Specificity of the short-window 4D-Var covariance construction conclusion to the Lorenz-96 model

Ascertain whether the conclusion that a four-dimensional variational system can build a fairly good approximation of flow-dependent state error covariance using a data assimilation window approximately equal to the model’s error doubling time is specific to the Lorenz-96 system or holds more generally.

Background

The authors observe that their first algorithm (A1), despite its simplicity, suggests that a 4D-Var system can reconstruct flow-dependent covariance using a data assimilation window of roughly one error doubling time, which is shorter than typical windows used to match ensemble Kalman filter performance.

They explicitly state uncertainty about whether this observation is particular to the Lorenz-96 model, raising an unresolved question about the generality of the result across other chaotic systems and data assimilation contexts.