Parametric Vertical Coordinates

See also

1. CF conventions on parametric vertical coordinates

2. Dataset.cf.decode_vertical_coords()

3. Dataset.cf.formula_terms

cf_xarray supports decoding parametric vertical coordinates encoded in the formula_terms attribute using Dataset.cf.decode_vertical_coords().

Decoding parametric coordinates

from cf_xarray.datasets import romsds

romsds

<xarray.Dataset> Size: 1kB
Dimensions:      (s_rho: 30, ocean_time: 2)
Coordinates:
  * s_rho        (s_rho) float64 240B -0.9833 -0.95 -0.9167 ... -0.05 -0.01667
    hc           float64 8B 20.0
    h            float64 8B 603.9
    Vtransform   float64 8B 2.0
    Cs_r         (s_rho) float64 240B -0.933 -0.8092 ... -0.0005206 -5.758e-05
    z_rho_dummy  (ocean_time, s_rho) float64 480B -1.149 0.2692 ... 0.1062
Dimensions without coordinates: ocean_time
Data variables:
    zeta         (ocean_time) float64 16B -0.1554 -0.1274
    temp         (ocean_time, s_rho) float64 480B 20.0 20.34 ... 29.66 30.0

xarray.Dataset

• Dimensions:
  • s_rho: 30
  • ocean_time: 2
• Coordinates: (6)
  • s_rho
    (s_rho)
    float64
    -0.9833 -0.95 ... -0.05 -0.01667

    long_name :

    S-coordinate at RHO-points

    valid_min :

    -1.0

    valid_max :

    0.0

    standard_name :

    ocean_s_coordinate_g2

    formula_terms :

    s: s_rho C: Cs_r eta: zeta depth: h depth_c: hc

    field :

    s_rho, scalar

    array([-0.983333, -0.95    , -0.916667, -0.883333, -0.85    , -0.816667,
           -0.783333, -0.75    , -0.716667, -0.683333, -0.65    , -0.616667,
           -0.583333, -0.55    , -0.516667, -0.483333, -0.45    , -0.416667,
           -0.383333, -0.35    , -0.316667, -0.283333, -0.25    , -0.216667,
           -0.183333, -0.15    , -0.116667, -0.083333, -0.05    , -0.016667])

  • hc
    ()
    float64
    20.0

    array(20.)

  • h
    ()
    float64
    603.9

    standard_name :

    sea_floor_depth_below_geopotential_datum

    array(603.9)

  • Vtransform
    ()
    float64
    2.0

    array(2.)

  • Cs_r
    (s_rho)
    float64
    -0.933 -0.8092 ... -5.758e-05

    array([-9.33010396e-01, -8.09234736e-01, -6.98779853e-01, -6.01008926e-01,
           -5.15058562e-01, -4.39938913e-01, -3.74609181e-01, -3.18031817e-01,
           -2.69209327e-01, -2.27207488e-01, -1.91168387e-01, -1.60316097e-01,
           -1.33957253e-01, -1.11478268e-01, -9.23404709e-02, -7.60741092e-02,
           -6.22718662e-02, -5.05823390e-02, -4.07037635e-02, -3.23781605e-02,
           -2.53860004e-02, -1.95414261e-02, -1.46880431e-02, -1.06952600e-02,
           -7.45515186e-03, -4.87981407e-03, -2.89916971e-03, -1.45919898e-03,
           -5.20560097e-04, -5.75774004e-05])

  • z_rho_dummy
    (ocean_time, s_rho)
    float64
    -1.149 0.2692 ... 0.7674 0.1062

    positive :

    up

    array([[-1.14890189,  0.26921425,  0.09477228,  0.51749981,  0.26544117,
            -0.94032808,  2.09387782, -0.40221365, -0.92953856, -0.74115275,
             0.52681666, -0.29616087,  0.05282064, -0.19265996, -0.3948643 ,
             1.63970789, -1.46314754,  0.29749193,  0.20838147,  0.05004918,
             0.29759451,  0.42917807,  0.69438305,  0.24254697, -0.21881533,
            -1.48468937,  0.74443594,  0.82408938, -1.36858291, -0.92691106],
           [ 0.09930769, -0.39083751,  1.39496101,  1.35875569, -1.3766136 ,
             0.18107347, -0.43299452,  0.62316888,  0.48955731, -0.64260337,
             0.82110821, -0.00297183, -0.95442581,  0.01668455, -0.23217898,
             1.26424081, -0.86347477,  1.97823489, -1.10410487, -1.78392418,
            -1.0738544 , -1.04064906,  1.14471348,  0.09361037, -1.47257204,
             0.04086832, -1.01189311, -1.23024409,  0.76735683,  0.10619519]])

• Data variables: (2)
  • zeta
    (ocean_time)
    float64
    -0.1554 -0.1274

    standard_name :

    sea_surface_height_above_geopotential_datum

    array([-0.155356, -0.127435])

  • temp
    (ocean_time, s_rho)
    float64
    20.0 20.34 20.69 ... 29.66 30.0

    coordinates :

    z_rho_dummy

    standard_name :

    sea_water_potential_temperature

    array([[20.        , 20.34482759, 20.68965517, 21.03448276, 21.37931034,
            21.72413793, 22.06896552, 22.4137931 , 22.75862069, 23.10344828,
            23.44827586, 23.79310345, 24.13793103, 24.48275862, 24.82758621,
            25.17241379, 25.51724138, 25.86206897, 26.20689655, 26.55172414,
            26.89655172, 27.24137931, 27.5862069 , 27.93103448, 28.27586207,
            28.62068966, 28.96551724, 29.31034483, 29.65517241, 30.        ],
           [20.        , 20.34482759, 20.68965517, 21.03448276, 21.37931034,
            21.72413793, 22.06896552, 22.4137931 , 22.75862069, 23.10344828,
            23.44827586, 23.79310345, 24.13793103, 24.48275862, 24.82758621,
            25.17241379, 25.51724138, 25.86206897, 26.20689655, 26.55172414,
            26.89655172, 27.24137931, 27.5862069 , 27.93103448, 28.27586207,
            28.62068966, 28.96551724, 29.31034483, 29.65517241, 30.        ]])

• Indexes: (1)
  • s_rho
    PandasIndex

    PandasIndex(Index([-0.983333,     -0.95, -0.916667, -0.883333,     -0.85, -0.816667,
           -0.783333,     -0.75, -0.716667, -0.683333,     -0.65, -0.616667,
           -0.583333,     -0.55, -0.516667, -0.483333,     -0.45, -0.416667,
           -0.383333,     -0.35, -0.316667, -0.283333,     -0.25, -0.216667,
           -0.183333,     -0.15, -0.116667, -0.083333,     -0.05, -0.016667],
          dtype='float64', name='s_rho'))

• Attributes: (0)

Now we decode the vertical coordinates in-place. Note the new z_rho variable. cf_xarray sees that s_rho has a formula_terms attribute, looks up the right formula using s_rho.attrs["standard_name"] and computes a new vertical coordinate variable.

romsds.cf.decode_vertical_coords(outnames={'s_rho': 'z_rho'})  # adds new z_rho variable
romsds.z_rho

<xarray.DataArray 'z_rho' (ocean_time: 2, s_rho: 30)> Size: 480B
-564.4 -491.5 -426.3 -368.5 -317.6 -273.1 ... -5.883 -4.08 -2.593 -1.399 -0.4837
Coordinates:
  * s_rho        (s_rho) float64 240B -0.9833 -0.95 -0.9167 ... -0.05 -0.01667
    hc           float64 8B 20.0
    h            float64 8B 603.9
    Vtransform   float64 8B 2.0
    Cs_r         (s_rho) float64 240B -0.933 -0.8092 ... -0.0005206 -5.758e-05
    z_rho_dummy  (ocean_time, s_rho) float64 480B -1.149 0.2692 ... 0.1062
    z_rho        (ocean_time, s_rho) float64 480B -564.4 -491.5 ... -0.4837
Dimensions without coordinates: ocean_time
Attributes:
    standard_name:  height_above_geopotential_datum

xarray.DataArray

'z_rho'

