“…In former studies about relations between QBO and long-term variations of atmospheric waves, QBO phases are usually defined by zonal wind directions at a single pressure level, mostly at 50 hPa (Holton and Tan, 1980;Merzlyakov et al, 2013;Merzlyakov et al, 2015;de Wit et al, 2016;Laskar et al, 2016), or the vertical shear of QBO wind, e.g., between 70 hPa and 10 hPa (Miyoshi and Hirooka, 2003). Moreover, most of these results are qualitatively.…”