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@@ -152,8 +152,8 @@
     "objectID": "unit_01/03_in_class_exercise.html#geometric-terrain-correction",
     "href": "unit_01/03_in_class_exercise.html#geometric-terrain-correction",
     "title": "3  In-class Exercise 3: Backscattering Coefficients",
-    "section": "3.2 Geometric terrain correction",
-    "text": "3.2 Geometric terrain correction\nLevel 1 SAR data, such as the “GRD” product only takes into account the ellipsoidal model of the earth (i.e. slant-range distortion; script Chapter 4), without the description of the relief. This makes mountains appear to lean towards the radar system as visible in the below plot of the GRD scene. This latter distortion originates from the side-looking geometry of the SAR system. Due to this, the radar pulse reaches mountain slope facing the sensor before it reaches the base. Consequently, these slopes appear compressed and leaning toward the sensor. During processing to a level 1C product, these slant range distortions are partly corrected using a terrain correction algorithm and a Digital Elevation Model (DEM). The most common algorithm for this is the Range Doppler Terrain Correction.\n\nFigure 1: Geometric terrain correction. The lower bar shows the GRD without geometric terrain correction in slant geometry. In areas where the ground is elevated, the time of the signal to travel to the earth’s surface and back to the sensor is distorted, causing geometric shifts (foreshortening, lengthening, etc). Using a DEM and the Range Doppler Terrain Correction, the distortions are corrected and the image is orthorectified. (Source: ESRI)\nLet’s visualize this geometric terrain correction (GTC) with some actual data using the xarray method hvplot of the gtc_dc object.\n\ngtc_dc.hvplot.image(x=\"x\", y=\"y\", robust=True, data_aspect=1, cmap=\"Greys_r\",\n                    groupby=\"band\", rasterize=True).\\\n                        opts(frame_height=600, framewise=False, aspect=True)\n\n\n\n\n\n  \n\n\n\n\nFigure 2: The ground range detected values and geometrically terrain corrected values can be selected on the right-hand side of the graphic.\nThe geometrically terrain corrected values from the gtc_dc object (Figure 1) can be approximated to a certain extent, as we have sufficiently detailed information of topography in this area. This corrects for at least one typically occurring distortion in mountainous regions: “foreshortening”.\n\nFigure 3: Side Looking radar distortions (script Chapter 4).\nForeshortening can be spotted by eye, as it often has a radiometric consequence, where unusually bright areas fringe mountain ridges; a phenomenon called “highlighting”. This geometric artifact occurs due to the compression of the distance in the image of slopes facing the radar system and the consequentially higher density of scatterers per unit length. Now let’s zoom in on an example from the same data cube and display the original and corrected values side-by-side.\n\nfor_dc = gtc_dc.sel(x=slice(9.651, 9.706), y=slice(47.134, 47.079)).band_data\n\nfig, ax = plt.subplots(1, 2, figsize=(20, 8))\n\nbbox = dict(boxstyle=\"round\", fc=\"0.8\")\n\n\nax[1].annotate(\n    \"foreshortening/layover\",\n    xy=(9.674, 47.092),\n    xytext=(0.574, 0.192),\n    textcoords=\"subfigure fraction\",\n    bbox=bbox,\n    arrowprops=dict(facecolor=\"red\", shrink=0.05),\n)\nax[1].annotate(\n    \"radar shadows\",\n    xy=(9.68, 47.119),\n    xytext=(0.6, 0.625),\n    textcoords=\"subfigure fraction\",\n    bbox=bbox,\n    arrowprops=dict(facecolor=\"red\", shrink=0.05),\n)\n\nax[0].axes.set_aspect(\"equal\")\nax[1].axes.set_aspect(\"equal\")\n\nfor_dc.sel(band=\"grd\").plot(ax=ax[0], robust=True, cmap=\"Greys_r\")\nfor_dc.sel(band=\"sig0_gtc\").plot(ax=ax[1], robust=True, cmap=\"Greys_r\")\n\n\n\n\n\n\n\n\nFigure 4: Close-up inspection of geometric distortions in side-looking radar\nAs we can see, not all the geometric distortions can be corrected by the algorithm. Some of the pixels at the mountain ranges appear stretched, as in these areas not enough valid measurements are available. Moreover, we can see dark areas which are indicating radar shadows. These are image areas that could not be captured by the radar sensor and have values close to the noise floor of the Sensor (minimum detectable signal strength) ~ -28dB. It is important to note, that radar shadows are not the same for every image, as they depend on the acquisition geometry, in particular, the incidence angle and the flight direction of the satellite.",
