Application of Manley‐Rowe Relation in Analyzing Nonlinear Interactions Between Planetary Waves and the Solar Semidiurnal Tide During 2009 Sudden Stratospheric Warming Event

Abstract

Upper mesospheric winds observed by the Svalbard specular meteor radar (16.01°E,78.16°N) are analyzed to study the tidal variabilities during the 2009 sudden stratospheric warming (SSW). We report a textbook case of nonlinear interactions between planetary waves (PWs) and the SW2 tide (SWm denotes semidiurnal westward propagating tidal mode with zonal wave number m). The Lomb‐Scargle algorithm, bispectrum, wavelet spectra, and Manley‐Rowe relations are combined to explore the frequency match, phase coherence, energy budget, and wave number relations among the interacting waves and their temporal evolution. Our results suggest that (1) 5, 10, 16 day PW normal modes interact with SW2 generating significant sidebands (S2Ss) at frequencies lower and higher than SW2, known as SW1 and SW3 enhancements, respectively; (2) SW2 is the main energy supplier for both SW1 and SW3, hence shrinks in the interactions; (3) whereas the PWs export relatively negligible energy to SW3 but accept energy from SW2 in generating SW1, therefore, the PWs is not subject to the interactions but controlled by external dynamics, which might in turn act as a key in switching on/off the SW1 and SW3 interactions independently; (4) the SW1 enhancement could be explained as a byproduct of the planetary wave amplification by stimulated tidal decay (PASTIDE); (5) PASTIDE contributes energy to the secondary PW in the late SSW stage reported in previous studies; and (6) one SW1 component associated with the 16 day PW is very close to the semidiurnal lunar mode in frequency, which might contaminate the estimation of the lunar tidal amplification in previous studies.

The 16‐Day Planetary Wave Triggers the SW1‐Tidal‐Like Signatures During 2009 Sudden Stratospheric Warming

“…In comparison with Manson et al (2009), our main improvements in the methodology were highlighted in section 5.2 in He et al (2018). To explain the oscillations, the existing studies have to deal with six wave components, namely, the semidiurnal migrating solar and lunar tides (SW2 and M2), nonmigrating solar tidal modes SW1 and SW3, and the upper sideband (USB) and lower sideband (LSB) of 16-day PW modulation on SW2 (modulation refers to the nonlinear interaction, see section 2 in He et al, 2017, for a review of the relevant terminologies). To explain the oscillations, the existing studies have to deal with six wave components, namely, the semidiurnal migrating solar and lunar tides (SW2 and M2), nonmigrating solar tidal modes SW1 and SW3, and the upper sideband (USB) and lower sideband (LSB) of 16-day PW modulation on SW2 (modulation refers to the nonlinear interaction, see section 2 in He et al, 2017, for a review of the relevant terminologies).…”

“…Pedatella & Forbes, 2010). He et al (2017) also pointed out that the secondary wave at 12.4 hr reads as identical as SW1 in analyses at low-frequency resolutions ( f > 1∕15d − ) and might have been reported as SW1, whereas the secondary wave at 11.6 hr might have been reported as SW3 (see the sketch in Figure 1). He et al (2017) also pointed out that the secondary wave at 12.4 hr reads as identical as SW1 in analyses at low-frequency resolutions ( f > 1∕15d − ) and might have been reported as SW1, whereas the secondary wave at 11.6 hr might have been reported as SW3 (see the sketch in Figure 1).…”

“…Specifically, He et al (2017) hypothesized that it is the PW normal mode 16-day wave, instead of qSPWs in general, that interacts nonlinearly with SW2, giving rise to the SW1-and SW3-like signatures in SSW 2009. Supporting the hypothesis are the spectral analyses on the mesospheric wind collected by the specular meteor radar (SMR) at Svalbard in 2009 SSW (He et al, 2017).…”

“…The zonal wave numbers m of the signatures were estimated from the coherency in the SMR mesospheric wind between northern Germany (Juliusruh) and northern China (Mohe; e.g., He et al, 2018). Given that the occurrence of the 12.4-hr wave is theoretically independent of the 11.6-hr wave (He et al, 2017), the 12.4-hr secondary wave during SSWs has not been explicitly substantiated. The associated error suggested that a single wave with the characteristic m = 3 or m = 2 is able to account for the zonal variation of the 11.6-or 12.0-hr oscillations within the tolerance of observational errors.…”

“…The estimation revealed that the 11.6-and 12.0-hr oscillations are characterized by m = 2.98 ± 0.12 and m = 1.95 ± 0.08, respectively. In the current work and as detailed in section 2, we combine two radars to diagnose the zonal wave number of a 12.4-hr oscillation in SSW 2009 that was suggested to be the secondary wave by the bispectral analysis using the single-radar observations collected at Svalbard (He et al, 2017). These results implied that SW1 and SW3 modes at the exact period of 12.0 hr did not enhance during SSW 2013 and that the 11.6-hr secondary wave might be misread as the SW3 enhancement in studies at low-frequency resolutions (e.g., Wu & Nozawa, 2015).…”