source-code/xarray/xarray_intro.ipynb

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   "source": [
    "# xarray package"
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   "metadata": {},
   "source": [
    "xarray is a crossbreed between numpy and pandas. It allows to annotate pure numerical (numpy-like) data with indices, attributes and so on."
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   "cell_type": "markdown",
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   "source": [
    "## Required imports"
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   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas.plotting import register_matplotlib_converters\n",
    "register_matplotlib_converters()\n",
    "import sys\n",
    "import xarray as xr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running example"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a 2D array of floating point values that represent temperatures of a plane. The dimensions are named `x` and `y`, and the coordinates for those dimensions are provided."
   ]
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   "execution_count": 2,
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     "end_time": "2019-07-03T04:48:30.222457Z",
     "start_time": "2019-07-03T04:48:29.895908Z"
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (x: 11, y: 11)&gt;\n",
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       "        17.54559125],\n",
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       "        20.44920664, 18.19519786, 20.08703814, 20.71606606, 22.47236078,\n",
       "        21.74689995],\n",
       "       [20.5625017 , 22.05083949, 21.95732169, 17.47612362, 19.87772883,\n",
       "        21.94072604, 22.00168891, 22.43482559, 24.79262302, 20.29191436,\n",
       "        18.30555044],\n",
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       "        18.73215314, 23.18644216, 21.44794374, 18.62120212, 16.86028957,\n",
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       "        22.80684945, 20.49398006, 20.2695466 , 21.78867674, 24.38193689,\n",
       "        24.61066743],\n",
       "       [19.99932104, 20.57241287, 23.59508175, 19.46785632, 20.68334031,\n",
       "        23.11870648, 16.31390571, 20.2654778 , 21.75407437, 19.08934392,\n",
       "        22.06232585],\n",
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       "        22.60296343, 23.34667823, 21.06888182, 18.52592886, 19.39018055,\n",
       "        22.55640252],\n",
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       "        19.86546734, 25.00695312, 19.97707261, 20.08962417, 20.41009906,\n",
       "        21.16657101],\n",
       "       [18.4188453 , 23.48988415, 21.95504864, 21.41116603, 23.55451612,\n",
       "        22.58808432, 20.92057409, 23.28880561, 22.25891661, 23.89341775,\n",
       "        22.87442428],\n",
       "       [21.85546146, 17.22067194, 22.12433162, 21.26206679, 21.34416812,\n",
       "        24.15464899, 21.57123663, 18.76124212, 22.15520087, 18.96670815,\n",
       "        21.9385253 ],\n",
       "       [21.47985149, 22.04392962, 22.22475834, 21.06548021, 24.33369792,\n",
       "        20.35700529, 22.4617063 , 21.67978738, 22.11073535, 17.08955224,\n",
       "        21.81306346]])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0\n",
       "  * y        (y) float64 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 11</li><li><span class='xr-has-index'>y</span>: 11</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-81b0252e-840f-4a0e-948c-80d694f13af6' class='xr-array-in' type='checkbox' checked><label for='section-81b0252e-840f-4a0e-948c-80d694f13af6' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>22.57 18.95 23.71 20.1 20.43 21.99 ... 22.46 21.68 22.11 17.09 21.81</span></div><div class='xr-array-data'><pre>array([[22.57434967, 18.9545404 , 23.71126177, 20.10369652, 20.42903562,\n",
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       "        21.74689995],\n",
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       "        18.30555044],\n",
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       "        23.96180751],\n",
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       "        24.61066743],\n",
       "       [19.99932104, 20.57241287, 23.59508175, 19.46785632, 20.68334031,\n",
       "        23.11870648, 16.31390571, 20.2654778 , 21.75407437, 19.08934392,\n",
       "        22.06232585],\n",
       "       [22.39604594, 19.2314135 , 19.17910261, 21.47735363, 17.52693194,\n",
       "        22.60296343, 23.34667823, 21.06888182, 18.52592886, 19.39018055,\n",
       "        22.55640252],\n",
       "       [22.32223847, 22.81747289, 18.37844145, 21.10576001, 22.24295744,\n",
       "        19.86546734, 25.00695312, 19.97707261, 20.08962417, 20.41009906,\n",
       "        21.16657101],\n",
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       "        22.87442428],\n",
       "       [21.85546146, 17.22067194, 22.12433162, 21.26206679, 21.34416812,\n",
       "        24.15464899, 21.57123663, 18.76124212, 22.15520087, 18.96670815,\n",
       "        21.9385253 ],\n",
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       "        20.35700529, 22.4617063 , 21.67978738, 22.11073535, 17.08955224,\n",
       "        21.81306346]])</pre></div></div></li><li class='xr-section-item'><input id='section-c39ae8cc-2bd6-4f9e-84a7-7f6caed91fb4' class='xr-section-summary-in' type='checkbox'  checked><label for='section-c39ae8cc-2bd6-4f9e-84a7-7f6caed91fb4' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.1 0.2 0.3 ... 0.7 0.8 0.9 1.0</div><input id='attrs-b5a18675-37fc-457a-91e2-778e10fa2350' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b5a18675-37fc-457a-91e2-778e10fa2350' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d3e2064b-a782-4bbc-bed0-19997c5cf15d' class='xr-var-data-in' type='checkbox'><label for='data-d3e2064b-a782-4bbc-bed0-19997c5cf15d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>y</span></div><div class='xr-var-dims'>(y)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.1 0.2 0.3 ... 0.7 0.8 0.9 1.0</div><input id='attrs-95c3e2ce-f591-4e05-88da-e95e1b30a881' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-95c3e2ce-f591-4e05-88da-e95e1b30a881' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-37136460-2a89-4394-8bcb-8e4498e9aa72' class='xr-var-data-in' type='checkbox'><label for='data-37136460-2a89-4394-8bcb-8e4498e9aa72' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-0e1e9643-dd26-4cba-9a46-3a05f0edcb9e' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-0e1e9643-dd26-4cba-9a46-3a05f0edcb9e' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
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       "        19.86546734, 25.00695312, 19.97707261, 20.08962417, 20.41009906,\n",
       "        21.16657101],\n",
       "       [18.4188453 , 23.48988415, 21.95504864, 21.41116603, 23.55451612,\n",
       "        22.58808432, 20.92057409, 23.28880561, 22.25891661, 23.89341775,\n",
       "        22.87442428],\n",
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       "        20.35700529, 22.4617063 , 21.67978738, 22.11073535, 17.08955224,\n",
       "        21.81306346]])\n",
       "Coordinates:\n",
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       "  * y        (y) float64 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "grid_size = 11\n",
    "temperature = xr.DataArray(np.random.normal(loc=21.0, scale=2.0, size=(grid_size, grid_size)),\n",
    "                           dims=('x', 'y'), coords={'x': np.linspace(0.0, 1.0, grid_size),\n",
    "                                                    'y': np.linspace(0.0, 1.0, grid_size)})\n",
    "temperature"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Accessing data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The elements can be accessed as you would do for a numpy array as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T05:01:08.509437Z",
     "start_time": "2019-07-03T05:01:08.480251Z"
    }
   },
   "outputs": [
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       "    y        float64 0.2</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-1411461e-8cec-41b1-a62e-668e17fa3bc5' class='xr-array-in' type='checkbox' checked><label for='section-1411461e-8cec-41b1-a62e-668e17fa3bc5' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>19.42</span></div><div class='xr-array-data'><pre>array(19.41716026)</pre></div></div></li><li class='xr-section-item'><input id='section-772ae929-2a01-4f54-bb47-a4d6afb1bbe5' class='xr-section-summary-in' type='checkbox'  checked><label for='section-772ae929-2a01-4f54-bb47-a4d6afb1bbe5' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>x</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.1</div><input id='attrs-111ac74c-192b-4d6d-a71d-6c4a838096c4' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-111ac74c-192b-4d6d-a71d-6c4a838096c4' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-55ddcc09-fabe-430f-8404-0ef31595ca3b' class='xr-var-data-in' type='checkbox'><label for='data-55ddcc09-fabe-430f-8404-0ef31595ca3b' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.1)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>y</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.2</div><input id='attrs-fd1a17c9-75a0-49a3-acc6-0c6defa0c760' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-fd1a17c9-75a0-49a3-acc6-0c6defa0c760' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-47fe90fd-80c5-4fe5-99bc-709bbdba8ad9' class='xr-var-data-in' type='checkbox'><label for='data-47fe90fd-80c5-4fe5-99bc-709bbdba8ad9' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.2)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-c9cb4a61-0c46-49ea-bac9-6d050007fd0d' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-c9cb4a61-0c46-49ea-bac9-6d050007fd0d' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
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       "<xarray.DataArray ()>\n",
       "array(19.41716026)\n",
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      ]
     },
     "execution_count": 3,
     "metadata": {},
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    }
   ],
   "source": [
    "temperature[1, 2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note however that the result is a new xarray, althought it contains only a single element.  An advantage of this is that the coordinates are part of the result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values of the xarray `temperature` can now be accessed by index, i.e., the value of the coordinates, e.g., the temperature at $x = 0.1$ and $y = 0.2$ is given by:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-02T14:46:35.996918Z",
     "start_time": "2019-07-02T14:46:35.966369Z"
    }
   },
   "outputs": [
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       "    y        float64 0.2</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-7cde21ca-a060-40c2-ba6f-6b39d84b7443' class='xr-array-in' type='checkbox' checked><label for='section-7cde21ca-a060-40c2-ba6f-6b39d84b7443' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>19.42</span></div><div class='xr-array-data'><pre>array(19.41716026)</pre></div></div></li><li class='xr-section-item'><input id='section-a4598339-9bca-442a-ac00-576eb24b2f9a' class='xr-section-summary-in' type='checkbox'  checked><label for='section-a4598339-9bca-442a-ac00-576eb24b2f9a' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>x</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.1</div><input id='attrs-7b6164f1-f389-48fc-82c7-2b40b8577338' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-7b6164f1-f389-48fc-82c7-2b40b8577338' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-53985033-206c-453f-85b0-2dce54d72838' class='xr-var-data-in' type='checkbox'><label for='data-53985033-206c-453f-85b0-2dce54d72838' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.1)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>y</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.2</div><input id='attrs-431e9b86-2e88-4d1a-80a5-826407293d6f' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-431e9b86-2e88-4d1a-80a5-826407293d6f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-148dff75-3dac-4fc3-82b6-fea470cdf123' class='xr-var-data-in' type='checkbox'><label for='data-148dff75-3dac-4fc3-82b6-fea470cdf123' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.2)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-c242f6bf-476d-4f00-8e3e-c15a4dd2c1de' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-c242f6bf-476d-4f00-8e3e-c15a4dd2c1de' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray ()>\n",
       "array(19.41716026)\n",
       "Coordinates:\n",
       "    x        float64 0.1\n",
       "    y        float64 0.2"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temperature.sel(x=0.1, y=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that using `float` coordinates may lead to unexpected results due to round off errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T04:59:13.433341Z",
     "start_time": "2019-07-03T04:59:13.409876Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "KeyError for 0.200000000001\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    temperature.sel(x=0.1, y=0.200000000001)\n",
    "except KeyError as e:\n",
    "    print(f'KeyError for {e}', file=sys.stderr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is straightforward to interpolate, as we'll discuss in a [later section](#Interpolation)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "xarrays can be indexed by slicing as well.  Note that you need to use the `slice` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T07:08:20.915039Z",
     "start_time": "2019-07-03T07:08:20.841836Z"
    }
   },
   "outputs": [
    {
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       "\n",
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       "\n",
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (x: 7, y: 2)&gt;\n",
       "array([[22.05083949, 21.95732169],\n",
       "       [21.46954344, 25.05141603],\n",
       "       [21.57348695, 19.76372872],\n",
       "       [20.57241287, 23.59508175],\n",
       "       [19.2314135 , 19.17910261],\n",
       "       [22.81747289, 18.37844145],\n",
       "       [23.48988415, 21.95504864]])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.2 0.3 0.4 0.5 0.6 0.7 0.8\n",
       "  * y        (y) float64 0.1 0.2</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 7</li><li><span class='xr-has-index'>y</span>: 2</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-3d344d44-bb5e-435d-96f3-c12f886f58b2' class='xr-array-in' type='checkbox' checked><label for='section-3d344d44-bb5e-435d-96f3-c12f886f58b2' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>22.05 21.96 21.47 25.05 21.57 19.76 ... 19.18 22.82 18.38 23.49 21.96</span></div><div class='xr-array-data'><pre>array([[22.05083949, 21.95732169],\n",
       "       [21.46954344, 25.05141603],\n",
       "       [21.57348695, 19.76372872],\n",
       "       [20.57241287, 23.59508175],\n",
       "       [19.2314135 , 19.17910261],\n",
       "       [22.81747289, 18.37844145],\n",
       "       [23.48988415, 21.95504864]])</pre></div></div></li><li class='xr-section-item'><input id='section-a97f27ff-b198-46b9-84ae-2534554821a1' class='xr-section-summary-in' type='checkbox'  checked><label for='section-a97f27ff-b198-46b9-84ae-2534554821a1' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.2 0.3 0.4 0.5 0.6 0.7 0.8</div><input id='attrs-2e0affde-f57a-41d5-85f5-b2efe6ee74eb' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2e0affde-f57a-41d5-85f5-b2efe6ee74eb' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d9670b7e-05ac-4a2e-8c9a-5c1aa7b3312b' class='xr-var-data-in' type='checkbox'><label for='data-d9670b7e-05ac-4a2e-8c9a-5c1aa7b3312b' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>y</span></div><div class='xr-var-dims'>(y)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.1 0.2</div><input id='attrs-b0e9e0c9-3594-4cdc-b776-2d1cb65cb2f6' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b0e9e0c9-3594-4cdc-b776-2d1cb65cb2f6' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-58b78149-732e-483c-bbf1-63118372c826' class='xr-var-data-in' type='checkbox'><label for='data-58b78149-732e-483c-bbf1-63118372c826' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.1, 0.2])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-3945ec1b-4d73-4d9c-8dd8-81331fb351f4' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-3945ec1b-4d73-4d9c-8dd8-81331fb351f4' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray (x: 7, y: 2)>\n",
       "array([[22.05083949, 21.95732169],\n",
       "       [21.46954344, 25.05141603],\n",
       "       [21.57348695, 19.76372872],\n",
       "       [20.57241287, 23.59508175],\n",
       "       [19.2314135 , 19.17910261],\n",
       "       [22.81747289, 18.37844145],\n",
       "       [23.48988415, 21.95504864]])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.2 0.3 0.4 0.5 0.6 0.7 0.8\n",
       "  * y        (y) float64 0.1 0.2"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temperature.sel(x=slice(0.2, 0.8), y=slice(0.1, 0.3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also possible to select values from an xarray using integer location indices on specific dimensions without worrying about the layout of the array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T05:00:57.912906Z",
     "start_time": "2019-07-03T05:00:57.892762Z"
    }
   },
   "outputs": [
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       "Coordinates:\n",
       "    x        float64 0.1\n",
       "    y        float64 0.2</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-81a402ae-dd78-467c-90e5-df401d26f2cf' class='xr-array-in' type='checkbox' checked><label for='section-81a402ae-dd78-467c-90e5-df401d26f2cf' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>19.42</span></div><div class='xr-array-data'><pre>array(19.41716026)</pre></div></div></li><li class='xr-section-item'><input id='section-be022359-0971-43ae-8b05-ee0c498cac18' class='xr-section-summary-in' type='checkbox'  checked><label for='section-be022359-0971-43ae-8b05-ee0c498cac18' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>x</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.1</div><input id='attrs-6149e920-d717-4061-abb0-17c078f7aacd' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-6149e920-d717-4061-abb0-17c078f7aacd' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ca6e0e3c-6548-410f-b8bb-a1ac15ebaef8' class='xr-var-data-in' type='checkbox'><label for='data-ca6e0e3c-6548-410f-b8bb-a1ac15ebaef8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.1)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>y</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.2</div><input id='attrs-6c998e7e-8ad6-43d2-b174-22df5f9e4af3' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-6c998e7e-8ad6-43d2-b174-22df5f9e4af3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e3b3b1e3-5050-4198-98ca-9b18f78d5791' class='xr-var-data-in' type='checkbox'><label for='data-e3b3b1e3-5050-4198-98ca-9b18f78d5791' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.2)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-57460dfd-9f34-4b45-9d2f-3da0b8e1b3d3' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-57460dfd-9f34-4b45-9d2f-3da0b8e1b3d3' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray ()>\n",
       "array(19.41716026)\n",
       "Coordinates:\n",
       "    x        float64 0.1\n",
       "    y        float64 0.2"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temperature.isel(x=1, y=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A scalar value can be obtained using the `float` constructor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-02T14:47:41.855378Z",
     "start_time": "2019-07-02T14:47:41.842593Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19.41716025838715"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(temperature.isel(x=1, y=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T07:21:03.186815Z",
     "start_time": "2019-07-03T07:21:03.145478Z"
    }
   },
   "source": [
    "As in pandas, direct access to the underlying numpy array is available as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T08:57:01.034727Z",
     "start_time": "2019-07-03T08:57:01.021467Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'> float64 (11, 11)\n"
     ]
    }
   ],
   "source": [
    "print(type(temperature.values), temperature.values.dtype, temperature.values.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Metadata"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Like a numpy array, the data type and shape of an xarray can be easily obtained."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T08:59:03.230436Z",
     "start_time": "2019-07-03T08:59:03.220621Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "float64 (11, 11)\n"
     ]
    }
   ],
   "source": [
    "print(temperature.dtype, temperature.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dimensions can be retrieved."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T07:37:15.883407Z",
     "start_time": "2019-07-03T07:37:15.866205Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('x', 'y')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temperature.dims"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coordinates associated with an xarray can be retrieved as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-02T14:50:47.268531Z",
     "start_time": "2019-07-02T14:50:47.235440Z"
    }
   },
   "outputs": [
