Solar Magnetic Carpet I: Simulation of Synthetic Magnetograms

This paper describes a new 2D model for the photospheric evolution of the magnetic carpet. It is the first in a series of papers working towards constructing a realistic 3D non-potential model for the interaction of small-scale solar magnetic fields. In the model, the basic evolution of the magnetic elements is governed by a supergranular flow profile. In addition, magnetic elements may evolve through the processes of emergence, cancellation, coalescence and fragmentation. Model parameters for the emergence of bipoles are based upon the results of observational studies. Using this model, several simulations are considered, where the range of flux with which bipoles may emerge is varied. In all cases the model quickly reaches a steady state where the rates of emergence and cancellation balance. Analysis of the resulting magnetic field shows that we reproduce observed quantities such as the flux distribution, mean field, cancellation rates, photospheric recycle time and a magnetic network. As expected, the simulation matches observations more closely when a larger, and consequently more realistic, range of emerging flux values is allowed (4×10¹⁶ – 10¹⁹ Mx). The model best reproduces the current observed properties of the magnetic carpet when we take the minimum absolute flux for emerging bipoles to be 4×10¹⁶ Mx. In future, this 2D model will be used as an evolving photospheric boundary condition for 3D non-potential modeling.     

Carbon dioxide on the satellites of Saturn: Results from the Cassini VIMS investigation and revisions to the VIMS wavelength scale

Several of the icy satellites of Saturn show the spectroscopic signature of the asymmetric stretching mode of C-O in carbon dioxide (CO₂) at or near the nominal solid-phase laboratory wavelength of 4.2675 μm (2343.3 cm⁻¹), discovered with the Visible-Infrared Mapping Spectrometer (VIMS) on the Cassini spacecraft. We report here on an analysis of the variation in wavelength and width of the CO₂ absorption band in the spectra of Phoebe, Iapetus, Hyperion, and Dione. Comparisons are made to laboratory spectra of pure CO₂, CO₂ clathrates, ternary mixtures of CO₂ with other volatiles, implanted and adsorbed CO₂ in non-volatile materials, and ab initio theoretical calculations of CO₂ * nH₂O. At the wavelength resolution of VIMS, the CO₂ on Phoebe is indistinguishable from pure CO₂ ice (each molecule’s nearby neighbors are also CO₂) or type II clathrate of CO₂ in H₂O. In contrast, the CO₂ band on Iapetus, Hyperion, and Dione is shifted to shorter wavelengths (typically ∼4.255 μm (∼2350.2 cm⁻¹)) and broadened. These wavelengths are characteristic of complexes of CO₂ with different near-neighbor molecules that are encountered in other volatile mixtures such as with H₂O and CH₃OH, and non-volatile host materials like silicates, some clays, and zeolites. We suggest that Phoebe’s CO₂ is native to the body as part of the initial inventory of condensates and now exposed on the surface, while CO₂ on the other three satellites results at least in part from particle or UV irradiation of native H₂O plus a source of C, implantation or accretion from external sources, or redistribution of native CO₂ from the interior.The analysis presented here depends on an accurate VIMS wavelength scale. In preparation for this work, the baseline wavelength calibration for the Cassini VIMS was found to be distorted around 4.3 μm, apparently as a consequence of telluric CO₂ gas absorption in the pre-launch calibration. The effect can be reproduced by convolving a sequence of model detector response profiles with a deep atmospheric CO₂ absorption profile, producing distorted detector profile shapes and shifted central positions. In a laboratory blackbody spectrum used for radiance calibration, close examination of the CO₂ absorption profile shows a similar deviation from that expected from a model. These modeled effects appear to be sufficient to explain the distortion in the existing wavelength calibration now in use. A modification to the wavelength calibration for 13 adjacent bands is provided. The affected channels span about 0.2 μm centered on 4.28 μm. The maximum wavelength change is about 10 nm toward longer wavelength. This adjustment has implications for interpretation of some of the spectral features observed in the affected wavelength interval, such as from CO₂, as discussed in this paper.     

