Laboratory investigations of beach morphology change under wave action are undertaken to gain insight into coastal processes, design coastal structures and validate the predictions of numerical models. For the results of such experiments to be reliable, it is necessary that they are repeatable. The equilibrium beach concept, that beach morphology will evolve to a quasi-static equilibrium shape for a given forcing suggests that experiments should be repeatable to some degree. However, sediment transport in turbulent breaking and broken waves is complex and highly variable and the level of repeatability at different temporal and spatial scales is challenging to measure, as such, previous work has restricted comparisons to small numbers of waves. Here we use the results of two identical, 20-h large-scale wave flume experiments to investigate the repeatability of sediment transport and beach morphology change under waves at timescales down to individual swash events. It is shown that while flow characteristics from identical swash events are very repeatable, the sediment transported can be very different in both magnitude and direction due to differences in turbulence, sediment advection and morphological feedback. Over longer periods containing multiple matching swash events however, the beach responds in a very similar manner, with the level of morphological repeatability increasing with time. The results also demonstrate that gross swash zone sediment transport remains high even as a beach profile approaches quasi-equilibrium, but the proportion of individual swash events that cause large sediment fluxes (>±7.5 kg/event/m) reduces with time. The results of this laboratory study indicate that beach morphology change has a level of determinism over timescales of several minutes and longer, giving confidence in the results from physical modelling studies. However, the large differences in sediment transport from apparently identical swash events questions the value in pursuing numerical predictions of sediment transport at the wave-by-wave timescale unless the reversals in sediment transport between apparently near identical swash events can also be predicted.

Morphodynamics of sandy beaches are governed by sediment transport processes. Conceptualising the process of subaqueous and subaerial sediment transport and quantifying the magnitude of sediment transport have proven to be a difficult challenge. The challenge is reflected by the many concepts available that describe sediment transport and its relationship with hydrodynamic processes and sediment compositions. This chapter gives an overview of the most important concepts that are currently available and widely used to describe sediment transport processes.

Concepts include timescale-dependent sediment transport as a function of different hydrodynamic processes such as waves, currents and turbulent forces. Also, the role of sediment properties and the most important modes of sediment transport, bedload and suspended load transport are discussed. In a further conceptualisation, cross-shore processes are distinguished from longshore processes given the nature of varying hydrodynamic gradients along the sandy beach. The rare measurements of sediment transport provide some evidence that help quantify the concepts.

Finally, reflection on current challenges that need to be addressed to achieve a more comprehensive and detailed model for sediment transport processes is made.

Although commonly used for the validation of morphological predictions, point-wise accuracy metrics, such as the root-mean-squared error (RMSE), are not well suited to demonstrate the quality of a high-variability prediction; in the presence of (often inevitable) location errors, the comparison of depth values per grid point tends to favour predictions that underestimate variability. In order to overcome this limitation, this paper presents a novel diagnostic tool that defines the distance between predicted and observed morphological fields in terms of an optimal sediment transport field, which moves the misplaced sediment from the predicted to the observed morphology. This optimal corrective transport field has the “cheapest” quadratic transportation cost and is relatively easily found through a parameter-free and symmetric solution procedure solving an elliptic partial differential equation. Our method, which we named effective transport difference (ETD), is a variation to a partial differential equation approach to the Monge–Kantorovich L² optimal transport problem. As a new error metric, we propose the root-mean-squared transport error (RMSTE) as the root-mean-squared value of the optimal transport field. We illustrate the advantages of the RMSTE for simple 1D and 2D cases as well as for more realistic morphological fields, generated with Delft3D, for an idealized case of a tidal inlet developing from an initially highly schematized geometry. The results show that by accounting for the spatial structure of morphological fields, the RMSTE, as opposed to the RMSE, is able to discriminate between predictions that differ in the misplacement distance of predicted morphological features, and avoids the consistent favouring of the underprediction of morphological variability that the RMSE is prone to.

