We introduce a hybrid method that integrates deep learning with model-analog forecasting, a straightforward yet effective approach that generates forecasts from similar initial climate states in a repository of model simulations. This hybrid framework employs a convolutional neural network to estimate state-dependent weights to identify analog states. The advantage of our method lies in its physical interpretability, offering insights into initial-error-sensitive regions through estimated weights and the ability to trace the physically-based temporal evolution of the system through analog forecasting. We evaluate our approach using the Community Earth System Model Version 2 Large Ensemble to forecast the El Ni\~no-Southern Oscillation (ENSO) on a seasonal-to-annual time scale. Results show a 10% improvement in forecasting sea surface temperature anomalies over the equatorial Pacific at 9-12 months leads compared to the traditional model-analog technique. Furthermore, our hybrid model demonstrates improvements in boreal winter and spring initialization when evaluated against a reanalysis dataset. Our deep learning-based approach reveals state-dependent sensitivity linked to various seasonally varying physical processes, including the Pacific Meridional Modes, equatorial recharge oscillator, and stochastic wind forcing. Notably, disparities emerge in the sensitivity associated with El Ni\~no and La Ni\~na events. We find that sea surface temperature over the tropical Pacific plays a more crucial role in El Ni\~no forecasting, while zonal wind stress over the same region exhibits greater significance in La Ni\~na prediction. This approach has broad implications for forecasting diverse climate phenomena, including regional temperature and precipitation, which are challenging for the traditional model-analog forecasting method.

翻译：我们提出了一种混合方法，将深度学习与模型模拟类比预报相结合。这种直接有效的方法通过从模型模拟库中寻找相似初始气候状态生成预报。该混合框架采用卷积神经网络估计状态依赖权重以识别模拟类比状态。该方法的优势在于其物理可解释性——通过估计权重揭示初始误差敏感区域，并借助类比预报追溯系统基于物理的时间演化过程。我们利用社区地球系统模型第二版大集合在季节至年际时间尺度上评估该方法对厄尔尼诺-南方涛动的预报能力。结果显示，相比传统模型类比技术，该方法在赤道太平洋9-12个月超前预报海表温度异常方面提升了10%。此外，在基于再分析数据集的评估中，该混合模型在北半球冬季和春季初始化阶段表现出改进。基于深度学习的方法揭示了与多种季节性变化物理过程——包括太平洋经向模态、赤道充电振荡和随机风强迫——相关的状态依赖敏感性。值得注意的是，与厄尔尼诺和拉尼娜事件相关的敏感性存在差异。研究发现，赤道太平洋海表温度对厄尔尼诺预报更为关键，而同一区域的纬向风应力对拉尼娜预测更具重要性。该方法对预报传统模型类比方法难以处理的气候现象（包括区域温度和降水）具有广泛适用性。