Wave run-up on embayed beaches. Study case: Itapocorói Bay, Southern Brazil

ABSTRACT This paper presents a new approach for estimating run-up on embayed beaches based on a study of the microtidal coast of Itapocorói Bay, Southern Brazil using the surf similarity parameter and wave height at break location. The four step methodology involved: 1) direct wave measurement (34 days), wave run-up measurement (19 days at 7 points within the bay), measurement of bathymetry and beach topography in the entire bay; 2) tests on available formulae to calculate wave run-up; 3) use of the SWAN spectral wave model to simulate wave parameters at breaking at each wave run-up measurement point and; 4) development of a new formula/approach to assess wave run-up on embayed beaches (in both exposed and protected areas). During the experiments the significant wave height varied from 0.5 m to 3.01 m, the mean wave period from 2.79 s to 7.76 s (the peak period varied between 2.95 s and 17.18 s), the mean wave direction from 72.5° to 141.9° (the peak direction varied from 39.2° to 169.8°) and the beach slope (tan β) from 0.041 to 0.201. The proposed formula is in good agreement with measured data for different wave conditions and varying degrees of protection. The analysis demonstrates that although R² varies from 0.52 to 0.75, the wave run-up distribution over the measurements agreed well with the proposed model, as shown by quantile-quantile analysis (R²=0.98 to 0.99). The errors observed in individual cases may be related to errors of measurements, modeling and to non-linear processes in the swash zone, such as infragavity waves.