Some remarks on the Gaussian beam summation method

Summary. Recently, a method using superposition of Gaussian beams has been proposed for the solution of high-frequency wave problems. The method is a potentially useful approach when the more usual techniques of ray theory fail: it gives answers which are finite at caustics, computes a nonzero field in shadow zones, and exhibits critical angle phenomena, including head waves. Subsequent tests by several authors have been encouraging, although some reported solutions show an unexplained dependence on the 'free' complex parameter ε which specifies the initial widths and phases of the Gaussian beams.
We use methods of uniform asymptotic expansions to explain the behaviour of the Gaussian beam method. We show how it computes correctly the entire caustic boundary layer of a caustic of arbitrary complexity, and computes correctly in a region of critical reflection. However, the beam solution for head waves and in edge-diffracted shadow zones are shown to have the correct asymptotic form, but with governing parameters that are explicitly ε-dependent. We also explain the mechanism by which the beam solution degrades when there are strong lateral inhomogeneities. We compare numerically our predictions for some representative, model problems, with exact solutions obtained by other means.     

A Global Synthesis of Managing Groundwater Dependent Ecosystems Under Sustainable Groundwater Policy

Groundwater is a vital water supply worldwide for people and nature. However, species and ecosystems that depend on groundwater for some or all of their water needs, known as groundwater dependent ecosystems (GDEs), are increasingly becoming threatened worldwide due to growing human water demands. Over the past two decades, the protection and management of GDEs have been incorporated into several water management policy initiatives worldwide including jurisdictions within Australia, the European Union, South Africa, and the United States. Among these, Australia has implemented the most comprehensive framework to manage and protect GDEs through its water policy initiatives. Using a science‐based approach, Australia has made good progress at reducing uncertainty when selecting management thresholds for GDEs in their water management plans. This has been achieved by incorporating appropriate metrics for GDEs into water monitoring programs so that information gathered over time can inform management decisions. This adaptive management approach is also accompanied by the application of the “Precautionary Principle” in cases where insufficient information on GDEs exist. Additionally, the integration of risk assessment into Australia's approach has enabled water managers to prioritize the most valuable and vulnerable ecologic assets necessary to manage GDEs under Australia's national sustainable water management legislation. The purpose of this paper is to: (1) compare existing global policy initiatives for the protection and management of GDEs; (2) synthesize Australia's adaptive management approach of GDEs in their state water plans; and (3) highlight opportunities and challenges of applying Australia's approach for managing GDEs under other water management policies worldwide.     

Response of low‐angle dunes to variable flow

Current understanding of bedform dynamics is largely based on field and laboratory observations of bedforms in steady flow environments. There are relatively few investigations of bedforms in flows dominated by unsteadiness associated with rapidly changing flows or tides. As a consequence, the ability to predict bedform response to variable flow is rudimentary. Using high‐resolution multibeam bathymetric data, this study explores the dynamics of a dune field developed by tidally modulated, fluvially dominated flow in the Fraser River Estuary, British Columbia, Canada. The dunes were dominantly low lee angle features characteristic of large, deep river channels. Data were collected over a field ca 1·0 km long and 0·5 km wide through a complete diurnal tidal cycle during the rising limb of the hydrograph immediately prior to peak freshet, yielding the most comprehensive characterization of low‐angle dunes ever reported. The data show that bedform height and lee angle slope respond to variable flow by declining as the tide ebbs, then increasing as the tide rises and the flow velocities decrease. Bedform lengths do not appear to respond to the changes in velocity caused by the tides. Changes in the bedform height and lee angle have a counterclockwise hysteresis with mean flow velocity, indicating that changes in the bedform geometry lag changes in the flow. The data reveal that lee angle slope responds directly to suspended sediment concentration, supporting previous speculation that low‐angle dune morphology is maintained by erosion of the dune stoss and crest at high flow, and deposition of that material in the dune trough.     

