A. Brad Murray

Formation of coastline features by large-scale instabilities induced by high-angle waves.

Alongshore sediment transport that is driven by waves is generally assumed to smooth a coastline. This assumption is valid for small angles between the wave crest lines and the shore, as has been demonstrated in shoreline models. But when the angle between the waves and the shoreline is sufficiently large, small perturbations to a straight shoreline will grow. Here we use a numerical model to investigate the implications of this instability mechanism for large-scale morphology over long timescales. Our simulations show growth of coastline perturbations that interact with each other to produce large-scale features that resemble various kinds of natural landforms, including the capes and cuspate forelands observed along the Carolina coast of southeastern North America. Wind and wave data from this area support our hypothesis that such an instability mechanism could be responsible for the formation of shoreline features at spatial scales up to hundreds of kilometres and temporal scales up to millennia.

A coupled geomorphic and ecological model of tidal marsh evolution

The evolution of tidal marsh platforms and interwoven channel networks cannot be addressed without treating the two-way interactions that link biological and physical processes. We have developed a 3D model of tidal marsh accretion and channel network development that couples physical sediment transport processes with vegetation biomass productivity. Tidal flow tends to cause erosion, whereas vegetation biomass, a function of bed surface depth below high tide, influences the rate of sediment deposition and slope-driven transport processes such as creek bank slumping. With a steady, moderate rise in sea level, the model builds a marsh platform and channel network with accretion rates everywhere equal to the rate of sea-level rise, meaning water depths and biological productivity remain temporally constant. An increase in the rate of sea-level rise, or a reduction in sediment supply, causes marsh-surface depths, biomass productivity, and deposition rates to increase while simultaneously causing the channel network to expand. Vegetation on the marsh platform can promote a metastable equilibrium where the platform maintains elevation relative to a rapidly rising sea level, although disturbance to vegetation could cause irreversible loss of marsh habitat.

Estimation of Discharge From Three Braided Rivers Using Synthetic Aperture Radar Satellite Imagery: Potential Application to Ungaged Basins

Analysis of 41 ERS 1 synthetic aperture radar images and simultaneous ground measurements of discharge for three large braided rivers indicates that the area of active flow on braided river floodplains is primarily a function of discharge. A power law correlation is found between satellite-derived effective width We and discharge Q, where We is the water surface area within a braided reach divided by the reach length. Synthetic values of We and Q generated from a cellular automata model of stream braiding display a similar power law correlation. Power functions that are fit through plots of We and Q represent satellite-derived rating curves that can subsequently be used to estimate instantaneous river discharge from space, with errors ranging from tens to hundreds of cubic meters per second. For ungaged rivers, changes in relative discharge can be determined from satellite data alone to determine the shape and timing of annual flows in glacierized basins. Absolute discharge can probably be estimated within a factor of 2. More accurate estimates will require either (1) one or more ground measurements of discharge acquired simultaneously with a satellite image acquisition, or (2) successful parameterization of known morphologic controls such as total sinuosity 5;P, valley slope, bank material and stability, and braid channel hydraulic geometry. Values of total sinuosity 5;P derived from satellite imagery and field measurements from two rivers of braid channel width, depth, velocity, water surface slope, and bed material grain size indicate that while the shape of satellite-derived We-Q rating curves may be influenced by all of these variables, the sensitivity of flow area to changing discharge is most dependent upon the degree of braiding. Efforts to monitor river discharge from space will be most successful for intensely braided rivers with high values of total sinuosity. Subsampling of existing daily discharge records from the Iskut River suggests that satellite return times of about 1 week are sufficient for approximating the shape and timing of the seasonal hydrograph in large, glacierized basins. Although errors are large, the presented technique represents the only currently available way to estimate discharge in ungauged braided rivers.

High-angle wave instability and emergent shoreline shapes : 2. Wave climate analysis and comparisons to nature

[1] Recent research has revealed that the plan view evolution of a coast due to gradients in alongshore sediment transport is highly dependant upon the angles at which waves approach the shore, giving rise to an instability in shoreline shape that can generate different types of naturally occurring coastal landforms, including capes, flying spits, and alongshore sand waves. This instability merely requires that alongshore sediment flux is maximized for a given deepwater wave angle, a maximum that occurs between 35 and 50 for several common alongshore sediment transport formulae. Here we introduce metrics that sum over records of wave data to quantify the long-term stability of wave climates and to investigate how wave climates change along a coast. For Long Point, a flying spit on the north shore of Lake Erie, Canada, wave climate metrics suggest that unstable waves have shaped the spit and, furthermore, that smaller-scale alongshore sand waves occur along the spit at the same locations where the wave climate becomes unstable. A shoreline aligned along the trend of the Carolina Capes, United States, would be dominated by high-angle waves; numerical simulations driven by a comparable wave climate develop a similarly shaped cuspate coast. Local wave climates along these simulated capes and the Carolina Capes show similar trends: Shoreline reorientation and shadowing from neighboring capes causes most of the coast to experience locally stable wave climates despite regional instability.

