You can run this notebook in a live session or view it on Github.

# Working with Multidimensional Coordinates

Author: Ryan Abernathey

Many datasets have physical coordinates which differ from their logical coordinates. Xarray provides several ways to plot and analyze such datasets.

    [1]:

    %matplotlib inline
    import numpy as np
    import pandas as pd
    import xarray as xr
    import cartopy.crs as ccrs
    from matplotlib import pyplot as plt

As an example, consider this dataset from the xarray-data repository.

    [2]:

    ds = xr.tutorial.open_dataset("rasm").load()
    ds

    ---------------------------------------------------------------------------
    gaierror                                  Traceback (most recent call last)
    File /usr/lib/python3/dist-packages/urllib3/connection.py:198, in HTTPConnection._new_conn(self)
        197 try:
    --> 198     sock = connection.create_connection(
        199         (self._dns_host, self.port),
        200         self.timeout,
        201         source_address=self.source_address,
        202         socket_options=self.socket_options,
        203     )
        204 except socket.gaierror as e:

    File /usr/lib/python3/dist-packages/urllib3/util/connection.py:60, in create_connection(address, timeout, source_address, socket_options)
         58     raise LocationParseError(f"'{host}', label empty or too long") from None
    ---> 60 for res in socket.getaddrinfo(host, port, family, socket.SOCK_STREAM):
         61     af, socktype, proto, canonname, sa = res

    File /usr/lib/python3.13/socket.py:977, in getaddrinfo(host, port, family, type, proto, flags)
        976 addrlist = []
    --> 977 for res in _socket.getaddrinfo(host, port, family, type, proto, flags):
        978     af, socktype, proto, canonname, sa = res

    gaierror: [Errno -2] Name or service not known

    The above exception was the direct cause of the following exception:

    NameResolutionError                       Traceback (most recent call last)
    File /usr/lib/python3/dist-packages/urllib3/connectionpool.py:787, in HTTPConnectionPool.urlopen(self, method, url, body, headers, retries, redirect, assert_same_host, timeout, pool_timeout, release_conn, chunked, body_pos, preload_content, decode_content, **response_kw)
        786 # Make the request on the HTTPConnection object
    --> 787 response = self._make_request(
        788     conn,
        789     method,
        790     url,
        791     timeout=timeout_obj,
        792     body=body,
        793     headers=headers,
        794     chunked=chunked,
        795     retries=retries,
        796     response_conn=response_conn,
        797     preload_content=preload_content,
        798     decode_content=decode_content,
        799     **response_kw,
        800 )
        802 # Everything went great!

    File /usr/lib/python3/dist-packages/urllib3/connectionpool.py:488, in HTTPConnectionPool._make_request(self, conn, method, url, body, headers, retries, timeout, chunked, response_conn, preload_content, decode_content, enforce_content_length)
        487         new_e = _wrap_proxy_error(new_e, conn.proxy.scheme)
    --> 488     raise new_e
        490 # conn.request() calls http.client.*.request, not the method in
        491 # urllib3.request. It also calls makefile (recv) on the socket.

    File /usr/lib/python3/dist-packages/urllib3/connectionpool.py:464, in HTTPConnectionPool._make_request(self, conn, method, url, body, headers, retries, timeout, chunked, response_conn, preload_content, decode_content, enforce_content_length)
        463 try:
    --> 464     self._validate_conn(conn)
        465 except (SocketTimeout, BaseSSLError) as e:

    File /usr/lib/python3/dist-packages/urllib3/connectionpool.py:1093, in HTTPSConnectionPool._validate_conn(self, conn)
       1092 if conn.is_closed:
    -> 1093     conn.connect()
       1095 # TODO revise this, see https://github.com/urllib3/urllib3/issues/2791

    File /usr/lib/python3/dist-packages/urllib3/connection.py:704, in HTTPSConnection.connect(self)
        703 sock: socket.socket | ssl.SSLSocket
    --> 704 self.sock = sock = self._new_conn()
        705 server_hostname: str = self.host

    File /usr/lib/python3/dist-packages/urllib3/connection.py:205, in HTTPConnection._new_conn(self)
        204 except socket.gaierror as e:
    --> 205     raise NameResolutionError(self.host, self, e) from e
        206 except SocketTimeout as e:

    NameResolutionError: <urllib3.connection.HTTPSConnection object at 0x7557b3530050>: Failed to resolve 'github.com' ([Errno -2] Name or service not known)

    The above exception was the direct cause of the following exception:

    MaxRetryError                             Traceback (most recent call last)
    File /usr/lib/python3/dist-packages/requests/adapters.py:667, in HTTPAdapter.send(self, request, stream, timeout, verify, cert, proxies)
        666 try:
    --> 667     resp = conn.urlopen(
        668         method=request.method,
        669         url=url,
        670         body=request.body,
        671         headers=request.headers,
        672         redirect=False,
        673         assert_same_host=False,
        674         preload_content=False,
        675         decode_content=False,
        676         retries=self.max_retries,
        677         timeout=timeout,
        678         chunked=chunked,
        679     )
        681 except (ProtocolError, OSError) as err:

