tutorials/rtc-qualitative-assessment.ipynb

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    "## Radiometric terrain correction qualitative assessment \n",
    "\n",
    "[sarsen](https://github.com/bopen/sarsen) radiometric correction implements the gamma flatting algorithm proposed by Small, David (2011). [Flattening Gamma: Radiometric Terrain Correction for SAR Imagery. Geoscience and Remote Sensing, IEEE Transactions on. 49. 3081 - 3093. 10.1109/TGRS.2011.2120616](https://www.researchgate.net/publication/224230688_Flattening_Gamma_Radiometric_Terrain_Correction_for_SAR_Imagery)\n",
    "\n",
    "In this notebook, we perform the same qualitative test done by the authors to evaluate the goodness of the gamma flattening correction. For an introduction to terrain correction, see [Customizable radiometric terrain corrections of Sentinel-1 products\n",
    "](https://planetarycomputer.microsoft.com/docs/tutorials/customizable-rtc-sentinel1/)."
   ]
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  {
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   "id": "6d604a80-9222-46f2-97cb-afe5bfb9bdbd",
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   "source": [
    "### Install Dependencies and Imports\n",
    "Additional dependencies: `sarsen==0.9.2`"
   ]
  },
  {
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   "execution_count": 1,
   "id": "ce375bf1-9ec8-4aa5-b3ce-cbfe5995c31e",
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   "source": [
    "# !pip install sarsen==0.9.2"
   ]
  },
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   "execution_count": 2,
   "id": "9f82185a-60a4-4651-8bdf-6fb1ee82c884",
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   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import Normalize\n",
    "from matplotlib import cm\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 7)\n",
    "plt.rcParams[\"font.size\"] = 14"
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
   "id": "1391c47f-d76e-4840-8eed-d547b4784331",
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   "source": [
    "import os\n",
    "import tempfile\n",
    "\n",
    "import numpy as np\n",
    "import xarray as xr\n",
    "from scipy.stats import gaussian_kde as kde\n",
    "from sarsen import apps, geocoding, orbit, scene\n",
    "\n",
    "import adlfs\n",
    "import planetary_computer\n",
    "import pystac_client\n",
    "import stackstac\n",
    "import rioxarray  # noqa: F401\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 7)"
   ]
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   "id": "86970ee8",
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   "source": [
    "### Processing definitions"
   ]
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   "execution_count": 4,
   "id": "107608ba-51f5-4a3d-ab70-bc9fb34eafed",
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    {
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       "'/tmp'"
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   "source": [
    "# create a temporary directory where to store downloaded data\n",
    "tmp_dir = tempfile.gettempdir()\n",
    "\n",
    "# DEM path\n",
    "dem_path = os.path.join(tmp_dir, \"South-of-Redmond-10m.tif\")\n",
    "\n",
    "# path to Sentinel-1 input product in the Planetary Computer\n",
    "product_folder = \"GRD/2021/12/17/IW/DV/S1B_IW_GRDH_1SDV_20211217T141304_20211217T141329_030066_039705_9048\"  # noqa: E501\n",
    "\n",
    "# band to be processed\n",
    "measurement_group = \"IW/VV\"\n",
    "\n",
    "tmp_dir"
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  },
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   "id": "4dd0a0f2-4476-48fa-bceb-6f5a872c59de",
   "metadata": {},
   "source": [
    "#### Area of interest definition: South-of-Redmond (Seattle, US)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8ec8652a-7736-40cc-b8d9-1134493e5888",
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   "source": [
    "lon, lat = [-121.95, 47.04]\n",
    "buffer = 0.2\n",
    "bbox = [lon - buffer, lat - buffer, lon + buffer, lat + buffer]"
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   "source": [
    "#### DEMs discovery\n",
    "\n",
    "Here we use the DEM with a 10-meter ground sample distance (GDS) available on the Planetary Computer. Note that **any DEM supported by GDAL/Proj can be used**.\n",
    "\n",
    "Using `pystac_client` we can search the Planetary Computer's STAC endpoint for items matching our query parameters.  \n",
    "As multiple DEMs acquired at different times are available in this area, we select the DEMs with 10-meter GDS and perform the average of the remaining DEMs along the time dimension."
   ]
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   "id": "e08b28b1-a706-4005-b1e8-633a748e7f69",
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   "source": [
    "catalog = pystac_client.Client.open(\n",
    "    \"https://planetarycomputer.microsoft.com/api/stac/v1\",\n",
    "    modifier=planetary_computer.sign_inplace,\n",
    ")\n",
    "search = catalog.search(\n",
    "    collections=\"3dep-seamless\", bbox=bbox, query={\"gsd\": {\"eq\": 10}}\n",
    ")\n",
    "items = search.item_collection()"
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   "cell_type": "markdown",
   "id": "7503fa77-ba5a-492c-9662-ae2f9b2ba5f4",
   "metadata": {},
   "source": [
    "Here we load the data into an xarray `DataArray` using stackstac."
   ]
  },
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   "cell_type": "code",
   "execution_count": 7,
   "id": "625eb3d3-90b0-429b-addc-e0ac59e60942",
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       "    resolution:  9.2592593e-05</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'stackstac-6fbfb106cd445ae5ea0f677ec80c3c41'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>time</span>: 4</li><li><span class='xr-has-index'>y</span>: 4321</li><li><span class='xr-has-index'>x</span>: 4321</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-29d5b192-5ced-49bf-8b61-f47a6d290fb2' class='xr-array-in' type='checkbox' checked><label for='section-29d5b192-5ced-49bf-8b61-f47a6d290fb2' 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>dask.array&lt;chunksize=(1, 1024, 1024), meta=np.ndarray&gt;</span></div><div class='xr-array-data'><table>\n",
       "    <tr>\n",
       "        <td>\n",
       "            <table>\n",
       "                <thead>\n",
       "                    <tr>\n",
       "                        <td> </td>\n",
       "                        <th> Array </th>\n",
       "                        <th> Chunk </th>\n",
       "                    </tr>\n",
       "                </thead>\n",
       "                <tbody>\n",
       "                    \n",
       "                    <tr>\n",
       "                        <th> Bytes </th>\n",
       "                        <td> 569.79 MiB </td>\n",
       "                        <td> 8.00 MiB </td>\n",
       "                    </tr>\n",
       "                    \n",
       "                    <tr>\n",
       "                        <th> Shape </th>\n",
       "                        <td> (4, 4321, 4321) </td>\n",
       "                        <td> (1, 1024, 1024) </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <th> Count </th>\n",
       "                        <td> 208 Tasks </td>\n",
       "                        <td> 100 Chunks </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                    <th> Type </th>\n",
       "                    <td> float64 </td>\n",
       "                    <td> numpy.ndarray </td>\n",
       "                    </tr>\n",
       "                </tbody>\n",
       "            </table>\n",
       "        </td>\n",
       "        <td>\n",
       "        <svg width=\"194\" height=\"184\" style=\"stroke:rgb(0,0,0);stroke-width:1\" >\n",
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       "  <text x=\"7.474299\" y=\"147.474299\" font-size=\"1.0rem\" font-weight=\"100\" text-anchor=\"middle\" transform=\"rotate(45,7.474299,147.474299)\">4</text>\n",
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       "        </td>\n",
       "    </tr>\n",
       "</table></div></div></li><li class='xr-section-item'><input id='section-a677ef22-e7ac-4fc0-ad83-ad2fd42a567e' class='xr-section-summary-in' type='checkbox'  checked><label for='section-a677ef22-e7ac-4fc0-ad83-ad2fd42a567e' class='xr-section-summary' >Coordinates: <span>(13)</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'>time</span></div><div class='xr-var-dims'>(time)</div><div class='xr-var-dtype'>datetime64[ns]</div><div class='xr-var-preview xr-preview'>2018-02-02 ... 2020-01-07</div><input id='attrs-53d19fe5-843e-49bf-83cd-14e19009a062' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-53d19fe5-843e-49bf-83cd-14e19009a062' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-bf7abc63-a59c-4d0b-99ae-b7a59e34a367' class='xr-var-data-in' type='checkbox'><label for='data-bf7abc63-a59c-4d0b-99ae-b7a59e34a367' 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;2018-02-02T00:00:00.000000000&#x27;, &#x27;2018-02-08T00:00:00.000000000&#x27;,\n",
