Corrections stemming from the non-osculating character of the Andoyer variables used in the description of rotation of the elastic Earth

We explore the evolution of the angular velocity of an elastic Earth model, within the Hamiltonian formalism. The evolution of the rotation state of the Earth is caused by the tidal deformation exerted by the Moon and the Sun. It can be demonstrated that the tidal perturbation to spin depends not only upon the instantaneous orientation of the Earth, but also upon its instantaneous angular velocity. Parameterizing the orientation of the Earth figure axis with the three Euler angles, and introducing the canonical momenta conjugated to these, one can then show that the tidal perturbation depends both upon the angles and the momenta. This circumstance complicates the integration of the rotational motion. Specifically, when the integration is carried out in terms of the canonical Andoyer variables (which are the rotational analogues to the orbital Delaunay variables), one should keep in mind the following subtlety: under the said kind of perturbations, the functional dependence of the angular velocity upon the Andoyer elements differs from the unperturbed dependence (Efroimsky in Proceedings of Journées 2004: Systèmes de référence spatio-temporels. l’Observatoire de Paris, pp 74–81, 2005; Efroimsky and Escapa in Celest. Mech. Dyn. Astron. 98:251–283, 2007). This happens because, under angular velocity dependent perturbations, the requirement for the Andoyer elements to be canonical comes into a contradiction with the requirement for these elements to be osculating, a situation that parallels a similar antinomy in orbital dynamics. Under the said perturbations, the expression for the angular velocity acquires an additional contribution, the so called convective term. Hence, the time variation induced on the angular velocity by the tidal deformation contains two parts. The first one comes from the direct terms, caused by the action of the elastic perturbation on the torque-free expressions of the angular velocity. The second one arises from the convective terms. We compute the variations of the angular velocity through the approach developed in Getino and Ferrándiz (Celest. Mech. Dyn. Astron. 61:117–180, 1995), but considering the contribution of the convective terms. Specifically, we derive analytical formulas that determine the elastic perturbations of the directional angles of the angular velocity with respect to a non-rotating reference system, and also of its Cartesian components relative to the Tisserand reference system of the Earth. The perturbation of the directional angles of the angular velocity turns out to be different from the evolution law found in Kubo (Celest. Mech. Dyn. Astron. 105:261–274, 2009), where it was stated that the evolution of the angular velocity vector mimics that of the figure axis. We investigate comprehensively the source of this discrepancy, concluding that the difference between our results and those obtained in Ibid. stems from an oversimplification made by Kubo when computing the direct terms. Namely, in his computations Kubo disregarded the motion of the tide raising bodies with respect to a non-rotating reference system when compared with the Earth rotational motion. We demonstrate that, from a numerical perspective, the convective part provides the principal contribution to the variation of the directional angles and of length of day. In the case of the x and y components in the Tisserand system, the convective contribution is of the same order of magnitude as the direct one. Finally, we show that the approximation employed in Kubo (Ibid.) leads to significant numerical differences at the level of a hundred micro-arcsecond.     

Meteorites at Meridiani Planum provide evidence for significant amounts of surface and near‐surface water on early Mars

Abstract– Six large iron meteorites have been discovered in the Meridiani Planum region of Mars by the Mars Exploration Rover Opportunity in a nearly 25 km‐long traverse. Herein, we review and synthesize the available data to propose that the discovery and characteristics of the six meteorites could be explained as the result of their impact into a soft and wet surface, sometime during the Noachian or the Hesperian, subsequently to be exposed at the Martian surface through differential erosion. As recorded by its sediments and chemical deposits, Meridiani has been interpreted to have undergone a watery past, including a shallow sea, a playa, an environment of fluctuating ground water, and/or an icy landscape. Meteorites could have been encased upon impact and/or subsequently buried, and kept underground for a long time, shielded from the atmosphere. The meteorites apparently underwent significant chemical weathering due to aqueous alteration, as indicated by cavernous features that suggest differential acidic corrosion removing less resistant material and softer inclusions. During the Amazonian, the almost complete disappearance of surface water and desiccation of the landscape, followed by induration of the sediments and subsequent differential erosion and degradation of Meridiani sediments, including at least 10–80 m of deflation in the last 3–3.5 Gy, would have exposed the buried meteorites. We conclude that the iron meteorites support the hypothesis that Mars once had a denser atmosphere and considerable amounts of water and/or water ice at and/or near the surface.     

