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.
In [1]: import numpy as np
In [2]: import pandas as pd
In [3]: import xarray as xr
In [4]: import netCDF4
In [5]: import cartopy.crs as ccrs
In [6]: import matplotlib.pyplot as plt
As an example, consider this dataset from the xarray-data repository.
In [7]: ds = xr.tutorial.open_dataset('rasm').load()
---------------------------------------------------------------------------
TimeoutError Traceback (most recent call last)
/usr/lib/python3.7/urllib/request.py in do_open(self, http_class, req, **http_conn_args)
1323 h.request(req.get_method(), req.selector, req.data, headers,
-> 1324 encode_chunked=req.has_header('Transfer-encoding'))
1325 except OSError as err: # timeout error
/usr/lib/python3.7/http/client.py in request(self, method, url, body, headers, encode_chunked)
1263 """Send a complete request to the server."""
-> 1264 self._send_request(method, url, body, headers, encode_chunked)
1265
/usr/lib/python3.7/http/client.py in _send_request(self, method, url, body, headers, encode_chunked)
1309 body = _encode(body, 'body')
-> 1310 self.endheaders(body, encode_chunked=encode_chunked)
1311
/usr/lib/python3.7/http/client.py in endheaders(self, message_body, encode_chunked)
1258 raise CannotSendHeader()
-> 1259 self._send_output(message_body, encode_chunked=encode_chunked)
1260
/usr/lib/python3.7/http/client.py in _send_output(self, message_body, encode_chunked)
1033 del self._buffer[:]
-> 1034 self.send(msg)
1035
/usr/lib/python3.7/http/client.py in send(self, data)
973 if self.auto_open:
--> 974 self.connect()
975 else:
/usr/lib/python3.7/http/client.py in connect(self)
1418
-> 1419 super().connect()
1420
/usr/lib/python3.7/http/client.py in connect(self)
945 self.sock = self._create_connection(
--> 946 (self.host,self.port), self.timeout, self.source_address)
947 self.sock.setsockopt(socket.IPPROTO_TCP, socket.TCP_NODELAY, 1)
/usr/lib/python3.7/socket.py in create_connection(address, timeout, source_address)
726 if err is not None:
--> 727 raise err
728 else:
/usr/lib/python3.7/socket.py in create_connection(address, timeout, source_address)
715 sock.bind(source_address)
--> 716 sock.connect(sa)
717 # Break explicitly a reference cycle
TimeoutError: [Errno 110] Connection timed out
During handling of the above exception, another exception occurred:
URLError Traceback (most recent call last)
<ipython-input-7-7ddfc509c01f> in <module>()
----> 1 ds = xr.tutorial.open_dataset('rasm').load()
/builds/AstraOS/buildsystem/tbs_build/python-xarray/python-xarray-0.11.3/xarray/tutorial.py in open_dataset(name, cache, cache_dir, github_url, branch, **kws)
69
70 url = '/'.join((github_url, 'raw', branch, fullname))
---> 71 _urlretrieve(url, localfile)
72 url = '/'.join((github_url, 'raw', branch, md5name))
73 _urlretrieve(url, md5file)
/usr/lib/python3.7/urllib/request.py in urlretrieve(url, filename, reporthook, data)
245 url_type, path = splittype(url)
246
--> 247 with contextlib.closing(urlopen(url, data)) as fp:
248 headers = fp.info()
249
/usr/lib/python3.7/urllib/request.py in urlopen(url, data, timeout, cafile, capath, cadefault, context)
220 else:
221 opener = _opener
--> 222 return opener.open(url, data, timeout)
223
224 def install_opener(opener):
/usr/lib/python3.7/urllib/request.py in open(self, fullurl, data, timeout)
523 req = meth(req)
524
--> 525 response = self._open(req, data)
526
527 # post-process response
/usr/lib/python3.7/urllib/request.py in _open(self, req, data)
541 protocol = req.type
542 result = self._call_chain(self.handle_open, protocol, protocol +
--> 543 '_open', req)
544 if result:
545 return result
/usr/lib/python3.7/urllib/request.py in _call_chain(self, chain, kind, meth_name, *args)
501 for handler in handlers:
502 func = getattr(handler, meth_name)
--> 503 result = func(*args)
504 if result is not None:
505 return result
