<h1>Measuring Landform Heights and Depths on Viking Images from Shadows.</h1></p>
<UL>
<B>QUICK STEPS: Measuring heights and depths: <BR></B>
<LI> Set scale
<LI> Measure length of shadow with measuring wand
<LI> Use the formula below to find the feature height or depth
</UL>
<BR><P>
You can measure the height or depth of a feature using the length of its shadow and a little trigonometry. If a crater rim or valley wall casts a clear shadow, the height of that valley wall or the depth of the crater can be estimated by measuring the shadow length and using simple trigonometry.</p>
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<IMG SRC = "GIFPICS/Shadows/ShadDiag.GIF">
<P>
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The formula for determining the height or depth "y" of a landform from cast shadows is </p>
y = x tan (90 - INA) </p>
where x is the length (horizontal distance) of the cast shadow.</P>
(90-INA) is equal to the sun's elevation angle. The INA angle is measured at the center of the image and can be found in the <a href="ina.htm">image header</a>.<P>
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In the example image below, depths at several points have already been computed. The image has been reduced to 41% of its size for display purposes. A full resolution version is located in the VOImages folder. To try these measurements yourself, open the file 430S34 using <CITE>FILE - Acquire -PDS</CITE>. Next select <CITE>PROCESS - Rank Filters - Median Filter (reduce noise)</CITE>. The reseau marks (the grid of black dots across the image) will still be present but other "noise" in the image will be removed. Since this is a "raw" image, you can either adjust contrast and brightness levels manually by using the sliders in the <b>Map</b> window or select <CITE>PROCESS - Equalize</CITE>.
<p>
The next step is to set the scale of the image and measure the length of the shadow. Refer to the section on <A HREF="SetScale.htm">Measuring distances and areas</A> in the tutorial for details on setting the scale and measuring distances. The scale of this image is 0.068 km/px. Be sure to measure across the length of the shadow from the landform to its corresponding spot on the terminus of the shadow. The shadow lengths at points A through E have already been calculated. Compare your answers with these and then try other areas on the image.
<p>
Now you need the sun's elevation angle. For this image, the INA is 81.33 degrees so the elevation angle (90 - INA) is 8.67 degrees. Now you can use the formula given above to find the depth of the valley and craters in the image. Compare your answers with those in the table.<P>
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<IMG SRC = "GIFPICS/SHADOWS/430S34Sh.GIF">
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<TABLE BORDER>
<CAPTION>Measuring Depths using Shadow Lengths and Sun Elevation Angles</CAPTION>
<col align=left>
<col align=left>
<col align=left>
<col align=left>
<col align=left>
<TR>
<TH><I> Area</I>
<TH><I> INA (degrees)</I>
<TH><I> 90 - INA (degrees)</I>
<TH><I> Shadow Length (km)</I>
<TH><I> Depth (km) </I>
<tr><td>A<td>81.33<td>8.67<td>3.67<td>0.6
<tr><td>B<td>" " <td>" "<td>1.43<td>0.2
<tr><td>C<td>" " <td>" "<td>2.92<td>0.5
<tr><td>D<td>" " <td>" "<td>2.38<td>0.4
<tr><td>E<td>" " <td>" "<td>2.17<td>0.3
</TABLE>
<P>
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Possible Problems or sources of error with measuring shadow length from Viking images:
<p>
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1. You may be measuring a shadow length for a feature that is far from the center of the picture, where there is a significantly different sun angle.</p>
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2. You may be measuring a change in the actual brightness of the martian surface that appears to be a shadow but really isn't. You should adjust the brightness and contrast levels back and forth to be sure you are really measuring only a cast shadow. Another way of making sure what you are seeing is indeed a shadow is to look at the shape of the shadow and see if the bumps and jiggles in the shadow outline match the topography of the feature casting the shadow. </p>
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3. Your picture may have been taken at an appreciable angle in which case there is foreshortening of the shadow.</p>
