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REVIEW 3 major objections 4 minor 85 references

Reconciling Jupiter's Vertical Motions with the Observed Cloud Structure in the Upper Troposphere

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Jupiter's bright zones are upwelling after all — once the eddies' Stokes drift is counted in, the paper argues, the cloud bands and the dynamics agree.

desk verdict A clean TEM-scaling argument that likely resolves Jupiter's upwelling-downwelling contradiction, but the sign and magnitude rest on a constant-K PV diffusion closure that the paper doesn't yet stress-test. read the letter →

arxiv 2509.02759 v1 pith:ZCOLJU3O submitted 2025-09-02 astro-ph.EP

João M. Mendonça , Tapio Schneider , Junjun Liu , Yuan Lian This is my paper · ORCID
classification astro-ph.EP
keywords JupitertransformedEulerianmeanatmosphericcirculationpotentialvorticitybeltsandzoneseddyfluxesammoniacloudsgeneralmodel
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Jupiter's cloud bands have long posed a puzzle: the bright zones appear to be upwelling and the dark belts downwelling, yet the momentum balance of the observed eddies implies the opposite sense of vertical motion. This paper argues that the contradiction dissolves when tracers are tracked by the transformed Eulerian mean (TEM) flow — the Eulerian mean plus an eddy-driven Stokes drift — rather than by the Eulerian mean alone. Using potential vorticity gradients implied by the observed winds and a mixing-length diffusivity, the authors estimate TEM upwelling in zones and downwelling in belts, about an order of magnitude stronger than the Eulerian mean vertical velocity. A global circulation model of Jupiter's upper troposphere reproduces the pattern. If right, the work reconciles dynamics with cloud appearance and identifies turbulent eddies, not the mean flow, as the main agents of vertical tracer transport.

What carries the argument

The load-bearing object is the transformed Eulerian mean (TEM) circulation, an approximation of the Lagrangian mean flow that adds a Stokes-drift term built from meridional eddy heat fluxes to the Eulerian mean. Its key identity, f v̄* = −v′q′, sets the TEM meridional flow by the eddy potential vorticity flux rather than the eddy momentum flux divergence; the TEM vertical flow follows from continuity. Combined with the downgradient diffusive closure v′q′ ∼ −K ∂yq̄, with diffusivity K estimated from observed eddy scales, and with Jupiter's mean potential vorticity gradient being barotropically dominated, this makes the TEM meridional flow converge in belts and diverge in zones — hence upwelli

What would settle it

Measure, at the cloud level and outside the equatorial jet, the meridional eddy flux of potential temperature (equivalently, the baroclinic part of the Eliassen-Palm flux). If that flux is too small for the Stokes-drift term to dominate the Eulerian mean meridional flow, or if its sign pattern is not what downgradient diffusion of potential vorticity implies, the claimed TEM upwelling in zones would not hold. A more direct falsification would be a cloud-tracking or tracer-inversion estimate of vertical velocity showing downwelling in the bright zones.

Watch

Extended reading notes

Core claim

The paper's central claim is that the apparent contradiction between Jupiter's cloud bands and its inferred vertical motions is an artifact of averaging. Nearly conserved tracers such as ammonia are advected not by the Eulerian mean flow but by the transformed Eulerian mean (TEM) circulation, which adds the eddies' Stokes drift. From the potential vorticity structure implied by the observed jets and a downgradient diffusive closure for the eddy potential vorticity flux, the TEM meridional flow is poleward almost everywhere, strongest in prograde jets; continuity then gives TEM upwelling in zones and downwelling in belts, with magnitudes about an order of magnitude stronger than the Eulerian

Load-bearing premise

Everything hinges on the assumption that eddy potential vorticity fluxes are downgradient and diffusive, with a single constant eddy diffusivity; if real Jupiter fluxes are counter-gradient, or if the jet cores act as strong transport barriers that shrink the diffusivity there, the computed sign of the vertical motion in zones and belts could change.

