The length and spacing of river tributaries.

River networks are composed of a mainstem and tributaries. These tributaries dissect landscapes, regulate water and habitat availability, and transport sediment and nutrients. Despite the importance of tributaries, we currently lack theory and data describing whether and how tributary length and spacing varies within watersheds, thereby limiting our ability to accurately describe river network geometry. We address this knowledge gap by analyzing 4,696 tributaries across six landscapes with varying climate, tectonic setting, and lithology. Our results show that both tributary length and spacing systematically increase with downstream distance along the mainstem river, following a power-law scaling. This power-law scaling can be modulated by basin shape, with tributaries becoming shorter and, in some cases, more closely spaced as basin elongate. Furthermore, the power-law scaling may break down in cases where river networks have been disturbed by pervasive faulting, raising the possibility that the scaling we observe is not unique to all branching networks, and instead may be universal across undisturbed fluvial networks. These findings can be used to improve predictions of river network geometry and potentially to distinguish fluvial river networks from other branching networks.

Self-formed bedrock waterfalls.

Waterfalls are inspiring landforms that set the pace of landscape evolution as a result of bedrock incision1-3. They communicate changes in sea level or tectonic uplift throughout landscapes2,4 or stall river incision, disconnecting landscapes from downstream perturbations3,5. Here we use a flume experiment with constant water discharge and sediment feed to show that waterfalls can form from a planar, homogeneous bedrock bed in the absence of external perturbations. In our experiment, instabilities between flow hydraulics, sediment transport and bedrock erosion lead to undulating bedforms, which grow to become waterfalls. We propose that it is plausible that the origin of some waterfalls in natural systems can be attributed to this intrinsic formation process and we suggest that investigations to distinguish self-formed from externally forced waterfalls may help to improve the reconstruction of Earth history from landscapes.