The calculation of climatically relevant singular vectors in the presence of weather noise as applied to the ENSO problem

An efficient technique for the extraction of climatically relevant singular vectors in the presence of weather noise is presented. This technique is particularly relevant to the analysis of coupled general circulation models where the fastest growing modes are connected with weather and not climate. Climatic analysis, however, requires that the slow modes relevant to oceanic adjustment be extracted, and so effective techniques are required to essentially filter the stochastic part of the system. The method developed here relies on the basic properties of the evolution of first moments in stochastic systems. The methodology for the climatically important ENSO problem is tested using two different coupled models. First, the method using a stochastically forced intermediate coupled model for which exact singular vectors are known is tested. Here, highly accurate estimates for the first few singular vectors are produced for the associated dynamical system without stochastic forcing. Then the methodology is applied to a relatively complete coupled general circulation model, which has been shown to have skill in the prediction of ENSO. The method is shown to converge rapidly with respect to the expansion basis chosen and also with respect to ensemble size. The first climatic singular vector calculated shows some resemblance to that previously extracted by other authors using observational datasets. The promising results reported here should hopefully encourage further investigation of the methodology in a range of coupled models and for a range of physical problems where there exists a clear separation of timescales.