Abstract
Abstract. 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.
Highlights
It is known that resolution impacts landscape evolution models (LEMs) (Schoorl et al, 2000)
It has been demonstrated that either distributing flow down all slopes or allowing flow to descend down the steepest slope, gives different outcomes for landscape evolution models (Schoorl et al, 2000; Pelletier, 2004)
For a model of channelized flow, it was, found that the routing of run-off led to a resolution dependence in the valley spacing, which could be overcome by the addition of a parameterized flow width that was less than the numerical grid spacing (Perron et al, 2008)
Summary
It is known that resolution impacts landscape evolution models (LEMs) (Schoorl et al, 2000). The resolution dependence of LEMs is caused by how run-off is routed down the model surface. For a model of channelized flow, it was, found that the routing of run-off led to a resolution dependence in the valley spacing, which could be overcome by the addition of a parameterized flow width that was less than the numerical grid spacing (Perron et al, 2008). The response time of LEMs to a change in external forcing is strongly dependent on the surface run-off (Armitage et al, 2018) This means that the model response time becomes likewise dependent on the chosen flow width. In LEMs developed for understanding long-term landscape evolution, the large timescales necessitate large spatial scales, where a single grid cell can be 1 km wide or more (Temme et al, 2017). If the width of the flow path for run-off is narrower than can be reasonably modelled, can the flow paths be treated as lines, from model node to node (Fig. 2), where water collects along these lines? To explore this idea and understand LEM sensitivity to resolution, I wish to explore how a simple LEM evolves under four scenarios (Fig. 2): (1) simple SFD from cell area to cell area, (2) an MFD version of this cell-to-cell algorithm, (3) a node-to-node SFD, and (4) a node-to-node MFD
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