def __init__(self, var, maxvalue=0., fillvalue=0., shoreline=None):
if var.getLongitude() is None:
var.getAxis(1).designateLongitude()
if var.getLatitude() is None:
var.getAxis(1).designateLatitude()
if var.getGrid() is None:
var.setGrid(create_grid(var.getLongitude(), var.getLatitude()))
self._bathy = var
self._xres, self._yres = resol(self.get_grid())
_GriddedBathyMasked_.__init__(self, shoreline=shoreline, fillvalue=fillvalue, maxvalue=maxvalue)
self._lon2d, self._lat2d = meshgrid(self.get_lon(), self.get_lat())
# self._lon2dp,self._lat2dp = meshbounds(self.get_lon(), self.get_lat())
self._xxs = self._yys = None
import pylab as P
# Création de bathymétries fictives à partir de Smith and Sandwell
import cdms2
from vacumm.config import data_sample
cdms2.axis.longitude_aliases.append('x')
cdms2.axis.latitude_aliases.append('y')
f = cdms2.open(data_sample('ETOPO2v2g_flt.grd'))
# - large
var_large = f('z', lon=(-7, -1), lat=(46, 49))
# - petite
var_small = f('z', lon=(-4.5, -.5), lat=(44.5, 46.5))
f.close()
# - regrillage de la large vers une grille moins fine
from vacumm.misc.grid import regridding, resol, create_grid
xr, yr = resol(var_large.getGrid())
grid_large = create_grid((-7., -1, xr * 4.5), (46., 49, yr * 4.5))
var_large = regridding.regrid2d(var_large, grid_large)
# On ajoute un traît de côte pour le masquage
from vacumm.bathy.bathy import GriddedBathy, GriddedBathyMerger
bathy_large = GriddedBathy(var_large, shoreline='i')
bathy_small = var_small
# Création de la grille finale de résolution intermédiaire
final_grid = create_grid((-6., .5, xr * 2.5), (45, 47., yr * 2.5))
# On crée maintenant le merger
merger = GriddedBathyMerger(final_grid)
# - ajout de la bathy basse resolution en premier (en dessous)
merger += bathy_large
def get_spec(var1, var2=None, dx=None, dy=None, verbose=False, fft=False, **kwargs):
"""Get the spectrum of a 2D variable
:Return: specvar,nbwave,dk
"""
# Get the resolution in meters
kwresol = kwfilter(kwargs, 'resol_')
if None in [dx, dy]:
if not cdms2.isVariable(var1):
raise TypeError('var1 must be a MV2 array to compute dx and dy')
kwresol.setdefault('proj', True)
ldx, ldy = resol(var1, **kwresol)
dx = dx or ldx
dy = dy or ldy
if N.ma.isMA(var1): var1= var1.filled(0.)
if N.ma.isMA(var2): var2 = var2.filled(0.)
# Part 1 - estimate of the wavenumbers
[kx,ky,kkx,kky,kk,Lx,Ly] = get_kxky(var1, dx, dy, verbose=verbose)
if verbose:
print "dx = %s, fy = %s " %(dx,dy)
print "kx = ",kx[0:3]
print "ky = ",ky[0:3]
print "kkx[0:3,2] = ",kkx[0:3,2]
print "kky[0:3,1] = ",kky[0:3,1]
print "kk[0:3,3] = ",kk[0:3,3]
print "shape",kx.shape,ky.shape,kkx.shape,kky.shape,kk.shape
# Part 2 - estimate of the spectrum
# - fast fourier transform
if fft:
hat_phi1=N.fft.fft2(var1)
hat_phi1=hat_phi1*hat_phi1.conj()
hat_phi1=hat_phi1.real.copy() # useless
else:
hat_phi1 = var1
if var2 is not None:
if fft:
hat_phi2=N.fft.fft2(var2)
hat_phi2=hat_phi2*hat_phi2.conj()
hat_phi2=hat_phi2.real.copy() # useless
else:
hat_phi2 = var2
hat_spec = hat_phi1 + hat_phi2
else:
hat_spec = hat_phi1
# - integration of the spectrum
# shift to have values centered on the intervals
dk = kx[1] - kx[0]
dk_half = dk/2 # half of the interval
k_= kx[0:min(var1.shape[1],var1.shape[0])/2] + dk
specvar = k_*0
for i in range(len(k_)):
