Jupiter's Mesoscale Waves Observed at 5 μm by Ground-based Observations and Juno JIRAM

VISIR (Lagage et al. 2004) returned to the 8.2 m UT3/Melipal telescope in 2015 after a 3 yr refurbishment. The new 1024 × 1024 Raytheon Aquarius IBC detector offers a pixel size of 00453 pixel^–1 over a 38'' × 38'' field of view, smaller than the disk of Jupiter at opposition but sufficient to oversample the 015 spatial resolution of the 5-μm imaging. Following interactions with Hans-Ulrich Kaufl in 2015 March, an M-band filter was located and inserted into VISIR. Given the high sky background, the individual integration times are usually a few milliseconds, and the upgraded VISIR now offers a new burst mode whereby all individual detector exposures are recorded, rather than just retaining the averages per nodding cycle. We were awarded Science Verification observations in Period 96 (2016 February), immediately prior to Juno's arrival at Jupiter, to test this new M-band "lucky-imaging" capability. Once validated, this became a part of our regular observing sequence in Period 98 (2016 December onward). We targeted all opportunities when Jupiter was available for more than 1 hr within a week of Juno's perijove encounters. Unfortunately, weather constraints at Paranal and scheduling competition for service-mode observations restricted the data set to six distinct epochs, as shown in Table 1. The epochs were primarily clustered during the 2016–17 apparition (centered on Jupiter's opposition on 2017 April 07). Regular observations at 7–20 μm (i.e., without burst mode) demonstrated the changes associated with the NEB expansion during this period (Fletcher et al. 2017b).

A single observing block has N_nod nodding cycles (usually four or five), each producing two files: the first performed chopping on Jupiter itself, the second performed chopping at a position 25'' away. The observations were designed such that the direction of the chop was determined by the particular hemisphere that we were focusing on: chopping the telescope north if we desired unobstructed views of the northern hemisphere, and chopping the telescope south if we wanted unobstructed views of the southern hemisphere. The total integration time divided by the number of nodding cycles and the 3–4 Hz chopping frequency determined the number of chopping cycles within each individual file. The individual integration time of each frame was 11.4–20.8 ms, depending on the chopping frequency used. We took the sum of the chop-nod position that encompassed only blank sky and subtracted this from every frame of the chop-nod position that targeted Jupiter alone (effectively discarding 50% of the data). This produced hundreds of individual frames for each nodding cycle. These were saved as both MP4 files for quick inspection and uncompressed TIFF files for further processing. The movies show Jupiter moving around on the detector and coming in and out of focus as the seeing varies over millisecond timescales.

The TIFF files were imported into AutoStakkert,⁹ a software tool developed by E. Kraaikamp to identify and stack those frames with the best image quality (Kraaikamp 2016). The software centers and aligns the individual frames using a "surface" mode to track individual bright features within an alignment box on Jupiter throughout the sequence. The frame quality is estimated via measurements of local gradients from frame to frame and used to rank the frames from best to worst. One large alignment point, encompassing the NEB and South Equatorial Belt (SEB) of Jupiter, was then used as the anchor to stack the top 2%, 5%, 10%, and 20% of frames. As more frames sometimes worsened the quality of the stack, we made a qualitative selection of one stack for continued analysis. The limb of the planet was fitted to assign latitudes, longitudes, and emission angles to each pixel, which were then projected onto a 025 resolution cylindrical map. No attempt was made to radiometrically calibrate the data.

The VISIR data were supplemented by a single mosaic 5-μm image from NIRI (Hodapp et al. 2003) on Gemini-North using a similar lucky-imaging process without adaptive optics. NIRI's 1024 × 1024 pixel InSb array and 00218 pixel^–1 scale limits the field of view to 22 × 22'', which was mosaicked across the disk to generate a map on 2017 February 5 (Table 1). Details of the wider Gemini/NIRI program will be described in a forthcoming paper.

