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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
[2]:
<xarray.DataArray 'air' (time: 730, lat: 25, lon: 53)> array([[[-31.2775 , -30.849998 , -30.475002 , ..., -39.7775 , -37.975 , -35.475002 ], [-28.575005 , -28.5775 , -28.874996 , ..., -41.9025 , -40.324997 , -36.85 ], [-19.149998 , -19.927498 , -21.3275 , ..., -41.675 , -39.454998 , -34.524998 ], ..., [ 23.15001 , 22.824997 , 22.849998 , ..., 22.747505 , 22.170013 , 21.795006 ], [ 23.174995 , 23.574997 , 23.592514 , ..., 23.022507 , 22.850006 , 22.397507 ], [ 23.470009 , 23.845001 , 23.950005 , ..., 23.872505 , 23.897507 , 23.82251 ]], [[-29.550003 , -29.650005 , -29.849998 , ..., -34.177498 , -32.3525 , -30.0775 ], [-25.3275 , -25.95 , -26.927498 , ..., -37.225 , -36.552498 , -34.550003 ], [-19.627502 , -21.0775 , -22.852497 , ..., -35.452496 , -34.277496 , -31.25 ], ... [ 23.215004 , 22.265 , 22.015007 , ..., 23.740005 , 23.195007 , 22.195 ], [ 24.3675 , 24.514992 , 23.895012 , ..., 23.415 , 22.995003 , 22.269997 ], [ 25.417496 , 25.592499 , 25.192497 , ..., 23.642502 , 23.190002 , 22.720001 ]], [[-28.935001 , -29.535 , -30.385002 , ..., -29.410004 , -28.960003 , -28.46 ], [-23.834995 , -24.060001 , -24.559998 , ..., -32.585 , -31.635002 , -30.035004 ], [-10.209999 , -10.784988 , -11.434998 , ..., -33.684998 , -31.035 , -27.135002 ], ..., [ 21.69001 , 21.990005 , 23.489998 , ..., 22.265007 , 22.015 , 21.415009 ], [ 23.390007 , 24.439995 , 24.94001 , ..., 22.415009 , 22.315002 , 21.640007 ], [ 24.840012 , 25.590004 , 25.54 , ..., 23.065002 , 22.715004 , 22.390007 ]]], dtype=float32) Coordinates: * lat (lat) float32 75.0 72.5 70.0 67.5 65.0 ... 25.0 22.5 20.0 17.5 15.0 * lon (lon) float32 200.0 202.5 205.0 207.5 ... 322.5 325.0 327.5 330.0 * time (time) datetime64[ns] 2013-01-01 2013-01-02 ... 2014-12-31
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()
[3]:
<cartopy.mpl.feature_artist.FeatureArtist at 0xffff58667590>

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
[4]:
<xarray.DataArray 'weights' (lat: 25)> array([0.25881907, 0.30070582, 0.34202015, 0.38268346, 0.42261827, 0.4617486 , 0.49999997, 0.5372996 , 0.57357645, 0.6087614 , 0.6427876 , 0.67559016, 0.70710677, 0.7372773 , 0.76604444, 0.7933533 , 0.81915206, 0.8433914 , 0.8660254 , 0.8870108 , 0.90630776, 0.9238795 , 0.9396926 , 0.95371693, 0.9659258 ], dtype=float32) Coordinates: * lat (lat) float32 75.0 72.5 70.0 67.5 65.0 ... 25.0 22.5 20.0 17.5 15.0 Attributes: standard_name: latitude long_name: Latitude units: degrees_north axis: Y
Weighted mean¶
[5]:
air_weighted = air.weighted(weights)
air_weighted
[5]:
DataArrayWeighted with weights along dimensions: lat
[6]:
weighted_mean = air_weighted.mean(("lon", "lat"))
weighted_mean
[6]:
<xarray.DataArray 'air' (time: 730)> array([ 6.092401 , 5.5279913, 5.6512904, 5.7862387, 5.911766 , 5.6834373, 5.976714 , 6.456723 , 6.571065 , 6.5046463, 6.1348996, 5.926867 , 5.826823 , 5.7228684, 5.578007 , 5.4655237, 5.09124 , 4.9860153, 5.228629 , 5.2516623, 5.4277263, 5.3877945, 5.433898 , 5.364401 , 5.4685388, 5.2290297, 5.3502855, 5.3418307, 5.37267 , 5.3595138, 5.140337 , 5.055567 , 5.072465 , 5.23522 , 5.3184857, 5.4991755, 5.720886 , 5.7286143, 5.7608094, 5.8255615, 6.268504 , 6.4369035, 6.5102324, 6.5647664, 6.6087837, 6.421267 , 5.914742 , 5.5546784, 5.329217 , 5.3359075, 5.07059 , 5.283736 , 5.595219 , 6.0546594, 6.5307307, 6.5074177, 6.391743 , 6.395127 , 6.3980885, 6.529374 , 6.4771113, 6.535766 , 6.692519 , 6.677368 , 6.511633 , 6.447034 , 6.860378 , 7.437535 , 7.698107 , 7.4842625, 7.2581897, 7.135959 , 7.0934076, 7.267086 , 7.3485355, 7.3217874, 7.2211447, 7.2129273, 7.284042 , 7.54338 , 7.8543735, 8.11584 , 8.261897 , 8.111622 , 8.219127 , 8.358713 , 8.716148 , 9.151885 , 9.370043 , 9.415864 , 9.073437 , 8.820656 , 8.804643 , 8.856381 , 9.0674515, 9.40715 , 9.696928 , 9.742079 , 9.659618 , 9.695613 , ... 16.536924 , 16.133308 , 16.05551 , 16.100082 , 15.909407 , 15.764092 , 15.631487 , 15.827746 , 16.026222 , 16.319872 , 16.156446 , 15.898447 , 15.830862 , 15.810077 , 15.589791 , 15.309618 , 15.105176 , 14.964679 , 14.966973 , 14.904602 , 14.61066 , 14.330113 , 14.255611 , 14.314032 , 13.940103 , 13.758864 , 13.820865 , 14.021832 , 13.888188 , 13.724708 , 13.190875 , 12.995149 , 12.66984 , 12.585032 , 12.377669 , 12.178653 , 12.082314 , 11.874204 , 11.660166 , 11.601135 , 11.558611 , 11.183846 , 11.237345 , 11.091917 , 10.472192 , 9.898911 , 9.431238 , 9.491593 , 9.688618 , 9.998573 , 9.7935505, 9.315284 , 9.2599325, 9.3849945, 9.343003 , 9.202585 , 9.472327 , 9.4242115, 9.050674 , 8.568184 , 7.7191467, 7.3312216, 7.4512987, 7.4235888, 7.5187955, 7.4950356, 7.623865 , 8.083244 , 8.04913 , 8.027267 , 8.069612 , 7.912531 , 8.042945 , 8.3448105, 8.507071 , 8.708198 , 8.60495 , 8.312464 , 8.257239 , 7.9841394, 7.693307 , 7.4219747, 7.4352374, 7.482958 , 7.6428432, 7.908468 , 8.036133 , 7.6254177, 7.753316 , 7.8504243, 7.6213007, 6.8473396, 6.4502635, 5.9852395, 5.5805774], dtype=float32) Coordinates: * time (time) datetime64[ns] 2013-01-01 2013-01-02 ... 2014-12-31
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()
[7]:
<matplotlib.legend.Legend at 0xffff583b4250>