+    "section": "3.2 Geometric Terrain Correction",
+    "text": "3.2 Geometric Terrain Correction\nLevel 1 SAR data, such as the “GRD” product only takes into account the ellipsoidal model of the earth (i.e. slant-range distortion; script Chapter 4), without the description of the relief. This makes mountains appear to lean towards the radar system as visible in the below plot of the GRD scene. This latter distortion originates from the side-looking geometry of the SAR system. Due to this, the radar pulse reaches mountain slope facing the sensor before it reaches the base. Consequently, these slopes appear compressed and leaning toward the sensor. During processing to a level 1C product, these slant range distortions are partly corrected using a terrain correction algorithm and a Digital Elevation Model (DEM). The most common algorithm for this is the Range Doppler Terrain Correction.\n\nFigure 1: Geometric terrain correction. The lower bar shows the GRD without geometric terrain correction in slant geometry. In areas where the ground is elevated, the time of the signal to travel to the earth’s surface and back to the sensor is distorted, causing geometric shifts (foreshortening, lengthening, etc). Using a DEM and the Range Doppler Terrain Correction, the distortions are corrected and the image is orthorectified. (Source: ESRI)\nLet’s visualize this geometric terrain correction (GTC) with some actual data using the xarray method hvplot of the gtc_dc object.\n\ngtc_dc.hvplot.image(x=\"x\", y=\"y\", robust=True, data_aspect=1, cmap=\"Greys_r\",\n                    groupby=\"band\", rasterize=True).\\\n                        opts(frame_height=600, framewise=False, aspect=True)\n\n\n\n\n\n  \n\n\n\n\nFigure 2: The ground range detected values and geometrically terrain corrected values can be selected on the right-hand side of the graphic.\nThe geometrically terrain corrected values from the gtc_dc object (Figure 1) can be approximated to a certain extent, as we have sufficiently detailed information of topography in this area. This corrects for at least one typically occurring distortion in mountainous regions: “foreshortening”.\n\nFigure 3: Side Looking radar distortions (script Chapter 4).\nForeshortening can be spotted by eye, as it often has a radiometric consequence, where unusually bright areas fringe mountain ridges; a phenomenon called “highlighting”. This geometric artifact occurs due to the compression of the distance in the image of slopes facing the radar system and the consequentially higher density of scatterers per unit length. Now let’s zoom in on an example from the same data cube and display the original and corrected values side-by-side.\n\nfor_dc = gtc_dc.sel(x=slice(9.651, 9.706), y=slice(47.134, 47.079)).band_data\n\nfig, ax = plt.subplots(1, 2, figsize=(20, 8))\n\nbbox = dict(boxstyle=\"round\", fc=\"0.8\")\n\n\nax[1].annotate(\n    \"foreshortening/layover\",\n    xy=(9.674, 47.092),\n    xytext=(0.574, 0.192),\n    textcoords=\"subfigure fraction\",\n    bbox=bbox,\n    arrowprops=dict(facecolor=\"red\", shrink=0.05),\n)\nax[1].annotate(\n    \"radar shadows\",\n    xy=(9.68, 47.119),\n    xytext=(0.6, 0.625),\n    textcoords=\"subfigure fraction\",\n    bbox=bbox,\n    arrowprops=dict(facecolor=\"red\", shrink=0.05),\n)\n\nax[0].axes.set_aspect(\"equal\")\nax[1].axes.set_aspect(\"equal\")\n\nfor_dc.sel(band=\"grd\").plot(ax=ax[0], robust=True, cmap=\"Greys_r\")\nfor_dc.sel(band=\"sig0_gtc\").plot(ax=ax[1], robust=True, cmap=\"Greys_r\")\n\n\n\n\n\n\n\n\nFigure 4: Close-up inspection of geometric distortions in side-looking