  A reservoir computer (RC) is a type of simplified recurrent neural network
architecture that has demonstrated success in the prediction of
spatiotemporally chaotic dynamical systems. A further advantage of RC is that
it reproduces intrinsic dynamical quantities essential for its incorporation
into numerical forecasting routines such as the ensemble Kalman filter -- used
in numerical weather prediction to compensate for sparse and noisy data. We
explore here the architecture and design choices for a "best in class" RC for a
number of characteristic dynamical systems, and then show the application of
these choices in scaling up to larger models using localization. Our analysis
points to the importance of large scale parameter optimization. We also note in
particular the importance of including input bias in the RC design, which has a
significant impact on the forecast skill of the trained RC model. In our tests,
the the use of a nonlinear readout operator does not affect the forecast time
or the stability of the forecast. The effects of the reservoir dimension,
spinup time, amount of training data, normalization, noise, and the RC time
step are also investigated. While we are not aware of a generally accepted best
reported mean forecast time for different models in the literature, we report
over a factor of 2 increase in the mean forecast time compared to the best
performing RC model of Vlachas et.al (2020) for the 40 dimensional
spatiotemporally chaotic Lorenz 1996 dynamics, and we are able to accomplish
this using a smaller reservoir size.
