3.3 Interpolating elevation data
Most sources of elevation data do not measure elevation at all locations. Interpolation is therefore necessary in order to estimate the elevation at locations in between measurement points. This learning object investigates methods for interpolating elevation.
Most data sources require some interpolation to produce a DEM. For example, the elevation of points in between contours on a paper map needs to be interpolated. Similarly, a field surveyor cannot visit every location in a study area and elevation for the unsurveyed locations must be interpolated. In LIDAR data, elevation for points on the ground’s surface beneath a tree canopy will also need to be interpolated.
Why interpolating elevation is different
Most GIS systems include general purpose tools for interpolating between measurement points. However, elevation has particular properties that make its interpolation rather different to other types of data.
Interpolating elevation, particularly from contour lines, therefore requires specialist rather than general purpose interpolation techniques.
Techniques for interpolating elevation
One of the earliest techniques for interpolating elevation from contours is the CONSURF algorithm developed by David Douglas. The CONSURF algorithm starts by converting all contours to a raster grid and then estimating the elevation values between contours along the four outside edges of this grid. In the next step, the gradient of each cell between the contours is estimated along the rows in the raster grid. Linear interpolation is used to also estimate the elevation values between contours along each row. The method then calculates gradients and interpolates elevation along the columns of the grid. Finally, gradients and elevation values between contours are calculated by looking along the two diagonals (top right / bottom left and bottom left / top right) in the grid. Out of the four interpolated elevation values (from the rows, from the columns and the two diagonals), the one associated with the steepest slope is retained and used in the final DEM.
Today, perhaps the most widely used technique for interpolating elevation from contours is Hutchinson’s ANUDEM algorithm, which can be used in the ArcGIS system via the TOPO TO RASTER command. This interpolation method not only uses contours, but also uses surface drainage lines such as streams and rivers. The ANUDEM method ensures that in the output raster grid of elevation, rivers and streams always flow downhill.
Checking the quality of an interpolated DEM
The technique used to interpolate a DEM can potentially have a large impact on the elevation values in each grid cell. Terrain ‘artifacts’ (spurious features caused by the interpolation method) can sometimes occur. As a result, several methods are used to check the accuracy of an interpolated DEM.
- Can you think of reasons why interpolating elevation might be different to interpolating, say, soil pH?
- In general, there tend to be few sharp breaks within an elevation surface. Cliffs and crags occur infrequently and overhangs are even rarer.
- In many cases, contours digitised from paper maps are often used to produce DEMs although LIDAR, radar and photogrammetry are becoming increasingly important. Unlike other types of data, interpolation of elevation therefore involves the use of polylines and not points.
- Although they do not directly measure elevation, streamlines can provide information about the shape of the land. For example, water should flow downhill along a streamline and this says something about the relative height of the land along a stream's course.
- Can you think what methods you might use to check how well an interpolation from contours has worked?
- If the original data set included spot heights (points) as well as contours (lines), then these spot heights can be used to check the quality of the interpolation. The elevation values for spot heights can be compared to those interpolated for the DEM.
- Another option is to produce contours from the interpolated DEM. These contours can then be compared back against the original contours used to produce the DEM in the first instance. If the two are substantially different, then this implies problems with the interpolation process.
- Many GIS analysts often calculate slope and aspect from the interpolated DEM too. Terrain 'artifacts' can often be detected by examining these slope and aspect maps and looking for abnormal features, such as very steep slopes, 'steps' in the terrain, or sudden changes in slope.
- Download the attached
zip file and undertake the activity, which involves interpolating an elevation model from contour data.
References (Essential reading for this learning object indicated by *)
The ANUDEM software (also implemented as TOPO TO RASTER within ArcGIS) is one of the best known methods for interpolating elevation from contours: http://fennerschool.anu.edu.au/research/products/anudem