On the period of the periodic orbits of the restricted three body problem

We will show that the period T of a closed orbit of the planar circular restricted three body problem (viewed on rotating coordinates) depends on the region it encloses. Roughly speaking, we show that, \(2 T=k\pi +\int _\Omega g\) where k is an integer, \(\Omega \) is the region enclosed by the periodic orbit and \(g:{\mathbb {R}}^2\rightarrow {\mathbb {R}}\) is a function that only depends on the constant C known as the Jacobian constant; it does not depend on \(\Omega \). This theorem has a Keplerian flavor in the sense that it relates the period with the space “swept” by the orbit. As an application we prove that there is a neighborhood around \(L_4\) such that every periodic solution contained in this neighborhood must move clockwise. The same result holds true for \(L_5\).     

ENSO,the IOD and the intraseasonal prediction of heat extremes across Australia using POAMA-2

The simulation and prediction of extreme heat over Australia on intraseasonal timescales in association with the El Niño–Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) is assessed using the Bureau of Meteorology’s Predictive Ocean Atmosphere Model for Australia (POAMA). The analysis is based on hindcasts over 1981–2010 and focuses on weeks 2 and 3 of the forecasts, i.e. beyond a typical weather forecast. POAMA simulates the observed increased probabilities of extreme heat during El Niño events, focussed over south eastern and southern Australia in SON and over northern Australia in DJF, and the decreased probabilities of extreme heat during La Niña events, although the magnitude of these relationships is smaller than observed. POAMA also captures the signal of increased probabilities of extreme heat during positive phases of the IOD across southern Australia in SON and over Western Australia in JJA, but again underestimates the strength of the relationship. Shortcomings in the simulation of extreme heat in association with ENSO and the IOD over southern Australia may be linked to deficiencies in the teleconnection with Indian Ocean SSTs. Forecast skill for intraseasonal episodes of extreme heat is assessed using the Symmetric Extremal Dependence Index. Skill is highest over northern Australia in MAM and JJA and over south-eastern and eastern Australia in JJA and SON, whereas skill is generally poor over south-west Western Australia. Results show there are windows of forecast opportunity related to the state of ENSO and the IOD, where the skill in predicting extreme temperatures over certain regions is increased.     

On the importance of initializing the stochastic part of the atmosphere for forecasting the 1997/1998 El Ni?o

The importance of initializing atmospheric intra-seasonal (stochastic) variations for prediction of the onset of the 1997/1998 El Ni?o is examined using the Australian Bureau of Meteorology coupled seasonal forecast model. A suite of 9-month forecasts was initialized on the 1st December 1996. Observed ocean initial conditions were used together with five different atmospheric initial conditions that sample a range of possible initial states of intra-seasonal (stochastic) variability, especially the Madden-Julian Oscillation (MJO), which is considered the primary stochastic variability of relevance to El Ni?o evolution. The atmospheric initial states were generated from a suite of atmosphere-only integrations forced by observed sea surface temperatures (SST). To the extent that low frequency variability of the tropical atmosphere is forced by slow variations in SST, these atmospheric states should all represent realistic low frequency atmospheric variability that was present in December 1996. However, to the extent that intra-seasonal variability is not constrained by SST, they should capture a range of intra-seasonal states, especially variations in the activity, phase and amplitude of the MJO. For each of these five states, a 20-member ensemble of coupled model forecasts was generated by the addition of small random perturbations to the SST field at the initial time. The ensemble mean from all five sets of forecasts resulted in El Ni?o but three of the sets produced substantially greater warming by months 4?C5 in the NINO3.4 region compared to the other two. The warmer group stemmed from stronger intra-seasonal westerly wind anomalies associated with the MJO that propagated eastward into the central Pacific during the first 1?C2?months of the forecast. These were largely absent in the colder group; the weakest of the colder group developed strong easterly wind anomalies, relative to the grand ensemble mean, that propagated into the central Pacific early in the forecast, thereby generating significantly weaker downwelling Kelvin waves in comparison to the warmer group. The strong reduction in downwelling Kelvin waves in the weakest case acted to limit the warming in the eastern Pacific, resulting in a ??Modoki?? type El Ni?o that is more focused in the central Pacific. Our results suggest that the intra-seasonal stochastic component of the atmospheric initial condition has an important and potentially predictable impact on the forecasts of the initial warming and flavour of the 1997/1998 El Ni?o. However, to the extent that atmospheric intra-seasonal variability is not predictable beyond a month or two, these results imply a limit to the accuracy with which the strength and perhaps the spatial distribution of an El Ni?o can ultimately be predicted. These results do not preclude a predictable role of the MJO and other intra-seasonal stochastic variability at longer lead times if some aspects of the stochastic variability are preconditioned by the evolving state of El Ni?o or other low frequency boundary forcing.     

