Short communication: flow as distributed lines within the landscape

Landscape evolution models (LEMs) aim to capture an aggregation of the processes of erosion and deposition within the earth's surface and predict the evolving topography. Over long timescales, i.e. greater than 1 million years, the computational cost is such that numerical resolution is coarse and all small-scale properties of the transport of material cannot be captured. A key aspect, therefore, of such a long timescale LEM is the algorithm chosen to route water down the surface. I explore the consequences of two end-member assumptions of how water flows over the surface of an LEM - either down a single flow direction (SFD) or down multiple flow directions (MFDs) - on model sediment flux and valley spacing. I find that by distributing flow along the edges of the mesh cells, node to node, the resolution dependence of the evolution of an LEM is significantly reduced. Furthermore, the flow paths of water predicted by this node-to-node MFD algorithm are significantly closer to those observed in nature. This reflects the observation that river channels are not necessarily fixed in space, and a distributive flow captures the sub-grid-scale processes that create non-steady flow paths. Likewise, drainage divides are not fixed in time. By comparing results between the distributive transport-limited LEM and the stream power model "Divide And Capture", which was developed to capture the sub-grid migration of drainage divides, I find that in both cases the approximation for sub-grid-scale processes leads to resolution-independent valley spacing. I would, therefore, suggest that LEMs need to capture processes at a sub-grid-scale to accurately model the earth's surface over long timescales.