Meteorology of the terrestrial planets

The thermodynamics, dynamics, weather and general circulation (climate) of the atmospheres of Venus, Earth and Mars is reviewed, in the light of present knowledge. These three terrestrial planets each have a gaseous sunlit envelope, but the realizations of motions in them are quite different. This makes comparisons of their meteorology very interesting and challenging.     

Structure and evolution of the terrestrial planets

Geo-scientific planetary research of the last 25 years has revealed the global structure and evolution of the terrestrial planets Moon, Mercury, Venus and Mars. The evolution of the terrestrial bodies involves a differentiation into heavy metallic cores, Fe-and Mg-rich silicate mantles and light Ca, Al-rich silicate crusts early in the history of the solar system. Magnetic measurements yield a weak dipole field for Mercury, a very weak field (and local anomalies) for the Moon and no measurable field for Venus and mars. Seismic studies of the Moon show a crust-mantle boundary at an average depth of 60 km for the front side, P- and S-wave velocities around 8 respectively 4.5 km s^–1 in the mantle and a considerable S-wave attenuation below a depth of 1000 km. Satellite gravity permits the study of lateral density variations in the lithosphere. Additional contributions come from photogeology, orbital particle, x-and -ray measurements, radar and petrology.The cratered surfaces of the smaller bodies Moon and Mercury have been mainly shaped by meteorite impacts followed by a period of volcanic flows into the impact basins until about 3×10⁹ yr before present. Mars in addition shows a more developed surface. Its northern half is dominated by subsidence and younger volcanic flows. It even shows a graben system (rift) in the equatorial region. Large channels and relics of permafrost attest the role of water for the erosional history. Venus, the most developed body except Earth, shows many indications of volcanism, grabens (rifts) and at least at northern latitudes collisional belts, i.e. mountain ranges, suggesting a limited plate tectonic process with a possible shallow subduction.List of Symbols and Abbreviations a=R _e mean equatorial radius (km) - A(r, t) heat production by radioactive elements (W m^–3) - A, B equatorial moments of inertia - b polar radius (km) - complex amplitude of bathymetry in the wave number (K) domain (m) - C polar moment of inertia - C _Fe moment of inertia of metallic core - C _Si moment of inertia of silicate mantle - C _p heat capacity at constant pressure (JK^–1 mole^–) - C _nm,J _nm,S _nm harmonic coefficients of degreen and orderm - C/(MR _e ² ) factor of moment of inertia - d distance (km) - d nondimensional radius of disc load of elastic bending model - D diameter of crater (km) - D flexural rigidity (dyn cm) - E Young modulus (dyn cm^–2) - E maximum strain energy - E energy loss during time interval t - f frequency (Hz) - f flattening - F magnetic field strength (Oe) (1 Oe=79.58A m^–1) - g acceleration or gravity (cms^–2) or (mGal) (1mGal=10^–3cms^–2) - mean acceleration - g _e equatorial surface gravity - complex amplitude of gravity anomaly in the wave number (K) domain - g free air gravity anomaly (FAA) - g Bouguer gravity anomaly - g _t gravity attraction of the topography - G gravitational constant,G=6.67×10^–11 m³kg^–1s^–2 - GM planetocentric gravitational constant - h relation of centrifugal acceleration (² R _e ) to surface acceleration (g _e ) at the equator - J magnetic flux density (magnetic field) (T) (1T=10⁹ nT=10⁹ =10⁴G (Gauss)) - J ₂ oblateness - J _nm seeC _nm - k ₍₀₎ (zero) pressure bulk modulus (Pa) (Pascal, 1 Pa=1 Nm^–2) - K wave number (km^–1) - K ^* thermal conductivity (Jm^–1s^–1K^–1) - L thickness of elastic lithosphere (km) - M mas of planet (kg) - M _Fe mass of metallic core - M _Si mass of silicate mantle - M(r) fractional mass of planet with fractional radiusr - m magnetic dipole moment (Am²) (1Am²=10³Gcm³) - m _b body wave magnitude - N crater frequency (km^–2) - N(D) cumulative number of cumulative frequency of craters with diameters D - P pressure (Pa) (1Pa=1Nm^–2=10^–5 bar) - P _z vertical (lithostatic) stress, see also _z (Pa) - P _n ^m (cos) Legendre polynomial - q surface load (dyn cm^–2) - Q seismic quality factor, 2E/E - Q _s ,Q _p seismic quality factor derived from seismic S-and P-waves - R=R ₀ mean radius of the planet (km) (2a+b)/3 - R _e =a mean equatorial radius of the planet - r distance from the center of the planet (fractional radius) - r _Fe radius of metallic core - S _nm seeC _nm - t time and age in a (years), d (days), h (hours), min (minutes), s (seconds) - T mean crustal thickness from Airy isostatic gravity models (km) - T temperature (°C or K) (0°C=273.15K) - T _m solidus temperature - T sideral period of rotation in d (days), h (hours), min (minutes), s (seconds), =2/T - U external potential field of gravity of a planet - V volume of planet - V _p ,V _s compressional (P), shear (S) wave velocity, respectively (kms^–1) - w deflection of lithosphere from elastic bending models (km) - z, Z depth (km) - z (K) admittance function (mGal m^–1) - thermal expansion (°C^–1) - viscosity (poise) (1 poise=1gcm^–1s^–1) - co-latitude (90°-) - longitude - Poisson ratio - density (g cm^–3) - mean density - ₀ zero pressure density - _m , _Si average density of silicate mantle (fluid interior) - average density of metallic core - _t , _top density of the topography - density difference between crustal and mantle material - electrical conductivity (^–1 m^–1) - _r , radial and azimuthal surface stress of axisymmetric load (Pa) - _z vertical (lithostatic) stress (seeP _z ) - _II second invariant of stress deviation tensor - latitude - angular velocity of a planet (=2/T) - ages in years (a), generally 0 years is present - B.P. before present - FAA Free Air Gravity Anomaly (see g - HFT High Frequency Teleseismic event - LTP Lunar Transient Phenomenon - LOS Line-Of-Sight - NRM Natural Remanent Magnetization Contribution No. 309, Institut für Geophysik der Universität, Kiel, F.R.G.     

