def __init__(self, nlon, nlat, rsphere=1e2, gridtype="regular", legfunc="stored"):
Spharmt.__init__(self, nlon, nlat, rsphere, gridtype, legfunc)
if self.gridtype == "gaussian":
raise Exception, "Can't deal with Gaussian grid at the moment."
else:
deltalat = 180.0 / (nlat - 1)
self.lats = 90 - deltalat * np.arange(nlat)
deltalon = 360.0 / nlon
self.lons = deltalon * np.arange(nlon)
return
def __init__(self,nlon,nlat,rsphere=1e2,gridtype='regular',legfunc='stored'):
Spharmt.__init__(self,nlon,nlat,rsphere,gridtype,legfunc)
if self.gridtype=='gaussian':
raise Exception, "Can't deal with Gaussian grid at the moment."
else:
deltalat = 180./(nlat-1)
self.lats = 90 - deltalat*np.arange(nlat)
deltalon = 360./nlon
self.lons = deltalon*np.arange(nlon)
return
def regrid_sphere(nlat,nlon,Nens,X):
"""
Truncate lat,lon grid to another resolution in spherical harmonic space. Triangular truncation
Inputs:
nlat : number of latitudes
nlon : number of longitudes
Nens : number of ensemble members
X : data array of shape (nlat*nlon,Nens)
ntrunc : triangular truncation (e.g., use 42 for T42)
Outputs :
lat_new : 2D latitude array on the new grid (nlat_new,nlon_new)
lon_new : 2D longitude array on the new grid (nlat_new,nlon_new)
X_new : truncated data array of shape (nlat_new*nlon_new, Nens)
"""
# Originator: Greg Hakim
# University of Washington
# May 2015
# create the spectral object on the original grid
specob_lmr = Spharmt(nlon,nlat,gridtype='regular',legfunc='computed')
# truncate to a lower resolution grid (triangular truncation)
# ifix = np.remainder(ntrunc,2.0).astype(int)
# nlat_new = ntrunc + ifix
# nlon_new = int(nlat_new*1.5)
ntrunc = 42
nlat_new = 64
nlon_new = 128
# create the spectral object on the new grid
specob_new = Spharmt(nlon_new,nlat_new,gridtype='regular',legfunc='computed')
# create new lat,lon grid arrays
dlat = 90./((nlat_new-1)/2.)
dlon = 360./nlon_new
veclat = np.arange(-90.,90.+dlat,dlat)
veclon = np.arange(0.,360.,dlon)
blank = np.zeros([nlat_new,nlon_new])
lat_new = (veclat + blank.T).T
lon_new = (veclon + blank)
# transform each ensemble member, one at a time
X_new = np.zeros([nlat_new*nlon_new,Nens])
for k in range(Nens):
X_lalo = np.reshape(X[:,k],(nlat,nlon))
Xbtrunc = regrid(specob_lmr, specob_new, X_lalo, ntrunc=nlat_new-1, smooth=None)
vectmp = Xbtrunc.flatten()
X_new[:,k] = vectmp
return X_new,lat_new,lon_new
def regrid_field(field, lat, lon, lat_new, lon_new):
nlat_old, nlon_old = np.size(lat), np.size(lon)
nlat_new, nlon_new = np.size(lat_new), np.size(lon_new)
spec_old = Spharmt(nlon_old, nlat_old, gridtype='regular', legfunc='computed')
spec_new = Spharmt(nlon_new, nlat_new, gridtype='regular', legfunc='computed')
#remove nans
field[np.isnan(field)] = 0
field_new = []
for field_old in field:
regridded_field = regrid(spec_old, spec_new, field_old, ntrunc=None, smooth=None)
field_new.append(regridded_field)
field_new = np.array(field_new)
return field_new
def regrid(self, ntrunc, inplace=False):
old_spec = Spharmt(self.nlon,
self.nlat,
gridtype='regular',
legfunc='computed')
ifix = ntrunc % 2
new_nlat = ntrunc + ifix
new_nlon = int(new_nlat * 1.5)
new_spec = Spharmt(new_nlon,
new_nlat,
gridtype='regular',
legfunc='computed')
include_poles = False if new_nlat % 2 == 0 else True
new_lat_2d, new_lon_2d, _, _ = generate_latlon(
new_nlat, new_nlon, include_endpts=include_poles)
new_lat = new_lat_2d[:, 0]
new_lon = new_lon_2d[0, :]
# new_value = []
# for old_value in self.value:
old_value = np.moveaxis(self.value, 0, -1)
regridded_value = regrid(old_spec,
new_spec,
old_value,
ntrunc=new_nlat - 1,
smooth=None)
new_value = np.moveaxis(regridded_value, -1, 0)
# new_value.append(regridded_value)
new_value = np.array(new_value)
if inplace:
self.value = new_value
self.lat = new_lat
self.lon = new_lon
self.nlat = np.size(new_lat)
self.nlon = np.size(new_lon)
self.ntrunc = ntrunc
else:
new_field = self.copy()
new_field.value = new_value
new_field.lat = new_lat
new_field.lon = new_lon
new_field.nlat = np.size(new_lat)
new_field.nlon = np.size(new_lon)
new_field.ntrunc = ntrunc
return new_field
def __init__(self,
lat,
lon,
rsphere=6.3712e6,
legfunc='stored',
trunc=None):
# Length of lat/lon arrays
self.nlat = len(lat)
self.nlon = len(lon)
if self.nlat % 2:
gridtype = 'gaussian'
else:
gridtype = 'regular'
self.s = Spharmt(self.nlon,
self.nlat,
gridtype=gridtype,
rsphere=rsphere,
legfunc=legfunc)
# Reverse latitude array if necessary
# self.ReverseLat = False
# if lat[0] < lat[-1]:
# lat = self._reverse_lat(lat)
# self.ReverseLat = True
# lat/lon in degrees
self.glat = lat
self.glon = lon
# lat/lon in radians
self.rlat = np.deg2rad(lat)
self.rlon = np.deg2rad(lon)
self.rlons, self.rlats = np.meshgrid(self.rlon, self.rlat)
# Constants
# Earth's angular velocity
self.omega = 7.292e-05 # unit: s-1
# Gravitational acceleration
self.g = 9.8 # unit: m2/s
# Misc
self.dtype = np.float32
def __init__(self, nlon, nlat, truncation, radius=6371200.):
"""
Initialize the spectral transforms engine.
Arguments:
* nlon: int
Number of longitudes in the transform grid.
* nlat: int
Number of latitudes in the transform grid.
* truncation: int
The spectral truncation (triangular). This is the maximum
number of spherical harmonic modes retained in the discrete
truncation. More modes means higher resolution.
"""
self.sh = Spharmt(nlon, nlat, gridtype='regular', rsphere=radius)
self.radius = radius
self.nlon = nlon
self.nlat = nlat
self.truncation = truncation
def __init__(self, H, W):
super(PowerSpectrum, self).__init__()
self.spharm = Spharmt(W, H, legfunc='stored')
self.spectrums = []
self.needs_sh = True
wavenum = 4.0
omega = 7.848e-6
re = 6.371e6
delat = 2.*math.pi/nlons_reg
lats = (0.5*math.pi-delat*numpy.indices(lats_reg.shape)[0,:,:])
lons = (delat*numpy.indices(lons_reg.shape)[1,:,:])
psi_reg_exact = rhwave(wavenum,omega,re,lats,lons)
delat = 2.*math.pi/nlons_gau
lats = (math.pi/180.)*numpy.transpose(gaulats*numpy.ones((nlons_gau,nlats_gau),'d'))
lons = (delat*numpy.indices(lons_gau.shape)[1,:,:])
psi_gau = rhwave(wavenum,omega,re,lats,lons)
# create Spharmt instances for regular and gaussian grids.
reggrid = Spharmt(nlons_reg,nlats_reg,gridtype='regular')
gaugrid = Spharmt(nlons_gau,nlats_gau,gridtype='gaussian')
# regrid from gaussian to regular grid.
psi_reg = regrid(gaugrid,reggrid,psi_gau)
print('reggrid error (should be less than 1.e-6):')
print(numpy.fabs(psi_reg-psi_reg_exact).max()/numpy.fabs(psi_reg_exact).max())
# spectrally interpolate to geodesic grid.
ntrunc = nlats_reg-1
latpts,lonpts = getgeodesicpts(7) # compute geodesic points
dataspec = reggrid.grdtospec(psi_reg_exact,ntrunc) # compute spectral coeffs
nlat = 0
class VectorWind(object):
"""Vector Wind computations (standard `numpy` interface)."""
def __init__(self, u, v, gridtype='regular', rsphere=6.3712e6):
"""Initialize a VectorWind instance.
**Arguments:**
*u*, *v*
Zonal and meridional wind components respectively. Their
types should be either `numpy.ndarray` or
`numpy.ma.MaskedArray`. *u* and *v* must have matching
shapes and contain no missing values. *u* and *v* may be 2
or 3-dimensional with shape (nlat, nlon) or
(nlat, nlon, nt), where nlat and nlon are the number of
latitudes and longitudes respectively and nt is the number
of fields. The latitude dimension must be oriented
north-to-south. The longitude dimension should be
oriented west-to-east.
**Optional argument:**
*gridtype*
Type of the input grid, either 'regular' for evenly-spaced
grids, or 'gaussian' for Gaussian grids. Defaults to
'regular'.
**See also:**
`~windspharm.tools.prep_data`,
`~windspharm.tools.recover_data`,
`~windspharm.tools.get_recovery`,
`~windspharm.tools.reverse_latdim`,
`~windspharm.tools.order_latdim`.
