Constraints on the latitudinal profile of Jupiter's deep jets
E. Galanti, Y. Kaspi, K. Duer, L. Fletcher, A. P. Ingersoll, C. Li, G. S. Orton, T. Guillot, S. M. Levin, S. J. Bolton
CConstraints on the latitudinal profile of Jupiter’s deep jets
E. Galanti , Y. Kaspi , K. Duerl , L. Fletcher , A. P. Ingersolll ,C. Li , G. S. Orton , T. Guillot , S. M. Levin , and S. J. Bolton (Geophysical Research Letters, submitted)February 23, 2021 Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot, Israel. School of Physics and Astronomy, University of Leicester, Leicester, UK California Institute of Technology, Pasadena, CA, USA Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI, USA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, USA Observatoire de la Cote d’Azur, Nice, France Southwest Research Institute, San Antonio, Texas, TX, USA
AbstractThe observed zonal winds at Jupiter’s cloud tops have been shown to be closely linked to theasymmetric part of the planet’s measured gravity field. However, other measurements suggestthat in some latitudinal regions the flow below the clouds might be somewhat different from theobserved cloud-level winds. Here we show, using both the symmetric and asymmetric parts ofthe measured gravity field, that the observed cloud-level wind profile between 25 ◦ S and 25 ◦ Nmust extend unaltered to depths of thousands of kilometers. Poleward, the midlatitude deepjets also contribute to the gravity signal, but might differ somewhat from the cloud-level winds.We analyze the likelihood of this difference and give bounds to its strength. We also find thatto match the gravity measurements, the winds must project inward in the direction parallel toJupiter’s spin axis, and that their decay inward should be in the radial direction.
The zonal (east-west) wind at Jupiter’s cloud level dominate the atmospheric circulation, and strongly relate tothe observed cloud bands
Fletcher et al. (2020). The structure of the flow beneath the cloud level has beeninvestigated by several of the instruments on board the Juno spacecraft by means of gravity, infrared and microwavemeasurements
Bolton et al. (2017). Particularly, the gravity measurements were used to infer that the winds extenddown to roughly 3000 km, and that the main north-south asymmetry in the cloud-level wind extends to these greatdepths
Kaspi et al. (2018), resulting in the substantial values of the odd gravity harmonics J , J , J , and J . Theexcellent match between the sign and value of the predicted odd harmonics using the cloud-level wind Kaspi (2013)and the Juno gravity measurements
Iess et al. (2018), led to the inference that the wind profile at depth is similarto that at the cloud level
Kaspi et al. (2018, 2020). Here, we revisit in more detail the relation between the exactmeridional profile of the zonal flow and the gravity measurements, and study how much of the cloud-level windmust be retained in order to match the gravity measurements.Since the gravity measurements are sensitive to mass distribution, they are not very sensitive to the shallowlevels (0.5-240 bar) probed by Juno’s microwave radiometer (MWR,
Janssen et al. , 2017), as the density in thisregion is low compared to the deeper levels. Yet, the gravity measurements have substantial implications on theMWR region, since if the flow profile at depth (below the MWR region) resembles that at the cloud level it is likelythat the flow profile within the MWR region is not very different. In such a case, where the flow is barotropic, thisimplies via thermal wind balance that latitudinal temperature gradients in the MWR region are small, which hasimportant implication to the MWR analysis of water and ammonia distribution
Li et al. (2017);
Ingersoll et al. (2017);
Li et al. (2020). Thus, it is important to determine how strong the gravity constraint on the temperaturedistribution is, and what is its latitudinal dependence. 1 a r X i v : . [ a s t r o - ph . E P ] F e b he determination of the zonal flow field at depth is based on the measurements of the odd gravity harmonics, J , J , J , and J , which are uniquely related to the flow field Kaspi (2013). Using only four numbers to determinea 2D (latitude and depth) field poses a uniqueness challenge, and solutions that are unrelated to the observed cloud-level wind can be found