# get indexes that satisfy two conditions
# integration over a spectral width
specvar[i] = ( hat_spec[ (kk<=k_[i]+dk_half) & (kk>k_[i]-dk_half) ] ).sum()
# Normalisation (Danioux 2011)
specvar /= (var1.shape[1]*var1.shape[0])**2 * dk
# Dimensionalization to be able to compare with the litterature
nbwave = k_*1000.0/2.0/N.pi # from rad/m to km/m
dk *= 1000.0/2.0/N.pi
specvar *= 2.0*N.pi/1000.0
if verbose:
if var2 is not None:
print "\n Normalized co-spectrum : \n",specvar
else:
print "\n Normalized spectrum : \n",specvar
return specvar,nbwave,dk
def energy_spectrum(var, dx=None, dy=None, ctime=None, dispfig=False, latmean=None, verbose=False):
"""Compute the energy spectrum of a 2D variable"""
# Guess dx and/or dy
if None in [dx, dy]:
if not cdms2.isVariable(var):
raise TypeError('var must be a MV2 array to compute dx and dy')
kwresol.setdefault('proj', True)
ldx, ldy = resol(var, **kwresol)
dx = dx or ldx
dy = dy or ldy
if latmean is None:
if not cdms2.isVariable(var):
raise Exception('You must provide explicitly latmean')
latmean = var.getLatitude().getValue().mean()
# Numpy arrays
sshbox = var.filled(0.) if N.ma.isMA(var) else var
#####################################################
# estimate of the spatial resolution and the latitude
#####################################################
grav = 9.81
#latmean = int(float(latmean))
#dx = int(grid[0])*np.cos(np.pi*latmean/180.)
f0 = 2*N.pi/(24.*3600.)*2.0*N.sin(N.pi*latmean/180.)
gof0 = grav/f0
if verbose:
print "the spatial resolution of the grid is constant \n dx = %s m, dy = %s m" %(dx,dy)
print "the averaged latitude is %s degrees\n" %(latmean)
###############################################
# 1ST PART ANALYZE FROM THE SEA SURFACE HEIGHT
# --------------------------------------------
###############################################
# zonal average and its removing from ssh
# mean on i (we erase 1 dimension)
# and duplication along i (depends on sshbox.mean(1).shape)
# then we need to transpose to have constant value along i and variations along j
#revoir sshbox = sshbox - N.tile( sshbox.mean(1),(sshbox.shape[1],1) ).T
# plot of ssh (box domain)
#if options.dispfig: plot.contour_xy(sshbox,sshbox.shape[0],sshbox.shape[1],'ssh_box_minus_iaverage')
# estimate of the rms to further check
sshbox_rms = N.sqrt( (sshbox**2).mean() )
if verbose: print "rms of the ssh over the region of interest (from physical field) : %s \n" %sshbox_rms
################################
# create a double periodic field
################################
ssh2per = N.tile( sshbox, (2,2) )
ssh2per[ssh2per.shape[0]/2:ssh2per.shape[0],0:ssh2per.shape[1]/2] = sshbox[::-1,::]
ssh2per[::,ssh2per.shape[1]/2:] = N.fliplr(ssh2per[::,0:ssh2per.shape[1]/2])
#if options.dispfig: plot.contour_xy(ssh2per,ssh2per.shape[0],ssh2per.shape[1],'ssh_double_periodic')
del sshbox
# estimate of the rms to further check
ssh2per_rms = N.sqrt( (ssh2per**2).mean() )
if verbose: print "rms of the double periodic ssh over the region of interest (from physical field) : %s \n" %ssh2per_rms
################################
# wavenumber spectrum of the ssh (double periodic field)
################################
# estimate of the spectrum
ssh2per_spec, ssh2per_k, dk = get_spec(ssh2per, dx=dx, dy=dy, fft='x2k', verbose=verbose) # sshbox in physical space
# make sure the FFT is correct : we must have the same rms either from physics or from wavenumbers
ssh2per_rmsk = N.sqrt( (ssh2per_spec*dk).sum() )
