A global wave parameter database for geophysical applications. Part 1: Wave-current–turbulence interaction parameters for the open ocean based on traditional parameterizations

Ocean surface mixing and drift are influenced by the mixed layer depth, buoyancy fluxes and currents below the mixed layer. Drift and mixing are also functions of the surface Stokes drift U_ss, volume Stokes transport T_S, a wave breaking height scale H_swg, and the flux of energy from waves to ocean turbulence Φ_oc. Here we describe a global database of these parameters, estimated from a well-validated numerical wave model, that uses traditional forms of the wave generation and dissipation parameterizations, and covers the years 2003–2007. Compared to previous studies, the present work has the advantage of being consistent with the known physical processes that regulate the wave field and the air–sea fluxes, and also consistent with a very large number of in situ and satellite observations of wave parameters. Consequently, some of our estimates differ significantly from previous estimates. In particular, we find that the mean global integral of Φ_oc is 68 TW, and the yearly mean value of T_S is typically 10–30% of the Ekman transport, except in well-defined regions where it can reach 60%. We also have refined our previous estimates of U_ss by using a better treatment of the high frequency part of the wave spectrum. In the open ocean, U_ss  0.013U₁₀, where U₁₀ is the wind speed at 10 m height.     

Upwelling into the thermocline of the Pacific Ocean

The established “island rule” and the recently introduced “separation formula” are combined to yield an analytical expression for the total upwelling into the thermocline in the Pacific. The combination of the two is achieved with the use of a hybrid model containing a stratified upper layer, a thick (slowly moving) homogenous intermediate layer and an inert lower layer. Both the upper and the intermediate layers are subject to diabatic cooling and heating (which need not be specified) and there is an exchange of mass between the two active layers. An attempt is made to examine the above analytical (hybrid) model numerically. Ideally, this should be done with a complete two-and-a-half layer model (with upwelling and downwelling), but such a model is much too complex for process-oriented studies (due to the required parameterization of vertical mixing). Consequently, we focus our attention on verifying that the separation formula and the island rule are consistent with each other in a much simpler, layer-and-a-half model (without upwelling). We first verified that the new “separation formula” provides a reasonable estimate of the wind-induced transport in an island-free basin. We then compare the wind-induced transport predicted by the separation formula and the island rule in an idealized basin containing an island. We show that in these idealized situations the two methods give results that are consistent with each other and the numerics. We then turned to an application of the (hybrid) two-and-a-half layer model to the Pacific where, in contrast to the idealized layer-and-a-half models (where the two methods address the same water mass), the two methods address two different water masses. While the separation formula addresses only thermocline water (σ_θ<26.20), the island rule addresses all the water down to 27.5σ_θ (i.e., both the upper and intermediate layer). This is why the application of the two methods to the Pacific gives two different results — an application of the formula gives zero warm water transport whereas an application of the island rule gives 16 Sv. Namely, the difference between the amount predicted by the island rule (16 Sv) and the amount predicted by the separation formula (zero) enters the Pacific as intermediate water and is then somehow upwelled into the thermocline. The upwelling should take place north of the southern western boundary currents separation (40°S).     

Reducing horizontal diffusion errors in σ-coordinate coastal ocean models with a second-order Lagrangian-interpolation finite-difference scheme

When a steep bottom slope exists, it is well known that conventional methods for calculating horizontal diffusion in sigma-coordinate coastal ocean models causes spurious transport (e.g. salinity, temperature, and sediments) and currents. In this study, a second-order accurate finite-difference algorithm and program have been developed to reduce the spurious numerical diffusion errors. In the proposed algorithm, the finite differencing is performed in the x–z coordinate system to approximate the horizontal gradient. Each variable in the finite differential formation is calculated in the sigma-coordinate grid cells using a second-order Lagrangian interpolation polynomial. In conjunction with a stepwise bottom boundary condition, numerical experiments show that the proposed finite-difference scheme considerably reduces numerical errors compared to conventional approaches when dealing with horizontal diffusion over steep topography, which often occurs in coastal oceans and navigation channels.     

