A multi-arc approach for chaotic orbit determination problems

Chaotic dynamical systems are characterized by the existence of a predictability horizon, connected to the notion of Lyapunov time, beyond which predictions of the state of the system are meaningless. In order to study the main features of orbit determination in the presence of chaos, Spoto and Milani (Celest Mech Dyn Astron 124:295–309, 2016) applied the classical least-squares fit and differential correction algorithm to determine a chaotic orbit and a dynamical parameter of a simple discrete system—Chirikov standard map (cf. Chirikov in Phys Rep 52:263, 1979)—with observations distributed beyond the predictability horizon. They found a time limit beyond which numerical calculations are affected by numerical instability: the computability horizon. In this article, we aim at pushing forward such inherent obstacle to numerical calculations in chaotic orbit determination by applying the classical and the constrained multi-arc method (cf. Alessi et al. in Mon Not R Astron Soc 423:2270–2278, 2012) to the same dynamical system. These strategies entail the determination of an orbit when observations are grouped in separate observed arcs. For each arc, a set of initial conditions is determined and, in the case of the constrained multi-arc method, all subsequent arcs are constrained to belong to the same trajectory. We show that the use of these techniques in place of the standard least-squares method has significant advantages: Not only can we perform accurate numerical calculations well beyond the computability horizon, in particular, the constrained multi-arc strategy improves considerably the determination of the dynamical parameter.     

Subsurface mass redistributions at Mount Etna (Italy) during the 1995–1996 explosive activity detected by microgravity studies

Gravity changes are presented from a series of field microgravity surveys conducted at Mt Etna between August 1994 and November 1996, a period including the 1995–1996 explosive summit activity. Data were collected along a microgravity network of 69 stations at a monthly to annual sampling rate, depending on each subarray of the network.
  Results show that seasonal changes in water level within the volcano may induce gravity changes of up to 20  μgal on Etna's southern slope, and indicate that significant magma movement occurred within and below Etna's edifice between 1994 and 1996. In particular, between September 1994 and October 1995, a mass increase of 2 × 10¹⁰  kg occurred 2000  m beneath the summit craters. Between October 1995 and July 1996 this mass was lost, while another 2 × 10¹⁰  kg was injected at about 1000  m  a.s.l. into the 1989 fracture system. From the gravity data alone, it is not possible to distinguish whether the first shallow intrusion (1994–1995) was then injected laterally into the 1989 fracture, or summit activity was fed by the first shallow intrusion, while new magma entered the 1989 fracture system.
  While magma was being redistributed within the volcanic edifice, measurements along an E–W-trending profile on the southern slope of the volcano detected some 1.5 × 10¹¹  kg of magma accumulating 2–3  km below sea level between October 1995 and November 1996.     

Single-point position estimation in interplanetary trajectories using star trackers

This study provides a single-point position estimation technique for interplanetary missions by observing visible planets using star trackers. Closed-form least-squares solution is obtained by minimizing the sum of the expected object-space squared distance errors. A weighted least-squares solution is provided by an iterative procedure. The weights are evaluated using the distances to the planets estimated by the least-squares solution. It is shown that the weighted approach only requires one iteration to converge and results in significant accuracy gains compared to simple least squares approach. The light-time correction is taken into account while the star-light aberration cannot be implemented in single-point estimation as it requires knowledge of the observer velocity. The proposed method is numerically validated through a statistical scenario as follows. A three-dimensional grid of test cases is generated: two dimensions sweep through the ecliptic plane and the third dimension sweeps through time from January 1, 2018 to January 1, 2043 in 5-year increments. The observer position is estimated at each test case and the estimate error is recorded. The results obtained show that a large majority of positions are well suited to position estimation by using star trackers pointing to visible planets, and reliable and accurate single-point position estimations can be provided in interplanetary missions. The proposed approach is suitable to be used to initiate a filtering technique to increase the estimation accuracy.     

