Roughness Spectra Derived from Multi-Scale LiDAR Point Clouds of a Gravel Surface: A Comparison and Sensitivity Analysis

The roughness spectrum (i.e., the power spectral density) is a derivative of digital terrain models (DTMs) that is used as a surface roughness descriptor in many geomorphological and physical models. Although light detection and ranging (LiDAR) has become one of the main data sources for DTM calculation, it is still unknown how roughness spectra are affected when calculated from different LiDAR point clouds, or when they are processed differently. In this paper, we used three different LiDAR point clouds of a 1 m × 10 m gravel plot to derive and analyze the roughness spectra from the interpolated DTMs. The LiDAR point clouds were acquired using terrestrial laser scanning (TLS), and laser scanning from both an unmanned aerial vehicle (ULS) and an airplane (ALS). The corresponding roughness spectra are derived first as ensemble averaged periodograms and then the spectral differences are analyzed with a dB threshold that is based on the 95% confidence intervals of the periodograms. The aim is to determine scales (spatial wavelengths) over which the analyzed spectra can be used interchangeably. The results show that one TLS scan can measure the roughness spectra for wavelengths larger than 1 cm (i.e., two times its footprint size) and up to 10 m, with spectral differences less than 0.65 dB. For the same dB threshold, the ULS and TLS spectra can be used interchangeably for wavelengths larger than about 1.2 dm (i.e., five times the ULS footprint size). However, the interpolation parameters should be optimized to make the ULS spectrum more accurate at wavelengths smaller than 1 m. The plot size was, however, too small to draw particular conclusions about ALS spectra. These results show that novel ULS data has a high potential to replace TLS for roughness spectrum calculation in many applications.