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2d_spec_estimate_eta.py
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2d_spec_estimate_eta.py
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def spec_est2(A,d1,d2,win=True):
""" computes 2D spectral estimate of A
obs: the returned array is fftshifted
and consistent with the f1,f2 arrays
d1,d2 are the sampling rates in rows,columns """
import numpy as np
l1,l2,l3 = A.shape
df1 = 1./(l1*d1)
df2 = 1./(l2*d2)
f1Ny = 1./(2*d1)
f2Ny = 1./(2*d2)
f1 = np.arange(-f1Ny,f1Ny-df1,df1)
f2 = np.arange(-f2Ny,f2Ny,df2)
if win == True:
wx = np.matrix(np.hanning(l1))
wy = np.matrix(np.hanning(l2))
window_s = np.repeat(np.array(wx.T*wy),l3).reshape(l1,l2,l3)
else:
window_s = np.ones((l1,l2,l3))
an = np.fft.fft2(A*window_s,axes=(0,1))
E = (an*an.conjugate()) / (df1*df2) / ((l1*l2)**2)
E = np.fft.fftshift(E)
E = E.mean(axis=2)
return np.real(E),f1,f2,df1,df2,f1Ny,f2Ny
def spec_est2_2(A,d1,d2,win=True):
""" computes 2D spectral estimate of A
obs: the returned array is fftshifted
and consistent with the f1,f2 arrays
d1,d2 are the sampling rates in rows,columns """
import numpy as np
l1,l2 = A.shape
df1 = 1./(l1*d1)
df2 = 1./(l2*d2)
f1Ny = 1./(2*d1)
f2Ny = 1./(2*d2)
f1 = np.arange(-f1Ny,f1Ny-df1,df1)
f2 = np.arange(-f2Ny,f2Ny,df2)
wx = np.matrix(np.hanning(l1))
wy = np.matrix(np.hanning(l2))
window_s = np.array(wx.T*wy)
an = np.fft.fft2(A*window_s,axes=(0,1))
E = (an*an.conjugate()) / (df1*df2) / ((l1*l2)**2)
E = np.fft.fftshift(E)
return np.real(E),f1,f2,df1,df2,f1Ny,f2Ny
if __name__=='__main__':
import matplotlib.pyplot as plt
import numpy as np
import scipy.signal
import scipy as sp
import glob, os
import seawater.csiro as sw
import aux_func_3dfields as my
plt.close('all')
plt.rcParams.update({'font.size': 24, 'legend.handlelength' : 1.5
, 'legend.markerscale': 14., 'legend.linewidth': 3.})
iz = 0 # vertical level [m]
data_path = '/Users/crocha/Data/llc4320/eta/2011*'
grid_path= '/Users/crocha/Data/llc4320/eta/'
grid = np.load(grid_path+'grid.npz')
lons = grid['lon'][300,:]
lats = grid['lat'][:,300]
flats = (lats>-62.)
flons = (lons<-49.)
lons=lons[flons]
lats=lats[flats]
# projection onto regular grid
lati = np.linspace(lats.min(),lats.max(),lats.size)
loni = np.linspace(lons.min(),lons.max(),lons.size)
loni,lati = np.meshgrid(loni,lati)
# griduv = np.load('grid_uv_i.npz')
# loni,lati = griduv['lon'],griduv['lat']
# dx,dy = griduv['dx'],griduv['dy']
dist,ang = sw.dist(loni[300,:],lati[300,:])
dx = dist.mean() # [km], about 1 km
dist,ang = sw.dist(loni[:,300],lati[:,300])
dy = dist.mean() # [km], about 1 km
files = sorted(glob.glob(data_path), key=os.path.getmtime)
Eetaw = np.zeros((lats.size,lons.size,np.array(files).size))
Eetawf = np.zeros((lats.size,lons.size,np.array(files).size))
Eugw = np.zeros((lats.size,lons.size,np.array(files).size))
Eugwf = np.zeros((lats.size,lons.size,np.array(files).size))
Evgw = np.zeros((lats.size,lons.size,np.array(files).size))
Evgwf = np.zeros((lats.size,lons.size,np.array(files).size))
