G. Schubert

University of Exeter, Exeter, England, United Kingdom

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Publications (390)1294.71 Total impact

  • W.B. Hubbard, G. Schubert, D. Kong, K. Zhang
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    ABSTRACT: The so-called theory of figures (TOF) uses potential theory to solve for the structure of highly distorted rotating liquid planets in hydrostatic equilibrium. An apparently divergent expansion for the gravitational potential plays a fundamental role in the traditional TOF. This questionable expansion, when integrated, leads to the standard geophysical expansion of the external gravitational potential on spherical-harmonics (via the usual J-coefficients). We show that this expansion is convergent and exact on the planet’s level surfaces, provided that rotational distortion does not exceed a critical value. We examine the general properties of the Maclaurin multipole expansion and discuss conditions for its convergence on the surface of both single and nested-concentric Maclaurin spheroids.
    Icarus 11/2014; 242:138–141. · 3.16 Impact Factor
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    D. Kong, X. Liao, K. Zhang, G. Schubert
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    ABSTRACT: The depth of penetration of Jupiter's zonal winds into the planet's interior is unknown. A possible way to determine the depth is to measure the effects of the winds on the planet's high-order zonal gravitational coefficients, a task to be undertaken by the Juno spacecraft. It is shown here that the equatorial winds alone largely determine these coefficients which are nearly independent of the depth of the non-equatorial winds.
    The Astrophysical Journal Letters 08/2014; 791(2):L24. · 6.35 Impact Factor
  • D Kong, X Liao, K Zhang, G Schubert
    Monthly Notices of the Royal Astronomical Society Letters 07/2014; 445:L26-L30. · 5.52 Impact Factor
  • Dali Kong, Xinhao Liao, Keke Zhang, Gerald Schubert
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    ABSTRACT: Both deep zonal winds, if they exist, and the basic rotational distortion of Jupiter contribute to its zonal gravity coefficients Jn for n ⩾ 2. In order to capture the gravitational signature of Jupiter that is caused solely by its deep zonal winds, one must take into account the full effect of rotational distortion by computing the coefficients Jn in non-spherical geometry. This represents a difficult and challenging problem because the widely-used spherical-harmonic-expansion method becomes no longer suitable. Based on the model of a polytropic Jupiter with index unity, we compute Jupiter's gravity coefficients J2, J4, J6, … , J12 taking into account the full effect of rotational distortion of the gaseous planet using a finite element method. For the model of deep zonal winds on cylinders parallel to the rotation axis, we also compute the variation of the gravity coefficients ΔJ2, ΔJ4, ΔJ6, … , ΔJ12 caused solely by the effect of the winds in non-spherical geometry. It is found that the effect of the zonal winds on lower-order coefficients is weak, ∣ΔJn/Jn∣ < 1%, for n = 2, 4, 6, but it is substantial for the high-degree coefficients with n ⩾ 8.
    Icarus 11/2013; 226(2):1425-1430. · 3.16 Impact Factor
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    ABSTRACT: [1] Gusty flow over rough terrain is likely to be a significant source of fast gravity waves and acoustic waves in the atmosphere of Mars, as it is in Earth's atmosphere. Accordingly, we have used a numerical model to study the dissipation in the thermosphere and exosphere of Mars of upward-propagating fast gravity waves and acoustic waves. Model simulations are performed for a range of wave periods and horizontal wavelengths. Wave amplitudes are constrained by the Mars Global Surveyor and Mars Odyssey aerobraking data, and gravity wave phase velocities are limited by occultation data. Dissipating gravity waves heat some regions of the thermosphere and cool others through the effects of sensible heat flux divergence, while acoustic waves mainly heat the Mars thermosphere. Heating rates can be on the order of several hundred Kelvin per day. The cycle-integrated effects on the Jeans escape flux are also investigated and found to be on the order of background values and even greater and might be a significant source of loss of the Martian atmosphere to space.
    Journal of Geophysical Research: Planets. 11/2013; 118(11).
