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# 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.

    [1]:

    %matplotlib inline
    import numpy as np
    import pandas as pd
    import xarray as xr
    import cartopy.crs as ccrs
    from matplotlib import pyplot as plt

As an example, consider this dataset from the xarray-data repository.

    [2]:

    ds = xr.tutorial.open_dataset('rasm').load()
    ds

    ---------------------------------------------------------------------------
    FileNotFoundError                         Traceback (most recent call last)
    <ipython-input-2-0eb806e38f7f> in <module>
    ----> 1 ds = xr.tutorial.open_dataset('rasm').load()
          2 ds

    /build/python-xarray-kTVyut/python-xarray-0.15.0/xarray/tutorial.py in open_dataset(name, cache, cache_dir, github_url, branch, **kws)
         76         # May want to add an option to remove it.
         77         if not _os.path.isdir(longdir):
    ---> 78             _os.mkdir(longdir)
         79
         80         url = "/".join((github_url, "raw", branch, fullname))

    FileNotFoundError: [Errno 2] No such file or directory: '/sbuild-nonexistent/.xarray_tutorial_data'

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.

    [3]:

    print(ds.xc.attrs)
    print(ds.yc.attrs)

    ---------------------------------------------------------------------------
    NameError                                 Traceback (most recent call last)
    <ipython-input-3-adcec99473e0> in <module>
    ----> 1 print(ds.xc.attrs)
          2 print(ds.yc.attrs)

    NameError: name 'ds' is not defined

## Plotting

Let’s examine these coordinate variables by plotting them.

    [4]:

    fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(14,4))
    ds.xc.plot(ax=ax1)
    ds.yc.plot(ax=ax2)

    ---------------------------------------------------------------------------
    NameError                                 Traceback (most recent call last)
    <ipython-input-4-06a89de0178b> in <module>
          1 fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(14,4))
    ----> 2 ds.xc.plot(ax=ax1)
          3 ds.yc.plot(ax=ax2)

    NameError: name 'ds' is not defined

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.

    [5]:

    ds.Tair[0].plot()

    ---------------------------------------------------------------------------
    NameError                                 Traceback (most recent call last)
    <ipython-input-5-01ef0c7cb560> in <module>
    ----> 1 ds.Tair[0].plot()

    NameError: name 'ds' is not defined

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.

    [6]:

    plt.figure(figsize=(14,6))
    ax = plt.axes(projection=ccrs.PlateCarree())
    ax.set_global()
    ds.Tair[0].plot.pcolormesh(ax=ax, transform=ccrs.PlateCarree(), x='xc', y='yc', add_colorbar=False)
    ax.coastlines()
    ax.set_ylim([0,90]);

    ---------------------------------------------------------------------------
    NameError                                 Traceback (most recent call last)
    <ipython-input-6-b7284116c837> in <module>
          2 ax = plt.axes(projection=ccrs.PlateCarree())
          3 ax.set_global()
    ----> 4 ds.Tair[0].plot.pcolormesh(ax=ax, transform=ccrs.PlateCarree(), x='xc', y='yc', add_colorbar=False)
          5 ax.coastlines()
          6 ax.set_ylim([0,90]);

    NameError: name 'ds' is not defined

## 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.

    [7]:

    # define two-degree wide latitude bins
    lat_bins = np.arange(0,91,2)
    # define a label for each bin corresponding to the central latitude
    lat_center = np.arange(1,90,2)
    # group according to those bins and take the mean
    Tair_lat_mean = ds.Tair.groupby_bins('xc', lat_bins, labels=lat_center).mean(dim=xr.ALL_DIMS)
    # plot the result
    Tair_lat_mean.plot()

    ---------------------------------------------------------------------------
    NameError                                 Traceback (most recent call last)
    <ipython-input-7-53c25972f9a2> in <module>
          4 lat_center = np.arange(1,90,2)
          5 # group according to those bins and take the mean
    ----> 6 Tair_lat_mean = ds.Tair.groupby_bins('xc', lat_bins, labels=lat_center).mean(dim=xr.ALL_DIMS)
          7 # plot the result
          8 Tair_lat_mean.plot()

    NameError: name 'ds' is not defined

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`.

Note: This group-by-latitude approach does not take into account the finite-size geometry of grid cells. It simply bins each value according to the coordinates at the cell center. Xarray has no understanding of grid cells and their geometry. More precise geographic regridding for Xarray data is available via the xesmf package.

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