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MITgcm ECCOv4 Example¶

Overview¶

This Jupyter notebook demonstrates how to use xarray and xgcm to analyze data from the ECCO v4r3 ocean state estimate.

Loading ECCO zarr data and converting to an xarray dataset
Visualize ocean depth using cartopy
Indexing and selecting data using xarray
Use dask cluster to speed up reading the data
Calculate and plot the horizontally integrated heat content anomaly
Use xgcm to compute the time-mean convergence of veritcally-integrated heat fluxes

Prerequisites¶

Concepts	Importance	Notes
Intro to Cartopy	Helpful
Xarray	Helpful	Slicing, indexing, basic statistics
Dask	Helpful

Time to learn: 1 hour

Imports¶

import xarray as xr
import numpy as np
from matplotlib import pyplot as plt
%matplotlib inline
import intake
import cartopy as cart
import pyresample
from dask_gateway import GatewayCluster
from dask.distributed import Client
import xgcm

Load the data¶

The ECCOv4r3 data was converted from its raw MDS (.data / .meta file) format to zarr format, using the xmitgcm package. Zarr is a powerful data storage format that can be thought of as an alternative to HDF. In contrast to HDF, zarr works very well with cloud object storage. Zarr is currently useable in python, java, C++, and julia. It is likely that zarr will form the basis of the next major version of the netCDF library.

If you’re curious, here are some resources to learn more about zarr:

The ECCO zarr data currently lives in Google Cloud Storage as part of the Pangeo Data Catalog. This means we can open the whole dataset using one line of code.

This takes a bit of time to run because the metadata must be downloaded and parsed. The type of object returned is an Xarray dataset.

cat = intake.open_catalog("https://raw.githubusercontent.com/pangeo-data/pangeo-datastore/master/intake-catalogs/ocean.yaml")
ds = cat.ECCOv4r3.to_dask()
ds

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[2], line 2
      1 cat = intake.open_catalog("https://raw.githubusercontent.com/pangeo-data/pangeo-datastore/master/intake-catalogs/ocean.yaml")
----> 2 ds = cat.ECCOv4r3.to_dask()
      3 ds

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/intake_xarray/base.py:8, in IntakeXarraySourceAdapter.to_dask(self)
      6 def to_dask(self):
      7     if "chunks" not in self.reader.kwargs:
----> 8         return self.reader(chunks={}).read()
      9     else:
     10         return self.reader.read()

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/intake/readers/readers.py:121, in BaseReader.read(self, *args, **kwargs)
    119 kw.update(kwargs)
    120 args = kw.pop("args", ()) or args
--> 121 return self._read(*args, **kw)

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/intake/readers/readers.py:1327, in XArrayDatasetReader._read(self, data, open_local, **kw)
   1325         f = fsspec.open(data.url, **(data.storage_options or {})).open()
   1326         return open_dataset(f, **kw)
-> 1327 return open_dataset(data.url, **kw)

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/xarray/backends/api.py:760, in open_dataset(filename_or_obj, engine, chunks, cache, decode_cf, mask_and_scale, decode_times, decode_timedelta, use_cftime, concat_characters, decode_coords, drop_variables, create_default_indexes, inline_array, chunked_array_type, from_array_kwargs, backend_kwargs, **kwargs)
    748 decoders = _resolve_decoders_kwargs(
    749     decode_cf,
    750     open_backend_dataset_parameters=backend.open_dataset_parameters,
   (...)    756     decode_coords=decode_coords,
    757 )
    759 overwrite_encoded_chunks = kwargs.pop("overwrite_encoded_chunks", None)
--> 760 backend_ds = backend.open_dataset(
    761     filename_or_obj,
    762     drop_variables=drop_variables,
    763     **decoders,
    764     **kwargs,
    765 )
    766 ds = _dataset_from_backend_dataset(
    767     backend_ds,
    768     filename_or_obj,
   (...)    779     **kwargs,
    780 )
    781 return ds

