Along shore 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.

[1] Contrary to traditional findings, the deepwater angle of wave approach strongly affects plan view coastal evolution, giving rise to an antidiffusional ''high wave angle'' instability for sufficiently oblique deepwater waves (with angles between wave crests and the shoreline trend larger than the value that maximizes alongshore sediment transport, $45°). A one-contour-line numerical model shows that a predominance of high-angle waves can cause a shoreline to self-organize into regular, quasiperiodic shapes similar to those found along many natural coasts at scales ranging from kilometers to hundreds of kilometers. The numerical model has been updated from a previous version to include a formulation for the widening of an overly thin barrier by the process of barrier overwash, which is assumed to maintain a minimum barrier width. Systematic analysis shows that the wave climate determines the form of coastal response. For nearly symmetric wave climates (small net alongshore sediment transport), cuspate coasts develop that exhibit increasing relative cross-shore amplitude and pointier tips as the proportion of high-angle waves is increased. For asymmetrical wave climates, shoreline features migrate in the downdrift direction, either as subtle alongshore sand waves or as offshore-extending ''flying spits,'' depending on the proportion of high-angle waves. Numerical analyses further show that the rate that the alongshore scale of model features increases through merging follows a diffusional temporal scale over several orders of magnitude, a rate that is insensitive to the proportion of high-angle waves. The proportion of high-angle waves determines the offshore versus alongshore aspect ratio of selforganized shoreline undulations.

River deltas rank among the most economically and ecologically valuable environments on Earth. Even in the absence of sea-level rise, deltas are increasingly vulnerable to coastal hazards as declining sediment supply and climate change alter their sediment budget, affecting delta morphology and possibly leading to erosion 1-3 . However, the relationship between deltaic sediment budgets, oceanographic forces of waves and tides, and delta morphology has remained poorly quantified. Here we show how the morphology of about 11,000 coastal deltas worldwide, ranging from small bayhead deltas to mega-deltas, has been affected by river damming and deforestation. We introduce a model that shows that present-day delta morphology varies across a continuum between wave (about 80 per cent), tide (around 10 per cent) and river (about 10 per cent) dominance, but that most large deltas are tide-and river-dominated. Over the past 30 years, despite sea-level rise, deltas globally have experienced a net land gain of 54 ± 12 square kilometres per year (2 standard deviations), with the largest 1 per cent of deltas being responsible for 30 per cent of all net land area gains. Humans are a considerable driver of these net land gains-25 per cent of delta growth can be attributed to deforestation-induced increases in fluvial sediment supply. Yet for nearly 1,000 deltas, river damming 4 has resulted in a severe (more than 50 per cent) reduction in anthropogenic sediment flux, forcing a collective loss of 12 ± 3.5 square kilometres per year (2 standard deviations) of deltaic land. Not all deltas lose land in response to river damming: deltas transitioning towards tide dominance are currently gaining land, probably through channel infilling. With expected accelerated sea-level rise 5 , however, recent land gains are unlikely to be sustained throughout the twenty-first century. Understanding the redistribution of sediments by waves and tides will be critical for successfully predicting human-driven change to deltas, both locally and globally. A new model for delta changeOn the basis of two recent quantitative studies 12,13 , we here introduce a ternary diagram that allows prognosis of delta morphology and morphologic change using sediment fluxes (Fig. 1a). We apply this approach on a global scale. First, we predict delta morphology for conditions that resemble a world without substantial human impact on the fluvial sediment supply. Next, we compare these predictions to the delta morphology that is expected on the basis of recent modifications to sediment fluxes due to both deforestation and river damming.

