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Table of Contents
1 Compare weighted and unweighted mean temperature
1.0.1 Data
1.0.2 Creating weights
1.0.3 Weighted mean
1.0.4 Plot: comparison with unweighted mean
Compare weighted and unweighted mean temperature¶
Author: Mathias Hauser
We use the air_temperature
example dataset to calculate the area-weighted temperature over its domain. This dataset has a regular latitude/ longitude grid, thus the grid cell area decreases towards the pole. For this grid we can use the cosine of the latitude as proxy for the grid cell area.
[1]:
%matplotlib inline
import cartopy.crs as ccrs
import matplotlib.pyplot as plt
import numpy as np
import xarray as xr
Data¶
Load the data, convert to celsius, and resample to daily values
[2]:
ds = xr.tutorial.load_dataset("air_temperature")
# to celsius
air = ds.air - 273.15
# resample from 6-hourly to daily values
air = air.resample(time="D").mean()
air
---------------------------------------------------------------------------
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 0x7f8ccf8fd400>: 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/air_temperature.nc (Caused by NameResolutionError("<urllib3.connection.HTTPSConnection object at 0x7f8ccf8fd400>: 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.load_dataset("air_temperature")
3 # to celsius
4 air = ds.air - 273.15
File /usr/lib/python3/dist-packages/xarray/tutorial.py:213, in load_dataset(*args, **kwargs)
176 def load_dataset(*args, **kwargs) -> Dataset:
177 """
178 Open, load into memory, and close a dataset from the online repository
179 (requires internet).
(...)
211 load_dataset
212 """
--> 213 with open_dataset(*args, **kwargs) as ds:
214 return ds.load()
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: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/air_temperature.nc (Caused by NameResolutionError("<urllib3.connection.HTTPSConnection object at 0x7f8ccf8fd400>: Failed to resolve 'github.com' ([Errno -3] Temporary failure in name resolution)"))
Plot the first timestep:
[3]:
projection = ccrs.LambertConformal(central_longitude=-95, central_latitude=45)
f, ax = plt.subplots(subplot_kw=dict(projection=projection))
air.isel(time=0).plot(transform=ccrs.PlateCarree(), cbar_kwargs=dict(shrink=0.7))
ax.coastlines()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In[3], line 5
1 projection = ccrs.LambertConformal(central_longitude=-95, central_latitude=45)
3 f, ax = plt.subplots(subplot_kw=dict(projection=projection))
----> 5 air.isel(time=0).plot(transform=ccrs.PlateCarree(), cbar_kwargs=dict(shrink=0.7))
6 ax.coastlines()
NameError: name 'air' is not defined

Creating weights¶
For a rectangular grid the cosine of the latitude is proportional to the grid cell area.
[4]:
weights = np.cos(np.deg2rad(air.lat))
weights.name = "weights"
weights
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In[4], line 1
----> 1 weights = np.cos(np.deg2rad(air.lat))
2 weights.name = "weights"
3 weights
NameError: name 'air' is not defined
Weighted mean¶
[5]:
air_weighted = air.weighted(weights)
air_weighted
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In[5], line 1
----> 1 air_weighted = air.weighted(weights)
2 air_weighted
NameError: name 'air' is not defined
[6]:
weighted_mean = air_weighted.mean(("lon", "lat"))
weighted_mean
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In[6], line 1
----> 1 weighted_mean = air_weighted.mean(("lon", "lat"))
2 weighted_mean
NameError: name 'air_weighted' is not defined
Plot: comparison with unweighted mean¶
Note how the weighted mean temperature is higher than the unweighted.
[7]:
weighted_mean.plot(label="weighted")
air.mean(("lon", "lat")).plot(label="unweighted")
plt.legend()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In[7], line 1
----> 1 weighted_mean.plot(label="weighted")
2 air.mean(("lon", "lat")).plot(label="unweighted")
4 plt.legend()
NameError: name 'weighted_mean' is not defined