Rossby wave phase tracing and its application to the structure of the Pacific–Japan teleconnection

Building upon the established Rossby wave ray tracing framework, we introduce a phase tracing approach, derived from two-dimensional spherical Rossby wave theory on a horizontally non-uniform basic flow, to explicitly diagnose the evolution of wave crests and troughs along stationary Rossby wave rays.

The method is first applied to a series of idealized basic flows and validated against forced solutions from a barotropic model, with a particular emphasis on contrasting flows with and without a mean meridional wind. The theoretical phase tracing accurately reproduces both the ray pathways and the spatial structure of the simulated responses, in agreement with the theoretical prediction that local zonal and meridional wave scales are primarily controlled by the background flow rather than by the forcing scale. Importantly, the inclusion of a mean meridional flow emerges as a key dynamical ingredient: it not only permits one-way propagation of stationary Rossby waves across tropical easterlies, but also substantially enlarges both zonal and meridional wave scales, with the zonal scale becoming dominant, thereby shaping zonally elongated wave-train structures.

The framework is further applied to climatological summertime flows to investigate the structure of the Pacific–Japan (PJ) teleconnection. In the lower troposphere, northward-propagating Rossby waves embedded in the monsoonal southwesterly exhibit a characteristic ‘− / + / −’ phase pattern, while in the upper troposphere the phase evolution of southeastward- and southwestward-propagating Rossby waves displays a complementary ‘+ / − / +’ structure. The phase transition points along the rays are found to coincide closely with the centers of positive and negative vorticity anomalies, providing a clear dynamical explanation for the formation of the zonally elongated tripolar structure of the PJ teleconnection.

In addition, the Li–Yang wave ray flux (WRF) is employed to quantify the intensity of wave propagation along the diagnosed ray pathways, offering a complementary measure of wave activity during propagation.

Together, the phase tracing framework and wave ray flux diagnostics enable a precise and physically constrained diagnosis of atmospheric teleconnection patterns, and hold broad applicability for understanding the structure and variability of Rossby wave–mediated teleconnections in a realistic, non-uniform background flow.