Isolating Zonal Influences on Global Climate Feedbacks Using Empirical Orthogonal Functions

It has recently become clear that the climate feedback parameter λ, which relates changes in surface temperatures to changes in top-of-atmosphere net flux, is a function of the pattern of surface warming. In order to understand this better, we have analyzed a large ensemble of model runs (the MPI Grand Ensemble) and estimated λ in a sliding 15-year window in each ensemble member. We then break λ down into its constituent feedbacks. The global averages of these feedbacks were used in multivariate empirical orthogonal function (EOF) analysis to create one set of principal components (PCs) that applied to the global EOFs of all feedbacks. Zonal feedbacks were then calculated and analyzed using single variable EOF analysis to produce EOFs and PCs for each feedback at each latitude. The zonal, feedback-specific PCs were regressed against the global, feedback-ambiguous PCs, and the coefficients that minimize the error in estimation were extracted. Each mode of the zonal EOFs was multiplied by the corresponding coefficient and all ten modes were summed to create one representative EOF for that latitude. The resulting EOF was regressed against the global EOF to determine the effect of the feedbacks at that latitude on the global average. To determine the physical driver of the resulting feedback patterns, temperature change at a given grid point per unit global temperature change corresponding to the feedbacks was calculated. This local temperature change was used to relate feedback variability to surface temperature patterns.