Detrended fluctuation analysis for spatial characterisation of landscapes

Abstract

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 x 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.

Long‐range correlations of soil water content time series under tillage and different cover crops in a semi‐arid vineyard

“…Subhakar and Chandrasekhar (2015, 2016) made use of DFA, MFDFA and multifractal singularity spectra of geophysical well‐log data to identify the tops of reservoir zones and to characterize sedimentation patterns and lithological differences. Castellanos, Morató, Aguado, Monte, and Tarquis (2018) analysed landscapes through MFDFA of altitude of data points along transects from different directions. Cao et al (2020) also made use of elevation data of terrain profiles of gully shoulder lines to detect active gully erosion sites.…”

The long-range correlation and evolution law of centennial-scale temperatures in Northeast China

“…This means that there are still significant correlations between long-separated time periods and that the past status can continue to affect the current and future statuses of the system. The DFA method has been successfully applied in many fields including noise analysis, medical physiology, geology, economics[ 21 – 24 ] and meteorology[ 25 – 30 ]. Generally speaking, the observation stations at Harbin, Changchun, and Shenyang are located in areas that represent the typical climate in the Northeast region.…”