Spherical harmonic transforms of 300-hPa wind by season

%config IPCompleter.greedy = True
%matplotlib inline
%config InlineBackend.figure_format='retina'

%load_ext autoreload
%autoreload 2

import warnings
warnings.filterwarnings("ignore")

import senpy as sp

import numpy  as np
import xarray as xr

import matplotlib
import matplotlib.pyplot as plt

from xspharm import xspharm

plt.style.use('science')

# era_ds = sp.ERA5_onelevel_vars(vars=['u10', 'v10']).mean('time').load()
era_ds = sp.ERA5_pressuelevel_vars(vars=['u', 'v']).sel(lev=300).groupby('time.month').mean('time').load()
era_ds

<xarray.Dataset>
Dimensions:  (month: 12, lat: 181, lon: 360)
Coordinates:
  * lon      (lon) float32 0.0 1.0 2.0 3.0 4.0 ... 355.0 356.0 357.0 358.0 359.0
  * lat      (lat) float32 -90.0 -89.0 -88.0 -87.0 -86.0 ... 87.0 88.0 89.0 90.0
    lev      int32 300
  * month    (month) int64 1 2 3 4 5 6 7 8 9 10 11 12
Data variables:
    u        (month, lat, lon) float32 4.266e-05 4.266e-05 ... 0.0001429
    v        (month, lat, lon) float32 -4.92e-05 -4.92e-05 ... -6.439e-05
Attributes:
    Conventions:  CF-1.6
    history:      2023-10-09 08:34:05 GMT by grib_to_netcdf-2.25.1: /opt/ecmw...

xarray.Dataset

• Dimensions:
  • month: 12
  • lat: 181
  • lon: 360
• Coordinates: (4)
  • lon
    (lon)
    float32
    0.0 1.0 2.0 ... 357.0 358.0 359.0

    units :

    degrees_east

    long_name :

    longitude

    array([  0.,   1.,   2., ..., 357., 358., 359.], dtype=float32)

  • lat
    (lat)
    float32
    -90.0 -89.0 -88.0 ... 89.0 90.0

    units :

    degrees_north

    long_name :

    latitude

    array([-90., -89., -88., -87., -86., -85., -84., -83., -82., -81., -80., -79.,
           -78., -77., -76., -75., -74., -73., -72., -71., -70., -69., -68., -67.,
           -66., -65., -64., -63., -62., -61., -60., -59., -58., -57., -56., -55.,
           -54., -53., -52., -51., -50., -49., -48., -47., -46., -45., -44., -43.,
           -42., -41., -40., -39., -38., -37., -36., -35., -34., -33., -32., -31.,
           -30., -29., -28., -27., -26., -25., -24., -23., -22., -21., -20., -19.,
           -18., -17., -16., -15., -14., -13., -12., -11., -10.,  -9.,  -8.,  -7.,
            -6.,  -5.,  -4.,  -3.,  -2.,  -1.,   0.,   1.,   2.,   3.,   4.,   5.,
             6.,   7.,   8.,   9.,  10.,  11.,  12.,  13.,  14.,  15.,  16.,  17.,
            18.,  19.,  20.,  21.,  22.,  23.,  24.,  25.,  26.,  27.,  28.,  29.,
            30.,  31.,  32.,  33.,  34.,  35.,  36.,  37.,  38.,  39.,  40.,  41.,
            42.,  43.,  44.,  45.,  46.,  47.,  48.,  49.,  50.,  51.,  52.,  53.,
            54.,  55.,  56.,  57.,  58.,  59.,  60.,  61.,  62.,  63.,  64.,  65.,
            66.,  67.,  68.,  69.,  70.,  71.,  72.,  73.,  74.,  75.,  76.,  77.,
            78.,  79.,  80.,  81.,  82.,  83.,  84.,  85.,  86.,  87.,  88.,  89.,
            90.], dtype=float32)

  • lev
    ()
    int32
    300

    units :

    millibars

    long_name :

    pressure_level

    array(300, dtype=int32)

  • month
    (month)
    int64
    1 2 3 4 5 6 7 8 9 10 11 12

    array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12])

• Data variables: (2)
  • u
    (month, lat, lon)
    float32
    4.266e-05 4.266e-05 ... 0.0001429

    units :

    m s**-1

    long_name :

    U component of wind

    standard_name :

    eastward_wind

    array([[[ 4.2661031e-05,  4.2661031e-05,  4.2661031e-05, ...,
              4.2661031e-05,  4.2661031e-05,  4.2661031e-05],
            [ 1.1175711e+00,  1.1388880e+00,  1.1607718e+00, ...,
              1.0522013e+00,  1.0742236e+00,  1.0956029e+00],
            [ 1.2989755e+00,  1.3317318e+00,  1.3654623e+00, ...,
              1.2049227e+00,  1.2359184e+00,  1.2669873e+00],
            ...,
            [ 9.5698261e-01,  9.8621190e-01,  1.0145204e+00, ...,
              8.6627144e-01,  8.9669335e-01,  9.2719775e-01],
            [-5.5998485e-03,  1.7559158e-02,  4.0160604e-02, ...,
             -7.8709498e-02, -5.3849284e-02, -2.8954612e-02],
            [ 4.2661031e-05,  4.2661031e-05,  4.2661031e-05, ...,
              4.2661031e-05,  4.2661031e-05,  4.2661031e-05]],
    
