],
projection=ccrs.PlateCarree()) # main axes
ax1.set_extent(
(lon_bnds[0], lon_bnds[1], lat_bnds[0], lat_bnds[1]))
# discrete colormap
cmap = plt.get_cmap('RdYlBu',
len(np.arange(10, 30)) -
1) #inferno similar to cmo thermal
eof[i, :, :].plot(ax=ax1,
cbar_kwargs={'label': 'Correlation'},
transform=ccrs.PlateCarree(),
x='lon',
y='lat',
add_colorbar=True,
cmap=cmap)
gl = map_stuff(ax1)
gl.xlocator = mticker.FixedLocator([100, 110, 120])
gl.ylocator = mticker.FixedLocator(np.arange(-35, -10, 5))
plt.text(116,
-24,
str(np.round(varfr[i].values, decimals=2)),
horizontalalignment='center',
verticalalignment='center',
transform=ccrs.PlateCarree(),
fontsize=8)
ax2 = fig.add_axes([0.5, 0.1, 0.55, 0.9]) # main axes
plt.plot(pcs.time_counter,
pcs[:, i].values,
linewidth=0.1,
color='k')
anomaly(ax2, pcs.time_counter.values, pcs.values[:, i], [0, 0])
ax2.set_xlim(
[pcs.time_counter[0].values, pcs.time_counter[-1].values])
plt.savefig(pathplots + 'eof_as' + eoftype + '_mode' + str(i) +
'_' + time + '_' + run + '_' + var + '.png',
dpi=300,
bbox_inches='tight',
pad_inches=0.1)
plt.show()
#----------------------------------------------
return pcs, eof, varfr
def calcEOF(xrdata, data_var, w, wei=True):
"""
input:
xrdata: xarray Dataset
data_var: string. Variable name to use on EOF.
w: string. variable for using weights. E.g. latitude
use as:
solver, eof1, var1 = calcEOF(xrdata, 'data_var')
"""
xrdata = xrdata - xrdata[data_var].mean(dim="time")
# Testing if we can select data from level, lat and time
try:
xrdata = xrdata.sel(level=1000,
latitude=slice(90, 20),
time=slice("1979-01-01", "2000-12-31"))
print(
'Data selection OK on first try. Level, lat and time slice done.')
except ValueError:
try:
print('valueError: Trying next')
xrdata = xrdata.sel(level=1000,
lat=slice(90, 20),
time=slice("1979-01-01", "2000-12-31"))
print(
'Data selection OK on second try. Level, lat and time slice done.'
)
except ValueError:
try:
print('valueError: Trying next')
xrdata = xrdata.sel(latitude=slice(90, 20),
time=slice("1979-01-01", "2000-12-31"))
print('Data selection OK on third try. No level cut')
except ValueError:
try:
print('valueError: Trying next')
xrdata = xrdata.sel(time=slice("1979-01-01", "2000-12-31"))
print('Data selection OK on fourth try. Only time slice.')
except:
raise TypeError(' Data out of limits')
xrdata = (xrdata.groupby('time.month') -
xrdata[data_var].groupby('time.month').mean())
# To ensure equal area weighting for the covariance matrix,
# the gridded data is weighted by the square root of the cosine of
# latitude. - NOAA
if wei == True:
coslat = np.cos(np.deg2rad(xrdata.coords[w].values)).clip(0., 1.)
# np.newaxis add a dimention to wgts. dont know what ... does
# i think its like a transposed. It took all the objects on a list and
# make a new list with lists inside (each list with only one object)
# just an adjustment of format
wgts = np.sqrt(coslat)[..., np.newaxis]
# The EOF analysis is handled by a solver class, and the EOF solution
# is computed when the solver class is created. Method calls are then used
# to retrieve the quantities of interest from the solver class.
# center = False do not remove mean from data
# solver = Eof(m_anomalie.hgt, weights=wgts, center=False)
"""
