  Reduced-order dynamical models play a central role in developing our
understanding of predictability of climate irrespective of whether we are
dealing with the actual climate system or surrogate climate-models. In this
context, the Linear-Inverse-Modeling (LIM) approach, by capturing a few
essential interactions between dynamical components of the full system, has
proven valuable in providing insights into predictability of the full system.
We demonstrate that Reservoir Computing (RC), a form of learning suitable for
systems with chaotic dynamics, provides an alternative nonlinear approach that
improves on the predictive skill of the LIM approach. We do this in the example
setting of predicting sea-surface-temperature in the North Atlantic in the
pre-industrial control simulation of a popular earth system model, the
Community-Earth-System-Model so that we can compare the performance of the new
RC based approach with the traditional LIM approach both when learning data is
plentiful and when such data is more limited. The improved predictive skill of
the RC approach over a wide range of conditions -- larger number of retained
EOF coefficients, extending well into the limited data regime, etc. -- suggests
that this machine-learning technique may have a use in climate predictability
studies. While the possibility of developing a climate emulator -- the ability
to continue the evolution of the system on the attractor long after failing to
be able to track the reference trajectory -- is demonstrated in the Lorenz-63
system, it is suggested that further development of the RC approach may permit
such uses of the new approach in more realistic predictability studies.