if verbose: print "rms of the ssh over the region of interest (from wave number fields) : %s \n" %ssh2per_rmsk
# figure
if dispfig: plot_loglog_kspec(ssh2per_spec, ssh2per_k, savefig='ssh2per_spec',
title='SPECTRUM OF SSH (double periodic)', subtitle=str(ctime),
xlabel='Wavenumber (cycles/km)', ylabel='SSH [m^2/(cycle/km)]',
slope=-5)
###########################################
# the ssh pectrum after doubling the domain
# is much better than the previous one
###########################################
####################################################
# 2ND PART ANALYZIS FROM THE GEOSTROPHIC VELOCITIES
# -------------------------------------------------
####################################################
###########################################
# estimate of the geostrophic velocities (from the spectrum of the periodic field of ssh)
###########################################
# estimate of the wavenumbers
kx,ky,kkx,kky,kk,Lx,Ly = get_kxky(ssh2per, dx, dy, verbose=verbose)
# estimate of the velocities from the spectrum of the ssh
ussh = -gof0*N.fft.ifft2( (kky*N.fft.fft2(ssh2per))*N.complex(0,1) ).real
vssh = gof0*N.fft.ifft2( (kkx*N.fft.fft2(ssh2per))*N.complex(0,1) ).real
#if options.dispfig: plot.contour_xy(ussh,ussh.shape[0],ussh.shape[1],'ussh (from double periodic field spectral method) ')
#if options.dispfig: plot.contour_xy(vssh,vssh.shape[0],vssh.shape[1],'vssh (from double periodic field and spectral method) ')
ssh2per_shape = ssh2per.shape
del ssh2per
#######################################################
# wavenumber co-spectrum of the geostrophic velocities (eke)
#######################################################
# estimate of the co-spectrum
uv2per_cospec,eke_k,dk = get_cospec(ussh, vssh, dx=dx, dy=dy, verbose=verbose, fft=True)
# estimate of the eke to further check
uv2per_rmsk = N.sqrt( ((uv2per_cospec*dk)/2.).sum() )
if verbose: print "eke over the region of interest (from physical field) : %s \n" %uv2per_rmsk
# make sure the FFT is correct : we must have the same rms either from physics or from wavenumbers
#ssh2per_rmsk = N.sqrt( (ssh2per_spec*dk).mean() )
#if verbose: print "eke over the region of interest (from physical field) : %s \n" %sshbox_rms
#if verbose: print "rms of the ssh over the region of interest (from wave number fields) : %s \n" %ssh2per_rmsk
#if verbose: print "rms difference (wavenumber - physics) : %s \n" %(ssh2per_rmsk-ssh2per_rms)
# figure
if dispfig:
plot_loglog_kspec(uv2per_cospec, eke_k, savefig='eke2per_spec',
title='SPECTRUM OF EKE', subtitle=str(ctime),
xlabel='Wavenumber (cycles/km)', ylabel='EKE [(m/s)^2/(cycle/km)]')
####################################################
# 3RD PART ESTIMATE OF THE FLUXES OF ENERGY
# -------------------------------------------------
####################################################
###########################################
# estimate of the production of eke
###########################################
# geostrophic velocities in the spectral space are non zero in the bottom-left corner
ug = ussh.copy() ; del ussh
ug[ssh2per_shape[0]/2:ssh2per_shape[0],::] = 0.
ug[::,ssh2per_shape[1]/2:] = 0.
vg = vssh.copy() ; del vssh
vg[ssh2per_shape[0]/2:ssh2per_shape[0],::] = 0.
vg[::,ssh2per_shape[1]/2:] = 0.