Diversity and Habitat Distribution of Birds in Coastal Marshes and Comparisons with Surrounding Upland Habitats in Southeastern South America

We studied variation in bird assemblages with plant associations for three different coastal marshes from Southeastern South America (SESA) and assessed how marsh bird assemblages related to nearby upland bird assemblages. We surveyed bird species and plant structure along the tidal gradient of each locality from the low tide level to the upper habitats bordering coastal marshes. Twenty species frequently used coastal marshes, including relatively few migratory species. We found that birds occurring in SESA coastal marshes do not have distributions constrained to coastal marshes. Nonetheless, four bird assemblages were recognized in association with vegetation types and/or sites. Among the recorded coastal marsh species, the bay-capped wren-spinetail (Spartonoica maluroides) is both the most frequent and the most habitat constrained. Bird richness increases steadily along the tidal gradient associated with the increase in vegetation structure, suggesting that bird richness is directly explained by vegetation and indirectly by the physical conditions influencing vegetation structure. Results highlight the importance of SESA middle marshes as habitat for conservation of some threatened SESA grassland birds.     

Zircon U-Pb geochronology and geochemistry of Late Devonian–Carboniferous granitoids in NW Iran: implications for the opening of Paleo-Tethys

ABSTRACT

We present zircon U-Pb crystallization ages combined with bulk rock major and trace element geochemistry and Sr-Nd-Pb and zircon in-situ Hf isotopic compositions of the Amand and Moro granitoid intrusions in northwest Iran. The Amand and Moro plutons include granite and syeno-diorite with LA-ICP-MS U-Pb zircon ages of 367 ± 6.8 Ma and 351 ± 1.3 Ma, respectively, representative of Late Devonian-Early Carboniferous magmatic activity in NW Iran. Geochemical characteristics such as typical enrichments in alkalis, Nb, Zr, Ga and Y, depletion in P and Sr and fractionated REE patterns with high Ga/Al ratios and Eu negative anomalies are consistent with A-type magmatic signatures. The granitoids are classified as A₂-type and within-plate granitoids. The bulk rock geochemistry (enrichments in Th, Nb and, high Th/Yb, Zr/Y ratios) along with low variation of ¹⁴³Nd/¹⁴⁴Nd_(i) and ⁸⁷Sr/⁸⁶Sr_(i) ratios and positive zircon εHf_(t) support the role of a mantle plume component for the evolution of the Amand and Moro A-type granitoids in an extensional tectonic environment. In fitting with wider regional knowledge, this magmatism occurred during Paleo-Tethys opening in northern Gondwana.     

The control of the production process of phytoplankton by the physical structure of the aquatic environment with special reference to its optical properties

This tutorial was designed for nonbiologists requiring an introduction to the nature and general timescales of phytoplankton responses to physical forcing in aquatic environments. As such, an effort was made to highlight biological markers which might assist in identifying, measuring and/or validating physical processes controlling the variability in the distribution, abundance, composition and activity of phytoplankton communities. Given the recent advances in environmental optics and remote sensing capabilities, a special emphasis was placed on the nature and utility of phytoplankton optical properties in current bio-optical modelling efforts to predict temporal and spatial variability in phytoplankton productivity and growth.     

Ephemeris errors of GPS satellites

Ephemeris errors are supposed to be a major factor limiting the usefulness ofGPS in high precision geodesy. Considerations of orbital mechanics suggest that, regardless of their complexity, the uncertainties in the solar radiation pressure model, the gravity field model, and the estimated initial state, may have simple effects on the ephemeris. This possibility has been tested by fitting linear combinations of simple functions—chosen on theoretical grounds—to simulated errors of three-day ephemerides. With a set of five functions for the across-track component, six for the radial, and seven for the along-track, it has been possible to fit the position errors to better than 1% of theirr.m.s values, in all the caces studied. The simulations included —besides solar radiation pressure errors—gravity field model and initial state uncertainties, as well as an unknown constant force along the axis of the solar panels. The solar radiation force was calculated taking into account the shape, orientation, and physical properties (reflectivity and specularity) of the main parts of the spacecraft, under various conditions of illumination (continuous sunlight, eclipses, etc.).     

Dynamic of the freshwater–saltwater interface in a karstic aquifer under extraordinary recharge action: the Merida Yucatan case study

A hydraulic analysis of the interface between freshwater–saltwater behavior was done in the Merida Yucatan zone, two machines that constantly register the groundwater levels were installed, and three electric conductivity logs were taken from wells. When comparing the measured results with the ones obtained using theoretical equations developed to calculate the freshwater–saltwater interface position, it was proved that in some cases these equations can be applied, and in others not. Two effects that rule the behavior of karst aquifers in extraordinary conditions were found.     

Coherent structure dynamics and sediment particle motion around a cylindrical pier in developing scour holes

Recent investigations on the dynamics of the turbulent horseshoe vortex system (THV) around cylindrical piers have shown that the rich coherent dynamics of the vortical structures is dominated by low-frequency bimodal fluctuations of the velocity field. In spite of these advances, many questions remain regarding the changes of the flow and sediment transport dynamics as scour progresses. In this investigation we carry out laboratory experiments to register the development of the scour hole around a cylindrical pier in a fine-sand bed (d ₅₀ = 0.36 mm). We use the bathymetry measured in the experiment to simulate the flow field employing the detached-eddy simulation approach (DES), which has shown to resolve most of the turbulent stresses around surface-mounted obstacles. From these simulations we compare the dynamics of the THV to the flat-bed case, and analyze the effects on particle transport and sediment flux using the Lagrangian particle model of Escauriaza and Sotiropoulos (2011b) to study the impact of the changes of the flow on the sediment dynamics.