Physical Variables

This notebook looks at some canonical transformations of sea surface height (SSH). These are derived variables that can be calculated from SSH and are often very good indicators of performance.

import autoroot
import typing as tp
from dataclasses import dataclass
import numpy as np
import pandas as pd
import xarray as xr
import metpy
from metpy.units import units
import xarray_dataclasses as xrdataclass
from oceanbench._src.geoprocessing import geostrophic_v2 as geocalc
import matplotlib.pyplot as plt
import seaborn as sns

sns.reset_defaults()
sns.set_context(context="talk", font_scale=0.7)

%load_ext autoreload
%autoreload 2

# file = "/gpfswork/rech/cli/uvo53rl/projects/jejeqx/data/natl60/NATL60-CJM165_GULFSTREAM_ssh_y2013.1y.nc"
file = "/Users/eman/code_projects/data/oceanbench-data-registry/osse_natl60/grid/gf_mod_ssh_daily.nc"

!ls $file

/Users/eman/code_projects/data/oceanbench-data-registry/osse_natl60/grid/gf_mod_ssh_daily.nc

da = xr.open_dataset(file)
# da["time"] = pd.to_datetime(da.time)
da = da.sortby("time")
# da = da.coarsen(lat=2, boundary="trim").mean()
da = da.sel(time=slice("2013-01-01", "2013-03-01"))
da

<xarray.Dataset>
Dimensions:  (time: 60, lat: 201, lon: 201)
Coordinates:
  * lon      (lon) float64 -65.0 -64.95 -64.9 -64.85 ... -55.1 -55.05 -55.0
  * lat      (lat) float64 33.0 33.05 33.1 33.15 33.2 ... 42.85 42.9 42.95 43.0
  * time     (time) datetime64[ns] 2013-01-01T12:00:00 ... 2013-03-01T12:00:00
Data variables:
    ssh      (time, lat, lon) float64 ...

xarray.Dataset

• Dimensions:
  • time: 60
  • lat: 201
  • lon: 201
• Coordinates: (3)
  • lon
    (lon)
    float64
    -65.0 -64.95 -64.9 ... -55.05 -55.0

    array([-65.  , -64.95, -64.9 , ..., -55.1 , -55.05, -55.  ])

  • lat
    (lat)
    float64
    33.0 33.05 33.1 ... 42.9 42.95 43.0

    array([33.  , 33.05, 33.1 , ..., 42.9 , 42.95, 43.  ])

  • time
    (time)
    datetime64[ns]
    2013-01-01T12:00:00 ... 2013-03-...

    array(['2013-01-01T12:00:00.000000000', '2013-01-02T12:00:00.000000000',
           '2013-01-03T12:00:00.000000000', '2013-01-04T12:00:00.000000000',
           '2013-01-05T12:00:00.000000000', '2013-01-06T12:00:00.000000000',
           '2013-01-07T12:00:00.000000000', '2013-01-08T12:00:00.000000000',
           '2013-01-09T12:00:00.000000000', '2013-01-10T12:00:00.000000000',
           '2013-01-11T12:00:00.000000000', '2013-01-12T12:00:00.000000000',
           '2013-01-13T12:00:00.000000000', '2013-01-14T12:00:00.000000000',
           '2013-01-15T12:00:00.000000000', '2013-01-16T12:00:00.000000000',
           '2013-01-17T12:00:00.000000000', '2013-01-18T12:00:00.000000000',
           '2013-01-19T12:00:00.000000000', '2013-01-20T12:00:00.000000000',
           '2013-01-21T12:00:00.000000000', '2013-01-22T12:00:00.000000000',
           '2013-01-23T12:00:00.000000000', '2013-01-24T12:00:00.000000000',
           '2013-01-25T12:00:00.000000000', '2013-01-26T12:00:00.000000000',
           '2013-01-27T12:00:00.000000000', '2013-01-28T12:00:00.000000000',
           '2013-01-29T12:00:00.000000000', '2013-01-30T12:00:00.000000000',
           '2013-01-31T12:00:00.000000000', '2013-02-01T12:00:00.000000000',
           '2013-02-02T12:00:00.000000000', '2013-02-03T12:00:00.000000000',
           '2013-02-04T12:00:00.000000000', '2013-02-05T12:00:00.000000000',
           '2013-02-06T12:00:00.000000000', '2013-02-07T12:00:00.000000000',
           '2013-02-08T12:00:00.000000000', '2013-02-09T12:00:00.000000000',
           '2013-02-10T12:00:00.000000000', '2013-02-11T12:00:00.000000000',
           '2013-02-12T12:00:00.000000000', '2013-02-13T12:00:00.000000000',
           '2013-02-14T12:00:00.000000000', '2013-02-15T12:00:00.000000000',
           '2013-02-16T12:00:00.000000000', '2013-02-17T12:00:00.000000000',
           '2013-02-18T12:00:00.000000000', '2013-02-19T12:00:00.000000000',
           '2013-02-20T12:00:00.000000000', '2013-02-21T12:00:00.000000000',
           '2013-02-22T12:00:00.000000000', '2013-02-23T12:00:00.000000000',
           '2013-02-24T12:00:00.000000000', '2013-02-25T12:00:00.000000000',
           '2013-02-26T12:00:00.000000000', '2013-02-27T12:00:00.000000000',
           '2013-02-28T12:00:00.000000000', '2013-03-01T12:00:00.000000000'],
          dtype='datetime64[ns]')

• Data variables: (1)
  • ssh
    (time, lat, lon)
    float64
    ...

    [2424060 values with dtype=float64]

• Indexes: (3)
  • lon
    PandasIndex

    PandasIndex(Index([              -65.0,              -64.95,               -64.9,
            -64.85000000000001,  -64.80000000000001,  -64.75000000000001,
            -64.70000000000002,  -64.65000000000002,  -64.60000000000002,
            -64.55000000000003,
           ...
            -55.45000000000054, -55.400000000000546,  -55.35000000000055,
            -55.30000000000055, -55.250000000000554,  -55.20000000000056,
            -55.15000000000056,  -55.10000000000056, -55.050000000000566,
            -55.00000000000057],
          dtype='float64', name='lon', length=201))

  • lat
    PandasIndex

    PandasIndex(Index([              33.0,              33.05, 33.099999999999994,
            33.14999999999999,  33.19999999999999, 33.249999999999986,
            33.29999999999998,  33.34999999999998,  33.39999999999998,
           33.449999999999974,
           ...
            42.54999999999946, 42.599999999999454,  42.64999999999945,
            42.69999999999945, 42.749999999999446,  42.79999999999944,
            42.84999999999944,  42.89999999999944, 42.949999999999434,
            42.99999999999943],
          dtype='float64', name='lat', length=201))

  • time
    PandasIndex

    PandasIndex(DatetimeIndex(['2013-01-01 12:00:00', '2013-01-02 12:00:00',
                   '2013-01-03 12:00:00', '2013-01-04 12:00:00',
                   '2013-01-05 12:00:00', '2013-01-06 12:00:00',
                   '2013-01-07 12:00:00', '2013-01-08 12:00:00',
                   '2013-01-09 12:00:00', '2013-01-10 12:00:00',
                   '2013-01-11 12:00:00', '2013-01-12 12:00:00',
                   '2013-01-13 12:00:00', '2013-01-14 12:00:00',
                   '2013-01-15 12:00:00', '2013-01-16 12:00:00',
                   '2013-01-17 12:00:00', '2013-01-18 12:00:00',
                   '2013-01-19 12:00:00', '2013-01-20 12:00:00',
                   '2013-01-21 12:00:00', '2013-01-22 12:00:00',
                   '2013-01-23 12:00:00', '2013-01-24 12:00:00',
                   '2013-01-25 12:00:00', '2013-01-26 12:00:00',
                   '2013-01-27 12:00:00', '2013-01-28 12:00:00',
                   '2013-01-29 12:00:00', '2013-01-30 12:00:00',
                   '2013-01-31 12:00:00', '2013-02-01 12:00:00',
                   '2013-02-02 12:00:00', '2013-02-03 12:00:00',
                   '2013-02-04 12:00:00', '2013-02-05 12:00:00',
                   '2013-02-06 12:00:00', '2013-02-07 12:00:00',
                   '2013-02-08 12:00:00', '2013-02-09 12:00:00',
                   '2013-02-10 12:00:00', '2013-02-11 12:00:00',
                   '2013-02-12 12:00:00', '2013-02-13 12:00:00',
                   '2013-02-14 12:00:00', '2013-02-15 12:00:00',
                   '2013-02-16 12:00:00', '2013-02-17 12:00:00',
                   '2013-02-18 12:00:00', '2013-02-19 12:00:00',
                   '2013-02-20 12:00:00', '2013-02-21 12:00:00',
                   '2013-02-22 12:00:00', '2013-02-23 12:00:00',
                   '2013-02-24 12:00:00', '2013-02-25 12:00:00',
                   '2013-02-26 12:00:00', '2013-02-27 12:00:00',
                   '2013-02-28 12:00:00', '2013-03-01 12:00:00'],
                  dtype='datetime64[ns]', name='time', freq=None))

• Attributes: (0)

Sea Surface Height

\[ \begin{aligned} \text{Sea Surface Height}[m]: && \eta &=\boldsymbol{\eta}(\vec{\mathbf{x}},t) && && \boldsymbol{\eta}: \boldsymbol{\Omega}\times\boldsymbol{T}\rightarrow\mathbb{R} \end{aligned} \]

da["ssh"] = da.ssh * units.meters
da["ssh"].attrs["units"] = "m"
da["ssh"].attrs["long_name"] = "Sea Surface Height"
da["ssh"].attrs["standard_name"] = "sea_surface_height"

da["lat"] = da.lat * units.degree_north
da["lat"].attrs["long_name"] = "Latitude"
da["lat"].attrs["standard_name"] = "latitude"

da["lon"] = da.lon * units.degree_east
da["lon"].attrs["long_name"] = "Longitude"
da["lon"].attrs["standard_name"] = "longitude"

fig, ax = plt.subplots()

da.ssh.isel(time=1).plot.pcolormesh(ax=ax, cmap="viridis")

plt.show()

Stream Function

\[ \begin{aligned} \text{Stream Function }[ms^{-1}]: && \psi &=\boldsymbol{\psi}(\vec{\mathbf{x}},t) && && \boldsymbol{\psi}: \boldsymbol{\Omega}\times\boldsymbol{T}\rightarrow\mathbb{R} \end{aligned} \]

\[ \psi = \frac{g}{f_0}\eta \]

Coriolis Parameter

\[ f_0 = 2\Omega\sin(\varphi) \]

where:

• \(\Omega\) - …

• \(\varphi\) - latitude (radians)

f0 = metpy.calc.coriolis_parameter(latitude=np.deg2rad(da.lat)).mean()
f0

<xarray.DataArray ()>
<Quantity(8.967442585730005e-05, '1 / second')>

xarray.DataArray

• [1/s] 8.967e-05

  8.967442585730005×10^-5 1/second
• Coordinates: (0)
• Indexes: (0)
• Attributes: (0)

Gravity

from metpy.constants import earth_gravity as GRAVITY

GRAVITY

9.80665 meter/second²

da["psi"] = geocalc.streamfunction(da, "ssh").psi

da

<xarray.Dataset>
Dimensions:  (time: 60, lat: 201, lon: 201)
Coordinates:
  * lon      (lon) float64 -65.0 -64.95 -64.9 -64.85 ... -55.1 -55.05 -55.0
  * lat      (lat) float64 33.0 33.05 33.1 33.15 33.2 ... 42.85 42.9 42.95 43.0
  * time     (time) datetime64[ns] 2013-01-01T12:00:00 ... 2013-03-01T12:00:00
Data variables:
    ssh      (time, lat, lon) float64 [m] 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0
    psi      (time, lat, lon) float64 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0

xarray.Dataset

• Dimensions:
  • time: 60
  • lat: 201
  • lon: 201
• Coordinates: (3)
  • lon
    (lon)
    float64
    -65.0 -64.95 -64.9 ... -55.05 -55.0

    long_name :

