COASTAL PROFILE MODELING: POSSIBILITIES AND LIMITATIONS Bart Grasmeijer1, Dirk-Jan Walstra2 Abstract: This paper discusses the possibilities and limitations of coastal profile models based on the comparison of the results from two cross-shore profile models with smalland large-scale wave flume data and field data on a storm time scale (days) and a seasonal time scale (months). The models differ with respect to the description of the randomness and directionality of the waves, the near-bed wave velocity asymmetry (higher harmonics), the wave breaking processes, the wave-induced streaming in the boundary layer, the waveinduced cross-shore and longshore currents, the generation of low-frequency processes and the wave-induced sand transport components. Results show that the bed profile evolution on a storm time scale can be predicted quite reasonably, provided that a variable bed roughness is applied. Breaker delay shifts the maximum undertow velocities shoreward. This shoreward shift of the undertow velocities appears to be of vital importance for proper simulation of nearshore profiles. 1.
INTRODUCTION In this paper, the question is addressed to what extent a coastal profile model is capable of predicting nearshore morphological changes on the time scale of storms and seasons, simplifying the coastal system to a longshore-averaged 2-D system. Observed and computed hydrodynamics, transport rates and morphological changes on storm (weeks) and seasonal (months) scales are compared using two cross-shore profile models. 2.
DESCRIPTION OF MODELS Herein, the attention is focused on the possibilities and limitations of two coastal profile models with respect to the predictability of sandy beaches. The modeling approaches that will be used are the parametric UNIBEST-model of Delft Hydraulics (Bosboom et al., 2000) and the probabilistic CROSMOR model of the University of Utrecht (Grasmeijer, 2002b). Both models are designed to compute cross-shore sediment transport and the resulting profile changes under the combined action of waves, longshore tidal currents and wind. The parametric model UNIBEST-TC is based on the Battjes and Janssen (1978) wave model and includes long wave and breaker delay effects (Roelvink et al., 1995). The probabilistic cross-shore profile model CROSMOR is based on a wave-bywave approach (Van Rijn and Wijnberg, 1996) but can also be applied in parametric mode (Grasmeijer, 2002b). Both the UNIBEST and the CROSMOR model include the effect of a surface roller on the undertow velocities. The transport module is based on TRANSPOR (Van Rijn, 1993) in both models. CROSMOR incorporates wave-related suspended transport, which is not included in the UNIBEST model.
1) Department of Physical Geography, University of Utrecht, PO Box 80115, 3508 TC Utrecht, The Netherlands; Tel: +31-30-2535735, Fax: +31-30-2531145, Email:
[email protected] 2) Delft Hydraulics, P.O.Box 177, 2600 MH, Delft, The Netherlands. 1
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COMPARISON WITH OBSERVATIONS Herein the models are tested against small-scale and large-scale laboratory experiments and field measurements near the coast of Egmond aan Zee in the Netherlands. 3.1. Small-scale wave flume experiments The data used here were obtained during experiments in a small-scale wave flume of Delft University of Technology in The Netherlands (Grasmeijer and Van Rijn, 1999). Measurements were done at a number of locations across a simulated shallow water bar built in fine sands (D50 = 0.10 mm) and subjected to irregular waves (JONSWAP spectrum). The wave height predictions by the CROSMOR model show good agreement with the measurements (Figure 1). Discrepancies are less than 5%. The shoaling near the bar crest is under-predicted by the UNIBEST model, causing wave heights to be underestimated with about 10%. Measured and predicted undertow velocities are compared in the lower panel of Figure 1. For both models, the predicted location of maximum undertow is near the bar crest, whereas the measured maximum is located more shoreward. The UNIBEST model produces smaller undertow velocities than the CROSMOR model. The effect of the roller was tested by running the models with and without roller (results not shown here). Neglecting the roller causes an immediate transfer of energy from organized wave motion to the undertow, resulting in smaller undertow velocities shoreward of the bar crest. However, the roller influence was found to be relatively small in this test case. wave height
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Figure 1. Measured and computed wave height and undertow velocities for small-scale wave flume experiments, Delft University of Technology, The Netherlands.
