You can run this notebook in a live session 
or view it on Github.
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 gridcell 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
- -31.2775 -30.849998 -30.475002 ... 23.065002 22.715004 22.390007
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 ], ..., [ 22.972504 , 22.24501 , 22.049995 , ..., 22.99501 , 22.720001 , 22.0225 ], [ 23.972504 , 23.647507 , 22.9225 , ..., 23.497498 , 23.622505 , 23.070007 ], [ 24.545006 , 24.372513 , 23.875 , ..., 23.975006 , 23.997505 , 24.100006 ]], [[-29.2775 , -29.1525 , -29.177502 , ..., -33.6525 , -31.599998 , -29.25 ], [-27.552498 , -26.900002 , -26.729996 , ..., -36.727497 , -35.5275 , -33.125 ], [-20.975002 , -20.474998 , -20.649998 , ..., -32.127495 , -30.350002 , -27.454998 ], ..., [ 23.395004 , 22.57251 , 22.425003 , ..., 22.625 , 21.850006 , 21.150002 ], [ 24.222504 , 23.674995 , 23.07251 , ..., 23.092514 , 22.850006 , 22.345009 ], [ 24.625 , 24.345001 , 24.095001 , ..., 24.174995 , 24.1725 , 24.32251 ]], ..., [[-13.055 , -13.154995 , -13.682495 , ..., -23.23 , -24.5075 , -25.780003 ], [ -6.6524963, -6.207489 , -6.404991 , ..., -20.155003 , -20.005001 , -19.477505 ], [ -6.757492 , -6.8074875, -6.8799896, ..., -16.435001 , -14.129997 , -11.229996 ], ..., [ 21.519997 , 20.870003 , 20.9225 , ..., 24.322502 , 23.895004 , 22.920006 ], [ 22.792511 , 22.897507 , 22.7725 , ..., 24.6175 , 24.097504 , 22.967506 ], [ 24.297493 , 24.620003 , 24.2975 , ..., 24.947502 , 24.542496 , 23.970001 ]], [[-25.130001 , -24.405003 , -23.755005 , ..., -24.1325 , -24.807495 , -25.685001 ], [-21.93 , -20.805 , -19.805004 , ..., -29.032505 , -28.0075 , -26.382504 ], [-14.830006 , -14.380005 , -13.959999 , ..., -28.579998 , -25.085 , -20.382504 ], ..., [ 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) - time(time)datetime64[ns]2013-01-01 ... 2014-12-31
array(['2013-01-01T00:00:00.000000000', '2013-01-02T00:00:00.000000000', '2013-01-03T00:00:00.000000000', ..., '2014-12-29T00:00:00.000000000', '2014-12-30T00:00:00.000000000', '2014-12-31T00:00:00.000000000'], dtype='datetime64[ns]') - lat(lat)float3275.0 72.5 70.0 ... 20.0 17.5 15.0
- standard_name :
- latitude
- long_name :
- Latitude
- units :
- degrees_north
- axis :
- Y
array([75. , 72.5, 70. , 67.5, 65. , 62.5, 60. , 57.5, 55. , 52.5, 50. , 47.5, 45. , 42.5, 40. , 37.5, 35. , 32.5, 30. , 27.5, 25. , 22.5, 20. , 17.5, 15. ], dtype=float32) - lon(lon)float32200.0 202.5 205.0 ... 327.5 330.0
- standard_name :
- longitude
- long_name :
- Longitude
- units :
- degrees_east
- axis :
- X
array([200. , 202.5, 205. , 207.5, 210. , 212.5, 215. , 217.5, 220. , 222.5, 225. , 227.5, 230. , 232.5, 235. , 237.5, 240. , 242.5, 245. , 247.5, 250. , 252.5, 255. , 257.5, 260. , 262.5, 265. , 267.5, 270. , 272.5, 275. , 277.5, 280. , 282.5, 285. , 287.5, 290. , 292.5, 295. , 297.5, 300. , 302.5, 305. , 307.5, 310. , 312.5, 315. , 317.5, 320. , 322.5, 325. , 327.5, 330. ], dtype=float32)
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 0x7f3e04414e50>
/home/docs/checkouts/readthedocs.org/user_builds/xray/conda/v0.15.1/lib/python3.8/site-packages/cartopy/io/__init__.py:260: DownloadWarning: Downloading: http://naciscdn.org/naturalearth/110m/physical/ne_110m_coastline.zip
