Fluctuations in Jupiter’s equatorial stratospheric oscillation

The equatorial stratospheres of Earth, Jupiter and Saturn all exhibit a remarkable periodic oscillation of their temperatures and winds with height. Earth’s quasi-biennial oscillation and Saturn’s quasi-periodic equatorial oscillation have recently been observed to experience disruptions in their vertical structure as a consequence of atmospheric events occurring far from the equator. Here we reveal that Jupiter’s quasi-quadrennial oscillation can also be perturbed by strong tropospheric activity at equatorial and off-equatorial latitudes. Observations of Jupiter’s stratospheric temperatures between 1980 and 2011 show two significantly different periods for the quasi-quadrennial oscillation, with a 5.7-yr period between 1980 and 1990 and a 3.9-yr period between 1996 and 2006. Major disruptions to the predicted quasi-quadrennial oscillation pattern in 1992 and 2007 coincided with marked planetary-scale disturbances in the equatorial and low-latitude troposphere, suggesting that they are connected to vertically propagating waves generated by meteorological sources in the deeper troposphere (that is 500–4,000-mbar pressures). Disruptions in Jupiter’s periodic oscillations are thus inherently different from those of Saturn or the Earth. This interconnectivity between the troposphere and stratosphere, which is probably common to all planetary atmospheres, shows that seemingly regular cycles of variability can switch between different modes when subjected to extreme meteorological events. Multi-decade observations of Jupiter’s stratospheric temperatures show that their quasiperiodic oscillation locked into a new period after a major atmospheric perturbation in 1992, from 5.7 years to 3.9 years. This is different from Earth (and presumably from Saturn), where the period returned to its original value after substantial atmospheric disruptions.

T he observed equatorial stratospheric oscillations on Earth, Jupiter and Saturn are thought to be linked to waves propagating upwards from the deeper atmosphere. Tropospheric convection produces a spectrum of waves that propagate into the stratosphere, where they can interact with the background winds and potentially break, depositing angular momentum into the zonal jets [1][2][3] . Once thought to be regular and stable, recent observations have shown that such oscillations are disrupted by horizontally propagating stratospheric waves on both Earth and Saturn. Earth's quasi-biennial oscillation (QBO) 4 recently experienced an anomalous, very short reversal period of only nine months, as compared with the mean of 28 months observed over the last 40 yr of observations 5,6 . This odd behaviour of the QBO was attributed to large amounts of wave activity originating from higher latitudes, moving horizontally equatorwards and penetrating farther south than normal. This disruption of Earth's QBO may be partially related to the weakening of meridional temperature gradients attributed to climate change 5,6 or to extreme El Niño events 7 . After this disruption the QBO re-established its nominal 28-month mean period 6 . Saturn's quasi-periodic equatorial oscillation (QPO) 3,8 , observed with a ~15-yr periodicity, was disrupted between 2011 and 2014 (ref. 9 ). An energetic convective storm erupted in 2010 at northern mid-latitudes [10][11][12] , spawning a large, hot stratospheric vortex that persisted for 3 yr near ~40° N (all latitudes in this paper are planetocentric) 13 . Waves emanating from this source travelled over 30,000 km to the equator, perturbing the QPO 9 .
Yearly infrared observations of Jupiter's quasi-quadrennial oscillation (QQO) 1,14 in the 1980s and 1990s estimated that the equatorial stratospheric temperatures oscillate with a 4-5-yr periodicity 15,16 . This was confirmed by a later study 17 , which reported a 4.5-yr periodicity of the QQO between 1980 and 2000. The increase of the data points in the temporal sampling and the addition of a subsequent decade of observations enables a more careful assessment of the supposed regularity of Jupiter's QQO. At higher pressures in the troposphere, several types of large-scale semiregular event (plume outbreaks; fades, revivals and expansions of belts; and other disturbances) can alter the banded morphology of clouds in Jupiter's weather layer 18 .