Study of the macrophyte assemblages and application of phytobenthic indices to assess the Ecological Status of the Marano‐Grado Lagoon (Italy)

Benthic macrophytes from 19 sites within the Marano‐Grado Lagoon were sampled in July 2007 in order to update the available information on the flora and vegetation and to assess the Ecological Status (ES) within the European Water Framework Directive (WFD). Data on macrophytes were analysed using two phytobenthic indices (EEI and R‐MaQI) recently set up to evaluate the ecological status of transitional environments in the Mediterranean eco‐region. Notwithstanding the extension (c. 160 km²) that places this lagoon as the second largest Italian transitional environment, ecological studies are relatively few. The present research revealed a relatively poor flora, mainly characterized by the dominance of low‐diversity settlements of Ulvaceae. Moreover, the absence of intensive aquaculture activities and commercial big harbours, which account for the new species introductions recorded in other lagoons, limits the presence of non‐autochthonous species. The comparison with previous data ( Curiel et al. 1998 ) highlighted the reduction of macrophyte coverage and biomass, especially Ulvaceae stands, and an increase in species richness. In particular, there was evidence of a worsening of the area north of the Grado bridge. This area, which in the past was colonized by widespread angiosperm coverage, at present is almost lacking in vegetation. According to these observations, by applying both the phytobenthic indices available in the literature for the transitional environments, the Marano‐Grado Lagoon showed a ‘Good–High’ quality in the central part of the basin and near the lagoon inlets and a ‘Poor–Bad’ quality in the northern and southern areas. The evaluation of some physico‐chemical parameters, coupled with the distribution of the angiosperms, also allowed a first delineation of the main lagoon water bodies.     

An individual-based population dynamic model for estimating biomass yield and nutrient fluxes through an off-shore mussel (Mytilus galloprovincialis) farm

The fluxes of carbon, nitrogen and phosphorus through an off-shore long-line Mytilus galloprovincialis farm during a typical rearing cycle were estimated by combining a simple population dynamic model, based on a new individual model, and a set of field data, concerning the composition of the seston, as well as that of mussel meat and faeces. The individual model, based on an energy budget, was validated against a set of original field data, which were purposely collected from July 2006 to May 2007 in the North-Western Adriatic Sea (Italy) and was further tested using historical data. The model was upscaled to the population level by means of a set of Monte Carlo simulations, which were used for estimating the size structure of the population. The daily fluxes of C, N and P associated with mussel filtration, excretion and faeces and pseudo-faeces production were integrated over the 10-month-long rearing cycle and compared with the total amount of C, N and P removed by harvesting. The results indicate that the individual model compares well with an existing literature model and provides reliable estimations of the growth of mussel specimen over a range of trophic conditions which are typical of the Northern Adriatic Sea coastal area. The results of the budget calculation indicate that, even though the harvest represents a net removal of phosphorus and nitrogen from the ecosystem, the mussel farm increases the retention time of both nutrients in the coastal area, via the deposition of faeces and pseudo-faeces on the sea-bed. In fact, the amount of nitrogen associated with deposition is approximately twice the harvested one and the amount of phosphorus is approximately five times higher. These findings are in qualitative agreement with the results of literature budget and model calculations carried out in a temperate coastal embayment. This agreement suggests that the proper assessment of the overall effect of long-line mussel farming on both the benthic and pelagic ecosystem asks for an integrated modelling approach, which should include the dynamic of early diagenesis processes, as well as of that of nutrients released from the surface sediment.     

Rotating magnetopolytropes: spherical figures of equilibrium due to balance of magnetic field and rotation

In this paper we compute spherical figures of equilibrium resulting from the balance of toroidal magnetic field and rotation. These two distortion effects are assumed to act on rotating magneto-polytropic constant-mass sequences, that is, sequences with each of their members having mass constant and equal to that of the corresponding nondistorted model.     

The effects of discharge and slope on hyporheic flow in step‐pool morphologies

This paper focuses on surface–subsurface water exchange in a steep coarse‐bedded stream with a step‐pool morphology. We use both flume experiments and numerical modelling to investigate the influence of stream discharge, channel slope and sediment hydraulic conductivity on hyporheic exchange. The model step‐pool reach, whose topography is scaled from a natural river, consists of three step‐pool units with 0.1‐m step heights, discharges ranging between base and over‐bankfull flows (scaled values of 0.3–4.5 l/s) and slopes of 4% and 8%. Results indicate that the deepest hyporheic flow occurs with the steeper slope and at moderate discharges and that downwelling fluxes at the base of steps are highest at the largest stream discharges. In contrast to findings in a pool‐riffle morphology, those in this study show that steep slopes cause deeper surface–subsurface exchanges than gentle slopes. Numerical simulation results show that the portion of the hyporheic zone influenced by surface water temperature increases with sediment hydraulic conductivity. These experiments and numerical simulations emphasize the importance of topography, sediment permeability and roughness elements along the channel surface in governing the locations and magnitude of downwelling fluxes and hyporheic exchange. Our results show that hyporheic zones in these steep streams are thicker than previously expected by extending the results from streams with pool‐riffle bed forms. Copyright © 2014 John Wiley & Sons, Ltd.     

