A comparison of empirical orthogonal decomposition methods in baroclinic flows

The relative merits of three contrasting empirical orthogonal decomposition methods in common use (namely, Proper Orthogonal Decomposition, Biorthogonal Decomposition and Multivariate Singular Systems Analysis) are considered as applied to baroclinic flow data. The regimes analysed are a steady, drifting wave, a modulated amplitude vacillating wave flow and a neighbouring multi-mode state which exhibits intermittency. The results are used to make a qualitative comparison of the methods in terms of convergence properties, variance capture and eigenfunction structure. The feasibility of using the resulting empirical orthogonal functions to transform partial differential equations to ordinary differential equations by Galerkin projection is mentioned.     

Pit crater formation on Kilauea volcano, Hawaii.

Most of the known pit craters in Hawaii occur along the East and Southwest Rift Zones of Kilauea volcano. The pit craters typically are either astride a single rift zone fracture or between a pair of rift zone fractures. These fractures are prominent in the pit crater walls. The pit craters are elliptical in plan view, with their major diameters ranging from 8 to 1140 m. They range in depth from 6 m to 186 m. They typically develop with initially steep, locally overhanging walls, but as the walls collapse, the craters fill with talus and become shaped like inverted elliptical cones. None of the craters apparently formed as eruptive vents, although some have been subsequently filled by lava. Devil's Throat is the best-exposed pit crater along the East Rift Zone. It is sited at a `waist' between two east-striking zones of ground cracks; the spacing between the crack zones decreases towards Devil's Throat. East-striking fractures are also prominent in the pit crater walls. Pit craters along the Southwest Rift Zone typically are elongate in plan view along the direction of the rift, have large caves at their bases along the long axes of the craters, and are smaller than those of the East Rift Zone. Some closely spaced pits there have coalesced to form a trough. Based on our observations and mechanical considerations, we infer that pit craters form by stoping over an underlying large-aperture rift zone fracture, and not by piston-like collapse over broad magma bodies or voids. Flow of magma along the underlying fracture may remove stoped blocks and prevent the fracture from being choked with debris. This mechanism is consistent with pit crater location, ground crack patterns, the preferred orientation of fractures in pit crater walls, and pit crater geometry (both in map view and cross-section). The mechanism also fits with observations of stoping into a gaping rift fracture that conducted lava from Kilauea caldera during the 1920s. Additionally, the ratio of pit crater width to depth of 0.5 to 2 is consistent with pit craters forming over a nearly vertical opening mode fracture.     

Fault-valve behaviour in optimally oriented shear zones: an example at the Revenge gold mine, Kambalda, Western Australia

Quartz vein systems developed in and adjacent to shear zones host major gold deposits in the Kambalda region of the Norseman–Wiluna greenstone belt. At the Revenge Mine, two groups of mineralised reverse shear zones formed as conjugate, near-optimally oriented sets during ESE subhorizontal shortening adjacent to a major transpressional shear system. The shear zones developed at temperatures of about 400°C in a transitional brittle–ductile regime. Deformation was associated with high fluid fluxes and involved fault-valve behaviour at transiently near-lithostatic fluid pressures. During progressive evolution of the shear system, early brittle and ductile deformation was overprinted by predominantly brittle deformation. Brittle shear failure was associated with fault dilation and the formation of fault-fill veins, particularly at fault bends and jogs. A transition from predominantly brittle shear failure to combined shear along faults and extension failure adjacent to faults occurred late during shear zone evolution and is interpreted as a response to a progressive decrease in maximum shear stress and a decrease in effective stresses. The formation of subhorizontal stylolites, locally subvertical extension veins and minor normal faults in association with thrust faulting, indicates episodic or transient reorientation of the near-field maximum principal stress from a subhorizontal to a near-vertical attitude during some fault-valve cycles. Local stress re-orientation is interpreted as resulting from near-total shear stress release and overshoot during some rupture events. Previously described fault-valve systems have formed predominantly in severely misoriented faults. The shear systems at Revenge Mine indicate that fault-valve action, and associated fluctuations in shear stress and fluid pressure, can influence the mechanical behaviour of optimally-oriented faults.     

Methane distribution and cycling in Tomales Bay, California

Cycling of methane (CH₄) in Tomales Bay, a 28-km² temperature estuary in northern California with relatively low inputs of organic carbon, was studied over a 1-yr period. Water column CH₄ concentrations showed spatial and temporal variability (range=8–100 nM), and were supersaturated with respect to the atmosphere by a factor of 2–37. Rates of net water column CH₄ production-oxidation were determined by in situ experiments, and were not found to be significantly different from zero. Fluxes across the sediment-water interface, determined by direct measurement using benthic chambers, varied from ?0.1 μmol m^?2 d^?1 to +16 μmol m^?2 d^?1 (positive fluxes into water). Methane concentrations in the two perennial creeks feeding the bay varied annually (140–950 nM); these creeks were a significant CH₄ source to the bay during winter. In addition, mass-balance calculations indicate a significant additional inter CH₄ source, which is hypothesized to result from storm-related runoff from dairy farms adjacent to the bay. Systemwide CH₄ budgets of the 16-km² inner bay indicate benthic production (110 mol d^?1) and atmospheric evasion (110 mol d^?1) dominated during summer, while atmospheric evasion (160 mol d^?1) and runoff from dairy farms (90 mol d^?1) dominated during winter.     

