International and Intergenerational Dimensions of Climate Change: North-South Cooperation in an Overlapping Generations Framework

Global environmental problems such as climate change have both an international and an intertemporal dimension. Recently, some papers have used an overlapping generations framework to analyze the climate change problem taking into account jointly the issues of intergenerational equity and intertemporal efficiency but without considering the international aspect of the problem. In this paper, we extend such approach by considering an overlapping generations model of climate-economy interactions where the world is split into two regions: North and South. We resort to numerical simulations of the calibrated model to analyze the effect of cooperation over economic and climate variables under two different scenarios: long-lived and short-lived governments. The main aim of our analysis is to test numrically whether John and Pecchenino´s (1997) theoretical result, which states that international agreements with transfers that lack an intergenerational perspective could actually harm the environment, applies low us to conclude that when we consider short lived governments: (1) the lack of cooperation always leads to higher environmental degradation, (2) the higher the welfare weight attached to the North under cooperation, the lower the environmental degradation in the long run, and (3) some cooperative scenarios may lead in the short run to higher environmental degradation than what it would arise in the non cooperative scenario.international environmental agreements, intergenerational externality, climate change

Secular changes in length of day: Effect of the mass redistribution

In this paper the secular change in the length of day due to mass redistribution effects is revisited using the Hamiltonian formalism of the Earth rotation theories. The framework is a two-layer deformable Earth model including dissipative effects at the core–mantle boundary, which are described through a coupling torque formulated by means of generalized forces. The theoretical development leads to the introduction of an effective time-averaged polar inertia moment, which allows us to quantify the level of core–mantle coupling throughout the secular evolution of the Earth. Taking advantage of the canonical procedure, we obtain a closed analytical formula for the secular deceleration of the rotation rate, numerical evaluation of which is performed using frequency-dependent Love numbers corresponding to solid and oceanic tides. With this Earth modeling, under the widespread assumption of totally coupled core and mantle layers in the long term response, a secular angular acceleration of − 1328.6′′ cy−2 is obtained, which is equivalent to an increase of 2.418 ms cy−1 in the length of day. The ocean tides and the semidiurnal band of the mass-redistribution-perturbing potential, mostly induced by the Moon, constitute the main part of this deceleration. This estimate is shown to be in very good agreement with recent observational values, and with other theoretical predictions including comparable modeling features

Forced nutations of a two-layer Earth in canonical formulation with dissipative Hori-like kernel

[EN] In this research, a modification of the Lie-Hori perturbation method developed by the authors in a recent investigation is used to compute the forced nutations of a non-rigid Earth model, including dissipative processes at the core-mantle boundary. The study is tackled within the Hamiltonian formalism of a two-layer Earth, where the viscous and electromagnetic couplings between mantle and core are introduced via generalized forces. The modified Lie-Hori method is introduced within the framework of the generalized Hamiltonian formalism. It, therefore, allows for calculating first-order perturbations in both conservative and non-conservative systems, while the classical Lie-Hori procedure is not designed to include generalized forces in the kernel to account for dissipative processes. Unlike other methods, this one presents the advantage of keeping the same dimensionality of the original problem, avoiding the doubling of the dimension of the phase space. With this mathematical refinement, differences in the derived nutation amplitudes at the microarcsecond level have been found when compared with the former, first approximation for dissipative systems based on damped oscillators —the only existing previous solution. Those figures are of relevance according to recent recommendations of the International Astronomical Union (IAU) and the International Association of Geodesy (IAG) based on the final report of the Joint Working Group on Theory of Earth rotation and validation.SIThis research has been partially supported by the Spanish project AYA2016-79775-P (AEI/FEDER, UE)

New measures for open-domain question answering evaluation within a time constraint

Previous works on evaluating the performance of Question Answering (QA) systems are focused on the evaluation of the precision. In this paper, we developed a mathematic procedure in order to explore new evaluation measures in QA systems considering the answer time. Also, we carried out an exercise for the evaluation of QA systems within a time constraint in the CLEF-2006 campaign, using the proposed measures. The main conclusion is that the evaluation of QA systems in realtime can be a new scenario for the evaluation of QA systems.This research has been partially supported by the framework of the project QALL-ME (FP6-IST-033860), which is a 6th Framenwork Research Programme of the European Union (EU), by the Spanish Government, project TEXT-MESS (TIN-2006-15265-C06-01) and by the Valencia Government under project number GV06-161