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/xarray/backends/zarr.py:1654, in ZarrBackendEntrypoint.open_dataset(self, filename_or_obj, mask_and_scale, decode_times, concat_characters, decode_coords, drop_variables, use_cftime, decode_timedelta, group, mode, synchronizer, consolidated, chunk_store, storage_options, zarr_version, zarr_format, store, engine, use_zarr_fill_value_as_mask, cache_members)
   1652 filename_or_obj = _normalize_path(filename_or_obj)
   1653 if not store:
-> 1654     store = ZarrStore.open_group(
   1655         filename_or_obj,
   1656         group=group,
   1657         mode=mode,
   1658         synchronizer=synchronizer,
   1659         consolidated=consolidated,
   1660         consolidate_on_close=False,
   1661         chunk_store=chunk_store,
   1662         storage_options=storage_options,
   1663         zarr_version=zarr_version,
   1664         use_zarr_fill_value_as_mask=None,
   1665         zarr_format=zarr_format,
   1666         cache_members=cache_members,
   1667     )
   1669 store_entrypoint = StoreBackendEntrypoint()
   1670 with close_on_error(store):

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/xarray/backends/zarr.py:714, in ZarrStore.open_group(cls, store, mode, synchronizer, group, consolidated, consolidate_on_close, chunk_store, storage_options, append_dim, write_region, safe_chunks, align_chunks, zarr_version, zarr_format, use_zarr_fill_value_as_mask, write_empty, cache_members)
    688 @classmethod
    689 def open_group(
    690     cls,
   (...)    707     cache_members: bool = True,
    708 ):
    709     (
    710         zarr_group,
    711         consolidate_on_close,
    712         close_store_on_close,
    713         use_zarr_fill_value_as_mask,
--> 714     ) = _get_open_params(
    715         store=store,
    716         mode=mode,
    717         synchronizer=synchronizer,
    718         group=group,
    719         consolidated=consolidated,
    720         consolidate_on_close=consolidate_on_close,
    721         chunk_store=chunk_store,
    722         storage_options=storage_options,
    723         zarr_version=zarr_version,
    724         use_zarr_fill_value_as_mask=use_zarr_fill_value_as_mask,
    725         zarr_format=zarr_format,
    726     )
    728     return cls(
    729         zarr_group,
    730         mode,
   (...)    739         cache_members=cache_members,
    740     )

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/xarray/backends/zarr.py:1858, in _get_open_params(store, mode, synchronizer, group, consolidated, consolidate_on_close, chunk_store, storage_options, zarr_version, use_zarr_fill_value_as_mask, zarr_format)
   1854 group = open_kwargs.pop("path")
   1856 if consolidated:
   1857     # TODO: an option to pass the metadata_key keyword
-> 1858     zarr_root_group = zarr.open_consolidated(store, **open_kwargs)
   1859 elif consolidated is None:
   1860     # same but with more error handling in case no consolidated metadata found
   1861     try:

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/api/synchronous.py:231, in open_consolidated(use_consolidated, *args, **kwargs)
    226 def open_consolidated(*args: Any, use_consolidated: Literal[True] = True, **kwargs: Any) -> Group:
    227     """
    228     Alias for :func:`open_group` with ``use_consolidated=True``.
    229     """
    230     return Group(
--> 231         sync(async_api.open_consolidated(*args, use_consolidated=use_consolidated, **kwargs))
    232     )

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/core/sync.py:163, in sync(coro, loop, timeout)
    160 return_result = next(iter(finished)).result()
    162 if isinstance(return_result, BaseException):
--> 163     raise return_result
    164 else:
    165     return return_result

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/core/sync.py:119, in _runner(coro)
    114 """
    115 Await a coroutine and return the result of running it. If awaiting the coroutine raises an
    116 exception, the exception will be returned.
    117 """
    118 try:
--> 119     return await coro
    120 except Exception as ex:
    121     return ex

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/api/asynchronous.py:408, in open_consolidated(use_consolidated, *args, **kwargs)
    403 if use_consolidated is not True:
    404     raise TypeError(
    405         "'use_consolidated' must be 'True' in 'open_consolidated'. Use 'open' with "
    406         "'use_consolidated=False' to bypass consolidated metadata."
    407     )
--> 408 return await open_group(*args, use_consolidated=use_consolidated, **kwargs)

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/api/asynchronous.py:857, in open_group(store, mode, cache_attrs, synchronizer, path, chunk_store, storage_options, zarr_version, zarr_format, meta_array, attributes, use_consolidated)
    855 try:
    856     if mode in _READ_MODES:
--> 857         return await AsyncGroup.open(
    858             store_path, zarr_format=zarr_format, use_consolidated=use_consolidated
    859         )
    860 except (KeyError, FileNotFoundError):
    861     pass