           [[-3.2249026e-04, -3.2249026e-04, -3.2249026e-04, ...,
             -3.2249026e-04, -3.2249026e-04, -3.2249026e-04],
            [ 7.7612197e-01,  7.4263918e-01,  7.0957458e-01, ...,
              8.7755048e-01,  8.4339768e-01,  8.0924189e-01],
            [ 8.7946057e-01,  8.5654765e-01,  8.3557618e-01, ...,
              9.5789462e-01,  9.3058711e-01,  9.0415740e-01],
    ...
            [ 2.4561417e+00,  2.4767909e+00,  2.4955268e+00, ...,
              2.3900282e+00,  2.4123766e+00,  2.4344604e+00],
            [ 1.3433924e+00,  1.3593796e+00,  1.3741091e+00, ...,
              1.2898577e+00,  1.3087554e+00,  1.3263352e+00],
            [-1.3097850e-04, -1.3097850e-04, -1.3097850e-04, ...,
             -1.3097850e-04, -1.3097850e-04, -1.3097850e-04]],
    
           [[ 1.4294278e-04,  1.4294278e-04,  1.4294278e-04, ...,
              1.4294278e-04,  1.4294278e-04,  1.4294278e-04],
            [ 1.4239448e+00,  1.4606490e+00,  1.4971709e+00, ...,
              1.3142494e+00,  1.3508402e+00,  1.3875641e+00],
            [ 1.4955662e+00,  1.5394915e+00,  1.5840343e+00, ...,
              1.3663207e+00,  1.4090148e+00,  1.4521546e+00],
            ...,
            [ 8.8072732e-02,  9.5349357e-02,  1.0228586e-01, ...,
              6.5601870e-02,  7.3517233e-02,  8.0901794e-02],
            [-8.0075037e-01, -7.9545748e-01, -7.9096913e-01, ...,
             -8.1793958e-01, -8.1150782e-01, -8.0585134e-01],
            [ 1.4294278e-04,  1.4294278e-04,  1.4294278e-04, ...,
              1.4294278e-04,  1.4294278e-04,  1.4294278e-04]]], dtype=float32)

  • v
    (month, lat, lon)
    float32
    -4.92e-05 -4.92e-05 ... -6.439e-05

    units :

    m s**-1

    long_name :

    V component of wind

    standard_name :

    northward_wind

    array([[[-4.91956853e-05, -4.91956853e-05, -4.91956853e-05, ...,
             -4.91956853e-05, -4.91956853e-05, -4.91956853e-05],
            [-7.11467803e-01, -7.06154764e-01, -7.00233519e-01, ...,
             -7.23533094e-01, -7.20069468e-01, -7.16146708e-01],
            [-1.16331327e+00, -1.16681063e+00, -1.16899872e+00, ...,
             -1.14482868e+00, -1.15226948e+00, -1.15822268e+00],
            ...,
            [ 1.37612486e+00,  1.34870219e+00,  1.32101035e+00, ...,
              1.45584297e+00,  1.42941284e+00,  1.40296805e+00],
            [ 1.25123727e+00,  1.24477315e+00,  1.23816872e+00, ...,
              1.26926410e+00,  1.26356578e+00,  1.25762558e+00],
            [-4.91956853e-05, -4.91956853e-05, -4.91956853e-05, ...,
             -4.91956853e-05, -4.91956853e-05, -4.91956853e-05]],
    
           [[ 2.61127279e-04,  2.61127279e-04,  2.61127279e-04, ...,
              2.61127279e-04,  2.61127279e-04,  2.61127279e-04],
            [ 2.31422448e+00,  2.30678678e+00,  2.29926276e+00, ...,
              2.33296275e+00,  2.32722259e+00,  2.32102108e+00],
            [ 1.91298687e+00,  1.88807070e+00,  1.86311257e+00, ...,
              1.98860371e+00,  1.96334195e+00,  1.93828714e+00],
    ...
              1.13175595e+00,  1.09039783e+00,  1.04891241e+00],
            [ 9.53117728e-01,  9.29101229e-01,  9.04685438e-01, ...,
              1.02475464e+00,  1.00112188e+00,  9.77232039e-01],
            [ 2.85783954e-05,  2.85783954e-05,  2.85783954e-05, ...,
              2.85783954e-05,  2.85783954e-05,  2.85783954e-05]],
    
