MJO Initiation Triggered by Amplification of Upper‐Tropospheric Dry Mixed Rossby‐Gravity Waves

A possibly important dynamical process for the Madden–Julian oscillation (MJO) convective initiation is proposed. An MJO event during the “CINDY2011” field campaign is triggered by eastward‐moving lower‐tropospheric mixed Rossby‐gravity (MRG) wave packets, and its leading precursor is predominance of upper‐tropospheric MRGs in the Indian Ocean (IO). Simple three‐dimensional model experiments reveal that the upper‐tropospheric MRGs in the IO are amplified particularly in the western IO (WIO) by their westward advection and wave accumulation due to the upper‐level convergence in mean easterlies of the Walker circulation. The model also predicts downward dispersion of the amplified upper‐tropospheric MRGs and resultant lower‐tropospheric MRG wave packet formation. This MRG evolution consistently explains the MJO initiation process during CINDY2011, which is further verified by ray tracing for MRGs. Upper‐tropospheric circumnavigating Kelvin waves assist the proposed mechanism by promoting MRG‐wave accumulation (advection) in their westerly (easterly) phases via enhanced zonal convergence and weakened easterlies (enhanced easterlies).

TAKASUKA ET AL. 10.1029/2021GL094239 2 of 11 It is non-trivial when MJO convection is triggered during the preconditioning, however. For instance, Xu and Rutledge (2016) showed that the transition into deep convection is sometimes more rapid than the prediction from the discharge-recharge mechanism. To fill this deficiency in thermodynamic-driven processes, we should scrutinize dynamic variations as external forcing at the 2 E S . Specifically, equatorially circumnavigating Kelvin waves (e.g., Chen & Zhang, 2019;Powell & Houze, 2015;Seo & Kim, 2003) and extratropical disturbances (e.g., Hsu et al., 1990;Ray & Zhang, 2010;Gahtan & Roundy, 2019) can trigger MJO convection by inducing upward motions directly, although it is still debated how robust and plausible the proposed processes are. This paper focuses on the 2 E S , particularly dynamic roles of mixed Rossby-gravity waves (MRGs) in triggering of MJO convection, which is motivated by several observational studies (Straub & Kiladis, 2003;Takasuka & Satoh, 2020;Takasuka et al., 2019;Yang & Ingersoll, 2011;Yasunaga et al., 2010). Field observations clearly detected MRGs enhanced in the mid-to-upper troposphere during the MJO-suppressed phase (Takasuka et al., 2019;Yasunaga et al., 2010), which supports a notion that those MRGs determine the timing of MJO convective outbreaks in the IO through rapid moistening and/or the development of low-level convergence. Moreover, some previous studies showed that eastward group velocity of MRGs assists the start of MJO propagation (Takasuka & Satoh, 2020;Takasuka et al., 2019;Yang & Ingersoll, 2011).
The aforementioned findings imply that mid-to-upper-tropospheric MRGs may be sometimes influential precursors of MJO initiation. A question here is how upper-tropospheric MRGs finally initiate MJO convection, which is more likely to be affected by lower-tropospheric moisture fields. Takasuka and Satoh (2020) statistically suggested that upper-tropospheric MRG energy input by more diabatic heating associated with MRG-convection coupling results in downward dispersion of MRGs and the formation of low-level MRG wave packets leading to MJO initiation. However, because upper-tropospheric diabatic heating is rooted in lower-tropospheric moisture/wind variations, diabatic processes may not be a primary trigger for low-level MRGs stemming from the upper troposphere. Hence, it is worth examining whether, as an intrinsic mechanism for MJO initiation in which amplification of upper-tropospheric MRGs is involved, there exists a process more in line with upper-tropospheric dynamics.
In this regard, we shed light on the dry interaction between upper-tropospheric MRGs and a sharp downward branch of the Walker circulation (WC) above the western IO (WIO), which is referred to as the "Wall" of WC by Kohyama et al. (2021). Because this "Wall" climatologically forces upper-tropospheric zonal convergence in easterlies over the IO, MRGs approaching there may be amplified by wave accumulation (Hoskins & Yang, 2016) and then be dispersed downward and eastward. Motivated by this insight, we aim to verify the possibility that dry MRG dynamics can play an essential role in MJO initiation, based on simple model simulations and observational data analyses. A possible role of circumnavigating Kelvin waves in the MJO-MRG relationship is also discussed.