**Examples:**
Initialize a `VectorWind` instance with zonal and meridional
components of the vector wind on the default regular
(evenly-spaced) grid:
from windspharm.standard import VectorWind
w = VectorWind(u, v)
Initialize a `VectorWind` instance with zonal and meridional
components of the vector wind specified on a Gaussian grid:
from windspharm.standard import VectorWind
w = VectorWind(u, v, gridtype='gaussian')
"""
# For both the input components check if there are missing values by
# attempting to fill missing values with NaN and detect them. If the
# inputs are not masked arrays then take copies and check for NaN.
try:
self.u = u.filled(fill_value=np.nan)
except AttributeError:
self.u = u.copy()
try:
self.v = v.filled(fill_value=np.nan)
except AttributeError:
self.v = v.copy()
if np.isnan(self.u).any() or np.isnan(self.v).any():
raise ValueError('u and v cannot contain missing values')
# Make sure the shapes of the two components match.
if u.shape != v.shape:
raise ValueError('u and v must be the same shape')
if len(u.shape) not in (2, 3):
raise ValueError('u and v must be rank 2 or 3 arrays')
nlat = u.shape[0]
nlon = u.shape[1]
try:
# Create a Spharmt object to do the computations.
self.gridtype = gridtype.lower()
self.s = Spharmt(nlon, nlat, gridtype=self.gridtype,
rsphere=rsphere)
except ValueError:
if self.gridtype not in ('regular', 'gaussian'):
err = 'invalid grid type: {0:s}'.format(repr(gridtype))
else:
err = 'invalid input dimensions'
raise ValueError(err)
# Method aliases.
self.rotationalcomponent = self.nondivergentcomponent
self.divergentcomponent = self.irrotationalcomponent
def magnitude(self):
"""Wind speed (magnitude of vector wind).
**Returns:**
*speed*
The wind speed.
**Example:**
Magnitude of the vector wind::
spd = w.magnitude()
"""
return (self.u ** 2 + self.v ** 2) ** 0.5
def vrtdiv(self, truncation=None):
"""Relative vorticity and horizontal divergence.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*vrt*, *div*
The relative vorticity and divergence respectively.
**See also:**
`~VectorWind.vorticity`, `~VectorWind.divergence`.
**Examples:**
Compute the relative vorticity and divergence::
vrt, div = w.vrtdiv()
Compute the relative vorticity and divergence and apply spectral
truncation at triangular T13::
vrtT13, divT13 = w.vrtdiv(truncation=13)
"""
vrtspec, divspec = self.s.getvrtdivspec(self.u,
self.v,
ntrunc=truncation)
vrtgrid = self.s.spectogrd(vrtspec)
divgrid = self.s.spectogrd(divspec)
return vrtgrid, divgrid
def vorticity(self, truncation=None):
"""Relative vorticity.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*vrt*
The relative vorticity.
**See also:**
`~VectorWind.vrtdiv`, `~VectorWind.absolutevorticity`.
**Examples:**
Compute the relative vorticity::
vrt = w.vorticity()
Compute the relative vorticity and apply spectral truncation at
triangular T13::
vrtT13 = w.vorticity(truncation=13)
"""
vrtspec, divspec = self.s.getvrtdivspec(self.u,
self.v,
ntrunc=truncation)
vrtgrid = self.s.spectogrd(vrtspec)
return vrtgrid
def divergence(self, truncation=None):
"""Horizontal divergence.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*div*
The divergence.
**See also:**
`~VectorWind.vrtdiv`.
**Examples:**
Compute the divergence::
div = w.divergence()
Compute the divergence and apply spectral truncation at
triangular T13::
divT13 = w.divergence(truncation=13)
"""
vrtspec, divspec = self.s.getvrtdivspec(self.u,
self.v,
ntrunc=truncation)
divgrid = self.s.spectogrd(divspec)
return divgrid
def planetaryvorticity(self, omega=None):
"""Planetary vorticity (Coriolis parameter).
**Optional argument:**
*omega*
Earth's angular velocity. The default value if not specified
is 7.292x10**-5 s**-1.
**Returns:**
*pvorticity*
The planetary vorticity.
**See also:**
`~VectorWind.absolutevorticity`.
**Example:**
Compute planetary vorticity using default values::
pvrt = w.planetaryvorticity()
Override the default value for Earth's angular velocity::
pvrt = w.planetaryvorticity(omega=7.2921150)
"""
if omega is None:
# Define the Earth's angular velocity.
omega = 7.292e-05
nlat = self.s.nlat
if self.gridtype == 'gaussian':
lat, wts = gaussian_lats_wts(nlat)
else:
if nlat % 2:
lat = np.linspace(90, -90, nlat)
else:
dlat = 180. / nlat
lat = np.arange(90 - dlat / 2., -90, -dlat)
try:
cp = 2. * omega * np.sin(np.deg2rad(lat))
except (TypeError, ValueError):
raise ValueError('invalid value for omega: {!r}'.format(omega))
indices = [slice(0, None)] + [np.newaxis] * (len(self.u.shape) - 1)
f = cp[indices] * np.ones(self.u.shape, dtype=np.float32)
return f
def absolutevorticity(self, omega=None, truncation=None):
"""Absolute vorticity (sum of relative and planetary vorticity).
**Optional arguments:**
*omega*
Earth's angular velocity. The default value if not specified
is 7.292x10**-5 s**-1.
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*avorticity*
The absolute (relative + planetary) vorticity.
**See also:**
`~VectorWind.vorticity`, `~VectorWind.planetaryvorticity`.
**Examples:**
Compute absolute vorticity::
avrt = w.absolutevorticity()
Compute absolute vorticity and apply spectral truncation at
triangular T13, also override the default value for Earth's
angular velocity::
avrt = w.absolutevorticity(omega=7.2921150, truncation=13)
"""
pvrt = self.planetaryvorticity(omega=omega)
rvrt = self.vorticity(truncation=truncation)
return pvrt + rvrt
def sfvp(self, truncation=None):
"""Streamfunction and velocity potential.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*sf*, *vp*
The streamfunction and velocity potential respectively.
**See also:**
`~VectorWind.streamfunction`, `~VectorWind.velocitypotential`.
**Examples:**
Compute streamfunction and velocity potential::
sf, vp = w.sfvp()
Compute streamfunction and velocity potential and apply spectral
truncation at triangular T13::
sfT13, vpT13 = w.sfvp(truncation=13)
"""
psigrid, chigrid = self.s.getpsichi(self.u, self.v, ntrunc=truncation)
return psigrid, chigrid
def streamfunction(self, truncation=None):
"""Streamfunction.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*sf*
The streamfunction.
**See also:**
`~VectorWind.sfvp`.
**Examples:**
Compute streamfunction::
sf = w.streamfunction()
Compute streamfunction and apply spectral truncation at
triangular T13::
sfT13 = w.streamfunction(truncation=13)
"""
psigrid, chigrid = self.sfvp(truncation=truncation)
return psigrid
def velocitypotential(self, truncation=None):
"""Velocity potential.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*vp*
The velocity potential.
**See also:**
`~VectorWind.sfvp`.
**Examples:**
Compute velocity potential::
vp = w.velocity potential()
Compute velocity potential and apply spectral truncation at
triangular T13::
vpT13 = w.velocity potential(truncation=13)
"""
psigrid, chigrid = self.sfvp(truncation=truncation)
return chigrid
def helmholtz(self, truncation=None):
"""Irrotational and non-divergent components of the vector wind.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*uchi*, *vchi*, *upsi*, *vpsi*
Zonal and meridional components of irrotational and
non-divergent wind components respectively.
**See also:**
`~VectorWind.irrotationalcomponent`,
`~VectorWind.nondivergentcomponent`.
**Examples:**
Compute the irrotational and non-divergent components of the
vector wind::
uchi, vchi, upsi, vpsi = w.helmholtz()
Compute the irrotational and non-divergent components of the
vector wind and apply spectral truncation at triangular T13::
uchiT13, vchiT13, upsiT13, vpsiT13 = w.helmholtz(truncation=13)
"""
psigrid, chigrid = self.s.getpsichi(self.u, self.v, ntrunc=truncation)
psispec = self.s.grdtospec(psigrid)
chispec = self.s.grdtospec(chigrid)
vpsi, upsi = self.s.getgrad(psispec)
uchi, vchi = self.s.getgrad(chispec)
return uchi, vchi, -upsi, vpsi
def irrotationalcomponent(self, truncation=None):
"""Irrotational (divergent) component of the vector wind.
.. note::
If both the irrotational and non-divergent components are
required then `~VectorWind.helmholtz` should be used instead.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*uchi*, *vchi*
The zonal and meridional components of the irrotational wind
respectively.
**See also:**
`~VectorWind.helmholtz`.
**Examples:**
Compute the irrotational component of the vector wind::
uchi, vchi = w.irrotationalcomponent()
Compute the irrotational component of the vector wind and apply
spectral truncation at triangular T13::
uchiT13, vchiT13 = w.irrotationalcomponent(truncation=13)
"""
psigrid, chigrid = self.s.getpsichi(self.u, self.v, ntrunc=truncation)
chispec = self.s.grdtospec(chigrid)
uchi, vchi = self.s.getgrad(chispec)
return uchi, vchi
def nondivergentcomponent(self, truncation=None):
"""Non-divergent (rotational) component of the vector wind.
.. note::
If both the non-divergent and irrotational components are
required then `~VectorWind.helmholtz` should be used instead.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*upsi*, *vpsi*
The zonal and meridional components of the non-divergent
wind respectively.
**See also:**
`~VectorWind.helmholtz`.
**Examples:**
Compute the non-divergent component of the vector wind::
upsi, vpsi = w.nondivergentcomponent()
Compute the non-divergent component of the vector wind and apply
spectral truncation at triangular T13::
upsiT13, vpsiT13 = w.nondivergentcomponent(truncation=13)
"""
psigrid, chigrid = self.s.getpsichi(self.u, self.v, ntrunc=truncation)
psispec = self.s.grdtospec(psigrid)
vpsi, upsi = self.s.getgrad(psispec)
return -upsi, vpsi
def gradient(self, chi, truncation=None):
"""Computes the vector gradient of a scalar field on the sphere.
