def windsfarm(): #Prepare wund for vector w = VectorWind(uwnd, vwnd) #Calculating basic variables eta = w.absolutevorticity() div = w.divergence() uchi, vchi = w.irrotationalcomponent() etax, etay = w.gradient(eta) planvor = w.planetaryvorticity S = -eta * div - uchi * etax - vchi * etay S = recover_data(S, uwnd_info) return(w, eta, div, uchi, vchi, etax, etay, planvor, S)
# either 2D or 3D arrays. The data read in is 3D and has latitude and # longitude as the last dimensions. The bundled tools can make the process of # re-shaping the data a lot easier to manage. uwnd, uwnd_info = prep_data(uwnd, "tyx") vwnd, vwnd_info = prep_data(vwnd, "tyx") # It is also required that the latitude dimension is north-to-south. Again the # bundled tools make this easy. lats, uwnd, vwnd = order_latdim(lats, uwnd, vwnd) # Create a VectorWind instance to handle the computations. w = VectorWind(uwnd, vwnd) # Compute components of rossby wave source: absolute vorticity, divergence, # irrotational (divergent) wind components, gradients of absolute vorticity. eta = w.absolutevorticity() div = w.divergence() uchi, vchi = w.irrotationalcomponent() etax, etay = w.gradient(eta) # Combine the components to form the Rossby wave source term. Re-shape the # Rossby wave source array to the 4D shape of the wind components as they were # read off files. S = -eta * div - (uchi * etax + vchi * etay) S = recover_data(S, uwnd_info) # Pick out the field for December and add a cyclic point (the cyclic point is # for plotting purposes). S_dec, lons_c = add_cyclic_point(S[11], lons) # Plot Rossby wave source.
# velocity in the Mercator projection
print np.shape(u)
um = u / coslat[:, None]
vm = v / coslat[:, None]
# um checked!!!
# Create a VectorWind instance to handle the computations.
# uwndT, uwnd_info = prep_data(uwnd, 'tyx')
# vwndT, vwnd_info = prep_data(vwnd, 'tyx')
#w = VectorWind(uwnd, vwnd)
# Compute absolute vorticity
w = VectorWind(u, v)
q = w.absolutevorticity()
#qbar = q
#qbar checked!!!
#----BetaM---------------------------------------------------------------------
print 'Calculate BetaM'
cos2 = coslat * coslat
# dum, cosuy=w.gradient(u*cos2[:,None])
# dum, cosuyy = w.gradient(cosuy/coslat[:,None])
#
# tmp = 2*e_omega *cos2/radius
# BetaM=tmp[:,None]-cosuyy
def calc_quantity(uwnd, vwnd, quantity, lat_axis, lon_axis, axis_order):
"""Calculate a single wind quantity.
Args:
uwnd (numpy.ndarray): Zonal wind
vwnd (numpy.ndarray): Meridional wind
quantity (str): Quantity to be calculated
lat_axis (list): Latitude axis values
lon_axis (list): Longitude axis values
axis_order (str): e.g. tyx
Design:
windsparm requires the input data to be on a global grid
(due to the spherical harmonic representation used),
latitude and longitude to be the leading axes and the
latitude axis must go from 90 to -90. The cdms2 interface
is supposed to adjust for these things but I've found that
things come back upsidedown if the lat axis isn't right, so
I've just used the standard interface here instead.