Observational Data
To provide observational evidence for our hypothesis, we analyze "MJO2" event initiated in mid-November 2011 during a field campaign CINDY2011 (Yoneyama et al., 2013). We use 3-hourly radiosonde observations at Gan Island (0.  7 E S, 73.  2 E E), 6-hourly atmospheric fields from ERA-Interim (Dee et al., 2011) with 27 vertical layers spanning 1,000-100 hPa, and 6-hourly rainfall data from the Global Satellite Mapping of Precipitation (GSMaP; Okamoto et al., 2005). A horizontal grid interval of the ERA-Interim (GSMaP) is ). The ERA-Interim data and others covered the entire period of October/November and November 2011, respectively. Note that the boreal-winter (November-March) climatology used in Section 4 is derived from the period of 1979-2012.
Anomalies are calculated by subtracting the mean during the data period. To capture MRG variations, we filter 6-hourly anomalies for westward-propagating wavenumbers and periods of 3.5-8 days (cf. Section 3), using fast Fourier transforms in space and a 101-point Lanczos filter in time (Duchon, 1979

Simple Dry Model
Based on Stechmann et al. (2008), a simple dry model with the barotropic and the first and second baroclinic modes for the vertical depth of  16 E H km is constructed on the equatorial  E -plane. Note that these three vertical modes can capture the main structure of equatorial waves (e.g., Haertel & Kiladis, 2004;Takayabu et al., 1996). The model equations are Equations 1-4 start with the three-dimensional Boussinesq system (Majda, 2003), and they have been nondimensionalized by the scaling used in Stechmann et al. (2008). The derivation of Equations 1-4 is provided in the supporting information (Text S1).
Solutions to the present model are numerically obtained for specific  1,2 E S distributions and initial conditions given to examine the interaction between WC and MRGs (see Section 4.1 for details). We assume a zonally periodic meridionally bounded channel of which the zonal and meridional extent is 40,000 km (nearly the circumference along the equator) and 8,000 km, respectively. In all simulations, a grid spacing of 100 km on the Arakawa C-grid and a time step of 15 min for the third-order Runge-Kutta scheme are used. For the fourth-order horizontal diffusion (the damping/cooling) term in Equations 1-4, we adopt

