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REVIEW 3 major objections 3 minor 58 references

Scaling Relations for Terrestrial Exoplanet Atmospheres from Baroclinic Criticality

T0 review · 3 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper derives two scaling equations that predict the equator-to-pole temperature contrast and bulk lapse rate of terrestrial exoplanet atmospheres from rotation rate, surface pressure, tropopause height, radius, and gravity, and…

desk verdict A clean extension of baroclinic criticality theory to exoplanets, with GCM support for the main trends; the main caveat is that the closure is only validated indirectly, with runs clustering near xi ~ 1. read the letter →

arxiv 1908.02661 v1 pith:6EWOOGJQ submitted 2019-08-07 astro-ph.EP physics.ao-phphysics.flu-dyn

Thaddeus D. Komacek , Malte F. Jansen , Eric T. Wolf , Dorian S. Abbot This is my paper · ORCID
classification astro-ph.EPphysics.ao-phphysics.flu-dyn
keywords barocliniccriticalityterrestrialexoplanetatmospheresequator-to-poletemperaturecontrastbulklapserateatmosphericheattransportgeneralcirculationmodelsExoCAMrotationscaling
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

The paper asks how fast-rotating terrestrial exoplanet atmospheres transport heat poleward, and derives closed-form scaling laws for two observable quantities: the equator-to-pole potential temperature contrast and the bulk lapse rate. The laws follow from balancing baroclinic eddy heat fluxes against radiative relaxation, building on a prior theory of baroclinic criticality. The paper compares the scalings against ExoCAM general circulation model simulations spanning rotation rates 0.0625 to 8 times Earth's and surface pressures 0.25 to 4 bars, and finds broad agreement wherever baroclinic instability is active. If the theory is right, future observations could use thermal phase curves and spectra to estimate a planet's rotation rate and surface pressure from its temperature structure.

What carries the argument

The central object is the baroclinic criticality parameter $\xi = s a / H$, where $s$ is the slope of mid-latitude isentropes, $a$ is planetary radius, and $H$ is the smaller of the tropopause height and the scale height. The argument runs through three steps: the isentropic slope is set by the distance eddies diffuse heat in one radiative relaxation time, $s \sim H/\sqrt{\tau_{\mathrm{rad}} D_{\mathrm{eddy}}}$; the eddy diffusivity obeys the geostrophic-turbulence closure $D_{\mathrm{eddy}} \sim \beta (\xi L_d)^3$ from Held & Larichev (1996), with $L_d$ the Rossby deformation length; and the horizontal and vertical eddy heat fluxes are related along isentropes, giving a constraint that separates the equator-to-pole and vertical contrasts. With the radiative relaxation timescale scaling $\tau_{\mathrm{rad}} \propto p/(gT^3)$, this machinery converts an abstract measure of instability into observable temperature contrasts.

What would settle it

Run a GCM at $16\Omega_\oplus$ and 1 bar: the theory predicts $\xi$ about three times Earth's value and an equator-to-pole potential temperature contrast near 218 K (for $\Delta_h \theta_{eq} = 242$ K), versus about 121 K at Earth's rotation; if the simulated contrast does not approach that value, or its growth with rotation deviates from the predicted $\Omega^{2/5}$ trend, the central scaling fails.

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Extended reading notes

Core claim

The central claim is that the baroclinic criticality parameter $\xi$—a measure of how slanted mid-latitude isentropes are, roughly the ratio of equator-to-pole to surface-to-tropopause potential temperature contrast—controls both heat transport and lapse rate, and that it scales as $\xi \propto (\Omega/\Omega_\oplus)^{2/5}(p/p_\oplus)^{-1/5}(H/H_\oplus)^{-3/5}(a/a_\oplus)^{3/5}(g/g_\oplus)^{-1/10}$. Combining this with the assumption that eddy heat flux is directed along isentropes yields equations (13) and (14), which predict the equator-to-pole potential temperature contrast and the bulk lapse rate (defined as the smaller of the surface-to-tropopause contrast and the contrast over one scale height) with no free parameters once the radiative-equilibrium contrast is fixed. The GCM comparisons show the equator-to-pole contrast increases with rotation rate and decreases with surface pressure, while the bulk lapse rate varies weakly and peaks near $\xi \approx 1$. The paper argues this confirms that baroclinic instabilities, not just radiative-convective balance, set the temperature structure of fast-rotating terrestrial exoplanets.

