Evolution of Mercury's obliquity

Mercury has a near-zero obliquity, i.e. its spin axis is nearly perpendicular to its orbital plane. The value of the obliquity must be known precisely in order to constrain the size of the planet's core within the framework suggested by Peale [Peale, S.J., 1976. Nature 262, 765-766]. Rambaux and Bois [Rambaux, N., Bois, E., 2004. Astron. Astrophys. 413, 381-393] have suggested that Mercury's obliquity varies on thousand-year timescales due to planetary perturbations, potentially ruining the feasibility of Peale's experiment. We use a Hamiltonian approach (free of energy dissipation) to study the spin-orbit evolution of Mercury subject to secular planetary perturbations. We can reproduce an obliquity evolution similar to that of Rambaux and Bois [Rambaux, N., Bois, E., 2004. Astron. Astrophys. 413, 381-393] if we integrate the system with a set of initial conditions that differs from the Cassini state. However the thousand-year oscillations in the obliquity disappear if we use initial conditions corresponding to the equilibrium position of the Cassini state. This result indicates that planetary perturbations do not force short-period, large amplitude oscillations in the obliquity of Mercury. In the absence of excitation processes on short timescales, Mercury's obliquity will remain quasi-constant, suggesting that one of the important conditions for the success of Peale's experiment is realized. We show that interpretation of data obtained in support of this experiment will require a precise knowledge of the spin-orbit configuration, and we provide estimates for two of the critical parameters, the instantaneous Laplace plane orientation and the orbital precession rate from numerical fits to ephemeris data. Finally we provide geometrical relationships and a scheme for identifying the correct initial conditions required in numerical integrations involving a Cassini state configuration subject to planetary perturbations.     

Exploring controls of the early and stepped deglaciation on the western margin of the British Irish Ice Sheet

New optically stimulated luminescence dating and Bayesian models integrating all legacy and BRITICE-CHRONO geochronology facilitated exploration of the controls on the deglaciation of two former sectors of the British–Irish Ice Sheet, the Donegal Bay (DBIS) and Malin Sea ice-streams (MSIS). Shelf-edge glaciation occurred ~27 ka, before the global Last Glacial Maximum, and shelf-wide retreat began 26–26.5 ka at a rate of ~18.7–20.7 m a^–1. MSIS grounding zone wedges and DBIS recessional moraines show episodic retreat punctuated by prolonged still-stands. By ~23–22 ka the outer shelf (~25 000 km²) was free of grounded ice. After this time, MSIS retreat was faster (~20 m a^–1 vs. ~2–6 m a^–1 of DBIS). Separation of Irish and Scottish ice sources occurred ~20–19.5 ka, leaving an autonomous Donegal ice dome. Inner Malin shelf deglaciation followed the submarine troughs reaching the Hebridean coast ~19 ka. DBIS retreat formed the extensive complex of moraines in outer Donegal Bay at 20.5–19 ka. DBIS retreated on land by ~17–16 ka. Isolated ice caps in Scotland and Ireland persisted until ~14.5 ka. Early retreat of this marine-terminating margin is best explained by local ice loading increasing water depths and promoting calving ice losses rather than by changes in global temperatures. Topographical controls governed the differences between the ice-stream retreat from mid-shelf to the coast.     

Tidal evolution of close binary asteroid systems

We provide a generalized discussion of tidal evolution to arbitrary order in the expansion of the gravitational potential between two spherical bodies of any mass ratio. To accurately reproduce the tidal evolution of a system at separations less than 5 times the radius of the larger primary component, the tidal potential due to the presence of a smaller secondary component is expanded in terms of Legendre polynomials to arbitrary order rather than truncated at leading order as is typically done in studies of well-separated system like the Earth and Moon. The equations of tidal evolution including tidal torques, the changes in spin rates of the components, and the change in semimajor axis (orbital separation) are then derived for binary asteroid systems with circular and equatorial mutual orbits. Accounting for higher-order terms in the tidal potential serves to speed up the tidal evolution of the system leading to underestimates in the time rates of change of the spin rates, semimajor axis, and mean motion in the mutual orbit if such corrections are ignored. Special attention is given to the effect of close orbits on the calculation of material properties of the components, in terms of the rigidity and tidal dissipation function, based on the tidal evolution of the system. It is found that accurate determinations of the physical parameters of the system, e.g., densities, sizes, and current separation, are typically more important than accounting for higher-order terms in the potential when calculating material properties. In the scope of the long-term tidal evolution of the semimajor axis and the component spin rates, correcting for close orbits is a small effect, but for an instantaneous rate of change in spin rate, semimajor axis, or mean motion, the close-orbit correction can be on the order of tens of percent. This work has possible implications for the determination of the Roche limit and for spin-state alteration during close flybys.     

