Storm wave run-up causes beach erosion, wave overtopping, and street flooding. Extreme runup estimates may be improved, relative to predictions from general empirical formulae with default parameter values, by using historical storm waves and eroded profiles in numerical runup simulations. A climatology of storm wave run-up at Imperial Beach, California is developed using the numerical model SWASH, and over a decade of hindcast spectral waves and observed depth profiles. For use in a local flood warning system, the relationship between incident wave energy spectra E(f) and SWASH-modeled shoreline water levels is approximated with the numerically simple integrated power law approximation (IPA). Broad and multi-peaked E(f) are accommodated by characterizing wave forcing with frequency-weighted integrals of E(f). This integral approach improves runup estimates compared to the more commonly used bulk parameterization using deep water wave height \(H_0\) and deep water wavelength \(L_0\) Hunt (Trans Am Soc Civ Eng 126(4):542–570, 1961) and Stockdon et al. (Coast Eng 53(7):573–588, 2006. https://doi.org/10.1016/j.coastaleng.2005.12.005). Scaling of energy and frequency contributions in IPA, determined by searching parameter space for the best fit to SWASH, show an \(H_0L_0\) scaling is near optimal. IPA performance is tested with LiDAR observations of storm run-up, which reached 2.5 m above the offshore water level, overtopped backshore riprap, and eroded the foreshore beach slope. Driven with estimates from a regional wave model and observed \(\beta _f\), the IPA reproduced observed run-up with \(<30\%\) error. However, errors in model physics, depth profile, and incoming wave predictions partially cancelled. IPA (or alternative empirical forms) can be calibrated (using SWASH or similar) for sites where historical waves and eroded bathymetry are available.

风暴波加速导致海滩侵蚀，波浪过顶和街道洪水。相对于具有默认参数值的一般经验公式的预测，可以通过在数值运行模拟中使用历史风暴波和侵蚀剖面来改善极端运行估计。使用数值模型SWASH以及超过十年的后播频谱波和观测到的深度剖面图，开发了加利福尼亚帝国海滩的风暴波传播气候学。为了在本地洪水预警系统中使用，入射波能谱E（f）与SWASH模型的海岸线水位之间的关系通过数字简单积分幂律近似（IPA）进行近似。宽峰和多峰E（f）通过用E（f）的频率加权积分来表征推力来适应。与更常用的使用深水波高度\（H_0 \）和深水波长\（L_0 \） Hunt的体积参数化方法相比，这种积分方法可改善启动估算（Trans Am Soc Civ Eng 126（4）：542–570，1961 ）和Stockdon等。（Coast Eng 53（7）：573-588，2006.https：//doi.org/10.1016/j.coastaleng.2005.12.005）。通过在参数空间中搜索最适合SWASH的方式确定IPA中能量和频率贡献的比例，并显示\（H_0L_0 \）缩放接近最佳。通过LiDAR观测暴风雨，测试了IPA的性能，暴风雨达到了离岸水位以上2.5 m，过高的后岸防波堤并侵蚀了前滩的坡度。根据区域波动模型的估计值并观察到\（\ beta _f \），IPA再现了观察到的运行，误差为（<30 \％\）。但是，模型物理，深度剖面和入射波预测中的误差已部分抵消。IPA（或替代的经验形式）可以在有历史波浪和侵蚀性测深的地方进行校准（使用SWASH或类似方法）。