Load-bearing premise

The predictions inherit the assumption that eddy mixing follows the quasi-geostrophic turbulence law $D_{\mathrm{eddy}} \sim \beta (\xi L_d)^3$, with the Rhines scale tied to the deformation radius; if atmospheres with very different rotation or pressure mix according to a different law, the derived rotation and pressure exponents would not hold.

Editorial extensions

If this is right

  • At fixed incident stellar flux, faster rotation widens the equator-to-pole potential temperature contrast, so fast rotators should have colder poles and larger sea-ice cover, an effect that could appear in orbital-phase albedo variations.
  • The bulk lapse rate is only weakly dependent on planetary parameters near Earth-like values and peaks near $\xi \approx 1$; for rotation rates above about $8\Omega_\oplus$, further spin-up should reduce it rather than increase it.
  • Spectroscopic retrievals that constrain the vertical temperature profile and tropopause height can directly test the predicted lapse rate, while full-phase thermal light curves can constrain the equator-to-pole contrast.
  • The theory applies only to planets with active baroclinic instability, roughly those with rotation periods of about three days or shorter; slowly rotating and tidally locked planets require separate treatments.
  • Extending the same reasoning to warm Jupiters and warm Neptunes is plausible, and the predicted increase of equator-to-pole contrast with rotation rate matches previous simulations of warm Jupiters.

Reading between the lines

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

  • A retrieved equator-to-pole contrast alone would not pin down rotation rate or surface pressure, because the scalings depend on the combination $\xi \sim \Omega^{2/5} p^{-1/5}$ together with tropopause height, radius, and gravity; independent estimates of pressure or tropopause height would be needed to break the degeneracy.
  • Because the theory fixes the radiative-equilibrium contrast $\Delta_h \theta_{eq}$ at one value, ice-albedo feedbacks are an unmodeled pathway; coupling the lapse-rate prediction to a sea-ice model might explain the anomalous ice-covered 2-4 bar cases noted in the paper.
  • The predicted $\Omega^{2/5}$ exponent could be checked before exoplanet spectroscopy is ready, using existing dry dynamical-core GCMs or rotating-tank experiments that vary rotation rate over a wider range than the present suite.
  • If the eddy-diffusivity closure survives, the same criticality balance may give testable predictions for the phase-curve amplitudes of fast-rotating gas giants as functions of their rotation rate and radiative timescale.
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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 / 3 minor

Summary. The manuscript derives scaling relations for the baroclinic criticality parameter, equator-to-pole potential temperature contrast, and bulk lapse rate of terrestrial exoplanet atmospheres. Building on Jansen & Ferrari (2013) and the Held-Larichev eddy-diffusivity closure, the authors obtain Equation (6) for the criticality parameter as a function of rotation rate, surface pressure, tropopause height, radius, and gravity, and then Equations (13) and (14) for the temperature contrast and lapse rate. The predictions are compared to ExoCAM GCM simulations with rotation rates from 0.0625 to 8 Earth values and surface pressures from 0.25 to 4 bars. The paper reports broad agreement for rotation rates greater than about one third of Earth's rotation rate and discusses observational tests of the scalings. Limitations of the theory for slowly rotating and tidally locked planets are acknowledged.

