Energy conversion and transfer within the atmosphere are fundamental to the dynamics that govern climate variability and weather patterns. A key aspect of these dynamics is energy transfer within the atmosphere, which occurs through mechanisms such as radiation, convection, and wave propagation by means of energy conversion. This energy conversion and transfer is crucial for maintaining the atmospheric thermal structure and driving large-scale circulation patterns that affect weather systems, climate variability, and extreme weather events. In turn, these structures and processes also have an impact on the energy conversion and transfer within them. Sudden stratospheric warmings (SSWs) are particularly significant events in this context.

An SSW is a kind of event involving a large and rapid temperature increase and sometimes a reversal of the zonal wind in the high-latitude region of the stratosphere (Scherhag, 1952). These events can have far-reaching effects, affecting not only changes in atmospheric circulation in the stratosphere, but also the winter troposphere and even the mesosphere. Sudden stratospheric warmings greatly affect the structural characteristics of and variations in the winter stratosphere as well as the entire atmospheric circulation. Since the discovery of SSWs, meteorological researchers have conducted extensive observations and research on them. Sudden stratospheric warmings are believed to be due to the interaction of upward-propagating planetary waves with zonal winds (Wüst and Bittner, 2011). Several phenomena related to the ocean–atmosphere system, such as the El Niño–Southern Oscillation (ENSO) and Madden–Julian Oscillation (MJO) outside the polar stratosphere, have been identified as possible modulators of the likelihood of SSWs (Baldwin et al., 2021). Roy and Kuttippurath (2022) studied the dynamic evolution and activities of waves in SSWs of arctic winters over the decade of 2011–2021. Many studies have been conducted on the impact of SSWs on stratospheric atmospheric fluctuations (Kalisch and Chun, 2021; Mitra et al., 2022). Recently, many studies have paid attention to variations in SSWs in the mesosphere and lower thermosphere (MLT) region. Long-term studies, such as that by Li QR et al. (2024), have shown that variations in planetary wave activity are a primary driver of arctic SSW frequency and characteristics, underscoring the critical role of wave–mean flow interactions. Some have studied atmospheric variations in the MLT regions during SSW periods. In particular, ground-based meteor radars, such as those deployed in the Chinese Meridian Project, have provided continuous and stable wind observations in the MLT region, greatly advancing our understanding of planetary wave behaviors during SSWs (Ma Z et al., 2024). Sudden stratospheric warmings have been found to be closely related to the cooling of the mesosphere and the warming of the lower part of the thermosphere (Chen X et al., 2012; Zorkaltseva et al., 2019; Kohma et al., 2021). For instance, Yang JF et al. (2024) reported a rapid increase of more than 50% in high-latitude mesospheric neutral air density around the onset of the major 2021 SSW, which they attributed to altered planetary waves and residual circulation. Energy deposition and redistribution during upper atmospheric disturbances often exhibit complex spatial patterns. In the mesosphere, gravity waves often play a more dominant role during SSW events, whereas modulations of gravity wave activity and wave forcing in the mesosphere have been observed, and these play a critical role in the recovery of the westward zonal-mean zonal winds in the mesosphere after the SSW event (Tomikawa et al., 2012). Recent observations using COSMIC (Constellation Observing System for Meteorology, Ionosphere, and Climate) data have also revealed enhanced gravity wave potential energy density during SSWs, with eastward and downward extensions and a strong relationship with zonal wind weakening (Zeng XY and Zhong G, 2024). However, existing research still lacks quantitative contributions to the energy transfer between the lower stratosphere and upper mesosphere during SSWs, which is also particularly valuable, as it would reveal the mechanisms behind these sudden temperature and wind changes and would provide important insights into mesosphere–stratosphere coupling. Such research would help explain the transmissions between different energy sources in the atmosphere. The physical mechanisms by which SSWs have an impact on the mesosphere are not well understood, and answering this question would extend scientific curiosity in a society extremely dependent on technology affected by space weather (Baldwin et al., 2021).

