Fractal dimension estimations of drainage network in the Carpathian–Pannonian system

Abstract

The development of drainage network in the intra-Carpathian realm is influenced by a complex Quaternary tectonic evolution manifested with differential vertical motions. The present-day configuration of the left-hand side tributary system of the Tisza river was studied by means of fractal analysis. Fractal dimensions describing the complexity of the network were obtained by different methods. These include the early estimations based on stream ordering hierarchy and the application of the box-counting and sandbox algorithms representing fixed-size algorithms considered as efficient tools in fractal set analysis. Besides calculations made for the entire drainage system, the region was subdivided into three distinct areas characterised by different Quaternary uplift history. These are the Apuseni Mts., the Transylvanian basin and a part of the Eastern Carpathians, investigated separately. The concept of multifractality was also taken into consideration and dimensions of both higher and lower orders were determined along with the corresponding singularity spectra. Non-space-filling and multifractal behaviour of the network structure was validated. However, small but tendentious variations of the support dimensions (D0) were observed in the three sub-regions. The Transylvanian basin is characterised by the lowest estimated dimensions, while higher values represent the Apuseni Mts., and the western slopes of the Eastern Carpathians. In addition, fractal dimension values showed consistency within each sub-region. Correlation of these measures with average uplift rates was performed. As a major outcome, differential uplift, affecting the morphology of catchments, appears to influence the obtained fractal dimensions, whereas surface lithology conceivably plays only a secondary role.