       "       &#x27;2018-02-08T00:00:00.000000000&#x27;, &#x27;2020-01-07T00:00:00.000000000&#x27;],\n",
       "      dtype=&#x27;datetime64[ns]&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>id</span></div><div class='xr-var-dims'>(time)</div><div class='xr-var-dtype'>&lt;U10</div><div class='xr-var-preview xr-preview'>&#x27;n48w122-13&#x27; ... &#x27;n48w123-13&#x27;</div><input id='attrs-fc23b22c-b91c-43f9-b814-f0a6e227b93f' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-fc23b22c-b91c-43f9-b814-f0a6e227b93f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c847904a-6e83-40c1-b3b5-3e364f77251e' class='xr-var-data-in' type='checkbox'><label for='data-c847904a-6e83-40c1-b3b5-3e364f77251e' 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;n48w122-13&#x27;, &#x27;n47w122-13&#x27;, &#x27;n47w123-13&#x27;, &#x27;n48w123-13&#x27;],\n",
       "      dtype=&#x27;&lt;U10&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>band</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>&lt;U4</div><div class='xr-var-preview xr-preview'>&#x27;data&#x27;</div><input id='attrs-7ef3ea35-0002-4f1e-bc91-56c8da0859c2' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-7ef3ea35-0002-4f1e-bc91-56c8da0859c2' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c4f7aab3-298c-41d9-8372-2a0856a5c64a' class='xr-var-data-in' type='checkbox'><label for='data-c4f7aab3-298c-41d9-8372-2a0856a5c64a' 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;data&#x27;, dtype=&#x27;&lt;U4&#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'>-122.2 -122.1 ... -121.8 -121.8</div><input id='attrs-befc0719-69dc-4bbd-b3b4-a6225fdcb12e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-befc0719-69dc-4bbd-b3b4-a6225fdcb12e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e9f7af31-13a9-4d23-a60e-7393cb0abdcf' class='xr-var-data-in' type='checkbox'><label for='data-e9f7af31-13a9-4d23-a60e-7393cb0abdcf' 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([-122.150001, -122.149908, -122.149815, ..., -121.750186, -121.750093,\n",
       "       -121.750001])</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'>47.24 47.24 47.24 ... 46.84 46.84</div><input id='attrs-6d57120a-f362-41d5-8fc7-8a8a5c69c0c9' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-6d57120a-f362-41d5-8fc7-8a8a5c69c0c9' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f39260ba-6521-4432-b070-3b64b815f80e' class='xr-var-data-in' type='checkbox'><label for='data-f39260ba-6521-4432-b070-3b64b815f80e' 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([47.24    , 47.239908, 47.239815, ..., 46.840185, 46.840093, 46.84    ])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>start_datetime</span></div><div class='xr-var-dims'>(time)</div><div class='xr-var-dtype'>&lt;U20</div><div class='xr-var-preview xr-preview'>&#x27;1952-01-01T00:00:00Z&#x27; ... &#x27;2017...</div><input id='attrs-687f5fff-a577-4878-80b1-2c3e15316cc9' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-687f5fff-a577-4878-80b1-2c3e15316cc9' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-922f8c43-e439-4b3c-b15d-f4b48ecd49e8' class='xr-var-data-in' type='checkbox'><label for='data-922f8c43-e439-4b3c-b15d-f4b48ecd49e8' 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;1952-01-01T00:00:00Z&#x27;, &#x27;1956-01-01T00:00:00Z&#x27;,\n",
       "       &#x27;1947-01-01T00:00:00Z&#x27;, &#x27;2017-09-14T00:00:00Z&#x27;], dtype=&#x27;&lt;U20&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>end_datetime</span></div><div class='xr-var-dims'>(time)</div><div class='xr-var-dtype'>&lt;U20</div><div class='xr-var-preview xr-preview'>&#x27;2016-12-31T00:00:00Z&#x27; ... &#x27;2019...</div><input id='attrs-d9205806-9ea5-4c01-a2bc-f048bba08f41' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d9205806-9ea5-4c01-a2bc-f048bba08f41' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-623dadb2-d26a-49d3-aa57-1aa516391f85' class='xr-var-data-in' type='checkbox'><label for='data-623dadb2-d26a-49d3-aa57-1aa516391f85' 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;2016-12-31T00:00:00Z&#x27;, &#x27;2016-12-31T00:00:00Z&#x27;,\n",
       "       &#x27;2016-12-31T00:00:00Z&#x27;, &#x27;2019-04-25T00:00:00Z&#x27;], dtype=&#x27;&lt;U20&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>proj:shape</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>{10812}</div><input id='attrs-fa407de8-7d0a-4038-9a1d-3de287413d8a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-fa407de8-7d0a-4038-9a1d-3de287413d8a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-af7a09e8-560d-4043-884d-7fc657c824f2' class='xr-var-data-in' type='checkbox'><label for='data-af7a09e8-560d-4043-884d-7fc657c824f2' 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({10812}, dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>proj:epsg</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>5498</div><input id='attrs-cdf0398e-83aa-4aea-b7bd-cce15c99ebf6' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-cdf0398e-83aa-4aea-b7bd-cce15c99ebf6' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-a7ffcac5-53f8-41ac-bf2d-00df32cc1872' class='xr-var-data-in' type='checkbox'><label for='data-a7ffcac5-53f8-41ac-bf2d-00df32cc1872' 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(5498)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>threedep:region</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>&lt;U7</div><div class='xr-var-preview xr-preview'>&#x27;n40w130&#x27;</div><input id='attrs-8bae5d77-05ee-42ba-925e-c0d6c08b566f' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-8bae5d77-05ee-42ba-925e-c0d6c08b566f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-4b44c7e7-8d45-42ed-9ed9-55aa015b6ac4' class='xr-var-data-in' type='checkbox'><label for='data-4b44c7e7-8d45-42ed-9ed9-55aa015b6ac4' 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;n40w130&#x27;, dtype=&#x27;&lt;U7&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>gsd</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>10</div><input id='attrs-4b730efa-a2ae-4cf0-846c-5ada3a0f5cea' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-4b730efa-a2ae-4cf0-846c-5ada3a0f5cea' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-18d8e21e-a9eb-48c1-8a3d-17ef5e59095e' class='xr-var-data-in' type='checkbox'><label for='data-18d8e21e-a9eb-48c1-8a3d-17ef5e59095e' 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(10)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>description</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>&lt;U1849</div><div class='xr-var-preview xr-preview'>&#x27;This tile of the 3D Elevation P...</div><input id='attrs-80a59015-04ed-4727-9705-3104adb09173' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-80a59015-04ed-4727-9705-3104adb09173' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-9e357051-be52-4c03-b09a-cc718ae5fbfe' class='xr-var-data-in' type='checkbox'><label for='data-9e357051-be52-4c03-b09a-cc718ae5fbfe' 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;This tile of the 3D Elevation Program (3DEP) seamless products is 1/3 arc-second resolution.  3DEP data serve as the elevation layer of The National Map, and provide basic elevation information for Earth science studies and mapping applications in the United States. Scientists and resource managers use 3DEP data for global change research, hydrologic modeling, resource monitoring, mapping and visualization, and many other applications. 3DEP data compose an elevation dataset that consists of seamless layers and a high resolution layer.  Each of these layers consists of the best available raster elevation data of the conterminous United States, Alaska, Hawaii, territorial islands, Mexico and Canada.  3DEP data are updated continually as new data become available. Seamless 3DEP data are derived from diverse source data that are processed to a common coordinate system and unit of vertical measure. These data are distributed in geographic coordinates in units of decimal degrees, and in conformance with the North American Datum of 1983 (NAD 83). All elevation values are in meters and, over the conterminous United States, are referenced to the North American Vertical Datum of 1988 (NAVD 88). The vertical reference will vary in other areas. Seamless 3DEP data are available nationally (except for Alaska) at resolutions of 1 arc-second (approximately 30 meters) and 1/3 arc-second (approximately 10 meters). In most of Alaska, only lower resolution source data are available. As a result, most seamless 3DEP data for Alaska are at 2 arc-second (approximately 60 meters) grid spacing. Part of Alaska is available at the 1 and 1/3 arc-second resolutions from interferometric synthetic aperture radar (ifsar) collections starting in 2010.  Plans are in place for collection of statewide ifsar in Alaska. All 3DEP products are public domain.&#x27;,\n",
