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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/python3.12/os.py:215, in makedirs(name, mode, exist_ok)
214 try:
--> 215 makedirs(head, exist_ok=exist_ok)
216 except FileExistsError:
217 # Defeats race condition when another thread created the path
File /usr/lib/python3.12/os.py:215, in makedirs(name, mode, exist_ok)
214 try:
--> 215 makedirs(head, exist_ok=exist_ok)
216 except FileExistsError:
217 # Defeats race condition when another thread created the path
File /usr/lib/python3.12/os.py:225, in makedirs(name, mode, exist_ok)
224 try:
--> 225 mkdir(name, mode)
226 except OSError:
227 # Cannot rely on checking for EEXIST, since the operating system
228 # 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:161, in open_dataset(name, cache, cache_dir, engine, **kws)
158 url = f"{base_url}/raw/{version}/{path.name}"
160 # retrieve the file
--> 161 filepath = pooch.retrieve(url=url, known_hash=None, path=cache_dir)
162 ds = _open_dataset(filepath, engine=engine, **kws)
163 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")