Editorial extensions

If this is right

  • The apparent conflict between eddy-momentum-based circulation inferences and cloud appearance in Jupiter's belts and zones is resolved: the eddy-driven (Stokes drift) component of the flow reverses the sign of vertical motion relative to the Eulerian mean.
  • Transient tracers such as ammonia in the upper troposphere are transported by a circulation whose upwelling regions coincide with the bright zones where ammonia ice clouds form.
  • The TEM vertical velocity below the cloud layer is about an order of magnitude larger than the Eulerian mean value, so turbulent eddies, not the mean meridional circulation, dominate vertical tracer transport in the upper troposphere.
  • The circulation is driven from the top down: shallow upper-tropospheric eddy fluxes force overturning cells that close in a deep frictional layer, consistent with the downward-control principle.
  • Simulations that reproduce the observed jet structure and energetics produce the same belt-zone pattern of TEM vertical motion, making the inference more than a scaling argument.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the TEM picture is right, the vertical motion that shapes Jupiter's ammonia cloud bands is largely a tracer-transport (Lagrangian) motion rather than a mass motion, and the Eulerian circulation could be nearly its reverse; a direct test would be measuring the meridional eddy heat flux at cloud level, since a small Eliassen-Palm contribution would make the TEM and Eulerian circulations coincide
  • The same argument, with adjusted parameters, should apply to Saturn and other giant planets whose banded cloud structure is also anticorrelated with the Eulerian-mean circulation inferred from eddy momentum fluxes; the mechanism predicts TEM upwelling in their bright zones as well.
  • The constant-diffusivity assumption yields a specific, testable relation between jet curvature and vertical velocity: upwelling should be strongest where the mean potential vorticity gradient is most positive (prograde jet cores) and downwelling where it is most negative; cloud-top ammonia contrast maps could be compared quantitatively with this pattern.
  • Because the TEM vertical velocity is an order of magnitude larger than the Eulerian one, global tracer budgets for Jupiter — for example, ammonia supply from depth or lightning occurrence in belts — may need to be re-evaluated in terms of Lagrangian-mean transport rather than Eulerian mean motion.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper addresses the apparent contradiction between two inferences about Jupiter's upper troposphere: eddy momentum flux convergence implies an Eulerian mean meridional circulation with downwelling in zones and upwelling in belts, while cloud and haze structure suggests upwelling in zones and downwelling in belts. The authors argue that the relevant tracer-transport circulation is the transformed Eulerian mean (TEM), not the Eulerian mean. Using the observed zonal wind profile, a downgradient potential vorticity flux closure v'q' ~ -K ∂y q̄ with a constant eddy diffusivity K, and neglecting the stretching contribution to the mean PV gradient, they infer a TEM meridional flow that is generally poleward and an order of magnitude stronger than the Eulerian mean. Its convergence/divergence pattern then implies TEM upwelling in zones and downwelling in belts, resolving the contradiction. The arguments are supplemented by GCM simulations from Young et al. (2019a,b), which qualitatively reproduce the sign pattern of the TEM vertical velocity.

Significance. If the central claim is correct, it is an important step: it would replace the apparent contradiction with a circulation whose vertical branches match the observed cloud structure and which is the relevant mean flow for ammonia and other tracers. The paper has real strengths: the scaling argument is transparent, it makes explicit use of observed Cassini eddy momentum fluxes and zonal winds, and the authors candidly acknowledge the main caveats, including the uncertain eddy diffusivity and the limitations of the GCM. The GCM data are made available. The result is also falsifiable in principle through future tracer or heat-flux observations. However, the chain from Eqs. (10)-(12) is the load-bearing part, and it currently rests on an unmeasured closure; the GCM provides only qualitative support. The manuscript is therefore promising but not yet conclusive.