**Argument:**
*chi*
A scalar field. Its shape must be either (nlat, nlon) or
(nlat, nlon, nfields) where nlat and nlon are the same
as those for the vector wind components that initialized the
`VectorWind` instance.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*uchi*, *vchi*
The zonal and meridional components of the vector gradient
respectively.
**Examples:**
Compute the vector gradient of absolute vorticity::
avrt = w.absolutevorticity()
avrt_zonal, avrt_meridional = w.gradient(avrt)
Compute the vector gradient of absolute vorticity and apply
spectral truncation at triangular T13::
avrt = w.absolutevorticity()
avrt_zonalT13, avrt_meridionalT13 = w.gradient(avrt, truncation=13)
"""
try:
chi = chi.filled(fill_value=np.nan)
except AttributeError:
pass
if np.isnan(chi).any():
raise ValueError('chi cannot contain missing values')
try:
chispec = self.s.grdtospec(chi, ntrunc=truncation)
except ValueError:
raise ValueError('input field is not compatitble')
uchi, vchi = self.s.getgrad(chispec)
return uchi, vchi
def truncate(self, field, truncation=None):
"""Apply spectral truncation to a scalar field.
This is useful to represent other fields in a way consistent
with the output of other `VectorWind` methods.
**Argument:**
*field*
A scalar field. Its shape must be either (nlat, nlon) or
(nlat, nlon, nfields) where nlat and nlon are the same
as those for the vector wind components that initialized the
`VectorWind` instance.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation. If not specified it will default to
*nlats - 1* where *nlats* is the number of latitudes.
**Returns:**
*truncated_field*
The field with spectral truncation applied.
**Examples:**
Truncate a scalar field to the computational resolution of the
`VectorWind` instance::
scalar_field_truncated = w.truncate(scalar_field)
Truncate a scalar field to T21::
scalar_field_T21 = w.truncate(scalar_field, truncation=21)
"""
try:
field = field.filled(fill_value=np.nan)
except AttributeError:
pass
if np.isnan(field).any():
raise ValueError('field cannot contain missing values')
try:
fieldspec = self.s.grdtospec(field, ntrunc=truncation)
except ValueError:
raise ValueError('field is not compatible')
fieldtrunc = self.s.spectogrd(fieldspec)
return fieldtrunc
class VectorWind(object):
"""Vector Wind computations (standard `numpy` interface)."""
def __init__(self, u, v, gridtype='regular', rsphere=6.3712e6):
"""Initialize a VectorWind instance.
**Arguments:**
*u*, *v*
Zonal and meridional wind components respectively. Their
types should be either `numpy.ndarray` or
`numpy.ma.MaskedArray`. *u* and *v* must have matching
shapes and contain no missing values. *u* and *v* may be 2
or 3-dimensional with shape (nlat, nlon) or
(nlat, nlon, nt), where nlat and nlon are the number of
latitudes and longitudes respectively and nt is the number
of fields. The latitude dimension must be oriented
north-to-south. The longitude dimension should be
oriented west-to-east.
**Optional arguments:**
*gridtype*
Type of the input grid, either 'regular' for evenly-spaced
grids, or 'gaussian' for Gaussian grids. Defaults to
'regular'.
*rsphere*
The radius in metres of the sphere used in the spherical
harmonic computations. Default is 6371200 m, the approximate
mean spherical Earth radius.
**See also:**
`~windspharm.tools.prep_data`,
`~windspharm.tools.recover_data`,
`~windspharm.tools.get_recovery`,
`~windspharm.tools.reverse_latdim`,
`~windspharm.tools.order_latdim`.
**Examples:**
Initialize a `VectorWind` instance with zonal and meridional
components of the vector wind on the default regular
(evenly-spaced) grid:
from windspharm.standard import VectorWind
w = VectorWind(u, v)
Initialize a `VectorWind` instance with zonal and meridional
components of the vector wind specified on a Gaussian grid:
from windspharm.standard import VectorWind
w = VectorWind(u, v, gridtype='gaussian')
"""
# For both the input components check if there are missing values by
# attempting to fill missing values with NaN and detect them. If the
# inputs are not masked arrays then take copies and check for NaN.
try:
self.u = u.filled(fill_value=np.nan)
except AttributeError:
self.u = u.copy()
try:
self.v = v.filled(fill_value=np.nan)
except AttributeError:
self.v = v.copy()
if np.isnan(self.u).any() or np.isnan(self.v).any():
raise ValueError('u and v cannot contain missing values')
# Make sure the shapes of the two components match.
if u.shape != v.shape:
raise ValueError('u and v must be the same shape')
if len(u.shape) not in (2, 3):
raise ValueError('u and v must be rank 2 or 3 arrays')
nlat = u.shape[0]
nlon = u.shape[1]
try:
# Create a Spharmt object to do the computations.
self.gridtype = gridtype.lower()
self.s = Spharmt(nlon,
nlat,
gridtype=self.gridtype,
rsphere=rsphere)
except ValueError:
if self.gridtype not in ('regular', 'gaussian'):
err = 'invalid grid type: {0:s}'.format(repr(gridtype))
else:
err = 'invalid input dimensions'
raise ValueError(err)
# Method aliases.
self.rotationalcomponent = self.nondivergentcomponent
self.divergentcomponent = self.irrotationalcomponent
def magnitude(self):
"""Wind speed (magnitude of vector wind).
**Returns:**
*speed*
The wind speed.
**Example:**
Magnitude of the vector wind::
spd = w.magnitude()
"""
return (self.u**2 + self.v**2)**0.5
def vrtdiv(self, truncation=None):
"""Relative vorticity and horizontal divergence.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*vrt*, *div*
The relative vorticity and divergence respectively.
**See also:**
`~VectorWind.vorticity`, `~VectorWind.divergence`.
**Examples:**
Compute the relative vorticity and divergence::
vrt, div = w.vrtdiv()
Compute the relative vorticity and divergence and apply spectral
truncation at triangular T13::
vrtT13, divT13 = w.vrtdiv(truncation=13)
"""
vrtspec, divspec = self.s.getvrtdivspec(self.u,
self.v,
ntrunc=truncation)
vrtgrid = self.s.spectogrd(vrtspec)
divgrid = self.s.spectogrd(divspec)
return vrtgrid, divgrid
def vorticity(self, truncation=None):
"""Relative vorticity.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*vrt*
The relative vorticity.
**See also:**
`~VectorWind.vrtdiv`, `~VectorWind.absolutevorticity`.
**Examples:**
Compute the relative vorticity::
vrt = w.vorticity()
Compute the relative vorticity and apply spectral truncation at
triangular T13::
vrtT13 = w.vorticity(truncation=13)
"""
vrtspec, divspec = self.s.getvrtdivspec(self.u,
self.v,
ntrunc=truncation)
vrtgrid = self.s.spectogrd(vrtspec)
return vrtgrid
def divergence(self, truncation=None):
"""Horizontal divergence.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*div*
The divergence.
**See also:**
`~VectorWind.vrtdiv`.
**Examples:**
Compute the divergence::
div = w.divergence()
Compute the divergence and apply spectral truncation at
triangular T13::
divT13 = w.divergence(truncation=13)
"""
vrtspec, divspec = self.s.getvrtdivspec(self.u,
self.v,
ntrunc=truncation)
divgrid = self.s.spectogrd(divspec)
return divgrid
def planetaryvorticity(self, omega=None):
"""Planetary vorticity (Coriolis parameter).
**Optional argument:**
*omega*
Earth's angular velocity. The default value if not specified
is 7.292x10**-5 s**-1.
**Returns:**
*pvorticity*
The planetary vorticity.
**See also:**
`~VectorWind.absolutevorticity`.
**Example:**
Compute planetary vorticity using default values::
pvrt = w.planetaryvorticity()
Override the default value for Earth's angular velocity::
pvrt = w.planetaryvorticity(omega=7.2921150)
"""
if omega is None:
# Define the Earth's angular velocity.
omega = 7.292e-05
nlat = self.s.nlat
if self.gridtype == 'gaussian':
lat, wts = gaussian_lats_wts(nlat)
else:
if nlat % 2:
lat = np.linspace(90, -90, nlat)
else:
dlat = 180. / nlat
lat = np.arange(90 - dlat / 2., -90, -dlat)
try:
cp = 2. * omega * np.sin(np.deg2rad(lat))
except (TypeError, ValueError):
raise ValueError('invalid value for omega: {!r}'.format(omega))
indices = [slice(0, None)] + [np.newaxis] * (len(self.u.shape) - 1)
f = cp[indices] * np.ones(self.u.shape, dtype=np.float32)
return f
def absolutevorticity(self, omega=None, truncation=None):
"""Absolute vorticity (sum of relative and planetary vorticity).
**Optional arguments:**
*omega*
Earth's angular velocity. The default value if not specified
is 7.292x10**-5 s**-1.
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*avorticity*
The absolute (relative + planetary) vorticity.
**See also:**
`~VectorWind.vorticity`, `~VectorWind.planetaryvorticity`.
**Examples:**
Compute absolute vorticity::
avrt = w.absolutevorticity()
Compute absolute vorticity and apply spectral truncation at
triangular T13, also override the default value for Earth's
angular velocity::
avrt = w.absolutevorticity(omega=7.2921150, truncation=13)
"""
pvrt = self.planetaryvorticity(omega=omega)
rvrt = self.vorticity(truncation=truncation)
return pvrt + rvrt
def sfvp(self, truncation=None):
"""Streamfunction and velocity potential.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*sf*, *vp*
The streamfunction and velocity potential respectively.
**See also:**
`~VectorWind.streamfunction`, `~VectorWind.velocitypotential`.
**Examples:**
Compute streamfunction and velocity potential::
sf, vp = w.sfvp()
Compute streamfunction and velocity potential and apply spectral
truncation at triangular T13::
sfT13, vpT13 = w.sfvp(truncation=13)
"""
psigrid, chigrid = self.s.getpsichi(self.u, self.v, ntrunc=truncation)
return psigrid, chigrid
def streamfunction(self, truncation=None):
"""Streamfunction.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*sf*
The streamfunction.