/usr/lib/python3.7/urllib/request.py in https_open(self, req)
1365 def https_open(self, req):
1366 return self.do_open(http.client.HTTPSConnection, req,
-> 1367 context=self._context, check_hostname=self._check_hostname)
1368
1369 https_request = AbstractHTTPHandler.do_request_
/usr/lib/python3.7/urllib/request.py in do_open(self, http_class, req, **http_conn_args)
1324 encode_chunked=req.has_header('Transfer-encoding'))
1325 except OSError as err: # timeout error
-> 1326 raise URLError(err)
1327 r = h.getresponse()
1328 except:
URLError: <urlopen error [Errno 110] Connection timed out>
In [8]: ds
Out[8]:
<xarray.Dataset>
Dimensions: (time: 3, x: 2, y: 2)
Coordinates:
lat (x, y) float64 42.25 42.21 42.63 42.59
lon (x, y) float64 -99.83 -99.32 -99.79 -99.23
* time (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
reference_time datetime64[ns] 2014-09-05
day (time) int64 6 7 8
Dimensions without coordinates: x, y
Data variables:
temperature (x, y, time) float64 11.04 23.57 20.77 ... 6.301 9.61 15.91
precipitation (x, y, time) float64 5.904 2.453 3.404 ... 3.435 1.709 3.947
In this example, the logical coordinates are x and y, while
the physical coordinates are xc and yc, which represent the
latitudes and longitude of the data.
In [9]: ds.xc.attrs
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-9-58b1081550ce> in <module>()
----> 1 ds.xc.attrs
/builds/AstraOS/buildsystem/tbs_build/python-xarray/python-xarray-0.11.3/xarray/core/common.py in __getattr__(self, name)
177 return source[name]
178 raise AttributeError("%r object has no attribute %r" %
--> 179 (type(self).__name__, name))
180
181 def __setattr__(self, name, value):
AttributeError: 'Dataset' object has no attribute 'xc'
In [10]: ds.yc.attrs
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-10-f2e4ac0aa2f2> in <module>()
----> 1 ds.yc.attrs
/builds/AstraOS/buildsystem/tbs_build/python-xarray/python-xarray-0.11.3/xarray/core/common.py in __getattr__(self, name)
177 return source[name]
178 raise AttributeError("%r object has no attribute %r" %
--> 179 (type(self).__name__, name))
180
181 def __setattr__(self, name, value):
AttributeError: 'Dataset' object has no attribute 'yc'
Plotting¶
Let’s examine these coordinate variables by plotting them.
In [11]: fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9,3))
In [12]: ds.xc.plot(ax=ax1);
In [13]: ds.yc.plot(ax=ax2);
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.
In [14]: ds.Tair[0].plot();
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.
In [15]: plt.figure(figsize=(7,2));
In [16]: ax = plt.axes(projection=ccrs.PlateCarree());
In [17]: ds.Tair[0].plot.pcolormesh(ax=ax, transform=ccrs.PlateCarree(),
....: x='xc', y='yc', add_colorbar=False);
....:
In [18]: ax.coastlines();
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.
# define two-degree wide latitude bins
In [19]: lat_bins = np.arange(0, 91, 2)
# define a label for each bin corresponding to the central latitude
In [20]: lat_center = np.arange(1, 90, 2)
# group according to those bins and take the mean
In [21]: Tair_lat_mean = (ds.Tair.groupby_bins('xc', lat_bins, labels=lat_center)
....: .mean(xr.ALL_DIMS))
....:
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-21-d7ce10b82be1> in <module>()
----> 1 Tair_lat_mean = (ds.Tair.groupby_bins('xc', lat_bins, labels=lat_center)
2 .mean(xr.ALL_DIMS))
/builds/AstraOS/buildsystem/tbs_build/python-xarray/python-xarray-0.11.3/xarray/core/common.py in __getattr__(self, name)
177 return source[name]
178 raise AttributeError("%r object has no attribute %r" %
--> 179 (type(self).__name__, name))
180
181 def __setattr__(self, name, value):
AttributeError: 'Dataset' object has no attribute 'Tair'
# plot the result
In [22]: Tair_lat_mean.plot();
Note that the resulting coordinate for the groupby_bins operation
got the _bins suffix appended: xc_bins. This help us distinguish
it from the original multidimensional variable xc.