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/core/group.py:559, in AsyncGroup.open(cls, store, zarr_format, use_consolidated)
    552         raise FileNotFoundError(store_path)
    553 elif zarr_format is None:
    554     (
    555         zarr_json_bytes,
    556         zgroup_bytes,
    557         zattrs_bytes,
    558         maybe_consolidated_metadata_bytes,
--> 559     ) = await asyncio.gather(
    560         (store_path / ZARR_JSON).get(),
    561         (store_path / ZGROUP_JSON).get(),
    562         (store_path / ZATTRS_JSON).get(),
    563         (store_path / str(consolidated_key)).get(),
    564     )
    565     if zarr_json_bytes is not None and zgroup_bytes is not None:
    566         # warn and favor v3
    567         msg = f"Both zarr.json (Zarr format 3) and .zgroup (Zarr format 2) metadata objects exist at {store_path}. Zarr format 3 will be used."

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/storage/_common.py:168, in StorePath.get(self, prototype, byte_range)
    166 if prototype is None:
    167     prototype = default_buffer_prototype()
--> 168 return await self.store.get(self.path, prototype=prototype, byte_range=byte_range)

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/zarr/storage/_fsspec.py:299, in FsspecStore.get(self, key, prototype, byte_range)
    297 try:
    298     if byte_range is None:
--> 299         value = prototype.buffer.from_bytes(await self.fs._cat_file(path))
    300     elif isinstance(byte_range, RangeByteRequest):
    301         value = prototype.buffer.from_bytes(
    302             await self.fs._cat_file(
    303                 path,
   (...)    306             )
    307         )

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/gcsfs/core.py:1119, in GCSFileSystem._cat_file(self, path, start, end, **kwargs)
   1117 else:
   1118     head = {}
-> 1119 headers, out = await self._call("GET", u2, headers=head)
   1120 return out

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/gcsfs/core.py:483, in GCSFileSystem._call(self, method, path, json_out, info_out, *args, **kwargs)
    479 async def _call(
    480     self, method, path, *args, json_out=False, info_out=False, **kwargs
    481 ):
    482     logger.debug(f"{method.upper()}: {path}, {args}, {kwargs.get('headers')}")
--> 483     status, headers, info, contents = await self._request(
    484         method, path, *args, **kwargs
    485     )
    486     if json_out:
    487         return json.loads(contents)

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/decorator.py:224, in decorate.<locals>.fun(*args, **kw)
    222 if not kwsyntax:
    223     args, kw = fix(args, kw, sig)
--> 224 return await caller(func, *(extras + args), **kw)

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/gcsfs/retry.py:135, in retry_request(func, retries, *args, **kwargs)
    133     if retry > 0:
    134         await asyncio.sleep(min(random.random() + 2 ** (retry - 1), 32))
--> 135     return await func(*args, **kwargs)
    136 except (
    137     HttpError,
    138     requests.exceptions.RequestException,
   (...)    141     aiohttp.client_exceptions.ClientError,
    142 ) as e:
    143     if (
    144         isinstance(e, HttpError)
    145         and e.code == 400
    146         and "requester pays" in e.message
    147     ):

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/gcsfs/core.py:476, in GCSFileSystem._request(self, method, path, headers, json, data, *args, **kwargs)
    473 info = r.request_info  # for debug only
    474 contents = await r.read()
--> 476 validate_response(status, contents, path, args)
    477 return status, headers, info, contents

File ~/micromamba/envs/po-cookbook-dev/lib/python3.13/site-packages/gcsfs/retry.py:120, in validate_response(status, content, path, args)
    118     raise requests.exceptions.ProxyError()
    119 elif "invalid" in str(msg):
--> 120     raise ValueError(f"Bad Request: {path}\n{msg}")
    121 elif error and not isinstance(error, str):
    122     raise HttpError(error)

ValueError: Bad Request: https://storage.googleapis.com/download/storage/v1/b/pangeo-ecco-eccov4r3/o/eccov4r3%2F.zattrs?alt=media
User project specified in the request is invalid.