#if options.dispfig: plot.contour_xy(ug,ug.shape[0],ug.shape[1],'ug (from the spectrum of the periodic ssh)')
#if options.dispfig: plot.contour_xy(vg,vg.shape[0],vg.shape[1],'vg (from the spectrum of the periodic ssh)')
u = N.fft.fft2(ug)
v = N.fft.fft2(vg)
ugx = N.fft.ifft2( (u*kkx)*N.complex(0,1) ).real
ugy = N.fft.ifft2( (u*kky)*1j ).real
vgx = N.fft.ifft2( (v*kkx)*1j ).real
vgy = N.fft.ifft2( (v*kky)*1j ).real
term_u = N.fft.fft2(ug*ugx + vg*ugy)
term_v = N.fft.fft2(ug*vgx + vg*vgy)
eke_prod = - ( u.conj()*term_u + v.conj()*term_v ).real
eke_prod_phys1=N.fft.ifft2(eke_prod).real
#if options.dispfig: plot.contour_xy(eke_prod_phys1,eke_prod_phys1.shape[0],eke_prod_phys1.shape[1],'eke_prod_phys1')
term_u = 1j*kkx*N.fft.fft2(ug*ug) + 1j*kky*N.fft.fft2(vg*ug)
term_v = 1j*kkx*N.fft.fft2(ug*vg) + 1j*kky*N.fft.fft2(vg*vg)
eke_prod = - ( u.conj()*term_u + v.conj()*term_v ).real
eke_prod_phys2=N.fft.ifft2(eke_prod).real
#if options.dispfig: plot.contour_xy(eke_prod_phys2,eke_prod_phys2.shape[0],eke_prod_phys2.shape[1],'eke_prod_phys2')
#if options.dispfig: plot.contour_xy(eke_prod_phys1-eke_prod_phys2,eke_prod_phys2.shape[0],eke_prod_phys2.shape[1],'diff_eke_prod')
phi = eke_prod_phys1-eke_prod_phys2
# estimate of the total energy flux of the momentum equation
gg_spec, gg_k, dk = get_spec(eke_prod, dx=dx, dy=dy, verbose=verbose, fft=False) # phi in Fourier space
# choose kmax1 such that it corresponds to gg_k(kmax1) < 1/(3*dx)*1000 [km/m] (2dx Shanon + take into account diffusion)
kmax1 = min( N.where(gg_k>= 1/(3.0*dx)*1000.)[0][0] - 1 ,gg_spec.shape[0])
if verbose: print "Shanon criterium kmax1 = %s, gg_k(kmax1) = %s, gg_k(kmax1+1) = %s, 1/(3.0*dx)*1000. = %s" %(kmax1,gg_k[kmax1],gg_k[kmax1+1],1/(3.0*dx)*1000.)
# integration from large scales to small ones (shift one large scales)
tpi = N.array( [sum(gg_spec[ i:kmax1 ]) for i in range(kmax1)] )
tpi[0]=0.
# figure
if dispfig:
plot_semilogx_kspec(tpi, gg_k[:kmax1], savefig='ssh_spec',
title='TOTAL ENERGY FLUX', subtitle=str(ctime),
xlabel='Wavenumber (cycles/km)', ylabel='Sum of EKE from small scales to k [(m/s)^2/(cycle/km)]')
if verbose: print "The end !"
del grav,f0,gof0,sshbox_rms,ssh2per_rms,dk,kx,ky,kkx,kky,kk,Lx,Ly,uv2per_rmsk,ug,vg,u,v,term_u,term_v,ugx,ugy,vgx,vgy,eke_prod,eke_prod_phys1,eke_prod_phys2,phi,gg_spec
gc.collect()
return ssh2per_spec, ssh2per_k, uv2per_cospec, eke_k, tpi, gg_k[:kmax1]
y = xyz.y z = xyz.z # %% Extensions # - en tenant compte des zones de selection et exclusion print 'Limites:', xyz.xmin, xyz.xmax, xyz.ymin, xyz.ymax # - donnees brutes print 'X min brut:', xyz.get_xmin(mask=False), xyz.get_x(mask=False).min() # %% Mean resolution print 'Resolution in degrees:', xyz.resol(deg=True) print 'Resolution in meters:', xyz.resol() # %% Automatic grid grid_auto = xyz.grid print 'Resolution of auto grid:', resol(grid_auto) # %% Interpolation on auto grid print 'Interpolation:' gridded_auto = xyz.togrid() # equivalent a : # >>> gridded_auto = xyz.togrid(xyz.grid) # %% Interpolation on manual grid print 'Interpolation and masking, then extraction' # - defintion grid_manual = create_grid((-5.3, -4.91, .01), (48.1, 48.41, .01)) # - interpolation gridded_manual = xyz.togrid(grid_manual, mask='h') # - extraction with margin xyz_up = xyz.clip(zone=(None, None, None, 48.3), margin=2)
y = xyz.y z = xyz.z # Extensions # - en tenant compte des zones de selection et exclusion print 'Limites :', xyz.xmin, xyz.xmax, xyz.ymin, xyz.ymax # - donnees brutes print 'X min brut :', xyz.get_xmin(mask=False), xyz.get_x(mask=False).min() # Resolution moyenne print 'Resolution geographique :', xyz.resol(deg=True) print 'Resolution metrique :', xyz.resol() # Definition auto d'une grille reguliere grid_auto = xyz.grid print 'Resolution grille auto :', resol(grid_auto) # Interpolation sur grille auto print 'Interpolation auto' gridded_auto = xyz.togrid() # equivalent a : # >>> gridded_auto = xyz.togrid(xyz.grid) # Interpolation sur grille manuelle print 'Interpolation et masquage manuels puis extraction' # - defintion de la grille grid_manual = create_grid((-5.3, -4.91, .01), (48.1, 48.41, .01)) # - interpolation gridded_manual = xyz.togrid(grid_manual, mask='h') # Extraction d'une sous-zone (xmin,ymin...) avec marge xyz_up = xyz.clip(zone=(None, None, None, 48.3), margin=2)
lonn, latn = get_xy(gg, num=True)
grid = create_grid(*gg)
print 'Dimensions : nx=%i ny=%i' % grid.shape[::-1]
print 'Axes : lon="%s" lat="%s" (%iD)' % (lon.id, lat.id,
lonn.ndim)
# Extension
print 'Zonal extent : %s -> %s [%s -> %s]' % (
lonn.min(), lonn.max(), lonlab(
lonn.min(), decimal=False), lonlab(lonn.max(), decimal=False))
print 'Meridional extent : %s -> %s [%s -> %s]' % (
latn.min(), latn.max(), latlab(
latn.min(), decimal=False), latlab(latn.max(), decimal=False))
# Resolution
lonres, latres = resol(gg, proj=False)
xres, yres = resol(gg, proj=True)
xres /= 1000.
