The authors thank two anonymous reviewers, the MæT group in Hokkaido University, Prof. Masahide Kimoto, Prof. Takeshi Enomoto, and Prof. Shoshiro Minobe for giving us insightful comments for the study. This study was partly supported by Research Program on Climate Change Adaptation, by Grants-in-Aid for Scientific Research on Innovative Areas 22106008, by the Core Research for Evolution Science and Technology, and for Scientific Research (B) 23340141, all funded by the Ministry of Education, Culture, Sports, Science, and Technology of Japan. Prof. Takashi Sakajo in Hokkaido University especially supported our work. Figures were drawn using Grid Application Development Software.
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Degrees of freedom are about 300 in the analysis period, because a low-pass filter was taken for the data.
The degrees of freedom of data in a single DJF season are about 9. If you statistically calculated the one-dimensional PDF in a phase space, you would require about 30 independent samples. The required number of winters can then be roughly estimated by 10d/2 of DJF seasons for the d-dimensional plot.