    Longitude

    standard_name :

    longitude

    array([-65.  , -64.95, -64.9 , ..., -55.1 , -55.05, -55.  ])

  • lat
    (lat)
    float64
    33.0 33.05 33.1 ... 42.9 42.95 43.0

    long_name :

    Latitude

    standard_name :

    latitude

    array([33.  , 33.05, 33.1 , ..., 42.9 , 42.95, 43.  ])

  • time
    (time)
    datetime64[ns]
    2013-01-01T12:00:00 ... 2013-03-...

    array(['2013-01-01T12:00:00.000000000', '2013-01-02T12:00:00.000000000',
           '2013-01-03T12:00:00.000000000', '2013-01-04T12:00:00.000000000',
           '2013-01-05T12:00:00.000000000', '2013-01-06T12:00:00.000000000',
           '2013-01-07T12:00:00.000000000', '2013-01-08T12:00:00.000000000',
           '2013-01-09T12:00:00.000000000', '2013-01-10T12:00:00.000000000',
           '2013-01-11T12:00:00.000000000', '2013-01-12T12:00:00.000000000',
           '2013-01-13T12:00:00.000000000', '2013-01-14T12:00:00.000000000',
           '2013-01-15T12:00:00.000000000', '2013-01-16T12:00:00.000000000',
           '2013-01-17T12:00:00.000000000', '2013-01-18T12:00:00.000000000',
           '2013-01-19T12:00:00.000000000', '2013-01-20T12:00:00.000000000',
           '2013-01-21T12:00:00.000000000', '2013-01-22T12:00:00.000000000',
           '2013-01-23T12:00:00.000000000', '2013-01-24T12:00:00.000000000',
           '2013-01-25T12:00:00.000000000', '2013-01-26T12:00:00.000000000',
           '2013-01-27T12:00:00.000000000', '2013-01-28T12:00:00.000000000',
           '2013-01-29T12:00:00.000000000', '2013-01-30T12:00:00.000000000',
           '2013-01-31T12:00:00.000000000', '2013-02-01T12:00:00.000000000',
           '2013-02-02T12:00:00.000000000', '2013-02-03T12:00:00.000000000',
           '2013-02-04T12:00:00.000000000', '2013-02-05T12:00:00.000000000',
           '2013-02-06T12:00:00.000000000', '2013-02-07T12:00:00.000000000',
           '2013-02-08T12:00:00.000000000', '2013-02-09T12:00:00.000000000',
           '2013-02-10T12:00:00.000000000', '2013-02-11T12:00:00.000000000',
           '2013-02-12T12:00:00.000000000', '2013-02-13T12:00:00.000000000',
           '2013-02-14T12:00:00.000000000', '2013-02-15T12:00:00.000000000',
           '2013-02-16T12:00:00.000000000', '2013-02-17T12:00:00.000000000',
           '2013-02-18T12:00:00.000000000', '2013-02-19T12:00:00.000000000',
           '2013-02-20T12:00:00.000000000', '2013-02-21T12:00:00.000000000',
           '2013-02-22T12:00:00.000000000', '2013-02-23T12:00:00.000000000',
           '2013-02-24T12:00:00.000000000', '2013-02-25T12:00:00.000000000',
           '2013-02-26T12:00:00.000000000', '2013-02-27T12:00:00.000000000',
           '2013-02-28T12:00:00.000000000', '2013-03-01T12:00:00.000000000'],
          dtype='datetime64[ns]')

• Data variables: (2)
  • ssh
    (time, lat, lon)
    float64
    [m] 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0

    units :

    m

    long_name :

    Sea Surface Height

    standard_name :

    sea_surface_height

    Magnitude

    [[[0.0 0.0 0.0 ... 0.0 0.0 0.0] [0.0 0.5274601962787064 0.5215055760227856 ... 0.531906899685309 0.5309050673837461 0.0] [0.0 0.532797112868378 0.5265096624938118 ... 0.5384498208113863 0.5365520567351275 0.0] ... [0.0 -0.12543447287080764 -0.12327818290848727 ... -0.1982068958479165 -0.19710730016125091 0.0] [0.0 -0.12731597737047365 -0.12554665184477803 ... -0.19204990596778784 -0.1902951824531404 0.0] [0.0 0.0 0.0 ... 0.0 0.0 0.0]] [[0.0 0.0 0.0 ... 0.0 0.0 0.0] [0.0 0.5393008378801131 0.5343245685393202 ... 0.5404921223474768 0.5420319195907619 0.0] [0.0 0.5408474624184129 0.5356400540091064 ... 0.5474284504746452 0.5485933791335439 0.0] ... [0.0 -0.11739143036408646 -0.1169736530073986 ... -0.20029922527105645 -0.19856698820461274 0.0] [0.0 -0.12003031488571676 -0.11954693266019144 ... -0.19199693661993045 -0.18932468930730623 0.0] [0.0 0.0 0.0 ... 0.0 0.0 0.0]] [[0.0 0.0 0.0 ... 0.0 0.0 0.0] [0.0 0.5272116224649942 0.5231640880831123 ... 0.5405480268943602 0.5424189575940782 0.0] [0.0 0.5265939935542825 0.5222266809212104 ... 0.5473287354179225 0.5489821365754443 0.0] ... [0.0 -0.09543377852141287 -0.09732591613065772 ... -0.20520827443078066 -0.2045688642473909 0.0] [0.0 -0.09475764032865742 -0.09648029268827862 ... -0.1956169620082138 -0.19550088658915293 0.0] [0.0 0.0 0.0 ... 0.0 0.0 0.0]] ... [[0.0 0.0 0.0 ... 0.0 0.0 0.0] [0.0 0.5431924117017981 0.5425313060476112 ... 0.5711585743958262 0.574486559126326 0.0] [0.0 0.5485255474375483 0.5463762774472194 ... 0.5688282377548372 0.5729731702890268 0.0] ... [0.0 -0.06966948694073988 -0.06864865877238163 ... -0.1587271965129317 -0.1576343270445825 0.0] [0.0 -0.06616817571754427 -0.06571839096436957 ... -0.15871194023495547 -0.15869658335968997 0.0] [0.0 0.0 0.0 ... 0.0 0.0 0.0]] [[0.0 0.0 0.0 ... 0.0 0.0 0.0] [0.0 0.5409536458092825 0.541412761965103 ... 0.5841225541955257 0.5863682487630513 0.0] [0.0 0.5453516095856129 0.5465233657381937 ... 0.5833180510688298 0.5866411511382449 0.0] ... [0.0 -0.05562449528910319 -0.05079445239898697 ... -0.16300438125527925 -0.16133805372246013 0.0] [0.0 -0.054759021556013865 -0.05047628005514776 ... -0.16191339688143136 -0.1595854649465261 0.0] [0.0 0.0 0.0 ... 0.0 0.0 0.0]] [[0.0 0.0 0.0 ... 0.0 0.0 0.0] [0.0 0.5367315631480529 0.5353015058041571 ... 0.5857868161934291 0.5875366156381135 0.0] [0.0 0.5447038693814195 0.5428811377400011 ... 0.5854428206044671 0.5880564638210437 0.0] ... [0.0 -0.03911645498057455 -0.03586781018737217 ... -0.16541374956681373 -0.162049593863412 0.0] [0.0 -0.04084287006693674 -0.03673480709780731 ... -0.16275756851503356 -0.15899018136284307 0.0] [0.0 0.0 0.0 ... 0.0 0.0 0.0]]]

    Units

    meter

  • psi
    (time, lat, lon)
    float64
    0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0

    long_name :

    Stream Function

    standard_name :

    stream_function

    units :

    meter ** 2 / second

    array([[[     0.        ,      0.        ,      0.        , ...,
                  0.        ,      0.        ,      0.        ],
            [     0.        ,  57682.19293724,  57031.00530849, ...,
              58168.47722114,  58058.91846293,      0.        ],
            [     0.        ,  58265.8294933 ,  57578.24410174, ...,
              58884.00048039,  58676.4640741 ,      0.        ],
            ...,
            [     0.        , -13717.31083437, -13481.50245582, ...,
             -21675.58516918, -21555.33516548,      0.        ],
            [     0.        , -13923.0691197 , -13729.57854531, ...,
             -21002.26672603, -20810.37300393,      0.        ],
            [     0.        ,      0.        ,      0.        , ...,
                  0.        ,      0.        ,      0.        ]],
    
           [[     0.        ,      0.        ,      0.        , ...,
                  0.        ,      0.        ,      0.        ],
            [     0.        ,  58977.06632896,  58432.86957203, ...,
              59107.34326923,  59275.73300233,      0.        ],
            [     0.        ,  59146.20268398,  58576.72893281, ...,
              59865.88888107,  59993.28359282,      0.        ],
    ...
            [     0.        ,  -6083.00473086,  -5554.79906179, ...,
             -17825.89517753, -17643.66829686,      0.        ],
            [     0.        ,  -5988.35792489,  -5520.00424949, ...,
             -17706.58689306, -17452.00802633,      0.        ],
            [     0.        ,      0.        ,      0.        , ...,
                  0.        ,      0.        ,      0.        ]],
    
           [[     0.        ,      0.        ,      0.        , ...,
                  0.        ,      0.        ,      0.        ],
            [     0.        ,  58696.09460474,  58539.70584933, ...,
              64060.69764154,  64252.05287532,      0.        ],
            [     0.        ,  59567.93310469,  59368.60212398, ...,
              64023.07884097,  64308.90263081,      0.        ],
            ...,
            [     0.        ,  -4277.71217455,  -3922.44564056, ...,
             -18089.37979453, -17721.48117446,      0.        ],
            [     0.        ,  -4466.51013277,  -4017.25901874, ...,
             -17798.90413592, -17386.90877757,      0.        ],
            [     0.        ,      0.        ,      0.        , ...,
                  0.        ,      0.        ,      0.        ]]])

• Indexes: (3)
  • lon
    PandasIndex

    PandasIndex(Index([              -65.0,              -64.95,               -64.9,
            -64.85000000000001,  -64.80000000000001,  -64.75000000000001,
            -64.70000000000002,  -64.65000000000002,  -64.60000000000002,
            -64.55000000000003,
           ...
            -55.45000000000054, -55.400000000000546,  -55.35000000000055,
            -55.30000000000055, -55.250000000000554,  -55.20000000000056,
            -55.15000000000056,  -55.10000000000056, -55.050000000000566,
            -55.00000000000057],
          dtype='float64', name='lon', length=201))

  • lat
    PandasIndex

    PandasIndex(Index([              33.0,              33.05, 33.099999999999994,
            33.14999999999999,  33.19999999999999, 33.249999999999986,
            33.29999999999998,  33.34999999999998,  33.39999999999998,
           33.449999999999974,
           ...
            42.54999999999946, 42.599999999999454,  42.64999999999945,
            42.69999999999945, 42.749999999999446,  42.79999999999944,
            42.84999999999944,  42.89999999999944, 42.949999999999434,
            42.99999999999943],
          dtype='float64', name='lat', length=201))

