Equation of state

pop_tools.eos implements the model’s equation of state.

%matplotlib inline
import xarray as xr

import pop_tools

Show check value

McDougall, T.J., D.R. Jackett, D.G. Wright, and R. Feistel, 2003: Accurate and Computationally Efficient Algorithms for Potential Temperature and Density of Seawater. J. Atmos. Oceanic Technol., 20, 730–741, doi:10.1175/1520-0426(2003)20<730:AACEAF>2.0.CO;2.

test value:

• \(rho = 1033.213387 kg/m^3\);

• \(S = 35.0\) PSU, \(theta = 20.0\) C, \(pressure = 2000.0\) dbars

pop_tools.eos(salt=35.0, temp=20.0, pressure=2000.0)

1033.2133865866824

Load POP dataset using dask

filepath = pop_tools.DATASETS.fetch("cesm_pop_monthly.T62_g17.nc")
ds = xr.open_dataset(filepath, decode_times=False, decode_coords=False, chunks={'z_t': 20})
ds

Downloading file 'cesm_pop_monthly.T62_g17.nc' from 'ftp://ftp.cgd.ucar.edu/archive/aletheia-data/cesm-data/ocn/cesm_pop_monthly.T62_g17.nc' to '/home/docs/.pop_tools/data'.

<xarray.Dataset>
Dimensions:       (time: 1, z_t: 60, nlat: 384, nlon: 320, lat_aux_grid: 395,
                   d2: 2)
Coordinates:
  * lat_aux_grid  (lat_aux_grid) float32 -79.49 -78.95 -78.42 ... 89.47 90.0
  * time          (time) float64 6.314e+04
  * z_t           (z_t) float32 500.0 1.5e+03 2.5e+03 ... 5.125e+05 5.375e+05
Dimensions without coordinates: nlat, nlon, d2
Data variables:
    SALT          (time, z_t, nlat, nlon) float32 dask.array<chunksize=(1, 20, 384, 320), meta=np.ndarray>
    TEMP          (time, z_t, nlat, nlon) float32 dask.array<chunksize=(1, 20, 384, 320), meta=np.ndarray>
    TLAT          (nlat, nlon) float64 dask.array<chunksize=(384, 320), meta=np.ndarray>
    TLONG         (nlat, nlon) float64 dask.array<chunksize=(384, 320), meta=np.ndarray>
    ULAT          (nlat, nlon) float64 dask.array<chunksize=(384, 320), meta=np.ndarray>
    ULONG         (nlat, nlon) float64 dask.array<chunksize=(384, 320), meta=np.ndarray>
    UVEL          (time, z_t, nlat, nlon) float32 dask.array<chunksize=(1, 20, 384, 320), meta=np.ndarray>
    VVEL          (time, z_t, nlat, nlon) float32 dask.array<chunksize=(1, 20, 384, 320), meta=np.ndarray>
    time_bound    (time, d2) float64 dask.array<chunksize=(1, 2), meta=np.ndarray>
Attributes:
    title:             g.e21.G1850ECOIAF.T62_g17.004
    history:           Sun May 26 14:13:02 2019: ncks -4 -L 9 cesm_pop_monthl...
    Conventions:       CF-1.0; http://www.cgd.ucar.edu/cms/eaton/netcdf/CF-cu...
    time_period_freq:  month_1
    model_doi_url:     https://doi.org/10.5065/D67H1H0V
    contents:          Diagnostic and Prognostic Variables
    source:            CCSM POP2, the CCSM Ocean Component
    revision:          $Id: tavg.F90 90507 2019-01-18 20:54:19Z altuntas@ucar...
    calendar:          All years have exactly  365 days.
    start_time:        This dataset was created on 2019-05-26 at 11:20:07.5
    cell_methods:      cell_methods = time: mean ==> the variable values are ...
    NCO:               netCDF Operators version 4.7.4 (http://nco.sf.net)

xarray.Dataset

• Dimensions:
  • time: 1
  • z_t: 60
  • nlat: 384
  • nlon: 320
  • lat_aux_grid: 395
  • d2: 2
• Coordinates: (3)
  • lat_aux_grid
    (lat_aux_grid)
    float32
    -79.49 -78.95 -78.42 ... 89.47 90.0

    long_name :

    latitude grid for transport diagnostics

    units :

    degrees_north

    valid_min :

    -79.48815

    valid_max :

    90.0

    array([-79.48815 , -78.952896, -78.418655, ...,  88.948814,  89.47441 ,
            90.      ], dtype=float32)

  • time
    (time)
    float64
    6.314e+04

    long_name :

    time

    units :

    days since 0000-01-01 00:00:00

    bounds :

    time_bound

    calendar :

    noleap

    array([63145.])