This thesis investigates the behaviour of the often used point-wise skill score, the MSESSini a.k.a. BSS, and develops new error metrics that, as opposed to point-wise metrics, take the spatial structure of morphological patterns into account. The MSESSini measures the relative accuracy of a morphological prediction over a prediction of zero morphological change, using the mean-squared error (MSE) as the accuracy measure. The main findings about the MSESSini are: 1) a generic ranking, based on values for MSESSini, has limited validity, since the zero change reference model fails to make model performance comparable across different prediction situations; 2) the combination of larger, persistent and smaller, intermittent scales of cumulative change may lead to an increase of skill with time, without the prediction on either of these scales becoming more skilful with time; 3) in the presence of inevitable location errors, the MSESSini favours predictions that underestimate the variance of cumulative bed changes and 4) existing methods to correct for measurement error are inconsistent in either their skill formulation or their suggested classification scheme. In order to overcome the inherent limitations of point-wise metrics, three novel diagnostic tools for the spatial validation of 2D morphological predictions are developed. First, a field deformation or warping method deforms the predictions towards the observations, minimizing the squared point-wise error. Error measures are formulated based on both the smooth displacement field between predictions and observations and the residual point-wise error field after the deformation. In contrast with the RMSE, the method captures the visual closeness of morphological patterns. Second, an optimal transport method defines the distance between predicted and observed morphological fields in terms of an optimal sediment transport field. The optimal corrective transport field moves the misplaced sediment from the predicted to the observed morphology at the lowest quadratic transportation cost. The root-mean-squared value of the optimal transport field, the RMSTE, is proposed as a new error metric. As opposed to the field deformation method, the optimal transport method is mass-conserving, parameter-free and symmetric. The RMSTE, unlike the RMSE, is able to discriminate between predictions that differ in the misplacement distance of predicted morphological features. It also avoids the consistent reward of the underestimation of morphological variability that the RMSE is prone to. Third, a scale-selective validation approach allows any metric to selectively address multiple spatial scales. It employs a smoothing filter in such a way that, in addition to the domain-averaged statistics, localized validation statistics and maps of prediction quality are obtained per scale (geographic extent or areal size of focus). The employed skill score weights how well the morphological structure and variability are simulated, while avoiding to reward the underestimation of variability. To fully describe prediction quality multiple metrics are required with a weighting determined by the goal of the simulation. Point-wise metrics should be supplemented with an error decomposition, as to avoid undesired underestimation of variability. Further, a set of performance metrics must include a metric, e.g. the RMSTE, that accounts for the spatial structure of the observed and predicted morphological fields.

The quality of morphodynamic predictions is often indicated by a skill score that weighs the mean-squared error of the prediction by that of the initial bed as the reference prediction. As simple as this Brier skill score (BSS) or meansquared- error skill score (MSESS) may seem, it is not well understood and, hence, sometimes misinterpreted. This chapter aims at improving the understanding of the MSESS. We review existing MSESS formulations and classifications, with and without an account of the measurement error. Using simple examples, we illuminate which aspects of prediction quality the MSESS actually measures. It is shown that the MSESS tends to favor model results that underestimate the variance of cumulative bed changes. We further demonstrate that the normalization by the observed cumulative change, which follows from the choice of the initial bed as the reference, is not effective in creating a level playing field over a wide range of prediction situations (trend, episodic event, different seasons). Also, it is shown that the combined presence of larger, persistent scales and smaller, intermittent scales in the cumulative bed changes may lead to an apparent increase of skill with time, although the prediction of neither of these scales becomes more skilful with time. Finally, in order to obtain a balanced appreciation of model performance, the use and development of a more extensive suite of validation measures is advocated.

This paper investigates the effect of wave-induced streaming on sediment transport by applying a newly developed numerical sediment transport model. The transport model solves the intra-wave oscillatory motion and sediment concentrations. The wave-induced streaming in the wave boundary layer, as occurs in propagating waves, is an integral part of the computed flow field. Comparison of the computed flow field with wave-current flume experiments gives good results. The model can also describe the horizontally uniform situation in an oscillating water tunnel, in which vertical orbital velocities and wave-induced streaming are absent. The model is successfully tested against measurements of sediment concentrations and net transport rates performed in a large-scale oscillating water tunnel. The importance of streaming is assessed by comparing model results for the case with wave-induced streaming and the case of the oscillating water tunnel. For a typical water tunnel condition, the effect of the absence of vertical velocities and streaming is found to be a 40% lower net transport rate than the corresponding situation under propagating waves. These differences result not only from the net transport by the streaming velocity, but are also due to an increased asymmetry in the model of near-bed velocity, bed shear-stress and resulting sediment concentrations. This result suggests that the differences in transport rates between water tunnel and propagating waves may not be insignificant.

Existing Boussinesq models are extended to include the computation of the vertical structure of the horizontal velocity. A time-domain model is tested against laboratory measurements of the vertical profile of the horizontal velocity in regular waves; good results are obtained, especially in the near-bed zone. A spectral model, which includes a dissipation formulation to account for wave breaking, is tested against laboratory measurements of bottom velocities in (partially) breaking irregular waves. For moderately long waves, the comparison on velocity variance and skewness, which are relevant to sediment transport, yields good results.

A frequency-domain Boussinesq model with good linear shoaling, improved linear dispersion characteristics and a dissipation formulation to account for wave breaking is extended to include the computation of the vertical structure of the horizontal velocity. The extended model is used to predict bottom velocities and resulting velocity variance and skewness in (partially) breaking irregular waves. The comparison of measured and computed velocity moments indicates that for moderately long waves the spectral Boussinesq model can be successfully used for sediment transport purposes. For shorter waves the crest velocity values of the higher waves are significantly underestimated, and as a result the velocity skewness as well.