The atmospheres of the terrestrial planets

Current knowledge of the atmospheres of Venus, Earth and Mars is reviewed, with emphasis on aspects where recent observational or theoretical work shows common processes at work. Selected problems of particular interest at the present time are described under the headings of composition, thermal structure, clouds, dynamics, weather and climate, and aeronomy. The overall problem remains the understanding of the origin and evolution of the planets, and the stability of their atmospheres and the surface environment or climate which they control. The latter depends on a complicated balance between radiative, dynamical and chemical processes which is only rather sketchily understood at present.     

Core formation in terrestrial planets

Calculations of the radial distribution of the energy released in core formation indicate that the cores of all the terrestrial planets may be expected to receive a disproportionate share of the gravitational energy released. Since the model of the process used in these calculations favors transfer of energy to the mantle, it is likely that other reasonable models of the process will result in even more energy being deposited in the cores of the early planets. The calculations also show that it is necessary for a certain amount of core phase to separate and accumulate, before the energy released by gravitational settling is sufficient to supply the latent heat of fusion of the core phase. The amount of melting required to reach this point varies according to the total mass of the planet, and mass fraction of core, but is not particularly great (<5% for the Earth to ～ 37% for the Moon). In the case of the Moon, this amount of segregation, although large, amounts to a surface layer about 260 km thick, similar to the proposed depth of early wholesale melting. Core separation in terrestrial planets appears to be a self-sustaining process even for fairly small bodies, provided that a small amount of a dense potential core phase is present. Although it seems likely to occur rapidly (within 10⁶–10⁷ years) even for small (Moon-size) bodies, detailed kinetic models will be necessary to specify the time scale.     