           [[-6.43892708e-05, -6.43892708e-05, -6.43892708e-05, ...,
             -6.43892708e-05, -6.43892708e-05, -6.43892708e-05],
            [-1.66790843e+00, -1.65821278e+00, -1.64771271e+00, ...,
             -1.69197237e+00, -1.68502700e+00, -1.67672622e+00],
            [-2.02232337e+00, -2.02113414e+00, -2.01861668e+00, ...,
             -2.01706362e+00, -2.02046800e+00, -2.02228212e+00],
            ...,
            [ 3.82978529e-01,  3.74244392e-01,  3.65538239e-01, ...,
              4.10737544e-01,  4.01318848e-01,  3.92008185e-01],
            [ 4.08034801e-01,  4.16305363e-01,  4.24647450e-01, ...,
              3.84193242e-01,  3.92050654e-01,  3.99832040e-01],
            [-6.43892708e-05, -6.43892708e-05, -6.43892708e-05, ...,
             -6.43892708e-05, -6.43892708e-05, -6.43892708e-05]]],
          dtype=float32)

• Indexes: (3)
  • lon
    PandasIndex

    PandasIndex(Float64Index([  0.0,   1.0,   2.0,   3.0,   4.0,   5.0,   6.0,   7.0,   8.0,
                    9.0,
                  ...
                  350.0, 351.0, 352.0, 353.0, 354.0, 355.0, 356.0, 357.0, 358.0,
                  359.0],
                 dtype='float64', name='lon', length=360))

  • lat
    PandasIndex

    PandasIndex(Float64Index([-90.0, -89.0, -88.0, -87.0, -86.0, -85.0, -84.0, -83.0, -82.0,
                  -81.0,
                  ...
                   81.0,  82.0,  83.0,  84.0,  85.0,  86.0,  87.0,  88.0,  89.0,
                   90.0],
                 dtype='float64', name='lat', length=181))

  • month
    PandasIndex

    PandasIndex(Int64Index([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], dtype='int64', name='month'))

• Attributes: (2)

  Conventions :

  CF-1.6

  history :

  2023-10-09 08:34:05 GMT by grib_to_netcdf-2.25.1: /opt/ecmwf/mars-client/bin/grib_to_netcdf.bin -S param -o /cache/data6/adaptor.mars.internal-1696840444.646768-21592-4-99a63a23-dfb8-4c0d-a57a-b5cc57604db5.nc /cache/tmp/99a63a23-dfb8-4c0d-a57a-b5cc57604db5-adaptor.mars.internal-1696840419.9374874-21592-6-tmp.grib

Xsp = xspharm(era_ds)
uv_tranc = Xsp.truncate(era_ds, ntrunc=24)
uv_taper = Xsp.exp_taper(era_ds, ntrunc=24)

cdict_u = sp.cmap.dict_cmap_contourf(levels=np.arange(-45, 45.01, step=5), name='RdBu_r', extend='both', add_norm=False)
cdict_v = sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1), name='RdBu_r', extend='both', add_norm=False)

plt.figure(figsize=(12, 8))
uv_taper['u'].plot.contourf(col='month', col_wrap=6, **cdict_u)

plt.figure(figsize=(12, 8))
uv_taper['v'].plot.contourf(col='month', col_wrap=6, **cdict_v)

<xarray.plot.facetgrid.FacetGrid at 0x7fb6e00e1f90>

<Figure size 1200x800 with 0 Axes>

<Figure size 1200x800 with 0 Axes>

sfvp_ds = Xsp.uv2sfvp(era_ds.u, era_ds.v)
sfvp_ds

<xarray.Dataset>
Dimensions:  (lon: 360, lat: 181, month: 12)
Coordinates:
  * lon      (lon) float32 0.0 1.0 2.0 3.0 4.0 ... 355.0 356.0 357.0 358.0 359.0
  * lat      (lat) float32 -90.0 -89.0 -88.0 -87.0 -86.0 ... 87.0 88.0 89.0 90.0
    lev      int32 300
  * month    (month) int64 1 2 3 4 5 6 7 8 9 10 11 12
Data variables:
    sf       (month, lat, lon) float32 -1.193e+08 -1.193e+08 ... 1.267e+08
    vp       (month, lat, lon) float32 5.162e+05 5.162e+05 ... -9.082e+05

xarray.Dataset

• Dimensions:
  • lon: 360
  • lat: 181
  • month: 12
• Coordinates: (4)
  • lon
    (lon)
    float32
    0.0 1.0 2.0 ... 357.0 358.0 359.0

    units :

    degrees_east

    long_name :

    longitude

    array([  0.,   1.,   2., ..., 357., 358., 359.], dtype=float32)

  • lat
    (lat)
    float32
    -90.0 -89.0 -88.0 ... 89.0 90.0

    units :

    degrees_north

    long_name :

