Atmospheric confinement of jet streams on Uranus and Neptune

Journal name:
Date published:
Published online

The observed cloud-level atmospheric circulation on the outer planets of the Solar System is dominated by strong east–west jet streams. The depth of these winds is a crucial unknown in constraining their overall dynamics, energetics and internal structures. There are two approaches to explaining the existence of these strong winds. The first suggests that the jets are driven by shallow atmospheric processes near the surface1, 2, 3, whereas the second suggests that the atmospheric dynamics extend deeply into the planetary interiors4, 5. Here we report that on Uranus and Neptune the depth of the atmospheric dynamics can be revealed by the planets’ respective gravity fields. We show that the measured fourth-order gravity harmonic, J4, constrains the dynamics to the outermost 0.15 per cent of the total mass of Uranus and the outermost 0.2 per cent of the total mass of Neptune. This provides a stronger limit to the depth of the dynamical atmosphere than previously suggested6, and shows that the dynamics are confined to a thin weather layer no more than about 1,000 kilometres deep on both planets.

At a glance


  1. Observed cloud-level zonally averaged zonal winds on Uranus and Neptune.
    Figure 1: Observed cloud-level zonally averaged zonal winds on Uranus and Neptune.

    a, Observations of Uranus from Voyager 2 (circles) and from HST measurements (squares)27, 28. The solid line is an empirical fit to the data28. b, Observations of Neptune from Voyager 2 (circles)29 and from HST measurements (squares)30. The solid line is an empirical fit to the data29, constrained to zero at the poles. The cloud-level atmospheric circulations on Uranus and Neptune have a generally similar structure, despite the differences in solar insolation (Uranus has an obliquity of 98°, whereas that of Neptune is 29°), and internal heating (Neptune’s internal/solar heating ratio is roughly1.6, whereas that of Uranus is only 0.06). Error bars represent cloud tracking and navigational errors27, 28, 29, 30.

  2. over a wide range of interior models for Neptune.
    Figure 2: over a wide range of interior models for Neptune.

    a, as a function of normalized core radius and core density, with J2 held constant at the mean observed value15 of J2 = 3,408.4×10−6. b, as a function of normalized core radius and J2, with the core density set to 1.01×104 kg m−3, and J2 = (3,408.4±4.5)×10−6 varying between the observed uncertainties (dashed lines). We specifically do not constrain the solution to J4, because we are interested in the possible range of given the other constraints. We allow the constant-density core to extend up to 30% of the planet’s radius (Fig. 3), its density to be up to 1.2×104kgm−3 (refs 16, 17, 19) and J2 to vary within the observed error estimates (see further details in Supplementary Information). A similar figure for Uranus appears as Supplementary Fig. 1.

  3. Radial density profiles for two different interior models of Uranus and Neptune.
    Figure 3: Radial density profiles for two different interior models of Uranus and Neptune.

    Interior profiles shown are the extreme cases of ρstatic(r) from our suite of interior models. For each planet, we show here one model that has a constant core density of ~1.2×104kgm−3 reaching 30% of the planet’s radius on Neptune (black) and 20% of the planet’s radius on Uranus (red), and another model that does not have a constant density core. We used a suite of more than 3,000 profiles for Neptune and more than 1,500 profiles for Uranus, which are between these two extreme cases. All cases are constrained to match the planets’ mass, J2, mean radius, and the atmospheric density and its derivative at 1bar, but are not constrained to the observed J4 (see Supplementary Information). Density profiles based on three-layer models6, 16, 19 were also used.

  4. as function of the decay height H for Uranus and Neptune.
    Figure 4: as function of the decay height H for Uranus and Neptune.

    a, Uranus; b, Neptune. All possible solutions for the range of interior models explored in this study are between the two blue lines for each planet. The dashed lines are the maximum and minimum possible values for calculated as the difference between the observed J4 and obtained from the interior models (Fig. 2 and Supplementary Fig. 1). Only solutions within the two dashed red lines are possible solutions for the dynamical contribution to J4, and therefore H must be limited to less than ~1,100km for both Uranus and Neptune. On Uranus, this depth corresponds to a pressure of roughly 2,000bar or the outermost 0.15% of the mass. For Neptune, this is equivalent to a pressure of roughly 4,000bar or the outermost 0.2% of the mass. For lower values of H (not shown), all values converge to zero. For each planet, the bottom half of the plot is the negative of the log-scale to reflect the negative numbers on a log-scale.


