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Models are attractive tools to deepen the understanding of atmospheric and climate processes. In practice, such investigations often involve numerical experiments that switch on or off individual factors ( such as latent heating, nonlinear coupling, or some climate forcing). However, as in general many factors can be considered, the analysis of these experiments is far from straightforward. In particular, as pointed out in an influential study on factor separation by Stein and Alpert, the analysis will often require the consideration of nonlinear interaction terms.

In the current paper an alternative factor separation methodology is proposed and analyzed. Unlike the classical method, sequential factor separation (SFS) does not involve the derivation of the interaction terms but, rather, provides some uncertainty measure that addresses the quality of the separation. The main advantage of the proposed methodology is that in the case of n factors it merely requires 2n simulations (rather than 2(n) for the classical analysis). The paper provides an outline of the methodology, a detailed mathematical analysis, and a theoretical intercomparison against the classical methodology. In addition, an example and an intercomparison using regional climate model experiments with n = 3 factors are presented. The results relate to the Mediterranean amplification and demonstrate that-at least in the particular example considered-the two methodologies yield almost identical results and that the SFS is rather insensitive with respect to design choices.