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Calculating Seasonal Averages from Time Series of Monthly Means

Author: Joe Hamman

The data used for this example can be found in the xarray-data repository. You may need to change the path to rasm.nc below.

Suppose we have a netCDF or xarray.Dataset of monthly mean data and we want to calculate the seasonal average. To do this properly, we need to calculate the weighted average considering that each month has a different number of days.

[1]:
%matplotlib inline
import numpy as np
import pandas as pd
import xarray as xr
import matplotlib.pyplot as plt

Open the Dataset

[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.

Now for the heavy lifting:

We first have to come up with the weights, - calculate the month length for each monthly data record - calculate weights using groupby('time.season')

Finally, we just need to multiply our weights by the Dataset and sum along the time dimension. Creating a DataArray for the month length is as easy as using the days_in_month accessor on the time coordinate. The calendar type, in this case 'noleap', is automatically considered in this operation.

[3]:
month_length = ds.time.dt.days_in_month
month_length
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[3], line 1
----> 1 month_length = ds.time.dt.days_in_month
      2 month_length

NameError: name 'ds' is not defined
[4]:
# Calculate the weights by grouping by 'time.season'.
weights = (
    month_length.groupby("time.season") / month_length.groupby("time.season").sum()
)

# Test that the sum of the weights for each season is 1.0
np.testing.assert_allclose(weights.groupby("time.season").sum().values, np.ones(4))

# Calculate the weighted average
ds_weighted = (ds * weights).groupby("time.season").sum(dim="time")
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[4], line 3
      1 # Calculate the weights by grouping by 'time.season'.
      2 weights = (
----> 3     month_length.groupby("time.season") / month_length.groupby("time.season").sum()
      4 )
      6 # Test that the sum of the weights for each season is 1.0
      7 np.testing.assert_allclose(weights.groupby("time.season").sum().values, np.ones(4))

NameError: name 'month_length' is not defined
[5]:
ds_weighted
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[5], line 1
----> 1 ds_weighted

NameError: name 'ds_weighted' is not defined
[6]:
# only used for comparisons
ds_unweighted = ds.groupby("time.season").mean("time")
ds_diff = ds_weighted - ds_unweighted
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[6], line 2
      1 # only used for comparisons
----> 2 ds_unweighted = ds.groupby("time.season").mean("time")
      3 ds_diff = ds_weighted - ds_unweighted

NameError: name 'ds' is not defined
[7]:
# Quick plot to show the results
notnull = pd.notnull(ds_unweighted["Tair"][0])

fig, axes = plt.subplots(nrows=4, ncols=3, figsize=(14, 12))
for i, season in enumerate(("DJF", "MAM", "JJA", "SON")):
    ds_weighted["Tair"].sel(season=season).where(notnull).plot.pcolormesh(
        ax=axes[i, 0],
        vmin=-30,
        vmax=30,
        cmap="Spectral_r",
        add_colorbar=True,
        extend="both",
    )

    ds_unweighted["Tair"].sel(season=season).where(notnull).plot.pcolormesh(
        ax=axes[i, 1],
        vmin=-30,
        vmax=30,
        cmap="Spectral_r",
        add_colorbar=True,
        extend="both",
    )

    ds_diff["Tair"].sel(season=season).where(notnull).plot.pcolormesh(
        ax=axes[i, 2],
        vmin=-0.1,
        vmax=0.1,
        cmap="RdBu_r",
        add_colorbar=True,
        extend="both",
    )

    axes[i, 0].set_ylabel(season)
    axes[i, 1].set_ylabel("")
    axes[i, 2].set_ylabel("")

for ax in axes.flat:
    ax.axes.get_xaxis().set_ticklabels([])
    ax.axes.get_yaxis().set_ticklabels([])
    ax.axes.axis("tight")
    ax.set_xlabel("")

axes[0, 0].set_title("Weighted by DPM")
axes[0, 1].set_title("Equal Weighting")
axes[0, 2].set_title("Difference")

plt.tight_layout()

fig.suptitle("Seasonal Surface Air Temperature", fontsize=16, y=1.02)
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[7], line 2
      1 # Quick plot to show the results
----> 2 notnull = pd.notnull(ds_unweighted["Tair"][0])
      4 fig, axes = plt.subplots(nrows=4, ncols=3, figsize=(14, 12))
      5 for i, season in enumerate(("DJF", "MAM", "JJA", "SON")):

NameError: name 'ds_unweighted' is not defined
[8]:
# Wrap it into a simple function
def season_mean(ds, calendar="standard"):
    # Make a DataArray with the number of days in each month, size = len(time)
    month_length = ds.time.dt.days_in_month

    # Calculate the weights by grouping by 'time.season'
    weights = (
        month_length.groupby("time.season") / month_length.groupby("time.season").sum()
    )

    # Test that the sum of the weights for each season is 1.0
    np.testing.assert_allclose(weights.groupby("time.season").sum().values, np.ones(4))

    # Calculate the weighted average
    return (ds * weights).groupby("time.season").sum(dim="time")