TY  - JOUR
A1  - Heckmann, Tobias
A1  - Schwanghart, Wolfgang
T1  - Geomorphic coupling and sediment connectivity in an alpine catchment - Exploring sediment cascades using graph theory
JF  - Geomorphology : an international journal on pure and applied geomorphology
N2  - Through their relevance for sediment budgets and the sensitivity of geomorphic systems, geomorphic coupling and (sediment) connectivity represent important topics in geomorphology. Since the introduction of the systems perspective to physical geography by Chorley and Kennedy (1971), a catchment has been perceived as consisting of landscape elements (e.g. landforms, subcatchments) that are coupled by geomorphic processes through sediment transport. In this study, we present a novel application of mathematical graph theory to explore the network structure of coarse sediment pathways in a central alpine catchment. Numerical simulation models for rockfall, debris flows, and (hillslope and channel) fluvial processes are used to establish a spatially explicit graph model of sediment sources, pathways and sinks. The raster cells of a digital elevation model form the nodes of this graph, and simulated sediment trajectories represent the corresponding edges. Model results are validated by visual comparison with the field situation and aerial photos. The interaction of sediment pathways, i.e. where the deposits of a geomorphic process form the sources of another process, forms sediment cascades, represented by paths (a succession of edges) in the graph model. We show how this graph can be used to explore upslope (contributing area) and downslope (source to sink) functional connectivity by analysing its nodes, edges and paths. The analysis of the spatial distribution, composition and frequency of sediment cascades yields information on the relative importance of geomorphic processes and their interaction (however regardless of their transport capacity). In the study area, the analysis stresses the importance of mass movements and their interaction, e.g. the linkage of large rockfall source areas to debris flows that potentially enter the channel network. Moreover, it is shown that only a small percentage of the study area is coupled to the channel network which itself is longitudinally disconnected by natural and anthropogenic barriers. Besides the case study, we discuss the methodological framework and alternatives for node and edge representations of graph models in geomorphology. We conclude that graph theory provides an excellent methodological framework for the analysis of geomorphic systems, especially for the exploration of quantitative approaches towards sediment connectivity.
KW  - Geomorphic coupling
KW  - Sediment connectivity
KW  - Sediment cascades
KW  - Graph theory
Y1  - 2013
U6  - https://doi.org/10.1016/j.geomorph.2012.10.033
SN  - 0169-555X
VL  - 182
IS  - 2
SP  - 89
EP  - 103
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Phillips, Jonathan D.
A1  - Schwanghart, Wolfgang
A1  - Heckmann, Tobias
T1  - Graph theory in the geosciences
JF  - Earth science reviews : the international geological journal bridging the gap between research articles and textbooks
N2  - Graph theory has long been used in quantitative geography and landscape ecology and has been applied in Earth and atmospheric sciences for several decades. Recently, however, there have been increased, and more sophisticated, applications of graph theory concepts and methods in geosciences, principally in three areas: spatially explicit modeling, small-world networks, and structural models of Earth surface systems. This paper reviews the contrasting goals and methods inherent in these approaches, but focuses on the common elements, to develop a synthetic view of graph theory in the geosciences. Techniques applied in geosciences are mainly of three types: connectivity measures of entire networks; metrics of various aspects of the importance or influence of particular nodes, links, or regions of the network; and indicators of system dynamics based on graph adjacency matrices. Geoscience applications of graph theory can be grouped in five general categories: (1) Quantification of complex network properties such as connectivity, centrality, and clustering; (2) Tests for evidence of particular types of structures that have implications for system behavior, such as small-world or scale-free networks; (3) Testing dynamical system properties, e.g., complexity, coherence, stability, synchronization, and vulnerability; (4) Identification of dynamics from historical records or time series; and (5) spatial analysis. Recent and future expansion of graph theory in geosciences is related to general growth of network-based approaches. However, several factors make graph theory especially well suited to the geosciences: Inherent complexity, exploration of very large data sets, focus on spatial fluxes and interactions, and increasing attention to state transitions are all amenable to analysis using graph theory approaches. (C) 2015 Elsevier B.V. All rights reserved.
KW  - Graph theory
KW  - Geosciences
KW  - Networks
KW  - Spatially explicit models
KW  - Structural models
KW  - Complexity
Y1  - 2015
U6  - https://doi.org/10.1016/j.earscirev.2015.02.002
SN  - 0012-8252
SN  - 1872-6828
VL  - 143
SP  - 147
EP  - 160
PB  - Elsevier
CY  - Amsterdam
ER  -