A cyclical period variation detected in the updated orbital period analysis of TV Columbae

Two CCD photometries of the intermediate polar TV Columbae are made for obtaining two updated eclipse timings with high precision. There is an interval time ～17 yr since the last mid-eclipse time observed in 1991. Thus, the new mid-eclipse times might offer an opportunity to check the previous orbital ephemerides. A calculation indicates that the orbital ephemeris derived by Augusteijn et al. (Astron. Astrophys. Suppl. Ser. 107:219, 1994) should be corrected. Based on the proper linear ephemeris (Hellier in Mon. Not. R. Astron. Soc. 264:132, 1993), the new orbital period analysis suggests a cyclical period variation in the O–C diagram of TV Columbae. Using Applegate’s mechanism to explain the periodic oscillation in the O–C diagram, the required energy is larger than the energy that a M0-type star can afford over a complete variation period of ～31.0(±3.0) yr. Thus, the light travel-time effect indicates that the tertiary component in TV Columbae may be a dwarf with a low mass, which is near the lower mass limit of ～0.08M _⊙ as long as the inclination of the third body is high enough.     

Stability and chemical equilibrium of amphibole in calc-alkaline magmas: an overview, new thermobarometric formulations and application to subduction-related volcanoes

This work focuses on a rigorous analysis of the physical–chemical, compositional and textural relationships of amphibole stability and the development of new thermobarometric formulations for amphibole-bearing calc-alkaline products of subduction-related systems. Literature experimental results (550–1,120°C, <1,200 MPa, −1 ≤ ΔNNO ≤ +5), H₂O–CO₂ solubility models, a multitude of amphibole-bearing calc-alkaline products (whole-rocks and glasses, representing 38 volcanoes worldwide), crustal and high-P (1–3 GPa) mantle amphibole compositions have been used. Calcic amphiboles of basalt-rhyolite volcanic products display tschermakitic pargasite (37%), magnesiohastingsite (32%) and magnesiohornblende (31%) compositions with aluminium number (i.e. Al# = ^[6]Al/Al_T) ≤ 0.21. A few volcanic amphiboles (~1%) show high Al# (>0.21) and are inferred to represent xenocrysts of crustal or mantle materials. Most experimental results on calc-alkaline suites have been found to be unsuitable for using in thermobarometric calibrations due to the high Al# (>0.21) of amphiboles and high Al₂O₃/SiO₂ ratios of the coexisting melts. The pre-eruptive crystallization of consistent amphiboles is confined to relatively narrow physical–chemical ranges, next to their dehydration curves. The widespread occurrence of amphiboles with dehydration (breakdown) rims made of anhydrous phases and/or glass, related to sub-volcanic processes such as magma mixing and/or slow ascent during extrusion, confirms that crystal destabilization occurs with relatively low T–P shifts. At the stability curves, the variance of the system decreases so that amphibole composition and physical–chemical conditions are strictly linked to each other. This allowed us to retrieve some empirical thermobarometric formulations which work independently with different compositional components (i.e. Si^*, Al_T, Mg^*, ^[6]Al^*) of a single phase (amphibole), and are therefore easily applicable to all types of calc-alkaline volcanic products (including hybrid andesites). The Si^*-sensitive thermometer and the fO₂–Mg^* equation account for accuracies of ±22°C (σ_est) and 0.4 log units (maximum error), respectively. The uncertainties of the Al_T-sensitive barometer increase with pressure and decrease with temperature. Near the P–T stability curve, the error is <11% whereas for crystal-rich (porphyritic index i.e. PI > 35%) and lower-T magmas, the uncertainty increases up to 24%, consistent with depth uncertainties of 0.4 km, at 90 MPa (~3.4 km), and 7.9 km, at 800 MPa (~30 km), respectively. For magnesiohornblendes, the ^[6]Al^*-sensitive hygrometer has an accuracy of 0.4 wt% (σ_est) whereas for magnesiohastingsite and tschermakitic pargasite species, H₂O_melt uncertainties can be as high as 15% relative. The thermobarometric results obtained with the application of these equations to calc-alkaline amphibole-bearing products were finally, and successfully, crosschecked on several subduction-related volcanoes, through complementary methodologies such as pre-eruptive seismicity (volcano-tectonic earthquake locations and frequency), seismic tomography, Fe–Ti oxides, amphibole–plagioclase, plagioclase–liquid equilibria thermobarometry and melt inclusion studies. A user-friendly spreadsheet (i.e. AMP-TB.xls) to calculate the physical–chemical conditions of amphibole crystallization is also provided.     

