  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.
