The theory and climatological characteristics of nonstationary horizontally Rossby waves

Atmospheric Rossby waves are a fundamental component of large-scale circulation and low-frequency atmospheric variability. In classical theory, quasi-stationary planetary waves are characterized by infinite periods and are typically regarded as slowly varying background disturbances, which limits their ability to explain the widespread intraseasonal oscillations (ISOs) observed in the atmosphere. Given that ISOs share comparable spatial and temporal scales with planetary waves, a nonstationary Rossby waves framework provides a promising theoretical basis for interpreting their propagation characteristics.

In this study, we develop a theoretical framework for nonstationary horizontally propagating Rossby waves embedded in a prescribed background flow. We systematically derive the necessary conditions for the existence of three propagating solution branches, expressed equivalently in terms of the supremum and infimum of phase speed and wave period. Both the phase-speed and period supremum and infimum are determined by the background wind field, while the supremum and infimum of the period additionally depend on the zonal wavenumber. Two distinct regimes of admissible phase-speed and period ranges emerge, reflecting different background-flow configurations.

By combining these theoretical constraints with atmospheric reanalysis data, we diagnose the climatological supremum and infimum of nonstationary Rossby wave speriods in both the upper and lower troposphere over key tropical regions. The results reveal pronounced seasonal and regional variations in the theoretical period ranges due to differences in background circulation between tropospheric layers. In the upper troposphere, the equatorial Indian–western Pacific region does not support eastward-propagating solutions, whereas in the lower troposphere, eastward-propagating nonstationary waves with intraseasonal periods become possible under monsoonal flow conditions, consistent with monsoon ISO characteristics. During boreal winter and spring, the theoretical period supremum and infimum of lower-tropospheric nonstationary waves over the equatorial Indian–western Pacific exhibit Madden–Julian Oscillation (MJO)-like features. Over the equatorial Atlantic, vertically asymmetric background flows lead to distinct propagation characteristics between the upper and lower troposphere, consistent with observed ISO structures.

This work extends the classical theory of Rossby waves propagation by incorporating nonstationary waves and provides a unified theoretical interpretation linking nonstationary planetary waves to tropical intraseasonal variability.