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       "  * x        (x) float64 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'x'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 11</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-629e80fe-7e8b-405a-b2ab-11ccadbc5b22' class='xr-array-in' type='checkbox' checked><label for='section-629e80fe-7e8b-405a-b2ab-11ccadbc5b22' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0</span></div><div class='xr-array-data'><pre>array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])</pre></div></div></li><li class='xr-section-item'><input id='section-b2d1e9c2-1cf6-4451-ace4-dfc0d2d852f1' class='xr-section-summary-in' type='checkbox'  checked><label for='section-b2d1e9c2-1cf6-4451-ace4-dfc0d2d852f1' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.1 0.2 0.3 ... 0.7 0.8 0.9 1.0</div><input id='attrs-6feff842-0e60-48a7-b5d1-299d9bea8d1a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-6feff842-0e60-48a7-b5d1-299d9bea8d1a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-aa2df6e9-aa23-40ed-8ebc-f4a2aada1517' class='xr-var-data-in' type='checkbox'><label for='data-aa2df6e9-aa23-40ed-8ebc-f4a2aada1517' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-8498f566-bb33-4203-8768-05257cd8c5c5' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-8498f566-bb33-4203-8768-05257cd8c5c5' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
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       "<xarray.DataArray 'x' (x: 11)>\n",
       "array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])\n",
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     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temperature.coords['x']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This can be quite convenient to reuse the same coordinates in a new xarray."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T08:49:44.720587Z",
     "start_time": "2019-07-03T08:49:44.684016Z"
    }
   },
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       "  * y        (y) float64 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 11</li><li><span class='xr-has-index'>y</span>: 11</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-9799f8d7-819b-4d50-8062-0a33f1feb40a' class='xr-array-in' type='checkbox' checked><label for='section-9799f8d7-819b-4d50-8062-0a33f1feb40a' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>1.137e+05 1.076e+05 1.116e+05 ... 1.091e+05 1.08e+05 1.055e+05</span></div><div class='xr-array-data'><pre>array([[113681.49891279, 107574.72543152, 111575.59481009,\n",
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       "...\n",
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       "...\n",
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     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pressure = xr.DataArray(np.random.normal(loc=1.1e5, scale=3e3, size=temperature.shape),\n",
    "                        dims=temperature.dims, coords=temperature.coords)\n",
    "pressure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Arbitrary attributes can be added to an xarray to store additional metadata."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T08:49:48.540207Z",
     "start_time": "2019-07-03T08:49:48.518321Z"
    }
   },
   "outputs": [
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (x: 11, y: 11)&gt;\n",
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       "       [113103.85808058, 112315.78201912, 111325.3225198 ,\n",
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       "        108412.79612146, 113464.00008095, 109669.15313825,\n",
       "        110895.25567714, 112177.8393465 ],\n",
       "       [105269.22608631, 111075.55262817, 111424.9642551 ,\n",
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       "Attributes:\n",
       "    units:    P\n",
       "    source:   random data</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 11</li><li><span class='xr-has-index'>y</span>: 11</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-ee9e459d-f033-4c22-9f02-709f428ad289' class='xr-array-in' type='checkbox' checked><label for='section-ee9e459d-f033-4c22-9f02-709f428ad289' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>1.137e+05 1.076e+05 1.116e+05 ... 1.091e+05 1.08e+05 1.055e+05</span></div><div class='xr-array-data'><pre>array([[113681.49891279, 107574.72543152, 111575.59481009,\n",
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       "...\n",
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       "        108412.79612146, 113464.00008095, 109669.15313825,\n",
       "        110895.25567714, 112177.8393465 ],\n",
       "       [105269.22608631, 111075.55262817, 111424.9642551 ,\n",
       "        110383.82876284, 111303.03171273, 105448.85423657,\n",
       "        108750.27693033, 113730.87292861, 109111.58741648,\n",
       "        107999.16111684, 105455.10927893]])</pre></div></div></li><li class='xr-section-item'><input id='section-f4280796-4aed-4020-a659-f980e1dcd560' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f4280796-4aed-4020-a659-f980e1dcd560' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.1 0.2 0.3 ... 0.7 0.8 0.9 1.0</div><input id='attrs-e3ba5c1c-4d14-4483-b165-733f6dee13d1' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e3ba5c1c-4d14-4483-b165-733f6dee13d1' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-8dc66782-b575-49b9-88e0-6c7a1fdeb64a' class='xr-var-data-in' type='checkbox'><label for='data-8dc66782-b575-49b9-88e0-6c7a1fdeb64a' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>y</span></div><div class='xr-var-dims'>(y)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.1 0.2 0.3 ... 0.7 0.8 0.9 1.0</div><input id='attrs-eebb82b1-d2c2-4d9a-a324-c6e0cab92270' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-eebb82b1-d2c2-4d9a-a324-c6e0cab92270' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-fff18534-b1b2-432b-bff2-32611970cf41' class='xr-var-data-in' type='checkbox'><label for='data-fff18534-b1b2-432b-bff2-32611970cf41' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-9a6b626e-6213-4977-b559-dfa2a6ac2c31' class='xr-section-summary-in' type='checkbox'  checked><label for='section-9a6b626e-6213-4977-b559-dfa2a6ac2c31' class='xr-section-summary' >Attributes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>units :</span></dt><dd>P</dd><dt><span>source :</span></dt><dd>random data</dd></dl></div></li></ul></div></div>"
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       "...\n",
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       "Attributes:\n",
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       "    source:   random data"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pressure.attrs['units'] = 'P'\n",
    "pressure.attrs['source'] = 'random data'\n",
    "pressure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## File I/O"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "xarrays can be stored in NetCDF format, which can be used with many scientific and visualization software packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T08:49:51.697985Z",
     "start_time": "2019-07-03T08:49:51.680769Z"
    }
   },
   "outputs": [],
   "source": [
    "pressure.to_netcdf('pressure.nc')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T08:52:16.632476Z",
     "start_time": "2019-07-03T08:52:16.482831Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "README.md  pressure.nc\txarray_intro.ipynb\n"
     ]
    }
   ],
   "source": [
    "!ls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To demonstrate that this is lossless, we remove the original xarray, and reinstantiate it from the NetCDF file that was saved to disk."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T08:49:55.748236Z",
     "start_time": "2019-07-03T08:49:55.734300Z"
    }
   },
   "outputs": [],
   "source": [
    "del pressure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T08:50:20.413543Z",
     "start_time": "2019-07-03T08:50:20.356292Z"
    }
   },
   "outputs": [
    {
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (x: 11, y: 11)&gt;\n",
       "array([[113681.498913, 107574.725432, 111575.59481 , 105268.331755,\n",
       "        109625.59509 , 104991.440633, 110784.111841, 110950.286334,\n",
       "        111124.931614, 113309.448581, 109734.979633],\n",
       "       [110998.756141, 106712.305662, 108917.282948, 112856.716736,\n",
       "        113099.547078, 109312.849482, 109775.158502, 113287.404479,\n",
       "        109254.30904 , 106667.410182, 110288.307568],\n",
       "       [112749.668448, 113377.665674, 113706.414489, 110715.658421,\n",
       "        112514.901296, 114745.365732, 112841.185821, 114133.981709,\n",
       "        105465.87295 , 108378.363935, 103719.789618],\n",
       "       [113290.604469, 109927.692258, 109425.15259 , 113713.423774,\n",
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       "       [109627.081189, 112740.067252, 108377.45039 , 107505.707448,\n",
       "        110478.222574, 107364.827535, 107961.32426 , 103974.634378,\n",
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       "       [113672.194942, 112076.062684, 117283.516963, 110135.756885,\n",
       "        105876.061492, 112767.346872, 108572.108514, 105801.444041,\n",
       "        114162.103277, 108063.749401, 113230.574748],\n",
       "       [105562.884675, 111931.725964, 114443.441506, 105743.69907 ,\n",
       "        108170.91687 , 104224.71099 , 111079.891767, 112118.399358,\n",
       "        107880.907105, 107551.983526, 109265.66716 ],\n",
       "       [111884.078477, 111561.62099 , 102016.299623, 106634.513225,\n",
       "        111803.305921, 110956.225149, 104412.047786, 113673.211901,\n",
       "        107817.708306, 112562.521756, 112868.449658],\n",
       "       [110479.491762, 110804.485959, 109768.562619, 108439.916164,\n",
       "        108707.403695, 108869.900765, 110133.578606, 111098.119789,\n",
       "        116551.329581, 107356.795406, 109389.384635],\n",
       "       [113103.858081, 112315.782019, 111325.32252 , 111398.456906,\n",
       "        108134.464681, 107956.058763, 108412.796121, 113464.000081,\n",
       "        109669.153138, 110895.255677, 112177.839347],\n",
       "       [105269.226086, 111075.552628, 111424.964255, 110383.828763,\n",
       "        111303.031713, 105448.854237, 108750.27693 , 113730.872929,\n",
       "        109111.587416, 107999.161117, 105455.109279]])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0\n",
       "  * y        (y) float64 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0\n",
       "Attributes:\n",
       "    units:    P\n",
       "    source:   random data</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 11</li><li><span class='xr-has-index'>y</span>: 11</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-9098e9a8-d11c-496e-8520-fb7265cb407b' class='xr-array-in' type='checkbox' checked><label for='section-9098e9a8-d11c-496e-8520-fb7265cb407b' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>1.137e+05 1.076e+05 1.116e+05 ... 1.091e+05 1.08e+05 1.055e+05</span></div><div class='xr-array-data'><pre>array([[113681.498913, 107574.725432, 111575.59481 , 105268.331755,\n",
       "        109625.59509 , 104991.440633, 110784.111841, 110950.286334,\n",
       "        111124.931614, 113309.448581, 109734.979633],\n",
       "       [110998.756141, 106712.305662, 108917.282948, 112856.716736,\n",
       "        113099.547078, 109312.849482, 109775.158502, 113287.404479,\n",
       "        109254.30904 , 106667.410182, 110288.307568],\n",
       "       [112749.668448, 113377.665674, 113706.414489, 110715.658421,\n",
       "        112514.901296, 114745.365732, 112841.185821, 114133.981709,\n",
       "        105465.87295 , 108378.363935, 103719.789618],\n",
       "       [113290.604469, 109927.692258, 109425.15259 , 113713.423774,\n",
       "        112717.066371, 108957.386358, 117603.927417, 110631.743102,\n",
       "        109361.445818, 109628.011845, 104525.926538],\n",
       "       [109627.081189, 112740.067252, 108377.45039 , 107505.707448,\n",
       "        110478.222574, 107364.827535, 107961.32426 , 103974.634378,\n",
       "        111042.077242, 109010.096849, 108773.650636],\n",
       "       [113672.194942, 112076.062684, 117283.516963, 110135.756885,\n",
       "        105876.061492, 112767.346872, 108572.108514, 105801.444041,\n",
       "        114162.103277, 108063.749401, 113230.574748],\n",
       "       [105562.884675, 111931.725964, 114443.441506, 105743.69907 ,\n",
       "        108170.91687 , 104224.71099 , 111079.891767, 112118.399358,\n",
       "        107880.907105, 107551.983526, 109265.66716 ],\n",
       "       [111884.078477, 111561.62099 , 102016.299623, 106634.513225,\n",
       "        111803.305921, 110956.225149, 104412.047786, 113673.211901,\n",
       "        107817.708306, 112562.521756, 112868.449658],\n",
       "       [110479.491762, 110804.485959, 109768.562619, 108439.916164,\n",
       "        108707.403695, 108869.900765, 110133.578606, 111098.119789,\n",
       "        116551.329581, 107356.795406, 109389.384635],\n",
       "       [113103.858081, 112315.782019, 111325.32252 , 111398.456906,\n",
       "        108134.464681, 107956.058763, 108412.796121, 113464.000081,\n",
       "        109669.153138, 110895.255677, 112177.839347],\n",
       "       [105269.226086, 111075.552628, 111424.964255, 110383.828763,\n",
       "        111303.031713, 105448.854237, 108750.27693 , 113730.872929,\n",
       "        109111.587416, 107999.161117, 105455.109279]])</pre></div></div></li><li class='xr-section-item'><input id='section-5a9e9151-c837-4c58-8358-5795bdbe1801' class='xr-section-summary-in' type='checkbox'  checked><label for='section-5a9e9151-c837-4c58-8358-5795bdbe1801' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.1 0.2 0.3 ... 0.7 0.8 0.9 1.0</div><input id='attrs-5fc1d8ed-fd27-4a0a-b406-151e56ab9483' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-5fc1d8ed-fd27-4a0a-b406-151e56ab9483' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-73c4e6a7-5398-445a-81d2-4b4a88e27512' class='xr-var-data-in' type='checkbox'><label for='data-73c4e6a7-5398-445a-81d2-4b4a88e27512' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>y</span></div><div class='xr-var-dims'>(y)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.1 0.2 0.3 ... 0.7 0.8 0.9 1.0</div><input id='attrs-2c62201f-6398-4637-a9d6-6ddfa685749e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2c62201f-6398-4637-a9d6-6ddfa685749e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-8011a4b2-ed70-4acc-bc34-cff3acaedfe6' class='xr-var-data-in' type='checkbox'><label for='data-8011a4b2-ed70-4acc-bc34-cff3acaedfe6' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-77acb4fe-0bbb-43f1-b78d-abd6acc0c1f3' class='xr-section-summary-in' type='checkbox'  checked><label for='section-77acb4fe-0bbb-43f1-b78d-abd6acc0c1f3' class='xr-section-summary' >Attributes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>units :</span></dt><dd>P</dd><dt><span>source :</span></dt><dd>random data</dd></dl></div></li></ul></div></div>"
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       "        111303.031713, 105448.854237, 108750.27693 , 113730.872929,\n",
       "        109111.587416, 107999.161117, 105455.109279]])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0\n",
       "  * y        (y) float64 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0\n",
       "Attributes:\n",
       "    units:    P\n",
       "    source:   random data"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pressure = xr.open_dataarray('pressure.nc')\n",
    "pressure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All metadata, including coordinates and attributes has been preserved."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical computations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numerical operations are broadcasted along the dimensions, so to initialize a 2D array of complex numbers, we can simply initialize the real values as an xarray with dimension `re`, the imaginary values as an xarray with dimension `im`, and add the two 1D arrays to obtain a complex-valued 2D array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T05:10:07.869657Z",
     "start_time": "2019-07-03T05:10:07.847281Z"
    }
   },
   "outputs": [],
   "source": [
    "real_vals = xr.DataArray(np.linspace(0.0, 1.0, 11), dims='re')\n",
    "im_vals = xr.DataArray(np.linspace(0.0j, 1.0j, 11), dims='im')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T05:10:33.039569Z",
     "start_time": "2019-07-03T05:10:32.986204Z"
    }
   },
   "outputs": [
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       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (re: 11, im: 11)&gt;\n",
       "array([[0. +0.j , 0. +0.1j, 0. +0.2j, 0. +0.3j, 0. +0.4j, 0. +0.5j,\n",
       "        0. +0.6j, 0. +0.7j, 0. +0.8j, 0. +0.9j, 0. +1.j ],\n",
       "       [0.1+0.j , 0.1+0.1j, 0.1+0.2j, 0.1+0.3j, 0.1+0.4j, 0.1+0.5j,\n",
       "        0.1+0.6j, 0.1+0.7j, 0.1+0.8j, 0.1+0.9j, 0.1+1.j ],\n",
       "       [0.2+0.j , 0.2+0.1j, 0.2+0.2j, 0.2+0.3j, 0.2+0.4j, 0.2+0.5j,\n",
       "        0.2+0.6j, 0.2+0.7j, 0.2+0.8j, 0.2+0.9j, 0.2+1.j ],\n",
       "       [0.3+0.j , 0.3+0.1j, 0.3+0.2j, 0.3+0.3j, 0.3+0.4j, 0.3+0.5j,\n",
       "        0.3+0.6j, 0.3+0.7j, 0.3+0.8j, 0.3+0.9j, 0.3+1.j ],\n",
       "       [0.4+0.j , 0.4+0.1j, 0.4+0.2j, 0.4+0.3j, 0.4+0.4j, 0.4+0.5j,\n",
       "        0.4+0.6j, 0.4+0.7j, 0.4+0.8j, 0.4+0.9j, 0.4+1.j ],\n",
       "       [0.5+0.j , 0.5+0.1j, 0.5+0.2j, 0.5+0.3j, 0.5+0.4j, 0.5+0.5j,\n",
       "        0.5+0.6j, 0.5+0.7j, 0.5+0.8j, 0.5+0.9j, 0.5+1.j ],\n",
       "       [0.6+0.j , 0.6+0.1j, 0.6+0.2j, 0.6+0.3j, 0.6+0.4j, 0.6+0.5j,\n",
       "        0.6+0.6j, 0.6+0.7j, 0.6+0.8j, 0.6+0.9j, 0.6+1.j ],\n",
       "       [0.7+0.j , 0.7+0.1j, 0.7+0.2j, 0.7+0.3j, 0.7+0.4j, 0.7+0.5j,\n",
       "        0.7+0.6j, 0.7+0.7j, 0.7+0.8j, 0.7+0.9j, 0.7+1.j ],\n",
       "       [0.8+0.j , 0.8+0.1j, 0.8+0.2j, 0.8+0.3j, 0.8+0.4j, 0.8+0.5j,\n",
       "        0.8+0.6j, 0.8+0.7j, 0.8+0.8j, 0.8+0.9j, 0.8+1.j ],\n",
       "       [0.9+0.j , 0.9+0.1j, 0.9+0.2j, 0.9+0.3j, 0.9+0.4j, 0.9+0.5j,\n",
       "        0.9+0.6j, 0.9+0.7j, 0.9+0.8j, 0.9+0.9j, 0.9+1.j ],\n",
       "       [1. +0.j , 1. +0.1j, 1. +0.2j, 1. +0.3j, 1. +0.4j, 1. +0.5j,\n",
       "        1. +0.6j, 1. +0.7j, 1. +0.8j, 1. +0.9j, 1. +1.j ]])\n",
       "Dimensions without coordinates: re, im</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span>re</span>: 11</li><li><span>im</span>: 11</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-5ccedf7a-c494-4da7-9f54-096fe4240f31' class='xr-array-in' type='checkbox' checked><label for='section-5ccedf7a-c494-4da7-9f54-096fe4240f31' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>0j 0.1j 0.2j 0.30000000000000004j ... (1+0.8j) (1+0.9j) (1+1j)</span></div><div class='xr-array-data'><pre>array([[0. +0.j , 0. +0.1j, 0. +0.2j, 0. +0.3j, 0. +0.4j, 0. +0.5j,\n",
       "        0. +0.6j, 0. +0.7j, 0. +0.8j, 0. +0.9j, 0. +1.j ],\n",
       "       [0.1+0.j , 0.1+0.1j, 0.1+0.2j, 0.1+0.3j, 0.1+0.4j, 0.1+0.5j,\n",
       "        0.1+0.6j, 0.1+0.7j, 0.1+0.8j, 0.1+0.9j, 0.1+1.j ],\n",
       "       [0.2+0.j , 0.2+0.1j, 0.2+0.2j, 0.2+0.3j, 0.2+0.4j, 0.2+0.5j,\n",
       "        0.2+0.6j, 0.2+0.7j, 0.2+0.8j, 0.2+0.9j, 0.2+1.j ],\n",
       "       [0.3+0.j , 0.3+0.1j, 0.3+0.2j, 0.3+0.3j, 0.3+0.4j, 0.3+0.5j,\n",
       "        0.3+0.6j, 0.3+0.7j, 0.3+0.8j, 0.3+0.9j, 0.3+1.j ],\n",
       "       [0.4+0.j , 0.4+0.1j, 0.4+0.2j, 0.4+0.3j, 0.4+0.4j, 0.4+0.5j,\n",
       "        0.4+0.6j, 0.4+0.7j, 0.4+0.8j, 0.4+0.9j, 0.4+1.j ],\n",
       "       [0.5+0.j , 0.5+0.1j, 0.5+0.2j, 0.5+0.3j, 0.5+0.4j, 0.5+0.5j,\n",
       "        0.5+0.6j, 0.5+0.7j, 0.5+0.8j, 0.5+0.9j, 0.5+1.j ],\n",
       "       [0.6+0.j , 0.6+0.1j, 0.6+0.2j, 0.6+0.3j, 0.6+0.4j, 0.6+0.5j,\n",
       "        0.6+0.6j, 0.6+0.7j, 0.6+0.8j, 0.6+0.9j, 0.6+1.j ],\n",
       "       [0.7+0.j , 0.7+0.1j, 0.7+0.2j, 0.7+0.3j, 0.7+0.4j, 0.7+0.5j,\n",
       "        0.7+0.6j, 0.7+0.7j, 0.7+0.8j, 0.7+0.9j, 0.7+1.j ],\n",
       "       [0.8+0.j , 0.8+0.1j, 0.8+0.2j, 0.8+0.3j, 0.8+0.4j, 0.8+0.5j,\n",
       "        0.8+0.6j, 0.8+0.7j, 0.8+0.8j, 0.8+0.9j, 0.8+1.j ],\n",
       "       [0.9+0.j , 0.9+0.1j, 0.9+0.2j, 0.9+0.3j, 0.9+0.4j, 0.9+0.5j,\n",
       "        0.9+0.6j, 0.9+0.7j, 0.9+0.8j, 0.9+0.9j, 0.9+1.j ],\n",
       "       [1. +0.j , 1. +0.1j, 1. +0.2j, 1. +0.3j, 1. +0.4j, 1. +0.5j,\n",
       "        1. +0.6j, 1. +0.7j, 1. +0.8j, 1. +0.9j, 1. +1.j ]])</pre></div></div></li><li class='xr-section-item'><input id='section-847089eb-b55c-4b66-87dc-597f9afb7080' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-847089eb-b55c-4b66-87dc-597f9afb7080' class='xr-section-summary'  title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-c890370e-aec5-4c4c-ad48-5d7727db8d74' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-c890370e-aec5-4c4c-ad48-5d7727db8d74' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray (re: 11, im: 11)>\n",
       "array([[0. +0.j , 0. +0.1j, 0. +0.2j, 0. +0.3j, 0. +0.4j, 0. +0.5j,\n",
       "        0. +0.6j, 0. +0.7j, 0. +0.8j, 0. +0.9j, 0. +1.j ],\n",
       "       [0.1+0.j , 0.1+0.1j, 0.1+0.2j, 0.1+0.3j, 0.1+0.4j, 0.1+0.5j,\n",
       "        0.1+0.6j, 0.1+0.7j, 0.1+0.8j, 0.1+0.9j, 0.1+1.j ],\n",
       "       [0.2+0.j , 0.2+0.1j, 0.2+0.2j, 0.2+0.3j, 0.2+0.4j, 0.2+0.5j,\n",
       "        0.2+0.6j, 0.2+0.7j, 0.2+0.8j, 0.2+0.9j, 0.2+1.j ],\n",
       "       [0.3+0.j , 0.3+0.1j, 0.3+0.2j, 0.3+0.3j, 0.3+0.4j, 0.3+0.5j,\n",
       "        0.3+0.6j, 0.3+0.7j, 0.3+0.8j, 0.3+0.9j, 0.3+1.j ],\n",
       "       [0.4+0.j , 0.4+0.1j, 0.4+0.2j, 0.4+0.3j, 0.4+0.4j, 0.4+0.5j,\n",
       "        0.4+0.6j, 0.4+0.7j, 0.4+0.8j, 0.4+0.9j, 0.4+1.j ],\n",
       "       [0.5+0.j , 0.5+0.1j, 0.5+0.2j, 0.5+0.3j, 0.5+0.4j, 0.5+0.5j,\n",
       "        0.5+0.6j, 0.5+0.7j, 0.5+0.8j, 0.5+0.9j, 0.5+1.j ],\n",
       "       [0.6+0.j , 0.6+0.1j, 0.6+0.2j, 0.6+0.3j, 0.6+0.4j, 0.6+0.5j,\n",
       "        0.6+0.6j, 0.6+0.7j, 0.6+0.8j, 0.6+0.9j, 0.6+1.j ],\n",
       "       [0.7+0.j , 0.7+0.1j, 0.7+0.2j, 0.7+0.3j, 0.7+0.4j, 0.7+0.5j,\n",
       "        0.7+0.6j, 0.7+0.7j, 0.7+0.8j, 0.7+0.9j, 0.7+1.j ],\n",
       "       [0.8+0.j , 0.8+0.1j, 0.8+0.2j, 0.8+0.3j, 0.8+0.4j, 0.8+0.5j,\n",
       "        0.8+0.6j, 0.8+0.7j, 0.8+0.8j, 0.8+0.9j, 0.8+1.j ],\n",
       "       [0.9+0.j , 0.9+0.1j, 0.9+0.2j, 0.9+0.3j, 0.9+0.4j, 0.9+0.5j,\n",
       "        0.9+0.6j, 0.9+0.7j, 0.9+0.8j, 0.9+0.9j, 0.9+1.j ],\n",
