Here we describe the technical background of the LAPSUS modelling framework. More detailed information concerning the different landscape forming processes can be found in the Modules Section.
Overview of the model
LAPSUS is a reduced-complexity multi-process landscape evolution model that deliberately uses process descriptions with simple parametrisation to enable wide applicability. Both short and long term applications can be made with varying temporal (usually annual) and spatial resolution.
The model has a top-level structure that reads input data and controls the modules. Each module calculates a landscape forming process, and results of these processes are added to the dynamic landscape (DEM) at the top-level. In this way, processes can interact over mutiple timesteps.
The discharge Q (m2 time-1) (or in the 3D model in m3 m-2 time-1 or m time-1) consists of the effective precipitation and the run-on from higher slopes calculated for the centre of a grid cell. Effective precipitation is calculated by correcting precipitation by an evaporation fraction and substracting infiltration. Both precipitation and infiltration are usually constant values over the whole catchment and thus effective precipitation as well. It is however possible to use soil type, land use or e.g. elevation dependent values. Discharge towards lower neighbouring grid cells is calculated following the multiple flow principle of routing discharge water (Holmgren, 1994):Where fraction fi of the amount of flow out of a grid cell in direction i is equal to the difference in slope gradient Λ in direction i powered by factor p, divided by the summation of slope gradient Λ for all lower neighbours j powered by p (Schoorl et al., 2000). For higher p, the steepest slope gradient will be more dominant, whereby the multiple flow routing changes to steepest decent routing if p → ∞. The applied method of flow diversion influences the discharge, as grid cells which would receive all discharge in case of steepest descent flow routing, receive less water when using multiple flow routing. Subsequently gully discharge and formation are influenced as well (Schoorl et al., 2000). Multiple flow routing mimics the diverging characteristics of water flow over convex surfaces and re-sedimentation more realistic than steepest descent (Quinn et al., 1991; Schoorl et al., 2000).
After each iteration the digital elevation model and soil depth map are corrected for net erosion and sedimentation (m time-1) and for example tectonic uplift or dust deposition (m time-1). Sinks, both artificial and natural, in the DEM can cause serious problems in landscape modelling and are often removed in advance (Martz and Garbrecht, 1998). LAPSUS handles sinks within the model, and treats sinks as a natural phenomenon.