major comments (3)
  1. [§2.2, Eqs. (10)–(12)] The headline claim—TEM vertical motion is positive in zones and negative in belts and an order of magnitude stronger than the Eulerian mean—rests entirely on the downgradient closure v′q′ ∼ −K∂y q̄ with constant K. Neither v′q′ nor K is measured on Jupiter. If K has local minima at prograde jet cores, as the paper acknowledges from transport-barrier studies, the product K∂y q̄ need not peak there; the convergence/divergence of v̄* and hence the sign of w̄* can change in individual bands. The GCM does not provide the missing test: its TEM and Eulerian meridional flows are comparable in magnitude, and its eddy velocities are a factor ~3 smaller, so its effective K differs from the 6×10^6 m^2 s^-1 assumed in Fig. 1. Please report local-K diagnostics from the GCM, or an observational constraint on v′q′, before the central sign claim is considered established.
  2. [§3.1.1, Fig. 4] The GCM is the only independent check of the scaling, yet Fig. 4 shows that the simulated TEM and Eulerian mean meridional flows are of similar magnitude, not an order apart. The text attributes this to weaker eddy amplitudes and smaller S, but that means the model does not reproduce the assumed K or the claimed dominance of the Stokes-drift contribution. To validate the observational inference, the model should be diagnosed to show whether the sign pattern of w̄* follows from the same balance (Eq. 10) and to identify why the magnitude ratio differs. Without this, the GCM supports qualitative sign consistency but not the 'order of magnitude' part of the central claim.
  3. [§2.2, Eq. (8)] The potential vorticity gradient in Eq. (8) contains a stretching term that is discarded on the authority of Read et al. (2006)'s ~10% estimate. This is defensible as a first-order scaling, but it becomes load-bearing where the barotropic part ∂y(f+ζ) is small, e.g., near retrograde jet cores and band edges, where the sign of ∂y q̄ may be controlled by the stretching term. The paper should either quantify the stretching contribution from the GCM temperature field at the levels shown in Fig. 1, or restrict the sign claim to latitudes where the barotropic term clearly dominates.
minor comments (4)
  1. [§2.2, after Eq. (12)] The eddy diffusivity is written as K ∼ V L ∼ 6 × 10^6 m s^-2; the units should be m^2 s^-1. The same typo appears in the Fig. 1 caption.
  2. [§3] In the list of tracers, 'hydrogen sulfilde (H2S)' should be 'hydrogen sulfide (H2S)'.
  3. [§3.1.1, Eqs. (13)–(15)] The S/I = 0.05 threshold is described as chosen for continuity with the standard TEM at 200 mbar. Since Fig. 5 extends the residual circulation to depth using this choice, a brief sensitivity test or a statement of how the deep pattern changes with the threshold would aid robustness.
  4. [Fig. 1] The four panels use two vertical axes with different scales and line styles; a small legend or explicit axis labels for the orange and dashed-blue curves in each panel would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the TEM upwelling-in-zones pattern follows from observed winds plus an openly stated downgradient PV closure; cloud structure is used only as an independent consistency check.

full rationale

Walking the derivation chain: the Eulerian mean meridional flow follows from Eq. (1)/(3), vbar ~ S/f, using the observed eddy momentum flux divergence S (Salyk et al. 2006). The TEM flow is then obtained from the standard identity f vbar* = -v'q' (Eq. 10) and the explicitly stated downgradient closure v'q' ~ -K d(y) qbar (Eq. 11), with K estimated as V L from observed eddy velocity and length scales (V ~ 3 m/s, L ~ 2000 km), not tuned to the cloud-implied vertical velocity. Equation (12) then maps the observed zonal-wind curvature, via the absolute vorticity gradient, into the TEM meridional flow; continuity gives the TEM vertical velocity. Zones and belts are defined by the observed meridional shear of the zonal wind (anticyclonic vs. cyclonic), independently of the cloud brightness used for comparison. The cloud/haze inference enters only as the benchmark in Figs. 1d and 4, not as a fitted target, so the sign of w* in zones and belts is not imposed by the cloud data. The GCM (Young et al. 2019) independently reproduces the same sign pattern without invoking the constant-K closure, serving as an external testbed. The constant-K downgradient assumption is explicitly acknowledged with caveats about jet-core transport barriers; this is a robustness limitation, not a circular step. The self-citations (Schneider and Liu 2009; Liu and Schneider 2010) support the shallow-layer/energetic context and jet-formation mechanisms, but the central TEM sign result does not reduce to them: Eqs. (10)-(12) plus observed winds suffice. No step reduces to its input by construction, so no circular steps are identified.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central inference uses one fitted parameter (K) and several standard dynamical assumptions. The key unverified element is the downgradient PV flux closure; the rest are standard GFD tools. No new entities are postulated.

