The impact of cloud inhomogeneities on the Earth radiation budget: the 14 October 1989 I.C.E. convective cloud case study

Through their multiple interactions with radiation, clouds have an important impact on the climate. Nonetheless, the simulation of clouds in climate models is still coarse. The present evolution of modeling tends to a more realistic representation of the liquid water content; thus the problem of its subgrid scale distribution is crucial. For a convective cloud field observed during ICE 89, Landsat TM data (resolution: 30m) have been analyzed in order to quantify the respective influences of both the horizontal distribution of liquid water content and cloud shape on the Earth radiation budget. The cloud field was found to be rather well-represented by a stochastic distribution of hemi-ellipsoidal clouds whose horizontal aspect ratio is close to 2 and whose vertical aspect ratio decreases as the cloud cell area increases. For that particular cloud field, neglecting the influence of the cloud shape leads to an over-estimate of the outgoing longwave flux; in the shortwave, it leads to an over-estimate of the reflected flux for high solar elevations but strongly depends on cloud cell orientations for low elevations. On the other hand, neglecting the influence of cloud size distribution leads to systematic over-estimate of their impact on the shortwave radiation whereas the effect is close to zero in the thermal range. The overall effect of the heterogeneities is estimated to be of the order of 10 W m⁻² for the conditions of that Landsat picture (solar zenith angle 65○, cloud cover 70%); it might reach 40 W m⁻² for an overhead sun and overcast cloud conditions.     

Distribution of magnetic energy in αΩ-dynamos,I: The method

Abstract

In this paper a method for solving the equation for the mean magnetic energy <BB> of a solar type dynamo with an axisymmetric convection zone geometry is developed and the main features of the method are described. This method is referred to as the finite magnetic energy method since it is based on the idea that the real magnetic field B of the dynamo remains finite only if <BB> remains finite. Ensemble averaging is used, which implies that fields of all spatial scales are included, small-scale as well as large-scale fields. The method yields an energy balance for the mean energy density ε ≡ B ²/8π of the dynamo, from which the relative energy production rates by the different dynamo processes can be inferred. An estimate for the r.m.s. field strength at the surface and at the base of the convection zone can be found by comparing the magnetic energy density and the outgoing flux at the surface with the observed values. We neglect resistive effects and present arguments indicating that this is a fair assumption for the solar convection zone. The model considerations and examples presented indicate that (1) the energy loss at the solar surface is almost instantaneous; (2) the convection in the convection zone takes place in the form of giant cells; (3) the r.m.s. field strength at the base of the solar convection zone is no more than a few hundred gauss; (4) the turbulent diffusion coefficient within the bulk of the convection zone is about 10¹⁴cm²s^?1, which is an order of magnitude larger than usually adopted in solar mean field models.     

Convective heat transfer in magmas near the liquidus

Natural convection in magmas at subliquidus temperatures is analyzed using Bingham plastic and power-law rheology models. Heat flux measurements were obtained at liquidus and subliquidus temperatures for degassed basaltic lava at atmospheric pressure. These measurements of heat flux ranged from 2 to 40 kW/m² and were obtained using two different types of convective heat flux probes. The agreement between the two different instruments and the theoretical calculations is excellent. A noticeable change in the trend of the convective heat flux data is observed in the vicinity of the liquidus temperature. Subliquidus convective heat flux rates (6–15 kW/m²) are attractive for energy extraction applications.     

The flux ejection dynamo effect

Abstract

The mean-field effects of cyclonic convection become increasingly complex when the cyclonic rotation exceeds ½-π. Net helicity is not required, with negative turbulent diffusion, for instance, appearing in mirror symmetric turbulence. This paper points out a new dynamo effect arising in convective cells with strong asymmetry in the rotation of updrafts as against downdrafts. The creation of new magnetic flux arises from the ejection of reserve flux through the open boundary of the dynamo region. It is unlike the familiar α-effect in that individual components of the field may be amplified independently. Several formal examples are provided to illustrate the effect. Occurrence in nature depends upon the existence of fluid rotations of the order of π in the convective updrafts. The flux ejection dynamo may possibly contribute to the generation of field in the convective core of Earth and in the convective zone of the sun and other stars.     