       "      dtype=&#x27;&lt;U1849&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>epsg</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>5498</div><input id='attrs-e1a22919-6070-4d1c-95da-c88b0d49764a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e1a22919-6070-4d1c-95da-c88b0d49764a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f5067b70-dce3-4936-8e67-4a4b43424d04' class='xr-var-data-in' type='checkbox'><label for='data-f5067b70-dce3-4936-8e67-4a4b43424d04' 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(5498)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-09b97f6e-13df-472a-825a-18a422614edc' class='xr-section-summary-in' type='checkbox'  checked><label for='section-09b97f6e-13df-472a-825a-18a422614edc' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>spec :</span></dt><dd>RasterSpec(epsg=5498, bounds=(-122.15000053746, 46.839907613503, -121.749907943107, 47.240000207856), resolutions_xy=(9.2592593e-05, 9.2592593e-05))</dd><dt><span>crs :</span></dt><dd>epsg:5498</dd><dt><span>transform :</span></dt><dd>| 0.00, 0.00,-122.15|\n",
       "| 0.00,-0.00, 47.24|\n",
       "| 0.00, 0.00, 1.00|</dd><dt><span>resolution :</span></dt><dd>9.2592593e-05</dd></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'stackstac-6fbfb106cd445ae5ea0f677ec80c3c41' (time: 4,\n",
       "                                                                y: 4321, x: 4321)>\n",
       "dask.array<getitem, shape=(4, 4321, 4321), dtype=float64, chunksize=(1, 1024, 1024), chunktype=numpy.ndarray>\n",
       "Coordinates: (12/13)\n",
       "  * time             (time) datetime64[ns] 2018-02-02 2018-02-08 ... 2020-01-07\n",
       "    id               (time) <U10 'n48w122-13' 'n47w122-13' ... 'n48w123-13'\n",
       "    band             <U4 'data'\n",
       "  * x                (x) float64 -122.2 -122.1 -122.1 ... -121.8 -121.8 -121.8\n",
       "  * y                (y) float64 47.24 47.24 47.24 47.24 ... 46.84 46.84 46.84\n",
       "    start_datetime   (time) <U20 '1952-01-01T00:00:00Z' ... '2017-09-14T00:00...\n",
       "    ...               ...\n",
       "    proj:shape       object {10812}\n",
       "    proj:epsg        int64 5498\n",
       "    threedep:region  <U7 'n40w130'\n",
       "    gsd              int64 10\n",
       "    description      <U1849 'This tile of the 3D Elevation Program (3DEP) sea...\n",
       "    epsg             int64 5498\n",
       "Attributes:\n",
       "    spec:        RasterSpec(epsg=5498, bounds=(-122.15000053746, 46.839907613...\n",
       "    crs:         epsg:5498\n",
       "    transform:   | 0.00, 0.00,-122.15|\\n| 0.00,-0.00, 47.24|\\n| 0.00, 0.00, 1...\n",
       "    resolution:  9.2592593e-05"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# select DEMs with resolution 10 meters\n",
    "dem_raster_all = stackstac.stack(items, bounds=bbox).squeeze()\n",
    "dem_raster_all"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19adb6a3-26a4-4fdb-862a-1f6aa4f2abf6",
   "metadata": {},
   "source": [
    "#### DEMs average along the time dimension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "65ae53fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "dem_raster_geo = dem_raster_all.compute().mean(\"time\")\n",
    "dem_raster_geo.rio.set_crs(dem_raster_all.rio.crs);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c508e760",
   "metadata": {},
   "source": [
    "#### Convert the DEM in UTM coordinates\n",
    "\n",
    "In order to facilitate the comparison between the RTC computed by sarsen with the RTC available on the Planetery Computer, here we convert the DEM in UTM.\n",
    "\n",
    "#### RESAMPLING UTM DEM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f6ad2b6e",
   "metadata": {},
   "outputs": [
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       "  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 &#x27;stackstac-6fbfb106cd445ae5ea0f677ec80c3c41&#x27; (y: 4487, x: 3100)&gt;\n",
       "array([[1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308],\n",
       "       [1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308],\n",
       "       [1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308],\n",
       "       ...,\n",
       "       [1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308],\n",
       "       [1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308],\n",
       "       [1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308]])\n",
       "Coordinates:\n",
       "  * x                (x) float64 5.643e+05 5.643e+05 ... 5.953e+05 5.953e+05\n",
       "  * y                (y) float64 5.233e+06 5.233e+06 ... 5.188e+06 5.188e+06\n",
       "    proj:shape       object {10812}\n",
       "    epsg             int64 5498\n",
       "    threedep:region  &lt;U7 &#x27;n40w130&#x27;\n",
       "    proj:epsg        int64 5498\n",
       "    gsd              int64 10\n",
       "    band             &lt;U4 &#x27;data&#x27;\n",
       "    description      &lt;U1849 &#x27;This tile of the 3D Elevation Program (3DEP) sea...\n",
       "    spatial_ref      int64 0\n",
       "Attributes:\n",
       "    _FillValue:  1.7976931348623157e+308</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'stackstac-6fbfb106cd445ae5ea0f677ec80c3c41'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>y</span>: 4487</li><li><span class='xr-has-index'>x</span>: 3100</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-a6d95a25-0579-4d3d-af53-86b290787f73' class='xr-array-in' type='checkbox' checked><label for='section-a6d95a25-0579-4d3d-af53-86b290787f73' 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>1.798e+308 1.798e+308 1.798e+308 ... 1.798e+308 1.798e+308 1.798e+308</span></div><div class='xr-array-data'><pre>array([[1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308],\n",
       "       [1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308],\n",
       "       [1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308],\n",
       "       ...,\n",
       "       [1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308],\n",
       "       [1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308],\n",
       "       [1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308]])</pre></div></div></li><li class='xr-section-item'><input id='section-e55ca0a2-fcfe-41b3-a1d1-0b95254cbfd1' class='xr-section-summary-in' type='checkbox'  checked><label for='section-e55ca0a2-fcfe-41b3-a1d1-0b95254cbfd1' class='xr-section-summary' >Coordinates: <span>(10)</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'>5.643e+05 5.643e+05 ... 5.953e+05</div><input id='attrs-39aba1fb-e659-40c9-95c6-5beaa4f8b7bb' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-39aba1fb-e659-40c9-95c6-5beaa4f8b7bb' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-80e6a681-3610-4964-8cae-2643ad6044aa' class='xr-var-data-in' type='checkbox'><label for='data-80e6a681-3610-4964-8cae-2643ad6044aa' 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'><dt><span>axis :</span></dt><dd>X</dd><dt><span>long_name :</span></dt><dd>x coordinate of projection</dd><dt><span>standard_name :</span></dt><dd>projection_x_coordinate</dd><dt><span>units :</span></dt><dd>metre</dd></dl></div><div class='xr-var-data'><pre>array([564332.162431, 564342.162431, 564352.162431, ..., 595302.162431,\n",
       "       595312.162431, 595322.162431])</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'>5.233e+06 5.233e+06 ... 5.188e+06</div><input id='attrs-d173ecf5-af34-401b-b737-c13f196fe3e0' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-d173ecf5-af34-401b-b737-c13f196fe3e0' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-663cfc09-0d10-4f7f-bea2-07b930b7349d' class='xr-var-data-in' type='checkbox'><label for='data-663cfc09-0d10-4f7f-bea2-07b930b7349d' 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'><dt><span>axis :</span></dt><dd>Y</dd><dt><span>long_name :</span></dt><dd>y coordinate of projection</dd><dt><span>standard_name :</span></dt><dd>projection_y_coordinate</dd><dt><span>units :</span></dt><dd>metre</dd></dl></div><div class='xr-var-data'><pre>array([5232593.548183, 5232583.548183, 5232573.548183, ..., 5187753.548183,\n",
       "       5187743.548183, 5187733.548183])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>proj:shape</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>{10812}</div><input id='attrs-80fd791f-8cfc-4547-a712-d17f30189885' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-80fd791f-8cfc-4547-a712-d17f30189885' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d490d180-eee6-4dba-9bee-62ed5c47fe20' class='xr-var-data-in' type='checkbox'><label for='data-d490d180-eee6-4dba-9bee-62ed5c47fe20' 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({10812}, dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>epsg</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>5498</div><input id='attrs-94937067-3575-4a05-b33c-1cf8c3986c6b' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-94937067-3575-4a05-b33c-1cf8c3986c6b' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-834f6565-4c70-4ec5-8ed3-baad069f12ab' class='xr-var-data-in' type='checkbox'><label for='data-834f6565-4c70-4ec5-8ed3-baad069f12ab' 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(5498)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>threedep:region</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>&lt;U7</div><div class='xr-var-preview xr-preview'>&#x27;n40w130&#x27;</div><input id='attrs-663f79fa-e4d5-470a-bdb3-b947a6133ebd' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-663f79fa-e4d5-470a-bdb3-b947a6133ebd' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f27836a3-d598-400b-bf20-5b8420aa89fa' class='xr-var-data-in' type='checkbox'><label