The ground-based observations are compared to partial maps of the NEB acquired by the JIRAM instrument on the Juno spacecraft. The JIRAM imager and spectrometer (Adriani et al. 2017) are mounted on the Juno spacecraft and have been operating since 2016 August. Juno approaches the planet every 53 days with different attitudes according to primary science objectives (Bolton et al. 2017). In the first part of the mission, most of the flybys were favorable to JIRAM, and the planet could be observed during the approach with good views of the northern hemisphere. The NEB was observed with variable coverage during orbits 1, 4, 5, 6, and 7 (during orbits 2 and 3, the instrument was not operating). The JIRAM imager has a channel working around 5-μm wavelength. Single images have a size of 432 × 128 pixels. Pixels are square-shaped with an angular resolution of 240 × 240 μm, which defines the spatial resolution at the cloud level as a function of the distance of the spacecraft from the planet. The images reported hereafter present an average spatial resolution of about 250 km at the cloud level, twice as good as the VLT resolution reported above. When the spacecraft's spinning plane intersects the planet, JIRAM can make scans from south to north, changing pointing approximately every 30 s (spacecraft spinning period). Maps of a limited range of latitudes can be built by mosaicking images from different observing sequences, although some artifacts occur because the atmosphere has evolved during the interval between sequences. Dates of the JIRAM data acquisitions are reported in Table 1.

Figure 3 shows the evolution of the NEB during a new phase of NEB expansion in 2017 (all latitudes are planetographic). During these expansion events, the dark coloration of the NEB is seen to extend from 17°N to 20°N, encroaching on the typically white North Tropical Zone (NTrZ; region [2] of Figure 1). This dark coloration coincides with warmer temperatures and bright 5-μm emission, implying the removal of the white NTrZ aerosols during an expansion. The first phase of the expansion in 2015–16 was documented by Fletcher et al. (2017b) but had stalled and regressed by the time of Juno's arrival in 2016 July and never spanned all longitudes. At its peak, the expanded region spanned ∼145° of longitude west of a large anticyclone (White Oval Z; 19 °N, 283 °W in 2016 February). The expanded region reached an unusual cyclone–anticyclone pair, which was observed during our first VLT lucky-imaging campaign in 2016 February (Figure 4), before Juno's arrival. The anticlockwise motion of the cyclone can be observed near 16°N, 55°W, embedded within the NEB. This cyclone will be labeled B1 for the purposes of this study. The anticlockwise motion of the anticyclone can be seen at 19°N, 43°W, nominally within the NTrZ. The expanded NEB had regressed at all longitudes by the time of Juno's arrival, and the NEB had its normal width in 2016 August (Figure 5(a)) and 2016 December (Figure 3).

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Maps in 2017 February and March (Figure 3) show a second phase of cloud clearing within the NTrZ, where the 5-μm emission is visible at latitudes poleward of the NEBn jet at 17°N (planetographic). This time, the expansion spread over all longitudes. At the end of an expansion episode, the undulations of the northern edge of the NEB transform into a chain of cyclones near 16°N (sometimes known as barges) and anticyclonic white ovals (AWOs) near 19°N (Fletcher et al. 2017b; Rogers 2017). This pattern of cyclone–anticyclone pairs can be seen in 2017 March (see Section 3.2). In addition, the southern edge of the NEB (region [3] in Figure 1) exhibits the familiar chain of 5-μm bright hot spots that move rapidly eastward with the prograde NEBs jet at 7°N. The influence of the NEB expansion and the presence of the NEB cyclones will be described in Section 3.2.

In this section, we present the chronology of the NEB wave activity as observed at 5 μm. The prerequisite for observing the waves at this wavelength is the presence of a relatively quiescent background 5-μm emission that can be modulated solely by the waves, rather than other phenomena, like vortices, convective plumes, and "rifts," which appear dark and cloudy against the bright background emission. For ground-based observers, these conditions were met in 2016 December and 2017 January–February (Figure 6), when the mesoscale waves were first identified at 5 μm. The 2016 February 5-μm observations (Figure 4) did not show the presence of waves, whereas the first JIRAM map (2016 August, Figure 5(a)) reveals hints of the wave pattern over a limited 12° longitude range to the west of a dark cyclone at 35°W, and these were clearly visible by the end of 2016 from the ground.