Here we characterize the long-term behaviour of the QQO using ground-based infrared images acquired over almost three Jovian years  at the Infrared Telescope Facility (IRTF) on Maunakea, Hawai'i, at 7.6-7.9 μm, sensing the 10-20-mbar pressure level (where the stratospheric temperature oscillations are observed). We employed a wavelet-transform analysis and a nonlinear least-squares curve-fitting analysis to characterize the long-term periodicity of the stratospheric brightness temperature oscillations, and determine whether, like the Earth's QBO or Saturn's QPO, the QQO can be disrupted by tropospheric convective events and/or stratospheric perturbations (Methods). An analysis of previously reported tropospheric meteorological activity, and of the longitudinal variance of the stratospheric brightness temperatures at the equatorial and off-equatorial latitudes, was also carried out to investigate the origin of the QQO disruptions.

Long-term QQO periodicity analysis
Figure 1e,f shows the ~7.9-μm brightness temperature and its temporal variance between ±30° latitudes for the 31 years analysed in this study, showing the dynamic nature of Jupiter's stratospheric temperatures. The QQO signal is clearly observed, with temperatures at the equator oscillating in time between lower and higher values, anticorrelated with those at approximately ±12° latitude, as suggested by refs. 1,14 . The variance of the temperatures for the entire Fluctuations in Jupiter's equatorial stratospheric oscillation Arrate Antuñano 1 ✉ , Richard G. Cosentino 2,3 , Leigh N. Fletcher 1 , Amy A. Simon 3 , Thomas K. Greathouse 4 and Glenn S. Orton 5 The equatorial stratospheres of Earth, Jupiter and Saturn all exhibit a remarkable periodic oscillation of their temperatures and winds with height. Earth's quasi-biennial oscillation and Saturn's quasi-periodic equatorial oscillation have recently been observed to experience disruptions in their vertical structure as a consequence of atmospheric events occurring far from the equator. Here we reveal that Jupiter's quasi-quadrennial oscillation can also be perturbed by strong tropospheric activity at equatorial and off-equatorial latitudes. Observations of Jupiter's stratospheric temperatures between 1980 and 2011 show two significantly different periods for the quasi-quadrennial oscillation, with a 5.7-yr period between 1980 and 1990 and a 3.9-yr period between 1996 and 2006. Major disruptions to the predicted quasi-quadrennial oscillation pattern in 1992 and 2007 coincided with marked planetary-scale disturbances in the equatorial and low-latitude troposphere, suggesting that they are connected to vertically propagating waves generated by meteorological sources in the deeper troposphere (that is 500-4,000-mbar pressures). Disruptions in Jupiter's periodic oscillations are thus inherently different from those of Saturn or the Earth. This interconnectivity between the troposphere and stratosphere, which is probably common to all planetary atmospheres, shows that seemingly regular cycles of variability can switch between different modes when subjected to extreme meteorological events.
observational data set shows that the QQO signal is most prominent between ±4° of the equator and at 12-14° north and south latitudes, in agreement with ref. 19 . The substantial temporal variance found at 26° N is not part of the QQO and represents the large stratospheric variability of the North Temperate Belt due to the presence of stratospheric wave activity 14,20 . Figure 1 provides our first hint that Jupiter's temperature oscillations have been disrupted at certain times, having a longer period between 1980 and 1990 and a shorter period between 1996 and 2006. This change in the QQO periodicity is better seen in Fig. 1g, where the brightness temperature of the equatorial latitudes between ±1° is shown. Thus, just like the QBO on Earth and the QPO on Saturn, the QQO on Jupiter could have also been modified by strong meteorological activity. However, unlike Earth, Jupiter's QQO appears to have been locked into a different period between 1996 and 2006, compared with 1980-1990. This change in the period has never been observed for Earth's QBO, which returned to the usual 28-month mean period after the 2016 disruption 6 . Observations of Saturn over more than a decade would be needed to know whether the 2011-2013 disruption of the QPO 9 had the same effect. However, a preliminary assessment in ref. 21 suggests that the QPO returned to the same 15-yr phase after the disturbance.
