Network analysis of sediment cascades derived from digital geomorphological maps Tobias Heckmann, Ludwig Hilger Cath. University of Eichstaett-Ingolstadt, Germany Karoline Meßenzehl, Thomas Hoffmann University of Bonn, Germany Joachim Götz, Johannes Buckel University of Salzburg, Austria contact | tobias.heckmann@ku.de Introduction Methods: From the geomorphological map to a functionally coupled network of landforms Selected results: Node, edge and network properties Conclusions and Outlook Sediment cascades represent a conceptual model of the functioning of sediment transfer through a catchment. Starting from sediment sources, different geomorphic processes mobilise or erode sediments; what is deposited on one landform may be remobilised by another geomorphic process and carried on towards the catchment outlet. Frequently, such cascades are decoupled by storage landforms acting as buffers or barriers to sediment transfer. The degree of (de-)coupling of all sediment cascades within a catchment can be called (sediment) connectivity. It is an important system property, governing the sediment delivery ratio and the sensitivity of the system to the up- and downstream propagation of change. The representation of cascading systems as networks is not new (see figure above). However, connectivity as a system property has previously not been tractable in a quantitative way (not in geomorphology - the analysis of ecosystems has made rich use of graph-theoretic indices to analyse landscape connectivity, see e.g. Pascual- Hortal & Saura, 2006). In the present contribution, we propose a network analysis framework that is supposed to be useful for the assessment of sediment connectivity. Our approach makes direct use of a „traditional“ geomorphological map, far beyond the mere visualisation of a geomorphic system. Fig. 1: Conceptual model of storage types and geomorphic processes forming a cascading system. This model represents an inter- pretation of a detailed geomorpho- logical map of the Reintal valley, Bavarian Alps (Schrott et al., 2003) References  Evans, I. S.: Geomorphometry and landform mapping: What is a landform?, Geomorphology, 137, 94–106, 2012.  Pascual-Hortal, L. and Saura, S.: Comparison and development of new graph-based landscape connectivity indices: towards the priorization of habitat patches and corridors for conservation, Landscape Ecol, 21, 959–967, doi:10.1007/s10980-006-0013-z, 2006.  Schrott, L., Hufschmidt, G., Hankammer, M., Hoffmann, T., and Dikau, R.: Spatial Distribution of Sediment Storage Types and Quantification of Valley Fill Deposits in an Alpine Basin, Reintal, Bavarian Alps, Germany, Geomorphology, 55, 45–63, 2003.  Otto, J.-C., Gustavsson, M., and Geilhausen, M.: Cartography: Design, Symbolisation and Visualisation of Geomorphological Maps, in: Geomorphological mapping: Methods and applications, Smith, M., Paron, P., Griffiths, J. S. (Eds.), Developments in earth surface processes, 15, Elsevier, Amsterdam [etc.], 253–295, 2012. 1 2 3 The geomorphological map Functional coupling of adjacent landforms The geomorphological map focuses on landforms and processes, it is created directly in a GIS, combining field observation, aerial photos and derivatives of high- resolution DEMs. Although landforms (e.g. talus cones) normally have an areal extent, their representation in digital geomorphological maps is frequently a scalable and rotatable point signature, and lines may represent parts of a landform boundary. Polygon features are reserved for genetic process domains and/or substrate (see Fig. 2). While that can be explained with scale issues, modelling areal features as points effectively prevents a GIS-based analysis of landform extent and topology. Fig. 2: Top left: Point signatures for landforms of an ArcGIS style file made available by Jan-Christoph Otto Right: An example of a digital geomorphological map making use of point, line and polygon signatures (Otto et al., 2012). Fig. 3: On the geomorphological map of the Gradental valley, arrows link pairs of adjacent landforms that are coupled by the activity of (at least) one geomorphic process. With the landform map in the background, and using diagnostic features indicative of the activity of geomorphic processes, directed line features are digitised. These lines represent either the functional coupling of adjacent landforms, or sediment re- distribution within one landform (Fig. 3). Creation