Formation of magnetic flux tubes in cylindrical wedge geometry

Three-dimensional (3D) MHD numerical simulations have not been able to demonstrate convincingly the spontaneous formation of large vertical flux tubes. Two-dimensional (2D) magnetoconvection in axisymmetric cylinders forms a central magnetic flux tube surrounded by annular convection rings. To study the robustness of this type of solution in three dimensions, the nonlinear resistive MHD equations are solved numerically in a 3D cylindrical wedge from an initially uniform vertical magnetic field. It is shown that the 2D result is retrieved for small domain radii. However, for larger radii the central axis loses its importance and in this case many convection cells form in the numerical domain. Magnetic flux is captured between cells where flow converges and the reduced amount of flux that congregates at the central axis is eroded by the surrounding convection.     

Magnetohydrodynamic simulation of a solar flare: 2. Flare model and simulation using active-region magnetic maps

The results of a three-dimensional MHD simulation and data obtained using specialized spacecraft made it possible to construct an electrodynamic model of solar flares. A flare results from explosive magnetic reconnection in a current sheet above an active region, and electrons accelerated in field-aligned currents cause hard X rays on the solar surface. In this review, we considered works where the boundary and initial conditions on the photosphere were specified directly from the magnetic maps, obtained by SOHO MDI in the preflare state, in order to simulate the formation of a current sheet. A numerical solution of the complete set of MHD equations, performed using the new-generation PERESVET program, demonstrated the formation of several current sheets before a series of flares. A comparison of the observed relativistic proton spectra and the simulated proton acceleration along a magnetic field singular line made it possible to estimate the magnetic reconnection rate during a flare (∼10⁷ cm s⁻¹). Great flares (of the X class) originate after an increase in the active region magnetic flux up to 10²² Mx.     

GPU-accelerated computing of three-dimensional solar wind background

High-performance computational models are required to make the real-time or faster than real-time numerical prediction of adverse space weather events and their influence on the geospace environment. The main objective in this article is to explore the application of programmable graphic processing units (GPUs) to the numerical space weather modeling for the study of solar wind background that is a crucial part in the numerical space weather modeling. GPU programming is realized for our Solar-Interplanetary-CESE MHD model (SIP-CESE MHD model) by numerically studying the solar corona/interplanetary solar wind. The global solar wind structures are obtained by the established GPU model with the magnetic field synoptic data as input. Meanwhile, the time-dependent solar surface boundary conditions derived from the method of characteristics and the mass flux limit are incorporated to couple the observation and the three-dimensional (3D) MHD model. The simulated evolution of the global structures for two Carrington rotations 2058 and 2062 is compared with solar observations and solar wind measurements from spacecraft near the Earth. The MHD model is also validated by comparison with the standard potential field source surface (PFSS) model. Comparisons show that the MHD results are in good overall agreement with coronal and interplanetary structures, including the size and distribution of coronal holes, the position and shape of the streamer belts, and the transition of the solar wind speeds and magnetic field polarities.     

Models for the origin and composition of the earth,and the hypothesis of potassium in the Earth's core

Progress in understanding the condensation of planetary constituents from a solar nebula necessitates a re-examination of models for the origin and composition of the Earth. All models which appear to be viable require the Earth to have an Fe–FeS core and the full, or nearly full, solar (i.e. chondritic) K/Si ratio. The crust and upper mantle do not contain the requisite potassium for the entire Earth to have the solar K/Si ratio. Therefore, these models require that much of the Earth's potassium, about 80–90%, must be in the deep interior—in the lower mantle or in the core.The hypothesis that a substantial fraction of the Earth's potassium is in the Fe–FeS core is based on the chalcophilic behavior of potassium. Data including the stability of K₂S, the occurrence of potassium in sulfide phases in meteorites and in metallurgical systems, and most importantly, experiments on potassium partitioning between solid silicates and Fe–FeS melts support this hypothesis. The present data appear to require at least several percent of the Earth's total potassium to be in the core. Incorporation of much larger amounts of potassium into the core, possibly most of the 80–90% of the Earth's potassium which is postulated to be in the deep interior, is not contradicted by the present data. Additional experimental data, at high pressures, are required before quantitative estimates of the core's potassium content can be made.It is likely that⁴⁰K is a significant heat source in the core. Decay of⁴⁰K is a plausible energy source to drive core convection to maintain the geomagnetic field, and to drive mantle convection and seafloor spreading.     

