tutorials/customizable-rtc-sentinel1.ipynb

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    "## Customizable radiometric terrain corrections of Sentinel-1 products\n",
    "\n",
    "The Planetary Computer includes both [Sentinel-1 Level-1 Ground Range Detected (GRD)](https://planetarycomputer.microsoft.com/dataset/sentinel-1-grd) and [Sentinel-1 Radiometrically Terrain Corrected (RTC)](https://planetarycomputer.microsoft.com/dataset/sentinel-1-rtc) collections. This tutorial explains the some background on Synthetic Aperture Radar (SAR), geometric and radiometric terrain correction, and introduces [sarsen](https://github.com/bopen/sarsen), an open-source library for working with SAR data. `sarsen` enables geometric and radiometric corrections using any digital elevation model (DEM) supported by GDAL / Proj.\n",
    "\n",
    "### Background\n",
    "\n",
    "The typical side-looking [Synthetic Aperture Radar (SAR)](https://earthdata.nasa.gov/learn/backgrounders/what-is-sar) system acquires data with uniform sampling in azimuth and slant range, where the azimuth and range represents the time when a given target is acquired and the absolute sensor-to-target distance, respectively.\n",
    "Because of this, the near range appears compressed with respect to the far range. Furthermore, any deviation of the target elevation from a smooth geoid results in additional local geometric and radiometric distortions known as foreshortening, layover and shadow.\n",
    "\n",
    "- Radar foreshortening: Terrain surfaces sloping towards the radar appear shortened relative to those sloping away from the radar.\n",
    "- Radar layover: It's an extreme case of foreshortening occurring when the terrain slope is greater than the angle of the incident signal.  \n",
    "- Radar shadows: They occur when ground points at the same azimuth but different slant ranges are aligned in the direction of the line-of-sight. This is usually due to a back slope with an angle steeper than the viewing angle. When this happens, the radar signal never reaches the farthest points, and thus there is no measurement, meaning that this lack of information is unrecoverable.\n",
    "\n",
    "### Geometric Terrain Correction\n",
    "\n",
    "The [Sentinel-1 GRD](https://planetarycomputer.microsoft.com/dataset/sentinel-1-grd) product already provides a geometric correction that removes the compression effect on the near-range. Geometric Terrain Correction *also* corrects for displacements due to target elevation. When applying geometric terrain correction, the resolution and accuracy of the input Digital Elevation Model (DEM). The Planetary Computer has a number of [DEMs](https://planetarycomputer.microsoft.com/catalog?tags=DEM) to choose from.\n",
    "\n",
    "### Radiometric Terrain Correction\n",
    "\n",
    "Terrain variations affect both the position of a given point on the Earth's surface *and* the brightness of the radar return. The `sarsen` radiometric terrain correction compensates for the backscatter modulation generated by the topography of the scene. This produces a more uniform backscatter image, emphasizing the radiometric differences of the terrain.\n",
    "\n",
    "The accuracy of Radiometric Terrain Corrected (RTC) products is also strongly affected by the resolution of the input DEM.\n",
    "\n",
    "This tutorial shows how to perform (i) geometric and (ii) radiometric terrain corrections on the Sentinel-1 GRD product using `sarsen`. We use a 10-meter resolution DEM, the same resolution of the DEM used to generate the [Sentinel-1 RTC product](https://planetarycomputer.microsoft.com/dataset/sentinel-1-rtc) available on the Planetary Computer. The comparison at the end of this notebook demonstrates that the RTC computed by `sarsen` is consistent with the RTC from the Planetary Computer.\n",
    "\n",
    "As an example, we use data covering the South-of-Redmond region (Seattle, US).\n",
    "\n",
    "Steps:\n",
    "\n",
    "- Download the Sentinel-1 GRD\n",
    "- Download the 10-meter DEM\n",
    "- Compute the GTC using `sarsen`\n",
    "- Compute the RTC using `sarsen`\n",
    "- Compare the GTC to the RTC\n",
    "- Compare the RTC computed using `sarsen` to the RTC already available on the Planetery Computer \n",
    "\n",
    "**Note**: Download/retrieval steps are slower on local machines compared to the Planetary Computer. In future versions, it will be possible to access data via [fsspec](https://filesystem-spec.readthedocs.io/en/latest/) without having to download data locally."