Early to mid‐Holocene climate change at Lago dell'Accesa (central Italy): climate signal or anthropogenic bias?

Despite the high potential of pollen records for climate reconstruction, pollen–climate relationships may be biased due to past and present human activities on the landscape. We use (i) transfer functions based on modern pollen–climate relationships to infer seasonal temperature and summer precipitation for the period 11 500–4500 cal. a BP and (ii) lake‐level change records based on different sedimentary proxies in multiple cores that are mainly indicative for summer hydrology at Lago dell'Accesa (central Italy). Quantitative reconstructions indicate lowest summer precipitation during two phases (8500–7700 cal. a BP and after 6000 cal. a BP) and a gradual winter temperature increase from 11 500 to ca. 8000 cal. a BP. Lowest summer precipitation was reconstructed during these phases characterised by vegetation shifts from open forests dominated by summergreen oaks (Quercus) to forests dominated by evergreen oaks (Quercus ilex), which are at present most abundant where summer drought is stronger. Similarly, the lake‐level record indicates two long‐lasting low summer precipitation phases (8800–7700 and 6400–4400 cal. a BP) that were interrupted by short‐term high summer precipitation events. Based on the broad agreement between the pollen‐inferred summer precipitation and the low‐frequency lake‐level changes, we suggest that the duration of the high summer precipitation events may have been too short to maintain drought‐sensitive trees, which may have been affected by high mortality rates when summer dry conditions returned. Although past and modern pollen–climate relationships may very likely have been affected by human activities since the Neolithic (i.e. when exploitation of the landscape started), we reject the hypothesis of a significant anthropogenic bias in the pollen‐based climate reconstruction. In addition, we suggest that pollen‐based and lake‐level reconstructions may have different inherent abilities of capturing high‐ and low‐frequency precipitation signals. Copyright © 2010 John Wiley & Sons, Ltd.     

Analysis of raw soils and their re-suspended PM10 fractions: Characterisation of source profiles and enrichment factors

In this work, the inorganic chemical profiles of soil samples collected at different sites in the Salentum peninsula (Italy, Apulia region) are discussed. The samples were re-suspended in the laboratory, for PM10 sampling, using a ventilated wooden chamber and were then chemically analysed measuring the abundances of 17 elements. Different land use categories of soils (olive grove, arable land, vineyards, sand, and urban dust) were included in the 50 samples analysed: 45 collected in background areas and five collected in the urban area of Lecce. The objectives were to compare the chemical profiles of raw soil and re-suspended PM10 for different crustal sources and to estimate the potential improvements in the calculation of the enrichment factors of atmospheric PM10. The variability of elemental abundances in samples of the same category of soil collected in different zones was of the same order of magnitude as the differences observed between the various categories of soil. This allows the calculation of a weighted average composition of soil and urban dust and the corresponding weighted average composition of re-suspended PM10. In re-suspended PM10 from average background soil, all of the elements except Ca, Na, K and V have larger abundances with respect to raw soil. In urban dust, this is limited to Ca, V and Mg. The crustal enrichment factors (EFs) of atmospheric PM10 were evaluated by considering different reference elements and different reference tables. Results indicated that it is possible to apply a two-threshold (S₁ and S₂) scheme for the interpretation of EF, with thresholds derived from uncertainty in soil categories and from the choice of the reference element. A specific element is likely of crustal origin if EF < S₁ and likely of anthropogenic origin if EF > S₂. Between the two thresholds, the element can be considered of mixed origin. The thresholds vary according to the geological composition used in the evaluation of EF. If the average composition of local re-suspended soils is used, the thresholds are S₁ = 2 and S₂ = 4. If raw soil is used, the thresholds become S₁ = 5 and S₂ = 10. If the average upper-crust composition from literature data is used, the thresholds further increase to S₁ = 10 and S₂ = 20.