Preconditioned Optimizing Utility for Large-dimensional analyses (POpULar)

I present the derivation of the Preconditioned Optimizing Utility for Large-dimensional analyses (POpULar), which is developed for adopting a non-diagonal background error covariance matrix in nonlinear variational analyses (i.e., analyses employing a non-quadratic cost function). POpULar is based on the idea of a linear preconditioned conjugate gradient method widely adopted in ocean data assimilation systems. POpULar uses the background error covariance matrix as a preconditioner without any decomposition of the matrix. This preconditioning accelerates the convergence. Moreover, the inverse of the matrix is not required. POpULar therefore allows us easily to handle the correlations among deviations of control variables (i.e., the variables which will be analyzed) from their background in nonlinear problems. In order to demonstrate the usefulness of POpULar, we illustrate two effects which are often neglected in studies of ocean data assimilation before. One is the effect of correlations among the deviations of control variables in an adjoint analysis. The other is the nonlinear effect of sea surface dynamic height calculation required when sea surface height observation is employed in a three-dimensional ocean analysis. As the results, these effects are not so small to neglect.     

Spatial and Temporal Variations of Sound Speed at the PN Section

Gridded sound speed data were calculated using Del Grosso's formulation from the temperature and salinity data at the PN section in the East China Sea covering 92 cruises between February 1978 and October 2000. The vertical gradients of sound speed are mainly related to the seasonal variations, and the strong horizontal gradients are mainly related to the Kuroshio and the upwelling. The standard deviations show that great variations of sound speed exist in the upper layer and in the slope zone. Empirical orthogonal function analysis shows that contributions of surface heating and the Kuroshio to sound speed variance are almost equivalent. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dissolved carbon and 33-133-133-1anomalies in the water column caused by hydrocarbon seeps on the northwestern Gulf of Mexico slope

Alkalinity, dissolved inorganic carbon (DIC), and ¹³C profiles from seep sites on the northwestern Gulf of Mexico upper slope show anomalously negative ¹³C values of up to –4.5 PDB, increased levels of DIC of up to 2.45 mmole/liter, and slight alkalinity rises of up to 2.54 meq/liter, relative to water column profiles from a seep-free site (0.63, 2.04 mmole/liter, and 2.39 meq/liter). The observed DIC enrichments coupled with the¹³C-depletions are attributed to the release of CO₂ by microbial oxidation of crude oil in the seep environment, and its migration into the water column. The ¹³C composition of the migrating CO₂ is estimated to be –26.0 on the basis of dissolved carbon inventory. Manifestation of DIC and ¹³C anomalies in the water column caused by hydrocarbon seepage holds promise to be useful for hydrocarbon reconnaissance surveys over large offshore tracts on account of the simplicity of sampling acquisition, and rapidity of analytical techniques in the laboratory.     

Geochemistry of suspended matter from the Baltic Sea 2. Results of bulk trace metal analysis by AAS

In 1984, on a transect covering the whole Baltic Sea and parts of the adjacent North Sea, 160 water samples were taken and analysed for their concentrations of particulate and dissolved metals. In addition, the suspended materials were investigated for their elemental bulk composition.The particulate fractions represented from about 5% (Cd, Cu and Ni) to 50% (Fe and Pb) of the total (particulate plus dissolved) concentrations. For some elements (Ba, Cd, Cu, Pb and Zn), the particulate matter from the surface microlayer was enriched with respect to those suspended materials taken from 0.2 m depth. This could reflect the atmospheric input of metal-rich aerosols. In anoxic deep waters, maximum contents of Zn (6400 μg g⁻¹), Cu (1330 μg g⁻¹) and Cd (12 μg g⁻¹) were observed in the particulate matter, indicating sulphidic forms. On the other hand, under oxic conditions the distribution coefficients (K_d) decreased with the water depth (Cd, Fe and Pb).Relative to global background levels, the particulate matter contained metal “excesses” amounting to more than 90% of the total contents (Cd, Mn, Pb and Zn). Automated electron probe X-ray microanalysis (EPXMA) revealed that the elemental composition of sediments is mainly governed by post-depositional processes of early diagenesis and is only weakly related to the composition of suspended matter in the overlying water body. For instance, in relation to surface mud sediments of the central Baltic net-sedimentation basins, Zn, Cd, Cu and Mn had 30–100% higher levels in the suspended materials. The general pattern of metal contents of particulate matter taken from 10 m depth on a transect between the Bothnian Bay and the North Sea were—possibly as a result of anthropogenic inputs—rather similar for Pb, Zn and Cu. For Fe and Mn, the distribution patterns along the transect were probably governed by the natural loading characteristics and by the biogeochemistry of those elements.     

Ocean Waves: Half-a-Century of Discovery

While the nature of most ocean waves has long been known and their basic physics understood since the nineteenth century, intense study of ocean waves during the second half of the twentieth century has taken the subject from the realm of mathematical exercises to that of practical engineering. Modern understanding of the generation, propagation and interactions of ocean waves with each other and with oceanic features has advanced to a quantitative level offering predictive capacity. This paper presents a brief qualitative review of advances in knowledge of sound waves, wind waves, tsunamis, tides, internal waves and long-period vorticity waves. The review is aimed at non-specialists who may benefit from an overview of the current state of the subject and access to a bibliography of general-interest references. This revised version was published online in August 2006 with corrections to the Cover Date.     

