Estimate of the Transition Value of Librational Invariant Curves

We investigate the break-down threshold of librational invariant curves. As a model problem, we consider a variant of a mapping introduced by M. Hénon, which well describes the dynamics of librational motions surrounding a stable invariant point. We verify in concrete examples the applicability of Greene's method, by computing the instability transition values of a sequence of periodic orbits approaching an invariant curve with fixed noble frequency. However, this method requires the knowledge of the location of the periodic orbits within a very good approximation. This task appears to be difficult to realize for a libration regime, due to the different topology of the phase space. To compute the break-down threshold, we tried an alternative method very easy to implement, based on the computation of the fast Lyapunov indicators and frequency analysis. Such technique does not require the knowledge of the periodic orbits, but again, it appears very difficult to have a precision better than Greene's method for the computation of the critical parameter.     

Normal Form Invariants Around Spin-orbit Periodic Orbits

We consider a model of spin-orbit interaction, describing the motion of an oblate satellite rotating about an internal spin-axis and orbiting about a central planet. The resulting second order differential equation depends upon the parameters provided by the equatorial oblateness of the satellite and its orbital eccentricity. Normal form transformations around the main spin-orbit resonances are carried out explicitly. As an outcome, one can compute some invariants; the fact that these quantities are not identically zero is a necessary condition to prove the existence of nearby periodic orbits (Birkhoff fixed point theorem). Moreover, the nonvanishing of the invariants provides also the stability of the spin-orbit resonances, since it guarantees the existence of invariant curves surrounding the periodic orbit.     

Geostationary secular dynamics revisited: application to high area-to-mass ratio objects

The long-term dynamics of the geostationary Earth orbits (GEO) is revisited through the application of canonical perturbation theory. We consider a Hamiltonian model accounting for all major perturbations: geopotential at order and degree two, lunisolar perturbations with a realistic model for the Sun and Moon orbits, and solar radiation pressure. The long-term dynamics of the GEO region has been studied both numerically and analytically, in view of the relevance of such studies to the issue of space debris or to the disposal of GEO satellites. Past studies focused on the orbital evolution of objects around a nominal solution, hereafter called the forced equilibrium solution, which shows a particularly strong dependence on the area-to-mass ratio. Here, we (i) give theoretical estimates for the long-term behavior of such orbits, and (ii) we examine the nature of the forced equilibrium itself. In the lowest approximation, the forced equilibrium implies motion with a constant non-zero average ‘forced eccentricity’, as well as a constant non-zero average inclination, otherwise known in satellite dynamics as the inclination of the invariant ‘Laplace plane’. Using a higher order normal form, we demonstrate that this equilibrium actually represents not a point in phase space, but a trajectory taking place on a lower-dimensional torus. We give analytical expressions for this special trajectory, and we compare our results to those found by numerical orbit propagation. We finally discuss the use of proper elements, i.e., approximate integrals of motion for the GEO orbits.     

Reconstructing the early 19th‐century Waal River by means of a 2D physics‐based numerical model

Suspended‐sediment concentration data are a missing link in reconstructions of the River Waal in the early 1800s. These reconstructions serve as a basis for assessing the long‐term effects of major interventions carried out between 1850 AD and the early 20th century. We used a 2D physics‐based morphodynamic model accounting for the influence of floodplain vegetation to fill in this gap. Historical discharge hydrographs were derived from a correlation between flow discharge records at Cologne and water level measurements of the Rhine branches in the Netherlands, taking into account the discharge distribution between the branches. Historical floodplain sedimentation rates were estimated using old cartographic information and recent geomorphologic field work. The computed historical sedimentation rates are found to be within the range of measured data, which suggests that fine suspended sediment concentrations in the early 1800s were comparable to contemporary ones. The computations show also how vegetation enhances the formation of natural levees close to the main channel and at the same time decreases the sedimentation rates in farther areas of the floodplain. A sensitivity analysis shows suspended sediment composition to have a strong influence on the resulting quantities and patterns of floodplain deposition. The reconstruction has also provided validation of the modelling tools to reproduce the effects of vegetation on sediment dynamics, enabling their implementation to study other cases. Copyright © 2010 John Wiley & Sons, Ltd.     

Cloud cover classification through simultaneous ground-based measurements of solar and infrared radiation

