Is Canyon Width a Diagnostic Indicator of the Discharge of Megafloods on Earth and Mars?

On Earth, large floods have carved steep-walled and amphitheater-headed canyons from the Pleistocene (e.g. Box Canyon, ID) through the Holocene (e.g. Asbyrgi Canyon, Iceland), to historic times (e.g. Canyon Lake Gorge, TX). The geologic record on Mars suggests that similar floods have carved canyons by waterfall retreat about 3.5 billion years ago, when the red planet was wetter and possibly warmer. We currently lack robust paleo-hydraulic tools to reconstruct the discharge of ancient floods, especially on Mars where sediment sizes are obscured from observation. To address this issue, we hypothesize that the width of canyon escarpment is controlled by the hydraulics of the canyon-carving flood due to focusing of the flood into the canyon head. We compiled field data from multiple canyons and floods on Earth and Mars and show that there is a correlation between estimated flood discharge and canyon headwall width. To explore what sets this relationship, we identified five important parameters using dimensional analysis: the Froude number, the ratio of backwater length to canyon length, the ratio of backwater length to flood width, the ratio of canyon width to flood width, and the topographic slope upstream of the canyon. We used the hydraulic numerical modeling suite ANUGA to simulate overland flow over different canyon geometries and flood parameters to systematically explore the relative bed shear stresses along the canyon rim as a metric for flow focusing. Results show that canyons that exceed a certain length, scaling with the hydraulic backwater length, have shear stresses at their heads that are significantly higher than near the canyon mouth. Shear stresses along the rim of the canyon sidewalls are limited, in comparison to stresses along the canyon head, when the flood width is of the order of the backwater length. Flow focusing only occurs for subcritical flow. Together, these results suggest that canyons may only grow from a perturbation that is large enough to instigate flow focusing. Once canyon growth is initiated, the equilibrium width of canyons may arise from the competition between the cross-stream backwater effects along the canyon sidewalls, which promote widening of the escarpment, and the geometry of the canyon flood system, which promote a drying of the canyon sidewalls. These results show promise for a new paleohydraulic tool to infer discharges of ancient floods on Earth and Mars.