To investigate the degree to which the CROSMOR model in probabilistic mode is capable of reproducing the wave height distribution correctly, measured and computed wave height distributions were compared (Figure 2). Both the measured and computed 2
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wave height distribution become narrower in the onshore direction, caused by the breaking of the largest waves. However, the shape of the measured and computed distributions differ at locations just shoreward of the bar crest (x > 12 m). The upper tail of the measured distribution extends to values greater than computed. For example, at x = 13 m, the largest wave height in the computed distribution is 0.21 m, while the maximum measured wave height is 0.29 m. 0.3
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Figure 2. Measured and computed wave height distributions for small-scale wave flume experiments, Delft University of Technology, The Netherlands. For locations see Figure 1.
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Moreover, at locations shoreward of the bar crest (breaking waves), the computed wave height distribution is too peaked with large probability density values in the upper tail of the distribution. This effect is most pronounced at x = 14.5 m, where the fraction of breaking waves was observed to be largest. It is interesting to see that the Rayleigh distribution represents the measured wave height distribution reasonably, consistent with findings by (Thornton and Guza, 1983) under field conditions and by (Baldock et al., 1998) for small-scale laboratory tests.
3.2. Large-scale wave flume tests The large-scale laboratory data used here was collected during the LIPII 1B test in the Delta Flume of Delft Hydraulics and is described in Roelvink and Reniers (1995). Test 1B represents erosive short-period (Tp = 5 s) storm waves with an offshore Hrms of 1.0 m. A small bar was present at the start of the experiment. Median sediment grain size was 0.22 mm. 0
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Figure 3 shows the measured and computed wave heights along the profile. The CROSMOR model computes the Hrms seaward of the bar crest quite accurately. Further shoreward however, Hrms is underestimated by about 20%. In probabilistic mode, the CROSMOR model predicts the significant wave heights quite accurately while the root-
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mean-square wave height is generally overestimated by about 20%, especially at locations near the bar crest, which is partly caused by the fact that the probabilistic model was calibrated focusing on the significant wave heights (Van Rijn and Wijnberg, 1996). The measured ratio H1/3/Hrms remains about 1.4 throughout the surf zone whereas the probabilistic mode results in a decrease of this ratio because of breaking of only the highest waves. Measured and computed morphological changes are presented in Figure 4. The measured profile evolution shows offshore bar migration over about 10 m during 18 hours of wave action, with erosion of the trough and growth of the bar. Generally, the predicted profile evolution shows offshore movement of sediment, erosion of the bar crest and flattening of the profile. The measured erosion in the trough is not predicted by the models, neither is the measured bar growth. The CROSMOR parametric and probabilistic modes produce comparable results. The UNIBEST and the CROSMOR models show a similar behaviour, flattening the profile. profile changes
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Figure 4. Measured and computed morphological changes after 18 hours of wave action for largescale wave flume experiments, LIPII, Delft Hydraulics, The Netherlands.
For the computations shown in Figure 4, the roughness height was taken to be constant over the entire profile. However, observations clearly showed a bed form pattern with ripple heights and lengths varying along the bed profile. No ripples or relatively small and flat ripples were found near the bar crest and further seaward whereas relatively large ripples were found in the trough shoreward of the bar crest. This argues for a roughness height varying across the profile, which is possible in the CROSMOR model. To test the effect on the model output, the roughness height ks was varied between 0.01 m on the bar crest and 0.03 m in the trough region. Figure 5 shows the computed profile based on these settings. As can be seen, the effect of using a varying wave-related roughness height is significant. Agreement between the measured and predicted profile is excellent.
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Figure 5. Measured and computed morphological changes after 18 hours of wave action for largescale wave flume experiments, LIPII, Delft Hydraulics, The Netherlands. The roughness height was varied across the profile.