       "       [1. +0.j , 1. +0.1j, 1. +0.2j, 1. +0.3j, 1. +0.4j, 1. +0.5j,\n",
       "        1. +0.6j, 1. +0.7j, 1. +0.8j, 1. +0.9j, 1. +1.j ]])\n",
       "Dimensions without coordinates: re, im"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vals = real_vals + im_vals\n",
    "vals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although this can be done in numpy as well, it requires fiddling with extra dimensions, using xarrays this can be expressed quite naturally."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another example is the computation and representation of volume data. A 3D Gaussian function is computed over the domain $[-3 : 3, -3 : 3, -3 : 3]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T09:31:13.037884Z",
     "start_time": "2019-07-03T09:31:12.962198Z"
    }
   },
   "outputs": [],
   "source": [
    "x_coords = xr.DataArray(np.linspace(-3.0, 3.0, 101), dims='x')\n",
    "y_coords = xr.DataArray(np.linspace(-3.0, 3.0, 101), dims='7')\n",
    "z_coords = xr.DataArray(np.linspace(-3.0, 3.0, 101), dims='z')\n",
    "X, Y, Z = np.meshgrid(x_coords, y_coords, z_coords)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T09:32:55.971171Z",
     "start_time": "2019-07-03T09:32:55.945115Z"
    }
   },
   "outputs": [],
   "source": [
    "def gaussian(X, Y, Z):\n",
    "    return np.exp(-(X**2 + Y**2 + Z**2))/np.sqrt(2.0*np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T09:52:57.927742Z",
     "start_time": "2019-07-03T09:52:57.705829Z"
    }
   },
   "outputs": [],
   "source": [
    "values = xr.DataArray(gaussian(X, Y, Z), dims=('x', 'y', 'z'),\n",
    "                      coords=(x_coords, y_coords, z_coords))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T09:53:05.449075Z",
     "start_time": "2019-07-03T09:53:05.438796Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(101, 101, 101)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data can be exported to NetCDF for visualization with, e.g., ParaView or VisIt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T09:53:57.493904Z",
     "start_time": "2019-07-03T09:53:57.415923Z"
    }
   },
   "outputs": [],
   "source": [
    "values.to_netcdf('gaussian.nc')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize two slices of the data volume, one along the $Z$-plane, the other along the $X$-plane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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n5LrtHWNlztl43xpBHo+/VpT3z2n+uawR4bX75cFic2oEYRCmPduuixL09/W/+vuoRC+ixyy/njl7cY1YHuvVSQg5D+owdZg6/DrgAPmV81A779wikLU23imRiiUhXhLhOQEeRXS5Of7pNl8foYixFYdMhC4Moo1OXGeiGlU0F6IZvfV3SKDnohiH7L6HFI3Q5iNkCnV4CnWYOnwNcID8SrmEnbdWlB9DkM8R4/6xwoJYj9sdWjd3riN5ImDT7arwDTbfrGh3gi3oijr6548mdJ4zN7H+qk34cIFesvqWil+WKqtp85FbhjpMHQaow9fKeV7HGYjIN4jID4vIdy3c/0Ui8lER+UD5+w1PdW7XzKmVwmvyydq260VZguyJcs8lRLl/jP72ZF+Rvb9DHNp+7vh7t2XhvGeuxbHXqr8Wdf8z7NO5Y649h739z7RLyfNBLX56qMPUYerw6+MpI8jfCOC3A/h9B7b5b1X1Fz/N6bxeHsPOOybIp0YsTo1WjGI8J8RLtt4ovEvnPLf9qWhWxL11GYjtmHm04zp7L8a4F83o7/dIRm/7TSqwB8tvLooxlxN3qI3RXJ5efV6FYz06afO9Kr4R1OIHQx2mDlOHr5snGyCr6n8jIp/+VI93jTyWnXeOlfcQG+8cMW6Pe1yElyIH7djnC3OWfWHRoTgk1uUm2KNYu0j2Qp1xgkgfsPv6WaHy5PXLe9vW88S+cM4JLm2+1w+1+GFQh6nD1OHb4KXF5X+eiHyniHybiPyMpY1E5CtE5P0i8v77Nx99yvN7FZxit5y27SlfDMvRisl2InvieYooSwiL9uHUVpP6Nz72mr81x9k7h+7cDlmCvu9cYctyccv8NVrDadu+NIkgT8RRLaYOH4Y6TB0+BHX45fOSivT+HICfpqofE5F3A/jDAD5zbkNVfS+A9wLAJ77js27iJ9BT23mLkYAzbbwxWjEKSghh1rqTMOabhcn9fqxRKOfO/dC6tfQV1D7Lab+u/iKPZoOZBWcbStluEtEIWu2/vrBEg7Yq7AxIiXCsiWL0v3s9inGocOTUohFWVV89q7SYOnxgO+owdZg6/Op5MQNkVf2b3fL7ROR3isgnq+qPPOd5vQRegyifIsijhTcXoVgS/fYrf1+Ij9l/c8/pVHTG2suhE+YqvooYp+LjtqB2eWhhRqTtRrP9Moaqa7+2WGf3nZMT91Q2H8X55UEtnoc63M6FOkwdvgVezABZRN4J4H9RVRWRL4C9vf76M5/WVfJQu2ZJlMfjL0Ur6nEWRHn/fEcLbPwS2I9UjFba3PmdRzc9qYtreSzPbzNBlMnmqlqFTEQmUYZJoUa3v5ZtQwjTnp5F0Kro+nHHoo8gi+J8DmsFl7xuqMVPA3WYOnwO1OGn48kGyCLyBwB8EYBPFpEPA/iNALYAoKrvAfClAH6NiOwA/BiAL1P+rFkVtXjMiMWhIpClFjmHohVzFt4opuOxeyFeEuG5CEv/9GcFf2VECOgtu663ZverPatprdl27X6PalQRj6U4xAtCRGtxiWSttl8v8n0Uo6+4XoxizE6Z2sQZaEUjz23zMXrx9FCLT4c6TB2mDt8eT9nF4p85cv9vh7UeIoXnFuXJ8U6w8uby28KMSI8W3jEx3hfwtq+f8lLl9FJu3KnMWXUAIJ1wuwjnAIi3AyrbTgQXgMgKkR7y4/xaZuQWSOkE2q0+F9c2C1Rb71GMx7b51kBxflqoxadBHaYOU4dvkxeTYkEel3PsrLHyd0nY50S5HWNeEJdy6ibbzGzfi3IfoZh7nFMKRlbTBwW6p+o61U9JGrJ27X2yiarIjDg3YZosL4nmZJtuNqiyT0CeWH1LwjonzmtZnd9GO5CQCnWYOtxvQx1+2XCA/AK5dDHIJey8uYjFXI7bOdGKXkh92znbboxQHMuFWxbm/WvWP99D+WHaacwkitEVhdT7Yrdem4BmbRagZq2PF0pfTlWdFJIsRTGq4Ba7r582dbZw5EDRiHRfIP02trze5ju3WGTu+IQ8J9Rh6jB1+LbhAPmVcoqlN9lvpZ13rHp5ycqby3FzoZ0T5CULL1SBXhbj6ZfAVJxt/ZEikYUvwLkr27cNAlyAbf+s2o4V27ZWCNKE2sVWVKHl28HtP8uTK+cF6Sw/qZafZq3V1vXLwwumQ6hV1siYWn0usl119VxD+zwR3XU23961e4A4E/LaoA5Th+0AqNebOnw9cIB85Zxq6S1tP5sPt5hnNoj5Qo5bv+9ctGIuWjIn5FORRj3GeN6TczzV3RPBRG+6yxQyLEpRxdLPq3MCc7MCc+72Ty6QGSGjirPvo4NY9kUevm0tPAmtyroX0DmxHC3Btv40AaXgEnIc6jB1mDr8+uAA+YVxyYKQxZyyFXbeqUUgbuWN0Yr+eHPRirAJ3TYtUjGKcXuMXpgx2bdu30U65p5/f/nWXO+phTe/fmLbabP5cl2eRjTcwqsRilJU4rafSqu8ll3eKyDxKEYOTWS9wX1tbj9GMI40tA85n2XzXdrio71HnhvqMHWYOkwd5gD5BXGuKB+rlH6IndfvL2HaOmjMc5u35w7nty1ZeDGOoi9HxXj8EgkBk8dtz2fvcs1GZtov+3Zfrxktr02R/VoUO06zrfOqahWtkQ8RKeLZCTOAhIyQFYhhYvlhE6rwukMnUSZ5cWPEo1p9XXV1nw+3VDRyrs03J879Neofg+JMXjLU4XZe1GHq8C3DAfIL4SERiwc/9gE7b60oj/v10Q9nSZQB7AnrmNfmojypnu4EuRdjP4Y/pt1u5zY5p0OX3WdW6jRC0FtpLj7WlrPmqhXrLsIiFlntdvDUtKBAlmb95e6c/YsnK5I//97yKxZhL3guqDlMe4K6OHuje/SiGpo4Y9ivP+5j2HYUZ/JSoQ5Th6nD3TY3rsMcIL9y1lZKn2vnrS0CmctxC7Hb90C0orf85iIVdftBiHsR7gV4Ivb1fNrzbNdm3TUe9aG36+z+FpUwy65sl7vemsXaq/ZdXdZq+1WLrhSS+O0axSh2n3YRDy84yUArHCnbeK/OsWgkBrPo5iqr52y+Y03s++iFr69HW7D5CLkmqMPUYYA6fG1wgPwCeKyoxdxxZ4s85rbr1s0VgYytg0Yrr99vzHELm3iSIMfOLnRBbvt5pATd+bTn5U9jKd9tjTj3wqyqiF41XYVZOrFuQpVVkFMRLTHBdrtPc7dcbL85yy+L1mrrHADsUs13y7tcn5eqQEKc5MTZSbTXKuU0EdJeNOciBcea2PfX89QoA6MX5KVBHaYOU4dntrlhHeYA+RVzLGpxbD2wn++21s4DsHd7vG9iz02WUbdZEuUx982XY2yiH3x5iFC4II9iPCfS/fOYYywM8W1VgRA6ey2LCW+x7QAgQKs96PvHCKSEav21ZUFC3rP8PNdNoQhi/TjdItQgE1uwRT/aa+G2Xh8Z6W2+EGSSC9e3Hur7c57C2mIRQq4B6jB1mDp8nXCA/Mwci1qcUym9dNzR0ltqPu/rliqkAVTbbq4IxAV2TbQi+jaxs/w6AY6x374J+yS60YlwCFPLr4pxdznmbL5lSpRisPNsXRPpZuE1Ecou1loqnosFGGOJYmRFjIqUptEDt/w86pF2uYpbtfvcPuy+HFQt6hE2sTW1L4Ul4gUuAXuV1chpNjoxEefezhvu7899ifkWR/tW4N7Vv+HoBXk6qMPUYeowdXiEA+RnZI2lt+o4Z+a79beXIhb98fr2Qb7PKMpxT7D3c9xiDDVS0aIPghDbdk2Yw0SQffvYCfCcGNtxUI9t92Hy3+47enmRFQhF2LRaaRZ56C09s+c6vctFfEvBSCopZjmhbqsq6Lp0VssPKddm+ECodl8qBwlZgU2sFdYexfBIh6WwTYtG+text/lqkQt8Z+xFMNprHvbE2c77eB7cudyqOJOngTpMHaYOH+cWdZgD5FfIoVma1or9ml/tc3aeLy9FLPr7J0UafcSis/H8PEZR7qMV1c7z6EYRP388z4WbE2SRJsTVUuy+m9YIs/S5b15noX5fs/RatbR01t/+snl6ZvulpIjRhRdNdGMwcQag5flmAEFbdXZfYS0linJInO38XTj3bb5DrLX4DokoLT5yTVCHqcPU4euGA+QXzJpem2vy3Tx6UI/RRSgOVUofsvNijN3yfgV1XT9ENOImtOhDDLXwI8QwsfN6MfZtTLCbEJdD1vWA6VkT5mm0InTL9dqsEOZpcYj9twrotq7afLnqKVSl2napFI1YFbUgFUsuRLfwbNu6fVJPoYMEi1iEKMhBkHa5bNMiCABqdXXeZcRoj5dMzu27AMmOt2Dz7TWxr2+ZaR5cey/lTujnxX1NHtxjtTEi5BJQh6nDdo2pw7cGB8jPxDm23qGIxdIxx2rpU0R57thjoYcXgYyivJcLN0Qr6r5VuKf5br2F19a3axDjNDLhEQsX47ruiDCvtfacZWEuOXDlPLzvpv2Sd3EthR/ZhPg4wYo61L7ENCtU7MstZ51EMUQDUKZJ9Xw3eDFLsel8WtS+YGTy+ro4u2WXcy0qGcW57td9MfTHOjUP7hi3aO+Rx4c6TB0+DnV47TGvDQ6QXyjntBMa9x1Fee7YvQDvR0UE47Sls4UgnY03yXWTToyrELcIiIvxRLx9P2m2XgmSWI5bEb4YplaeRzF6QR7FeBTm8XssdB6eRyIA+wHfizBgdl8v0n7bl1GcuSrQKgCsrZCdiD+W1OOq2BdOViBoa3gPWJW1REHWVCus1Suts527FXBkIGl9PXrx7m0+F+e+iX3/PphrO7QcndgvFjkVRi/IS4Q6TB2mDt8uHCA/A+dWTC9tMy3Y2N/XhFIm988Vg8xVSu9HJcIqOy/G0Amw2XZ9lKKPVrggbza+PWrBRwhNmGPo7TzUIowYpoI8FeZioXV2nz3H/lf73BUudtkkamEb1srlmgcnpYK6RTCyAhttNl/OQEpFZDv7L4QixrX1kG2zk4wQI7wZfZsKNdYKaxEplh+wA2qfTsCENwcgINR93eYLXVX13nSoHsEqNt9c26E6DeqMmNbiEfEvnGkBySGOifOtRS/I40Idpg5Th/ehDjc4QH5izq2YPmbr7T1OmArx3H1z94/5bkuFIEt2Xs2PG6IVo4Xn9/c5bsVdquul/JKvuW9FxFx0e0F2wQ7BxHg/cqFVgE24jwmzMea9WSV16b8pLtTaCbNFCiJMfEW6aIf0x/MHtehEOwfLjwtRagHJGDXxnp2iiljsvxiD5cJFKV8ceW9qVBdYC6uk+j7QpBNxnlh+nVjO2nguxDP3HeLcQpFbEmfyeFCHqcPllh8V1OH13IoOc4B8RSy1DjpWKT3mu83Zeb58yM6Lcdpwvlp5YgUeY6FIiG2bOBFjqUUec9GKUAS8rq8CrVWw7XnovDCjravXauYSdc6aRS1EayMgF2KgWHjqUQl7zKz2XOw+O37O0zy68sioll95sP5cNAOhRG5yEfoYbb1mqQ3xJUgV6SDYs/lsutO+8rp8qQRAcnvdve1Qnwd3jKUWRITcItRh6jB1+DrgAPmFcWrF9F4Rx0KE45il52Lqx6y5U0PEYq6/ptt41k8zVHHebO24QYDNttl8m00T5O3Gj9ty20zgS0RiRox9uRdiqctNgGMnxrFUKwt0Inx9vpvfr0PhRp8Hp4p6f8pS16WuWb1XSqtKFeZUm9WbWOeS4xaL5VeXQ1lfbD5Vxf0OpZJasNuVHpzRoyYt0uDTo25gBSg5lXPOCmxCnRI1ZyBs2nSo6u+Z3L1/xorqri+nf7WFnPcKRerj+TpZzp1jJTV5qVCHqcPUYeowB8hPyDk5b+dOY3osajHmu7XH60S/i0z05zJXJQ3M2HnixRwt4jFGK8wmRBNnkZoP1ouxC3Bb1kmEwoU3it0GikjDixyaCPfiLIMwG9N1oZ+pSSzSkFUg5XGySi0OUQhQ1qdJNEKRskx6ec4vi+WwqZRza5GbFsUIdTankBUZdj37ohHA7u+rqvsm9qlGNKaWXQjBWg7V90CY5MGN9C2H1kQvLiHOt2LvkceBOkwdpg5Th9fAAfIrpo9AzLFUELKUD7eU7+aP1ee79VXSk0IRF92h4XzNcRNMLbxYRLkKtee7NTHeFGtrE1sEYhO15raFoIjSxDjIvDCLKAIGS68T4X699tGK7stNVWqj+JqTBqlRjKxSrTIRiziY7phY9q/b5PpPRFqgtaF98xdVLEphDevtmiYAIZfcN+SJzZdSnlRV903sXdwkLOfBadoXTO/LuTcF6oxQ9oUi1y6k5HahDlOHqcPXCQfIT8SloxazH+6wLNSj5bcm382LPWqLoE3Yq5IWOWzn9QUhPgOTWXsmzJtNi1ZsN8ti3NYXYQ46iVAEaX+9AFuUYv92vS4TYW7XZ1IUgqkwK6QKdL0d2u3c/blg77Ig+3Ky56JqX0a7YsHtkll7lisniNl7eNqfnVOrhhZpy7jPEIkTm0+C7FdVlyb29lwUuVwLLW2H+jy4atHN5MGdWihyaYuPYk/OgTpMHaYOU4fXwgHyK+eYpTeKuVt6031kstxHLPYfr4l3teuO2HkSmijHiL1oBTBtFxSCW3FFdEOLULgY93beJuRq10VRBLEPdJQmwkHy1Oarywsf7olIl6hEyYwDLJohGgApOW4QSCfzAi2vQbuOu/I/lEiGaZEWMbfn7foUYxFumUYxtNvX+3TmYs+NNh8wLQhBKq9f2n/OfQRjnAbVCUFqHtwosqdafIRcE9Rh6jB1+PrgAPkJOLel0OQYK6MWc/v0BSH9fXMFIXP5brXlkAu7oImuNFEOnSj3vTVj+QsBVcjd4mtV0vt2XhAT5U3UKsybTozduuutvSDZBNkjFm7zFbEucYbF6MWIQqpIqwpUushFOUZWMasPgqSeb2YFI15sIpiKtFt+Owg2JZeuPqafzqZUSUcT2axSvrwUkgXlYUpUo9l8NlNTaT2UtRaExBhMzLNO8uD8iydkmbQjqu+DUigyEVz7dltsTH9q9OIcrj16QS4LdZg6TB2mDp8CB8gvgDW23qH9RkuvLwiZRiWGRvThQJ9Nj0oUCy+IIGxiJ7xlfZgK8JydF4PZeS7MW7f2ArDdtiKQbemtuYlaK6I30cRYShRjE0pUIjQB9miFC7GLcECuUYwguUUroBA0oZ5c0xKJ6HFrTyXU5QxBLsqYNdgvegBJQ2lYb/enIuQpCGIRqphDraY2a09KP89WZS1SqqldIKXl2uXcipklAzkBqp3NB2tzpKJQLYUk5b6QtfqmOSjyrjWTl9BmeAKA4M+v5MHNFYpMCkuG6IXft0aEWUlNnhvqMHWYOkwd7uEA+QVyajP6yb4HLL2ePpJR89+63Lf5Y7coiIvytChk3s4zQe5sv/LnFdJu45mFV4o+Su/MKK0gJEwiEVrEtoiu5GLtZQQUkS7/ASCalJbjdL/AofuRi97WK1sApTDDq6ERJttJsehsXagWoH09qK2T9jxUTNyjABqsyX3QLkKRrRgkBkBjs/yCmK0YiuVp0RT7QglBalW02EOW18OE2qMNZgGivtY2DWqrpg4iSNBppGGIEnihyCUjEec2rSfkMaAOU4epw7cNB8jPzFKO2dI2xyqmp/vN231LBSH9/fuW3lR4/f5+utK+hVAQ1Fy30c6zghBUwY71T2vkYhOtoGMT86T4w/PcoihiSNPIBbSKdCiSGmCVF37/JGrhonLM2kOpoBZA65Gl/bKXaEcVi1YEBGj5FZ80l+pqQEITdvuVL0glP84lbQexYo5SYZ6y5bdtN95rc9/mg1uNCjtWzqV/J2oeXNxY83rPg7Ncudag3u2/vaiDWHSrb1xfG3t277MxejH3vhsrqdeI+S1HL8jTQR2mDlOHl7lVHeYA+ZE5lPd2rihP75+JVBwpCBnz3QA0Sy/si3K19KSz9DwqEUO18frm8ybATZjdzttsPK/N/m86O88sPUUUYLspAhwUMViEIoaETbHwNh6tgCJKQnRhRmp2HjKCmnhLLsKs7T8wFWXpBGXSUmiw9sb/WWK19jJCFeqkAUldtDN2GqAqCBKQcrSUMgkWyYAgwPIKa8V0ktqQf5da9GK0+aRES1Iqszfldj8QkVMuOW9m/6WULQ8uANilmTy4MGlcryUa4sv+XloqFOmXL5EDd2iba85/I5eDOkwdpg5Th0+FA+RH5BJFIaseZyHnbVbID4r7sL9bdGV1teyG7b1ApC6HZt+Ndl7obDyRFq0I/XLwAg6UXLYxx62z86DFzkstclFsvKB5IsRB7Re33S7CoP6BH8SjVCkDaK15SqEHNBXx9cIPa/WjbvdpKyrprcFQSkUiBCrZ9hRFFgHUilxCeeycBTFYtXQqkQXkZoXa612quIsdKgHQ5BaZb1dEtQiq9w7NqewfpPbl9H6bbvH10Yv+/TPKYF8oYuc1X0n9WFyrOJPLQB2mDlOHqcPnwAHyC+OcopC5+46tD8MxestvrJauuW2d5edN6WsRSIlm+MxMNZoR0P1HqYb2aIVbe1YM4kUgm5DNwivLW7fwQsZGTFyjJGzErb1dEWNF0FSjFUFTFeaQE+CRC52PXAAm1C7ETh+5yDaFEiJ2yCHWCEaz92Jbrg2JBDuUhqJiwuvr62PU0whQBTSaZdfVctSoxnZjtp1XVQN9pAI+gVQ5riAlq5zWbFOcaraIk6pCNFguXLH4JtZx126on9mpvpcGi8/vW6qkPrdIhJCnhjpMHaYOU4c5QH7BHLL1RlGeq5iuEY3ByvOcNxdf38e36xvRu6UXguVP1T6aJYrRbD37UG+rtWc2nrUWalXSbud5X827jVX2boJiGwcxLhaeWXuKTdghSkKAImLXIhe6Q1TrbhnzfYtYaCqCDItauCBrn/+WgUO/ekW6yEVot8VEGIAJtMQi0AEpbAEASTYIYrlvEQFJNtYfMytCsHIVi7aY5efRHT8d+0VeXhOxCEZWa03kL7eIHc/7cprwlu1Tax3kbYo8P87z4IJYq6GQAZT8OMD2C6VZfbP+rHYa2Qplaj9OADr07hxz4EaL79Kthgh5LKjD1GHq8G3CAfIjcY6td0rUYun2msdfKggZ7xtz4eaO0+fPeYP6Zum19b29539m5WmtkBax6mdvLB9gFp7ntUlfmuHV0Z7f5hGKIsiiGSGnZuflVAW5F2OPZCxhRSFeQZxNnEv/n3rpS5FFkW6oppLLlkq/zlAa2rfnZJag2HSlGpCLhamSkRCKrWdVzEGkVEj3Mz/ZbE8o1c52TS2KIUGhqXt9xeIk42tXc926xvUumJ4zORaKHHpPzdlr54juOdGLa7T3yMOhDlOHqcPU4XPhAPmZWFMYspa+pdBeRMMFtmwzZ+nVcxosPY9a1PVdQYgXhXhVtPfZ7GdnCsXO8+UgbZrSuhy8AESxjakWgbidtwkZG9nZsiTEshyxQ8xlOd8j5h1QLLwq1GlXhVhyMgF2Ifact87mm8OjFOViFaG2/xosWiEICHFTLT7RBECQwqZaeBI2EOly5dzaCxsAu87mi6XiOwLI1oi+2HzeG1TVLL4YABSbLwbALD5FTOVYSYsFqwCCWX4pA9Fy65BRBRjApHG95wLOWXzHKqmB6axO0/vPi1IwukEeA+owdZg6vJ5b02EOkF8I+9OO7tt6a8X8tIppF+yuhZBbemHaiH6/Wtq23WyC/aouQm1iLNhuUHPctl2em1dJ93beNpoY7wmz7LCRhIBkVdJaRDq/MWHWjJB3EzEOurNii5xKxCK3yIXm4nN1gtyLh1VF9BfTVteKl1CXNUS7HSJyjsXu20CLSIe8Qww7qAQk3WAX7iyiIRk2b5OVi0jYdAUkdfIkABGhRk2ka15vxR9+2kEsAiFZkZJdf399s+b6vZITSsgjTwpFYjTR7QtFgna2Yi79OItoL1VSa9rPhZt9f65oNcQcOPIcUIepwwB12Ll1HeYA+Rk4JWqxtqXQOceoRSYyte72C0n6dkPT4/htr4YO0ltN0z9vPu82XrX4vNE8zJ4KXXN5s/AsD64WfNQij4xa8JGLnae7GqWQnICy3gW6z3/z6IXkUZi7NkP2DWXRCLFqZ5Em3iomqQEojeNLVEC8JU8711AsvyzR7D21quuAjKyhWZYq9gVVbL52/dp11O4a22uIYgF6BbpFNII5d/U19+hEtfby8LqXKaP8PdGEc5q7Nscxe+9Yq6Fj3Fr0gjwu1GHqMHX48D6zx78hHeYA+QVySl/O0dbbLyJpxxptPaCPijRbz6MWLsatZdB8QYj32GyV1FNLz+08i2JYrlso05VuylSlMSTEkBDELTwT4y3ui7WXEfMOm/ymVEPvsElvWrQi3zeBTrsmxkWYkZMJcBe5gObW1NIZIhf1WpVohUgo0QqBFGsPIVabT+MGEpJZfmFrYiwB6O08wKIVErz42VrUl7CFipeuRKvmLgUdGUCO1sQeUESPGmTUaAUgiFW7ppGMlAQI9r3jjevreyaYtRdE6hSnSC0KNldJ7fZeL5Z+rNHeYzN68tqgDlOHqcO3DQfIj8DBJPozc94O7Td3n+e82f0yEeW5iumW8+bi6+2DAiRYe5qpGHe5cC7KQ75b30bI7jNbz5vP91XS28HO28q9FYYgVTHe5DeI6Q1ELd8tFGEOaQdJ92bnpfsWrdjtgGw2n5USl2hHFeguBw6YinQfoulsPQSrnhYJwGZjMhs20E0R2hSR4xYQQYgJWW29aEYKW4s4THLfAIHWKmQETNoOBW2tgzS0amWbLaqdauqehufBAfZa+HYxdsfSgIRcrD2rmk7IJbphxS7+3hgrqc3Ss0pqa15v0Zc0aOrBxvKPkAN3bQUi5GFQh6nD1GHq8EPgAPmVMddzc3+beRFf+sIYK6ZHwrDfJKdOmq3nVdJuQdm+bulZQUgAioXl1p62dfAG9N2UpX0/TbfsOisPxcLz3DZ0+W7Iu1a8oBmS0r4g56k4mwUVej8MCLlEGBRAhCBBI6aFEbkUbwAluuEXJFqBSk4QiQCCFbBIqbDWhCyhPd/O5rPgQrtWqNXXZim6jZq0WX9aHla0vS5eOB2CIKUmXF6VPXkvhBI+6Sqp594v51ZKr7EICXnpUIepw9Th64cD5AvzWG2Fjj5uteCmwrrUNsjXHauYNierRSssooGuWnpaEBJrEci0z6ZbepuYbZ14ZbTNxFSrpIudF2GCHHWHTbHtYnqDkC23LeR7xN2bIrgWuajRinRvYptSE+OcgJRMOHpbbyZyYU7aELkIrnilGj1GwItDYrQvAwmQuIV6k3tVRLcKNwqoQkOsRSk5RKh6JCJii/tq89n0ojtkDcihbK+CTcxAyYdL2UpMrHCknW7MrsbSWX6AlGpqIHc2X1f0UVRcQmlaP3mPzLcaGkVaQtjrxXkubDNEzoU6TB2mDlOHHwoHyC+MNU3p+7y3uZZCvs1cS6HR1mvHbDlv/VSmfTN6760ZO1GOEU2Uw7IoT9oIhVztvBisv2ZfJb0Ry3ELmrDJ98XOK8Lsdt7uDUIvzLsixvdvmhjvdtDUWXulureuAyZz2KP/1d19edVGmyKQuDHh9ide1mGzKSJ9D8l3EAnQTYJmWw/NkE2G5gCJd/YQOQAbQCRbs3tLkaszQCFskBTYljBKUkHWkkumQIpa8+A2sb0HmrWn5SmVHLlokQv/krXiEVmupC7vjVZJHRCyfWkcajVUe3iGtk+f/zaK9qEqakKeA+owdZg6TB3mAPkVsMZum9zXW2+d8C4ff/gCkNaUvr+vF/L540xtPbebplZf+QC6lVf+27JXSee9KmmB1srnauO5tZesCKTlttmyps7aK2Kt2SIaEzGe+6XrIi5S7xcRiwe49RfEAgQuSqViWn05WeuhMuWRnXeALcPOP+SEHGO5BqViXGca8pdmRKFUl2dIvbY6XO9DSJA6BWoQLFZS+7ZL0QcpOXD9NociDZfsxUnIc0Adpg5Th28LDpCfmUvYekvH63tuTm7XKEQfuWjV10sV01VoY4tahCAtaiFj5MIKQkKJWLioxJBKxXTGJvTN502MY7YpS0NOiMkKQqCKze7HIbtSMb17Y3ZeSkC6t8hFShat2DVrT+/vAQC621UR1l2qlp5mrRGLiUVVv0laZEglQDbRxDoESCofn20qUYwASVs7pxihmhE0Q2NEUIXqXZ0utTxIXczBohUaLA/OJVmgyMGkOakiqVh7Ji3XVgFAsOksvL6SOgXAbb6UBUhaZoNya8++UMdKatEAJIsySG7rzakcIg9FpP39NxaJPIRb78NJngbqMHUYoA4vcas6zAHyBTmW93ascvoSTemXzmUiwINQ15ZCJWJhEYrp+pojVyqmTZs85w2TnDf7s0rpUBrRb0Lez3crYhygiFLEWNOkSjrkXbXzZPcGYfeWFUncvwF2bwFZIfdvAbudRSbevGlRivt7E2SgLLu1VyIXOU8EZtImp7+W5RtHRCznDYBsIrDd2gYpQbZbs/ZSgugdsAuQlKBbhSSBbFouWX280uxeS39Pr5rOEpEllF6dGZqtiEMwzYNLwbe36unaUL57y5i7ZuIWRGz2JkVn7XlLodL3M1jz+7reLbqZVkPS9+4sUZ167XrL9ABrmtUv7bN4/5Xkv5HzoA5Th6nD1OFLwAHyK+PU9kRhYfvQifIx288P4Zv16WB1uxkbrz5WaS4PoDZhF8GedTX5G6qkJ9XS3kOzaxNU89nc0lM1Ac62nWZtYpxSFWQdrD2vnq6zEYkAKNadX4AQ7LF33gE+2TopeV0p2XKM5TxDtR0VodmTAfa8Qin4mLkOfpn9ejX5m3mtuteg2n0BgJ+eANDp09CxfHogiM3etBRB8F6ca6GdR64B6jB1ePG1og5fDRwgPyNLtt5cBGSxAMTtmGG9HT9M9nUR7ntu9sev+W7S9eL022U5FqG2AoNWMe1iHbqoxabYekGKvTdELqy/plVMR5Tm86UIJOb7WiVtRSBqkYt7KwjBmx83Oy8ni1bs7k2A37wF3e2gOUPvdyaSRYzzznLm8i5N7LwqFDP9N/tID0JAKE1FwyaWCmqrpJaU2q/6O1M/9S+RYDafABAJJYIRILk0r09Sp0mNEARJyDFAxYoyoli0JCMgiUJDRlLBxsIS2AGlWb1ar8zg0YlWSW3rzeLT7JZZEfxgPTfd8nPBHi28EKT24vSIhvfiTDntia7bgcC+GM/l1S1FHG7V3iNPA3WYOkwdxmR76rDBAfITcYqtd2wbr5o+tM2Y9zYWk4zthpZaCpnYmqUnAfV2LNafC7Jbepbb1vLevGI6lp6a/d9Gki2X2ZlitpmXYmfnxa5KemrnmRhrSsCbN5bvljPymzfQe8tzy7sddGfRi+wiDdR1WiMaQ4uh/gtLypdfuU6aikjGiLDd2LXbxFJVHCC5tJAPAZJLP84YrZa5VM/UKvYyGxREoJqwkQBAoBIQZQcNAVkCNmi2XwypfKcExKDQEsnYueiqlop3P3+U24qdmDhbW1A7nk2z6vlu01ZD3otT1Gy8XjQ9otHed14sEqZ9Sbv35VhFfYiH2nuEzEEdpg5Th6nDa+EA+Yo4Vmgy+RW+5nidlWe3R3Hf32bu8L1NNWvjIddKaXQV061CeqZnplo0YrJcbDzPu9Jd6uy9XG2+vOusvdREpEUw2hecIgGI0KyQUKy28qVlj19+watC3Eb09cXa0wRI9D6gJScuqj2Q25XI0+dfr4vM2n062HxFTy0SIf1rNq2uVvXXcbpvOiEw0IviNeSZEXJJqMPUYerwdcAB8pUwW1jSRScm20r79exN6ceem9Mqai8SKVGMgFpNLTVigUnEwqMWm5CrrRckW9W0JETJk4KQmO+t+XzppxmSNaK35vO7ViV9b8Uh+uYN8MYiGvnNG+hbZfmtNxal6KIVmjPymx1ySiUPLpu9B9TohS3vF4d41AIAwiYil8hFiBHhziIXeZcQdmZthZQQ9A4oFl6wg1gEw6MUQRDuS2P7sEOUN2btyQ5R7i1yke+telq0FookKKJEZLEjh6DYoC17JXUMJsAxALsASCkGCcmiG1YoAiAKsldNF8Hue3EGAXKwZvXaRTQ8WuL23Nis3o5x3ZEFQuagDlOHqcPXAwfIL5jRpju23bFtan5bl/sWpB0/7AmxC3XLiXJrz6MWsRQd+H+R3sqzX9ejrRclIyCZpaednaep5rtJui/CfF9z3OTNm9Z0fncPLdaevvXGqqNTQr7fIZdK6Xy/q1GKfH/flrvIhQs0gL2WOf11s+Wd5bwFgW48mmF5cMjZKqp9/+j5asXaCwIVgcQNJN6XiukMCSVxUDNCiNAcoSEi5h2yWF/OJBsEJEBQrmGx+SQgo7RsEoUWQZZi7eUizjrJa9OauxhK0QdQIhydnWsTUkkT5XKZQpByX6g9Sg+95/TANlXYr9ymI68b6jB1mDp8m3CAfGUstRW6xH7729h/3zSUqmjHb48V0/0fgPK/WXrN1usqpSd/Wi0866mZa8sgTcksvVL00aIVc38t/23E10nQmvfWr9di4dUiCrVqag0BuolWJFIEGyLFkiy2ZErAxtRStLThUe2eu1lvHiPYs0IF7doJEPocNLHr7g3s6+uUm7U3+7oGTIpjlgqUxqb0e7045VB9NyG3AXWYOkwdfv1wgHwhDuWUndoS6BB9/tlc5XTdrnvMuRZCffSirpPWlN6O4dGI1qDeKqubned5VqFGMBSx/Pdf1B7FiB69QCkKcUtPbSYjSTsENVsvpBKt2O1s2lLNFrUodp6+eQv5zRvLZXM7LyWkt94gv7kv0Yodki/vEvIuF1svT4tDul/NHo1o12laHBI2qf73KIYLfxVotMhFKD05A1zYkhWcxHuoJEjY2G3N0LhByPfIqgghIcoOItkiFxJgrYEyott5khE9ihGsQhpBW/RBXajb66XlPglqTenFIhkptdcfefoeQ9oXYH9feYGIV1CPtMb2WvcZZ3I6l0MRD+bk3SbUYeowdZg6fCk4QH4m1s7ctBR5WGo31N83m/MmvbUX2vpuW7fy/Bg1QuFC3Yp+96qmTaSLrVcsPXFRRlc9XaYxDZohVaAt3w3lT3LJdytTmGqZpUnTzloIeZV0b+e9uUe63wFZsfvxN9XGS292s9Zeum85cEvXOG5jvR3v7CMTNhHxbiriHioQEcimFE/EeyAEaAjA/T0kbqC7+2L3RWiyZQUsxy9Es081IasJetCEINGsPdisUBAgiiKL1VX79Zaa+2ZV1CbG3WumxZ4Va0rfV9n79LP1dS/iZjZem83J7/ei8zGiMVdB3W+/v/64gN5iiyHy+FCHqcPUYerwEhwgvzCWIhHTGYX2IyGnTpU6VkLPrfcohS37/f257i/3Z+bLzYbqG9K3imnxT6xqa0w/a+k1a69WRJflZudpLQCZt/PsL6fD1h7QohjpvkQrAORdrmLS8ucywiZDEFAb4e8SNMZaVa05QybV4MXCK8tSbD5RrX077bpIvV5AsOsnCii6amoXV9SiaI8o+V97fVuVddu23RjbBvXvC484rIkK3JqQkuuCOkwdpg4TDpBfEUtiOsfYX3P+eEV8Q5vW1PfxIhB/XC8osGppE+wwfPhD8GiFFYhIsfVMkHMRkWR/apEL0dRsvXRvwuyWXt5ZYYgXhNzvahGI3u9qf02LXLSK6fTmHnmXkd7skN7Y+vRmh3RvXwDpzQ45TYtDdKa/jpQelWETASTEbSgVyEDcWlW2hIB4V0Rt01dcWyVN2NxDQ0AIARqtR6hEy41DVmCT7DkGhcRSHAMgpx2CROQSxQgaoZI7Mc71+irsemc1W9XyDKW9LvWvRCuyFYmotmhFCKizOUnA3nSnS6UbayMPtq1ZcXYe87bca7fkyPVDHaYOU4dvAw6QL8ApPS1n958RzlPy5fqoxaIV2An1oahFb/X4f998jFS0D71OhNqrpt3WC131tEUr7Jd5KKIcNJX+k1ptPeSd/S9WHnJn6fk0pd5fs8zOlFNCenNfxHhq56X7PF0ull7uIhCauvZCMQC7ZlsBgOaI2OXGSciWQwYXqOwXEiFGyMa+NCRGaEy1Lyfu7216pRBLL85ig7mlCUCK9YmMGsWoX2rlGzS4tad+vRVZWnshu+5SKqdbtKJ/Pf2L2U69VINnIC9EL7ySujawL9XR/fvLr1cIgrSk6ANzeWwPraqmyN8W1GHqMHWYOnxJOEC+UdZWVdftpUUxRl2fWkeHPwjSCclkfbW4uuppx5erpae14Xz7c0tvrjq6beOWnttOLtAAajQDsByzcUlyRk5iDeK94X3pM9lXVSMrVNrjQqQ1z++/b93q666BVVNLszvRLLylumQ5cs3bdsvWHSHk6aEOU4fJy4UD5CtmFN8xP67245RpFbb/mhUpNs/QRsi2Gf+6FkLF5gsAar/NUvXb57vVqEWe/nnEAqViGskjGOV/ae2TvTjkTSkOKYUffeQi3Zs47t6y6IYmRdplpDclcnHfBHAizLGLTvh0oDkiJkWOgpC8YCQg5oC+yjrvEiRbjlyI1qczbGKbcSpGyP3Oohf+XN3mK0UVfi1CgFmfYrM5hZARS3FIKNEh1Vivu1uq9hrI5DWqz61GLLQW+fj7oH8PeBV2baHkFdBDXtsp9h4htwZ1mDpMHX6dcID8DJxayLFEtVe623b8aWuh1ccbPpzTx2r/w/Dn60VQLSZbp12uVlcQAjXbCtr12dT6S15y+e9C1v33IpDcTV+ai7Vnwpxn7by8S0WkFelNqoKc3tj/PFhI6b5dx3g3tVm9gjhHqdaetR0S5F00YQ5i1l5KkHK+VgUuNhWqZmv6nlKx9wDJCtUMaOiuhwLleqmEWigSyuxOolq/FIMosspEiL162l+rcbrT/ddZLLpyypynhRACcs7oe3BaJXW+iMXGghNySajD1GHq8Onckg5frjEkebEs9d5cwnX9UJ7cZPuZTQIwa0V55AJoVpag2XpVnIvV57lPkxyo3Fl/e5betCK62nmp3J8yNNm6WiDij3Gv9a9f79tqKvtnrceYWHrA3uPXpu9qdqQvj8+rVYu3pvyWDzhYf30z+q7B/1ipvvS6jMz1Zj2FU774CbllqMPU4SWowy8TRpBfIOc0tD+2j0dLlnpvyrD7tBDEm5qj2n2jZRTKD16PXkysPo9WSJ5EL6RGLVrrnSpQuf1y17RrUYuuGER3pShktxC56Kw9t/M0WUTD+26mH2uiPOHHANkKEjLi24fIRSyCGBM0B0hIyNGKQySEGrnQXUKOpRo6JoRSSKG7BNlYBproXelVGevzt9w3uy6KgJATcthM2zINsznVKJFIsVRbG6H6V/pv1ip5rxaB23v9+6m8V3L//rI2SEj2flKd76np259a2MGpTslLgjpMHaYO3zYcIL8gHlqFPTnWil+je1OWiqz6tTvdB50Itw+5E6po+C/0JsQtaqH1V3v76/tUlp6W6v02LQrgAjzOxuTRipwU+T4hd3ZeTop0n6D3irzT+h+YirNsBdgpwsbE2f6bsIauSXsIihQEYaNd0UiJfOwSwrbrFZoVCO15TPtxyszzV8t58+vl11DKtRNFUJvOtF53RdtGAGD+Be0Kn6fr5SxXb1I1/VBec9Uzef1Qh6nD1GHqMMAUi6sjHIhgnCr83i6o3V5j8zW7aa9C+kjVrgxi7LbdhAO/bKdVzId/AbsYz4lyf3vc7tBj23/de+xJ4cR4Xr3111meS8gKweqrqedesmOv49wX9qHbhJAp1GHqMHX49cMI8ivgHKsPOD8vaf+D2B+z77O5f7/d1slyL9LN1htmcKqFECi2XifS/su/j1So57JNpy21opC2LucSvbjPSG8ycs5IP5bPjFxkm+u+m84zA5Bdgm4D0n2yKuk+Fy+ZbeczTaHM8iTedshtzOB5cRmQ2OXASbtO5UJPrmfXrskLREb610ubW1ctv9JS8yKCG0JAyjMhkRlo5ZHXBHWYOkwdvi2eLIIsIr9QRP6iiHxIRP61mftFRL6+3P9BEfm8pzq310Sfs/a4j3Par9Wxhc3sNpPIRfvF7jYfAKucHtBetMs+Js4tWuD/+whC/39yvEGUJwUh902ke9Gu//sIRcp7jzPt+VnWeZFL/eLp7ErbqazXUjne5wPuR3/6L7kljr0el3z/rBkAtAb2NK2eG2rxw6EOgzpMHb56nuQqiUgE8DsA/CIAnwPgnxGRzxk2+0UAPrP8fQWAf/8pzo08jKWG9C336oEMwrpvm+3/8m0zMrV9c9K9FkJ7DzWIcz1eJ9bAfiuiNsPTY+ZrrT/2Odf9IRXU5PVALb5OqMPUYXJ5jg6QReSrReQnPvBxvgDAh1T1+1T1DYBvBvAlwzZfAuD3qfFnAbxDRN71wMclK7lUm5g1swx5/tZijlexu6roerRAu7y2TgT3ZlDqD5XypPH8KLJjxMLJC9vV7WvLofnn0M8cZTt0kY0+gjG2ITrAUt6bF+jMcWxGLXJzUItfMNRh6jB5OayJIL8TwHeIyB8s1tw5n+BPBfD93e0Pl3WnbkOuGc91m71rZv0BMcsnVPKOonxs/SFmoxdHClbq+j7fr2PuC2xJiI8V4KyFfTVfHiLyJ0Tk3cO69554GGoxOQx1mDpMAKwYIKvq/xlmtf0eAL8SwPeKyP9FRH76CY8z9yqP76A129iGIl8hIu8Xkfffv/noCadBXjRSmnzO3jWz/oAd5VOUriFsF1rwLKw/xKxFFg7nfdX1/vyHa6Az10R1/tx0oZ3QqeQbb+/zQvkMAF8rIr+xW/f5Jx7jYlpMHb5SqMPUYQJgZQ6ymhfxQ+VvB+AnAvgWEfmtKx/nwwB+anf70wD8wBnb+Pm8V1U/X1U/f3v3E1aeAjnEpT6IS8LQC4mWX8VzggPAhCl007cOBTESwkSUJYSu8f5Q1BLDrEhLEV3/P4pwGO7f2z4KQhRIXBJbKeflz6GdezVh+uexIvdMF6IJVkMyf19eWE9eJR8B8AsA/GQR+S9E5Bzxu5gWU4cvD3WYOkxeDmtykH+tiPyPAH4rgP8OwN+rqr8GwN8P4JeufJzvAPCZIvIZInIH4MsAfOuwzbcC+BWlgvoLAXxUVX9w7RMhz8PSB19VZueYP5m96VnDwdu2rohgJ8ghCkIIVVhnH2pBpPdEeTyHOP+lcFnWH/uc6/64hS3kQoiq7lT1XwbwhwD8aQA/6cRjUIuvEOowdZhcnjV9kD8ZwD+pqn+1X6mqWUR+8ZoHUdWdiHw1gD8GIAL4BlX9bhH5ynL/ewC8D8C7AXwIwN8G8KvWP43bwafRVNVHbTGkWYFO2MxEWH68mU44+9tM9i/LIlCRGsXQIPOPMp1ztUQAAhRpErWo7Ze6dTq0g5StTQNq3TBbP0q9172IRdgM//e+GGT4vx9FESkRjD5iIdJevy6Co6VZpkqwSMXwGns3U19e4tjrcckZktZEvSaFPeRc3uMLqvqNIvIXAHzVKQegFl8G6jCow9Thq+foAFlVf8OB+/4/ax9IVd8HE95+XS/4ihPF/lZwMT6VrHpWkv8owv3nLisg5UOf1YRt/FyqSt1dtQhvJyaKIjzlv01MX0RIUTqqtwnrJUYoANnEInZmj0mZh16CIGwi8s5EOm5jaxafFNhGhFIsIsnOIyEjbkvTeT/xzbwFGN9uW8S3B0ix9MI2IGwjQnlsf1z7cmjrJJb//mVS7jdbL1Qbs/6vD+ziHCbXq7+G9fr6NVWZjSTl7vXqAxT9fADtdX8Yx1o49VCkT0NV/4Ph9v8I4FefcRxq8RlQh6nD1OHbgt2ir4xDH4xTP3j+gW63j+/vwtCLR338I/aU9sURPrXQaJeNkYPuV3//5XXsi6yPSMhW9iw/XzdGLpboIyb79mO373he/TRY5bkv5gRiOf9tso3Of6k6/es4d//4Pjl2mxAyhTq8vzwHdXj5furw88Oppl8Ql7TrNOvRXKy5D1w+sfrWCxN6K2ki5uUXtYlNrjaeQsv/AJHcxLj+tciF22AqpbCi/PJv0Ypmp/m6AMt3022E5AzNEQAgQaFJkbdnRC62EXFr0Yt4V5ZDaIUiYRqdqNGLEqXwCAb8eXRiPP/8BYpQbb5esBXBIhULESZ7TU5/L52bAnfJ3DkKP3lOqMPUYeowdRjgAPlFco6VpzlDYly8P2dFKPPWIxZbJdrc9PCWj93uqs3cU1XkLHW95pZb1dtD2e8XqcJgAmxRjKydVQWpuV0mPlJ+tatFI3zCehFI3DRrrzxHs+2iCfAm2u2sCJtUl+OdAtghJ0H0WZZKQ/l034nW21Ebzzt9JCNuY/kfEO8CJAbEjX0xhCiId5sqwqGsd0EOmwgp5yex/G0iECMkbpoQB3/+Hr1w27NZo/YX7DpWOw/dtbbbGb1d1/3l9t9mWZ1GMPqgl7UBbdOwtqlbtb6fDonxObYdrT7ykqAOU4epw7cNB8g3gGadVBIfi2oUzYZmRVZF9Dwrr6YYt9f91RnzVl7Nd9NUc7vsWyCUyETultUKYYD6H0AtrrBlKa2I7HYfxbDbpRAkCiSXvLmoCP5Fk+zM83ZfFLwQxNsTSWknZDltLVrhjzNGLibWpEiz9aQvYgkTQUYV5NBFLUrhTJf/5tfS/+dhnb8ux8h6WGDX7E8IOQ51mDq8BHX4ZcIB8jPgUYSHov5zM8R6WyDIOSOWX/gmrCuPN6ew9bHa/9z9yfgLGYISHJkUhmQIBO0Xd5aIiF395V4rhSVYBbUEIBTLL0YgwX7tbyKws+hEjhEighAjtEQrJOxa5GKbyvPKCKlco4WZnbxopMcFOWyLtXcXETelQGQTETZm7cVtmI1chBgRYqw2pBeK1KKQaBEMjbE+7ybOnc1XrtcketEXiui0MGQvotT9zdmv09f5fKH2vMtJRKSf0vWBZLZAIheEOkwdpg6fc/zb0WEOkK+YMUKRs7qG1/uzKELwD5N/sLWzAlskwwXXthn/pBNnIGdBDkBQQVKzoyBArJXAihwiskR7/BChwfPTimAFgaQE7Mr6ImIiAZISwnYDTQnhbmO2U0qId5v63Mwizcg7E+gcBTkpJLaWRDm23kP9tKh9U/vQWXtu54VNwOZtm2LfBcS7Tc13cxEOd5tqR/a2nmw2wHZjIlyeqy/r8JclIodYIxhZA1Kx9/y6VktVgZQ7oZ6xYAEXaLX7s9t6OhVU1fo+GIV6FEj27iRkGeowdZg6/DrhAPlG0V5l12xfhDurQoaig+mHXhC6+en3Kqi7djiT9TXnS1sRiB+m5oZJsfhym9WpzJLUtxqa2nxqUY6ktgxAc0AI5eDbWIUloNl7PjOTBKlRJi8E6WdnGu08t/Sm24TpbE31QUqkoixXG2+ooG4Ri/lo19oiEIs6nSeiFF9CLg91mDp8CtThp4UD5Avw0KrnuWKQUwpE1liFfo6aFTnM9+XMqgi5bQ9I+QXbLKN2vN7mM8F266jadxoQkMv9AeKFIqUgxH+VI8NsPxGLWoQIhPLWLEUUClgxxSYBKZXIwBa6K8vem7P80m7FIXYtY+6v5a6Jd4lqaFJgM7QFcmtvUwpSSiEI4FGMYu11xSHxbou4tYjGJFrRRy+2WyCU5xW751ueu4Y4uT41aiERWWOx8QJyXxTSFYvkyeuyH73o/9foRC0C0UXx7vPklloO9QJ+ihU3Vxjy0GIRVmHfFtRh6jB1mDp8SThAfkWsaTjvdp7nwWlWqGQTvL3jAVIsnpzLl4sXhYhApItW5CLSWZCg9UMv3Yc+F1spZdhjB0GCIKjnvwVkRGREQGD5XBLNAowb5LxFyMmEabMBsgA5QZJZcZoTkHYmeikh5AyN0T7AJcdKs2KD9qGWUjFuFlyyCuti8WnO0G2YiknSia3XF32EKF2OW5zYeZuP29o22w3C3dZy8rYbhLfdWXP67Qay3Vr1dyfOiBG62U5svRwiNG6KKBd7TwJyyR2062jthZL6NS9/KuV1GL88XVibredfpkCppnbRLe8HF+wlffWK6rX4a2LnMS+6r1lMyW1AHaYOU4dvAw6QXxhLUZA+kmHLJ/hyM2TV2TqQafNyrZXRvnrMf8Ow3BdY+/JkhqHaKqebwck9PI9qdNXTqFXFtiwh1GuhIUD8utTlYq2hq2IG9pYDAESb6cnFGwDiUHkNtPZCvX3X/3kEo1p6ImW2Ke8X2k1xOum32f7qbE21WKZbV66XXVNpkaRi9c1J3Jib2F7fudeu+2I6ELWY236JWyrkINcHdZg6TB0mHCA/E2srqJdaAc0WfsB6cHoV9LiNJ/zX6EbXg7PPhfOIBjzykS2ikbNpi3pRgQAp25+IRTg8gpFLD077ha1IpTjEihlCjVxkCQgAUthCZGcpbW5xwQpF1KcJTVtoShDNZu/Zz2+ElOy56NSi2gBIb+5bbtvGohx5F2vBiK/zfZyxXVHrpxnq/97OC9sSxbjbWuQiRlu33Zpgb8qyBMhmC2w29qUUt1YUU6IVVhCyaVEdt/RKQYhfv6TBohRaGtV3EYuUm61Xrb1JIUgXxeisul5Lx96b++t0su30/5xNNy/UayMfFHryGFCHqcPUYerwEhwgX4hD+W/nNJxfYrT3zMKb2W5oMSSjSBch7sXb2hVJzXvzz5d/aK0q12y9lFtAoX7Yxap3EcwK9HY3QQVRBUBAKDldUBPmFLZQTRBNZmdlgcQE5C1EAnSbIZqhbvHpnYnzXSn0SAlB79r5w74kVLVGMZC1zuykWcv/TbWmDonD2Fezt/bCJgJBEHs7725b7bzwtjuz9GKE3L0N2BRrb7Npdt5mAy3ibLbettp7KWzKl1csghy7qmkpy1JeD0FSr57GpHI6V7F2W69ZfL6tXz9fP3mfYF5A+2jG0tS6Y7uiS/brPJQbR4vwNqEOU4epw/tQh8+DA+RXzFxUY/yCONaMvt9v79hRqgXUPrD9sQGEZveZEPcfQrGCEO8R2c3m1FcD239vzK515iK3uKSz9uwvw6c5hRbLL0YgJXgjeLf8Qow2K5TbfuijEj5FqtTn7PTXzItD9mw9j6gUC68WgYjdB/Gq6VCrv+F9N/sq6Rk7D8P1GQtA+oId/wIcb+futfP7ll77UXjnhG1OpNfsR8g1Qx2mDlOHrxMOkF8wNcfriLiuiYzYr7yALFpmRvJKaiAUZTW70T5sWaQUjlikIsCmObUfi1rsJPtFvFG391CnQhUxgQgi1YIC7JdrtfmQkWSDgIQUNgh5V4RuixCTiZcqdJMgKUDvLIohxY6UrJAYa+6XVAG1/DiEANmkcn0EsklAjVy4XbWZtaTaDEvTdkUerQjeX7NUSYdSMe0FIZAAedsdwp0tY7O16IWIRS3i1gpb4rZGLnLYIgez/CZRi1JUU/ttaqhRC6tSt2vcem/a69FsPo9ieCFQi0a5ZZa1WXe5E2Bf7+SZa3X4PXfo/vXHIuS5oA5Th6nDtwkHyFeCzszk1LcUQj/FqSqQgRzsF30OoVRPa5k/XiGdzWMC7paRRS9S8mM3UfY8OECazQdrK5TElpNmJLXZiASKINnaCkERww6AImhCVmu3EzWbeIaIoBm6VUjemcVnT9ymMAWAnBEkQOJ9sfbeQEteXIgROfXCrFDN9ef9nDhUcY4tctELcy0AibGrkt5CthubtenuDijCLHd30G0R6bhF3t6ZSMcN0qZbjlu7vmFr4oyIpBvsNCJ3+W5eJb3LASlL+dKU+hr4l6bnu6XUquTd7nMhroJcbT//QrbrkrttZm0/nf5fup6EXDvUYVCHqcNXAwfIV0TOingggKE52zSaC43O947n1pDaHjZd6mgjteX+/+RxvR+n23x71l6rpBbNrXoanmBXpFfMIlNsIFKmR0Vo1p4INKVm7ZXCDy+YEVUgWEV33iUIzPZT7arRs04ayYuEGrkIm1ijI/D+miGYQBdLEcXyq9OY+rmF2M6/nGuzKmVq6XUV03u2nl2VvYb1S6+DRy2mr6vubXMKvejOWXm3VshBSA91mDpMHb4OOEB+Io7Zb2vtOQnBCkQWtu/tQIQWxZgrKun38cIP1Mpo298qpssHOTRrL2WBBIVoKyJxOy9lndp8EKRgImo9H+28EwISIkQUQawYQjRDNEHC1qqkNwpohuSEvC1NdvIOqncmS5pLlXUpAgGgxdoLRTyRcy0OgSpyTAjbXK9DFZpeUPrqab9ubu2J1GlMq0B7U/rNxiy8IMXOs2iFbrZAiVxo3CJvzOZLm7taELKLd0idtZdgzeg9apE1IOUWwfCem2PVdI1eeLW0arndpjXNSdttj0xkTCIUffHMKMBjkccxm84jIIe2Gbd/yP2EzEEdpg5Th6nDa+EA+RlZajE0V4k9WwhS8tkQMBSE2K/1XMTJ9/Uq6iz2uNa8vsuDk5L7VvKiwlBhq+UDjmIbpmTFIClJEWKvxLXbu2xRgiBFPMTtvIBQrL0kG4h6Pp7ZegKLMkjxpWRjwuwWnugGAlh0I++sylrEtg0C3N+bNRnvLZKRFXp/D9naE7F2RJ1IzAhG/dITmebB9WIcY41UWOsgs/awKct3b2t23tasPZUA3dy1VkJhixRtfQ4bpLC1qnJskHQDhSBpLOJsOW67bNXTuxywK8K8Sy7STZBTAlJWpISa95a6/La+3VTWdtvtvbHwo9p+9XqVvLmaRzgVyyb4+yI6V429VFjCSAh5TKjD1GHq8HT7OW5RhzlAfmWc2qqobzM0Xa+eKoe+9+b+41mhSIzF9QKqUPen4TZfVtSWQ/WxShHDXCV1hkyb2Ptfte1KVXUoQixmeUnYACEVmy/Z9KearfWQN7GPEVCFwmw+7JJVLgNAKE+iNH6v23f0ggyvkO7y4OCV0y7SvZVXq6K9crpVSqsEayfU/x+qypuN16qkfTrTJfrXoFp8HpRp3z81QJPzvED2uAgvieNSW6HFc7zyiAO5DajD1OElqMPXAwfIF+RQD07gNHuvFXasE2KtajktEGnH9giF5b950UgO5YOn2JvuNAet61WLSCdY306VVijSfuSXyIZFUnbJ9A8AYg4IxSIMEhAhEAWCZmTP9OoKRQSKkBNStN6aosnOD4BobjNFqT+fN2YBSrCG9pqB+51NJ6pqgp2sKb3uUlUsLY3q6zVEO/+67PluEtpyFWOxL4XtptxvzechAXp3B0RrSp+3dxaxKJGLFM3ay2FT/iJ24Q67cFeiFVYQojBrL2msUYsWubCIRfbpTTtLz6IWqBXSbvHZ1K6KlLwgBPBm9eO0pmOEordBD7UVMqt4XbShHm/Yf80+i/evfGxynVCHqcPUYerwJeAA+ZlZO5PTOcerYlxE2quo+7y4iWB7hCArNCi8Wb1mIAE1eoGkSMFEGWh2n2Qgdp8ZK1RpldQqxebTUM5JkSQ2IYbNWIRQxLeLJAQtMy6JNJuv2HnhvkQFNEPifYlYZGi4h+QNkNVEWbN90W1S/fBK/5MeM1+eXvSBItalIMTsuvLxCbHOzlSbzw9V0nnztmrnpfg25E0R4HiHXbwrzfqn+W7JK6arGAd4M3qfsckrpndpX5RTEdqUSvV00hrV6Kum+yr50Y6b5sLtC3V/299/l+QWbT3y9FCHqcPU4WVuVYc5QH4FzEUvxmKPyX25VVFXEZ7JnWvHn1p7nv/kvTi9UMIiGpi0Kpoep1l7dpzBairFI6oCCMov9IAoudhYEUGT5YFJW1YJFrGQCJVkzydESE4AcotUqEAlWSW0CiSqtSDyE0qAxGDFJC4q0wvX7L1ejPs8uFg+Mp19J3FTq6Pty60sT6qkpdp4cBvPG9J3X002LWycWHt91bQ3n5+18XRa37L0Wvdi1/fcHH/xH7L95prVHxLRuZmbaPOR1wR1mDpMHb4tOEB+YczZe+2+FmXoq6iBsCe6tUG7SM1/cysvlmMtNav39SYEatXQCsSoULXemyH6B02KbpnyTiMXFtnYQRBDEWRk3IvZfC45Nvvpxm5LsEOFFq0ALJLRnpwWgSvRirCDBBNnkQDNqUUxUnmL73YtcqF39VukHndOVPyadvlrtVikRCnsicZJtEI3VgFtzefN5uurpHPY1IKQ+/g2JLFm9Dvd4B7bErnY1GjFfY7VzktZsEsBSVFsPZR1XeQit6IQj1qkauehFPbM99xMqQluK/7olrVf32y5uZZDHgEZq6aP2YKEPDfUYeowdZhwgHxhjuW/zXEJe88jFBiiHHPN6lXKByS0lkJ9s3opVs7Yasg+tBkxBuTUPkz2Y79VUjvWzUewgWKXBNZVyEQ5i9iXgiqCBgA7SNggIAMCCLTafHb08uEW69GJJBYVUEWUNxYNUBN2KcKMEGHJeoDE+ybElshXfvZ3gjJXPW03JsJcoxI1ytGEWYPNymQN57e1+fxYJb2LxdqTDXayhUJwj2218yzHbYMM1Hw3VWCXrGLaRdiqpkdbz0TZhTblkvOmQEq5ivJcSyG/Dq1Hp06E91BT+v4aHis6WcM5tt415L2Rh0Mdpg5Th6nDD4UD5FfGIYuubdOKRCbrdVow0q/3YwO5CU5hbEzvRSG2rwmCyNTaczfN7CcT7WxabxXAqrXlUBZt9pZP24mAILlO8xk0IYcI0QQgTJrYa4jlG8SE16w7aZUpqtCwASTb+qyAip2kdkUg0olxf42HSugaNfH1waw9t/U0xGrl7VVLiyAHe04Kaf/VbD1//m7l+ZSlqujsPVufyzSz9XXQ9l3jr0uvU6PQ5U6M+/fOKL5L75e99SuiDpcQbEKeG+owdZg6fP1wgPwIHIpenNoeaM1+s7lxWRHQmtVntF6cXjE99uI0a88+PAnZ2ukEQUSotwHTbbeAYP3fC1Nrb5da2lgM1pMTAAICgp+DAFHahzWUXDA7mmKLeysWQYbm0NoUiSBms/Oy7BCKtefRCtEMiakuIydIVqjmplzdFKflQrblUaR7cZZgM2ENYuzLOW5KhMKsvdpwvkQrdqE0okfYt/NKn837HJHyUDFdqqV3SUoUY7DzUr/crLreykvJ/zK8Yjql3EUytNp3LuRLPTf7HqZzUYZDQn2uhXfwmFcStSCXgTpsUIepw0tQhw/DAfIL5OTZnEobIhxoVg9gkgPn0Q9vXO6zNOVgWhWKVbhUSS2dmCaxyASA0mpI6rJ/XndJEIPnwVnUAggW8ZAMIJaKaC1CbL/fi2Nojxcw7eMpEYAiyj20iLRVTFsrIslNmCWnIsqDvQf7guou2ESUtc9/816gbu/tCbPUpvO14XzcAhAT5rBtwlyqpCd2nkbssq1POZqFV20+F+OW7+ZV02bZubWnnShjEOPDFdMW+WgC7e+P0a5bynlr69r6S87aRMhTQh2mDlOHbxsOkJ+BU6IXc1GQsUhk1TGwfwyVDAmx5jf5Npozavk1PDev/IIVmfSyd01ze8+sPYUUS6qkpxXrSUpenamtr08IJTYCBLesxHLwAnKz9sSmQ7Venanmwbl1Bi1TuQZ7zkH9+ZXnrmV7lSLQ9l/7J6QyjVoA+4LcVUOjs+sggiybzsYLQFcl7TaeW5i5iHPWUOw9X28WaNLQbD0tLZrKdfR19vr69W3tg1zjpt855f48XzE9FnhM7zseFThm+c0d45RoA4WbXBLqMHWYOnx4n0PHuQU4QH4hjAUil2hWnxEmvTgBlCgE0E95CqBWTAOASqukTikjWsmGba/2i9i3DQqkoFXLYmler8HOuUyiZBae2n0ipvsumDEovL9RgIkSYNELDVKiFREbJBPssj6JVVzHfI+YdwAUISTEfG/PKWytQU+JXEiJVvj/crGmldnjtXRBBqoI+/8qwAhWJQ3YFKUhYoxWWG9Nn7K0bz5vVdKKZudlAPcpluiE4D4Fi1iUyMXOZm2t1l5KwG5nfVBrpCKXfpudxZcVyCnvVUxPBHtYD/TRh2kfTifn/QjGIdY0pb/VvpvkeaEOU4epw9Nj3jIcID8T5+bAzTHae33xiOfAzbUaGqMfxyqpc6meDmJN5720OWWtdRgpSRFty4NTBbBBWwYgJXcLKF84pe0QEBGLzdeOvquth/xXf819k2Q5caXIQqCIsitFJBmhRDwAlIpqrULtJyMu1AuoRy2AVuiBLnIBWAFLjVbEktcmtem8IiAhIummiLE1n1fIpEq6t/P6NkJeHd3P0qRl/W7Xlr19UBVlbRXUOeUmyr3Fp/bl6+8jX1+f/xFbbxTQOVvvEtxS1II8HdRhgDpMHV7LrekwB8gviDVthkZBXxJ4s+oWjlEjIVpmdMolx0vqh7KvpHZrb+44Wn7x2nH816gdx1bb+pJKt2dVxQAkKCQLgigSzH4LalXVWU2cWhN7KcexymtFs/sUgEgugi7IXRgk1AcXKAJEPHIhOGgvdcJcBblEM7IUYQ4RKrHYd6Gtl9iazdeqcKnV0rn+t+eTVKqdl7IglUiPW3ouwGbjteCLV0HbNtqCMp34zr12fXRirm3QUkuhOdZWVK8R2FtuK0SeH+owdZg6TB0GOEB+NA5VUK8+xoy91+6bthnqZ3TqoxIAkBGKlWYRCJ/eVCD116VXUgOA7DKwCQjl13AsFdJpZztbepjWFkIiJgohAve7NrWpiFmJGlvVtX/mUhZsSs5Zb/P1uXIhaBFfQUJADAGbYu1FCYhF5rKEavMl2SBosvw4TW1q1JwAaI1UuJ0naB/o3uKr0Qrbq65rkYyS7wbUFkgerajLCJNohee47TQidXZe7a3Z9dm8T6FGK9zO02LneZ/NXW0+PzSiz1NLb6+Cepdr3ptbelkVedciEWPFtAl5nkQ2Rkuvt/zGqAWb0pPngDpMHaYOY/Y+fz+3+6jDIxwgvzBOiV7M9eJcjGSUN7/EWO0ZF3oXce0qqr3dkORSfAE7L49ipGSN6vs8OACWk1bEzg5vhSAilru13UzbDgVxUbZtpLMMRdHlvnnFdBFvCHIRZoUgoIixBASJJotaZnWCWkTDbT5otfNMjA/96u0iF+VLAjAxrtOTloiFmaihFXsg1hw3r45WBZLGmu82aT4/VEl7lKJvI5Szffmp9qLc8t20WLD7opxbtELN6vP3RW/ptcjVvKXX3zfH3H19G6Jj3HrOG3kZUIcB6jB1+NbhAPkRuUT0YtXjDK2GbJ3utRqq54RRzN2amwq9rS+2nNiHxqc+Db59bGJercFsAupWk1f7AqhN1JHtmCmbGHvBCFAa15ti14piCJBUILDIRTPw1L4IpEQh7DTsOZb/VdpLtbWbbMD0+vQ5cNpHifrIBWTmv1QLz6y6WIpAOpHWUJ9LKhXTdj2KbQex511svayYWHo5t2tX17mV5+uqtYpBZPtIQ+ur6VGLvp1Qv/3aauexYOSUlkKX4NpsPXJZqMPUYerw43ONOswB8iNzSJxP6bO5dKzZIo+9go/DldSAFYSEUlxiFp81pE8pI2SrVpZQbqsgBymTH2XsAMQo5ddtQIj+YQnForPHaFGKIvTl8yRlvaoJ5Saa8AYAm5iR1fLiggTkUOy8kBEkF5sv1uUgucQPtEYzpFSGmyB7gUiJXByMWpRrXIXZ8ub6I/msS7kYjXkQ4+Q5b6WPpkcrcmmj5EUgGV4ZvR+5eLNrwnx/j1oJvdu1Ppu7XS7V0Yr7+1ytvN0uVcHOqVl61qC+NaPvc+H6aIa/hybC20UiFtsTrWwp9NC+nNcoyuTyUIepw9Th4XpSh4/CAfIzc644r9tvyI/L+5XUoSyPhSLZNqsWn8/shOAWk1t8lgeXUslt8w9iLHl1yWy7nD0a0Cw8t/lq9x4xAd6hibc3HEqQ0oaoPDcIgkhpam8V3SJARLa+m6IICGY7Klw2y3Fzi3TgsDhXUXZLT1uhSEKo61ykLd8tlMhCqMUfLsyAWXjJys+xS2bnZW3N57NKtfM8ajHaeS6kKVmkoFZOpybKXigy5rvVFkKjKOt8QcihhvT9tnYt5q/lmpZCh/Yj5DGhDlOHqcPL3KoOc4D8AlmT/7a4r7ZWQ2P0YlJ13Vl8faFIWIiy2LGnMztlNPG2df5BLtGILKVVkQv91OZLJQcuwEQoiIm3F5skteOI239qoiVQJBUAlpNXc+V8Wcyms5y48sEWINTnG5q114nyJIdP23Vo4tymX/UohV2XUK3G1Fl4feQi9RaeSr0O3j7IIzetCT3q/1QKQ3o7z/PgvF0Q0EcUOgHWbqpSdUFur2lv9e312+xFdBDcQ1GLc2HeG3lJUIepw9Th24YD5BfAXBTinCKRpRy4Op2pW3xo++UhBywHALuEsIlI5QMvnosGAJtYG9cHFWgWi0QUKw/32c7Fq6GDQN3aC4PNF30br6A2IfbG7EHUlqMiiAl7CsXmy4oYzGALwaqpzeZT7NzGE0UoYhuL9Qeg3ufL7YIuXOcq6II+kpEm+WvN6uvFOOeynJsg77KtPxStqMu5VUn3dl7O3pTexHa3y3UKU7P5LGqRdl1RSBHlvEvV2hsLQvopTvMYxch5VcX0XvTjzKKQW41akOeBOkwdpg5Th3s4QH4CHrvVkN0/tfGO7aPu3eUinqo1D84LRQAgS+m9mVEb1yfYPtX+UwWyICFDpAg3LBLgbpxkjwbs23zIADbN4nOCCDYwqy8I0Jw9wSZoiVoAG2RrUy/lfEtvzSitZVIWacIsQPDcN1lQ4/46aotW+I917SIXLsYAWrSiRCnczkvZBBlwMTZhzhl1dqZURFh9eWePtWjn5WkboSq8LspDxfRcI/pxpqZaLFJFdmr5tWuiB4X3Ejlvx7jWvDfyOFCHqcPUYerwKXCA/MpZalg/N6vTXKGI7aPujpVcNysUmW9T5FES3cuDQ7bHyBArKJmx+ZC8WloBCCTbeaZk0QwRO2YQt/ZMwE33fOao9h1iBItmFOH1whKFVmtPtTWyF9g5ChTo+n7uPddJUGMavbA8t3IuGupt1Rah8OIPACbE3XKbhcmWbX2z8NzOMwHuZmdKzc5zW6637Pp8NzumDiI6L2ZzxRzjth61mBPYpYrpW44+kNuBOgxQh6nD1wYHyE/EsejFGnvvnErq8b7JsUuhiN22QhHf1gpCchUbfywNAnExUxPEHIrFFzqrLs7bfGa1hUkjem8tZI9jRSYpu80HbIoFuOnXByCWxzNrr1h4obPzgmW/+TaAff/M2XpzEYzZ/LdekHNn87nodmLs1h7gUQlfNhsPwMTO80bzqm7boUQcmjB7lfRo56XsFdGY2HY2ram9d+p637ZGKqY9OP39MLH8BpGejUzMiHu7lstRi3NsvWuOWpDHgzpMHaYOT7dzqMP7cID8ijlWST0WitQIxYJwZ5g4V6uniLOE2HKkyudFSwuiHAJSslZEEaG0LDpg80VBSoo2QZLsRTGc3qn01S7eLuqAWX6eX6cqVYS1RCkAKyyxKVQ9982PW726A9fZRbkJ9LSnqEUpgBKVKOtTngqzF37YchNjy30rUYk8F63oms8rZu08F2UX22rrFVGulp1HMhby3ew55EXhnbP0TqmYJuTaoA6X7ajD1OErgwPkJ+Sc6MXabY5ZfHPb94UiTs4ZMcayjU4a1+esiOW22X8AYDM8SZSaS3XI5gOK4Gab6ckeWsovdCmCX4SwO+2wtyzleqJub3dag/sAj4pYtETQhFxEgCLU/YP0kQzF9JrlTpz9frPeSp5btfb6xvLNwssqTYA7Mc7Z7Tpf7iy68t9FWbXlui3ZeX6fv34uyn0/zbFaelLgMWPNjQUh0+syFel+vzkYtSDPDXXYHoM6TB1uj0cdnoMD5BfGKLD+xl1r8fmHbK5QxAg1zw2dOHuhCIDZxvWaUSqqM0Jwcba+nKnmlxXxOmDz2blaZprNAmX9O2MSxFhsvmxWnwQgZmnLAdgJSiV1s/ZiaAIcglQRD0HrsjWpr1dgYuUdqtvpNaC39Vx4ARfVFqHoBdvz2kYxtoiCRzG0Lc9EK7wIBEBtPr9XJd3ZeSm55ZdrQcikGEQVuXiLS43ovSBkzHfTTqTHiMVTWHqEPAXUYeowdZhwgHxFnBq9cJYa19sxigB7E/tSEOLC1otzrLM/6Z7NBwSIlry2YgUCpc1QaufSTl9gD1EiGRnQYPurFGFTVJsvBliUpEQkREwcmzA3AQ4yFeOThFnb+l6Y3Wr0CAVQxFhRBdq3SakXbK35bim11kG9GE+iFdqaz7so93YegCrKfWRiv5Cku0+bpWfPrYnyGlgQQkiDOkwdBqjD1wAHyE/Mua2GTm1av7ZQZE/M1aIWS3lwHvmYa0fkEQyv1J7YfGKinlKriAbK7SDWfkjstt/nth+q5daef3EfbTmYAPq0qR7REGki3X8RZDQxXvNSVDuvE2Jf30cpgD5y0QQZaBaeb5Nye/4uxt46CChirKiC6mLcZmbat/P6Yo/eztOZ++213893G22zpV6b4/1LVdlLnNuM/hZsPfL4UIepw9Rh6vAxOEB+Bi6dA+dv1qVCEc1WxAGgtg3yKITvUy0+oNp8Ls7N5mvibMUfgtBXRpcIhmiA5oRQvkxEBKoWFYlRsKvXwSqrRQQ5eFP6FnHwSuoaCQhNkGOZ1SkIsCu2n12D6bJHbHxbXx6vf5D9D7znu9XrqE2k88KyC3NdnkQvpmLsy72d5wUdfbQiJa2TBWS37VQnzefHKml73cv6PBXlrIq8a1GKXpSrbdcLeG/5lf19eWSpIGRNNIM5b+QpoQ77daAOU4fXb3NLOswB8ivmWKFIH6FY2q//kthvZ6R7UYoxgjFn86FUVYvaL/IQUKMY9svc8uD8V3ofRaguX0QLWNSIhU6WgwhUrDLacuiKVahNiLU7dr/s+NPNWP6i7H9kz4lxH6moy3lc10UlugiF57j5a1EFeCFaUcU7D/+LKB+y8/pKaX+8uUrpPqpwKHetrV8W6kPrT92GkJcIdZg6TB2+TjhAfibOiV6cau/ZcYa+m7rcuF5CWMyDU1Vr6Z4tFy7ikHADKFXVvXhnFJFWAEkRYzB7CopWsXIIqQKvKoiljVCMJtDIragEmOa4jZGLesQTrL1+eU6Y7Xo3O8+jEYBHNMrsVZP1Lcetj1CkZFEHO07La6tiPCO6h+w8O+epKE+f4zTf7VIFIXOcY+vdUtSCPB3UYeqwracOr+HWdJgD5BfMGnFeikJM1meFK+fc7E4Aal9OAHsV1bmbL8mPn5CKbTa1+STLpIk9klVP+7mFIAg5lArsDC3N54Oa2NrzEKRk20pS5LKNWX/F0guK5A3qU7smQZow9zlwfp9dg3Y913zPTSIXebqu2Xha7/f7PKetX/YoRi/G9r3YohS+PvfFHr2F1wlyKwjJE0Feili0+/NEpMc2QqOdZ895ersX5cdsJ0TIc0Idpg63bajDtwQHyK+QQxGMtcUnxyqqgfKB6XLf+mlQgXmbz/tzAoBK6dupQChRjtkoBgAp1lco9p5VWVt0wxraC5C0s/zEFybLKlKa0QPJi0z8y8qFuRfaU4V5EOQmVr2V5/ZcE6Kcm3j3hR8WxegEOHvuW5djthCtaNGSJrr2WMuiXJ/HIMrHr8G6yMGhCMO5BSGEvESowwB1mDp8zXCA/IycW0m9d5whwuHH9Q9cnwe31ILI9wMAeLGIV1iX4/Vth3qbrxdn78+JDOSgQFIT5U2s4pxSRlCbFrVZetmiKUEwrdPwqAhqW6EgJoSW69bsPhGbDcq/S6QUkCToQtRCsPY3cy/AbZ1f76kY++0+UlErnTtBnotWNNHtohtdEUgvynmX9toEHct1s3PMw+15O8/X9YxRi0l19Z7td5mIxK3ZeuRpoQ5Th6nDx7lFHeYA+ZlZkwMH4CSLb+m4vTgDQA5hz+Lr2w7NVVSnnFrzeS8qKeLcmtgPTfPL9rkcP8aAnIDQWX45S620lgBombM0Jau4BiwqUtsEBUGIFrGwHDeBhBaNcfuvP89q8dXLNL1/9voPouBa0yIYU0G2c+4iDv5dV6qhff0oxrbcpin1SEVv6bVtdH7Zz6VrPj9XJe23p62D+uWp6Oa9bfeF8pgon2vp3aIok6eHOkwdpg4vc6s6zAHyK+aYOB9bDzSLr6+43ms75GJeCkbqcVWr7dc3sfeCkxYJKVEMWOFIrlXOrbracux82ZraBxErPimPkeCC2wRSBMhBEKDQZNENCQAUsNZFAOAFJX7e7Tn4/YfotaEXil6k+8hGFciZKEXOLoq9QE6bzY+iPB5vrrn8GHGYi1jMifLafLfZ6/KAfDdCrgXqMHWYOnydcID8Alhj8R0S15MeK++3HJrLg+vPqf8CcDGuDexHcS4RDAk+m5MJaZ8vJzmbyGqoOW4igoiAVM4vIiBBIarwKVMtp02r4LrgeNGJi6yE0scT7Tm0iuqWJ3eKq9rr02jzzQmxX7dpZKPZcqMgA/ORiLp9nlZH++M2W04xjTRMC0H617U+j04w5yIEc6J8TrX0HIxakJcGdZg6DFCHL3Hca4ED5FfOXPQCKPlunXCNeXBl77ouq5YcNuBgRTWwZ/OFEKBJW+V0EITcaq4nkYLcohshu+iGIrj9+ZblMLX8qnVX1lm1dG/5oR7DrstUhPsvpVM6NfV61ISxu38QYbt/X4jtWPtRCmBqzy0Jch+t6IV8rkLazmXezrtUpXQvnnNiy6gFuQWow9Rh2546fE1wgPxCeMroxdrjrrH5NGub6anbz6MYflz/gIYwFpYAKA3tg3+IQ/eBHyy/3iJEsIJqj2h403ufQrW/pjXykrSKtDfDn2viP7kG/e1BjG2dTsS4XgMdb0/tvzyI6FS8l0V5FLuxCKSd32mivP/cj0cXzoFRC/JSoQ5Th6nD3TY3rsMcIL8gzhXnJnrzeXD9cSfrB5vPhSPk5WrsXKIatT8nMLH6+nLksWjEzrXsAItiYBNqhbVFPUygk29T+nq6vedTqtrMTeV8S9U1cunxKS5GfeRiGtlwRMTU/dA111Hw9tdPBPWAGNv+87ltc9EKAMi7PN23CvW+lefn1U9baseeNp+fe14u8HvP/4yoxVLEgqJMXjrUYeowdZg6DHCA/OJ4SATjWPN64IE2nz1I2fo0qw+lotcsx1Z9XUXfm9onKwqR0Ft+bXt/flK2sYdv1t40x20aleiv6ym2njOx92ZFuYmwbzPJTRvE1dfPifEYqdDJ+vkcNzv2umhFf94PsfPG+/yx5qAok9cCdZg6XLenDt8sHCBfOafagYdsvr2ikjwtGmnFJM3q64tCxqlV67FVZyIewJzll7vvglqUgi4ike24CWq5cr0WdE8r43RlnhNjoOWyjdv1eW0TkT5i4fnx9wVwOVphj3e8CGTu/KfrT7PzHsv+I+SaoA53J0wdnj3/6Xrq8EuAA+RXytroxd5+Z9h8APYiICj75qx7EQygs/rsBgAXS5lUWFsltFlwQVsEIgdMLD/Aqq17267adSrICV30olvfW3vFwpOF76m+gnyprc6cANvlGKIBnTj77VGMffulaEW/3yjIdfsVEQvbdrn5/Ll23hwPiVoQ8tqgDlOHqcPXCwfIL5Dehju43RkW33j8VTZfF3GoDJXVtqrlw2mZrrOJZCsmqXZfSgiletrOS2quG4rQaijLYWr72bryuDJv4YUFW+9QMcgxJoI1J8xDdMM3XxJi/78U2ejz0eby2/r92+PO57nNie25dt54f38Njm03uw0tPfLCoA5Th6nDtw0HyDfCOZXXvs/YxL7er61opI9iTKdQbeI8jZp064ccvZxNVN3ys1mn+u1nZqLKHpWQ7td8ey6Tp/6AH9FLltliocggeEuiPH+cThiPPFa/z5oikOm5nH5B1u7DiAUhDepw98Sow8O5UIdfGhwgv2AuWSgyt+1amw/AEMEAPH+tF2dgpmjEVsK7cY4V1m739VEMxVAQ4sul2ASAFZL4mXT23zSi0YvZ9Pkcu65zzOWiOWOEwu/PMyJ6qFDEjzEXrfBzmItYzBWB9Oesw/qH2HlzYvuQPpuMWpCXDHWYOkwdvk04QH7hrBVnAHsCfaztkB8fOG7zARYhALBv9U2iAkMLIjuB0vdSaoU1MLX7JEidsQkAQvY8tmm1NVJ5Pl2um9t/tn2zAP3Mpbu/XafzxGAUpbFIZFx3KBfO79+PJOjevr0YT/dfznGbHms5WvFcdt7SYxDy0qAOU4epw7fHaV7PmYjIZ4vIfy8ib4nI1xzY7htF5C+LyAfK3+c+xfndGg+1Ww7lS/Xrj1lM/bpRjKbHG1voNHHaz+lqFtpe0UUvXmf+zR1vfKzJeevCeQ8RifH850R5/5rNX+f9Yy0XgZwCbbrXDXX4ZUEdpg6fA3X46XiqCPLfAPBrAfySFdv+elX9lsc9ndfFmugFsB+VcC5l8/Xrx3y4KjIzfTpt9ZEoRmf5eQEJYE3oQz2vvoq7i2aUymtHchepGQtBvNDkTA6JqZ1XF8mYiVLY/6nFNveldGq0Yu5xJtuuyam7kJ3HqMWLhTr8AKjD1OHpcajD186TDJBV9YcB/LCI/KNP8XjXyCXEGXiYzdcXZHjRCICumT1wqKG9rS4iUo5RWw8NIu3iPRHpkiNnj9msPzv3+Uppt/QmX0xpZrsjzInIbF/LFbba9L7R+tuPBlmkYyrG/XGPCf+4/d7xL2TnzW27uB1F+cmhDj8c6jB1eHxM6vD18iQpFifydSLyQRH5bSLytrkNROQrROT9IvL++zcfferze/GcYsGctu36D9OxX9t1u876cvKi4HRRge649jdtvTMeN2etf+Njr/lbexw/T89pO0eUD12bdozlaMUxTtv2cd5L5MVDHX4g1GHq8CGowy+fl1ak968D+CEAdwDeC+BrAfyb40aq+t5yPz7xHZ91Mz+B+sjC0W0vaPMBmFh95UjtmHtFIy3i0bf7GaMYyKmdSxetsG3a8cdIhh3fikl8eYxo1HMYikAkCFJ62Ftm3t5bihYsLM+I8ZovszU2Xn8OS9GK8b7+mEv3j+dybNvZ7RixeA1Qhw9AHaYOU4dvg0cbIIvIVwH48nLz3ar6A8f2UdUfLItvicjvBbBYSHLLPJbNB+zP1HRIoMecuGr1DW2IbL99gQaWLT9N7fF728/Oeyric2INoFZi1/1EoOv04yhjocW+6O1HaIDDQmzrumszY9Udsg7H81pj5Y3HnLu/P5c5KMovF+rw40Edpg5P9qcOXx2PlmKhqr9DVT+3/B0VZQAQkXeV/wIrJPmuxzq/W+FUu+Vcq++YOIzW28jcr/N+24mt1/16H4Vqr3q5W+dVzv3fGpb2G48/ew7dOZ4jyj2jdbi3zwpRXjrm3H5roJ33sqEOvwyow9Rh6vDr40lSLETknQDeD+DvBJBF5NcB+BxV/Zsi8j4A/2IR798vIp8CQAB8AMBXPsX5vUYey+Ybt+8/uGPRiG3bogazhSNLfT3L6WhKnZ3XzjF01l4/bapvO0Yz2qbTqEd7TvsWH4BJpOMYawVuzGEb910jxqOFt3eMMwT51CKQufNas/3edoxYvAiow5eHOkwdrvtRh6+Op+pi8UMAPm3hvnd3y1/8FOdzTTyGzefbA9Om92ty4k4V6CXLL+XusbscOf+Ij/Zf229esO05ds/lgflvc+ILzIjhgmjaMdbZbZcU5PHYc/fPnd8IRfn1QR1+PKjD1OFxPXX49fPSivTII7IkzsByFGPvGMMXwaFj9vd5v05fDywL9Fwf0PH85qIrc7lw0+c4FZOwcN5zLAlx/3iTdUfE75iVOR53b/8Dgn/ocdcK5SVEmRCyD3WYOkwdfh1wgHwFXMLmA9YVjfjjjeLs2/RishTFAMYCEmCSDj9MmepMohnAtPoa06gGsB+dGK9PygnncqztT89eS6UzohTAXEHK+dGKtee6Zp/Z7RixIDcGdbicR31c6jB1+HXDAfIVcYrNB+CkKMYo6GNO3Nxx5+w+v7+3/Pp9jQWRtpOb3NwTawx5c/1z6B7/XA4J02xBx1we3IHK61mxPBClOEeQFx/nQtEKijK5ZajDvgt1eOmxDj4OdfjFwAEyWc2hqMeh7fpWROP9o0CP9+/tOxOlGR+vF5il4pdLsrZ4Yj56cF6kYtx37v4laM0R8nqhDs9DHSaXhgPkK+MxbT7fB9i3+pzjje0PRzKAI7bfwiotDer37bu2/JCIxcjBfLPFaMHxyMapYjy7zQnRCoB2HiGXhjpMHaYOv344QL5SLmnzAesE2h8XWBZoWzct3jgk0gAQZoVh/3wnldjzT2b5vhM59DhLbYiO2XaHtjtXkE+1Itfuu7ctRZmQPajDs09m+b4ToQ4P21KHL8qjTRRCXhfHPoSn9mCcqx4+51c4cJp4HeuROfd3iFP3eQpRnr2WJwrjJUWZEHIZqMOX2Yc6TC4BI8hXzCk2H/DwKMa471KeWr/tXOP4URTmohnAUkQD0JmCkUPoCU3qDx7nUJTgBLtt7RcW8LzRiqXHJ4Q0qMProA6v23ft45OHwwHyDbDW5qvbHykCOdSrc27fudw43xaYt/1s/Vxlddt+Vqxnq7EPc+i5nvML/tDUqYsCe0LE43DkhKJMyEuEOnwY6vDxfWe3pw4/Ghwgk1keKs7AvODNfUks5tEtNJo/dPyxyGQNl7CxDonxocc4RZCBZTE815pduz8h5OmhDp8GdZhcEg6Qb4RTbT5gvdUHHG7jc2okY9xnTrzmLMDp/fN24GNyTNwO5eUd2v+xIhXH9l/chxELQs6COvz4UIfJpeAA+cY41eYDjgs0sJwX1+8/d4w1Ij2730zO3NJjHmJtP9FzOFeIgfPFGHg8QQYoyoRcAurwFOrwaVCHnwYOkG+Qc6IYF3vsA5bhoS+NY18Oczlza8/nkhwT4zWP+diifA4UZEIuC3V4/7iXgjpMLgEHyDfMOUUjzrl237HjzAnAoYjG3HHWiONTsEb01wjemuMwWkHI64Q6/LhQh8m5cIB845wbxThWPAI8XKTHcwSWz3ONYD8Wj1F1fCkxXnus2f0oyIQ8CdThh0MdJpeGA2RyNmty4pxD1danHO/cnqI9DxHrh1iBlxJk4PFFmRDyOqAOn7gvdZishANkAmBddGBx3xXRB2BfTNZEM5aOeUzkDj2HxxKrc37pX1qITznm7L6MVhDybFCHHw51mFwKDpDJHudUWNd9V1h+zqGK6/GYztpjP0S4zz3m6uOcIJynFntQlAm5DqjD5x1z9XGow+QIHCCTWR4qzsB6EV0r0P2xTzn+7HFeWG/OkacUZICiTMhLhDp8WajD5BQ4QCaLPLQN0akiOidGh8R6jRi9xOKQkXNbAl3CoqQgE/KyoQ6vgzpMLg0HyOQol+jXeWo0w1lTgb3mcV8aD+mTSUEm5PagDl8e6jA5BAfIZDUPsfvqMU7IjRt5qEg/N5doHk9RJuS2oQ4/DOowWQsHyOQkHlJlXY9xgZY/h0TuOUX7kjMoXTLqQjEm5HqgDh+GOkwuAQfI5GwuOVXqudbfHEvieEnBfqypRAEKMiFkPdThx4E6TDhAJg/mEpZfPdYFBXrkMcX0Elw6T4+iTMjtQB2+DNRh4nCATC7CJSy/yfGeccrSx+YxC1YoxoTcLtTh9VCHyTE4QCYX55KW396xL9R/86l57CpuCjIhpIc6vA91mJwCB8jk0XhMgQYuU2TyGDxlSyMKMiHkENThJ3gs6vBVwgEyeXRG8XgsoQZebr/NS0EhJoScA3X4clCHb4Pn/5lHbg6Ky3nwuhFCLgX15Dx43W4HRpDJs/DYtt+1QDEmhDwW1OF1UIdvEw6QybOyJDy3KNgUYULIc0AdblCHicMBMnmR3FJkg4JMCHmJUIfJLcMBMnnRPGVhyVNBISaEvCaow+QW4QCZvCqOidpLEG4KLyHkmqEOk1uAA2RyVTxHpINCTAghDeowuQY4QCZXDUWTEEKeF+oweY2wDzIhhBBCCCEdHCATQgghhBDSwQEyIYQQQgghHRwgE0IIIYQQ0sEBMiGEEEIIIR0cIBNCCCGEENLBATIhhBBCCCEdHCATQgghhBDSwQEyIYQQQgghHRwgE0IIIYQQ0sEBMiGEEEIIIR0cIBNCCCGEENLBATIhhBBCCCEdHCATQgghhBDSwQEyIYQQQgghHRwgE0IIIYQQ0sEBMiGEEEIIIR0cIBNCCCGEENLBATIhhBBCCCEdHCATQgghhBDSwQEyIYQQQgghHRwgE0IIIYQQ0sEBMiGEEEIIIR0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      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure, axes = plt.subplots(nrows=1, ncols=2, figsize=(10, 5))\n",
    "z_slice = values.sel(z=0.0)\n",
    "tick_locs = list(range(0, 101, 25))\n",
    "tick_vals = np.linspace(values.coords['x'].values[0], values.coords['y'].values[-1], 5)\n",
    "axes[0].imshow(z_slice, origin='lower', aspect='equal', cmap='coolwarm')\n",
    "axes[0].set_title('Z slice')\n",
    "axes[0].set_xlabel(z_slice.dims[0])\n",
    "axes[0].set_xticks(tick_locs)\n",
    "axes[0].set_xticklabels(f'{x:.1f}' for x in tick_vals)\n",
    "axes[0].set_ylabel(z_slice.dims[1])\n",
    "axes[0].set_yticks(tick_locs)\n",
    "axes[0].set_yticklabels(f'{x:.1f}' for x in tick_vals)\n",
    "x_slice = values.sel(x=0.0)\n",
    "axes[1].imshow(x_slice, origin='lower', aspect='equal', cmap='coolwarm')\n",
    "axes[1].set_title('X slice')\n",
    "axes[1].set_xlabel(x_slice.dims[0])\n",
    "axes[1].set_xticks(tick_locs)\n",
    "axes[1].set_xticklabels(f'{x:.1f}' for x in tick_vals)\n",
    "axes[1].set_ylabel(x_slice.dims[1])\n",
    "axes[1].set_yticks(tick_locs)\n",
    "axes[1].set_yticklabels(f'{x:.1f}' for x in tick_vals)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that labels and tick values are set according to information contained in the xarray representing the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpolation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is straightforward to interpolate data for coordinates that are missing in the xarray, e.g.,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0002448162927385368"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(values.interp(x=np.pi/2.0, y=np.pi/2.0, z=np.pi/2.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The interpolation is linear, and this function is highly non-linear, so the actual function values at the given point is different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00024331787691818835"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gaussian(np.pi/2.0, np.pi/2.0, np.pi/2.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, other interpolation methods are available for 1-D interpolation, e.g., quadratic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0002433054503600994"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(values.interp(x=np.pi/2.0, y=np.pi/2.0, z=np.pi/2.0, method=\"quadratic\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interpolation can be done for an entire plane of 3D data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</defs>\n",