• ocean_time: 2
• s_rho: 30

• -564.4 -491.5 -426.3 -368.5 -317.6 ... -4.08 -2.593 -1.399 -0.4837

  array([[-5.64429324e+02, -4.91450849e+02, -4.26256914e+02,
          -3.68475346e+02, -3.17601624e+02, -2.73057273e+02,
          -2.34234039e+02, -2.00525627e+02, -1.71349093e+02,
          -1.46158464e+02, -1.24452423e+02, -1.05777507e+02,
          -8.97284995e+01, -7.59468652e+01, -6.41177903e+01,
          -5.39667363e+01, -4.52557099e+01, -3.77793350e+01,
          -3.13612443e+01, -2.58507156e+01, -2.11194386e+01,
          -1.70587808e+01, -1.35773854e+01, -1.05989166e+01,
          -8.06028479e+00, -5.91015794e+00, -4.10756442e+00,
          -2.62091623e+00, -1.42726108e+00, -5.11575009e-01],
         [-5.64427498e+02, -4.91445649e+02, -4.26248698e+02,
          -3.68464458e+02, -3.17588384e+02, -2.73041973e+02,
          -2.34216943e+02, -2.00506973e+02, -1.71329089e+02,
          -1.46137295e+02, -1.24430250e+02, -1.05754470e+02,
          -8.97047209e+01, -7.59224493e+01, -6.40928273e+01,
          -5.39413039e+01, -4.52298746e+01, -3.77531540e+01,
          -3.13347664e+01, -2.58239829e+01, -2.10924871e+01,
          -1.70316416e+01, -1.35500851e+01, -1.05714786e+01,
          -8.03272936e+00, -5.88250307e+00, -4.07982620e+00,
          -2.59310925e+00, -1.39939890e+00, -4.83670483e-01]])

• Coordinates: (7)
  • s_rho
    (s_rho)
    float64
    -0.9833 -0.95 ... -0.05 -0.01667

    long_name :

    S-coordinate at RHO-points

    valid_min :

    -1.0

    valid_max :

    0.0

    standard_name :

    ocean_s_coordinate_g2

    formula_terms :

    s: s_rho C: Cs_r eta: zeta depth: h depth_c: hc

    field :

    s_rho, scalar

    array([-0.983333, -0.95    , -0.916667, -0.883333, -0.85    , -0.816667,
           -0.783333, -0.75    , -0.716667, -0.683333, -0.65    , -0.616667,
           -0.583333, -0.55    , -0.516667, -0.483333, -0.45    , -0.416667,
           -0.383333, -0.35    , -0.316667, -0.283333, -0.25    , -0.216667,
           -0.183333, -0.15    , -0.116667, -0.083333, -0.05    , -0.016667])

  • hc
    ()
    float64
    20.0

    array(20.)

  • h
    ()
    float64
    603.9

    standard_name :

    sea_floor_depth_below_geopotential_datum

    array(603.9)

  • Vtransform
    ()
    float64
    2.0

    array(2.)

  • Cs_r
    (s_rho)
    float64
    -0.933 -0.8092 ... -5.758e-05

    array([-9.33010396e-01, -8.09234736e-01, -6.98779853e-01, -6.01008926e-01,
           -5.15058562e-01, -4.39938913e-01, -3.74609181e-01, -3.18031817e-01,
           -2.69209327e-01, -2.27207488e-01, -1.91168387e-01, -1.60316097e-01,
           -1.33957253e-01, -1.11478268e-01, -9.23404709e-02, -7.60741092e-02,
           -6.22718662e-02, -5.05823390e-02, -4.07037635e-02, -3.23781605e-02,
           -2.53860004e-02, -1.95414261e-02, -1.46880431e-02, -1.06952600e-02,
           -7.45515186e-03, -4.87981407e-03, -2.89916971e-03, -1.45919898e-03,
           -5.20560097e-04, -5.75774004e-05])