free parameters (3)
  • Eddy diffusivity K = ~6e6 m^2/s
    Mixing length estimate K ~ V L with V ~ 3 m/s (Salyk et al. 2006) and L ~ 2000 km. Controls magnitude of TEM meridional flow, not its sign.
  • Layer thickness H = 20 km
    Used to convert horizontal divergence to vertical velocity w ~ (H/2) div v. Affects magnitude only.
  • S/I threshold = 0.05
    Ad hoc cutoff in the modified TEM formulation (Eq. 15) to keep the standard TEM at 200 mbar; does not affect the central claim.
assumptions (6)
  • domain assumption Quasigeostrophic scaling: f vbar ~ S outside equatorial region
    Used to relate eddy momentum flux divergence to Eulerian mean meridional flow (Eq. 1).
  • domain assumption Downgradient diffusive PV flux closure: v'q' ~ -K ∂y qbar
    Central closure for inferring TEM meridional flow (Eq. 11); unverified and potentially modified by jet transport barriers.
  • domain assumption Mean PV gradient dominated by barotropic term; stretching neglected (~10%)
    Used to approximate ∂y qbar from observed zonal winds (Section 2.2).
  • domain assumption TEM circulation closes at depth via downward control
    Assumed to link upper-tropospheric horizontal divergence to lower-tropospheric vertical motion (Haynes et al. 1991).
  • domain assumption Tracers such as ammonia are advected by the TEM (Lagrangian mean) flow
    Required to interpret TEM vertical motion as relevant for cloud structure.
  • domain assumption Statistically steady state over decadal timescales
    Allows neglect of time derivatives in zonal momentum balance; supported by Voyager/Cassini wind comparisons.

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Cite this review

Pith. "Pith review of Reconciling Jupiter's Vertical Motions with the Observed Cloud Structure in the Upper Troposphere." pith.science (2026). https://pith.science/paper/ZCOLJU3O

@misc{pith2026250902759,
  author       = {Pith},
  title        = {Pith review of: Reconciling Jupiter's Vertical Motions with the Observed Cloud Structure in the Upper Troposphere},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZCOLJU3O}},
  note         = {Machine review of arXiv:2509.02759}
}
read the original abstract

The eddy fluxes of angular momentum in Jupiter's upper troposphere are known to converge in prograde jets and diverge in retrograde jets. Away from the equator, this implies convergence of the Eulerian mean meridional flow in zones (anticyclonic shear) and divergence in belts (cyclonic shear). It indicates lower-tropospheric downwelling in zones and upwelling in belts because the mean meridional circulation almost certainly closes at depth. Yet the observed banded structure of Jupiter's clouds and hazes suggests that there is upwelling in the brighter zones and downwelling in the darker belts. Here, we show that this apparent contradiction can be resolved by considering not the Eulerian but the transformed Eulerian mean circulation, which includes a Stokes drift owing to eddies and is a better approximation of the Lagrangian mean transport of tracers such as ammonia. The potential vorticity structure inferred from observations paired with mixing length arguments suggests that there is transformed Eulerian mean upwelling in zones and downwelling in belts. Simulations with a global circulation model of Jupiter's upper atmosphere demonstrate the plausibility of these inferences and allow us to speculate on the band structure at deeper levels.

Figures

Figures reproduced from arXiv: 2509.02759 by the authors.

Figure 1
Figure 1. Zonal, meridional, and vertical velocities in Jupiter’s upper troposphere. (a) [PITH_FULL_IMAGE:figures/full_fig_p039_1.png] view at source ↗
Figure 2
Figure 2. Mean flow fields in the latitude-pressure plane in the upper atmosphere of the [PITH_FULL_IMAGE:figures/full_fig_p040_2.png] view at source ↗
Figure 3
Figure 3. Latitude-pressure contour map representing the mass mixing ratio of ice NH [PITH_FULL_IMAGE:figures/full_fig_p041_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Simulated zonal (left panel), meridional (middle panel) and vertical (right panel) [PITH_FULL_IMAGE:figures/full_fig_p042_4.png]
Figure 5
Figure 5. Figure 5: The Eulerian and transformed Eulerian mean vertical flow fields in the latitude [PITH_FULL_IMAGE:figures/full_fig_p043_5.png]

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    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.