3.3. Field measurements Egmond aan Zee The data used here were obtained during measurements near the coast of Egmond aan Zee, The Netherlands. Hydrodynamic process measurements were carried out in an area of about 500x500 m2 in the nearshore by use of instrumented tripods and poles during the period between 12 October and 20 November 1998 (Soulsby, 2000). Offshore wave conditions were measured by a directional wave buoy, located in 16-m water depth, 5 km offshore. The median grain size of the bed material was about 0.225 mm. Six hydrodynamic events have been selected for model comparisons (Van Rijn, 2001). Two typical hydrodynamic events of the storm period with a relatively large wave angle (24 degrees to shore normal) and a relatively small wave angle (3 degrees) are shown herein. The characteristics of these two events are: •
Burst 9416: 28-10-98 08:00 - 09:00; flood case, H1/3,offshore= 3.16 m, Tp= 8.3 s, angle = 24 degreees from the south-west quadrant, water level elevation of +1.4 m, longshore velocity to the north;
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Burst 9431: 28-10-98 23:00 - 24:00; flood case, H1/3,offshore= 4.55 m, Tp= 8.3 s, angle = 3 degrees, waves almost perpendicular to the shoreline, water elevation +1.6 m, longshore velocity to the north.
The computed hydrodynamic results for the two events, based on the best run, are shown in Figure 6 and Figure 7. All hydrodynamic runs were done by using the individual measured profiles (closest to the date of the event considered) of the measurement transect. The figures show computed and measured root-mean-square wave heights, longshore current velocities and cross-shore current velocities. The computed current velocities are depth-averaged values, whereas the measured velocities are local values at about 1 m above the bed. The computed results are summarised as follows: Wave height The computed wave heights seaward of the surf zone show differences up to 0.4 m, due to differences in bed roughness used in the models. The computed wave heights at the outer
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bar are reasonably close (within 0.2 m) and show good agreement with measured values. The computed wave heights of both models at the inner bar are reasonably close together (within 0.1 m). The least satisfactory results are obtained for the measurement station on the landward flank of the inner bar, where waves are reforming. The wave height in this latter station is over-predicted by both models. The UNIBEST model shows a more gradual wave height variation across the nearshore profile than the CROSMOR model. Best wave height predictions are obtained using the CROSMOR model in parametric mode. wave height
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Figure 6. Measured and computed wave heights, longshore current velocities and cross-shore current velocities, 28 October 1998, 08:00 h, Egmond aan Zee, the Netherlands.
Longshore velocity The type of applied boundary condition (tidal velocity, no tidal velocity or water surface slope) has a strong effect on the computed longshore velocities seaward of the outer bar. The computed longshore velocities at the outer bar show a large variability. The largest difference between the model results including tidal velocities is about 0.4 m/s (Figure 6); Both models yield peak values near the bar crest or just landward of it (Figure 6), due to 7
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inclusion of a surface roller. The computed longshore velocities at the inner bar also show a large variability; the largest difference between the model results is about 0.3 m/s. Both models show a gradual behaviour with peak values at the landward flank of the inner bar. The peak values are somewhat under-predicted for most events. The UNIBEST model results are poor to reasonable in this zone, whereas the CROSMOR model results are reasonable to good. Generally both model produce reasonable results in the surf zone for incident wave angles (to shore normal) larger than 5 degrees. The computed longshore velocities deviate substantially from measured values for incident angles smaller than 5 degrees (Figure 7).
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Figure 7. Measured and computed wave heights, longshore current velocities and cross-shore current velocities, 28 October 1998, 23:00 h, Egmond aan Zee, the Netherlands.