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    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 7)"
   ]
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    "import os\n",
    "import tempfile\n",
    "\n",
    "import rioxarray\n",
    "\n",
    "from sarsen import apps\n",
    "\n",
    "import adlfs\n",
    "import planetary_computer\n",
    "import pystac_client\n",
    "import stackstac"
   ]
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   "source": [
    "### Processing definitions"
   ]
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     "data": {
      "text/plain": [
       "'/tmp'"
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    "# 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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   "source": [
    "#### Area of interest definition: South-of-Redmond (Seattle, US)"
   ]
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   "id": "51cfd0f3-1be4-493a-a419-b56425c139eb",
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    "lon, lat = [-121.95, 47.04]\n",
    "buffer = 0.2\n",
    "bbox = [lon - buffer, lat - buffer, lon + buffer, lat + buffer]"
   ]
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    "#### DEMs discovery\n",
    "\n",
    "Here we use the [USGS 3dep-seamles DEM](https://planetarycomputer.microsoft.com/dataset/3dep-seamless) with a 10-meter ground sample distance (GDS). 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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    "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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    "Here we load the data into an xarray `DataArray` using stackstac."
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       "Coordinates: (12/13)\n",
       "  * time             (time) datetime64[ns] 2018-02-02 2018-02-08 ... 2020-01-07\n",
       "    id               (time) &lt;U10 &#x27;n48w122-13&#x27; &#x27;n47w122-13&#x27; ... &#x27;n48w123-13&#x27;\n",
       "    band             &lt;U4 &#x27;data&#x27;\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",
       "    threedep:region  &lt;U7 &#x27;n40w130&#x27;\n",
       "    ...               ...\n",
       "    proj:epsg        int64 5498\n",
       "    proj:shape       object {10812}\n",
       "    gsd              int64 10\n",
       "    end_datetime     (time) &lt;U20 &#x27;2016-12-31T00:00:00Z&#x27; ... &#x27;2019-04-25T00:00...\n",
       "    description      &lt;U1849 &#x27;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</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-91c9486d3e17af5ae0ea1ccefd39911d'</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-10d923c1-a98a-42fd-992a-ee2507d2a37c' class='xr-array-in' type='checkbox' checked><label for='section-10d923c1-a98a-42fd-992a-ee2507d2a37c' 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",
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       "\n",
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       "\n",
       "  <!-- Text -->\n",
       "  <text x=\"84.948598\" y=\"154.948598\" font-size=\"1.0rem\" font-weight=\"100\" text-anchor=\"middle\" >4321</text>\n",
       "  <text x=\"164.948598\" y=\"74.948598\" font-size=\"1.0rem\" font-weight=\"100\" text-anchor=\"middle\" transform=\"rotate(-90,164.948598,74.948598)\">4321</text>\n",
       "  <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",
       "</svg>\n",
       "        </td>\n",
       "    </tr>\n",
       "</table></div></div></li><li class='xr-section-item'><input id='section-bec312e6-dfa6-4924-884e-b017d082a09a' class='xr-section-summary-in' type='checkbox'  checked><label for='section-bec312e6-dfa6-4924-884e-b017d082a09a' 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-a9053b61-3fae-409a-b9d0-32a8cb0e3004' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a9053b61-3fae-409a-b9d0-32a8cb0e3004' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-12d299fc-c774-4615-9e48-ac9afe09ed99' class='xr-var-data-in' type='checkbox'><label for='data-12d299fc-c774-4615-9e48-ac9afe09ed99' 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-b7600d4c-cf75-4f5a-a853-40284a263fa7' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b7600d4c-cf75-4f5a-a853-40284a263fa7' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-42959a23-a0df-4ec8-b75b-ccf7316a4204' class='xr-var-data-in' type='checkbox'><label for='data-42959a23-a0df-4ec8-b75b-ccf7316a4204' 