       "</svg>\n",
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       "  --xr-background-color: var(--jp-layout-color0, white);\n",
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       "  --xr-background-color-row-even: #111111;\n",
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       "\n",
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       "  display: block;\n",
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       "  max-width: 700px;\n",
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       "\n",
       ".xr-text-repr-fallback {\n",
       "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
       "  display: none;\n",
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       "\n",
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       "  padding-top: 6px;\n",
       "  padding-bottom: 6px;\n",
       "  margin-bottom: 4px;\n",
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       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
       "  margin-top: 0;\n",
       "  margin-bottom: 0;\n",
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       "\n",
       ".xr-obj-type,\n",
       ".xr-array-name {\n",
       "  margin-left: 2px;\n",
       "  margin-right: 10px;\n",
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       "\n",
       ".xr-obj-type {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-sections {\n",
       "  padding-left: 0 !important;\n",
       "  display: grid;\n",
       "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
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       "\n",
       ".xr-section-item {\n",
       "  display: contents;\n",
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       "  display: none;\n",
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       "\n",
       ".xr-section-item input + label {\n",
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       "\n",
       ".xr-section-item input:enabled + label {\n",
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       "  color: var(--xr-font-color2);\n",
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       "\n",
       ".xr-section-item input:enabled + label:hover {\n",
       "  color: var(--xr-font-color0);\n",
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       "\n",
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       "  grid-column: 1;\n",
       "  color: var(--xr-font-color2);\n",
       "  font-weight: 500;\n",
       "}\n",
       "\n",
       ".xr-section-summary > span {\n",
       "  display: inline-block;\n",
       "  padding-left: 0.5em;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in + label:before {\n",
       "  display: inline-block;\n",
       "  content: '►';\n",
       "  font-size: 11px;\n",
       "  width: 15px;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
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       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (y: 101, z: 101)&gt;\n",
       "array([[2.49746212e-11, 3.56682222e-11, 5.05751404e-11, ...,\n",
       "        5.05751404e-11, 3.56682222e-11, 2.49746212e-11],\n",
       "       [3.56682222e-11, 5.09405954e-11, 7.22303385e-11, ...,\n",
       "        7.22303385e-11, 5.09405954e-11, 3.56682222e-11],\n",
       "       [5.05751404e-11, 7.22303385e-11, 1.02417762e-10, ...,\n",
       "        1.02417762e-10, 7.22303385e-11, 5.05751404e-11],\n",
       "       ...,\n",
       "       [5.05751404e-11, 7.22303385e-11, 1.02417762e-10, ...,\n",
       "        1.02417762e-10, 7.22303385e-11, 5.05751404e-11],\n",
       "       [3.56682222e-11, 5.09405954e-11, 7.22303385e-11, ...,\n",
       "        7.22303385e-11, 5.09405954e-11, 3.56682222e-11],\n",
       "       [2.49746212e-11, 3.56682222e-11, 5.05751404e-11, ...,\n",
       "        5.05751404e-11, 3.56682222e-11, 2.49746212e-11]])\n",
       "Coordinates:\n",
       "  * y        (y) float64 -3.0 -2.94 -2.88 -2.82 -2.76 ... 2.82 2.88 2.94 3.0\n",
       "  * z        (z) float64 -3.0 -2.94 -2.88 -2.82 -2.76 ... 2.82 2.88 2.94 3.0\n",
       "    x        float64 2.344</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span class='xr-has-index'>y</span>: 101</li><li><span class='xr-has-index'>z</span>: 101</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-ceae6b18-c3fa-4437-80d6-3aae8526a0d7' class='xr-array-in' type='checkbox' checked><label for='section-ceae6b18-c3fa-4437-80d6-3aae8526a0d7' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>2.497e-11 3.567e-11 5.058e-11 ... 5.058e-11 3.567e-11 2.497e-11</span></div><div class='xr-array-data'><pre>array([[2.49746212e-11, 3.56682222e-11, 5.05751404e-11, ...,\n",
       "        5.05751404e-11, 3.56682222e-11, 2.49746212e-11],\n",
       "       [3.56682222e-11, 5.09405954e-11, 7.22303385e-11, ...,\n",
       "        7.22303385e-11, 5.09405954e-11, 3.56682222e-11],\n",
       "       [5.05751404e-11, 7.22303385e-11, 1.02417762e-10, ...,\n",
       "        1.02417762e-10, 7.22303385e-11, 5.05751404e-11],\n",
       "       ...,\n",
       "       [5.05751404e-11, 7.22303385e-11, 1.02417762e-10, ...,\n",
       "        1.02417762e-10, 7.22303385e-11, 5.05751404e-11],\n",
       "       [3.56682222e-11, 5.09405954e-11, 7.22303385e-11, ...,\n",
       "        7.22303385e-11, 5.09405954e-11, 3.56682222e-11],\n",
       "       [2.49746212e-11, 3.56682222e-11, 5.05751404e-11, ...,\n",
       "        5.05751404e-11, 3.56682222e-11, 2.49746212e-11]])</pre></div></div></li><li class='xr-section-item'><input id='section-69882ac0-a5d0-402e-b8da-6cb18a17b71a' class='xr-section-summary-in' type='checkbox'  checked><label for='section-69882ac0-a5d0-402e-b8da-6cb18a17b71a' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>y</span></div><div class='xr-var-dims'>(y)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-3.0 -2.94 -2.88 ... 2.88 2.94 3.0</div><input id='attrs-650bdd96-aa8c-4813-91a3-4f786602d803' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-650bdd96-aa8c-4813-91a3-4f786602d803' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d4c941f2-bcb3-437c-bdd0-14ecd87f9afe' class='xr-var-data-in' type='checkbox'><label for='data-d4c941f2-bcb3-437c-bdd0-14ecd87f9afe' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([-3.  , -2.94, -2.88, -2.82, -2.76, -2.7 , -2.64, -2.58, -2.52, -2.46,\n",
       "       -2.4 , -2.34, -2.28, -2.22, -2.16, -2.1 , -2.04, -1.98, -1.92, -1.86,\n",
       "       -1.8 , -1.74, -1.68, -1.62, -1.56, -1.5 , -1.44, -1.38, -1.32, -1.26,\n",
       "       -1.2 , -1.14, -1.08, -1.02, -0.96, -0.9 , -0.84, -0.78, -0.72, -0.66,\n",
       "       -0.6 , -0.54, -0.48, -0.42, -0.36, -0.3 , -0.24, -0.18, -0.12, -0.06,\n",
       "        0.  ,  0.06,  0.12,  0.18,  0.24,  0.3 ,  0.36,  0.42,  0.48,  0.54,\n",
       "        0.6 ,  0.66,  0.72,  0.78,  0.84,  0.9 ,  0.96,  1.02,  1.08,  1.14,\n",
       "        1.2 ,  1.26,  1.32,  1.38,  1.44,  1.5 ,  1.56,  1.62,  1.68,  1.74,\n",
       "        1.8 ,  1.86,  1.92,  1.98,  2.04,  2.1 ,  2.16,  2.22,  2.28,  2.34,\n",
       "        2.4 ,  2.46,  2.52,  2.58,  2.64,  2.7 ,  2.76,  2.82,  2.88,  2.94,\n",
       "        3.  ])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>z</span></div><div class='xr-var-dims'>(z)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-3.0 -2.94 -2.88 ... 2.88 2.94 3.0</div><input id='attrs-ff8a27f6-1b3c-47ca-9b6f-9d5adcdd54a3' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ff8a27f6-1b3c-47ca-9b6f-9d5adcdd54a3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-03a69b69-f2e7-4b3f-afc0-081f3dba5187' class='xr-var-data-in' type='checkbox'><label for='data-03a69b69-f2e7-4b3f-afc0-081f3dba5187' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([-3.  , -2.94, -2.88, -2.82, -2.76, -2.7 , -2.64, -2.58, -2.52, -2.46,\n",
       "       -2.4 , -2.34, -2.28, -2.22, -2.16, -2.1 , -2.04, -1.98, -1.92, -1.86,\n",
       "       -1.8 , -1.74, -1.68, -1.62, -1.56, -1.5 , -1.44, -1.38, -1.32, -1.26,\n",
       "       -1.2 , -1.14, -1.08, -1.02, -0.96, -0.9 , -0.84, -0.78, -0.72, -0.66,\n",
       "       -0.6 , -0.54, -0.48, -0.42, -0.36, -0.3 , -0.24, -0.18, -0.12, -0.06,\n",
       "        0.  ,  0.06,  0.12,  0.18,  0.24,  0.3 ,  0.36,  0.42,  0.48,  0.54,\n",
       "        0.6 ,  0.66,  0.72,  0.78,  0.84,  0.9 ,  0.96,  1.02,  1.08,  1.14,\n",
       "        1.2 ,  1.26,  1.32,  1.38,  1.44,  1.5 ,  1.56,  1.62,  1.68,  1.74,\n",
       "        1.8 ,  1.86,  1.92,  1.98,  2.04,  2.1 ,  2.16,  2.22,  2.28,  2.34,\n",
       "        2.4 ,  2.46,  2.52,  2.58,  2.64,  2.7 ,  2.76,  2.82,  2.88,  2.94,\n",
       "        3.  ])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>x</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>2.344</div><input id='attrs-b91f24b4-17d7-4a6a-acda-d3f06b06aa59' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b91f24b4-17d7-4a6a-acda-d3f06b06aa59' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-049021fe-288c-4f1a-8c6e-ff21140c0101' class='xr-var-data-in' type='checkbox'><label for='data-049021fe-288c-4f1a-8c6e-ff21140c0101' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(2.34447213)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f4cadf2e-b427-4b3a-92ed-f960fbcefb74' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-f4cadf2e-b427-4b3a-92ed-f960fbcefb74' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray (y: 101, z: 101)>\n",
       "array([[2.49746212e-11, 3.56682222e-11, 5.05751404e-11, ...,\n",
       "        5.05751404e-11, 3.56682222e-11, 2.49746212e-11],\n",
       "       [3.56682222e-11, 5.09405954e-11, 7.22303385e-11, ...,\n",
       "        7.22303385e-11, 5.09405954e-11, 3.56682222e-11],\n",
       "       [5.05751404e-11, 7.22303385e-11, 1.02417762e-10, ...,\n",
       "        1.02417762e-10, 7.22303385e-11, 5.05751404e-11],\n",
       "       ...,\n",
       "       [5.05751404e-11, 7.22303385e-11, 1.02417762e-10, ...,\n",
       "        1.02417762e-10, 7.22303385e-11, 5.05751404e-11],\n",
       "       [3.56682222e-11, 5.09405954e-11, 7.22303385e-11, ...,\n",
       "        7.22303385e-11, 5.09405954e-11, 3.56682222e-11],\n",
       "       [2.49746212e-11, 3.56682222e-11, 5.05751404e-11, ...,\n",
       "        5.05751404e-11, 3.56682222e-11, 2.49746212e-11]])\n",
       "Coordinates:\n",
       "  * y        (y) float64 -3.0 -2.94 -2.88 -2.82 -2.76 ... 2.82 2.88 2.94 3.0\n",
       "  * z        (z) float64 -3.0 -2.94 -2.88 -2.82 -2.76 ... 2.82 2.88 2.94 3.0\n",
       "    x        float64 2.344"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values.interp(x=np.pi/1.34)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc-hr-collapsed": true
   },
   "source": [
    "## Combining data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Concatenate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `cnocatinate` function works similarly to what you would expect from numpy's counterpart. Two or more `DataArray`s are concatenated as in the following example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_vals = np.arange(0.0, 2.0*np.pi, 0.3)\n",
    "signal1 = xr.DataArray(np.cos(x_vals), dims=('x', ), coords=(x_vals.copy(), ))\n",
    "x_vals += 5.0*np.pi\n",
    "signal2 = xr.DataArray(np.cos(x_vals), dims=('x', ), coords=(x_vals.copy(), ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "signal = xr.concat((signal1, signal2), dim='x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f976813ae50>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/AVCf/d+b5/vNzCw/Zx81M0ucA4GZWeKca8jMKqmKSRybyoHAzCqnqkkci1K1IOdbQ2ZWOVVN4liEuSA3ffIUwY+C3P2PT5dWJwcCM6ucqiZxLEIVg5wDgZlVTlWTOBahikHOgcDMKqfJ6dOrGOQcCMyscpqcxLGKQc6jhsyskpqaxHHu31SlUUMOBGZmY1a1IOdbQ2ZmiXMgMDNLnAOBmVniHAjMzBKXq7NY0iXA3wBrgReB3+z18HlJLwI/AF4DzkREazH72+JULY+JmVVb3hbBLuBgRKwHDmbL/VwTERvmgsAQ+9fS/Y9Ps2n3I6zb9QU27X5k5PlEqpjHxMyqLW8g2Arsyz7vA7aNef9KK+OkXMU8JmZWbXkDweURcQwge7+sz3YBPCTpsKQdQ+yPpB2SJiVNzs7O5qz2eJRxUq5iHhMzq7YF+wgkfRn48R6r/nQR37MpImYkXQY8LOkbEfHoIvYnIvYAewBarVYsZt+ylHFSXrl8GdM9/n4TknWZ2Wgs2CKIiHdFxM/0eD0AHJe0AiB7P9Hnb8xk7yeA+4CN2aqB9q+rMpJLVTGPiZlVW95bQ/uBm7PPNwMPdG8g6SJJF899Bq4Djgy6f52VcVJucrIuMxsNRQx/l0XSm4DPAWuAbwHviYjvSloJ3B0RWyT9JO1WALRvRX0mIj483/4LfW+r1YrJycmh6z1OHsppZlUh6XDXyM12eZ5AUJY6BQIzs6roFwg8s9jMLHEOBGZmiXMgMDNLnAOBmVni/IQyM6sEj7ArjwOBmZVuLi/XXEqWubxcQBLBoOwg6FtDZla6lJMlViFjsAOBmZUu5WSJVQiCDgRmVroy8nJVRRWCoAOBmZUu5WSJVQiCDgRmVrqUkyVWIQh61JCZVcK2q1clceLvNvdvLnPUkAOBmVnJyg6CvjVkZpY4twgaoOzJKGZWbw4EY1b0STv1GZlmll+uW0OSLpH0sKTns/c39tjmSklPdLy+L+n92boPSZruWLclT32qbhQzCKswGcXM6i1vH8Eu4GBErAcOZsvniIjnImJDRGwAfh54hR89uhLgY3PrI+JAzvpU2ihO2lWYjGJm9ZY3EGwF9mWf9wHbFtj+V4B/jYhv5vzeWhrFSbsKk1HMrN7yBoLLI+IYQPZ+2QLbbwc+21W2U9KTkvb2urU0R9IOSZOSJmdnZ/PVuiSjOGlXYTKKmdXbgoFA0pclHenx2rqYL5J0IfDrwN92FN8JvBnYABwDPtpv/4jYExGtiGhNTEws5qsrYxQn7ZRnZJpZMRYcNRQR7+q3TtJxSSsi4pikFcCJef7UDcBjEXG842+f/SzpE8DfDVbtehrVDMKyJ6OYWb3lHT66H7gZ2J29PzDPtjfRdVtoLohkizcCR3LWp/J80jazqsnbR7AbuFbS88C12TKSVko6OwJI0uuz9fd27f/nkp6S9CRwDfCBnPUxM7NFytUiiIjv0B4J1F0+A2zpWH4FeFOP7d6b5/vNrL48I746PLPYzMbOM+LnN+4g6aRzZjZ2nhHfXxnPMHYgMLOx84z4/soIkg4EZjZ2nhHfXxlB0oHAzMbOM+L7KyNIOhCY2dh5Rnx/ZQRJjxoq2TCjAzzszprAkyt7K+MZxg4EJRpmCJ2H3Zk137iDpG8NlWiY0QEedmdmRXMgKNEwowM87M7MiuZAUKJhRgd42J2ZFc2BoETDjA7wsDszK5o7i0s0zOiAMkYUmBXBo93yGeXxU0QU8ofGqdVqxeTkZNnVMLMBdY92g3ZL1nMHBlPU8ZN0OCJa3eW+NWRmI+fRbvmM+vj51lDFdDf/rvmpCb7yjVk3p63WPNotn1Efv1yBQNJ7gA8BbwE2RkTP+zWSNgMfB5YAd0fE3JPMLgH+BlgLvAj8ZkS8nKdOddZrstj/+9q3zq735DGri+4LmuWvX8rLr5w+bzuPdhvMyuXLmO5x0i/q+OW9NXQEeDfwaL8NJC0B7qD98PqrgJskXZWt3gUcjIj1wMFsOVm9mn/d3Jy2quuVT//f//MMS5fonO082m1wox4tmCsQRMSzEbHQWWkjcDQiXoiIV4F7gK3Zuq3AvuzzPmBbnvrU3aDNPDenrcp6XdCc/mFw0YUXOMnckEadpG8cfQSrgJc6lqeAt2efL4+IYwARcUzSZf3+iKQdwA6ANWvWjKiq5erX/Ou1nVlV9btQ+d6p0zzxwevGXJvmGGX+oQVbBJK+LOlIj9fWhfad+xM9yhY9ZjUi9kREKyJaExMTi929Fno1/7q5OW1V59nv9bNgiyAi3pXzO6aA1R3LVwAz2efjklZkrYEVwImc31VrvSaLedSQ1c1t11/Zc8y7L2Cqaxy3hg4B6yWtA6aB7cBvZev2AzcDu7P3B8ZQn0pzjnarO89+r59cM4sl3Qj8FTABnASeiIjrJa2kPUx0S7bdFuAvaQ8f3RsRH87K3wR8DlgDfAt4T0R8d6Hv9cxiM7PF6zez2CkmzMwS4RQTZmbWkwOBmVniHAjMzBLnQGBmlrhadhZLmgW+OeTulwLfLrA6TeHj0puPS28+Lv1V+dj8REScNyO3loEgD0mTvXrNU+fj0puPS28+Lv3V8dj41pCZWeIcCMzMEpdiINhTdgUqyselNx+X3nxc+qvdsUmuj8DMzM6VYovAzMw6OBCYmSUuqUAgabOk5yQdlZT085E7SXpR0lOSnpCUbDY/SXslnZB0pKPsEkkPS3o+e39jmXUsQ5/j8iFJ09lv5oksw3BSJK2W9BVJz0p6WtIfZeW1+80kEwgkLQHuAG4ArgJuknRVubWqlGsiYkPdxj8X7JPA5q6yXcDBiFgPHMyWU/NJzj8uAB/LfjMbIuLAmOtUBWeAP46ItwDvAG7Nzim1+80kEwiAjcDRiHghIl4F7gEGfdymJSAiHgW6n4exFdiXfd4HbBtnnaqgz3FJXkQci4jHss8/AJ6l/Yz22v1mUgoEq4CXOpansjJrP0P6IUmHJe0ouzIVc3lEHIP2//jAZSXXp0p2Snoyu3VU+dsfoyRpLXA18E/U8DeTUiBQjzKPnW3bFBFvo33b7FZJv1h2hazy7gTeDGwAjgEfLbU2JZL0BuDzwPsj4vtl12cYKQWCKWB1x/IVwExJdamUiJjJ3k8A99G+jWZtxyWtAMjeT5Rcn0qIiOMR8VpE/BD4BIn+ZiQtpR0EPh0R92bFtfvNpBQIDgHrJa2TdCGwHdhfcp1KJ+kiSRfPfQauA47Mv1dS9gM3Z59vBh4osS6VMXeiy9xIgr8ZSQL+Gng2Iv6iY1XtfjNJzSzOhrj9JbAE2BsRHy63RuWT9JO0WwEAFwCfSfW4SPos8E7aaYSPAx8E7gc+B6wBvgW8JyKS6jjtc1zeSfu2UAAvAn8wd188FZJ+Afh74Cngh1nx/6DdT1Cr30xSgcDMzM6X0q0hMzPrwYHAzCxxDgRmZolzIDAzS5wDgZlZ4hwIzMwS50BgZpY4BwKzAkj6r1kCttdls7WflvQzZdfLbBCeUGZWEEn/E3gdsAyYioiPlFwls4E4EJgVJMthdQj4T+C/R8RrJVfJbCC+NWRWnEuANwAX024ZmNWCWwRmBZG0n/aT79YBKyJiZ8lVMhvIBWVXwKwJJL0POBMRn8mej/1VSb8cEY+UXTezhbhFYGaWOPcRmJklzoHAzCxxDgRmZolzIDAzS5wDgZlZ4hwIzMwS50BgZpa4/w/0VLRunHqKSwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "signal.plot.line('o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, the coordinates of the `DataArray`s can overlap, as the next example illustrates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_vals = np.linspace(0.0, 2.0*np.pi, 11)\n",
    "signal1 = xr.DataArray(np.sin(x_vals), dims=('x', ), coords=(x_vals.copy(), ))\n",
    "x_vals = np.linspace(0.0, np.pi, 20)\n",
    "signal2 = xr.DataArray(np.sin(x_vals), dims=('x', ), coords=(x_vals.copy(), ))\n",
    "signal = xr.concat((signal1, signal2), dim='x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure, axes = plt.subplots(nrows=1, ncols=1)\n",
    "_ = signal.plot.line('bo', ax=axes, alpha=0.5)\n",
    "_ = signal.plot.line('ro', ax=axes, alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `merge`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two (or more) `DataArray` objects can be merged into a single `DataSet` object.  The coordinates are taken into account, and if one of the arrays has no values for the some coordinates, those are considered missing values, and represented as `NaN`.\n",
    "\n",
    "Consider two `DataArray`s, one representing temperature measurements, the other pressure values.  Both data sets have $x$ and $y$ dimensions, but the coordinates differ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "temperature = xr.DataArray(np.random.normal(loc=20.0, scale=5.0, size=(5, 5)),\n",
    "                           dims=('x', 'y'), coords={'x': np.linspace(0.0, 1.0, 5),\n",
    "                                                    'y': np.linspace(0.0, 5.0, 5)},\n",
    "                           name='temperature')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "pressure = xr.DataArray(np.random.normal(loc=1001.0, scale=100.0, size=(5, 5)),\n",
    "                        dims=('x', 'y'), coords={'x': np.linspace(0.0, 2.0, 5),\n",
    "                                                 'y': np.linspace(0.0, 3.0, 5)},\n",
    "                        name='pressure')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When the data is merged into a `DataSet`, missing values are present."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       ".xr-var-data,\n",
       ".xr-attrs {\n",
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       "\n",
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       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
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       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
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       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
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       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:      (x: 7, y: 9)\n",
       "Coordinates:\n",
       "  * x            (x) float64 0.0 0.25 0.5 0.75 1.0 1.5 2.0\n",
       "  * y            (y) float64 0.0 0.75 1.25 1.5 2.25 2.5 3.0 3.75 5.0\n",
       "Data variables:\n",
       "    temperature  (x, y) float64 17.95 nan 12.78 nan nan ... nan nan nan nan nan\n",
       "    pressure     (x, y) float64 1.028e+03 1.041e+03 nan ... 1.048e+03 nan nan</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-20967950-0ac5-4858-887c-ba4a61b1211e' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-20967950-0ac5-4858-887c-ba4a61b1211e' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 7</li><li><span class='xr-has-index'>y</span>: 9</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-1d837a4e-f28e-483a-9b5d-0e0497fcba2e' class='xr-section-summary-in' type='checkbox'  checked><label for='section-1d837a4e-f28e-483a-9b5d-0e0497fcba2e' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.25 0.5 0.75 1.0 1.5 2.0</div><input id='attrs-f5a605ce-a7df-4117-b9aa-3100f210087d' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-f5a605ce-a7df-4117-b9aa-3100f210087d' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c84bbc57-6d25-4daf-8cc3-467d6f78bb3b' class='xr-var-data-in' type='checkbox'><label for='data-c84bbc57-6d25-4daf-8cc3-467d6f78bb3b' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.  , 0.25, 0.5 , 0.75, 1.  , 1.5 , 2.  ])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>y</span></div><div class='xr-var-dims'>(y)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.75 1.25 1.5 ... 3.0 3.75 5.0</div><input id='attrs-1671c4d2-b93e-479d-8774-2bad8928bd1b' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1671c4d2-b93e-479d-8774-2bad8928bd1b' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d379120d-5eec-4574-b3ca-874f2b22d308' class='xr-var-data-in' type='checkbox'><label for='data-d379120d-5eec-4574-b3ca-874f2b22d308' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.  , 0.75, 1.25, 1.5 , 2.25, 2.5 , 3.  , 3.75, 5.  ])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-530f54d2-90b4-4db8-8c0c-591799a272fa' class='xr-section-summary-in' type='checkbox'  checked><label for='section-530f54d2-90b4-4db8-8c0c-591799a272fa' class='xr-section-summary' >Data variables: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>temperature</span></div><div class='xr-var-dims'>(x, y)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>17.95 nan 12.78 nan ... nan nan nan</div><input id='attrs-87bb2012-6d17-46c6-8740-80b7913e853c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-87bb2012-6d17-46c6-8740-80b7913e853c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2147ed33-f2c9-42fd-b83f-22a2b513f615' class='xr-var-data-in' type='checkbox'><label for='data-2147ed33-f2c9-42fd-b83f-22a2b513f615' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[17.94960783,         nan, 12.78179366,         nan,         nan,\n",
       "        15.34804566,         nan, 16.50947814, 18.45371695],\n",
       "       [23.16431556,         nan, 16.7211818 ,         nan,         nan,\n",
       "        16.14457474,         nan, 19.28489001, 19.86366115],\n",
       "       [14.06485946,         nan, 27.00412885,         nan,         nan,\n",
       "        15.23882881,         nan, 13.7426183 , 15.07335772],\n",
       "       [ 8.32511351,         nan, 24.26735521,         nan,         nan,\n",
       "        20.46706844,         nan, 20.03878593, 23.282952  ],\n",
       "       [15.97616991,         nan, 14.81847599,         nan,         nan,\n",
       "        22.43793148,         nan, 17.08504234, 22.20120769],\n",
       "       [        nan,         nan,         nan,         nan,         nan,\n",
       "                nan,         nan,         nan,         nan],\n",
       "       [        nan,         nan,         nan,         nan,         nan,\n",