Significance. If the scalings hold, they provide compact, observationally relevant predictions for how the circulation of Earth-like exoplanets depends on basic planetary parameters. The paper connects a well-established body of geophysical fluid dynamics to exoplanet observations, and the GCM comparison is a reasonable and transparent test. The authors are honest about key inputs, such as the Earth-normalized criticality and the model-derived tropopause height and albedo, and they explicitly delimit the regime of applicability. The main weakness is that the validation is concentrated near the marginally critical regime, so the claim of applicability throughout the baroclinically unstable regime is not yet strongly supported.

major comments (3)
  1. [Section 2.1, Equations (5)-(6) and Figures 2-4] The exponents in Equations (6), (13), and (14) all inherit the Held-Larichev closure D_eddy ~ beta (xi L_d)^3 from Equation (5). The GCM comparisons test the integrated scaling rather than this closure directly, and the simulated runs lie mostly at or near xi ~ 1 (as noted in the discussion of Figure 4). Consequently, the paper's claim of applicability 'throughout the baroclinically unstable regime' rests largely on extrapolation to strongly supercritical states (xi >> 1) that the suite does not sample. I recommend adding a simulation or reanalysis at higher rotation rate or lower pressure that pushes xi well above 1, or substantially softening the scope claim to the near-critical regime.
  2. [Section 4.1, Figure 2 (right panel)] The pressure scaling is not a fully independent prediction because the predicted criticality uses the tropopause height H taken from the GCM experiments (the text states this explicitly). Since H enters Equation (6) with an exponent -3/5 and itself varies with surface pressure, the agreement between theory and model in Figure 2 partly reflects the model's H rather than a pure a priori prediction. The disclosure is appreciated, but the discussion should distinguish which parts of the pressure dependence are predicted and which are diagnosed, and should quantify the sensitivity to the choice of H (e.g., using a fixed H would change the predicted exponent to -1/5).
  3. [Section 4.2, Equation (13) and Figure 3] The fixed equilibrium equator-to-pole contrast Delta_h_theta_eq = 242 K is derived using an albedo of 0.55 taken from the Earth-like simulation, and the manuscript notes that albedo changes due to sea ice are ignored. For the 2 and 4 bar cases, which are ice-covered, the change in Delta_h_theta_eq is not accounted for and is invoked as the reason for the discrepancy. This is an acknowledged limitation, but it directly affects the pressure scaling that is a central target of the paper. Please estimate how Delta_h_theta_eq changes with the simulated albedo across the suite, so readers can judge how much of the apparent pressure trend in Figure 3 is attributable to the fixed Delta_h_theta_eq assumption.
minor comments (3)
  1. [Abstract] The word 'baroclincally' is a typo and should be 'baroclinically'.
  2. [Section 4.2, paragraph 1] The phrase 'there is no tunable parameter in our equations' is misleading because the theory is anchored by setting xi = xi_Earth for Earth-like parameters and by fixing Delta_h_theta_eq with an albedo taken from the model. These are inputs rather than tunable fits, but a more precise statement would acknowledge them as calibration choices.
  3. [Figure 2 caption] The caption refers to 'the arrow' but the figure does not visibly include an arrow in the rendered version; please either include the arrow in the figure or remove the reference.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the scaling theory is derived from stated closures and validated against GCMs without fitting the target outputs.

full rationale

The derivation chain is algebraic and self-contained: Eqs. (1)-(6) combine the Jansen-Ferrari criticality definition with the Held-Larichev eddy-diffusivity closure and the Showman-Guillot radiative-timescale scaling to produce Eq. (6); Eqs. (7)-(12) then derive the temperature-contrast scalings from a Newtonian-heating balance, with Eqs. (13)-(14) obtained by substitution. No step inverts a target output to define an input. The GCM comparison is not circular: ξ is measured from simulated isentropic slopes via Eq. (15), the theory is anchored by setting ξ=ξ_Earth at Earth parameters rather than fitting it, and the quoted statement in Sec. 4.2, 'there is no tunable parameter in our equations,' is accurate. The use of the model's albedo (0.55) to set Δhθeq=242 K and the use of GCM-computed tropopause heights in the pressure scaling are model-derived inputs, but they are diagnostics of the radiative state and geometry, not fits to the equator-to-pole contrast or bulk lapse rate being predicted; they do not force the predicted values, and the paper explicitly notes limitations (e.g., ignoring albedo changes with ice cover). The Jansen-Ferrari theory is prior work by a co-author, but it is an external, published theoretical result with stated assumptions that do not include the exoplanet scaling targets, so the self-citation is not load-bearing in a circular sense. Overall, no circular step is identifiable under the quoted-equation standard.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The theory inherits the Jansen and Ferrari (2013) closure assumptions and adds a normalization at Earth, a model-derived radiative equilibrium contrast, and model-derived tropopause heights for the pressure scaling. The central claim therefore rests on these inputs plus standard geostrophic turbulence scalings.

