Rational approximations in the parabolic equation method for water waves

Approximations based on minimax principles are developed in order to allow for large-angle propagation in the parabolic equation method. Numerical studies show that the minimax approximations do not cause any significant degradation of accuracy at small angles of incidence when compared with an existing model based on a (1,1) Padé approximant, and that they allow for much more successful treatment of large angles of incidence than is possible using the previously available methods.     

On the energy integral for first post-Newtonian approximation

The post-Newtonian approximation for general relativity is widely adopted by the geodesy and astronomy communities. It has been successfully exploited for the inclusion of relativistic effects in practically all geodetic applications and techniques such as satellite/lunar laser ranging and very long baseline interferometry. Presently, the levels of accuracy required in geodetic techniques require that reference frames, planetary and satellite orbits and signal propagation be treated within the post-Newtonian regime. For arbitrary scalar W and vector gravitational potentials \(W^j (j=1,2,3)\), we present a novel derivation of the energy associated with a test particle in the post-Newtonian regime. The integral so obtained appears not to have been given previously in the literature and is deduced through algebraic manipulation on seeking a Jacobi-like integral associated with the standard post-Newtonian equations of motion. The new integral is independently verified through a variational formulation using the post-Newtonian metric components and is subsequently verified by numerical integration of the post-Newtonian equations of motion.     

Lead and Mg isotopic age constraints on the evolution of the HED parent body

The large collection of howardite‐eucrite‐diogenite (HED) meteorites allows us to study the initial magmatic differentiation of a planetesimal. We report Pb‐Pb ages of the unequilibrated North West Africa (NWA) 4215 and Dhofar 700 diogenite meteorites and their mass‐independent ²⁶Mg isotope compositions (²⁶Mg*) to better understand the timing of differentiation and crystallization of their source reservoir(s). NWA 4215 defines a Pb‐Pb age of 4484.5 ± 7.9 Myr and has a ²⁶Mg* excess of +2.3 ± 1.6 ppm whereas Dhofar 700 has a Pb‐Pb age of 4546.4 ± 4.7 Myr and a ²⁶Mg* excess of +25.5 ± 1.9 ppm. We interpret the young age of NWA 4215 as a thermal overprint, but the age of Dhofar 700 is interpreted to represent a primary crystallization age. Combining our new data with published Mg isotope and trace element data suggests that approximately half of the diogenites for which such data are available crystallized within the first 1–2 Myr of our solar system, consistent with a short‐lived, early‐formed magma ocean undergoing convective cooling. The other half of the diogenites, including both NWA 4215 and Dhofar 700, are best explained by their crystallization in slowly cooled isolated magma chambers lasting over at least ~20 Myr.     

Geochemical and oxygen isotope perspective of a new R chondrite Dhofar 1671: Affinity with ordinary chondrites

Dhofar 1671 is a relatively new meteorite that previous studies suggest belongs to the Rumuruti chondrite class. Major and REE compositions are generally in agreement with average values of the R chondrites (RCs). Moderately volatile elements such as Se and Zn abundances are lower than the R chondrite values that are similar to those in ordinary chondrites (OCs). Porphyritic olivine pyroxene (POP), radial pyroxene (RP), and barred olivine (BO) chondrules are embedded in a proportionately equal volume of matrix, one of the characteristic features of RCs. Microprobe analyses demonstrate compositional zoning in chondrule and matrix olivines showing Fa‐poor interior and Fa‐rich outer zones. Precise oxygen isotope data for chondrules and matrix obtained by laser‐assisted fluorination show a genetic isotopic relationship between OCs and RCs. On the basis of our data, we propose a strong affinity between these groups and suggest that OC chondrule precursors could have interacted with a ¹⁷O‐rich matrix to form RC chondrules (i.e., ?¹⁷O shifts from ~1‰ to ~3‰). These interactions could have occurred at the same time as “exotic” clasts in brecciated samples formed such as NWA 10214 (LL3–6), Parnallee (LL3), PCA91241 (R3.8–6), and Dhofar 1671 (R3.6). We also infer that the source of the oxidation and ¹⁷O enrichment is the matrix, which may have been enriched in ¹⁷O‐rich water. The abundance of matrix in RCs relative to OCs, ensured that these rocks would be apparently more oxidized and appreciably ¹⁷O‐enriched. In situ analysis of Dhofar 1671 is recommended to further strengthen the link between OCs and RCs.     