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-57e30ea4-5976-44a4-8eb8-50931f9a5b27' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-57e30ea4-5976-44a4-8eb8-50931f9a5b27' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-a511007d-3a29-4462-95ca-92577bea3384' class='xr-var-data-in' type='checkbox'><label for='data-a511007d-3a29-4462-95ca-92577bea3384' 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-bf1bd81b-1f83-4634-a291-fc9d3726030a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-bf1bd81b-1f83-4634-a291-fc9d3726030a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-4c79c43a-e6e5-4a38-a114-922b57de08ae' class='xr-var-data-in' type='checkbox'><label for='data-4c79c43a-e6e5-4a38-a114-922b57de08ae' 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-0d26d4c4-45e2-42d7-802f-aeb6c5b53775' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0d26d4c4-45e2-42d7-802f-aeb6c5b53775' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2f1c3d8e-1b73-44db-8bfe-6127bfc9ef64' class='xr-var-data-in' type='checkbox'><label for='data-2f1c3d8e-1b73-44db-8bfe-6127bfc9ef64' 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>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-2503182e-7023-4ccd-a0c0-6e6a22fac826' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2503182e-7023-4ccd-a0c0-6e6a22fac826' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f7a58b75-87b4-4636-b96a-a3c6347d71b2' class='xr-var-data-in' type='checkbox'><label for='data-f7a58b75-87b4-4636-b96a-a3c6347d71b2' 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>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-b8fb67be-e23d-42b4-b9dc-a48aec29f88d' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b8fb67be-e23d-42b4-b9dc-a48aec29f88d' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-db53578e-5719-49d5-a62c-d8ef11ef8ea6' class='xr-var-data-in' type='checkbox'><label for='data-db53578e-5719-49d5-a62c-d8ef11ef8ea6' 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>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-e70fbcd4-de06-4c5b-863d-73f9bcb10e00' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e70fbcd4-de06-4c5b-863d-73f9bcb10e00' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-cc0d2db1-52cc-4a4d-854f-4e751e51c4bd' class='xr-var-data-in' type='checkbox'><label for='data-cc0d2db1-52cc-4a4d-854f-4e751e51c4bd' 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>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-21a3a884-7ae8-4e55-9739-e0c38c59f6c2' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-21a3a884-7ae8-4e55-9739-e0c38c59f6c2' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-321ce8ce-8da0-4ad7-b8d4-2cd3797ab8b4' class='xr-var-data-in' type='checkbox'><label for='data-321ce8ce-8da0-4ad7-b8d4-2cd3797ab8b4' 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>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-3eef1607-c52f-4d58-a41b-38de045da9ee' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3eef1607-c52f-4d58-a41b-38de045da9ee' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e4d557be-14b5-402c-8133-80a84117cc18' class='xr-var-data-in' type='checkbox'><label for='data-e4d557be-14b5-402c-8133-80a84117cc18' 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>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-e10f0fdb-9acc-43a7-b9f2-0e613ca3d673' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e10f0fdb-9acc-43a7-b9f2-0e613ca3d673' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d09603cf-9aaf-4724-8787-8b3cb4ba04a1' class='xr-var-data-in' type='checkbox'><label for='data-d09603cf-9aaf-4724-8787-8b3cb4ba04a1' 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>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-d66959e8-9696-40bd-8750-fb85251c1b1a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d66959e8-9696-40bd-8750-fb85251c1b1a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-7fea8bb8-3fa2-40a9-9b9b-e9904e4b12b7' class='xr-var-data-in' type='checkbox'><label for='data-7fea8bb8-3fa2-40a9-9b9b-e9904e4b12b7' 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-52047797-2882-4644-bef3-c2f9d7f8856c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-52047797-2882-4644-bef3-c2f9d7f8856c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d2489f1a-f88a-408f-9457-ddd8abd1d78c' class='xr-var-data-in' type='checkbox'><label for='data-d2489f1a-f88a-408f-9457-ddd8abd1d78c' 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-682d5cf5-4038-482f-be1b-9667f349c98a' class='xr-section-summary-in' type='checkbox'  checked><label for='section-682d5cf5-4038-482f-be1b-9667f349c98a' 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-91c9486d3e17af5ae0ea1ccefd39911d' (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",
       "    threedep:region  <U7 'n40w130'\n",