To understand how the periodicity observed in Fig. 1 changes, we employed both a wavelet-transform analysis and a nonlinear least-squares curve-fitting analysis. Detailed information on these techniques is given in Methods. In Fig. 2 the power spectrum of the stratospheric temperature variability over time for the equatorial latitudes between ±1° and 11-13°, north and south, are shown. The QQO is clearly observed, particularly during 1980-1988 and 1996-2006, with markedly different periods, at both the equatorial and off-equatorial latitudes. At the equator, the wavelet-transform analysis shows predominant periods of 5:0 þ1:8 �1:0 I yr between 1980 and 1988 and 3.9 ± 0.7 yr between 1995 and 2006 (see Fig. 2d). Between 1989-1994 and 2007-2011, when the QQO signal becomes irregular and disorganized, no significant periodicity is observed. In short, Jupiter's equatorial oscillation should not be described as 'quadrennial' at all, as we do not know what the nominal period is. References 1,14,19 reported a potential anticorrelation of the stratospheric temperatures between the equatorial and off-equatorial latitudes, which is confirmed in Fig. 1. However, at 12° N and 12° S the period seems to vary between ~7-7.5 yr and 3-4 yr, maybe due to weaker meridional temperature gradients making the off-equatorial latitudes susceptible to localized convective weather events. The variability of the period of the off-equatorial latitudes is most prominent in the northern hemisphere, where the wavelet-transform analysis shows a dominant 7-8-yr periodicity between 1986 and 2000, compared with the ~3-yr periodicity found in 1980-1986 and 2000-2006. The observed longer periodicity at the off-equatorial latitudes might not be associated with the QQO and could be part of a completely different phenomenon, similar to the Earth's semi-annual oscillations 22 observed in the equatorial and tropical upper stratosphere. However, further observations will be needed to understand the nature of these longer periodicities and their relation to the QQO. All the results from the wavelet-transform analysis are shown in Table 1.
To increase confidence in the two discrete periods at the equatorial latitudes, Fig. 3 showcases the nonlinear Levenberg-Marquardt method to derive the best sinusoidal modelled amplitude, period, phase and offset constant to represent the time series. This confirms the wavelet analysis in the previous figure, and shows how well the newly proposed periods fit the data (Extended Data Fig. 1) for the fits at the off-equatorial latitudes. Model 1 attempts to reproduce the initial QQO discovery by fitting only the data between 1980 and 1990, where previous studies estimated the QQO period to be ~4-5 yr (refs. 1,14 ). However, further observations added to our study reveal an equatorial QQO period of 5:7 þ1:1 �0:8 I years for this time interval. Model 4 was developed to fit only the data between 1996 and 2006, revealing a 3.9 ± 0.2-yr period, statistically different from that found in Model 1 for 1980-1990. This change in the QQO period between 1980-1990 and 1996-2006 is larger than the 20% variability usually observed at the Earth's QBO 2 . Model 2 attempts to fit data that span from 1980 to late 2000 23 , and reproduces an approximate 4.5-yr QQO period consistent with analysis carried out in ref. 17 . However, this model does not adequately fit the observations, mainly before 1992, where the model phase departs from the data by almost 180°. Model 3 fits the observations between 1990 and late 2011, finding a 4.2-yr period. However, this latter model temperatures at ±12°. f, The high variances of the data at the equator and ±12° show that the QQO is most prominent at these latitudes. g, The brightness temperature as a function of time for the equatorial latitudes between ±1°. The error bars represent the s.d. of the average at each latitude of the zonal-mean brightness temperatures corresponding to observations taken on the same date. In the cases where a single image is available on a single observing night, we represent the errors as the root square of the estimated average absolute calibration uncertainty and the zonal variability (Methods).
does not adequately reproduce the 2007-2008 data, with the 2008 observations departing by 180° from the model phase. If Jupiter's QQO had precisely followed the periodicities derived by our model, then local temperature minima were expected to be observed in 1991-1992 and late 2007-2008. However, the observations from these epochs show the complete opposite, with a stratosphere ~3 K warmer than expected, displaying instead early temperature maxima. Our observations also show that the QQO signal is not just delayed during these two epochs (for example, slowing down the descending pattern of temperature anomalies for a short time), but instead it becomes irregular and disorganized over a longer time span. Understanding how Jovian tropospheric and stratospheric activity could have disturbed the QQO during these two epochs is essential to further our knowledge in the vertical coupling of the gas giant atmosphere.