The atmospheric energy cycle is a useful tool for diagnosing atmospheric circulation because it can reflect the physical mechanisms of multilevel interactions and transformations in the climate system. The energetic transfer diagnostics in the atmosphere during SSWs are important for understanding the influences of SSWs on the entire atmospheric circulation. The Lorenz energy cycle diagnostic, introduced by Lorenz (1955), has proved to be particularly useful in analyzing atmospheric energetics. Over the years, various multiscale energetics analyses have been conducted on the energetics averaged over a specific domain (e.g., Julian and Labitzke, 1965; Trenberth, 1973). However, these analyses do not distinguish between different spatial locations, which limits their ability to capture regional variations. This information is especially relevant for SSW events, which are transient events that occur over a short period each year, marked by a rapid temperature increase within just a few days. Because these events are nonstationary, the time–mean decomposition method fails to effectively separate such short-term, dynamic processes. Beyond externally driven formation processes, emerging studies propose that SSWs may originate from intrinsic atmospheric dynamics. In foundational work, Plumb (1981) theorized that temporal growth in these events could stem from resonant interactions between stationary planetary waves and decelerating progressive waves. His analysis further distinguished between displacement-type SSWs (characterized by polar vortex shifting) and split-type SSWs (featuring vortex fragmentation), positing fundamentally distinct generation pathways for these phenomena. To unravel the atmospheric system’s preferential selection of specific formation mechanisms, comprehensive energy budget analyses can serve as crucial investigative tools, particularly for differentiating between competing dynamic processes. Liang XS (2016) found the multiscale window transform (MWT) of Liang XS and Anderson (2007) to be a powerful method of overcoming the difficulties mentioned above. This discovery has also led to a new diagnostic methodology, that is, the localized energetics analysis and theory of canonical transfer (MS-ECT). These two methods have been applied successfully to oceanic and atmospheric diagnoses (Yang Y, et al., 2017; Wei JN and Zhang J, 2021; Wang ML and Liang XS, 2022; Ma JW and Liang XS, 2023).

Xu F and Liang XS (2017) applied the MWT and the localized multiscale energy and vorticity analysis (MS-EVA) to diagnose the energetic transforms during a 2012–2013 SSW event in the stratosphere. They applied the multiscale method to their study, conducted some vorticity analyses, and used the theory of canonical transfer. From their study, we can conclude that in the stage of rapid warming, the temperature rise is mainly due to a strong poleward heat flux and a canonical transfer through baroclinic instability, which extracts the available potential energy (APE) from the mean window. At that time, a portion of the SSW-scale APE is converted to the SSW-scale kinetic energy (KE). However, how the energy transfer in the mesosphere occurs during SSW events is unknown. Open questions are whether it is similar to or opposite of the situation in the stratosphere, what influence it has, and whether different characteristics correspond to different SSW events.

With the aim of deeply understanding how the energy is transferred in the middle atmosphere, especially in the mesosphere, during SSWs and identifying whether the energy transfer characteristics are different between different SSW events, we use the MWT and MS-ECT to analyze the energy transfer at different scales during the 2023 SSW and the 2012–2013 SSW for comparisons based on Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) reanalysis data. This energetic diagnosis helps us understand more about the mechanisms of SSWs in the middle atmosphere. In addition, it contributes to understanding the relationship between different energy sources in the atmosphere, as well as the energy coupling and transmission at different altitudes. Much of this variation in predictive skill is likely linked to limitations in the predictive skill of key tropospheric drivers of the SSW process (Baldwin et al., 2021). As noted by Noguchi et al. (2016), predictions of SSW events are also sensitive to the background stratospheric state prior to the SSW. Given the relevance of SSW events to the entire atmosphere, the predictability of SSWs can be improved by numerical simulation.

The data and the MWT and MS-ECT methods used are introduced in Section 2. The results are shown in Section 3. Sections 4 and 5 present the discussion and conclusions, respectively.

