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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
---------------------------------------------------------------------------
gaierror                                  Traceback (most recent call last)
File /usr/lib/python3/dist-packages/urllib3/connection.py:198, in HTTPConnection._new_conn(self)
    197 try:
--> 198     sock = connection.create_connection(
    199         (self._dns_host, self.port),
    200         self.timeout,
    201         source_address=self.source_address,
    202         socket_options=self.socket_options,
    203     )
    204 except socket.gaierror as e:

File /usr/lib/python3/dist-packages/urllib3/util/connection.py:60, in create_connection(address, timeout, source_address, socket_options)
     58     raise LocationParseError(f"'{host}', label empty or too long") from None
---> 60 for res in socket.getaddrinfo(host, port, family, socket.SOCK_STREAM):
     61     af, socktype, proto, canonname, sa = res

File /usr/lib/python3.13/socket.py:977, in getaddrinfo(host, port, family, type, proto, flags)
    976 addrlist = []
--> 977 for res in _socket.getaddrinfo(host, port, family, type, proto, flags):
    978     af, socktype, proto, canonname, sa = res

gaierror: [Errno -3] Temporary failure in name resolution

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

NameResolutionError                       Traceback (most recent call last)
File /usr/lib/python3/dist-packages/urllib3/connectionpool.py:787, in HTTPConnectionPool.urlopen(self, method, url, body, headers, retries, redirect, assert_same_host, timeout, pool_timeout, release_conn, chunked, body_pos, preload_content, decode_content, **response_kw)
    786 # Make the request on the HTTPConnection object
--> 787 response = self._make_request(
    788     conn,
    789     method,
    790     url,
    791     timeout=timeout_obj,
    792     body=body,
    793     headers=headers,
    794     chunked=chunked,
    795     retries=retries,
    796     response_conn=response_conn,
    797     preload_content=preload_content,
    798     decode_content=decode_content,
    799     **response_kw,
    800 )
    802 # Everything went great!

File /usr/lib/python3/dist-packages/urllib3/connectionpool.py:488, in HTTPConnectionPool._make_request(self, conn, method, url, body, headers, retries, timeout, chunked, response_conn, preload_content, decode_content, enforce_content_length)
    487         new_e = _wrap_proxy_error(new_e, conn.proxy.scheme)
--> 488     raise new_e
    490 # conn.request() calls http.client.*.request, not the method in
    491 # urllib3.request. It also calls makefile (recv) on the socket.

File /usr/lib/python3/dist-packages/urllib3/connectionpool.py:464, in HTTPConnectionPool._make_request(self, conn, method, url, body, headers, retries, timeout, chunked, response_conn, preload_content, decode_content, enforce_content_length)
    463 try:
--> 464     self._validate_conn(conn)
    465 except (SocketTimeout, BaseSSLError) as e:

File /usr/lib/python3/dist-packages/urllib3/connectionpool.py:1093, in HTTPSConnectionPool._validate_conn(self, conn)
   1092 if conn.is_closed:
-> 1093     conn.connect()
   1095 # TODO revise this, see https://github.com/urllib3/urllib3/issues/2791

File /usr/lib/python3/dist-packages/urllib3/connection.py:704, in HTTPSConnection.connect(self)
    703 sock: socket.socket | ssl.SSLSocket
--> 704 self.sock = sock = self._new_conn()
    705 server_hostname: str = self.host

File /usr/lib/python3/dist-packages/urllib3/connection.py:205, in HTTPConnection._new_conn(self)
    204 except socket.gaierror as e:
--> 205     raise NameResolutionError(self.host, self, e) from e
    206 except SocketTimeout as e:

NameResolutionError: <urllib3.connection.HTTPSConnection object at 0x7fec4b7fd7f0>: Failed to resolve 'github.com' ([Errno -3] Temporary failure in name resolution)

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

MaxRetryError                             Traceback (most recent call last)
File /usr/lib/python3/dist-packages/requests/adapters.py:667, in HTTPAdapter.send(self, request, stream, timeout, verify, cert, proxies)
    666 try:
--> 667     resp = conn.urlopen(
    668         method=request.method,
    669         url=url,
    670         body=request.body,
    671         headers=request.headers,
    672         redirect=False,
    673         assert_same_host=False,
    674         preload_content=False,
    675         decode_content=False,
    676         retries=self.max_retries,
    677         timeout=timeout,
    678         chunked=chunked,
    679     )
    681 except (ProtocolError, OSError) as err:

File /usr/lib/python3/dist-packages/urllib3/connectionpool.py:841, in HTTPConnectionPool.urlopen(self, method, url, body, headers, retries, redirect, assert_same_host, timeout, pool_timeout, release_conn, chunked, body_pos, preload_content, decode_content, **response_kw)
    839     new_e = ProtocolError("Connection aborted.", new_e)
--> 841 retries = retries.increment(
    842     method, url, error=new_e, _pool=self, _stacktrace=sys.exc_info()[2]
    843 )
    844 retries.sleep()

