The most common detachment‐limited river incision models ignore the effects of sediment on fluvial erosion, yet steep reaches of mountain rivers often host clusters of large (>1 m) blocks. We argue that this distribution of blocks is a manifestation of an autogenic negative feedback in which fast vertical river incision steepens adjacent hillslopes, which deliver blocks to the channel. Blocks inhibit incision by shielding the bed and enhancing form drag. We explore this feedback with a 1‐D channel‐reach model in which block delivery by hillslopes depends on the river incision rate. Results indicate that incision‐dependent block delivery can explain the block distribution in Boulder Creek, Colorado. The proposed negative feedback may significantly slow knickpoint retreat, channel adjustment, and landscape response compared to rates predicted by current theory. The influence of hillslope‐derived blocks may complicate efforts to extract base level histories from river profiles.

Abstract. Models of landscape evolution by river erosion are often either transport-limited (sediment is always available but may or may not be transportable) or detachmentlimited (sediment must be detached from the bed but is then always transportable). While several models incorporate elements of, or transition between, transport-limited and detachment-limited behavior, most require that either sediment or bedrock, but not both, are eroded at any given time. Modeling landscape evolution over large spatial and temporal scales requires a model that can (1) transition freely between transport-limited and detachment-limited behavior, (2) simultaneously treat sediment transport and bedrock erosion, and (3) run in 2-D over large grids and be coupled with other surface process models. We present SPACE (stream power with alluvium conservation and entrainment) 1.0, a new model for simultaneous evolution of an alluvium layer and a bedrock bed based on conservation of sediment mass both on the bed and in the water column. The model treats sediment transport and bedrock erosion simultaneously, embracing the reality that many rivers (even those commonly defined as "bedrock" rivers) flow over a partially alluviated bed. SPACE improves on previous models of bedrockalluvial rivers by explicitly calculating sediment erosion and deposition rather than relying on a flux-divergence (Exner) approach. The SPACE model is a component of the Landlab modeling toolkit, a Python-language library used to create models of Earth surface processes. Landlab allows efficient coupling between the SPACE model and components simulating basin hydrology, hillslope evolution, weathering, lithospheric flexure, and other surface processes. Here, we first derive the governing equations of the SPACE model from existing sediment transport and bedrock erosion formulations and explore the behavior of local analytical solutions for sediment flux and alluvium thickness. We derive steadystate analytical solutions for channel slope, alluvium thickness, and sediment flux, and show that SPACE matches predicted behavior in detachment-limited, transport-limited, and mixed conditions. We provide an example of landscape evolution modeling in which SPACE is coupled with hillslope diffusion, and demonstrate that SPACE provides an effective framework for simultaneously modeling 2-D sediment transport and bedrock erosion.

Despite considerable community effort, there is no general set of equations to model long-term landscape evolution. In order to determine a suitable set of landscape evolution process laws for a site where postglacial erosion has incised valleys up to 50 m deep, we generate a set of alternative models and perform a multimodel analysis. The most basic model we consider includes stream power channel incision, uniform lithology, hillslope transport by linear diffusion, and surface-water discharge proportional to drainage area. We systematically add one, two, or three elements of complexity to this model from one of four categories: hillslope processes, channel processes, surface hydrology, and representation of geologic materials. We apply methods of formal model analysis to the 37 alternative models. The global Method of Morris sensitivity analysis method is used to identify model input parameters that most and least strongly influence model outputs. Only a few parameters are identified as important, and this finding is consistent across two alternative model outputs: one based on a collection of topographic metrics and one that uses an objective function based on a topographic difference. Parameters that control channel erosion are consistently important, while hillslope diffusivity is important for only select model outputs. Uncertainty in initial and boundary conditions is associated with low sensitivity. Sensitivity analysis provides insight to model dynamics and is a critical step in using model analysis for mechanistic hypothesis testing in landscape evolution theory.

Abstract. Models of landscape evolution by river erosion are often either transport-limited (sediment is always available, but may or may not be transportable) or detachment-limited (sediment must be detached from the bed, but is then always transportable). While several models incorporate elements of, or transition between, transport-limited and detachment-limited behavior, most require that either sediment or bedrock, but not both, are eroded at any given time. We present SPACE (Stream Power with Alluvium Conservation and Entrainment) 1.0, a new model for simultaneous evolution of an alluvium layer and a bedrock bed based on conservation of sediment mass both on the bed and in the water column. The model treats sediment transport and bedrock erosion simultaneously, embracing the reality that many rivers (even those commonly defined as "bedrock" rivers) flow over a partially alluviated bed. The SPACE model is a component of the Landlab modeling toolkit, a Python-language library used to create models of earth surface processes. Landlab allows efficient coupling between the SPACE model and components simulating basin hydrology, hillslope evolution, weathering, lithospheric flexure, and other surface processes. Here, we first derive the governing equations of the SPACE model from existing sediment transport and bedrock erosion formulations and explore the behavior of local analytical solutions for sediment flux and alluvium thickness. We derive steady-state analytical solutions for channel slope, alluvium thickness, and sediment flux, and show that SPACE matches predicted behavior in detachment-limited, transport-limited, and mixed conditions. We provide an example of landscape evolution modeling in which SPACE is coupled with hillslope diffusion, and demonstrate that SPACE provides an effective framework for simultaneously modeling 2-D sediment transport and bedrock erosion.

