1. A trendy concept for old questions

1.1. A recent and spectacular scientific upturn

1“Old wine in new bottle”, here is Bracken's skepticism (Bracken et al., 2015) regarding the concept of hydro-sedimentary connectivity at the conclusion of a special issue of Earth Surface Processes and Landforms, dealing specifically with connectivity. This skepticism is due to the recent and spectacular infatuation of geomorphologists for this concept, particularly perceptible in the rhythm of publications mentioning the term connectivity in their title (fig. 1). However, we should remind that the scientific milestones of hydro-sedimentary connectivity were raised nearly half a century ago with the successful formalization of the functioning of open systems in geomorphology (Chorley and Kennedy, 1971; Schumm, 1977). These authors have shown that the continuum between supply, transport and deposition depends not only on the volume of sediment supplied by upstream sources, but also on the connecting patterns between the different components of the system. McGuiness et al. (1971) for instance illustrate that sedimentary signals can be largely desynchronized at various points in a watershed (exhibiting a “spatial and temporal paradox”) (fig. 2). In this way, the ability of a watershed to efficiently transfer sediments is related to its ability to propagate disturbances associated with external forcing, i.e. “sensitivity” (Brunsden and Thornes, 1979). These pioneering studies carried out during the 1970s have emphasized two main applications of the connectivity concept for geomorphologists. This term is used both to predict the volume of sediment exported to the outlet of a catchment, as well as to explain the rhythmicity of sediment signals and, therefore, the way in which they are a proxy of past and present environmental changes (e.g., climatic, anthropogenic, tectonic, etc.).

1.2. Connectivity and exportation of sediments

2A large part of the studies using the term connectivity is aimed at explaining why the proportion of sediment exported to the outlet of catchment areas remains low, well below the supply of sediment from upstream sediment sources. This refers to the sediment delivery problem (Walling, 1983), exhibited from sediment balances carried out at the scale of catchment areas of several thousand square kilometres. In these catchments the rate of exported sediment (relatively to sediments supplied by sources) is estimated to be between 1% and 15% (Slaymaker, 1977; Milliman and Meade, 1983; Trimble, 1983; Milliman and Syvitski, 1992). The geomorphic inefficiency of catchment basins is directly related to the disorganization of the sediment cascade. A sediment cascade can be defined as the flowpath (direction) of sediments between various types of sediment sources, temporary sinks, and the outlet. Following these studies at a large scale, it is assumed that geomorphological processes within the catchment can have antagonistic effects. More specifically, the coupling patterns between geomorphological processes may explain the rate of sediment export in general (Fryirs, 2013) and the trend to sediment impoundment (Walling, 1983) in particular.

3To explore such complexity of catchments, Harvey (1997) suggests a focus at several spatial scales, trying to open up the “black boxes” that remain along sediment pathways. The coupling zones between components such as “buffers”, “barriers”, “blankets” (Fryirs, 2013) are of prime importance. A spatial organization of sediment cascade as a whole emerges from the combination of all buffers, barriers and blankets. Nevertheless this global pattern (i.e. efficiency of the cascade to deliver sediments at the outlet) remains difficult to predict.

4The concept of connectivity leads to considering the catchments as a complex system, whose behaviour results from the emergence of a multitude of local interactions (Miall, 1996; Schumm, 2005). In other words, the first step is to study on a fine-scale the functioning of connectors and regulators, which locally activate or hinder sediment flows in sediment cascades. Then, the question is to predict how the combination of existing coupling patterns affect the global sediment delivery: the development of modelling methods is then required. Such developments can be made through graph theory (Heckmann et al., 2015; Cossart and Fressard, 2017) or the use of differential equations (Cossart, 2016). Such geomorphic expertise has been widely developed in France, with several studies on the development of geographical methods to predict the emergence catchments functioning based from local interactions (Delahaye et al., 2002; Douvinet et al., 2008; Viel, 2012; Reulier, 2015; Reulier et al., 2016).

1.3. Connectivity and sedimentary signals

5Harvey (1997) also argues for a focus on the sediment variability over time. Indeed, the coupling of geomorphic processes may contribute efficiently to a sedimentary export, or on the contrary may be antagonistic, causing hindrances. Such combinations can throw a disturbance on classical interpretations of the sedimentary signals i.e. “sedimentological anarchy” (Walker, 1990), so that “erratic behavior –of the geomorphological system– may be exhibited” (Bravard, 1998).

6This question refers to the modeling of self-organised critical systems (SOC: Self-Organized Criticality) defined by Bak et al. (1987, 1988). This is a group of models that describe a dynamic system that spontaneously places itself in a critical situation (self-organized criticality): stresses are accumulated locally up to a breaking point that corresponds to the critical threshold of the system's resistance to this constraint. In geomorphology, the self-organization of sedimentary cascades is characterized in particular by non-linear temporal dynamics in the occurrence of disturbance events in the system or by the existence of a mechanism by which the same process can initiate both low and high magnitude events (Roussel et al., 2016). In other words, the sedimentary cascades can be considered a jerky conveyor belt (Ferguson, 1981). There are many examples in which the sedimentary signal is characterized by sporadic pulses (Fort, 1987) thus reflecting the internal self-organization of a sedimentary cascade and not the response to external forces (Heckmann and Schwanghart, 2013). So the concept of connectivity finally invites us to go beyond the sometimes simplistic interpretations of peaks and pulsations of sediment, interpretations often based on Anthropogenic-Climatic-Tectonic forces.