radar\nAs we can see, not all the geometric distortions can be corrected by the algorithm. Some of the pixels at the mountain ranges appear stretched, as in these areas not enough valid measurements are available. Moreover, we can see dark areas which are indicating radar shadows. These are image areas that could not be captured by the radar sensor and have values close to the noise floor of the Sensor (minimum detectable signal strength) ~ -28dB. It is important to note, that radar shadows are not the same for every image, as they depend on the acquisition geometry, in particular, the incidence angle and the flight direction of the satellite.",
     "crumbs": [
       "Unit 1",
       "<span class='chapter-number'>3</span>  <span class='chapter-title'>Backscattering Coefficients</span>"

unit_01/03_in_class_exercise.html

@@ -287,7 +287,7 @@ <h2 id="toc-title">Table of contents</h2>
 
   <ul>
   <li><a href="#loading-backscatter-data" id="toc-loading-backscatter-data" class="nav-link active" data-scroll-target="#loading-backscatter-data"><span class="header-section-number">3.1</span> Loading Backscatter Data</a></li>
-  <li><a href="#geometric-terrain-correction" id="toc-geometric-terrain-correction" class="nav-link" data-scroll-target="#geometric-terrain-correction"><span class="header-section-number">3.2</span> Geometric terrain correction</a></li>
+  <li><a href="#geometric-terrain-correction" id="toc-geometric-terrain-correction" class="nav-link" data-scroll-target="#geometric-terrain-correction"><span class="header-section-number">3.2</span> Geometric Terrain Correction</a></li>
   <li><a href="#backscattering-coefficients" id="toc-backscattering-coefficients" class="nav-link" data-scroll-target="#backscattering-coefficients"><span class="header-section-number">3.3</span> Backscattering Coefficients</a></li>
   <li><a href="#radiometric-terrain-correction" id="toc-radiometric-terrain-correction" class="nav-link" data-scroll-target="#radiometric-terrain-correction"><span class="header-section-number">4</span> Radiometric Terrain Correction</a></li>
   </ul>
@@ -1366,7 +1366,7 @@ <h2 data-number="3.1" class="anchored" data-anchor-id="loading-backscatter-data"
 </div>
 </section>
 <section id="geometric-terrain-correction" class="level2" data-number="3.2">
-<h2 data-number="3.2" class="anchored" data-anchor-id="geometric-terrain-correction"><span class="header-section-number">3.2</span> Geometric terrain correction</h2>
+<h2 data-number="3.2" class="anchored" data-anchor-id="geometric-terrain-correction"><span class="header-section-number">3.2</span> Geometric Terrain Correction</h2>
 <p>Level 1 SAR data, such as the “GRD” product only takes into account the ellipsoidal model of the earth (i.e.&nbsp;slant-range distortion; script Chapter 4), without the description of the relief. This makes mountains appear to lean towards the radar system as visible in the below plot of the GRD scene. This latter distortion originates from the side-looking geometry of the SAR system. Due to this, the radar pulse reaches mountain slope facing the sensor before it reaches the base. Consequently, these slopes appear compressed and leaning toward the sensor. During processing to a level 1C product, these slant range distortions are partly corrected using a terrain correction algorithm and a Digital Elevation Model (DEM). The most common algorithm for this is the Range Doppler Terrain Correction.</p>
 <p><img src="https://www.esri.com/arcgis-blog/wp-content/uploads/2024/05/emenezes-esriBlog-GP-tool-fig_Apply-Geometric-Terrain-Correction-detailed.png" class="img-fluid"></p>
 <p><em>Figure 1: Geometric terrain correction. The lower bar shows the GRD without geometric terrain correction in slant geometry. In areas where the ground is elevated, the time of the signal to travel to the earth’s surface and back to the sensor is distorted, causing geometric shifts (foreshortening, lengthening, etc). Using a DEM and the Range Doppler Terrain Correction, the distortions are corrected and the image is orthorectified. (Source: ESRI)</em></p>