Temperature induced decoupling of enzymatic hydrolysis and carbon remineralization in long-term incubations of Arctic and temperate sediments

Extracellular enzymatic hydrolysis of high-molecular weight organic matter is the initial step in sedimentary organic carbon degradation and is often regarded as the rate-limiting step. Temperature effects on enzyme activities may therefore exert an indirect control on carbon mineralization. We explored the temperature sensitivity of enzymatic hydrolysis and its connection to subsequent steps in anoxic organic carbon degradation in long-term incubations of sediments from the Arctic and the North Sea. These sediments were incubated under anaerobic conditions for 24 months at temperatures of 0, 10, and 20 °C. The short-term temperature response of the active microbial community was tested in temperature gradient block incubations. The temperature optimum of extracellular enzymatic hydrolysis, as measured with a polysaccharide (chondroitin sulfate), differed between Arctic and temperate habitats by about 8-13 °C in fresh sediments and in sediments incubated for 24 months. In both Arctic and temperate sediments, the temperature response of chondroitin sulfate hydrolysis was initially similar to that of sulfate reduction. After 24 months, however, hydrolysis outpaced sulfate reduction rates, as demonstrated by increased concentrations of dissolved organic carbon (DOC) and total dissolved carbohydrates. This effect was stronger at higher incubation temperatures, particularly in the Arctic sediments. In all experiments, concentrations of volatile fatty acids (VFA) were low, indicating tight coupling between VFA production and consumption. Together, these data indicate that long-term incubation at elevated temperatures led to increased decoupling of hydrolytic DOC production relative to fermentation. Temperature increases in marine sedimentary environments may thus significantly affect the downstream carbon mineralization and lead to the increased formation of refractory DOC.     

The economics of boldness: equity,action, and hope

Equity is usually interpreted in terms of the concept of justice, such that an equitable share of the atmospheric space is understood in terms of past emissions. This emphasizes the collective nature of sharing the burden of mitigation and the duty to act for those who have emitted the most. An alternative is considered: the aggregate costs and benefits to all Parties that could result from both increasing the level of collective ambition and implementing a climate regime that supports bold actions across all Parties. The regional impacts and carbon flow costs across differentiated scenarios are assessed and it is argued that the majority of developing-country Parties would be better off if a high ambition outcome to which all contributed, but some more than others. Moreover, those with middle or low emissions would have proportionally more to gain (or lose) relative to the level of ambition compared to those that have had higher emissions. The climate regime should be built on the principle of common but differentiated responsibility and respective capabilities (CBDR&RC), in which all act early even if some do much more; one that accounts for justice but does not forget hope.

Policy relevance

Differing interpretations of equity and the principles of the United Nations Framework Convention on Climate Change (UNFCCC) are discussed, with a focus on how these can enhance or hinder collective action. Whilst the climate change negotiations are usually taken as games in which one party gains and another loses, and interactions are dogged by continuous conflict, it is explored instead how negotiation responses can be framed in terms of cooperation. This would emphasize the gains that could be achieved by common but differentiated collective action, which could result in a collective avoidance of impacts. The possibilities that this shift of perspective could bring are explored by comparing costs under global cooperation (or lack of it). It is found that cooperation reduces the total costs for these regions. Thus, thinking in terms of cooperation focuses the options for negotiation on the means and interpretations of the UNFCCC principles that spur action and avoid climate impacts through collective action.     

The freshwater lens of Benjamín Aceval,Chaco, Paraguay: a terrestrial analogue of an oceanic island lens

The occurrence of a freshwater lens in the Paraguayan Chaco, 900 km away from the ocean, is reported. It is located underneath sandstone hills, surrounded by lowlands with predominantly saline groundwater. Its geometry was delineated using geoelectrical and electromagnetic investigations. The unusual height of the fresh groundwater level can be attributed to the presence of a confining layer at depth. The lens receives its recharge exclusively from rainfall during the hot and humid summer months. It predominantly contains water predating the atmospheric atomic bomb tests, some of it probably up to a thousand or more years old. The water balance shows that extraction currently does not exceed recharge in normal years. However, the available volume of groundwater leaves little room for a further increase of extraction in the future. Recharge is augmented by return flow from thousands of latrines and cess pits, and this has lead to widespread contamination of the groundwater by faecal bacteria.     

Catastrophic,rainfall-induced debris flows in Andean villages of Tarapacá, Atacama Desert,northern Chile

In March 2012, during the rainy season in the Altiplano plateau, a >100-year return period rainfall event affected the deeply incised valleys of the Precordillera of the Tarapacá Region, northern Chile. This extreme event in a very arid region triggered a number of debris and mud flows that caused severe damage and destruction in several small villages along the Camiña and Tarapacá valleys. The highly vulnerable location of the villages on top of alluvial fans due to socioeconomic and cultural reasons is a key factor to explain the level of destruction in most villages. In this paper, this unusual, remarkable landslide event is described, and the hazard faced by these settlements for future rainfall episodes and possible mitigation measures are discussed.