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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: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 0x7f453803c170>: 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/air_temperature.nc (Caused by NewConnectionError('<urllib3.connection.HTTPSConnection object at 0x7f453803c170>: 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.load_dataset("air_temperature")
3 # to celsius
4 air = ds.air - 273.15
File /usr/lib/python3/dist-packages/xarray/tutorial.py:207, in load_dataset(*args, **kwargs)
170 def load_dataset(*args, **kwargs) -> Dataset:
171 """
172 Open, load into memory, and close a dataset from the online repository
173 (requires internet).
(...)
205 load_dataset
206 """
--> 207 with open_dataset(*args, **kwargs) as ds:
208 return ds.load()
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/air_temperature.nc (Caused by NewConnectionError('<urllib3.connection.HTTPSConnection object at 0x7f453803c170>: Failed to establish a new connection: [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
