The separation between stratosphere and troposphere is explained by the radiative-convective equilibrium15,16, that is Manabe’s Nobel Prize-winning work. The border, the tropopause is controlled by localized tropospheric mesoscale convective activity, with geographical and climatological modulations such as IMC “stratospheric fountain”17 and annual cycle18,19,20. Our recent observations have revealed that convective activity along the equator has SLBCs around lands centered at coastlines11,12, by which the tropopause (its potential temperature) reflects the surface humidity (equivalent potential temperature) quickly. The stratosphere is stabilized strongly with ozone ultraviolet heating centered at the upper (stratopause) level15,13, which provides suitable media for various types of neutral waves (in a situation similar to the ocean). At the equatorial stratosphere the thermal-wind equilibrium with almost zero meridional temperature gradient does not determine the vertical shear of zonal wind. From a viewpoint of the zonal-mean angular momentum budget any wave forcing is inevitably necessary to generate and maintain an equatorial “superrotation” (westerly)3.
The period of 2–3 years of QBO is not a multiple of the annual cycle, but is maintained robustly and almost zonally-uniformly in the equatorial stratosphere1,2,3,4,5,6. After sixty years since its discovery, we get spatiotemporally continuous JRA-55 data for making truly zonal-mean interannual-vertical section of QBO and its composite plot (Methods), shown by contours of Figs. 1(a) and (b). Zonal-wind amplitude and downward phase progression are around ±20 m/s and (20–40 km)/(around 27 months/2) ≈ – 1.5 km/month, respectively, and the easterly phase is somewhat stronger and slower than the westerly phase. These features must be determined by zonal phase velocities (so-called critical-level condition) and momentum flux divergences (mean-flow acceleration) of waves interacting the mean flow7,8,9. QBO is recognized clearly inside the tropics (latitude < 23.4º) where annual insolation cycle is weaker than diurnal cycle, but it affects the global tropospheric weather and climate5,6,21. All the foregoing studies considered planetary-scale equatorial (eastward Kelvin and westward mixed Rossby-gravity) waves, otherwise extratropical planetary (Rossby) or broad-band smaller-scale (inertio-gravity) waves to explain the zonally homogeneous feature of QBO22,23. Those waves might contribute to the total amount of momentum fluxes, but their variability could never explain the robustness of QBO.
Here we calculate the vertical flux of zonal momentum associated with “SLBC waves” corresponding to longitudinally-30° high-passed deviations from daily-mean of the JRA-55 data (Methods), and plot its vertical gradient as shown by color-codes in Fig. 1. Because a wave momentum flux is conserved for linear non-dissipative waves, its vertical gradient consists of absorbed waves accelerating the mean wind. In the stratosphere the upward fluxes of zonal momentum decrease upward in zonal-wind vertical shears of the same directions, just as expected from the QBO theory7,8,9. The momentum flux gradient per unit mass ±2 m/s/month corresponds to a zonal wind acceleration ±30 m/s/1.25 year. Therefore, the “SLBC waves” analyzed here are responsible to generate the zonal-mean zonal flow oscillation, although the other waves satisfying critical layers may contribute also to modifying the descending speed of the zonal flow pattern.
In the troposphere of this zonal-mean plot, the zonal flow and the vertical gradient of zonal momentum are both weak, because wave forcing and wave-mean flow interaction are zonally inhomogeneous, as shown later. Some phases of QBO seem to be connected to the upper-tropospheric (counter-monsoon) annual cycle of westerly/easterly in northern winter/summer, and westerly phases near the lowest level are longer than easterly phases. Such “calendar lock” of QBO (with about 5-year interval as the least common multiple between annual cycle and QBO) has been recognized already in foregoing studies24,25,26,27. Because the lower-tropospheric SLBC is modulated by the seasonal (monsoon) cycle, QBO is somewhat synchronized seasonally if it is generated basically by SLBC. During QBO was disrupted around 201628 (and also 2020 but is not seen well in the data until 2019), the diurnal wave momentum flux is also somewhat unusual, which is possibly due to a “super-El Nino” event during 2014–16.
