Alluvial rivers are an integral part of sedimentary systems, moving sediment from erosional source regions to sinks in which it is deposited and stored. Understanding their behaviour is crucial to interpreting landforms that develop along stream, such as cut-and-fill terrace sequences, and stratigraphic records preserved downstream. As such, a series of recent analogue and numerical modelling studies have explored how external forcings such as changes in sediment supply, precipitation rate, and base level—which, in turn, are associated with changing environmental or tectonic conditions—translate into aggradation and incision along alluvial rivers and variations in the amount of sediment they transport. In almost all cases, these studies have employed a simplified, linear geometry in which water and sediment are supplied only at the river inlet or increase continuously downstream. This simplification leads to difficulties when attempting to apply resulting concepts in field settings, where rivers form branching networks. For example, the system length is often emphasised as a key control on a river's response time, but a river network has no single length.

Here, we explore the effects of network geometries on estimates of their sensitivity to external forcing. We use a physically based model describing the long profile evolution of and sediment transport by alluvial (transport limited) rivers. We analyse large sets of randomly generated network topologies to assess the range of possible behaviours. We show how the effects of an isolated event, such as a large landslide, propagate through an entire catchment. We also investigate responses to pervasive changes in sediment production or precipitation rate. We find that sensitivity to external forcing—as well as the extent to which the network response lags behind the imposed forcing—varies significantly throughout a river network, with important implications for interpreting distributions of fluvial terraces and their ages. Nevertheless, properties that integrate over the entire catchment, such as the total sediment export, do behave in similar ways to the simplified linear case. We show that variability in sediment export is closely related to the mean catchment length (i.e., the mean distance from channel heads to the catchment outlet), more so than the maximum trunk-stream length, as might otherwise be assumed. We conclude that accounting for network geometry is critical when interpreting landforms and patterns of sediment transport within specific catchments, while linear models remain useful for predicting river networks' general behaviour.