       "    ...               ...\n",
       "    proj:epsg        int64 5498\n",
       "    proj:shape       object {10812}\n",
       "    gsd              int64 10\n",
       "    end_datetime     (time) <U20 '2016-12-31T00:00:00Z' ... '2019-04-25T00:00...\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": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dem_raster_all = stackstac.stack(items, bounds=bbox).squeeze()\n",
    "dem_raster_all"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55b7fc2e-c6ba-49d5-a04d-a6b61d7a89ab",
   "metadata": {},
   "source": [
    "#### DEMs average along the time dimension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8bdf169d-28dc-41aa-a34b-29e3aa462e51",
   "metadata": {},
   "outputs": [],
   "source": [
    "dem_raster_geo = dem_raster_all.compute()\n",
    "if \"time\" in dem_raster_geo.dims:\n",
    "    dem_raster_geo = dem_raster_geo.mean(\"time\")\n",
    "_ = dem_raster_geo.rio.set_crs(dem_raster_all.rio.crs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b400b893-0441-4709-88d0-bf95ff4eb00b",
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "dddaccb5-2cee-4c65-880a-c33f7f3a4d1a",
   "metadata": {},
   "outputs": [
    {
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       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;stackstac-d90c33d750479ce84c6f5eda1b1f3eec&#x27; (y: 3000, x: 2900)&gt;\n",
       "array([[ 196.68109131,  196.14202881,  194.11082458, ...,  820.71972656,\n",
       "         820.05755615,  819.68597412],\n",
       "       [ 196.68109131,  196.14202881,  195.13980103, ...,  817.84838867,\n",
       "         814.0760498 ,  814.61773682],\n",
       "       [ 197.03511047,  195.65205383,  195.13980103, ...,  812.12884521,\n",
       "         810.13116455,  809.48669434],\n",
       "       ...,\n",
       "       [ 602.28057861,  607.78918457,  609.63909912, ..., 4130.93261719,\n",
       "        4135.22167969, 4137.34033203],\n",
       "       [ 597.96710205,  602.36712646,  603.93676758, ..., 4133.00195312,\n",
       "        4137.37695312, 4139.43896484],\n",
       "       [ 594.58496094,  599.09234619,  600.71466064, ..., 4135.22558594,\n",
       "        4139.52978516, 4141.82373047]])\n",
       "Coordinates:\n",
       "  * x                (x) float64 5.65e+05 5.65e+05 ... 5.94e+05 5.94e+05\n",
       "  * y                (y) float64 5.22e+06 5.22e+06 ... 5.19e+06 5.19e+06\n",
       "    proj:shape       object {10812}\n",
       "    band             &lt;U4 &#x27;data&#x27;\n",
       "    threedep:region  &lt;U7 &#x27;n40w130&#x27;\n",
       "    epsg             int64 5498\n",
       "    proj:epsg        int64 5498\n",
       "    description      &lt;U1849 &#x27;This tile of the 3D Elevation Program (3DEP) sea...\n",
       "    gsd              int64 10\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-d90c33d750479ce84c6f5eda1b1f3eec'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>y</span>: 3000</li><li><span class='xr-has-index'>x</span>: 2900</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-a66737d2-a716-458f-bfde-4871b89b2748' class='xr-array-in' type='checkbox' checked><label for='section-a66737d2-a716-458f-bfde-4871b89b2748' 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>196.7 196.1 194.1 193.7 ... 4.133e+03 4.135e+03 4.14e+03 4.142e+03</span></div><div class='xr-array-data'><pre>array([[ 196.68109131,  196.14202881,  194.11082458, ...,  820.71972656,\n",
       "         820.05755615,  819.68597412],\n",
       "       [ 196.68109131,  196.14202881,  195.13980103, ...,  817.84838867,\n",
       "         814.0760498 ,  814.61773682],\n",
       "       [ 197.03511047,  195.65205383,  195.13980103, ...,  812.12884521,\n",
       "         810.13116455,  809.48669434],\n",
       "       ...,\n",
       "       [ 602.28057861,  607.78918457,  609.63909912, ..., 4130.93261719,\n",
       "        4135.22167969, 4137.34033203],\n",
       "       [ 597.96710205,  602.36712646,  603.93676758, ..., 4133.00195312,\n",
       "        4137.37695312, 4139.43896484],\n",
       "       [ 594.58496094,  599.09234619,  600.71466064, ..., 4135.22558594,\n",
       "        4139.52978516, 4141.82373047]])</pre></div></div></li><li class='xr-section-item'><input id='section-bb7ac606-8309-49b1-85b9-3a0a4e05b737' class='xr-section-summary-in' type='checkbox'  checked><label for='section-bb7ac606-8309-49b1-85b9-3a0a4e05b737' 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'>5.65e+05 5.65e+05 ... 5.94e+05</div><input id='attrs-abbff2b2-a709-49fe-8b80-9bff294f1a25' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-abbff2b2-a709-49fe-8b80-9bff294f1a25' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-1e2ccd26-e883-41fd-8ce4-5bf148104e4c' class='xr-var-data-in' type='checkbox'><label for='data-1e2ccd26-e883-41fd-8ce4-5bf148104e4c' 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([565002.162431, 565012.162431, 565022.162431, ..., 593972.162431,\n",