Displacement of large-scale open solar magnetic fields from the zone of active longitudes and the heliospheric storm of November 3–10, 2004: 2. “Explosion” of singularity and dynamics of sunspot formation and energy release

A more detailed scenario of one stage (August–November 2004) of the quasibiennial MHD process “Origination ... and dissipation of the four-sector structure of the solar magnetic field” during the decline phase of cycle 23 has been constructed. It has been indicated that the following working hypothesis on the propagation of an MHD disturbance westward (in the direction of solar rotation) and eastward (toward the zone of active longitudes) with the displacement of the large-scale open solar magnetic field (LOSMF) from this zone can be constructed based on LOSMF model representations and data on sunspot formation, flares, active filaments, and coronal ejections as well as on the estimated contribution of sporadic energy release to the flare luminosity and kinetic energy of ejections: (1) The “explosion” of the LOSMF singularity and the formation in the explosion zone of an anemone active region (AR), which produced the satellite sunspot formation that continued west and east of the “anemone,” represented a powerful and energy-intensive source of MHD processes at this stage. (2) This resulted in the origination of two “governing” large-scale MHD processes, which regulated various usual manifestations of solar activity: the fast LOSMF along the neutral line in the solar atmosphere, strongly affecting the zone of active longitudes, and the slow LOSMF in the outer layers of the convection zone. The fronts of these processes were identified by powerful (about 10³¹ erg) coronal ejections. (3) The collision of a wave reflected from the zone of active longitudes with the eastern front of the hydromagnetic impulse of the convection zone resulted in an increase in LOSMF magnetic fluxes, origination of an active sector boundary in the zone of active longitudes, shear-convergent motions, and generation and destabilization of the flare-productive AR 10696 responsible for the heliospheric storm of November 3–10, 2004.     

Topological semi-dynamos

Abstract

Magnetic field generation in a continuous medium in processes without self-excitation—the so-called semi-dynamo, involving as essential elements both magnetohydrodynamic processes and the presence of an impressed e.m.f.—has been studied for the case of the topological pumping effect on the magnetic field generation by an impressed e.m.f. operating in a three-dimensional Bénard convection layer.

Under conditions of interest for astrophysical applications the magnetic flux produced can exceed substantially that excited by the e.m.f. in the absence of motion.

The results obtained permitted an evaluation of the general quasi-steady magnetic field of the Sun generated by an azimuthal Coriolis e.m.f. which is active in the outermost layers of the convective envelope, taking into account small-scale convective and turbulent motions. In the polar regions of the Sun this field can reach ～10^?1 G.     

Nonlinear dynamics of boussinesq convection in a deep rotating spherical shell-i

Abstract

Convection in a rotating spherical shell has wide application for understanding the dynamics of the atmospheres and interiors of many celestial bodies. In this paper we review linear results for convection in a shell of finite depth at substantial but not asymptotically large Taylor numbers, present nonlinear multimode calculations for similar conditions, and discuss the model and results in the context of the problem of solar convection and differential rotation. Detailed nonlinear calculations are presented for Taylor number T = 10⁵, Prandtl number P = 1, and Rayleigh number R between 1 |MX 10⁴ and 4 |MX 10⁴ (which is between about 4 and 16 times critical) for a shell of depth 20% of the outer radius. Sixteen longitudinal wave numbers are usually included (all even wave numbers m between 0 and 30) the amplitudes of which are computed on a staggered grid in the meridian plane.

The kinetic energy spectrum shows a peak in the wave number range m = 12–18 at R = 10⁴, which straddles the critical wave number m = 14 predicted by linear theory. These are modes which peak near the equator. The spectrum shows a second strong peak at m = 0, which represents the differential rotation driven by the peak convective modes. As R is increased, the amplitude of low wave numbers increases relative to high wave numbers as convection fills in in high and middle latitudes, and as the longitudinal scale of equatorial convection grows. By R = 3 |MX 10⁴, m = 8 is the peak convective mode. There is a clear minimum in the total kinetic energy at middle latitudes relative to low and high, well into the nonlinear regime, representing the continued dominance of equatorial and polar modes found in the linear case. The kinetic energy spectrum for m > 0 is maintained primarily by buoyancy work in each mode, but with substantial nonlinear transfer of kinetic energy from the peak modes to both lower and higher wave numbers.

