Four‐Dimensional Generalization of Ensemble Singular Vector: Formulation and Experiments With the Lorenz 96 Model

Abstract Motivated by the need to extend sensitivity analysis beyond spatial variations to include temporal evolution, we propose a four‐dimensional generalization to the ensemble singular vector approach, termed 4DEnSV. This generalization enables user‐defined norms that flexibly target spatiotemporal evolutions of interest. Experiments with the Lorenz '96 model demonstrate that 4DEnSV successfully identifies perturbations yielding the largest response under a user‐defined norm. By defining norms to reflect temporal objectives, 4DEnSV can extract initial perturbations responsible for specific temporal changes, such as shifts in peak timing. The proposed method offers a novel framework for sensitivity analysis and related applications, particularly for understanding the temporal evolution of weather systems.