Initial and model uncertainties are the main sources of forecast errors, making the single and deterministic forecasts unreliable. To estimate these uncertainties, a growing consensus shifts towards ensemble forecasting, aiming to provide the probability density distribution of the atmosphere. However, current ensemble methods either focus on single-source uncertainties or employ a simple superposition of the two, neglecting the nonlinear interaction between them, and thus fail to reflect the real forecast uncertainty. Motivated by this, this study extends the CNOP approach, defined as the optimal growth considering nonlinear interaction between initial and model parameters, to the scenario of ensemble forecasts and proposes an orthogonal CNOPs method (O-CNOP-IPs). This method concerns the nonlinear effect of initial and model parametric uncertainties through a joint optimization strategy and enhances the estimation of this effect by providing diversity and independent CNOPs (via orthogonality). To evaluate the performance of O-CNOP-IPs, extensive experiments are conducted for North Atlantic Oscillation (NAO) ensemble forecasts in the realistically configured Community Earth System Model (CESM). Our findings reveal that the O-CNOP-IPs method outperforms existing methods in forecast skill and reliability, improving deterministic skill by 17.5 % and probabilistic skill by 52 %–63 %. Our dynamic analysis also unveils that this method undergoes rapid development in the early stage and effectively neutralizes errors in control forecasts, significantly enhancing the reliability of ensemble forecasts. It is expected that O-CNOP-IPs plays a significant role in accurately representing the forecast uncertainty of other high-impact weather and climate phenomena.

中文翻译：

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考虑初始和模型参数不确定性之间非线互作用的条件非线性最优扰动集成预测的扩展


初始和模型的不确定性是预测误差的主要来源，使得单一和确定性的预测不可靠。为了估计这些不确定性，越来越多的共识转向集成预报，旨在提供大气的概率密度分布。然而，目前的集成方法要么关注单一来源的不确定性，要么采用两者的简单叠加，忽略了它们之间的非线性相互作用，因此无法反映真正的预报不确定性。受此启发，本研究将 CNOP 方法（定义为考虑初始参数和模型参数之间的非线互的最优增长）扩展到集成预报的场景，并提出了一种正交 CNOPs 方法 （O-CNOP-IPs）。该方法通过联合优化策略关注初始和模型参数不确定性的非线性效应，并通过提供多样性和独立的 CNOPs（通过正交性）来增强对这种效应的估计。为了评估 O-CNOP-IP 的性能，在真实配置的社区地球系统模型 （CESM） 中对北大西洋涛动 （NAO） 集合预报进行了广泛的实验。我们的研究结果表明，O-CNOP-IPs 方法在预测技能和可靠性方面优于现有方法，将确定性技能提高了 17.5%，概率技能提高了 52 %–63 %。我们的动力学分析还揭示了该方法在早期经历了快速发展，并有效地抵消了控制预报中的误差，显著提高了集成预报的可靠性。预计 O-CNOP-IP 在准确表示其他高影响天气和气候现象的预报不确定性方面发挥着重要作用。