For R = 1 to 2 |MX 10⁴, the differential rotation takes the form of an equatorial acceleration, with angular velocity generally decreasing with latitude away from the equator (as on the sun) and decreasing inwards. By R = 4 |MX 10⁴, this equatorial profile has completely reversed, with angular velocity increasing with depth and latitude. Also, a polar vortex which has positive rotation relative to the reference frame (no evidence of which has been seen on the sun) builds up as soon as polar modes become important. Meridional circulation is quite weak relative to differential rotation at R = 10⁴, but grows relative to it as R is increased. This circulation takes the farm of a single cell of large latitudinal extent in equatorial regions, with upward flow near the equator, together with a series of narrower cells in high latitudes. It is maintained primarily by axisymmetric buoyancy forces. The differential rotation is maintained at all R primarily by Reynolds stresses, rather than meridional circulation. Angular momentum transport toward the equator for R = 1–2 |MX 10⁴ maintains the equatorial acceleration while radially inward transport maintains the opposite profile at R = 4 |MX 10⁴.

The total heat flux out the top of the convective shell always shows two peaks for the range of R studied, one at the equator and the other near the poles (no significant variation with latitude is seen on the sun), while heat flux in at the bottom shows only a polar peak at large R. The meridional circulation and convective cells transport heat toward the equator to maintain this difference.

The helicity of the convection plus the differential rotation produced by it suggest the system may be capable of driving a field reversing dynamo, but the toroidal field may migrate with lime in each cycle toward the poles and equator, rather than just toward the equator as apparently occurs on the sun.

We finally outline additions to the physics of the model to make it more realistic for solar application.     

太阳等离子体和磁场输出源表面结构的一种MHD模型

以观测到的光球视向磁场、Ｋ－日冕亮度作为输入,以相应的统计结果为约束条件,利用磁流体力学方程组,给出了等离子体及磁场各参数在源表面上的二维分布．其结果与同期的卫星观测数据和已有的统计结果相比较,显示出相当程度的一致性．     

Long wavelength thermal convection between non-conducting boundaries

Non-linear Rayleigh-Bénard convection in a fluid layer is considered as a model of convection in the Earth's upper mantle. Previous studies have shown that when the temperature is held fixed at one of the boundaries of the layer, convection takes place in cells of width of the order of the layer depth or less. We investigate the effects of a different thermal boundary condition, in which the flux of heat is held fixed on both layer boundaries; then if this flux is just greater than that required for the onset of convection, motion takes place on horizontal scales much greater than the layer depth. An analytical treatment of the equations, based on an expansion in the depth-to-width ratio of the cells, shows that cells of a definite horizontal scale are the fastest growing according to linearised theory, but that these cells are unstable to ones of larger wavelength than themselves. Thus the dominant wavelength lengthens with time. The results hold whether the heat flux is generated internally of comes from beneath the layer. These results produce flow patterns similar to those found when the heat flux is much greater than the critical value. The results have important consequences for the understanding of mantle convection.     

Generation and evolution of interplanetary slow shocks

It is well known that most MHD shocks observed within 1 AU are MHD fast shocks. Only a very limited number of MHD slow shocks are observed within 1 AU. In order to understand why there are only a few MHD slow shocks observed within 1 AU, we use a one-dimensional, time-dependent MHD code with an adaptive grid to study the generation and evolution of interplanetary slow shocks (ISS) in the solar wind. Results show that a negative, nearly square-wave perturbation will generate a pair of slow shocks (a forward and a reverse slow shock). In addition, the forward and the reverse slow shocks can pass through each other without destroying their characteristics, but the propagating speeds for both shocks are decreased. A positive, square-wave perturbation will generate both slow and fast shocks. When a forward slow shock (FSS) propagates behind a forward fast shock (FFS), the former experiences a decreasing Mach number. In addition, the FSS always disappears within a distance of 150R_⊙ (where R_⊙ is one solar radius) from the Sun when there is a forward fast shock (with Mach number \geq1.7) propagating in front of the FSS. In all tests that we have performed, we have not discovered that the FSS (or reverse slow shock) evolves into a FFS (or reverse fast shock). Thus, we do not confirm the FSS-FFS evolution as suggested by Whang (1987).     