The data used in this study are the reanalysis product of MERRA-2 because of its high quality and availability at low altitudes. Along with the enhancements of MERRA-2 in meteorological assimilation, it takes significant steps toward the target of an earth system reanalysis set by the Global Modeling and Assimilation Office (GMAO) at the National Aeronautics and Space Administration (NASA). The MERRA-2 is the first long-term global reanalysis to assimilate space-based observations of aerosols and represent their interactions with other physical processes in the climate system (Gelaro et al., 2017). The data quality in the middle atmosphere improved after 2004 when the Earth Observing System (EOS) Aura satellite data were assimilated (Gelaro et al., 2017; Wargan et al., 2017). Many studies have used the MERRA-2 reanalysis database to investigate SSW events in the middle atmosphere. Koushik et al. (2020) used MERRA-2 data to study abrupt changes in stratopause winds during three SSW events. Eswaraiah et al. (2020) studied the mesosphere winds during a 2019 SSW using MERRA-2 data. Tang et al. (2023) used MERRA-2 data to analyze different quasi-2-day wave behaviors in two major SSW events in the summer mesosphere. In summary, MERRA-2 data in the mesosphere have repeatedly been applied in research on SSW events, and the data quality is very reliable.

The atmospheric parameters needed included temperature, geopotential, wind, and vertical pressure velocity. We used data provided through the following two websites: https://disc.gsfc.nasa.gov/datasets/M2I6NVANA_5.12.4/summary?keywords=merra-2 and https://disc.gsfc.nasa.gov/datasets/M2I3NVASM_5.12.4/summary?keywords=merra-2. The M2I6NVANA_5.12.4 data have a 6-hour resolution and include the parameters of temperature, wind speed, surface pressure, and specific humidity, whereas the M2I3NVASM_5.12.4 data have a 3-hour resolution and include the parameters of temperature, wind speed, vertical pressure velocity, and surface potential height. We use pressure and surface potential height data to calculate the geopotential. By combining the two datasets, we were able to obtain all the parameters needed. The data include 25 vertical levels, ranging from 10 to 0.01 hPa. We use a resolution of $ 0.5{\text{°}}\times 0.625{\text{°}} $ in the horizontal direction.

Figure 1 shows the variations in the polar temperature and zonal wind at 60°N at 10 hPa from November 24, 2022, to March 31, 2023, from the MERRA-2 database. Two obvious warming phases were observed. The zonal wind has reversed three times: on January 26–30, February 14–22, and February 24–March 9 (marked with blue squares). According to the definition provided by the World Meteorological Organization, SSWs can be divided into major warmings and minor warmings. In addition to the temperature gradient reversal, major SSWs have a reversal of the zonal-mean wind from eastward to westward at 60° (Chandran and Collins, 2014). Therefore, this SSW is a major event. According to the period of temperature increase, we define this SSW period from January 1, 2023, to March 9, 2023 (marked with vertical green lines).

We apply the MWT and MS-ECT methods to analyze this SSW event. The MWT method was proposed by Liang XS and Anderson (2007) in an attempt to separate nonstationary processes while preserving spatial localization. It is a functional analysis tool that decomposes a functional space into a direct sum of orthogonal subspaces, each with an exclusive range of scales, while preserving its local properties. The subspace is called a scale window. The MWT method was developed to provide a faithful representation of the multiscale energies on the resulting scale windows and hence makes the MS-ECT analysis possible. In this framework, a functional space can be decomposed into several scales. Taking three scales as an example, a functional space $ {u}\left({t}\right) $ can then be written as

where $ {(\cdot )}^{\sim \varpi } $ denotes a subspace with $ \varpi $ being its index. In this work, $ {(\cdot )}^{\sim 0} $ denotes the large-scale window, $ {(\cdot )}^{\sim 1} $ denotes the SSW-scale window, and $ {(\cdot )}^{\sim 2} $ denotes the synoptic-scale window. More detailed derivations are shown in Liang XS (2016).

The first step of the MWT is to determine the scales of subspaces. Because the MWT requires that the number of time steps be a power of 2, we choose the period from November 24, 2022, to March 31, 2023 (128 days, $ {2}^{7} $). The SSW event is included in this period. Because the resolution of data is 6 hours, the number of data points in this period is 512 (2⁹).

The determination of scales can be achieved through the characteristics of the SSW and the wavelet spectral analysis. During SSWs, the temperature increases sharply in a week or less. The entire SSW can last for 1 or 2 months (Butler et al., 2015). The variation in temperature at 10 hPa in this period and the wavelet spectrum of the period are shown in Figure 2. During the period of temperature increase, there are clearly two peaks. One is at 64 days and the other corresponds to a period of 16 days. Frequencies with a periodicity of 8 days also occur.

