Abstract Applications of graph theory have proliferated across the academic spectrum in recent years. Whereas geosciences and landscape ecology have made rich use of graph theory, its use seems limited in physical geography, and particularly in geomorphology. Common applications of graph theory—analyses of connectivity, path or transport efficiencies, subnetworks, network structure, system behaviour and dynamics, and network optimization or engineering—all have uses or potential uses in geomorphology and closely related fields. In this paper, we give a short introduction to graph theory and review previous geomorphological applications or works in related fields that have been particularly influential. Network-like geomorphic systems can be classified into nonspatial or spatially implicit system components linked by statistical/causal relationships and spatial units linked by some spatial relationship, for example by fluxes of matter and/or energy. We argue that, if geomorphic system properties and behaviour (e.g., complexity, sensitivity, synchronisability, historical contingency, connectivity etc.) depend on system structure and if graph theory is able to quantitatively describe the configuration of system components, then graph theory should provide us with tools that help in quantifying system properties and in inferring system behaviour.

Graph theory - recent developments of its application in geomorphology

In recent years the concept of connectivity has emerged in sediment management to describe transfer of sediment from different sections of landscapes at various spatial and temporal scales. The sediment connectivity concept has two distinct components: structural and functional. Structural and functional sediment connectivities have a hard and soft nature, respectively, in which the former relates to physical characteristics and the latter to soil erosion and sediment transport processes. Although there has been an increase in sediment connectivity studies over the last decade, disagreement and confusion seems to remain about conceptual and especially methodological approaches, related indices, methods of quantifying sediment connectivity at a range of spatial and temporal scales, and the current situation in sediment connectivity research. A review of the relevant literature is needed to address these issues and provide a holistic overview of different aspects of sediment connectivity which would enlighten the directions of future research. In this review, 117 papers have been classified into five different categories, namely (i) developing conceptual frameworks; (ii) depicting spatial and temporal distribution of sediment source and sink areas; (iii) developing sediment connectivity indices; (iv) using and developing models; or (v) investigating sediment delivery likelihood through a network analysis approach. The reviewed contributions within each category were 8%, 23%, 55%, 10% and 4% papers respectively. The results indicated that more studies at both global and local scales are necessary to achieve a comprehensive conceptualization of sediment yield and related processes using sediment connectivity. Most studies have concentrated on static characteristics rather than dynamic aspects of connectivity, leading to mainly structural-based methods and indices, resulting in less attention being paid to functional connectivity. Process-based sediment connectivity studies, by focusing on spatio-temporal variations of sediment transport throughout a watershed, will therefore be a crucial aspect in future studies.

Sediment connectivity concepts and approaches

In agricultural lands, the way in which slope position affects the detachment of material and the runoff generation is not clear. There are complex interactions between slope position, slope gradient and a series of soil characteristics, and their impact on runoff generation and soil erosion may vary from site to site. We designed an experiment to investigate the initial hydrological responces of soils located on different slope positions (footslope, backslope and shoulder) in runoff and soil detachment generation. To achieve these goals, 25 high-intensity low frequency rainfall events were simulated in experiments with a return period of 5 years, on 0.25 m2 circular plots to measure the detachment along a hillslope in the Celler del Roure vineyards in Eastern Spain. The results of this investigation showed that soil erosion rates (3 Mg ha−1 h−1) were high and there were no significant differences between sites in relation to slope position; all the plots generated runoff (runoff coefficient of 24.8%). These results allow us to conclude that soil detachment and runoff generation in Mediterranean vineyards, where tillage is millennia-old management practice, could be also evenly distributed. Therefore, the used management practices in these vineyards contribute to creating net source areas of runoff and erosion with no areas that could act as a sink under intensive rainfall events. Based on our research and a literature review, we propose to implement nature-based solutions that would contribute to reducing soil erosion in agricultural land by creating sink areas in the form of hedgerows, ponds, or vegetation strips where the surface wash deposits and water can sediment and infiltrate. We also discussed other management practices contributing to reduction of erosion,such as mulching and inter-row crops. We state that there is an urgent need to apply strategies to reduce soil loss in vineyards.

Is the hillslope position relevant for runoff and soil loss activation under high rainfall conditions in vineyards

New trends related to market incomes, cultural human development, non-sustainable soil management practices, and climate change are affecting land abandonment in Mediterranean sloping vineyards. It...

https://journals.sagepub.com/doi/pdf/10.1177/1178622119839403

Analysis of Weather-Type-Induced Soil Erosion in Cultivated and Poorly Managed Abandoned Sloping Vineyards in the Axarquía Region (Málaga, Spain):

Mapping water and sediment connectivity.

A graph theory tool for assessing structural sediment connectivity: Development and application in the Mercurey vineyards (France).

In France, in the context of regulatory mapping (PPRNs –Prevention Plans of Natural Risk based on French regulatory rules), landslide hazard assessment follows an empirical approach and uses basic available data. Therefore, the results are closely linked to the quality of the expertise and divergent opinions may arise in some specific cases. In recent years, numerical approaches using GIS, the availability of new databases, the development of new acquisition tools in the field and web visualization services have improved the knowledge of phenomena and different landslide-prone areas. Numerical approaches using GIS, that allow the transparency and traceability of results, have various levels of complexity and require different quantities of input data. However, they are often neglected by experts and new data and tools are not currently used to develop regulatory mapping documents. Numerous scientific examples show that these numerical approaches, web services and new tools can be a significant help in improving knowledge and provide a credible alternative to the expert approach, even in a regulatory context such as a PPRN. Thus, through this synthesis carried out as part of the regulatory mapping of landslide hazards and risks in France, a state-of-the-art spatial assessment of current landslide hazards is performed. The new tools and newly available databases to support this type of analysis are then described. Finally, the perspectives and limitations of alternative approaches and new tools and data are discussed, leading to some considerations for the improvement of the current method of producing landslide hazard maps for PPRNs in France.

Mathieu Fressard

Papers

A graph theory tool for assessing structural sediment connectivity: Development and application in the Mercurey vineyards (France).

Improvement of landslide hazard assessments for regulatory zoning in France: STATE–OF–THE-ART perspectives and considerations