**See also:**
`~VectorWind.sfvp`.
**Examples:**
Compute streamfunction::
sf = w.streamfunction()
Compute streamfunction and apply spectral truncation at
triangular T13::
sfT13 = w.streamfunction(truncation=13)
"""
psigrid, chigrid = self.sfvp(truncation=truncation)
return psigrid
def velocitypotential(self, truncation=None):
"""Velocity potential.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*vp*
The velocity potential.
**See also:**
`~VectorWind.sfvp`.
**Examples:**
Compute velocity potential::
vp = w.velocity potential()
Compute velocity potential and apply spectral truncation at
triangular T13::
vpT13 = w.velocity potential(truncation=13)
"""
psigrid, chigrid = self.sfvp(truncation=truncation)
return chigrid
def helmholtz(self, truncation=None):
"""Irrotational and non-divergent components of the vector wind.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*uchi*, *vchi*, *upsi*, *vpsi*
Zonal and meridional components of irrotational and
non-divergent wind components respectively.
**See also:**
`~VectorWind.irrotationalcomponent`,
`~VectorWind.nondivergentcomponent`.
**Examples:**
Compute the irrotational and non-divergent components of the
vector wind::
uchi, vchi, upsi, vpsi = w.helmholtz()
Compute the irrotational and non-divergent components of the
vector wind and apply spectral truncation at triangular T13::
uchiT13, vchiT13, upsiT13, vpsiT13 = w.helmholtz(truncation=13)
"""
psigrid, chigrid = self.s.getpsichi(self.u, self.v, ntrunc=truncation)
psispec = self.s.grdtospec(psigrid)
chispec = self.s.grdtospec(chigrid)
vpsi, upsi = self.s.getgrad(psispec)
uchi, vchi = self.s.getgrad(chispec)
return uchi, vchi, -upsi, vpsi
def irrotationalcomponent(self, truncation=None):
"""Irrotational (divergent) component of the vector wind.
.. note::
If both the irrotational and non-divergent components are
required then `~VectorWind.helmholtz` should be used instead.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*uchi*, *vchi*
The zonal and meridional components of the irrotational wind
respectively.
**See also:**
`~VectorWind.helmholtz`.
**Examples:**
Compute the irrotational component of the vector wind::
uchi, vchi = w.irrotationalcomponent()
Compute the irrotational component of the vector wind and apply
spectral truncation at triangular T13::
uchiT13, vchiT13 = w.irrotationalcomponent(truncation=13)
"""
psigrid, chigrid = self.s.getpsichi(self.u, self.v, ntrunc=truncation)
chispec = self.s.grdtospec(chigrid)
uchi, vchi = self.s.getgrad(chispec)
return uchi, vchi
def nondivergentcomponent(self, truncation=None):
"""Non-divergent (rotational) component of the vector wind.
.. note::
If both the non-divergent and irrotational components are
required then `~VectorWind.helmholtz` should be used instead.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*upsi*, *vpsi*
The zonal and meridional components of the non-divergent
wind respectively.
**See also:**
`~VectorWind.helmholtz`.
**Examples:**
Compute the non-divergent component of the vector wind::
upsi, vpsi = w.nondivergentcomponent()
Compute the non-divergent component of the vector wind and apply
spectral truncation at triangular T13::
upsiT13, vpsiT13 = w.nondivergentcomponent(truncation=13)
"""
psigrid, chigrid = self.s.getpsichi(self.u, self.v, ntrunc=truncation)
psispec = self.s.grdtospec(psigrid)
vpsi, upsi = self.s.getgrad(psispec)
return -upsi, vpsi
def gradient(self, chi, truncation=None):
"""Computes the vector gradient of a scalar field on the sphere.
**Argument:**
*chi*
A scalar field. Its shape must be either (nlat, nlon) or
(nlat, nlon, nfields) where nlat and nlon are the same
as those for the vector wind components that initialized the
`VectorWind` instance.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Returns:**
*uchi*, *vchi*
The zonal and meridional components of the vector gradient
respectively.
**Examples:**
Compute the vector gradient of absolute vorticity::
avrt = w.absolutevorticity()
avrt_zonal, avrt_meridional = w.gradient(avrt)
Compute the vector gradient of absolute vorticity and apply
spectral truncation at triangular T13::
avrt = w.absolutevorticity()
avrt_zonalT13, avrt_meridionalT13 = w.gradient(avrt, truncation=13)
"""
try:
chi = chi.filled(fill_value=np.nan)
except AttributeError:
pass
if np.isnan(chi).any():
raise ValueError('chi cannot contain missing values')
try:
chispec = self.s.grdtospec(chi, ntrunc=truncation)
except ValueError:
raise ValueError('input field is not compatitble')
uchi, vchi = self.s.getgrad(chispec)
return uchi, vchi
def truncate(self, field, truncation=None):
"""Apply spectral truncation to a scalar field.
This is useful to represent other fields in a way consistent
with the output of other `VectorWind` methods.
**Argument:**
*field*
A scalar field. Its shape must be either (nlat, nlon) or
(nlat, nlon, nfields) where nlat and nlon are the same
as those for the vector wind components that initialized the
`VectorWind` instance.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation. If not specified it will default to
*nlats - 1* where *nlats* is the number of latitudes.
**Returns:**
*truncated_field*
The field with spectral truncation applied.
**Examples:**
Truncate a scalar field to the computational resolution of the
`VectorWind` instance::
scalar_field_truncated = w.truncate(scalar_field)
Truncate a scalar field to T21::
scalar_field_T21 = w.truncate(scalar_field, truncation=21)
"""
try:
field = field.filled(fill_value=np.nan)
except AttributeError:
pass
if np.isnan(field).any():
raise ValueError('field cannot contain missing values')
try:
fieldspec = self.s.grdtospec(field, ntrunc=truncation)
except ValueError:
raise ValueError('field is not compatible')
fieldtrunc = self.s.spectogrd(fieldspec)
return fieldtrunc
grav = 9.80616 # gravity
hbar = 10.e3 # resting depth
umax = 80. # jet speed
phi0 = np.pi / 7.
phi1 = 0.5 * np.pi - phi0
phi2 = 0.25 * np.pi
en = np.exp(-4.0 / (phi1 - phi0)**2)
alpha = 1. / 3.
beta = 1. / 15.
hamp = 120. # amplitude of height perturbation to zonal jet
efold = 3. * 3600. # efolding timescale at ntrunc for hyperdiffusion
ndiss = 8 # order for hyperdiffusion
# setup up spherical harmonic instance, set lats/lons of grid
x = Spharmt(nlons, nlats, rsphere=rsphere, gridtype=gridtype)
delta = 2. * np.pi / nlons
lats1d = 0.5 * np.pi - delta * np.arange(nlats)
lons1d = np.arange(-np.pi, np.pi, delta)
lons, lats = np.meshgrid(lons1d, lats1d)
f = 2. * omega * np.sin(lats) # coriolis
# zonal jet.
vg = np.zeros((nlats, nlons), np.float32)
u1 = (umax / en) * np.exp(1. / ((lats1d - phi0) * (lats1d - phi1)))
ug = np.zeros((nlats), np.float32)
ug = np.where(np.logical_and(lats1d < phi1, lats1d > phi0), u1, ug)
ug.shape = (nlats, 1)
ug = ug * np.ones(
(nlats, nlons), dtype=np.float32) # broadcast to shape (nlats,nlonss)
# height perturbation.
# ERA
smatch, ematch = find_date_indices(ERA20C_time,stime,etime)
ERA20C = ERA20C - np.mean(ERA20C[smatch:ematch,:,:],axis=0)
# -----------------------------------
# Regridding the data for comparisons
# -----------------------------------
print('\n regridding data to a common T42 grid...\n')
iplot_loc= False
#iplot_loc= True
# create instance of the spherical harmonics object for each grid
specob_lmr = Spharmt(nlon,nlat,gridtype='regular',legfunc='computed')
specob_tcr = Spharmt(nlon_TCR,nlat_TCR,gridtype='regular',legfunc='computed')
specob_era20c = Spharmt(nlon_ERA20C,nlat_ERA20C,gridtype='regular',legfunc='computed')
# truncate to a lower resolution grid (common:21, 42, 62, 63, 85, 106, 255, 382, 799)
ntrunc_new = 42 # T42
ifix = np.remainder(ntrunc_new,2.0).astype(int)
nlat_new = ntrunc_new + ifix
nlon_new = int(nlat_new*1.5)
# lat, lon grid in the truncated space
dlat = 90./((nlat_new-1)/2.)
dlon = 360./nlon_new
veclat = np.arange(-90.,90.+dlat,dlat)
veclon = np.arange(0.,360.,dlon)
blank = np.zeros([nlat_new,nlon_new])
lat2_new = (veclat + blank.T).T
# grid, time step info
nlons = 128 # number of longitudes
ntrunc = 42 # spectral truncation (for alias-free computations)
nlats = (nlons/2)+1 # for regular grid.
gridtype = 'regular'
#nlats = nlons/2 # for gaussian grid.
#gridtype = 'gaussian'
dt = 900 # time step in seconds
itmax = 8*(86400/dt) # integration length in days
umax = 50. # jet speed
jetexp = 10 # parameter controlling jet width
# create spherical harmonic instance.
rsphere = 6.37122e6 # earth radius
sp = Spharmt(nlons,nlats,rsphere=rsphere,gridtype=gridtype)
# create model instance using default parameters.
model = TwoLayer(sp,dt,ntrunc)
# vort, div initial conditions
psipert = np.zeros((sp.nlat,sp.nlon,2),np.float32)
psipert[:,:,1] = 5.e6*np.sin((model.lons-np.pi))**12*np.sin(2.*model.lats)**12
psipert = np.where(model.lons[:,:,np.newaxis] > 0., 0, psipert)
ug = np.zeros((sp.nlat,sp.nlon,2),np.float32)
vg = np.zeros((sp.nlat,sp.nlon,2),np.float32)
ug[:,:,1] = umax*np.sin(2.*model.lats)**jetexp
vrtspec, divspec = sp.getvrtdivspec(ug,vg,model.ntrunc)
vrtspec = vrtspec + model.lap*sp.grdtospec(psipert,model.ntrunc)
vrtg = sp.spectogrd(vrtspec)
lyrthkspec = model.nlbalance(vrtspec)
class TransformsEngine(object):
"""A spectral transforms engine based on pyspharm."""
def __init__(self, nlon, nlat, truncation, radius=6371200.):
"""
Initialize the spectral transforms engine.
