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：我们提出一种混合方法，将深度学习与模式相似预报相结合——这是一种直接而有效的技术，通过从模式模拟数据库中的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的权重，以识别相似状态。本方法的优势在于其物理可解释性：通过估计的权重揭示初始误差敏感区域，并可追溯基于物理过程的系统时间演化。我们利用社区地球系统模式第二版大集合评估该方法对厄尔尼诺-南方涛动（ENSO）在季节到年际尺度上的预报能力。结果显示，相较于传统模式相似技术，该方法在热带太平洋海表温度异常超前9-12个月的预报中提升约10%。此外，基于再分析资料的评估表明，该混合模型在北半球冬春季初始化阶段具有改进效果。基于深度学习的方法揭示了与多种季节变化物理过程相关的状态依赖敏感性，包括太平洋经向模、赤道充放电振荡以及随机风强迫。值得注意的是，厄尔尼诺和拉尼娜事件在敏感性上呈现显著差异：热带太平洋海表温度对厄尔尼诺预报更为关键，而同区域纬向风应力在拉尼娜预报中更为重要。该方法对包括区域气温和降水在内的多样化气候现象预报具有广泛适用性，而传统模式相似预报方法在处理这些现象时面临挑战。