# solver.eofAsCovariance Returns the EOFs expressed as the covariance between each PC and the input
# data set at each point in space. they are not actually the EOFs. They tell you how each point in space
# varies like the given mode. The eofs method provides the raw EOFs (eigenvectors of the covariance
# matrix) which are the spatial patterns the PCs are the coefficeints of.
# “The covariance matrix is used for the EOF analysis.” - NOAA """
solver = Eof(xrdata[data_var], weights=wgts)
else:
solver = Eof(xrdata[data_var])
# solver = Eof(s_anomalie.hgt, weights=wgts, center=False)
# Retrieve the leading EOF, expressed as the covariance between the leading PC
# time series and the input SLP anomalies at each grid point.
eof1 = solver.eofsAsCovariance(pcscaling=1)
var1 = solver.varianceFraction().sel(mode=0)
return solver, eof1, var1
klrat = {}
for ii in range(8):
covu = cov(umeana[ii, :]**2)
covv = cov(vmeana[ii, :]**2)
covuv = cov(umeana[ii, :] * vmeana[ii, :])
varmax = 0.5 * (covu + covv + sqrt((covu - covv)**2 + 4 * covuv**2))
varmax
varmin = covu**2 + covv**2 - varmax
varmin
import xarray as xray
uvmat = xray.concat((umeana, vmeana), dim='uv')
from eofs.xarray import Eof
solver = Eof(uvmat.isel(distance=ii).T)
evec1x = solver.eofs(neofs=1)[0][0].values
evec1y = solver.eofs(neofs=1)[0][1].values
maxtheta_rad = arctan(evec1y / evec1x)
maxtheta = arctan(evec1y / evec1x) * 180 / pi
maxtheta
eig1 = solver.eigenvalues()[0].values
eig2 = solver.eigenvalues()[1].values
maxvar = 2 * sqrt(5.991 * eig1)
minvar = 2 * sqrt(5.991 * eig2)
fig, ax = plt.subplots(subplot_kw={'aspect': 'equal'})
hist2d(umean[ii, :], vmean[ii, :], 30)
def eof_analyse(xarray_DataArray, neofs):
solver = Eof(xarray_DataArray)
eofs = solver.eofs(neofs)
return eofs
import numpy as np
import xarray as xr
from eofs.xarray import Eof
from eofs.examples import example_data_path
# Read SST anomalies using the xarray module. The file contains November-March
# averages of SST anomaly in the central and northern Pacific.
filename = example_data_path('sst_ndjfm_anom.nc')
sst = xr.open_dataset(filename)['sst']
# Create an EOF solver to do the EOF analysis. Square-root of cosine of
# latitude weights are applied before the computation of EOFs.
coslat = np.cos(np.deg2rad(sst.coords['latitude'].values))
wgts = np.sqrt(coslat)[..., np.newaxis]
solver = Eof(sst, weights=wgts)
# Retrieve the leading EOF, expressed as the correlation between the leading
# PC time series and the input SST anomalies at each grid point, and the
# leading PC time series itself.
eof1 = solver.eofsAsCorrelation(neofs=1)
pc1 = solver.pcs(npcs=1, pcscaling=1)
# Plot the leading EOF expressed as correlation in the Pacific domain.
clevs = np.linspace(-1, 1, 11)
ax = plt.axes(projection=ccrs.PlateCarree(central_longitude=190))
fill = eof1[0].plot.contourf(ax=ax,
levels=clevs,
cmap=plt.cm.RdBu_r,
add_colorbar=False,
transform=ccrs.PlateCarree())
def LFCA(da, N=30, L=1/10, fs=12, order=3, landmask=None, monthly=True):
"""Perform LFCA (as per Wills et al, 2018, GRL) on a dataarray.
Parameters
----------
da : xarray.DataArray
Data to perform LFCA on (time x lat x lon)
N : int
Number of EOFs to retain
L : float
Cutoff frequency for lowpass filter (e.g. 1/10 for per decade)
fs : float
Sampling frequency (1/12 for monthly)
order : int
Order of the Butterworth filter
landmask : xarray.DataArray or None
If None, do not perform any masking
If DataArray, indicates land locations
monthly : bool
If True, perform lowpass filtering for each month separately
Returns
-------
LFPs : numpy.ndarray
2D array of N spatial patterns (nlat*nlon x N)
LFCs : numpy.ndarray
2D array of N time series (ntime x N)
"""
from eofs.xarray import Eof
# remove empirical seasonal cycle
da = da.groupby('time.month') - da.groupby('time.month').mean('time')
ntime, nlat, nlon = da.shape
if landmask is not None:
# expand land mask to ntime
lnd_mask = np.repeat(is_land.values[np.newaxis, :, :], ntime, axis=0)
da = da.where(lnd_mask)
coslat = np.cos(np.deg2rad(da['lat'].values)).clip(0., 1.)
