A hydrodynamically consistent "slope-area" relationship foranalysing fluvial landscape with wide rivers
Résumé
Landforms and channel networks have long been analysed through co-variation betweentopographic slope and drainage area, which is derived from easy-to-implement flow routingalgorithms (D8 or Dinf) relying on topographic slopes. The slope-area relationship has beensuccessful to identify morphologic regions in landscapes likely reflecting the erosion and transportprocesses that shape them. But the implicit assumption for using the slope-area relationship isthat channels are narrower than the DEM resolution and that, at this scale, the flow is correctlyrouted. These assumptions are no more valid for very high-resolution DEM (HRDEM, <2 m) thatare now widely available with unprecedented level of vertical accuracy (< 20 cm). In wide rivers, thedrainage area algorithm puts the total river discharge in one of the pixel of each channel sectionand let the others with unrealistically low areas. In other words, D8 or Dinf algorithms are notadapted to resolve the lateral extent of rivers.In this study, we propose a new topographic analysis relying on realistic hydraulic simulations ofsurface flow. For this, we use a particle-based hydraulic model, Floodos, which solves the 2Dshallow water equations, and we present an analysis of the 1m LiDAR DEM of the Elder creekwatershed in California, for which channels are up to ten meters wide. By simulating channel flowswith water depth, hydraulic slope, specific discharge and bed shear stress, the hydraulic modelreveals landscape patterns that are not described by the slope-area relationship. Additionally, theflow model handles very well the small irregularities of the topography.We introduce new geomorphic descriptors: the hydraulic slope and the specific drainage area (orspecific discharge). The catchment organization is then analysed through a new framework calledthe hydraulic slope-area diagram. This diagram has several benefits over the classical slope-areadiagram. It correctly classifies pixels located in the river for a given discharge in the fluvial domainleading to a sharper transition between the colluvial and fluvial domain. The hillslope-to-valleytransition is also insensitive to the DEM resolution. Channel width can also be automaticallycalculated based on a joint analysis of Dinf and 2D shallow water simulation. Finally, the capabilityto perform the hydraulic slope-area for various discharges brings a richer description of landscapeorganization by highlighting discharge-dependent regions such as floodplain areas and fluvialterraces.