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 flow 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.