DEM visualisation techniques: Local relief model

Trend removal is a very useful tool to extract topographic detail from DEMs. It can help us to distinguish between positive and negative deviations or “anomalies” from the general (smoothed) forms of the earth surface. But what about measuring the height or depth of these deviations? For trend removal, we simply subtract a smoothed version of the DEM from the original DEM. Any local topographic “anomalies” will smoothed rather than being removed completely. Because of this, more prominent relief features will to a certain extent still be present in smoothed version of the DEM. Ad a result of this, the relative height of such local relief features will be underestimated.

To be able to display (and/or measure) the relative height/depth of local relief “anomalies” it would therefore be good to cut out these features from the DEM and then subtract this “purged” DEM from the original DEM. Trend removal is used as a first step in this process: it results in a difference map containing positive and negative values for positive and negative local relief features, respectively.

In a second step, we can delineate the boundaries between positive and negative local relief features by finding the positions where trend removal values are zero. If we extract the DEM elevation values at these positions and fill the interjacent areas using interpolation, we have a purged DEM in which the local relief features are actually cut out.

Shaded relief image (illumination azimuth 315°, elevation 45°, no vertical exaggeration) overlaid with the zero contours derived from the trend removal map.

Shaded relief image (illumination azimuth 315°, elevation 45°, no vertical exaggeration) overlaid with the zero contours derived from the trend removal map. LIDAR data (c) LGL/LAD.

Shaded relief image (illumination azimuth 315°, elevation 45°, no vertical exaggeration) of the purged DEM. Note that while almost all relief detail has been cut out, part of the largest burial mound is still present in the purged DEM because its diameter  strongly exceeds the ow-pass filter diameter used for trend removal.

Shaded relief image (illumination azimuth 315°, elevation 45°, no vertical exaggeration) of the purged DEM. Note that while almost all relief detail has been cut out, part of the largest burial mound is still present in the purged DEM because its diameter strongly exceeds the ow-pass filter diameter used for trend removal. LIDAR data (c) LGL/LAD.

By subtracting this purged DEM from the original DEM we get what I call a Local Relief Model (LRM), which is a digital model of local relief features. This can be displayed as an image using greyscale or colour mapping. I usually use blue colours for negative and red to yellow colours for positive relief features to make it easier to intuitively read the image.

Colour-coded LRM. Note the strong circular artefact around the largest burial mound. The profile across a smaller burial mound conveys realistic relative height values.

Colour-coded LRM. Note the strong circular artefact around the largest burial mound. The profile across a smaller burial mound conveys realistic relative height values. LIDAR data (c) LGL/LAD.

The LRM does represent the height and depth of local relief features more realistically than the simple trend removal. However, because it is based on the same general approach it also suffers from the same computation artefacts as simple trend removal: there can be apparent ditches or banks which are not actually present.

When working with LRM, I usually display a colour-coded LRM as an overlay over (i.e., multiply by) a shaded relief image. That way, I can visually combine overall landscape forms and local relief details. Using vertical illumination, I see almost only the LRM colours, and by manipulating shaded relief illumination direction I can easily further enhance visibility of certain features. The colour-coding helps a lot to avoid errors due to optical illusions (i.e., apparent relief inversion).

Colour-coded LRM overlaid over a shaded relief image.

Colour-coded LRM overlaid over a shaded reliuef image. LIDAR data (c) LGL/LAD.

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