Gravitational potential energy of terrestrial planets

Summary The gravitational potential energies of Mercury, Venus and Mars have been computed on the basis of density models and compared to that of the Earth. It has been stated that the specific potential energy per unit mass is very close as regards the pair Earth and Venus, as well as the pair Mercury and Mars.Dedicated to the Memory of K. P     

A simple model of convection in the terrestrial planets

Abstract

In this paper we study analytically the simplest fluid mechanical model which can mimic the convective behavior which is thought to occur in the solid mantles of the terrestrial planets. The convecting materials are polycrystalline rocks, whose creep behavior depends very strongly on temperature and probably also on pressure. As a simple model of this situation, we consider the flow of a Newtonian viscous fluid, whose viscosity depends strongly on temperature (only), and in fact has an infinite viscosity below a certain temperature, and a constant viscosity above this temperature. This model would also be directly relevant to the convection of a melt beneath its own solid phase (e.g. water below ice, though in that case there are other physical complications).

As a consequence of this assumption, there is a vigorous convection zone overlain by a stagnant lid, as also observed in analogous laboratory experiments (Nataf and Richter, 1982). The analysis is then very similar to that of Roberts (1979), but the extension to variable viscosity introduces important differences, most notably that the boundary between the lid and the convecting zone is unknown, and not horizontal. The resulting buoyancy induced stresses near this boundary are much larger than the stresses produced by buoyancy in the side-wall plumes, and mean that the dynamics of this region, and hence also the heat flux, are independent of the rest of the cell. We give a first order approximation for the Nusselt number-Rayleigh number relationship.     

Geophysical observations pertaining to solid-state convection in the terrestrial planets

We present a broad-based review of the observational evidence that pertains to or otherwise implies solid-state convection to be occurring (or have occurred) in the interiors of the terrestrial planets.For the Earth, the motion of the plates is prima facie evidence of large-scale mantle convection. Provided we understand upper-mantle thermal conductivity correctly, heat flow beneath the old ocean basins may be too high to be transported conductively from the upper mantle through the base of the lithosphere and therefore convection on a second smaller scale might be operative. The horizontal scale of plate dimensions implies, due to typical cell aspect ratios observed in convection, that the motion extends to the core-mantle boundary. Improved global data coverage and viscoelastic modeling of isostatic rebound due to Pleistocene deglaciation imply a uniform mantle viscosity, and thus indicate that whole-mantle convection could exist. Additionally, there is some seismic evidence of lithospheric penetration to depths deeper than 700 km. We discuss some salient features and assumption boundedness of arguments for convection confined to the upper mantle and for convection which acts throughout the mantle since the vertical length scale has a profound effect upon the relevance of geophysical observations. The horizontal form of mantle convection may be fully three-dimensional with complex planform and, therefore, searching for correlative gravity patterns in the ocean basins may not be useful without additional geophysical constraints. Many long-wavelength gravity anomalies may arise from beneath the lithosphere and must be supported dynamically, although thermal convection is not a unique explanation. Topography is an additional geophysical constraint, but for wavelengths greater than a few hundred kilometers, a general lack of correlation exists between oceanic residual gravity and topography, except at specific locations such as Hawaii. Theoretical calculations predict a complex relationship between these two observational types. Oceanic gravity data alone shows no regular planform and there is no correlation with any small-scale convective pattern predicted by laboratory experiments.All of the observational evidence argues against Martian plate tectonics occurring now or over much of the history of this planet, but lack of plate tectonics is not an argument against interior convection. The Tharsis uplift on Mars may have resulted from convective processes in the mantle, and the present-day gravity anomaly associated with Tharsis must be supported by the finite strength of the lithosphere or by mantle convection. Stresses imparted by the present topographic load would be greater than a kilobar, in excess of long-term finite strength. Observed fracture patterns are probably a direct result of this load, and the key question concerns the level of resultant strain relief. The global topographic and geomorphic dichotomy between the northern and southern hemisphere required a solid-state flow process to create the accompanying center-of-figure to center-of-mass offset.Lunar heat flow values, in analogy with oceanic heat flow on the Earth, strongly imply a convective mechanism of heat transport in the interior which, based on seismic Q values, is limited to the lower mantle. The presence of moonquakes in this region does not preclude solid-state convective processes. Lunar conductivity profiles provide no information on convection because of the difficulty in conductivity modeling, uniqueness of models, and the uncertainty in the conductivity-temperature relationship. The excess oblateness of the lunar figure over the hydrostatic value does not require convective support; in fact, such a mechanism is unlikely.The presence of a dipole magnetic field on Mercury does not provide a constraint on mantle convection unless its existence can be inextricably linked to a molten core. The non-hydrostatic shape of the equatorial figure, required for the observed $\text{3}\text{2}$ resonance between Mercury's rotational and orbital periods, is most likely related to surface processes, as opposed to convection. The $\text{3n}\text{2}$ resonance implies escape from a 2n resonance and, therefore, is related to the question of a molten core. Further dynamical data is needed to constrain interior models.Interpretation of limited radar imagery for the surface of Venus is enigmatic in terms of plate tectonics and therefore interior convection. Linear tensional and possibly compressional features are observed, but there are also crustal regions which appear to show large impact structures and are thus geologically old and may not have been recycled.     