  • time
    PandasIndex

    PandasIndex(DatetimeIndex(['2013-01-01 12:00:00', '2013-01-02 12:00:00',
                   '2013-01-03 12:00:00', '2013-01-04 12:00:00',
                   '2013-01-05 12:00:00', '2013-01-06 12:00:00',
                   '2013-01-07 12:00:00', '2013-01-08 12:00:00',
                   '2013-01-09 12:00:00', '2013-01-10 12:00:00',
                   '2013-01-11 12:00:00', '2013-01-12 12:00:00',
                   '2013-01-13 12:00:00', '2013-01-14 12:00:00',
                   '2013-01-15 12:00:00', '2013-01-16 12:00:00',
                   '2013-01-17 12:00:00', '2013-01-18 12:00:00',
                   '2013-01-19 12:00:00', '2013-01-20 12:00:00',
                   '2013-01-21 12:00:00', '2013-01-22 12:00:00',
                   '2013-01-23 12:00:00', '2013-01-24 12:00:00',
                   '2013-01-25 12:00:00', '2013-01-26 12:00:00',
                   '2013-01-27 12:00:00', '2013-01-28 12:00:00',
                   '2013-01-29 12:00:00', '2013-01-30 12:00:00',
                   '2013-01-31 12:00:00', '2013-02-01 12:00:00',
                   '2013-02-02 12:00:00', '2013-02-03 12:00:00',
                   '2013-02-04 12:00:00', '2013-02-05 12:00:00',
                   '2013-02-06 12:00:00', '2013-02-07 12:00:00',
                   '2013-02-08 12:00:00', '2013-02-09 12:00:00',
                   '2013-02-10 12:00:00', '2013-02-11 12:00:00',
                   '2013-02-12 12:00:00', '2013-02-13 12:00:00',
                   '2013-02-14 12:00:00', '2013-02-15 12:00:00',
                   '2013-02-16 12:00:00', '2013-02-17 12:00:00',
                   '2013-02-18 12:00:00', '2013-02-19 12:00:00',
                   '2013-02-20 12:00:00', '2013-02-21 12:00:00',
                   '2013-02-22 12:00:00', '2013-02-23 12:00:00',
                   '2013-02-24 12:00:00', '2013-02-25 12:00:00',
                   '2013-02-26 12:00:00', '2013-02-27 12:00:00',
                   '2013-02-28 12:00:00', '2013-03-01 12:00:00'],
                  dtype='datetime64[ns]', name='time', freq=None))

• Attributes: (0)

fig, ax = plt.subplots()

da.psi.isel(time=10).plot.pcolormesh(ax=ax, cmap="viridis")

plt.show()

Velocities

\[\begin{split} \begin{aligned} \text{U Velocity}[ms^{-1}]: && u &=\boldsymbol{u}(\vec{\mathbf{x}},t) && && \boldsymbol{\psi}: \boldsymbol{\Omega}\times\boldsymbol{T}\rightarrow\mathbb{R} \\ \text{V Velocity}[ms^{-1}]: && v &=\boldsymbol{v}(\vec{\mathbf{x}},t) && && \boldsymbol{\psi}: \boldsymbol{\Omega}\times\boldsymbol{T}\rightarrow\mathbb{R} \end{aligned} \end{split}\]

\[ \begin{aligned} u = -\frac{\partial \psi}{\partial y} && v = \frac{\partial \psi}{\partial x} \end{aligned} \]

da = da.assign = geocalc.geostrophic_velocities(da, variable="psi")

[autoreload of jupyter_client.provisioning.provisioner_base failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 365, in update_class
    update_instances(old, new)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 323, in update_instances
    object.__setattr__(ref, "__class__", new)
TypeError: can't apply this __setattr__ to KernelProvisionerMeta object
]
[autoreload of pygments.token failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 365, in update_class
    update_instances(old, new)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 323, in update_instances
    object.__setattr__(ref, "__class__", new)
TypeError: __class__ assignment: '_TokenType' object layout differs from '_TokenType'
]
[autoreload of pygments.style failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 365, in update_class
    update_instances(old, new)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 323, in update_instances
    object.__setattr__(ref, "__class__", new)
TypeError: can't apply this __setattr__ to StyleMeta object
]
[autoreload of pygments.lexer failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 365, in update_class
    update_instances(old, new)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 323, in update_instances
    object.__setattr__(ref, "__class__", new)
TypeError: can't apply this __setattr__ to LexerMeta object
]
[autoreload of prompt_toolkit.shortcuts.progress_bar.formatters failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 365, in update_class
    update_instances(old, new)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 319, in update_instances
    refs = gc.get_referrers(old)
           ^^^^^^^^^^^^^^^^^^^^^
KeyboardInterrupt
]
[autoreload of jedi.inference.cache failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 365, in update_class
    update_instances(old, new)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 323, in update_instances
    object.__setattr__(ref, "__class__", new)
TypeError: can't apply this __setattr__ to CachedMetaClass object
]
[autoreload of jedi.inference.filters failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 365, in update_class
    update_instances(old, new)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 323, in update_instances
    object.__setattr__(ref, "__class__", new)
TypeError: can't apply this __setattr__ to _OverwriteMeta object
]
[autoreload of typing_extensions failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 365, in update_class
    update_instances(old, new)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 323, in update_instances
    object.__setattr__(ref, "__class__", new)
TypeError: can't apply this __setattr__ to _ProtocolMeta object
]
[autoreload of urllib3.exceptions failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 349, in update_class
    if update_generic(old_obj, new_obj):
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 309, in update_function
    setattr(old, name, getattr(new, name))
ValueError: __init__() requires a code object with 1 free vars, not 0
]
[autoreload of urllib3.util.connection failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 475, in superreload
    module = reload(module)
             ^^^^^^^^^^^^^^
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/importlib/__init__.py", line 169, in reload
    _bootstrap._exec(spec, module)
  File "<frozen importlib._bootstrap>", line 621, in _exec
  File "<frozen importlib._bootstrap_external>", line 940, in exec_module
  File "<frozen importlib._bootstrap>", line 241, in _call_with_frames_removed
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/urllib3/util/connection.py", line 8, in <module>
    from .wait import NoWayToWaitForSocketError, wait_for_read
ImportError: cannot import name 'NoWayToWaitForSocketError' from 'urllib3.util.wait' (/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/urllib3/util/wait.py)
]
[autoreload of urllib3._collections failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 349, in update_class
    if update_generic(old_obj, new_obj):
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 309, in update_function
    setattr(old, name, getattr(new, name))
ValueError: __init__() requires a code object with 1 free vars, not 0
]
[autoreload of urllib3.connection failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 475, in superreload
    module = reload(module)
             ^^^^^^^^^^^^^^
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/importlib/__init__.py", line 169, in reload
    _bootstrap._exec(spec, module)
  File "<frozen importlib._bootstrap>", line 621, in _exec
  File "<frozen importlib._bootstrap_external>", line 940, in exec_module
  File "<frozen importlib._bootstrap>", line 241, in _call_with_frames_removed
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/urllib3/connection.py", line 15, in <module>
    from .util.proxy import create_proxy_ssl_context
ImportError: cannot import name 'create_proxy_ssl_context' from 'urllib3.util.proxy' (/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/urllib3/util/proxy.py)
]
[autoreload of urllib3.response failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 349, in update_class
    if update_generic(old_obj, new_obj):
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 309, in update_function
    setattr(old, name, getattr(new, name))
ValueError: __init__() requires a code object with 1 free vars, not 0
]
[autoreload of urllib3.connectionpool failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 349, in update_class
    if update_generic(old_obj, new_obj):
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 309, in update_function
    setattr(old, name, getattr(new, name))
ValueError: __init__() requires a code object with 1 free vars, not 0
]
[autoreload of urllib3.poolmanager failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 349, in update_class
    if update_generic(old_obj, new_obj):
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 309, in update_function
    setattr(old, name, getattr(new, name))
ValueError: __init__() requires a code object with 1 free vars, not 0
]
[autoreload of requests.packages.urllib3.util.retry failed: Traceback (most recent call last):
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 276, in check
    superreload(m, reload, self.old_objects)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 500, in superreload
    update_generic(old_obj, new_obj)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 397, in update_generic
    update(a, b)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 365, in update_class
    update_instances(old, new)
  File "/Users/eman/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/extensions/autoreload.py", line 323, in update_instances
    object.__setattr__(ref, "__class__", new)
TypeError: can't apply this __setattr__ to _RetryMeta object
]

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File ~/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/core/async_helpers.py:129, in _pseudo_sync_runner(coro)
    121 """
    122 A runner that does not really allow async execution, and just advance the coroutine.
    123 
   (...)
    126 Credit to Nathaniel Smith
    127 """
    128 try:
--> 129     coro.send(None)
    130 except StopIteration as exc:
    131     return exc.value

File ~/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/IPython/core/interactiveshell.py:3278, in InteractiveShell.run_cell_async(self, raw_cell, store_history, silent, shell_futures, transformed_cell, preprocessing_exc_tuple, cell_id)
   3274     return error_before_exec(e)
   3276 # Give the displayhook a reference to our ExecutionResult so it
   3277 # can fill in the output value.
-> 3278 self.displayhook.exec_result = result
   3280 # Execute the user code
   3281 interactivity = "none" if silent else self.ast_node_interactivity

File ~/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/traitlets/traitlets.py:745, in TraitType.__set__(self, obj, value)
    743     raise TraitError('The "%s" trait is read-only.' % self.name)
    744 else:
--> 745     self.set(obj, value)

File ~/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/traitlets/traitlets.py:719, in TraitType.set(self, obj, value)
    718 def set(self, obj, value):
--> 719     new_value = self._validate(obj, value)
    720     try:
    721         old_value = obj._trait_values[self.name]

File ~/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/traitlets/traitlets.py:751, in TraitType._validate(self, obj, value)
    749     return value
    750 if hasattr(self, "validate"):
--> 751     value = self.validate(obj, value)
    752 if obj._cross_validation_lock is False:
    753     value = self._cross_validate(obj, value)

File ~/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/traitlets/traitlets.py:2311, in Instance.validate(self, obj, value)
   2309 def validate(self, obj, value):
   2310     assert self.klass is not None
-> 2311     if isinstance(value, self.klass):  # type:ignore[arg-type]
   2312         return value
   2313     else:

TypeError: isinstance() arg 2 must be a type, a tuple of types, or a union

fig, ax = plt.subplots(ncols=2, figsize=(10,4))

da.u.isel(time=10, lat=slice(1,-1), lon=slice(1,-1)).plot.pcolormesh(ax=ax[0], cmap="gray")
da.v.isel(time=10, lat=slice(1,-1), lon=slice(1,-1)).plot.pcolormesh(ax=ax[1], cmap="gray")

plt.tight_layout()
plt.show()

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
/Users/eman/code_projects/oceanbench/jbook/content/geoprocess/physical_variables.ipynb Cell 24 line 3
      <a href='vscode-notebook-cell:/Users/eman/code_projects/oceanbench/jbook/content/geoprocess/physical_variables.ipynb#X31sZmlsZQ%3D%3D?line=0'>1</a> fig, ax = plt.subplots(ncols=2, figsize=(10,4))
----> <a href='vscode-notebook-cell:/Users/eman/code_projects/oceanbench/jbook/content/geoprocess/physical_variables.ipynb#X31sZmlsZQ%3D%3D?line=2'>3</a> da.u.isel(time=10, lat=slice(1,-1), lon=slice(1,-1)).plot.pcolormesh(ax=ax[0], cmap="gray")
      <a href='vscode-notebook-cell:/Users/eman/code_projects/oceanbench/jbook/content/geoprocess/physical_variables.ipynb#X31sZmlsZQ%3D%3D?line=3'>4</a> da.v.isel(time=10, lat=slice(1,-1), lon=slice(1,-1)).plot.pcolormesh(ax=ax[1], cmap="gray")
      <a href='vscode-notebook-cell:/Users/eman/code_projects/oceanbench/jbook/content/geoprocess/physical_variables.ipynb#X31sZmlsZQ%3D%3D?line=5'>6</a> plt.tight_layout()

File ~/miniconda3/envs/oceanbench_311/lib/python3.11/site-packages/xarray/core/common.py:278, in AttrAccessMixin.__getattr__(self, name)
    276         with suppress(KeyError):
    277             return source[name]
--> 278 raise AttributeError(
    279     f"{type(self).__name__!r} object has no attribute {name!r}"
    280 )

AttributeError: 'Dataset' object has no attribute 'u'

Kinetic Energy

\[\begin{split} \begin{aligned} E &= \frac{1}{2}\int \mathbf{u}^2dr \\ E &\approx \frac{1}{2} \mathbb{E}\left[ \mathbf{u}^2\right] \\ &= \frac{1}{2} \mathbb{E}\left[ u^2 + v^2\right] \end{aligned} \end{split}\]

da = geocalc.kinetic_energy(da, variables=["u", "v"])

fig, ax = plt.subplots()

da.ke.isel(time=1, lat=slice(1,-1), lon=slice(1,-1)).plot.pcolormesh(ax=ax, cmap="YlGnBu_r", robust=True)

plt.show()

Relative Vorticity

Somtimes called the vertical vorticity.

\[ \zeta = \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y} \]

