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.