for='data-f27836a3-d598-400b-bf20-5b8420aa89fa' 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;n40w130&#x27;, dtype=&#x27;&lt;U7&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>proj:epsg</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>5498</div><input id='attrs-da3a0e22-ffff-4ac1-a727-5213e97ffb0e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-da3a0e22-ffff-4ac1-a727-5213e97ffb0e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c494d40e-1fd1-489c-8e52-3de8c6296afc' class='xr-var-data-in' type='checkbox'><label for='data-c494d40e-1fd1-489c-8e52-3de8c6296afc' 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(5498)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>gsd</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>10</div><input id='attrs-42d3404d-e52d-4d45-a33b-40ca69c27bc0' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-42d3404d-e52d-4d45-a33b-40ca69c27bc0' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-dafd5188-2f4e-4f74-ba55-5f5f1673b43b' class='xr-var-data-in' type='checkbox'><label for='data-dafd5188-2f4e-4f74-ba55-5f5f1673b43b' 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(10)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>band</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>&lt;U4</div><div class='xr-var-preview xr-preview'>&#x27;data&#x27;</div><input id='attrs-aee5e0a9-2f0e-4276-930e-b23a46bb79fc' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-aee5e0a9-2f0e-4276-930e-b23a46bb79fc' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-cf10bb10-5615-4a79-8b21-02c57182b5ff' class='xr-var-data-in' type='checkbox'><label for='data-cf10bb10-5615-4a79-8b21-02c57182b5ff' 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;data&#x27;, dtype=&#x27;&lt;U4&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>description</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>&lt;U1849</div><div class='xr-var-preview xr-preview'>&#x27;This tile of the 3D Elevation P...</div><input id='attrs-2a80610b-d611-4e8e-916f-a180b6df0dd9' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2a80610b-d611-4e8e-916f-a180b6df0dd9' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-df626d44-0757-49ae-bf2b-9cba68ecb126' class='xr-var-data-in' type='checkbox'><label for='data-df626d44-0757-49ae-bf2b-9cba68ecb126' 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;This tile of the 3D Elevation Program (3DEP) seamless products is 1/3 arc-second resolution.  3DEP data serve as the elevation layer of The National Map, and provide basic elevation information for Earth science studies and mapping applications in the United States. Scientists and resource managers use 3DEP data for global change research, hydrologic modeling, resource monitoring, mapping and visualization, and many other applications. 3DEP data compose an elevation dataset that consists of seamless layers and a high resolution layer.  Each of these layers consists of the best available raster elevation data of the conterminous United States, Alaska, Hawaii, territorial islands, Mexico and Canada.  3DEP data are updated continually as new data become available. Seamless 3DEP data are derived from diverse source data that are processed to a common coordinate system and unit of vertical measure. These data are distributed in geographic coordinates in units of decimal degrees, and in conformance with the North American Datum of 1983 (NAD 83). All elevation values are in meters and, over the conterminous United States, are referenced to the North American Vertical Datum of 1988 (NAVD 88). The vertical reference will vary in other areas. Seamless 3DEP data are available nationally (except for Alaska) at resolutions of 1 arc-second (approximately 30 meters) and 1/3 arc-second (approximately 10 meters). In most of Alaska, only lower resolution source data are available. As a result, most seamless 3DEP data for Alaska are at 2 arc-second (approximately 60 meters) grid spacing. Part of Alaska is available at the 1 and 1/3 arc-second resolutions from interferometric synthetic aperture radar (ifsar) collections starting in 2010.  Plans are in place for collection of statewide ifsar in Alaska. All 3DEP products are public domain.&#x27;,\n",
       "      dtype=&#x27;&lt;U1849&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>spatial_ref</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0</div><input id='attrs-9e2ea439-937b-45a1-99e7-91e42b271f53' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-9e2ea439-937b-45a1-99e7-91e42b271f53' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f98d9fa1-039e-477d-92d8-b7c8c4ebf063' class='xr-var-data-in' type='checkbox'><label for='data-f98d9fa1-039e-477d-92d8-b7c8c4ebf063' 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'><dt><span>crs_wkt :</span></dt><dd>PROJCS[&quot;WGS 84 / UTM zone 10N&quot;,GEOGCS[&quot;WGS 84&quot;,DATUM[&quot;WGS_1984&quot;,SPHEROID[&quot;WGS 84&quot;,6378137,298.257223563,AUTHORITY[&quot;EPSG&quot;,&quot;7030&quot;]],AUTHORITY[&quot;EPSG&quot;,&quot;6326&quot;]],PRIMEM[&quot;Greenwich&quot;,0,AUTHORITY[&quot;EPSG&quot;,&quot;8901&quot;]],UNIT[&quot;degree&quot;,0.0174532925199433,AUTHORITY[&quot;EPSG&quot;,&quot;9122&quot;]],AUTHORITY[&quot;EPSG&quot;,&quot;4326&quot;]],PROJECTION[&quot;Transverse_Mercator&quot;],PARAMETER[&quot;latitude_of_origin&quot;,0],PARAMETER[&quot;central_meridian&quot;,-123],PARAMETER[&quot;scale_factor&quot;,0.9996],PARAMETER[&quot;false_easting&quot;,500000],PARAMETER[&quot;false_northing&quot;,0],UNIT[&quot;metre&quot;,1,AUTHORITY[&quot;EPSG&quot;,&quot;9001&quot;]],AXIS[&quot;Easting&quot;,EAST],AXIS[&quot;Northing&quot;,NORTH],AUTHORITY[&quot;EPSG&quot;,&quot;32610&quot;]]</dd><dt><span>semi_major_axis :</span></dt><dd>6378137.0</dd><dt><span>semi_minor_axis :</span></dt><dd>6356752.314245179</dd><dt><span>inverse_flattening :</span></dt><dd>298.257223563</dd><dt><span>reference_ellipsoid_name :</span></dt><dd>WGS 84</dd><dt><span>longitude_of_prime_meridian :</span></dt><dd>0.0</dd><dt><span>prime_meridian_name :</span></dt><dd>Greenwich</dd><dt><span>geographic_crs_name :</span></dt><dd>WGS 84</dd><dt><span>horizontal_datum_name :</span></dt><dd>World Geodetic System 1984</dd><dt><span>projected_crs_name :</span></dt><dd>WGS 84 / UTM zone 10N</dd><dt><span>grid_mapping_name :</span></dt><dd>transverse_mercator</dd><dt><span>latitude_of_projection_origin :</span></dt><dd>0.0</dd><dt><span>longitude_of_central_meridian :</span></dt><dd>-123.0</dd><dt><span>false_easting :</span></dt><dd>500000.0</dd><dt><span>false_northing :</span></dt><dd>0.0</dd><dt><span>scale_factor_at_central_meridian :</span></dt><dd>0.9996</dd><dt><span>spatial_ref :</span></dt><dd>PROJCS[&quot;WGS 84 / UTM zone 10N&quot;,GEOGCS[&quot;WGS 84&quot;,DATUM[&quot;WGS_1984&quot;,SPHEROID[&quot;WGS 84&quot;,6378137,298.257223563,AUTHORITY[&quot;EPSG&quot;,&quot;7030&quot;]],AUTHORITY[&quot;EPSG&quot;,&quot;6326&quot;]],PRIMEM[&quot;Greenwich&quot;,0,AUTHORITY[&quot;EPSG&quot;,&quot;8901&quot;]],UNIT[&quot;degree&quot;,0.0174532925199433,AUTHORITY[&quot;EPSG&quot;,&quot;9122&quot;]],AUTHORITY[&quot;EPSG&quot;,&quot;4326&quot;]],PROJECTION[&quot;Transverse_Mercator&quot;],PARAMETER[&quot;latitude_of_origin&quot;,0],PARAMETER[&quot;central_meridian&quot;,-123],PARAMETER[&quot;scale_factor&quot;,0.9996],PARAMETER[&quot;false_easting&quot;,500000],PARAMETER[&quot;false_northing&quot;,0],UNIT[&quot;metre&quot;,1,AUTHORITY[&quot;EPSG&quot;,&quot;9001&quot;]],AXIS[&quot;Easting&quot;,EAST],AXIS[&quot;Northing&quot;,NORTH],AUTHORITY[&quot;EPSG&quot;,&quot;32610&quot;]]</dd><dt><span>GeoTransform :</span></dt><dd>564327.1624312083 10.0 0.0 5232598.548182782 0.0 -10.0</dd></dl></div><div class='xr-var-data'><pre>array(0)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-5ebc71ec-6137-48ba-9158-077fe28050ab' class='xr-section-summary-in' type='checkbox'  checked><label for='section-5ebc71ec-6137-48ba-9158-077fe28050ab' class='xr-section-summary' >Attributes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>_FillValue :</span></dt><dd>1.7976931348623157e+308</dd></dl></div></li></ul></div></div>"
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       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308],\n",
       "       ...,\n",
       "       [1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308],\n",
       "       [1.79769313e+308, 1.79769313e+308, 1.79769313e+308, ...,\n",
       "        1.79769313e+308, 1.79769313e+308, 1.79769313e+308],\n",
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       "Coordinates:\n",
       "  * x                (x) float64 5.643e+05 5.643e+05 ... 5.953e+05 5.953e+05\n",
       "  * y                (y) float64 5.233e+06 5.233e+06 ... 5.188e+06 5.188e+06\n",
       "    proj:shape       object {10812}\n",
       "    epsg             int64 5498\n",
       "    threedep:region  <U7 'n40w130'\n",
       "    proj:epsg        int64 5498\n",
       "    gsd              int64 10\n",
       "    band             <U4 'data'\n",
       "    description      <U1849 'This tile of the 3D Elevation Program (3DEP) sea...\n",
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       "Attributes:\n",