Note that the u,v velocities can be calculated from the stream function as

\[\begin{split} \begin{aligned} u &= -\frac{\partial \psi}{\partial y} && && v = \frac{\partial \psi}{\partial x}\\ \end{aligned} \end{split}\]

So plugging these into the equation, we get:

\[\begin{split} \begin{aligned} \zeta &= \frac{\partial}{\partial x}\left(\frac{\partial \psi}{\partial x}\right) - \frac{\partial}{\partial y}\left( -\frac{\partial \psi}{\partial y}\right) \\ \zeta &= \frac{\partial^2 \psi}{\partial x^2}+ \frac{\partial^2 \psi}{\partial y^2}\\ \zeta &=\nabla^2\psi \end{aligned} \end{split}\]

We can also calculate a normalized version

\[ \bar{\zeta} = \frac{\zeta}{f_0} \]

Note: This is closely related to the geostrophic eqns:

\[ \begin{aligned} \text{Relative Vorticity }[s^{-1}]: && \zeta &=\boldsymbol{\zeta}(\vec{\mathbf{x}},t) && && \boldsymbol{\xi}: \boldsymbol{\Omega}\times\boldsymbol{T}\rightarrow\mathbb{R} \end{aligned} \]

\[ \zeta = \nabla^2\psi \]

da = geocalc.relative_vorticity(da, variables=["u", "v"])
# da = geocalc.coriolis_normalized(da, "vort_r")

fig, ax = plt.subplots()

da.vort_r.isel(time=1).plot.pcolormesh(ax=ax, cmap="RdBu_r")

plt.show()

Absolute Vorticity

Somtimes called the horizontal divergence.

\[ \zeta = \frac{\partial v}{\partial x} + \frac{\partial u}{\partial y} \]

Note that the u,v velocities can be calculated from the stream function as

\[\begin{split} \begin{aligned} u &= -\frac{\partial \psi}{\partial y} && && v = \frac{\partial \psi}{\partial x}\\ \end{aligned} \end{split}\]

So plugging these into the equation, we get:

\[\begin{split} \begin{aligned} \zeta &= \frac{\partial}{\partial x}\left(\frac{\partial \psi}{\partial x}\right) + \frac{\partial}{\partial y}\left( -\frac{\partial \psi}{\partial y}\right) \\ \zeta &= \frac{\partial^2 \psi}{\partial x^2} - \frac{\partial^2 \psi}{\partial y^2} \end{aligned} \end{split}\]

We can also calculate a normalized version

\[ \bar{\zeta} = \frac{\zeta}{f_0} \]

da = geocalc.absolute_vorticity(da, variables=["u", "v"])
da = geocalc.coriolis_normalized(da, "vort_a")

fig, ax = plt.subplots()

da.vort_a.isel(time=10).plot.pcolormesh(ax=ax, cmap="RdBu_r")

plt.show()

Divergence

\[ \nabla \cdot \vec{\mathbf{u}} = \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} \]

da = geocalc.divergence(da, variables=["u", "v"])
da = geocalc.coriolis_normalized(da, "div")

fig, ax = plt.subplots()

da.div.isel(time=10).plot.pcolormesh(ax=ax, cmap="RdBu_r")

plt.show()

Enstropy

This is a summarization of the relative vorticity

\[\begin{split} \begin{aligned} Z &= \frac{1}{2}\int \zeta^2 dr \\ Z &\approx \frac{1}{2} \mathbb{E}\left[ \zeta^2 \right] \\ \end{aligned} \end{split}\]

da = geocalc.enstrophy(da, variable="vort_r")
da = geocalc.coriolis_normalized(da, "ens")

fig, ax = plt.subplots()

da.ens.isel(time=10).plot.pcolormesh(ax=ax, cmap="RdBu_r")

plt.show()

Strain

Shear Strain

We also have the Shearing Deformation given by:

\[ S_s = \frac{\partial v}{\partial x} + \frac{\partial u}{\partial y} \]

da = geocalc.shear_strain(da, variables=["u", "v"])
da

<xarray.Dataset>
Dimensions:       (time: 60, lat: 201, lon: 201)
Coordinates:
  * lon           (lon) float64 -65.0 -64.95 -64.9 -64.85 ... -55.1 -55.05 -55.0
  * lat           (lat) float64 33.0 33.05 33.1 33.15 ... 42.85 42.9 42.95 43.0
  * time          (time) datetime64[ns] 2013-01-01 2013-01-02 ... 2013-03-01
Data variables:
    ssh           (time, lat, lon) float64 <Quantity([[[ 0.52873772  0.528737...
    psi           (time, lat, lon) float64 <Quantity([[[ 57821.90125565  5782...
    u             (time, lat, lon) float64 <Quantity([[[ 0.09819786  0.098197...
    v             (time, lat, lon) float64 <Quantity([[[ 0.06750432 -0.067504...
    ke            (time, lat, lon) float64 <Quantity([[[7.09982675e-03 7.0998...
    vort_r        (time, lat, lon) float64 <Quantity([[[-21.03727654 -13.1933...
    vort_a        (time, lat, lon) float64 <Quantity([[[26.01496319 33.858852...
    div           (time, lat, lon) float64 <Quantity([[[-22.41076683 -11.8198...
    ens           (time, lat, lon) float64 <Quantity([[[1.31080192e+08 5.1554...
    shear_strain  (time, lat, lon) float64 <Quantity([[[ 1.24743972e-08 -1.24...

xarray.Dataset

• Dimensions:
  • time: 60
  • lat: 201
  • lon: 201
• Coordinates: (3)
  • lon
    (lon)
    float64
    -65.0 -64.95 -64.9 ... -55.05 -55.0

    long_name :

    Longitude

    standard_name :

    longitude

    _metpy_axis :

    x,longitude

    array([-65.  , -64.95, -64.9 , ..., -55.1 , -55.05, -55.  ])

  • lat
    (lat)
    float64
    33.0 33.05 33.1 ... 42.9 42.95 43.0

    long_name :

    Latitude

    standard_name :

    latitude

    _metpy_axis :

    y,latitude

    array([33.  , 33.05, 33.1 , ..., 42.9 , 42.95, 43.  ])

  • time
    (time)
    datetime64[ns]
    2013-01-01 ... 2013-03-01

    _metpy_axis :

    time

    array(['2013-01-01T00:00:00.000000000', '2013-01-02T00:00:00.000000000',
           '2013-01-03T00:00:00.000000000', '2013-01-04T00:00:00.000000000',
           '2013-01-05T00:00:00.000000000', '2013-01-06T00:00:00.000000000',
           '2013-01-07T00:00:00.000000000', '2013-01-08T00:00:00.000000000',
           '2013-01-09T00:00:00.000000000', '2013-01-10T00:00:00.000000000',
           '2013-01-11T00:00:00.000000000', '2013-01-12T00:00:00.000000000',
           '2013-01-13T00:00:00.000000000', '2013-01-14T00:00:00.000000000',
           '2013-01-15T00:00:00.000000000', '2013-01-16T00:00:00.000000000',
           '2013-01-17T00:00:00.000000000', '2013-01-18T00:00:00.000000000',
           '2013-01-19T00:00:00.000000000', '2013-01-20T00:00:00.000000000',
           '2013-01-21T00:00:00.000000000', '2013-01-22T00:00:00.000000000',
           '2013-01-23T00:00:00.000000000', '2013-01-24T00:00:00.000000000',
           '2013-01-25T00:00:00.000000000', '2013-01-26T00:00:00.000000000',
           '2013-01-27T00:00:00.000000000', '2013-01-28T00:00:00.000000000',
           '2013-01-29T00:00:00.000000000', '2013-01-30T00:00:00.000000000',
           '2013-01-31T00:00:00.000000000', '2013-02-01T00:00:00.000000000',
           '2013-02-02T00:00:00.000000000', '2013-02-03T00:00:00.000000000',
           '2013-02-04T00:00:00.000000000', '2013-02-05T00:00:00.000000000',
           '2013-02-06T00:00:00.000000000', '2013-02-07T00:00:00.000000000',
           '2013-02-08T00:00:00.000000000', '2013-02-09T00:00:00.000000000',
           '2013-02-10T00:00:00.000000000', '2013-02-11T00:00:00.000000000',
           '2013-02-12T00:00:00.000000000', '2013-02-13T00:00:00.000000000',
           '2013-02-14T00:00:00.000000000', '2013-02-15T00:00:00.000000000',
           '2013-02-16T00:00:00.000000000', '2013-02-17T00:00:00.000000000',
           '2013-02-18T00:00:00.000000000', '2013-02-19T00:00:00.000000000',
           '2013-02-20T00:00:00.000000000', '2013-02-21T00:00:00.000000000',
           '2013-02-22T00:00:00.000000000', '2013-02-23T00:00:00.000000000',
           '2013-02-24T00:00:00.000000000', '2013-02-25T00:00:00.000000000',
           '2013-02-26T00:00:00.000000000', '2013-02-27T00:00:00.000000000',
           '2013-02-28T00:00:00.000000000', '2013-03-01T00:00:00.000000000'],
          dtype='datetime64[ns]')

• Data variables: (10)
  • ssh
    (time, lat, lon)
    float64
    <Quantity([[[ 0.52873772 0.5287...

    units :

    m

    long_name :

    Sea Surface Height

    standard_name :

    sea_surface_height

    Magnitude

    [[[0.5287377235934707 0.5287377235934707 0.522969079741927 ... 0.5411993453411955 0.5406936933399921 0.5406936933399921] [0.5287377235934707 0.5287377235934707 0.522969079741927 ... 0.5411993453411955 0.5406936933399921 0.5406936933399921] [0.5386593697200855 0.5386593697200855 0.5317972916949067 ... 0.5503102679827852 0.5472362034113286 0.5472362034113286] ... [-0.14953106401257885 -0.14953106401257885 -0.14543524615326275 ... -0.17598567550767183 -0.17592814053862824 -0.17592814053862824] [-0.1564428243843681 -0.1564428243843681 -0.1526108154264891 ... -0.16950291316128438 -0.17007242266885556 -0.17007242266885556] [-0.1564428243843681 -0.1564428243843681 -0.1526108154264891 ... -0.16950291316128438 -0.17007242266885556 -0.17007242266885556]] [[0.5391389026408514 0.5391389026408514 0.5330762839513563 ... 0.536576341409434 0.5375850924283004 0.5375850924283004] [0.5391389026408514 0.5391389026408514 0.5330762839513563 ... 0.536576341409434 0.5375850924283004 0.5375850924283004] [0.5429088065119245 0.5429088065119245 0.5369101565200166 ... 0.5438399434161332 0.5418302937209541 0.5418302937209541] ... [-0.10293197607496386 -0.10293197607496386 -0.10169449147177415 ... -0.18793466136830417 -0.1866449023215486 -0.1866449023215486] [-0.10546162065251329 -0.10546162065251329 -0.1036485558207519 ... -0.18133018358240693 -0.17791136460703794 -0.17791136460703794] [-0.10546162065251329 -0.10546162065251329 -0.1036485558207519 ... -0.18133018358240693 -0.17791136460703794 -0.17791136460703794]] [[0.5402870194100985 0.5402870194100985 0.5356310394772633 ... 0.5479772674895839 0.5501420586773289 0.5501420586773289] [0.5402870194100985 0.5402870194100985 0.5356310394772633 ... 0.5479772674895839 0.5501420586773289 0.5501420586773289] [0.5406876636755815 0.5406876636755815 0.5356638522281901 ... 0.5558092187020827 0.557005916024521 0.557005916024521] ... [-0.13445553928942483 -0.13445553928942483 -0.1338641543559391 ... -0.1924576556647342 -0.191740634466255 -0.191740634466255] [-0.13860817144495502 -0.13860817144495502 -0.13767411322544076 ... -0.18129368141715724 -0.1802944949661698 -0.1802944949661698] [-0.13860817144495502 -0.13860817144495502 -0.13767411322544076 ... -0.18129368141715724 -0.1802944949661698 -0.1802944949661698]] ... [[0.5433101122506314 0.5433101122506314 0.5430574255187012 ... 0.5689346550538082 0.5727583405716874 0.5727583405716874] [0.5433101122506314 0.5433101122506314 0.5430574255187012 ... 0.5689346550538082 0.5727583405716874 0.5727583405716874] [0.5511900954974471 0.5511900954974471 0.5492376538303079 ... 0.5657574188396578 0.5696000446977054 0.5696000446977054] ... [-0.06326424798004898 -0.06326424798004898 -0.0634393010040546 ... -0.15456124599463805 -0.15337259502744321 -0.15337259502744321] [-0.05877586481294284 -0.05877586481294284 -0.061237361532658546 ... -0.15585711415935316 -0.15770489788422143 -0.15770489788422143] [-0.05877586481294284 -0.05877586481294284 -0.061237361532658546 ... -0.15585711415935316 -0.15770489788422143 -0.15770489788422143]] [[0.5367400858536936 0.5367400858536936 0.5362331610834976 ... 0.5844879348834278 0.5867649100557852 0.5867649100557852] [0.5367400858536936 0.5367400858536936 0.5362331610834976 ... 0.5844879348834278 0.5867649100557852 0.5867649100557852] [0.5389199720033089 0.5389199720033089 0.5373913866110094 ... 0.5833074193388187 0.5869104732767194 0.5869104732767194] ... [-0.07104319616733296 -0.07104319616733296 -0.06756085264368931 ... -0.1610185973242123 -0.16158134082912548 -0.16158134082912548] [-0.06806466313594035 -0.06806466313594035 -0.06531996664222713 ... -0.16039820717747472 -0.1619364901419632 -0.1619364901419632] [-0.06806466313594035 -0.06806466313594035 -0.06531996664222713 ... -0.16039820717747472 -0.1619364901419632 -0.1619364901419632]] [[0.541107855033267 0.541107855033267 0.5400384057555375 ... 0.5888172262601357 0.590241946440579 0.590241946440579] [0.541107855033267 0.541107855033267 0.5400384057555375 ... 0.5888172262601357 0.590241946440579 0.590241946440579] [0.5464211687853855 0.5464211687853855 0.5489003946148437 ... 0.5884807444197748 0.591795974946214 0.591795974946214] ... [-0.04676019392651611 -0.04676019392651611 -0.040990601725933634 ... -0.16754683885569496 -0.16454667695037542 -0.16454667695037542] [-0.04819953656600751 -0.04819953656600751 -0.0421048047341123 ... -0.1648261777380988 -0.15993202552378355 -0.15993202552378355] [-0.04819953656600751 -0.04819953656600751 -0.0421048047341123 ... -0.1648261777380988 -0.15993202552378355 -0.15993202552378355]]]