       "       593982.162431, 593992.162431])</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'>5.22e+06 5.22e+06 ... 5.19e+06</div><input id='attrs-943a30a9-494f-4bd9-bce7-e23b4422e110' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-943a30a9-494f-4bd9-bce7-e23b4422e110' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-71d32f4f-8726-4e2c-ab05-c53ecb67200f' class='xr-var-data-in' type='checkbox'><label for='data-71d32f4f-8726-4e2c-ab05-c53ecb67200f' 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([5219993.548183, 5219983.548183, 5219973.548183, ..., 5190023.548183,\n",
       "       5190013.548183, 5190003.548183])</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-626de40e-0e25-45c0-861e-b6b86de5834a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-626de40e-0e25-45c0-861e-b6b86de5834a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-9efa51ce-6da7-45f9-bb62-8c5c87bb5af3' class='xr-var-data-in' type='checkbox'><label for='data-9efa51ce-6da7-45f9-bb62-8c5c87bb5af3' 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>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-ca5f304e-7944-4b68-ab84-e5c747069199' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ca5f304e-7944-4b68-ab84-e5c747069199' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0b0cb2e5-6f8a-49f8-bc2e-d27550fc25c0' class='xr-var-data-in' type='checkbox'><label for='data-0b0cb2e5-6f8a-49f8-bc2e-d27550fc25c0' 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>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-505774cf-0467-4104-b61e-1da779a6fd49' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-505774cf-0467-4104-b61e-1da779a6fd49' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-9c440679-4e25-40a4-8211-49a3fb2d550a' class='xr-var-data-in' type='checkbox'><label for='data-9c440679-4e25-40a4-8211-49a3fb2d550a' 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>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-2622cd36-2a66-4b68-b73e-7ae3c3943a81' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2622cd36-2a66-4b68-b73e-7ae3c3943a81' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-27ad5a66-7b9e-4838-a330-a6f915201a47' class='xr-var-data-in' type='checkbox'><label for='data-27ad5a66-7b9e-4838-a330-a6f915201a47' 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>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-55d6e6e6-cebc-421d-ba05-08af5c0e5496' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-55d6e6e6-cebc-421d-ba05-08af5c0e5496' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-360dfcc9-cbf4-40d1-8bda-69289fe9739c' class='xr-var-data-in' type='checkbox'><label for='data-360dfcc9-cbf4-40d1-8bda-69289fe9739c' 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>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-3c2a0e17-2562-4052-b3c6-8a9dde4eb887' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3c2a0e17-2562-4052-b3c6-8a9dde4eb887' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2f4ca21f-5ac6-40b6-a2b5-7feca01a9659' class='xr-var-data-in' type='checkbox'><label for='data-2f4ca21f-5ac6-40b6-a2b5-7feca01a9659' 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>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-97520cc5-438e-4ec5-be05-a6a453ca4e08' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-97520cc5-438e-4ec5-be05-a6a453ca4e08' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-965e5dea-eb38-457f-bc78-6a9747e4eafd' class='xr-var-data-in' type='checkbox'><label for='data-965e5dea-eb38-457f-bc78-6a9747e4eafd' 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>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-490e993b-f121-4abe-85d7-0c279e882410' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-490e993b-f121-4abe-85d7-0c279e882410' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-61e3039b-3411-40fa-886c-aa610497c6f0' class='xr-var-data-in' type='checkbox'><label for='data-61e3039b-3411-40fa-886c-aa610497c6f0' 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-0dbbcc3b-ee2c-4f33-8057-f0e0e730b453' class='xr-section-summary-in' type='checkbox'  checked><label for='section-0dbbcc3b-ee2c-4f33-8057-f0e0e730b453' 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-d90c33d750479ce84c6f5eda1b1f3eec' (y: 3000, x: 2900)>\n",