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Timeline of the NEB cyclones.—Given the potential importance of cyclogenesis in the origins of the wave pattern (Simon et al. 2015), we now discuss their chronology in detail. In the August and December images, the waves appear to be located to the west of two cyclones. Figure 6 shows that the cyclone B1 moved 4° westward (from 90°W to 94°W) over 30 days between the December and January observations (013 day^–1). This slow motion is consistent with the weak winds in the center of the NEB. Extrapolating backward, this same cyclone B1 is observed at 75°W in 2016 August (Figure 5(a)) and 55°W in 2016 February (Figure 4). Indeed, B1 is the same cyclone that marked the westward extension of the stalled 2015–16 expansion and had been apparent in ground-based data since at least 2015 October (Fletcher et al. 2017b). This cyclone showed no wave pattern in 2016 August, but one had developed by 2016 December, 4 months later. The longevity of cyclone B1, which existed long before waves were identified, suggests that the waves may not originate from cyclone formation but rather from processes at work once the cyclone was already mature. Cyclone B1 was last definitively observed at 106°W in 2017 March (Figure 5(c)), at which time its wave train was no longer visible (it is visible in 2017 February in Gemini/NIRI observations; Figure 6). The second cyclone, B2 (35°W in 2016 August), formed within the previously expanded sector of the NEB and was the first to exhibit the wave train in the Juno observations at 35°W. It was observed again near 58°W in 2016 December, this time without visible waves, but B2 is not visible in either the January VISIR maps or the 2017 February Gemini/NIRI maps (Figure 3), suggesting that the cyclone had dissipated.

Early views of the waves.—Observations between 2016 August (JIRAM), 2016 December, and 2017 January (VLT) suggest that the waves occurred in longitudinally confined packets. The NEB had its regular width (7°N–17°N) at this stage, before the onset of the new 2017 expansion event. On 2016 August 27, the waves extended some 12° west of cyclone B2, but these had vanished by 2016 December when B2 was at 58°W, indicating a lifetime shorter than 4 months. Conversely, the December data showed a longitudinally confined wave train between 80°W and 105°W that had not been present in August. Hubble imaging on December 11 (Figure 6) also reported the wave between 70°W and 100°W (Simon et al. 2018). The waves appeared to exist within two 10° longitude wide packets on either side of cyclone B1 at 92°W that were latitudinally wider to the east (∼3°) than to the west (∼1°). This tapering could be related to a dark striation 1° further south in Figure 6, which extended from the southeast to the northwest. The wavelength was 13 in the January image and exhibited a slight tilt from southeast to northwest. The cyclone B1 and wave pattern moved ∼2° westward (to 94°W) by January 11. The waves retained their 12–14 wavelength and northwesterly tilt and extended from 95°W to 117°W longitude. The latitudinal extent remained ∼2° across the wave train. Once again, there is a qualitative suggestion that they existed in two distinct packets of approximately 10° longitude, although this could be a property of the underlying background emission rather than of the wave itself. JIRAM observations on 2017 February 2 (PJ4) only caught a small glimpse of the waves between 68°W and 82°W, extending over ∼14° longitude (Figure 5(b)), and they were also detectable in Gemini/NIRI observations on February 5. There is a considerable amount of small structure at the same spatial scale that could support the presence of a more extensive wave pattern, as suggested by Hubble imaging on February 1, which reports waves from 25°W to 75°W (Simon et al. 2018).

Mature wave pattern.—In 2017 February–March, the NEB had expanded northward to 21°N (Figures 3 and 7), and a cyclone–anticyclone pattern formed from the "bulges" on the northern edge of the NEB that characterize expansion phases¹⁰ (Fletcher et al. 2017b). The February images reveal dark cyclones every ∼22° of longitude in the 250°–340° range at 16°N (Figure 7). By March, these had been joined by anticyclones near 20°N, with the anticyclones generally occurring to the northwest of the cyclones, although this pairing was not always consistent. The presence of this cyclone–anticyclone pattern caused the surrounding NEB to become turbulent and chaotic. With these features strongly modulating the background 5-μm flux, it proved impossible to observe the mesoscale waves in the 220°W–320°W longitude range sampled by the VLT data.