# constant for geostrophic vel.
f = np.repeat(sw.cor(lats),lons.size).reshape(lats.size,lons.size)
C = 9.81/f
kk = 0
for file in sorted(files):
data = np.load(file)
print kk
ix,jx,kx = data['eta'].shape
etai = np.zeros((lats.size,lons.size,kx))
ugi = np.zeros((lats.size,lons.size,kx))
vgi = np.zeros((lats.size,lons.size,kx))
# mask bad data
ETA = data['eta']
deta = np.diff(ETA,axis=2).sum(axis=2) == 0 # points where variable doesn't
# change over time
#ETA[deta] = np.nan
#ETA = np.ma.masked_array(ETA,np.isnan(ETA))
for i in range(kx):
etaaux=ETA[:,flons,i]
etaaux=etaaux[flats,:]
interp_eta = sp.interpolate.interp2d(lons,lats,etaaux,kind='linear')
etai[:,:,i] = interp_eta(loni[300,:],lati[:,300])
ugi[:,:,i],b = -C*sp.gradient(etai[:,:,i],dy*1.e3)
a,vgi[:,:,i] = C*sp.gradient(etai[:,:,i],dx*1.e3)
Eetaw[:,:,kk],lw,kw,dlw,dkw,flNyw,fkNyw = spec_est2(etai,dy,dx)
Eetawf[:,:,kk],lwf,kwf,dlwf,dkwf,flNywf,fkNywf = spec_est2_2(etai.mean(axis=2),dy,dx)
Eugw[:,:,kk],l,k,dl,dk,flNy,fkNy = spec_est2(ugi,dy,dx)
Eugwf[:,:,kk],_,_,_,_,_,_ = spec_est2_2(ugi.mean(axis=2),dy,dx)
Evgw[:,:,kk],_,_,_,_,_,_ = spec_est2(vgi,dy,dx)
Evgwf[:,:,kk],_,_,_,_,_,_ = spec_est2_2(vgi.mean(axis=2),dy,dx)
kk = kk + 1
del data,etai,ix,jx,kx,ETA,ugi,vgi,etaaux
Ew = Eetaw.mean(axis=2)
Ewf = Eetawf.mean(axis=2)
Eu = Eugw.mean(axis=2)
Euf = Eugwf.mean(axis=2)
Ev = Evgw.mean(axis=2)
Evf = Evgwf.mean(axis=2)
Eg = (Eu+Ev)/2.
Egf = (Euf+Evf)/2.
# isotropic spectral estimate
ki,li = np.meshgrid(kw,lw)
K = np.sqrt(ki**2+li**2)
K = np.ma.masked_array(K,K<1.e-10)
phi = np.math.atan2(dlw,dkw)
dK = dkw*np.cos(phi)
Ki = np.arange(K.min(),K.max(),dK)
K_w = (Ki[1:]+Ki[0:-1])/2.
dK2 = dK/2.
Eiso_w = np.zeros(K_w.size)
for i in range(K_w.size):
f = (K>=K_w[i]-dK2)&(K<K_w[i]+dK2)
dtheta = (2*np.pi)/np.float(f.sum())
Eiso_w[i] = ((Ew[f].sum()))*K_w[i]*dtheta
ki,li = np.meshgrid(kwf,lwf)
K = np.sqrt(ki**2+li**2)
K = np.ma.masked_array(K,K<0.0023)
phi = np.math.atan2(dlwf,dkwf)
dK = dkwf*np.cos(phi)
Ki = np.arange(K.min(),K.max(),dK)
K_wf = (Ki[1:]+Ki[0:-1])/2.
dK2 = dK/2.