  • Dali Kong, Keke Zhang, Gerald Schubert
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    ABSTRACT: Hubbard recently derived an important iterative equation for calculating the gravitational coefficients of a Maclaurin spheroid that does not require an expansion in a small distortion parameter. We show that this iterative equation, which is based on an incomplete solution of the Poisson equation, diverges when the distortion parameter is not sufficiently small. We derive a new iterative equation that is based on a complete solution of the Poisson equation and, hence, always converges when calculating the gravitational coefficients of a Maclaurin spheroid.
    The Astrophysical Journal 01/2013; 764(1):67. · 6.73 Impact Factor
  • Dali Kong, Keke Zhang, Gerald Schubert, John Anderson
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    ABSTRACT: We present a new three-dimensional numerical method for calculating the non-spherical shape and internal structure of a model of a rapidly rotating gaseous body with a polytropic index of unity. The calculation is based on a finite-element method and accounts for the full effects of rotation. After validating the numerical approach against the asymptotic solution of Chandrasekhar that is valid only for a slowly rotating gaseous body, we apply it to models of Jupiter and a rapidly rotating, highly flattened star (α Eridani). In the case of Jupiter, the two-dimensional distributions of density and pressure are determined via a hybrid inverse approach by adjusting an a priori unknown coefficient in the equation of state until the model shape matches the observed shape of Jupiter. After obtaining the two-dimensional distribution of density, we then compute the zonal gravity coefficients and the total mass from the non-spherical model that takes full account of rotation-induced shape change. Our non-spherical model with a polytropic index of unity is able to produce the known mass of Jupiter with about 4% accuracy and the zonal gravitational coefficient J 2 of Jupiter with better than 2% accuracy, a reasonable result considering that there is only one parameter in the model. For α Eridani, we calculate its rotationally distorted shape and internal structure based on the observationally deduced rotation rate and size of the star by using a similar hybrid inverse approach. Our model of the star closely approximates the observed flattening.
    The Astrophysical Journal 01/2013; 763(2):116. · 6.73 Impact Factor
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    ABSTRACT: In the context of an International Space Science Institute (ISSI) working group, we have conducted a project to compare the most recent General Circulation Models (GCMs) of the Venus atmospheric circulation. A common configuration has been decided, with simple physical parametrization for the solar forcing and the boundary layer scheme.
    Towards Understanding the Climate of Venus. 01/2013;
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    ABSTRACT: In studying the hydrothermal evolution of primitive asteroids we have assumed that they were lithified. Disgarding this assumption solves a number of problems.
    Lunar and Planetary Science ConferenceLunar and Planetary Science Conference; 01/2013
  • Journal of the Atmospheric Sciences 12/2012; 69(12):3800-3811. · 2.67 Impact Factor
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    ABSTRACT: To help understand the large disparity in the results of circulation modeling for the atmospheres of Titan and Venus, where the whole atmosphere rotates faster than the surface (superrotation), the atmospheric angular momentum budget is detailed for two General Circulation Models (GCMs). The LMD GCM is tested for both Venus (with simplified and with more realistic physical forcings) and Titan (realistic physical forcings). The Community Atmosphere Model is tested for both Earth and Venus with simplified physical forcings. These analyses demonstrate that errors related to atmospheric angular momentum conservation are significant, especially for Venus when the physical forcings are simplified. Unphysical residuals that have to be balanced by surface friction and mountain torques therefore affect the overall circulation. The presence of topography increases exchanges of angular momentum between surface and atmosphere, reducing the impact of these numerical errors. The behavior of GCM dynamical cores with regard to angular momentum conservation under Venus conditions provides an explanation of why recent GCMs predict dissimilar results despite identical thermal forcing. The present study illustrates the need for careful and detailed analysis of the angular momentum budget for any GCM used to simulate superrotating atmospheres.
