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
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)
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
# 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)
def __init__(self, H, W):
super(PowerSpectrum, self).__init__()
self.spharm = Spharmt(W, H, legfunc='stored')
self.spectrums = []
self.needs_sh = True
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()
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
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)
# 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
