When modeling terrain with lidar, it is important to be aware of the difference between elevation data quality and positional accuracy. In many instances, users of lidar data focus solely on point cloud accuracy as specified by sensor manufacturers, but an accurate lidar point cloud does not necessarily result in accurate modeling of the terrain, nor will it create accurate volumetric calculations: elevation data must also faithfully represent the terrain detail. Therefore, users should also consider point density as it relates to terrain roughness or smoothness, as this is an equally important aspect of accurate terrain modeling.
Terrain modeling methodologies (e.g., polygon-based Regular Triangulated Networks (RTNs) versus Triangulated Irregular Networks (TINs) versus Voxel-Based Networks) also affect the terrain model quality. Terrain analysis is sensitive to whether the software represents the point cloud as a TIN, a gridded surface, or an RTN. Methods that involve gridding the data are sensitive to grid cell size (post spacing). Note that lidar point density is an important factor when choosing grid cell size.
The Figure below illustrates the relationship between terrain roughness and point density. While the point cloud in this example may have a vertical accuracy of RMSEV = 10-cm, TIN interpolation based on surrounding areas of low point density places the vertical position of point A at point A’, resulting in a vertical error of 2 meters in this example. The remedy is to obtain the point cloud at a higher density so that it more accurately represents the terrain detail. Attempting to use a low-density point cloud to represent terrain with high frequencies of undulation will result in inaccurate volume estimations, regardless of what software or modeling algorithms are used. Smoother terrain may be adequately represented with a lower density point cloud. Very smooth or flat terrain can be accurately modeled using a point cloud with nominal post spacing (NPS) of a few meters or coarser.
The Nyquist-Shannon sampling theorem, which is well-known and widely used in signal processing, may be used to determine the point density required to accurately represent the project terrain. According to the Nyquist-Shannon sampling theorem, if a signal x(t) contains no frequencies higher than B Hz, then a sampling rate of greater than 2B samples per second (or 2B Hz) will be needed in order to reconstruct the original signal without aliasing.
For example, let us assume that the undulation rate of the terrain represents the highest frequency of the signal to be modeled, and the nominal point spacing represents the sampling rate needed to model the terrain without aliasing. If we want to accurately model rocky terrain where the spikes caused by these rocks appear every 30 cm on average, the nominal point spacing of the lidar data used to model this terrain should be less than 15 cm.