Nutation of the non-rigid Earth: Effect of the mass redistribution

[EN] In this research, we computed the nutation of the figure axis for a non-rigid Earth model due to the mass redistribution resulting from the lunisolar attraction on the deformable Earth, thus extending our previous work on the precessional motion. The basic Earth model is a two-layer structure composed of a fluid core and an anelastic mantle. We used the Hamiltonian approach, leading to closed-form analytical formulae that describe the nutations in longitude and obliquity of the figure axis as a sum of Poisson and Oppolzer terms. Those formulae were evaluated assuming different Earth rheologies by means of the Love number formalism. In particular, we first computed the effect using the standard model of the International Earth Rotation and Reference Systems Service Conventions (2010) solid tides, and then the Love numbers computed by Williams and Boggs, accounting for the complete oceanic tide contribution, which should provide more consistent and updated values for the nutations. The main amplitudes correspond to the 18.6 yr nutation component and reach 201 μas and −96 μas in the in-phase components in longitude and obliquity, respectively. The obtained values differ greatly from those considered in the current nutation model, IAU2000, of the International Astronomical Union (IAU) – and later similar studies – which includes this effect under the denomination of non-linear terms and derives its numerical contribution on the basis of the Sasao, Okubo, and Saito framework. The differences are significant and reach more than 30 μas for some nutation amplitudes. They can be likely attributed to several factors: an incomplete modelling of the redistribution potential; a different treatment of the permanent tide; and the use of different oceanic tide models.S

Precession of the non-rigid Earth: Effect of the mass redistribution

[EN] This research is focused on determining the contribution to the precession of the Earth’s equator due to the mass redistribution stemming from the gravitational action of the Moon and the Sun on a rotating solid Earth. In the IAU2006 precession theory, this effect is taken into account through a contribution of −0.960 mas cy−1 for the precession in longitude (with the unspecific name of non-linear effect). In this work, the revised value of that second-order contribution reaches −37.847 mas cy−1 when using the Love numbers values given in IERS Conventions, and −43.945 mas cy−1 if those values are supplemented with the contributions of the oceanic tides. Such variations impose a change of the first-order precession value that induces relative changes of the Earth’s dynamical ellipticity of about 7.3 and 8.5 ppm, respectively. The corresponding values for the obliquity rate are 0.0751 and 0.9341 mas cy−1, respectively, in contrast to 0.340 mas cy−1 considered in IAU2006. The fundamentals of the modeling have been revisited by giving a clear construction of the redistribution potential of the Earth through the corresponding changes in the Earth tensor of inertia. The dynamical problem is tackled within the Hamiltonian framework of a two-layer Earth model, introduced and developed by Getino and Ferrándiz. This approach allows for the achievement of closed-analytical formulae for the precession in longitude and obliquity. It makes it possible to obtain numerical values for different Earth models once a set of associated Love numbers is selected. The research is completed with a discussion on the permanent tide and the related estimation of the variation of the second degree zonal Stokes parameter, J2, and also the indirect effects on nutations arising from the relative change of the Earth’s dynamicalSIThis work has been partially supported by the Spanish project AYA2016-79775-P (AEI/FEDER, UE)

Earth’s Rotation: A Challenging Problem in Mathematics and Physics

A suitable knowledge of the orientation and motion of the Earth in space is a common need in various fields. That knowledge has been ever necessary to carry out astronomical observations, but with the advent of the space age, it became essential for making observations of satellites and predicting and determining their orbits, and for observing the Earth from space as well. Given the relevant role it plays in Space Geodesy, Earth rotation is considered as one of the three pillars of Geodesy, the other two being geometry and gravity. Besides, research on Earth rotation has fostered advances in many fields, such as Mathematics, Astronomy and Geophysics, for centuries. One remarkable feature of the problem is in the extreme requirements of accuracy that must be fulfilled in the near future, about a millimetre on the tangent plane to the planet surface, roughly speaking. That challenges all of the theories that have been devised and used to-date; the paper makes a short review of some of the most relevant methods, which can be envisaged as milestones in Earth rotation research, emphasizing the Hamiltonian approach developed by the authors. Some contemporary problems are presented, as well as the main lines of future research prospected by the International Astronomical Union/International Association of Geodesy Joint Working Group on Theory of Earth Rotation, created in 2013.This work has been partially supported by the Spanish government under Grants AYA2010-22039-C02-01 and AYA2010-22039-C02-02 from Ministerio de Economía y Competitividad (MINECO), the University of Alicante under Grant GRE11-08 and the Generalitat Valenciana, Grant GV/2014/072

