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The Madden-Julian Oscillation (MJO) is a dominant intraseasonal variability originating in the tropics and influencing global weather and climate. Despite this dominance, we still lack reliable precursor signals triggering nonlinear initiation of primary MJO events. Here for the first time, we deal with this question from the point of view of nonlinearity, with successful implementation of conditional nonlinear optimal perturbation (CNOP). Our results show that relative to random perturbations, CNOPs of moisture have the most potential to trigger the strongest primary MJO events more than 15-20 days in advance from the given non-MJO reference states. The CNOPs manifest as a moist equator and aggregate in the lower troposphere, with stronger signals over the western Indian Ocean than over the eastern one. These CNOPs can also capture the observational moist precursor conditions of primary MJO events. This work also implies the necessity of utilizing nonlinear optimal moist initialization in subseasonal predictions.

Plain Language Summary As a dominant intraseasonal (20-90 days) variability prevailing in the tropics, the Madden-Julian Oscillation (MJO) casts significant impacts on global weather and climate. However, we still lack reliable precursor signals for MJOs initiating over the western Indian Ocean, especially for primary events, that is, those without an immediately preceding MJO event. Here for the first time, we deal with this topic from the point of view of nonlinearity, with the successful implementation of conditional nonlinear optimal perturbation (CNOP). In particular, we find that our CNOPs can identify the optimal precursors of primary MJO initiation. We examined four non-MJO reference states, selected based on both circulation- and convection-based MJO indices. Although different reference states produce different CNOPs, all tend to manifest as a moist equator and aggregate in the lower troposphere, with stronger signals over the western Indian Ocean than over the eastern Indian Ocean. These CNOP-type moist precursor conditions are also found preceding the onset of observed primary events. We find that, relative to random perturbations, CNOPs of moisture have the most potential to trigger the strongest MJO event more than 15-20 days in advance. This work implies the necessity of utilizing nonlinear optimal moist initialization to improve subseasonal (15-60 days) predictions.