File /usr/lib/python3/dist-packages/urllib3/util/retry.py:519, in Retry.increment(self, method, url, response, error, _pool, _stacktrace)
    518     reason = error or ResponseError(cause)
--> 519     raise MaxRetryError(_pool, url, reason) from reason  # type: ignore[arg-type]
    521 log.debug("Incremented Retry for (url='%s'): %r", url, new_retry)

MaxRetryError: HTTPSConnectionPool(host='github.com', port=443): Max retries exceeded with url: /pydata/xarray-data/raw/master/rasm.nc (Caused by NameResolutionError("<urllib3.connection.HTTPSConnection object at 0x7fec4b7fd7f0>: Failed to resolve 'github.com' ([Errno -3] Temporary failure in name resolution)"))

During handling of the above exception, another exception occurred:

ConnectionError                           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:167, in open_dataset(name, cache, cache_dir, engine, **kws)
    164 downloader = pooch.HTTPDownloader(headers=headers)
    166 # retrieve the file
--> 167 filepath = pooch.retrieve(
    168     url=url, known_hash=None, path=cache_dir, downloader=downloader
    169 )
    170 ds = _open_dataset(filepath, engine=engine, **kws)
    171 if not cache:

File /usr/lib/python3/dist-packages/pooch/core.py:239, in retrieve(url, known_hash, fname, path, processor, downloader, progressbar)
    236 if downloader is None:
    237     downloader = choose_downloader(url, progressbar=progressbar)
--> 239 stream_download(url, full_path, known_hash, downloader, pooch=None)
    241 if known_hash is None:
    242     get_logger().info(
    243         "SHA256 hash of downloaded file: %s\n"
    244         "Use this value as the 'known_hash' argument of 'pooch.retrieve'"
   (...)
    247         file_hash(str(full_path)),
    248     )

File /usr/lib/python3/dist-packages/pooch/core.py:807, in stream_download(url, fname, known_hash, downloader, pooch, retry_if_failed)
    803 try:
    804     # Stream the file to a temporary so that we can safely check its
    805     # hash before overwriting the original.
    806     with temporary_file(path=str(fname.parent)) as tmp:
--> 807         downloader(url, tmp, pooch)
    808         hash_matches(tmp, known_hash, strict=True, source=str(fname.name))
    809         shutil.move(tmp, str(fname))

File /usr/lib/python3/dist-packages/pooch/downloaders.py:220, in HTTPDownloader.__call__(self, url, output_file, pooch, check_only)
    218     # pylint: enable=consider-using-with
    219 try:
--> 220     response = requests.get(url, timeout=timeout, **kwargs)
    221     response.raise_for_status()
    222     content = response.iter_content(chunk_size=self.chunk_size)

File /usr/lib/python3/dist-packages/requests/api.py:73, in get(url, params, **kwargs)
     62 def get(url, params=None, **kwargs):
     63     r"""Sends a GET request.
     64
     65     :param url: URL for the new :class:`Request` object.
   (...)
     70     :rtype: requests.Response
     71     """
---> 73     return request("get", url, params=params, **kwargs)

File /usr/lib/python3/dist-packages/requests/api.py:59, in request(method, url, **kwargs)
     55 # By using the 'with' statement we are sure the session is closed, thus we
     56 # avoid leaving sockets open which can trigger a ResourceWarning in some
     57 # cases, and look like a memory leak in others.
     58 with sessions.Session() as session:
---> 59     return session.request(method=method, url=url, **kwargs)

File /usr/lib/python3/dist-packages/requests/sessions.py:589, in Session.request(self, method, url, params, data, headers, cookies, files, auth, timeout, allow_redirects, proxies, hooks, stream, verify, cert, json)
    584 send_kwargs = {
    585     "timeout": timeout,
    586     "allow_redirects": allow_redirects,
    587 }
    588 send_kwargs.update(settings)
--> 589 resp = self.send(prep, **send_kwargs)
    591 return resp

File /usr/lib/python3/dist-packages/requests/sessions.py:703, in Session.send(self, request, **kwargs)
    700 start = preferred_clock()
    702 # Send the request
--> 703 r = adapter.send(request, **kwargs)
    705 # Total elapsed time of the request (approximately)
    706 elapsed = preferred_clock() - start

File /usr/lib/python3/dist-packages/requests/adapters.py:700, in HTTPAdapter.send(self, request, stream, timeout, verify, cert, proxies)
    696     if isinstance(e.reason, _SSLError):
    697         # This branch is for urllib3 v1.22 and later.
    698         raise SSLError(e, request=request)
--> 700     raise ConnectionError(e, request=request)
    702 except ClosedPoolError as e:
    703     raise ConnectionError(e, request=request)

ConnectionError: HTTPSConnectionPool(host='github.com', port=443): Max retries exceeded with url: /pydata/xarray-data/raw/master/rasm.nc (Caused by NameResolutionError("<urllib3.connection.HTTPSConnection object at 0x7fec4b7fd7f0>: Failed to resolve 'github.com' ([Errno -3] Temporary failure in name resolution)"))

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")