Eiso_wf = np.zeros(K_wf.size)
for i in range(K_wf.size):
f = (K>=K_wf[i]-dK2)&(K<K_wf[i]+dK2)
dtheta = (2*np.pi)/np.float(f.sum())
Eiso_wf[i] = ((Ewf[f].sum()))*K_wf[i]*dtheta
# isotropic spectral estimate
ki,li = np.meshgrid(k,l)
K = np.sqrt(ki**2+li**2)
K = np.ma.masked_array(K,K<1.e-10)
phi = np.math.atan2(dl,dk)
dK = dk*np.cos(phi)
Ki = np.arange(K.min(),K.max(),dK)
K_g = (Ki[1:]+Ki[0:-1])/2.
dK2 = dK/2.
Eiso_g = np.zeros(K_g.size)
for i in range(K_g.size):
f = (K>=K_g[i]-dK2)&(K<K_g[i]+dK2)
dtheta = (2*np.pi)/np.float(f.sum())
Eiso_g[i] = ((Eg[f].sum()))*K_g[i]*dtheta
# isotropic spectral estimate
ki,li = np.meshgrid(k,l)
K = np.sqrt(ki**2+li**2)
K = np.ma.masked_array(K,K<1.e-10)
phi = np.math.atan2(dl,dk)
dK = dk*np.cos(phi)
Ki = np.arange(K.min(),K.max(),dK)
K_gf = (Ki[1:]+Ki[0:-1])/2.
dK2 = dK/2.
Eiso_gf = np.zeros(K_g.size)
for i in range(K_gf.size):
f = (K>=K_gf[i]-dK2)&(K<K_gf[i]+dK2)
dtheta = (2*np.pi)/np.float(f.sum())
Eiso_gf[i] = ((Egf[f].sum()))*K_gf[i]*dtheta
# save for comparison
fno = 'outputs/Eiso_eta_small'
np.savez(fno,Ew=Eiso_w,Ewf=Eiso_wf,K_w = K_w,K_wf=K_wf, Eiso_g=Eiso_g,Eiso_gf=Eiso_gf,
K_g=K_g,K_gf=K_gf)
# integrating in k or l
Elw = 2*(Ew.sum(axis=1)*dkw)[lw.size/2:]
Ekw = 2*(Ew.sum(axis=0)*dlw)[kw.size/2:]
kxw = kw[kw.size/2:]
lyw = lw[lw.size/2:]
Elwf = 2*(Ewf.sum(axis=1)*dkw)[lw.size/2:]
Ekwf = 2*(Ewf.sum(axis=0)*dlw)[kw.size/2:]
# mask low wavenumbers
kref = 0.0022
fw = (K_w > kref); K_w = K_w[fw]; Eiso_w = Eiso_w[fw]
fw = (K_wf > kref); K_wf = K_wf[fw]; Eiso_wf = Eiso_wf[fw]
fw = (kxw > kref); kxw = kxw[fw]; Ekw = Ekw[fw]
fw = (lyw > kref); lyw = lyw[fw]; Elw = Elw[fw]
# plotting
ks = np.array([1.e-3,1])
Es2 = .2e-7*(ks**(-3))
Es3 = .5e-11*(ks**(-5))
fig = plt.figure(facecolor='w', figsize=(12.,8.5))
plt.loglog(kxw,Ekw,color='b',label='Ek',linewidth=4.,alpha=.5)
plt.loglog(lyw,Elw,color='g',label='El',linewidth=4.,alpha=.5)
plt.loglog(K_w,Eiso_w,color='m',linewidth=4.,alpha=.5)
plt.loglog(K_wf,Eiso_wf,color='r',linewidth=4.,alpha=.5)
plt.loglog(ks,Es2,'--', color='k',linewidth=2.,alpha=.5)
plt.loglog(ks,Es3,'--', color='k',linewidth=2.,alpha=.5)
plt.text(0.0011686481894527252, 5.4101984795026086/2.,u'k$^{-3}$')
plt.text(0.0047869726184615827, 5.5118532543417871/2.,u'k$^{-5}$')
plt.axis((1./(1000),1.,.4e-7,10))
plt.ylabel('Spectral density [m$^2$/(cycles/km)]')
plt.xlabel('Wavenumber [cycles/km]')
plt.savefig('figs/Eiso_eta')