Dynamic parameter sensitivity in numerical modelling of cyclone-induced waves: a multi-look approach using advanced meta-modelling techniques

The knowledge and prediction of cyclones as well as wave models experienced significant improvements in this last decade, opening the perspective of a better understanding of the wave sensitivity to the cyclone characteristics (e.g. track angle of approach θ, forward speed V f, radius of maximum wind R m, landfall position x o, etc.). Physically, waves are strongly linked to the time-varying evolution of the relative cyclone position. Thus, even assuming the main cyclone characteristics to be stationary, exploring the role played by each of them should necessarily be conducted in a dynamic manner. This problem is investigated using the advanced statistical tools of variance-based global sensitivity analysis (VBSA) in different ways to provide an overall view of wave height sensitivity to cyclone characteristics: (1) step-by-step: by computing the time series of sensitivity measures; (2) aggregated: by summarising the time-varying information into a single sensitivity indicator; (3). mode-based: by studying the sensitivity with respect to the occurrence of specific temporal patterns (e.g. up-down translation of the overall series). Yet, applying this multi-look dynamic sensitivity analysis faces two major difficulties: (1) VBSA requires a large number of simulations (typically > 10,000), which appears to be incompatible with the large computation time cost of numerical codes (>several hours for a single run); (2) integrating the time dimension imposes to process a large amount of information via vectors of large size (e.g. series of significant wave height H S discretised over several hundreds of time steps). In this study, we propose a joint procedure combining kriging meta-modelling (to overcome the 1st issue) and principal component analysis techniques (to overcome the 2nd issue by summarising the time information into a limited number of components). The applicability of this strategy is tested and demonstrated on a real case (Sainte-Suzanne city, located at Reunion Island) using a set of 100 cyclone-induced H S series, each of them being computed for different scenarios of cyclone characteristics, i.e. using only 100 long-running simulations. The key role of R m over the whole evolution of H S is shown by means of the aggregated option, with a more specific influence in the vicinity of Sainte-Suzanne (when the cyclone eye is located less than 200 km away from the site) as highlighted by the step-by-step option. The step-by-step option also highlights the influence of the landfall position on the H S peak reached in strong interaction with θ and R m. Finally, the role of V f in the occurrence of a turning point marking a shift near landfall between regimes of low-to-high H S values is also identified. The above results provide guidelines for future research efforts on cyclone characteristics prediction.