Title: Using Deep Learning to Identify Initial Error Sensitivity for Interpretable ENSO Forecasts

Abstract: We introduce an interpretable-by-design method, optimized model-analog, 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 initial analog states that lead to shadowing target trajectories. The advantage of our method lies in its inherent interpretability, offering insights into initial-error-sensitive regions through estimated weights and the ability to trace the physically-based 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 equatorial Pacific sea surface temperature anomalies at 9-12 months leads compared to the original (unweighted) model-analog technique. Furthermore, our model demonstrates improvements in boreal winter and spring initialization when evaluated against a reanalysis dataset. Our approach reveals state-dependent regional sensitivity linked to various seasonally varying physical processes, including the Pacific Meridional Modes, equatorial recharge oscillator, and stochastic wind forcing. Additionally, disparities emerge in the sensitivity associated with El Ni\~no versus La Ni\~na events. El Ni\~no forecasts are more sensitive to initial uncertainty in tropical Pacific sea surface temperatures, while La Ni\~na forecasts are more sensitive to initial uncertainty in tropical Pacific zonal wind stress. This approach has broad implications for forecasting diverse climate phenomena, including regional temperature and precipitation, which are challenging for the original model-analog approach.