Fractal modeling of airborne laser altimetry data

Airborne laser altimetry is a remote sensing technique that can provide high resolution data on the roughness of the landscape both for estimating water balance components and for distinguishing between landscapes. Models of the scale-dependent roughness are needed to find scales most appropriate for these purposes. Our objectives were to apply fractal scaling to high-resolution profiling laser altimetry data and to determine fractal parameters for differentiating land cover. Data were collected at the USDA-ARS jornada Experimental Range in New Mexico over grass-dominated and shrub-dominated sites along four transects at each site. Scale-dependent root-meansquare (RMS) roughness and data power spectrums were computed from 100,000 data points (∼2 km) from each transect. A linearity measure and piecewise linear approximation were applied to find intervals of the fractal scaling. The RMS roughness data had two intervals of self-affine fractal scaling on grass transects and four such intervals on shrub transects. Reduction in the number of data points did not lead to a decrease in roughness but caused a smoothing dependency of fractal dimension on scale. Ten- and hundred-meter scales were appropriate for distinguishing between grass and shrub transects on the basis of fractal dimensions.