When separating scales, we aim to assign large-scale processes to represent background variations, mesoscale dynamics to capture the two distinct warming phases and wind reversals, and small-scale components to filter out weather noise. The determination of scale windows is based on the characteristic temporal scales of SSW events and is supported by the wavelet spectral analysis (Figure 2). The chosen thresholds are physically meaningful for the following reasons:

(1) Large-scale window (>64 days): This window captures the seasonal-scale background circulation, including the gradual evolution of the polar vortex and long-term trends. The multi-month scale is relevant for the preconditioning and slow recovery phases associated with SSWs (Butler et al., 2015).

(2) SSW-scale window (8–64 days): This window encompasses the full life cycle of an SSW event, from its initiation through its peak and subsequent decay, which typically spans several weeks to 2 months. It directly captures planetary wave activity with periods of ~10–30 days, which are the primary drivers of SSW dynamics (Baldwin et al., 2021). The wavelet spectrum (Figure 2) shows distinct peaks at periods of approximately 16 days and 8 days during the warming phases, firmly situating these dominant signals within this scale window.

(3) Synoptic-scale window (<8 days): This window filters higher frequency transients, including synoptic-scale weather disturbances and gravity waves. These processes can interact with the mean flow and planetary waves during SSWs, contributing to localized energy transfers and mesospheric effects (Tomikawa et al., 2012). The spectral power at periods below 8 days represents this background of higher frequency variability.

To assess potential edge effects arising from the fixed 128-day analysis window required for the MWT, we conduct a sensitivity test. The window is shifted forward and backward by ±3 days (i.e., analyzing periods from November 21, 2022, to March 28, 2023, and from November 27, 2022, to April 3, 2023). The MWT decomposition is repeated for these adjusted windows. The resulting scale-separated fields, particularly within the SSW-scale window during the core event period (January–March 2023), show highly consistent spatial patterns and magnitudes of energy terms compared with the original window. This result confirms that the chosen 128-day window does not introduce significant boundary artifacts that would affect the primary conclusions of this study.

On the basis of the MWT, we can form a localized multiscale energetics function from the original function, including temperature T, winds $ \boldsymbol{v}=(u,v,w) $, and geopotential $ {\phi } $ in the isobaric coordinate system. According to the definition of multiscale energy, the kinetic energy (KE) $ {K}^{\varpi } $ and the available potential energy (APE) $ {A}^{\varpi } $ in the $ \varpi $ subspace are

where $ {\nu }_{h} $ is the horizontal wind, g is the gravitational acceleration, $ {c}_{P} $ is the specific heat at constant pressure, and $ L=-\partial \overline{T}/\partial z $ is the lapse rate. In addition, $ \widehat{(\cdot )}_{h}^{\sim \varpi } $ denotes the MWT on the window at horizontal component $ h $, and $ \overline{(\cdot )} $ denotes the average value. The equations of energy balance can be inferred as

where

and

are the change rates of KE and APE respectively;

is the convergence of flux of KE on window $ \varpi $;

is the convergence of pressure flux, where Φ is the geopotential function;

is the buoyancy conversion, where $\omega =\dfrac{{\mathrm{d}}p}{{\mathrm{d}}t}, \alpha =\dfrac{R}{p}T $ is the specific volume;

and

are canonical transfers of KE and APE to window $ \varpi $, respectively;

is the convergence of flux of APE on window $ \varpi $;

is the apparent source–sink (usually negligible); and $ F_{K}^{\varpi } $ and $ F_{A}^{\varpi } $ are the frictional dissipation of KE and APE, respectively. For convenience, $ \nabla \cdot Q_{K}^{\varpi } $, $ \nabla \cdot Q_{P}^{\varpi } $, and $ \nabla \cdot Q_{A}^{\varpi } $ are written as $ \Delta Q_{K}^{\varpi } $, $ \Delta Q_{P}^{\varpi } $, and $ \Delta Q_{A}^{\varpi } $, respectively. Above are expressions for energy per unit mass (with units of $ {\text{m}}^{2}\text{/}{\text{s}}^{\text{3}} $). This is called the MS-ECT method.

