Exercise : Measuring heights of trees outside the forest (TOF) in digital orthophotos (DOP)

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Shadows in orthorectified remote sensing images

Figure A: Shadow length s and object height h

A simple application of the intercept theorem in elementary geometry is to determine the height of a tree by measuring the shadow length. According to Fig. A the shadow length \(s_1\) and the height \(h_1\) of a man-made object such as an overhead line tower were measured on the ground. If the lenght of a tree's shadow \(h_2\) is determined at the same time of the day we are able to compute \(h_2=s_2*\frac{h_1}{s_1}\).

We may also use trigonometry if we know the sun elevation \(\alpha\). The height of a tree is then computed \(h_2=s_2*\tan \alpha\).

Digitizing shadow length and measuring sun azimuth in digital orthophotos

Figure B: Overhead line tower (220 kV)
Figure C: Digitized shadow length and measured azimuth of an overhead line tower

Load and display German Geoadata using QGIS 2.10 following the Exercise: Displaying German Geobasis data (GBD) or load the saved project file .\GBData\display_gbd.qgs where the project coordinate reference system (CRS) is set to ETRS89/UTM32N (EPSG:25832).

  1. Create a new shapefile layer
    1. Select Layer --> New --> New Shapefile Layer.
      • As layer type, select Line. Click the Specify CRS button and select ETRS89/UTM32N (EPSG:25832).
      • To add an attibute:
        • For the attribute's name type Class into the Name field of the New attribute section.
        • Select Whole number as data type.
        • Confirm with Add to attributes list.
        • Confirm with OK and enter path and name (e.g. measure_shadow_length.shp) in the following menu.
    2. Zoom in to the overhead line tower 220kV shown in Fig. A. Click Add feature QGIS 2.0 AddLine.png to start digitizing. Simply click at first on the top of the shadow of the tower second add another node in the center of the base of the tower (Fig. B). Finish the line geometry by right-clicking and entering the attributes in the appearing window (just use an increasing number for the ID, and Class = 1 in case of a man-made object).
    3. Change the display style of the new line. Select the shapefile in the Layers window. Layer --> Properties --> Style --> Single Symbol. Click on "Simple line" and change the Color according to your preferences and increae the Pen width to 0.5.
    4. Do not forget to save your changes by clicking again the Toggle editing button QGIS 2.0 Edit.png! Confirm Save to stop editing and save the changes permanently.


  1. Measure the sun azimuth at the time of image acquisition
    1. Install the CadTools plugin using Plugins --> Manage and install plugins.
    2. We use the "Show azimuth" function of CadTools to calculate the azimuth between two points which have to be selected first. Zoom in to the overhead line tower and the digitized shadow lenght. Select the shapefile in the Layers window. Activate Select 2 Vertex Points QGIS 2.0 Select2Points.png left before Show Azimuth QGIS 2.0 ShowAzimuth.png and click at first on the node on top of the shadow of the line tower and second on the node near the base of the line tower. Calculate the azimuth by clicking Show Azimuth QGIS 2.0 ShowAzimuth.png. Make a note of the result in unit degrees.

Estimating sun elevation

If the position of the area of interest (WGS84 / Long/Lat) and date and exact time of the digital image acquisition is given we are able to compute the sun elevation \(\alpha\) using the Solar Geometry Calculator of the U.S. National Oceanic and Atmospheric Administration (NOAA). We assume that the date of the image flight is correctly indicated in the metadata as 2010-04-30 but the exact acquisition time is not known. We may construct a table for the day of the image aqcuision listing sun elevation and azimuth with a time intervall of 15 seconds.

  1. Find the position of the overhead line tower changing the project coordinate system from UTM to Long/Lat. Open Project Properties --> Project Properties --> CRC. Type into the text field "Filter": 4326 and than click on WGS84 to select geographic coordinates. Place the cursor on the line tower and make a note of the coordinates shown below the viewer in unit decimal degrees. Do not forget to switch the project CRS back to ETRS89 / UTM zone 32N, EPSG:25832 before we continue.
  2. Fill out the fields of the Solar Geometry Calculator and click Submit Query.
    Solar calculator.png
  3. Search in the resulting list for the sun azimuth calculated using the CadTools plugin (Fig. C) and report the corresponding sun elevation and acquisition time.

Calculating individual tree heights

  1. Vector --> Geometry Tools --> Export/Add geometry columns and select the vector layer measure_shadow_length. click OK and Yes. Close the dialog with OK and Close.
  2. Select measure_shadow_length in the layers window. Right click Open Atrribute table. Report the shadow length of the overhead line tower. The height of the tower was measured as 32.1m by a clinometer device. Compute the sun elevation \( \alpha \) and compare the result of the solar geometry calculator.
  3. Digitze additional tree shadows.
  4. Right click Open Atrribute table. Toggle editing mode QGIS 2.0 Edit.png. Add a new column QGIS 2.0 AddColumn.png Name: height, Type: Decimal number (real), Width: 10, Precision: 1. OK. Save the edits.
  5. Open Field Calculator QGIS 2.0 FieldCalcualtor.png and click the checkbox "Update existing field" on. Select height from the drop list and type an expression to calculate the tree heights.OK.
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