Ventilation of the North Pacific subtropical pycnocline and mode water formation

The annual subduction rate of the North Pacific was calculated based on isopycnally averaged hydrographic climatology (HydroBase), high-resolution winter mixed-layer climatology (NWMLC), and various wind stress climatologies from ship reports, numerical weather prediction products, and satellite products. The calculation was performed using Lagrangian coordinates in the same manner as in previous works, except a less smoothed oceanic climatology (HydroBase and NWMLC) was used instead of a World Ocean Atlas. Differences in the wind stress climatologies have very little effect on subduction rate estimates. The subduction rate census for density classes showed peaks corresponding to subtropical mode water (STMW), central mode water (CMW), and eastern subtropical mode water (ESTMW). The deeper mixed layer and the associated sharper mixed-layer fronts in the present climatology resulted in a larger lateral induction, which boosted the subduction rate, especially for the potential density anomaly (σ_θ) range of the lighter STMW (25.0 < σ_θ < 25.2 kg m⁻³) and lighter CMW (26.0 < σ_θ < 26.2 kg m⁻³), compared to previous estimates. The renewal time of permanent pycnocline water was estimated as the volume of water divided by the subduction rate for each σ_θ class: 2–4 years for ESTMW (24.5 < σ_θ < 25.2 kg m⁻³), 2 years for the lighter STMW (25.0 < σ_θ < 25.3 kg m⁻³), 5–9 years for the denser STMW (25.3 < σ_θ < 25.6 kg m⁻³), 10–20 years for the lighter CMW (26.0 < σ_θ < 26.2 kg m⁻³), 20–30 years for the middle CMW (26.2 < σ_θ < 26.3 kg m⁻³), and 60 years or longer for the denser CMW (26.3 < σ_θ < 26.6 kg m⁻³). A comparison of the water volume and subduction rate in potential temperature–salinity (θ–S) space indicated that the upper permanent pycnocline water (25.0 < σ_θ < 26.2 kg m⁻³) was directly maintained by nondiffusive subduction of winter surface water, including STMW and lighter CMW. The lower permanent pycnocline water (26.2 < σ_θ < 26.6 kg m⁻³) may be maintained through the subduction of fresher and colder water from the subarctic–subtropical transition region and subsequent mixing with saltier and warmer water. Diagnosis of the potential vorticity (PV) of the subducted water demonstrated that the low PV of STMW was mainly due to the large subduction rate, whereas that of both ESTMW and CMW was due mainly to the small density advection rate (cross-isopycnal flow). Additionally, a relatively large subduction rate probably contributes to the low PV of part of the lighter CMW (ESTMW) formed in the region around 38°N and 170°W (28°N and 145°W), which is characterized by a relatively thick winter mixed layer and an associated mixed-layer front, causing a large lateral induction rate.     

Effects of bottom topography and density stratification on the formation of western boundary currents

A wind-driven, general circulation for a two-layer ocean with continental shelf-slope along the western boundary is studied numerically. Special attention is focused on the formation process of the western boundary current in the subtropical gyre. The western boundary current develops in the upper layer along the western boundary on the shelf-slope with a bottom trapped poleward flow in the lower layer. The poleward undercurrent is concentrated approximately along the contour lines of the potential vorticity,f/D, wheref is the Coriolis parameter andD the depth of the ocean. The separation of upper- and lower-layer flows on the shelf-slope represents a typical transient response. As the response approaches a steady state, the poleward undercurrent decreases in amplitude, and the motion tends to be confined to the upper layer. The flow pattern becomes similar to that found in a flat bottom ocean. A steady-state response is expected to be isostatic (no motion in the lower layer), even on the shelf-slope, as conservation of potential vorticity would suggest.The remarkable increase in transport of the western boundary current produced by the formation of an anticyclonic vortex on the shelf-slope extending throughout the hemisphere (Holland, 1973) does not occur in the wind-driven general circulation.     

The β-induced drift of separated boundary currents

Western boundary currents flow poleward from low latitudes until they ultimately separate from the coast and turn eastward into the ocean interior. The separation is mainly due to either: (i) the variation of the Coriolis parameter with latitude (β) which causes vanishing of the near-wall depth; (ii) vanishing wind stress curl over the ocean interior which forces zero meridional transport; or (iii) opposing currents that flow toward the equator and force the northward flowing currents to turn offshore (Agra and Nof, Deep Sea Research I, 40, 2259–2282). Here, we focus on the third kind of separated currents and show that, due to β, such separated currents migrate along the wall. A nonlinear “reduced gravity” one-and-a-half layer model is used to compute the desired migration speed. Solutions of the primitive equations are constructed analytically assuming that the translation rate is steady. It is found that the migration rate along the wall is given by βR_d² cosα/2 sinγ, where R_d is the Rossby radius, α an angle that measures the inclination of the joint offshore currents relative to the north, and γ is the angle between the axis of the joint offshore currents and the wall. The migration meridional component can be either northward or southward (depending on the inclination of the wall) but the zonal component is always westward. When the separated joint offshore flow is in the east-west direction (i.e. α = π/2 or 3π/2 so that the separated flow is zonal) no migration is taking place. It turns out that the above migration formula is so robust that it is also describes the migration rate in a two-and-a-half layer model where one current is allowed to, at least partially, dive under the other. For most separated currents the computed migration rate is a few centimeters per second.Possible application of this theory to the Confluence zone in the South Atlantic (where significant seasonal movement of the separation latitude has been observed) is discussed.     