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      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# find the UTM zone and project in UTM\n",
    "t_srs = dem_raster_geo.rio.estimate_utm_crs()\n",
    "dem_raster = dem_raster_geo.rio.reproject(t_srs, resolution=(10, 10))\n",
    "dem_raster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5c4a8e3b",
   "metadata": {},
   "outputs": [
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       ".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;stackstac-6fbfb106cd445ae5ea0f677ec80c3c41&#x27; (y: 1500, x: 1400)&gt;\n",
       "array([[ 840.86486816,  837.69940186,  836.6675415 , ..., 1222.60290527,\n",
       "        1224.68151855, 1229.60192871],\n",
       "       [ 847.59912109,  843.43511963,  841.19110107, ..., 1226.77722168,\n",
       "        1229.88330078, 1235.05480957],\n",
       "       [ 853.09313965,  849.24804688,  847.56011963, ..., 1231.57214355,\n",
       "        1235.27197266, 1240.26989746],\n",
       "       ...,\n",
       "       [1057.71154785, 1056.44726562, 1053.34716797, ..., 1967.21203613,\n",
       "        1966.72473145, 1967.17895508],\n",
       "       [1053.78833008, 1052.40124512, 1049.59545898, ..., 1970.66943359,\n",
       "        1969.1439209 , 1969.60314941],\n",
       "       [1049.06298828, 1048.03967285, 1045.55126953, ..., 1973.11730957,\n",
       "        1971.60437012, 1971.93334961]])\n",
       "Coordinates:\n",
       "  * x                (x) float64 5.79e+05 5.79e+05 ... 5.93e+05 5.93e+05\n",
       "  * y                (y) float64 5.21e+06 5.21e+06 ... 5.195e+06 5.195e+06\n",
       "    proj:shape       object {10812}\n",
       "    epsg             int64 5498\n",
       "    threedep:region  &lt;U7 &#x27;n40w130&#x27;\n",
       "    proj:epsg        int64 5498\n",
       "    gsd              int64 10\n",
       "    band             &lt;U4 &#x27;data&#x27;\n",
       "    description      &lt;U1849 &#x27;This tile of the 3D Elevation Program (3DEP) sea...\n",
       "    spatial_ref      int64 0\n",
       "Attributes:\n",
       "    _FillValue:  1.7976931348623157e+308</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'stackstac-6fbfb106cd445ae5ea0f677ec80c3c41'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>y</span>: 1500</li><li><span class='xr-has-index'>x</span>: 1400</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-cf63a2f1-014f-42cf-bd0f-3497a9be8fb2' class='xr-array-in' type='checkbox' checked><label for='section-cf63a2f1-014f-42cf-bd0f-3497a9be8fb2' 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>840.9 837.7 836.7 835.7 ... 1.988e+03 1.973e+03 1.972e+03 1.972e+03</span></div><div class='xr-array-data'><pre>array([[ 840.86486816,  837.69940186,  836.6675415 , ..., 1222.60290527,\n",
       "        1224.68151855, 1229.60192871],\n",
       "       [ 847.59912109,  843.43511963,  841.19110107, ..., 1226.77722168,\n",
       "        1229.88330078, 1235.05480957],\n",
       "       [ 853.09313965,  849.24804688,  847.56011963, ..., 1231.57214355,\n",
       "        1235.27197266, 1240.26989746],\n",
       "       ...,\n",
       "       [1057.71154785, 1056.44726562, 1053.34716797, ..., 1967.21203613,\n",
       "        1966.72473145, 1967.17895508],\n",
       "       [1053.78833008, 1052.40124512, 1049.59545898, ..., 1970.66943359,\n",
       "        1969.1439209 , 1969.60314941],\n",
       "       [1049.06298828, 1048.03967285, 1045.55126953, ..., 1973.11730957,\n",
       "        1971.60437012, 1971.93334961]])</pre></div></div></li><li class='xr-section-item'><input id='section-31851537-2709-43e4-9205-f7d44c7e3f7a' class='xr-section-summary-in' type='checkbox'  checked><label for='section-31851537-2709-43e4-9205-f7d44c7e3f7a' class='xr-section-summary' >Coordinates: <span>(10)</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'>5.79e+05 5.79e+05 ... 5.93e+05</div><input id='attrs-aa9e7463-9b45-4fee-90b0-eec08cb8c2b5' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-aa9e7463-9b45-4fee-90b0-eec08cb8c2b5' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b40ff3d0-1996-41fa-bd49-f32c95522d96' class='xr-var-data-in' type='checkbox'><label for='data-b40ff3d0-1996-41fa-bd49-f32c95522d96' 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'><dt><span>axis :</span></dt><dd>X</dd><dt><span>long_name :</span></dt><dd>x coordinate of projection</dd><dt><span>standard_name :</span></dt><dd>projection_x_coordinate</dd><dt><span>units :</span></dt><dd>metre</dd></dl></div><div class='xr-var-data'><pre>array([579002.162431, 579012.162431, 579022.162431, ..., 592972.162431,\n",
       "       592982.162431, 592992.162431])</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'>5.21e+06 5.21e+06 ... 5.195e+06</div><input id='attrs-cd23da6b-10e5-405b-aebb-e5e93bee9388' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-cd23da6b-10e5-405b-aebb-e5e93bee9388' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-96a4e926-8d32-4692-b517-f39a561ab65d' class='xr-var-data-in' type='checkbox'><label for='data-96a4e926-8d32-4692-b517-f39a561ab65d' 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'><dt><span>axis :</span></dt><dd>Y</dd><dt><span>long_name :</span></dt><dd>y coordinate of projection</dd><dt><span>standard_name :</span></dt><dd>projection_y_coordinate</dd><dt><span>units :</span></dt><dd>metre</dd></dl></div><div class='xr-var-data'><pre>array([5209993.548183, 5209983.548183, 5209973.548183, ..., 5195023.548183,\n",
       "       5195013.548183, 5195003.548183])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>proj:shape</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>{10812}</div><input id='attrs-ac78e93b-9470-4f3e-b4e1-88483d526d33' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ac78e93b-9470-4f3e-b4e1-88483d526d33' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-bee6ce79-f733-4d1c-a177-61ef12176108' class='xr-var-data-in' type='checkbox'><label for='data-bee6ce79-f733-4d1c-a177-61ef12176108' 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({10812}, dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>epsg</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>5498</div><input id='attrs-28406bc8-3951-43b3-abe7-4cb98e703caa' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-28406bc8-3951-43b3-abe7-4cb98e703caa' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b9beb01c-dd75-4202-9b94-887711486fc3' class='xr-var-data-in' type='checkbox'><label for='data-b9beb01c-dd75-4202-9b94-887711486fc3' 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(5498)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>threedep:region</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>&lt;U7</div><div class='xr-var-preview xr-preview'>&#x27;n40w130&#x27;</div><input id='attrs-0f22a600-ffad-4d7c-a148-e1ad59d2ab80' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0f22a600-ffad-4d7c-a148-e1ad59d2ab80' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e73b4471-b895-43b4-9b0f-7516e2b7307d' class='xr-var-data-in' type='checkbox'><label for='data-e73b4471-b895-43b4-9b0f-7516e2b7307d' 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;n40w130&#x27;, dtype=&#x27;&lt;U7&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>proj:epsg</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>5498</div><input id='attrs-18481140-91ac-44fe-98c0-f7e69b383a1e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-18481140-91ac-44fe-98c0-f7e69b383a1e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-97d2ba1d-c009-4871-a1a3-88d81570645a' class='xr-var-data-in' type='checkbox'><label for='data-97d2ba1d-c009-4871-a1a3-88d81570645a' 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(5498)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>gsd</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>10</div><input id='attrs-64daf218-19b9-4d1a-b2b7-43666f26dc99' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-64daf218-19b9-4d1a-b2b7-43666f26dc99' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-fabaa0b9-0aeb-4a2e-8604-d27ad6ea59aa' class='xr-var-data-in' type='checkbox'><label for='data-fabaa0b9-0aeb-4a2e-8604-d27ad6ea59aa' 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(10)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>band</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>&lt;U4</div><div class='xr-var-preview xr-preview'>&#x27;data&#x27;</div><input id='attrs-6da8c812-f489-4904-9526-709f2078afbc' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-6da8c812-f489-4904-9526-709f2078afbc' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f1695c18-7370-43fa-be5e-99ac168ae9b8' class='xr-var-data-in' type='checkbox'><label for='data-f1695c18-7370-43fa-be5e-99ac168ae9b8' 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;data&#x27;, dtype=&#x27;&lt;U4&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>description</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>&lt;U1849</div><div class='xr-var-preview xr-preview'>&#x27;This tile of the 3D Elevation P...</div><input id='attrs-35a0ce0b-8a3b-4853-8a51-a51784d4769b' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-35a0ce0b-8a3b-4853-8a51-a51784d4769b' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-eccdab43-cc3b-4035-b535-6fa8946f6213' class='xr-var-data-in' type='checkbox'><label for='data-eccdab43-cc3b-4035-b535-6fa8946f6213' 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;This tile of the 3D Elevation Program (3DEP) seamless products is 1/3 arc-second resolution.  