M.J.F. Stive

Approaches to long-term modelling of coastal morphology: A review

Aspects of long-term mathematical modelling of coastal morphology are inventoried and discussed. They concern reduction techniques for input data, process descriptions and output data, as well as model concepts ranging from statistical extrapolation of the past coastal behaviour, via semi-empirical behaviour models, to formally integrated descriptions of the constituent small-scale processes. All approaches have in common that they reduce the need for detailed descriptions in space and time of the underlying physical processes. They lead not only to more transparent and robust models which require less computational effort, but also to a better insight into which aspects of coastal behaviour are relevant from a long-term point of view and which are not (“signal” vs. “noise”).

Variability of shore and shoreline evolution

Shore and shoreline evolution both due to natural and human-induced causes or factors can be variable over a wide range of different temporal and/or spatial scales. Our capability to understand and especially predict this variability is still limited. This can lead to misinterpretation of coastal change information, which hampers informed decision making and the subsequent design and implementation of (soft) engineering interventions. Collecting and describing example observations of shore and shoreline variability is one way to support and improve such human intervention. This paper describes causes and factors for the variability and the resulting possible evolutions of wave-dominated shores and shorelines, which are illustrated by a number of case studies. The new element of this work is that the variability is described in terms of a range of different time and space scales, which helps to structure such analysis. However, it is difficult to generalise the results for arbitrary situations, especially on decadal time scales. Scientific and engineering improvements require more quantitative insight into the physical mechanisms behind the free and forced shore behaviour responsible for the variability.

Modelling shoreface profile evolution

Current knowledge of hydro-, sediment and morpho-dynamics in the shoreface environment is insufficient to undertake shoreface-profile evolution modelling on the basis of first physical principles. We propose a simple, panel-type model to map observed behaviour. The internal dynamics are determined by slope-dependent, wave-induced cross-shoreface transports, while the external driving factors are lateral sediment supply and sea-level rise. This model concept is tested with reasonable success against the observed behaviour of the Central Holland Coast, considering two hindcast periods, one covering the evolution over the last century, the other the Subboreal/Subatlantic evolution. A limitation of this model is that the cross-shoreface dynamics are solely steered by the variations of shoaling, short waves. Since a variety of other wave and current dynamics may be expected to be present in the coastal boundary layer, it may well be that the effects of the mechanisms and conditions which are not represented are hidden in the coefficients of the sediment-transport formula. This limits the accuracy of the coefficients as used, and our findings should be considered as an-order-of-magnitude estimate only. Indeed, behaviour-oriented modelling implies that generalization of results to arbitrary situations and conditions is not straightforward. Yet, we expect that some of the conclusions are more generally applicable. This concerns the substantiation of the assumption that the upper shoreface responds on a much smaller time scale than the lower shoreface, and the idea that the shoreface profile is not always and everywhere in equilibrium with its forcing. A worthwhile observation from the Holland Coast application is, that the bottom slope effect on the transport is only important at geological time scales. The profile evolution at the engineering time scales (say 10 to 100 years) is effectively quasi-static, in that there is no feedback between the long-term averaged transport and the state of the profile. This implies that at these smaller scales the profile changes can be predicted on the basis of a static sediment balance. This does not mean that the gravitational downslope transport is unimportant as a physical phenomenon in coastal profile evolution: It is only unimportant if a highly aggregated model like this is applied at relatively short time scales.

CROSS-SHORE MEAN FLOW IN THE SURF ZONE

Abstract The seaward mean returnflow or undertow in the surf zone, which compensates for the shoreward mass flux above the wave trough level, is found to be driven by the force imbalance between the wave momentum flux on the one hand and the set-up on the other hand, in qualitative agreement with the model of Dyhr-Nielsen and Sorensen (1970). A model, which quantifies this imbalance, is shown to yield theoretical results in good accordance with experiments when the proper boundary conditions are accounted for.