We construct a simple morphodynamic model to investigate the long-term dynamic evolution of a coastal barrier system experiencing sea-level rise. Using a simplified barrier geometry, the model includes a dynamic shoreface profile that can be out of equilibrium and explicitly treats barrier sediment overwash as a flux. With barrier behavior primarily controlled by the maximum potential overwash flux and the rate of shoreface response, the modeled barrier system demonstrates four primary behaviors: height drowning, width drowning, constant landward retreat, and a periodic retreat. Height drowning occurs when overwash fluxes are insufficient to maintain the landward migration rate required to keep pace with sea-level rise. On the other hand, width drowning occurs when the shoreface response rate is insufficient to maintain the barrier geometry during overwash-driven landward migration. During periodic barrier retreat, the barrier experiences oscillating periods of rapid overwash followed by periods of relative stability as the shoreface resteepens. This periodic retreat, which occurs even with a constant sea-level rise rate, arises when overwash rates and shoreface response rates are large and of similar magnitude. We explore the occurrence of these behaviors across a wide range of parameter values and find that in addition to the maximum overwash flux and the shoreface response rate, barrier response can be particularly sensitive to the sea-level rise rate and back-barrier lagoon slope. Overall, our findings contrast with previous research which has primarily associated complex barrier behavior with changes in external forcing such as sea-level rise rate, sediment supply, or back-barrier geometry.

[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.

[1] The transport of fine sediment and organic matter plays an important role in the nutrient dynamics of shallow aquatic systems, and the fate of these particles is closely linked to vegetation. We describe the mean and turbulent flow near circular patches of synthetic vegetation and examine how the spatial distribution of flow is connected to the spatial distribution of suspended sediment deposition. Patches of rigid, emergent, and flexible, submerged vegetation were considered, with two different stem densities. For the rigid emergent vegetation, flow adjustment was primarily two-dimensional, with flow deflected in the horizontal plane. Horizontal shear layers produced a von Kármán vortex street. Flow through the patch shifted the vortex street downstream, resulting in a region directly downstream of the patch in which both the mean and turbulent velocities were diminished. Net deposition was enhanced within this region. In contrast, for the flexible, submerged vegetation, flow adjustment was three-dimensional, with shear layers formed in the vertical and horizontal planes. Because of strong vertical circulation, turbulent kinetic energy was elevated directly downstream of the patch. Consistent with this, deposition was not enhanced at any point in the wake. This comparison suggests that morphological feedbacks differ between submerged and emergent vegetation.

River deltas, low-lying landforms that host high concentrations of human population and ecosystem services, face a new, and mostly unknown, future over the coming decades and centuries. Even as some deltas experience decreased sediment supply from damming, others will see increased sediment discharge from land-use changes. There are proposals to actively use riverine sediment supply to build new land and counteract delta loss. We present a novel approach to understanding the morphology of deltas by quantifying the balance between river inputs and the largely overlooked ability of waves to spread sediments along the coast. Defining a fluvial dominance ratio-river sediment input versus the potential maximum alongshore sediment transport away from the delta mouth-allows a quantitative assessment of this sediment transport balance. For a series of deltas on Java, Indonesia, that exhibit a large range of sediment loads but have a homogeneous drainage lithology and wave climate, and for more eclectic global examples, shoreline deflection increases along with this fluvial dominance ratio. The fluvial dominance ratio also predicts the observed transition from cuspate, wave-dominated deltas to fluvially dominated deltas with protruding, crenulated shorelines. Not only does this approach provide a more quantitative foundation for paleoenvironmental reconstructions and delta management, perhaps more importantly, this simple metric of fluvial dominance has a predictive application in determining potential morphology of deltas created by engineered sediment diversions.

Accelerated sea level rise and the potential for an increase in frequency of the most intense hurricanes due to climate change threaten the vitality and habitability of barrier islands by lowering their relative elevation and altering frequency of overwash. High-density development may further increase island vulnerability by restricting delivery of overwash to the subaerial island. We analyzed pre-Hurricane Sandy and post-Hurricane Sandy (2012) lidar surveys of the New Jersey coast to assess human influence on barrier overwash, comparing natural environments to two developed environments (commercial and residential) using shore-perpendicular topographic profiles. The volumes of overwash delivered to residential and commercial environments are reduced by 40% and 90%, respectively, of that delivered to natural environments. We use this analysis and an exploratory barrier island evolution model to assess long-term impacts of anthropogenic structures. Simulations suggest that natural barrier islands may persist under a range of likely future sea level rise scenarios (7-13 mm/yr), whereas developed barrier islands will have a long-term tendency toward drowning.