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 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')

In [8]: ds
Dimensions:  (time: 36, x: 275, y: 205)
  * time     (time) datetime64[ns] 1980-09-16T12:00:00 1980-10-17 ...
    xc       (y, x) float64 189.2 189.4 189.6 189.7 189.9 190.1 190.2 190.4 ...
    yc       (y, x) float64 16.53 16.78 17.02 17.27 17.51 17.76 18.0 18.25 ...
Dimensions without coordinates: x, y
Data variables:
    Tair     (time, y, x) float64 nan nan nan nan nan nan nan nan nan nan ...
    title: /workspace/jhamman/processed/R1002RBRxaaa01a/lnd/temp/
    institution: U.W.
    source: RACM R1002RBRxaaa01a
    output_frequency: daily
    output_mode: averaged
    convention: CF-1.4
    references: Based on the initial model of Liang et al., 1994, JGR, 99, 14,415- 14,429.
    comment: Output from the Variable Infiltration Capacity (VIC) model.
    nco_openmp_thread_number: 1
    NCO: "4.6.0"
    history: Tue Dec 27 14:15:22 2016: ncatted -a dimensions,,d,,
Tue Dec 27 13:38:40 2016: ncks -3
history deleted for brevity

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
OrderedDict([('long_name', 'longitude of grid cell center'),
             ('units', 'degrees_east'),
             ('bounds', 'xv')])

In [10]: ds.yc.attrs
OrderedDict([('long_name', 'latitude of grid cell center'),
             ('units', 'degrees_north'),
             ('bounds', 'yv')])


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()

# 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.