Cross-shore velocities The models produce velocities in the range of 0 to -0.1 m/s seaward of the surf zone; the computed velocities of both models are reasonably close together at the seaward flank of outer bar (Figure 6 and Figure 7). Both models yield offshore-directed velocities in the range of -0.1 to -0.25 m/s at the outer bar, which is in reasonable agreement with measured 8
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values during minor storm events. Onshore-directed velocities are also present, but the models cannot predict onshore-directed velocities. The relatively large offshore-directed velocities just seaward of the outer bar crest during storm events are considerably underpredicted by the models. Both models yield offshore-directed velocities in the range of -0.1 to -0.3 m/s at the inner bar, which is in reasonable agreement with measured values during minor storm events. The relatively large offshore-directed velocities at the bar crest during storm events are considerably under-predicted by both models, although the CROSMOR model results are most consistent in this zone. Offshore-directed rip currents due to circulation effects (rips) have been observed during post–storm events with relatively low waves; the profile models do not include these effects. Morphological changes: storm and seasonal scale To investigate whether the cross-shore profile models are capable of predicting nearshore morphological changes near the coast of Egmond aan Zee on short-term storm and medium-term seasonal scales, measured and computed profile changes are compared for a storm scale time period of 7 days between 24 and 31 October 1998, a seasonal scale time period of 4 months between 24 October 1998 and 25 February 1999 and a seasonal scale time period of 8 months between September 1999 and May 2000. The latter includes a shoreface nourishment. The short-term storm-scale period was characterized by high-energy wave conditions with a Hrms wave height between 0.6 and 3.5 m, a wave spectrum period Tp between 4 and 11 s and wave directions between -33 and 61° relative to shore normal. Measured and predicted morphological changes on a short-term storm scale period (7 days) are shown in Figure 8. Observations showed the outer bar to migrate about 50 m offshore and the inner bar about 10 m offshore. The troughs remained stable and the changes near the beach were small during this period. Predictions by the CROSMOR model (parametric and probabilistic mode) show a flattening of the outer and inner nearshore bar with too much offshore transport of sediment. The UNIBEST model also tends to flatten the outer bar and to a lesser extent the inner nearshore bar, although the predicted morphological changes are much smaller compared to the predictions by CROSMOR, which is likely due to the smaller undertow velocities predicted by UNIBEST.
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Figure 8. Measured and computed morphological changes for a 7 days storm period during the EU-COAST3D measurements in 1998 near the coast of Egmond aan Zee, The Netherlands.
The medium-term seasonal scale period (4 months) was characterized by high-energy wave conditions with maximum Hrms of about 4.5 m. Two severe storms occurred with Hrms > 3 m and three moderate storms with 2 < Hrms < 3 m while Hrms < 1.0 m during about 45% of the time. Wave period Tp ranged between 4 and 11 s with an average of 6.0 s. The incident wave direction was predominantly southwest and storm setup often exceeded 0.80 m. Measured and predicted morphological changes during this seasonal-scale period are shown in Figure 9. Observations show erosion and significant offshore migration of both outer (~100 m) and inner (~50 m) nearshore bar. The CROSMOR model were done in parametric mode because the probabilistic mode runs were rather time consuming and the differences between the two modes for the storm time scale runs were small (see Figure 4 and Figure 8). The CROSMOR model predicts offshore migration of the outer bar, which is in line with the measured morphological development, but the predicted migration is too large and the model flattens the profile. The UNIBEST model tends to migrate the outer bar onshore and also flattens the profile. Neither one of the models predicts the offshore migration of the inner bar. Both models flatten the inner nearshore zone (x > 4650 m) and the formation of a step in the profile at a water depth between 3 and 4 m.
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Figure 9. Measured and computed morphological changes during a 4-month winter period near the coast of Egmond aan Zee, The Netherlands.
