Detrended fluctuation analysis for spatial characterisation of landscapes

The interactions among abiotic, biotic, and anthropic factors and their influence at different scales create a complex dynamic in landscape evolution. Scaling and multifractal analysis have the potential to characterise landscapes in terms of the statistical signature of the selected measure, in this case, altitude. This work evaluates the multifractality of altitude data points along transects that are obtained in several directions using Detrended Fluctuation Analysis (DFA) in a protected area adjacent to Madrid. The study data set consist of a matrix 2048 × 2048 pixels obtained at a 5 m resolution and extracted from a digital terrain model (DTM) using a Geographic Information System (GIS). We found that the distribution of altitude fluctuations at small scales revealed a non-Gaussian character in the statistical moments, indicating that Fractional Brownian modelling is not appropriate. Generalised Hurst dimensions (H(q)) were calculated on several transects crossing the area under study, all of which exhibited multifractality within a certain scale range. The results show a persistent behaviour in all directions because all of the H(q) values exceeded 0.5 and because there were differences in the intensities of the multifractality. The analysis of the directionality by means of a generalised Hurst rose plot showed differences in the scaling characteristics both along and across rivers and reservoirs. This indicates a clear anisotropy that is mainly due to the directions of the two river basins located in the area and the basement movement as a consequence of gradual tectonic displacement, which must be considered in two-dimensional DFAs.