Resonant forcing of Mercury's libration in longitude

The period of free libration of Mercury's longitude about the position it would have had if it were rotating uniformly at 1.5 times its orbital mean motion is close to resonance with Jupiter's orbital period. The Jupiter perturbations of Mercury's orbit thereby lead to amplitudes of libration at the 11.86 year period that may exceed the amplitude of the 88 day forced libration determined by radar. Mercury's libration in longitude may be thus dominated by only two periods of 88 days and 11.86 years, where other periods from the planetary perturbations of the orbit have much smaller amplitudes.     

Radar observations and a physical model of contact binary Asteroid 4486 Mithra

Arecibo (2380 MHz, 12.6 cm) and Goldstone (8560 MHz, 3.5 cm) delay-Doppler radar images obtained in July and August of 2000 reveal that 4486 Mithra is an irregular, significantly bifurcated object, with a central valley ∼380 m deep and a long axis potentially exceeding 2 km. With its bimodal appearance, Mithra is a strong candidate for a contact binary asteroid. Sequences of Goldstone images spanning up to 3 h per day show very little rotation and establish that Mithra is an unusually slow rotator. We used Goldstone and Arecibo data to estimate Mithra’s 3D shape and spin state. We obtain prograde (λ = 337°, β = 19°) and retrograde (λ = 154°, β = −19°) models that give comparable fits, have very similar shapes roughly resembling an hourglass, and have a rotation period of 67.5 ± 6.0 h. The dimensions of these two models are very similar; for the prograde solution the maximum dimensions are X = 2.35 ± 0.15 km, Y = 1.65 ± 0.10 km, Z = 1.44 ± 0.10 km. Dynamical analysis of our models suggests that in the past, Mithra most likely went through a period of even slower rotation with its obliquity close to 90°. The spin rate is predicted to be increasing due to thermal torque (YORP), while the obliquity, which is currently +68° and +106° for the prograde and retrograde models, respectively, is predicted to move away from 90°.     

Physical modeling of near-Earth Asteroid (29075) 1950 DA

Near-Earth Asteroid (29075) 1950 DA may closely encounter Earth in 2880. The probability of Earth impact may be as high as 1/300, but the outcome of the encounter depends critically on the physical properties of the asteroid [Giorgini et al., 2002. Science 196, 132-136]. We have used Arecibo and Goldstone radar data and optical lightcurves to estimate the shape, spin state, and surface structure of 1950 DA. The data allow two distinct models. One rotates prograde and is roughly spheroidal with mean diameter 1.16±0.12 km. The other rotates retrograde and is oblate and about 30% larger. Both models suggest a nickel-iron or enstatite chondritic composition. Ground-based observations should be able to determine which model is correct within the next several decades.     

Hydrologic indicators of hydraulic conditions that drive flow–biota relationships

Abstract

This article tests the association between streamflow alteration and the alteration of ecologically significant hydraulic environments. There has been a recent shift in environmental flow assessments to develop rapid desktop-based approaches that are applicable in a regional context. Streamflow statistics (e.g. minimum monthly flow) are often chosen to predict the impact of streamflow alteration on aquatic ecosystems. The assumption that the flow–biota relationship will be obscured by the effect of how streamflow interacts with channel morphology is often acknowledged, but not quantified. In this study, streamflow statistics are derived for 19 reaches in four river systems in Victoria, Australia. Hydraulic metrics were used to quantify ecologically significant surface flow conditions (Froude number) and the area of bench inundation, shallow and deep water. Multivariate analysis was used to investigate the correlation between streamflow statistics altered with regulation and the hydraulic metrics. It was found that streamflow statistics have a weak correlation to surface flow condition and the area of shallow water under natural streamflow conditions. The results show that hydrologic statistics have limited utility in quantifying changes in hydraulic environments. A similar magnitude of flow alteration can produce diverse hydraulic results. The confounding influence of channel morphology prevents streamflow statistics being an adequate surrogate for the assessment of hydraulic alteration. Modelling flow–biota relationships in a regional context is limited by the inadequacy of streamflow statistics to model ecologically significant hydraulic function. Improving knowledge of ecohydraulically significant hydrologic statistics will improve the effectiveness of environmental flow planning to sustain instream habitat conditions. A probabilistic approach is required to enable a risk-based approach to desktop generalization of flow–biota relations.

Editor Z.W. Kundzewicz; Guest editor M. Acreman

Citation Turner, M. and Stewardson, M., 2014. Hydrologic indicators of hydraulic conditions that drive flow–biota relationships. Hydrological Sciences Journal, 59 (3–4), 659–672.     

