Method: Measuring Profiles using Straight-Edge Shadow Back to main page

The topographical cross-sectional profile of dune features (eg., cornices, troughs, avalanche tongues) can be measured by making use of the shadow cast by a straight-edge, as described by Werner et al (1986) and Anderson (1988). Here is a variation of that technique.

 Fig 1. Side view

In figure 1 to the right, a square aluminum extruded tube casts a shadow on a surface of interest. The tube is rotated such that it casts a minimum-width shadow (ie., its top and bottom surfaces are parallel to the light source rays).

Figure 2 below shows the same scene as viewed from above. Both the upper and lower edges of the tube cast a shadow edge that we can use to determine the profile of the surface, assuming the surface profile is uniform over the span of each shadow edge (we can obtain some confidence that the profile is uniform if, as in figure 2, the two shadow edges have identical shape).

 Fig 2. Top view

Scale can be obtained from the width of the shadow, which is cast by the known width of the tube (recall that the tube was rotated such that the shadow had minimum width). From this the profile of the surface can be obtained from either shadow edge, with respect to a baseline (in this case, a line drawn between the knickpoints where the shadow crosses from white to purple).

Whether the tube needs to be level or aligned with the object of interest depends what is being measured (in figure 2, the desired surface profile is with respect to the purple surface, and so a slight skew caused by the bar not being level makes little difference).

The ideal light would be a point source at infinite distance perpendicular to the bar. The best angle of the light involves a trade-off between sensitivity (the lower the light angle, the longer the shadow) and the distance over which the object profile ought to be uniform (the longer the shadow, the greater the span).

To minimize distortion, try to photograph from directly above the shadow, perpendicular to the surface, as far away as possible and with maximum zoom (ie., smallest field of view). This minimizes the variation of angle of view over the photographic frame. (To get a feel for this, try photographing the inside of an open box -- how far back do you have to go, using how much zoom, to not see the walls of the box?) (Can you tell that figure 2 was generated with a not-great-choice 35° field of view from not very high above the surface? Notice how little of the light-facing white surface of the square tube is visible.)

Square-tube extruded aluminum is rigid, light, and fairly inexpensive, available at hardware stores. Rigidity can be assessed while at the store simply by sighting along a piece of the desired length. Of course other geometries can be used, such as a square tube (or right-angle extrusion) resting on the surface.

#### Example: Finding the profile of the toe of an avalanche tongue

 Fig 3. Avalanche tongue

Here the straight-edge is provided by the vertical leg of an right-angle-bar of extruded aluminum, with the vertical leg placed on the shadow side, resting on the surface of an avalanche tongue (figure 3). This was a 1-meter length of 1/16-inch aluminum with 3/4-inch equal-length right-angle legs (width), which costs maybe US\$10 for an 8-ft length at a hardware store.

The height of the bar will be used to scale the shadow, so it is important the bar be resting on the surface of the sand, as shown in figure 4, not pressed into the sand. (The bamboo skewers at either end of the bar in figure 4 prevent the bar from sliding downslope.)

(A longer square tube elevated by supports would have been better, but this right-angle piece was on-hand for other reasons.)

Fig 4. Side view of straight edge resting upon avalanche tongue

The shadow is photographed perpendicular to the surface (figure 5). A photographic reference scale was placed in the photo for redundant scale; the rise of the bar is also known.

Fig 5. View perpendicular to slipface

If we assume:

• the angle-bar is resting on the surface, and
• the surface is unchanging perpendicular to the bar for the span of the shadow,

then the minimum shadow length will be cast at the points at which the bar is resting on the surface, and that shadow length, cast by the known height of the bar, can be used to scale other parts of the shadow. The measurements can be carried out easily using a photo-editing package such as Photoshop, either by measuring lengths in pixels and scaling externally (eg., using a spreadsheet program) or in the tool itself, if it supports that (eg., Photoshop Extended).

In this case, the measurements were taken with respect to a base line drawn between the endpoints where the shadow hits the slipface outside the avalanche tongue (resulting in the cyan area in figure 6).

An estimated equal-scaled profile of the object can be obtained by vertically scaling the photo (figure 5) in a photo editor by the scaling factor found above. Figure 6 shows the avalanche tongue's profile-above-surface in equal horizontal and vertical scale, with the profile coloured cyan. Photoshop Extended CS3 can provide the area of the shape, which in this case is 142 cm2. Of course scaling the profile in this manner assumes object's profile was constant over the span of the shadow (otherwise the oblique profile obtained from the shadow cannot be mapped to the perpendicular profile without knowing more about the surface variations).

Fig 6. Scaled to true dimensions

The profile obtained here is an estimate of that of the avalanche tongue not at the point at which the bar rests but between the minimum and maximum points of the shadow. You'll notice the avalanche tongue narrows slightly in that interval and the surface isn't constant, which means this profile is an approximation.

#### References

Anderson, R.S. 1988. The pattern of grainfall deposition in the lee of aeolian dunes. Sedimentology 35:175-188

Werner, B.T.; Livi, R.; Haff, P.K.; Anderson, R.S. 1986. Measurement of eolian sand ripple cross-sectional shapes. Geology 14:743-745.