wgts = np.sqrt(coslat)[..., np.newaxis]
solver = Eof(da, weights=wgts)
eofs = solver.eofs(eofscaling=0) # normalized st L2 norm = 1
eigenvalues = solver.eigenvalues()
# Low pass filter data
if monthly:
fs = 1
nyq = 0.5 * fs # Nyquist frequency
low = L / nyq
sos = butter(order, low, btype='low', output='sos') # Coefficients for Butterworth filter
if monthly:
X_tilde = np.empty((da.shape))
for kk in range(12):
X_tilde[kk::12, :, :] = sosfiltfilt(sos, da.values[kk::12, :, :], padtype='even', axis=0)
else:
X_tilde = sosfiltfilt(sos, da.values, axis=0)
a_k = eofs.values[:N, :, :].reshape((N, nlat*nlon))
sigma_k = np.sqrt(eigenvalues.values[:N])
if landmask is not None:
lnd_mask_vec = is_land.values.flatten()
else:
lnd_mask_vec = np.ones((nlat*nlon,), dtype=bool)
PC_tilde = np.empty((ntime, N))
for kk in range(N):
PC_tilde[:, kk] = 1/sigma_k[kk]*np.dot(X_tilde.reshape((ntime, nlat*nlon))[:, lnd_mask_vec],
a_k[kk, lnd_mask_vec])
R = np.dot(PC_tilde.T, PC_tilde)/(N - 1)
R_eigvals, e_k = np.linalg.eig(R) # eigenvalues already sorted
# eigenvalues are in columns
u_k = np.dot((a_k.T)/sigma_k, e_k)
LFPs = np.dot(sigma_k*(a_k.T), e_k)
# Time series:
LFCs = np.dot(da.values.reshape((ntime, nlat*nlon))[:, lnd_mask_vec], u_k[lnd_mask_vec, :])
return LFPs, LFCs
from esmtools.stats import*
from eofs.xarray import Eof
# --- read netcdf file
dset = xr.open_dataset('asstdt_pacific.nc')
# --- select djf months
sst = dset['sst'].sel(time=np.in1d(dset['time.month'], [1, 2, 12]))
# --- square-root of cosine of latitude weights
coslat = np.cos(np.deg2rad(sst.coords['lat'].values))
wgts = np.sqrt(coslat)[..., np.newaxis]
# --- eof solver
solver = Eof(sst, weights=wgts)
# --- eof results
eofs = solver.eofsAsCorrelation(neofs=2)
pcs = solver.pcs(npcs=2, pcscaling=1)
variance_fractions = solver.varianceFraction()
north_test = solver.northTest(vfscaled=True)
# --- spatial patterns
fig, ax = plot.subplots(axwidth=5, nrows=2, tight=True, proj='pcarree',
proj_kw={'lon_0': 180})
# --- format options
ax.format(land=False, coast=True, innerborders=True, borders=True,
large='15px', labels=False,
latlim=(31, -31), lonlim=(119, 291),
geogridlinewidth=0,
r = 6.371 * 10**6 coslats = np.cos((np.pi / 180) * latts) coslats = coslats[:-1, :-1] areas = r**2 * coslats * dlats * dlons Q_s = Q_s[:, :-1, :-1] Qr = Qr[:, :-1, :-1] sst = sst[:, :-1, :-1] tendsst = tendsst[:, :-1, :-1] tot_area = np.sum(areas) weights = areas / tot_area #Calculate EOFs for SST, Qs and Qo. Should weight by area? solver = Eof(sst, weights=weights) sst_eof = solver.eofs(neofs=3, eofscaling=2) sst_eof_varfracs = solver.varianceFraction() solver = Eof(Qr, weights=weights) Qo_eof = solver.eofs(neofs=3, eofscaling=2) Qo_pc = solver.pcs(npcs=3, pcscaling=2) Qo_eof_varfracs = solver.varianceFraction() Qo_rec = solver.reconstructedField(5) Qo_rec_var = Qo_rec.var(dim='time') #get projection (pseudo-PCs) associated with Qo EOFs
def orthoModes(cls, data, nModes):
# type: (np.ndarray, int) -> np.ndarray
eof = Eof(data, None, False, False)
result = eof.eofs(0, nModes) # type: np.ndarray
result = result / (np.std(result) * math.sqrt(data.shape[1]))
return result.transpose()
def main():
ens = sys.argv[1]
sYear = sys.argv[2]
eYear = sys.argv[3]
if int(sYear) < 1920:
raise ValueError("Starting year must be 1920 or later.")
