Abstract. The longitudinal profiles of bedrock channels are a major component of the relief structure of mountainous drainage basins and therefore limit the elevation of peaks and ridges. Further, bedrock channels communicate tectonic and climatic signals across the landscape, thus dictating, to first order, the dynamic response of mountainous landscapes to external forcings. We review and explore the stream-power erosion model in an effort to (1) elucidate its consequences in terms of large-scale topographic (fluvial) relief and its sensitivity to tectonic and climatic forcing, (2) derive a relationship for system response time to tectonic perturbations, (3) determine the sensitivity of model behavior to various model parameters, and (4) integrate the above to suggest useful guidelines for further study of bedrock channel systems and for future refinement of the streampower erosion law. Dimensional analysis reveals that the dynamic behavior of the stream-power erosion model is governed by a single nondimensional group that we term the uplift-erosion number, greatly reducing the number of variables that need to be considered in the sensitivity analysis. The degree of nonlinearity in the relationship between stream incision rate and channel gradient (slope exponent n) emerges as a fundamental unknown. The physics of the active erosion processes directly influence this nonlinearity, which is shown to dictate the relationship between the uplift-erosion number, the equilibrium stream channel gradient, and the total fluvial relief of mountain ranges. Similar[y, the predicted response time to changes in rock uplift rate is shown to depend on climate, rock strength, and the magnitude of tectonic perturbation, with the slope exponent n controlling the degree of dependence on these various factors. For typical drainage basin geometries the response time is relatively insensitive to the size of the system. Work on the physics of bedrock erosion processes, their sensitivity to extreme floods, their transient responses to sudden changes in climate or uplift rate, and the scaling of local rock erosion studies to reach-scale modeling studies are most sorely needed.

[1] Developing a quantitative understanding of the factors that control the rate of river incision into bedrock is critical to studies of landscape evolution and the linkages between climate, erosion, and tectonics. Current models of long-term river network incision differ significantly in their treatment of the role of sediment flux. We analyze the implications of various sediment-fluxdependent incision models for large-scale topography, in an attempt (1) to identify quantifiable and diagnostic differences between models that could be detected from topographic data or from the transient responses of perturbed systems and (2) to explain the apparent ubiquity of mixed bedrockalluvial channels in active orogens. Although certain forms of the various models can be discarded as inconsistent with morphological data, we find that the relative intrinsic concavity indices of detachment-and transport-limited systems (defined herein) largely dictate whether the various models can be tied to distinctive steady state morphologies. Preliminary data suggest that no such diagnostic differences may exist, and other methods must be developed to test models. Accordingly, we develop and explore differences in the scaling behavior of topographic relief and the extent of detachment-versus transport-limited channels as a function of rock uplift rate that may allow discrimination among various models. Further, we explore potentially diagnostic differences in the rates and patterns of transient channel response to changes in rock uplift rate. In addition to general differences between detachment-and transport-limited systems our analysis identifies an interesting hysteresis in landscape evolution: ''hybrid'' channels at the threshold between detachment-and transport-limited conditions are expected to act as detachment-limited systems in response to an increase in rock uplift rate (or base level fall) and as transport-limited systems in response to a decrease in rock uplift rate, especially during postorogenic topographic decline. The analyses presented set the stage for field studies designed to test quantitatively the various river incision models that have been proposed.INDEX TERMS: 1815 Hydrology: Erosion and sedimentation; 1824 Hydrology: Geomorphology (1625); 8107 Tectonophysics: Continental neotectonics; KEYWORDS: Tectonic geomorphology, Erosion, Sediment-flux, Bedrock channels, Relief Motivation[2] Spurred by the recognition that river incision into bedrock importantly influences the style and tempo of landscape evolution in mountainous regions, the morphology of the resulting landscapes, and orogenic evolution in general, much research over the past decade has been devoted to understanding this process [e.g., Seidl and Dietrich, 1992;Howard et al., 1994;Wohl et al., 1994; Tinkler and Wohl, 1998;Whipple et al., 2000a]. Bedrock channels set much of the relief structure of unglaciated mountainous landscapes and convey signals of tectonic and climatic change across landscapes, thus setting, to first order, landscape response time...

Abstract. Catchment morphology and drainage density are strongly influenced by hillslope processes. The consequences of several different hillslope process laws are explored in a series of experiments with a numerical model of drainage basin evolution. Five different models are considered, including a simple diffusive-advective process transition, a runoff generation threshold, an erosion threshold, and two types of thresholdactivated landsliding. These different hillslope processes alter both the visual appearance of the landscape and the predicted relationship between slope and contributing area. On the basis of the different threshold theories, we derive expressions for the relationships between drainage density and environmental factors such as rainfall, relief, and mean erosion rate. These relationships vary depending on the dominant hillslope threshold. In particular, the sign of the predicted relationship between drainage density and relief is positive in semiarid, low-relief landscapes and negative in humid landscapes dominated by a saturation threshold and/or in high-relief landscapes dominated by simple threshold landsliding.

[1] Mechanistic theories of fluvial erosion are essential for quantifying large-scale orogenic denudation. We examine the topographic implications of two leading classes of river erosion model, detachment-limited and transport-limited, in order to identify diagnostic and testable differences between them. Several formulations predict distinctly different longitudinal profile shapes, which are shown to be closely linked to terrain morphology. Of these, some can be rejected on the basis of unrealistic morphology and slope-area scaling. An expression is derived for total drainage basin relief and its apportionment between hillslope and fluvial components. Relief and valley density are found to vary with tectonic forcing in a manner that reflects erosion physics; these properties therefore constitute an additional set of testable predictions. Finally, transient responses to tectonic perturbations are shown to depend strongly on the degree of nonlinearity in the incision process. These findings indicate that given proper constraints, fluvial erosion theories can be tested on the basis of observed topography. INDEX TERMS:1824 Hydrology: Geomorphology (1625); 1625 Global Change: Geomorphology and weathering (1824, 1886); 3210 Mathematical Geophysics: Modeling; 8110 Tectonophysics: Continental tectonics-general (0905); KEYWORDS: Landscape evolution, topography, geomorphology, erosion, streams, relief Citation: Tucker, G. E., and K. X. Whipple, Topographic outcomes predicted by stream erosion models: Sensitivity analysis and intermodel comparison,

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