Are anharmonicity corrections needed for temperature-profile calculations of interiors of terrestrial planets?

It is shown that there is linearity between the thermal pressure P_TH and T between the Debye temperature θ and some high temperature $\text{T}{}^1$. $\text{T}{}^1$ has been measured at 1 atm and is reported for several minerals including, for example, MgO (1300 K) and forsterite (1200 K). The change in thermal pressure from room temperature for five solids, so far measured, indicate striking linearity with T at high temperatures.It is further shown that the value of $\text{T}{}^1$ increases greatly as the pressure increases. It is therefore concluded that P_TH is probably linear with T for mantle minerals under mantle conditions. The proportionality constant is derived from the measurements of thermal expansivity and bulk modulus at high temperature and zero pressure.The argument is then reversed. Assuming that the thermal pressure is in fact linear with T for the various shells in a planet, the resulting density and temperature profile of the planet is derived. The resulting density profile of the Earth compares favorably with corresponding values of recent seismic profiles.     

Formation of strong stationary vortex turbulence in the terrestrial magnetosheath

The microscopic consequences of the presence of nonlinear vortex structures in the near-Earth plasma dispersive medium are studied in this work. In dispersive media, strongly localized vortex structures contain trapped particles, cause pronounced density fluctuations, and intensify transfer processes, mixing in a medium; i.e., they can form strong vortex turbulence. Turbulence is represented as a gas in the ensemble of strongly localized (therefore, weakly interacting) identical vortices composing the ground state. Vortices with different amplitudes are randomly located in space (since they interact with one another) and are described statistically. It is assumed that the steady turbulent state is formed through a balance of mutually competing effects: spontaneous generation of vortices due to nonlinear steepening of the disturbance front, ^noise transfer to small scales, and collisional or collisionless damping of disturbances in the HF region. Noise scaling in the inertial interval takes place since structures merge during their collision. A magnetized plasma medium in the magnetosheath is considered. A new type of turbulent fluctuation spectra with respect to wavenumbers k ^−8/3, which is in satisfactory agreement with satellite observations in space plasma, has been determined. The medium particle diffusion on an ensemble of vortices has also been studied. It has been established that the interaction between structures themselves and between structures and medium particles causes anomalous diffusion in the medium. The effective diffusion coefficient square roothly depends on the noise stationary level.     

The palaeomagnetism of muddy sediment cores from the Inner Sound,Northwest Scotland,and the glacial and post-glacial history of sedimentation in the area

Josephinite is a terrestrial iron-nickel alloy with an intergrown magnesium silicate, and arsenide and sulphide phases, and andradite garnet; several specimens have been found to contain elemental silicon and CaO · 2“FeO”. Josephinite is not awaruite, an iron-nickel mineral formed by serpentinization of ultramafic rocks. Because of its geologic setting and unique mineralogy we propose that josephinite might have originated in the region of the coremantle boundary, was transported via a deep-mantle “plume” and diatreme mechanism into lithosphere mantle that has been emplaced in the Klamaths by ophiolite obduction. Regardless of such a hypothesis, we report here the discovery of terrestrial silicon occurring with josephinite, which seems to preclude a lithosphere environment of origin for josephinite.     

