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Erosion following human disturbance threatens ecosystem health and inhibits effective land use. Mountaintop removal/valley fill (MTR/VF) mined landscapes of the Appalachian Coalfields region, USA, provide a unique opportunity to quantify the geomorphic trajectory of disturbed lands. Here we assess how MTR/VF-induced changes to topography and vegetation influence spatiotemporal erosion patterns in five mined watersheds. We use landscape evolution models starting from pre- and post-MTR/VF topographic data to isolate the influence of mining-induced topographic change. We then constrain ranges of erodibility from incision depths of gully features on mine margins, and use those estimates to model the influence of vegetation recovery trends on erosion. Topographic alterations alone reduce total sediment export from mined catchments. Model runs that incorporate the disturbance and recovery of vegetation in mined watersheds show that complete vegetation recovery keeps millennial sediment export from mined catchments within the range of unmined catchments. If vegetation recovery is anything less than complete, vegetation disturbance drives greater total sediment export from mined catchments than unmined catchments. Full vegetation recovery causes sediment fluxes to decline over millennia beyond the recovery period, while watersheds without full recovery experience fluxes that increase over the same time period. Spatiotemporal erosion trends depend on 1) the extent of vegetation recovery and 2) the extent to which MTR/VF creates slope–area disequilibrium. Valley fills and mine scarps experience erosion rates several times higher than those found in the unmined landscapes. Rapid erosion of mined areas drives deposition in colluvial hollows, headwater stream valleys, and below scarps. Our experiments suggest that reclamation focused on maximizing vegetation recovery and reducing hotspots of slope–area disequilibrium would reduce MTR's influence on Appalachian watersheds both during and long after the vegetation recovery period. Insights from MTR/VF-influenced landscapes can inform mined land management as the renewable energy transition drives increased surface mining. [Display omitted] • We model 10,000 years of erosion beginning from both pre- and post-mining topography. • Mining-driven topographic changes alone reduce total erosion due to ridge flattening. • Incomplete vegetation recovery increases erosion in mined over unmined basins. • Erosion is focused in valley fills, deposition in low-order valleys and below scarps. • Vegetation recovery sets decadal sediment pulses and millennial landscape trajectory. [ABSTRACT FROM AUTHOR]

Constraining Earth's sediment mass balance over geologic time requires a quantitative understanding of how landscapes respond to transient tectonic perturbations. However, the mechanisms by which bedrock lithology governs landscape response remain poorly understood. Rock type influences the size of sediment delivered to river channels, which controls how efficiently rivers respond to tectonic forcing. The Mendocino triple junction region of northern California, USA, is one landscape in which large boulders, delivered by hillslope failures to channels, may alter the pace of landscape response to a pulse of rock uplift. Boulders frequently delivered by earthflows in one lithology, the Franciscan mélange, have been hypothesized to steepen channels and slow river response to rock uplift, helping to preserve high-elevation, low-relief topography. Channels in other units (the Coastal Belt and the Franciscan schist) may experience little or no erosion inhibition due to boulder delivery. Here we investigate spatial patterns in channel steepness, an indicator of erosion resistance, and how it varies between mélange and non-mélange channels. We then ask whether lithologically controlled boulder delivery to rivers is a possible cause of steepness variations. We find that mélange channels are steeper than Coastal Belt channels but not steeper than schist channels. Though channels in all units steepen with increasing proximity to mapped hillslope failures, absolute steepness values near failures are much higher (~2x) in the mélange and schist than in Coastal Belt units. This could reflect reduced rock erodibility or increased erosion rates in the mélange and schist, or disproportionate steepening due to enhanced boulder delivery by hillslope failures in those units. To investigate the possible influence of lithology-dependent boulder delivery, we map boulders at failure toes in the three units. We find that boulder size, frequency, and concentration are greatest in mélange channels and that Coastal Belt channels have the lowest concentrations. Using our field data to parameterize a mathematical model for channel slope response to boulder delivery, we find that the modeled influence of boulders in the mélange could be strong enough to account for some observed differences in channel steepness between lithologies. At the landscape scale, we lack the data to fully disentangle boulder-induced steepening from that due to spatially varying erosion rates and in situ rock erodibility. However, our boulder mapping and modeling results suggest that lithology-dependent boulder delivery to channels could retard landscape adjustment to tectonic forcing in the mélange and potentially also in the schist. Boulder delivery may modulate landscape response to tectonics and help preserve high-elevation, low-relief topography at the Mendocino triple junction and elsewhere. [ABSTRACT FROM AUTHOR]