A self-consistent estimate of O+ + N2– rate coefficient and total EUV solar flux with λ < 1050 Å using EISCAT observations

There are differences between existing models of solar EUV with < 1050 Å and between laboratory measurements of the O⁺ + N₂ – reaction rate coefficient, both parameters being crucial for the F2-region modeling. Therefore, indirect aeronomic estimates of these parameters may be useful for qualifying the existing EUV models and the laboratory measured O⁺ + N₂ – rate coefficient. A modified self-consistent method for daytime F2-region modeling developed by Mikhailov and Schlegel was applied to EISCAT observations (32 quiet summer and equinoctial days) to estimate the set of main aeronomic parameters. Three laboratory measured temperature dependencies for the O⁺ + N₂ – rate coefficient were used in our calculations to find self-consistent factors both for this rate coefficient and for the solar EUV flux model from Nusinov. Independent of the rate coefficient used, the calculated values group around the temperature dependence recently measured by Hierl et al. in the 850–1400 K temperature range. Therefore, this rate coefficient may be considered as the most preferable and is recommended for aeronomic calculations. The calculated EUV flux shows a somewhat steeper dependence on solar activity than both, the Nusinov and the EUVAC models predict. In practice both EUV models may be recommended for the F2-region electron density calculations with the total EUV flux shifted by ±25% for the EUVAC and Nusinov models, correspondingly.     

Geophysical evidence on the structure of the Taupo Volcanic Zone and its hydrothermal circulation

The Taupo Volcanic Zone (TVZ) of New Zealand is characterised by extensive volcanism and by high rates of magma production. Associated with this volcanism are numerous high-temperature (> 250 °C) geothermal systems through which the natural heat output of 4200 ± 500 MW is channelled. Outside the geothermal fields the heat flow is negligible. The average heat flux from the central 6000 km² of the TVZ, which contains most of the geothermal fields, is 700 mW/m³. This heat flux appears to be more concentrated along the eastern margin of the TVZ.Schlumberger resistivity measurements (AB/2 of 500 m and 1000 m) have identified 17 distinct geothermal fields with natural heat outputs greater than 20 MW. An additional six, low-heat-output geothermal fields also occur, and may represent formerly more active systems now in decline. Two extinct fields have also been identified. The average spacing between fields is 10–15 km. The distribution of geothermal fields does not appear to be directly associated with individual volcanic features except for the geothermal system that occurs within Lake Taupo and which occupies the vent of the 1800 yr.B.P. Taupo eruption. The positions of the geothermal fields do not appear to have varied for at least the last 200,000 years. These data are consistent with a model of large-scale convection occurring throughout the TVZ, in which the geothermal fields represent the upper portion of the rising, high-temperature, convective plumes. The majority of the recharge to the convection system is provided by the downward movement of cold meteoric water between the fields which suppresses the heat flow in these regions.Gravity measurements indicate that to a depth of about 2.5 km the upper layers of the TVZ consist of low-density pyroclastic infill. A seismic refraction interface with velocity change from 3.2 km/s to 5.5 km/s occurs at a similar depth. The cross-sectional area of the convection plumes (identified electrically) appears to increase at depths of 1–2 km, consistent with a decrease in permeability at the depth at which the velocity and density increase.The seismicity is dominated by swarm activity which accounts for about half of all earthquakes and is highly variable in both space and time. The small number of seismic events (and swarms) that have well determined depths show a cut off of seismicity at depths of 7–9 km. The depth of the transition from brittle to ductile behaviour of the rocks is identified with the transition from a regime where heat is transported by (hydrothermal) convection and pore pressures are near-hydrostatic to a regime where heat transport is dominantly conductive and pore pressures are lithostatic. Within the convective region, temperatures are moderated by the circulation of water so that the depth of the transition from convective to conductive heat transfer can be linked to the bottom of the seismogenic zone. Rocks must become ductile within about 1 km of the bottom of the overlying convective zone.Seismic refraction studies suggest that the crust beneath the TVZ is highly thinned with a seismic velocity of about 7.5 km/ s, typical of the upper mantle, occurring at depth of 15 km. Seismological studies indicate the upper mantle is highly attenuating beneath the TVZ. Conductive heat transfer between the bottom of the convective system, at about 8 km, and the base of the material with crustal velocities, at 15 km, is not able to provide all the heat that is discharged at the surface. Repeated intrusion from the mantle may provide the additional heat transport required.     