       "array([[ 196.68109131,  196.14202881,  194.11082458, ...,  820.71972656,\n",
       "         820.05755615,  819.68597412],\n",
       "       [ 196.68109131,  196.14202881,  195.13980103, ...,  817.84838867,\n",
       "         814.0760498 ,  814.61773682],\n",
       "       [ 197.03511047,  195.65205383,  195.13980103, ...,  812.12884521,\n",
       "         810.13116455,  809.48669434],\n",
       "       ...,\n",
       "       [ 602.28057861,  607.78918457,  609.63909912, ..., 4130.93261719,\n",
       "        4135.22167969, 4137.34033203],\n",
       "       [ 597.96710205,  602.36712646,  603.93676758, ..., 4133.00195312,\n",
       "        4137.37695312, 4139.43896484],\n",
       "       [ 594.58496094,  599.09234619,  600.71466064, ..., 4135.22558594,\n",
       "        4139.52978516, 4141.82373047]])\n",
       "Coordinates:\n",
       "  * x                (x) float64 5.65e+05 5.65e+05 ... 5.94e+05 5.94e+05\n",
       "  * y                (y) float64 5.22e+06 5.22e+06 ... 5.19e+06 5.19e+06\n",
       "    proj:shape       object {10812}\n",
       "    band             <U4 'data'\n",
       "    threedep:region  <U7 'n40w130'\n",
       "    epsg             int64 5498\n",
       "    proj:epsg        int64 5498\n",
       "    description      <U1849 'This tile of the 3D Elevation Program (3DEP) sea...\n",
       "    gsd              int64 10\n",
       "    spatial_ref      int64 0\n",
       "Attributes:\n",
       "    _FillValue:  1.7976931348623157e+308"
      ]
     },
     "execution_count": 8,
     "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",
    "\n",
    "# crop DEM to our area of interest and save it\n",
    "dem_corners = dict(x=slice(565000, 594000), y=slice(5220000, 5190000))\n",
    "\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": 9,
   "id": "825373fa-d2ab-4b46-b2ad-0fdb9589e076",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://ai4edatasetspublicassets.blob.core.windows.net/assets/notebook-output/tutorials-customizable-rtc-sentinel1.ipynb/9.png\"/>"
      ],
      "text/plain": [
       "<Figure size 720x504 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dem_raster.plot()\n",
    "plt.title(\"DEM in UTM coordinates\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00e88577-3a05-4865-ae1a-e80fd2ae8f8a",
   "metadata": {},
   "source": [
    "### Define GRD parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "49dc13e7-f72d-4c1c-9c48-e5f466a394c3",
   "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": "116c7c85-a65e-4e74-a8a8-f0bdd952c198",
   "metadata": {},
   "source": [
    "### Retrieve Sentinel-1 GRD\n",
    "\n",
    "We'll use the Planetary Compueter's [SAS API](https://planetarycomputer.microsoft.com/docs/concepts/sas/) to get a read-only token for the Sentinel-1 GRD container."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "976ee57b-f766-4102-b24e-55f1b787a3b5",
   "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": 11,
     "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": 12,
   "id": "6ebd58bb-5584-4a7d-aeef-ffea00290b9a",
   "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": "9371be6b-5b88-4eb5-91b2-dfcb4ac23030",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Processing\n",
    "\n",
    "#### 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": 13,
   "id": "9f44371e-dedb-4a06-b16e-c4d748216ace",
   "metadata": {},
   "outputs": [],
   "source": [
    "gtc = apps.terrain_correction(\n",
    "    product_urlpath=grd_local_path,\n",
    "    measurement_group=measurement_group,\n",
    "    dem_urlpath=dem_path,\n",
    "    output_urlpath=os.path.join(\n",
    "        tmp_dir, os.path.basename(product_folder) + \".10m.GTC.tif\"\n",
    "    ),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7c3ac2e9-4d7d-45cc-9b06-d1bf223354c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://ai4edatasetspublicassets.blob.core.windows.net/assets/notebook-output/tutorials-customizable-rtc-sentinel1.ipynb/14.png\"/>"
      ],
      "text/plain": [
       "<Figure size 720x504 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gtc.plot(vmax=0.4);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c9cd051-776b-41dd-a03e-341f3a3271b1",
   "metadata": {},
   "source": [
    "#### RTC\n",
    "\n",
    "`sarsen` implements the radiometric terrain-correction [Gamma Flattening](https://ieeexplore.ieee.org/document/5752845) algorithm.\n",
    "\n",
    "#### Input parameters\n",
    "- `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.\n",
    "\n",