2. Why applying the conceptual framework offered by connectivity?

2.1. A framework for studying networks and interactions

7In many scientific disciplines, it appears that the term connectivity makes it possible to decipher the functioning of networks and interactions, and thus the functioning of the systems linked to them. For example, ecological connectivity is defined as “all the functional and effective linkages necessary for the functioning, stability and resilience of ecosystems over the long term” (Bennett, 2004). In geography, the connectivity of a network is seen as “all the links that connect one place to another” (Pumain and Saint-Julien, 2010). In these two definitions, we emphasize the need to study both the unitary links between two places, two objects, and the assemblage formed by these links on a larger scale. For this reason, several authors suggest to distinguish the term “coupling” for the study of elementary links, and to use the term “connectivity” for the study of the assemblage of these links (Faulkner, 2008; Heckmann and Schwanghart, 2013). In the latter case, the emphasis is then placed on identifying the zones which are organized into an effective sedimentary cascade, which can ensure a transfer to the outlet, and the zones which are disconnected from the cascade, and which do not contribute to the sediment supply at the outlet.

8Connectivity is therefore a time-tested concept progressively defined in various sciences, and quite recently in geomorphology (Cossart and Fressard, 2017). This concept is by no means innovative (Bracken et al., 2015) but have been used in different disciplinary fields to study networks of various types. In this issue of the journal Géomorphologie: Relief, Processus, Environnement, the article by Bourgeois et al. shows that the conceptual framework of connectivity is robust, allowing comparisons and even dialogue between disciplines. Without doubt, it will be possible to lift the locks in geomorphology by drawing inspiration from the developments produced by ecologists, sociologists and mathematicians who preceded us in mobilizing this concept. The way in which our colleagues have measured connectivity through indicators and the way they have formalized their datasets to make these measurements will certainly lead to applications for modelling sediment cascades.

2.2. Structural connectivity

9In geomorphology, the concept of connectivity encourages the study of the arrangement of links that feed a sedimentary cascade at the catchment scale (Cavalli et al., 2013). This study can focus on the structure or skeleton of the cascade (structural connectivity) in three main aspects. The first is to identify chains of links ensuring an efficient coupling, structuring the cascade. The second is to carry out a typology of these links: typology of the sediment sources/stores connected in a recurrent way, typology of the processes ensuring the connection. The third is geometric and aims to identify places where sediment flows particularly converge in the sedimentary cascade. A hierarchy of these convergence points may be proposed according to the size of the area that contributes to feeding this point, or according to the number of links that feed it. Such method allows the identification of some hotspots, which play a major role in the functioning of the sedimentary cascade. The article written by Fressard et al. in this issue makes such a study in an agricultural catchment area. It exhibits how some disruptions at these hotspots disorganize the sediment cascade, and consequently prevent soil losses.

2.3. Functional connectivity

10To complement a focus on structural connectivity, some studies can be carried out on the elementary processes and interactions that exist locally within the catchment area (e.g. local interactions between geomorphological processes, interactions between landscape/anthropic processes and infrastructures, etc). Within the framework of these functional studies, i.e. “process-based connectivity” (Bracken et al., 2015) the challenge is methodological, inherent in any study of a complex system whose behaviour emerges from local interactions. The article by Reulier et al. exhibits an example of methodological development based on Agent-Based Systems. This tool makes it possible to implement the interactions that exist locally between geomorphological processes and anthropogenic infrastructures, and then to predict the importance of the latter in hindering or exacerbating sediment flows.

3. Some perspectives

11Connectivity makes it possible to characterize spatial patterns within sedimentary cascades, to understand how they provide coherence and consistency to the network. Such patterns directly reflect the resilience properties of the sedimentary cascade and its sensitivity to change (Brunsden and Thornes, 1979). In this way, numerous articles have been published some methods to characterize, but also to measure connectivity (Cavalli et al., 2013): examples of some indices are presented in this issue.

12While they are efficient, we still have to make progress in the development of some indices that allow comparisons between study cases, and comparison through time. We also have to make progress in the interpretation of connectivity. What does high connectivity mean? At the scale of the whole catchment area: is it an ability of the network to react to external forcing? Is connectivity necessarily benefic? For example, the Water Framework Directive (2000/60/EC) requires the improvement of hydro-sedimentary connectivity in catchment areas by dismantling obsolete structures. The objective is to restore the quality of watercourses, but what about the risk of flooding or the spread of pollution? (Viel et al., 2014). At an intra-network scale: what are the hotspots identified by their ability to be well connected to all components of a sedimentary cascade? Geomorphologists assume that the dysfunction of such hotspots (e.g. disruption), can lead to a significant change in the initial organization of the sedimentary cascade (fig. 3). A concomitant question regards the meaning of a “geomorphological organization”. In the articles in this issue, it can correspond to the complexity of the mutual interactions that characterize the sedimentary cascade. Second, it can correspond to the space required for the development of upstream/downstream spatial relationships between geomorphological processes (fig. 3A). Within a sedimentary cascade, the dysfunction of the point with the highest connectivity would lead to a split into several independent systems, as equivalent as possible, so that none of them could reach the level of organization of the initial system (fig. 3B). Interpretation of connectivity values is however at its beginning.

13In conclusion, geomorphological connectivity is conducive to geographical reasoning: the community of geographers (including human geographers) has developed a scientific expertise of a spatial analysis of networks. This expertise confers a scientific legitimacy on our community, a legitimacy that is complementary to that of geosciences for the study of sedimentary cascades. Secondly, the recurrent use of the connectivity concept is probably due to the trivialization of numeric tools (e.g. mathematics, computing) allowing the modelling of geomorphological systems: it is now possible for us to support the reasoning formalized by the pioneers of the 1970s. For our community this conjunction is thus a wonderful opportunity!