Software package in C

Midterm Working Report for EoCoE Project

Release 2.1 of MLD2P4 package

The Optimized Retrieval Code (ORM) was originally designed to be the scientific code used as the reference for the ESA operational Near Real Time Analysis of MIPAS measurements on ENVISAT. After the end of ENVISAT mission, occurred on April 2017, this code has been adapted and improved to perform the reanalysis of the full MIPAS mission.

Position determination of photon emitters and associated strong field parallax effects are investigated using relativistic optics when the photon orbits are confined to the equatorial plane of the Schwarzschild spacetime. We assume the emitter is at a fixed space position and the receiver moves along a circular geodesic orbit. This study requires solving the inverse problem of determining the (spatial) intersection point of two null geodesic initial data problems, serving as a simplified model for applications in relativistic astrometry as well as in radar and satellite communications.

We investigate the scattering of a spinning test particle by a Kerr black hole within the Mathisson-Papapetrou-Dixon model to linear order in spin. The particle's spin and orbital angular momentum are taken to be aligned with the black hole's spin. Both the particle's mass and spin length are assumed to be small in comparison with the characteristic length scale of the background curvature, in order to avoid backreaction effects. We analytically compute the modifications due to the particle's spin to the scattering angle, the periastron shift, and the condition for capture by the black hole, extending previous results valid for the nonrotating Schwarzschild background. Finally, we discuss how to generalize the present analysis beyond the linear approximation in spin, including spin-squared corrections in the case of a black-hole-like quadrupolar structure for the extended test body.

Consider a dynamic general relativistic spacetime in which the proper infinitesimal interval along one spatial coordinate direction decreases monotonically with time, while the corresponding intervals increase along other spatial directions. In a system undergoing such complete anisotropic collapse/expansion, we look for the formation of a cosmic double-jet configuration: free test particles in the ambient medium, relative to the collapsing system, gain energy from the gravitational field and asymptotically line up parallel and antiparallel to the direction of collapse such that their Lorentz factors approach infinity. A strong burst of electromagnetic radiation is expected to accompany this event if some of the free test particles carry electric charge. Previous work in this direction involved mainly Ricci-flat spacetimes; hence, we concentrate here on inhomogeneous perfect fluid spacetimes. We briefly explore the possible connection between these theoretical cosmic jets and astrophysical jets. We also discuss other general relativistic scenarios for the formation of cosmic jets.

We compute the (center-of-mass frame) scattering angle ? of hyperboliclike encounters of two spinning black holes, at the fourth post-Newtonian approximation level for orbital effects, and at the next-to-next-to-leading order for spin-dependent effects. We find it convenient to compute the gauge-invariant scattering angle (expressed as a function of energy, orbital angular momentum and spins) by using the effective-one-body formalism. The contribution to scattering associated with nonlocal, tail effects is computed by generalizing to the case of unbound motions the method of time localization of the action introduced in the case of (small-eccentricity) bound motions by Damour et al. [Phys. Rev. D 91, 084024 (2015)PRVDAQ1550-799810.1103/PhysRevD.91.084024].

In this work we present an analytical gravitational self-force calculation of the spin-orbit precession along an eccentric orbit around a Schwarzschild black hole, following closely the recent prescription of Akcay, Dempsey, and Dolan, giving results to six post-Newtonian orders expanded in small eccentricity through e2. We then transcribe this quantity within the effective-one-body (EOB) formalism, thereby determining several new, linear-in-mass-ratio contributions in the post-Newtonian expansion of the spin-orbit couplings entering the EOB Hamiltonian. Namely, we determine the second gyrogravitomagnetic ratio gS*(r,pr,p?) up to order pr2/r4 included.

The precession angular velocity of a gyroscope moving along a general geodesic in the Kerr spacetime is analyzed using the geometric properties of the spacetime. Natural frames along the gyroscope world line are explicitly constructed by boosting frames adapted to fundamental observers. A novel geometrical description is given to Marck's construction of a parallel propagated orthonormal frame along a general geodesic, identifying and clarifying the special role played by the Carter family of observers in this general context, thus extending previous discussion for the equatorial plane case.

The scattering of spinning test particles by a Schwarzschild black hole is studied. The motion is described according to the Mathisson-Papapetrou-Dixon model for extended bodies in a given gravitational background field. The equatorial plane is taken as the orbital plane, the spin vector being orthogonal to it with constant magnitude. The equations of motion are solved analytically in closed form to first-order in spin and the solution is used to compute corrections to the standard geodesic scattering angle as well as capture cross section by the black hole.