Note that no data has been actually download yet. Xarray uses the approach of lazy evaluation, in which loading of data and execution of computations is delayed as long as possible (i.e. until data is actually needed for a plot). The data are represented symbolically as dask arrays. For example:

SALT       (time, k, face, j, i) float32 dask.array<shape=(288, 50, 13, 90, 90), chunksize=(1, 50, 13, 90, 90)>

The full shape of the array is (288, 50, 13, 90, 90), quite large. But the chunksize is (1, 50, 13, 90, 90). Here the chunks correspond to the individual granuales of data (objects) in cloud storage. The chunk is the minimum amount of data we can read at one time.

# a trick to make things work a bit faster
coords = ds.coords.to_dataset().reset_coords()
ds = ds.reset_coords(drop=True)

Visualizing Data¶

A Direct Plot¶

Let’s try to visualize something simple: the Depth variable. Here is how the data are stored:

Depth      (face, j, i) float32 dask.array<shape=(13, 90, 90), chunksize=(13, 90, 90)>

Although depth is a 2D field, there is an extra, dimension (face) corresponding to the LLC face number. Let’s use xarray’s built in plotting functions to plot each face individually.

coords.Depth.plot(col='face', col_wrap=5)

This view is not the most useful. It reflects how the data is arranged logically, rather than geographically.

A Pretty Map¶

To make plotting easier, we can define a quick function to plot the data in a more geographically friendly way. Eventually these plotting functions may be provided by the gcmplots package: https://github.com/xecco/gcmplots. For now, it is easy enough to roll our own.

class LLCMapper:

    def __init__(self, ds, dx=0.25, dy=0.25):
        # Extract LLC 2D coordinates
        lons_1d = ds.XC.values.ravel()
        lats_1d = ds.YC.values.ravel()

        # Define original grid
        self.orig_grid = pyresample.geometry.SwathDefinition(lons=lons_1d, lats=lats_1d)

        # Longitudes latitudes to which we will we interpolate
        lon_tmp = np.arange(-180, 180, dx) + dx/2
        lat_tmp = np.arange(-90, 90, dy) + dy/2

        # Define the lat lon points of the two parts.
        self.new_grid_lon, self.new_grid_lat = np.meshgrid(lon_tmp, lat_tmp)
        self.new_grid  = pyresample.geometry.GridDefinition(lons=self.new_grid_lon,
                                                            lats=self.new_grid_lat)

    def __call__(self, da, ax=None, projection=cart.crs.Robinson(), lon_0=-60, **plt_kwargs):

        assert set(da.dims) == set(['face', 'j', 'i']), "da must have dimensions ['face', 'j', 'i']"

        if ax is None:
            fig, ax = plt.subplots(figsize=(12, 6), subplot_kw={'projection': projection})
        else:
            m = plt.axes(projection=projection)
            
        field = pyresample.kd_tree.resample_nearest(self.orig_grid, da.values,
                                                    self.new_grid,
                                                    radius_of_influence=100000,
                                                    fill_value=None)

        vmax = plt_kwargs.pop('vmax', field.max())
        vmin = plt_kwargs.pop('vmin', field.min())

        
        x,y = self.new_grid_lon, self.new_grid_lat

        # Find index where data is splitted for mapping
        split_lon_idx = round(x.shape[1]/(360/(lon_0 if lon_0>0 else lon_0+360)))


        p = ax.pcolormesh(x[:,:split_lon_idx], y[:,:split_lon_idx], field[:,:split_lon_idx],
                         vmax=vmax, vmin=vmin, transform=cart.crs.PlateCarree(), zorder=1, **plt_kwargs)
        p = ax.pcolormesh(x[:,split_lon_idx:], y[:,split_lon_idx:], field[:,split_lon_idx:],
                         vmax=vmax, vmin=vmin, transform=cart.crs.PlateCarree(), zorder=2, **plt_kwargs)

        ax.add_feature(cart.feature.LAND, facecolor='0.5', zorder=3)
        label = ''
        if da.name is not None:
            label = da.name
        if 'units' in da.attrs:
            label += ' [%s]' % da.attrs['units']
        cb = plt.colorbar(p, shrink=0.4, label=label)
        return ax

mapper = LLCMapper(coords)
mapper(coords.Depth);

We can use this with any 2D cell-centered LLC variable.

