A probabilistic approach for channel initiation

The channel head represents an important transition point from hillslope to fluvial processes. There is a nonlinear threshold transition across the channel head with sediment transport much larger in channels than on hillslopes. Deterministic specific catchment area, a, thresholds for channel initiation, sometimes dependent on slope, S , in the form of aS α ≥ C , have been suggested. In this paper the channel initiation problem is viewed probabilistically with a spatially variable probability of channel initiation that depends on slope, specific catchment area, and the probability distributions of median grain size, surface roughness, and excess rainfall rate. The channel initiation threshold C is cast as a random variable to characterize the variability of aS α at channel heads. Using field measurements from the Idaho Batholith, we show that median grain size measurements at each channel head explain a significant part of the observed variability of aS α . We then characterize the variability of model inputs (median grain size, roughness, and excess rainfall) using probability distributions and show that the probability distribution of area‐slope threshold derived from these inputs matches the probability distribution of area‐slope thresholds measured at field channel head locations. A gamma probability distribution provides a reasonable match to the distributions of area‐slope threshold measured and modeled at channel heads in our study area and in other published channel head data.