Evidence of Hierarchy in the Drainage Basins Size Distribution of Greece Derived from ASTER GDEM-v2 Data

Filippos Vallianatos,Maria Kouli

doi:10.3390/app10010248

Abstract

The drainage basins of Greece are analyzed in terms of hierarchy and discussed in view of Tsallis Entropy. This concept has been successfully used in a variety of complex systems, where fractality, memory and long-range interactions are dominant. The analysis indicates that the statistical distribution of drainage basins’ area in Greece, presents a hierarchical pattern that can be viewed within the frame of non-extensive statistical physics. Our work was based on the analysis of the ASTER GDEM v2 Digital Elevation Model of Greece, which offers a 30 m resolution, creating an accurate drainage basins’ database. Analyzing the drainage size (e.g., drainage basin area)-frequency distribution we discuss the connection of the observed power law exponents with the Tsallis entropic parameters, demonstrating the hierarchy observed in drainage areas for the set created for all over Greece and the subsets of drainages in the internal and external Hellenides that are the main tectonic structures in Greece. Furthermore, we discuss in terms of Tsallis entropy, the hierarchical patterns observed when the drainages are classified according to their relief or the Topographic Position Index (TPI). The deviation of distribution from power law for large drainages area is discussed.

Highlights

Nature displays power laws in frequency distributions of diverse phenomena [1,2]
We note that recent applications to solid earth physics [31,32,33,37] and to natural hazards [29,30,38] supports the applicability of non-extensive statistical physics in complex geosystems
In the present work we study the hierarchical pattern of drainages area distribution in Greece as extracted from an ASTER GDEM v2 Digital Elevation Model, offering a 30m resolution, enabling the creation of an accurate drainage basins’ database within a geographical information systems (GIS) environment

Summary

Introduction

Nature displays power laws in frequency distributions of diverse phenomena [1,2]. Scaling theories as expressed by power laws play an important role in quantification of scale invariance in Earth systems. The continuous evolution of the aforementioned processes, in a dynamical non-linear feedback indicates a system in a dynamical non-equilibrium stage where long-range interactions and memory effects are dominant In this context, geomorphologists have studied the evolution of drainages in time and found it to be driven by local conditions due to erosion, natural damming, tectonic motion, as well as volcanic activity [14,15,16]. We note that recent applications to solid earth physics (in regional or planetary scale) [31,32,33,37] and to natural hazards [29,30,38] supports the applicability of non-extensive statistical physics in complex geosystems To our knowledge, this is the first time that Tsallis entropy is used to express and interpret the drainage basins area distribution, within an effort to present scaling laws as extracted from first principles and not in an empirical basis. It shall be demonstrated that drainage systems are sub-additive systems with significant long range interaction where non-extensive statistical physics could be used to understand the observed hierarchical processes

Drainage Basins Extraction

Hierarchical Drainage Basins Analysis

The drainage areaQ-exponential distribution for

Discussion

Concluding Remarks