You can run this notebook in a live session 
or view it on Github.
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:174, in HTTPConnection._new_conn(self)
173 try:
--> 174 conn = connection.create_connection(
175 (self._dns_host, self.port), self.timeout, **extra_kw
176 )
178 except SocketTimeout:
File /usr/lib/python3/dist-packages/urllib3/util/connection.py:73, in create_connection(address, timeout, source_address, socket_options)
69 return six.raise_from(
70 LocationParseError("'%s', label empty or too long" % host), None
71 )
---> 73 for res in socket.getaddrinfo(host, port, family, socket.SOCK_STREAM):
74 af, socktype, proto, canonname, sa = res
File /usr/lib/python3.12/socket.py:964, in getaddrinfo(host, port, family, type, proto, flags)
963 addrlist = []
--> 964 for res in _socket.getaddrinfo(host, port, family, type, proto, flags):
965 af, socktype, proto, canonname, sa = res
gaierror: [Errno -3] Temporary failure in name resolution
During handling of the above exception, another exception occurred:
NewConnectionError Traceback (most recent call last)
File /usr/lib/python3/dist-packages/urllib3/connectionpool.py:716, in HTTPConnectionPool.urlopen(self, method, url, body, headers, retries, redirect, assert_same_host, timeout, pool_timeout, release_conn, chunked, body_pos, **response_kw)
715 # Make the request on the httplib connection object.
--> 716 httplib_response = self._make_request(
717 conn,
718 method,
719 url,
720 timeout=timeout_obj,
721 body=body,
722 headers=headers,
723 chunked=chunked,
724 )
726 # If we're going to release the connection in ``finally:``, then
727 # the response doesn't need to know about the connection. Otherwise
728 # it will also try to release it and we'll have a double-release
729 # mess.
File /usr/lib/python3/dist-packages/urllib3/connectionpool.py:405, in HTTPConnectionPool._make_request(self, conn, method, url, timeout, chunked, **httplib_request_kw)
404 try:
--> 405 self._validate_conn(conn)
406 except (SocketTimeout, BaseSSLError) as e:
407 # Py2 raises this as a BaseSSLError, Py3 raises it as socket timeout.
File /usr/lib/python3/dist-packages/urllib3/connectionpool.py:1059, in HTTPSConnectionPool._validate_conn(self, conn)
1058 if not getattr(conn, "sock", None): # AppEngine might not have `.sock`
-> 1059 conn.connect()
1061 if not conn.is_verified:
File /usr/lib/python3/dist-packages/urllib3/connection.py:363, in HTTPSConnection.connect(self)
361 def connect(self):
362 # Add certificate verification
--> 363 self.sock = conn = self._new_conn()
364 hostname = self.host
File /usr/lib/python3/dist-packages/urllib3/connection.py:186, in HTTPConnection._new_conn(self)
185 except SocketError as e:
--> 186 raise NewConnectionError(
187 self, "Failed to establish a new connection: %s" % e
188 )
190 return conn
NewConnectionError: <urllib3.connection.HTTPSConnection object at 0x7f3fa95feb70>: Failed to establish a new connection: [Errno -3] Temporary failure in name resolution
During handling of the above exception, another exception occurred:
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:800, in HTTPConnectionPool.urlopen(self, method, url, body, headers, retries, redirect, assert_same_host, timeout, pool_timeout, release_conn, chunked, body_pos, **response_kw)
798 e = ProtocolError("Connection aborted.", e)
--> 800 retries = retries.increment(
801 method, url, error=e, _pool=self, _stacktrace=sys.exc_info()[2]
802 )
803 retries.sleep()
File /usr/lib/python3/dist-packages/urllib3/util/retry.py:592, in Retry.increment(self, method, url, response, error, _pool, _stacktrace)
591 if new_retry.is_exhausted():
--> 592 raise MaxRetryError(_pool, url, error or ResponseError(cause))
594 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 NewConnectionError('<urllib3.connection.HTTPSConnection object at 0x7f3fa95feb70>: Failed to establish a new connection: [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: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: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:208, in HTTPDownloader.__call__(self, url, output_file, pooch, check_only)
206 output_file = open(output_file, "w+b")
207 try:
--> 208 response = requests.get(url, **kwargs)
209 response.raise_for_status()
210 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 NewConnectionError('<urllib3.connection.HTTPSConnection object at 0x7f3fa95feb70>: Failed to establish a new connection: [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")
