Extratropical low-frequency variability as a low-dimensional problem I: A simplified model

It is shown that the low-frequency and large-scale variability of an intermediate complexity reference model can be reproduced faithfully by a simplified model of 10 independent variables and 10 equations. The reference model is quasi-geostrophic and baroclinic. The low-order model is based on the truncated projection of the reference-model equations on the empirical orthogonal functions of its output. A closure term is shown to be essential for good performance of the low-order model. This closure term is meant to reproduce all the neglected scales and all the scale interactions, mainly baroclinic eddy forcing, that drive the large-scale flow. The closure is built as an empirically defined function of the large-scale flow of the model, relying on an extensive previously computed library of tendency differences between the full and truncated model. Two other parametrization schemes, a time-mean and a stochastic one, are tested; comparisons of these two with the former underline the importance of the how dependence of the formulation. The low-order and reference models exhibit the same climate, as well as the same low-frequency variability and weather regimes.