Kong et al. (2018), although the origin of such internal flow structure, completely unrelatedto the cloud-level winds, is not clear. In addition, these solutions require a flow of about 1 m s − at depth of 0.8 theradius of Jupiter ( ∼ Liu et al. (2008);
Wicht et al. (2019) is expectedto dampen such strong flows
Cao and Stevenson (2017);
Duer et al. (2019);
Moore et al. (2019). Recently, (
Galantiand Kaspi , 2021) showed that the interaction of the flow with the magnetic field in the semiconducting region canbe used as an additional constraint on the structure of the flow below the cloud level. With some modification ofthe observed cloud-level wind, well within its uncertainty range
Tollefson et al. (2017), a solution can be found thatexplains the odd gravity harmonics and abides the magnetic field constraints.All of the above mentioned studies assumed that if the internal flow is related to the observed surface winds,it will manifest its entire latitudinal profile. However, some evidence suggests that at some latitudinal regionsthe flow below the clouds might be different from the winds at the cloud level. The Galileo probe, entering theJovian atmosphere around planetocentric latitude 6.5 ◦ N Orton et al. (1998), measured winds that strengthenedfrom 80 ms − at the cloud level to ∼
160 ms − at a depth of 4 bars, from where it remains approximately constantuntil a depth of 20 bars where the probe stopped transmitting data Atkinson et al. (1998). Such a baroclinic sheargot further support in studies of equatorial hot spots
Li et al. (2006);
Choi et al. (2013). Recently,
Duer et al. (2020) showed that the MWR measurements of brightness temperature correlate to the zonal wind’s latitudinalprofile. They found that profiles differing to a limited extent from the cloud-level can still be consistent with bothMWR and gravity. Emanating from the correlations between MWR and the zonal winds,
Fletcher et al. (2021)suggested that the winds at some latitudes might strengthen from the cloud level to a depth of 4-8 bars, i.e. not farfrom where water is expected to be condensing, and only then begin to decay downward. Alternatively, based onstability considerations, it was suggested that while westward jets are not altered much with depth, the eastwardjets might increase by 50-100%
Dowling (1995);
Dowling (2020).Furthermore, in the
Kaspi et al. (2018) and
Galanti and Kaspi (2021) studies, the observed cloud-level wind hasbeen assumed to be projected into the planet interior along the direction parallel to the spin axis of Jupiter, basedon theoretical arguments (
Busse , 1970, 1976) and 3D simulations of the flow in a Jovian-like planet (e.g.,
Busse ,1994;
Kaspi et al. , 2009;
Christensen , 2001;
Heimpel et al. , 2016). Theoretically this requires the flow to be nearlybarotropic, which is not necessarily the case, particularly when considering the 3D nature of the planetary interior.Another assumption made is that the flow decays in the radial direction. This was based on the reasoning that anymechanism acting to decay the flow, such as the increasing conductivity (
Cao and Stevenson , 2017), compressibility(
Kaspi et al. , 2009), or the existence of a stable layer (
Debras and Chabrier , 2019;
Christensen et al. , 2020), willdepend on pressure and temperature, which to first order are a function of depth. However, if the internal flow isorganized in cylinders it might be the case that the mechanism acting to decay it strengthens also in the directionparallel to the spin axis.Here we investigate what can be learned about the issues discussed above, based on the measured gravity field,considering both the symmetric and asymmetric components of the gravity field measurements. We study theability to fit the gravity measurements with a cloud-level wind that is limited to a specific latitudinal range, thusidentifying the regions where the observed cloud-level wind is likely to extend deep, and the regions where theinterior flow might differ (section 3). We also examine whether a stronger wind at the 4-8 bar level is compatiblewith the gravity measurements, and if the assumptions regarding the relation of the internal flow to the cloud levelcan be relaxed (section 4). Finally, we examine the latitudinal dependence of the wind-induced gravity harmonicswhen magnetohydrodynamics considerations are used as additional constraints (section 5).