Nitrogen inputs to seventy-four southern New England estuaries: Application of a watershed nitrogen loading model

Excess nitrogen inputs to estuaries have been linked to deteriorating water quality and habitat conditions which in turn have direct and indirect impacts on aquatic organisms. This paper describes the application of a previously verified watershed loading model to estimate total nitrogen loading rates and relative source contributions to 74 small-medium sized embayment-type estuaries in southern New England. The study estuaries exhibited a gradient in nitrogen inputs of a factor of over 7000. On an areal basis, the range represented a gradient of approximately a factor of 140. Therefore, all other factors being equal, the study design is sufficient to evaluate ecological effects conceptually tied to excess nitrogen along a nitrogen gradient. In addition to providing total loading inputs rates to the study estuaries, the model provides an estimate of the relative contribution of the nitrogen sources from each watershed to each associated estuary. Cumulative results of this analysis reveal the following source ranking (means): direct atmospheric deposition (37%), ≈wastewater (36%), >indirect atmospheric deposition (16%) > fertilizer (12%). However, for any particular estuary the relative magnitudes of these source types vary dramatically. Together with scientific evidence on symptoms of eutrophication, the results of this paper can be used to develop empirical pressure-state models to determine critical nitrogen loading limits for the protection of estuarine water quality.     

Prawn postlarvae fishing in coastal Bangladesh: Challenges for sustainable livelihoods

Fishing for prawn (Macrobrachium rosenbergii) postlarvae is a major contributor to the livelihoods of the coastal poor in Bangladesh, including women. A study of coastal livelihoods along the lower Pasur River in southwest Bangladesh indicates that on average 40% of total annual income comes from postlarvae fishing during the few months involved. However, indiscriminate fishing of wild postlarvae, with high levels of by-catch, has an impact on biodiversity in coastal ecosystems. This has provoked imposition of restrictions on postlarvae collection. The ban has, however, not been firmly enforced because of the lack of alternative livelihoods for coastal poor. A conceptual framework, drawn from an approach to poverty reduction known as the sustainable livelihoods approach, is applied to understanding the role of prawn postlarvae fishing. Evidence from this study suggests that postlarvae fishers faced a number of livelihood constraints, including poor livelihood assets. This paper concludes that wider livelihood options need to be found for postlarvae fishers to support their livelihoods.     

Can marine fisheries and aquaculture meet fish demand from a growing human population in a changing climate?

Expansion in the world's human population and economic development will increase future demand for fish products. As global fisheries yield is constrained by ecosystems productivity and management effectiveness, per capita fish consumption can only be maintained or increased if aquaculture makes an increasing contribution to the volume and stability of global fish supplies. Here, we use predictions of changes in global and regional climate (according to IPCC emissions scenario A1B), marine ecosystem and fisheries production estimates from high resolution regional models, human population size estimates from United Nations prospects, fishmeal and oil price estimations, and projections of the technological development in aquaculture feed technology, to investigate the feasibility of sustaining current and increased per capita fish consumption rates in 2050. We conclude that meeting current and larger consumption rates is feasible, despite a growing population and the impacts of climate change on potential fisheries production, but only if fish resources are managed sustainably and the animal feeds industry reduces its reliance on wild fish. Ineffective fisheries management and rising fishmeal prices driven by greater demand could, however, compromise future aquaculture production and the availability of fish products.     

High‐ to ultrahigh‐temperature metamorphism in the lower crust: An example resulting from Hikurangi Plateau collision and slab rollback in New Zealand

Lower crustal xenoliths erupted from an intraplate diatreme reveal that a portion of the New Zealand Gondwana margin experienced high‐temperature (HT) to ultrahigh‐temperature (UHT) granulite facies metamorphism just after flat slab subduction ceased at c. 110–105 Ma. P–T calculations for garnet–orthopyroxene‐bearing felsic granulite xenoliths indicate equilibration at ~815 to 910°C and 0.7 to 0.8 GPa, with garnet‐bearing mafic granulite xenoliths yielding at least 900°C. Supporting evidence for the attainment of HT and UHT conditions in felsic granulite comes from re‐integration of exsolution in feldspar (~900–950°C at 0.8 GPa), Ti‐in‐zircon thermometry on Y‐depleted overgrowths on detrital zircon grains (932°C ± 24°C at aTiO₂ = 0.8 ± 0.2), and correlation of observed assemblages and mineral compositions with thermodynamic modelling results (≥850°C at 0.7 to 0.8 GPa). The thin zircon overgrowths, which were mainly targeted by drilling through the cores of grains, yield a U–Pb pooled age of 91.7 ± 2.0 Ma. The cause of Late Cretaceous HT‐UHT metamorphism on the Zealandia Gondwana margin is attributed to collision and partial subduction of the buoyant oceanic Hikurangi Plateau in the Early Cretaceous. The halt of subduction caused the fore‐running shallowly dipping slab to rollback towards the trench position and permitted the upper mantle to rapidly increase the geothermal gradient through the base of the extending (former) accretionary prism. This sequence of events provides a mechanism for achieving regional HT–UHT conditions in the lower crust with little or no sign of this event at the surface.