    latitude

    array([-90., -89., -88., -87., -86., -85., -84., -83., -82., -81., -80., -79.,
           -78., -77., -76., -75., -74., -73., -72., -71., -70., -69., -68., -67.,
           -66., -65., -64., -63., -62., -61., -60., -59., -58., -57., -56., -55.,
           -54., -53., -52., -51., -50., -49., -48., -47., -46., -45., -44., -43.,
           -42., -41., -40., -39., -38., -37., -36., -35., -34., -33., -32., -31.,
           -30., -29., -28., -27., -26., -25., -24., -23., -22., -21., -20., -19.,
           -18., -17., -16., -15., -14., -13., -12., -11., -10.,  -9.,  -8.,  -7.,
            -6.,  -5.,  -4.,  -3.,  -2.,  -1.,   0.,   1.,   2.,   3.,   4.,   5.,
             6.,   7.,   8.,   9.,  10.,  11.,  12.,  13.,  14.,  15.,  16.,  17.,
            18.,  19.,  20.,  21.,  22.,  23.,  24.,  25.,  26.,  27.,  28.,  29.,
            30.,  31.,  32.,  33.,  34.,  35.,  36.,  37.,  38.,  39.,  40.,  41.,
            42.,  43.,  44.,  45.,  46.,  47.,  48.,  49.,  50.,  51.,  52.,  53.,
            54.,  55.,  56.,  57.,  58.,  59.,  60.,  61.,  62.,  63.,  64.,  65.,
            66.,  67.,  68.,  69.,  70.,  71.,  72.,  73.,  74.,  75.,  76.,  77.,
            78.,  79.,  80.,  81.,  82.,  83.,  84.,  85.,  86.,  87.,  88.,  89.,
            90.], dtype=float32)

  • lev
    ()
    int32
    300

    units :

    millibars

    long_name :

    pressure_level

    array(300, dtype=int32)

  • month
    (month)
    int64
    1 2 3 4 5 6 7 8 9 10 11 12

    array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12])

• Data variables: (2)
  • sf
    (month, lat, lon)
    float32
    -1.193e+08 -1.193e+08 ... 1.267e+08

    units :

    m**2/s

    long_name :

    streamfunction

    standard_name :

    eastward_wind

    array([[[-1.19294160e+08, -1.19294160e+08, -1.19294160e+08, ...,
             -1.19294160e+08, -1.19294160e+08, -1.19294160e+08],
            [-1.19348784e+08, -1.19349664e+08, -1.19350584e+08, ...,
             -1.19346400e+08, -1.19347160e+08, -1.19347952e+08],
            [-1.19121000e+08, -1.19124128e+08, -1.19127424e+08, ...,
             -1.19112816e+08, -1.19115344e+08, -1.19118080e+08],
            ...,
            [ 1.29473208e+08,  1.29478128e+08,  1.29482320e+08, ...,
              1.29454272e+08,  1.29461280e+08,  1.29467600e+08],
            [ 1.29019072e+08,  1.29022416e+08,  1.29025544e+08, ...,
              1.29007792e+08,  1.29011768e+08,  1.29015520e+08],
            [ 1.28884400e+08,  1.28884400e+08,  1.28884400e+08, ...,
              1.28884400e+08,  1.28884400e+08,  1.28884400e+08]],
    
           [[-1.25387040e+08, -1.25387040e+08, -1.25387040e+08, ...,
             -1.25387040e+08, -1.25387040e+08, -1.25387040e+08],
            [-1.25356448e+08, -1.25345496e+08, -1.25334664e+08, ...,
             -1.25389920e+08, -1.25378664e+08, -1.25367496e+08],
            [-1.25042128e+08, -1.25029480e+08, -1.25017192e+08, ...,
             -1.25082328e+08, -1.25068552e+08, -1.25055160e+08],
    ...
              1.22922552e+08,  1.22928448e+08,  1.22933576e+08],
            [ 1.22383728e+08,  1.22386112e+08,  1.22388192e+08, ...,
              1.22374744e+08,  1.22378040e+08,  1.22381024e+08],
            [ 1.21898008e+08,  1.21898008e+08,  1.21898008e+08, ...,
              1.21898008e+08,  1.21898008e+08,  1.21898008e+08]],
    
           [[-1.22305680e+08, -1.22305680e+08, -1.22305680e+08, ...,
             -1.22305680e+08, -1.22305680e+08, -1.22305680e+08],
            [-1.22404856e+08, -1.22409368e+08, -1.22413928e+08, ...,
             -1.22391480e+08, -1.22395904e+08, -1.22400352e+08],
            [-1.22170096e+08, -1.22177120e+08, -1.22184344e+08, ...,
             -1.22150104e+08, -1.22156576e+08, -1.22163232e+08],
            ...,
            [ 1.27294176e+08,  1.27293136e+08,  1.27291480e+08, ...,
              1.27293560e+08,  1.27294384e+08,  1.27294592e+08],
            [ 1.26806360e+08,  1.26806136e+08,  1.26805752e+08, ...,
              1.26805976e+08,  1.26806272e+08,  1.26806400e+08],
            [ 1.26725872e+08,  1.26725872e+08,  1.26725872e+08, ...,
              1.26725872e+08,  1.26725872e+08,  1.26725872e+08]]],
          dtype=float32)

  • vp
    (month, lat, lon)
    float32
    5.162e+05 5.162e+05 ... -9.082e+05

    units :

    m**2/s

    long_name :

    velocity potential

    standard_name :

    eastward_wind

    array([[[  516159.56 ,   516159.56 ,   516159.53 , ...,   516159.56 ,
               516159.56 ,   516159.56 ],
            [  567505.7  ,   567647.2  ,   567864.1  , ...,   567512.1  ,
               567440.44 ,   567437.5  ],
            [  592520.7  ,   588031.9  ,   583728.5  , ...,   607027.6  ,
               602025.9  ,   597187.75 ],
            ...,
            [-1089888.1  , -1068719.2  , -1047417.5  , ..., -1152358.5  ,
             -1131731.6  , -1110900.2  ],
            [-1076806.2  , -1070958.   , -1065024.1  , ..., -1093762.1  ,
             -1088215.8  , -1082561.4  ],
            [ -940297.44 ,  -940297.44 ,  -940297.5  , ...,  -940297.44 ,
              -940297.44 ,  -940297.44 ]],
    