We present a multimodel analysis for mechanistic hypothesis testing in landscape evolution theory. The study site is a watershed with well-constrained initial and boundary conditions in which a river network locally incised 50 m over the last 13 ka. We calibrate and validate a set of 37 landscape evolution models designed to hierarchically test elements of complexity from four categories: hillslope processes, channel processes, surface hydrology, and representation of geologic materials. Comparison of each model to a base model, which uses stream power channel incision, uniform lithology, hillslope transport by linear diffusion, and surface water discharge proportional to drainage area, serves as a formal test of which elements of complexity improve model performance. Model fit is assessed using an objective function based on a direct difference between observed and simulated modern topography. A hybrid optimization scheme identifies optimal parameters and uncertainty. Multimodel analysis determines which elements of complexity improve simulation performance. Validation tests which model improvements persist when models are applied to an independent watershed. The three most important model elements are (1) spatial variation in lithology (differentiation between shale and glacial till), (2) a fluvial erosion threshold, and (3) a nonlinear relationship between slope and hillslope sediment flux. Due to nonlinear interactions between model elements, some process representations (e.g., nonlinear hillslopes) only become important when paired with the inclusion of other processes (e.g., erosion thresholds). This emphasizes the need for caution in identifying the minimally sufficient process set. Our approach provides a general framework for hypothesis testing in landscape evolution.

Abstract. Models of landscape evolution provide insight into the geomorphic history of specific field areas, create testable predictions of landform development, demonstrate the consequences of current geomorphic process theory, and spark imagination through hypothetical scenarios. While the last 4 decades have brought the proliferation of many alternative formulations for the redistribution of mass by Earth surface processes, relatively few studies have systematically compared and tested these alternative equations. We present a new Python package, terrainbento 1.0, that enables multi-model comparison, sensitivity analysis, and calibration of Earth surface process models. Terrainbento provides a set of 28 model programs that implement alternative transport laws related to four process elements: hillslope processes, surface-water hydrology, erosion by flowing water, and material properties. The 28 model programs are a systematic subset of the 2048 possible numerical models associated with 11 binary choices. Each binary choice is related to one of these four elements – for example, the use of linear or nonlinear hillslope diffusion. Terrainbento is an extensible framework: base classes that treat the elements common to all numerical models (such as input/output and boundary conditions) make it possible to create a new numerical model without reinventing these common methods. Terrainbento is built on top of the Landlab framework such that new Landlab components directly support the creation of new terrainbento model programs. Terrainbento is fully documented, has 100 % unit test coverage including numerical comparison with analytical solutions for process models, and continuous integration testing. We support future users and developers with introductory Jupyter notebooks and a template for creating new terrainbento model programs. In this paper, we describe the package structure, process theory, and software implementation of terrainbento. Finally, we illustrate the utility of terrainbento with a benchmark example highlighting the differences in steady-state topography between five different numerical models.

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Geomorphologists often rely on simple models of river channel incision for predicting rates of landscape evolution and channel response to perturbations, as well as extracting climatic and tectonic signals from river longitudinal profiles. Recent work has shown that large, hillslope‐derived blocks delivered to rivers may noticeably alter the form and evolution of river profiles from the behavior predicted by the most common models. Here we use a 1‐D model of river reach erosion and hillslope block delivery to explore the conditions under which block delivery strongly influences channel evolution. We use global sensitivity analysis to understand which model parameters most strongly affect the channel longitudinal profile. We explore the effects of blocks on the relationship between erosion rate and channel gradient, and on the erosion rate‐channel steepness exponent ϕ, and find that block effects result in highly variable slope and ϕ over the range of erosion rates and climatic conditions (discharge mean and variability) tested. The influence of blocks on erosion rate‐slope scaling may be approximated by a piecewise model: The erosion threshold imposed by blocks scales linearly with erosion rate when blocks are infrequently mobile and remains constant when blocks are frequently mobile. We explore the implications of this variable‐threshold model for the erosion rate‐channel steepness relationship and find that erosion rate‐dependent thresholds imposed by hillslope‐derived blocks cause significant departures from previous models but may be consistent with existing field data sets. Our work has implications for landscape evolution modeling and the inversion of channel profiles for forcing information.