Optimising global landscape evolution models with ¹⁰Be

Abstract

By simulating erosion and deposition, landscape evolution models (LEMs) offer powerful insights into Earth surface processes and dynamics. Stream-power-based LEMs are often constructed from parameters describing drainage area (m), slope (n), substrate erodibility (K), hillslope diffusion (D), and a critical drainage area (Ac) that signifies the downslope transition from hillslope diffusion to advective fluvial processes. In spite of the widespread success of such models, the parameter values are highly uncertain mainly because the advection and diffusion equations amalgamate physical processes and material properties that span widely differing spatial and temporal scales. Here, we use a global catalogue of catchment-averaged cosmogenic 10Be-derived denudation rates with the aim to optimise a set of LEMs via a Monte Carlo-based parameter search. We consider three model scenarios: advection-only, diffusion-only, and an advection–diffusion hybrid. In each case, we search for a parameter set that best approximates denudation rates at the global scale, and we directly compare denudation rates from the modelled scenarios with those derived from 10Be data. We find that optimised ranges can be defined for many LEM parameters at the global scale. In the absence of diffusion, n∼1.3, and with increasing diffusivity the optimal n increases linearly to a global maximum of n∼2.3. Meanwhile, we find that the diffusion-only model yields a slightly lower misfit when comparing model outputs with observed erosion rates than the advection-only model and is optimised when the concavity parameter is raised to a power of 2. With these examples, we suggest that our approach provides baseline parameter estimates for large-scale studies spanning long timescales and diverse landscape properties. Moreover, our direct comparison of model-predicted versus observed denudation rates is preferable to methods that rely upon catchment-scale averaging or amalgamation of topographic metrics. We also seek to optimise the K and D parameters in LEMs with respect to precipitation and substrate lithology. Despite the potential bias due to factors such as lithology, these optimised models allow us to effectively control for topography and specifically target the relationship between denudation and precipitation. All models suggest a general increase in exponents with precipitation in line with previous studies. When isolating K under globally optimised models, we observe a positive correlation between K or D and precipitation > 1500 mm yr−1, plus a local maximum at ∼300 mm yr−1, which is compatible with the long-standing hypothesis that semi-arid environments are among the most erodible.