International and Intergenerational Dimensions of Climate Change: North-South Cooperation in an Overlapping Generations Framework

Global environmental problems such as climate change have both an international and an intertemporal dimension. Recently, some papers have used an overlapping generations framework to analyze the climate change problem taking into account jointly the issues of intergenerational equity and intertemporal efficiency but without considering the international aspect of the problem. In this paper, we extend such approach by considering an overlapping generations model of climate-economy interactions where the world is split into two regions: North and South. We resort to numerical simulations of the calibrated model to analyze the effect of cooperation over economic and climate variables under two different scenarios: long-lived and short-lived governments. The main aim of our analysis is to test numrically whether John and Pecchenino´s (1997) theoretical result, which states that international agreements with transfers that lack an intergenerational perspective could actually harm the environment, applies low us to conclude that when we consider short lived governments: (1) the lack of cooperation always leads to higher environmental degradation, (2) the higher the welfare weight attached to the North under cooperation, the lower the environmental degradation in the long run, and (3) some cooperative scenarios may lead in the short run to higher environmental degradation than what it would arise in the non cooperative scenario.Financial support from grants 9/UPV 00I01.I01-14548/2002 and SEC2001-0687 is gratefully acknowledged

Secular changes in length of day: Effect of the mass redistribution

[EN] In this paper the secular change in the length of day due to mass redistribution effects is revisited using the Hamiltonian formalism of the Earth rotation theories. The framework is a two-layer deformable Earth model including dissipative effects at the core–mantle boundary, which are described through a coupling torque formulated by means of generalized forces. The theoretical development leads to the introduction of an effective time-averaged polar inertia moment, which allows us to quantify the level of core–mantle coupling throughout the secular evolution of the Earth. Taking advantage of the canonical procedure, we obtain a closed analytical formula for the secular deceleration of the rotation rate, numerical evaluation of which is performed using frequency-dependent Love numbers corresponding to solid and oceanic tides. With this Earth modeling, under the widespread assumption of totally coupled core and mantle layers in the long term response, a secular angular acceleration of − 1328.6′′ cy−2 is obtained, which is equivalent to an increase of 2.418 ms cy−1 in the length of day. The ocean tides and the semidiurnal band of the mass-redistribution-perturbing potential, mostly induced by the Moon, constitute the main part of this deceleration. This estimate is shown to be in very good agreement with recent observational values, and with other theoretical predictions including comparable modeling features.SIThis research has been developed within the framework of the IAU/IAG Joint Working Group 3.1: Improving Theories and Models of the Earth’s Rotation (ITMER)

The Rotation of the Nonrigid Earth at the Second Order. II. The Poincaré Model: Nonsingular Complex Canonical Variables and Poisson Terms

[EN] We develop a Hamiltonian analytical theory for the rotation of a Poincaré Earth model (rigid mantle and liquid core) at the second order with respect to the lunisolar potential and moving ecliptic term. Since the Andoyer variables considered in the first-order solution present virtual singularities, i.e., vanishing divisors, we introduce a set of nonsingular complex canonical variables. This choice allows for applying the Hori canonical perturbation method in a standard way. We derive analytical expressions for the first- and second-order solutions of the precession and nutation of the angular momentum axis (Poisson terms). Contrary to first-order theories, there is a part of the Poisson terms that does depend on the Earth's structure. The resulting numerical amplitudes, not incorporated in the International Astronomical Union nutation standard, are not negligible considering current accuracies. They are at the microarcsecond level for a few terms, with a very significant contribution in obliquity of about 40 μas for the nutation argument with period −6798.38 days. The structure-dependent amplitudes present a large amplification with respect to the rigid model due to the fluid core resonance. The features of such resonance, however, are different from those found in first-order solutions. The most prominent is that it does not depend directly on the second-order nutation argument but rather on the combination of first-order arguments generating it. It entails that some first-order approaches, like those based on the transfer function, cannot be applied to obtain the second-order contributions.S