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

ImportErrorTraceback (most recent call last)
<ipython-input-4-9588a3d4fb24> in <module>()
----> 1 import netCDF4

ImportError: No module named 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')

IOErrorTraceback (most recent call last)
<ipython-input-7-7588dce177cb> in <module>()
----> 1 ds = xr.tutorial.load_dataset('rasm')

/srv/build/xarray/python-xarray-0.9.6/xarray/tutorial.py in load_dataset(name, cache, cache_dir, github_url, branch, **kws)
     68 
     69         url = '/'.join((github_url, 'raw', branch, fullname))
---> 70         _urlretrieve(url, localfile)
     71         url = '/'.join((github_url, 'raw', branch, md5name))
     72         _urlretrieve(url, md5file)

/usr/lib/python2.7/urllib.pyc in urlretrieve(url, filename, reporthook, data, context)
     96     else:
     97         opener = _urlopener
---> 98     return opener.retrieve(url, filename, reporthook, data)
     99 def urlcleanup():
    100     if _urlopener:

/usr/lib/python2.7/urllib.pyc in retrieve(self, url, filename, reporthook, data)
    243             except IOError:
    244                 pass
--> 245         fp = self.open(url, data)
    246         try:
    247             headers = fp.info()

/usr/lib/python2.7/urllib.pyc in open(self, fullurl, data)
    206         if not hasattr(self, name):
    207             if proxy:
--> 208                 return self.open_unknown_proxy(proxy, fullurl, data)
    209             else:
    210                 return self.open_unknown(fullurl, data)

/usr/lib/python2.7/urllib.pyc in open_unknown_proxy(self, proxy, fullurl, data)
    225         """Overridable interface to open unknown URL type."""
    226         type, url = splittype(fullurl)
--> 227         raise IOError, ('url error', 'invalid proxy for %s' % type, proxy)
    228 
    229     # External interface

IOError: [Errno url error] invalid proxy for https: '127.0.0.1:9'

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

AttributeErrorTraceback (most recent call last)
<ipython-input-9-58b1081550ce> in <module>()
----> 1 ds.xc.attrs

/srv/build/xarray/python-xarray-0.9.6/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

AttributeErrorTraceback (most recent call last)
<ipython-input-10-f2e4ac0aa2f2> in <module>()
----> 1 ds.yc.attrs

/srv/build/xarray/python-xarray-0.9.6/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);

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();

In [19]: plt.tight_layout();

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()

AttributeErrorTraceback (most recent call last)
<ipython-input-22-d2cf517792bc> in <module>()
----> 1 Tair_lat_mean = ds.Tair.groupby_bins('xc', lat_bins, labels=lat_center).mean()

/srv/build/xarray/python-xarray-0.9.6/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();

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.