  1. Read, P. L. Clearer circulation on Uranus. Nature 325, 197198 (1987)
  2. Lian, Y. & Showman, A. P. Generation of equatorial jets by large-scale latent heating on the giant planets. Icarus 207, 373393 (2010)
  3. Liu, J. & Schneider, T. Mechanisms of jet formation on the giant planets. J. Atmos. Sci. 67, 36523672 (2010)
  4. Suomi, V. E., Limaye, S. S. & Johnson, D. R. High winds of Neptune — a possible mechanism. Science 251, 929932 (1991)
  5. Aurnou, J., Heimpel, M. & Wicht, J. The effects of vigorous mixing in a convective model of zonal flow on the ice giants. Icarus 190, 110126 (2007)
  6. Hubbard, W. B. et al. Interior structure of Neptune — comparison with Uranus. Science 253, 648651 (1991)
  7. Hubbard, W. B. Gravitational signature of Jupiter’s deep zonal flows. Icarus 137, 357359 (1999)
  8. Kaspi, Y., Hubbard, W. B., Showman, A. P. & Flierl, G. R. Gravitational signature of Jupiter’s internal dynamics. Geophys. Res. Lett. 37 L01204 (2010)
  9. Kong, D., Zhang, K. & Schubert, G. On the variation of zonal gravity coefficients of a giant planet caused by its deep zonal flows. Astrophys. J. 748, 143 (2012)
  10. Kaspi, Y. Inferring the depth of the zonal jets on Jupiter and Saturn from odd gravity harmonics. Geophys. Res. Lett. 40, 676680 (2013)
  11. Hubbard, W. B. Planetary Interiors (Van Nostrand Reinhold, 1984)
  12. Zharkov, V. N. & Trubitsyn, V. P. Physics of Planetary Interiors (Pachart Publishing House, 1978)
  13. Helled, R., Anderson, J. D., Podolak, M. & Schubert, G. Interior models of Uranus and Neptune. Astrophys. J. 726, 15 (2011)
  14. Jacobson, R. A. The gravity field of the Uranian system and the orbits of the Uranian satellites and rings. Bull. Am. Astron. Soc. 39 (3). 453453 (2007)
  15. Jacobson, R. A. The orbits of the Neptunian satellites and the orientation of the pole of Neptune. Astrophys. J. 137, 43224329 (2009)
  16. Hubbard, W. B. & Marley, M. S. Optimized Jupiter, Saturn, and Uranus interior models. Icarus 78, 102118 (1989)
  17. Podolak, M., Weizman, A. & Marley, M. Comparative models of Uranus and Neptune. Planet. Space Sci. 43, 15171522 (1995)
  18. Fortney, J. J. & Nettelmann, N. The interior structure, composition, and evolution of giant planets. Space Sci. Rev. 152, 423447 (2010)
  19. Nettelmann, N., Helled, R., Fortney, J. J. & Redmer, R. New indication for a dichotomy in the interior structure of Uranus and Neptune from the application of modified shape and rotation data. Planet. Space Sci. 77, 143151 (2013)
  20. Kaspi, Y., Flierl, G. R. & Showman, A. P. The deep wind structure of the giant planets: results from an anelastic general circulation model. Icarus 202, 525542 (2009)
  21. Schneider, T. & Liu, J. Formation of jets and equatorial superrotation on Jupiter. J. Atmos. Sci. 66, 579601 (2009)
  22. Liu, J., Goldreich, P. M. & Stevenson, D. J. Constraints on deep-seated zonal winds inside Jupiter and Saturn. Icarus 196, 653664 (2008)
  23. Pedlosky, J. Geophysical Fluid Dynamics (Spinger, 1987)
  24. Pearl, J. C. & Conrath, B. J. The albedo, effective temperature, and energy balance of Neptune, as determined from Voyager data. J. Geophys. Res. 96, 1892118930 (1991)
  25. Helled, R., Anderson, J. D. & Schubert, G. Uranus and Neptune: shape and rotation. Icarus 210, 446454 (2010)
  26. Karkoschka, E. Neptune’s rotational period suggested by the extraordinary stability of two features. Icarus 215, 439448 (2011)
  27. Hammel, H. B., de Pater, I., Gibbard, S., Lockwood, G. W. & Rages, K. Uranus in 2003: zonal winds, banded structure, and discrete features. Icarus 175, 534545 (2005)
  28. Sromovsky, L. A. & Fry, P. M. Dynamics of cloud features on Uranus. Icarus 179, 459484 (2005)
  29. Sromovsky, L. A., Limaye, S. S. & Fry, P. M. Dynamics of Neptune’s major cloud features. Icarus 105, 110141 (1993)
  30. Sromovsky, L. A., Fry, P. M., Dowling, T. E., Baines, K. H. & Limaye, S. S. Neptune’s atmospheric circulation and cloud morphology: changes revealed by 1998 HST imaging. Icarus 150, 244260 (2001)

Download references

Author information


  1. Department for Environmental Sciences and Center for Planetary Science, Weizmann Institute of Science, Rehovot 76100, Israel

    • Yohai Kaspi &
    • Oded Aharonson
  2. Lunar and Planetary Laboratory, University of Arizona, Tucson, Arizona 85721, USA

    • Adam P. Showman &
    • William B. Hubbard
  3. Department of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125, USA

    • Oded Aharonson
  4. Department of Geophysics and Planetary Science, Tel Aviv University, Tel Aviv 69978, Israel

    • Ravit Helled


Y.K. and A.P.S. initiated and designed the research. Y.K. performed the dynamical gravity harmonics calculations and wrote the paper. R.H. performed the static interior model calculations and their interpretation. All authors contributed to the discussion of the results.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary Information (228 KB)

    This file contains Supplementary Text and Data 1-2, Supplementary Table 1, Supplementary Figure 1 and additional references.

Additional data