Abstract
This study develops an extended theoretical framework of Rossby wave ray and phase tracing that simultaneously predicts wave trajectories and the spatial evolution of crests and troughs. The formulation is derived from two-dimensional spherical Rossby wave theory on a horizontally non-uniform basic flow, allowing both zonal and meridional background winds to influence wave propagation and phase evolution. The framework is applied to diagnose stationary Rossby wave behavior under idealized and realistic atmospheric conditions: Validation in idealized basic states shows that the predicted phase evolution accurately reproduces the structure of forced responses in a barotropic model. The results demonstrate the important role of mean meridional flow: it permits one-way cross-equatorial propagation across the easterlies and substantially enlarges meridional scale of waves, thereby shaping zonally elongated structures in meridionally propagating wave trains. Application to the observed boreal-summer circulation further reveals that the Pacific-Japan (PJ) teleconnection arises from coherent phase evolution of multilevel Rossby wave trains. In the lower troposphere, northward-propagating waves embedded in the monsoonal southwesterlies generate a meridionally elongated ‘− / + / −’ phase consistent with observed tripolar anomaly pattern. In the upper troposphere, southeastward-to-southwestward propagating waves form a complementary ‘+ / − / +’ pattern. These features cannot be captured within the traditional zonal-flow-only framework, underscoring the dynamical importance of mean meridional flow. Overall, our results establish wave phase evolution as a key dynamical constraint on wave propagation and teleconnection structure, offering a new pathway for diagnosing teleconnection patterns and understanding their variabilities and potential future changes.