and analysis of a graph representing sediment cascades Using standard GIS procedures, the start and end nodes of the line features are intersected with the landform polygons. The result is an edgelist (Fig. 4) that can be converted to a graph. While the mapped landforms form the nodes of the graph, the edges linking some of the nodes represent functional coupling, i.e. active or probable sediment transport between the corresponding landforms inferred from diagnostic features. Analysis of the network includes * the classification of nodes (sediment sources, sinks, links) based on the node degree * statistics of paths, i.e. edge sequences, that represent sediment cascades: their length and the corresponding succession of geomorphic processes * ranking edges by their importance (here: „betweenness centrality“) * identifying number and size of connected components (subgraphs) within the system * computing indices relating to network structure (density, connectivity) edgeID fromStorage toStorage process 1 X010201 X0102 uvial transport 2 X010202 X0102 debris fall 3 X010501 X0105 debris fall 4 X010502 X0105 uvial transport 5 X011501 X0115 debris fall 6 X012001 X0120 debris fall 7 X013601 X0136 debris ow Fig. 4: Edgelist generated from the intersection of sediment pathways and mapped landforms bedrock 0.83 colluvial deposit 0.83 debris cone 0.42 debris ow channel 1.00 talus sheet 0.75 hillslope debris ows 0.50 alluvial 0.58 moraine deposit 0.33 protalus rampart 0.08 bedrock 1.00 alluvial plain 0.75 moraine 0.58 mire 0.50 talus sheet 1.00 debris cone 0.42 talus cone 0.25 rock glacier 0.42 complex valley ll deposit 0.42 alluvial fan 0.33 glacier 0.17 rock fall deposit 0.17 lake 0.25 mass movement 0.08 1 2 3 4 5 6 Path length distribution path length [edges] Frequency 0 100 200 300 400 1 2 5 0.002 0.010 0.050 0.200 1.000 Degree distribution log Node degree log Emp. CDF 1 2 5 10 20 50 100 0.005 0.020 0.050 0.200 Degree distribution log Node degree log Emp. CDF 1 2 3 4 5 Path length distribution path length [edges] Frequency 0 50 100 150 200 250 graph density: 0,003 graph density: 0,001 edge betweenness centrality edge betweenness centrality < System structure > The two graphs summarize the topology of landforms coupled by active sediment transfer, and thus the configuration of the catchment‘s sediment cascades. The edge thickness represents the number of edges linking the respective landform, while the number associated with each node is the relative node strength (weight of incoming and outgoing edges) Sediment cascades originating from the spatial and functional interaction of geomorphic processes have often been conceptualised as networks. However, the tools of graph theory have not yet been applied to such networks. We have proposed a framework enabling the use of geomorphological maps for analytical instead of only visualising purposes. The map is used for the set-up and analysis of graph models representing the spatial configuration, topology and coupling of landforms within a study area. While geomorphic coupling needs to be inferred from diagnostic features through expert knowledge, the assessment of the overall system configuration becomes less subjective, as it is calculated from all coupling relationships between adjacent landforms. Future work needs to * explore graph theoretic analysis of such networks * link graph properties to geomorphic system properties, such as connectivity and its consequences (e.g. sediment delivery) This can be achieved by comparative studies. One measure of connectivity could arise from the comparison of actual graph properties with those of a completely coupled network of ow lines in the same study area. Cooperation is highly welcome ! “The general-purpose geomorphological map may be dead, but long live geomorphological maps! [...] With the abundance of data now available, and the range of visualisation techniques, geomorphological mapping is more important than ever before.” (Evans, 2012) Gradental catchment, Upper Tauern, Austria (geom. map by J. Götz and J. Buckel) Val Müschauns catchment, Swiss Alps (geom. map by K. Meßenzehl and T. Hoffmann) Legend 5 Start/end nodes of edges Geomorphic coupling speicher_3D_V22 landform alluvial fan alluvial plain bedrock complex valley ll deposit debris cone glacier lake mass movement mire moraine regolith rock fall deposits rock glacier (active) rock glacier (inactive) talus cone talus sheet