Wave Runup Analysis
The sites at which wave runup was recorded span the study area; a total of 26 wave runup records were recorded at 21 of the 26 sites with beaches. Four sites were chosen to record multiple wave conditions based on their beach morphology, location within the study area, the ability to film storms at the sites, and accessibility during storm conditions.
The equations used to hindcast cumulative wave impact height were chosen by maximizing the R^{2} and minimizing the root mean square (RMS) error of the predicted versus observed wave runup. The figure below displays examples of raw predicted wave runup versus observed wave runup.
Raw, predicted wave runup versus observed wave runup from the Nielsen and Hanslow equations


The following tables show the R^{2} and root mean square (RMS) errors for each method separated by beach material type.
Root mean square error for predicted versus observed, raw wave runup data
Beach Material 
Hunt (mean) 
CERC (mean) 
Mase (mean) 
N & H (mean) 
Mase (2%) 
N & H (2%) 
A & S (2%) 
Cobble 
0.86 
0.91 
0.75 
0.27 
1.72 
0.70 
N/A 
Mix 
1.18 
1.22 
1.11 
0.35 
2.51 
0.99 
3.92 
Sand 
0.57 
0.58 
0.57 
0.21 
1.34 
0.49 
2.33 
All 
0.75 
0.78 
0.71 
0.25 
1.64 
0.63 
2.63 
R^{2} values for predicted versus observed, raw wave runup data
Beach Material 
Hunt (mean) 
CERC (mean) 
Mase (mean) 
N & H (mean) 
Mase (2%) 
N & H (2%) 
A & S (2%) 
Cobble 
0.38 
0.40 
0.36 
0.38 
0.37 
0.39 
N/A 
Mix 
0.92 
0.92 
0.93 
0.92 
0.95 
0.95 
0.02 
Sand 
0.49 
0.50 
0.49 
0.49 
0.41 
0.42 
0.35 
All 
0.48 
0.48 
0.48 
0.48 
0.45 
0.45 
0.18 
The R^{2} values are similar for each wave runup equation with the exception of the Ahrens and Seelig equation. These R^{2} values indicate each method accounts for the variability in observed wave runup equally well. The scatter in the case of the Ahrens and Seelig equation is probably due to the difficulty of obtaining representative grain sizes for the surf and swash zones. The RMS errors indicate the Nielsen and Hanslow equations came closest to predicting both the mean and 2% wave runup. This result is likely because the Nielsen and Hanslow equations were developed for natural sand beaches. The other equations investigated were based on laboratory data for smooth, impermeable slopes, with the exception of the Ahrens and Seelig equation. Thus, the higher errors are a result of wave runup being overestimated because the beaches in the field are rough and permeable. The recorded wave runup data shows the Nielsen and Hanslow equations are the most appropriate for predicting wave runup at the sites and will be the method employed and discussed from this point forward.
As discussed in the Geology section, a variety of beach materials are present at the study sites. Due to the presence of these different materials, wave runup reduction factors need to be applied to predict wave runup at different sites. A wave runup reduction factor is defined as the ratio of observed runup to predicted runup. The measured runup was intended to be used to verify which method to use to predict runup, not determine our own method of prediction. Thus, the wave runup reduction factors deemed appropriate for this study were to be reasonable according to published data (CERC, 1984). It is also desirable not to skew the predicted versus observed wave runup in the direction of over or under prediction and reduce RMS error. Adhering to these criteria, wave runup reduction factors were determined for each beach type. These reduction factors and the RMS error values are given in the table below.
Wave runup reduction factors for different beach material and RMS errors for reduced and unreduced predicted runup. Bold type indicates the reduction factors determined for this study.
Beach Material 
Reduction Factor 
RMS Error (m) 

N & H (mean) 
N & H (2%) 

Cobble 
0.65 
0.20 
0.38 
Cobble 
1.00 
0.27 
0.70 
Mix 
0.85 
0.26 
0.77 
Mix 
1.00 
0.35 
0.99 
Sand 
1.00 
0.21 
0.49 
Sand 
1.00 
0.21 
0.49 
All 
Y 
0.22 
0.52 
All 
N 
0.25 
0.63 
For hindcasting WIH the Nielsen and Hanslow equations will be used with the reduction factors in bold print in the above table.
Cumulative Wave Impact Height Area (WIHA)