An Approach to Generating Mutually Independent Initial Perturbations for Ensemble Forecasts: Orthogonal Conditional Nonlinear Optimal Perturbations

Conditional nonlinear optimal perturbation (CNOP) is the initial perturbation that satisfies a certain physical constraint and causes the largest nonlinear evolution at prediction time. To yield mutually independent initial perturbations in ensemble forecasts, orthogonal CNOPs are developed. Orthogonal CNOPs are then applied to a Lorenz-96 model to generate initial perturbations for ensemble forecasting, as compared with orthogonal singular vectors (SVs). When the initial analysis errors are fast growing, the ensemble forecasts generated by orthogonal CNOPs of the control forecasts perform much more skillfully. Nevertheless, for slow-growing initial analysis errors, the ensemble forecasts generated by orthogonal SVs achieve higher skill when the ensemble initial perturbations are large, whereas the ensemble forecasts generated by orthogonal CNOPs achieve almost the same forecast skill as those generated by orthogonal SVs when the ensemble initial perturbations are sufficiently small. The initial analysis errors that possess much faster growth behavior are easily influenced by nonlinearity, and extreme events (extreme here refers to strong), because of strong nonlinear instability, may be much more likely to cause fast growth of initial analysis errors. Therefore, the ensemble forecasts generated by orthogonal CNOPs may have higher skill than those generated by orthogonal SVs for extreme events; in particular, the ensemble forecasts generated by orthogonal CNOPs, compared with those generated by orthogonal SVs, require a much smaller number of ensemble members to achieve high skill. Therefore, orthogonal CNOPs may provide another useful technique to generate initial perturbations for ensemble forecasting.