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Long‐term erosion can threaten infrastructure and buried waste, with consequences for management of natural systems. We develop erosion projections over 10 ky for a 5 km²watershed in New York, USA. Because there is no single landscape evolution model appropriate for the study site, we assess uncertainty in projections associated withmodel structureby considering a set of alternative models, each with a slightly different governing equation. In addition to model structure uncertainty, we consider the following uncertainty sources: selection of a final model set; each model's parameter values estimated through calibration; simulation boundary conditions such as the future incision of downstream rivers and future climate; and initial conditions (e.g., site topography which may undergo near‐term anthropogenic modification). We use an analysis‐of‐variance approach to assess and partition uncertainty in projected erosion into the variance attributable to each source. Our results suggest one sixth of the watershed will experience erosion exceeding 5 m in the next 10 ky. Uncertainty in projected erosion increases with time, and the projection uncertainty attributable to each source manifests in a distinct spatial pattern. Model structure uncertainty is relatively low, which reflects our ability to constrain parameter values and reduce the model set through calibration to the recent geologic past. Beyond site‐specific findings, our work demonstrates what information prediction‐under‐uncertainty studies can provide about geomorphic systems. Our results represent the first application of a comprehensive multi‐model uncertainty analysis for long‐term erosion forecasting.

 

We review select mature geomorphic transport laws for use in temperate ridge and valley landscapes and compile parameter estimates for use in applications. This work is motivated by a case study of sensitivity analysis, calibration, validation, multimodel comparison, and prediction under uncertainty, which required bounding values for parameter ranges. Considered geomorphic transport formulae span hillslope sediment transport, soil production, and erosion by surface water. We compile or derive estimates for the parameters in these transport formulae. Additionally, we address a common challenge—connecting changes in precipitation distribution to changes in effective erodibility—by using a simple hydrologic model and a method to estimate precipitation distribution parameters using commonly available data. While some parameters are reasonably well constrained, others span orders of magnitude. Some, such as soil infiltration capacity, have a direct physical meaning but are challenging to measure on geologically relevant timescales. Through the process of compiling these ranges we identify common challenges in parameter determination. The issue of comparable units derives from considering an exponent as an empirically inferred coefficient rather than as an expression of a fundamental relationship. The issue of appropriate timescales derives from the mismatch between human measurement and geologic timescales. This contribution thus serves both as a practical compilation for applications and as a synthesis of outstanding challenges in parameter selection for geomorphic transport laws.

 

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.

 

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. Numerical simulation of the form and characteristics of Earth's surface provides insight into its evolution. Landlab is an open-source Python package that contains modularized elements of numerical models for Earth's surface, thus reducing time required for researchers to create new or reimplement existing models. Landlab contains a gridding engine which represents the model domain as a dual graph of structured quadrilaterals (e.g., raster) or irregular Voronoi polygon–Delaunay triangle mesh (e.g., regular hexagons, radially symmetric meshes, and fully irregular meshes). Landlab also contains components – modular implementations of single physical processes – and a suite of utilities that support numerical methods, input/output, and visualization. This contribution describes package development since version 1.0 and backward-compatibility-breaking changes that necessitate the new major release, version 2.0. Substantial changes include refactoring the grid, improving the component standard interface, dropping Python 2 support, and creating 31 new components – for a total of 58 components in the Landlab package. We describe reasons why many changes were made in order to provide insight for designers of future packages. We conclude by discussing lessons about the dynamics of scientific software development gained from the experience of using, developing, maintaining, and teaching with Landlab.