yres /= 1000.
print 'Zonal resolution : %g° / %gkm' % (lonres, xres)
print 'Meridional resolution: %g° / %gkm' % (latres, yres)
# Plot
if options.plot or options.out:
xmin, ymin, xmax, ymax = scalebox(grid, 1 / options.zoom)
for att in 'xmin', 'xmax', 'ymin', 'ymax':
if getattr(options, att) is not None:
exec att + " = %s" % getattr(options, att)
if options.figsize is not None:
try:
if grid is None:
sys.exit('Variable "%s" has no grid'%options.vname)
else: # loop on all variables
for vname in f.listvariables():
grid = f[vname].getGrid()
if grid is not None: break
else:
sys.exit('No variable with a grid found')
grid = (grid.getLongitude().clone(), grid.getLatitude().clone())
# VACUMM path
here = os.path.dirname(__file__)
for rpath in [os.path.join(here, '../lib/python')]:
path = os.path.abspath(rpath)
sys.path.append(path)
# Resolution
try:
from vacumm.misc.grid import resol
except:
sys.exit('Error when loading vacumm')
xres, yres = resol(grid, proj=options.meters)
if options.meters:
units = 'km'
xres /= 1000.
yres /= 1000.
else:
units = '°'
print 'dx=%(xres)g%(units)s, dy=%(yres)g%(units)s'%locals()
f.close()
y = xyz.y z = xyz.z # Extensions # - en tenant compte des zones de selection et exclusion print 'Limites :', xyz.xmin, xyz.xmax, xyz.ymin, xyz.ymax # - donnees brutes print 'X min brut :', xyz.get_xmin(mask=False), xyz.get_x(mask=False).min() # Resolution moyenne print 'Resolution geographique :', xyz.resol(deg=True) print 'Resolution metrique :', xyz.resol() # Definition auto d'une grille reguliere grid_auto = xyz.grid print 'Resolution grille auto :', resol(grid_auto) # Interpolation sur grille auto print 'Interpolation auto' gridded_auto = xyz.togrid() # equivalent a : # >>> gridded_auto = xyz.togrid(xyz.grid) # Interpolation sur grille manuelle print 'Interpolation et masquage manuels puis extraction' # - defintion de la grille grid_manual = create_grid((-5.3, -4.91, .01), (48.1, 48.41, .01)) # - interpolation gridded_manual = xyz.togrid(grid_manual, mask='h') # Extraction d'une sous-zone (xmin,ymin...) avec marge xyz_up = xyz.clip(zone=(None, None, None, 48.3), margin=2)
# Dimension
gg = (lon, lat)
lonn, latn = get_xy(gg, num=True)
grid = create_grid(*gg)
print 'Dimensions : nx=%i ny=%i'%grid.shape[::-1]
print 'Axes : lon="%s" lat="%s" (%iD)'%(lon.id, lat.id, lonn.ndim)
# Extension
print 'Zonal extent : %s -> %s [%s -> %s]'%(
lonn.min(), lonn.max(), lonlab(lonn.min(), decimal=False), lonlab(lonn.max(), decimal=False))
print 'Meridional extent : %s -> %s [%s -> %s]'%(
latn.min(), latn.max(), latlab(latn.min(), decimal=False), latlab(latn.max(), decimal=False))
# Resolution
lonres, latres = resol(gg, proj=False)
xres, yres = resol(gg, proj=True)
xres /= 1000.