As another correlation with the tropospheric seasons, the semiannual oscillation (SAO) in the upper stratosphere with exactly 6-month periodicity29 is confirmed for the zonal-mean zonal wind analyses in Fig. 1. Westerly and easterly maxima appear around equinoxes and solstices, respectively. Below the upper limit of JRA-55 (2 hPa or roughly 40 km altitude), some portions of the SAO signals appear both in the zonal flow and the “SLBC wave” momentum flux gradient. Because the QBO periodicity is close to the least common multiple with 0.5 year of SAO, the QBO-composite analysis of Fig. 1(b) shows clear signals of SAO. The semiannual variability has been known well as the basic tropospheric seasonal mode at the equator where the sun passes twice a year. It is reasonable that SAO is robust in the upper stratosphere after “SLBC waves” and their annual/interannual amplitude modulations are suppressed with the tropospheric circulations (shown later) and the lower-middle stratospheric QBO.
In QBO-composite longitudinal-vertical plots (Fig. 2) the bidirectional “SLBC waves” are separated and interacted with the mean zonal flow. In the stratosphere (above about 18 km altitude), the zonal flow (contours) and the vertical flux of zonal momentum (color-codes) are both almost zonally uniform. For the easterly-westerly transition phase at 26 km altitude shown in Fig. 2(a), the easterly (westerly) shear above (below) about 32 km altitude is associated with a weak negative (positive) momentum flux, suggesting absorption of positive (negative) zonal momentum associated with eastward (westward) waves. For the westerly-easterly transition phase shown in Fig. 2(b), everything is reversed. In the troposphere, the global zonal (Walker) circulation with surface convergence in the western Pacific (to the east of IMC), the wave-zonal flow interactions are not zonally uniform (stronger in particular around coastal lands), although the relationship between the shear and absorbed wave directions is similar to that in the stratosphere. Just below the tropopause (15–18 km altitude), a westerly (easterly) shear in the eastern (western) hemisphere is associated with positive (negative) momentum flux, suggesting absorption of westward (eastward) waves. Below 15 km altitude, everything is reversed from above.
We have analyzed more detailed structures of “SLBC waves” based on the JRA-55 data (Methods). In the stratosphere zonal-temporal structures of zonal wind fluctuations in a westerly-easterly transition phase show that the zonal propagation velocities of dominant waves are relatively fast (roughly ±30 m/s) and relatively continuous without clear land-sea contrasts, as shown in Fig. 3(a). Meridional-temporal structures of meridional wind fluctuations show that they are much faster but relatively weak, as shown in Fig. 3(b). These are results of the Walker and meridional (Hadley) circulations interacting with zonally slow and meridional components of “SLBC waves”. Zonally slower waves are absorbed by the zonal wind around ±15 m/s at maximum of the Walker circulation, and meridional waves are absorbed by the meridional wind around ±5 m/s at maximum of the Hadley circulation. Typical “SLBC waves” with phase velocities ±5 m/s perpendicular to coastlines making angles > 60° with meridians (that is, < 30° with the equator) have zonal phase velocities faster than ±15 m/s, and constitute dominant parts of zonal wind fluctuations in the stratosphere. Their meridional phase velocities are around ±5 m/s, and they do not constitute dominant meridional wind fluctuations.
