Estimating prediction horizon of reservoir computer on L63 system when observed variables are incomplete

Reservoir computer (RC) is an attractive neural computing framework that can well predict the dynamics of chaotic systems. Previous knowledge of the RC performance is established on the case that all variables in a chaotic system are completely observed. However, in practical circumstances the observed variables from a dynamical system are usually incomplete, among which there is a lack of understanding of the RC performance. Here we utilize mean error growth curve to estimate the RC prediction horizon on the Lorenz63 system (L63), and particularly we investigate the scenario of univariate time series. Our results demonstrate that the prediction horizon of RC outperforms that of local dynamical analogs of L63, and the state-space embedding technique can improve the RC prediction in case of incomplete observations. We then test the conclusion on the more complicated systems, and extend the method to estimate the intraseasonal predictability of atmospheric circulation indices. These results could provide indications for future developments and applications of the RC.