Parallel implementations of streamline simulators

We discuss various strategies for parallelizing streamline simulators and present a single-phase shared memory implementation. The choice of a shared memory programming model is motivated by its suitability for streamline simulation, as well as the rapid advance of multicore processors, which are readily available at low-cost. We show that streamline-based methods are easily parallelizable on shared memory architectures through their decomposition of the multidimensional transport equations into a large set of independent 1D transport solves. We tested both a specialized explicit load balancing algorithm that optimizes the streamline load distribution across threads to minimize the time that any of the threads are idle, and the dynamic load balancing algorithms provided by OpenMP on the shared memory machines. Our results clearly indicate that built-in schedulers are competitive with specialized load balancing strategies as long as the number of streamlines per thread is sufficiently high, which is the case in field applications. The average workload per thread is nominally insensitive to workload variations between individual streamlines, and any load balancing advantage offered by explicit strategies is not sufficient to overcome associated computational and parallel overhead. In terms of the allocation of streamlines or streamline segments to threads, we investigated both the distributed approach, in which threads are assigned streamline segments, and the owner approach, in which threads own complete streamlines. We found that the owner approach is most suitable. The slight advantage that the distributed approach has in terms of load balancing is not enough to compensate for the additional overheads. Moreover, the owner approach allows straightforward re-use of existing sequential codes, which is not the case for the distributed approach in case of implicit or adaptive implicit solution strategies. The tracing and mapping stages in streamline simulation have low parallel efficiency. However, in real-field models, the computational burden of the streamline solves is significantly heavier than that of the tracing and mapping stages, and therefore, the impact of these stages is limited. We tested the parallelization on three shared memory systems: a 24 dual-core processor Sun SPARC server; an eight-way Sun Opteron server, representative of the state-of-the-art shared memory systems in use in the industry; and the very recently released Sun Niagara II multicore machine that has eight floating point compute units on the chip. We test a single-phase flow problem on three heterogeneous reservoirs with varying well placements (this system gives the worst case scenario as the tracing and mapping costs are not negligible compared to the transport costs). For the SPARC and Opteron system, we find parallel efficiencies ranging between 60 and 75 for the tracer flow problems. The sublinear speedup is mostly due to communication overheads in the tracing and mapping stages. In applications with more complex physics, the relative contributions of these stages will decrease significantly, and we predict the parallel performance to be nearly linear. On the Niagara II, we obtain almost perfect linear scalability even for the single-phase flow problem thanks to the lowered communication costs on these architectures that have a shared cache. This result is all the more satisfactory considering that future server designs will be akin to this system.     

Maximum extent and readvance dynamics of the Irish Sea Ice Stream and Irish Sea Glacier since the Last Glacial Maximum

The BRITICE-CHRONO Project has generated a suite of recently published radiocarbon ages from deglacial sequences offshore in the Celtic and Irish seas and terrestrial cosmogenic nuclide and optically stimulated luminescence ages from adjacent onshore sites. All published data are integrated here with new geochronological data from Wales in a revised Bayesian analysis that enables reconstruction of ice retreat dynamics across the basin. Patterns and changes in the pace of deglaciation are conditioned more by topographic constraints and internal ice dynamics than by external controls. The data indicate a major but rapid and very short-lived extensive thin ice advance of the Irish Sea Ice Stream (ISIS) more than 300 km south of St George's Channel to a marine calving margin at the shelf break at 25.5 ka; this may have been preceded by extensive ice accumulation plugging the constriction of St George's Channel. The release event between 25 and 26 ka is interpreted to have stimulated fast ice streaming and diverted ice to the west in the northern Irish Sea into the main axis of the marine ISIS away from terrestrial ice terminating in the English Midlands, a process initiating ice stagnation and the formation of an extensive dead ice landscape in the Midlands.     

Bedload tracing in a high‐sediment‐load mountain stream

This paper reports a radiofrequency identification (RFID) tracing experiment implemented in a high‐sediment‐load mountain stream typical of alpine gravel‐bed torrents. The study site is the Bouinenc Torrent, a tributary to the Bléone River in southeast France that drains a 38·9‐km² degraded catchment. In spring 2008, we deployed 451 tracers with b‐axis ranging from 23 to 520 mm. Tracers were seeded along eight cross‐sections located in the upstream part of the lowest 2·3 km of the stream. Three tracer inventories were implemented in July 2008, 2009 and 2010. Recovery rates calculated for mobile tracers declined from 78% in 2008 to 45% in 2009 and 25% in 2010. Observations of tracer displacement revealed very high sediment dispersion, with frontrunners having travelled more than 2 km only three months after their deployment. The declining recovery rate over time was interpreted as resulting from rapid dispersion rather than deep burial. We evaluated that 64% of the tracers deployed in the active channel were exported from the 2·3‐km study reach three years after the onset of the tracing experiment. Travel distances were characterized by right‐skewed and heavy‐tailed distributions, correctly fitted by a power‐law function. This supports the idea that in gravel‐bed rivers with abundant sediment supply relative to transport capacity, bedload transport can be viewed as a superdiffusive sediment dispersion process. It is also shown that tracers initially deployed in the low‐flow channel were characterized by a 15‐ to 30‐fold increase of mobility compared to tracers deployed in gravel bars. Copyright © 2011 John Wiley & Sons, Ltd.