Sea surface temperature (SST) not only has profound effects on global weather and climate variations (Shiozaki et al., 2021;Soulard et al., 2019;Taguchi et al., 2012), but also is vital for climate predictions (e.g., Xie et al., 2019). The first leading mode of North Pacific SST (referred to as the first leading mode hereafter for simplicity) is one of the most documented modes of SST variability (Fang & Yang, 2016;Mantua et al., 1997). The first leading mode plays an important role in ecosystem and climate system variations (