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 km2 watershed in New York, USA. Because there is no single landscape evolution model appropriate for the study site, we assess uncertainty in projections associated with model structure by 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. Plain Language Summary: Erosion of ground material is a hazard to buildings and other infrastructure, and can pose an environmental risk when it occurs in areas such as radioactive waste repositories and post‐industrial sites. We make projections for erosion over the next 10,000 years and assess uncertainty sources at a 5 km2 watershed in New York state. Natural systems, like the study site, are not as well understood as engineered systems. However, information from studies like this one can provide useful insights to guide management decisions. Parts of the watershed experienced up to 50 m of erosion over the past 13,000 years. The type of model used to simulate land surface evolution over thousands of years is a Landscape Evolution Model (LEM). We use a set of alternative LEMs identified by prior work as successful in simulating this watershed from 13,000 years ago to the present. We consider uncertainty in future climate, incision of downstream rivers, the models used and their parameters, and small changes to the initial topography. We find that just under 20% of the study site will experience erosion exceeding 5 m at +10,000 years. The most important uncertainty source varies across the watershed and increases with time. Key Points: Projections of erosion to 10 ky and uncertainty assessment demonstrate that the dominant uncertainty sources vary in space and timeTwo alternative approaches to model selection result in similar projections and uncertainty at 10 kyVariation across alternative models is subtle and initial conditions influence the location of gullies that drain low‐relief areas [ABSTRACT FROM AUTHOR]

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. Key Points: Multiple landscape evolution models are developed for application in a well‐constrained site undergoing locally rapid (4 m/ka) erosionGlobal sensitivity analysis reveals that uncertainty in initial and boundary conditions has low impact on model output metricsGlobal sensitivity analysis finds that channel erosion parameters dominate and that select metrics are sensitive to hillslope diffusivity [ABSTRACT FROM AUTHOR]

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. Key Points: We provide a compilation of parameter ranges for mature geomorphic transport laws in terrestrial geomorphologyA simple hydrological model connects changes in the precipitation distribution with erodibility coefficientsCommon challenges include incomparable units and mismatch between observation and simulation timescales [ABSTRACT FROM AUTHOR]

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. Key Points: Comparison of calibrated models at a well‐constrained field site serves as a formal hypothesis test of landscape evolution theoryRepresenting subtle lithologic contrasts, fluvial incision thresholds, and nonlinear hillslope transport improves simulation results mostModel structure improvements are not always linearly additive [ABSTRACT FROM AUTHOR]

Surface mining may be humanity's most tangible impact on Earth's surface and will become more prevalent as the energy transition progresses. Prediction of post-mining landscape change can help mitigate environmental damage, but requires understanding how mining changes geomorphic processes and variables. Here we investigate surface mining's complex influence on surface processes in a case study of mountaintop removal/valley fill (MTR/VF) coal mining in the Appalachian Coalfields, USA. The future of MTR/VF landscapes is unclear because mining's effects on geomorphic processes are poorly understood. We use geospatial analysis—leveraging the existence of pre- and post-MTR/VF elevation models—and synthesis of literature to ask how MTR/VF alters topography, hydrology, and land-surface erodibility and how these changes could be incorporated into numerical models of post-MTR/VF landscape evolution. MTR/VF reduces slope and area–slope product, and rearranges drainage divides. Creation of closed depressions alters flow routing and casts doubt on the utility of models that assume steady flow. MTR/VF creates two contrasting hydrologic domains, one in which overland flow is generated efficiently due to a lack of infiltration capacity, and one in which waste rock deposits act as extensive subsurface reservoirs. This dichotomy creates localized hotspots of overland flow and erosion. Loss of forest cover probably reduces cohesion in near-surface soils for at least the timescale of vegetation recovery, while waste rock fills and minesoils also likely experience reduced erosion resistance. Our analysis suggests three necessary ingredients for numerical modeling of post-MTR/VF landscape change: 1) accurate routing and accumulation of unsteady overland flow and accompanying sediment across low-gradient, depression-rich, engineered landscapes, 2) separation of the landscape into cut, filled, and unmined regions, and 3) incorporation of vegetation recovery trajectories. Improved modeling of post-mining landscape evolution will mitigate environmental degradation from past mining and reduce the impacts of future mining that supports the energy transition. [Display omitted] • Mountaintop removal mining flattens topography and moves drainage divides. • Cut and filled domains generate different quantities of erosive runoff. • Creation of many closed depressions reduces applicability of common models. • Vegetation loss and material property changes increase erodibility. • Our work reveals the necessary elements for models of post-mining landscape change. [ABSTRACT FROM AUTHOR]

Models of landscape evolution provide insight into the development 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 four 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 modeling 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 model elements: hillslope processes, surface-water hydrology, erosion by flowing water, and material properties. The 28 model programs stem from 13 binary choices related to one of these four elements -- for example, the use of linear or non-linear hillslope diffusion. terrainbento is an extensible framework: model base classes that treat the elements common to all models (such as input/output and boundary conditions) make it possible to create a new model without re-inventing these common methods. terrainbento is built on top of the Landlab framework, such that new Landlab components directly support the creation of new terrainbento models. terrainbento is fully documented, has 100% unit test coverage including numerical comparison with % all available 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 model 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 process models. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]