Arguments:
* nlon: int
Number of longitudes in the transform grid.
* nlat: int
Number of latitudes in the transform grid.
* truncation: int
The spectral truncation (triangular). This is the maximum
number of spherical harmonic modes retained in the discrete
truncation. More modes means higher resolution.
"""
self.sh = Spharmt(nlon, nlat, gridtype='regular', rsphere=radius)
self.radius = radius
self.nlon = nlon
self.nlat = nlat
self.truncation = truncation
def vrtdiv_spec_from_uv_grid(self, u, v):
"""
Compute spectral vorticity and divergence from grid u and v.
"""
try:
vrt, div = self.sh.getvrtdivspec(u, v, ntrunc=self.truncation)
except ValueError:
msg = ('u and v must be 2d or 3d arrays with shape ({y}, {x}) '
'or ({y}, {x}, :)'.format(y=self.nlat, x=self.nlon))
raise ValueError(msg)
return vrt, div
def uv_grid_from_vrtdiv_spec(self, vrt, div):
"""
Compute grid u and v from spectral vorticity and divergence.
"""
try:
u, v = self.sh.getuv(vrt, div)
except ValueError:
nspec = (self.truncation + 1) * (self.truncation + 2) // 2
msg = ('vrt and div must be 1d or 2d arrays with shape '
'(n) or (n, :) where n <= {}'.format(nspec))
raise ValueError(msg)
return u, v
def spec_to_grid(self, scalar_spec):
"""
Transform a scalar field from spectral to grid space.
"""
try:
scalar_grid = self.sh.spectogrd(scalar_spec)
except ValueError:
nspec = (self.truncation + 1) * (self.truncation + 2) // 2
msg = ('scalar_spec must be a 1d or 2d array with shape '
'(n) or (n, :) where n <= {}'.format(nspec))
raise ValueError(msg)
return scalar_grid
def grid_to_spec(self, scalar_grid):
"""
Transform a scalar field from grid to spectral space.
"""
try:
scalar_spec = self.sh.grdtospec(scalar_grid,
ntrunc=self.truncation)
except ValueError:
msg = ('scalar_grid must be a 2d or 3d array with shape '
'({y}, {x}) or ({y}, {x}, :)'.format(y=self.nlat,
x=self.nlon))
raise ValueError(msg)
return scalar_spec
def grad_of_spec(self, scalar_spec):
"""
Return zonal and meridional gradients of a spectral field.
"""
try:
dsdx, dsdy = self.sh.getgrad(scalar_spec)
except ValueError:
nspec = (self.truncation + 1) * (self.truncation + 2) // 2
msg = ('scalar_spec must be a 1d or 2d array with shape '
'(n) or (n, :) where n <= {}'.format(nspec))
raise ValueError(msg)
return dsdx, dsdy
@property
def wavenumbers(self):
"""
Wavenumbers corresponding to the spectral fields.
"""
return getspecindx(self.truncation)
@property
def grid_latlon(self):
"""
Return the latitude and longitude coordinate vectors of the
model grid.
"""
lats, _ = gaussian_lats_wts(self.nlat)
lons = np.arange(0., 360., 360. / self.nlon)
return lats, lons
class spectral:
def __init__(self, lat, lon, rsphere=6.3712e6, legfunc='stored'):
# Length of lat/lon arrays
self.nlat = len(lat)
self.nlon = len(lon)
if self.nlat % 2:
gridtype = 'gaussian'
else:
gridtype = 'regular'
self.s = Spharmt(self.nlon,
self.nlat,
gridtype=gridtype,
rsphere=rsphere,
legfunc=legfunc)
# Reverse latitude array if necessary
# self.ReverseLat = False
# if lat[0] < lat[-1]:
# lat = self._reverse_lat(lat)
# self.ReverseLat = True
# lat/lon in degrees
self.glat = lat
self.glon = lon
# lat/lon in radians
self.rlat = np.deg2rad(lat)
self.rlon = np.deg2rad(lon)
self.rlons, self.rlats = np.meshgrid(self.rlon, self.rlat)
# Constants
# Earth's angular velocity
self.omega = 7.292e-05 # unit: s-1
# Gravitational acceleration
self.g = 9.8 # unit: m2/s
# Misc
self.dtype = np.float32
def _reverse_lat(self, var):
if len(np.shape(var)) == 1:
return (var[::-1])
if len(np.shape(var)) == 2:
return (var[::-1, :])
if len(np.shape(var)) == 3:
return (var[:, ::-1, :])
def planetaryvorticity(self, omega=None):
pass
def uv2vrt(self, u, v, trunc=None):
"""
Calculate relative vorticity from horizonal wind field
Input: u and v (grid)
Output: relative vorticity (grid)
"""
vrts, _ = self.s.getvrtdivspec(u, v, ntrunc=trunc)
vrtg = self.s.spectogrd(vrts)
return (vrtg)
def uv2div(self, u, v, trunc=None):
pass
def uv2sfvp(self, u, v, trunc=None):
"""
Calculate geostrophic streamfuncion and
velocity potential from u and v winds
"""
psig, chig = self.s.getpsichi(u, v, ntrunc=trunc)
return (psig, chig)
def uv2vrtdiv(self, u, v, trunc=None):
"""
Calculate relative vorticity and divergence
from u and v winds
"""
vrts, divs = self.s.getvrtdivspec(u, v, ntrunc=trunc)
vrtg = self.s.spectogrd(vrts)
divg = self.s.spectogrd(divs)
return (vrtg, divg)
def vrtdiv2uv(self, vrt, div, realm='grid', trunc=None):
"""
# Get u,v from vrt, div fields
# Input either in grid space
# or in spectral space
"""
if realm in ['g', 'grid']:
vrts = self.s.grdtospec(vrt, trunc)
divs = self.s.grdtospec(div, trunc)
elif realm in ['s', 'spec', 'spectral']:
vrts = vrt
divs = div
ug, vg = self.s.getuv(vrts, divs)
return (ug, vg)
def gradient(self, var, trunc=None):
"""
Calculate horizontal gradients
"""
# if self.ReverseLat is True:
# var = self._reverse_lat(var)
try:
var = var.filled(fill_value=np.nan)
except AttributeError:
pass
if np.isnan(var).any():
raise ValueError('var cannot contain missing values')
try:
varspec = self.s.grdtospec(var, ntrunc=trunc)
except ValueError:
raise ValueError('input field is not compatitble')
dxvarg, dyvarg = self.s.getgrad(varspec)
return (dxvarg, dyvarg)
from spharm import Spharmt, getspecindx
import matplotlib.pyplot as plt
import numpy as np
# set up orthographic map projection.
map = Basemap(projection='ortho',lat_0=30,lon_0=-60,resolution='l')
# draw coastlines, country boundaries, fill continents.
map.drawcoastlines()
# draw the edge of the map projection region (the projection limb)
map.drawmapboundary()
# draw lat/lon grid lines every 30 degrees.
map.drawmeridians(np.arange(0,360,30))
map.drawparallels(np.arange(-90,90,30))
min = int(raw_input('input degree (m) of legendre function to plot:'))
nin = int(raw_input('input order (n) of legendre function to plot:'))
nlons = 720; nlats = 361
x = Spharmt(nlons,nlats,legfunc='computed')
ntrunc = nlats-1
indxm, indxn = getspecindx(ntrunc)
nm = -1
i = 0
for m,n in zip(indxm,indxn):
if m == min and n == nin:
nm = i
exit
else:
i = i + 1
if nm < 0:
raise ValueError('invalid m,n - must fit within triangular truncation at wavenumber '+repr(ntrunc))
coeffs = np.zeros((ntrunc+1)*(ntrunc+2)/2,np.complex)
coeffs[nm] = 1.
spharmonic = x.spectogrd(coeffs)
# grid, time step info
nlons = 128 # number of longitudes
ntrunc = 42 # spectral truncation (for alias-free computations)
nlats = (nlons/2)+1 # for regular grid.
gridtype = 'regular'
#nlats = nlons/2 # for gaussian grid.