Disruption origins
The abrupt change observed in Earth's QBO has been partially attributed to weaker temperature gradients from a changing climate and to an extreme El Niño event, where stratospheric waves from higher latitudes could propagate further towards the equator and affect the regular descent of the jets 5-7 . Jupiter's climate, however, is unlikely to be changing, and given its low obliquity there are few similarities between the abrupt change in Earth's QBO and the QQO disruptions discovered here. Jupiter does, however, exhibit a plethora of energetic and convective events at multiple latitudes, and if these events serve to weaken latitudinal temperature contrasts, then they might alter the transmissivity of the atmosphere to wave propagation, allowing waves from higher latitudes to reach, and possibly alter, the QQO region. Pursuing this hypothesis, we investigated the temperature gradients in Fig. 1, focusing on higher latitudes away from the off-equatorial jets, postulating that energetic events associated with the 21° N jet 24,25 might produce substantial waves that could alter the QQO. However, the meridional temperature gradient with respect to latitude (Extended Data Fig. 2) indicates no clear behavioural changes near the disruptive events of 1992 and 2007, either before or after.
Saturn's QPO was disrupted by strong convective activity at northern mid-latitudes that produced a large, hot stratospheric anticyclone 9 . Waves emitted by this unusual phenomenon are thought to have propagated horizontally through the stratosphere to modify the equatorial oscillation 9 . Similarly, ref. 26 reported that Earth's QBO disruption was associated with record stratospheric tropical wave activity. We therefore searched for similar hot stratospheric vortices and strong stratospheric wave activity that could have disrupted Jupiter's QQO, by analysing the longitudinal variance of the 7.9-μm brightness temperature at the equatorial and tropical latitudes between 1980 and 2011 (see Methods for a detailed description). The variance as a function of latitude and date is shown in Fig.  4. High variance would indicate the presence of either stratospheric vortices or wave patterns that could potentially alter the QQO, while low variance would be indicative of either a quiescent state of the stratosphere or a homogeneously warm latitudinal band. Figure  4 shows that, during the dates preceding the 2007 QQO disruption, the variance at tropical and equatorial latitudes was very low, with no signs of stratospheric vortices or other substantial perturbations. This reveals that the physical phenomena perturbing the QQO are completely different from those observed on Earth and Saturn. Unfortunately, the limited observations in 1991 and 1992 do not enable us to confidently compute the longitudinal variance during     that disruption event. This study also shows that the largest longitudinal variability at the tropical latitudes is unexpectedly found at the times when the QQO was most prominent (that is 1980-1990 and 1996-2005). These large variabilities correspond to the presence of (1) tropospheric wave activity usually observed at the northern boundary of the north equatorial belt at 16-18° N (ref. 27 ), and (2) stratospheric wave activity over the north temperate belt at 21-27° N (ref. 14 ). Unlike the energetic stratospheric activity that disrupted the QBO on Earth and the QPO on Saturn, these are not one-off events and are commonly observed on Jupiter. Given that the equatorial stratospheric temperature oscillations are thought to be driven by vertically propagating waves, rather than by waves propagating horizontally (that is, meridionally), it is hard to determine whether this correlation between a prominent QQO and the presence of strong extratropical stratospheric variability is a mere coincidence, or is revealing something about the dynamical processes sustaining the regular oscillations. Future numerical modelling work, and extension of the observational time series, are highly desirable to address this question. The anomalous QQO period changes observed in 1992 and 2007 coincided with marked planetary-scale disturbances observed much deeper in Jupiter's troposphere (500-4,000 mbar compared with 10-20 mbar) at equatorial and tropical latitudes during 1990-1992 and 2006-2007. During these two epochs, nearly contemporaneous disturbances occurred at equatorial and tropical latitudes, completely altering Jupiter's banded cloud morphology. These were parts of rare events known as 'global upheavals' 28,29 , which usually involve multiple energetic convective events in the cloud decks. Between 1990-1992 and 2006-2007, these global upheavals involved three different types of tropospheric activity.

