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    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Compare-weighted-and-unweighted-mean-temperature\" data-toc-modified-id=\"Compare-weighted-and-unweighted-mean-temperature-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Compare weighted and unweighted mean temperature</a></span><ul class=\"toc-item\"><li><ul class=\"toc-item\"><li><span><a href=\"#Data\" data-toc-modified-id=\"Data-1.0.1\"><span class=\"toc-item-num\">1.0.1&nbsp;&nbsp;</span>Data</a></span></li><li><span><a href=\"#Creating-weights\" data-toc-modified-id=\"Creating-weights-1.0.2\"><span class=\"toc-item-num\">1.0.2&nbsp;&nbsp;</span>Creating weights</a></span></li><li><span><a href=\"#Weighted-mean\" data-toc-modified-id=\"Weighted-mean-1.0.3\"><span class=\"toc-item-num\">1.0.3&nbsp;&nbsp;</span>Weighted mean</a></span></li><li><span><a href=\"#Plot:-comparison-with-unweighted-mean\" data-toc-modified-id=\"Plot:-comparison-with-unweighted-mean-1.0.4\"><span class=\"toc-item-num\">1.0.4&nbsp;&nbsp;</span>Plot: comparison with unweighted mean</a></span></li></ul></li></ul></li></ul></div>"
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    "# Compare weighted and unweighted mean temperature\n",
    "\n",
    "\n",
    "Author: [Mathias Hauser](https://github.com/mathause/)\n",
    "\n",
    "\n",
    "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.\n"
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   "source": [
    "%matplotlib inline\n",
    "\n",
    "import cartopy.crs as ccrs\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import xarray as xr"
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    "### Data\n",
    "\n",
    "Load the data, convert to celsius, and resample to daily values"
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    "ds = xr.tutorial.load_dataset(\"air_temperature\")\n",
    "\n",
    "# to celsius\n",
    "air = ds.air - 273.15\n",
    "\n",
    "# resample from 6-hourly to daily values\n",
    "air = air.resample(time=\"D\").mean()\n",
    "\n",
    "air"
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   "source": [
    "Plot the first timestep:"
   ]
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    "projection = ccrs.LambertConformal(central_longitude=-95, central_latitude=45)\n",
    "\n",
    "f, ax = plt.subplots(subplot_kw=dict(projection=projection))\n",
    "\n",
    "air.isel(time=0).plot(transform=ccrs.PlateCarree(), cbar_kwargs=dict(shrink=0.7))\n",
    "ax.coastlines()"
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   "source": [
    "### Creating weights\n",
    "\n",
    "For a rectangular grid the cosine of the latitude is proportional to the grid cell area."
   ]
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   "source": [
    "weights = np.cos(np.deg2rad(air.lat))\n",
    "weights.name = \"weights\"\n",
    "weights"
   ]
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   "source": [
    "### Weighted mean"
   ]
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   "source": [
    "air_weighted = air.weighted(weights)\n",
    "air_weighted"
   ]
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   "source": [
    "weighted_mean = air_weighted.mean((\"lon\", \"lat\"))\n",
    "weighted_mean"
   ]
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   "source": [
    "### Plot: comparison with unweighted mean\n",
    "\n",
    "Note how the weighted mean temperature is higher than the unweighted."
   ]
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   "outputs": [],
   "source": [
    "weighted_mean.plot(label=\"weighted\")\n",
    "air.mean((\"lon\", \"lat\")).plot(label=\"unweighted\")\n",
    "\n",
    "plt.legend()"
   ]
  }
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