Riparian Vegetation as a Primary Control on Channel Characteristics in Multi-Thread Rivers

Vegetation has been recognized as a primary control on river planform, particularly as a determinant of whether a river will adopt a braided or single-thread pattern (e.g. Millar [2000]). Studies have shown that overall behavior of the system correlates with vegetation type or density, shifting between a single-thread channel and a multi-thread system as vegetation changes [Mackin, 1956; Brice, 1964; Nevins, 1969; Goodwin, 1996; Ward and Tockner, 2000]. Murray and Paola [1994] concluded that braiding is the main mode of instability for unconstrained flow over a noncohesive bed. In other words, in the absence of cohesion to stabilize the banks and/or discourage formation of new channels, the flow tends to create new channels until a braided system develops. There-

Rapid wetland expansion during European settlement and its implication for marsh survival under modern sediment delivery rates

Fluctuations in sea-level rise rates are thought to dominate the formation and evolution of coastal wetlands. Here we demonstrate a contrasting scenario in which land-use–related changes in sediment delivery rates drive the formation of expansive marshland, and vegetation feedbacks maintain their morphology despite recent sediment supply reduction. Stratigraphic analysis and radiocarbon dating in the Plum Island Estuary (Massachusetts, United States) suggest that salt marshes expanded rapidly during the eighteenth and nineteenth centuries due to increased rates of sediment delivery following deforestation associated with European settlement. Numerical modeling coupled with the stratigraphic observations suggests that existing marshland could survive, but not form under the low suspended sediment concentrations observed in the estuary today. These results suggest that many of the expansive marshes that characterize the modern North American coast are metastable relicts of high nineteenth century sediment delivery rates, and that recent observations of degradation may represent a slow return to pre-settlement marsh extent. In contrast to ecosystem management practices in which restoring pre-anthropogenic conditions is seen as a way to increase ecosystem services, our results suggest that widespread efforts to restore valuable coastal wetlands actually prevent some systems from returning to a natural state.

Fetch-limited self-organization of elongate water bodies

Naturally occurring elongate bodies that are segmented or appear to be in the process of segmentation occur in a variety of environments and scales. A simple, process-based numerical model of planform shoreline evolution demonstrates that fetch controls on alongshore sediment transport can result in the segmentation of an elongate water body into smaller, rounded lakes or ponds. The shape of elongate water bodies leaves their long coasts prone to a high-angle-wave instability in shoreline shape that results in the formation of capes that grow through interactions with one another along the same coast. In a numerical model, as capes extend farther offshore, a new behavior emerges, whereby capes on opposing coasts attract one another laterally as they grow, suggesting a novel mechanism for large-scale shoreline self-organization through fetch-limiting interactions. We demonstrate these interactions through analysis of local net sediment flux and coastline stability. Ensemble model runs suggest that, for a symmetric wind distribution, the initial segmentation of a water body requires four lengths per initial width, yet water bodies with higher initial aspect ratios segment to one final round water body per factor of two of the initial aspect ratio. Wave-dominated elongate water bodies with coasts consisting of clastic sediment (and a lack of vegetation) are most likely to undergo this predicted segmentation.

Validation of Braided-Stream Models: Spatial state-space plots, self-affine scaling, and island shapes

We present a comprehensive approach for validating braided-stream models and apply it to a specific cellular braided-stream model. The approach involves quantitative comparison of modeled and natural braided streams in terms of two main aspects: the sequential organization of their plan patterns studied using their state-space characteristics and the hierarchical organization of their patterns studied in the framework of self-affine scaling. These two aspects of braided streams are complementary to each other and taken together provide a sensitive test of the validity of a model of braided streams. The simple model we examine produces patterns that are similar to those of natural braided rivers in terms of both sequential organization and self-affine scaling. This finding supports the conclusion that the nonlinear interactions between water and sediment in the model are the primary mechanisms responsible for shaping braided rivers in nature.

A New Quantitative Test of Geomorphic Models, Applied to a Model of Braided Streams

Recent simple cellular models of self-organized geomorphic patterns embody a new understanding of complex, spatially extended systems. Such models can be difficult to test quantitatively because the statistics traditionally used can be insensitive even to visually obvious variations in a complex pattern. Here we develop a new approach to evaluating such models. We begin by applying to spatial patterns the state-space reconstruction techniques developed for dynamical systems, producing plots that summarize the patterns in a way that preserves more information than do the statistics usually used in geomorphology. Methods exist for characterizing some aspects of such plots. Here we develop a complementary method for quantitatively comparing state-space plots in a way that more directly evaluates the similarity between the typical features of spatial patterns. An application of this method to the patterns produced by a cellular braided-stream model and real braided streams indicates that this approach provides a relatively sensitive way of comparing model-generated and real spatial patterns.

Beach and sea-cliff dynamics as a driver of long-term rocky coastline evolution and stability

We investigate rocky coastline evolution over millennial time scales using exploratory analytical and numerical models based on interactions between beaches and sea cliffs. In the models, wave-driven sea-cliff retreat is a nonlinear function of beach width, where cliff retreat is maximized by sediment abrasion and minimized by either a lack of beach sediment or too much sediment (which prevents waves from reaching the sea cliff). As sea cliffs retreat, beach sediment is produced and distributed alongshore by wave-driven sediment transport, and local beach widths determine future cliff retreat rates. Numerical experiments indicate that through such interactions, rocky coastlines can reach an equilibrium configuration where headlands and embayments remain stable through time, even in the absence of alongshore variations in sea-cliff lithology. Furthermore, the equilibrium coastline configuration, or the alongshore proportion of rocky headland to cliff-backed pocket beach, can be predicted analytically. Initial tests suggest that predictions match well qualitatively with actual landscapes.