Simultaneous measurements of downwelling short-wave solar irradiance and incoming total radiation flux were performed at the Reeves Nevè glacier station (1200 m MSL) in Antarctica on 41 days from late November 1994 to early January 1995, employing the upward sensors of an albedometer and a pyrradiometer. The downwelling short-wave radiation measurements were analysed following the Duchon and O'Malley [J. Appl. Meteorol. 38 (1999) 132] procedure for classifying clouds, using the 50-min running mean values of standard deviation and the ratio of scaled observed to scaled clear-sky irradiance. Comparing these measurements with the Duchon and O'Malley rectangular boundaries and the local human observations of clouds collected on 17 days of the campaign, we found that the Duchon and O'Malley classification method obtained a success rate of 93% for cirrus and only 25% for cumulus. New decision criteria were established for some polar cloud classes providing success rates of 94% for cirrus, 67% for cirrostratus and altostratus, and 33% for cumulus and altocumulus.The ratios of the downwelling short-wave irradiance measured for cloudy-sky conditions to that calculated for clear-sky conditions were analysed in terms of the Kasten and Czeplak [Sol. Energy 24 (1980) 177] formula together with simultaneous human observations of cloudiness, to determine the empirical relationship curves providing reliable estimates of cloudiness for each of the three above-mentioned cloud classes. Using these cloudiness estimates, the downwelling long-wave radiation measurements (obtained as differences between the downward fluxes of total and short-wave radiation) were examined to evaluate the downwelling long-wave radiation flux normalised to totally overcast sky conditions. Calculations of the long-wave radiation flux were performed with the MODTRAN 3.7 code [Kneizys, F.X., Abreu, L.W., Anderson, G.P., Chetwynd, J.H., Shettle, E.P., Berk, A., Bernstein, L.S., Robertson, D.C., Acharya, P., Rothman, L.S., Selby, J.E.A., Gallery, W.O., Clough, S.A., 1996. In: Abreu, L.W., Anderson, G.P. (Eds.), The MODTRAN 2/3 Report and LOWTRAN 7 MODEL. Contract F19628-91-C.0132, Phillips Laboratory, Geophysics Directorate, PL/GPOS, Hanscom AFB, MA, 261 pp.] for both clear-sky and cloudy-sky conditions, considering various cloud types characterised by different cloud base altitudes and vertical thicknesses. From these evaluations, best-fit curves of the downwelling long-wave radiation flux were defined as a function of the cloud base height for the three polar cloud classes. Using these relationship curves, average estimates of the cloud base height were obtained from the three corresponding sub-sets of long-wave radiation measurements. The relative frequency histograms of the cloud base height defined by examining these three sub-sets were found to present median values of 4.7, 1.7 and 3.6 km for cirrus, cirrostratus/altostratus and cumulus/altocumulus, respectively, while median values of 6.5, 1.8 and 2.9 km were correspondingly determined by analysing only the measurements taken together with simultaneous cloud observations.     

Tectonics,sea-level changes and palaeoenvironments in the early Pleistocene of Rome (Italy)

The historical site of the Monte Mario lower Pleistocene succession (Rome, Italy) is an important marker of the Pliocene/Pleistocene boundary. Recently, the Monte Mario site was excavated and restudied. A spectacular angular unconformity characterizes the contact between the Monte Vaticano and the Monte Mario formations, which marks the Pliocene/Pleistocene boundary. Biostratigraphical analyses carried out on ostracod, foraminifer, and calcareous nannofossil assemblages indicate an Early Pliocene age (topmost Zanclean, 3.81–3.70 Ma) for the underlying Monte Vaticano Formation, whereas the Monte Mario Formation has been dated as early Pleistocene (Santernian, 1.66–1.59 Ma). Palaeomagnetic analyses point to C2Ar and C1r2r polarity chrons for the Monte Vaticano and the Monte Mario formations, respectively. The Monte Mario Formation consists of two obliquity-forced depositional sequences (MM1 and MM2) characterized by transgressive systems tracts of littoral marine environments at depths, respectively, of 40–80 m and 15–20 m. The data obtained from foraminifer and ostracod assemblages allow us to reconstruct early Pleistocene relative sea-level changes near Rome. At the Plio/Pleistocene transition, a relative sea-level drop of at least 260 m occurred, as a result of both tectonic uplift of the central Tyrrhenian margin and glacio-eustatic changes linked to early Pleistocene glaciation (Marine Isotope Stage 58).     

Continuous in situ measurements of volcanic gases with a diode-laser-based spectrometer: CO<Subscript>2</Subscript> and H<Subscript>2</Subscript>O concentration and soil degassing at Vulcano (Aeolian islands: Italy)

We report on a continuous-measurement campaign carried out in Vulcano (Aeolian islands, Sicily), devoted to the simultaneous monitoring of CO₂ and H₂O concentrations. The measurements were performed with an absorption spectrometer based on a semiconductor laser source emitting around a 2-μm wavelength. The emitted radiation was selectively absorbed by two molecular ro-vibrational transitions specific of the investigated species. Data for CO₂ and H₂O concentrations, and CO₂ soil diffusive flux using an accumulation chamber configuration, were collected at several interesting sampling points on the island (Porto Levante beach- PLB, Fossa Grande Crater – FOG- and Valley of Palizzi, PAL). CO₂/H₂O values, measured on the ground, are very similar (around 0.019 (± 0.006)) and comparable to the previous discrete detected values of 0.213 (Fumarole F5-La Fossa crater rim) and 0.012 (Fumarole VFS – Baia Levante beach) obtaid during the 1977–1993 heating phase of the crater fumaroles.