Notably, the canonical transfers ($ \Gamma _{K}^{\varpi } $ and $ \Gamma _{A}^{\varpi } $) are essential in the MS-ECT, which means the energy transfer between different subspaces. This energy transfer has an important property; that is, this kind of cross-scale transfer neither generates nor destroys energy, then it characterizes the redistribution of energy between different subspaces. The canonical APE transfer $ \Gamma _{A}^{\varpi } $ measures the rate of APE exchange between scales attributable to correlations between velocity and temperature gradients. In quasi-geostrophic theory, such a transfer is directly associated with baroclinic instability, which converts mean-state APE into eddy APE. Thus, a positive $ \Gamma _{A}^{0\rightarrow 1} $ indicates that baroclinic instability is transferring APE from the large-scale background to the SSW-scale disturbances. The canonical KE transfer and canonical APE transfer rigorously correspond to the barotropic instability process and baroclinic instability process in classical geophysical fluid dynamics while avoiding the global limitations inherent in classical theories. Consequently, these canonical energy transfers can authentically characterize both the temporal intermittency and spatial inherent spatial localization of fluid destabilization processes (Liang XS and Robinson, 2005).

Through energetics analyses, we can compare the energy transfer mechanism and its effect on the temperature and zonal wind between different SSW events and altitudes. Figures 10a and 10b display the time evolution of the SSW-scale energetic terms accumulated over 60°N–90°N at 0.01–10 hPa for the 2023 SSW and the temperature variation at the north pole at two altitudes. As shown in Figures 10a and 10b, the APE balance on the SSW scale is mainly among baroclinic canonical transfer and transport. The canonical transfer contributes the most to the SSW-scale APE. For the SSW-scale KE, the balance is mainly among the pressure fluxes $ \Delta Q_{P}^{1} $. We can also see that the SSW-scale temperature at 10 hPa generally follows the canonical transfer of APE ($ \Gamma _{A}^{0\rightarrow 1} $) and the variation in $ \Delta Q_{P}^{1} $ but that it is out of phase with the transport of SSW-scale APE ($ \Delta Q_{A}^{1} $) from January 25 to February 20.

Different SSW events exhibit distinct characteristics, and no universally accepted consensus has yet been established. Therefore, detailed investigations of typical cases remain essential. To identify systematic patterns in energy transport during SSWs, we conduct a comparative analysis of two distinct SSW events: 2023 SSW and 2012–2013 SSW. Both the 2023 and 2012–2013 SSWs are major SSWs. The 2012–2013 SSW lasted for an extraordinarily long time (2 months). It is unique in that, prior to the major warming, two minor warmings occurred in December 2012. The 2023 SSW also lasted for a long time (nearly 3 months) and two warmings also occurred. To compare the differences and similarities between the different SSW events, we analyze energetic variations in the 2012–2013 SSW in the middle atmosphere (the same SSW event explored by Xu F and Liang XS (2017); they also used the multiscale energy method to analyze this SSW event). Figures 10c and 10d display the time evolution of the SSW-scale energetic terms in the 2012–2013 SSW. An obvious result is that the energy terms are relatively smaller than those in the 2023 SSW. This difference is likely because the temperature had increased twice by a total of ~70° in the 2023 SSW (see Figure 1), whereas it had increased only once and by a total of ~40° in the 2012–2013 SSW. Moreover, the canonical transfer of APE ($ \Gamma _{A}^{0\rightarrow 1} $) is positive during warming; that is, the direction of the canonical transfer of APE is always through baroclinic instability in both SSWs.