We examine several aspects of the flow structure that might influence the ability to explain the gravity measurements.First, stemming from the notion that at some latitudinal regions the flow below the cloud level might differ fromthe observed, we set cases in which the cloud-level wind is truncated at a specific latitude (Fig. 1a). The truncationis done by applying a shifted hemispherically symmetric hyperbolic tangent function with a transition width of 5 ◦ ,to allow a smooth truncation of the wind from the observed flow. The result is a wind profile that equatorward ofthe truncation latitude is kept as in the cloud-top observations, and poleward decays quickly to zero. We examine18 cases with truncation latitudes ◦ , ◦ , ◦ , ..., ◦ . Note that all of the cloud-level wind setups used in this studyare based on the analysis of the HST Jupiter images during Juno’s PJ3 ( Tollefson et al. , 2017)[, Figure 1a, grayline], and that in all figures and calculations we use the planetocentric latitude.2 u ( m s - ) Wind truncated outside a latitudinal region (a)
ObsLat 20Lat 25Lat 50Lat 75 -80 -60 -40 -20 0 20 40 60 80
Latitude -50050100150 u ( m s - ) (b) Random winds outside 25S-25N region
Figure 1: (a) The observed wind (
Tollefson et al. , 2017) (gray), and variant examples with the wind truncatedpoleward of the latitudes 20 ◦ , 25 ◦ , 50 ◦ , and 75 ◦ . (b) The case of wind truncated poleward of the 25 ◦ latitude(black), along with examples of random jets added in the truncated regions.Next, we examine cases in which a different wind structure exists poleward of the truncation latitude. Assuch, unknown wind structures could possibly replace the observed cloud-level wind at shallow depths of around 5-10 bars (e.g., as can be inferred from MWR, depending on how microwave brightness temperatures are interpreted,see Fletcher et al. ◦ S − ◦ N , and replaced with 1000 random wind structuresthat mimic the latitudinal scale and strength of the observed winds (Fig. 1b).The cloud-level wind profile is first projected inward in the direction parallel to the spin axis ( Kaspi et al. ,2010), and then made to decay radially assuming a combination of functions (Fig. 2a), that allow a search forthe optimal decay profile (
Kaspi et al. , 2018;
Galanti and Kaspi , 2021, see also supporting information - SI). Inaddition, we examine two additional cases: a case in which the cloud-level wind is both projected and decays in theradial direction (Fig. 2b), and a case in which the wind is both projected and decays in the direction of the spinaxis (Fig. 2c).Given a zonal flow structure, thermal wind balance is used to calculate an anomalous density structure associatedwith large-scale flow in fast rotating gas giants. The density field is then integrated to give the 1-bar gravity fieldin terms of the zonal gravity harmonics (
Kaspi et al. , 2010). Using an adjoint based optimization, a solutionfor the flow structure is searched for, such that the model solution for the gravity field is best fitted to the partof the measured gravity field that can be attributed to the wind (
Galanti and Kaspi , 2016). The odd gravityharmonics are attributed solely to the wind, therefore we use the Juno measured values J = ( − . ± . × − , J = ( − . ± . × − , J = (12 . ± . × − , and J = ( − . ± . × − ( Iess et al. , 2018). Thelowest even harmonics J and J are dominated by the planet’s density structure and shape and cannot be used inour analysis, but interior models can give a reasonable estimate for the expected wind contribution for the highereven harmonics J , J , and J ( Guillot et al. , 2018). Based on the Juno measurements and the range of interiormodel solutions, the expected wind-induced even harmonics are estimated as ∆ J = 1 × − ± (0 . × − , ∆ J = 3 . × − ± (2 .
46 + 0 . × − , and ∆ J = − × − ± (6 .
