Recovering climate predictability from sparse observations via dynamical system deep learning

Real-world climate systems are intrinsically high-dimensional and only partially observable, making the recovery of large-scale dynamics and climate predictability from sparse observations a major challenge for climate prediction. In this study, we investigate whether latent predictability can be reconstructed from incomplete observations using the Dynamical System Deep Learning (DSDL) framework, which is grounded in nonlinear dynamical embedding theory. A series of representative nonlinear chaotic systems, including the Lorenz’ 63 system, a seven-dimensional hyperchaotic system, the Lorenz’ 96 system, the multi-scale coupled Lorenz’ 96 system, and the Kuramoto–Sivashinsky equation, are employed to evaluate the capability of DSDL under missing-variable conditions. Compared with several representative data-driven forecasting approaches, DSDL exhibits a stronger capability to recover latent large-scale dynamics and predictability from sparse observations, accompanied by longer effective prediction times and lower prediction variability. Furthermore, DSDL is applied to one-month-lead hindcasts of summer precipitation over China during 2000–2022. The results show that the framework successfully reconstructs the dominant large-scale drought–flood anomaly patterns and captures part of the interannual variability associated with the evolution of the East Asian summer monsoon and large-scale air–sea interactions. In several extreme years, including the 2020 Yangtze River flooding and the 2022 severe drought event, DSDL reproduces the observed spatial anomaly structures with considerable skill. These findings suggest that sparse observations may still retain recoverable information associated with low-frequency climate dynamics and predictability, highlighting the potential of DSDL, as a dynamics-informed framework grounded in nonlinear embedding theory, for seasonal climate prediction under incomplete observational conditions.