Influences of Initial Perturbation Amplitudes and Ensemble Sizes on the Ensemble Forecasts Made by CNOPs Method

The initial perturbation amplitude and ensemble size are important for ensemble forecast. The present study explores the impacts of initial perturbation amplitude and ensemble size on the ensemble forecast skill using a new strategy that applies orthogonal conditional nonlinear optimal perturbations (CNOPs) to the Lorenz-96 model. It is found that due to the effect of nonlinearity, the CNOPs-based ensemble forecast can achieve higher skills when the initial perturbation amplitude is appropriately smaller than the amplitude of initial analysis errors, and the highest skill of the CNOPs-based ensemble forecasts is always higher than that of its linear counterpart i.e., singular vectors (SVs)-based ensemble forecast. The results also show that an appropriate ensemble size is helpful for achieving higher skills in ensemble forecast. A better spread-skill relationship and a much flatter Talagrand diagram are found in CNOPs-based ensemble forecast, which indicates the reliability of the corresponding ensemble forecast system and makes the above results much solid. It is therefore inferred that the highest skill of CNOPs-based ensemble forecast is mostly likely achieved when initial perturbation amplitudes are properly smaller than those of initial analysis errors and the ensemble size is appropriate.