Observational Evidence of MRG Variations Leading to MJO Initiation
S rainfall variations in the time-longitude sections), stems from amplification of upper-tropospheric MRGs. In Figure 1a, the wavelet analysis (Torrence & Compo, 1998) for radiosonde-derived meridional winds at Gan highlights significant 4-5.5-day period variations at 300-200 hPa during November 5-12 (shading), after enhanced lower-tropospheric variations in the 6-8-days cycle (contours). These wind variations, detected from a 3.5-8-days-filtered data, are associated with cross-equatorial circulations with equatorially symmetric meridional wind signals (Figure 1b), indicating the robust MRG structure. This amplification of upper-tropospheric MRGs is followed by re-intensification of lower-tropospheric MRGs in the end of November during the MJO-active phase (Figures 1a and 1b).
The aforementioned fact is reinforced by the time-longitude diagrams of equatorial MRG-filtered meridional wind anomalies in the upper/lower troposphere and non-filtered precipitation field (Figures 1c  and 1d). The eastward propagation of MJO2 precipitation in the IO appears to collocate with the eastward formation of lower-tropospheric MRG wave packets beginning with northerlies in  45 E - 60 E E ( Figure 1c). In fact, low-level MRG circulations successively trigger MJO convection from the WIO (Text S2 and Figure S1), consistent with the view that MRGs can actively contribute to MJO convective initiation (Takasuka & Satoh, 2020;Takasuka et al., 2019). Before this situation, around November 10, upper-tropospheric MRG variations begin to strengthen over the WIO in conjunction with the slowdown of their westward propagation (Figure 1d; magenta lines), which slightly precedes the development of the lower-tropospheric MRG wave E. This evolution is also reconfirmed from the MRG-related eddy kinetic energy (EKE) field, defined by where primes denote MRG-filtered values; the positive tendency and subsequent accumulation of upper-level EKE is evidently observed over the WIO before MJO2 initiation (Figure 1e).  (Figures 2b and 2c); the Wall and associated upper-tropospheric zonal convergence over the WIO are reproduced. As expected, the same features as climatology are also realized in the 11 days running mean zonal-vertical circulations before MJO2 initiation (during November 5-15; Figure 2d), except for stronger zonal convergence than for the climatology (or the model), which will be discussed later.
Under the simulated WC, we examine how upper-tropospheric MRGs as observed before MJO initiation evolve. Referring to observations (Figure 1d and Figure S4), we set the initial MRG structure as the zonal wavenumber-8 mode confined in   7500 9000 E x km (i.e., the eastern side of the Wall) with maximum amplitudes at the model top, in the manner of Aiyyer and Molinari (2003) (see Text S3 and Figure S2 for details). This setting is somewhat arbitrary, because what is the ultimate source of such MRGs is still unclear. As one speculation, meridionally asymmetric external environments of the IO (e.g., SST) might be likely to induce equatorially anti-symmetric modes when the basin-scale convective variability is realized. This idea will be tested in our future work. Here, from the initial condition prepared by superimposing the derived MRG field onto the steady state obtained from a 200-days spin-up integration, we run the model for 30 days.   (     4500 5500 E x km) until around day 15 when they begin to exhibit eastward group velocity (red arrow), and then lower-tropospheric MRG wave packets are radiated eastward (blue arrow).
In Figures 3b and 3d, which are the same as Figures 3a and 3c but for the observed MJO2, the processes predicted by the model are similarly detected. After November 5, upper-tropospheric MRGs propagating westward with small positive group velocity are decelerated (magenta lines) and amplified in  45 E - 60 E E, where the zonal convergence associated with the Wall is realized. Then, lower-tropospheric MRG wave packets moving eastward are established, which characterizes MJO2 initiation.
Despite much consistency between the model and MJO2, there are some noteworthy differences. One is faster group velocity of the lower-tropospheric MRGs in the model (Figures 3a and 3b). This is attributed to the doppler shift by stronger background low-level westerlies (Figures 3c and 3d) and deeper equivalent depth in the dry model. The latter reflects the limitation that dry dynamics cannot represent wave-convection coupling effects that are important after MJO initiation.
Another difference is the stronger upper-tropospheric background zonal convergence around the Wall before MJO2 initiation (Figures 3c and 3d). This is because the observed background WC for MRGs are contributed by not only the climatology but also large-scale circumnavigating Kelvin waves with their evolution slower than MRGs. In fact, upper-tropospheric westerlies associated with circumnavigating Kelvin waves intrude into the WIO (Figure 3e; pink square), in agreement with the stronger background westerlies to the west of  50 E E than the boreal-winter mean (Figure 3d). This process, which is not incorporated in the model, promotes convergence with climatological upper-level easterlies. Considering that zonal convergence can amplify MRGs (see Section 4.2), upper-tropospheric circumnavigating Kelvin waves could serve as a catalyst of MRG-induced MJO initiation.