Tides in a body librating about a spin–orbit resonance: generalisation of the Darwin–Kaula theory

The Darwin-Kaula theory of bodily tides is intended for celestial bodies rotating without libration. We demonstrate that this theory, in its customary form, is inapplicable to a librating body. Specifically, in the presence of libration in longitude, the actual spectrum of Fourier tidal modes differs from the conventional spectrum rendered by the Darwin–Kaula theory for a nonlibrating celestial object. This necessitates derivation of formulae for the tidal torque and the tidal heating rate, that are applicable under libration. We derive the tidal spectrum for longitudinal forced libration with one and two main frequencies, generalisation to more main frequencies being straightforward. (By main frequencies we understand those emerging due to the triaxiality of the librating body.) Separately, we consider a case of free libration at one frequency (once again, generalisation to more frequencies being straightforward). We also calculate the tidal torque. This torque provides correction to the triaxiality-caused physical libration. Our theory is not self-consistent: we assume that the tidal torque is much smaller than the permanent-triaxiality-caused torque, so the additional libration due to tides is much weaker than the main libration due to the permanent triaxiality. Finally, we calculate the tidal dissipation rate in a body experiencing forced libration at the main mode, or free libration at one frequency, or superimposed forced and free librations.     

Analysis of radial movement of an unconfined leaky aquifer due to well pumping and injection

Radial movement of an unconfined leaky aquifer was studied with respect to hydraulic forces that are induced by well recharge and discharge. New analytic solutions in the velocity and displacement fields were found and applied to describe transient movement in an unconfined leaky aquifer. Linear momentum and mass balance of saturated porous sediments, the Darcy-Gersevanov law, and the analytic solution of hydraulic drawdown for unsteady flow within the unconfined leaky aquifer were introduced to find the new solutions. Analytic results indicate that the nonlinear relation between the initial hydraulic head (h₀) and the well function has an insignificant effect on the aquifer transient movement when the drawdown s<0.02h ₀. When the well function is simplified with different assumptions and pumping conditions, the new solutions correspondingly reduce to cases that are similar to the Hantush-Jacob, Muskat, and Theis transient movement of a confined leaky aquifer. It was found that large leakance is important in slowing radial movement and reducing aquifer deformation. Flow velocity in the aquifer is more responsive to leakance than to cumulative displacement within the aquifer. The zones and boundary with tensile stress can be located using the same approach applied to a confined aquifer for risk assessment of earth fissuring.

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Résumé Le mouvement radial dans un aquifère semi-perméable libre a été étudié en considérant les forces hydrauliques induites par la recharge et le prélèvement au niveau d’un puits. De nouvelles solutions analytiques des champs de vitesse et de déplacement ont été trouvées et appliquées pour décrire le mouvement transitoire dans un aquifère semi-perméable libre. Pour trouver les nouvelles solutions, le moment linéaire et le bilan de masse dans les sédiments poreux saturés, la loi de Darcy-Gersevanov, et la solution analytique du rabattement hydraulique pour un écoulement transitoire dans un aquifère semi-perméable libre sont pris en compte. Les résultats analytiques montrent que la relation non-linéaire entre le potentiel hydraulique initial (h₀) et la fonction de puits a un effet insignifiant sur le mouvement transitoire de l’aquifère quand le rabattements s <0.02h₀. Si la fonction de puits est simplifiée en tenant compte de différentes hypothèses et conditions de pompage, les nouvelles solutions se réduisent en conséquence à des cas similaires au mouvement transitoire dans un aquifère semi-perméable captif selon Hantush-Jacob, Muskat, et Theis. Il s’est avéré qu’une drainance élevée est importante pour le ralentissement du mouvement radial et la réduction de la déformation de l’aquifère. La vitesse d’écoulement dans l’aquifère est plus sensible à la drainance qu’au déplacement cumulé dans l’aquifère. Les zones et la frontière présentant des contraintes de traction peuvent être localisées en utilisant la même approche appliquée à un aquifère captif pour l’évaluation des risques de fissuration du sol.

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Resumen Se ha estudiado el movimiento radial en un acuífero no confinado con fuga en relación a las fuerzas hidráulicas que son inducidas por la descarga y recarga del pozo. Se encontraron nuevas soluciones analíticas en los campos de desplazamiento y velocidad, las cuales se aplicaron para describir el movimiento transitorio en un acuífero no confinado con fuga. Se han introducido cálculos de balance de masa y momentum lineal de los sedimentos porosos saturados, la Ley Darcy-Gersevanov, y la solución analítica de descenso hidráulico para flujo sin régimen permanente dentro del acuífero no confinado con goteo para encontrar las nuevas soluciones. Los resultados analíticos indican que la relación no lineal entre la presión hidráulica inicial (h₀) y la función del pozo tiene efecto insignificante en el movimiento transitorio del acuífero cuando el descenso s < 0.02h₀. Cuando se simplifica la función del pozo en base a diferentes supuestos y condiciones de bombeo se reducen las nuevas soluciones a casos que son similares a el movimiento transitorio Hantush-Jacob, Muskat, y Theis de un acuífero confinado con goteo. Se encontró que las fugas grandes son importantes en la disminución del movimiento radial y en la reducción de la deformación del acuífero. La velocidad de flujo en el acuífero responde más a las fugas que al desplazamiento acumulativo dentro del acuífero. Pueden localizarse zonas y límites con esfuerzos tensionales usando el mismo enfoque aplicado a acuíferos confinados para evaluación de riesgo de generación de fracturas en el terreno.

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