           [[  400139.2  ,   400139.2  ,   400139.16 , ...,   400139.12 ,
               400139.2  ,   400139.2  ],
            [ 1100254.2  ,  1098188.6  ,  1095975.6  , ...,  1105524.8  ,
              1103926.9  ,  1102168.6  ],
            [ 1299695.4  ,  1290220.   ,  1280618.4  , ...,  1327220.2  ,
              1318209.8  ,  1309030.   ],
    ...
            [ -693785.3  ,  -665017.8  ,  -636149.1  , ...,  -779247.1  ,
              -750923.25 ,  -722428.3  ],
            [ -687886.6  ,  -676003.4  ,  -664062.8  , ...,  -723106.4  ,
              -711446.75 ,  -699704.   ],
            [ -580482.2  ,  -580482.2  ,  -580482.25 , ...,  -580482.2  ,
              -580482.2  ,  -580482.2  ]],
    
           [[  526928.25 ,   526928.3  ,   526928.3  , ...,   526928.25 ,
               526928.3  ,   526928.3  ],
            [  353591.94 ,   354493.22 ,   355523.3  , ...,   351641.62 ,
               352168.3  ,   352817.7  ],
            [  342114.75 ,   338211.06 ,   334538.7  , ...,   355145.25 ,
               350588.97 ,   346242.9  ],
            ...,
            [ -813308.   ,  -794145.8  ,  -775002.2  , ...,  -870695.75 ,
              -851604.   ,  -832467.6  ],
            [ -880271.94 ,  -875928.6  ,  -871583.44 , ...,  -893228.6  ,
              -888928.2  ,  -884607.2  ],
            [ -908229.9  ,  -908229.94 ,  -908229.94 , ...,  -908229.9  ,
              -908229.94 ,  -908229.94 ]]], dtype=float32)

• Indexes: (3)
  • lon
    PandasIndex

    PandasIndex(Float64Index([  0.0,   1.0,   2.0,   3.0,   4.0,   5.0,   6.0,   7.0,   8.0,
                    9.0,
                  ...
                  350.0, 351.0, 352.0, 353.0, 354.0, 355.0, 356.0, 357.0, 358.0,
                  359.0],
                 dtype='float64', name='lon', length=360))

  • lat
    PandasIndex

    PandasIndex(Float64Index([-90.0, -89.0, -88.0, -87.0, -86.0, -85.0, -84.0, -83.0, -82.0,
                  -81.0,
                  ...
                   81.0,  82.0,  83.0,  84.0,  85.0,  86.0,  87.0,  88.0,  89.0,
                   90.0],
                 dtype='float64', name='lat', length=181))

  • month
    PandasIndex

    PandasIndex(Int64Index([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], dtype='int64', name='month'))

• Attributes: (0)

cdict_sf = sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*1e6, name='RdBu_r', extend='both', add_norm=False)
cdict_vp = sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*1e6, name='RdBu_r', extend='both', add_norm=False)

plt.figure(figsize=(12, 8))
(sfvp_ds['sf']-sfvp_ds['sf'].mean('lon')).plot.contourf(col='month', col_wrap=6, **cdict_sf)

plt.figure(figsize=(12, 8))
sfvp_ds['vp'].plot.contourf(col='month', col_wrap=6, **cdict_vp)

<xarray.plot.facetgrid.FacetGrid at 0x7fb711c94700>

<Figure size 1200x800 with 0 Axes>

<Figure size 1200x800 with 0 Axes>

vordiv_ds = Xsp.uv2vordiv(era_ds.u, era_ds.v, ntrunc=24)
vordiv_ds

<xarray.Dataset>
Dimensions:  (lon: 360, lat: 181, month: 12)
Coordinates:
  * lon      (lon) float32 0.0 1.0 2.0 3.0 4.0 ... 355.0 356.0 357.0 358.0 359.0
  * lat      (lat) float32 -90.0 -89.0 -88.0 -87.0 -86.0 ... 87.0 88.0 89.0 90.0
    lev      int32 300
  * month    (month) int64 1 2 3 4 5 6 7 8 9 10 11 12
Data variables:
    vor      (month, lat, lon) float32 5.107e-06 5.107e-06 ... -3.351e-06
    div      (month, lat, lon) float32 2.686e-07 2.686e-07 ... -5.619e-08

xarray.Dataset

• Dimensions:
  • lon: 360
  • lat: 181
  • month: 12
• Coordinates: (4)
  • lon
    (lon)
    float32
    0.0 1.0 2.0 ... 357.0 358.0 359.0

    units :

    degrees_east

    long_name :

    longitude

    array([  0.,   1.,   2., ..., 357., 358., 359.], dtype=float32)