    Units

    meter

  • psi
    (time, lat, lon)
    float64
    <Quantity([[[ 57821.90125565 57...

    long_name :

    Stream Function

    standard_name :

    stream_function

    Magnitude

    [[[57821.90125564999 57821.90125564999 57191.051705336016 ... 59184.68403060519 59129.386746566895 59129.386746566895] [57821.90125564999 57821.90125564999 57191.051705336016 ... 59184.68403060519 59129.386746566895 59129.386746566895] [58906.91640971854 58906.91640971854 58156.490668797655 ... 60181.03977717361 59844.86505353895 59844.86505353895] ... [-16352.475021501155 -16352.475021501155 -15904.56301285357 ... -19245.508496074934 -19239.21656502796 -19239.21656502796] [-17108.333943395653 -17108.333943395653 -16689.271649017723 ... -18536.564103552515 -18598.844741081328 -18598.844741081328] [-17108.333943395653 -17108.333943395653 -16689.271649017723 ... -18536.564103552515 -18598.844741081328 -18598.844741081328]] [[58959.35735341538 58959.35735341538 58296.35919086291 ... 58679.11980675888 58789.43518468958 58789.43518468958] [58959.35735341538 58959.35735341538 58296.35919086291 ... 58679.11980675888 58789.43518468958 58789.43518468958] [59371.62793606834 59371.62793606834 58715.6252866981 ... 59473.455560102295 59253.68352370711 59253.68352370711] ... [-11256.47422356339 -11256.47422356339 -11121.14491124438 ... -20552.23024054018 -20411.184279721954 -20411.184279721954] [-11533.112058255538 -11533.112058255538 -11334.838224189552 ... -19829.97524464943 -19456.09873767124 -19456.09873767124] [-11533.112058255538 -11533.112058255538 -11334.838224189552 ... -19829.97524464943 -19456.09873767124 -19456.09873767124]] [[59084.913544129704 59084.913544129704 58575.74311820474 ... 59925.90662111572 60162.644679913916 60162.644679913916] [59084.913544129704 59084.913544129704 58575.74311820474 ... 59925.90662111572 60162.644679913916 60162.644679913916] [59128.727352230926 59128.727352230926 58579.33146751169 ... 60782.39612326511 60913.26500460888 60913.26500460888] ... [-14703.840049903138 -14703.840049903138 -14639.167151219664 ... -21046.857572614415 -20968.445295436803 -20968.445295436803] [-15157.965177984068 -15157.965177984068 -15055.818083638842 ... -19825.98342696648 -19716.714014690915 -19716.714014690915] [-15157.965177984068 -15157.965177984068 -15055.818083638842 ... -19825.98342696648 -19716.714014690915 -19716.714014690915]] ... [[59415.514081810186 59415.514081810186 59387.88066998743 ... 62217.77258838436 62635.92464484224 62635.92464484224] [59415.514081810186 59415.514081810186 59387.88066998743 ... 62217.77258838436 62635.92464484224 62635.92464484224] [60277.25628945315 60277.25628945315 60063.7404303662 ... 61870.31518097279 62290.538522360985 62290.538522360985] ... [-6918.475713921085 -6918.475713921085 -6937.619229159158 ... -16902.567577575715 -16772.578632611734 -16772.578632611734] [-6427.633398903149 -6427.633398903149 -6696.818694215915 ... -17044.281621641367 -17246.35225763646 -17246.35225763646] [-6427.633398903149 -6427.633398903149 -6696.818694215915 ... -17044.281621641367 -17246.35225763646 -17246.35225763646]] [[58697.02663402816 58697.02663402816 58641.59016203386 ... 63918.654084786176 64167.66040247961 64167.66040247961] [58697.02663402816 58697.02663402816 58641.59016203386 ... 63918.654084786176 64167.66040247961 64167.66040247961] [58935.41545341288 58935.41545341288 58768.251830182686 ... 63789.5548164623 64183.57896060727 64183.57896060727] ... [-7769.168891061938 -7769.168891061938 -7388.345442351116 ... -17608.73306244806 -17670.27378088253 -17670.27378088253] [-7443.441341952366 -7443.441341952366 -7143.285777946805 ... -17540.88820061214 -17709.11233463343 -17709.11233463343] [-7443.441341952366 -7443.441341952366 -7143.285777946805 ... -17540.88820061214 -17709.11233463343 -17709.11233463343]] [[59174.67879868238 59174.67879868238 59057.72555745243 ... 64392.09837922697 64547.903471079786 64547.903471079786] [59174.67879868238 59174.67879868238 59057.72555745243 ... 64392.09837922697 64547.903471079786 64547.903471079786] [59755.73418664917 59755.73418664917 60026.858308694245 ... 64355.3012700375 64717.84951198376 64717.84951198376] ... [-5113.619088001549 -5113.619088001549 -4482.665827772383 ... -18322.650985007058 -17994.558137268945 -17994.558137268945] [-5271.023268297389 -5271.023268297389 -4604.51326449356 ... -18025.123890812647 -17489.907329862595 -17489.907329862595] [-5271.023268297389 -5271.023268297389 -4604.51326449356 ... -18025.123890812647 -17489.907329862595 -17489.907329862595]]]

    Units

    meter2/second

  • u
    (time, lat, lon)
    float64
    <Quantity([[[ 0.09819786 0.0981...

    long_name :

    Zonal Velocity

    standard_name :

    zonal_velocity

    Magnitude

    [[[0.09819786441965409 0.09819786441965409 0.0873757791160496 ... 0.09017386176441615 0.06475341982072315 0.06475341982072315] [-0.09819707644478928 -0.09819707644478928 -0.08737507798147337 ... -0.09017313817701987 -0.06475290021606878 -0.06475290021606878] [-0.17615502417141773 -0.17615502417141773 -0.1628996138865662 ... -0.17001370722584153 -0.13490419721012975 -0.13490419721012975] ... [0.11631903145771667 0.11631903145771667 0.11332102526424069 ... -0.11032240989974279 -0.1087707344099209 -0.1087707344099209] [0.06817922362939374 0.06817922362939374 0.07078149643964901 ... -0.06394748659901 -0.05776217297454113 -0.05776217297454113] [-0.06817862581508027 -0.06817862581508027 -0.07078087580788645 ... 0.06394692588973762 0.05776166649981131 0.05776166649981131]] [[0.037312004931693 0.037312004931693 0.03794512461895319 ... 0.07189030892150577 0.04201618316661254 0.04201618316661254] [-0.03731170552679018 -0.03731170552679018 -0.037944820133669246 ... -0.07188973204789473 -0.04201584601369714 -0.04201584601369714] [-0.06347083722336684 -0.06347083722336684 -0.05854163917994366 ... -0.17159953669821296 -0.13101029161609834 -0.13101029161609834] ... [0.026483813230523068 0.026483813230523068 0.03192811557377507 ... -0.1415618310883438 -0.1688764492892659 -0.1688764492892659] [0.02495300677083217 0.02495300677083217 0.019275348546363317 ... -0.0651481162104417 -0.08614966215317785 -0.08614966215317785] [-0.024952787975958252 -0.024952787975958252 -0.019275179534769715 ... 0.06514754497371772 0.08614890676908211 0.08614890676908211]] [[0.003965310872847362 0.003965310872847362 0.00032475881780463247 ... 0.07751545192115608 0.06793390175117876 0.06793390175117876] [-0.003965279053772268 -0.003965279053772268 -0.00032475621182256274 ... -0.07751482990938013 -0.06793335662519899 -0.06793335662519899] [0.0024213914193914657 0.0024213914193914657 0.0114517597933893 ... -0.150584017677278 -0.1393853617498071 -0.1393853617498071] ... [0.07448419996298912 0.07448419996298912 0.0654855198490467 ... -0.17306020128648453 -0.1890602124781547 -0.1890602124781547] [0.04096253648174631 0.04096253648174631 0.03758232690513567 ... -0.11012405753026708 -0.11290740168810641 -0.11290740168810641] [-0.04096217731088231 -0.04096217731088231 -0.037581997372886 ... 0.11012309193203315 0.11290641168473943 0.11290641168473943]] ... [[0.07799084109886471 0.07799084109886471 0.06116779555337048 ... -0.03144617405265558 -0.03125871514390142 -0.03125871514390142] [-0.07799021527239558 -0.07799021527239558 -0.06116730472105244 ... 0.031445921717279036 0.03125846431276503 0.03125846431276503] [-0.16438765515429185 -0.16438765515429185 -0.14394939328429202 ... 0.08347681356174544 0.06646683628987174 0.06646683628987174] ... [-0.07540788999423918 -0.07540788999423918 -0.05243366682389291 ... -0.02148301946296358 0.031265095115431955 0.031265095115431955] [-0.04427446312137081 -0.04427446312137081 -0.021720446827330667 ... 0.01278274717927639 0.04273485037301418 0.04273485037301418] [0.04427407491061696 0.04427407491061696 0.021720256376437652 ... -0.012782635096609148 -0.04273447566201139 -0.04273447566201139]] [[0.021575065451689822 0.021575065451689822 0.011463347096494315 ... -0.011683958882978185 0.0014406880926144184 0.0014406880926144184] [-0.02157489232562921 -0.02157489232562921 -0.011463255110489451 ... 0.011683865126703476 -0.0014406765320193594 -0.0014406765320193594] [-0.12308533873783908 -0.12308533873783908 -0.11233972249444192 ... 0.05476583886477182 0.04024363505412906 0.04024363505412906] ... [-0.05021644304764882 -0.05021644304764882 -0.02927444361257268 ... -0.04809954177888681 -0.004066086656309194 -0.004066086656309194] [-0.02938094764739113 -0.02938094764739113 -0.0221046245244926 ... -0.006119673755550516 0.0035032760280027846 0.0035032760280027846] [0.029380690027105364 0.029380690027105364 0.02210443070502303 ... 0.006119620096556062 -0.003503245310308396 -0.003503245310308396]] [[0.052587650959453024 0.052587650959453024 0.0877100805037041 ... -0.003330273799101673 0.015380742122142738 0.015380742122142738] [-0.05258722897728936 -0.05258722897728936 -0.08770937668657458 ... 0.0033302470757908256 -0.015380618701554934 -0.015380618701554934] [-0.18087878719297384 -0.18087878719297384 -0.21805567417344626 ... 0.02412125410458975 -0.007466827455070019 -0.007466827455070019] ... [0.020091745737492683 0.020091745737492683 -0.00488367353277767 ... -0.07601742208427498 -0.0872591163797205 -0.0872591163797205] [0.014198013012393054 0.014198013012393054 0.010990759513772218 ... -0.026837238674171184 -0.04552000281570274 -0.04552000281570274] [-0.014197888520282998 -0.014197888520282998 -0.010990663143749146 ... 0.02683700335783102 0.045519603683711364 0.045519603683711364]]]

