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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Working with Multidimensional Coordinates
Author
Step1:  As an example, consider this dataset from the xarray-data repository.
Step2:  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.
Step3:  Plotting
Let's examine these coordinate variables by plotting them.
Step4:  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.
Step5:  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.
Step6:  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.
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Python Code:
%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
Explanation: 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.
End of explanation
ds = xr.tutorial.open_dataset('rasm').load()
ds
Explanation: As an example, consider this dataset from the xarray-data repository.
End of explanation
print(ds.xc.attrs)
print(ds.yc.attrs)
Explanation: 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.
End of explanation
fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(14,4))
ds.xc.plot(ax=ax1)
ds.yc.plot(ax=ax2)
Explanation: Plotting
Let's examine these coordinate variables by plotting them.
End of explanation
ds.Tair[0].plot()
Explanation: 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.
End of explanation
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]);
Explanation: 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.
End of explanation
# 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()
Explanation: 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.
End of explanation
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