  • lat
    (lat)
    float32
    -90.0 -89.0 -88.0 ... 89.0 90.0

    units :

    degrees_north

    long_name :

    latitude

    array([-90., -89., -88., -87., -86., -85., -84., -83., -82., -81., -80., -79.,
           -78., -77., -76., -75., -74., -73., -72., -71., -70., -69., -68., -67.,
           -66., -65., -64., -63., -62., -61., -60., -59., -58., -57., -56., -55.,
           -54., -53., -52., -51., -50., -49., -48., -47., -46., -45., -44., -43.,
           -42., -41., -40., -39., -38., -37., -36., -35., -34., -33., -32., -31.,
           -30., -29., -28., -27., -26., -25., -24., -23., -22., -21., -20., -19.,
           -18., -17., -16., -15., -14., -13., -12., -11., -10.,  -9.,  -8.,  -7.,
            -6.,  -5.,  -4.,  -3.,  -2.,  -1.,   0.,   1.,   2.,   3.,   4.,   5.,
             6.,   7.,   8.,   9.,  10.,  11.,  12.,  13.,  14.,  15.,  16.,  17.,
            18.,  19.,  20.,  21.,  22.,  23.,  24.,  25.,  26.,  27.,  28.,  29.,
            30.,  31.,  32.,  33.,  34.,  35.,  36.,  37.,  38.,  39.,  40.,  41.,
            42.,  43.,  44.,  45.,  46.,  47.,  48.,  49.,  50.,  51.,  52.,  53.,
            54.,  55.,  56.,  57.,  58.,  59.,  60.,  61.,  62.,  63.,  64.,  65.,
            66.,  67.,  68.,  69.,  70.,  71.,  72.,  73.,  74.,  75.,  76.,  77.,
            78.,  79.,  80.,  81.,  82.,  83.,  84.,  85.,  86.,  87.,  88.,  89.,
            90.], dtype=float32)

  • lev
    ()
    int32
    300

    units :

    millibars

    long_name :

    pressure_level

    array(300, dtype=int32)

  • month
    (month)
    int64
    1 2 3 4 5 6 7 8 9 10 11 12

    array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12])

• Data variables: (2)
  • vor
    (month, lat, lon)
    float32
    5.107e-06 5.107e-06 ... -3.351e-06

    units :

    1/s

    long_name :

    Vorticity

    standard_name :

    eastward_wind

    array([[[ 5.10664449e-06,  5.10664449e-06,  5.10664449e-06, ...,
              5.10664404e-06,  5.10664404e-06,  5.10664404e-06],
            [ 6.59592570e-06,  6.58750787e-06,  6.57875216e-06, ...,
              6.61913600e-06,  6.61174090e-06,  6.60400383e-06],
            [ 7.70266797e-06,  7.68870268e-06,  7.67442179e-06, ...,
              7.74265300e-06,  7.72964631e-06,  7.71631676e-06],
            ...,
            [-6.49623416e-06, -6.49364529e-06, -6.48921787e-06, ...,
             -6.49289632e-06, -6.49586400e-06, -6.49697540e-06],
            [-5.39715256e-06, -5.39581515e-06, -5.39406892e-06, ...,
             -5.39871598e-06, -5.39860321e-06, -5.39808207e-06],
            [-5.28060718e-06, -5.28060718e-06, -5.28060718e-06, ...,
             -5.28060764e-06, -5.28060764e-06, -5.28060764e-06]],
    
           [[ 7.66751054e-06,  7.66751054e-06,  7.66751054e-06, ...,
              7.66750964e-06,  7.66750964e-06,  7.66750964e-06],
            [ 8.73002864e-06,  8.69771247e-06,  8.66527625e-06, ...,
              8.82617496e-06,  8.79427171e-06,  8.76222020e-06],
            [ 9.36883589e-06,  9.30620990e-06,  9.24389224e-06, ...,
              9.55834730e-06,  9.49493005e-06,  9.43175019e-06],
    ...
             -1.36275958e-05, -1.36325471e-05, -1.36349390e-05],
            [-1.14112572e-05, -1.14103950e-05, -1.14086915e-05, ...,
             -1.14087889e-05, -1.14104532e-05, -1.14112754e-05],
            [-9.83651262e-06, -9.83651262e-06, -9.83651262e-06, ...,
             -9.83651171e-06, -9.83651080e-06, -9.83651171e-06]],
    
           [[ 5.05260414e-06,  5.05260459e-06,  5.05260459e-06, ...,
              5.05260414e-06,  5.05260414e-06,  5.05260414e-06],
            [ 6.49120057e-06,  6.49233789e-06,  6.49316826e-06, ...,
              6.48595460e-06,  6.48800824e-06,  6.48975674e-06],
            [ 7.48046659e-06,  7.48428010e-06,  7.48785669e-06, ...,
              7.46763089e-06,  7.47213971e-06,  7.47641843e-06],
            ...,
            [-5.11284361e-06, -5.10530208e-06, -5.09599295e-06, ...,
             -5.12471979e-06, -5.12256292e-06, -5.11860071e-06],
            [-3.75939135e-06, -3.75718719e-06, -3.75454329e-06, ...,
             -3.76334401e-06, -3.76247090e-06, -3.76115281e-06],
            [-3.35103755e-06, -3.35103755e-06, -3.35103755e-06, ...,
             -3.35103778e-06, -3.35103755e-06, -3.35103755e-06]]],
          dtype=float32)