       "                nan,         nan,         nan,         nan]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>pressure</span></div><div class='xr-var-dims'>(x, y)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.028e+03 1.041e+03 nan ... nan nan</div><input id='attrs-f3a285a0-42e4-499b-b308-2ff689db0878' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-f3a285a0-42e4-499b-b308-2ff689db0878' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-7589d0a1-abe3-4b71-a4ba-1c00b34c1110' class='xr-var-data-in' type='checkbox'><label for='data-7589d0a1-abe3-4b71-a4ba-1c00b34c1110' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[1028.26532482, 1041.24862092,           nan,  993.99663901,\n",
       "        1033.62119861,           nan,  947.8055489 ,           nan,\n",
       "                  nan],\n",
       "       [          nan,           nan,           nan,           nan,\n",
       "                  nan,           nan,           nan,           nan,\n",
       "                  nan],\n",
       "       [ 925.9805478 ,  869.42080766,           nan, 1014.82220261,\n",
       "        1009.19783666,           nan, 1153.45178938,           nan,\n",
       "                  nan],\n",
       "       [          nan,           nan,           nan,           nan,\n",
       "                  nan,           nan,           nan,           nan,\n",
       "                  nan],\n",
       "       [1088.40426085, 1015.11683227,           nan,  923.85667441,\n",
       "         848.34917168,           nan, 1076.30438976,           nan,\n",
       "                  nan],\n",
       "       [1083.10427344, 1102.9111203 ,           nan, 1216.31839467,\n",
       "        1042.69602967,           nan, 1009.28499864,           nan,\n",
       "                  nan],\n",
       "       [1030.20353522,  957.03409707,           nan,  858.01495721,\n",
       "         970.70383648,           nan, 1047.99748065,           nan,\n",
       "                  nan]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-92bddd00-cf80-4fe4-8f71-8c70fdd3c39f' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-92bddd00-cf80-4fe4-8f71-8c70fdd3c39f' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:      (x: 7, y: 9)\n",
       "Coordinates:\n",
       "  * x            (x) float64 0.0 0.25 0.5 0.75 1.0 1.5 2.0\n",
       "  * y            (y) float64 0.0 0.75 1.25 1.5 2.25 2.5 3.0 3.75 5.0\n",
       "Data variables:\n",
       "    temperature  (x, y) float64 17.95 nan 12.78 nan nan ... nan nan nan nan nan\n",
       "    pressure     (x, y) float64 1.028e+03 1.041e+03 nan ... 1.048e+03 nan nan"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = xr.merge((temperature, pressure))\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the missing data which shows up as yellow in the plot below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure, axes = plt.subplots(nrows=1, ncols=2, figsize=(10, 5))\n",
    "missing_temp = np.where(np.isnan(data['temperature']), 1, 0)\n",
    "_ = axes[0].imshow(missing_temp)\n",
    "missing_pressure = np.where(np.isnan(data['pressure']), 1, 0)\n",
    "_ = axes[1].imshow(missing_pressure)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `combine_first`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This operation combines values from two `DataArrays`, using the second to fill holes in the first.  Coordinates for which there is no data in either `DataArray` will be filled with `NaN`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "temp1 = xr.DataArray(np.random.normal(loc=20.0, scale=5.0, size=(5, 5)),\n",
    "                     dims=('x', 'y'), coords={'x': np.linspace(0.0, 1.0, 5),\n",
    "                                              'y': np.linspace(0.0, 5.0, 5)},\n",
    "                     name='temperature')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30.160769229047233"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(temp1[0, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "temp2 = xr.DataArray(np.random.normal(loc=1001.0, scale=100.0, size=(5, 5)),\n",
    "                     dims=('x', 'y'), coords={'x': np.linspace(0.0, 2.0, 5),\n",
    "                                              'y': np.linspace(0.0, 3.0, 5)},\n",
    "                     name='temperature2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "973.5678681652961"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(temp2[0, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;temperature&#x27; (x: 7, y: 9)&gt;\n",
       "array([[  30.16076923, 1160.79185574,   32.54207966, 1113.94567685,\n",
       "         963.00125932,   20.6026758 , 1057.81260007,   13.57095518,\n",
       "          19.26529006],\n",
       "       [  16.78341091,           nan,   23.31879872,           nan,\n",
       "                  nan,   19.11640522,           nan,   21.39861491,\n",
       "          22.84965373],\n",
       "       [  13.32311252,  845.73365403,   23.39301521, 1000.36159348,\n",
       "        1040.53659612,   26.07197081,  939.0366407 ,   19.28379623,\n",
       "          21.42944587],\n",
       "       [  21.83136225,           nan,   24.74226117,           nan,\n",
       "                  nan,   21.8661864 ,           nan,   20.2430489 ,\n",
       "          11.04595042],\n",
       "       [  22.8803161 , 1067.44064587,   22.89817798,  878.59124927,\n",
       "         952.56961473,   17.06882593,  981.04218973,   22.01254996,\n",
       "          24.510231  ],\n",
       "       [ 860.50703651, 1111.03335793,           nan, 1185.63298016,\n",
       "        1007.7042812 ,           nan,  974.22068628,           nan,\n",
       "                  nan],\n",
       "       [1007.9544592 ,  907.82943711,           nan, 1106.23513447,\n",
       "        1115.1015106 ,           nan,  922.54767734,           nan,\n",
       "                  nan]])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.25 0.5 0.75 1.0 1.5 2.0\n",
       "  * y        (y) float64 0.0 0.75 1.25 1.5 2.25 2.5 3.0 3.75 5.0</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'temperature'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 7</li><li><span class='xr-has-index'>y</span>: 9</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-89156ee2-e548-4e0f-aaf2-33811e58c4a9' class='xr-array-in' type='checkbox' checked><label for='section-89156ee2-e548-4e0f-aaf2-33811e58c4a9' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>30.16 1.161e+03 32.54 1.114e+03 963.0 ... 1.115e+03 nan 922.5 nan nan</span></div><div class='xr-array-data'><pre>array([[  30.16076923, 1160.79185574,   32.54207966, 1113.94567685,\n",
       "         963.00125932,   20.6026758 , 1057.81260007,   13.57095518,\n",
       "          19.26529006],\n",
       "       [  16.78341091,           nan,   23.31879872,           nan,\n",
       "                  nan,   19.11640522,           nan,   21.39861491,\n",
       "          22.84965373],\n",
       "       [  13.32311252,  845.73365403,   23.39301521, 1000.36159348,\n",
       "        1040.53659612,   26.07197081,  939.0366407 ,   19.28379623,\n",
       "          21.42944587],\n",
       "       [  21.83136225,           nan,   24.74226117,           nan,\n",
       "                  nan,   21.8661864 ,           nan,   20.2430489 ,\n",
       "          11.04595042],\n",
       "       [  22.8803161 , 1067.44064587,   22.89817798,  878.59124927,\n",
       "         952.56961473,   17.06882593,  981.04218973,   22.01254996,\n",
       "          24.510231  ],\n",
       "       [ 860.50703651, 1111.03335793,           nan, 1185.63298016,\n",
       "        1007.7042812 ,           nan,  974.22068628,           nan,\n",
       "                  nan],\n",
       "       [1007.9544592 ,  907.82943711,           nan, 1106.23513447,\n",
       "        1115.1015106 ,           nan,  922.54767734,           nan,\n",
       "                  nan]])</pre></div></div></li><li class='xr-section-item'><input id='section-d8f914a9-abee-461f-84ec-6728f3303dd0' class='xr-section-summary-in' type='checkbox'  checked><label for='section-d8f914a9-abee-461f-84ec-6728f3303dd0' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.25 0.5 0.75 1.0 1.5 2.0</div><input id='attrs-99f75381-b0d1-4998-aacb-0cbeb0b8e832' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-99f75381-b0d1-4998-aacb-0cbeb0b8e832' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f87421ce-fbc9-47c3-9786-413cef08c890' class='xr-var-data-in' type='checkbox'><label for='data-f87421ce-fbc9-47c3-9786-413cef08c890' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.  , 0.25, 0.5 , 0.75, 1.  , 1.5 , 2.  ])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>y</span></div><div class='xr-var-dims'>(y)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.75 1.25 1.5 ... 3.0 3.75 5.0</div><input id='attrs-15a93c68-a0cb-4669-8fe3-7df1af0a5cba' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-15a93c68-a0cb-4669-8fe3-7df1af0a5cba' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-fe85729b-8b76-4231-b9c5-9f9f1177f0fd' class='xr-var-data-in' type='checkbox'><label for='data-fe85729b-8b76-4231-b9c5-9f9f1177f0fd' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.  , 0.75, 1.25, 1.5 , 2.25, 2.5 , 3.  , 3.75, 5.  ])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-a0f3a12a-eccd-4115-beea-ecdb5c4621e5' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-a0f3a12a-eccd-4115-beea-ecdb5c4621e5' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'temperature' (x: 7, y: 9)>\n",
       "array([[  30.16076923, 1160.79185574,   32.54207966, 1113.94567685,\n",
       "         963.00125932,   20.6026758 , 1057.81260007,   13.57095518,\n",
       "          19.26529006],\n",
       "       [  16.78341091,           nan,   23.31879872,           nan,\n",
       "                  nan,   19.11640522,           nan,   21.39861491,\n",
       "          22.84965373],\n",
       "       [  13.32311252,  845.73365403,   23.39301521, 1000.36159348,\n",
       "        1040.53659612,   26.07197081,  939.0366407 ,   19.28379623,\n",
       "          21.42944587],\n",
       "       [  21.83136225,           nan,   24.74226117,           nan,\n",
       "                  nan,   21.8661864 ,           nan,   20.2430489 ,\n",
       "          11.04595042],\n",
       "       [  22.8803161 , 1067.44064587,   22.89817798,  878.59124927,\n",
       "         952.56961473,   17.06882593,  981.04218973,   22.01254996,\n",
       "          24.510231  ],\n",
       "       [ 860.50703651, 1111.03335793,           nan, 1185.63298016,\n",
       "        1007.7042812 ,           nan,  974.22068628,           nan,\n",
       "                  nan],\n",
       "       [1007.9544592 ,  907.82943711,           nan, 1106.23513447,\n",
       "        1115.1015106 ,           nan,  922.54767734,           nan,\n",
       "                  nan]])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.25 0.5 0.75 1.0 1.5 2.0\n",
       "  * y        (y) float64 0.0 0.75 1.25 1.5 2.25 2.5 3.0 3.75 5.0"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = temp1.combine_first(temp2)\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the origin of the data, either `temp1` in blue or `temp2` in red, as well as the missing data which shows up in white."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_map = np.empty(data.shape)\n",
    "with np.errstate(invalid='ignore'):\n",
    "    data_map[data.values < 200.0] = -1.0\n",
    "    data_map[data.values >= 200.0] = 1.0\n",
    "data_map[np.isnan(data.values)] = 0.0\n",
    "_ = plt.imshow(data_map, cmap='bwr')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot below illustrates that the `combine_first` operator is not symmetric, i.e., `temp1.combine_first(temp2)` is not the same `DataArray` as `temp2.combine_first(temp1)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = temp2.combine_first(temp1)\n",
    "data_map = np.empty(data.shape)\n",
    "with np.errstate(invalid='ignore'):\n",
    "    data_map[data.values < 200.0] = -1.0\n",
    "    data_map[data.values >= 200.0] = 1.0\n",
    "data_map[np.isnan(data.values)] = 0.0\n",
    "_ = plt.imshow(data_map, cmap='bwr')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a second example, `combine_first` can also be used to concatenate two 1D `DataArray`'s. Data along the same dimension can be combined from several xarrays. Consider a sinusoidal signal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(15,)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_vals = np.linspace(0.0, 2.0*np.pi, 15)\n",
    "signal = xr.DataArray(np.sin(x_vals), dims=('x',), coords=(x_vals,), name='signal')\n",
    "signal.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = signal.plot.line('o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a second xarray by interpolating the signal.  Since this is 1D data, we can use quadratic interpolation, which is obviously better than the default, linear."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(62,)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_vals = np.arange(0.1, 2.0*np.pi, 0.1)\n",
    "interp_signal = signal.interp(x=x_vals, method='quadratic')\n",
    "interp_signal.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "  fill: currentColor;\n",
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;signal&#x27; (x: 62)&gt;\n",
       "array([ 0.10318894,  0.20264376,  0.29836444,  0.39035099,  0.47860341,\n",
       "        0.56312169,  0.64375288,  0.71753198,  0.78331803,  0.84111103,\n",
       "        0.89091097,  0.93216473,  0.96365124,  0.9853265 ,  0.99719052,\n",
       "        0.99924235,  0.99146638,  0.97385707,  0.94641442,  0.90913843,\n",
       "        0.86265968,  0.8082609 ,  0.74597955,  0.67581562,  0.5979443 ,\n",
       "        0.51487769,  0.42743617,  0.33561975,  0.23942843,  0.14036215,\n",
       "        0.04123119, -0.05789976, -0.15703071, -0.25590868, -0.35136437,\n",
       "       -0.44244516, -0.52915105, -0.61148204, -0.68816475, -0.75700325,\n",
       "       -0.81795917, -0.87103252, -0.91609399, -0.95171653, -0.97750573,\n",
       "       -0.99346159, -0.99958412, -0.99588178, -0.98236804, -0.95904304,\n",
       "       -0.92590681, -0.88309627, -0.83195232, -0.77281532, -0.70568526,\n",
       "       -0.63056215, -0.54917135, -0.46402519, -0.37514489, -0.28253045,\n",
       "       -0.18618189, -0.08609919])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ... 5.7 5.8 5.9 6.0 6.1 6.2</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'signal'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 62</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-ea771692-fbc8-433f-9fe9-d429d9b3a008' class='xr-array-in' type='checkbox' checked><label for='section-ea771692-fbc8-433f-9fe9-d429d9b3a008' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>0.1032 0.2026 0.2984 0.3904 0.4786 ... -0.3751 -0.2825 -0.1862 -0.0861</span></div><div class='xr-array-data'><pre>array([ 0.10318894,  0.20264376,  0.29836444,  0.39035099,  0.47860341,\n",
       "        0.56312169,  0.64375288,  0.71753198,  0.78331803,  0.84111103,\n",
       "        0.89091097,  0.93216473,  0.96365124,  0.9853265 ,  0.99719052,\n",
       "        0.99924235,  0.99146638,  0.97385707,  0.94641442,  0.90913843,\n",
       "        0.86265968,  0.8082609 ,  0.74597955,  0.67581562,  0.5979443 ,\n",
       "        0.51487769,  0.42743617,  0.33561975,  0.23942843,  0.14036215,\n",
       "        0.04123119, -0.05789976, -0.15703071, -0.25590868, -0.35136437,\n",
       "       -0.44244516, -0.52915105, -0.61148204, -0.68816475, -0.75700325,\n",
       "       -0.81795917, -0.87103252, -0.91609399, -0.95171653, -0.97750573,\n",
       "       -0.99346159, -0.99958412, -0.99588178, -0.98236804, -0.95904304,\n",
       "       -0.92590681, -0.88309627, -0.83195232, -0.77281532, -0.70568526,\n",
       "       -0.63056215, -0.54917135, -0.46402519, -0.37514489, -0.28253045,\n",
       "       -0.18618189, -0.08609919])</pre></div></div></li><li class='xr-section-item'><input id='section-6ff0b143-d1c8-4fbe-a076-c49af02d2ec0' class='xr-section-summary-in' type='checkbox'  checked><label for='section-6ff0b143-d1c8-4fbe-a076-c49af02d2ec0' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.1 0.2 0.3 0.4 ... 5.9 6.0 6.1 6.2</div><input id='attrs-a0d37c05-6ef7-4786-b0cf-c704703605d8' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a0d37c05-6ef7-4786-b0cf-c704703605d8' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-12c2f5ea-6935-4971-9e20-ea648ccbc4dd' class='xr-var-data-in' type='checkbox'><label for='data-12c2f5ea-6935-4971-9e20-ea648ccbc4dd' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. , 1.1, 1.2, 1.3, 1.4,\n",
       "       1.5, 1.6, 1.7, 1.8, 1.9, 2. , 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8,\n",
       "       2.9, 3. , 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4. , 4.1, 4.2,\n",
       "       4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5. , 5.1, 5.2, 5.3, 5.4, 5.5, 5.6,\n",
       "       5.7, 5.8, 5.9, 6. , 6.1, 6.2])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-b6f8989e-813a-4c8a-803d-94f659646681' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-b6f8989e-813a-4c8a-803d-94f659646681' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'signal' (x: 62)>\n",
       "array([ 0.10318894,  0.20264376,  0.29836444,  0.39035099,  0.47860341,\n",
       "        0.56312169,  0.64375288,  0.71753198,  0.78331803,  0.84111103,\n",
       "        0.89091097,  0.93216473,  0.96365124,  0.9853265 ,  0.99719052,\n",
       "        0.99924235,  0.99146638,  0.97385707,  0.94641442,  0.90913843,\n",
       "        0.86265968,  0.8082609 ,  0.74597955,  0.67581562,  0.5979443 ,\n",
       "        0.51487769,  0.42743617,  0.33561975,  0.23942843,  0.14036215,\n",
       "        0.04123119, -0.05789976, -0.15703071, -0.25590868, -0.35136437,\n",
       "       -0.44244516, -0.52915105, -0.61148204, -0.68816475, -0.75700325,\n",
       "       -0.81795917, -0.87103252, -0.91609399, -0.95171653, -0.97750573,\n",
       "       -0.99346159, -0.99958412, -0.99588178, -0.98236804, -0.95904304,\n",
       "       -0.92590681, -0.88309627, -0.83195232, -0.77281532, -0.70568526,\n",
       "       -0.63056215, -0.54917135, -0.46402519, -0.37514489, -0.28253045,\n",
       "       -0.18618189, -0.08609919])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ... 5.7 5.8 5.9 6.0 6.1 6.2"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interp_signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure, axes = plt.subplots(nrows=1, ncols=1)\n",
    "_ = signal.plot.line('r-o', ax=axes)\n",
    "_ = interp_signal.plot.line('b.', ax=axes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Combine the original and the interpolated signal into a single xarray."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(77,)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combined = signal.combine_first(interp_signal)\n",
    "combined.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = combined.plot.line('.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Split-apply-combine: grouping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As in pandas, data in `DataArray`s can be grouped using the `group_by` method.  It is mostly done for data with categorical coordinates, and works similar to its pandas counterpart.  However, xarray has the `groupby_bins` method that is very convenient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "coords = np.arange(0.0, 20.0, 1.0)\n",
    "temperature = xr.DataArray(np.random.normal(loc=20.0, scale=2.0, size=(coords.shape[0], coords.shape[0])),\n",
    "                           dims=('x', 'y'), coords={'x': coords, 'y': coords}, name='temperature')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data may be grouped by $x$ coordinates, e.g., into 5 bins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "bins = np.arange(-0.1, 20.1, 4.0)\n",
    "labels = np.arange(2.0, 19.0, 4.0)\n",
    "x_groups = temperature.groupby_bins('x', bins, labels=labels)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "As labels for the bins, the midpoint of the bin intervals is chosen.  The resulting groups show that each of the five groups contains 4 indices along the $x$-axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{2.0: [0, 1, 2, 3],\n",
       " 6.0: [4, 5, 6, 7],\n",
       " 10.0: [8, 9, 10, 11],\n",
       " 14.0: [12, 13, 14, 15],\n",
       " 18.0: [16, 17, 18, 19]}"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_groups.groups"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "For each of these groups, we can print the label, the group's shape, and the average over the group."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
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    {
     "name": "stdout",
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     "text": [
      "2.0 (4, 20): 19.740039\n",
      "6.0 (4, 20): 19.956380\n",
      "10.0 (4, 20): 19.833710\n",
      "14.0 (4, 20): 20.210349\n",
      "18.0 (4, 20): 19.883434\n"
     ]
    }
   ],
   "source": [
    "for label, group in x_groups:\n",
    "    print(f'{label} {group.shape}: {float(group.mean()):.6f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the `apply` method on a group-by object will perform the same computation, but combine the results back into a `DataArray` with the appropriate coordinates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;temperature&#x27; (x: 5)&gt;\n",
       "array([19.74003914, 19.95637965, 19.83371025, 20.2103495 , 19.88343436])\n",
       "Coordinates:\n",