yres /= 1000.
print 'Zonal resolution : %g° / %gkm'%(lonres, xres)
print 'Meridional resolution: %g° / %gkm'%(latres, yres)
# Plot
if options.plot or options.out:
xmin, ymin, xmax, ymax = scalebox(grid, 1/options.zoom)
for att in 'xmin', 'xmax', 'ymin', 'ymax':
if getattr(options, att) is not None: exec att+" = %s"%getattr(options, att)
if options.figsize is not None:
try:
options.figsize = eval(options.figsize)
# -*- coding: utf8 -*-
# Création de bathymétries fictives à partir de Smith and Sandwell
import cdms2
from vacumm.config import data_sample
cdms2.axis.longitude_aliases.append('x')
cdms2.axis.latitude_aliases.append('y')
f = cdms2.open(data_sample('ETOPO2v2g_flt.grd'))
# - large
var_large = f('z', lon=(-7, -1), lat=(46, 49))
# - petite
var_small = f('z', lon=(-4.5, -.5), lat=(44.5, 46.5))
f.close()
# - regrillage de la large vers une grille moins fine
from vacumm.misc.grid import regridding, resol, create_grid
xr, yr = resol(var_large.getGrid())
grid_large = create_grid((-7., -1, xr*4.5), (46., 49, yr*4.5))
var_large = regridding.regrid2d(var_large, grid_large)
# On ajoute un traît de côte pour le masquage
from vacumm.bathy.bathy import GriddedBathy, GriddedBathyMerger
bathy_large = GriddedBathy(var_large, shoreline='i')
bathy_small = var_small
# Création de la grille finale de résolution intermédiaire
final_grid = create_grid((-6., .5, xr*2.5), (45, 47., yr*2.5))
# On crée maintenant le merger
merger = GriddedBathyMerger(final_grid)
# - ajout de la bathy basse resolution en premier (en dessous)
merger += bathy_large
# - puis ajout de celle haute résolution
def barotropic_geostrophic_velocity(ssh,
dxy=None,
gravity=default_gravity,
cyclic=False,
format_axes=True,
getu=True,
getv=True,
filter=None):
"""Get barotropic geostropic velocity from SSH on a C-grid
.. note:: ssh is supposed to be at T points,
ubt is computed at V points,
and vbt is computed at U points.
.. todo:: Rewrite it using :mod:`vacumm.data.misc.arakawa` and defining
a limited number of algorithms for different staggering configurations.
:Params:
- **ssh**: Sea surface height.
- **dxy**, optional: Horizontal resolutions (m).
Resolution along X and Y are respectively at U and V points.
Possible forms:
- ``res``: A scalar meaning a constant resolution along X and Y.
- ``(dx,dy)``: A tuple of resolutions along X and Y.
- ``None``: Resolution is estimated using
:func:`~vacumm.misc.grid.misc.resol`.
:Return: ``(ubt,vbt)``
"""
if not getu and not getv: return
# Init masked
if getu: ugbt = format_var(ssh * MV2.masked, 'ugbt', format_axes=False)
if getv: vgbt = format_var(ssh * MV2.masked, 'vgbt', format_axes=False)
# Grid
tgrid = ssh.getGrid()
if getu: ugrid = shiftgrid(tgrid, ishift=0.5)
if getv: vgrid = shiftgrid(tgrid, jshift=0.5)
if format_axes:
if getv: format_grid(ugrid, 'u')
if getu: format_grid(vgrid, 'v')
if getu: set_grid(ugbt, vgrid)
if getv: set_grid(vgbt, ugrid)
# Resolutions
if dxy is None:
dxt, dyt = resol(ssh, proj=True, mode='local')
dxu = 0.5 * (dxt[:, 1:] + dxt[:, :-1])
del dxt
dyv = 0.5 * (dyt[1:, :] + dyt[:-1, :])
del dyt
elif not isinstance(dxy, (list, tuple)):
dxu = dyv = dxy
else:
dxu, dyv = dxy
if getv and isinstance(dxu, N.ndarray):
if cdms2.isVariable(dxu): dxu = dxu.asma()
if dxu.ndim == 1: dxu.shape = 1, -1
if dxu.shape[1] == ssh.shape[-1]:
dxu = dxu[:, :-1]
if getu and isinstance(dyv, N.ndarray):
if cdms2.isVariable(dyv): dyv = dyv.asma()
if dyv.ndim == 1: dyv.shape = -1, 1
if dyv.shape[0] == ssh.shape[-2]:
dyv = dyv[:-1]
# Get geostrophic factor
f0 = coriolis_parameter(ssh, gravity=gravity, fromvar=True).asma()
bad = f0 == 0.
