Exploring the Predictable Lead Time of Ensemble Forecast Based on Conditional Nonlinear Optimal Perturbation

Ensemble forecast generate multiple predictions from a set of initial conditions, thereby producing the probability density distribution (PDF) of a variable and quantifying forecast uncertainty beyond a single deterministic forecast. However, studies focusing on the predictable lead time of ensemble forecast remain limited. In this study, orthogonal conditional nonlinear optimal perturbations (O-CNOPs) are applied to the Lorenz-96 model to investigate the predictable lead time of ensemble forecast, which is then compared with that obtained from a single deterministic forecast. Results show that the maximum predictable lead time revealed by the ensemble distribution generated with O-CNOPs is 18.5 days, 2.5 days longer than that revealed by the ensemble distribution generated with singular vectors (SVs), which is 16 days. Consistent results are obtained from the ensemble mean analysis, which reveals a longer predictable lead time for O-CNOPs (21.75 days) than for SVs (18 days). In addition, compared with ensemble forecasts generated with SVs, the ensemble forecasts generated with O-CNOPs exhibit higher deterministic forecast skill, probabilistic forecast skill, reliability, and resolution over the same forecast periods. These results collectively highlight the advantage of O-CNOPs in constructing physically consistent nonlinear ensemble distributions and provide a methodological framework for more accurate quantification of ensemble forecast lead time.