  • div
    (month, lat, lon)
    float32
    2.686e-07 2.686e-07 ... -5.619e-08

    units :

    1/s

    long_name :

    Divergence

    standard_name :

    eastward_wind

    array([[[ 2.68555738e-07,  2.68555766e-07,  2.68555823e-07, ...,
              2.68555709e-07,  2.68555709e-07,  2.68555709e-07],
            [ 5.97945586e-08,  3.62248329e-08,  1.26115935e-08, ...,
              1.30191893e-07,  1.06783091e-07,  8.33156832e-08],
            [ 8.51454161e-08,  4.46646027e-08,  3.86137344e-09, ...,
              2.04618175e-07,  1.65125471e-07,  1.25300346e-07],
            ...,
            [ 1.31365402e-06,  1.26991017e-06,  1.22551990e-06, ...,
              1.44031605e-06,  1.39892575e-06,  1.35668211e-06],
            [ 5.18144191e-07,  5.11901703e-07,  5.05385401e-07, ...,
              5.35065055e-07,  5.29742238e-07,  5.24096492e-07],
            [-1.03782384e-07, -1.03782334e-07, -1.03782277e-07, ...,
             -1.03782504e-07, -1.03782490e-07, -1.03782419e-07]],
    
           [[ 4.35565880e-07,  4.35565880e-07,  4.35565880e-07, ...,
              4.35565880e-07,  4.35565880e-07,  4.35565880e-07],
            [-1.30896183e-06, -1.32669561e-06, -1.34399590e-06, ...,
             -1.25316240e-06, -1.27219482e-06, -1.29079490e-06],
            [-2.72672310e-06, -2.74941794e-06, -2.77149638e-06, ...,
             -2.65478684e-06, -2.67942301e-06, -2.70339638e-06],
    ...
              1.31575757e-06,  1.24913299e-06,  1.18185289e-06],
            [ 4.89920069e-07,  4.69256406e-07,  4.48391432e-07, ...,
              5.50511345e-07,  5.30566638e-07,  5.10363179e-07],
            [-4.12945838e-08, -4.12945127e-08, -4.12944701e-08, ...,
             -4.12947827e-08, -4.12947259e-08, -4.12946548e-08]],
    
           [[ 4.08585151e-07,  4.08585151e-07,  4.08585095e-07, ...,
              4.08585265e-07,  4.08585208e-07,  4.08585208e-07],
            [ 6.91978244e-07,  6.67523636e-07,  6.42919133e-07, ...,
              7.64399829e-07,  7.40420660e-07,  7.16278862e-07],
            [ 1.06389018e-06,  1.02354147e-06,  9.82772008e-07, ...,
              1.18240280e-06,  1.14332170e-06,  1.10381757e-06],
            ...,
            [ 4.53696089e-07,  4.20692686e-07,  3.87585430e-07, ...,
              5.51485186e-07,  5.19152593e-07,  4.86536067e-07],
            [ 1.76823363e-07,  1.74568783e-07,  1.72231879e-07, ...,
              1.82956342e-07,  1.81030856e-07,  1.78981907e-07],
            [-5.61949349e-08, -5.61949065e-08, -5.61948497e-08, ...,
             -5.61950770e-08, -5.61950202e-08, -5.61949918e-08]]],
          dtype=float32)

• Indexes: (3)
  • lon
    PandasIndex

    PandasIndex(Float64Index([  0.0,   1.0,   2.0,   3.0,   4.0,   5.0,   6.0,   7.0,   8.0,
                    9.0,
                  ...
                  350.0, 351.0, 352.0, 353.0, 354.0, 355.0, 356.0, 357.0, 358.0,
                  359.0],
                 dtype='float64', name='lon', length=360))

  • lat
    PandasIndex

    PandasIndex(Float64Index([-90.0, -89.0, -88.0, -87.0, -86.0, -85.0, -84.0, -83.0, -82.0,
                  -81.0,
                  ...
                   81.0,  82.0,  83.0,  84.0,  85.0,  86.0,  87.0,  88.0,  89.0,
                   90.0],
                 dtype='float64', name='lat', length=181))

  • month
    PandasIndex

    PandasIndex(Int64Index([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], dtype='int64', name='month'))

• Attributes: (0)

cdict_vor = sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*2e-6, name='RdBu_r', extend='both', add_norm=False)
cdict_div = sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*2e-6, name='RdBu_r', extend='both', add_norm=False)

plt.figure(figsize=(12, 8))
vordiv_ds['vor'].plot.contourf(col='month', col_wrap=6, **cdict_vor)

plt.figure(figsize=(12, 8))
vordiv_ds['div'].plot.contourf(col='month', col_wrap=6, **cdict_div)

