Bridging scales from single denudational events to continental-scale landscape evolution with stochastic theory

I will present work demonstrating how stochastic theory can be used to establish a scale-bridging understanding of landscape evolution. The scales of interest here include individual erosional events to continental-scale landscape evolution. The theory is used to embrace the unknowability of erosional processes operating at small scales over the lifetime of a landscape. It is used to establish analytical expectations of landscape form and its variance when the probabilities of forces driving and resisting denudation have defined distributions. The results provide a basis for the widely used stream power erosional model that is rooted in first principles. It also quantifies the (often considerable) uncertainty in predictions generated using deterministic models such as stream power, e.g. when probability distributions of driving and resisting forces significantly overlap.  Landscape form and its variance can be estimated for arbitrary stochastic driving forces and erosional thresholds extremely precisely and efficiently with a simple algorithmic approach that has links to cellular automata. I demonstrate how such approaches can be used to generate predictions that match those of partial differential equations (PDEs, e.g. the stream power model) at large scales, whilst avoiding many of the limitations, pitfalls and challenges with modelling landscape evolution with PDEs (e.g. assumptions of continuity, numerical stability, management of shockwaves). Stochastic theory is shown to provide means to relate physics-, laboratory- and field-based insights and measurement to landscape form at larger scales. I speculate on how this work might be useful for developing a better, probabilistic, understanding of landscape evolution across scales.