Dynamic modelling framework to track sediment provenance and solve lakes in long-term landscape evolution models

Many laws have been developed to describe the different aspects of landscape evolution at large spatial and temporal scales. Natural landscapes have heterogeneous properties (lithologies, climates, tectonics, etc.) that are associated with multiple coexisting processes. In turn, this can demand different mathematical expressions to model landscape evolution as a function of time and or space. Landscape Evolution Models are mostly designed to facilitate the combination of different landscape-wide laws in a plug-and-play way and many frameworks are being developed in this aim. However, most current frameworks cannot capture important landscape processes such as lake dynamics and full sediment tracing because they are optimized for speed and handle fluxes separately. Several processes require information from more than the immediate neighboring cells within a time step and demand an integrated knowledge from the entire upstream trajectory. Lakes for example require knowledge of all upstream water and sediment fluxes to be filled. These can only be known if all the laws controlling those have been processed. Tackling these situation with a grid logic requires substantial amount of numerical refactoring from existing models.

We present an alternative method to tackle landscape evolution modelling in heterogeneous landscapes with a framework inspired from Lagrangian and cellular automaton methods. Our framework only relies on the assumption that upstream nodes needs to be processed before the downstream ones, including lakes with outlets, in order to process all selected governing equations on a pixel-to-pixel basis. This way, we ensure that the true content of sediment and water fluxes can be known and tracked at any points. We first utilise graph theory to (i) find the most comprehensive path to reroute water through depressions and (ii) determine a generic multiple flow topological order (any node is processed after all potential upstream ones). Particles that register and track all fluxes simultaneously can then "roll" on the landscape and merge between each other while interacting with the grid.

This formulation makes possible a number of generic features. (i) The laws can be dynamically adapted to the environment (e.g. switching from single to multiple flow function of water content, adapting erodibility function of the sediment composition and quantity), (ii) Depressions can be explicitly managed, filled (or not) and separated from the rest of the landscape (e.g. sedimentation or evaporation in lakes) as a function function of inputted fluxes and parameters, (iii) full provenance, transport time, and deposition tracking as the particle can always keep in memory where the fluxes are from and in what proportions. In this contribution, we demonstrate the impact the importance of considering these additional elements in landscape evolution. In particular, lake dynamic can significantly impact the long-term signal propagation from source to sink.