Multifractal approach to gully network interpretation of an alluvial badland terrain

Abstract

Badlands are intensely gullied lands, undergoing heavy soil losses, bereft of sustainability and are degenerative to the verdant ecosystem. This paper aims at using multifractal and lacunarity analysis to badlands systems, with the objective of offering geomorphic correlation and interpretation of multifractal parameters to understand the nature of patterns and the operative processes in badlands. Interpretability of the parameters, namely generalised dimension (Dq) versus exponent (Q), multifractal function of the component (f(α)) versus Holder’s exponent (α), (Δα), Δf (α) and lacunarity (Ʌ or λ), provides an efficient approach to comprehend and resolve the dynamic problem of badlands patterns. Four badlands sites were selected in the study area and the analysis was done using ImageJ software. The analysis showed that the sigmoidal curves of Dq versus Q decreasing towards higher values of Q (Q > 0) and the high values of Dq indicate that the badlands are typical multifractal patterns and have been densely dissected. The graphs of f(α) versus (α) are hump-shaped and are right-skewed with negative values of Δf (α), which suggests that erosion processes are active on a finer scale in the area. The greater values (Δα) show greater complexity in the study area, while the decrease in (Δα) may be indicative of adjustment of forms. The lacunarity values are very low, suggesting high intensity of dissection and homogeneity of the pattern of the system. This study may provide a basis for priority ranking for land conservation measures and in monitoring thereof in the badland areas.