94 + 0 . × − . Note that the uncertaintyassociated with each even harmonic has contributions from both the measurement and the range of interior modelsolutions (first and second uncertainties, respectively). The large uncertainties in the estimated wind-induced evenharmonics suggest that our analysis is limited to their order of magnitude and sign.Finally, in order to isolate the latitudinal dependence from the general ability to fit the gravity harmonics, wefirst optimize the cloud-level wind so that the odd gravity harmonics are fitted perfectly ( Galanti and Kaspi , 2021).The modified wind is very similar to the observed (Fig. S1), well within the uncertainty of the cloud-level windobservation (
Tollefson et al. , 2017), therefore retaining all the observed latitudinal structure responsible for the3 a) -1-0.500.510 0.5 1 (b) -1-0.500.510 0.5 1 (c) -1-0.500.510 0.5 1 -120-80-4004080120 u ( m s - ) Figure 2: Options of cloud-level wind projection and decay profiles, shown for an example of a sharp decay at a3000 km distance from the surface. (a) Projection in the direction parallel to the spin axis and decay in the radialdirection. (b) Projection and decay in the radial direction. (c) Projection and decay in the direction parallel to thespin axis.wind-induced gravity harmonics.
We begin by analyzing the effect of the cloud-level wind latitudinal truncation on the ability to explain the gravityharmonics. For each wind setup, the internal flow structure is modified until the best fit to the 4 odd harmonicsand the 3 even harmonics is reached (Fig. 3). The cost-function (Fig. 3a), a measure for the overall differencebetween the measurements and the model solution (see SI), reveals the contribution of each latitudinal region tothe solution. First, as expected, when the cloud-level wind is retained at all latitudes, the solution for the oddharmonics is very close to the measurements (Fig. 3b-d, red dots). Importantly, the same optimal flow structureexplains very well the even harmonics (Fig. 3e-f, red dots). This is additional evidence that the observed cloud-levelwind is dynamically related to the gravity field.Examining the latitudinal dependence of the truncation, it is evident that truncating the observed cloud-levelwind closer to the equator than ◦ S − ◦ N prevents any flow structure that could explain the gravity harmonics.It is most apparent in the odd harmonics (Fig. 3b-d) where the optimal solutions (dark blue circles) are close tozero and far from the measured values. It is also the case for ∆ J , but for ∆ J and ∆ J the solutions are alwaysinside the uncertainty: in ∆ J because the measured value is very small, and in ∆ J because the uncertainty isvery large. Considering the cloud-level wind profile (Fig. 1a, black), it is not surprising that truncating the windspoleward of ◦ S − ◦ N makes the difference in the solution, as this is where the positive (negative) jet in thenorthern (southern) hemisphere are found, and project strongly on the low order odd harmonics. Note that even a5 ◦ difference (Fig. 1a, red, truncation at ◦ S − ◦ N ) prevents a physical solution from being reached. Once theseopposing jets are included, the flow structure contains enough asymmetry to explain very well J and J whichhave the largest values of the odd harmonics.However, with the ◦ S − ◦ N truncation, the model solutions for J and J are still outside the measureduncertainty. Only when the influence of the zonal winds throughout the ◦ S − ◦ N range (Fig. 1a, cyan) isincluded, then the lower odd harmonics can be explained with the cloud-level wind profile. The optimal decayfunction for each case (Fig. 3g), emphasize the robustness of the solutions. When only the equatorial region isretained, the optimization is trying (with no success) to include as much mass in the region where the cloud-levelwind is projected inward. But once the winds at ◦ S − ◦ N are included, then the decay function of the windsettles on a similar profile, with some small variations between the cases. Note that repeating these experiments withthe exact Tollefson et al. (2017) cloud-level wind profile, does not change substantially the main results (Fig. S2),thus ensuring the robustness of the results.The same methodology can be applied to a cloud-level wind that is truncated equatorward of a latitudinal region(Fig. S3). The analysis shows that a wind truncated equatorward of a latitude larger than ◦ S − ◦ N does notallow a plausible solution to be reached. Consistently with the above experiment, the deep jets at ◦ S − ◦ N are4 Truncation latitude C o s t f un c t i on (a) -4 0-8-40 J J (b) -8 -4 004812 J J (c) J J (d) J J (e) J J (f) Depth (km) D e c a y f un c t i on (g) Figure 3: Latitude-dependent solutions as function of the truncation latitude. (a) The overall fit of the modelsolution to the