To quantitatively assess the relative contributions of different processes to the SSW-scale APE variations, we calculate correlation coefficients between the APE changes and their major source terms $ \Gamma _{A}^{0\rightarrow 1},\Gamma _{A}^{2\rightarrow 1} $, and $ \Delta Q_{A}^{1} $. For the 2023 SSW, the correlation between APE changes and $ \Gamma _{A}^{0\rightarrow 1} $ is strikingly high (r = 0.90), whereas its correlation with the advective flux convergence ($ \Delta Q_{A}^{1} $) is r = −0.61. This finding indicates that the canonical transfer from the large-scale window explains approximately 81% (i.e., 0.9²) of the variance in the SSW-scale APE growth, quantitatively confirming its dominant role. The negative correlation with advection suggests that the advective export of APE often occurs during phases of APE increase driven by baroclinic instability. A similar pattern holds for the 2012–2013 SSW, with $ \Gamma _{A}^{0\rightarrow 1} $ showing a high correlation (r = 0.87) and advection a strong negative correlation (r = −0.87). An interesting finding is that the canonical transfer from the synoptic-scale window ($ \Gamma _{A}^{2\rightarrow 1} $) shows a moderate negative correlation in 2023 (r = −0.62) and a weak one in 2012–2013 (r = −0.20), indicating it is not a primary source for the SSW-scale APE accumulation. These statistical metrics robustly support our conclusion that baroclinic instability, acting through the canonical transfer $ \Gamma _{A}^{0\rightarrow 1} $, is the principal driver of APE variability during these major SSWs, whereas advective processes largely act as a counterbalancing sink or spatial redistributor.

Because planetary-scale waves can be generated spontaneously by baroclinic instability (Hartmann, 1979; Domeisen and Plumb, 2012), this result confirms the propagation of planetary waves in SSWs at 10 and 0.01 hPa. The SSW-scale temperature at 10 hPa generally follows the canonical transfer of APE ($ \Gamma _{A}^{0\rightarrow 1} $), which is similar to that of the 2023 SSW event. It can be inferred that the variation in temperature is associated with the canonical transfer. However, the variation in $ \Delta Q_{P}^{1} $ seems different from that of the 2023 SSW event because no correlation with temperature is displayed. This difference may arise from event-specific external forcing or variations in nonlocal energy transport that modulate the pressure flux convergence.

As for the energy flow, some differences also exist between the different SSW events. In the 2012–2013 SSW, the pressure work $ \Delta Q_{P}^{0} $ always provides energy for $ {K}^{0} $; however, the direction of the pressure work $ \Delta Q_{P}^{0} $ totally reverses in the 2023 SSW event. The large-scale KE mainly dissipates through pressure work. This dissipation is probably due to the different pressure distributions during the different SSW events.

In the stratosphere, we found that buoyancy conversion is important and that the SSW-scale temperature generally follows the variation in the pressure working rate but is out of phase with the APE transport ($ \Delta Q_{A}^{1} $) on the SSW window from 100 to 10 hPa (see Figure 10 in Xu F and Liang XS, 2017). As for the similarities, the direction of canonical transfer of APE is always from large scale to SSW scale through baroclinic instability in the stratosphere and mesosphere. From January 25 to February 20, the APE transport ($ \Delta Q_{A}^{1} $) is out of phase with the SSW-scale temperature in both the stratosphere and the mesosphere; that is, the outer transfer of APE is correlated with the SSW-scale temperature in the stratosphere and mesosphere.

Although our analysis highlights the importance of APE transport and baroclinic instability in the mesospheric cooling observed during the 2023 SSW, we note that other physical processes may also have contributed. For example, gravity wave drag can drive residual circulation that leads to adiabatic cooling, and nonlocal radiative cooling resulting from CO₂ emission is a persistent energy loss mechanism in the mesosphere. These processes are not explicitly separated in our energetic budget but are partly absorbed in the residual terms (e.g., $ F_{K}^{\varpi } $, $ F_{A}^{\varpi } $) and in the reanalysis thermodynamics. Future studies using high-resolution models that explicitly resolve gravity waves and interactive radiation would help quantify the relative roles of these mechanisms in concert with the energy transfer pathways identified here.

Regarding the reliability of MERRA-2 data in the mesosphere, it is noteworthy that several recent studies have utilized MERRA-2 reanalysis data to investigate dynamic processes in the MLT region during SSW events. For instance, Gong Y et al. (2025) utilized MERRA-2 data to analyze diurnal tidal variations in the MLT region during the 2020 SSW, demonstrating its applicability in capturing mesospheric wind and temperature structures. Similarly, Yang JF et al. (2017) used MERRA wind data to investigate the longitudinal and event-specific responses of zonal winds from the stratosphere to the lower thermosphere during several SSW events. Koushik et al. (2020) used MERRA-2 data to examine tropical stratopause zonal winds during major SSWs, validating the reanalysis against Rocketsonde observations up to ~65 km. Becker and Oberheide (2023) also utilized MERRA-2 data to identify nonmigrating tidal components in the southern summer mesosphere, further supporting its utility in mesospheric studies. Although the MERRA-2 reanalysis has been widely used for mesospheric studies, its vertical resolution (25 levels from 10 to 0.01 hPa) is relatively coarse for resolving fine vertical gradients. Moreover, above ~70 km, reanalysis uncertainties grow because of sparse direct observations and greater model influence. Therefore, although the qualitative features of energy fluxes (e.g., direction of transfer, phase relationships) are considered robust, their quantitative magnitudes in the upper mesosphere (especially near 0.01 hPa) should be viewed with appropriate caution.