    "**Note:** As the RTC generation step loads data into the memory, it may take several minutes (about 10 minutes on the Planetary Computer). The performances will be improved in the next releases of `sarsen`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "bc90978d-3c8b-4c9e-b77b-781fd04e6f20",
   "metadata": {},
   "outputs": [],
   "source": [
    "rtc = apps.terrain_correction(\n",
    "    grd_local_path,\n",
    "    measurement_group=measurement_group,\n",
    "    dem_urlpath=dem_path,\n",
    "    correct_radiometry=\"gamma_bilinear\",\n",
    "    output_urlpath=os.path.join(\n",
    "        tmp_dir, os.path.basename(product_folder) + \".10m.RTC.tif\"\n",
    "    ),\n",
    "    grouping_area_factor=(3, 3),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecae137d-447e-43a6-b74e-5165f858bb4e",
   "metadata": {},
   "source": [
    "### Comparison between GTC and RTC\n",
    "\n",
    "Let's visualize the geometrically and radiometrically terrain corrected data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e0c8af4d-01e9-42bf-b219-ca7ec2641b47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://ai4edatasetspublicassets.blob.core.windows.net/assets/notebook-output/tutorials-customizable-rtc-sentinel1.ipynb/16.png\"/>"
      ],
      "text/plain": [
       "<Figure size 2160x864 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(nrows=1, ncols=2, figsize=(30, 12))\n",
    "\n",
    "gtc.plot(ax=axes[0], vmax=0.4)\n",
    "axes[0].grid(c=\"red\")\n",
    "axes[0].set(title=\"GTC\")\n",
    "\n",
    "rtc.plot(ax=axes[1], vmax=0.4)\n",
    "axes[1].grid(c=\"red\")\n",
    "axes[1].set(title=\"RTC\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a421b9a-5f5b-47cd-88ce-f23b7bc9353d",
   "metadata": {},
   "source": [
    "### Comparison between Planetary Computer RTC and sarsen RTC\n",
    "\n",
    "Finally, let's compare the pre-computed Sentinel-1 RTC with the customizable RTC from sarsen. We'll use the Planetary Computer's STAC API to find the matching scene from the Sentinel-1 RTC collection.\n",
    "\n",
    "Note: accessing data from the `sentinel-1-rtc` collection requires an account on the Planetary Computer. See [When an account is needed](https://planetarycomputer.microsoft.com/docs/concepts/sas/#when-an-account-is-needed) for more."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "11747c3b-036d-4668-817e-423c6d95bb58",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found 1 items\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Item id=S1B_IW_GRDH_1SDV_20211217T141304_20211217T141329_030066_039705_rtc>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "search = catalog.search(\n",
    "    collections=[\"sentinel-1-rtc\"], datetime=\"2021-12-17\", bbox=bbox\n",
    ")\n",
    "items = search.get_all_items()\n",
    "print(f\"Found {len(items)} items\")\n",
    "item = items[0]\n",
    "item"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b4dd404-2467-490f-b226-4bfa91b8497d",
   "metadata": {},
   "source": [
    "We'll load up the pre-computed RTC data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5c64895d-3ed8-4498-8230-a1e3eaa97ff2",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
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       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
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       "\n",
       ".xr-attrs dd {\n",
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       "\n",
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (band: 1, y: 3000, x: 2900)&gt;\n",
       "[8700000 values with dtype=float32]\n",
       "Coordinates:\n",
       "  * x            (x) float64 5.65e+05 5.65e+05 5.65e+05 ... 5.94e+05 5.94e+05\n",
       "  * y            (y) float64 5.22e+06 5.22e+06 5.22e+06 ... 5.19e+06 5.19e+06\n",
       "    spatial_ref  int64 0\n",
       "Dimensions without coordinates: band\n",
       "Attributes:\n",
       "    Matrix_Element:   _1_1\n",
       "    Polarization:     VV\n",
       "    SARPixelContent:  intensity\n",
       "    Scale:            linear\n",
       "    _FillValue:       -32768.0\n",
       "    scale_factor:     1.0\n",
       "    add_offset:       0.0\n",