measurements (cost function). Each case is assigned with a different color that is used in thefollowing panels, ranging from latitude 5 ◦ (blue) to 90 ◦ (no truncation, red). (b-f) the solutions for the differentgravity harmonics (colors), and the measurement (black). (g) the decay function associated with each solution.necessary to fit gravity harmonics. Specifically, there is a gradual deterioration of the solution in the truncationregion of 0 ◦ to 20 ◦ , which is related solely to the even harmonics ∆ J , ∆ J , and ∆ J . Once the wind is truncatedinside 10 ◦ S-10 ◦ N the solution for ∆ J and ∆ J is outside the uncertainty range, and ∆ J moves further away fromthe measurement. This is due to the strong eastward jets at 6 ◦ S and 6 ◦ N. Next, we examine several variants to the wind setups. In section 3 we showed that the jets between 25 ◦ S and25 ◦ N are crucial for explaining the gravity harmonics, and therefore should not differ much below the cloud level.However, in the regions where the wind is truncated it should be examined whether a flow below the cloud levelthat is completely different might still allow matching the gravity harmonics. We therefore examine a case wherethe cloud-level wind is truncated poleward of ◦ S − ◦ N , and in the truncated regions random jets are added tosimulate different possible scenarios (Fig. 1b, see SI for definition). The gravity harmonic solutions for 1000 differentcases is shown in Fig. 4 (a-c). The largest effect the random jets have is on J and J , with considerable effect also onthe other odds and even harmonics. About 4% of the cases provide a good match to all the measurements (green),therefore it is statistically possible that some combination of jets unseen at the cloud level at the mid-latitudes,with amplitude of up to ± m s − , are responsible for part of the gravity signal. Doubling (halving) the randomjets strength results in only 1.1% (1.2%) of the solutions to fit the gravity measurement (SI, Fig. S7), suggestingthat if alternative jets exists in the mid-latitudes, their amplitude should be around ± m s − . These results areconsistent with Duer et al. (2020) who did a similar analysis, but taking the full cloud level winds and showed thatsolutions differing from the cloud level are possible but statistically unlikely ( ∼ ).Aside from modifications to the cloud-level wind, we also examine cases in which the projection of the flowbeneath the cloud level is modified. For simplicity, we examine these cases with the observed cloud-level wind5 J J (a) J J (b) J J (c) J J J J J J J -15-10-505101520 J n (d) MeasurementsKaspi 2018Radial projectionZ decayDoubled wind
Figure 4: (a-c) Solutions with the cloud-level wind truncated poleward of ◦ S − ◦ N and replaced with random jetsthere (Fig. 1b). Shown are the solutions for 1000 random cases (gray), and within those the solution which matchesall the gravity harmonics (green). Also shown are the solution with no random winds (blue, corresponding to the25 ◦ case in Fig. 3), the solution with no truncation of the winds (red, corresponding to the 90 ◦ case in Fig. 3) andthe Juno measurements (black). (d) Solutions for cases with cloud-level wind projected in the radial direction (blue;Fig. 2b) and wind decayed in the direction parallel to the spin axis (magenta; Fig. 2c), and a doubled cloud-levelwind (green). Also shown are the measurements (black), and the solution with the unaltered cloud-level wind (red; Kaspi et al. , 2018).spanning the full latitudinal range. Projecting the wind radially and keeping the decay radial (Fig. 2b), we findthat there is no plausible solution for flow structure under these assumptions that would give a good fit to thegravity measurements (Fig. 4d, blue). The best-fit model solution for all J n is far from the measurements, welloutside their uncertainty range, and does not even match J in sign. Next, we consider a case in which the decay ofthe winds is in the direction parallel to the spin axis (Fig. 2c). Here the optimal solution for the odd harmonics isfar from the measured values (Fig. 4d, magenta), while for the even harmonics the solution is within the uncertaintyrange. However, in this case the winds needs to be very deep, extending to ∼ km, where the interaction withthe magnetic field is extremely strong ( Cao and Stevenson , 2017;
Galanti et al. , 2017;
Galanti and Kaspi , 2021).Finally, following the suggestion that the cloud-level wind might get stronger with depth before they decay (e.g.,
Fletcher et al. , 2021), we conduct an experiment in which we double the cloud-level wind. Interestingly, a plausiblesolution can be achieved (Fig. 4d, green crosses), with a decay profile similar to the
Kaspi et al. (2018) solution,but with the winds decaying more baroclinicaly in the upper 2000 km, and then decaying slower (Fig. S6).
