Testing and calibrating parametric wave transformation models on natural beaches

TLDR: In this article, the authors compare different parametric wave transformation models with extensive observations from six field experiments on barred and unbarred beaches and show that the default model provides the best predictions for all data records or at all experiments.

About: This article is published in Coastal Engineering.The article was published on 2008-03-01 and is currently open access. It has received 92 citations till now. The article focuses on the topics: Wave height.

Figures

Figure 1: Water depth (relative to mean sea level) (solid curves), pressure sensor locations (diamonds), and tidal levels (dotted lines) versus distance offshore for (A) SandyDuck, (B) Duck94, (C) Egmond, (D) Terschelling, (E) NCEX, and (F) SwashX. The most offshore sensors for Egmond (15 m depth) and Terschelling (9 m depth) are not shown.

Figure 7: Universal empirical curves averaged over the two Duck experiments for the TG (blue), Whit (red), Lipp (green), Bald (cyan), BJ (black), and Jan (brown) models. The diamonds are the average of the binned values of the best-fit γ from Duck94 and

Table 3: Median percent errors for the six tuned models for all six experiments. Results for BJ, BS, and Nairn are identical, and are listed as BJ.

Figure 8: Percent of data records for the TG model versus the difference between the bestfit γ (γbest-fit) and the γ based on the universal curves (γuc, e.g., Figure 7) for SandyDuck (blue curve), Duck94 (black curve), SwashX (red curve), NCEX (green curve), Egmond (cyan curve), and Terschelling (yellow curve). The vertical grey dashed line represents perfect agreement, and values less (greater) than 0 occur when the universal curve over(under-) estimates the best-fit γ.

Figure 4: Number of records (histograms) versus the best-fit γ for the TG (solid curve), Whit (dashed-dotted curve), Lipp (dotted curve), Bald (dashed curve), BJ (solid curve with circles), and Jan (solid curve with diamonds) models for SandyDuck. Histograms of the best-fit γ at the other experiments are similar.

Figure 9: (A) Weighted rms percent error versus the number of tuning locations used with the TG model at SandyDuck, and (B) the scatter (defined as one standard deviation of the best-fit γ) of the best-fit γ versus the deep-water wave height Ho when the TG model is tuned using data from all sensors (solid curve), 2 offshore sensors and 2 shallow sensors (dashed curve), and 3 shallow sensors, but only 1 offshore sensor (dashed-dotted curve). In (A) two different sets of sensors were tested (i.e., there are 2 symbols in the vertical) for 3, 4, and 6 tuning locations.

Frequently asked questions

Q1. What are the contributions in this paper?

In this paper, several parametric models for the transformation of wave heights across the surfzone were tested and calibrated with observations collected along crossshore transects at 6 experiments on barred and unbarred beaches. 

Q2. What is the effect of the NCEX data on the model accuracy?

Model accuracy decreases with decreasing water depth, partially owing to the accumulation of errors with increasing distance from the location of model initialization. 

Q3. How many sensors are needed to tune the models?

To tune the models accurately, data must span the surfzone, which may require at least three to five sensors depending on tidal and wave height ranges. 

Q4. What is the way to optimize the wave heights?

To optimize predictions of the cross-shore distribution of wave heights, data are needed from at least two sensors spanning the surfzone, which changes in width and location with changing wave conditions and tidal levels. 

Q5. How many times was the bathymetry surveyed?

The bathymetry was surveyed approximately every other day from about 8-m water depth to above the high tide shoreline along cross-shore transects located about 20 m alongshore of the instrumented transects. 

Q6. What was the frequency used for the wave spectra?

The energyweighted (centroidal) frequency was used as the representative frequency when wave spectra were available (Duck94, SandyDuck, SwashX, and NCEX). 

Q7. How many meters of wave height were measured at the offshore sensors?

Root-mean-square wave heights at the most offshore sensors ranged from 0.19 to 3.93 m (Egmond) and from 0.12 to 1.84 m (Terschelling). 

Q8. How many sensors are needed to span the width of the surfzone?

At SandyDuck, three sensors are needed close to the shore to ensure that at least two sensors are located in the surfzone during all tidal stages for small waves, and at least one (or ideally two) sensors are needed in deeper water to span the width of the wider surfzone during large waves (not shown). 

Q9. What was the wave height at the offshore sensor?

Root-mean-square wave heights at the most offshore sensor (h ≈ 5 m) ranged from 0.20 to 2.10 m (SandyDuck) and from 0.14 to 2.92 m (Duck94). 

Q10. What is the relationship between the best-fit and the offshore wave height?

The dependence of the best-fit γ on the offshore wave height may be related to variations in B (which relates the dissipation in a hydraulic jump to that in a breaking wave) or to other parameterized processes, such as infragravity wave generation and differences in breaking-wave dissipation in spilling and plunging waves. 

Q11. Why does the wave model at Egmond have a larger spread?

The larger spread at Egmond and Terschelling (Figure 8, cyan and yellow curves) likely occurs because the lack of sensors in shallow water decreases best-fit γ for small Ho. 

Q12. What is the effect of using the universal curves on the prediction of waves?

Similar to previous results [Ruessink, personal communication], use of γ = 0.42 in the TG model for large deep-water waves (Ho > 1.5 m) causes too much dissipation in the outer surfzone, and thus the predicted waves are smaller than the observed waves. 

Q13. What is the effect of using the universal curves on the prediction of surfzone waves?

use of the default value of γ = 0.42 in the TG model may result in significant underprediction of surfzone wave heights when Ho is large. 

Q14. what is the criterion for the maximum height of periodic waves?

1"Q "lnQ = H rmsH m# $ %& ' (2, (4)where Hm is found by extending the Miche criterion for the maximum height of periodic waves of constant form [Miche, 1951] to! 

Q15. Does the inclusion of the NCEX data change the curves significantly?

Inclusion of the data from Egmond and Terschelling reduces the values of γ estimated for small Ho (see above), but does not change significantly the values estimated for Ho > 1.5 m.