Convective outbreaks at the zonal jet at 21° N in early 1990 and
2007 25,[30][31][32] . Observations of these vigorous outbreaks showed that they completely altered the coloration of the north temperate belt (that is 21°-28° N) at visible wavelengths, sensing the ~700-mbar pressure level, while no changes were observed in the stratosphere 32 or deeper in the troposphere 33 .

Equatorial zone (EZ) disturbances at ±7° between January and
April 1992 and April 2006 and September 2007 33,34 . These were part of a quasiperiodic pattern of cloud-clearing events that completely altered the appearance at the EZ at the ~700-mbar  pressure level (visible wavelengths) and at the 1-4-bar level (5 μm wavelength). During these events the usually visibly white and 5-μm dark EZ appeared visibly dark and 5-μm bright. Observations at 2.12 μm, sensing stratospheric hazes, of the same epochs showed a complex temporal variability not related to the EZ disturbances, suggesting that the EZ disturbances were confined to the cloud deck. 3. South equatorial belt fading and revival cycles at 7-17° S in 1989-1990, 1992-1993 and 2007 29,35-41 . These events were observed to markedly alter the troposphere at 500-mbar-4-bar pressure levels without altering the stratosphere 12 .
The contemporaneity of the disruptions of the stratospheric QQO and the anomalies observed at tropospheric levels suggest that, unlike on Earth and Saturn, disruptions of Jupiter's stratospheric temperature oscillations are not limited to horizontally propagating waves from large stratospheric perturbations at higher latitudes. Instead, the QQO period is highly sensitive to tropospheric meteorology, indicative of strong coupling between the troposphere and stratosphere. However, previous studies of the north temperate belt outbreaks and the EZ disturbances reported these events to occur quasiperiodically with 5-yr (ref. 28 ) and 7-yr (refs. 33,34 ) intervals, something not observed in the QQO disruptions. We therefore suggest that vertically propagating waves from a chain of these disturbances in the weather layer (that is, the global upheaval, rather than an individual tropospheric event) could be responsible for the disruptions of the QQO and the change in its periodicity.

Discussion
The distinction between the disruption mechanisms for Earth's and Saturn's oscillations (horizontally propagating waves from strong stratospheric wave activity) and the Jovian one (vertically propagating waves from energetic tropospheric activity) provides a new constraint on numerical atmospheric simulations of disturbed equatorial oscillations in planetary atmospheres, as tropospheric wave creation mechanisms can easily be reproduced while Saturn's hot stratospheric vortex remains nearly impossible to model. The lock of Jupiter's equatorial stratospheric temperature oscillation into different phases and periods that differ by more than 20% (a phenomenon not witnessed on Earth or Saturn) means that it cannot be accurately described as quadrennial. Indeed, we propose that these phenomena should be more generically referred to as the JESO and SESO (Jupiter equatorial stratospheric oscillation and Saturn equatorial stratospheric oscillation), so as not to directly imply their periods. We hope that future observations will be able to determine whether or not a UESO (Uranus) and/or a NESO (Neptune) also exist. We predict that future global-scale upheavals will similarly perturb Jupiter's QQO into a new phase and period, and will seek to test this hypothesis via continued monitoring of variable phenomena in the Jovian atmosphere.

methods
Ground-based observations and data reduction. This study uses 7.6-7.9-μm images of Jupiter captured between 1980 and 2011 by five different instruments mounted at NASA's 3-m IRTF. The 7.6-7.9-μm radiance, originating from a pressure region spanning approximately 10-20 mbar in Jupiter's stratosphere 14 , reveals the CH 4 emission and allows estimates of stratospheric temperatures. The ground-based observations used in this study include 1980-2000 data used in refs. 14-17 as well as additional observations never published before. A summary of the dates and instruments is shown in Table 2. A description of the different instruments is found in the previously mentioned references and references therein.