Amplification of Upper-Tropospheric MRGs and Its Impacts on the Lower Troposphere
To reveal why upper-tropospheric MRGs are amplified around the Wall and then lower-tropospheric MRG wave packets are formed there, we conduct the EKE budget analysis. The budget equation for the model is where E v is the three-dimensional wind vector; E w is vertical velocity; and overbars (primes) denote 11 days running mean (deviations from the mean of the 30 days simulation  Figures 3a and 3b). This comparison shows physical consistency with each other; upper-tropospheric MRGs are amplified by EKE advection by background flows ( m e E A K ) and the barotropic conversion from the background ( m e E K K ). In Figures 4b and 4e, the decomposition of these terms,

Summary and Discussion
In this study, we have presented a new pathway to MJO initiation that stems from dry upper-tropospheric westward-propagating MRGs above the IO. This is inspired by initiation processes of the "MJO2" event during CINDY2011, in which upper-tropospheric MRG amplification in the WIO is followed by MJO2 initiation ( Figure 1). Here we hypothesize that the interaction between MRGs and the Walker circulation (WC) is potentially important.
To test our hypothesis, we perform numerical simulations using a simple dry model with three vertical modes, comparing the model output with observations for MJO2. The model captures the essence of the boreal-winter mean WC above the IO: upper-level zonal convergence in mean easterlies blowing into the WIO, where the "Wall" (i.e., the zonally narrow downward branch of WC) exists (Figures 2b and 2c). In the model with this idealized WC, upper-tropospheric MRGs propagating into the Wall are amplified in the inner region of the Wall. Then, lower-tropospheric MRG wave packets start to propagate eastward (Figures 3a and 3c), resembling the processes of MJO2 initiation triggered by low-level MRG wave packets with eastward group velocity (Figures 3b and 3d).
The energetics for this MRG evolution is discussed by both the model experiment and observations (Figure 4). The initial amplification of upper-tropospheric MRGs in the Wall results from MRG energy advection to the Wall and wave accumulation due to upper-level easterlies of WC and their zonal convergence arising from the Wall. Subsequently, the eastward-downward dispersion of the amplified upper-level MRG energy is activated, which forms lower-tropospheric MRG wave packets leading to MJO initiation.
A difference of WC between the model and MJO2 (Figures 2b-2d) has implication that upper-tropospheric circumnavigating Kelvin waves make the presented mechanism more efficient by modulating background WC additionally. For MJO2, upper-level zonal convergence in the Wall are enhanced by cooperation between the westerly phase of Kelvin waves propagating into the WIO and climatological easterlies of WC above the IO (Figure 3e), which promotes MRG-wave accumulation. In addition, upper-tropospheric Kelvin-wave westerly anomalies help the realization of positive ground group velocity of MRGs by weakening upper-tropospheric mean easterlies, which is advantageous to triggering the wave accumulation (Hoskins & Yang, 2016). Furthermore, the easterly phase of Kelvin waves before the westerly phase can enhance westward advection of MRG energy into the WIO. For these reasons, equatorial circumnavigation of Kelvin waves assists MRG-induced MJO initiation cooperatively with the climatological WC.
The idea proposed in this study for MJO initiation does not require moist processes at all, which provides several debatable topics. First, we may reconsider roles of diabatic processes in the similar MRG-related mechanism suggested by Takasuka and Satoh (2020) and Takasuka et al. (2019). A possible interpretation for this is that dry dynamics are sufficient for an initial trigger of amplification of upper-tropospheric MRGs, although diabatic heating can accelerate and/or maintain MRG amplification in a later stage when MRGconvection coupling becomes evident. Second, our idea does not necessarily contradict with the preexisting hypotheses that put emphasis on moisture variations (e.g., Benedict & Randall, 2007;Zhao et al., 2013), because we have addressed MJO initiation in terms of convective triggering by gravity wave dynamics (e.g., Tulich & Mapes, 2008), assuming a favorable environment for organized convection regulated by moisture fields. Nevertheless, if dry MRG dynamics by itself can determine the timing of MJO initiation, it would be misleading to emphasize only the moisture variations for understanding MJO initiation. Because a simple dynamical model theoretically predicts the dry interaction between upper-tropospheric MRGs and WC as observed for a single MJO event, the next step is to examine its robustness and relationship with moist processes statistically for multiple cases.