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How Well Can Hillslope Evolution Models “Explain” Topography? Simulating Soil Transport and Production with High-Resolution Topographic Data

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How Well Can Hillslope Evolution Models “Explain” Topography? Simulating Soil Transport and Production with High-Resolution Topographic Data How well can hillslope evolution models “explain” topography? Simulating soil transport and production with high-resolution topographic data Joshua J. Roering Department of Geological Sciences, University of Oregon, Eugene, Oregon 97403-1272, USA ABSTRACT nonlinear slope- and depth-dependent model form and sediment yield (Gabet et al., 2003; accounts for how soil thickness controls the Roering et al., 2004; Yoo et al., 2005). Quan- The morphology of hillslopes is a direct magnitude of biogenic disturbances that titatively exploring these feedbacks between refl ection of tectonic forcing and climatic and drive transport; this model best preserved hillslope topography and climatic and tectonic biologic processes that drive soil production, the current landscape form, particularly the processes requires that we posit equations to mobilization, and transport. Soil transport narrow, sharply convex hilltops characteris- represent transport on hillslopes, an endeavor on hillslopes affects river incision by provid- tic of the Oregon Coast Range. According to that has occupied geologists for nearly 100 yr. ing tools for channel abrasion and controls our formulation, which provides an explicit In 1909, G.K. Gilbert (Gilbert, 1909) ex pounded the distribution of sediment that infl uences linkage for relating the distribution of biota upon the ideas of Davis (1892) and proposed a aquatic habitat. Although numerous hillslope to hillslope processes, the degree of hilltop process-based explanation for the convex form transport relationships have been proposed convexity varies nonlinearly with the ratio of “debris”-mantled hillslopes. For a one-dimen- over the past 60+ years, a comprehensive of erosion rate to maximum soil production sional hillslope that erodes at a spatially constant analysis of model predictions for a real land- rate, highlighting the profound infl uence of rate, sediment fl ux must increase linearly with scape has not been performed. Here, we use soil depth on hillslope evolution. distance from the drainage divide (i.e., hilltop). high-resolution topographic data obtained To accommodate the progressive downslope via airborne laser swath mapping (ALSM) to Keywords: hillslope evolution, soil transport, increase in fl ux, slopes become monotonically simulate the long-term evolution of Oregon nonlinear transport, airborne lidar. steeper as increasing gravitational acceleration Coast Range hillslopes and test three pub- facilitates transport via disturbances (such as lished transport models and a new model INTRODUCTION those associated with biogenic activity). The that accounts for nonlinear depth- and slope- progressive downslope increase in slope angle dependent transport. Analysis of one-dimen- In hilly and mountainous landscapes, the defi nes a convex form between hilltops and sional, steady-state solutions for these four downslope movement of soil on hillslopes mod- channels, which is commonly observed for models suggests that plots of gradient-cur- ulates landscape form and sediment delivery to natural slopes. Several decades after Gilbert’s vature may be diagnostic for distinguishing channels. The coupling between rock uplift and work, his conceptual framework was cast into model predictions. To evaluate two-dimen- topographic relief thus depends on the effi cacy equations by Culling (1963) and since the 1960s, sional model predictions for our fi eld site, of diverse climate-related hillslope processes, dozens of quantitative hillslope evolution models we assumed local steady-state erosion for a such as frost heave, bioturbation, and shallow have emerged, virtually all of which incorporate 72,000 m2 sequence of hillslopes and valleys. landsliding. With increasing rates of rock uplift slope angle as the primary control on sediment After calibrating each of the four models, and erosion, for example, mass wasting pro- transport rates (e.g., Ahnert, 1976; Arrowsmith we imposed constant base-level lowering for cesses promote rapid sediment fl uxes on steep et al., 1996; Avouac and Peltzer, 1993; Braun cells within the valley network, simulated slopes and may limit further topographic devel- and Sambridge, 1997; Culling, 1963; Dietrich 500,000 yr of soil production and transport, opment (e.g., Burbank et al., 1996; Montgom- and Perron, 2006; Hanks, 2000; Howard, 1997; and determined which transport model ery and Brandon, 2002). As a result, decipher- Istanbulluoglu et al., 2004; Kirkby, 1971; Kooi best preserved morphologic patterns that ing rates of tectonic forcing from topographic and Beaumont, 1994; Koons, 1989; Tucker and describe the current