In Jupiter, the increased conductivity with depth (e.g.,
French et al. , 2012;
Wicht et al. , 2019) suggests that theflow might be reduced to very small values in the semiconducting region (deeper than 2000 km,
Cao and Stevenson ,2017). Using flow estimates in the semiconducting region based on past magnetic secular variations (
Moore et al. ,2019),
Galanti and Kaspi (2021) gave a revised wind decay profile that can explain both the gravity harmonicsand the constraints posed by the secular variations. We follow this approach, setting the flow strength in thesemiconducting region (deeper than 2000 km, see
Galanti and Kaspi , 2021) to be a sharp exponential function(Fig. 5g, right part). Given this inner profile of the decay function, the outer part of the decay function can besearched for, together with the optimal cloud-level wind, that will result in the best fit to the odd measured gravityharmonics. The optimal cloud-level wind (Fig. S1b) is very similar to the observed wind, with deviations that are6 Truncation latitude C o s t f un c t i on (a) -4 0 4-8-40 J J (b) -8 -4 004812 J J (c) J J (d) -4 0 404 J J (e) J J (f) Depth (km) D e c a y f un c t i on (g) Figure 5: Same as Fig. 3, but for a case where the flow profile in the semiconducting region is restricted to complywith secular variations consideration.within the uncertainties.Using the modified cloud-level wind, the shape of the decay function in the outer neutral region is optimizedto allow the best-fit to the odd and even gravity harmonics (Fig. 5b-g). In addition to the odd harmonics, whichare expected to fit the measurements, the model also fits very well the even harmonics, despite the limited range ofpossible decay profiles in the outer region (Fig. 5g). The latitudinal dependence reveals that the range of ◦ S − ◦ N is needed in order to allow a good fit, especially for J and J . Similar to the case with gravity-only constraints,fitting the even harmonics, as well as J and J ., requires mostly the cloud-level wind inside the ◦ S − ◦ N region.Thus, even when including the strong magnetic constraint, the dominance of the ◦ S − ◦ N region remains robust. References
Atkinson, D. H., J. B. Pollack, and A. Seiff, The Galileo probe doppler wind experiment: Measurement of the deepzonal winds on Jupiter,
J. Geophys. Res. , , 22,911–22,928, doi:10.1029/98JE00060, 1998.Bolton, S. J., et al., Jupiter’s interior and deep atmosphere: The initial pole-to-pole passes with the Juno spacecraft, Science , , 821–825, doi:10.1126/science.aal2108, 2017.Busse, F. H., Thermal instabilities in rapidly rotating systems, J. Fluid Mech. , , 441–460, doi:10.1017/S0022112070001921, 1970.Busse, F. H., A simple model of convection in the Jovian atmosphere, Icarus , , 255–260, doi:10.1016/0019-1035(76)90053-1, 1976.Busse, F. H., Convection driven zonal flows and vortices in the major planets, Chaos , (2), 123–134, doi:10.1063/1.165999, 1994.Cao, H., and D. J. Stevenson, Zonal flow magnetic field interaction in the