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2d_spec_estimate_uv_nondiv.py
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/
2d_spec_estimate_uv_nondiv.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)
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 ps(u,v,dx,dy):
""" decompose the vector field (u,v) into potential (up,vp)
and solenoidal (us,vs) fields using 2D FT a la Smith JPO 2008 """
ix,jx,kx = u.shape
dl = 1./(ix*dy)
dk = 1./(jx*dx)
kNy = 1./(2*dx)
lNy = 1./(2*dy)
k = np.arange(-kNy,kNy,dk)
k = np.fft.fftshift(k)
l = np.arange(-lNy,lNy,dl)
l = np.fft.fftshift(l)
K,L = np.meshgrid(k,l)
THETA = (np.arctan2(L,K))
THETA = np.repeat(THETA,kx).reshape(ix,jx,kx)
U = np.fft.fft2(u,axes=(0,1))
V = np.fft.fft2(v,axes=(0,1))
P = U*np.cos(THETA) + V*np.sin(THETA)
S = -U*np.sin(THETA) + V*np.cos(THETA)
# back to physical space
up = np.real(np.fft.ifft2(P*np.cos(THETA),axes=(0,1)))
vp = np.real(np.fft.ifft2(P*np.sin(THETA),axes=(0,1)))
us = np.real(np.fft.ifft2(-S*np.sin(THETA),axes=(0,1)))
vs = np.real(np.fft.ifft2(S*np.cos(THETA),axes=(0,1)))
return up,vp,us,vs
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/uv/'+str(iz)+'m/*'
grid_path= '/Users/crocha/Data/llc4320/uv/'
grid = np.load(grid_path+'grid.npz')
lons = grid['lon'][300,:]
lats = grid['lat'][:,300]
# 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)
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)
Eund = np.zeros((lats.size,lons.size,np.array(files).size))
Evnd = np.zeros((lats.size,lons.size,np.array(files).size))
Eud = np.zeros((lats.size,lons.size,np.array(files).size))
Evd = np.zeros((lats.size,lons.size,np.array(files).size))
# save loni and lati in order to put SSH in the same grid
lonuv,latuv = loni[300,:],lati[:,300]
np.savez('grid_uv_i',lon=lonuv,lat=latuv,dx=dx,dy=dy)
kk = 0
for file in sorted(files):
data = np.load(file)
print kk
ix,jx,kx = data['u'].shape
ui = np.zeros((ix,jx,kx))
vi = np.zeros((ix,jx,kx))
for i in range(kx):
interp_u = sp.interpolate.interp2d(lons,lats,data['u'][:,:,i],kind='linear')
ui[:,:,i] = interp_u(loni[300,:],lati[:,300])
interp_v = sp.interpolate.interp2d(lons,lats,data['v'][:,:,i],kind='linear')
vi[:,:,i] = interp_v(loni[300,:],lati[:,300])
# apply spectral window before decomposing the flow
l1,l2,l3 = ui.shape
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)
# decompose the flow
#up,vp,us,vs = ps(ui*window_s,vi*window_s,dx,dy)
up,vp,us,vs = ps(ui,vi,dx,dy)
Eund[:,:,kk],lnd,knd,dlnd,dknd,flNynd,fkNynd = spec_est2(us,dy,dx,win=True)
Evnd[:,:,kk],_,_,_,_,_,_ = spec_est2(vs,dy,dx,win=True)
Eud[:,:,kk],ld,kd,dld,dkd,flNyd,fkNyd = spec_est2(up,dy,dx,win=True)
Evd[:,:,kk],_,_,_,_,_,_ = spec_est2(vp,dy,dx,win=True)
kk = kk + 1
del data, ui,vi,ix,jx,kx,us,vs,up,vp
Eund = Eund.mean(axis=2)
Evnd = Evnd.mean(axis=2)
End = (Eund+Evnd)/2
Eud = Eud.mean(axis=2)
Evd = Evd.mean(axis=2)
Ed = (Eud+Evd)/2
# isotropic spectral estimate
ki,li = np.meshgrid(knd,lnd)
K = np.sqrt(ki**2+li**2)
K = np.ma.masked_array(K,K<1.e-10)
phi = np.math.atan2(dlnd,dknd)
dK = dknd*np.cos(phi)
Ki = np.arange(K.min(),K.max(),dK)
K_nd = (Ki[1:]+Ki[0:-1])/2.
dK2 = dK/2.
Eiso_nd = np.zeros(K_nd.size)
for i in range(K_nd.size):
f = (K>=K_nd[i]-dK2)&(K<K_nd[i]+dK2)
dtheta = (2*np.pi)/np.float(f.sum())
Eiso_nd[i] = ((End[f].sum()))*K_nd[i]*dtheta
# isotropic spectral estimate
ki,li = np.meshgrid(kd,ld)
K = np.sqrt(ki**2+li**2)
K = np.ma.masked_array(K,K<1.e-10)
phi = np.math.atan2(dld,dkd)
dK = dkd*np.cos(phi)
Ki = np.arange(K.min(),K.max(),dK)
K_d = (Ki[1:]+Ki[0:-1])/2.
dK2 = dK/2.
Eiso_d = np.zeros(K_d.size)
for i in range(K_d.size):
f = (K>=K_d[i]-dK2)&(K<K_d[i]+dK2)
dtheta = (2*np.pi)/np.float(f.sum())
Eiso_d[i] = ((Ed[f].sum()))*K_d[i]*dtheta
fno='outputs/Eiso_KE_nondiv_div'
np.savez(fno,Eiso_d=Eiso_d,K_d=K_d,Eiso_nd=Eiso_nd,K_nd=K_nd)
# integrating in k or l
Elm = 2*(Em.sum(axis=1)*dkm)[lm.size/2:]
Ekm = 2*(Em.sum(axis=0)*dlm)[km.size/2:]
kxm = kw[km.size/2:]
lym = lw[lm.size/2:]
# plotting
ks = np.array([1.e-3,1])
Es2 = .2e-4*(ks**(-2))
Es3 = .5e-6*(ks**(-3))
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(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$^{-2}$')
plt.text(0.0047869726184615827, 5.5118532543417871/2.,u'k$^{-3}$')
plt.axis((1./(1000),1.,.4e-5,10))
plt.ylabel('Spectral density [(m$^2$s$^{-2}$)/(cycles/km)]')
plt.xlabel('Wavenumber [cycles/km]')
plt.savefig('figs/Eiso_uv_nondiv')