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So was the fine-scale (12 wavelength) wave pattern truly absent when the cyclone–anticyclone wave pattern (22°–24° wavelength) developed, or is this just a consequence of the visibility at 5 μm? Hubble imaging on February 1 and Gemini/NIRI imaging on February 5 showed waves in a relatively quiescent sector of the NEB over 160°W–200°W (Figure 7, top) but not over the more complex 250°W–320°W domain sampled by the VLT on February 6 (Figure 7, middle). This is consistent with turbulent activity removing all signatures of the waves. Further Hubble imaging on April 3 showed waves at (a) 5°W–55°W and (b) 235°W–305°W (Figure 7, bottom). The former are readily visible in the March 27 JIRAM observations (Figure 5(c)) spanning 45°W–85°W. But the latter were not visible in the VLT images 18 days earlier (Figure 7). This suggests that the waves can still be present but not visible at 5 μm due to strong variation in the underlying emission. The Hubble observations in 2017 April (Simon et al. 2018) show a large-scale NEB rifting event (turbulent white cloud structures, sheared east near the NEBs and west near the NEBn) that spanned from 90°W to 220°W during this period, and it is notable that the waves are only visible outside of this longitude range.

Hubble imaging and amateur observations (Simon et al. 2018), as well as Juno observations from PJ7 (Figure 5(e)), suggest that the NEB wave was present away from the prominent rifting zone until at least 2017 July. Waves were not visible in the 260°W–305°W range sampled by JIRAM during PJ6 but were visible 7–8 weeks later, spanning from 280°W to 30°W, confirming that they can develop and disappear over monthly timescales. We can conclude that the mesoscale waves form only in a relatively quiescent NEB, away from prominent rifts, and initially in association with preexisting cyclones.

The primary conclusion of this work is that the mesoscale wave activity observed at visible wavelengths (Simon et al. 2015, 2018) also serves to modulate the 5-μm emission from Jupiter's deeper troposphere. This provides a new window for tracking this unusual phenomenon. However, the detection alone need not necessarily imply that the wave pattern is deep. First, there is a nonnegligible contribution from reflected sunlight at 5 μm, which reflects off of the same tropospheric clouds that are evident in the visible-light imaging (Bjoraker et al. 2015). A modulation of the upper tropospheric clouds could therefore influence the reflected sunlight contribution, but aerosols within the belts are expected to have a low albedo at 5 μm. However, the upper tropospheric aerosols can modulate the 5-μm radiance in the absence of reflected sunlight simply via absorption and scattering. Giles et al. (2015) required a cloud at p < 1.2 bar to reproduce Cassini VIMS spectra of both cloudy zones and cloud-free belts. Lower pressures were also permitted by the data, implying that this cloud could reside at the NH₃ condensation level near 800 mbar. Furthermore, Galileo NIMS analyses by Irwin et al. (2001), Nixon et al. (2001), and Irwin & Dyudina (2002) place the primary cloud decks in the 1–2 bar range, and Sromovsky & Fry (2010) suggested a spatially variable cloud base between 0.79 and 1.27 bar. Although optical thickness variations of a deeper cloud were also required to fit the 5-μm spectra, we have no way to determine whether the mesoscale wave modulation exists in the upper layer, the deeper layer, or both.

Each of these works are consistent with a possible source of 5-μm modulation in the 0.8–1.2 bar range without having to assume that the mesoscale wave is present at higher pressures. Near-infrared spectroscopy of the NEB is required to better constrain the altitude of the wave pattern, as described by A. Adriani et al. (2018, in preparation) using JIRAM data. Their analysis also suggests that the data can be explained by waves in the upper layer, the deeper layer, or a combination of both. Although we cannot distinguish these possibilities, we favor a lower pressure for the reasons outlined above.

Finally, the calibrated Juno JIRAM data sets allow us to provide a quantitative estimate of the brightness amplitude of the wave pattern. The 2017 May observations (PJ5) have a mean brightness temperature at 16°N of 210 ± 15 K, where the large range is a result of the extreme variability seen in Figure 5(c). The wave amplitude is 7–10 K peak to peak (approximately 2 μW cm⁻² sr⁻¹ μm⁻¹), where we caution the reader that this is a brightness temperature resulting from aerosol modulation, rather than a physical temperature variation. The cyclone near 106°W reaches brightness temperatures of ∼195 K, compared to a background of ∼220 K. We find the same range of brightness temperatures in the PJ7 data. Via an analysis of Cassini VIMS spectra, Giles et al. (2015) demonstrated that changes of 2 μW cm⁻² sr⁻¹ μm⁻¹ could easily be reproduced by changes in the opacity of a p = 0.8 bar cloud of 10%–20%, which suggests that upper tropospheric modulation of the deeper 5-μm radiance is a reasonable hypothesis.