#gridtype = 'gaussian'
dt = 1800 # time step in seconds
itmax = int(5*(86400/dt)) # integration length in days
umax = 50. # jet speed
jetexp = 6 # parameter controlling jet width
# create spherical harmonic instance.
rsphere = 6.37122e6 # earth radius
sp = Spharmt(nlons,nlats,rsphere=rsphere,gridtype=gridtype)
# create model instance using default parameters.
model = TwoLevel(sp,dt,ntrunc)
# vort, div initial conditions
psipert = np.zeros((sp.nlat,sp.nlon,2),np.float32)
psipert[:,:,1] = 5.e6*np.sin((model.lons-np.pi))**12*np.sin(2.*model.lats)**12
psipert = np.where(model.lons[:,:,np.newaxis] > 0., 0, psipert)
ug = np.zeros((sp.nlat,sp.nlon,2),np.float32)
vg = np.zeros((sp.nlat,sp.nlon,2),np.float32)
ug[:,:,1] = umax*np.sin(2.*model.lats)**jetexp
vrtspec, tmpspec = sp.getvrtdivspec(ug,vg,model.ntrunc)
vrtspec = vrtspec + model.lap[:,np.newaxis]*sp.grdtospec(psipert,model.ntrunc)
thetaspec = model.nlbalance(vrtspec)
divspec = np.zeros(thetaspec.shape, thetaspec.dtype)
spec1 = None; spec2 = None; spec3 = None; spec4 = None
for date in dates:
# get first guess for expt 1 (hybrid gain)
datapath = '/scratch3/BMC/gsienkf/whitaker/%s' % expt1
print datapath
print date
filename = os.path.join(os.path.join(datapath,date),'sfg_%s_fhr06_ensmean.nc4' % date)
nc = Dataset(filename)
if spec1 is None:
lons = nc['lon'][:]
lats = nc['lat'][::-1]
nlats = len(lats); nlons = len(lons)
lons2, lats2 = np.meshgrid(lons, lats)
re = 6.3712e6; ntrunc=nlats-1
spec = Spharmt(nlons,nlats,rsphere=re,gridtype='regular',legfunc='computed')
indxm, indxn = getspecindx(ntrunc)
degree = indxn.astype(np.float)
if var == 'pressfc':
fg1 = nc[var][0,::-1,...]
else:
fg1 = nc[var][0,nlev,::-1,...]
nc.close()
# get first guess for expt 2 (hybrid cov/envar)
datapath = '/scratch3/BMC/gsienkf/whitaker/%s' % expt2
print datapath
print date
filename = os.path.join(os.path.join(datapath,date),'sfg_%s_fhr06_ensmean.nc4' % date)
nc = Dataset(filename)
if var == 'pressfc':
# set model parameters. nlons = 128 # number of longitudes ntrunc = 42 # spectral truncation (for alias-free computations) nlats = (nlons / 2) + 1 # for regular grid. gridtype = 'regular' dt = 900 # time step in seconds tdiab = 12. * 86400 # thermal relaxation time scale tdrag = 4. * 86400. # lower layer drag efold = 4 * dt # hyperdiffusion time scale rsphere = 6.37122e6 # earth radius jetexp = 2 umax = 40 moistfact = 0.1 # create spherical harmonic instance. sp = Spharmt(nlons, nlats, rsphere=rsphere, gridtype=gridtype) # create model instance. model =\ TwoLevel(sp,dt,ntrunc,efold=efold,tdiab=tdiab,tdrag=tdrag,jetexp=jetexp,umax=umax,moistfact=moistfact) # initial state is equilbrium jet + random noise. vg = np.zeros((sp.nlat, sp.nlon, 2), np.float32) ug = model.uref vrtspec, divspec = sp.getvrtdivspec(ug, vg, model.ntrunc) psispec = np.zeros(vrtspec.shape, vrtspec.dtype) psispec.real += npran.normal(scale=1.e4, size=(psispec.shape)) psispec.imag += npran.normal(scale=1.e4, size=(psispec.shape)) vrtspec = vrtspec + model.lap[:, np.newaxis] * psispec thetaspec = model.nlbalance(vrtspec) divspec = np.zeros(thetaspec.shape, thetaspec.dtype)
import matplotlib.pyplot as plt
import numpy as np
# set up orthographic map projection.
map = Basemap(projection='ortho', lat_0=30, lon_0=-60, resolution='l')
# draw coastlines, country boundaries, fill continents.
map.drawcoastlines()
# draw the edge of the map projection region (the projection limb)
map.drawmapboundary()
# draw lat/lon grid lines every 30 degrees.
map.drawmeridians(np.arange(0, 360, 30))
map.drawparallels(np.arange(-90, 90, 30))
min = int(raw_input('input degree (m) of legendre function to plot:'))
nin = int(raw_input('input order (n) of legendre function to plot:'))
nlons = 720
nlats = 361
x = Spharmt(nlons, nlats, legfunc='computed')
ntrunc = nlats - 1
indxm, indxn = getspecindx(ntrunc)
nm = -1
i = 0
for m, n in zip(indxm, indxn):
if m == min and n == nin:
nm = i
exit
else:
i = i + 1
if nm < 0:
raise ValueError(
'invalid m,n - must fit within triangular truncation at wavenumber ' +
repr(ntrunc))
coeffs = np.zeros((ntrunc + 1) * (ntrunc + 2) / 2, np.complex)
f = f - f.mean(axis=0) a = a - a.mean(axis=0) covfa = (f*a).mean(axis=0) varf = (f**2).mean(axis=0) vara = (a**2).mean(axis=0) return covfa/(np.sqrt(varf)*np.sqrt(vara)) def getmse(f,a): return ((f-a)**2).mean(axis=0) nlonsin = 800; nlatsin = 400 nlons = 360; nlats = 181 ntrunc = 20 latbound = 20. sin = Spharmt(nlonsin,nlatsin) sout = Spharmt(nlons,nlats) delta = 360./nlons lats = 90.-delta*np.arange(nlats) coslats = np.cos((np.pi/180.)*lats) coslats = coslats[:,np.newaxis]*np.ones((nlats,nlons)) latnh = lats.tolist().index(latbound) latsh = lats.tolist().index(-latbound) coslatsnh = coslats[0:latnh+1,:] coslatssh = coslats[latsh:,:] coslatstr = coslats[latnh:latsh+1,:] lons = delta*np.arange(nlons) lons, lats = np.meshgrid(lons,lats[::-1]) filename = varshort
def main():
# non-linear barotropically unstable shallow water test case
# of Galewsky et al (2004, Tellus, 56A, 429-440).
# "An initial-value problem for testing numerical models of the global
# shallow-water equations" DOI: 10.1111/j.1600-0870.2004.00071.x
# http://www-vortex.mcs.st-and.ac.uk/~rks/reprints/galewsky_etal_tellus_2004.pdf
# requires matplotlib for plotting.
# grid, time step info
nlons = 256 # number of longitudes
ntrunc = int(nlons/3) # spectral truncation (for alias-free computations)
nlats = int(nlons/2) # for gaussian grid.
dt = 150 # time step in seconds
itmax = 6*int(86400/dt) # integration length in days
# parameters for test
rsphere = 6.37122e6 # earth radius
omega = 7.292e-5 # rotation rate
grav = 9.80616 # gravity
hbar = 10.e3 # resting depth
umax = 80. # jet speed
phi0 = np.pi/7.; phi1 = 0.5*np.pi - phi0; phi2 = 0.25*np.pi
en = np.exp(-4.0/(phi1-phi0)**2)
alpha = 1./3.; beta = 1./15.
hamp = 120. # amplitude of height perturbation to zonal jet
efold = 3.*3600. # efolding timescale at ntrunc for hyperdiffusion
ndiss = 8 # order for hyperdiffusion
# setup up spherical harmonic instance, set lats/lons of grid
x = Spharmt(nlons,nlats,ntrunc,rsphere,gridtype='gaussian')
lons,lats = np.meshgrid(x.lons,x.lats)
f = 2.*omega*np.sin(lats) # coriolis
# zonal jet.
vg = np.zeros((nlats,nlons),np.float)
u1 = (umax/en)*np.exp(1./((x.lats-phi0)*(x.lats-phi1)))
ug = np.zeros((nlats),np.float)
ug = np.where(np.logical_and(x.lats < phi1, x.lats > phi0), u1, ug)
ug.shape = (nlats,1)
ug = ug*np.ones((nlats,nlons),dtype=np.float) # broadcast to shape (nlats,nlonss)
# height perturbation.
hbump = hamp*np.cos(lats)*np.exp(-((lons-np.pi)/alpha)**2)*np.exp(-(phi2-lats)**2/beta)
# initial vorticity, divergence in spectral space
vrtspec, divspec = x.getvrtdivspec(ug,vg)
vrtg = x.spectogrd(vrtspec)
divg = x.spectogrd(divspec)
# create hyperdiffusion factor
hyperdiff_fact = np.exp((-dt/efold)*(x.lap/x.lap[-1])**(ndiss/2))
# solve nonlinear balance eqn to get initial zonal geopotential,
# add localized bump (not balanced).
vrtg = x.spectogrd(vrtspec)
tmpg1 = ug*(vrtg+f); tmpg2 = vg*(vrtg+f)
tmpspec1, tmpspec2 = x.getvrtdivspec(tmpg1,tmpg2)
tmpspec2 = x.grdtospec(0.5*(ug**2+vg**2))
phispec = x.invlap*tmpspec1 - tmpspec2
phig = grav*(hbar + hbump) + x.spectogrd(phispec)
phispec = x.grdtospec(phig)
# initialize spectral tendency arrays
ddivdtspec = np.zeros(vrtspec.shape+(3,), np.complex)
dvrtdtspec = np.zeros(vrtspec.shape+(3,), np.complex)
dphidtspec = np.zeros(vrtspec.shape+(3,), np.complex)
nnew = 0; nnow = 1; nold = 2
# time loop.
time1 = time.time()
for ncycle in range(itmax+1):
t = ncycle*dt
# get vort,u,v,phi on grid
vrtg = x.spectogrd(vrtspec)
ug,vg = x.getuv(vrtspec,divspec)
phig = x.spectogrd(phispec)
print('t=%6.2f hours: min/max %6.2f, %6.2f' % (t/3600.,vg.min(), vg.max()))
# compute tendencies.
tmpg1 = ug*(vrtg+f); tmpg2 = vg*(vrtg+f)
ddivdtspec[:,nnew], dvrtdtspec[:,nnew] = x.getvrtdivspec(tmpg1,tmpg2)
dvrtdtspec[:,nnew] *= -1
tmpg = x.spectogrd(ddivdtspec[:,nnew])
tmpg1 = ug*phig; tmpg2 = vg*phig
tmpspec, dphidtspec[:,nnew] = x.getvrtdivspec(tmpg1,tmpg2)
dphidtspec[:,nnew] *= -1
tmpspec = x.grdtospec(phig+0.5*(ug**2+vg**2))
