Description of soil micro‐topography and fractional wetted area under runoff using fractal dimensions

Abstract

Understanding the connections between the micro‐topography of a surface and the patterns of shallow overland flow is important to the study of runoff and infiltration processes. In slopes with micro‐topographic features parallel to the flow, water tends to concentrate in channels and only a fraction of the slope contributes to the overland flow. This study aimed to formulate the relevance of the fractal approach for understanding the relation of surface roughness to overland flow patterns. Laboratory experiments of simulated runoff over a bare soil slope were used to test the efficacy of two fractal parameters (fractal dimension [FD] and vertical intercept [VIC] from the Fourier power spectrum method) to describe how main surface micro‐topographic features can influence runoff, infiltration and erosion processes. The fractal parameters behaved differently for the distinctive initial surface treatments (smooth, three rills, and five rills). The anisotropy of the surface was evident based on the change of the fractal parameters with direction. The rose plots of the fractal parameters provided important information about the magnitude of the concentrated flow erosion of a surface and its main direction; in the direction perpendicular to the rills, the FD values were lower and the VIC greater. The minimum FD decreased and the maximum VIC increased with runoff time. A linear relationship between the infiltration depth and the percentage of wetted area was observed. Furthermore, a relationship between the fraction of wetted area and the fractal parameters has been developed, indicating that vertical variations (VIC) in roughness had more impact on fraction of wetted area than horizontal variations (FD) of the surface. Finally, a decrease in the minimum FD and an increase in the maximum VIC were related to greater scour volumes. The scour volume of an initially smooth surface seems to be well‐represented by a power relationship with the maximum VIC. By defining indicators of rill erosion and associating them with flow patterns through these fractal parameters, a better description of shallow overland flow can be achieved. © 2018 John Wiley & Sons, Ltd.

Interactions of Microtopography, Slope and Infiltration Cause Complex Rainfall‐Runoff Behavior at the Hillslope Scale for Single Rainfall Events

“…In short, there is a complex spatiotemporal dependence of both the hydrodynamic and hydrological response on MT throughout a rainfall-runoff event. This dependence is not well captured by simple statistical models of MT that are typically used to transfer measured MT into simpler structural proxies (Smith, 2014), as they neglect key aspects such as surface detention and lag times (Antoine et al, 2011), MT anisotropy (García-Serrana et al, 2018;Viero & Valipour, 2017) and spatial variation (Kamphorst et al, 2005), interactions with infiltration and storm -2-…”

“…In short, there is a complex spatiotemporal dependence of both the hydrodynamic and hydrological response on MT throughout a rainfall‐runoff event. This dependence is not well captured by simple statistical models of MT that are typically used to transfer measured MT into simpler structural proxies (Smith, 2014), as they neglect key aspects such as surface detention and lag times (Antoine et al., 2011), MT anisotropy (García‐Serrana et al., 2018; Viero & Valipour, 2017) and spatial variation (Kamphorst et al., 2005), interactions with infiltration and storm properties (Fernández‐Pato et al., 2016; Thompson et al., 2010; Yang & Chu, 2013). Most importantly, such proxies are limited to represent mostly local, patch‐scale areas, thus not addressing multiscale interactions at the larger hillslope and catchment scales (Antoine et al., 2009; Descroix et al., 2007).…”

Hilltop curvature as a proxy for erosion rate: wavelets enable rapid computation and reveal systematic underestimation

“…Similarly, hillslope geomorphic transport laws formulated for soil-mantled landscapes allow for estimation of uplift and erosion rates as well as prediction of the migration of hillcrests in response to landscape transience (Forte and Whipple, 2018;Mohren et al, 2020;Mudd, 2017;Mudd andFurbish, 2007, 2005;Roering, 2008;Roering et al, 2007Roering et al, , 2001Roering et al, , 1999. Over 100 years ago, it was proposed that hillslope form, specifically slope and curvature, may be an effective predictor of erosion rate, as hillslopes steepen and lengthen to accommodate increases in baselevel lowering (Gilbert, 1909(Gilbert, , 1877. However, hillslopes do not continue to steepen as baselevel lowering progressively increases to faster and faster rates (e.g., Howard, 1994;Penck, 1953;Schumm, 1967;Strahler, 1950).…”

Hilltop curvature as a proxy for erosion rate: Wavelets enable rapid computation and reveal systematic underestimation

“…While hillslope spectra will vary between landscapes and likely exhibit a combination of different spectral slopes depending on the scale of analysis, red noise surfaces generally best describe topographic noise in natural landscapes while white noise surfaces are comparatively the least likely (e.g. Booth et al, 2009;García-Serrana et al, 2018;Marshall and Roering, 2014;Pelletier and Field, 2016;Perron et al, 2008). We generated each noisy surface of values normally distributed about 0 with the standard deviation ranging from -1 m (pits) to 1 m (mounds; Konowalczyk, 2021).…”