Modeling of waves and currents in the nearshore parametric vs. probabilistic approach
Introduction
Morphodynamic coastal profile models aim at predicting cross-shore bathymetric evolution by accounting explicitly for the various hydrodynamic processes involved (Roelvink and Brøker, 1993). With the increase in process knowledge and computing power, profile models have become standard tools in coastal management and are used for hind- and forecasting studies of nearshore bathymetry, often in response to human interference in the nearshore, for instance related to implementation of a shoreface nourishment. The models generally consist of three main modules. In the hydrodynamic module, the cross-shore evolution of wave height, orbital velocities and time-averaged (over many wave periods) cross-shore and longshore currents is computed. These are then used as input in the sediment transport module. From the cross-shore gradients in the sediment transport rates, morphological changes are computed in the bed-update module, after which the whole procedure is repeated.
Two main approaches in process-based profile modeling can be distinguished. In the first approach, known as parametric, the natural random wave field is assumed to be narrow banded in frequency and direction. Its description is then reduced to a single representative wave height, period, and direction. All subsequent computations of hydrodynamics and sediment transport are then based on this single wave approach. Examples of parametric morphodynamic models are Roelvink and Stive (1989) and Nairn and Southgate (1993). In the second, probabilistic (or wave-by-wave) approach the computation of hydrodynamics and sand transport is based on a discrete number of wave classes. The method is probabilistic in the sense that each wave class has a certain probability of occurrence. The hydrodynamic and sediment transport computations are performed separately for each wave class. In the bed-update module, the transport rates are then combined using the probability density function of the wave classes to yield bathymetric change. Van Rijn and Wijnberg (1996) argued that the probabilistic approach is better suited for profile modeling because of the strong non-linear dependence of the sediment transport on wave height, which would not be captured correctly with the single-wave parametric approach.
Previous probabilistic modeling studies have mainly focussed on modeling histograms of wave height and associated statistics and on longshore currents Mase and Iwagaki, 1982, Mizuguchi, 1982, Dally and Dean, 1986, Van Rijn and Wijnberg, 1996. A comparison between measured and computed orbital velocities and undertow has not been made. Furthermore, whether the probabilistic approach indeed outperforms the parametric approach both regarding hydrodynamics and sediment transport is unknown. The probabilistic approach is rather time-consuming because all wave classes (generally 10–12) are propagated shoreward separately and independently. In contrast, the parametric approach transforms only one representative wave shoreward. Therefore, if the same accuracy can be reached, the computationally quicker parametric approach would be better suitable for long-term morphological computations than the computationally intensive probabilistic approach.
In this paper we present the hydrodynamic module (Section 2) of a process-based morphodynamic profile model that can be used in both parametric and probabilistic mode. The described hydrodynamic processes are directly relevant for the modeling of sediment transport rates and include cross-shore wave transformation (shoaling, refraction, and dissipation), orbital motion, and time-averaged cross-shore and longshore currents. In the probabilistic mode, the present model is an extension of the work by Van Rijn and Wijnberg (1996). Here, we address whether and to what extent a probabilistic approach is necessary to accurately predict nearshore hydrodynamics. The need for a probabilistic approach in sediment transport and morphodynamic modeling is detailed in a future contribution. In Section 3, parametric and probabilistic predictions are compared to extensive laboratory and field measurements, the latter being collected at the barred beaches at Duck, NC, and Egmond aan Zee, Netherlands. Our main findings are discussed and summarized in 4 Discussion, 5 Conclusions, respectively.
Section snippets
Wave transformation
The wave model consists of two coupled differential equation describing the time-averaged wave and roller energy balances. With the assumption of longshore uniform bathymetry, the former readsin which x is the cross-shore direction, positive onshore, H is the wave height, cg,r the relative wave group velocity, θ is the angle of incidence, g is acceleration of gravity, ρ is the water density, Dbr and Dbf are the wave energy dissipation by breaking and bottom friction,
Model data comparison
In this section, we compare probabilistic and parameter model predictions to high-quality data, collected in small-scale and large-scale laboratory tests and during two extensive field experiments. An overview of the applied data sets, including a list of parameters available from the data, is provided in Table 1. In all data sets, the parameters were collected at several cross-shore locations across one or two nearshore bars.
Discussion
Predictions of nearshore hydrodynamics in probabilistic mode may rely, at least partly, on the accuracy of the computed wave–height probability density function (pdf). Both the small-scale laboratory experiments and the Egmond field data indicated that the present model predicts measured pdfs that are too broad and thus extend to too large wave heights, in particular within the surf zone. Interestingly, a Rayleigh wave–height distribution appears to fit the measured pdfs reasonably well, both
Conclusions
In this paper, we have presented a hydrodynamic model that can predict the cross-shore transformation of wave height, on- and offshore orbital motion, and time-averaged cross-shore and longshore currents in a parametric and probabilistic mode. In the parametric mode, the computations are based on the root-mean-square wave height, the peak period and the energy-weighted mean angle of incidence, while in the probabilistic mode a discrete number of classes with their own wave height, period, and
Acknowledgements
The present work was performed as part of the COAST3D project funded by the European Commission's research program MAST under contract number MAS3-CT97-0086. We would like to thank Steve Elgar, Robert Guza, and Falk Feddersen for providing the Duck94 data. Background data for Egmond was provided by Rijkswaterstaat in the framework of the Kust*2000 program. The second author was funded partly through the Delft Cluster project Coasts 03.01.03.
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