The explicit analytical computation of first-order metric perturbations in black hole spacetimes is described in the case of a perturbing mass moving on an equatorial circular orbit. The perturbation equations can be separated into an angular part and a radial part. The latter satisfies a single inhomogeneous radial Schrödingerlike equation with a Dirac-delta singular source term, whose solutions are built up through Green's function techniques. Various types of approximate analytical homogeneous solutions (and corresponding Green's functions) can be constructed: Post-Newtonian solutions (expanded in powers of 1=c), Mano-Suzuki-Takasugi solutions (expanded in series of hypergeometric functions), Wentzel-Kramers- Brillouin (WKB) solutions (large l expansion). The perturbed black-hole metric constructed by suitably combining these different kind of solutions can then be used to compute, in analytical form, gauge-invariant quantities. These include several "potentials" entering the effective-one-body formalism (shortly reviewed here). The latter formalism is a new way of describing the gravitational interaction of two masses which has played a crucial role in the recent detection of gravitationalwaves.

Deviation and precession effects of a bunch of spinning particles in the field of a weak gravitational plane wave are studied according to the Mathisson-Papapetrou-Dixon (MPD) model. Before the passage of the wave the particles are at rest with an associated spin vector aligned along a given direction with constant magnitude. The interaction with the gravitational wave causes the particles to keep moving on the 2-plane orthogonal to the direction of propagation of the wave, with the transverse spin vector undergoing oscillations around the initial orientation. The transport equations for both the deviation vector and spin vector between two neighboring world lines of such a congruence are then solved by a suitable extension of the MPD model off the spinning particle's world line. In order to obtain measurable physical quantities a "laboratory" is set up by constructing a Fermi coordinate system attached to a reference world line. The exact transformation between TT coordinates and Fermi coordinates is derived too.

MIPAS on ENVISAT performed almost continuous and global measurements of atmospheric temperature and composition from June 2002 to April 2012. These data are very useful for understanding atmosphere climatology from the upper troposphere to the mesosphere, including trends in composition and variability, as a reference for middle atmosphere ozone and general circulation as well as improvement of tropospheric composition retrievals. The ESA Level 2 processor, based on the Optimized Retrieval Model (ORM), originally designed for the Near Real Time analysis and developed by an European Consortium led by IFAC, is currently improved and used for the reanalysis of the full MIPAS mission. The maintenance and the upgrade of the ESA processor are made in the frame of the MIPAS Quality Working Group, where a fruitful collaboration among Level 1, Level 2 and validation teams is exploited. This collaboration is essential to improve the accuracy of the products and their characterization. This paper is meant to describe the most recent upgrades in the MIPAS processor, in particular the full mission was recently reprocessed with L1 V7 and L2 V7 processors, containing significant improvements with respect to previous version 6, and further improvements are in preparation, that will be collected in version 8 of the ESA processor. The improvements include both L1 and L2 processors, as well as the auxiliary data. In the L1 processor the correction of the instrumental drift caused by the ageing of the detectors has been implemented in order to reduce the non negligible systematic error in the trend estimation. Furthermore, the measured daily gain instead of the weekly gain is now used for the radiometric calibration that allows to better take account for the discontinuities in the gain that occasionally occur in MIPAS band B. Improvements in the L2 processor include a different approach for retrieving atmospheric continuum, the use of an a posteriori regularization with altitude dependent constraint, a better approach for handling interfering species, a reduced bias in CFC-11, the handling of horizontal inhomogeneities and the use of ECMWF altitude/pressure relation to determine more accurate altitudes. Improvements in the auxiliary data consist in the use of microwindows with larger information content, an improved spectroscopic database and diurnally varying climatological dataset. Furthermore, additional species are provided in the new processors, leading to a total of 22 retrieved species by the L2 version 8 processor. Each of these changes has a different impact on the Level 2 products. The individual contributions, as well as the cumulative effects, will be evaluated with a comparison with previous versions of MIPAS products and corresponding results of validation. Improvements in the trend determination will also be evaluated, as well as the quality of the new retrieved species.

