Particle motion on burned and vegetated hillslopes

Abstract

Climate change is causing increasingly widespread, frequent, and intense wildfires across the western United States. Many geomorphic effects of wildfire are relatively well studied, yet sediment transport models remain unable to account for the rapid transport of sediment released from behind incinerated vegetation, which can fuel catastrophic debris flows. This oversight reflects the fundamental inability of local, continuum-based models to capture the long-distance particle motions characteristic of steeplands. Probabilistic, particle-based nonlocal models may address this deficiency, but empirical data are needed to constrain their representation of particle motion in real landscapes. Here we present data from field experiments validating a generalized Lomax model for particle travel distance distributions. The model parameters provide a physically intuitive mathematical framework for describing the transition from light- to heavy-tailed distributions along a continuum of behavior as particle size increases and slopes get steeper and/or smoother. We show that burned slopes are measurably smoother than vegetated slopes, leading to 1) lower rates of experimental particle disentrainment and 2) runaway motion that produces the heavy-tailed travel distances often associated with nonlocal transport. Our results reveal that surface roughness is a key control on steepland sediment transport, particularly after wildfire when smoother surfaces may result in the preferential delivery of coarse material to channel networks that initiate debris flows. By providing a first-order framework relating the statistics of particle motion to measurable surface characteristics, the Lomax model both advances the development of nonlocal sediment transport theory and reveals insights on hillslope transport mechanics.

Rarefied particle motions on hillslopes: 2. Analysis

“…Although this idea is most applicable to processes such as rock fall and the subsequent motions of the rock material over talus or scree slopes, our description of the motions of individual particles nonetheless may be entirely relevant to conditions that are not strictly rarefied, but where during the collective motions of many particles the effects of particle-surface interactions dominate over effects of particle-particle interactions in determining the behavior of the particles -akin to granular shear flows at high Knudsen number (Kumaran, 2005(Kumaran, , 2006. We note that laboratory experiments (Kirkby and Statham, 1975;Gabet and Mendoza, 2012) and field-based experiments (DiBiase et al, 2017;Roth et al, 2020) designed to mimic particle motions and travel distances on hillslopes effectively focus on rarefied conditions. The formulation of rarefied particle motions presented in the first companion paper (Furbish et al, 2020a) is based on a description of the kinetic energy balance of a cohort of particles treated as a rarefied granular gas, and a description of particle deposition that depends on the energy state of the particles.…”

“…As described in our first companion paper (Furbish et al, 2020a), we are focused on rarefied motions of particles which, once entrained, travel downslope over the land surface. This notably includes the dry ravel of particles down rough hillslopes following disturbances (Roering and Gerber, 2005;Doane, 2018;Doane et al, 2019;Roth et al, 2020) or upon their release from obstacles (e.g., vegetation) following failure of the obstacles (Lamb et al, 2011(Lamb et al, , 2013DiBiase and Lamb, 2013;DiBiase et al, 2017;Doane et al, 2018Doane et al, , 2019, and the motions of rock fall material over the rough surfaces of talus and scree slopes (Gerber and Scheidegger, 1974;Kirkby and Statham, 1975;Statham, 1976;Tesson et al, 2020). By "rarefied motions" we are referring to the situation in which moving particles may frequently interact with the surface, but rarely interact with each other.…”

“…We also report laboratory experiments designed to clarify how the size and shape of particles influence their motions and disentrainment based on high-speed imaging. In Section 4 we compare the formulation with the field-based measurements of travel distances reported by DiBiase et al (2017) and Roth et al (2020).…”

Particle energy partitioning and transverse diffusion during rarefied travel on an experimental hillslope

“…Particle dispersion is a key element of sediment transport (Samson et al, 1998;Furbish and Haff, 2010;Tucker and Bradley, 2010;Furbish et al, 2012a). Particles starting at the same location, when subjected to the same macroscopic forcing, spread spatially over time in both laboratory and field settings (Schumm, 1967;Samson et al, 1998).…”

“…Particle dispersion is a key element of sediment transport (Samson et al, 1998;Furbish and Haff, 2010;Tucker and Bradley, 2010;Furbish et al, 2012a). Particles starting at the same location, when subjected to the same macroscopic forcing, spread spatially over time in both laboratory and field settings (Schumm, 1967;Samson et al, 1998). In a simplified way, the spreading behavior of particles on a hillslope is akin to particle behavior on a Galton board, which serves to illustrate the dispersion process due to particle collisions with roughness elements (pegs) attached to the board ( Figure 9) (Galton, 1894).…”