Selecting data¶

The entire ECCOv4e3 dataset is contained in a single Xarray.Dataset object. How do we find a view specific pieces of data? This is handled by Xarray’s indexing and selecting functions. To get the SST from January 2000, we do this:

sst = ds.THETA.sel(time='2000-01-15', k=0)
sst

Still no data has been actually downloaded. That doesn’t happen until we call .load() explicitly or try to make a plot.

mapper(sst, cmap='RdBu_r');

Do some Calculations¶

Now let’s start doing something besides just plotting the existing data. For example, let’s calculate the time-mean SST.

mean_sst = ds.THETA.sel(k=0).mean(dim='time')
mean_sst

As usual, no data was loaded. Instead, mean_sst is a symbolic representation of the data that needs to be pulled and the computations that need to be executed to produce the desired result. In this case, the 288 original chunks all need to be read from cloud storage. Dask coordinates this automatically for us. But it does take some time.

%time mean_sst.load()

mapper(mean_sst, cmap='RdBu_r');

Speeding things up with a Dask Cluster¶

How can we speed things up? In general, the main bottleneck for this type of data analysis is the speed with which we can read the data. With cloud storage, the access is highly parallelizeable.

From a Pangeo environment, we can create a Dask cluster to spread the work out amongst many compute nodes. This works on both HPC and cloud. In the cloud, the compute nodes are provisioned on the fly and can be shut down as soon as we are done with our analysis.

The code below will create a cluster with five compute nodes. It can take a few minutes to provision our nodes.

cluster = GatewayCluster()
cluster.scale(5)
client = Client(cluster)
cluster

Now we re-run the mean calculation. Note how the dashboard helps us visualize what the cluster is doing.

%time ds.THETA.isel(k=0).mean(dim='time').load()

Spatially-Integrated Heat Content Anomaly¶

Now let’s do something harder. We will calculate the horizontally integrated heat content anomaly for the full 3D model domain.

# the monthly climatology
theta_clim = ds.THETA.groupby('time.month').mean(dim='time')
# the anomaly
theta_anom = ds.THETA.groupby('time.month') - theta_clim
rho0 = 1029
cp = 3994
ohc = rho0 * cp * (theta_anom *
                   coords.rA *
                   coords.hFacC).sum(dim=['face', 'j', 'i'])
ohc

# actually load the data
ohc.load()
# put the depth coordinate back for plotting purposes
ohc.coords['Z'] = coords.Z
ohc.swap_dims({'k': 'Z'}).transpose().plot(vmax=1e20)

Spatial Derivatives: Heat Budget¶

As our final exercise, we will do something much more complicated. We will compute the time-mean convergence of vertically-integrated heat fluxes. This is hard for several reasons.

The first reason it is hard is because it involves variables located at different grid points. Following MITgcm conventions, xmitgcm (which produced this dataset) labels the center point with the coordinates j, i, the u-velocity point as j, i_g, and the v-velocity point as j_g, i. The horizontal advective heat flux variables are

ADVx_TH    (time, k, face, j, i_g) float32 dask.array<shape=(288, 50, 13, 90, 90), chunksize=(1, 50, 13, 90, 90)>
ADVy_TH    (time, k, face, j_g, i) float32 dask.array<shape=(288, 50, 13, 90, 90), chunksize=(1, 50, 13, 90, 90)>

Xarray won’t allow us to add or multiply variables that have different dimensions, and xarray by itself doesn’t understand how to transform from one grid position to another.

That’s why xgcm was created.

Xgcm allows us to create a Grid object, which understands how to interpolate and take differences in a way that is compatible with finite volume models such at MITgcm. Xgcm also works with many other models, including ROMS, POP, MOM5/6, NEMO, etc.

A second reason this is hard is because of the complex topology connecting the different MITgcm faces. Fortunately xgcm also supports this.