    Units

    meter/second

  • v
    (time, lat, lon)
    float64
    <Quantity([[[ 0.06750432 -0.0675...

    long_name :

    Meridional Velocity

    standard_name :

    meridional_velocity

    Magnitude

    [[[0.06750431775135449 -0.06750431775135449 -0.1298047063259371 ... -0.07061896037932272 -0.005917108810921311 0.0059171088109191946] [0.06754244022098707 -0.06754244022098707 -0.12987801239197724 ... -0.07065884181598076 -0.005920450446071049 0.005920450446068932] [0.08039042720301767 -0.08039042720301767 -0.16119631320350009 ... -0.09594085866976668 -0.03601319647542027 0.03601319647541709] ... [-0.05484206312475332 0.05484206312475272 0.08888520493881685 ... -0.020919427488586793 0.0007703800590178284 -0.0007703800590172231] [-0.0513512342092973 0.05135123420929699 0.0813387227054365 ... -0.013753191828417378 -0.00763177133178166 0.00763177133178166] [-0.051392852685358544 0.05139285268535824 0.08140464504860691 ... -0.013764338335286985 -0.007637956629902871 0.007637956629902871]] [[0.07094439333630936 -0.07094439333630724 -0.14715302433454497 ... 0.0006204836022630252 0.011804342764499001 -0.011804342764499001] [0.07098445855836712 -0.070984458558365 -0.14723612771057196 ... 0.0006208340149191742 0.011811009163235594 -0.011811009163235594] [0.07027521892368803 -0.0702752189236859 -0.14426073198054104 ... -0.0658186663537867 -0.023543392676673356 0.023543392676672294] ... [-0.01656963543182914 0.016569635431828537 0.017151728219470787 ... 0.06088578153139991 0.017269578259540622 -0.017269578259540928] [-0.024296163666577837 0.024296163666577535 0.02337775988809213 ... 0.0933445712359963 0.04581423891595195 -0.045814238915951044] [-0.024315854903244446 0.02431585490324414 0.023396706788887205 ... 0.09342022392211477 0.04585136984055283 -0.04585136984055192]] [[0.05448399258448515 -0.054483992584484095 -0.11017257790216871 ... 0.04306998101882859 0.025332254159629627 -0.025332254159630686] [0.05451476194001607 -0.05451476194001501 -0.11023479689638015 ... 0.04309430441173383 0.02534656032732519 -0.025346560327326247] [0.058854817296059 -0.058854817296059 -0.12190171319313808 ... 0.02848289818042913 0.014019515463255802 -0.014019515463255802] ... [-0.007918508822232911 0.00791850882223261 -0.002537015863560402 ... 0.03499201640974932 0.009600749637720871 -0.009600749637721173] [-0.012516944224980555 0.012516944224980254 -0.011587201468701345 ... 0.05189834844751845 0.013389701858133415 -0.013389701858133114] [-0.012527088794076288 0.012527088794075984 -0.011596592512059262 ... 0.0519404103415652 0.013400553768410366 -0.013400553768410062]] ... [[0.002956924691962738 -0.002956924691962738 -0.0109359607008966 ... 0.09510485068307512 0.044744534213623156 -0.04474453421362422] [0.002958594589171245 -0.002958594589171245 -0.010942136688501698 ... 0.09515856031088635 0.044769803295714554 -0.044769803295715616] [0.02287319076442783 -0.022873190764426773 -0.05621226462840667 ... 0.08730933959137964 0.045017024460818754 -0.0450170244608177] ... [0.0023439199013350434 -0.0023439199013350434 -0.003412445253400445 ... 0.05749095458029332 0.015915764229673068 -0.015915764229672162] [0.03298554255716074 -0.03298554255716059 -0.019032758006677846 ... -0.004642362867939182 -0.024761417801299444 0.024761417801299444] [0.033012276247877635 -0.03301227624787749 -0.019048183427228634 ... -0.0046461253494230635 -0.0247814861110465 0.0247814861110465]] [[0.005932002675843634 -0.005932002675843634 -0.009621404056396941 ... 0.07549478547178676 0.02664502429049792 -0.026645024290495804] [0.00593535272217257 -0.00593535272217257 -0.009626837659700863 ... 0.07553742048777444 0.0266600718335768 -0.026660071833574682] [0.01790764142470459 -0.01790764142470459 -0.019116462634373402 ... 0.10064159234931398 0.04221039811004085 -0.04221039811004085] ... [-0.046627782266086125 0.04662778226608628 0.10501871273426736 ... 0.02532173809602415 -0.007535006653059108 0.007535006653060319] [-0.03678059055480797 0.036780590554808125 0.07736353539475609 ... -0.016662972696605306 -0.020613920702779617 0.020613920702780224] [-0.03681040000634491 0.036810400006345056 0.07742623598015423 ... -0.016676477484580923 -0.020630627603373287 0.020630627603373895]] [[0.012514630079563535 -0.012514630079561419 -0.029091239062632782 ... 0.0640795713959629 0.016671988467829905 -0.01667198846782779] [0.012521697606813102 -0.012521697606810983 -0.029107668083985527 ... 0.06411575977021786 0.01668140382665807 -0.016681403826655953] [-0.029044558052472774 0.029044558052472774 0.04824212736052566 ... 0.09630938179960388 0.038838497219137076 -0.038838497219137076] ... [-0.07725351823170648 0.07725351823170648 0.13196438991341425 ... 0.0716080593406061 0.0401714808246869 -0.04017148082468599] [-0.08167308719333999 0.08167308719333977 0.14062871268411786 ... 0.09908625923548725 0.06558459528073543 -0.06558459528073513] [-0.08173928052786336 0.08173928052786314 0.14074268760219896 ... 0.09916656536973092 0.06563774942494845 -0.06563774942494814]]]

    Units

    meter/second

  • ke
    (time, lat, lon)
    float64
    <Quantity([[[7.09982675e-03 7.09...

    long_name :

    Kinetic Energy

    standard_name :

    kinetic_energy

    Magnitude

    [[[0.0070998267458282985 0.0070998267458282985 0.012241894280249733 ... 0.006559181455282193 0.002114008777579552 0.0021140087775795395] [0.007102323526654701 0.007102323526654701 0.012251351177579573 ... 0.006561933387733854 0.0021139949099382715 0.002113994909938259] [0.018746606663358225 0.018746606663358225 0.026260267797396625 ... 0.01905465450348315 0.009748046372643402 0.009748046372643288] ... [0.008268884483520355 0.008268884483520322 0.010371117211977074 ... 0.006304328286268553 0.005915833074754441 0.00591583307475444] [0.0036426778947624937 0.003642677894762478 0.005813004024793969 ... 0.0021392156638999054 0.001697356280200707 0.001697356280200707] [0.003644775162585848 0.0036447751625858322 0.005818324307810563 ... 0.002139333170277923 0.0016973742491578506 0.0016973742491578506]] [[0.00321264632893983 0.003212646328939679 0.011546922526575534 ... 0.002584300758365105 0.0009523510779960575 0.0009523510779960575] [0.0032154783630712214 0.0032154783630710714 0.011559143339090184 ... 0.0025842595043960915 0.0009524156268503727 0.0009524156268503727] [0.004483576786303705 0.004483576786303556 0.012119141154718106 ... 0.016889248917816214 0.008858993924031581 0.008858993924031555] ... [0.0004879725907864782 0.0004879725907864682 0.0006567931725034643 ... 0.01187341520688707 0.0144087467289062 0.014408746728906205] [0.0006064780579091665 0.0006064780579091592 0.00045902935948453986 ... 0.006478743012500602 0.004760354388277305 0.004760354388277263] [0.0006069512137243818 0.0006069512137243745 0.0004594692173313829 ... 0.0064857704268803185 0.00476199112688158 0.004761991126881538]] [[0.0014921145691322772 0.0014921145691322198 0.0060690511949495875 ... 0.003931834275751658 0.0026283690539734405 0.0026283690539734674] [0.0014937913536754545 0.001493791353675397 0.00607590795669165 ... 0.003932833964305657 0.002628694531396601 0.002628694531396628] [0.001734876327679194 0.001734876327679194 0.007495585240893792 ... 0.011743410934293732 0.009812412941974527 0.009812412941974527] ... [0.002805299413047165 0.0028052994130471623 0.0021473948796959233 ... 0.015587137240869353 0.017917969167945597 0.0179179691679456] [0.0009173016438748358 0.000917301643874832 0.0007733472667403794 ... 0.007410373309254807 0.006463682735904558 0.0064636827359045535] [0.0009174139618514166 0.0009174139618514127 0.0007734437422131795 ... 0.007412450801560599 0.006463716320411961 0.006463716320411957]] ... [[0.0030456573494711523 0.0030456573494711523 0.001930547224655242 ... 0.005016897242999961 0.0014895903072208326 0.00148959030722088] [0.003045613480088839 0.003045613480088839 0.0019305847610739694 ... 0.0050219987965449174 0.0014907134391646893 0.001490713439164737] [0.01377324201143614 0.013773242011436116 0.011940623260784898 ... 0.00729564959115263 0.0032221864088452824 0.0032221864088452347] ... [0.0028459219169435766 0.0028459219169435766 0.0013804670996032315 ... 0.0018833649918997106 0.0006154088617957739 0.0006154088617957596] [0.0015241370512379432 0.001524137051237938 0.00041701184385982925 ... 9.24750792234595e-05 0.0012196976239672096 0.0012196976239672096] [0.0015250020461285542 0.0015250020461285495 0.00041730141446776406 ... 9.249112038780777e-05 0.0012201787319895173 0.0012201787319895173]] [[0.0002503360524954579 0.0002503360524954579 0.00011198987133557807 ... 0.002917988764305115 0.0003560164508107126 0.00035601645081065624] [0.00025035219539954774 0.00025035219539954774 0.00011204111052719865 ... 0.0029212072991229216 0.00035641748952069317 0.00035641748952063674] [0.007735342116802194 0.007735342116802194 0.0064928261968898076 ... 0.006564013608583823 0.0017006339354890326 0.0017006339354890326] ... [0.002347920615705647 0.002347920615705654 0.005942961536594133 ... 0.0014773781697712594 3.665469297913035e-05 3.665469297913947e-05] [0.001108025963109584 0.0011080259631095896 0.0032368655170722386 ... 0.00015755253298109384 0.00021860333483443253 0.00021860333483444502] [0.001109115247547983 0.0011091152475479883 0.003241713937423847 ... 0.00015777732570995364 0.0002189477615066328 0.00021894776150664533]] [[0.0014610384997307884 0.001461038499730762 0.004269679206082753 ... 0.002058641096933645 0.0002572612138496546 0.00025726121384961933] [0.0014611047812331654 0.001461104781233139 0.004270095550017451 ... 0.00206096059824905 0.00025741633263533193 0.00025741633263529664] [0.016780361004432292 0.016780361004432292 0.024937789945752666 ... 0.00492866596110003 0.000782091189242353 0.000782091189242353] ... [0.0031858921629783305 0.0031858921629783305 0.00871922523619719 ... 0.005453181311433291 0.004613950631508897 0.00461395063150886] [0.0034360383725954994 0.003436038372595481 0.009948615812940874 ... 0.0052691620744683065 0.0031867048972397246 0.0031867048972397047] [0.0034414450098235634 0.003441445009823545 0.009964649394914768 ... 0.005277116218228675 0.0031901742345472345 0.0031901742345472146]]]

    Units

    meter2/second2

  • vort_r
    (time, lat, lon)
    float64
    <Quantity([[[-21.03727654 -13.19...

