On least squares estimation of generalized covariance functions

Least squares estimation (LSE) is theoretically related to quadratic unbiased estimation of variance components. It is argued that these methods of estimation of variance components essentially generalize LSE though they are not formally equivalent.     

Bi-dimensional observation of waves near the mesopause at auroral latitudes

During a campaign of optical observations at high latitude, a bi-dimensional study of the wave structure of the OH layer has been performed in December 1981 from Sodankyla (Finland). This site is one of the three stations of the EISCAT ionosphere sounding system. It has been found that a wave field covering an area of 1 million km² may extend to latitudes as high as 70°N. The OH wave structure shows many similarities with noctilucent clouds. The fairly large horizontal wavelength, of the order of 40 km cannot easily be explained by a wave motion at an interface. The observed wave structure seems to be a result of the propagation of an internal gravity wave in the 80–100 km region. This wave structure was often recorded during the same time as an active aurora was present. As a result, it appears that the perturbation might be correlated with particle precipitations at auroral latitudes.     

The Preboreal climate reversal and a subsequent solar‐forced climate shift

Accurate chronologies are essential for linking palaeoclimate archives. Carbon‐14 wiggle‐match dating was used to produce an accurate chronology for part of an early Holocene peat sequence from the Borchert (The Netherlands). Following the Younger Dryas–Preboreal transition, two climatic shifts could be inferred. Around 11 400 cal. yr BP the expansion of birch (Betula) forest was interrupted by a dry continental phase with dominantly open grassland vegetation, coeval with the PBO (Preboreal Oscillation), as observed in the GRIP ice core. At 11 250 cal. yr BP a sudden shift to a humid climate occurred. This second change appears to be contemporaneous with: (i) a sharp increase of atmospheric ¹⁴C; (ii) a temporary decline of atmospheric CO₂; and (iii) an increase in the GRIP ¹⁰Be flux. The close correspondence with excursions of cosmogenic nuclides points to a decline in solar activity, which may have forced the changes in climate and vegetation at around 11 250 cal. yr BP. Copyright © 2004 John Wiley & Sons, Ltd.     

Secular resonances: New results

We integrated numerically, in the frame of the four body problem Sun-Jupiter-Saturn-asteroid the orbit of the asteroid 1974 MA, an Earth-crosser, which is located in a region where three resonances overlap: the two secular resonances ₅ and ₁₆ and the mean motion resonance 5/1. The numerical integration yields a qualitative orbital evolution of this particular region.     

Constraining the origin and evolution of confined turbidite systems: southern Cretan margin,Eastern Mediterranean Sea (34°30–36°N)

Bathymetric, 9.5-kHz long-range sidescan sonar (OKEAN), seismic reflection and sediment-core data are used in the analysis of two tectonic troughs south of Crete, Eastern Mediterranean Sea. Here, up to 1.2 s two-way travel time (TWTT) of strata have accumulated since the Middle Miocene in association with extension in the South Aegean region. The study area comprises >100-km- long by >25-km-wide basins filled by sediments subdivided into two seismic units: (1) an upper Unit 1 deposited in sub-basins which follow the present-day configuration of the southern Cretan margin; (2) a basal Unit 2, more than 500 ms (TWTT) thick, accumulated in deeper half-graben/grabens distinct from the present-day depocentres. Both units overlap a locally stratified Unit 3 comprising the pre-Neogene core complex of Crete and Gavdos. In this work, the interpreted seismic units are correlated with the onshore stratigraphy, demonstrating that denudation processes occurring on Crete and Gavdos in response to major tectonic events have been responsible for high sedimentation rates along the proximal southern Cretan margin. Consequently, topographically confined sedimentary units have been deposited south of Crete in the last 12 Ma, including turbidites and other mass-flow deposits fed by evolving transverse and axial channel systems. Surface processes controlling facies distribution include the direct inflow of sediment from alluvial-fan systems and incising mountain rivers onto the Cretan slope, where significant sediment instability processes occur at present. In this setting, seismic profiles reveal eight different types of stratigraphic contacts on basin-margin highs, and basinal areas show evidence of halokinesis and/or fluid escape. The acquired data also show that significant changes to the margin’s configuration occurred in association with the post-Alpine tectonic and eustatic episodes affecting the Eastern Mediterranean.     