From planetesimals to terrestrial planets: N-body simulations including the effects of nebular gas and giant planets

We present results from a suite of N-body simulations that follow the formation and accretion history of the terrestrial planets using a new parallel treecode that we have developed. We initially place 2000 equal size planetesimals between 0.5 and 4.0 AU and the collisional growth is followed until the completion of planetary accretion (>100 Myr). A total of 64 simulations were carried out to explore sensitivity to the key parameters and initial conditions. All the important effect of gas in laminar disks are taken into account: the aerodynamic gas drag, the disk-planet interaction including Type I migration, and the global disk potential which causes inward migration of secular resonances as the gas dissipates. We vary the initial total mass and spatial distribution of the planetesimals, the time scale of dissipation of nebular gas (which dissipates uniformly in space and exponentially in time), and orbits of Jupiter and Saturn. We end up with 1-5 planets in the terrestrial region. In order to maintain sufficient mass in this region in the presence of Type I migration, the time scale of gas dissipation needs to be 1-2 Myr. The final configurations and collisional histories strongly depend on the orbital eccentricity of Jupiter. If today’s eccentricity of Jupiter is used, then most of bodies in the asteroidal region are swept up within the terrestrial region owing to the inward migration of the secular resonance, and giant impacts between protoplanets occur most commonly around 10 Myr. If the orbital eccentricity of Jupiter is close to zero, as suggested in the Nice model, the effect of the secular resonance is negligible and a large amount of mass stays for a long period of time in the asteroidal region. With a circular orbit for Jupiter, giant impacts usually occur around 100 Myr, consistent with the accretion time scale indicated from isotope records. However, we inevitably have an Earth size planet at around 2 AU in this case. It is very difficult to obtain spatially concentrated terrestrial planets together with very late giant impacts, as long as we include all the above effects of gas and assume initial disks similar to the minimum mass solar nebular.     

Oxidation of CO on surface hematite in high CO2 atmospheres

We propose a mechanism for the oxidation of gaseous CO into CO₂ occurring on the surface mineral hematite (Fe₂O₃(s)) in hot, CO₂-rich planetary atmospheres, such as Venus. This mechanism is likely to constitute an important source of tropospheric CO₂ on Venus and could at least partly address the CO₂ stability problem in Venus’ stratosphere, since our results suggest that atmospheric CO₂ is produced from CO oxidation via surface hematite at a rate of 0.4 petagrammes (Pg) CO₂ per (Earth) year on Venus which is about 45% of the mass loss of CO₂ via photolysis in the Venusian stratosphere. We also investigated CO oxidation via the hematite mechanism for a range of planetary scenarios and found that modern Earth and Mars are probably too cold for the mechanism to be important because the rate-limiting step, involving CO(g) reacting onto the hematite surface, proceeds much slower at lower temperatures. The mechanism may feature on extrasolar planets such as Gliese 581c or CoRoT-7b assuming they can maintain solid surface hematite which, e.g. starts to melt above about 1200 K. The mechanism may also be important for hot Hadean-type environments and for the emerging class of hot Super-Earths with planetary surface temperatures between about 600 and 900 K.     

A parallel global-implicit 2-D solver for reactive transport problems in porous media based on a reduction scheme and its application to the MoMaS benchmark problem

In this article, an approach for the efficient numerical solution of multi-species reactive transport problems in porous media is described. The objective of this approach is to reformulate the given system of partial and ordinary differential equations (PDEs, ODEs) and algebraic equations (AEs), describing local equilibrium, in such a way that the couplings and nonlinearities are concentrated in a rather small number of equations, leading to the decoupling of some linear partial differential equations from the nonlinear system. Thus, the system is handled in the spirit of a global implicit approach (one step method) avoiding operator splitting techniques, solved by Newton’s method as the basic algorithmic ingredient. The reduction of the problem size helps to limit the large computational costs of numerical simulations of such problems. If the model contains equilibrium precipitation-dissolution reactions of minerals, then these are considered as complementarity conditions and rewritten as semismooth equations, and the whole nonlinear system is solved by the semismooth Newton method.     

Erosion rates on different timescales derived from cosmogenic 10Be and river loads: implications for landscape evolution in the Rhenish Massif, Germany

We determined erosion rates on timescales of 10¹–10⁴ years for two catchments in the northeastern Rhenish Massif, in order to unravel the Quaternary landscape evolution in a Variscan mountain range typical of central Europe. Spatially averaged erosion rates derived from in situ produced ¹⁰Be concentrations in stream sediment of the Aabach and M?hne watersheds range from 47 ± 6 to 65 ± 14 mm/ka and integrate over the last 9–13 ka. These erosion rates are similar to local rates of river incision and rock uplift in the Quaternary and to average denudation rates since the Mesozoic derived from fission track data. This suggests that rock uplift is balanced by denudation, i.e., the landscape is in a steady state. Short-term erosion rates were derived from suspended and dissolved river loads subsequent to (1) correcting for atmospheric and anthropogenic inputs, (2) establishing calibration curves that relate the amount of suspended load to discharge, and (3) estimating the amount of bedload. The resulting solid mass fluxes (suspended and bedload) agree with those derived from the sediment volume trapped in three reservoirs. However, resulting geogenic short-term erosion rates range from 9 to 25 mm/ka and are only about one-third of the rates derived from ¹⁰Be. Model simulations in combination with published sediment yield data suggest that this discrepancy is caused by at least three factors: (1) phases with higher precipitation and/or lower evapotranspiration, (2) rare flood events not captured in the short-term records, and (3) prolonged periods of climatic deterioration with increased erosion and sediment transport on hillslopes.     