Connectivity of molten Fe alloy in peridotite based on in situ electrical conductivity measurements: implications for core formation in terrestrial planets

The connectivity of molten Fe-S in peridotite has been experimentally investigated by means of in situ electrical conductivity measurements at high temperatures and 1 GPa. Starting materials were powdered mixtures of peridotite KLB-1 with various amounts (0, 3, 6, 13, 19, 24 vol.%) of the 1 GPa eutectic composition in the Fe-FeS binary system. At temperatures above the eutectic point in the Fe-FeS system (∼980 °C) and below the solidus of KLB1 (∼1200 °C), molten Fe-S in a solid silicate matrix interconnects when the volume fraction is over ∼5%. Conductivity-temperature paths indicate that in the presence of partial silicate melting the connectivity of molten Fe-S in a peridotite matrix is inhibited. Based on observations of retrieved samples, the percolation threshold of Fe-S melts in the presence of low to moderate degrees of silicate melt is estimated at 13±2 vol.%. These results indicate that if the volume fraction of Fe-alloy in a planetesimal was initially greater than 5%, and if early heating by decay of radionuclides raised the temperature of the interior above the Fe-alloy melting point, initial metal segregation was controlled by permeable flow of molten iron alloy in a solid silicate matrix. These conditions were likely met by many terrestrial objects in the early solar nebula. Efficient removal of residual Fe-alloy (5 vol.%) from silicate requires high-degree melting of silicate so that metal can segregate as droplets. Giant impacts during the final stage of accretion of large planetary objects could supply the energy required for high-degrees of melting. Alternatively, if initial metal segregation were delayed until a planetary object grew to large size (∼1000 km in diameter), release of gravitational potential energy due to metal segregation could contribute enough heat to form a magma ocean.     

Global electromagnetic induction in the Moon and planets

A summary of experiments and analyses concerning electromagnetic induction in the Moon and other extraterrestrial bodies is presented. Magnetic step-transient measurements made on the lunar dark side show the eddy current response to be the dominant induction mode of the Moon. Analysis of the poloidal field decay of the eddy currents has yielded a range of monotonic conductivity profiles for the lunar interior: the conductivity rises from 3·10^?4 mho/m at a depth of 170 km to 10^?2 mho/m at 1000 km depth. The static magnetization field induction has been measured and the whole-Moon relative magnetic permeability has been calculated to be $\text{μ}\text{μ}{}_0\text{= 1.01 ± 0.06}$. The remanent magnetic fields, measured at Apollo landing sites, range from 3 to 327 γ. Simultaneous magnetometer and solar wind spectrometer measurements show that the 38-γ remanent field at the Apollo 12 site is compressed to 54 γ by a solar wind pressure increase of 7·10^?8 dyn/cm². The solar wind confines the induced lunar poloidal field; the field is compressed to the surface on the lunar subsolar side and extends out into a cylindrical cavity on the lunar antisolar side. This solar wind confinement is modeled in the laboratory by a magnetic dipole enclosed in a superconducting lead cylinder; results show that the induced poloidal field geometry is modified in a manner similar to that measured on the Moon. Induction concepts developed for the Moon are extended to estimate the electromagnetic response of other bodies in the solar system.     

Analytic base of geodynamo-like scaling laws in the planets,geomagnetic periodicities and inversions

Scaling laws for hydromagnetic dynamo in planets initially express the characteristic strength of the magnetic field through the primary values, such as the size of the conductive core of the planet, the angular rotation rate, electrical conductivity and energy flows. Most of the earlier proposed scaling laws based only on observations and assumptions about force balances. Recent and my new approaches to fully take into account the energy and induction balance has additionally expressed here in terms of primary values such important characteristics as forces, magnitudes, energies, scales and orientations of hydromagnetic fields. The direct numerical simulation of the hydromagnetic dynamo and modeling ability in a fairly wide range of parameters for the first time allowed direct test such laws. The obtained numerical geodynamo-like results for the Earth, Jupiter and partially Saturn postulated previously not identified analytically simplest law that predicts the field strength is only depended on the specific energy density of convection and the size of the dynamo area. This simplest and already widely used law was original way analytically grounded here along with other previously known and new laws. This analytic identifies the physics determining geomagnetic periodicities for jerk, secular variations and inversions. Mean period between the inversions is found to be roughly proportional to the intensity of the geomagnetic field that is confirmed by some paleomagnetic researches. Possible dynamos in Mercury, Ganymede, Uranus and Neptune are also discussed.     

