Lagrangian framework to simulate landscapes with local sinks and independently solved fluxes of water, sediment, and tracers

Abstract:

Natural landscapes have heterogeneous properties (lithologies, climates, etc.) that are associated with multiple coexisting processes. In turn, this can demand different mathematical expressions in parallel to model the evolution of a single landscape. Landscape Evolution Models are mostly designed in Eulerian grids, which has the advantage of making the combination of different landscape-wide laws easy in a plug-and-play way and many frameworks are being developed in this aim. However, several processes demand an integrated knowledge from the entire upstream trajectory. Topographic depressions are a perfect example: to determine if an internal lake will be filled with water and/or sediment and hence transfer these fluxes downstream, one needs to know the final state of all the fluxes upstream of the lake. These can only be known if all the laws affecting sediment and water have been processed. Tackling this situation with a grid logic requires many adaptation, e.g. separating the model into sub-domains, and adapting such models to new formulations typically requires a substantial amount of numerical refactoring.

We present an alternative method to tackle landscape evolution modelling in heterogeneous landscapes by developing a Lagrangian framework not tied a set of fixed formulations for fixed processes. It only relies on the assumption that upstream nodes needs to be processed before the downstream ones, acknowledging lakes with outlets. We utilise graph theory to find the most comprehensive path to reroute water through depressions and use an adequate topological sorting compatible with multiple flow. Equations are then expressed in series of flexible functional descriptions of particles' actions: interactions with the grid (e.g. erosion), interactions with external data (e.g. precipitation), splitting the fluxes (e.g. steepest descent) and merging with other particles. The framework therefore allows (i) dynamically adaption of laws to the environment, (ii) explicit management of lakes (filled or not, evaporation), (iii) intrinsic evolution of fluxes (e.g. grainsize fining during transport) and (iv) full provenance and deposition tracking. In this contribution, we present in detail the structure of the model and apply theoretical cases focusing on the handling of depressions in the landscape.