    Journal of Geophysical Research 12/2012; 117(E12):12004-. · 3.17 Impact Factor
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    ABSTRACT: The lack of magnetic anomalies within the major impact basins (Hellas, Argyre, and Isidis) has led many investigators to the conclusion that Mars' dynamo shut down prior to the time when these basins formed (∼4.0 Ga). We test this hypothesis by analyzing gravity and magnetic anomalies in the regions surrounding Tyrrhenus Mons and Syrtis Major, two volcanoes that were active during the late Noachian and Hesperian. We model magnetic anomalies that are associated with gravity anomalies and generally find that sources located below Noachian surface units tend to favor paleopoles near the equator and sources located below Hesperian surface features favor paleopoles near the geographical poles, suggesting polar wander during the Noachian-Hesperian. Both paleopole clusters have positive and negative polarities, indicating reversals of the field during the Noachian and Hesperian. Magnetization of sources below Hesperian surfaces is evidence that the dynamo persisted beyond the formation of the major impact basins. The demagnetization associated with the volcanic construct of Syrtis Major implies dynamo cessation occurred while it was geologically active approximately 3.6 billion years ago. Timing of dynamo activity is fundamentally linked to Mars' climate via the stability of its atmosphere, and is coupled to the extent and duration of surface geologic activity. Thus, the dynamo history is key for understanding both when Mars was most geologically active and when it may have been most hospitable to life.
    Journal of Geophysical Research 10/2012; 117(E10):10007-. · 3.17 Impact Factor
  • Keke Zhang, D. Kong, G. Schubert, J. Anderson
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    ABSTRACT: An accurate calculation of the rotationally distorted shape and internal structure of Jupiter is required to understand the high-precision gravitational field that will be measured by the Juno spacecraft now on its way to Jupiter. We present a three-dimensional non-spherical numerical calculation of the shape and internal structure of a model of Jupiter with a polytropic index of unity. The calculation is based on a finite element method and accounts for the full effects of rotation. After validating the numerical approach against the asymptotic solution of Chandrasekhar (1933) that is valid only for a slowly rotating gaseous planet, we apply it to a model of Jupiter whose rapid rotation causes a significant departure from spherical geometry. The two-dimensional distribution of the density and the pressure within Jupiter is then determined via a hybrid inverse approach by matching the a priori unknown coefficient in the equation of state to the observed shape of Jupiter. After obtaining the two-dimensional distribution of Jupiter's density, we then compute the zonal gravity coefficients and the total mass from the non-spherical Jupiter model that takes full account of rotation-induced shape changes. Our non-spherical model with a polytrope of unit index is able to produce the known mass and zonal gravitational coefficients of Jupiter. Chandrasekhar, S. 1933, The equilibrium of distorted polytropes, MNRAS 93, 390
  • X. Zhan, G. Schubert
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    ABSTRACT: It is generally believed that Ganymede's core is composed of an Fe-FeS alloy and that convective motions inside it are responsible for generating the satellite's magnetic field. Analysis of the melting behavior of Fe-FeS alloys at Ganymede's core pressures suggests that, besides the growth of a solid inner core, convection can be driven by two novel mechanisms: Fe snow and FeS flotation. To advance our understanding of magnetic field generation in Ganymede, we construct dynamo models in which deep inner core growth, Fe-snow and FeS flotation drive convection. Although a dynamo can be found in each of these cases, the dynamos have different characteristics. For example, some dynamos are dipole dominant and others are not. It is found that multipole-dominant magnetic fields are generated in all Fe-snow cases, while dipole dominant dynamos are found in FeS flotation cases and in inner core growth cases. Ganymede's present dipole-dominant magnetic field suggests that the Fe-snow process does not play a primary role in driving Ganymede's core convection. The reason that Fe-snow driven convection does not produce a dipole-dominant dynamo can be related to the buoyancy flux. In Fe-snow cases, the buoyancy source is located at the core-mantle boundary (CMB), and the buoyancy flux peaks there, while in the other two cases, the buoyancy source is located at the inner core boundary where the buoyancy flux peaks.