  • z_rho_dummy
    (ocean_time, s_rho)
    float64
    -1.149 0.2692 ... 0.7674 0.1062

    positive :

    up

    array([[-1.14890189,  0.26921425,  0.09477228,  0.51749981,  0.26544117,
            -0.94032808,  2.09387782, -0.40221365, -0.92953856, -0.74115275,
             0.52681666, -0.29616087,  0.05282064, -0.19265996, -0.3948643 ,
             1.63970789, -1.46314754,  0.29749193,  0.20838147,  0.05004918,
             0.29759451,  0.42917807,  0.69438305,  0.24254697, -0.21881533,
            -1.48468937,  0.74443594,  0.82408938, -1.36858291, -0.92691106],
           [ 0.09930769, -0.39083751,  1.39496101,  1.35875569, -1.3766136 ,
             0.18107347, -0.43299452,  0.62316888,  0.48955731, -0.64260337,
             0.82110821, -0.00297183, -0.95442581,  0.01668455, -0.23217898,
             1.26424081, -0.86347477,  1.97823489, -1.10410487, -1.78392418,
            -1.0738544 , -1.04064906,  1.14471348,  0.09361037, -1.47257204,
             0.04086832, -1.01189311, -1.23024409,  0.76735683,  0.10619519]])

  • z_rho
    (ocean_time, s_rho)
    float64
    -564.4 -491.5 ... -1.399 -0.4837

    standard_name :

    height_above_geopotential_datum

    array([[-5.64429324e+02, -4.91450849e+02, -4.26256914e+02,
            -3.68475346e+02, -3.17601624e+02, -2.73057273e+02,
            -2.34234039e+02, -2.00525627e+02, -1.71349093e+02,
            -1.46158464e+02, -1.24452423e+02, -1.05777507e+02,
            -8.97284995e+01, -7.59468652e+01, -6.41177903e+01,
            -5.39667363e+01, -4.52557099e+01, -3.77793350e+01,
            -3.13612443e+01, -2.58507156e+01, -2.11194386e+01,
            -1.70587808e+01, -1.35773854e+01, -1.05989166e+01,
            -8.06028479e+00, -5.91015794e+00, -4.10756442e+00,
            -2.62091623e+00, -1.42726108e+00, -5.11575009e-01],
           [-5.64427498e+02, -4.91445649e+02, -4.26248698e+02,
            -3.68464458e+02, -3.17588384e+02, -2.73041973e+02,
            -2.34216943e+02, -2.00506973e+02, -1.71329089e+02,
            -1.46137295e+02, -1.24430250e+02, -1.05754470e+02,
            -8.97047209e+01, -7.59224493e+01, -6.40928273e+01,
            -5.39413039e+01, -4.52298746e+01, -3.77531540e+01,
            -3.13347664e+01, -2.58239829e+01, -2.10924871e+01,
            -1.70316416e+01, -1.35500851e+01, -1.05714786e+01,
            -8.03272936e+00, -5.88250307e+00, -4.07982620e+00,
            -2.59310925e+00, -1.39939890e+00, -4.83670483e-01]])

• Indexes: (1)
  • s_rho
    PandasIndex

    PandasIndex(Index([-0.983333,     -0.95, -0.916667, -0.883333,     -0.85, -0.816667,
           -0.783333,     -0.75, -0.716667, -0.683333,     -0.65, -0.616667,
           -0.583333,     -0.55, -0.516667, -0.483333,     -0.45, -0.416667,
           -0.383333,     -0.35, -0.316667, -0.283333,     -0.25, -0.216667,
           -0.183333,     -0.15, -0.116667, -0.083333,     -0.05, -0.016667],
          dtype='float64', name='s_rho'))

• Attributes: (1)

  standard_name :

  height_above_geopotential_datum

Formula terms

To see whether decoding is possible, use the Dataset.cf.formula_terms attribute

romsds.cf.formula_terms

{'s_rho': {'s': 's_rho',
  'C': 'Cs_r',
  'eta': 'zeta',
  'depth': 'h',
  'depth_c': 'hc'}}