Comparison of measured and computed undertow velocities showed the computed values to be too large on the seaward flank of a bar and too small on the shoreward flank, which basically means that the models produce an insufficient shoreward shift of the maximum undertow velocities, despite inclusion of a surface roller in both models. This was most clear in small-scale wave flume experiments (Figure 1) and field measurements near Egmond aan Zee (Figure 6 and Figure 7). To test whether the inaccurate prediction of the undertow velocities may be responsible for the flattening of the profile, Grasmeijer (2002a) adjusted the undertow velocities in the CROSMOR model approximate to the measured values by use of a spatial averaging method seaward of each computational grid point (delay factor). Predictions of the profile evolution in the outer nearshore bar region clearly improved based on this method (Grasmeijer, 2002a). However, prediction of the inner nearshore bar region remained difficult. The model predictions did reveal some 10
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offshore migration of the inner nearshore bar, which was in line with the measured morphological changes, but the predicted bar growth was not observed in the measurements. Morphological changes: a shoreface nourishment In August 1999 a shoreface nourishment was implemented along the Egmond aan Zee coast to stabilize the existing coastline. In terms of design dimensions in total 900.000 m3 of sediment was involved and this sediment was supplied on the seaward flank of the outer nearshore bar at about 700 m offshore (Figure 10). For the nourished zone, the amount of sediment supplied was equivalent to an average vertical change in seabed elevation of about 2 m and, in a longshore direction the amount of nourished sediment per cross-section was in the order of 400 m3/m. The nourishment with a total length of about 2.2 km is located in the depth interval between –5 and –7 m below NAP. Figure 10 shows the crossshore profile just before and after the implementation of the nourishment, respectively. The basic assumption underlying the design and implementation of the shoreface nourishment is that eventually sand will be carried to the shore. This section will focus on the medium-term developments of the shoreface nourishment near the coast of Egmond aan Zee in 8 months after the implementation. The cross-shore profile changes predicted by the model are compared to observed profile changes for a morphodynamic period from September 1999 to May 2000 (winter period). The 8-month winter period immediately after implementation of the nourishment is characterized by high-energy wave conditions with maximum Hrms of about 3.8 m. Three severe storms occurred with Hrms > 3 m and about eight moderate storms with 2 < Hrms < 3 m while Hrms < 1.0 m during about 45% of the time. Wave period Tp ranged between 4 and 11 s with an average of 6.4 s. The incident wave direction was predominantly southwest and storm setup often exceeded 0.80 m.
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Figure 10. Shoreface nourishment near the coast of Egmond aan Zee, The Netherlands.
Figure 11 shows the measured and predicted morphological changes of the nourished profile. The measurements show the nourished area to be rather stable. The development of the nourishment and outer bar area shows the formation of a trough between the nourishment and the outer bar. The nourishment starts to behave like an outer bar and the original outer bar is forced to migrate onshore. During this migration, the original inner bar reduces or disappears. In other words, the implementation of the shoreface nourishment 11
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sets the bar system back in time in the overall offshore bar migration cycle (Wijnberg, 1995; Van Enckevort, 2001). The outer bar migrates about 100 m onshore filling up the trough between the outer and inner nearshore bar. The model predictions also show a filling of the trough between the outer and inner nearshore bar but this is a result from offshore transport of sand from the beach. Both models tend to flatten the profile, especially in the inner nearshore zone. 3
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Figure 11. Measured and predicted morphological changes after the implementation of a shoreface nourishment near Egmond aan Zee for the period between September 1999 and May 2000.
Predictions of the profile evolution in the outer nearshore bar region clearly improve by including a breaker delay effect in the UNIBEST model (Figure 12). Apparently, breaker delay is of vital importance for proper simulation of the nearshore profile. 3
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Figure 12. Measured and predicted morphological changes after the implementation of a shoreface nourishment near Egmond aan Zee for the period between September 1999 and May 2000.