free parameters (3)
  • Earth criticality xi_Earth = approximately 1
    Sets the normalization of Eq. 6; the theory curve is anchored to match GCM and Earth values at Earth rotation rate and 1 bar (Section 4.1).
  • Radiative equilibrium equator-to-pole contrast Delta_h_theta_eq = 242 K
    Fixed input for Eqs. 13 and 14, computed with an assumed albedo of 0.55 taken from the Earth-like simulation (Section 4.2).
  • Tropopause height H for pressure scaling = Taken from GCM for each surface pressure
    Used in the predicted criticality for the pressure comparison, rather than predicted by the theory (Section 4.1).
assumptions (5)
  • domain assumption Baroclinic instability dominates poleward heat transport in mid-latitudes of fast-rotating terrestrial planets.
    Foundation of the criticality framework (Sections 1 and 2.1).
  • domain assumption Eddy diffusivity follows D_eddy ~ beta (xi L_d)^3 (Held and Larichev 1996).
    Leads to Eq. 5 and the exponents in Eq. 6 (Section 2.1).
  • domain assumption Radiative relaxation timescale scales as tau_rad proportional to p/(g T^3).
    Used to turn Eq. 4 into Eq. 6; cited to Showman and Guillot (2002).
  • domain assumption Vertical radiative equilibrium contrast is negligible, Delta_v_theta_eq approximately 0.
    Required to derive Eqs. 11 and 12 from Eq. 10 (Section 2.2).
  • domain assumption Eddy heat flux is directed along isentropes, giving F_eddy,v ~ s F_eddy,h.
    Used in Eq. 9 to close the system (Section 2.2).

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Pith. "Pith review of Scaling Relations for Terrestrial Exoplanet Atmospheres from Baroclinic Criticality." pith.science (2026). https://pith.science/paper/6EWOOGJQ

@misc{pith2026190802661,
  author       = {Pith},
  title        = {Pith review of: Scaling Relations for Terrestrial Exoplanet Atmospheres from Baroclinic Criticality},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6EWOOGJQ}},
  note         = {Machine review of arXiv:1908.02661}
}
read the original abstract

The macroturbulent atmospheric circulation of Earth-like planets mediates their equator-to-pole heat transport. For fast-rotating terrestrial planets, baroclinic instabilities in the mid-latitudes lead to turbulent eddies that act to transport heat poleward. In this work, we derive a scaling theory for the equator-to-pole temperature contrast and bulk lapse rate of terrestrial exoplanet atmospheres. This theory is built on the work of Jansen & Ferrari (2013), and determines how unstable the atmosphere is to baroclinic instability (the baroclinic "criticality") through a balance between the baroclinic eddy heat flux and radiative heating/cooling. We compare our scaling theory to General Circulation Model (GCM) simulations and find that the theoretical predictions for equator-to-pole temperature contrast and bulk lapse rate broadly agree with GCM experiments with varying rotation rate and surface pressure throughout the baroclincally unstable regime. Our theoretical results show that baroclinic instabilities are a strong control of heat transport in the atmospheres of Earth-like exoplanets, and our scalings can be used to estimate the equator-to-pole temperature contrast and bulk lapse rate of terrestrial exoplanets. These scalings can be tested by spectroscopic retrievals and full-phase light curves of terrestrial exoplanets with future space telescopes.

Figures

Figures reproduced from arXiv: 1908.02661 by the authors.