       "    long_name:        Sentinel-1 Calibrated and Terrain Corrected VV</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'></div><ul class='xr-dim-list'><li><span>band</span>: 1</li><li><span class='xr-has-index'>y</span>: 3000</li><li><span class='xr-has-index'>x</span>: 2900</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-0eaa44fe-4725-4b78-b001-134ac954ff38' class='xr-array-in' type='checkbox' checked><label for='section-0eaa44fe-4725-4b78-b001-134ac954ff38' 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>...</span></div><div class='xr-array-data'><pre>[8700000 values with dtype=float32]</pre></div></div></li><li class='xr-section-item'><input id='section-1b81bab1-d2e5-4a46-b27e-353d32d826d4' class='xr-section-summary-in' type='checkbox'  checked><label for='section-1b81bab1-d2e5-4a46-b27e-353d32d826d4' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>5.65e+05 5.65e+05 ... 5.94e+05</div><input id='attrs-5c81d6c4-edd2-4b7b-be5e-d9c2fb34a84f' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-5c81d6c4-edd2-4b7b-be5e-d9c2fb34a84f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-58c39b39-bb85-4e52-9114-10eaa5c5d01a' class='xr-var-data-in' type='checkbox'><label for='data-58c39b39-bb85-4e52-9114-10eaa5c5d01a' 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([565005., 565015., 565025., ..., 593975., 593985., 593995.])</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'>5.22e+06 5.22e+06 ... 5.19e+06</div><input id='attrs-618fee52-a8ad-4989-a94a-7bb9da0f684f' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-618fee52-a8ad-4989-a94a-7bb9da0f684f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-8f6bd00b-3b18-4044-9288-a918e5859ff8' class='xr-var-data-in' type='checkbox'><label for='data-8f6bd00b-3b18-4044-9288-a918e5859ff8' 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([5219995., 5219985., 5219975., ..., 5190025., 5190015., 5190005.])</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-414b8359-2069-4df6-8d05-2ed3704d88c1' class='xr-var-attrs-in' type='checkbox' ><label for='attrs-414b8359-2069-4df6-8d05-2ed3704d88c1' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-1d7a5757-ac50-42e4-889a-3ccc95fe8bf7' class='xr-var-data-in' type='checkbox'><label for='data-1d7a5757-ac50-42e4-889a-3ccc95fe8bf7' 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>514080.0 10.0 0.0 5295360.0 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-b64c054b-45d9-4e68-b4f6-346d9f5db55f' class='xr-section-summary-in' type='checkbox'  checked><label for='section-b64c054b-45d9-4e68-b4f6-346d9f5db55f' class='xr-section-summary' >Attributes: <span>(8)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>Matrix_Element :</span></dt><dd>_1_1</dd><dt><span>Polarization :</span></dt><dd>VV</dd><dt><span>SARPixelContent :</span></dt><dd>intensity</dd><dt><span>Scale :</span></dt><dd>linear</dd><dt><span>_FillValue :</span></dt><dd>-32768.0</dd><dt><span>scale_factor :</span></dt><dd>1.0</dd><dt><span>add_offset :</span></dt><dd>0.0</dd><dt><span>long_name :</span></dt><dd>Sentinel-1 Calibrated and Terrain Corrected VV</dd></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray (band: 1, y: 3000, x: 2900)>\n",
       "[8700000 values with dtype=float32]\n",
       "Coordinates:\n",
       "  * x            (x) float64 5.65e+05 5.65e+05 5.65e+05 ... 5.94e+05 5.94e+05\n",
       "  * y            (y) float64 5.22e+06 5.22e+06 5.22e+06 ... 5.19e+06 5.19e+06\n",
       "    spatial_ref  int64 0\n",
       "Dimensions without coordinates: band\n",
       "Attributes:\n",
       "    Matrix_Element:   _1_1\n",
       "    Polarization:     VV\n",
       "    SARPixelContent:  intensity\n",
       "    Scale:            linear\n",
       "    _FillValue:       -32768.0\n",
       "    scale_factor:     1.0\n",
       "    add_offset:       0.0\n",
       "    long_name:        Sentinel-1 Calibrated and Terrain Corrected VV"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rtc_pc = rioxarray.open_rasterio(item.assets[\"vv\"].href).drop(\"band\").sel(dem_corners)\n",
    "rtc_pc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1abc6292-455b-409a-b80e-4be005955207",
   "metadata": {},
   "source": [
    "And plot the results, with the pre-computed RTC on the left and sarsen's RTC on the right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "2ebe759d-5d53-40fc-badf-a4aafe13a91a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://ai4edatasetspublicassets.blob.core.windows.net/assets/notebook-output/tutorials-customizable-rtc-sentinel1.ipynb/20.png\"/>"
      ],
      "text/plain": [
       "<Figure size 2160x864 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(ncols=2, figsize=(30, 12))\n",
    "\n",
    "rtc_pc.plot(ax=axes[0], vmax=0.4)\n",
    "axes[0].grid(c=\"red\")\n",
    "axes[0].set(title=\"Planetary Computer RTC\")\n",
    "\n",
    "rtc.plot(ax=axes[1], vmax=0.4)\n",
    "axes[1].grid(c=\"red\")\n",
    "axes[1].set(title=\"sarsen RTC\")\n",
    "\n",
    "plt.tight_layout();"
   ]
  }
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