Abstract This study applies a systematic strategy for stochastic modeling of atmospheric low-frequency variability to a realistic barotropic model climate. This barotropic model climate has reasonable approximations of the Arctic Oscillation (AO) and Pacific/North America (PNA) teleconnections as its two leading principal patterns of low-frequency variability. The systematic strategy consists first of the identification of slowly evolving climate modes and faster evolving nonclimate modes by use of an empirical orthogonal function (EOF) decomposition. The low-order stochastic climate model predicts the evolution of these climate modes a priori without any regression fitting of the resolved modes. The systematic stochastic mode reduction strategy determines all correction terms and noises with minimal regression fitting of the variances and correlation times of the unresolved modes. These correction terms and noises account for the neglected interactions between the resolved climate modes and the unresolved nonclimate modes. Low-order stochastic models with only four resolved modes capture the statistics of the original barotropic model modes quite well. A budget analysis establishes that the low-order stochastic models are dominated by linear dynamics and additive noise. The linear correction terms and the additive noise stem from the linear coupling between resolved and unresolved modes, and not from nonlinear interactions between resolved and unresolved modes as assumed in previous studies.