Raw MIRLIN, MIRAC and MIRSI data (1994-2011) are reduced using the Data Reduction Manager software 42 written in IDL (Interactive Data Language). The reduction technique includes the following steps: (1) subtraction of the sky emission using chop-nodded images; (2) correction of the spurious pixels and non-uniformities in the detector by flat fielding; (3) coadding multiple corrected images separated by less than an hour to increase the signal-to-noise ratio; (4) geometric calibration of the images by limb-fitting; (5) projection of the images as cylindrical maps of 0.5° × 0.5° (longitude-latitude) or 1° × 1° spatial resolution, depending on the quality of the image, to assign longitudes, latitudes and emission angles to each pixel. The BOLO-1 and AT1 data used in this study (captured between 1980 and 1981 and between 1982 and 1992, respectively) were previously reduced and projected into 1° × 2° (longitude-latitude) cylindrical maps in ref. 15 . Information for these observations and reduction techniques are described in that paper.  To avoid radiometric calibration differences between the previously reduced and published data and the new data reduced in this study, we recalibrated all the data in a systematic way. Each cylindrical map is radiometrically calibrated by scaling the radiance to match the Voyager IRIS and Cassini CIRS observations from 1979 and 2000, respectively, at mid-latitudes. To do so, we compute the zonal average of the radiance within 20 ∘ longitude around the central meridian for each latitude, creating a latitude-radiance profile for each cylindrical map. These profiles are then compared one by one with the zonally averaged radiance of the IRIS and CIRS observations to obtain a scaling factor for each cylindrical map. This calibration technique has been widely used in previous studies and assumes that Jupiter's zonal average brightness at mid-latitudes remains mostly invariant with time (e.g. 42 ).
The reduced and calibrated data are then used to compute the 7.9-μm zonally averaged brightness temperatures for each observing date. This is computed by binning the radiance corresponding to emission angles smaller than 75° of all images captured in a single observation night in latitudinal bins of 1°, and converting them to brightness temperatures. Radiances corresponding to emission angles greater than 75° are omitted from the average to avoid strong limb brightening and convolution of the edge of the planet's disk with deep space. Zonally averaged brightness temperatures shown in this study might differ from those shown in refs. 14,17 , as these previous studies used yearly brightness temperatures corresponding to annual averages of the stratospheric zonal-mean temperatures.
The data reduction process introduces diverse systematic errors to the final radiance (brightness temperatures) from various sources. The largest uncertainties are introduced during the absolute radiometric calibration process due to (1) differences in the radiance between Voyager IRIS and Cassini CIRS that would lead to an overall 0.4-K difference in the temperatures between the older (1980s) and newer (1990s and 2000s) observations and (2) radiometric scaling error, which we estimate to be 0.95 K in the worst cases, less than 0.05 K in the best cases and 0.30 K on average. We estimate these uncertainties by looking for the scaling factor required to minimize differences in (1) the Voyager IRIS and Cassini CIRS final radiances and (2) the zonal-mean brightnesses of different observations captured during a single night (and repeat this for all the available observing dates). Error bars shown in Fig. 1 represent the s.d. of the average at each latitude of the zonal-mean brightness temperatures corresponding to observations taken on the same date. This s.d. not only includes the contribution from the longitudinal variability, but also accounts for the calibration uncertainty. In the cases where a single image is available on a single observing night we represent the errors as the root square of the estimated average radiometric scaling uncertainty and the zonal variability.

Wavelet-transform analysis.
To study the long-term periodicity of the Jovian QQO we perform a wavelet-transform analysis. This is a powerful tool used to analyse potential changes within a time series 43 . Unlike the Fourier transform or the Lomb-Scargle method 44 , the wavelet-transform analysis provides accurate time-frequency analysis for signals where sinusoidal functions with a single frequency cannot reproduce the observations, by expanding a set of functions, called wavelets, given by the user. This technique is widely used in geophysics and has been previously used to analysed the long-term variability of Jupiter's 1-4-bar-level atmosphere 33 . Here we follow ref. 33 and use the most commonly used wavelet function, that is the Morlet wavelet, which consists of a plane wave modulated by a Gaussian 45,46 . This wavelet is defined as where ω 0 is a wavenumber and t is time.
