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()
---------------------------------------------------------------------------
gaierror                                  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)
   1243         """Send a complete request to the server."""
-> 1244         self._send_request(method, url, body, headers, encode_chunked)
   1245 

/usr/lib/python3.7/http/client.py in _send_request(self, method, url, body, headers, encode_chunked)
   1289             body = _encode(body, 'body')
-> 1290         self.endheaders(body, encode_chunked=encode_chunked)
   1291 

/usr/lib/python3.7/http/client.py in endheaders(self, message_body, encode_chunked)
   1238             raise CannotSendHeader()
-> 1239         self._send_output(message_body, encode_chunked=encode_chunked)
   1240 

/usr/lib/python3.7/http/client.py in _send_output(self, message_body, encode_chunked)
   1025         del self._buffer[:]
-> 1026         self.send(msg)
   1027 

/usr/lib/python3.7/http/client.py in send(self, data)
    965             if self.auto_open:
--> 966                 self.connect()
    967             else:

/usr/lib/python3.7/http/client.py in connect(self)
   1398 
-> 1399             super().connect()
   1400 

/usr/lib/python3.7/http/client.py in connect(self)
    937         self.sock = self._create_connection(
--> 938             (self.host,self.port), self.timeout, self.source_address)
    939         self.sock.setsockopt(socket.IPPROTO_TCP, socket.TCP_NODELAY, 1)

/usr/lib/python3.7/socket.py in create_connection(address, timeout, source_address)
    706     err = None
--> 707     for res in getaddrinfo(host, port, 0, SOCK_STREAM):
    708         af, socktype, proto, canonname, sa = res

/usr/lib/python3.7/socket.py in getaddrinfo(host, port, family, type, proto, flags)
    747     addrlist = []
--> 748     for res in _socket.getaddrinfo(host, port, family, type, proto, flags):
    749         af, socktype, proto, canonname, sa = res

gaierror: [Errno -3] Temporary failure in name resolution

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()

/opt/build/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 -3] Temporary failure in name resolution>

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

/opt/build/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

/opt/build/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);
../_images/xarray_multidimensional_coords_8_2.png

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();
../_images/xarray_multidimensional_coords_10_1.png

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();
_build/html/_static/xarray_multidimensional_coords_12_0.png

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))

/opt/build/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();
../_images/xarray_multidimensional_coords_14_1.png

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.