    Journal of Geophysical Research 08/2012; 117(E8):8011-. · 3.17 Impact Factor
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    ABSTRACT: Our fundamental understanding of the interior of the Earth comes from seismology, geodesy, geochemistry, geomagnetism, geothermal studies, and petrology. For the Earth, measurements in those disciplines of geophysics have revealed the basic internal layering of the Earth, its dynamical regime, its thermal structure, its gross compositional stratification, as well as significant lateral variations in these quantities. Planetary interiors not only record evidence of conditions of planetary accretion and differentiation, they exert significant control on surface environments. We present recent advances in possible in-situ investigations of the interior of Mars, experiments and strategies that can provide unique and critical information about the fundamental processes of terrestrial planet formation and evolution. Such investigations applied on Mars have been ranked as a high priority in virtually every set of European, US and international high-level planetary science recommendations for the past 30 years. New seismological methods and approaches based on the cross-correlation of seismic noise by two seismic stations/landers on the surface of Mars and on joint seismic/orbiter detection of meteorite impacts, as well as the improvement of the performance of Very Broad-Band (VBB) seismometers have made it possible to secure a rich scientific return with only two simultaneously recording stations. In parallel, use of interferometric methods based on two Earth-Mars radio links simultaneously from landers tracked from Earth has increased the precision of radio science experiments by one order of magnitude. Magnetometer and heat flow measurements will complement seismic and geodetic data in order to obtain the best information on the interior of Mars. In addition to studying the present structure and dynamics of Mars, these measurements will provide important constraints for the astrobiology of Mars by helping to understand why Mars failed to sustain a magnetic field, by helping to understand the planet’s climate evolution, and by providing a limit for the energy available to the chemoautotrophic biosphere through a measurement of the surface heat flow. The landers of the mission will also provide meteorological stations to monitor the climate and obtain new measurements in the atmospheric boundary layer.
    Planetary and Space Science 08/2012; · 2.11 Impact Factor
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    ABSTRACT: We examine the angular momentum budget for different Venus general circulation models. We find that if there is weak angular momentum forcing, numerical diffusion and residual numerical torques can dominate and give unphysical results.
    LPI Contributions. 06/2012;
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    ABSTRACT: Expressions for momentum and heat fluxes using density as the vertical coordinate are derived. These are applied in the evaluation of fluxes using data from super-pressure balloons drifting on constant density surfaces in the Antarctic lower stratosphere during the VORCORE campaign (September 2005 to February 2006). We focus on the core months of October and November. Vertical fluxes of zonal and meridional momentum are calculated using wind, pressure and height data and the vertical flux of sensible heat is calculated using temperature and height data. Calculations were performed in three band passes covering 1-13 h. We find that the largest fluxes are in the vicinity of the Antarctic Peninsula. In October the fluxes in the low period band pass (1-5 h) account for the main part of the total flux of zonal momentum, consistent with topographically forced waves. During November the vertical fluxes of zonal momentum are found mainly in longer period band passes, consistent with weaker winds. The peak campaign-averaged flux of zonal momentum in the vicinity of the Antarctic Peninsula is ˜-30 mPa. These values are ˜60% larger over the peninsula than those inferred by other authors. The flux of zonal momentum provides a zonal body force of ˜5 m s-1 day-1 assuming a saturated spectrum. We infer downward sensible heat fluxes of ˜3 W m-2. The corresponding cooling rates assuming a saturated spectrum are ˜0.6 K day-1, a significant fraction of the net radiative imbalance in the springtime Antarctic lower stratosphere.