Population displacement after cyclone and its consequences: empirical evidence from coastal Bangladesh

This study investigates the disaster-induced population displacement scenario at individual household level in Bangladesh. ‘Population displacement’ is seen here as an alternative adaptation option to natural hazard for the survivors after cyclone Aila. The changes both in origin and destination community due to population displacement are described here on the basis of social ‘inclusion’ and ‘exclusion’ concept. The field survey was conducted during March–July 2010, and a sample of 280 respondents from 12 villages in southwest coastal Bangladesh was interviewed. Findings show that at the end of emergency aid, male members of the family started moving towards nearer cities to find an income. Based on the income and asset distribution at the community level, this study developed a societal cluster of displacement and demonstrates the societal changes because of cyclone-induced population displacement.     

Evolution of the mass function of dark matter haloes

We use a high-resolution ΛCDM numerical simulation to calculate the mass function of dark matter haloes down to the scale of dwarf galaxies, back to a redshift of 15, in a  50 h ⁻¹ Mpc  volume containing 80 million particles. Our low-redshift results allow us to probe low-σ density fluctuations significantly beyond the range of previous cosmological simulations. The Sheth & Tormen mass function provides an excellent match to all of our data except for redshifts of 10 and higher, where it overpredicts halo numbers increasingly with redshift, reaching roughly 50 per cent for the  10¹⁰–10¹¹ M_⊙  haloes sampled at redshift 15. Our results confirm previous findings that the simulated halo mass function can be described solely by the variance of the mass distribution, and thus has no explicit redshift dependence. We provide an empirical fit to our data that corrects for the overprediction of extremely rare objects by the Sheth & Tormen mass function. This overprediction has implications for studies that use the number densities of similarly rare objects as cosmological probes. For example, the number density of high-redshift  ( z ≃ 6) QSOs  , which are thought to be hosted by haloes at 5σ peaks in the fluctuation field, are likely to be overpredicted by at least a factor of 50 per cent. We test the sensitivity of our results to force accuracy, starting redshift and halo-finding algorithm.     

Efficient block preconditioners for the coupled equations of pressure and deformation in highly discontinuous media

Large‐scale simulations of flow in deformable porous media require efficient iterative methods for solving the involved systems of linear algebraic equations. Construction of efficient iterative methods is particularly challenging in problems with large jumps in material properties, which is often the case in geological applications, such as basin evolution at regional scales. The success of iterative methods for this type of problems depends strongly on finding effective preconditioners. This paper investigates how the block‐structured matrix system arising from single‐phase flow in elastic porous media should be preconditioned, in particular for highly discontinuous permeability and significant jumps in elastic properties. The most promising preconditioner combines algebraic multigrid with a Schur complement‐based exact block decomposition. The paper compares numerous block preconditioners with the aim of providing guidelines on how to formulate efficient preconditioners. Copyright © 2010 John Wiley & Sons, Ltd.     

Implementing quality control on a random number stream to improve a stochastic weather generator

For decades, stochastic modellers have used computerized random number generators to produce random numeric sequences fitting a specified statistical distribution. Unfortunately, none of the random number generators we tested satisfactorily produced the target distribution. The result is generated distributions whose mean even diverges from the mean used to generate them, regardless of the length of run. Non‐uniform distributions from short sequences of random numbers are a major problem in stochastic climate generation, because truly uniform distributions are required to produce the intended climate parameter distributions. In order to ensure generation of a representative climate with the stochastic weather generator CLIGEN within a 30‐year run, we tested the climate output resulting from various random number generators. The resulting distributions of climate parameters showed significant departures from the target distributions in all cases. We traced this failure back to the uniform random number generators themselves. This paper proposes a quality control approach to select only those numbers that conform to the expected distribution being retained for subsequent use. The approach is based on goodness‐of‐fit analysis applied to the random numbers generated. Normally distributed deviates are further tested with confidence interval tests on their means and standard deviations. The positive effect of the new approach on the climate characteristics generated and the subsequent deterministic process‐based hydrology and soil erosion modelling are illustrated for four climatologically diverse sites. Copyright © 2007 John Wiley & Sons, Ltd.