    Magnitude

    [[[-21.037276539504088 -13.193387615039205 -5.726909927294198 ... 7.968321109675717 3.238196234652759 -0.23769832250910775] [-22.435305149645565 -11.834032855099853 -2.381367034988031 ... 10.685345664356323 6.46991224104165 -3.466024362338599] [-26.321470334800143 -14.489692482167449 -2.821565743378921 ... 6.144348397961585 10.600913718918411 7.6816166278134554] ... [21.613558472434004 10.207372479110525 -3.3371318841652973 ... 4.010363387987696 1.5745565308409932 -2.0215530380440994] [19.9992202554098 9.820337936718612 -3.452168627983166 ... -5.293389123075981 2.000887572027651 2.4308666563282277] [20.409433454211985 9.458479855399847 -4.271892662860473 ... -4.534357294848219 1.1061847671140776 3.3327559525703108]] [[-22.190926398319167 -13.784160571495606 -5.038368896891508 ... -0.17389879737669142 -2.6833055415486387 -3.302541085733476] [-22.135599970515713 -13.880131700733939 -5.372205988249708 ... 6.953720122704274 1.1072788583924416 -7.09988830320995] [-22.37510686304138 -13.300949369994491 -4.803346712633632 ... 6.318727975802327 8.245730355846039 3.7063548018849386] ... [6.774529992693016 2.8396456040399682 -1.8710967229620887 ... -5.1991983373815245 -7.650449445868605 -2.369852965295829] [11.060006779079139 3.0487264861832193 -4.468123004567845 ... -1.1759911912143393 -11.624367145284856 -14.979869041555117] [10.253692580332649 3.8779192752223235 -3.8115176657344954 ... 2.285488099711323 -8.594336284770554 -18.05304108337324]] [[-16.96025363956064 -10.66795317867214 -4.195554035109316 ... -2.899196392853458 -4.943772052992825 -7.901923056683961] [-17.441716970139343 -10.217704233155139 -2.955332953310177 ... -1.3323117309490446 -3.732628302495408 -9.127579890718842] [-18.981060608989637 -10.897292010862802 -2.5354467100752625 ... -0.36324321112007707 -1.9867515815239463 -5.130423287371658] ... [4.856763833301946 -0.2622189144085565 -5.672587706420773 ... -3.4216986703790035 -4.3940972058287695 -1.1765318679121348] [7.4462385759841725 -0.17767429604614107 -8.48597392337007 ... -6.332988466072976 -4.9409518700135555 -2.834421008245024] [6.967594396441242 0.31275651955046224 -9.466647189851914 ... -4.539618474962985 -4.544894549284441 -3.243086801124563]] ... [[0.44874533840861236 -1.9481678854769902 -4.427365375172547 ... -4.2078993082340865 -8.852606370673657 -13.836832978497261] [-1.6870503442507647 0.18593374758063008 0.42364860330252685 ... -3.364795109038946 -8.886412841380347 -13.828661066752263] [-7.889756753416843 -3.7220923797292746 0.18117753028989225 ... -4.15452301429976 -9.47714615158215 -13.376285267266054] ... [-2.6100947093952045 1.2500854557923817 2.0112337666701388 ... -0.33030983107777734 -1.4979156696090925 -7.736865185447668] [-17.014583317048597 -2.140054754028148 4.673306253635758 ... -1.6400383068152928 4.306722708747072 10.072182694774314] [-13.767914672994012 -5.41778438055305 3.011942800498298 ... -8.287433676133624 -0.03456359489502653 14.436785697328823]] [[-1.380514321897645 -1.6275360980561397 -0.16146768171489373 ... -3.582339230086374 -5.641380018888482 -7.870005745237936] [-2.6661275564806197 -0.3453213628658879 0.8558336369571985 ... -6.275032745844693 -7.314408983254165 -6.212241962602232] [-7.423114888832164 -1.6679136736339104 2.6570600559490094 ... -4.168540444302742 -9.98619102740848 -11.442422923069232] ... [14.537546961275774 12.517223690543343 6.119127896892292 ... -0.7994179594543755 1.9021879789206293 2.469838031157601] [12.545265507285583 8.813149286012136 4.740940115937365 ... -2.310046046816606 3.4037658858831032 8.566696312990196] [13.621942555729635 7.771106843819947 1.7842274998667564 ... -6.802601967457243 2.0122821915464515 9.97759119719846]] [[-5.937583104436881 -0.40844206168311464 3.846664524570144 ... -3.5609068189306576 -3.9311646529894158 -4.523009199058629] [-1.4842107257993244 -4.868984188051464 -4.449014907850407 ... -7.0148414650178035 -6.311655850921424 -2.1520695380659234] [12.198353739184324 2.546463882357658 -4.831555349554623 ... -5.391840157801834 -10.58048012535021 -9.136347968901259] ... [31.46076716619934 13.363929961313875 -3.809867018168988 ... -1.4724503359490198 -8.924085911983626 -14.384554294401678] [31.523738720322463 15.903658377207062 0.8210664497756265 ... 1.315155046444602 -13.308038310960196 -24.776803964122877] [31.10924713587112 16.39505778650966 1.7368859184954006 ... 4.247505153340107 -10.617364769567622 -27.529235530590284]]]

    Units

    dimensionless

  • vort_a
    (time, lat, lon)
    float64
    <Quantity([[[26.01496319 33.8588...

    Magnitude

    [[[26.01496318720537 33.85885211167025 41.325329799415265 ... 55.02056083638517 50.29043596136222 46.81454140420035] [24.680144778960337 35.28141707350605 44.734082893617874 ... 57.80079559296223 53.58536216964755 43.649425566267304] [20.857153915237493 32.68893176787019 44.35705850665872 ... 53.32297264799922 57.77953796895605 54.86024087785109] ... [80.42212608152012 69.01594008819664 55.47143572492082 ... 62.818930997073814 60.38312413992711 56.78701457104202] [78.86299253079643 68.68411021210525 55.41160364740348 ... 53.57038315231066 60.86465984741429 61.29463893171487] [79.3283655685759 68.37741196976377 54.64703945150345 ... 54.38457481951571 60.025116881478006 62.25168806693424]] [[24.861313328390292 33.26807915521385 42.013870829817954 ... 46.878340929332765 44.368934185160825 43.749698640975986] [24.97984995809019 33.235318227871964 41.743243940356194 ... 54.06917005131018 48.222728786998346 40.015561625395954] [24.803517386996255 33.877674880043145 42.37527753740401 ... 53.49735222583996 55.42435460588368 50.88497905192257] ... [65.58309760177913 61.648213213126084 56.93747088612403 ... 53.609369271704594 51.158118163217516 56.43871464379029] [69.92377905446578 61.912498761569864 54.395649270818794 ... 57.68778108417231 47.23940513010179 43.883903233831525] [69.17262469469658 62.79685138958625 55.107414448629434 ... 61.204420214075256 50.32459582959337 40.86589103099069]] [[30.09198608714882 36.38428654803732 42.85668569160014 ... 44.153043333856 42.10846767371663 39.1503166700255] [29.67373295846656 36.897745695450766 44.16011697529573 ... 45.783138197656854 43.38282162611049 37.987870037887056] [28.197563641047996 36.28133223917484 44.64317753996237 ... 46.81538103891756 45.19187266851369 42.04820096266598] ... [63.665331442388066 58.54634869467756 53.13597990266535 ... 55.38686893870712 54.414470403257354 57.632035741173986] [66.31001085137082 58.6860979793405 50.37779835201657 ... 52.53078380931367 53.92282040537308 56.02935126714162] [65.88652651080517 59.231688633914395 49.452284924512014 ... 54.37931363940095 54.37403756507948 55.675845313239364]] ... [[47.50098506511807 45.10407184123247 42.62487435153692 ... 42.844340418475376 38.199633356035804 33.2154067482122] [45.428399584355134 47.30138367618653 47.53909853190843 ... 43.75065481956696 38.22903708722555 33.28678886185364] [39.28886749662079 43.45653187030836 47.35980178032753 ... 43.02410123573788 37.70147809845548 33.80233898277159] ... [56.19847289969091 60.0586530648785 60.81980137575626 ... 58.47825777800834 57.310651939477026 51.071702423638456] [41.84918895833805 56.723717521358495 63.5370785290224 ... 57.223733968571345 63.17049498413372 68.93595497016096] [45.151017441369916 53.50114773381088 61.93087491486223 ... 50.6314984382303 58.8843685194689 73.35571781169276]] [[45.67172540481181 45.42470362865332 46.89077204499456 ... 43.46990049662309 41.410859707820975 39.18223398147152] [44.44932237212528 46.77012856574001 47.9712835655631 ... 40.84041718276121 39.80104094535174 40.90320796600367] [39.75550936120547 45.510710576403724 49.835684305986646 ... 43.010083805734894 37.192433222629155 35.736201326968406] ... [73.34611457036189 71.32579129962946 64.9276955059784 ... 58.009149649631745 60.710755588006755 61.27840564024372] [71.40903778267223 67.67692156139877 63.60471239132401 ... 56.553726228570035 62.26753816126975 67.43046858837684] [72.54087467009356 66.69003895818388 60.703159614230685 ... 52.11633014690669 60.93121430591038 68.89652331156239]] [[41.11465662227258 46.64379766502634 50.898904251279596 ... 43.491332907778805 43.12107507372004 42.52923052765083] [45.631239202806576 42.24646574055444 42.66643502075549 ... 40.100608463588095 40.80379407768448 44.96338039053998] [59.376977989221956 49.7250881323953 42.34706890048301 ... 41.786784092235806 36.59814412468742 38.042276281136374] ... [90.26933477528546 72.1724975704 54.99870059091713 ... 57.3361172731371 49.884481697102494 44.424013314684444] [90.3875109957091 74.7674306525937 59.68483872516227 ... 60.178927321831246 45.555733964426445 34.08696831126377] [90.02817925023506 75.31398990087358 60.65581803285933 ... 63.16643726770404 48.30156734479631 31.389696583773645]]]

    Units

    dimensionless

  • div
    (time, lat, lon)
    float64
    <Quantity([[[-22.41076683 -11.81...

    Magnitude

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    Units

    dimensionless

  • ens
    (time, lat, lon)
    float64
    <Quantity([[[1.31080192e+08 5.15...

