  The El Ni\~no Southern Oscillation (ENSO) is a semi-periodic fluctuation in
sea surface temperature (SST) over the tropical central and eastern Pacific
Ocean that influences interannual variability in regional hydrology across the
world through long-range dependence or teleconnections. Recent research has
demonstrated the value of Deep Learning (DL) methods for improving ENSO
prediction as well as Complex Networks (CN) for understanding teleconnections.
However, gaps in predictive understanding of ENSO-driven river flows include
the black box nature of DL, the use of simple ENSO indices to describe a
complex phenomenon and translating DL-based ENSO predictions to river flow
predictions. Here we show that eXplainable DL (XDL) methods, based on saliency
maps, can extract interpretable predictive information contained in global SST
and discover SST information regions and dependence structures relevant for
river flows which, in tandem with climate network constructions, enable
improved predictive understanding. Our results reveal additional information
content in global SST beyond ENSO indices, develop understanding of how SSTs
influence river flows, and generate improved river flow prediction, including
uncertainty estimation. Observations, reanalysis data, and earth system model
simulations are used to demonstrate the value of the XDL-CN based methods for
future interannual and decadal scale climate projections.