ddivdtspec[:,nnew] += -x.lap*tmpspec
# update vort,div,phiv with third-order adams-bashforth.
# forward euler, then 2nd-order adams-bashforth time steps to start.
if ncycle == 0:
dvrtdtspec[:,nnow] = dvrtdtspec[:,nnew]
dvrtdtspec[:,nold] = dvrtdtspec[:,nnew]
ddivdtspec[:,nnow] = ddivdtspec[:,nnew]
ddivdtspec[:,nold] = ddivdtspec[:,nnew]
dphidtspec[:,nnow] = dphidtspec[:,nnew]
dphidtspec[:,nold] = dphidtspec[:,nnew]
elif ncycle == 1:
dvrtdtspec[:,nold] = dvrtdtspec[:,nnew]
ddivdtspec[:,nold] = ddivdtspec[:,nnew]
dphidtspec[:,nold] = dphidtspec[:,nnew]
vrtspec += dt*( \
(23./12.)*dvrtdtspec[:,nnew] - (16./12.)*dvrtdtspec[:,nnow]+ \
(5./12.)*dvrtdtspec[:,nold] )
divspec += dt*( \
(23./12.)*ddivdtspec[:,nnew] - (16./12.)*ddivdtspec[:,nnow]+ \
(5./12.)*ddivdtspec[:,nold] )
phispec += dt*( \
(23./12.)*dphidtspec[:,nnew] - (16./12.)*dphidtspec[:,nnow]+ \
(5./12.)*dphidtspec[:,nold] )
# implicit hyperdiffusion for vort and div.
vrtspec *= hyperdiff_fact
divspec *= hyperdiff_fact
# switch indices, do next time step.
nsav1 = nnew; nsav2 = nnow
nnew = nold; nnow = nsav1; nold = nsav2
time2 = time.time()
print('CPU time = ',time2-time1)
# make a contour plot of potential vorticity in the Northern Hem.
fig = plt.figure(figsize=(12,4))
# dimensionless PV
pvg = (0.5*hbar*grav/omega)*(vrtg+f)/phig
print('max/min PV',pvg.min(), pvg.max())
lons1d = (180./np.pi)*x.lons-180.; lats1d = (180./np.pi)*x.lats
levs = np.arange(-0.2,1.801,0.1)
cs=plt.contourf(lons1d,lats1d,pvg,levs,extend='both')
cb=plt.colorbar(cs,orientation='horizontal') # add colorbar
cb.set_label('potential vorticity')
plt.grid()
plt.xlabel('degrees longitude')
plt.ylabel('degrees latitude')
plt.xticks(np.arange(-180,181,60))
plt.yticks(np.arange(-5,81,20))
plt.axis('equal')
plt.axis('tight')
plt.ylim(0,lats1d[0])
plt.title('PV (T%s with hyperdiffusion, hour %6.2f)' % (ntrunc,t/3600.))
plt.savefig("output_swe.pdf")
plt.show()
def __init__(self, u, v, gridtype='regular', rsphere=6.3712e6):
"""Initialize a VectorWind instance.
**Arguments:**
*u*, *v*
Zonal and meridional wind components respectively. Their
types should be either `numpy.ndarray` or
`numpy.ma.MaskedArray`. *u* and *v* must have matching
shapes and contain no missing values. *u* and *v* may be 2
or 3-dimensional with shape (nlat, nlon) or
(nlat, nlon, nt), where nlat and nlon are the number of
latitudes and longitudes respectively and nt is the number
of fields. The latitude dimension must be oriented
north-to-south. The longitude dimension should be
oriented west-to-east.
**Optional arguments:**
*gridtype*
Type of the input grid, either 'regular' for evenly-spaced
grids, or 'gaussian' for Gaussian grids. Defaults to
'regular'.
*rsphere*
The radius in metres of the sphere used in the spherical
harmonic computations. Default is 6371200 m, the approximate
mean spherical Earth radius.
**See also:**
`~windspharm.tools.prep_data`,
`~windspharm.tools.recover_data`,
`~windspharm.tools.get_recovery`,
`~windspharm.tools.reverse_latdim`,
`~windspharm.tools.order_latdim`.
**Examples:**
Initialize a `VectorWind` instance with zonal and meridional
components of the vector wind on the default regular
(evenly-spaced) grid:
from windspharm.standard import VectorWind
w = VectorWind(u, v)
Initialize a `VectorWind` instance with zonal and meridional
components of the vector wind specified on a Gaussian grid:
from windspharm.standard import VectorWind
w = VectorWind(u, v, gridtype='gaussian')
"""
# For both the input components check if there are missing values by
# attempting to fill missing values with NaN and detect them. If the
# inputs are not masked arrays then take copies and check for NaN.
try:
self.u = u.filled(fill_value=np.nan)
except AttributeError:
self.u = u.copy()
try:
self.v = v.filled(fill_value=np.nan)
except AttributeError:
self.v = v.copy()
if np.isnan(self.u).any() or np.isnan(self.v).any():
raise ValueError('u and v cannot contain missing values')
# Make sure the shapes of the two components match.
if u.shape != v.shape:
raise ValueError('u and v must be the same shape')
if len(u.shape) not in (2, 3):
raise ValueError('u and v must be rank 2 or 3 arrays')
nlat = u.shape[0]
nlon = u.shape[1]
try:
# Create a Spharmt object to do the computations.
self.gridtype = gridtype.lower()
self.s = Spharmt(nlon,
nlat,
gridtype=self.gridtype,
rsphere=rsphere)
except ValueError:
if self.gridtype not in ('regular', 'gaussian'):
err = 'invalid grid type: {0:s}'.format(repr(gridtype))
else:
err = 'invalid input dimensions'
raise ValueError(err)
# Method aliases.
self.rotationalcomponent = self.nondivergentcomponent
self.divergentcomponent = self.irrotationalcomponent
class VectorWind(object):
"""Vector Wind computations (standard :py:mod:`numpy` interface)."""
def __init__(self, u, v, gridtype='regular'):
"""Initialize a VectorWind instance.
**Arguments:**
*u*, *v*
Zonal and meridional wind components respectively. Their
types should be either :py:class:`numpy.ndarray` or
:py:class:`numpy.ma.MaskedArray`. *u* and *v* must have
matching shapes and contain no missing values. *u* and *v*
may be 2 or 3-dimensional with shape (nlat, nlon) or
(nlat, nlon, nt), where nlat and nlon are the number of
latitudes and longitudes respectively and nt is the number
of fields. The latitude dimension must be oriented
north-to-south. The longitude dimension should be
oriented west-to-east.
**Optional argument:**
*gridtype*
Type of the input grid, either 'regular' for evenly-spaced
grids, or 'gaussian' for Gaussian grids. Defaults to
'regular'.
**Examples:**
Initialize a VectorWind instance with zonal and meridional
components of the vector wind on the default regular
(evenly-spaced) grid:
from windspharm.standard import VectorWind
w = VectorWind(u, v)
Initialize a VectorWind instance with zonal and meridional
components of the vector wind specified on a Gaussian grid:
from windspharm.standard import VectorWind
w = VectorWind(u, v, gridtype='gaussian')
"""
# For both the input components check if there are missing values by
# attempting to fill missing values and detect them. If the inputs are
# not masked arrays then this check isn't needed so take a copy.
try:
self.u = u.filled()
if (self.u == u.fill_value).any():
raise ValueError('u and v cannot contain missing values')
except AttributeError:
self.u = u.copy()
try:
self.v = v.filled()
if (self.v == v.fill_value).any():
raise ValueError('u and v cannot contain missing values')
except AttributeError:
self.v = v.copy()
# Check for NaN values.
if np.isnan(self.u).any() or np.isnan(self.v).any():
raise ValueError('u and v cannot contain missing values')
# Make sure the shapes of the two components match.
if u.shape != v.shape:
raise ValueError('u and v must be the same shape')
if len(u.shape) not in (2, 3):
raise ValueError('u and v must be rank 2 or 3 arrays')
try:
# Get the number of latitudes and longitudes.
nlat = u.shape[0]
nlon = u.shape[1]
except AssertionError:
raise ValueError('nlon must be >= 4 and nlat must be >= 3')
try:
# Create a Spharmt object to do the computations.
self.gridtype = gridtype.lower()
self.s = Spharmt(nlon, nlat, gridtype=self.gridtype)
except ValueError:
if self.gridtype not in ('regular', 'gaussian'):
err = 'invalid grid type: {0:s}'.format(repr(gridtype))
else:
err = 'invalid input dimensions'
raise ValueError(err)
# Method aliases.
self.rotationalcomponent = self.nondivergentcomponent
self.divergentcomponent = self.irrotationalcomponent
def magnitude(self):
"""Wind speed (magnitude of vector wind).
**Example:**
spd = w.magnitude()
"""
return (u ** 2 + v ** 2) ** 0.5
def vrtdiv(self, truncation=None):
"""Relative vorticity and horizontal divergence.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Examples:**
Compute the relative vorticity and divergence:
vrt, div = w.vrtdiv()
Compute the relative vorticity and divergence and apply spectral
truncation at triangular T13:
vrtT13, divT13 = w.vrtdiv(truncation=13)
"""
vrtspec, divspec = self.s.getvrtdivspec(self.u,
self.v,
ntrunc=truncation)
vrtgrid = self.s.spectogrd(vrtspec)
divgrid = self.s.spectogrd(divspec)
return vrtgrid, divgrid
def vorticity(self, truncation=None):
"""Relative vorticity.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Examples:**
Compute the relative vorticity:
vrt = w.vorticity()
Compute the relative vorticity and apply spectral truncation at
triangular T13:
vrtT13 = w.vorticity(truncation=13)
"""
vrtspec, divspec = self.s.getvrtdivspec(self.u,
self.v,
ntrunc=truncation)
vrtgrid = self.s.spectogrd(vrtspec)
return vrtgrid
def divergence(self, truncation=None):
"""Horizontal divergence.
**Optional argument:**
*truncation*
Truncation limit (triangular truncation) for the spherical
harmonic computation.