3DEP data serve as the elevation layer of The National Map, and provide basic elevation information for Earth science studies and mapping applications in the United States. Scientists and resource managers use 3DEP data for global change research, hydrologic modeling, resource monitoring, mapping and visualization, and many other applications. 3DEP data compose an elevation dataset that consists of seamless layers and a high resolution layer.  Each of these layers consists of the best available raster elevation data of the conterminous United States, Alaska, Hawaii, territorial islands, Mexico and Canada.  3DEP data are updated continually as new data become available. Seamless 3DEP data are derived from diverse source data that are processed to a common coordinate system and unit of vertical measure. These data are distributed in geographic coordinates in units of decimal degrees, and in conformance with the North American Datum of 1983 (NAD 83). All elevation values are in meters and, over the conterminous United States, are referenced to the North American Vertical Datum of 1988 (NAVD 88). The vertical reference will vary in other areas. Seamless 3DEP data are available nationally (except for Alaska) at resolutions of 1 arc-second (approximately 30 meters) and 1/3 arc-second (approximately 10 meters). In most of Alaska, only lower resolution source data are available. As a result, most seamless 3DEP data for Alaska are at 2 arc-second (approximately 60 meters) grid spacing. Part of Alaska is available at the 1 and 1/3 arc-second resolutions from interferometric synthetic aperture radar (ifsar) collections starting in 2010.  Plans are in place for collection of statewide ifsar in Alaska. All 3DEP products are public domain.&#x27;,\n",
       "      dtype=&#x27;&lt;U1849&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>spatial_ref</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0</div><input id='attrs-391cd60e-75fc-4622-b76f-f44742ab8143' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-391cd60e-75fc-4622-b76f-f44742ab8143' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-7d1eee41-bd0c-48a2-9f2b-7c74ab2e1259' class='xr-var-data-in' type='checkbox'><label for='data-7d1eee41-bd0c-48a2-9f2b-7c74ab2e1259' 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'><dt><span>crs_wkt :</span></dt><dd>PROJCS[&quot;WGS 84 / UTM zone 10N&quot;,GEOGCS[&quot;WGS 84&quot;,DATUM[&quot;WGS_1984&quot;,SPHEROID[&quot;WGS 84&quot;,6378137,298.257223563,AUTHORITY[&quot;EPSG&quot;,&quot;7030&quot;]],AUTHORITY[&quot;EPSG&quot;,&quot;6326&quot;]],PRIMEM[&quot;Greenwich&quot;,0,AUTHORITY[&quot;EPSG&quot;,&quot;8901&quot;]],UNIT[&quot;degree&quot;,0.0174532925199433,AUTHORITY[&quot;EPSG&quot;,&quot;9122&quot;]],AUTHORITY[&quot;EPSG&quot;,&quot;4326&quot;]],PROJECTION[&quot;Transverse_Mercator&quot;],PARAMETER[&quot;latitude_of_origin&quot;,0],PARAMETER[&quot;central_meridian&quot;,-123],PARAMETER[&quot;scale_factor&quot;,0.9996],PARAMETER[&quot;false_easting&quot;,500000],PARAMETER[&quot;false_northing&quot;,0],UNIT[&quot;metre&quot;,1,AUTHORITY[&quot;EPSG&quot;,&quot;9001&quot;]],AXIS[&quot;Easting&quot;,EAST],AXIS[&quot;Northing&quot;,NORTH],AUTHORITY[&quot;EPSG&quot;,&quot;32610&quot;]]</dd><dt><span>semi_major_axis :</span></dt><dd>6378137.0</dd><dt><span>semi_minor_axis :</span></dt><dd>6356752.314245179</dd><dt><span>inverse_flattening :</span></dt><dd>298.257223563</dd><dt><span>reference_ellipsoid_name :</span></dt><dd>WGS 84</dd><dt><span>longitude_of_prime_meridian :</span></dt><dd>0.0</dd><dt><span>prime_meridian_name :</span></dt><dd>Greenwich</dd><dt><span>geographic_crs_name :</span></dt><dd>WGS 84</dd><dt><span>horizontal_datum_name :</span></dt><dd>World Geodetic System 1984</dd><dt><span>projected_crs_name :</span></dt><dd>WGS 84 / UTM zone 10N</dd><dt><span>grid_mapping_name :</span></dt><dd>transverse_mercator</dd><dt><span>latitude_of_projection_origin :</span></dt><dd>0.0</dd><dt><span>longitude_of_central_meridian :</span></dt><dd>-123.0</dd><dt><span>false_easting :</span></dt><dd>500000.0</dd><dt><span>false_northing :</span></dt><dd>0.0</dd><dt><span>scale_factor_at_central_meridian :</span></dt><dd>0.9996</dd><dt><span>spatial_ref :</span></dt><dd>PROJCS[&quot;WGS 84 / UTM zone 10N&quot;,GEOGCS[&quot;WGS 84&quot;,DATUM[&quot;WGS_1984&quot;,SPHEROID[&quot;WGS 84&quot;,6378137,298.257223563,AUTHORITY[&quot;EPSG&quot;,&quot;7030&quot;]],AUTHORITY[&quot;EPSG&quot;,&quot;6326&quot;]],PRIMEM[&quot;Greenwich&quot;,0,AUTHORITY[&quot;EPSG&quot;,&quot;8901&quot;]],UNIT[&quot;degree&quot;,0.0174532925199433,AUTHORITY[&quot;EPSG&quot;,&quot;9122&quot;]],AUTHORITY[&quot;EPSG&quot;,&quot;4326&quot;]],PROJECTION[&quot;Transverse_Mercator&quot;],PARAMETER[&quot;latitude_of_origin&quot;,0],PARAMETER[&quot;central_meridian&quot;,-123],PARAMETER[&quot;scale_factor&quot;,0.9996],PARAMETER[&quot;false_easting&quot;,500000],PARAMETER[&quot;false_northing&quot;,0],UNIT[&quot;metre&quot;,1,AUTHORITY[&quot;EPSG&quot;,&quot;9001&quot;]],AXIS[&quot;Easting&quot;,EAST],AXIS[&quot;Northing&quot;,NORTH],AUTHORITY[&quot;EPSG&quot;,&quot;32610&quot;]]</dd><dt><span>GeoTransform :</span></dt><dd>564327.1624312083 10.0 0.0 5232598.548182782 0.0 -10.0</dd></dl></div><div class='xr-var-data'><pre>array(0)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-1c463c76-9414-40c6-ae53-30da7e1d2050' class='xr-section-summary-in' type='checkbox'  checked><label for='section-1c463c76-9414-40c6-ae53-30da7e1d2050' class='xr-section-summary' >Attributes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>_FillValue :</span></dt><dd>1.7976931348623157e+308</dd></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'stackstac-6fbfb106cd445ae5ea0f677ec80c3c41' (y: 1500, x: 1400)>\n",
       "array([[ 840.86486816,  837.69940186,  836.6675415 , ..., 1222.60290527,\n",
       "        1224.68151855, 1229.60192871],\n",
       "       [ 847.59912109,  843.43511963,  841.19110107, ..., 1226.77722168,\n",
       "        1229.88330078, 1235.05480957],\n",
       "       [ 853.09313965,  849.24804688,  847.56011963, ..., 1231.57214355,\n",
       "        1235.27197266, 1240.26989746],\n",
       "       ...,\n",
       "       [1057.71154785, 1056.44726562, 1053.34716797, ..., 1967.21203613,\n",
       "        1966.72473145, 1967.17895508],\n",
       "       [1053.78833008, 1052.40124512, 1049.59545898, ..., 1970.66943359,\n",
       "        1969.1439209 , 1969.60314941],\n",
       "       [1049.06298828, 1048.03967285, 1045.55126953, ..., 1973.11730957,\n",
       "        1971.60437012, 1971.93334961]])\n",
       "Coordinates:\n",
       "  * x                (x) float64 5.79e+05 5.79e+05 ... 5.93e+05 5.93e+05\n",
       "  * y                (y) float64 5.21e+06 5.21e+06 ... 5.195e+06 5.195e+06\n",
       "    proj:shape       object {10812}\n",
       "    epsg             int64 5498\n",
       "    threedep:region  <U7 'n40w130'\n",
       "    proj:epsg        int64 5498\n",
       "    gsd              int64 10\n",
       "    band             <U4 'data'\n",
       "    description      <U1849 'This tile of the 3D Elevation Program (3DEP) sea...\n",
       "    spatial_ref      int64 0\n",
       "Attributes:\n",
       "    _FillValue:  1.7976931348623157e+308"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# crop DEM to our area of interest and save it\n",
    "dem_corners = dict(x=slice(579000, 593000), y=slice(5210000, 5195000))\n",
    "\n",
    "dem_raster = dem_raster.sel(**dem_corners)\n",
    "dem_raster.rio.to_raster(dem_path)\n",
    "dem_raster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7082c7d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://ai4edatasetspublicassets.blob.core.windows.net/assets/notebook-output/tutorials-rtc-qualitative-assessment.ipynb/11.png\"/>"
      ],
      "text/plain": [
       "<Figure size 720x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 469,
       "width": 666
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dem_raster.plot()\n",
    "_ = plt.title(\"DEM in UTM coordinates\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4445aa2a-abf4-4162-ab0b-b22ae069e4e4",
   "metadata": {},
   "source": [
    "### Define GRD parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0c35e4ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "grd_account_name = \"sentinel1euwest\"\n",
    "grd_storage_container = \"s1-grd\"\n",
    "grd_product_folder = f\"{grd_storage_container}/{product_folder}\"\n",
    "grd_local_path = os.path.join(tmp_dir, product_folder)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac695ed8-10bb-4efe-a43e-372c289605e3",
   "metadata": {},
   "source": [
    "### Retrieve Sentinel-1 GRD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "81012b36",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['s1-grd/GRD/2021/12/17/IW/DV/S1B_IW_GRDH_1SDV_20211217T141304_20211217T141329_030066_039705_9048/manifest.safe']"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grd_token = planetary_computer.sas.get_token(\n",
    "    grd_account_name, grd_storage_container\n",
    ").token\n",