<xarray.plot.facetgrid.FacetGrid at 0x7fb64063e3e0>

<Figure size 1200x800 with 0 Axes>

<Figure size 1200x800 with 0 Axes>

absvor = Xsp.uv2absvor(era_ds.u, era_ds.v, ntrunc=24)
cdict_vor = sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*2e-5, name='RdBu_r', extend='both', add_norm=False)

plt.figure(figsize=(12, 8))
absvor.plot.contourf(col='month', col_wrap=6, **cdict_vor)

<xarray.plot.facetgrid.FacetGrid at 0x7fb62036afb0>

<Figure size 1200x800 with 0 Axes>

uv_rot_ds = Xsp.sf2uv(sfvp_ds['sf'])

plt.figure(figsize=(12, 8))
uv_rot_ds['u_rot'].plot.contourf(col='month', col_wrap=6, **cdict_u)

plt.figure(figsize=(12, 8))
uv_rot_ds['v_rot'].plot.contourf(col='month', col_wrap=6, **cdict_v)

<xarray.plot.facetgrid.FacetGrid at 0x7fb62012c610>

<Figure size 1200x800 with 0 Axes>

<Figure size 1200x800 with 0 Axes>

uv_div_ds = Xsp.vp2uv(sfvp_ds['vp'])
plt.figure(figsize=(12, 8))
uv_div_ds['u_div'].plot.contourf(col='month', col_wrap=6, **cdict_v)

plt.figure(figsize=(12, 8))
uv_div_ds['v_div'].plot.contourf(col='month', col_wrap=6, **cdict_v)

<xarray.plot.facetgrid.FacetGrid at 0x7fb5c05dea70>

<Figure size 1200x800 with 0 Axes>

<Figure size 1200x800 with 0 Axes>

plt.figure(figsize=(12, 8))

ax1 = plt.subplot(2, 2, 1)
uv_rot_ds['u_rot'].mean('lon').plot.contourf( **sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*5, name='RdBu_r', extend='both', add_norm=False) )

ax2 = plt.subplot(2, 2, 2)
uv_div_ds['v_div'].mean('lon').plot.contourf( **sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*0.1, name='RdBu_r', extend='both', add_norm=False) )

ax3 = plt.subplot(2, 2, 3)
era_ds['u'].mean('lon').plot.contourf( **sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*5, name='RdBu_r', extend='both', add_norm=False) )

ax4 = plt.subplot(2, 2, 4)
era_ds['v'].mean('lon').plot.contourf( **sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*0.1, name='RdBu_r', extend='both', add_norm=False) )


for ax in [ax1, ax2, ax3, ax4]:
    sp.set_latticks(ax, lats=np.arange(-90, 90.01, step=30), axis='x')
    sp.set_monticks(ax, axis='y', option='b')
    # ax.set_yticks(minor=False)
plt.tight_layout()

# plt.subplot(2, 2, 3)
# uv_rot_ds['u_rot'].sel(lat=slice(-5, 5)).mean('lat').plot.contourf( **sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*1, name='RdBu_r', extend='both', add_norm=False) )

# plt.subplot(2, 2, 4)
# uv_div_ds['v_div'].sel(lat=slice(-5, 5)).mean('lat').plot.contourf( **sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*0.1, name='RdBu_r', extend='both', add_norm=False) )

plt.figure(figsize=(12, 8))

ax1 = plt.subplot(2, 2, 1)
uv_rot_ds['u_rot'].sel(lat=slice(-5, 5)).mean('lat').plot.contourf( **sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*1, name='RdBu_r', extend='both', add_norm=False) )

ax2 = plt.subplot(2, 2, 2)
uv_div_ds['v_div'].sel(lat=slice(-5, 5)).mean('lat').plot.contourf( **sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*0.3, name='RdBu_r', extend='both', add_norm=False) )

ax3 = plt.subplot(2, 2, 3)
era_ds['u'].sel(lat=slice(-5, 5)).mean('lat').plot.contourf( **sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*1, name='RdBu_r', extend='both', add_norm=False) )

ax4 = plt.subplot(2, 2, 4)
era_ds['v'].sel(lat=slice(-5, 5)).mean('lat').plot.contourf( **sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*0.3, name='RdBu_r', extend='both', add_norm=False) )


for ax in [ax1, ax2, ax3, ax4]:
    sp.set_lonticks(ax, lons=np.arange(0, 360.01, step=60), axis='x')
    sp.set_monticks(ax, axis='y', option='b')
    # ax.set_yticks(minor=False)
plt.tight_layout()

# plt.subplot(2, 2, 3)
# uv_rot_ds['u_rot'].sel(lat=slice(-5, 5)).mean('lat').plot.contourf( **sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*1, name='RdBu_r', extend='both', add_norm=False) )

# plt.subplot(2, 2, 4)
# uv_div_ds['v_div'].sel(lat=slice(-5, 5)).mean('lat').plot.contourf( **sp.cmap.dict_cmap_contourf(levels=np.arange(-10, 10.01, step=1)*0.1, name='RdBu_r', extend='both', add_norm=False) )