warnings.warn('Downloading: {}'.format(url), DownloadWarning)
Creating weights¶
For a 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
- 0.25881907 0.30070582 0.34202015 ... 0.9396926 0.95371693 0.9659258
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) - lat(lat)float3275.0 72.5 70.0 ... 20.0 17.5 15.0
- standard_name :
- latitude
- long_name :
- Latitude
- units :
- degrees_north
- axis :
- Y
array([75. , 72.5, 70. , 67.5, 65. , 62.5, 60. , 57.5, 55. , 52.5, 50. , 47.5, 45. , 42.5, 40. , 37.5, 35. , 32.5, 30. , 27.5, 25. , 22.5, 20. , 17.5, 15. ], dtype=float32)
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
- time: 730
- 6.092401 5.5279922 5.6512914 5.786239 ... 6.4502645 5.985239 5.5805774
array([ 6.092401 , 5.5279922, 5.6512914, 5.786239 , 5.9117665, 5.6834373, 5.9767127, 6.456724 , 6.5710645, 6.504647 , 6.134899 , 5.926867 , 5.8268237, 5.7228684, 5.5780067, 5.4655232, 5.09124 , 4.9860163, 5.22863 , 5.2516627, 5.4277263, 5.3877945, 5.4338994, 5.364401 , 5.4685388, 5.2290297, 5.350285 , 5.3418307, 5.372671 , 5.3595133, 5.1403375, 5.0555673, 5.0724645, 5.23522 , 5.3184857, 5.4991755, 5.720886 , 5.7286143, 5.7608094, 5.825561 , 6.268504 , 6.436903 , 6.510233 , 6.564767 , 6.6087847, 6.4212685, 5.9147425, 5.5546775, 5.329217 , 5.3359075, 5.0705895, 5.283736 , 5.5952206, 6.05466 , 6.530731 , 6.507418 , 6.3917418, 6.3951263, 6.3980885, 6.5293736, 6.4771113, 6.535765 , 6.692519 , 6.6773686, 6.511633 , 6.4470334, 6.860378 , 7.437535 , 7.6981063, 7.484263 , 7.2581897, 7.135959 , 7.093408 , 7.267086 , 7.348537 , 7.3217864, 7.221145 , 7.212927 , 7.2840424, 7.54338 , 7.854373 , 8.11584 , 8.261896 , 8.111622 , 8.219126 , 8.358713 , 8.716147 , 9.151885 , 9.370043 , 9.415865 , 9.073439 , 8.820655 , 8.804644 , 8.856381 , 9.0674515, 9.40715 , 9.696928 , 9.742079 , 9.659618 , 9.695613 , 9.561744 , 9.4079895, 9.617972 , 9.76423 , 9.68687 , 9.507037 , 9.583357 , 9.536606 , 9.149774 , 9.206877 , 9.712005 , 9.949959 , 10.212819 , 10.352596 , 10.463948 , 10.969345 , 11.17319 , 11.37765 , 11.666062 , 11.5937605, 11.5184355, 11.372785 , 11.2966 , 11.389726 , 11.630326 , 12.04973 , 12.28303 , 12.51103 , 12.665153 , 12.658167 , 12.697796 , 12.935123 , 13.231032 , 13.601825 , 13.677147 , 13.944387 , 14.055336 , 14.044068 , 14.039132 , 14.049725 , 14.107756 , 14.125751 , 14.220755 , 14.389268 , 14.666479 , 14.894946 , 15.093599 , 15.187727 , 15.229364 , 15.385192 , 15.517196 , 15.576119 , 15.46246 , 15.336645 , 15.5871935, 15.935525 , 16.160788 , 16.362488 , 16.402073 , 16.613111 , 16.690079 , 16.710402 , 16.957804 , 17.036436 , 17.024513 , 17.113266 , 17.403803 , 17.471989 , 17.354223 , 17.286469 , 17.469456 , 17.691341 , 17.808374 , 18.005512 , 18.180136 , 18.14735 , 18.087774 , 18.541489 , 18.812765 , 18.772768 , 18.774654 , 18.75971 , 18.61955 , 18.493517 , 18.666697 , 18.623306 , 18.700373 , 18.745745 , 18.938585 , 19.04691 , 19.034967 , 18.728828 , 18.678013 , 18.704285 , 18.970568 , 19.138163 , 19.204895 , 19.254156 , 19.216059 , 19.307415 , 19.161972 , 19.060398 , 19.24664 , 19.396854 , 19.503927 , 19.524248 , 19.532833 , 19.501417 , 19.38236 , 19.44305 , 19.590784 , 19.67537 , 19.759476 , 19.736116 , 19.748497 , 19.778793 , 19.929216 , 19.915003 , 19.93247 , 19.816433 , 19.897675 , 19.921324 , 20.089659 , 20.174969 , 20.020954 , 19.916275 , 19.674044 , 19.609095 , 19.70313 , 19.742498 , 19.547344 , 19.40055 , 19.364971 , 19.30133 , 19.32931 , 19.252117 , 19.19223 , 19.12292 , 19.05988 , 18.91547 , 18.972017 , 19.109762 , 19.17509 , 18.943657 , 18.778591 , 18.799852 , 18.990286 , 19.173693 , 19.13864 , 19.046425 , 18.653067 , 18.528996 , 18.39046 , 18.382334 , 18.224634 , 18.074722 , 17.809874 , 17.728031 , 17.559685 , 17.185799 , 17.007568 , 16.844471 , 16.628885 , 16.632135 , 16.684452 , 16.7827 , 16.902582 , 16.982395 , 16.94174 , 16.731483 , 16.569954 , 16.642183 , 16.44107 , 16.32606 , 16.18429 , 15.9199915, 15.794434 , 15.333749 , 15.139457 , 15.239242 , 15.183755 , 15.217643 , 15.256958 , 15.194689 , 15.338222 , 15.195775 , 14.989729 , 15.019909 , 14.836974 , 14.780034 , 14.746626 , 14.643647 , 14.434376 , 14.174599 , 13.690615 , 13.393573 , 13.324159 , 13.234417 , 13.105837 , 12.825273 , 12.590388 , 12.360748 , 12.4433975, 12.511931 , 12.623505 , 12.464619 , 11.873396 , 11.3994465, 11.027147 , 11.073167 , 10.917732 , 10.710046 , 10.599323 , 10.606334 , 10.488928 , 10.463197 , 10.3303175, 10.669272 , 10.642239 , 10.355392 , 10.218304 , 10.060601 , 9.39898 , 8.9061985, 8.508362 , 8.3262005, 8.183812 , 8.244926 , 8.287311 , 8.149289 , 7.8001986, 7.683447 , 7.886427 , 7.908317 , 8.032764 , 8.3206215, 8.253178 , 7.9912343, 7.34998 , 6.836603 , 6.3923655, 6.120939 , 5.973691 , 5.8665175, 5.5887747, 5.2916183, 5.564002 , 5.691005 , 5.80986 , 6.1114473, 6.0680313, 6.117207 , 6.0920706, 5.9908032, 5.9610896, 5.9642596, 5.702404 , 5.974395 , 5.7453547, 5.720085 , 5.7497687, 5.9001875, 5.3603168, 4.975006 , 5.034215 , 4.940766 , 4.8569155, 5.053116 , 5.1932135, 5.154923 , 4.8237185, 4.9460754, 5.5160084, 6.096235 , 6.306667 , 6.5905867, 6.879803 , 7.4664016, 7.676546 , 7.454749 , 7.2756977, 6.8854356, 6.8190045, 7.000944 , 6.9153275, 6.518248 , 6.376813 , 6.1025376, 5.836243 , 6.2818537, 6.7731247, 6.2265654, 5.8736043, 5.888508 , 6.1134453, 6.2495136, 6.5044417, 6.24279 , 5.889445 , 5.349453 , 5.1401687, 4.6669383, 4.414816 , 4.721158 , 4.9752355, 4.608664 , 4.661077 , 4.349577 , 4.6422057, 5.1544943, 5.759283 , 5.732609 , 6.1441774, 6.4816713, 6.8110523, 6.8179736, 6.5025144, 6.6047516, 6.3821716, 5.914061 , 5.7290044, 5.559222 , 5.483134 , 5.661207 , 5.625481 , 5.448103 , 5.1356015, 4.9774427, 5.2434754, 5.8586645, 6.168095 , 6.305263 , 6.4765425, 6.870062 , 7.175213 , 7.3970156, 7.301994 , 7.3982806, 7.2345557, 7.2241607, 7.2945085, 7.289131 , 7.447318 , 7.640786 , 7.600175 , 7.36517 , 7.075017 , 6.9393187, 6.971508 , 6.862118 , 7.409107 , 7.8365316, 8.264829 , 8.424241 , 8.335242 , 8.2654295, 8.436648 , 8.637371 , 8.597472 , 8.744505 , 9.08334 , 9.472183 , 9.498424 , 9.722453 , 9.790919 , 9.929076 , 9.949384 , 9.750111 , 9.586125 , 9.281569 , 9.379645 , 9.647652 , 10.149494 , 10.374341 , 10.813217 , 11.019511 , 11.4107485, 11.348444 , 11.275326 , 11.391884 , 11.480863 , 11.496771 , 11.4580965, 11.741908 , 12.039109 , 12.119159 , 12.294326 , 12.496779 , 12.63022 , 