Figure 1
Figure 1. — Potential temperature (left), zonal wind (center), and eddy component of the zonal wind (right) maps at the lowest atmospheric model level for rotation rates of 1, 2, and 8 Ω. The surface pressure for these simulations is 1 bar. Eddies that form from baroclinic instabilities are apparent in the mid-latitudes. that the width of tropical regions decreases and the num￾ber of zonal jets increases with increasing rota… view at source ↗
Figure 2
Figure 2. — Scaling for the criticality parameter (dashed lines) compared to GCM results (solid lines) for separately varying rotation rate (left panel) and surface pressure (right panel). For the simulations varying rotation rate (left panel), we keep the surface pressure fixed to 1 bar. For the simulations varying surface pressure (right panel), we keep the rotation rate fixed to that of Earth. We find good agreement betwee… view at source ↗
Figure 3
Figure 3. — Scaling for the equator-to-pole temperature contrast (dashed lines) compared to GCM results (solid lines) with varying rotation rate (left panel) and surface pressure (right panel). The equator-to-pole temperature contrast increases with increasing rotation rate and decreasing surface pressure in both our theory and GCM experiments. As a result, we find that our scaling explains the qualitative trends in equator-t… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: — Scaling for the bulk lapse rate (dashed lines) compared to GCM results for the mid-latitude bulk lapse rate with varying rotation rate (left panel) and surface pressure (right panel). Overall, the variations in bulk lapse rate with planetary parameters are relatively…

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Works this paper leans on

58 extracted references · 57 canonical work pages

  1. [1]

    2019, Publications of the Astronomical Society of the Pacific, 131, 064402

    Baker, A., Blake, C., & Halverson, S. 2019, Publications of the Astronomical Society of the Pacific, 131, 064402

    work page 2019

  2. [2]

    & Seager, S

    Benneke, B. & Seager, S. 2012, The Astrophysical Journal, 753, 100

    work page 2012

  3. [3]

    & Vallis, G

    Chai, J. & Vallis, G. 2014, Journal of the Atmospheric Sciences, 71, 2300

    work page 2014

  4. [4]

    1947, Journal of Meteorology, 4, 135

    Charney, J. 1947, Journal of Meteorology, 4, 135

    work page 1947

  5. [5]

    & Kaspi, Y

    Chemke, R. & Kaspi, Y. 2017, The Astrophysical Journal, 841, 1

    work page 2017

  6. [6]

    D., Seager, S., & Charbonneau, D

    Wellnitz, D. D., Seager, S., & Charbonneau, D. 2009, The Astrophysical Journal, 700, 915

    work page 2009

  7. [7]

    Cowan, N. B. & Strait, T. E. 2013, The Astrophysical Journal Letters, 765, L17

    work page 2013

  8. [8]

    & Jansen, M

    Cronin, T. & Jansen, M. 2016, Geophysical Research Letters, 43, 449

    work page 2016

Show all 58 references
  1. [9]

    2016, The Astrophysical Journal, 829, 52

    Kreidberg, L., & Parmentier, V. 2016, The Astrophysical Journal, 829, 52

    2016

  2. [10]

    2018, The Astronomical Journal, 155, 200

    Feng, Y., Robinson, T., Fortney, J., Lupu, R., Marley, M., Lewis, N., Macintosh, B., & Line, M. 2018, The Astronomical Journal, 155, 200

    2018

  3. [11]

    1979, Icarus, 40, 205

    Gierasch, P., Ingersoll, A., & Pollard, D. 1979, Icarus, 40, 205

    1979

  4. [12]

    2016, The Astrophysical Journal, 817, 17

    Greene, T., Line, M., Montero, C., Fortney, J., Lustig-Yaeger, J., & Luther, K. 2016, The Astrophysical Journal, 817, 17

    2016

  5. [13]

    2018, The Astrophysical Journal, 852, 67

    Haqq-Misra, J., Wolf, E., Josh, M., Zhang, X., & Kopparapu, R. 2018, The Astrophysical Journal, 852, 67

    2018

  6. [14]

    2000, in Program in Geophysical Fluid Dynamics (Woods

    Held, I. 2000, in Program in Geophysical Fluid Dynamics (Woods

    2000

  7. [15]

