Extreme Water Levels for Australian Beaches using Empirical Equations for Shoreline Wave Setup

Empirical equations for wave breaking and wave setup are compared with archived shoreline wave setup measurements to investigate the contribution of wind waves to extreme Mean Total Water Levels (MTWL, the mean height of the shoreline), for natural beaches exposed to open ocean wind waves. A broad range of formulations is compared through linear regression and quantile regression analysis of the highest measured values. Shoreline wave setup equations are selected based on the availability of local beach slope data and the ability of the quantile regression to show a good representation of the highest measured levels. Wave parameters from an existing spectral wave hindcast are used as input to the selected equations and are combined with a storm tide time series to quantify the relative contribution of shoreline wave setup to the extreme MTWL climate along Australian beaches. A multipass analysis is provided to understand the ability to capture the shoreline wave setup estimates with and without considering beach slope. The national scale analysis which does not include beach slope indicates there are multiple contributing factors to MTWL. Examples are provided at two locations of differing local beach slope to show the importance of including local beach slope in determining the contribution of waves to MTWL. A tool is in development for further investigation of wave setup for Australian beaches. Plain Language Summary Understanding how high ocean water levels can reach up the coast is important for designing coastal protection from coastal inundation and erosion. This is particularly important as climate change affects wind and weather conditions and sea level rise with the subsequent modification to the occurrence of the largest storm-driven water levels. While the height of storm-driven water levels are well understood for protected harbors and estuaries, new research is providing estimates of how high water levels can reach for coastlines exposed to dangerous wave/surf conditions. This study uses mathematical model simulations spanning similar to 30 years of historical water levels and ocean waves. Statistical analysis is performed to determine how high the largest storm events will likely reach on natural sandy beaches directly exposed to large wave/surf conditions. The study demonstrates that estimates are very sensitive to local beach characteristics. The paper presents the science behind a tool (which is in development) to allow further investigation of the contribution of waves/surf to the highest water levels for individual beaches.