The chronology of the NEB wave described above raises several intriguing possibilities, which we summarize here.

• 1.  
  Mesoscale waves were first observed at 5 μm in mid-2016 in association with two cyclones, B1 and B2, that were related to the stalled 2015–16 expansion of the NEB. Cyclone B1 had been present since at least 2015 October and had been part of a cyclone–anticyclone pair that marked the western edge of the expanded NEB sector. Given the rarity of the mesoscale waves and their redetection during a period when the NEB has been observed to sporadically expand into the NTrZ, we speculate that the NEB expansion conditions (and the resulting cyclogenesis) may be influencing the environmental conditions permitting the propagation of these waves.
• 2.  
  The wave trains were initially restricted in longitude to packets ∼10° wide, meaning that only ∼7–10 wave crests were visible in the early detections. These packets appeared to the west of B1 and B2 and had lifetimes of a few months. The packets were latitudinally wider in the east than in the west, and the wave crests appeared to be sheared from southeast to northwest. Such a morphology is likely related to the changing wind across the NEB (centered on the westward NEBn jet at 17°N) and the visibly bright and 5-μm dark elongated rifts that could be seen in Figure 6 stretching across the NEB from southeast to northwest. The wave trains expanded to span ∼40°–50° longitude some 6–8 months after they were first detected and were most visible in 2017 March and April.
• 3.  
  The waves were not visible when the NEB became chaotic. At 5 μm, the presence of a closely packed pattern of cyclones and anticyclones (typical of the end stages of an NEB expansion and contraction event) rendered the small-scale wave pattern invisible, although it could still be detected in visible light. However, strong rifting activity that is bright in the visible and dark at 5 μm (which was present from 90°W to 220°W in 2017 March) caused the wave pattern to be invisible at all wavelengths and potentially disrupted it completely. We suggest that relatively quiescent NEB conditions are therefore needed for the wave pattern to propagate.
• 4.  
  The waves retained their 11–14 wavelength (a wavenumber of 260–330) at all epochs without notable increases or decreases with time. Simon et al. (2015) pointed out that this and the ∼2° latitudinal extent of the waves are on the same scale as the atmospheric deformation radius (see Figure 8(f)), which may be playing a role in setting the length scale for these waves.

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By analogy to waves associated with cyclones and anticyclones on Earth and in general circulation models, Simon et al. (2018) proposed both pure gravity waves (GWs; under the action of gravity and buoyancy forces) and/or inertio-gravity waves (IGWs; with wavelengths long enough to require consideration of the Coriolis term) as plausible explanations for the observed mesoscale wave pattern. In this analysis, we also consider short-wavelength Rossby waves (RWs), although we note that Jovian RWs typically have much longer wavelengths and a very different morphology than the mesoscale waves described here (e.g., NEB thermal waves with a 22°–24° longitude wavelength were identified in the NEB in 2015–16; Fletcher et al. 2017b). We utilize Jupiter's zonal-mean temperature structure retrieved from Cassini Composite Infrared Spectrometer (CIRS) data by Fletcher et al. (2016a) to explore the dispersion relationships of these three wave types. Although more recent Earth-based temperature observations are available, their analysis is ongoing, and the Cassini thermal structure from 2000 December can be used as a good qualitative proxy for present-day conditions within the NEB.