**Examples:**
Compute the divergence:
div = w.divergence()
Compute the divergence and apply spectral truncation at
triangular T13:
divT13 = w.divergence(truncation=13)
"""
vrtspec, divspec = self.s.getvrtdivspec(self.u,
self.v,
ntrunc=truncation)
divgrid = self.s.spectogrd(divspec)
return divgrid
def planetaryvorticity(self, omega=None):
"""Planetary vorticity (Coriolis parameter).
**Optional argument:**
*omega*
Earth's angular velocity. The default value if not specified
is 7.292x10**-5 s**-1.
**Example:**
Compute planetary vorticity using default values:
pvrt = w.planetaryvorticity()
Override the default value for Earth's angular velocity:
pvrt = w.planetaryvorticity(omega=7.2921150)
"""
if omega is None:
# Define the Earth's angular velocity.
omega = 7.292e-05
nlat = self.s.nlat
if self.gridtype == 'gaussian':
lat, wts = gaussian_lats_wts(nlat)
else:
if nlat % 2:
lat = np.linspace(90, -90, nlat)
else:
dlat = 180. / nlat
lat = np.arange(90 - dlat / 2., -90, -dlat)
try:
cp = 2. * omega * np.sin(np.deg2rad(lat))
except TypeError, ValueError:
raise ValueError('invalid value for omega: {!r}'.format(omega))
indices = [slice(0, None)] + [np.newaxis] * (len(self.u.shape) - 1)
f = cp[indices] * np.ones(self.u.shape, dtype=np.float32)
return f
def __init__(self, u, v, gridtype='regular', rsphere=6.3712e6):
"""Initialize a VectorWind instance.
**Arguments:**
*u*, *v*
Zonal and meridional wind components respectively. Their
types should be either `numpy.ndarray` or
`numpy.ma.MaskedArray`. *u* and *v* must have matching
shapes and contain no missing values. *u* and *v* may be 2
or 3-dimensional with shape (nlat, nlon) or
(nlat, nlon, nt), where nlat and nlon are the number of
latitudes and longitudes respectively and nt is the number
of fields. The latitude dimension must be oriented
north-to-south. The longitude dimension should be
oriented west-to-east.
**Optional argument:**
*gridtype*
Type of the input grid, either 'regular' for evenly-spaced
grids, or 'gaussian' for Gaussian grids. Defaults to
'regular'.
**See also:**
`~windspharm.tools.prep_data`,
`~windspharm.tools.recover_data`,
`~windspharm.tools.get_recovery`,
`~windspharm.tools.reverse_latdim`,
`~windspharm.tools.order_latdim`.
**Examples:**
Initialize a `VectorWind` instance with zonal and meridional
components of the vector wind on the default regular
(evenly-spaced) grid:
from windspharm.standard import VectorWind
w = VectorWind(u, v)
Initialize a `VectorWind` instance with zonal and meridional
components of the vector wind specified on a Gaussian grid:
from windspharm.standard import VectorWind
w = VectorWind(u, v, gridtype='gaussian')
"""
# For both the input components check if there are missing values by
# attempting to fill missing values with NaN and detect them. If the
# inputs are not masked arrays then take copies and check for NaN.
try:
self.u = u.filled(fill_value=np.nan)
except AttributeError:
self.u = u.copy()
try:
self.v = v.filled(fill_value=np.nan)
except AttributeError:
self.v = v.copy()
if np.isnan(self.u).any() or np.isnan(self.v).any():
raise ValueError('u and v cannot contain missing values')
# Make sure the shapes of the two components match.
if u.shape != v.shape:
raise ValueError('u and v must be the same shape')
if len(u.shape) not in (2, 3):
raise ValueError('u and v must be rank 2 or 3 arrays')
nlat = u.shape[0]
nlon = u.shape[1]
try:
# Create a Spharmt object to do the computations.
self.gridtype = gridtype.lower()
self.s = Spharmt(nlon, nlat, gridtype=self.gridtype,
rsphere=rsphere)
except ValueError:
if self.gridtype not in ('regular', 'gaussian'):
err = 'invalid grid type: {0:s}'.format(repr(gridtype))
else:
err = 'invalid input dimensions'
raise ValueError(err)
# Method aliases.
self.rotationalcomponent = self.nondivergentcomponent
self.divergentcomponent = self.irrotationalcomponent
class PowerSpectrum(EvaluationMethod):
def __init__(self, H, W):
super(PowerSpectrum, self).__init__()
self.spharm = Spharmt(W, H, legfunc='stored')
self.spectrums = []
self.needs_sh = True
def _calc_energy_spectrum(self, div_vort):
sh = self.spharm.grdtospec(div_vort)
u, v = self.spharm.getuv(sh[..., 1], sh[..., 0])
u_sh = pysh.expand.SHExpandDH(u)
u_spectrum = pysh.spectralanalysis.spectrum(u_sh) # <-> u^2
v_sh = pysh.expand.SHExpandDH(v)
v_spectrum = pysh.spectralanalysis.spectrum(v_sh) # <-> v^2
return 0.5 * (u_spectrum + v_spectrum) # <-> 0.5 * (u^2 + v^2)
def set_shape(self, shape):
self.shape = shape
self.spectrums = [[] for _ in range(self.shape[-1])]
self.energy_spectrum = []
def evaluate_SR_sh(self, i, LR, SR, SR_sh):
for c in range(SR_sh.shape[-1]):
self.spectrums[c] += [
pysh.spectralanalysis.spectrum(sh) for sh in SR_sh[..., c]
]
self.energy_spectrum += [self._calc_energy_spectrum(img) for img in SR]
def finalize(self):
spectrums = np.asarray(self.spectrums) # C x N x L
mean_spectrum = np.mean(spectrums, axis=1)
for c, spectrum in enumerate(mean_spectrum):
np.savetxt(self.dir / f'spectrum_channel_{c}.csv', spectrum)
energy_spectrum = np.mean(np.asarray(self.energy_spectrum), axis=0)
np.savetxt(self.dir / 'energy_spectrum.csv', energy_spectrum)
self.summarize({'SR': self.dir}, self.dir)
def summarize(self, paths, outdir):
p = paths[next(iter(paths))]
C = len(glob(str(p / 'spectrum_channel_*.csv')))
for c in range(C):
plt.figure(figsize=(10, 5))
plt.xscale('log')
plt.yscale('log')
plt.xlabel('wavenumber')
plt.ylabel('energy')
for name, path in paths.items():
spectrum = np.loadtxt(path / f'spectrum_channel_{c}.csv')
x = np.arange(1, 1 + spectrum.shape[0])
plt.plot(x, spectrum, label=name)
plt.plot(x, x**(-5 / 3) * spectrum[0], '--')
plt.legend()
plt.savefig(outdir / f'spectrum_channel_{c}.png')
plt.figure(figsize=(10, 5))
plt.xscale('log')
plt.yscale('log')
plt.xlabel('wavenumber')
plt.ylabel('energy')
for name, path in paths.items():
spectrum = np.loadtxt(path / 'energy_spectrum.csv')
x = np.arange(1, 1 + spectrum.shape[0])
plt.plot(x, spectrum, label=name)
plt.plot(x, x**(-5 / 3) * spectrum[0], '--')
plt.legend()
plt.savefig(outdir / 'energy_spectrum.png')
date, date)
nc = Dataset(fcstfile)
if ntime is None:
times = nc['time'][:].tolist()
levels = nc['plev'][:].tolist()
ntime = times.index(fhour)
nlev = levels.index(level)
lons = nc['longitude'][:]
lats = nc['latitude'][:]
nlons = len(lons)
nlats = len(lats)
re = 6.3712e6
ntrunc = nlats - 1
spec = Spharmt(nlons,
nlats,
rsphere=re,
gridtype='regular',
legfunc='computed')
indxm, indxn = getspecindx(ntrunc)
degree = indxn.astype(np.float)
if int(nc['time'][ntime]) != fhour:
raise ValueError('incorrect forecast time')
fcst_data1 = nc[varnc][ntime, nlev, ...]
nc.close()
if fhour > 9:
fcstfile = '%s/%s/fv3longcontrol2_historyp_%s_latlon.nc' % (datapath2,
date, date)
else:
fcstfile = '%s/%s/fv3control2_historyp_%s_latlon.nc' % (datapath2,
date, date)
nc = Dataset(fcstfile)
# parameters for test rsphere = 6.37122e6 # earth radius omega = 7.292e-5 # rotation rate grav = 9.80616 # gravity hbar = 10.e3 # resting depth umax = 80. # jet speed phi0 = np.pi/7.; phi1 = 0.5*np.pi - phi0; phi2 = 0.25*np.pi en = np.exp(-4.0/(phi1-phi0)**2) alpha = 1./3.; beta = 1./15. hamp = 120. # amplitude of height perturbation to zonal jet efold = 3.*3600. # efolding timescale at ntrunc for hyperdiffusion ndiss = 8 # order for hyperdiffusion # setup up spherical harmonic instance, set lats/lons of grid x = Spharmt(nlons,nlats,rsphere=rsphere,gridtype=gridtype) delta = 2.*np.pi/nlons lats1d = 0.5*np.pi-delta*np.arange(nlats) lons1d = np.arange(-np.pi,np.pi,delta) lons,lats = np.meshgrid(lons1d,lats1d) f = 2.*omega*np.sin(lats) # coriolis # zonal jet. vg = np.zeros((nlats,nlons),np.float32) u1 = (umax/en)*np.exp(1./((lats1d-phi0)*(lats1d-phi1))) ug = np.zeros((nlats),np.float32) ug = np.where(np.logical_and(lats1d < phi1, lats1d > phi0), u1, ug) ug.shape = (nlats,1) ug = ug*np.ones((nlats,nlons),dtype=np.float32) # broadcast to shape (nlats,nlonss) # height perturbation. hbump = hamp*np.cos(lats)*np.exp(-(lons/alpha)**2)*np.exp(-(phi2-lats)**2/beta)
