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Abstract The extent to which climate and tectonics can be coupled rests on the degree to which topography and erosion rates scales linearly. The stream power incision model (SPIM) is commonly used to interpret such relationships, but is limited in probing mechanisms. A promising modification to stream power models are stochastic‐threshold incision models (STIM) which incorporate both variability in discharge and a threshold to erosion. In this family of models, the form of the topography erosion rate relationship is largely controlled by runoff variability. Applications of STIM typically assume temporally variable, but spatially uniform and synchronous runoff generating events, an assumption that is likely broken in regions with complicated orography. To address this limitation, we develop a new 1D STIM model, which we refer to as spatial‐STIM. This modified version of STIM allows for stochasticity in both time and space and is driven by empirical relationships between topography and runoff statistics. Coupling between mean runoff and runoff variability via topography in spatial‐STIM generates highly nonlinear relationships between steady‐state topography and erosion rates. We find that whether the daily statistics of runoff are spatially linked or unlinked, which sets whether there is spatial synchronicity in the recurrence interval of runoff generating events, is a fundamental control on landscape evolution. Many empirical topography—erosion rate data sets are based on data that span across the endmember scenarios of linked versus unlinked behavior. It is thus questionable whether singular SPIM relationships fit to those data can be meaningfully related to their associated hydroclimatic conditions. 

Abstract Mountain topography alters the phase, amount, and spatial distribution of precipitation. Past efforts focused on how orographic precipitation can alter spatial patterns in mean runoff, with less emphasis on how time‐varying runoff statistics may also vary with topography. Given the importance of the magnitude and frequency of runoff events to fluvial erosion, we evaluated whether orographic patterns in mean runoff and daily runoff variability can be constrained using the global WaterGAP3 water model data. Model runoff data are validated against observational data in the contiguous United States, showing agreement with mean runoff in all settings and daily runoff variability in settings where rainfall‐runoff predominates. In snowmelt‐influenced settings, runoff variability is overestimated by the water model data. Cognizant of these limitations, we use the water model data to develop relationships between mean runoff and daily runoff variability and how these are mediated by snowmelt fraction in mountain topography globally. A global analysis of topographic controls on hydroclimatic variables using a random forest model was ambiguous. Instead, relationships between topography and runoff parameters are better assessed at the mountain range scale. Rulesets linking topography to mean runoff and snowmelt fraction are developed for three mid‐latitude mountain landscapes—British Columbia, European Alps, and Greater Caucasus. Increasing topographic elevation and relief together leads to higher mean runoff and lower runoff variability due to the increasing contribution of snowmelt. The three sets of empirical relationships developed here serve as the basis for a suite of numerical experiments in our companion manuscript (Part 2, Forte & Rossi, 2024a,https://doi.org.10.1002/2023JF007327). 

Abstract Generalizable relationships for how subdaily rainfall statistics imprint into runoff statistics are lacking. We use the Colorado Front Range, known for destructive rainfall‐triggered floods and landslides, to assess whether orographic patterns in runoff generation are a direct consequence of rainstorm climatology. Climatological analysis relies on a dense network of tipping‐bucket rain gauges and gridded precipitation frequency estimates from the National Oceanic and Atmospheric Administration to evaluate relationships among subdaily rainfall statistics, topography, and flood frequency throughout the South Platte River basin. We find that event‐scale rainfall statistics only weakly depend on elevation, suggesting that orographic gradients in runoff “extremes” are not simply a consequence of rainfall patterns. In contrast, bedrock exposure strongly varies with elevation in a way that plausibly explains enhanced runoff generation at lower elevations via reduced water storage capacity. These findings are suggestive of feedbacks between bedrock river evolution and hillslope hydrology not typically included in models of landscape evolution. 

Gravel‐bed rivers that incise into bedrock are common worldwide. These systems have many similarities with other alluvial channels: they transport large amounts of sediment and adjust their forms in response to discharge and sediment supply. At the same time, the occurrence of bedrock incision implies behaviour that falls on a spectrum between fully detachment‐limited ‘bedrock channels’ and fully transport‐limited ‘alluvial channels’. Here, we present a mathematical model of river profile evolution that integrates bedrock erosion, gravel transport and the formation of channels whose hydraulic geometry is consistent with that of near‐threshold alluvial channels. We combine theory for five interrelated processes: bedload sediment transport in equilibrium gravel‐bed channels, channel width adjustment to flow and sediment characteristics, abrasion of bedrock by mobile sediment, plucking of bedrock and progressive loss of gravel‐sized sediment due to grain attrition. This model contributes to a growing class of models that seek to capture the dynamics of both bedrock incision and alluvial sediment transport. We demonstrate the model's ability to reproduce expected fluvial features such as inverse power law scaling between slope and area, and width and depth consistent with near‐threshold channel theory, and we discuss the role of sediment characteristics in influencing the mode of channel behaviour, erosional mechanism, channel steepness and profile concavity. 

Increased access to high-resolution topography has revolutionized our ability to map out fine-scale topographic features at watershed to landscape scales. As our “vision” of the land surface has improved, so has the need for more robust quantification of the accuracy of the geomorphic maps we derive from these data. One broad class of mapping challenges is that of binary classification whereby remote sensing data are used to identify the presence or absence of a given feature. Fortunately, there is a large suite of metrics developed in the data sciences well suited to quantifying the pixel-level accuracy of binary classifiers. This analysis focuses on how these metrics perform when there is a need to quantify how the number and extent of landforms are expected to vary as a function of the environmental forcing (e.g., due to climate, ecology, material property, erosion rate). Results from a suite of synthetic surfaces show how the most widely used pixel-level accuracy metric, the F1 score, is particularly poorly suited to quantifying accuracy for this kind of application. Well-known biases to imbalanced data are exacerbated by methodological strategies that calibrate and validate classifiers across settings where feature abundances vary. The Matthews correlation coefficient largely removes this bias over a wide range of feature abundances such that the sensitivity of accuracy scores to geomorphic setting instead embeds information about the size and shape of features and the type of error. If error is random, the Matthews correlation coefficient is insensitive to feature size and shape, though preferential modification of the dominant class can limit the domain over which scores can be compared. If the error is systematic (e.g., due to co-registration error between remote sensing datasets), this metric shows strong sensitivity to feature size and shape such that smaller features with more complex boundaries induce more classification error. Future studies should build on this analysis by interrogating how pixel-level accuracy metrics respond to different kinds of feature distributions indicative of different types of surface processes.