Substorm associated radar auroral surges: a statistical study and possible generation model

Substorm-associated radar auroral surges (SARAS) are a short lived (15–90 minutes) and spatially localised (5° of latitude) perturbation of the plasma convection pattern observed within the auroral E-region. The understanding of such phenomena has important ramifications for the investigation of the larger scale plasma convection and ultimately the coupling of the solar wind, magnetosphere and ionosphere system. A statistical investigation is undertaken of SARAS, observed by the Sweden And Britain Radar Experiment (SABRE), in order to provide a more extensive examination of the local time occurrence and propagation characteristics of the events. The statistical analysis has determined a local time occurrence of observations between 1420 MLT and 2200 MLT with a maximum occurrence centred around 1700 MLT. The propagation velocity of the SARAS feature through the SABRE field of view was found to be predominately L-shell aligned with a velocity centred around 1750 ms^–1 and within the range 500 m s^–1 and 3500 m s^–1. This comprehensive examination of the SARAS provides the opportunity to discuss, qualitatively, a possible generation mechanism for SARAS based on a proposed model for the production of a similar phenomenon referred to as sub-auroral ion drifts (SAIDs). The results of the comparison suggests that SARAS may result from a similar geophysical mechanism to that which produces SAID events, but probably occurs at a different time in the evolution of the event.     

Multimoment convecting flux tube model of the polar wind system with return current and microprocesses

Multimoment fluid simulation frameworks, which effectively account for anomalous transport due to microprocesses, combine best features of small-scale kinetic and global-scale MHD models. The most practical models of this type, 1D flux tube models, have been successfully used for realistic simulations of space plasmas including polar wind and magnetosphere–ionosphere coupling processes characterized by a wide range of temporal and spatial scales. Our earlier flux tube models with field-aligned current and microprocesses have been formulated for spatially stationary flux tubes. However, horizontal convection due to electric fields is an important aspect of the high-latitude ionosphere–polar wind system and typical time scales of the polar wind upflow are comparable to the transit time across the polar cap. To take into account this important feature we have added flux tube convection to our earlier model. Using typical convecting flux tube that starts outside auroral oval, then enters and leaves downward current region, it has been shown that anomalous transport effects due to current-driven microinstabilities significantly alter dynamics of several plasma moments and should be taken into account for an accurate interpretation and prediction of the observed data. Future applications of our new model have also been discussed.     

The rapid dissipation of magnetic fields in highly conducting fluids

Abstract

This paper treats the dynamical conditions that obtain when long straight parallel twisted flux tubes in a highly conducting fluid are packed together in a broad array. It is shown that there is generally no hydrostatic equilibrium. In place of equilibrium there is a dynamical nonequilibrium, leading to neutral point reconnection and progressive coalescence of neighboring tubes (with the same sense of twisting), forming tubes of larger diameter and reduced twist. The magnetic energy in the twisting of each tube declines toward zero, dissipated into small-scale motions of the fluid and thence into heat.

The physical implications are numerous. For instance, it has been suggested that the subsurface magnetic field of the sun is composed of close-packed twisted flux tubes. Any such structures are short lived, at best.

The footpoints of the filamentary magnetic fields above bipolar magnetic regions on the sun are continually shuffled and rotated by the convection, so that the fields are composed of twisted rubes. The twisting and mutual wrapping is converted directly into fluid motion and heat by the dynamical nonequilibrium, so that the work done by the convection of the footpoints goes directly into heating the corona above. This theoretical result is the final step, then, in understanding the assertion by Rosner, Tucker, and Valana, and others, that the observed structure of the visible corona implies that it is heated principally by direct dissipation of the supporting magnetic field. It is the dynamical nonequilibrium that causes the dissipation, in spite of the high electrical conductivity. It would appear that any bipolar magnetic field extending upward from a dense convective layer into a tenuous atmosphere automatically produces heating, and a corona of some sort, in the sun or any other convective star.