Network geometries influence responses of alluvial river systems to external forcing

Alluvial rivers transport sediment from erosional source regions to sedimentary basins downstream. Erosion and precipitation rates control their sediment and water supplies, tectonic processes drive uplift or subsidence along their lengths, while sea or lake levels set their base levels. Changes in these external conditions cause them to adjust their slopes and sediment transport rates. Geomorphic and stratigraphic archives that develop alongside and downstream of alluvial rivers may therefore record information about past climatic and/or tectonic change and their influence on landscapes. Much recent work has aimed to understand precisely how alluvial rivers respond to changes in external forcing, using a range of numerical and laboratory modelling approaches. Many of these conceptual studies have used a simplified, one-dimensional spatial domain in which sediment and water discharge are either held constant or increase continuously downstream (e.g., according to Hack's law). Such studies have emphasised, among other important findings, that the timescales over which a system responds to external forcing is strongly influenced by its length. However, in real rivers, water and sediment accumulate at discrete intervals as tributary streams coalesce. This discrepancy complicates the application to real catchments of concepts developed in one-dimensional modelling studies, since, for example, the 'length' of a river network is not clearly defined. Here, we explore how incorporating realistic network geometries influences the behaviour of an alluvial river model. We use a model describing the long-profile evolution of transport-limited gravel-bed rivers which takes a non-linear diffusive form. We construct networks by linking individual segments, so that their sediment and water supplies are set by segments immediately upstream and their base levels are set by segments immediately downstream. We show that significant complexity can arise locally, so that studies aiming to understand specific segments within a catchment should take into account the geometry of that catchment. However, properties that integrate over the entire catchment, such as its total sediment export, are adequately predicted by a simplified one-dimensional model—provided an appropriate lengthscale is chosen. We conclude that, while care is required in some circumstances, one-dimensional models can provide useful insights into the general behaviour of alluvial river networks.