# define the connectivity between faces
face_connections = {'face':
                    {0: {'X':  ((12, 'Y', False), (3, 'X', False)),
                         'Y':  (None,             (1, 'Y', False))},
                     1: {'X':  ((11, 'Y', False), (4, 'X', False)),
                         'Y':  ((0, 'Y', False),  (2, 'Y', False))},
                     2: {'X':  ((10, 'Y', False), (5, 'X', False)),
                         'Y':  ((1, 'Y', False),  (6, 'X', False))},
                     3: {'X':  ((0, 'X', False),  (9, 'Y', False)),
                         'Y':  (None,             (4, 'Y', False))},
                     4: {'X':  ((1, 'X', False),  (8, 'Y', False)),
                         'Y':  ((3, 'Y', False),  (5, 'Y', False))},
                     5: {'X':  ((2, 'X', False),  (7, 'Y', False)),
                         'Y':  ((4, 'Y', False),  (6, 'Y', False))},
                     6: {'X':  ((2, 'Y', False),  (7, 'X', False)),
                         'Y':  ((5, 'Y', False),  (10, 'X', False))},
                     7: {'X':  ((6, 'X', False),  (8, 'X', False)),
                         'Y':  ((5, 'X', False),  (10, 'Y', False))},
                     8: {'X':  ((7, 'X', False),  (9, 'X', False)),
                         'Y':  ((4, 'X', False),  (11, 'Y', False))},
                     9: {'X':  ((8, 'X', False),  None),
                         'Y':  ((3, 'X', False),  (12, 'Y', False))},
                     10: {'X': ((6, 'Y', False),  (11, 'X', False)),
                          'Y': ((7, 'Y', False),  (2, 'X', False))},
                     11: {'X': ((10, 'X', False), (12, 'X', False)),
                          'Y': ((8, 'Y', False),  (1, 'X', False))},
                     12: {'X': ((11, 'X', False), None),
                          'Y': ((9, 'Y', False),  (0, 'X', False))}}}

# create the grid object
grid = xgcm.Grid(ds, periodic=False, face_connections=face_connections)
grid

Now we can use the grid object we created to take the divergence of a 2D vector

# vertical integral and time mean of horizontal diffusive heat flux
advx_th_vint = ds.ADVx_TH.sum(dim='k').mean(dim='time')
advy_th_vint = ds.ADVy_TH.sum(dim='k').mean(dim='time')

# difference in the x and y directions
diff_ADV_th = grid.diff_2d_vector({'X': advx_th_vint, 'Y': advy_th_vint}, boundary='fill')
# convergence
conv_ADV_th = -diff_ADV_th['X'] - diff_ADV_th['Y']
conv_ADV_th

# vertical integral and time mean of horizontal diffusive heat flux
difx_th_vint = ds.DFxE_TH.sum(dim='k').mean(dim='time')
dify_th_vint = ds.DFyE_TH.sum(dim='k').mean(dim='time')

# difference in the x and y directions
diff_DIF_th = grid.diff_2d_vector({'X': difx_th_vint, 'Y': dify_th_vint}, boundary='fill')
# convergence
conv_DIF_th = -diff_DIF_th['X'] - diff_DIF_th['Y']
conv_DIF_th

# convert to Watts / m^2 and load
mean_adv_conv = rho0 * cp * (conv_ADV_th/coords.rA).fillna(0.).load()
mean_dif_conv = rho0 * cp * (conv_DIF_th/coords.rA).fillna(0.).load()

ax = mapper(mean_adv_conv, cmap='RdBu_r', vmax=300, vmin=-300);
ax.set_title(r'Convergence of Advective Flux (W/m$^2$)');

ax = mapper(mean_dif_conv, cmap='RdBu_r', vmax=300, vmin=-300)
ax.set_title(r'Convergence of Diffusive Flux (W/m$^2$)');

ax = mapper(mean_dif_conv + mean_adv_conv, cmap='RdBu_r', vmax=300, vmin=-300)
ax.set_title(r'Convergence of Net Horizontal Flux (W/m$^2$)');

ax = mapper(ds.TFLUX.mean(dim='time').load(), cmap='RdBu_r', vmax=300, vmin=-300);
ax.set_title(r'Surface Heat Flux (W/m$^2$)');

Summary¶

In this example we used xarray and cartopy to visualize ocean depth and ocean heat content anomalies. Then, we used xgcm to easily work with variables that have different dimensions.

What’s next?¶

In our last example, we will visualize ocean currents.

Resources and references¶

This notebook is based on the ECCOv4 example from the Pangeo physical oceanography gallery: http://gallery.pangeo.io/repos/pangeo-gallery/physical-oceanography/04_eccov4.html

Example Workflows

MOM6/CESM Ocean Model Analysis

Example Workflows

Gulf Stream Currents