landscape form. Mod- metrics requires information on hillslope pro- Slingerland, 1994; van der Beek and Braun, els for which fl ux varies proportionally with cess mechanics and rates (e.g., Ahnert, 1970b; 1998; Willett, 1999; Willgoose et al., 1991). hillslope gradient generated broadly convex Ahnert, 1984; Whipple et al., 2005). In the Linear slope-dependent transport models hilltops inconsistent with the sharp-crested, absence of overland fl ow, mass transport on soil- predict convex hillslopes and have a straight- steep-sided slopes of our study site, whereas mantled slopes is often driven by disturbances forward mathematical form, making them the two nonlinear slope-dependent models associated with biological activity (i.e., biotur- simple to implement in analytical and numeri- produced convex-planar slopes consistent bation). This explicit linkage between biology cal models of landscape evolution (Koons, with current hillslope form. Our proposed and sediment transport suggests that ecological 1989). Importantly, linear models predict that changes associated with long-term climatic fl uc- steady-state hillslopes exhibit constant curva- †E-mail: [email protected] tuations may induce fi rst-order shifts in hillslope ture ( Fernandes and Dietrich, 1997). Despite the GSA Bulletin; September/October 2008; v. 120; no. 9/10; p. 1248–1262; doi: 10.1130/B26283.1; 12 fi gures; 1 table. 1248 For permission to copy, contact [email protected] © 2008 Geological Society of America How well can hillslope evolution models “explain” topography? visually and computationally appealing nature ing of the valley network. Using the assumption SOIL PRODUCTION MODEL of the linear transport model, the prediction of of locally steady-state topography, they com- constant curvature slopes is inconsistent with pared their results with the initial topographic The presence or absence of soil has a pro- frequently observed convex-planar slopes in form (i.e., current topography) to assess model found infl uence on the mechanics and rates of soil-mantled regions (Carson and Petley, 1970; success. Essentially, they inquired as to how well surfi cial processes as well as feedbacks with Penck, 1953; Strahler, 1950; Young, 1961). To a previously calibrated transport model can pre- ecological processes. Following insights fi rst account for this discrepancy, a raft of trans- serve current landscape form. Here, we adopt a proposed by Gilbert (1877), recent studies have port models emerged in the 1980s and 1990s; similar approach, but instead test a diverse suite demonstrated that the rate of soil production, ε, these models incorporated a nonlinearity in the of representative transport models to systemati- declines exponentially with slope-normal soil fl ux-slope relationship such that transport rates cally determine which best preserves diagnostic depth according to: increase rapidly as slopes approach a critical properties of current topography in the Oregon angle (Anderson, 1994; Anderson and Hum- Coast Range. We also propose a new transport ε −μθ phrey, 1989; Andrews and Bucknam, 1987; model for which fl ux depends nonlinearly on ε = 0 e h cos , (3) cosθ Gabet, 2000; Howard, 1994; Kirkby, 1984; slope and soil depth. Because the depth depen- Roering et al., 1999). Put simply, the fl ux-slope dency depends on the vertical distribution of ε nonlinearity enables nearly steep and planar biological activity in soil, this new formulation where 0 is the maximum production rate asso- (low convexity) sideslopes to erode at rates com- enables us to calibrate and test the model with ciated with zero soil depth, μ is the exponential mensurate with highly convex hilltops. More fi eld-generated biological data. Our results are decay constant, and θ is local slope in degrees recently, several studies have proposed that fl ux useful for predicting sediment yield to channel (Heimsath et al., 2001b). The cosine term in the rates depend on slope angle and soil depth (e.g., networks as well as interpreting and predicting exponential function is included to convert ver- Furbish and Fagherazzi, 2001; Heimsath et al., morphologic response to tectonic and climatic tical soil depth to slope-normal soil depth and 2002; Heimsath et al., 2005; Mudd and Furbish, perturbations in real landscapes. the cosine term in the denominator is included 2007; Yoo et al., 2005), enabling these models to convert soil production measured slope-nor- to be directly coupled with representations of MASS CONSERVATION LAWS FOR mal into a vertical reference frame. Here, we depth-dependent biological processes. HILLSLOPE EVOLUTION express soil depth, h, in a vertical orientation to Despite the widespread availability of com- facilitate presentation and interpretation of our putational resources and high-resolution topo- Landscapes result from the coupled infl uence simulation results. Equation 3 is equivalent to graphic data (via airborne laser altimetry), few of tectonic
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