Quasi-3D modelling of nearshore currents

Abstract Existing concepts of wave-induced nearshore current models, in the cross-shore vertical plane (2DV) and depth-integrated (2DH), are combined to a quasi-3D mathematical model. This combination is tested for reproducing correct results in 2DV and 2DH situations. The importance of the various contributions to the wave-induced secondary circulation in the vertical plane is investigated for realistic parameter ranges, which leads to the conclusion that both the non-breaking and the breaking fraction of a random wave field in the surf zone generate important secondary currents. Additional computations show the relevance of a 3D-approach of nearshore currents, even in seemingly simple situations like a plane sloping beach with obliquely incident waves.

Impact of sea-level rise on the morphological equilibrium state of tidal inlets

Abstract This study addresses the question whether the geomorphology of a tidal inlet (i.e. the coastal inlet and associated tidal basin) can maintain equilibrium under a rising relative sea level. When a tidal inlet system is exposed to a constant rate of sea-level rise (SLR), the system will be permanently in a state that deviates from the Equilibrium State corresponding to zero SLR. This is a physical requirement to create a permanent incentive to import sediment into the system. In case the rate of sediment import matches the rate of sea-level rise, a new state of dynamic morphological equilibrium is reached. If the actual import rate is less than this, the system’s morphological state will deviate increasingly from its equilibrium and finally degenerate. In this case SLR has exceeded an upper boundary (named ‘state limit’, denoted as SLRlimit), and the system will not be able to reach a state of dynamic morphological equilibrium any longer and drown. Because the SLRlimit predictions are sensitive to a variation of internal sediment exchange rate and availability of sediment at the seaward boundary of the system, we assess the SLRlimit predictions quasi-probabilistically to gain quantitative insight into the inherent uncertainties. This technique leads to an estimate of the probability distribution for the SLRlimit of two selected tidal inlet systems in the Dutch Wadden Sea. The calculated probabilities comply with the available fragmentary geological data, which suggest that the former tidal inlets in the western region of the Netherlands were drowned under the influence of a sea-level rise of 80 cm to a few metres per century.

Holocene Evolution of the Coast of Holland

Abstract The Holocene evolution of the coast of Holland was controlled by the complex interaction of such diverse parameters as wave and tidal climate, the rate of sea-level rise, and the morphology of the pre-transgressional surface. The latter, in combination with the rate of sea-level rise, mainly determines the location of sediments sources and sinks, while the hydrodynamic parameters mainly determine the rate and direction of sediment transport. In the early Holocene the low sea level in the shallow southern North Sea strongly affected wave climate and tidal regime. However, the barrier and back-barrier sedimentary record since 5000 14C yrs B.P. gives us no reason to assume major changes in these parameters since then, so we conclude that breaks in barrier development are due to variations in rate of sea-level rise inl combination with the morphology of the pre-transgressional surface. The transformation from an open “tide-dominated” to a closed “wave-dominated” coast, which occurred in the Subboreal period, and the concomitant change in barrier movement from transgressive to regressive around 5000 yrs B.P. are the main events in the development of the coast of Holland up to the Middle Ages. The morphology of the pre-transgressional surface gives a shoreline in the late Atlantic which consists of two protruding headlands separated by a large tidal basin. The southern headland is the alluvial plain of the Rhine and the Meuse, the northern headland constitutes the moraines of the Texel High. The tidal basin in between is connected to the North Sea by a large number of inlets. The rate of sea-level rise at that time (1 m/century) outran the supply of sediment to the tidal basin. After 6000 yrs B.P. the rate of sea-level rise decreased gradually, whereas the rate of sediment supply remained constant. This led to a gradual decrease in the tidal prisms of the inlets as the tidal basin was filled in with sediment. Shortly before 5000 yrs B.P. the first channels silted up and closed; the last tidal channel disappeared around 3300 yrs B.P., leaving two inlets along the coast which were both connected to the river Rhine. The closure of the first inlets occurred at the same time as the barrier began prograding because (1) the rate of sea-level rise diminished considerably, (2) not all the sand supplied by longshore and cross-shore transport disappeared into the tidal basin, but instead could be used for barrier progradation; and (3) ebb-tidal deltas of the closed inlets provided major sand sources. The prograding barrier sequence enclosed between the two headlands roughly forms a closed system. Using the relationships between tidal prism, cross-sectional area of inlets and volume of the ebb-tidal delta, and the results of modelling of longshore transport along the Subboreal coast under present-day wave conditions, a simple sand budget for the coast of Holland is given which shows that a large part of the sand now stored in the barrier sequence was obtained by cross-shore transport from the North Sea.