Diet shifts of Caribbean grunts (Haemulidae) and snappers (Lutjanidae) and the relation with nursery-to-coral reef migrations

The spatial size distribution of grunts and snappers have previously indicated the separation of juveniles in nursery habitats from the adults on the coral reef. This implies life cycle migrations from nursery habitats (such as seagrass beds and mangroves) to the coral reef. If diet shifts are related to such migrations, then the diets of these fish must change before or around the fish size at which such migrations take place. A wide size range of juveniles of two grunt species (Haemulon sciurus and Haemulon flavolineatum) and of two snapper species (Lutjanus apodus and Ocyurus chrysurus) were caught in seagrass beds and mangroves, and their gut contents identified and quantified. Regression analysis between fish size and dietary importance of small crustaceans showed a negative relationship in all four species. Positive relations were found for H. sciurus, L. apodus and O. chrysurus between fish length and the dietary importance of decapods, and for L. apodusand O. chrysurus between fish length and prey fish importance. Critical changes in the fish diets with fish size were examined by application of a Canonical Correspondence Analysis (CCA). The CCA yielded three clusters of size-classes of fishes with similar diets, and application of a Mantel test showed that each of these clusters had significantly different diets, and that each cluster diet was significantly specialised. The size at which a fish species ‘switched’ from one cluster to another was compared with size-at-maturity data and with the typical size at which these species migrate from the nursery habitats to the coral reef. H. sciurus and H. flavolineatum may be prompted to migrate from the nursery habitats to coral reef habitats because of dietary changes, or because of the development of the gonads. For L. apodus and O. chrysurus, a dietary changeover forms a more likely explanation for nursery-to-reef migrations than does sexual maturation because these species reach maturity at sizes much larger than the maximum size of individuals found in nursery habitats. Although other factors may theoretically initiate or promote the migration patterns, the results of this study indicate that ontogenetic dietary changes may crucially influence the nursery-to-coral reef migrations of these reef fish species.     

Preliminary attempt to characterize the rotation of seafloor in the Pito Deep area of the Easter Microplate using a submersible magnetometer

Several mechanisms have been proposed to account for the rotation of the nearly north-south abyssal hill fabric formed on the East Pacific Rise north of the Easter Microplate to the nearly east-west trends in the northern microplate interior. Proposed mechanisms include rigid microplate rotation, transform fault – parallel shear, and bookshelf faulting during the transfer of lithosphere from the Nazca Plate to the microplate. We used a submersible magnetometer on a NAUTILE dive program to measure the magnetic vector rotation of a pillow basalt and dike spur near Pito Deep, the present location of the tip of the propagating rift system that created the microplate. Our results, although too limited to draw strong conclusions from, suggest clockwise rotations of the seafloor magnetic vectors inconsistent with the transform-parallel shear model, and larger than can be explained solely by rigid microplate rotation.     

The dimensions of sand ripples in full-scale oscillatory flows

New large-scale experiments have been carried out in two oscillatory flow tunnels to study ripple regime sand suspension and net sand transport processes in full-scale oscillatory flows. The paper focuses on ripple dimensions and the new data are combined with existing data to make a large dataset of ripple heights and lengths for flows with field-scale amplitudes and periods. A feature of the new experiments is a focus on the effect of flow irregularity. The combined dataset is analysed to examine the range of hydraulic conditions under which oscillatory flow ripples occur, to examine the effects of flow irregularity and ripple three-dimensionality on ripple dimensions and to test and improve existing methods for predicting ripple dimensions.The following are the main conclusions. (1) The highest velocities in a flow time-series play an important role in determining the type of bedform occurring in oscillatory flow. Bedform regime is well characterised by mobility number based on maximum velocity in the case of regular flow and based on the mean of the highest one tenth peak velocities in the case of irregular flow. (2) For field-scale flows, sand size is the primary factor determining whether equilibrium ripples will be 2D or 3D. 2D ripples occur when the sand D₅₀ ≥ 0.30 mm and 3D ripples occur when D₅₀ ≤ 0.22 mm (except when the flow orbital diameter is low). (3) Ripple type (2D or 3D) is the same for regular and irregular flows and ripple dimensions produced by equivalent regular and irregular flows follow a similar functional dependence on mobility number, with mobility number based on maximum velocity in the case of regular flow and based on the mean of the highest one tenth velocities in the case of irregular flow. For much of the ripple regime, ripple dimensions have weak dependency on mobility number and ripple dimensions are similar for regular and irregular flows with the same flow orbital amplitude. However, differences in ripples produced by equivalent regular and irregular flows become significant at the high mobility end of the ripple regime. (4) Ripple dimensions predicted using the Wiberg and Harris formulae are in poor agreement with measured ripple dimensions from the large-scale experiments. Predictions based on the Mogridge et al. and the Nielsen formulae show better overall agreement with the data but also show systematic differences in cases of 3D ripples and ripples generated by irregular flows. (5) Based on the combined large-scale data, modifications to the Nielsen ripple dimension equations are proposed for the heights and lengths of 2D ripples. The same equations apply to regular and irregular flows, but with mobility number appropriately defined. 3D ripples are generally smaller than 2D ripples and estimates of 3D ripple height and length may be obtained by applying multipliers of 0.55 and 0.73 respectively to the 2D formulae. The proposed modified Nielsen formulae provide an improved fit to the large-scale data, accounting for flow irregularity and ripple three-dimensionality.     

A relation in families of periodic solutions

We show the existence of a general relation between the parameters of periodic solutions in dynamical systems with ignorable coordinates. In particular, for time-independent systems with an axis of symmetry, the relation takes the form T/A=–/E, whereT is the period,A is the angular momentum, is the angle through which the system has rotated after one period, andE is the energy.