Numerical storm surge models are essential to forecasting coastal flood hazard and informing the design of coastal defences. However, such models rely on a variety of inputs, many of which carry uncertainty. An awareness and understanding of the sensitivity of model outputs with respect to those uncertain inputs is therefore essential when interpreting model results. Here, we use an unstructured-mesh numerical coastal ocean model, Thetis, and its adjoint, to perform a sensitivity analysis for a hindcast of the 5th/6th December 2013 North Sea surge event, with respect to the bottom friction coefficient, bathymetry and wind stress forcing. The results reveal spatial and temporal patterns of sensitivity, providing physical insight into the mechanisms of surge generation and propagation. For example, the sensitivity of the skew surge to the bathymetry reveals the protective effect of a sand bank off the UK east coast. The results can also be used to propagate uncertainties through the numerical model; based on estimates of model input uncertainties, we estimate that modelled skew surges carry uncertainties of around 5 cm and 15 cm due to bathymetry and bottom friction, respectively. While these uncertainties are small compared with the typical spread in an ensemble storm surge forecast due to uncertain meteorological inputs, the adjoint-derived model sensitivities can nevertheless be used to inform future model calibration and data acquisition efforts in order to reduce uncertainty. Our results demonstrate the power of adjoint methods to gain insight into a storm surge model, providing information complementary to traditional ensemble uncertainty quantification methods.

数值风暴潮模型对于预测沿海洪灾危害和为沿海防御设计提供信息至关重要。但是，此类模型依赖于多种输入，其中许多带有不确定性。因此，在解释模型结果时，对模型输出相对于那些不确定输入的敏感性的认识和理解是必不可少的。在这里，我们使用非结构化网格数值沿海海洋模型Thetis，及其伴随物，针对底部摩擦系数，测深法和风应力强迫，对2013年12月5日至6日北海突增事件的后遗症进行敏感性分析。结果揭示了灵敏度的时空分布，为电涌产生和传播的机理提供了物理见识。例如，偏斜浪涌对测深的敏感性揭示了英国东海岸以外的沙洲的保护作用。结果还可以用于通过数值模型传播不确定性。根据模型输入不确定性的估计，我们估计，由于测深法和底部摩擦，建模的斜度波动分别带来约5 cm和15 cm的不确定性。尽管由于不确定的气象输入，这些不确定性与整体风暴潮预报中的典型传播相比很小，但是，可以将伴随得出的模型敏感性用于未来的模型校准和数据采集工作，以减少不确定性。我们的结果证明了伴随方法能够深入了解风暴潮模型，并提供与传统整体不确定性量化方法相辅相成的信息。