A New Alternative to Saving Our Beaches from Sea-Level Rise: The Sand Engine

ABSTRACT Stive, M.J.F.; de Schipper, M.A.; Luijendijk, A.P.; Aarninkhof, S.G.J.; van Gelder-Maas, C.; van Thiel de Vries, J.S.M.; de Vries, S.; Henriquez, M.; Marx, S., and Ranasinghe, R., 2013. A new alternative to saving our beaches from local sea-level rise: the sand engine. A boldly innovative soft engineering intervention, comprising an unprecedented 21.5 Mm3 sand nourishment known as the Sand Engine, has recently been implemented in the Netherlands. The Sand Engine nourishment is a pilot project to test the efficacy of local mega-nourishments as a counter measure for the anticipated enhanced coastal recession in the 21st century. The proposed concept, a single mega-nourishment, is expected to be more efficient, economical, and environmentally friendly in the long term than traditional beach and shoreface nourishments presently being used to negate coastal recession. Preliminary numerical model results indicate that this local nourishment will result in the widening of the beach along a 10 to 20 km stretch of the coastline and a beach area gain of 200 ha over a 20-year period. First observations show indeed a redistribution of the sand feeding the adjacent coasts, roughly 40% toward the south and 60% toward the north. While the jury is still out on this globally unique intervention, if proven successful, it may well become a global generic solution for combating sea-level-rise driven coastal recession on open coasts.

Living with sea-level rise and climate change: a case study of the Netherlands

Abstract Based on historical hindsight, this paper shows that sea-level rise has played a fundamental role in the development of the low-lying environment of the Netherlands. It was beneficial in morphological terms during the mid-Holocene, but from Roman times, it has been a threat to the coastal zone evolution and human habitation. Collective human response started to play a role in coastal evolution as early as the ninth century, while its influence started to become a major factor during the nineteenth and twentieth century. Throughout its history, Dutch society has always been receptive to new technologies, approaches, and policies in its dealings with the many water-related challenges. The success of concerted human response explains why the water boards were successful as the first democratic institutions in the Netherlands. Development of technology and increasing financial means (the Dutch Golden Age) gave rise to increasingly viable flood abatement measures and reclamation projects, which took place on increasingly larger scales. This culminated in large-scale works such as the closure of the Zuiderzee and the Delta Project in the twentieth century. During this project, a turning point in thinking emerged; while flood protection remained a top priority, human interventions were considered in a broader, more holistic context with natural values being weighed against socioeconomic interests. In the face of the challenges of the twenty-first century, policy and management approaches as well as science and technology approaches need to be adapted further in accordance to the principles of working with nature in a trans-disciplinary way. The success of this adaptation will to a large extent determine the viability of the Dutch society as a whole.

Numerical modelling of shoal pattern formation in well-mixed elongated estuaries

Abstract The formation of channel and shoal patterns in a schematic estuary is investigated using a 2-D depth-averaged numerical model based on a description of elementary flow and sediment transport processes. The schematisations apply to elongated inland estuaries, sandy, well-mixed and tide-dominated. The model results show how, due to non-linear interactions, a simple and regular pattern of initially grown perturbations merges to complex larger-scale channel/shoal patterns. The emerging patterns are validated with field observations. The overall pattern agrees qualitatively with patterns observed in the Westerschelde, The Netherlands, and in the Patuxent River estuary, Virginia. Quantitative comparison of the number of channels and meander length scales with observations and with an analytical model gives reasonable accordance. Complementary to other research approaches, this model provides a tool to study the morphodynamic behaviour of channels and shoals in estuaries.