    "grd_fs = adlfs.AzureBlobFileSystem(grd_account_name, credential=grd_token)\n",
    "grd_fs.ls(f\"{grd_product_folder}/manifest.safe\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0b1daaa9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/tmp/GRD/2021/12/17/IW/DV/S1B_IW_GRDH_1SDV_20211217T141304_20211217T141329_030066_039705_9048\n"
     ]
    }
   ],
   "source": [
    "grd_fs.get(grd_product_folder, grd_local_path, recursive=True)\n",
    "!ls -d {grd_local_path}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dbe585a-5467-445e-a9cb-cd8c5b66fe8e",
   "metadata": {},
   "source": [
    "### Process"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54a3d505-a01c-4a88-a939-0169264609d0",
   "metadata": {},
   "source": [
    "#### GTC\n",
    "\n",
    "Here we compute the geometric terrain correction.\n",
    "\n",
    "Input parameters:\n",
    "- `product_urlpath`: product path\n",
    "- `measurement_group`: band to be processed in the form {swath}/{polarization} (see [xarray-sentinel](https://pypi.org/project/xarray-sentinel/) for more details)\n",
    "- `dem_urlpath`: path to the input DEM. sarsen supports all DEMs supported by GDAL/Proj for ECEF-translation. \n",
    "- `interp_method`: interpolation method, sarsen supports all interpolation methods supported by [xarray.Dataset.interp](https://xarray.pydata.org/en/stable/generated/xarray.Dataset.interp.html)\n",
    "- `chunks`: dask chunks\n",
    "- `output_urlpath`: output path\n",
    "\n",
    "The output is the input SAR image resampled on DEM coordinates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "41add520",
   "metadata": {},
   "outputs": [],
   "source": [
    "gtc_path = os.path.basename(product_folder) + \".GTC.tif\"\n",
    "\n",
    "gtc = apps.terrain_correction(\n",
    "    grd_local_path,\n",
    "    measurement_group,\n",
    "    dem_path,\n",
    "    interp_method=\"nearest\",\n",
    "    override_product_files=\"{dirname}/{prefix}{swath}-{polarization}{ext}\",\n",
    "    chunks=2048,\n",
    "    output_urlpath=gtc_path,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "27a84435",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://ai4edatasetspublicassets.blob.core.windows.net/assets/notebook-output/tutorials-rtc-qualitative-assessment.ipynb/16.png\"/>"
      ],
      "text/plain": [
       "<Figure size 720x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 447,
       "width": 629
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = gtc.plot(vmax=0.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7399622",
   "metadata": {},
   "source": [
    "#### RTC\n",
    "`sarsen` implements the radiometric terrain-correction [Gamma Flattening](https://ieeexplore.ieee.org/document/5752845) algorithm.\n",
    "\n",
    "#### Input parameters\n",
    "- `correct_radiometry`: `correct_radiometry`: default `None`. If `correct_radiometry=None`the radiometric terrain correction is not applied. `correct_radiometry=gamma_bilinear` applies the gamma flattening classic algorithm using bilinear interpolation to compute the weights. `correct_radiometry=gamma_nearest` applies the gamma flattening using nearest neighbours instead of bilinear interpolation. 'gamma_nearest' significantly reduces the processing time.\n",
    "- `grouping_area_factor`: scaling factor for the size of the image pixel where the areas are summed. By default, the `grouping_area_factor` is `(1, 1)`, which corresponds to Sentinel-1 input product pixel size. The `grouping_area_factor` shall be increased if the DEM resolution is lower than the Sentinel-1 input product resolution to avoid gaps and distortions the normalization factor. It can be also used to to speed up the computation or  the DEM resolution is lower than the Sentinel-1 input product resolution.  \n",
    "\n",
    "\n",
    "**Note**: The `grouping_area_factor` can be increased (i) to speed up the processing or (ii) when the input DEM resolution is low. The Gamma Flattening usually works properly if the pixel size of the input DEM is much smaller than the pixel size of the input Sentinel-1 product. Otherwise, the output may have radiometric distortions. This problem can be avoided by increasing the `grouping_area_factor`. Be aware that `grouping_area_factor` too high may degrade the final result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8416dd32-afa0-434a-8c9c-5d44bdd06cf9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\", \"divide by zero\", RuntimeWarning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "bfdd3e96",
   "metadata": {},
   "outputs": [],
   "source": [
    "rtc_path = os.path.basename(grd_local_path) + \".RTC.tif\"\n",
    "\n",
    "rtc = apps.terrain_correction(\n",
    "    grd_local_path,\n",
    "    measurement_group,\n",
    "    dem_path,\n",
    "    interp_method=\"nearest\",\n",
    "    override_product_files=\"{dirname}/{prefix}{swath}-{polarization}{ext}\",\n",
    "    correct_radiometry=\"gamma_nearest\",\n",
    "    output_urlpath=rtc_path,\n",
    "    grouping_area_factor=(1, 1),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "849a9019",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://ai4edatasetspublicassets.blob.core.windows.net/assets/notebook-output/tutorials-rtc-qualitative-assessment.ipynb/19.png\"/>"
      ],
      "text/plain": [
       "<Figure size 720x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 447,
       "width": 629
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = rtc.plot(vmax=0.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "646acd93",
   "metadata": {},
   "source": [
    "### Gamma vs Local incidence Angle\n",
    "\n",
    "The backscattering depends on the ground material, the roughness and the local incidence angle. Small values of the local incidence angle correspond usually to higher values of backscattering, while high values of radar incidence angle corresponds to zones with low backscattering. The aim of the radiometric terrain correction is to remove the contribution due to the local incidence angle. \n",
    "For evaluating the goodness of the radiometric correction we will compare the incidence angle versus backscattering before and after the correction."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bc92d66",
   "metadata": {},
   "source": [
    "#### Compute local incidence angle and ellipsoid incidence angle"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f93af76d",
   "metadata": {},
   "source": [
    "![SNOWFALL](https://forum.step.esa.int/uploads/default/original/3X/e/3/e372bf0efa0133c63977111b15614bc0c7d96fd8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e8499527-c404-4c45-b266-c0ec077db4d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "dem = scene.open_dem_raster(dem_path)\n",
    "\n",
    "\n",
    "orbit_ecef = xr.open_dataset(\n",
    "    grd_local_path,\n",
    "    engine=\"sentinel-1\",\n",
    "    group=f\"{measurement_group}/orbit\",\n",
    "    override_product_files=\"{dirname}/{prefix}{swath}-{polarization}{ext}\",\n",
    ")\n",
    "dem_ecef = scene.convert_to_dem_ecef(dem, source_crs=t_srs)\n",
    "dem_ecef_1 = scene.convert_to_dem_ecef(dem + 1, source_crs=t_srs)\n",
    "ellissoid_normal = dem_ecef - dem_ecef_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a5f3dd32-007b-4c1c-9cda-88592fe78dd4",
   "metadata": {},
   "outputs": [],
   "source": [
    "acquisition = apps.simulate_acquisition(\n",
    "    dem_ecef, orbit_ecef.position, coordinate_conversion=None, correct_radiometry=True\n",
    ")\n",
    "oriented_area = scene.compute_dem_oriented_area(dem_ecef)\n",
    "dem_normal = -oriented_area / np.sqrt(xr.dot(oriented_area, oriented_area, dims=\"axis\"))\n",
    "\n",
    "# compute direction target sensor\n",
    "orbit_interpolator = orbit.OrbitPolyfitIterpolator.from_position(orbit_ecef.position)\n",
    "position_ecef = orbit_interpolator.position()\n",
    "velocity_ecef = orbit_interpolator.velocity()\n",
    "acquisition = geocoding.backward_geocode(dem_ecef, orbit_ecef.position, velocity_ecef)\n",
    "slant_range = np.sqrt((acquisition.dem_distance**2).sum(dim=\"axis\"))\n",
    "dem_direction = acquisition.dem_distance / slant_range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "920ee292-f695-44d4-9178-950fb5703a4b",
   "metadata": {},
   "outputs": [],
   "source": [
    "angle = np.arccos(xr.dot(dem_normal, dem_direction, dims=\"axis\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a2797f82-5471-4a75-9878-317e9b23865d",
   "metadata": {},
   "outputs": [],
   "source": [
    "ellipsoid_incidence = np.arccos(xr.dot(ellissoid_normal, dem_direction, dims=\"axis\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c69085f",
   "metadata": {},
   "source": [
    "#### Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "a45cd942",
   "metadata": {},
   "outputs": [],
   "source": [
    "ellipsoid_incidence = ellipsoid_incidence.load()\n",
    "angle = angle.load()\n",
    "gtc = gtc.load()\n",
    "rtc = rtc.load()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5311f17d-aa35-4725-8e28-dd91719cf91c",
   "metadata": {},
   "source": [
    "#### GTC and RTC distribution of foreslope, backslope, and flat terrain \n",
    "\n",
    "We classify taking into account the local incidence angle and the ellipsoid incidence angle\n",