    & Hou, A

    Held, I. & Hou, A. 1980, Journal of the Atmospheric Sciences, 37, 515

    1980

  8. [16]

    & Larichev, V

    Held, I. & Larichev, V. 1996, Journal of the Atmospheric Sciences, 53, 946

    1996

  9. [17]

    & Ferrari, R

    Jansen, M. & Ferrari, R. 2012a, Journal of the Atmospheric Sciences, 69, 695 —. 2012b, Journal of the Atmospheric Sciences, 70, 1456 —. 2013, Journal of the Atmospheric Sciences, 70, 2948

    2013

  10. [18]

    Jansen, T., Scharf, C., Way, M., & Genio, A. D. 2019, The Astrophysical Journal, 875, 79

    2019

  11. [19]

    & Flierl, G

    Kaspi, Y. & Flierl, G. 2006, Journal of the Atmospheric Sciences, 64, 3177

    2006

  12. [20]

    & Schneider, T

    Kaspi, Y. & Schneider, T. 2011, Journal of the Atmospheric Sciences, 68, 2459 —. 2013, Journal of the Atmospheric Sciences, 70, 2596

    2011

  13. [21]

    & Showman, A

    Kaspi, Y. & Showman, A. 2015, The Astrophysical Journal, 804, 60

    2015

  14. [22]

    & Fujii, Y

    Kawahara, H. & Fujii, Y. 2010, The Astrophysical Journal, 720, 1333

    2010

  15. [23]

    & Abbot, D

    Koll, D. & Abbot, D. 2016, The Astrophysical Journal, 825, 99

    2016

  16. [24]

    & Abbot, D

    Komacek, T. & Abbot, D. 2019, The Astrophysical Journal, 871, 245

    2019

  17. [25]

    2017, The Astrophysical Journal, 845, 5

    Grimm, S., & Heng, K. 2017, The Astrophysical Journal, 845, 5

    2017

  18. [26]

    2016, The Astrophysical Journal, 819, 84

    Meadows, V., Terrien, R., & Mahadevan, S. 2016, The Astrophysical Journal, 819, 84

    2016

  19. [27]

    & Loeb, A

    Kreidberg, L. & Loeb, A. 2016, The Astrophysical Journal Letters, 832, L12

    2016

  20. [28]

    & Showman, A

    Lian, Y. & Showman, A. 2008, Icarus, 194, 597

    2008

  21. [29]

    & Yung, Y

    Line, M. & Yung, Y. 2013, The Astrophysical Journal, 779, 3

    2013

  22. [30]

    2018, The Astronomical Journal, 156, 301

    Fujii, Y., Luger, R., & Robinson, T. 2018, The Astronomical Journal, 156, 301

    2018

  23. [31]

    & Seager, S

    Madhusudhan, N. & Seager, S. 2009, The Astrophysical Journal, 707, 24

    2009

  24. [32]

    & Brunini, A

    Miguel, Y. & Brunini, A. 2010, Monthly Notices of the Royal Astronomical Society, 406, 1935

    2010

  25. [33]

    & Snellen, I

    Molliere, P. & Snellen, I. 2019, Astronomy & Astrophysics, 622, A139

    2019

  26. [34]

    2017, The Astrophysical Journal, 850, 121

    Fortney, J. 2017, The Astrophysical Journal, 850, 121

    2017

  27. [35]

    2018, The Astrophysical Journal Letters, 858, L14

    Olson, S., Schwieterman, E., Reinhard, C., Ridgewell, A., Kane, S., Meadows, V., & Lyons, T. 2018, The Astrophysical Journal Letters, 858, L14

    2018

  28. [36]

    2010, Principles of Planetary Climate (Cambridge: Cambridge University Press)

    Pierrehumbert, R. 2010, Principles of Planetary Climate (Cambridge: Cambridge University Press)

    2010

  29. [37]

    2016, Nature Communications, 7, 10627

    Popp, M., Schmidt, H., & Marotzke, J. 2016, Nature Communications, 7, 10627

    2016

  30. [38]