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CONCLUSIONS Two process-based cross-shore profile model have been compared with hydrodynamic and morphodynamic data of laboratory and field measurements on the time scale of storms and seasons. Both models produce reasonably good results for wave height and current velocities in 3D field conditions after proper calibration of key parameters and coefficients. The models cannot represent the relatively large reduction in wave height across the inner bar at Egmond aan Zee completely, although the CROSMOR model in parametric mode performs best in this zone, probably due to the use of a locally varying wave breaking parameter. The CROSMOR model in probabilistic mode yields good results for H1/3, but the Hrms-values are over-predicted systematically (10% to 15%). The measured values of H1/3/Hrms near the coast of Egmond aan Zee were about 1.35 close to the Rayleigh-related value of 1.41. More research is necessary to improve the simulation of the wave spectrum in the surf zone with breaking waves. With respect to the hydrodynamic parameters, there is no advantage of a multi-wave approach above a single-wave approach. Waves and currents in the nearshore are predicted with at least the same accuracy. Differences between a single-wave and a multi-wave approach are generally less than 10%. A major advantage of the single-wave approach is the relatively small computation time, which is an advantage for morphological modelling. Most important parameters determining model performance are the bed roughness height, the wave-related suspended transport and breaker delay. The short-term bed profile evolution can be modelled quite reasonably by the CROSMOR model, provided that a variable bed roughness (across the profile) is applied. The variable bed roughness is the primary cause of sand transport gradients and hence bed level changes in a barred nearshore zone. Although the effect of the wave-related suspended transport on the shortterm bed evolution is not substantial, the effect on long-term bed evolution is significant because the wave-related transport is an additional onshore transport component. On long term, this will lead to accretion of the beach. Breaker delay, as included in the UNIBEST model, shifts the maximum undertow velocities shoreward. This shoreward shift of the undertow velocities appears to be of vital importance for proper simulation of nearshore profiles (Grasmeijer, 2002a, b). The behaviour of a relatively large sand nourishment in the outer bar zone is less difficult to model than the natural behaviour of the inner bar, which is dominated by small residual transport processes. The simulation of the inner bar behaviour on the storm time scale and seasonal time scale is rather problematic due to the presence of 3D effects. Much more research is required to improve on this (including the chronology of wave events). ACKNOWLEDGEMENTS This work was undertaken as part of the COAST3D project funded by the European Commission’s research program MAST under Contract Number MAS3-CT97-0086. REFERENCES Baldock, T. E., P. Holmes, S. Bunker and P. Van Weert (1998). Cross-shore hydrodynamics within an unsaturated surf zone. Coastal Engineering 34: 173-196. 13
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Battjes, J. A. and J. P. F. M. Janssen (1978). Energy loss and set-up due to breaking of random waves. Proceedings Coastal Engineering, ASCE. pp. 569-587 Bosboom, J., S. G. J. Aarninkhof, A. J. H. M. Reniers, J. A. Roelvink and D. J. R. Walstra (2000). Unibest-TC 2.0 Overview of model formulations. H2305.42. Delft, The Netherlands Grasmeijer, B. T. (2002a). Modelling cross-shore bar behavior on storm and seasonal time scales. Proceedings Coastal Engineering, ASCE Grasmeijer, B. T. (2002b). Process-based cross-shore modelling of barred beaches. Ph.D. Thesis Physical Geography. Utrecht, The Netherlands, University of Utrecht, 250 pp. Grasmeijer, B. T. and L. C. Van Rijn (1999). Transport of fine sands by currents and waves III: breaking waves over barred profile with ripples. Journal of Waterway, Port, Coastal and Ocean Engineering 125(2): 71-79. Roelvink, J. A., T. J. G. P. Meijer, K. T. Houwman, R. Bakker and R. Spanhoff (1995). Field validation and application of a coastal profile model, New York, ASCE. pp. 818-828 Soulsby, R. L. (2000). Coastal study of three-dimensional sand transport processes and morphodynamics (Project COAST-3D), Hamburg, Germany. pp. Thornton, E. B. and R. T. Guza (1983). Transformation of wave height distribution. Journal of Geophysical Research 88(C10): 5925-5938. Van Enckevort, I. M. J. (2001). Daily to yearly nearshore bar behaviour. Ph.D. Thesis, University of Utrecht pp. Van Rijn, L. C. (1993). Principles of sediment transport in rivers, estuaries and coastal seas. Amsterdam, Aqua Publications. Van Rijn, L. C. (2001). Simulation of nearshore hydrodynamics and morphodynamics on the time scale of storms and seasons using Profile and Area models; comparison of field data and model results; COAST3D Experiments 1998-1999, Egmond, The Netherlands. Z2394. Delft, The Netherlands, WL|Delft Hydraulics Van Rijn, L. C. and K. M. Wijnberg (1996). One-dimensional modelling of individual waves and wave-induced longshore currents in the surf zone. Coastal Engineering 28: 121-145. Wijnberg, K. M. (1995). Morphologic behaviour of a barred coast over a period of decades. Ph.D. Thesis, University of Utrecht pp.
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