    " the image in three zone:\n",
    "- foreslope, small incidence angles that correspond to high backscattering zones.\n",
    "- flat terrain\n",
    "- backslope, big incidence angles that correspond to low backscattering zones\n",
    "\n",
    "\n",
    "We will show that the radiometric correction mitigate the effect of the foreslope and backslope."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "fec9e2e8-0dc7-49e5-a9ea-a12bbce248e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# foreslope backslope and flat terrain\n",
    "gtc_foreslope = xr.where(angle < ellipsoid_incidence - 0.20, gtc, np.nan)\n",
    "gtc_backslope = xr.where(angle > ellipsoid_incidence + 0.20, gtc, np.nan)\n",
    "gtc_flat = xr.where(\n",
    "    (angle < ellipsoid_incidence + 0.20) & (angle > ellipsoid_incidence - 0.20),\n",
    "    gtc,\n",
    "    np.nan,\n",
    ")\n",
    "\n",
    "rtc_foreslope = xr.where(angle < ellipsoid_incidence - 0.20, rtc, np.nan)\n",
    "rtc_backslope = xr.where(angle > ellipsoid_incidence + 0.20, rtc, np.nan)\n",
    "rtc_flat = xr.where(\n",
    "    (angle < ellipsoid_incidence + 0.20) & (angle > ellipsoid_incidence - 0.20),\n",
    "    rtc,\n",
    "    np.nan,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e3abd619-34e2-4fec-845d-89e85adf4049",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://ai4edatasetspublicassets.blob.core.windows.net/assets/notebook-output/tutorials-rtc-qualitative-assessment.ipynb/26.png\"/>"
      ],
      "text/plain": [
       "<Figure size 2160x648 with 6 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 631,
       "width": 2109
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(nrows=1, ncols=3, figsize=(30, 9))\n",
    "\n",
    "dem_raster.plot(ax=axes[0])\n",
    "axes[0].grid(c=\"red\")\n",
    "axes[0].set_title(\"DEM\")\n",
    "\n",
    "gtc.plot(ax=axes[1], vmax=0.4)\n",
    "axes[1].grid(c=\"red\")\n",
    "axes[1].set_title(\"GTC\")\n",
    "\n",
    "\n",
    "angle.plot(ax=axes[2])\n",
    "axes[2].grid(c=\"red\")\n",
    "axes[2].set_title(\"Incidence Angle\")\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "8923dfd6-b740-4a72-9f88-a67e07d47df6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://ai4edatasetspublicassets.blob.core.windows.net/assets/notebook-output/tutorials-rtc-qualitative-assessment.ipynb/27.png\"/>"
      ],
      "text/plain": [
       "<Figure size 2160x648 with 6 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 631,
       "width": 2114
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(nrows=1, ncols=3, figsize=(30, 9))\n",
    "\n",
    "gtc_backslope.plot(ax=axes[0], vmax=0.4)\n",
    "axes[0].grid(c=\"red\")\n",
    "axes[0].set_title(\"GTC basckslope\")\n",
    "\n",
    "gtc_foreslope.plot(ax=axes[1], vmax=0.4)\n",
    "axes[1].grid(c=\"red\")\n",
    "axes[1].set_title(\"GTC foreslope\")\n",
    "\n",
    "\n",
    "gtc_flat.plot(ax=axes[2], vmax=0.4)\n",
    "axes[2].grid(c=\"red\")\n",
    "axes[2].set_title(\"GTC flat terrain\")\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10bcc74a-902c-4fb3-ac85-f0012e307f68",
   "metadata": {},
   "source": [
    "#### GTC and RTC distribution of foreslope backslope and flat terrain in db"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "12ef90a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "gtc_backslope_db = np.log(gtc_backslope)\n",
    "gtc_foreslope_db = np.log(gtc_foreslope)\n",
    "gtc_flat_db = np.log(gtc_flat)\n",
    "\n",
    "rtc_backslope_db = np.log(rtc_backslope)\n",
    "rtc_foreslope_db = np.log(rtc_foreslope)\n",
    "rtc_flat_db = np.log(rtc_flat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "68081745-5198-441f-87bf-b9b7e49d81ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'gamma_T DB')"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"https://ai4edatasetspublicassets.blob.core.windows.net/assets/notebook-output/tutorials-rtc-qualitative-assessment.ipynb/29.png\"/>"
      ],
      "text/plain": [
       "<Figure size 2160x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 724,
       "width": 1717
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(nrows=1, ncols=2, figsize=(30, 12))\n",
    "\n",
    "gtc_backslope_db_h = xr.plot.hist(\n",
    "    gtc_backslope_db,\n",
    "    range=[-10, 5],\n",
    "    bins=50,\n",
    "    color=[0, 1, 0, 0.4],\n",
    "    density=True,\n",
    "    ax=axes[0],\n",
    "    label=\"backslope\",\n",
    ")\n",
    "gtc_foreslope_db_h = xr.plot.hist(\n",
    "    gtc_foreslope_db,\n",
    "    range=[-10, 5],\n",
    "    bins=50,\n",
    "    color=[1, 0, 0, 0.4],\n",
    "    density=True,\n",
    "    ax=axes[0],\n",
    "    label=\"foreslope\",\n",
    ")\n",
    "gtc_flat_db_h = xr.plot.hist(\n",
    "    gtc_flat_db,\n",
    "    range=[-10, 5],\n",
    "    bins=50,\n",
    "    color=[0, 0, 1, 0.4],\n",
    "    density=True,\n",
    "    ax=axes[0],\n",
    "    label=\"flat\",\n",
    ")\n",
    "\n",
    "rtc_backslope_db_h = xr.plot.hist(\n",
    "    rtc_backslope_db,\n",
    "    range=[-10, 5],\n",
    "    bins=50,\n",
    "    color=[0, 1, 0, 0.4],\n",
    "    density=True,\n",
    "    ax=axes[1],\n",
    "    label=\"backslope\",\n",
    ")\n",
    "rtc_foreslope_db_h = xr.plot.hist(\n",
    "    rtc_foreslope_db,\n",
    "    range=[-10, 5],\n",
    "    bins=50,\n",
    "    color=[1, 0, 0, 0.4],\n",
    "    density=True,\n",
    "    ax=axes[1],\n",
    "    label=\"foreslope\",\n",
    ")\n",
    "rtc_flat_db_h = xr.plot.hist(\n",
    "    rtc_flat_db,\n",
    "    range=[-10, 5],\n",
    "    bins=50,\n",
    "    color=[0, 0, 1, 0.4],\n",
    "    density=True,\n",
    "    ax=axes[1],\n",
    "    label=\"flat\",\n",
    ")\n",
    "axes[0].legend()\n",
    "axes[1].legend()\n",
    "\n",
    "axes[0].set_title(\"GTC distribution\")\n",
    "axes[0].set_xlabel(\"beta DB\")\n",
    "\n",
    "axes[1].set_title(\"RTC distribution\")\n",
    "axes[1].set_xlabel(\"gamma_T DB\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cff38443-b393-4ace-bf3f-bc64318347a1",
   "metadata": {},
   "source": [
    "**Before the radiometic correction the distribution of backslope flat terrain and foreslope are separate, after they  overlap completely.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "456b4611",
   "metadata": {},
   "source": [
    "#### RTC and GTC scatterplots incidence angle vs backcattering\n",
    "\n",
    "We compare the incidence_angle-backscattering scatterplots of the GTC and the RTC to show that in the former there is a correlation between the incidence angle and backscattering, while in the RTC the correlation has been removed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "82786f69",
   "metadata": {},
   "outputs": [],
   "source": [
    "def makeColours(vals):\n",
    "    colours = np.zeros((len(vals), 3))\n",
    "    norm = Normalize(vmin=vals.min(), vmax=vals.max())\n",
    "\n",
    "    # Can put any colormap you like here.\n",
    "    colours = [cm.ScalarMappable(norm=norm, cmap=\"plasma\").to_rgba(val) for val in vals]\n",
    "\n",
    "    return colours\n",
    "\n",
    "\n",
    "def plot_density(x, y, ax=None):\n",
    "    if ax is None:\n",
    "        ax = plt\n",
    "    mask = np.logical_and(np.isfinite(y), np.isfinite(x))\n",
    "    samples = np.stack([x[mask], y[mask]])\n",
    "\n",
    "    densObj = kde(samples)\n",
    "    colours = makeColours(densObj.evaluate(samples))\n",
    "    fig = ax.scatter(samples[0], samples[1], color=colours)\n",
    "    return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "92dc79c9-099b-4c28-b41d-a46ce68cdb87",
   "metadata": {},
   "outputs": [],
   "source": [
    "gtc_db = np.log(gtc).load()\n",
    "rtc_db = np.log(rtc).load()\n",
    "angle = angle.load()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "498a010d-6465-4cce-89c9-1feeb5cd5a0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'local incidence angle')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"https://ai4edatasetspublicassets.blob.core.windows.net/assets/notebook-output/tutorials-rtc-qualitative-assessment.ipynb/32.png\"/>"
      ],
      "text/plain": [
       "<Figure size 2160x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 724,
       "width": 1734
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(nrows=1, ncols=2, figsize=(30, 12))\n",
    "\n",
    "fig = plot_density(\n",
    "    angle[::10, ::10].data.ravel(), gtc_db[::10, ::10].data.ravel(), ax=axes[0]\n",
    ")\n",
    "fig = plot_density(\n",
    "    angle[::10, ::10].data.ravel(), rtc_db[::10, ::10].data.ravel(), ax=axes[1]\n",
    ")\n",
    "\n",
    "axes[0].set_title(\"GTC\")\n",
    "axes[0].set_ylabel(\"beta DB\")\n",
    "axes[0].set_xlabel(\"local incidence angle\")\n",
    "\n",
    "axes[1].set_title(\"RTC\")\n",
    "axes[1].set_ylabel(\"gamma_T DB\")\n",
    "axes[1].set_xlabel(\"local incidence angle\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9a66c4d-ec35-49a9-8b71-1594615d6403",
   "metadata": {},
   "source": [
    "**Note that in the first plot there is a clear correlation between the angle of incidence and backscattering, while in the second graph there is no correlation.**"
   ]
  }
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