A Numerical Model of Retreating Alluvial Fan Coasts
Abstract
A numerical model has been developed that simulates the wave-driven retreat of partially-consolidated alluvial- fan shores over millennium time-scales. It has been developed to reproduce the shore profiles and coastal erosion rates observed along the Pleistocene glacial-outwash fan built by the Waitaki River on the east coast of New Zealand's South Island. This cliffed shore is currently fronted by a narrow sand-and-gravel beach. The nearshore seabed is formed in Pleistocene substrate and has only a thin and patchy cover of sand. The motivation is to examine the sensitivity of the erosion rates to wave-climate change, sea-level rise, and river sediment supplies. The model is forced by two wave conditions that, when randomly sampled, represent the storm-wave and normal-swell climates of the prototype coast. These each operate for a fixed proportion of the model's yearly time-step. Morphological change is driven by a series of coupled process models. These include scour of the nearshore seabed by shoaling waves, cross-shore exchanges of sand and gravel between the nearshore and beach, berm construction during normal wave conditions, berm overtopping by storm waves with consequent beach stripping and scour of the exposed sub-aerial substrate and cliff-toe notch-cutting, gravity-failure of the cliffs and talus construction between storm events, and beach sediment abrasion. The scour, notching, and transport models are generally based on energetics principles and are calibrated with linear scaling coefficients to match field observations from the prototype coast. Negative feedback regulates the rate of cliff erosion through the protection that is afforded by cliff and substrate material added to the beach. The starting model condition is a sloping alluvial fan inundated by the sea-level rise that followed the last glacial epoch, and the model is run for 6000 years to the present assuming a stable sea level. Initially, the gentle slope of the alluvial fan results in quite rapid rates of seafloor lowering under the shoaling and breaking waves, which in turn results in the rapid development of a large gravel barrier fed by the material excavated from the nearshore. As the nearshore profile approaches equilibrium, this onshore supply lessens and abrasion begins to reduce the beach volume. As a result, the beach size reduces to a threshold at which storm waves periodically overtop and strip part or all of the beach. The associated scour of the substrate beneath the sub- aerial beach initiates a proto-cliff. The modeled shore then settles into a mode of ongoing retreat with gradually increasing cliff height and a landward-translating nearshore profile. From this stage, the beach volume settles to an equilibrium value, while the cliff retreat rate declines in inverse proportion to the cliff height. The equilibrium volume and retreat rates are a function of the wave climate and the substrate material properties. The model was verified from the nearshore and shore-cliff profiles of the prototype coast, assuming that these have evolved over the past ~ 6000 year sea-level still-stand. The current model formulation is 1-d, assuming zero divergence in the longshore transport field. Work-in- progress is expanding the model to 2-d, to include wave refraction, longshore transport divergence, river sediment inputs, and longshore variability in substrate topography and material properties.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2006
- Bibcode:
- 2006AGUFM.H32C..08H
- Keywords:
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- 1824 Geomorphology: general (1625);
- 1847 Modeling;
- 4217 Coastal processes;
- 4546 Nearshore processes