    Magnitude

    [[[131080191.69164084 51554986.80239767 9714014.36235932 ... 18805794.68154839 3105734.761284585 16734.404780279732] [149080897.2236682 41478551.09275353 1679618.7376747949 ... 33817008.591446154 12398090.889155956 3558125.4662555614] [205200458.7029598 62183673.29159319 2357970.58942573 ... 11181748.049929108 33284699.134116694 17476855.42009979] ... [138360010.64000311 30859292.293718286 3298411.0511227828 ... 4763492.542646453 734301.7297713707 1210398.3312139767] [118463391.74869329 28563465.78404132 3529734.4945164076 ... 8298998.33313679 1185778.057324194 1750170.2978413524] [123372945.81783083 26497245.07073828 5405037.356517193 ... 6089610.462371741 362421.0242244676 3289766.4075571294]] [[145850829.02517873 56275411.99602425 7518616.97083602 ... 8956.765278788436 2132545.4269705643 3230386.5583948996] [145124464.93429664 57061766.186090805 8547977.085540026 ... 14321630.015842974 363138.2963960357 14930043.35287267] [148281944.45982242 52399038.351722956 6833542.623560643 ... 11825441.239757424 20137998.01327598 4068665.7989731166] ... [13593033.14178139 2388285.932236713 1036932.5616439411 ... 8006280.5862762565 17335322.895168263 1663415.8645869005] [36230040.73996766 2752928.7009340087 5913005.418559022 ... 409605.87147469545 40021805.09973213 66462101.50263642] [31140000.92856487 4454054.889336715 4302827.2468091585 ... 1547091.374024299 21876745.883192945 96529215.57992949]] [[85196689.9012346 33707010.621858075 5213587.583219915 ... 2489506.745519378 7238938.922122881 18493692.367158215] [90102430.41068512 30921794.563813906 2586847.749840429 ... 525738.4492353012 4126553.932809166 24675690.9226111] [106708493.33305238 35171850.0904671 1904000.2893688695 ... 39079.86443824743 1169082.5303196402 7795867.200599943] ... [6986376.844320732 20365.077455667804 9530605.099300317 ... 3467700.3168215244 5718700.553166919 409982.6009300648] [16422222.413928255 9349.905961839468 21328554.4422381 ... 11878878.224244576 7230682.348318789 2379505.716992789] [14378836.93243988 28971.486505995734 26543025.21743479 ... 6103750.1176401125 6117946.268065142 3115122.8717175303]] ... [[59642.7879996033 1124115.137090958 5805622.117915169 ... 5244314.326495836 23211346.97771367 56706315.96820037] [842973.8872053779 10239.399356090644 53158.11764512042 ... 3353322.200688808 23388965.181671187 56639355.2452505] [18436788.077860408 4103291.132636285 9722.248259448197 ... 5112112.16710762 26601932.818371277 52994290.27852673] ... [2017764.9267765034 462846.98686478124 1198072.6102118143 ... 32314.767517365195 664557.806395196 17729157.362102453] [85743394.26988043 1356462.5443123025 6468543.764499104 ... 796647.1747075578 5493534.505359591 30047284.241454776] [56142838.689717405 8693636.344194006 2686899.8308595256 ... 20342211.605166715 353.8309746211842 61730394.950889885]] [[564468.7051248433 784547.595470431 7721.990373269082 ... 3800943.851390451 9426028.489040704 18344595.284642935] [2105328.567092641 35318.71778995147 216938.55313244314 ... 11662456.290014854 15845885.605579028 11430224.53598979] [16320385.036537113 823958.1886323829 2091032.472975172 ... 5146667.066914267 29536414.56552357 38778769.782737255] ... [62595094.20572079 46405992.22049335 11090141.749836344 ... 189280.48389481968 1071679.4466514138 1806737.1870533172] [46614147.95779074 23004896.80574943 6657129.041744415 ... 1580517.5036553387 3431447.8151464267 21736257.94215223] [54958658.71699185 17886435.31039397 942884.4937465654 ... 13705918.870254533 1199322.009002604 29485564.591354407]] [[10441849.719163796 49410.46664203517 4382547.789648599 ... 3755599.345084363 4577206.483811343 6059167.776222081] [652452.9026021294 7021578.643656709 5862539.178364434 ... 14574503.100571811 11798985.220039574 1371736.316011512] [44071768.95764764 1920582.9875768283 6914041.059361536 ... 8610573.019552955 33156508.19698539 24723121.305740118] ... [293154559.53765225 52896436.76167316 4299101.217432337 ... 642154.2289454561 23587695.961573616 61284529.4234082] [294329284.43791586 74912124.26206127 199670.84183340106 ... 512285.36318610783 52454906.94652986 181822910.51481876] [286640160.35407084 79612990.85194267 893512.4834203789 ... 5343500.630527056 33388085.155043963 224463814.52523753]]]

    Units

    second

  • shear_strain
    (time, lat, lon)
    float64
    <Quantity([[[ 1.24743972e-08 -1....

    long_name :

    Shear Strain

    standard_name :

    shear_strain

    Magnitude

    [[[1.2474397182089499e-08 -1.2474397182084205e-08 -2.331109069820465e-08 ... -1.1839393741431339e-08 1.867907970833252e-09 -1.8679079707375373e-09] [1.4473626828582738e-08 -1.4473626828581255e-08 -2.8169917765829206e-08 ... -1.574746954886321e-08 -2.7511906295783844e-09 2.7511906294818226e-09] [1.5969924145668166e-08 -1.5969924145674942e-08 -3.242391763141154e-08 ... -1.849044873168907e-08 -6.430145894086086e-09 6.430145894186036e-09] ... [-1.517728482357792e-08 1.5177284823509786e-08 2.4334736254963516e-08 ... -2.443927056449629e-09 -8.459453264093e-10 8.459453263355022e-10] [-1.5254523682158755e-08 1.5254523682186866e-08 2.4309883260953682e-08 ... -4.540296296453036e-09 -1.616091471079642e-09 1.6160914710250084e-09] [-1.4518735836181996e-08 1.4518735836150709e-08 2.2702435299981857e-08 ... -2.9778551608107324e-09 -3.4614637811454496e-09 3.461463781200189e-09]] [[1.4563043464116463e-08 -1.4563043464116225e-08 -3.036048723722723e-08 ... 6.919083477470534e-09 6.025468126918232e-09 -6.025468126822094e-09] [1.4483849592150259e-08 -1.4483849592149954e-08 -2.996544508539012e-08 ... -3.2733633130189863e-09 6.065584483776432e-10 -6.065584484742049e-10] [1.4780571021076917e-08 -1.4780571020981626e-08 -3.033578568836372e-08 ... -1.0326211223076325e-08 -3.666703493095661e-09 3.6667034929050788e-09] ... [-6.49196551426963e-09 6.491965514270689e-09 7.125416146439271e-09 ... 1.7541955089272278e-08 6.4913182379310425e-09 -6.49131823779467e-09] [-6.533090886764542e-09 6.533090886790694e-09 6.374324911847682e-09 ... 2.4897360131165722e-08 1.129931667891158e-08 -1.1299316678797654e-08] [-8.239869642189756e-09 8.239869642161698e-09 7.751800189425913e-09 ... 3.206251476999853e-08 1.7579879957197642e-08 -1.7579879957307757e-08]] [[1.068476588947577e-08 -1.0684765889378626e-08 -2.131022042379655e-08 ... 1.02909069177805e-08 6.332168406053679e-09 -6.332168406150876e-09] [1.1373330488394894e-08 -1.1373330488490185e-08 -2.31460682583771e-08 ... 8.067300129858348e-09 4.605022554282619e-09 -4.605022554184363e-09] [1.2170342110195869e-08 -1.2170342110290948e-08 -2.5334530508172438e-08 ... 6.2761165429845615e-09 3.35583700036405e-09 -3.355837000454471e-09] ... 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[-2.06890292901274e-08 2.0689029290115117e-08 3.431214352023529e-08 ... 2.4616813794547713e-08 1.4297318183127492e-08 -1.4297318183035377e-08] [-2.3534309528735714e-08 2.3534309528715914e-08 4.044557086327088e-08 ... 2.693798272482858e-08 1.730279797248796e-08 -1.730279797254217e-08] [-2.4549004928462438e-08 2.454900492847906e-08 4.242377931599652e-08 ... 3.3015064931315216e-08 2.2908396185368703e-08 -2.290839618531153e-08]]]

    Units

    1/second

• Indexes: (3)
  • lon
    PandasIndex

    PandasIndex(Float64Index([              -65.0,              -64.95,               -64.9,
                   -64.85000000000001,  -64.80000000000001,  -64.75000000000001,
                   -64.70000000000002,  -64.65000000000002,  -64.60000000000002,
                   -64.55000000000003,
                  ...
                   -55.45000000000054, -55.400000000000546,  -55.35000000000055,
                   -55.30000000000055, -55.250000000000554,  -55.20000000000056,
                   -55.15000000000056,  -55.10000000000056, -55.050000000000566,
                   -55.00000000000057],
                 dtype='float64', name='lon', length=201))

  • lat
    PandasIndex

    PandasIndex(Float64Index([              33.0,              33.05, 33.099999999999994,
                   33.14999999999999,  33.19999999999999, 33.249999999999986,
                   33.29999999999998,  33.34999999999998,  33.39999999999998,
                  33.449999999999974,
                  ...
                   42.54999999999946, 42.599999999999454,  42.64999999999945,
                   42.69999999999945, 42.749999999999446,  42.79999999999944,
                   42.84999999999944,  42.89999999999944, 42.949999999999434,
                   42.99999999999943],
                 dtype='float64', name='lat', length=201))

  • time
    PandasIndex

    PandasIndex(DatetimeIndex(['2013-01-01', '2013-01-02', '2013-01-03', '2013-01-04',
                   '2013-01-05', '2013-01-06', '2013-01-07', '2013-01-08',
                   '2013-01-09', '2013-01-10', '2013-01-11', '2013-01-12',
                   '2013-01-13', '2013-01-14', '2013-01-15', '2013-01-16',
                   '2013-01-17', '2013-01-18', '2013-01-19', '2013-01-20',
                   '2013-01-21', '2013-01-22', '2013-01-23', '2013-01-24',
                   '2013-01-25', '2013-01-26', '2013-01-27', '2013-01-28',
                   '2013-01-29', '2013-01-30', '2013-01-31', '2013-02-01',
                   '2013-02-02', '2013-02-03', '2013-02-04', '2013-02-05',
                   '2013-02-06', '2013-02-07', '2013-02-08', '2013-02-09',
                   '2013-02-10', '2013-02-11', '2013-02-12', '2013-02-13',
                   '2013-02-14', '2013-02-15', '2013-02-16', '2013-02-17',
                   '2013-02-18', '2013-02-19', '2013-02-20', '2013-02-21',
                   '2013-02-22', '2013-02-23', '2013-02-24', '2013-02-25',
                   '2013-02-26', '2013-02-27', '2013-02-28', '2013-03-01'],
                  dtype='datetime64[ns]', name='time', freq=None))

• Attributes: (0)

fig, ax = plt.subplots()

da.shear_strain.isel(time=10).plot.pcolormesh(ax=ax, cmap="RdBu_r")

plt.show()

Normal Strain

Sometimes called Stretching Deformation.

\[ \sigma_n = \frac{\partial u}{\partial x} - \frac{\partial v}{\partial y} \]

da = geocalc.tensor_strain(da, variables=["u", "v"])

fig, ax = plt.subplots()

da.tensor_strain.isel(time=10).plot.pcolormesh(ax=ax, cmap="RdBu_r")

plt.show()

Strain Magnitude

Often, we are interested in the give by:

\[ \sigma = \sqrt{\sigma_n^2 + \sigma_s^2} \]

Note: Also known as the total deformation.

The normal and shear strains are coordinate invariant. The vorticity and divergence and strain magnitude is coordinate invariant!

Often times, we use the relative strain magnitude:

\[ \bar{\sigma} = \frac{\sigma}{f_0} \]

da = geocalc.strain_magnitude(da, variables=["u", "v"])
da = geocalc.coriolis_normalized(da, variable="strain")

import cmocean as cmo

fig, ax = plt.subplots()

da.strain.isel(time=10).plot.pcolormesh(ax=ax, cmap=cmo.cm.speed, robust=True)

plt.show()

Okubo-Weiss Parameter

OW parameter [Okubo, 1970; Weiss, 1991] describes the relative dominance of deformation with respect to rotation of the flow.

This is a combination of the Strain (deformation rate) and the vorticity

\[ \sigma_o = \sigma_n^2 + \sigma_s^2 - \zeta^2 \]

where:

\[\begin{split} \begin{aligned} \text{Normal Strain}: && && \sigma_n &= \frac{\partial u}{\partial x} - \frac{\partial v}{\partial y} \\ \text{Shear Strain}: && && \sigma_s &= \frac{\partial v}{\partial x} + \frac{\partial u}{\partial y} \\ \text{Relative Vorticity}: && && \zeta &= \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y} \end{aligned} \end{split}\]

Sources:

• Wiki

• Paper

• Eddy-Tracker Python Lib

da = geocalc.okubo_weiss_param(da, variables=["u", "v"])

import cmocean as cmo

fig, ax = plt.subplots()

da.ow.isel(time=10).plot.contourf(ax=ax, cmap="cividis")

plt.show()