Ensemble forecasts are frequently utilized to assess the uncertainties of prediction systems.
There is a consensus that generating initial perturbations with specific structures is
more conducive to characterizing the growth dynamics of analysis errors, demonstrating
higher forecast skills. However, the widely used methods, such as linear singular vectors
(SVs) and orthogonal conditional nonlinear optimal perturbations (O-CNOPs) exhibit
strong linear-assumption dependence and the overestimation of growing properties for
analysis errors, respectively, severely limiting the ability to capture analysis errors and
forecast skills. To tackle these challenges, a theoretical framework is established to solve
the optimal distribution of the nonlinear growing-type initial perturbations by variational
inference (VI) incorporated with the concept of CNOPs, marked as VI-CNOPs. As the
distribution is obtained, diverse initial perturbations for ensemble forecasts can be easily
sampled in it. To evaluate the reliability of VI-CNOPs, a series of ensemble forecast experiments
are then conducted using the Lorenz-96 model.We compare the deterministic and
probabilistic forecast skills of VI-CNOPs, O-CNOPs, and SVs under various optimization
durations. The results reveal that, as the optimization durations extend, the forecast skills
of VI-CNOPs progressively improve, consistently outperforming O-CNOPs and SVs. This
trend remains consistent across various forecast lead times. Further analysis reveals that
VI-CNOPs more effectively capture the covariance matrix of analysis errors, aligning with
the fundamental concept of perturbation generation methods for ensemble forecasts.
Moreover, unlike O-CNOPs and SVs, VI-CNOPs do not require the utilization of adjoint
and tangent linear models, largely expanding its application. These results indicate the
novelty and efficacy of VI-CNOPs for ensemble forecasts.

Ensemble forecast,nonlinear,Artificial Intelligence