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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

    ---------------------------------------------------------------------------
    PermissionError                           Traceback (most recent call last)
    File /usr/lib/python3/dist-packages/pooch/utils.py:262, in make_local_storage(path, env)
        258 if action == "create":
        259     # When running in parallel, it's possible that multiple jobs will
        260     # try to create the path at the same time. Use exist_ok to avoid
        261     # raising an error.
    --> 262     os.makedirs(path, exist_ok=True)
        263 else:

    File /usr/lib/python3.13/os.py:217, in makedirs(name, mode, exist_ok)
        216 try:
    --> 217     makedirs(head, exist_ok=exist_ok)
        218 except FileExistsError:
        219     # Defeats race condition when another thread created the path

    File /usr/lib/python3.13/os.py:217, in makedirs(name, mode, exist_ok)
        216 try:
    --> 217     makedirs(head, exist_ok=exist_ok)
        218 except FileExistsError:
        219     # Defeats race condition when another thread created the path

    File /usr/lib/python3.13/os.py:227, in makedirs(name, mode, exist_ok)
        226 try:
    --> 227     mkdir(name, mode)
        228 except OSError:
        229     # Cannot rely on checking for EEXIST, since the operating system
        230     # could give priority to other errors like EACCES or EROFS

    PermissionError: [Errno 13] Permission denied: '/sbuild-nonexistent'

    The above exception was the direct cause of the following exception:

    PermissionError                           Traceback (most recent call last)
    Cell In[2], line 1
    ----> 1 ds = xr.tutorial.open_dataset("rasm").load()
          2 ds

    File /usr/lib/python3/dist-packages/xarray/tutorial.py:165, in open_dataset(name, cache, cache_dir, engine, **kws)
        162 downloader = pooch.HTTPDownloader(headers=headers)
        164 # retrieve the file
    --> 165 filepath = pooch.retrieve(
        166     url=url, known_hash=None, path=cache_dir, downloader=downloader
        167 )
        168 ds = _open_dataset(filepath, engine=engine, **kws)
        169 if not cache:

    File /usr/lib/python3/dist-packages/pooch/core.py:227, in retrieve(url, known_hash, fname, path, processor, downloader, progressbar)
        222 action, verb = download_action(full_path, known_hash)
        224 if action in ("download", "update"):
        225     # We need to write data, so create the local data directory if it
        226     # doesn't already exist.
    --> 227     make_local_storage(path)
        229     get_logger().info(
        230         "%s data from '%s' to file '%s'.",
        231         verb,
        232         url,
        233         str(full_path),
        234     )
        236     if downloader is None:

    File /usr/lib/python3/dist-packages/pooch/utils.py:276, in make_local_storage(path, env)
        272 if env is not None:
        273     message.append(
        274         f"Use environment variable '{env}' to specify a different location."
        275     )
    --> 276 raise PermissionError(" ".join(message)) from error

    PermissionError: [Errno 13] Permission denied: '/sbuild-nonexistent' | Pooch could not create data cache folder '/sbuild-nonexistent/.cache/xarray_tutorial_data'. Will not be able to download data files.

In this example, the logical coordinates are `x` and `y`, while the physical coordinates are `xc` and `yc`, which represent the longitudes and latitudes of the data.

    [3]:

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

    ---------------------------------------------------------------------------
    NameError                                 Traceback (most recent call last)
    Cell In[3], line 1
    ----> 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)
    Cell In[4], line 2
          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)
    Cell In[5], line 1
    ----> 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)
    Cell In[6], line 4
          2 ax = plt.axes(projection=ccrs.PlateCarree())
          3 ax.set_global()
    ----> 4 ds.Tair[0].plot.pcolormesh(
          5     ax=ax, transform=ccrs.PlateCarree(), x="xc", y="yc", add_colorbar=False
          6 )
          7 ax.coastlines()
          8 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("yc", lat_bins, labels=lat_center).mean(
        dim=xr.ALL_DIMS
    )
    # plot the result
    Tair_lat_mean.plot()

    ---------------------------------------------------------------------------
    NameError                                 Traceback (most recent call last)
    Cell In[7], line 6
          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("yc", lat_bins, labels=lat_center).mean(
          7     dim=xr.ALL_DIMS
          8 )
          9 # plot the result
         10 Tair_lat_mean.plot()

    NameError: name 'ds' is not defined

The resulting coordinate for the `groupby_bins` operation got the `_bins` suffix appended: `yc_bins`. This help us distinguish it from the original multidimensional variable `yc`.

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.