  This paper explores the potential of a hybrid modeling approach that combines
machine learning (ML) with conventional physics-based modeling for weather
prediction beyond the medium range. It extends the work of Arcomano et al.
(2022), which tested the approach for short- and medium-range weather
prediction, and the work of Arcomano et al. (2023), which investigated its
potential for climate modeling. The hybrid model used for the forecast
experiments of the paper is based on the low-resolution, simplified
parameterization atmospheric general circulation model (AGCM) SPEEDY. In
addition to the hybridized prognostic variables of SPEEDY, the current version
of the model has three purely ML-based prognostic variables. One of these is
6~h cumulative precipitation, another is the sea surface temperature, while the
third is the heat content of the top 300 m deep layer of the ocean. The model
has skill in predicting the El Ni\~no cycle and its global teleconnections with
precipitation for 3-7 months depending on the season. The model captures
equatorial variability of the precipitation associated with Kelvin and Rossby
waves and MJO. Predictions of the precipitation in the equatorial region have
skill for 15 days in the East Pacific and 11.5 days in the West Pacific. Though
the model has low spatial resolution, for these tasks it has prediction skill
comparable to what has been published for high-resolution, purely
physics-based, conventional operational forecast models.