Reference:
ajdawson.github.io/windspharm
"""
check_global(lat_axis, lon_axis)
# Make latitude and longitude the leading coordinates
uwnd, uwnd_info = prep_data(numpy.array(uwnd), axis_order)
vwnd, vwnd_info = prep_data(numpy.array(vwnd), axis_order)
# Make sure latitude dimension is north-to-south
lats, uwnd, vwnd = order_latdim(lat_axis, uwnd, vwnd)
flip_lat = False if lats[0] == lat_axis[0] else True
w = VectorWind(uwnd, vwnd)
data_out = {}
if quantity == 'rossbywavesource':
eta = w.absolutevorticity()
div = w.divergence()
uchi, vchi = w.irrotationalcomponent()
etax, etay = w.gradient(eta)
data_out['rws1'] = (-eta * div) / (1.e-11)
data_out['rws2'] = (-(uchi * etax + vchi * etay)) / (1.e-11)
data_out['rws'] = data_out['rws1'] + data_out['rws2']
elif quantity == 'magnitude':
data_out['spd'] = w.magnitude()
elif quantity == 'vorticity':
data_out['vrt'] = w.vorticity()
elif quantity == 'divergence':
div = w.divergence()
data_out['div'] = div / (1.e-6)
elif quantity == 'absolutevorticity':
avrt = w.absolutevorticity()
data_out['avrt'] = avrt / (1.e-5)
elif quantity == 'absolutevorticitygradient':
avrt = w.absolutevorticity()
ugrad, vgrad = w.gradient(avrt)
avrtgrad = numpy.sqrt(numpy.square(ugrad) + numpy.square(vgrad))
data_out['avrtgrad'] = avrtgrad / (1.e-5)
elif quantity == 'planetaryvorticity':
data_out['pvrt'] = w.planetaryvorticity()
elif quantity == 'irrotationalcomponent':
data_out['uchi'], data_out['vchi'] = w.irrotationalcomponent()
elif quantity == 'nondivergentcomponent':
data_out['upsi'], data_out['vpsi'] = w.nondivergentcomponent()
elif quantity == 'streamfunction':
sf = w.streamfunction()
data_out['sf'] = sf / (1.e+6)
elif quantity == 'velocitypotential':
vp = w.velocitypotential()
data_out['vp'] = vp / (1.e+6)
else:
sys.exit('Wind quantity not recognised')
# Return data to its original shape
for key in data_out.keys():
data_out[key] = recover_structure(data_out[key], flip_lat, uwnd_info)
return data_out
def compute_rws(ds_u,
ds_v,
lat_coord='lat',
lon_coord='lon',
time_coord='time'):
"""
Computation of absolute vorticity, divergence, and Rossby wave source.
Outputs xarray datasets of each.
Args:
ds_u (xarray data array): Zonal (u) wind (m/s).
ds_v (xarray data array): Meridional (v) wind (m/s).
lat_coord (str): Latitude coordinate. Defaults to ``lat``.
lon_coord (str): Longitude coordinate. Defaults to ``lon``.
time_coord (str): Time coordinate. Defaults to ``time``.
Returns:
Xarray datasets for absolute vorticity, divergence, and Rossby wave source.
"""
from windspharm.standard import VectorWind
from windspharm.tools import prep_data, recover_data, order_latdim
# grab lat and lon coords
lats = ds_u.coords[lat_coord].values
lons = ds_u.coords[lon_coord].values
time = ds_u.coords[time_coord].values
_, wnd_info = prep_data(ds_u.values, 'tyx')
# reorder dims into lat, lon, time
uwnd = ds_u.transpose(lat_coord, lon_coord, time_coord).values
vwnd = ds_v.transpose(lat_coord, lon_coord, time_coord).values
# reorder lats to north-south direction
lats, uwnd, vwnd = order_latdim(lats, uwnd, vwnd)
# initialize wind vector instance
w = VectorWind(uwnd, vwnd)
# Absolute vorticity (sum of relative and planetary vorticity).
eta = w.absolutevorticity()
# Horizontal divergence.
div = w.divergence()
# Irrotational (divergent) component of the vector wind.
uchi, vchi = w.irrotationalcomponent()
# Computes the vector gradient of a scalar field on the sphere.
etax, etay = w.gradient(eta)
# Compute rossby wave source
S = -eta * div - (uchi * etax + vchi * etay)
# recover data shape
S = recover_data(S, wnd_info)
div = recover_data(div, wnd_info)
eta = recover_data(eta, wnd_info)
# assemble xarray datasets
data_rws = xr.Dataset({
'rws': (['time', 'lat', 'lon'], S),
},
coords={
'time': (['time'], time),
'lat': (['lat'], lats),
'lon': (['lon'], lons)
},
attrs={'long_name': 'Rossby wave source'})
data_div = xr.Dataset(
{
'div': (['time', 'lat', 'lon'], div),
},
coords={
'time': (['time'], time),
'lat': (['lat'], lats),
'lon': (['lon'], lons)
},
attrs={'long_name': 'Horizontal divergence (300-mb)'})
data_eta = xr.Dataset(
{
'eta': (['time', 'lat', 'lon'], eta),
},
coords={
'time': (['time'], time),
'lat': (['lat'], lats),
'lon': (['lon'], lons)
},
attrs={
'long_name':
'Absolute vorticity (sum of relative and planetary vorticity)'
})
return data_eta, data_div, data_rws