In this study, we use in particular the 'wavelet.pro' code written in IDL 43 . This function computes the one-dimensional wavelet transform by translating and changing the wavenumber of the function given in equation (1) and allows the user to set a significance level to use. Here we set a significance level of 0.98. We also set the PAD keyword, which minimizes the errors introduced by the temporal boundaries of our data set. The time series analysed by the wavelet-transform analysis must be evenly spaced in time. As our observations are not obtained on a regular basis, we interpolate the 7.9-μm radiance onto a regular grid of 2 d using a basic linear interpolation and then smooth the interpolated radiance with a boxcar average of 10 d. This grid provides the best representation of our data.
Nonlinear Levenberg-Marquardt analysis. We used a nonlinear least-square minimization and curve-fitting Python package (https://doi.org/10.5281/ zenodo.11813) utilizing the Levenberg-Marquardt method to find the best sinusoidal modelled amplitude, period, phase and offset constant given by where A is the amplitude, ϕ is the phase and C is a constant or the approximate mean temperature of observational data spanned by the model for a specific latitude. To establish the significance of the results of our models fitted to the data, we varied the range of data included in both models 1 and 4. The indices of the equatorial data for models 1 and 4 presented throughout this paper are 0-49 and 63-130, respectively. We rooted the beginning of the observations because of how sparse the data are around 1980-1983, so the 0 index position was held constant. To be systematic in this analysis, the same initial conditions for model 1 and model 4 were used while the indices were altered from the base values presented earlier.
The internal Levenberg-Marquardt method parameters such as tolerance, iteration limits and the 'throttle' lambda variable were also held constant in this exploration.
The indices for model 1 were varied by ±1, which produced an increase in the period uncertainty by 20% while the period itself did not change. Extending model 1 to include points later in time did not find converged solutions, probably because of the spacing of data points between 1991 and 1994. The indices for model 4 were varied by ±10, and over this range the QQO model period varied within the range of 3.84-4.22 yr with an uncertainty range of 0.1-0.56 yr. When leaving model 1 constant, these variations in model 4 data produced P-test probabilities that varied in the range of 1.11-3.77%.
Longitudinal variance analysis. To investigate potential sources responsible for the observed QQO disruptions around 1992 and late 2007, we searched for hot stratospheric vortices and strong stratospheric wave activity that, as on Saturn, could have disrupted the stratospheric temperature oscillations. One way to do this is by analysing how the 7.9-μm brightness temperatures vary with longitude and date, as localized stratospheric vortices and wave activity would result in large longitudinal variability of the brightness temperature.
In this study, we first compute the variance at longitudes within ±40° of the central meridian for each latitude and date. However, due to the different observing settings used and the very different weather conditions during each of the observing runs, global maps of Jupiter were not always acquired, resulting in cases where the presence of vortices or wave activity could have been missed because we were viewing a 'quiet' side of Jupiter. To try to solve this problem, we search for the largest variance at each latitude using a 60-d temporal resolution boxcar. In most cases, this temporal resolution is long enough to have at least two images available. Epochs where only one image is available in a 60-d window are not taken into account. This solution only partially addresses the problem, as there is always a small chance that the available images in a 60-d window span similar longitudes, but is the best that can be done with this limited data set. To analyse the robustness of the obtained results we show the number of images available at each latitude over the 60-d windows in Fig. 4.

Data availability
This work relies on ground-based data acquired at the IRTF. Jupiter images at 7.6-7.9 μm are available from A.A. and from L.N.F., and are in the process of being archived with NASA's Planetary Data System. The cylindrical maps and the emission angle files used in this study to compute the zonal-mean brightness temperatures can be found at https://doi.org/10.5281/zenodo.3764712.