We take the dispersion relationship for linear GWs as (Holton & Alexander 2000; Sánchez-Lavega et al. 2011)

$$\begin{eqnarray}&&{\omega }^{2}={({c}_{x}-u)}^{2}{k}^{2}=\displaystyle \frac{{N}^{2}{k}^{2}}{{k}^{2}+{m}^{2}+1/(4{H}^{2})}.\end{eqnarray} \tag{ 1 }$$

Here ω is the intrinsic frequency; c_x is the longitudinal phase speed of the waves; u is the zonal wind determined from the thermal wind shear dT/dy (where y is the north–south distance); k and m are the zonal and vertical wavenumbers, respectively; N is the Brunt Väisälä frequency; and H is the scale height. Note that we take the meridional wavenumber to be zero, as the wave crests are nearly zonal, i.e., perpendicular to longitude and flow direction. The dispersion relationship for IGWs (e.g., accounting for the Coriolis parameter f) is given by (Section 4.6.3 of Andrews et al. 1987)

$$\begin{eqnarray}&&{\omega }^{2}={({c}_{x}-u)}^{2}{k}^{2}={f}^{2}+\displaystyle \frac{{N}^{2}{k}^{2}}{{m}^{2}+1/(4{H}^{2})}.\end{eqnarray} \tag{ 2 }$$

Finally, the dispersion relationship for a quasi-geostrophic RW reduces to (Sánchez-Lavega et al. 2011)

$$\begin{eqnarray}&&{c}_{x}-u=-\displaystyle \frac{{\beta }_{e}}{{k}^{2}+({f}^{2}/{N}^{2})({m}^{2}+(1/4{H}^{2}))}.\end{eqnarray} \tag{ 3 }$$

Here we have introduced the latitudinal gradient of the quasi-geostrophic potential vorticity (${\beta }_{e}={{dq}}_{G}/{dy}$, the "effective beta"; Andrews et al. 1987), evaluated following the method of Fletcher et al. (2016b). This is related to the change in the Coriolis parameter with latitude, which provides the restoring force for RWs.

Note that we consider only GWs, IGWs, and RWs, rather than Kelvin–Helmholtz instabilities, because the Richardson number (${N}^{2}/{({du}/{dz})}^{2}$) is positive and much larger than one throughout the 80–800 mbar range sampled here. The dispersion relationships above rely on parameters that can be derived from the CIRS temperature measurements in the 0.1–0.8 bar range: zonal winds are estimated from the thermal wind equation (Andrews et al. 1987), and the buoyancy frequency utilized the measured and dry adiabatic lapse rates (using the local gravity and specific heat capacity). The mean zonal phase speed of the waves, c_x, is estimated to be −15.5 ± 10 m s⁻¹ (from an average of the 2016–17 measurements of Simon et al. 2018), implying a slow westward motion with respect to the cloud-tracked zonal winds at 16°N (u ∼ −10 m s⁻¹ in the center of the NEB; Figure 8(c)). These dispersion relationships should strictly rely on constant N and u with altitude, which is not the case in Figure 8, and so should be considered only as approximations. These equations can be rearranged to estimate m to assess the likelihood of vertical propagation, first for GWs,

$$\begin{eqnarray}&&{m}^{2}=\displaystyle \frac{{N}^{2}}{{({c}_{x}-u)}^{2}}-{k}^{2}-\displaystyle \frac{1}{4{H}^{2}}\mathrm{,}\end{eqnarray} \tag{ 4 }$$

second for IGWs,

$$\begin{eqnarray}&&{m}^{2}=\displaystyle \frac{{N}^{2}{k}^{2}}{{({c}_{x}-u)}^{2}{k}^{2}-{f}^{2}}-\displaystyle \frac{1}{4{H}^{2}},\end{eqnarray} \tag{ 5 }$$

and finally for RWs,

$$\begin{eqnarray}&&{m}^{2}=\displaystyle \frac{{N}^{2}}{{f}^{2}}\left(\displaystyle \frac{{\beta }_{e}}{u-{c}_{x}}-{k}^{2}\right)-\displaystyle \frac{1}{4{H}^{2}}.\end{eqnarray} \tag{ 6 }$$

If ${m}^{2}\gt 0$, then real solutions can be found, and vertical propagation of this wave type is permitted. If ${m}^{2}\lt 0$, then the solutions are imaginary, and the wave could be trapped in the vertical at the level that it is observed.

