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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
---------------------------------------------------------------------------
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/python3.13/os.py:217, in makedirs(name, mode, exist_ok)
216 try:
--> 217 makedirs(head, exist_ok=exist_ok)
218 except FileExistsError:
219 # Defeats race condition when another thread created the path
File /usr/lib/python3.13/os.py:217, in makedirs(name, mode, exist_ok)
216 try:
--> 217 makedirs(head, exist_ok=exist_ok)
218 except FileExistsError:
219 # Defeats race condition when another thread created the path
File /usr/lib/python3.13/os.py:227, in makedirs(name, mode, exist_ok)
226 try:
--> 227 mkdir(name, mode)
228 except OSError:
229 # Cannot rely on checking for EEXIST, since the operating system
230 # 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.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: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.
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