A sample of 6C radio sources designed to find objects at redshift z > 4 — I. The radio data

We describe the selection of a sample of 34 radio sources from the 6C survey from a region of sky covering 0.133 sr. The selection criteria for this sample, hereafter called 6C*, were chosen to optimize the chances of finding radio galaxies at redshift z  > 4. Optical follow-up observations have already led to the discovery of the most distant known radio galaxy at z  = 4.41. We present VLA radio maps and derive radio spectra for all the 6C* objects.     

Measuring Ω0 using cluster evolution

The evolution of the abundance of galaxy clusters depends sensitively on the value of the cosmological density parameter, Ω₀. Recent ASCA data are used to quantify this evolution as measured by the cluster X-ray temperature function. A χ² minimization fit to the cumulative temperature function, as well as a maximum-likelihood estimate (which requires additional assumptions about cluster luminosities), leads to the estimate Ω₀ ≈ 0.45 ± 0.25 (1σ statistical error). Various systematic uncertainties are considered, none of which significantly enhances the probability that Ω₀ = 1. These conclusions hold for models with or without a cosmological constant, i.e., with Λ₀ = 0 or Λ₀ = 1 − Ω₀. The statistical uncertainties are at least as large as any of the individual systematic errors that have been considered here, suggesting that additional temperature measurements of distant clusters will allow an improvement in this estimate. An alternative method that uses the highest redshift clusters to place an upper limit on Ω₀ is also presented and tentatively applied, with the result that Ω₀  1 can be ruled out at the 98 per cent confidence level. Whilst this method does not require a well-defined statistical sample of distant clusters, there are still modelling uncertainties that preclude a firmer conclusion at this time.     

Neutral hydrogen absorption observations of the central region of NGC 3628

Using MERLIN with 0.2-arcsec resolution we have observed neutral hydrogen absorption against the central region of the starburst galaxy NGC 3628. The central region resolves into ∼16 continuum components at 1.4 GHz. From comparison with published 15-GHz data, we infer that these components are supernova remnants, although three components may be consistent with a weak active galactic nucleus. Neutral hydrogen absorption is seen against the continuum emission with column densities ∼10²² cm⁻². The absorption appears to be from two separate absorbing structures. Assuming a simple morphology, the main velocity structure can be attributed to a ring of neutral gas with a radius 130 pc rotating around a central starburst with a velocity gradient of 1270 km s⁻¹ kpc⁻¹. From simple assumptions, the mass interior to this ring is 0.9 × 10⁹ M_⊙. The second absorption structure may represent outflow from the starburst region or a large-scale galactic structure. Alternatively the absorption structure may be non-axisymmetric, such as a bar.     

Carbon dioxide concentration and atmospheric flux in the Hudson River

We made direct measurements of the partial pressure of CO₂ (P_{CO 2}) in the tidal-freshwater portion of the Hudson River Estuary over a 3.5-yr period. At all times the Hudson was supersaturated in CO₂ with respect to the atmosphere. P_{CO 2} in surface water averaged 1125±403 (SD) μatm while the atmosphere averaged 416±68 μatm. Weekly samples at a single, mid-river station showed a pronounced and reproducible seasonal cycle with highest values (～2000 μatm) in mid-to-late summer, and lowest values (～500 μatm) generally in late winter. Samples taken along the length of the 190-km section of river showed a general decline in CO₂ from north to south. This decline was most pronounced in summer and very slight in spring. Diel and vertical variation were small relative to the standing stock of CO₂. Over six diel cycles, all taken during the algal growing season, the mean range was 300±114 μatm. CO₂ tended to increase slightly with depth, but the gradient was small, about 0.5 μmol m^?1, or an increase of 190 μatm from top to within 1 m of the bottom. For a large subset of the samples (n=452) we also calculated CO₂ from measurements of pH and total DIC. Calculated and measured values of CO₂ were in reasonably good agreement and a regression of calculated versus measured values had a slope of 0.85±0.04 and an r₂ of 0.60. Combining our measurements with recent experimental studies of gas exchange in the Hudson, we estimate that the Hudson releases CO₂ at a rate of 70–162 g C m^?2 yr^?1 from the river to the atmosphere.