Statistical and physical characterization of rainfall-driven overland flow morphologies

Environmental transport processes are highly coupled with the shape of landscapes. Modern catchment analysis with high-resolution data and huge computational powers demand more detailed within-cell metrics for surface evolution modeling. This dissertation involves experiments and numerical simulations of rainfall-driven sediment transport at laboratory scales of which areas were less than the common computational cell sizes at catchment scales. The objective was a stochastic and physical study of unchanneled overland flow morphologies. In the first step, a detailed laboratory study was conducted to highlight the effects of morphological changes on hysteretic sediment transport under a time-varying rainfall. A rainfall pattern composed of seven sequential stepwise varying rainfall intensities was applied to a 5-m×2-m soil erosion flume. Clockwise hysteresis loops in the sediment concentration versus discharge curves were measured for the total eroded soil and the finer particle sizes. However, for larger particle sizes, hysteresis effects decreased and suspended concentrations tended to vary linearly with discharge. Overall, it is found that hysteresis varies amongst particle sizes and that the predictions of the HR model are consistent with hysteretic behavior of different sediment size classes. After demonstrating the role of morphological changes (generation of a shield layer on the topsoil) on erosion patterns, overland flow morphologies were statistically characterized. To do so, the catchment-scale network analyses were applied on the micro-roughnesses of unchanneled surfaces at the laboratory scale (2-m×1-m flume). The scaling relation between the drainage area and stream length (Hack¿s law), along with exceedance probabilities of drainage area, discharge, and upstream flow network length, is well known for catchment-scale channelized fluvial regions. It was found that the relationships for the overland flow network were the same as those found for large-scale catchments and for laboratory experiments with observable channels. In addition, the scaling laws were temporally invariant, even though the network dynamically changed over the course of the experiment.

In the next step, we tested the applicability of a physically-based catchment scale landscape evolution model (LEM) at laboratory scale and in absence of rills. We modeled the overland flow as a network that preserves the water flux for each cell in the discretized domain. This network represented the surface flow and determined the evolution direction. The spectral analysis confirmed that the model predictions capture the main characteristics of the measured morphology. However, the model could not reproduce the experimental scaling relation as the micro-roughnesses of the surface were not produced by the model. In order to modify the LEM, it was solved as a stochastic partial differential equation. The results showed that an extra term for roughness was necessary to simulate more details of the morphology. Furthermore, a new deterministic approach (diffusion coefficient as a step function of curvature) was proposed and tested to improve the model predictions in the statistical sense.\ Besides the scientific contributions, useful modeling, optimization and data analysis tools (C++ and Python codes) were provided for future geomorphological studies.