Calibration and verification of a parametric wave model on barred beaches

Since its introduction in 1978, the Battjes and Janssen model has proven
to be a popular framework for estimating the cross-shore
root-mean-square wave height H-rms transformation of random breaking
waves in shallow water. Previous model tests have shown that wave
heights in the bar trough of single bar systems and in the inner troughs
of multiple bar systems are overpredicted by up to 60\% when standard
settings for the free model parameter gamma (a wave height-to-depth
ratio) are used. In this paper, a new functional form for gamma is
derived empirically by an inverse modelling of gamma from a
high-resolution (in the cross-shore) 300-h H-rms data set collected at
Duck, NC, USA. We find that, in contrast to the standard setting, gamma
is not cross-shore constant, but depends systematically on the product
of the local wavenumber k and water depth It. Model verification with
other data at Duck, and data collected at Egmond and Terschelling
(Netherlands), spanning a total of about 1600 h, shows that cross-shore
H-rms profiles modelled with the locally varying gamma are indeed in
better agreement with measurements than model predictions using the
cross-shore constant gamma. In particular, model accuracy in inner bar
troughs increases by up to 80\%. Additional verifications with data
collected on planar laboratory beaches show the new functional form of
gamma to be applicable to non-barred beaches as well. Our optimum gamma
cannot. be compared directly to field and laboratory measurements of
height-to-depth ratios and we do not know of a physical mechanism why
gamma should depend positively on kh.