  • z_t
    (z_t)
    float32
    500.0 1.5e+03 ... 5.375e+05

    long_name :

    depth from surface to midpoint of layer

    units :

    centimeters

    positive :

    down

    valid_min :

    500.0

    valid_max :

    537500.0

    array([5.000000e+02, 1.500000e+03, 2.500000e+03, 3.500000e+03, 4.500000e+03,
           5.500000e+03, 6.500000e+03, 7.500000e+03, 8.500000e+03, 9.500000e+03,
           1.050000e+04, 1.150000e+04, 1.250000e+04, 1.350000e+04, 1.450000e+04,
           1.550000e+04, 1.650984e+04, 1.754790e+04, 1.862913e+04, 1.976603e+04,
           2.097114e+04, 2.225783e+04, 2.364088e+04, 2.513702e+04, 2.676542e+04,
           2.854837e+04, 3.051192e+04, 3.268680e+04, 3.510935e+04, 3.782276e+04,
           4.087846e+04, 4.433777e+04, 4.827367e+04, 5.277280e+04, 5.793729e+04,
           6.388626e+04, 7.075633e+04, 7.870025e+04, 8.788252e+04, 9.847059e+04,
           1.106204e+05, 1.244567e+05, 1.400497e+05, 1.573946e+05, 1.764003e+05,
           1.968944e+05, 2.186457e+05, 2.413972e+05, 2.649001e+05, 2.889385e+05,
           3.133405e+05, 3.379793e+05, 3.627670e+05, 3.876452e+05, 4.125768e+05,
           4.375392e+05, 4.625190e+05, 4.875083e+05, 5.125028e+05, 5.375000e+05],
          dtype=float32)

• Data variables: (9)
  • SALT
    (time, z_t, nlat, nlon)
    float32
    dask.array<chunksize=(1, 20, 384, 320), meta=np.ndarray>

    long_name :

    Salinity

    units :

    gram/kilogram

    coordinates :

    TLONG TLAT z_t time

    grid_loc :

    3111

    cell_methods :

    time: mean

    Array Chunk Bytes 28.12 MiB 9.38 MiB Shape (1, 60, 384, 320) (1, 20, 384, 320) Dask graph 3 chunks in 2 graph layers Data type float32 numpy.ndarray

  • TEMP
    (time, z_t, nlat, nlon)
    float32
    dask.array<chunksize=(1, 20, 384, 320), meta=np.ndarray>

    long_name :

    Potential Temperature

    units :

    degC

    coordinates :

    TLONG TLAT z_t time

    grid_loc :

    3111

    cell_methods :

    time: mean

    Array Chunk Bytes 28.12 MiB 9.38 MiB Shape (1, 60, 384, 320) (1, 20, 384, 320) Dask graph 3 chunks in 2 graph layers Data type float32 numpy.ndarray

  • TLAT
    (nlat, nlon)
    float64
    dask.array<chunksize=(384, 320), meta=np.ndarray>

    long_name :

    array of t-grid latitudes

    units :

    degrees_north

    Array Chunk Bytes 0.94 MiB 0.94 MiB Shape (384, 320) (384, 320) Dask graph 1 chunks in 2 graph layers Data type float64 numpy.ndarray

  • TLONG
    (nlat, nlon)
    float64
    dask.array<chunksize=(384, 320), meta=np.ndarray>

    long_name :

    array of t-grid longitudes

    units :

    degrees_east

    Array Chunk Bytes 0.94 MiB 0.94 MiB Shape (384, 320) (384, 320) Dask graph 1 chunks in 2 graph layers Data type float64 numpy.ndarray

  • ULAT
    (nlat, nlon)
    float64
    dask.array<chunksize=(384, 320), meta=np.ndarray>

    long_name :

    array of u-grid latitudes

    units :

    degrees_north

    Array Chunk Bytes 0.94 MiB 0.94 MiB Shape (384, 320) (384, 320) Dask graph 1 chunks in 2 graph layers Data type float64 numpy.ndarray

  • ULONG
    (nlat, nlon)
    float64
    dask.array<chunksize=(384, 320), meta=np.ndarray>

    long_name :

    array of u-grid longitudes

    units :

    degrees_east

    Array Chunk Bytes 0.94 MiB 0.94 MiB Shape (384, 320) (384, 320) Dask graph 1 chunks in 2 graph layers Data type float64 numpy.ndarray

  • UVEL
    (time, z_t, nlat, nlon)
    float32
    dask.array<chunksize=(1, 20, 384, 320), meta=np.ndarray>

    long_name :

    Velocity in grid-x direction

    units :

    centimeter/s

    coordinates :

    ULONG ULAT z_t time

    grid_loc :

    3221

    cell_methods :

    time: mean

    Array Chunk Bytes 28.12 MiB 9.38 MiB Shape (1, 60, 384, 320) (1, 20, 384, 320) Dask graph 3 chunks in 2 graph layers Data type float32 numpy.ndarray

  • VVEL
    (time, z_t, nlat, nlon)
    float32
    dask.array<chunksize=(1, 20, 384, 320), meta=np.ndarray>

    long_name :

    Velocity in grid-y direction

    units :

    centimeter/s

    coordinates :

    ULONG ULAT z_t time

    grid_loc :