It is clearly confirmed (Fig. 4) that the stratospheric “SLBC waves” are originated from the surface SLBCs. They are robust, in spite of amplitude modulations with seasonal (annual and semiannual) cycles of insolation and intraseasonal variations propagating over open oceans10,12. SLBC is a sum of internal gravity waves propagating land- and seaward, as well as upward in latitudes < 30º30,31, and appears dominantly in a narrower latitude range (< about 20º) because the Coriolis force is too weak to develop a vortex such as tropical cyclones. The equatorial SLBC is somewhat larger horizontally and vertically than the other (higher) latitude regions, which corresponds to horizontal and vertical wavelengths of 103 km and 10 km, respectively, of internal gravity waves with 1-day periodicity of 102 times of Väisälä-Brunt period (as expected from the dispersion relation). Dominance of SLBC is the reason why IMC with the longest coastlines has the most active convection on Earth11,12. Waves are longer and faster on sea than on land32, and are much slower than cumulonimbus gust (~20 m/s). The amplitude is proportional to the sea-land temperature contrast, determined mainly by the land surface temperature with daytime heating and nighttime cooling. In small islands, directions of SLBCs are unclear33 or SLBCs disappear34. Therefore, the fractal structures of coastlines35 are truncated at a 101 km scale in generating SLBCs, which are not chaotic but following the land-sea temperature contrast.
Because the coastlines and SLBCs are localized and in various directions, the “SLBC wave” momentum flux divergences may generate meridional flows and longer equatorial (Kelvin and mixed Rossby-gravity) waves36,37,38,39 which have been considered to generate QBO. Kawatani et al.24 estimated contribution of internal gravity waves (zonal wavenumber 12, same as the longitudinally 30° filter used in this study) to eastward or westward acceleration of QBO in a high-resolution general circulation model was 50–75% or more, although the diurnal mode forced at the surface was not focused. In the actual atmosphere analyzed in this study, roughly a half of such acceleration is directly due to “SLBC waves”, of which almost fixed wave parameters (phase velocity and momentum flux) and geographical locations robustize the QBO features (amplitude and period). The other (equatorial) waves, including those which generated by localized “SLBC wave” forcing, should contribute to variabilities of QBO. Interannual and intraseasonal variations may modulate SLBC amplitudes, “SLBC wave” momentum flux and then QBO. The “SLBC waves” are interacted with the meridional and zonal circulations, which may be related to the material transport13,40. Some earlier works claimed existence of tropospheric QBO or downward controls of the troposphere by the stratospheric QBO41,42,43, but results of this study suggest that upward controls of QBO by the tropospheric “SLBC waves” are more essential.
In the laboratory experiments9 and their simulations44, nonlinear interactions of same or opposite waves, that is just as “SLBC waves”, are necessary before any wave absorption mechanisms. In bifurcation theory45 the wave momentum fluxes must exceed a threshold for generating QBO-like oscillations, but their increase does not contribute to the amplitude but to the descending speed. If the SLBCs are intensified with larger land-sea temperature contrasts, stronger “SLBC wave” momentum fluxes make the QBO period shorter. Assuming that the typical land/seaward phase velocities of “SLBC waves” are not changed, more north-south oriented coastlines (generating more east-west “SLBC waves”) decrease the QBO zonal-wind amplitudes down to ±5 m/s. These features are consistent with detailed examination on the laboratory experiments44.
In this article we have demonstrated observational evidence that the “SLBC waves” originated from the equatorial tropospheric SLBCs play a principal role to maintain the stratospheric QBO robustly. The convective activity with SLBC separates the troposphere from the radiatively-equilibrated stratosphere, and in the latter any periodicity other than multiples of a year may be dominant near the equator. Essentially the period and structure of QBO may be dependent on the number and location of coastlines, that is, the distribution of lands. For example, if coastlines are less (more), the period of QBO becomes longer (shorter). IMC with the longest coastline is most responsible to produce QBO, which has been confirmed by the standard mechanistic model. The coastlines are the triple boundary among land, sea and air constructing the Earth system, and our present results suggest even the QBO is not occurred incidentally but is controlled under the Earth system. As Himalaya-Tibet in the mid-latitudes, the present coastline distribution in the tropics is the geologically most important product of plate tectonics in Mesozoic-Cenozoic (recent 100 million years). As in the surface rainfall distribution and the tropospheric convective cloud activity, the strongest SLBCs along the world’s longest coastline surrounding major islands of IMC is most responsible in the generation of bidirectional (sea- and land-ward) gravity waves interacting with QBO. IMC produces both volcano ashes and QBO winds dispersing them to make global cooling such as the most gigantic Toba 74,000 years ago46.