River network scaling laws describe how their shape varies with their size. However, the regional variation of this size-dependence remains poorly understood. Here we show that river network scaling laws vary systematically with the climatic aridity index. We find that arid basins do not change their proportions with size, while humid basins do. To explore why, we study an aspect ratio L ⊥ / L ∥ between basin width L ⊥ and basin length L ∥ . We find that the aspect ratio exhibits a dependence on climate and argue that this can be understood as a structural consequence of the confluence angle. We then find that, in humid basins, the aspect ratio decreases with basin size, which we attribute to a common hydrogeological hierarchy. Our results offer an explanation of the variability in network scaling exponents and suggest that the absence of self-similarity in humid basins can be understood as a morphological expression of subsurface processes.

Streams shape landscapes through headward growth and lateral migration. When these streams are primarily fed by groundwater, recent work suggests that their tips advance to maximize the symmetry of the local Laplacian field associated with groundwater flow. We explore the extent to which such forcing is responsible for the lateral migration of streams by studying two features of groundwater-fed streams in Bristol, Florida: their confluence angle near junctions and their curvature. First, we find that, while streams asymptotically form a 72° angle near their tips, they simultaneously exhibit a wide 120° confluence angle within approximately 10 m of their junctions. We show that this wide angle maximizes the symmetry of the groundwater field near the junction. Second, we argue that streams migrate laterally within valleys and present a new spectral analysis method to relate planform curvature to the surrounding groundwater field. Our results suggest that streams migrate laterally in response to fluxes from the surrounding groundwater table, providing evidence of a new mechanism that complements Laplacian growth at their tips.

Valleys that form around a stream head often develop characteristic finger-like elevation contours. We study the processes involved in the formation of these valleys and introduce a theoretical model that indicates how shape may inform the underlying processes. We consider valley growth as the advance of a moving boundary travelling forward purely through linearly diffusive erosion, and we obtain a solution for the valley shape in three dimensions. Our solution compares well to the shape of slowly growing groundwater-fed valleys found in Bristol, Florida. Our results identify a new feature in the formation of groundwater-fed valleys: a spatially variable diffusivity that can be modelled by a fixed-height moving boundary.

River networks exhibit a complex ramified structure that has inspired decades of studies. However, an understanding of the propagation of a single stream remains elusive. Here we invoke a criterion for path selection from fracture mechanics and apply it to the growth of streams in a diffusion field. We show that, as it cuts through the landscape, a stream maintains a symmetric groundwater flow around its tip. The local flow conditions therefore determine the growth of the drainage network. We use this principle to reconstruct the history of a network and to find a growth law associated with it. Our results show that the deterministic growth of a single channel based on its local environment can be used to characterize the structure of river networks.

A concept for how such seepage channel systems form was first proposed by T. Dunne in the early 1980s [2]. A small bulge in the sidewall of a stream focuses ground water flow. This results in a larger flux and therefore a higher erosion rate in this direction. Over time such small perturbations grow into newly formed streams, but how they do so and how erosion depends on the water flux is unclear. The theory of diffusive growth provides a theoretical framework to describe channelization in response to groundwater flow. For this system the underlying physical equations are well-defined, and numerical and analytical predictions can be obtained and tested in the field. If a stream advances at a rate v ∼ q , where q is the discharge of ground water into the tip, theory predicts that η has to be smaller than a critical value η to obtain ramified networks [3]. We test this hypothesis by measuring erosion rates in a field site in the Florida Panhandle, which provides a natural laboratory to study channel incision by re-emerging groundwater flow [4].

River networks exhibit a complex ramified structure that has inspired decades of studies. Yet, an understanding of the propagation of a single stream remains elusive. Here we invoke a criterion for path selection from fracture mechanics and apply it to the growth of streams in a diffusion field. We show that a stream will follow local symmetry in order to maximize the water flux and that its trajectory is defined by the local field in its vicinity. We also study the growth of a real network. We use this principle to construct the history of a network and to find a growth law associated with it. The results show that the deterministic growth of a single channel based on its local environment can be used to characterize the structure of river networks.