semi-conducting region of giant planets, Icarus , , 59–72, doi:10.1016/j.icarus.2017.05.015, 2017.7hoi, D. S., A. P. Showman, A. R. Vasavada, and A. A. Simon-Miller, Meteorology of Jupiter’s equatorial hot spotsand plumes from Cassini, Icarus , (2), 832–843, doi:10.1016/j.icarus.2013.02.001, 2013.Christensen, U. R., Zonal flow driven by deep convection in the major planets, Geophys. Res. Lett. , , 2553–2556,doi:10.1029/2000GL012643, 2001.Christensen, U. R., J. Wicht, and W. Dietrich, Mechanisms for Limiting the Depth of Zonal Winds in the GasGiant Planets, Astrophys. J. , (1), 61, doi:10.3847/1538-4357/ab698c, 2020.Debras, F., and G. Chabrier, New models of Jupiter in the context of Juno and Galileo, Astrophys. J. , , 100–,doi:10.3847/1538-4357/aaff65, 2019.Dowling, T. E., Estimate of Jupiter’s deep zonal-wind profile from Shoemaker-Levy 9 data and Arnold’s secondstability criterion, Icarus , , 439–442, doi:10.1006/icar.1995.1169, 1995.Dowling, T. E., Jupiter-style Jet Stability, The Planatary Science Journal , , 6, doi:10.3847/PSJ/ab789d, 2020.Duer, K., E. Galanti, and Y. Kaspi, Analysis of Jupiter’s deep jets combining Juno gravity and time-varyingmagnetic field measurements, Astrophys. J. Let. , (2), L22, doi:10.3847/2041-8213/ab288e, 2019.Duer, K., E. Galanti, and Y. Kaspi, The Range of Jupiter’s Flow Structures that Fit the Juno Asymmetric GravityMeasurements, J. Geophys. Res. (Planets) , (8), e06292, doi:10.1029/2019JE006292, 2020.Fletcher, L. N., Y. Kaspi, T. Guillot, and A. P. Showman, How Well Do We Understand the Belt/Zone Circulationof Giant Planet Atmospheres?, Space Sci. Rev. , (2), 30, doi:10.1007/s11214-019-0631-9, 2020.Fletcher, L. N., et al., Jupiter’s temperate belt/zone contrasts revealed at depth by Juno microwave observations, submitted , 2021.French, M., A. Becker, W. Lorenzen, N. Nettelmann, M. Bethkenhagen, J. Wicht, and R. Redmer, Ab initio simu-lations for material properties along the Jupiter adiabat, Astrophys. J. Sup. , (1), 5, doi:10.1088/0067-0049/202/1/5, 2012.Galanti, E., and Y. Kaspi, An Adjoint-based Method for the Inversion of the Juno and Cassini Gravity Measurementsinto Wind Fields, Astrophys. J. , (2), 91, doi:10.3847/0004-637X/820/2/91, 2016.Galanti, E., and Y. Kaspi, Combined magnetic and gravity measurements probe the deep zonal flows of the gasgiants, MNRAS , (2), 2352–2362, doi:10.1093/mnras/staa3722, 2021.Galanti, E., H. Cao, and Y. Kaspi, Constraining Jupiter’s internal flows using Juno magnetic and gravity measure-ments, Geophys. Res. Lett. , (16), 8173–8181, doi:10.1002/2017GL074903, 2017.Guillot, T., et al., A suppression of differential rotation in Jupiter’s deep interior, Nature , , 227–230, doi:10.1038/nature25775, 2018.Heimpel, M., T. Gastine, and J. Wicht, Simulation of deep-seated zonal jets and shallow vortices in gas giantatmospheres, Nature Geoscience , , 19–23, doi:10.1038/ngeo2601, 2016.Iess, L., et al., Measurement of Jupiter’s asymmetric gravity field, Nature , , 