if int(eYear) > 2100:
raise ValueError("End year must be 2100 or earlier.")
print("Computing NPGO for ensemble number " + ens + "...")
filepath = ('/glade/scratch/rbrady/EBUS_BGC_Variability/' +
'global_residuals/SST/remapped/remapped.SST.' + ens +
'.192001-210012.nc')
print("Global residuals loaded...")
ds = xr.open_dataset(filepath)
ds = ds['SST'].squeeze()
# Make time dimension readable through xarray.
ds['time'] = pd.date_range('1920-01', '2101-01', freq='M')
# Reduce to time period of interest.
ds = ds.sel(time=slice(sYear + '-01', eYear + '-12'))
# Slice down to Northeast Pacific domain.
ds = ds.sel(lat=slice(25, 62), lon=slice(180, 250))
# Take annual JFM means.
month = ds['time.month']
JFM = (month <= 3)
ds_winter = ds.where(JFM).resample('A', 'time')
# Compute EOF
coslat = np.cos(np.deg2rad(ds_winter.lat.values))
wgts = np.sqrt(coslat)[..., np.newaxis]
solver = Eof(ds_winter, weights=wgts, center=False)
print("NPGO computed.")
eof = solver.eofsAsCorrelation(neofs=2)
variance = solver.varianceFraction(neigs=2)
# Reconstruct the monthly index of SSTa by projecting
# these values onto the annual PC timeseries.
pseudo_pc = solver.projectField(ds, neofs=2, eofscaling=1)
# Set up as dataset.
ds = eof.to_dataset()
ds['pc'] = pseudo_pc
ds['variance_fraction'] = variance
ds = ds.rename({'eofs': 'eof'})
ds = ds.sel(mode=1)
# Invert to the proper values for the bullseye.
if ds.sel(lat=45.5, lon=210).eof < 0:
pass
else:
ds['eof'] = ds['eof'] * -1
ds['pc'] = ds['pc'] * -1
# Change some attributes for the variables.
ds['eof'].attrs['long_name'] = 'Correlation between PC and JFM SSTa'
ds['pc'].attrs['long_name'] = 'Principal component for NPGO'
# Add a description of methods for clarity.
ds.attrs[
'description'] = 'Second mode of JFM SSTa variability over 25-62N and 180-110W.'
ds.attrs[
'anomalies'] = 'Anomalies were computed by removing the ensemble mean at each grid cell.'
ds.attrs['weighting'] = (
'The native grid was regridded to a standard 1deg x 1deg (180x360) grid.'
+ 'Weighting was computed via the sqrt of the cosine of latitude.')
print("Saving to netCDF...")
ds.to_netcdf('/glade/p/work/rbrady/NPGO/NPGO.' + ens + '.' + str(sYear) +
'-' + str(eYear) + '.nc')
# Begining
"""
# Create an EOF solver to do the EOF analysis.
# Square-root of cosine of
# latitude weights are applied before the computation of EOFs.
# scaling values to avoid overrepresented areas
# np.clip: Given an interval, values outside the interval are clipped to
# the interval edges. For example, if an interval of [0, 1] is specified,
# values smaller than 0 become 0, and values larger than 1 become 1.
coslat = np.cos(np.deg2rad(m_anomalie.coords['lat'].values)).clip(0., 1.)
# np.newaxis add a dimention to wgts. dont know what ... does
# i think its like a transposed. It took all the objects on a list and
# make a new list with lists inside (each list with only one object)
# just an adjustment of format
wgts = np.sqrt(coslat)[..., np.newaxis]
solver = Eof(m_anomalie.hgt, weights=wgts)
# Retrieve the leading EOF, expressed as the covariance between the leading PC
# time series and the input SLP anomalies at each grid point.
eof1 = solver.eofsAsCovariance(neofs=2)
# Plot the leading EOF expressed as covariance in the European/Atlantic domain.
clevs = np.linspace(-75, 75, 11)
proj = ccrs.Orthographic(0, 90)
ax = plt.axes(projection=proj)
ax.coastlines()
ax.set_global()
eof1.sel(mode=0).plot.contourf(ax=ax,
levels=clevs,
cmap=plt.cm.RdBu_r,
transform=ccrs.PlateCarree(),