    3221

    cell_methods :

    time: mean

    Array Chunk Bytes 28.12 MiB 9.38 MiB Shape (1, 60, 384, 320) (1, 20, 384, 320) Dask graph 3 chunks in 2 graph layers Data type float32 numpy.ndarray

  • time_bound
    (time, d2)
    float64
    dask.array<chunksize=(1, 2), meta=np.ndarray>

    long_name :

    boundaries for time-averaging interval

    units :

    days since 0000-01-01 00:00:00

    Array Chunk Bytes 16 B 16 B Shape (1, 2) (1, 2) Dask graph 1 chunks in 2 graph layers Data type float64 numpy.ndarray

• Indexes: (3)
  • lat_aux_grid
    PandasIndex

    PandasIndex(Index([-79.48815155029297, -78.95289611816406, -78.41865539550781,
           -77.88441467285156, -77.35017395019531, -76.81593322753906,
           -76.28169250488281, -75.74745178222656, -75.21321868896484,
            -74.6789779663086,
           ...
            85.26966857910156,  85.79525756835938,  86.32085418701172,
            86.84644317626953,  87.37203979492188,  87.89762878417969,
            88.42322540283203,  88.94881439208984,  89.47441101074219,
                         90.0],
          dtype='float32', name='lat_aux_grid', length=395))

  • time
    PandasIndex

    PandasIndex(Index([63145.0], dtype='float64', name='time'))

  • z_t
    PandasIndex

    PandasIndex(Index([          500.0,          1500.0,          2500.0,          3500.0,
                    4500.0,          5500.0,          6500.0,          7500.0,
                    8500.0,          9500.0,         10500.0,         11500.0,
                   12500.0,         13500.0,         14500.0,         15500.0,
            16509.83984375, 17547.904296875, 18629.126953125,  19766.02734375,
           20971.138671875,    22257.828125,   23640.8828125,    25137.015625,
           26765.419921875, 28548.365234375,    30511.921875, 32686.798828125,
            35109.34765625,  37822.76171875,  40878.46484375,  44337.76953125,
              48273.671875,  52772.80078125,   57937.2890625,  63886.26171875,
              70756.328125,        78700.25,   87882.5234375,   98470.5859375,
             110620.421875,     124456.6875,    140049.71875,   157394.640625,
             176400.328125,   196894.421875,    218645.65625,    241397.15625,
                264900.125,    288938.46875,    313340.46875,    337979.34375,
              362767.03125,     387645.1875,     412576.8125,       437539.25,
              462519.03125,    487508.34375,     512502.8125,        537500.0],
          dtype='float32', name='z_t'))

• Attributes: (12)

  title :

  g.e21.G1850ECOIAF.T62_g17.004

  history :

  Sun May 26 14:13:02 2019: ncks -4 -L 9 cesm_pop_monthly.T62_g17.nc cesm_pop_monthly.T62_g17.nc Sun May 26 14:12:41 2019: ncks -v SALT,TEMP,UVEL,VVEL,lat_aux_grid -O g.e21.G1850ECOIAF.T62_g17.004.pop.h.0172-12.nc cesm_pop_monthly.T62_g17.nc none

  Conventions :

  CF-1.0; http://www.cgd.ucar.edu/cms/eaton/netcdf/CF-current.htm

  time_period_freq :

  month_1

  model_doi_url :

  https://doi.org/10.5065/D67H1H0V

  contents :

  Diagnostic and Prognostic Variables

  source :

  CCSM POP2, the CCSM Ocean Component

  revision :

  $Id: tavg.F90 90507 2019-01-18 20:54:19Z altuntas@ucar.edu $

  calendar :

  All years have exactly 365 days.

  start_time :

  This dataset was created on 2019-05-26 at 11:20:07.5

  cell_methods :

  cell_methods = time: mean ==> the variable values are averaged over the time interval between the previous time coordinate and the current one. cell_methods absent ==> the variable values are at the time given by the current time coordinate.

  NCO :

  netCDF Operators version 4.7.4 (http://nco.sf.net)

Compute in situ density

%%time
rho = pop_tools.eos(ds.SALT, ds.TEMP, depth=ds.z_t * 1e-2)

CPU times: user 14.7 ms, sys: 0 ns, total: 14.7 ms
Wall time: 14.4 ms

Visualize density field

h = rho.isel(time=0, z_t=0).plot()

/home/docs/checkouts/readthedocs.org/user_builds/pop-tools/conda/latest/lib/python3.9/site-packages/dask/core.py:121: RuntimeWarning: invalid value encountered in _compute_eos
  return func(*(_execute_task(a, cache) for a in args))

h = rho.isel(time=0, nlon=200).plot(yincrease=False)

%load_ext watermark
%watermark -d -iv -m -g -h

Compiler    : GCC 11.3.0
OS          : Linux
Release     : 5.15.0-1004-aws
Machine     : x86_64
Processor   : x86_64
CPU cores   : 2
Architecture: 64bit

Hostname: build-21213814-project-451810-pop-tools

Git hash: d3c80c0576ae4838c0e04a0157734eb0c977e613

pop_tools: 2023.3.0.post2+dirty
xarray   : 2023.6.0