    2017, The Astrophysical Journal, 846, 69

    Rauscher, E. 2017, The Astrophysical Journal, 846, 69

    2017

  31. [39]

    1975, Journal of Fluid Mechanics, 69, 417

    Rhines, P. 1975, Journal of Fluid Mechanics, 69, 417

    1975

  32. [40]

    2004, Journal of the Atmospheric Sciences, 61, 1317

    Schneider, T. 2004, Journal of the Atmospheric Sciences, 61, 1317

    2004

  33. [41]

    & Walker, C

    Schneider, T. & Walker, C. 2006, Journal of the Atmospheric Sciences, 63, 1569

    2006

  34. [42]

    & Guillot, T

    Showman, A. & Guillot, T. 2002, Astronomy and Astrophysics, 385, 166

    2002

  35. [43]

    2015, The Astrophysical Journal, 801, 95

    Showman, A., Lewis, N., & Fortney, J. 2015, The Astrophysical Journal, 801, 95

    2015

  36. [44]

    2015, Astronomy & Astrophysics, 576, A59

    Snellen, I., de Kok, R., Birkby, J., Brandl, B., Brogi, M., Keller, C., Kenworthy, M., Schwarz, H., & Stuik, R. 2015, Astronomy & Astrophysics, 576, A59

    2015

  37. [45]

    2001, Journal of the Atmospheric Sciences, 58, 3650

    Sobel, A., Nilsson, J., & Polvani, L. 2001, Journal of the Atmospheric Sciences, 58, 3650

    2001

  38. [46]

    1978, Journal of the Atmospheric Sciences, 35, 561

    Stone, P. 1978, Journal of the Atmospheric Sciences, 35, 561

    1978

  39. [47]

    2006, Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation (Cambridge: Cambridge University Press)

    Vallis, G. 2006, Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation (Cambridge: Cambridge University Press)

    2006

  40. [48]

    2015, The Astrophysical Journal, 802, 107

    Waldmann, I., Tinetti, G., Rocchetto, M., Barton, E., Yurchenko, S., & Tennyson, J. 2015, The Astrophysical Journal, 802, 107

    2015

  41. [49]

    2018, Quarterly Journal of the Royal Meteorological Society, 144, 2537

    Wang, Y., Read, P., Tabataba-Vakili, F., & Young, R. 2018, Quarterly Journal of the Royal Meteorological Society, 144, 2537

    2018

  42. [50]

    2017, The Astrophysical Journal Supplement Series, 231, 12

    Tsigaridis, K. 2017, The Astrophysical Journal Supplement Series, 231, 12

    2017

  43. [51]

    1978, Journal of the Atmospheric Sciences, 35, 1399 —

    Williams, G. 1978, Journal of the Atmospheric Sciences, 35, 1399 —. 1979, Journal of the Atmospheric Sciences, 36, 932

    1978

  44. [52]

    & Holloway, J

    Williams, G. & Holloway, J. 1982, Nature, 297, 295

    1982

  45. [53]

    2017, The Astrophysical Journal Letters, 839, L1

    Wolf, E. 2017, The Astrophysical Journal Letters, 839, L1

    2017

  46. [54]

    2017, The Astrophysical Journal, 837, 107

    Wolf, E., Shields, A., Kopparapu, R., Haqq-Misra, J., & Toon, O. 2017, The Astrophysical Journal, 837, 107

    2017

  47. [55]

    2015, The Astrophysical Journal, 806, 180

    Wordsworth, R. 2015, The Astrophysical Journal, 806, 180

    2015

  48. [56]

    2019, The Astrophysical Journal Letters, 876, L27

    Yang, H., Komacek, T., & Abbot, D. 2019, The Astrophysical Journal Letters, 876, L27

    2019

  49. [57]

    2014, The Astrophysical Journal Letters, 787, L2

    Yang, J., Boue, G., Fabrycky, D., & Abbot, D. 2014, The Astrophysical Journal Letters, 787, L2

    2014

  50. [58]

    2019, Icarus, 326, 225

    Young, R., Read, P., & Wang, Y. 2019, Icarus, 326, 225

    2019

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