A hydrodynamically consistent "slope-area" relationship for analysing fluvial landscape with wide rivers.

Landforms and channel networks have long been analysed through co-variation between topographic slope and drainage area, which is derived from easy-to-implement flow routing algorithms (D8 or Dinf) relying on topographic slopes. The slope-area relationship has been successful to identify morphologic regions in landscapes likely reflecting the erosion and transport processes that shape them. But the implicit assumption for using the slope-area relationship is that channels are narrower than the DEM resolution and that, at this scale, the flow is correctly routed. These assumptions are no more valid for very high-resolution DEM (HRDEM, <2 m) that are now widely available with unprecedented level of vertical accuracy (< 20 cm). In wide rivers, the drainage area algorithm puts the total river discharge in one of the pixel of each channel section and let the others with unrealistically low areas. In other words, D8 or Dinf algorithms are not adapted to resolve the lateral extent of rivers.

In this study, we propose a new topographic analysis relying on realistic hydraulic simulations of surface flow. For this, we use a particle-based hydraulic model, Floodos, which solves the 2D shallow water equations, and we present an analysis of the 1m LiDAR DEM of the Elder creek watershed in California, for which channels are up to ten meters wide. By simulating channel flows with water depth, hydraulic slope, specific discharge and bed shear stress, the hydraulic model reveals landscape patterns that are not described by the slope-area relationship. Additionally, the flow model handles very well the small irregularities of the topography.

We introduce new geomorphic descriptors: the hydraulic slope and the specific drainage area (or specific discharge). The catchment organization is then analysed through a new framework called the hydraulic slope-area diagram. This diagram has several benefits over the classical slope-area diagram. It correctly classifies pixels located in the river for a given discharge in the fluvial domain leading to a sharper transition between the colluvial and fluvial domain. The hillslope-to-valley transition is also insensitive to the DEM resolution. Channel width can also be automatically calculated based on a joint analysis of Dinf and 2D shallow water simulation. Finally, the capability to perform the hydraulic slope-area for various discharges brings a richer description of landscape organization by highlighting discharge-dependent regions such as floodplain areas and fluvial terraces.