Four-dimensional ensemble singular vector: Theoretical framework and experiments with the Lorenz 96 model

Ensemble simulations can be employed in sensitivity analysis to ascertain the extent to which factors influence the simulation results. Large-size ensembles reduce sampling errors and are expected to provide better sensitivity analysis. We performed a very first try at applying 1000-member ensemble sensitivity analysis, focusing on identifying the sensitives in heavy rainfall cases. In this study, the 1000-member ensemble simulations of Typhoon Hagibis (2009), which brought extreme rainfall and caused disaster in Japan, were conducted with the non-hydrostatic model (NHM) of the Japan Meteorological Agency (JMA) with 5-km grid spacing (5 km). With the Hagibis case, we expanded the traditional analysis for targeting the sensitivity of rainfall temporal changes to identify what factors impact rainfall evolution. The aim is to identify the factors that influence the timing and location of heavy rainfall, leveraging the ability of large ensembles to carry out promising sensitivity analysis.
The analysis over the surface level reasonably revealed strong sensitivity areas near the typhoon center and the associated rain bands, indicating that the typhoon itself significantly influences its accompanying rainfall. The results also showed that the rainfall was sensitive to dynamical variables (winds) mainly over the typhoon center and to thermal dynamical variables (temperature, water vapor, and pressure) over the rain band of the typhoon. In comparison to a 2D distribution target, employing the rainfall evolution target resulted in clearer sensitivities to horizontal wind over a wider area near the typhoon center and over a region away from the typhoon near Hokkaido, Japan. These results imply that a larger-scale environmental condition is more important for simulating rainfall evolution.