The effectiveness of machine learning methods in the nonlinear coupled data assimilation

Implementing the strongly coupled data assimilation (SCDA) in coupled earth system models remains big challenging, primarily due to accurately estimating the coupled cross background-error covariance. In this work, through simplified two-variable one-dimensional assimilation experiments focusing on the air–sea interactions over the tropical pacific, we aim to clarify that SCDA based on the variance–covariance correlation, such as the ensemble-based SCDA, is limited in handling the inherent nonlinear relations between cross-sphere variables and provides a background matrix containing linear information only. These limitations also lead to the analysis distributions deviating from the truth and miscalculating the strength of rare extreme events. However, free from linear or Gaussian assumptions, the application of the data-driven machine learning (ML) method, such as multilayer perceptron, on SCDA circumvents the expensive matrix operations by avoiding the explicit calculation of background matrix. This strategy presents comprehensively superior performance than the conventional ensemble-based assimilation strategy, particularly in representing the strongly nonlinear relationships between cross-sphere variables and reproducing long-tailed distributions, which help capture the occurrence of small probability events. It is also demonstrated to be cost-effective and has great potential to generate a more accurate initial condition for coupled models, especially in facilitating prediction tasks of the extreme events.