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.load_dataset('rasm')
---------------------------------------------------------------------------
ConnectionRefusedError                    Traceback (most recent call last)
/usr/lib/python3.5/urllib/request.py in do_open(self, http_class, req, **http_conn_args)
   1253             try:
-> 1254                 h.request(req.get_method(), req.selector, req.data, headers)
   1255             except OSError as err: # timeout error

/usr/lib/python3.5/http/client.py in request(self, method, url, body, headers)
   1106         """Send a complete request to the server."""
-> 1107         self._send_request(method, url, body, headers)
   1108 

/usr/lib/python3.5/http/client.py in _send_request(self, method, url, body, headers)
   1151             body = _encode(body, 'body')
-> 1152         self.endheaders(body)
   1153 

/usr/lib/python3.5/http/client.py in endheaders(self, message_body)
   1102             raise CannotSendHeader()
-> 1103         self._send_output(message_body)
   1104 

/usr/lib/python3.5/http/client.py in _send_output(self, message_body)
    933 
--> 934         self.send(msg)
    935         if message_body is not None:

/usr/lib/python3.5/http/client.py in send(self, data)
    876             if self.auto_open:
--> 877                 self.connect()
    878             else:

/usr/lib/python3.5/http/client.py in connect(self)
   1252 
-> 1253             super().connect()
   1254 

/usr/lib/python3.5/http/client.py in connect(self)
    848         self.sock = self._create_connection(
--> 849             (self.host,self.port), self.timeout, self.source_address)
    850         self.sock.setsockopt(socket.IPPROTO_TCP, socket.TCP_NODELAY, 1)

/usr/lib/python3.5/socket.py in create_connection(address, timeout, source_address)
    711     if err is not None:
--> 712         raise err
    713     else:

/usr/lib/python3.5/socket.py in create_connection(address, timeout, source_address)
    702                 sock.bind(source_address)
--> 703             sock.connect(sa)
    704             return sock

ConnectionRefusedError: [Errno 111] Connection refused

During handling of the above exception, another exception occurred:

URLError                                  Traceback (most recent call last)
<ipython-input-7-45e669c5b239> in <module>()
----> 1 ds = xr.tutorial.load_dataset('rasm')

/home/gladk/18/python-xarray-0.9.2/xarray/tutorial.py in load_dataset(name, cache, cache_dir, github_url, **kws)
     54 
     55         url = '/'.join((github_url, 'raw', 'master', fullname))
---> 56         _urlretrieve(url, localfile)
     57 
     58     ds = _open_dataset(localfile, **kws).load()

/usr/lib/python3.5/urllib/request.py in urlretrieve(url, filename, reporthook, data)
    186     url_type, path = splittype(url)
    187 
--> 188     with contextlib.closing(urlopen(url, data)) as fp:
    189         headers = fp.info()
    190 

/usr/lib/python3.5/urllib/request.py in urlopen(url, data, timeout, cafile, capath, cadefault, context)
    161     else:
    162         opener = _opener
--> 163     return opener.open(url, data, timeout)
    164 
    165 def install_opener(opener):

/usr/lib/python3.5/urllib/request.py in open(self, fullurl, data, timeout)
    464             req = meth(req)
    465 
--> 466         response = self._open(req, data)
    467 
    468         # post-process response

/usr/lib/python3.5/urllib/request.py in _open(self, req, data)
    482         protocol = req.type
    483         result = self._call_chain(self.handle_open, protocol, protocol +
--> 484                                   '_open', req)
    485         if result:
    486             return result

/usr/lib/python3.5/urllib/request.py in _call_chain(self, chain, kind, meth_name, *args)
    442         for handler in handlers:
    443             func = getattr(handler, meth_name)
--> 444             result = func(*args)
    445             if result is not None:
    446                 return result

/usr/lib/python3.5/urllib/request.py in https_open(self, req)
   1295         def https_open(self, req):
   1296             return self.do_open(http.client.HTTPSConnection, req,
-> 1297                 context=self._context, check_hostname=self._check_hostname)
   1298 
   1299         https_request = AbstractHTTPHandler.do_request_

/usr/lib/python3.5/urllib/request.py in do_open(self, http_class, req, **http_conn_args)
   1254                 h.request(req.get_method(), req.selector, req.data, headers)
   1255             except OSError as err: # timeout error
-> 1256                 raise URLError(err)
   1257             r = h.getresponse()
   1258         except:

URLError: <urlopen error [Errno 111] Connection refused>

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 9.346 6.683 17.17 ...
    precipitation   (x, y, time) float64 5.904 2.453 3.404 9.847 9.195 ...

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-9-824248f2223e> in <module>()
----> 1 ds.xc.attrs

/home/gladk/18/python-xarray-0.9.2/xarray/core/common.py in __getattr__(self, name)
    166                     return source[name]
    167         raise AttributeError("%r object has no attribute %r" %
--> 168                              (type(self).__name__, name))
    169 
    170     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-faf38965074d> in <module>()
----> 1 ds.yc.attrs

/home/gladk/18/python-xarray-0.9.2/xarray/core/common.py in __getattr__(self, name)
    166                     return source[name]
    167         raise AttributeError("%r object has no attribute %r" %
--> 168                              (type(self).__name__, name))
    169 
    170     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();

In [19]: plt.tight_layout();
examples/../_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 [20]: lat_bins = np.arange(0, 91, 2)

# define a label for each bin corresponding to the central latitude
In [21]: lat_center = np.arange(1, 90, 2)

# group according to those bins and take the mean
In [22]: Tair_lat_mean = ds.Tair.groupby_bins('xc', lat_bins, labels=lat_center).mean()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-22-83b74688111e> in <module>()
----> 1 Tair_lat_mean = ds.Tair.groupby_bins('xc', lat_bins, labels=lat_center).mean()

/home/gladk/18/python-xarray-0.9.2/xarray/core/common.py in __getattr__(self, name)
    166                     return source[name]
    167         raise AttributeError("%r object has no attribute %r" %
--> 168                              (type(self).__name__, name))
    169 
    170     def __setattr__(self, name, value):

AttributeError: 'Dataset' object has no attribute 'Tair'

# plot the result
In [23]: 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.