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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 -3] Temporary failure in name resolution
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 0x7fda3dbc0c20>: Failed to resolve 'github.com' ([Errno -3] Temporary failure in name resolution)
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 0x7fda3dbc0c20>: Failed to resolve 'github.com' ([Errno -3] Temporary failure in name resolution)"))
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 0x7fda3dbc0c20>: Failed to resolve 'github.com' ([Errno -3] Temporary failure in name resolution)"))
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.