**1. Introduction**

It has been 10 years since academician Duzheng Ye left us. His pass away was a great loss not only to the atmospheric science community in China but also to the international atmospheric science community. This article is written to commemorate the 10th anniversary of his pass away and to remember his great contributions to the development of atmospheric dynamics.

It is well known that the theory of Rossby wave energy dispersion [1] proposed by Duzheng Ye more than 70 years ago is one of the classical theories of atmospheric dynamics. The theory of Rossby wave energy dispersion is not only widely used in weather forecasting but also inspire the development of planetary wave dynamics, especially the study on the propagating characteristics of quasi-stationary planetary waves in two- and three-dimensional spherical atmosphere [2–11] and the teleconnection mechanism of global atmospheric circulation anomalies [12–20]. Under the guidance of the theory of Rossby wave energy dispersion proposed by academician Ye, the research on the dynamic processes of the variability of the East Asian monsoon system has been made in recent years. In particular, our research group studied the dynamic processes of the impacts of the East Asian/Pacific (EAP) and Silk Road (SR) pattern teleconnection wave trains on the variability

**Citation:** Huang, R.; Huangfu, J.; Liu, Y.; Lu, R. The Guiding Role of Rossby Wave Energy Dispersion Theory for Studying East Asian Monsoon System Dynamics. *Atmosphere* **2023**, *14*, 962. https://doi.org/10.3390/ atmos14060962

Academic Editor: Anthony R. Lupo

Received: 14 April 2023 Revised: 24 May 2023 Accepted: 28 May 2023 Published: 31 May 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

of the East Asian summer monsoon system [16,21]. In addition, significant progress has achieved in the studies on the dynamic processes of the variability of the East Asian winter monsoon system due to the oscillations of the propagating waveguides of quasi-stationary planetary waves in the three-dimensional spherical atmosphere [22–25]. Thus, this paper presents a brief review of the recent studies on the dynamic processes of the interannual and interdecadal variabilities of the East Asian summer monsoon system and the dynamical impact of the interannual and interdecadal oscillations of the propagating waveguides of quasi-stationary planetary waves on the East Asian winter monsoon system. Besides, under the guidance of the theory of Rossby wave energy dispersion, some studies in China and abroad related to the dynamic processes of the East Asian monsoon system are simply reviewed in this paper. Many figures in this paper are the result of our recent analysis using 60-year reanalysis data and summer precipitation data in eastern China for 1961–2020.

#### **2. The Guiding Role of the Theory of Rossby Wave Energy Dispersion in the Study on Quasi-Stationary Planetary Wave Propagation in a Three-Dimensional Spherical Atmosphere**

The theory of Rossby wave energy dispersion proposed by academician Ye has not only benefited the study on the two-dimensional propagation of quasi-stationary planetary waves in the spherical atmosphere but also played a guiding role in the study on the threedimensional propagation of quasi-stationary planetary waves in the spherical atmosphere during boreal winter.

### *2.1. Study on the Propagating Waveguides of Quasi-Stationary Planetary Waves in the Spherical Atmosphere during Boreal Winter*

After academician Duzheng Ye proposed the theory of Rossby wave energy dispersion, many meteorologists focused on the energy dispersion of planetary waves in the vertical direction of the atmosphere. For example, several meteorologists [26,27] applied the concepts of the wave refraction index and energy, respectively, to study the vertical propagating characteristics of quasi-stationary planetary waves in the basic flow with a vertical wind shear. Later, Dickinson [5] applied the concept of waveguides to study the vertical propagating characteristics of quasi-stationary planetary waves in the ideal basic flow in boreal winter and proposed that quasi-stationary planetary waves can propagate from the troposphere to the stratosphere over high latitudes, which is called the polar waveguide. After the Dickinson's study, Matsuno [6,7] studied the vertical propagation of quasi-stationary planetary waves from the troposphere to the stratosphere in the actual basic flow in boreal winter and proposed the dynamic mechanism of the stratospheric sudden warming. He noted that the propagation of tropospheric quasi-stationary planetary waves into the stratosphere and their interaction with the stratospheric basic flow leads to the stratospheric sudden warming in boreal winter. Thus, the theory of Rossby wave energy dispersion guided the study on the propagating characteristics of quasi-stationary planetary waves in the atmosphere from the troposphere to the stratosphere, which established the theoretical basis for the study on the mechanism of tropospheric-stratospheric interactions.