220–222, doi:10.1038/nature25776,2018.Ingersoll, A. P., et al., Implications of the ammonia distribution on Jupiter from 1 to 100 bars as measured by theJuno microwave radiometer, Geophys. Res. Lett. , (15), 7676–7685, doi:10.1002/2017GL074277, 2017.Janssen, M. A., et al., MWR: Microwave Radiometer for the Juno Mission to Jupiter, Space Sci. Rev. , (1-4),139–185, doi:10.1007/s11214-017-0349-5, 2017.Kaspi, Y., Inferring the depth of the zonal jets on Jupiter and Saturn from odd gravity harmonics, Geophys. Res.Lett. , , 676–680, doi:10.1029/2009GL041385, 2013.Kaspi, Y., G. R. Flierl, and A. P. Showman, The deep wind structure of the giant planets: Results from an anelasticgeneral circulation model, Icarus , (2), 525–542, doi:10.1016/j.icarus.2009.03.026, 2009.8aspi, Y., W. B. Hubbard, A. P. Showman, and G. R. Flierl, Gravitational signature of Jupiter’s internal dynamics, Geophys. Res. Lett. , , L01,204, doi:10.1029/2009GL041385, 2010.Kaspi, Y., E. Galanti, A. P. Showman, D. J. Stevenson, T. Guillot, L. Iess, and S. J. Bolton, Comparison of theDeep Atmospheric Dynamics of Jupiter and Saturn in Light of the Juno and Cassini Gravity Measurements, Space Sci. Rev. , (5), 84, doi:10.1007/s11214-020-00705-7, 2020.Kaspi, Y., et al., Jupiter’s atmospheric jet streams extend thousands of kilometres deep, Nature , , 223–226,doi:10.1038/nature25793, 2018.Kong, D., K. Zhang, G. Schubert, and J. D. Anderson, Origin of Jupiter’s cloud-level zonal winds remains a puzzleeven after Juno, Proc. Natl. Acad. Sci. U.S.A. , (34), 8499–8504, doi:10.1073/pnas.1805927115, 2018.Li, C., et al., The distribution of ammonia on Jupiter from a preliminary inversion of Juno microwave radiometerdata, Geophys. Res. Lett. , (11), 5317–5325, doi:10.1002/2017GL073159, 2017.Li, C., et al., The water abundance in Jupiter’s equatorial zone, Nature Astronomy , , 609–616, doi:10.1038/s41550-020-1009-3, 2020.Li, L., A. P. Ingersoll, A. R. Vasavada, A. A. Simon-Miller, A. D. Del Genio, S. P. Ewald, C. C. Porco, andR. A. West, Vertical wind shear on Jupiter from Cassini images, J. Geophys. Res. (Planets) , (E4), E04004,doi:10.1029/2005JE002556, 2006.Liu, J., P. M. Goldreich, and D. J. Stevenson, Constraints on deep-seated zonal winds inside Jupiter and Saturn, Icarus , , 653–664, doi:10.1016/j.icarus.2007.11.036, 2008.Moore, K. M., H. Cao, J. Bloxham, D. J. Stevenson, J. E. P. Connerney, and S. J. Bolton, Time variation ofJupiter’s internal magnetic field consistent with zonal wind advection, Nature Astronomy , , 730–735, doi:10.1038/s41550-019-0772-5, 2019.Orton, G. S., et al., Characteristics of the Galileo probe entry site from earth-based remote sensing observations, J. Geophys. Res. , , 22,791–22,814, doi:10.1029/98JE02380, 1998.Tollefson, J., et al., Changes in Jupiter’s zonal wind profile preceding and during the Juno mission, Icarus , ,163–178, doi:10.1016/j.icarus.2017.06.007, 2017.Wicht, J., T. Gastine, L. D. V. Duarte, and W. Dietrich, Dynamo action of the zonal winds in Jupiter, Astron. andAstrophys. ,629