Linear Inverse Modeling (LIM) and its implications for MJO predictability and mechanisms

Linear Inverse Modeling (LIM) is a multi-channel statistical technique in which one builds an evolution operator that predicts the evolution of multivariate anomalies, based on covariance and lag covariance matrices built from historical data samples. Previous studies show that the MJO can be well predicted by LIM, but their use of an EOF basis makes the nature of the derived evolution operator rather opaque. I will make attempt to make clearer the nature of LIM and demonstrate it for the MJO using a simpler, spatial basis (longitide bins). The importance of additional variables, resolution, etc. to prediction skill may allow deductions about MJO mechanisms and their linearity, while illustrating the pitfalls of overfitting. One final result of this exploration will be an optimized LIM to compare to existing statistical predictions in a familiar spatial framework (time-longitude sections of OLR).