f0[bad] = 1.
f0[bad] = N.ma.masked
del bad
gf = gravity / f0
del f0
# Computes
sshm = ssh.asma()
sshm = sshm * gf
del gf
if getu:
ugbt[..., :-1, :] = -N.ma.diff(sshm, axis=-2) / dyv
del dyv
if getv:
vgbt[..., :-1] = N.ma.diff(sshm, axis=-1) / dxu
del dxu
del sshm
if getu and cyclic:
ugbt[..., -1] = ugbt[..., 0]
if not getu: return vgbt
elif not getv: return ugbt
return ugbt, vgbt
def barotropic_geostrophic_velocity(ssh, dxy=None, gravity=default_gravity, cyclic=False,
format_axes=True, getu=True, getv=True, filter=None):
"""Get barotropic geostropic velocity from SSH on a C-grid
.. note:: ssh is supposed to be at T points,
ubt is computed at V points,
and vbt is computed at U points.
.. todo:: Rewrite it using :mod:`vacumm.data.misc.arakawa` and defining
a limited number of algorithms for different staggering configurations.
:Params:
- **ssh**: Sea surface height.
- **dxy**, optional: Horizontal resolutions (m).
Resolution along X and Y are respectively at U and V points.
Possible forms:
- ``res``: A scalar meaning a constant resolution along X and Y.
- ``(dx,dy)``: A tuple of resolutions along X and Y.
- ``None``: Resolution is estimated using
:func:`~vacumm.misc.grid.misc.resol`.
:Return: ``(ubt,vbt)``
"""
if not getu and not getv: return
# Init masked
if getu: ugbt = format_var(ssh*MV2.masked, 'ugbt', format_axes=False)
if getv: vgbt = format_var(ssh*MV2.masked, 'vgbt', format_axes=False)
# Grid
tgrid = ssh.getGrid()
if getu: ugrid = shiftgrid(tgrid, ishift=0.5)
if getv: vgrid = shiftgrid(tgrid, jshift=0.5)
if format_axes:
if getv: format_grid(ugrid, 'u')
if getu: format_grid(vgrid, 'v')
if getu: set_grid(ugbt, vgrid)
if getv: set_grid(vgbt, ugrid)
# Resolutions
if dxy is None:
dxt, dyt = resol(ssh, proj=True, mode='local')
dxu = 0.5*(dxt[:, 1:]+dxt[:, :-1]) ; del dxt
dyv = 0.5*(dyt[1:, :]+dyt[:-1, :]) ; del dyt
elif not isinstance(dxy, (list, tuple)):
dxu = dyv = dxy
else:
dxu, dyv = dxy
if getv and isinstance(dxu, N.ndarray):
if cdms2.isVariable(dxu): dxu = dxu.asma()
if dxu.ndim==1: dxu.shape = 1, -1
if dxu.shape[1]==ssh.shape[-1]:
dxu = dxu[:, :-1]
if getu and isinstance(dyv, N.ndarray):
if cdms2.isVariable(dyv): dyv = dyv.asma()
if dyv.ndim==1: dyv.shape = -1, 1
if dyv.shape[0]==ssh.shape[-2]:
dyv = dyv[:-1]
# Get geostrophic factor
f0 = coriolis_parameter(ssh, gravity=gravity, fromvar=True).asma()
bad = f0==0.
f0[bad] = 1.
f0[bad] = N.ma.masked ; del bad
gf = gravity/f0 ; del f0
# Computes
sshm = ssh.asma()
sshm = sshm*gf ; del gf
if getu: ugbt[..., :-1, :] = -N.ma.diff(sshm, axis=-2)/dyv ; del dyv
if getv: vgbt[..., :-1] = N.ma.diff(sshm, axis=-1)/dxu ; del dxu
del sshm
if getu and cyclic:
ugbt[..., -1] = ugbt[..., 0]
if not getu: return vgbt
elif not getv: return ugbt
return ugbt, vgbt