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. (C) 2003 Elsevier Science B.V. All rights reserved.