Tidal Habitats Support Large Numbers of Invasive Blue Catfish in a Chesapeake Bay Subestuary

The introduction of a non-native freshwater fish, blue catfish Ictalurus furcatus, in tributaries of Chesapeake Bay resulted in the establishment of fisheries and in the expansion of the population into brackish habitats. Blue catfish are an invasive species in the Chesapeake Bay region, and efforts are underway to limit their impacts on native communities. Key characteristics of the population (population size, survival rates) are unknown, but such knowledge is useful in understanding the impact of blue catfish in estuarine systems. We estimated population size and survival rates of blue catfish in tidal habitats of the James River subestuary. We tagged 34,252 blue catfish during July–August 2012 and 2013; information from live recaptures (n = 1177) and dead recoveries (n = 279) were used to estimate annual survival rates and population size using Barker’s Model in a Robust Design and allowing for heterogeneity in detection probabilities. The blue catfish population in the 12-km study area was estimated to be 1.6 million fish in 2013 (95% confidence interval [CI] adjusted for overdispersion: 926,307–2,914,208 fish). Annual apparent survival rate estimates were low: 0.16 (95% CI 0.10–0.24) in 2012–2013 and 0.44 (95% CI 0.31–0.58) in 2013–2014 and represent losses from the population through mortality, permanent emigration, or both. The tagged fish included individuals that were large enough to exhibit piscivory and represented size classes that are likely to colonize estuarine habitats. The large population size that we estimated was unexpected for a freshwater fish in tidal habitats and highlights the need to effectively manage such species.     

Trace metal distributions in Saint John Harbour sediments

The concentration and areal distribution of selected trace metals (Cu, Zn, Pb, Cd, Mo, Ni, Mn and Hg) in surficial sediments of Saint John Harbour, New Brunswick, Canada, were studied to determine the extent of anthropogenic input and to estimate the effects of dumping dredged material in the outer harbour. Hg and Cd are of especial concern, since the disposal of dredge material containing these two elements is regulated under the Ocean Dumping Control Act.The concentrations of all metals are low: Cu 16, Zn 53, Pb 24, Cd 0.16, Mo 3, Ni 16, Mn 296 and Hg 0.04 μg g^?1. Hg and Cd levels in sediments are well below the permissible limits of 0.75 and 0.6 μg g^?1, respectively, set by the Ocean Dumping Control Act.The mean concentrations of trace elements are similar to the low mean values in the unpolluted Bay of Fundy. There is an overall decline in concentrations of metals in the sediments from the inner to the outer harbour. Comparison of the metal levels in the sediments from different areas within the harbour indicate that there is a detectable anthropogenic input in the Courtenay Bay area. Trace metal levels at the dumpsite are significantly lower than in the Courtenay Bay area, where the bulk of the dredged material originates.     

GMOS spectroscopy of the S0 galaxy NGC 3115

We present Gemini Multi-Object Spectrograph longslit spectroscopy of the isolated S0 galaxy NGC 3115. We have determined kinematical data and Lick/IDS absorption line-strength indices for the major axis out to around 9 kpc and for the minor axis out to around 5 kpc (around 2R _e ). Using stellar population models which include the effects of variable [α/Fe] ratios, we derive metallicities, abundance ratios and ages for the stellar population of NGC 3115. We find that [α/Fe] remains fairly constant with increasing radius at around  [α/Fe]= 0.17  for the major axis but increases rapidly for the minor axis to around  [α/Fe]= 0.3  . We also find that to first order, this behaviour can be explained by a simple spheroid + disc model, where the spheroid has  [α/Fe]= 0.3  and the disc shows close to solar abundance ratios. The disc also appears considerably younger than the spheroid, having an age of around 6 Gyr compared to 12 Gyr for the spheroid. We compare these results to those previously presented for the globular cluster system of NGC 3115.     