    File /usr/lib/python3/dist-packages/urllib3/connectionpool.py:841, in HTTPConnectionPool.urlopen(self, method, url, body, headers, retries, redirect, assert_same_host, timeout, pool_timeout, release_conn, chunked, body_pos, preload_content, decode_content, **response_kw)
        839     new_e = ProtocolError("Connection aborted.", new_e)
    --> 841 retries = retries.increment(
        842     method, url, error=new_e, _pool=self, _stacktrace=sys.exc_info()[2]
        843 )
        844 retries.sleep()

    File /usr/lib/python3/dist-packages/urllib3/util/retry.py:519, in Retry.increment(self, method, url, response, error, _pool, _stacktrace)
        518     reason = error or ResponseError(cause)
    --> 519     raise MaxRetryError(_pool, url, reason) from reason  # type: ignore[arg-type]
        521 log.debug("Incremented Retry for (url='%s'): %r", url, new_retry)

    MaxRetryError: HTTPSConnectionPool(host='github.com', port=443): Max retries exceeded with url: /pydata/xarray-data/raw/master/rasm.nc (Caused by NameResolutionError("<urllib3.connection.HTTPSConnection object at 0x7557b3530050>: Failed to resolve 'github.com' ([Errno -2] Name or service not known)"))

    During handling of the above exception, another exception occurred:

    ConnectionError                           Traceback (most recent call last)
    Cell In[2], line 1
    ----> 1 ds = xr.tutorial.open_dataset("rasm").load()
          2 ds

    File /usr/lib/python3/dist-packages/xarray/tutorial.py:167, in open_dataset(name, cache, cache_dir, engine, **kws)
        164 downloader = pooch.HTTPDownloader(headers=headers)
        166 # retrieve the file
    --> 167 filepath = pooch.retrieve(
        168     url=url, known_hash=None, path=cache_dir, downloader=downloader
        169 )
        170 ds = _open_dataset(filepath, engine=engine, **kws)
        171 if not cache:

    File /usr/lib/python3/dist-packages/pooch/core.py:239, in retrieve(url, known_hash, fname, path, processor, downloader, progressbar)
        236 if downloader is None:
        237     downloader = choose_downloader(url, progressbar=progressbar)
    --> 239 stream_download(url, full_path, known_hash, downloader, pooch=None)
        241 if known_hash is None:
        242     get_logger().info(
        243         "SHA256 hash of downloaded file: %s\n"
        244         "Use this value as the 'known_hash' argument of 'pooch.retrieve'"
       (...)
        247         file_hash(str(full_path)),
        248     )

    File /usr/lib/python3/dist-packages/pooch/core.py:807, in stream_download(url, fname, known_hash, downloader, pooch, retry_if_failed)
        803 try:
        804     # Stream the file to a temporary so that we can safely check its
        805     # hash before overwriting the original.
        806     with temporary_file(path=str(fname.parent)) as tmp:
    --> 807         downloader(url, tmp, pooch)
        808         hash_matches(tmp, known_hash, strict=True, source=str(fname.name))
        809         shutil.move(tmp, str(fname))

    File /usr/lib/python3/dist-packages/pooch/downloaders.py:220, in HTTPDownloader.__call__(self, url, output_file, pooch, check_only)
        218     # pylint: enable=consider-using-with
        219 try:
    --> 220     response = requests.get(url, timeout=timeout, **kwargs)
        221     response.raise_for_status()
        222     content = response.iter_content(chunk_size=self.chunk_size)

    File /usr/lib/python3/dist-packages/requests/api.py:73, in get(url, params, **kwargs)
         62 def get(url, params=None, **kwargs):
         63     r"""Sends a GET request.
         64
         65     :param url: URL for the new :class:`Request` object.
       (...)
         70     :rtype: requests.Response
         71     """
    ---> 73     return request("get", url, params=params, **kwargs)

    File /usr/lib/python3/dist-packages/requests/api.py:59, in request(method, url, **kwargs)
         55 # By using the 'with' statement we are sure the session is closed, thus we
         56 # avoid leaving sockets open which can trigger a ResourceWarning in some
         57 # cases, and look like a memory leak in others.
         58 with sessions.Session() as session:
    ---> 59     return session.request(method=method, url=url, **kwargs)

    File /usr/lib/python3/dist-packages/requests/sessions.py:589, in Session.request(self, method, url, params, data, headers, cookies, files, auth, timeout, allow_redirects, proxies, hooks, stream, verify, cert, json)
        584 send_kwargs = {
        585     "timeout": timeout,
        586     "allow_redirects": allow_redirects,
        587 }
        588 send_kwargs.update(settings)
    --> 589 resp = self.send(prep, **send_kwargs)
        591 return resp

    File /usr/lib/python3/dist-packages/requests/sessions.py:703, in Session.send(self, request, **kwargs)
        700 start = preferred_clock()
        702 # Send the request
    --> 703 r = adapter.send(request, **kwargs)
        705 # Total elapsed time of the request (approximately)
        706 elapsed = preferred_clock() - start