Guided by the theory of Rossby wave energy dispersion and based on the studies made by Matsuno [6,7], Huang and Gambo [10,11] systematically studied the characteristics of the three-dimensional propagations of quasi-stationary planetary waves in a spherical atmosphere using the wave refraction index and the E-P flux, respectively.

Huang and Gambo [11] studied the characteristics of three-dimensional propagation of quasi-stationary planetary waves in the actual basic flow using the wave refraction index. Figure 1 shows the vertical distribution of boreal winter Q0 and a schematic diagram of the propagating waveguides of quasi-stationary planetary waves in the three-dimensional atmosphere, where Q0 = Qk + k2/cos2ϕ (Qk is the square of the refraction index for wavenumber k, calculated from the basic flow and related parameters; k is the wavenumber, and ϕ is latitude). In Figure 1, we can see that the propagations of quasi-stationary planetary waves in the three-dimensional atmosphere in boreal winter exist two waveguides. The first waveguide is called the polar waveguide [5], i.e., quasi-stationary planetary waves

can propagate from the troposphere to the stratosphere at high latitudes through this waveguide. Similarly, Figure 1 shows that quasi-stationary planetary waves can also propagate from the lower troposphere at mid-latitudes to the upper troposphere at low latitudes through the second waveguide. This propagating waveguide over low latitudes is called the "low-latitude waveguide" or "alternate waveguide". As shown in Figure 1, if there is a quasi-stationary planetary wave generated by a forcing source at low or mid-latitudes, it cannot propagate directly from the troposphere to the stratosphere at mid-latitudes but can propagate quasi-horizontally from the troposphere at low or midlatitudes to high latitudes and then to the stratosphere at high latitudes through the polar waveguide, and it can also propagate to the upper troposphere at low latitudes through the low-latitude waveguide. This schematic picture indicates that the propagations of quasi-stationary planetary waves in the three-dimensional atmosphere in boreal winter are not limited to the propagation through polar waveguide but also exist the propagation through the low-latitude waveguide.

**Figure 1.** The vertical distribution of Q0 (refraction index, dashed lines) and a schematic diagram of the waveguides of the three-dimensional propagations of quasi-stationary planetary waves in boreal winter (from Huang and Gambo [11]).

### *2.2. Waveguides of Quasi-Stationary Planetary Wave Propagation Characterized by the E-P Flux*

The characteristics of three-dimensional propagations of quasi-stationary planetary waves in the atmosphere over the Northern Hemisphere can also be studied in terms of the wave energy flux. Eliassen and Palm [27] studied the vertical propagation of waves using the concept of energy flux, which was generalized by Andrews and McIntyre [28] in the 1970s, and they proposed the E-P flux under the β-plane approximation. Later, Edmon et al. [29] extended it to a sphere under the assumption that Δf/f is small within the Rossby deformation radius.

Since the E-P flux of quasi-stationary planetary waves is parallel to the group velocity of the wave, meaning the E-P flux can represent the propagation of wave energy. Therefore, the E-P flux can be used to graphically characterize the propagations of quasi-stationary planetary waves in the three-dimensional atmosphere. Figure 2 shows the distributions of the E-P fluxes of quasi-stationary planetary waves averaged for 60 winters which were recently calculated by using the NCEP/NCAR reanalysis data from 1961 to 2020. As clearly shown in Figure 2, there are two propagating waveguides of quasi-stationary planetary waves in the three-dimensional atmosphere in boreal winter. The first waveguide is the propagation of planetary waves from the troposphere to the stratosphere at high-latitudes

via the polar waveguide, while the other is the propagation of planetary waves from the mid-latitude region to the upper troposphere at low latitudes via the low-latitude waveguide. Comparing Figures 1 and 2, the propagating characteristics of quasi-stationary planetary waves in the spherical atmospherie during boreal winter (as shown in Figure 2) are consistent with the results analyzed earlier using the wave refraction index.

**Figure 2.** E-P flux cross sections (vector scale: m<sup>3</sup> s−2; *Y*-axis denotes vertical levels, units: hPa) of quasi-stationary planetary waves averaged for 60 winters from the NCEP/NCAR [30] reanalysis data for 1961–2020.