Carbon tetrachloride (CCl?) is a strong ozone-depleting atmospheric gas regulated by the Montreal protocol. Recently it received increasing interest because it was found that at the surface its atmospheric concentration declines with a rate almost three times smaller than its lifetime-limited rate. Indeed there is a discrepancy between atmospheric observations and the estimated distribution based on the reported production and consumption (the so called "mystery of CCl?"). We use for the first time the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) measurements to estimate CCl? distribution, its trend, and atmospheric lifetime in the upper troposphere / lower stratosphere (UTLS) region. In particular, here we use MIPAS product generated with Version 7 of the Level 2 algorithm operated by the European Space Agency. The CCl? zonal means show features typical of long-lived species of anthropogenic origin that are destroyed primarily in the stratosphere: larger amounts are found in the troposphere, monotonically decreasing with altitude. We calculate CCl? trends as a function of both latitude and altitude: negative trends are found at all latitudes in the UTLS, apart from a region in the Southern mid-latitudes between 50 and 10 hPa where the trend is slightly positive. At the lowest altitudes sounded by the MIPAS scan we find trend values consistent with those determined on the basis of long-term ground-based measurements. CCl? global average lifetime of 46(38 - 60) years has been estimated using the tracer-tracer linear correlations approach and the CFC-11 as the reference tracer. This estimated value is consistent with the most recent literature result of 44(36 - 58) years.

The workshop Mathematical Approach to Climate Change Impacts (MAC2I) has been styled to drive the attention within Italian academy and public research institutions towards applied mathematics research in environmental problems related to climate change. A number of renowned specialists delivered plenary lectures to introduce the hottest issues, contributed talks were selected in order to exemplify recent successful mathematical developments in this applicative field and two tutorials introduced the mathematical modelling tools to approach clue subjects. The program has been structured into four thematic sessions, respectively glaciology, hydrology, ecosystem science and environmental monitoring. Panel discussions and brain-storming were included as an opportunity for the emergence of new ideas in the right atmosphere to foster scientific international collaborations. The workshop, appropriate also within a PhD course program, was conceived in the context of the excellence project of applied mathematics MATH-TECH, funded by the Italian Ministry of Education, University and Research (MIUR) awarded to the Institute for Applied Mathematics (IAC) "M. Picone" of the National Research Council (CNR) and to the Istituto Nazionale di Alta Matematica (INDAM) (2015-2017).

The melting of glaciers coming with climate change threatens the heritage of the last glaciation of Europe likely contained in subglacial lakes in Greenland and Svalbard, which look fated to disappear. This aspect urges specialists to focus their studies (theoretical, numerical and on-field) on such fascinating objects. Along this line we have approached the validation of the conjecture of the existence of a subglacial lake beneath the Amundsenisen Plateau at South-Spitzbergen, Svalbard, where Ground Penetrating Radar measurements have revealed several flat signal spots, sign of the presence of a body of water. The whole investigation aspects and tools, mathematical modeling and numerical simulation procedure, the computational algorithm and the numerical results obtained on the real study case, have been sketched at workshop time, and the decision has been discussed to undertake drilling operations above the presumed ice/water front, where subglacial lake water bio-chemicals might be traceable. This investigation is a follow-up of the multi and interdisciplinary research activities based at the Arctic Station ''Dirigibile Italia'', coordinated by the ''Dipartimento Scienze del Sistema Terra e Tecnologie per l'Ambiente'' of CNR (I) and of the transnational project 'SvalGlac - Sensitivity of Svalbard Glaciers to Climate Change' funded by ESF-ERANET PolarClimate Consortium (PNRA for Italy).

We give a general inequality for the total variation distance between a Poisson distributed random variable and a first order stochastic integral with respect to a point process with stochastic intensity, constructed by embedding in a bivariate Poisson process. We apply this general inequality to first order stochastic integrals with respect to a class of nonlinear Hawkes processes, which is of interest in queueing theory, providing explicit bounds for the Poisson approximation, a quantitative Poisson limit theorem, confidence intervals and asymptotic estimates of the moments.

We give general bounds in the Gaussian and Poisson approximations of innovations (or Skorohod integrals) defined on the space of point processes with Papangelou conditional intensity. We apply the general results to Gibbs point processes with pair potential and determinantal point processes. In particular, we provide explicit error bounds and quantitative limit theorems for stationary, inhibitory and finite range Gibbs point processes with pair potential and beta-Ginibre point processes.