    Journal of Geophysical Research 05/2012; 117(D9):9105-. · 3.17 Impact Factor
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    ABSTRACT: In the analysis I model crustal magnetic anomalies near the Tyrrhenus Mons and Syrtis Major volcanoes and the heavily cratered highlands between Arabia Terra and the Hellas impact basin. I first map the gravity anomalies in each region to identify the locations of anomalous crustal density. The gravity data are inverted to determine the depth and thickness of the layer, which are used as inputs to the magnetic inversion to reduce the inherent non-uniqueness in the horizontal position of magnetic sources. Magnetic anomalies are modeled where there is a gravity minimum or maximum in close proximity to a peak in the total magnetic field. Geologic processes such as magmatism, cratering, and serpentinization produce gravity and magnetic anomalies. All three components of the low altitude and mapping altitude magnetic field data are inverted using the same conjugate gradient iterative technique used by Langlais et al. (2004) and Langlais and Purucker (2007). The resulting paleopoles span a range of latitudes for sources below Noachian and Hesperian aged crusts. Magnetic sources that favor low latitude paleopoles are generally located below or immediately adjacent to Noachian surface units, and sources that favor middle to high latitude paleopoles are located below or immediately adjacent to Hesperian features. The cluster of paleopoles near the geographical pole associated with younger units is strong evidence that the dynamo was active during the Hesperian. Opposite polarities of paleomagnetic poles clustered in the same region are strong evidence for reversals of the magnetic field in the Noachian and Hesperian. The paleopole distributions determined support the case for true polar wander, magnetic reversals, and a dynamo that remained active into the Hesperian.
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    Dali Kong, Keke Zhang, Gerald Schubert
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    ABSTRACT: Rapidly rotating giant planets are usually marked by the existence of strong zonal flows at the cloud level. If the zonal flow is sufficiently deep and strong, it can produce hydrostatic-related gravitational anomalies through distortion of the planet's shape. This paper determines the zonal gravity coefficients, J 2n , n = 1, 2, 3, ..., via an analytical method taking into account rotation-induced shape changes by assuming that a planet has an effective uniform density and that the zonal flows arise from deep convection and extend along cylinders parallel to the rotation axis. Two different but related hydrostatic models are considered. When a giant planet is in rigid-body rotation, the exact solution of the problem using oblate spheroidal coordinates is derived, allowing us to compute the value of its zonal gravity coefficients , without making any approximation. When the deep zonal flow is sufficiently strong, we develop a general perturbation theory for estimating the variation of the zonal gravity coefficients, , caused by the effect of the deep zonal flows for an arbitrarily rapidly rotating planet. Applying the general theory to Jupiter, we find that the deep zonal flow could contribute up to 0.3% of the J 2 coefficient and 0.7% of J 4. It is also found that the shape-driven harmonics at the 10th zonal gravity coefficient become dominant, i.e., for n ≥ 5.
    The Astrophysical Journal 03/2012; 748(2):143. · 6.73 Impact Factor
  • B. J. Travis, G. Schubert
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    ABSTRACT: A numerical model of fluid flow and heat and salt transport in Enceladus results in long-lasting transient flow restricted to polar regions with a very non-uniform ice shell distribution.

Publication Stats

8k Citations
1,294.71 Total Impact Points


  • 2000–2014
    • University of Exeter
      • Department of Mathematics
      Exeter, England, United Kingdom
  • 1977–2013
    • University of California, Los Angeles
      • • Department of Earth and Space Sciences (ESS)
      • • Institute of Geophysics and Planetary Physics
      Los Angeles, California, United States
  • 1994–2010
    • California Institute of Technology
      • • Jet Propulsion Laboratory
      • • Division of Geological and Planetary Sciences
      Pasadena, CA, United States
  • 1979–2010
    • CSU Mentor
      Long Beach, California, United States
  • 2009
    • University of California, Santa Cruz
      Santa Cruz, California, United States
  • 2004
    • Clemson University
      • Department of Physics and Astronomy
      Anderson, Indiana, United States
    • Johns Hopkins University
      • Department of Earth and Planetary Sciences
      Baltimore, Maryland, United States
  • 2003
    • Embry-Riddle Aeronautical University
      • Department of Physical Sciences
      Daytona Beach, FL, United States
  • 1996–1997
    • Rutgers, The State University of New Jersey
      • Department of Mechanical and Aerospace Engineering
      New Brunswick, NJ, United States
  • 1994–1995
    • The Scripps Research Institute
      La Jolla, California, United States
  • 1989
    • University of Southern California
      Los Angeles, California, United States
    • University of Texas at Austin
      Austin, Texas, United States
  • 1988
    • University of Münster
      Muenster, North Rhine-Westphalia, Germany
  • 1982
    • Goethe-Universität Frankfurt am Main
      Frankfurt, Hesse, Germany