       "  * x        (x) float64 2.0 6.0 10.0 14.0 18.0</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'temperature'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 5</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-5628442d-405b-451f-af79-d61e6d3faab0' class='xr-array-in' type='checkbox' checked><label for='section-5628442d-405b-451f-af79-d61e6d3faab0' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>19.74 19.96 19.83 20.21 19.88</span></div><div class='xr-array-data'><pre>array([19.74003914, 19.95637965, 19.83371025, 20.2103495 , 19.88343436])</pre></div></div></li><li class='xr-section-item'><input id='section-f0e55d4e-a82b-49c3-b90e-4c830b3637ff' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f0e55d4e-a82b-49c3-b90e-4c830b3637ff' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>2.0 6.0 10.0 14.0 18.0</div><input id='attrs-927ebcb3-17cf-4f43-9d3f-e904d0867eb7' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-927ebcb3-17cf-4f43-9d3f-e904d0867eb7' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-6f8aa579-10ec-406f-8caf-cdead624bb9a' class='xr-var-data-in' type='checkbox'><label for='data-6f8aa579-10ec-406f-8caf-cdead624bb9a' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([ 2.,  6., 10., 14., 18.])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f6f556e5-3faf-4855-bc55-263dfda86c0b' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-f6f556e5-3faf-4855-bc55-263dfda86c0b' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'temperature' (x: 5)>\n",
       "array([19.74003914, 19.95637965, 19.83371025, 20.2103495 , 19.88343436])\n",
       "Coordinates:\n",
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     "execution_count": 61,
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   "source": [
    "x_groups.apply(np.mean).rename({'x_bins': 'x'})"
   ]
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  {
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   "source": [
    "Although there seems to be no way to bin directly in two dimensions, this can easily be achieved by using `apply` at two levels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;temperature&#x27; (x: 5, y: 5)&gt;\n",
       "array([[20.27900716, 19.84760764, 19.45199068, 19.38471107, 19.73687915],\n",
       "       [19.92500993, 19.86829183, 20.6684436 , 19.39024996, 19.92990292],\n",
       "       [20.61101087, 19.40372366, 20.07905835, 18.72817246, 20.34658592],\n",
       "       [20.01903605, 20.80194921, 20.4077706 , 20.69507883, 19.12791281],\n",
       "       [19.37891485, 20.40884597, 20.23977211, 19.05371739, 20.33592149]])\n",
       "Coordinates:\n",
       "  * x        (x) float64 2.0 6.0 10.0 14.0 18.0\n",
       "  * y        (y) float64 2.0 6.0 10.0 14.0 18.0</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'temperature'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 5</li><li><span class='xr-has-index'>y</span>: 5</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-33aa2a82-271d-4167-8799-6c2c845ba0ee' class='xr-array-in' type='checkbox' checked><label for='section-33aa2a82-271d-4167-8799-6c2c845ba0ee' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>20.28 19.85 19.45 19.38 19.74 19.93 ... 19.38 20.41 20.24 19.05 20.34</span></div><div class='xr-array-data'><pre>array([[20.27900716, 19.84760764, 19.45199068, 19.38471107, 19.73687915],\n",
       "       [19.92500993, 19.86829183, 20.6684436 , 19.39024996, 19.92990292],\n",
       "       [20.61101087, 19.40372366, 20.07905835, 18.72817246, 20.34658592],\n",
       "       [20.01903605, 20.80194921, 20.4077706 , 20.69507883, 19.12791281],\n",
       "       [19.37891485, 20.40884597, 20.23977211, 19.05371739, 20.33592149]])</pre></div></div></li><li class='xr-section-item'><input id='section-00128003-da2b-4581-b7cd-88314b4d2faa' class='xr-section-summary-in' type='checkbox'  checked><label for='section-00128003-da2b-4581-b7cd-88314b4d2faa' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>2.0 6.0 10.0 14.0 18.0</div><input id='attrs-601b3b13-7411-4d77-b606-cb2edb5aa873' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-601b3b13-7411-4d77-b606-cb2edb5aa873' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-91b789b6-ca5d-459d-bea3-725b3ea77adf' class='xr-var-data-in' type='checkbox'><label for='data-91b789b6-ca5d-459d-bea3-725b3ea77adf' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([ 2.,  6., 10., 14., 18.])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>y</span></div><div class='xr-var-dims'>(y)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>2.0 6.0 10.0 14.0 18.0</div><input id='attrs-2d79f025-3f30-4425-ae26-047c0c254587' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2d79f025-3f30-4425-ae26-047c0c254587' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-34b5a2fb-e5a0-42d7-8a69-417ef760e384' class='xr-var-data-in' type='checkbox'><label for='data-34b5a2fb-e5a0-42d7-8a69-417ef760e384' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([ 2.,  6., 10., 14., 18.])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-20ef01ec-3def-47c7-ad15-04efe0a9d47f' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-20ef01ec-3def-47c7-ad15-04efe0a9d47f' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'temperature' (x: 5, y: 5)>\n",
       "array([[20.27900716, 19.84760764, 19.45199068, 19.38471107, 19.73687915],\n",
       "       [19.92500993, 19.86829183, 20.6684436 , 19.39024996, 19.92990292],\n",
       "       [20.61101087, 19.40372366, 20.07905835, 18.72817246, 20.34658592],\n",
       "       [20.01903605, 20.80194921, 20.4077706 , 20.69507883, 19.12791281],\n",
       "       [19.37891485, 20.40884597, 20.23977211, 19.05371739, 20.33592149]])\n",
       "Coordinates:\n",
       "  * x        (x) float64 2.0 6.0 10.0 14.0 18.0\n",
       "  * y        (y) float64 2.0 6.0 10.0 14.0 18.0"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coarse_temp = x_groups.apply(lambda x: x.groupby_bins('y', bins, labels=labels).apply(np.mean))\\\n",
    "                      .rename({'x_bins': 'x', 'y_bins': 'y'})\n",
    "coarse_temp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify, compare the upper-left and lower-right elements of `coarse_temp` with the explicitely computed mean value of those subarrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isclose(temperature[0:4, 0:4].mean(), coarse_temp[0, 0], rtol=1.0e-7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isclose(temperature[-4:, -4:].mean(), coarse_temp[-1, -1], rtol=1.0e-7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the coarsening process by plotting a heatmap of the original and the coarsened data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vmin = float(temperature.min())\n",
    "vmax = float(temperature.max())\n",
    "figure, axes = plt.subplots(nrows=1, ncols=2, figsize=(10, 5))\n",
    "# plot of tempeature\n",
    "t_plot = axes[0].imshow(temperature, cmap='coolwarm', origin='lower',\n",
    "                        vmin=vmin, vmax=vmax)\n",
    "axes[0].set_xlabel('$x$')\n",
    "tick_pos = list(range(0, 20, 5))\n",
    "axes[0].set_xticks(tick_pos)\n",
    "axes[0].set_xticklabels(f'{float(x):.1f}' for x in temperature.coords['x'][tick_pos])\n",
    "axes[0].set_ylabel('$y$')\n",
    "axes[0].set_yticks(tick_pos)\n",
    "axes[0].set_yticklabels(f'{float(x):.1f}' for x in temperature.coords['y'][tick_pos])\n",
    "figure.colorbar(t_plot, ax=axes[0])\n",
    "# plot of coarse_temp\n",
    "c_plot = axes[1].imshow(coarse_temp, cmap='coolwarm', origin='lower',\n",
    "                        vmin=vmin, vmax=vmax)\n",
    "axes[1].set_xlabel('$x$')\n",
    "axes[1].set_xticks(range(len(coarse_temp.coords['x'])))\n",
    "axes[1].set_xticklabels(f'{float(x):.1f}' for x in coarse_temp.coords['x'])\n",
    "axes[1].set_ylabel('$y$')\n",
    "axes[1].set_yticks(range(len(coarse_temp.coords['y'])))\n",
    "axes[1].set_yticklabels(f'{float(x):.1f}' for x in coarse_temp.coords['y'])\n",
    "figure.colorbar(t_plot, ax=axes[1])\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time series"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Working with multi-dimensional time series data is straightforward with xarray.  A sequence of timestamps can be created using pandas. We will use this to index a 3D array, where the third dimension represents time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_coords = np.linspace(-2.0, 2.0, 5)\n",
    "y_coords = np.linspace(-3.0, 3.0, 7)\n",
    "timestamps = pd.date_range('2019-07-01', freq='6H', periods=10)\n",
    "data = xr.DataArray(np.empty((len(x_coords), len(y_coords), len(timestamps))),\n",
    "                    dims=('x', 'y', 't'), coords=(x_coords, y_coords, timestamps))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We initialize the data, starting from random values at $t = 0$, and computing the data at $t + 1$ from the data at time $t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "data[:, :, 0] = np.random.normal(loc=0.0, scale=1.0,\n",
    "                                 size=(data.coords['x'].shape[0], data.coords['y'].shape[0]))\n",
    "for t in range(1, data.coords['t'].shape[0]):\n",
    "    data[:, :, t] = data[:, :, t - 1] + np.random.normal(loc=0.0, scale=0.1, size=data[:, :, 0].shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each timestamp, we can print the mean and standard deviation over the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean: -0.015, stddev: 0.295 (2019-07-01 06:00)\n",
      "mean: -0.007, stddev: 0.088 (2019-07-01 12:00)\n",
      "mean: +0.015, stddev: 0.074 (2019-07-01 18:00)\n",
      "mean: +0.014, stddev: 0.080 (2019-07-02 00:00)\n",
      "mean: -0.030, stddev: 0.123 (2019-07-02 06:00)\n",
      "mean: +0.021, stddev: 0.103 (2019-07-02 12:00)\n",
      "mean: -0.020, stddev: 0.101 (2019-07-02 18:00)\n",
      "mean: +0.007, stddev: 0.078 (2019-07-03 00:00)\n",
      "mean: -0.025, stddev: 0.089 (2019-07-03 06:00)\n"
     ]
    }
   ],
   "source": [
    "for t, time in enumerate(data.coords['t'][1:]):\n",
    "    diff = data.isel(t=t) - data.isel(t=t - 1)\n",
    "    time_str = time.dt.strftime('%Y-%m-%d %H:%M').item()\n",
    "    print(f'mean: {float(diff.mean()):+0.3f}, stddev: {float(diff.std()):0.3f} ({time_str})')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean_data = data.mean(dim=('x', 'y'))\n",
    "mean_data.name = 'mean values'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = mean_data.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the plot's $x$-axis is labeled appropriately, i.e, with the date and time only."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data can be indexed by a string representing a timestamp."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-attrs dt {\n",
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       "\n",
       ".xr-attrs dt:hover span {\n",
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       "\n",
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (x: 5, y: 7)&gt;\n",
       "array([[-0.3412283 , -0.44141319, -3.12353046,  0.4575659 ,  0.67887657,\n",
       "         0.48948429, -0.44117579],\n",
       "       [-0.12299757,  0.44510657,  0.67707235, -0.56301321,  1.64253884,\n",
       "        -0.07242632,  0.62863607],\n",
       "       [ 0.65069085,  0.60879499,  2.13238478, -1.16405391,  0.9204897 ,\n",
       "         0.79807465,  0.55849914],\n",
       "       [ 0.25519679, -0.57028363, -0.90245524,  0.34766021,  1.85823148,\n",
       "         1.07159815, -2.82977829],\n",
       "       [-1.5539603 , -1.42375053, -1.08684066,  0.2109889 , -0.29453301,\n",
       "         0.46183656,  0.01838815]])\n",
       "Coordinates:\n",
       "  * x        (x) float64 -2.0 -1.0 0.0 1.0 2.0\n",
       "  * y        (y) float64 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0\n",
       "    t        datetime64[ns] 2019-07-02T06:00:00</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 5</li><li><span class='xr-has-index'>y</span>: 7</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-a696173e-17bf-444e-9e5c-b994ea90772b' class='xr-array-in' type='checkbox' checked><label for='section-a696173e-17bf-444e-9e5c-b994ea90772b' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>-0.3412 -0.4414 -3.124 0.4576 0.6789 ... 0.211 -0.2945 0.4618 0.01839</span></div><div class='xr-array-data'><pre>array([[-0.3412283 , -0.44141319, -3.12353046,  0.4575659 ,  0.67887657,\n",
       "         0.48948429, -0.44117579],\n",
       "       [-0.12299757,  0.44510657,  0.67707235, -0.56301321,  1.64253884,\n",
       "        -0.07242632,  0.62863607],\n",
       "       [ 0.65069085,  0.60879499,  2.13238478, -1.16405391,  0.9204897 ,\n",
       "         0.79807465,  0.55849914],\n",
       "       [ 0.25519679, -0.57028363, -0.90245524,  0.34766021,  1.85823148,\n",
       "         1.07159815, -2.82977829],\n",
       "       [-1.5539603 , -1.42375053, -1.08684066,  0.2109889 , -0.29453301,\n",
       "         0.46183656,  0.01838815]])</pre></div></div></li><li class='xr-section-item'><input id='section-30b582cb-8df2-4933-846a-d9f1efb09fa9' class='xr-section-summary-in' type='checkbox'  checked><label for='section-30b582cb-8df2-4933-846a-d9f1efb09fa9' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-2.0 -1.0 0.0 1.0 2.0</div><input id='attrs-daf88b51-07f1-4ca8-88b0-92aa0dd28b92' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-daf88b51-07f1-4ca8-88b0-92aa0dd28b92' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-99935070-c4df-46cf-b582-c5837647d1a7' class='xr-var-data-in' type='checkbox'><label for='data-99935070-c4df-46cf-b582-c5837647d1a7' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([-2., -1.,  0.,  1.,  2.])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>y</span></div><div class='xr-var-dims'>(y)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0</div><input id='attrs-1652a8bd-143c-4eb5-a0f1-0e39d12bb89e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1652a8bd-143c-4eb5-a0f1-0e39d12bb89e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-57f84df5-517a-4155-aef9-275e0ba8d299' class='xr-var-data-in' type='checkbox'><label for='data-57f84df5-517a-4155-aef9-275e0ba8d299' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([-3., -2., -1.,  0.,  1.,  2.,  3.])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>t</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>datetime64[ns]</div><div class='xr-var-preview xr-preview'>2019-07-02T06:00:00</div><input id='attrs-94cd2368-0f6e-4f29-be7b-b0c0113ba985' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-94cd2368-0f6e-4f29-be7b-b0c0113ba985' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-29c9d24f-4748-4409-8deb-15372d7fa3d7' class='xr-var-data-in' type='checkbox'><label for='data-29c9d24f-4748-4409-8deb-15372d7fa3d7' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(&#x27;2019-07-02T06:00:00.000000000&#x27;, dtype=&#x27;datetime64[ns]&#x27;)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-4b616341-a37d-4659-a5f6-8d33ed3ce1c9' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-4b616341-a37d-4659-a5f6-8d33ed3ce1c9' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray (x: 5, y: 7)>\n",
       "array([[-0.3412283 , -0.44141319, -3.12353046,  0.4575659 ,  0.67887657,\n",
       "         0.48948429, -0.44117579],\n",
       "       [-0.12299757,  0.44510657,  0.67707235, -0.56301321,  1.64253884,\n",
       "        -0.07242632,  0.62863607],\n",
       "       [ 0.65069085,  0.60879499,  2.13238478, -1.16405391,  0.9204897 ,\n",
       "         0.79807465,  0.55849914],\n",
       "       [ 0.25519679, -0.57028363, -0.90245524,  0.34766021,  1.85823148,\n",
       "         1.07159815, -2.82977829],\n",
       "       [-1.5539603 , -1.42375053, -1.08684066,  0.2109889 , -0.29453301,\n",
       "         0.46183656,  0.01838815]])\n",
       "Coordinates:\n",
       "  * x        (x) float64 -2.0 -1.0 0.0 1.0 2.0\n",
       "  * y        (y) float64 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0\n",
       "    t        datetime64[ns] 2019-07-02T06:00:00"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.sel(t='2019-07-02 06:00:00')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When indexing with a date, all data for that date is returned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;t&#x27; (t: 4)&gt;\n",
       "array([&#x27;2019-07-02T00:00:00.000000000&#x27;, &#x27;2019-07-02T06:00:00.000000000&#x27;,\n",
       "       &#x27;2019-07-02T12:00:00.000000000&#x27;, &#x27;2019-07-02T18:00:00.000000000&#x27;],\n",
       "      dtype=&#x27;datetime64[ns]&#x27;)\n",
       "Coordinates:\n",
       "  * t        (t) datetime64[ns] 2019-07-02 ... 2019-07-02T18:00:00</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'t'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>t</span>: 4</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-b2a82d7c-f705-49f9-9b8e-a7b1529c0988' class='xr-array-in' type='checkbox' checked><label for='section-b2a82d7c-f705-49f9-9b8e-a7b1529c0988' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>2019-07-02 2019-07-02T06:00:00 2019-07-02T12:00:00 2019-07-02T18:00:00</span></div><div class='xr-array-data'><pre>array([&#x27;2019-07-02T00:00:00.000000000&#x27;, &#x27;2019-07-02T06:00:00.000000000&#x27;,\n",
       "       &#x27;2019-07-02T12:00:00.000000000&#x27;, &#x27;2019-07-02T18:00:00.000000000&#x27;],\n",
       "      dtype=&#x27;datetime64[ns]&#x27;)</pre></div></div></li><li class='xr-section-item'><input id='section-3b08394d-1754-40b6-af79-b7d6903b66b5' class='xr-section-summary-in' type='checkbox'  checked><label for='section-3b08394d-1754-40b6-af79-b7d6903b66b5' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>t</span></div><div class='xr-var-dims'>(t)</div><div class='xr-var-dtype'>datetime64[ns]</div><div class='xr-var-preview xr-preview'>2019-07-02 ... 2019-07-02T18:00:00</div><input id='attrs-d3847d5e-110c-4904-b553-6c137a396c9f' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d3847d5e-110c-4904-b553-6c137a396c9f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ca684cff-3d25-4ed4-997f-0fcc76f40e08' class='xr-var-data-in' type='checkbox'><label for='data-ca684cff-3d25-4ed4-997f-0fcc76f40e08' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;2019-07-02T00:00:00.000000000&#x27;, &#x27;2019-07-02T06:00:00.000000000&#x27;,\n",
       "       &#x27;2019-07-02T12:00:00.000000000&#x27;, &#x27;2019-07-02T18:00:00.000000000&#x27;],\n",
       "      dtype=&#x27;datetime64[ns]&#x27;)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-3e0050a7-c609-4e44-b220-5176f25680ba' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-3e0050a7-c609-4e44-b220-5176f25680ba' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 't' (t: 4)>\n",
       "array(['2019-07-02T00:00:00.000000000', '2019-07-02T06:00:00.000000000',\n",
       "       '2019-07-02T12:00:00.000000000', '2019-07-02T18:00:00.000000000'],\n",
       "      dtype='datetime64[ns]')\n",
       "Coordinates:\n",
       "  * t        (t) datetime64[ns] 2019-07-02 ... 2019-07-02T18:00:00"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.sel(t='2019-07-02').coords['t']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data can also be sliced along the time coordinate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
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       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;t&#x27; (t: 3)&gt;\n",
       "array([&#x27;2019-07-02T06:00:00.000000000&#x27;, &#x27;2019-07-02T12:00:00.000000000&#x27;,\n",
       "       &#x27;2019-07-02T18:00:00.000000000&#x27;], dtype=&#x27;datetime64[ns]&#x27;)\n",
       "Coordinates:\n",
       "  * t        (t) datetime64[ns] 2019-07-02T06:00:00 ... 2019-07-02T18:00:00</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'t'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>t</span>: 3</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-b6817239-8b29-4ff6-91b8-a86e33d18ead' class='xr-array-in' type='checkbox' checked><label for='section-b6817239-8b29-4ff6-91b8-a86e33d18ead' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>2019-07-02T06:00:00 2019-07-02T12:00:00 2019-07-02T18:00:00</span></div><div class='xr-array-data'><pre>array([&#x27;2019-07-02T06:00:00.000000000&#x27;, &#x27;2019-07-02T12:00:00.000000000&#x27;,\n",
       "       &#x27;2019-07-02T18:00:00.000000000&#x27;], dtype=&#x27;datetime64[ns]&#x27;)</pre></div></div></li><li class='xr-section-item'><input id='section-959915f4-f286-433e-bebf-fa0c41cd1ed2' class='xr-section-summary-in' type='checkbox'  checked><label for='section-959915f4-f286-433e-bebf-fa0c41cd1ed2' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>t</span></div><div class='xr-var-dims'>(t)</div><div class='xr-var-dtype'>datetime64[ns]</div><div class='xr-var-preview xr-preview'>2019-07-02T06:00:00 ... 2019-07-...</div><input id='attrs-91bb4f20-f0aa-4958-a0bc-c53c06e6a034' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-91bb4f20-f0aa-4958-a0bc-c53c06e6a034' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-7937054c-6da7-4df3-887f-5b2affd95e7f' class='xr-var-data-in' type='checkbox'><label for='data-7937054c-6da7-4df3-887f-5b2affd95e7f' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;2019-07-02T06:00:00.000000000&#x27;, &#x27;2019-07-02T12:00:00.000000000&#x27;,\n",
       "       &#x27;2019-07-02T18:00:00.000000000&#x27;], dtype=&#x27;datetime64[ns]&#x27;)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-0328761b-3e82-4533-86f7-198f6ec149d0' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-0328761b-3e82-4533-86f7-198f6ec149d0' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 't' (t: 3)>\n",
       "array(['2019-07-02T06:00:00.000000000', '2019-07-02T12:00:00.000000000',\n",
       "       '2019-07-02T18:00:00.000000000'], dtype='datetime64[ns]')\n",
       "Coordinates:\n",
       "  * t        (t) datetime64[ns] 2019-07-02T06:00:00 ... 2019-07-02T18:00:00"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.sel(t=slice('2019-07-02 02:00:00', '2019-07-02 20:00:00')).coords['t']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the values at some point in time is now easy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = data.sel(t='2019-07-02 06:00:00').plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Time data can be resampled using the `groupby` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<defs>\n",
       "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
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       "</symbol>\n",
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       "</defs>\n",
       "</svg>\n",
       "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
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       "\n",
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       "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