Figure 8 shows these calculated quantities—temperatures, wind shears, Rossby deformation radius (${L}_{D}={NH}/f$), and m²—for the GW, IGW, and RW cases. These are provided at 16°N (the latitude of the cyclone chain in the NEB) and 20°N (the latitude of the associated anticyclones in the NTrZ). Before describing the results, we first caution the reader that the parameters in Figure 8 are subject to large uncertainties—wind shears and static stability both require derivatives of the retrieved temperatures with latitude and altitude, and estimates of the winds (and associated vorticity gradients) require integration of these gradients with altitude. This can serve to magnify the 1–2 K uncertainties on the T(p) profile in Figure 8(a), even if we consider the CIRS inversions to be "ideal" (Fletcher et al. 2016b). Additional errors arise from assumptions on vertical smoothing and variable information content with height, zonal averaging over Jupiter's spatially variable temperatures (Fletcher et al. 2016a), and the altitude level of the cloud-tracked zonal winds. Quantifying the effects of these unknowns in a meaningful way is challenging, but the parameters in Figure 8 represent our best estimate from the CIRS data and are sufficient to show qualitative trends, rather than quantitative values.

With these caveats in mind, we explore the implications of the vertical wavenumbers in Figure 8. In the GW case, we find that vertical propagation is allowed at all altitudes sampled (m is always real in Figure 8(g)). The value of m varies considerably within the c_x = −(15 ± 10) m s⁻¹ uncertainly envelope quoted by Simon et al. (2018), but the central value of m ∼ 1 × 10⁻³ m⁻¹ near 500–700 mbar is equivalent to a vertical wavelength of ∼6 km, or a third of a scale height. For IGWs in Figure 8(h), we find that m² < 0 for high pressures, but that vertical propagation is allowed for lower pressures. The transition between these regimes is sensitive to c_x, with more westward phase speeds (c_x ≈ −25 m s⁻¹) able to propagate vertically at deeper pressures (p < 500 mbar), whereas slower phase speeds (c_x ≈ −5 m s⁻¹) could only propagate in the upper troposphere (p < 300 mbar). Closer inspection of Equation (2) shows that IGW vertical propagation is inhibited when the intrinsic frequency ω is smaller than the Coriolis parameter f, which is the case for p > 400 mbar for waves with a c_x = −15 m s⁻¹ phase speed. The IGWs are not conclusively ruled out for higher pressures (p > 500 mbar), provided they form at the altitude at which they are observed, which is estimated to be ∼500 mbar from Hubble data (Simon et al. 2018). Finally, the vertical wavenumber for RWs is found to be negative almost everywhere—this is because ${k}^{2}\gg {\beta }_{e}/(u-{c}_{x})$ in Equation (6) for this short-period wave (so the value of c_x has negligible influence on m²), with the second term only gaining prominence when u ≈ c_x, which is the case for c_x = −5 m s⁻¹ in Figure 8(i). Given that the mesoscale wave bears little resemblance to RWs previously identified on Jupiter and the fact that vertical propagation is prohibited, we deem this to be the least likely explanation for these waves. Given that both c_x and the background zonal u from the thermal wind equation are significantly uncertain, these estimates of m² should be considered as qualitative guides only.

Frustratingly, further progress on identifying the nature of this wave pattern cannot be extracted from these measurements alone. Preliminary GCM modeling (Simon et al. 2018) is similarly inconclusive. Both GWs and IGWs are plausible explanations, with the former propagating more easily in the vertical throughout the upper troposphere. It is reasonable to hypothesize that the 5-μm brightness and the Hubble reflectivity are being modulated by the same aerosol layers somewhere in the 400–800 mbar range. Finally, it has been previously noted that the latitudinal gradient of quasi-geostropic potential vorticity (${\beta }_{e}={{dq}}_{G}/{dy}$, the "effective beta"; Andrews et al. 1987) changes sign across the NEB (Li et al. 2006; Rogers 2016). Figure 8(d) shows a complex vertical structure at 16°N–21°N, with the gradient changing sign several times in the 400–1000 mbar range. Such sign changes are a necessary (but not sufficient) condition for baroclinic instability following the Charney–Stern criterion (Charney & Stern 1962). While not conclusive, it is at the very least suggestive of mesoscale GWs or IGWs related to instabilities in the upper tropospheric aerosol layers (400–800 mbar), modulating both the Hubble reflectivity and the 5-μm brightness.