12.644609 , 12.698251 , 12.771256 , 12.8391485, 12.969559 , 13.328925 , 13.524718 , 13.442509 , 13.43661 , 13.444263 , 13.500961 , 13.596045 , 13.940781 , 14.161496 , 14.333419 , 14.536955 , 14.600366 , 14.704756 , 15.068306 , 15.144813 , 15.133619 , 15.378984 , 15.531531 , 15.775833 , 15.857242 , 15.643098 , 15.790469 , 15.875157 , 15.876257 , 15.883789 , 16.18826 , 16.136084 , 16.061764 , 16.140556 , 16.192955 , 16.183643 , 16.596642 , 16.691175 , 16.750244 , 16.765684 , 16.822803 , 16.830599 , 17.189337 , 17.297546 , 17.34677 , 17.249882 , 17.421677 , 17.662115 , 17.73621 , 17.911348 , 18.158567 , 18.063082 , 18.149403 , 18.307577 , 18.539606 , 18.647154 , 18.710331 , 18.558868 , 18.850899 , 18.846672 , 18.771374 , 18.881458 , 18.969193 , 19.0445 , 19.062105 , 18.9497 , 18.962055 , 19.090527 , 19.243608 , 19.44696 , 19.593018 , 19.392294 , 19.387154 , 19.369015 , 19.36154 , 19.38268 , 19.553045 , 19.74886 , 20.010616 , 20.067825 , 19.960098 , 19.71552 , 19.759594 , 19.94238 , 19.978153 , 19.960987 , 20.020414 , 20.074722 , 20.038465 , 19.872437 , 20.054897 , 20.122032 , 20.110695 , 20.11393 , 19.893097 , 19.756624 , 19.817728 , 19.870953 , 20.03211 , 19.948633 , 19.85636 , 19.89647 , 19.88095 , 20.027094 , 20.135996 , 20.0121 , 19.980116 , 19.959826 , 20.002214 , 19.86149 , 19.853733 , 19.663826 , 19.39195 , 19.252623 , 19.327692 , 19.449005 , 19.417816 , 19.292124 , 19.140076 , 19.20655 , 19.26588 , 19.160797 , 19.017757 , 18.7078 , 18.320269 , 18.16304 , 17.959549 , 17.953415 , 17.640057 , 17.511862 , 17.214102 , 17.160482 , 17.318962 , 17.481031 , 17.470463 , 17.67231 , 17.652508 , 17.61472 , 17.517643 , 17.6717 , 17.708685 , 17.484276 , 17.331753 , 17.202616 , 17.068213 , 16.910051 , 16.536924 , 16.133308 , 16.05551 , 16.100082 , 15.909406 , 15.764091 , 15.631487 , 15.827745 , 16.026222 , 16.319872 , 16.156448 , 15.898445 , 15.830862 , 15.810078 , 15.589792 , 15.309618 , 15.105176 , 14.96468 , 14.966973 , 14.904603 , 14.61066 , 14.330112 , 14.255611 , 14.31403 , 13.940103 , 13.758863 , 13.820865 , 14.021832 , 13.888187 , 13.724709 , 13.190875 , 12.995149 , 12.669842 , 12.585032 , 12.377669 , 12.178653 , 12.082313 , 11.874204 , 11.660166 , 11.601137 , 11.558611 , 11.183846 , 11.237345 , 11.091917 , 10.472193 , 9.898911 , 9.431238 , 9.491593 , 9.688618 , 9.998573 , 9.793551 , 9.315285 , 9.259933 , 9.3849945, 9.343004 , 9.202585 , 9.472328 , 9.424212 , 9.050674 , 8.568184 , 7.7191467, 7.3312225, 7.4512987, 7.4235888, 7.518795 , 7.4950347, 7.623865 , 8.083245 , 8.049131 , 8.027269 , 8.069612 , 7.912531 , 8.042945 , 8.34481 , 8.507071 , 8.708198 , 8.604949 , 8.312463 , 8.257239 , 7.9841394, 7.693307 , 7.421974 , 7.4352374, 7.4829583, 7.642844 , 7.908468 , 8.036132 , 7.625418 , 7.7533164, 7.850424 , 7.6213007, 6.8473396, 6.4502645, 5.985239 , 5.5805774], dtype=float32) - time(time)datetime64[ns]2013-01-01 ... 2014-12-31
array(['2013-01-01T00:00:00.000000000', '2013-01-02T00:00:00.000000000', '2013-01-03T00:00:00.000000000', ..., '2014-12-29T00:00:00.000000000', '2014-12-30T00:00:00.000000000', '2014-12-31T00:00:00.000000000'], dtype='datetime64[ns]')
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 0x7f3e04040a90>