       "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
       "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
       "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
       "  --xr-background-color: var(--jp-layout-color0, white);\n",
       "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
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       "\n",
       "html[theme=dark],\n",
       "body.vscode-dark {\n",
       "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
       "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
       "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
       "  --xr-border-color: #1F1F1F;\n",
       "  --xr-disabled-color: #515151;\n",
       "  --xr-background-color: #111111;\n",
       "  --xr-background-color-row-even: #111111;\n",
       "  --xr-background-color-row-odd: #313131;\n",
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       "\n",
       ".xr-wrap {\n",
       "  display: block;\n",
       "  min-width: 300px;\n",
       "  max-width: 700px;\n",
       "}\n",
       "\n",
       ".xr-text-repr-fallback {\n",
       "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
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       "\n",
       ".xr-header {\n",
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       "  padding-bottom: 6px;\n",
       "  margin-bottom: 4px;\n",
       "  border-bottom: solid 1px var(--xr-border-color);\n",
       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
       "  margin-top: 0;\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-obj-type,\n",
       ".xr-array-name {\n",
       "  margin-left: 2px;\n",
       "  margin-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-obj-type {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-sections {\n",
       "  padding-left: 0 !important;\n",
       "  display: grid;\n",
       "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
       "}\n",
       "\n",
       ".xr-section-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-section-item input {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-item input + label {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label {\n",
       "  cursor: pointer;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label:hover {\n",
       "  color: var(--xr-font-color0);\n",
       "}\n",
       "\n",
       ".xr-section-summary {\n",
       "  grid-column: 1;\n",
       "  color: var(--xr-font-color2);\n",
       "  font-weight: 500;\n",
       "}\n",
       "\n",
       ".xr-section-summary > span {\n",
       "  display: inline-block;\n",
       "  padding-left: 0.5em;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in + label:before {\n",
       "  display: inline-block;\n",
       "  content: '►';\n",
       "  font-size: 11px;\n",
       "  width: 15px;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (x: 5, y: 7, day: 3)&gt;\n",
       "array([[[-0.46291318, -0.39637169, -0.07841252],\n",
       "        [-0.39702317, -0.44815594, -0.4006401 ],\n",
       "        [-2.96951364, -3.1924674 , -3.22419747],\n",
       "        [ 0.63984448,  0.43730983,  0.55409257],\n",
       "        [ 0.55182783,  0.70007055,  0.79375391],\n",
       "        [ 0.27841046,  0.40519602,  0.15229262],\n",
       "        [-0.33689048, -0.41237619, -0.46285354]],\n",
       "\n",
       "       [[-0.3200796 , -0.08341457,  0.14228792],\n",
       "        [ 0.33866051,  0.36467424,  0.26528276],\n",
       "        [ 0.73958916,  0.73287116,  0.62997225],\n",
       "        [-0.17944376, -0.53313053, -0.55882628],\n",
       "        [ 1.67114844,  1.5620275 ,  1.42223704],\n",
       "        [-0.20170789, -0.09616273,  0.01273292],\n",
       "        [ 0.5997237 ,  0.54545052,  0.55801778]],\n",
       "\n",
       "       [[ 0.56069543,  0.61593755,  0.76182785],\n",
       "        [ 0.48387653,  0.50353675,  0.41104512],\n",
       "        [ 2.01396939,  2.09066303,  2.02752534],\n",
       "        [-1.2154396 , -1.23475548, -1.26299435],\n",
       "        [ 0.78624824,  0.95478107,  0.71358529],\n",
       "        [ 0.89168616,  0.73441534,  0.70084937],\n",
       "        [ 0.62710838,  0.62141553,  0.48262359]],\n",
       "\n",
       "       [[ 0.30075387,  0.22651747,  0.35977035],\n",
       "        [-0.71448025, -0.56899808, -0.67843257],\n",
       "        [-0.62399081, -0.89999181, -0.94120974],\n",
       "        [ 0.43679156,  0.40165305,  0.44681311],\n",
       "        [ 2.41439815,  1.82721954,  1.79978283],\n",
       "        [ 1.05004863,  1.06567837,  0.89642676],\n",
       "        [-2.60614422, -2.83196682, -2.80953678]],\n",
       "\n",
       "       [[-1.59392823, -1.51303191, -1.45941633],\n",
       "        [-1.54059522, -1.44898541, -1.49102598],\n",
       "        [-1.36019679, -1.15860528, -1.318973  ],\n",
       "        [-0.18104163,  0.20354281,  0.2574422 ],\n",
       "        [-0.20565196, -0.33182611, -0.39025233],\n",
       "        [ 0.41837562,  0.52777681,  0.75237673],\n",
       "        [-0.15815372,  0.12664222,  0.2733762 ]]])\n",
       "Coordinates:\n",
       "  * x        (x) float64 -2.0 -1.0 0.0 1.0 2.0\n",
       "  * y        (y) float64 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0\n",
       "  * day      (day) int64 1 2 3</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 5</li><li><span class='xr-has-index'>y</span>: 7</li><li><span class='xr-has-index'>day</span>: 3</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-49fcd72c-2584-4bfa-a651-d69bd2f9ad0e' class='xr-array-in' type='checkbox' checked><label for='section-49fcd72c-2584-4bfa-a651-d69bd2f9ad0e' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>-0.4629 -0.3964 -0.07841 -0.397 ... 0.7524 -0.1582 0.1266 0.2734</span></div><div class='xr-array-data'><pre>array([[[-0.46291318, -0.39637169, -0.07841252],\n",
       "        [-0.39702317, -0.44815594, -0.4006401 ],\n",
       "        [-2.96951364, -3.1924674 , -3.22419747],\n",
       "        [ 0.63984448,  0.43730983,  0.55409257],\n",
       "        [ 0.55182783,  0.70007055,  0.79375391],\n",
       "        [ 0.27841046,  0.40519602,  0.15229262],\n",
       "        [-0.33689048, -0.41237619, -0.46285354]],\n",
       "\n",
       "       [[-0.3200796 , -0.08341457,  0.14228792],\n",
       "        [ 0.33866051,  0.36467424,  0.26528276],\n",
       "        [ 0.73958916,  0.73287116,  0.62997225],\n",
       "        [-0.17944376, -0.53313053, -0.55882628],\n",
       "        [ 1.67114844,  1.5620275 ,  1.42223704],\n",
       "        [-0.20170789, -0.09616273,  0.01273292],\n",
       "        [ 0.5997237 ,  0.54545052,  0.55801778]],\n",
       "\n",
       "       [[ 0.56069543,  0.61593755,  0.76182785],\n",
       "        [ 0.48387653,  0.50353675,  0.41104512],\n",
       "        [ 2.01396939,  2.09066303,  2.02752534],\n",
       "        [-1.2154396 , -1.23475548, -1.26299435],\n",
       "        [ 0.78624824,  0.95478107,  0.71358529],\n",
       "        [ 0.89168616,  0.73441534,  0.70084937],\n",
       "        [ 0.62710838,  0.62141553,  0.48262359]],\n",
       "\n",
       "       [[ 0.30075387,  0.22651747,  0.35977035],\n",
       "        [-0.71448025, -0.56899808, -0.67843257],\n",
       "        [-0.62399081, -0.89999181, -0.94120974],\n",
       "        [ 0.43679156,  0.40165305,  0.44681311],\n",
       "        [ 2.41439815,  1.82721954,  1.79978283],\n",
       "        [ 1.05004863,  1.06567837,  0.89642676],\n",
       "        [-2.60614422, -2.83196682, -2.80953678]],\n",
       "\n",
       "       [[-1.59392823, -1.51303191, -1.45941633],\n",
       "        [-1.54059522, -1.44898541, -1.49102598],\n",
       "        [-1.36019679, -1.15860528, -1.318973  ],\n",
       "        [-0.18104163,  0.20354281,  0.2574422 ],\n",
       "        [-0.20565196, -0.33182611, -0.39025233],\n",
       "        [ 0.41837562,  0.52777681,  0.75237673],\n",
       "        [-0.15815372,  0.12664222,  0.2733762 ]]])</pre></div></div></li><li class='xr-section-item'><input id='section-e076ca9f-763e-4836-96de-67b41fe8fa16' class='xr-section-summary-in' type='checkbox'  checked><label for='section-e076ca9f-763e-4836-96de-67b41fe8fa16' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-2.0 -1.0 0.0 1.0 2.0</div><input id='attrs-ab4ba453-ba1a-4e77-9a13-3d0521e394d8' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ab4ba453-ba1a-4e77-9a13-3d0521e394d8' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-75d694d0-94e6-4c73-bc48-047d0e40cf55' class='xr-var-data-in' type='checkbox'><label for='data-75d694d0-94e6-4c73-bc48-047d0e40cf55' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([-2., -1.,  0.,  1.,  2.])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>y</span></div><div class='xr-var-dims'>(y)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0</div><input id='attrs-2be1c60f-1a73-4a27-985a-7b6457cf2e6b' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2be1c60f-1a73-4a27-985a-7b6457cf2e6b' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-667ce0e5-8e49-4e3b-8d30-81b5e815a7cf' class='xr-var-data-in' type='checkbox'><label for='data-667ce0e5-8e49-4e3b-8d30-81b5e815a7cf' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([-3., -2., -1.,  0.,  1.,  2.,  3.])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>day</span></div><div class='xr-var-dims'>(day)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>1 2 3</div><input id='attrs-475486e9-eaa7-4997-be0b-ff9db206a382' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-475486e9-eaa7-4997-be0b-ff9db206a382' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e46573db-09a7-4550-a91e-c93dfd5bda75' class='xr-var-data-in' type='checkbox'><label for='data-e46573db-09a7-4550-a91e-c93dfd5bda75' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([1, 2, 3])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-7c2a542e-5266-4dee-82ef-8344603076ed' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-7c2a542e-5266-4dee-82ef-8344603076ed' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray (x: 5, y: 7, day: 3)>\n",
       "array([[[-0.46291318, -0.39637169, -0.07841252],\n",
       "        [-0.39702317, -0.44815594, -0.4006401 ],\n",
       "        [-2.96951364, -3.1924674 , -3.22419747],\n",
       "        [ 0.63984448,  0.43730983,  0.55409257],\n",
       "        [ 0.55182783,  0.70007055,  0.79375391],\n",
       "        [ 0.27841046,  0.40519602,  0.15229262],\n",
       "        [-0.33689048, -0.41237619, -0.46285354]],\n",
       "\n",
       "       [[-0.3200796 , -0.08341457,  0.14228792],\n",
       "        [ 0.33866051,  0.36467424,  0.26528276],\n",
       "        [ 0.73958916,  0.73287116,  0.62997225],\n",
       "        [-0.17944376, -0.53313053, -0.55882628],\n",
       "        [ 1.67114844,  1.5620275 ,  1.42223704],\n",
       "        [-0.20170789, -0.09616273,  0.01273292],\n",
       "        [ 0.5997237 ,  0.54545052,  0.55801778]],\n",
       "\n",
       "       [[ 0.56069543,  0.61593755,  0.76182785],\n",
       "        [ 0.48387653,  0.50353675,  0.41104512],\n",
       "        [ 2.01396939,  2.09066303,  2.02752534],\n",
       "        [-1.2154396 , -1.23475548, -1.26299435],\n",
       "        [ 0.78624824,  0.95478107,  0.71358529],\n",
       "        [ 0.89168616,  0.73441534,  0.70084937],\n",
       "        [ 0.62710838,  0.62141553,  0.48262359]],\n",
       "\n",
       "       [[ 0.30075387,  0.22651747,  0.35977035],\n",
       "        [-0.71448025, -0.56899808, -0.67843257],\n",
       "        [-0.62399081, -0.89999181, -0.94120974],\n",
       "        [ 0.43679156,  0.40165305,  0.44681311],\n",
       "        [ 2.41439815,  1.82721954,  1.79978283],\n",
       "        [ 1.05004863,  1.06567837,  0.89642676],\n",
       "        [-2.60614422, -2.83196682, -2.80953678]],\n",
       "\n",
       "       [[-1.59392823, -1.51303191, -1.45941633],\n",
       "        [-1.54059522, -1.44898541, -1.49102598],\n",
       "        [-1.36019679, -1.15860528, -1.318973  ],\n",
       "        [-0.18104163,  0.20354281,  0.2574422 ],\n",
       "        [-0.20565196, -0.33182611, -0.39025233],\n",
       "        [ 0.41837562,  0.52777681,  0.75237673],\n",
       "        [-0.15815372,  0.12664222,  0.2733762 ]]])\n",
       "Coordinates:\n",
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       "  * y        (y) float64 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0\n",
       "  * day      (day) int64 1 2 3"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.groupby('t.day').mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, it is more convenient to use the `resample` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (x: 5, y: 7, t: 3)&gt;\n",
       "array([[[-0.46291318, -0.39637169, -0.07841252],\n",
       "        [-0.39702317, -0.44815594, -0.4006401 ],\n",
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       "        [ 0.63984448,  0.43730983,  0.55409257],\n",
       "        [ 0.55182783,  0.70007055,  0.79375391],\n",
       "        [ 0.27841046,  0.40519602,  0.15229262],\n",
       "        [-0.33689048, -0.41237619, -0.46285354]],\n",
       "\n",
       "       [[-0.3200796 , -0.08341457,  0.14228792],\n",
       "        [ 0.33866051,  0.36467424,  0.26528276],\n",
       "        [ 0.73958916,  0.73287116,  0.62997225],\n",
       "        [-0.17944376, -0.53313053, -0.55882628],\n",
       "        [ 1.67114844,  1.5620275 ,  1.42223704],\n",
       "        [-0.20170789, -0.09616273,  0.01273292],\n",
       "        [ 0.5997237 ,  0.54545052,  0.55801778]],\n",
       "\n",
       "       [[ 0.56069543,  0.61593755,  0.76182785],\n",
       "        [ 0.48387653,  0.50353675,  0.41104512],\n",
       "        [ 2.01396939,  2.09066303,  2.02752534],\n",
       "        [-1.2154396 , -1.23475548, -1.26299435],\n",
       "        [ 0.78624824,  0.95478107,  0.71358529],\n",
       "        [ 0.89168616,  0.73441534,  0.70084937],\n",
       "        [ 0.62710838,  0.62141553,  0.48262359]],\n",
       "\n",
       "       [[ 0.30075387,  0.22651747,  0.35977035],\n",
       "        [-0.71448025, -0.56899808, -0.67843257],\n",
       "        [-0.62399081, -0.89999181, -0.94120974],\n",
       "        [ 0.43679156,  0.40165305,  0.44681311],\n",
       "        [ 2.41439815,  1.82721954,  1.79978283],\n",
       "        [ 1.05004863,  1.06567837,  0.89642676],\n",
       "        [-2.60614422, -2.83196682, -2.80953678]],\n",
       "\n",
       "       [[-1.59392823, -1.51303191, -1.45941633],\n",
       "        [-1.54059522, -1.44898541, -1.49102598],\n",
       "        [-1.36019679, -1.15860528, -1.318973  ],\n",
       "        [-0.18104163,  0.20354281,  0.2574422 ],\n",
       "        [-0.20565196, -0.33182611, -0.39025233],\n",
       "        [ 0.41837562,  0.52777681,  0.75237673],\n",
       "        [-0.15815372,  0.12664222,  0.2733762 ]]])\n",
       "Coordinates:\n",
       "  * t        (t) datetime64[ns] 2019-07-01 2019-07-02 2019-07-03\n",
       "  * x        (x) float64 -2.0 -1.0 0.0 1.0 2.0\n",
       "  * y        (y) float64 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 5</li><li><span class='xr-has-index'>y</span>: 7</li><li><span class='xr-has-index'>t</span>: 3</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-2b06545d-9c4e-441e-a2e1-2976a86b54de' class='xr-array-in' type='checkbox' checked><label for='section-2b06545d-9c4e-441e-a2e1-2976a86b54de' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>-0.4629 -0.3964 -0.07841 -0.397 ... 0.7524 -0.1582 0.1266 0.2734</span></div><div class='xr-array-data'><pre>array([[[-0.46291318, -0.39637169, -0.07841252],\n",
       "        [-0.39702317, -0.44815594, -0.4006401 ],\n",
       "        [-2.96951364, -3.1924674 , -3.22419747],\n",
       "        [ 0.63984448,  0.43730983,  0.55409257],\n",
       "        [ 0.55182783,  0.70007055,  0.79375391],\n",
       "        [ 0.27841046,  0.40519602,  0.15229262],\n",
       "        [-0.33689048, -0.41237619, -0.46285354]],\n",
       "\n",
       "       [[-0.3200796 , -0.08341457,  0.14228792],\n",
       "        [ 0.33866051,  0.36467424,  0.26528276],\n",
       "        [ 0.73958916,  0.73287116,  0.62997225],\n",
       "        [-0.17944376, -0.53313053, -0.55882628],\n",
       "        [ 1.67114844,  1.5620275 ,  1.42223704],\n",
       "        [-0.20170789, -0.09616273,  0.01273292],\n",
       "        [ 0.5997237 ,  0.54545052,  0.55801778]],\n",
       "\n",
       "       [[ 0.56069543,  0.61593755,  0.76182785],\n",
       "        [ 0.48387653,  0.50353675,  0.41104512],\n",
       "        [ 2.01396939,  2.09066303,  2.02752534],\n",
       "        [-1.2154396 , -1.23475548, -1.26299435],\n",
       "        [ 0.78624824,  0.95478107,  0.71358529],\n",
       "        [ 0.89168616,  0.73441534,  0.70084937],\n",
       "        [ 0.62710838,  0.62141553,  0.48262359]],\n",
       "\n",
       "       [[ 0.30075387,  0.22651747,  0.35977035],\n",
       "        [-0.71448025, -0.56899808, -0.67843257],\n",
       "        [-0.62399081, -0.89999181, -0.94120974],\n",
       "        [ 0.43679156,  0.40165305,  0.44681311],\n",
       "        [ 2.41439815,  1.82721954,  1.79978283],\n",
       "        [ 1.05004863,  1.06567837,  0.89642676],\n",
       "        [-2.60614422, -2.83196682, -2.80953678]],\n",
       "\n",
       "       [[-1.59392823, -1.51303191, -1.45941633],\n",
       "        [-1.54059522, -1.44898541, -1.49102598],\n",
       "        [-1.36019679, -1.15860528, -1.318973  ],\n",
       "        [-0.18104163,  0.20354281,  0.2574422 ],\n",
       "        [-0.20565196, -0.33182611, -0.39025233],\n",
       "        [ 0.41837562,  0.52777681,  0.75237673],\n",
       "        [-0.15815372,  0.12664222,  0.2733762 ]]])</pre></div></div></li><li class='xr-section-item'><input id='section-95b65f2b-8bd6-4960-a59c-18e94d0e8b77' class='xr-section-summary-in' type='checkbox'  checked><label for='section-95b65f2b-8bd6-4960-a59c-18e94d0e8b77' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>t</span></div><div class='xr-var-dims'>(t)</div><div class='xr-var-dtype'>datetime64[ns]</div><div class='xr-var-preview xr-preview'>2019-07-01 2019-07-02 2019-07-03</div><input id='attrs-8a1693ad-fc17-4e1c-b1c1-d8e932f7d953' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-8a1693ad-fc17-4e1c-b1c1-d8e932f7d953' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b79a2cef-05bc-41a3-aac6-e71e40b35b9c' class='xr-var-data-in' type='checkbox'><label for='data-b79a2cef-05bc-41a3-aac6-e71e40b35b9c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;2019-07-01T00:00:00.000000000&#x27;, &#x27;2019-07-02T00:00:00.000000000&#x27;,\n",
       "       &#x27;2019-07-03T00:00:00.000000000&#x27;], dtype=&#x27;datetime64[ns]&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-2.0 -1.0 0.0 1.0 2.0</div><input id='attrs-089bdcd2-e5dd-4cfe-8d9a-b4689e5579ff' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-089bdcd2-e5dd-4cfe-8d9a-b4689e5579ff' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2b66e5b3-6de6-49a8-9f82-52b4a9472323' class='xr-var-data-in' type='checkbox'><label for='data-2b66e5b3-6de6-49a8-9f82-52b4a9472323' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([-2., -1.,  0.,  1.,  2.])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>y</span></div><div class='xr-var-dims'>(y)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0</div><input id='attrs-0b1916cf-1007-464a-b412-9276672027a3' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0b1916cf-1007-464a-b412-9276672027a3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e23ed9ea-7bb2-4fc6-99af-736ef3701631' class='xr-var-data-in' type='checkbox'><label for='data-e23ed9ea-7bb2-4fc6-99af-736ef3701631' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([-3., -2., -1.,  0.,  1.,  2.,  3.])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-c36a244d-7f37-4a4a-a260-5bb43e7cc160' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-c36a244d-7f37-4a4a-a260-5bb43e7cc160' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
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       "        [-0.33689048, -0.41237619, -0.46285354]],\n",
       "\n",
       "       [[-0.3200796 , -0.08341457,  0.14228792],\n",
       "        [ 0.33866051,  0.36467424,  0.26528276],\n",
       "        [ 0.73958916,  0.73287116,  0.62997225],\n",
       "        [-0.17944376, -0.53313053, -0.55882628],\n",
       "        [ 1.67114844,  1.5620275 ,  1.42223704],\n",
       "        [-0.20170789, -0.09616273,  0.01273292],\n",
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       "\n",
       "       [[ 0.56069543,  0.61593755,  0.76182785],\n",
       "        [ 0.48387653,  0.50353675,  0.41104512],\n",
       "        [ 2.01396939,  2.09066303,  2.02752534],\n",
       "        [-1.2154396 , -1.23475548, -1.26299435],\n",
       "        [ 0.78624824,  0.95478107,  0.71358529],\n",
       "        [ 0.89168616,  0.73441534,  0.70084937],\n",
       "        [ 0.62710838,  0.62141553,  0.48262359]],\n",
       "\n",
       "       [[ 0.30075387,  0.22651747,  0.35977035],\n",
       "        [-0.71448025, -0.56899808, -0.67843257],\n",
       "        [-0.62399081, -0.89999181, -0.94120974],\n",
       "        [ 0.43679156,  0.40165305,  0.44681311],\n",
       "        [ 2.41439815,  1.82721954,  1.79978283],\n",
       "        [ 1.05004863,  1.06567837,  0.89642676],\n",
       "        [-2.60614422, -2.83196682, -2.80953678]],\n",
       "\n",
       "       [[-1.59392823, -1.51303191, -1.45941633],\n",
       "        [-1.54059522, -1.44898541, -1.49102598],\n",
       "        [-1.36019679, -1.15860528, -1.318973  ],\n",
       "        [-0.18104163,  0.20354281,  0.2574422 ],\n",
       "        [-0.20565196, -0.33182611, -0.39025233],\n",
       "        [ 0.41837562,  0.52777681,  0.75237673],\n",
       "        [-0.15815372,  0.12664222,  0.2733762 ]]])\n",
       "Coordinates:\n",
       "  * t        (t) datetime64[ns] 2019-07-01 2019-07-02 2019-07-03\n",
       "  * x        (x) float64 -2.0 -1.0 0.0 1.0 2.0\n",
       "  * y        (y) float64 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.resample(t='24H').mean()"
   ]
  }
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