The hypothesis that predictability depends on the atmospheric state in the planetary-scale low-frequency variability in boreal winter was examined. We first computed six typical weather patterns from 500-hPa geopotential height anomalies in the Northern Hemisphere using self-organising map (SOM) and k-clustering analysis. Next, using 11 models from the subseasonal-to-seasonal (S2S) operational and reforecast archive, we computed each model’s climatology as a function of lead time to evaluate model bias. Although the forecast bias depends on the model, it is consistently the largest when the forecast begins from the atmospheric state with a blocking-like pattern in the eastern North Pacific. Moreover, the ensemble-forecast spread based on S2S multi-model forecast data was compared with empirically estimated Fokker-Planck equation (FPE) parameters based on reanalysis data. The multi-model mean ensemble-forecast spread was correlated with the diffusion tensor norm; they are large for the cases when the atmospheric state started from a cluster with a blocking-like pattern. As the multi-model mean is expected to substantially reduce model biases and may approximate the predictability inherent in nature, we can summarise that the atmospheric state corresponding to the cluster was less predictable than others.

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Physicists have established a general approach for explaining the phase transition behavior using order parameters in phenomenological theories. Order parameters are generally accounted for by single molecular properties in mean-field theories. Such theories build on physicists’ hypotheses, which are validated by agreement between the observed and predicted values, such as the theoretical estimation of phase transition temperatures. In this study, we report chemical-data-driven methods for finding and scrutinizing physical assumptions on which physical theories are based. We demonstrate the effectiveness of our methodology by validating the assumption of the widely accepted phenomenological Landau theory for liquid-crystalline (LC) phases, wherein the symmetry of the lower-temperature phase explains phase transition. Furthermore, our method suggests that the importance of molecular flexibility is underestimated in the major mean-field theories for LC phases, compared with the widely incorporated molecular shape and intermolecular electrostatic interactions.