Quality assessment of GPS reprocessed terrestrial reference frame

The International GNSS Service (IGS) contributes to the construction of the International Terrestrial Reference Frame (ITRF) by submitting time series of station positions and Earth Rotation Parameters (ERP). For the first time, its submission to the ITRF2008 construction is based on a combination of entirely reprocessed GPS solutions delivered by 11 Analysis Centers (ACs). We analyze the IGS submission and four of the individual AC contributions in terms of the GNSS frame origin and scale, station position repeatability and time series seasonal variations. We show here that the GPS Terrestrial Reference Frame (TRF) origin is consistent with Satellite laser Ranging (SLR) at the centimeter level with a drift lower than 1 mm/year. Although the scale drift compared to Very Long baseline Interferometry (VLBI) and SLR mean scale is smaller than 0.4 mm/year, we think that it would be premature to use that information in the ITRF scale definition due to its strong dependence on the GPS satellite and ground antenna phase center variations. The new position time series also show a better repeatability compared to past IGS combined products and their annual variations are shown to be more consistent with loading models. The comparison of GPS station positions and velocities to those of VLBI via local ties in co-located sites demonstrates that the IGS reprocessed solution submitted to the ITRF2008 is more reliable and precise than any of the past submissions. However, we show that some of the remaining inconsistencies between GPS and VLBI positioning may be caused by uncalibrated GNSS radomes.     

Ages and composition of gas trapped in Allan Hills and Byrd core ice

Gas is extracted from large (6–31 kg) Antarctic ice samples to obtain sufficient CO₂ for¹⁴C measurements with small low-level proportional counters. The¹⁴C ages of Byrd core ice are in accord with glaciological estimates ranging from (2.2_−1.1^+1.4)×10³ yr at 271 m depth to more than 8 × 10³ yr at 1071 m depth. The CO₂ abundances in gas extracted from Byrd core ice range from 0.0216 to 0.051%, with below present-day atmosphere CO₂ abundances for ice from 1068 and 1469 m depths. The CO₂ abundance in gas from Allan Hills surface ice samples ranges between four and six times the atmospheric value and the CO₂ had a specific activity three times that of contemporary carbon. A possible explanation for the anomalously high specific activity is surface melting with the incorporation into CO₂ of¹⁴C produced by cosmic ray spallation of oxygen in ice. The CO₂ abundance in gas extracted from subsurface Allan Hills ice ranged from 0.030 to 0.065%, and the specific activities are below contemporary carbon, indicating ages greater than 5×10³ yr. The¹⁸O/¹⁶O ratio of oxygen in the trapped gas is the same as that of atmospheric oxygen and differs markedly from the¹⁸O/¹⁶O ratio in the ice. The O₂, N₂, and Ar abundances and isotopic compositions are similar to those in contemporary air, except for positive¹⁵N/¹⁴N ratios in a few samples.     

Fragility analysis of low‐rise masonry in‐filled reinforced concrete buildings by a coefficient‐based spectral acceleration method

This study presents a seismic fragility analysis of low‐rise masonry in‐filled (MI) reinforced concrete (RC) buildings using a proposed coefficient‐based spectral acceleration method. The coefficient‐based method, without requiring any complicated finite element analysis, is a simplified procedure for assessing the spectral acceleration demand (or capacity) of buildings subjected to earthquakes. This paper begins with a calibration of the proposed coefficient‐based method for low‐rise MI RC buildings using published experimental results obtained from shaking table tests. Spectral acceleration‐based fragility curves for low‐rise MI RC buildings under various inter‐story drift limits are then constructed using the calibrated coefficient‐based method. A comparison of the experimental and estimated results indicates that the simplified coefficient‐based method can provide good approximations of the spectral accelerations at peak loads of low‐rise MI RC buildings, if a proper set of drift‐related factors and initial fundamental periods of structures are used. Moreover, the fragility curves constructed using the coefficient‐based method can provide a satisfactory vulnerability evaluation for low‐rise MI RC buildings under a given performance level. Copyright © 2011 John Wiley & Sons, Ltd.