Ar,Kr, and Xe in terrestrial materials

³⁶Ar, ⁸⁴Kr, and ¹³²Xe abundances along with Kr and Xe isotopic compositions are reported for two African shales and samples of chert from the Gunflint Formation in Canada. It is observed that these data and similar abundance data from other terrestrial materials show correlations between ³⁶Ar-⁸⁴Kr and between ⁸⁴Kr-¹³²Xe. The elemental ratios defined by all the above data differ significantly from and show greater variations than those measured in carbonaceous chondrites, a well-investigated class of extraterrestrial material. Physical absorption and equilibrium solubility acting on the atmosphere are investigated as explanations for the observations. The Kr and Xe isotopic spectra are also consistent with a mass-dependent incorporation process acting on a reservoir of atmospheric composition.     

Pb-derived ages for the reconstruction of terrestrial contaminant history into the Mexican Pacific coast: Potential and limitations

²¹⁰Pb is widely used for dating recent sediments in the aquatic environment; however, our experiences working in shallow coastal environments in the Pacific coast of Mexico have demonstrated that the potential of ²¹⁰Pb for reliable historical reconstructions might be limited by the low ²¹⁰Pb atmospheric fallout, sediment mixing, abundance of coarse sediments and the lack of ¹³⁷Cs signal for ²¹⁰Pb corroboration. This work discusses the difficulties in obtaining adequate sedimentary records for geochronological reconstruction in such active and complex settings, including examples of ²¹⁰Pb geochronologies based on sediment profiles collected in two contrasting areas coastal areas (mudflats associated to coastal lagoons of Sinaloa State and the continental shelf of the Gulf of Tehuantepec), in which geochemical data was used to support the temporal frame established and the changes in sediment supply recorded in the sediment cores which were related to the development of land-based activities during the last century.     

Convection-driven zonal flows in the major planets

The major planets produce heat flux from their interiors that is comparable to the radiative flux they receive from the sun. The dynamics of convection flows carrying the heat flux are discussed, and the dominating effect of the Coriolis force is demonstrated. The characteristic high-velocity jets in the atmospheres of Jupiter and Saturn can be explained on the basis of Reynolds stresses generated by the fluctuating convective motions. A simple annulus model, which elucidates the more complex mathematical analysis of the spherical case given in an earlier paper (Busse, 1983), is considered in detail. Various aspects of the observational evidence are discussed in relation to the model.     

Early physical conditions of the planets and satellites

An understanding of the origin of the Solar System is proving hard to achieve and there is still no finally accepted account. A wider range of reliable data, and especially for the outer Solar System, has become available over the last decade due to the use of space vehicles, and particularly the two Voyager probes which are now passing out of the Solar System. The planetary and satellite systems can, therefore, be viewed now more nearly as a whole than previously and consequences for the theory of the origin of the System should follow. The subject is here reviewed again but emphasis is placed on the relative planetology of the whole System. The only reliable data available to us are associated with the System as it is now and this will be the starting point for our discussion.     

Cation distribution in low-calcium pyroxenes: Dependence on temperature and calcium content and the thermal history of lunar and terrestrial pigeonites

Four pyroxenes with compositions En₄₈Fs₄₈Wo₄, En_47·5Fs_47·5Wo₅, En₄₅Fs₄₅Wo₁₀ and En₄₀Fs₄₀Wo₂₀, synthesized at 1200°C at atmospheric pressure, were heat-treated at 500, 600, 700, and 800°C for various lengths of time. These pyroxenes are variously ordered with respect to Fe²⁺ and Mg²⁺ without unmixing. The Fe²⁺-Mg²⁺ distribution over the two nonequivalent sites M1 and M2, determined through Mössbauer spectroscopy, is found to be a function of both temperature and concentration of Ca²⁺ at the M2 site. The preference of Fe²⁺ for the M2 site increases with decreasing temperature and increasing Ca²⁺. These data can be used to determine cation equilibration temperatures of lunar and terrestrial pigeonites. The lunar pigeonites usually indicate equilibration temperatures of 700–860°C, except the pigeonite from rock 14053, which may have been subjected to shock heating due to meteoritic impact.