It is important to acknowledge the limitations of MERRA-2 in the mesosphere. Above ~60 km, direct observations become sparse, and reanalysis fields rely more heavily on model physics and prior forecasts. This necessity can introduce uncertainties in derived variables such as vertical motion and temperature gradients, which propagate into the computed energy fluxes. Although the overall patterns of energy transfer (e.g., sign of fluxes, scale-to-scale directions) are likely credible, their exact magnitudes near 0.01 hPa should be interpreted with caution. Future work using high-resolution models or enhanced observational datasets would help to better quantify mesospheric energetics during SSWs. Therefore, although the qualitative features and trends in the mesosphere are considered robust, quantitative interpretations in the 60–80 km region should be made with caution.

The 2023 SSW from January 1 to March 9 has two obvious temperature warming peaks and three zonal wind reversals. To clarify the energy transfer processes during SSWs to better understand the dynamic coupling of the middle atmosphere, we adopt the MWT and the MWT-based MS-ECT to investigate this major 2023 SSW event. We reconstruct the fields on three orthogonal subspaces, that is, a large-scale window (>64 days), an SSW window (8–64 days), and a synoptic-scale window (<8 days). The energetic transfer in the mesosphere is analyzed and compared with that in the stratosphere in the 2012–2013 SSW. The main conclusions can be summarized as follows:

(1) On the vertical transfer aspect, the KE transfers downward before the SSW. Pressure flux plays a critical role in coupling the mesosphere and stratosphere during SSW events.

(2) On the energetic flow paths, the SSW-scale KE has three different energy sources for the following warming, and both barotropic instability and baroclinic instability provide KE and APE in the stratosphere. In the mesosphere, a main energy source, APE transport $ \Delta {Q}_{A} $, provides the cooling, and baroclinic instability provides the APE.

(3) The energy terms of the 2012–2013 SSW event in the mesosphere are relatively smaller than those in 2023 SSW event. Although the specific energy flow paths vary between SSW events, a consistent feature is the dominant role of baroclinic instability in transferring APE from large-scale to SSW-scale windows in both the stratosphere and mesosphere. This feature suggests a robust mechanism underlying SSW dynamics, despite event-specific differences in external forcing or the background state. In both SSWs, energetic term fluctuations increase when the temperature changes. Moreover, baroclinic instability always exists during warming in both SSWs.

Through these energy transfer results derived from the SSW events, we have obtained a better understanding of the conversions between different energy sources and have learned about physical mechanisms of multilevel interactions and transformations in the middle atmosphere. However, this study also has certain limitations. First, the energetic diagnostics are derived entirely from reanalysis data (MERRA-2). Although MERRA-2 is reliable for large-scale stratospheric dynamics, its uncertainty increases in the mesosphere, and the vertical resolution is coarse for resolving fine-scale gravity wave processes. Second, the MWT framework assumes orthogonality between scale windows, which is a mathematical convenience that may not fully hold for nonlinear, interacting geophysical flows. Nevertheless, the MWT provides a robust and localizable decomposition suitable for diagnosing scale interactions in transient events like SSWs. Future work utilizing higher resolution models and constrained by dedicated mesospheric observations will help validate and refine the energy pathways identified here. Several issues still remain. First, the mechanisms between energetic transfers and atmospheric variations are deserving of study. Moreover, one may wonder about the underlying relationship between the energy in the stratosphere and that in the mesosphere. A possible approach is studying the energetic flow in more previous SSW events that include a greater range of height. We will explore these problems in future studies.