    File /usr/lib/python3/dist-packages/requests/adapters.py:700, in HTTPAdapter.send(self, request, stream, timeout, verify, cert, proxies)
        696     if isinstance(e.reason, _SSLError):
        697         # This branch is for urllib3 v1.22 and later.
        698         raise SSLError(e, request=request)
    --> 700     raise ConnectionError(e, request=request)
        702 except ClosedPoolError as e:
        703     raise ConnectionError(e, request=request)

    ConnectionError: HTTPSConnectionPool(host='github.com', port=443): Max retries exceeded with url: /pydata/xarray-data/raw/master/rasm.nc (Caused by NameResolutionError("<urllib3.connection.HTTPSConnection object at 0x7557b3530050>: Failed to resolve 'github.com' ([Errno -2] Name or service not known)"))

In this example, the logical coordinates are `x` and `y`, while the physical coordinates are `xc` and `yc`, which represent the longitudes and latitudes of the data.

    [3]:

    print(ds.xc.attrs)
    print(ds.yc.attrs)

    ---------------------------------------------------------------------------
    NameError                                 Traceback (most recent call last)
    Cell In[3], line 1
    ----> 1 print(ds.xc.attrs)
          2 print(ds.yc.attrs)

    NameError: name 'ds' is not defined

## Plotting

Let’s examine these coordinate variables by plotting them.

    [4]:

    fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(14, 4))
    ds.xc.plot(ax=ax1)
    ds.yc.plot(ax=ax2)

    ---------------------------------------------------------------------------
    NameError                                 Traceback (most recent call last)
    Cell In[4], line 2
          1 fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(14, 4))
    ----> 2 ds.xc.plot(ax=ax1)
          3 ds.yc.plot(ax=ax2)

    NameError: name 'ds' is not defined

Note that the variables `xc` (longitude) and `yc` (latitude) are two-dimensional scalar fields.

If we try to plot the data variable `Tair`, by default we get the logical coordinates.

    [5]:

    ds.Tair[0].plot()

    ---------------------------------------------------------------------------
    NameError                                 Traceback (most recent call last)
    Cell In[5], line 1
    ----> 1 ds.Tair[0].plot()

    NameError: name 'ds' is not defined

In order to visualize the data on a conventional latitude-longitude grid, we can take advantage of xarray’s ability to apply cartopy map projections.

    [6]:

    plt.figure(figsize=(14, 6))
    ax = plt.axes(projection=ccrs.PlateCarree())
    ax.set_global()
    ds.Tair[0].plot.pcolormesh(
        ax=ax, transform=ccrs.PlateCarree(), x="xc", y="yc", add_colorbar=False
    )
    ax.coastlines()
    ax.set_ylim([0, 90]);

    ---------------------------------------------------------------------------
    NameError                                 Traceback (most recent call last)
    Cell In[6], line 4
          2 ax = plt.axes(projection=ccrs.PlateCarree())
          3 ax.set_global()
    ----> 4 ds.Tair[0].plot.pcolormesh(
          5     ax=ax, transform=ccrs.PlateCarree(), x="xc", y="yc", add_colorbar=False
          6 )
          7 ax.coastlines()
          8 ax.set_ylim([0, 90]);

    NameError: name 'ds' is not defined

## Multidimensional Groupby

The above example allowed us to visualize the data on a regular latitude-longitude grid. But what if we want to do a calculation that involves grouping over one of these physical coordinates (rather than the logical coordinates), for example, calculating the mean temperature at each latitude. This can be achieved using xarray’s `groupby` function, which accepts multidimensional variables. By default, `groupby` will use every unique value in the variable, which is probably not what we want. Instead, we can use the `groupby_bins` function to specify the output coordinates of the group.

    [7]:

    # define two-degree wide latitude bins
    lat_bins = np.arange(0, 91, 2)
    # define a label for each bin corresponding to the central latitude
    lat_center = np.arange(1, 90, 2)
    # group according to those bins and take the mean
    Tair_lat_mean = ds.Tair.groupby_bins("yc", lat_bins, labels=lat_center).mean(
        dim=xr.ALL_DIMS
    )
    # plot the result
    Tair_lat_mean.plot()

    ---------------------------------------------------------------------------
    NameError                                 Traceback (most recent call last)
    Cell In[7], line 6
          4 lat_center = np.arange(1, 90, 2)
          5 # group according to those bins and take the mean
    ----> 6 Tair_lat_mean = ds.Tair.groupby_bins("yc", lat_bins, labels=lat_center).mean(
          7     dim=xr.ALL_DIMS
          8 )
          9 # plot the result
         10 Tair_lat_mean.plot()

    NameError: name 'ds' is not defined

The resulting coordinate for the `groupby_bins` operation got the `_bins` suffix appended: `yc_bins`. This help us distinguish it from the original multidimensional variable `yc`.

Note: This group-by-latitude approach does not take into account the finite-size geometry of grid cells. It simply bins each value according to the coordinates at the cell center. Xarray has no understanding of grid cells and their geometry. More precise geographic regridding for xarray data is available via the xesmf package.