Eddy viscosities and velocities in combined wave-current flows

The eddy viscosities for the steady and the periodic components of combined wave-current flows have been studied quantitatively from the presently available experimental data. It has been found that inside the boundary interaction layer [z < δ] the eddy viscosity ε_c for the steady flow is increased in the presence of waves while outside the boundary interaction layer [z >δ] it is affected little by the wave motion, and that the eddy viscosity ε_w for the wave motion in the boundary layer is independent of the current strength U^*. On the other hand, a new eddy viscosity model is presented to give a good prediction of the velocity distributions of the waves and currents in comparison with experimental data.     

An experimental study of turbulent boundary layer with slit suction

Experiments are performed on a flat plate with a transverse suction slit in the Reynolds number range 5 × 10⁵ < R_e < 1.1 × 10⁶. Mean velocity profiles, RMS values are measured with hot wire anemometry. Friction velocity is numerically calculated. The experiments showed that a classical boundary layer parameter α is related to the suction coefficient S_c with an equation of the form: .The value of A seems to depend strongly on the relative location with respect to suction slit and possibly weakly on Reynolds number.     

Modification of the damping function in the k–ε model to analyse oscillatory boundary layers

A simple relationship has been developed between the wall coordinate y⁺ and Kolmogorov's length scale using direct numerical simulation (DNS) data for a steady boundary layer. This relationship is then utilized to modify two popular versions of low Reynolds number k–ε model. The modified models are used to analyse a transitional oscillatory boundary layer. A detailed comparison has been made by virtue of velocity profile, turbulent kinetic energy, Reynolds stress and wall shear stress with the available DNS data. It is observed that the low Reynolds number models used in the present study can predict the boundary layer properties in an excellent manner.     

Stable carbon isotope distribution of particulate organic matter in the ocean: a model study

The stable carbon isotopic composition of particulate organic matter in the ocean, δ¹³C_POC, shows characteristic spatial variations with high values in low latitudes and low values in high latitudes. The lowest δ¹³C_POC values (−32‰ to −35‰) have been reported in the Southern Ocean, whereas in arctic and subarctic regions δ¹³C_POC values do not drop below −27‰. This interhemispheric asymmetry is still unexplained. Global gradients in δ¹³C_POC are much greater than in δ¹³C_DIC, suggesting that variations in isotopic fractionation during organic matter production are primarily responsible for the observed range in δ¹³C_POC. Understanding the factors that control isotope variability is a prerequisite when applying δ¹³C_POC to the study of marine carbon biogeochemistry. The present model study attempts to reproduce the δ¹³C_POC distribution pattern in the ocean. The three-dimensional (3D) Hamburg Model of the Oceanic Carbon Cycle version 3.1 (HAMOCC3.1) was combined with two different parametrizations of the biological fractionation of stable carbon isotopes. In the first parametrization, it is assumed that the isotopic fractionation between CO₂ in seawater and the organic material produced by algae, _P, is a function of the ambient CO₂ concentration. The two parameters of this function are derived from observations and are not based on an assumption of any specific mechanism. Thus, this parametrization is purely empirical. The second parametrization is based on fractionation models for microalgae. It is supported by several laboratory experiments. Here the fractionation, _P, depends on the CO₂ concentration in seawater and on the (instantaneous) growth rates, μ_i, of the phytoplankton. In the Atlantic Ocean, where most field data are available, both parametrizations reproduce the latitudinal variability of the mean δ¹³C_POC distribution. The interhemispheric asymmetry of δ¹³C_POC can mostly be attributed to the interhemispheric asymmetry of CO₂ concentration in the water. However, the strong seasonal variations of δ¹³C_POC as reported by several authors, can only be explained by a growth rate-dependent fractionation, which reflects variations in the cellular carbon demand.     

A comparison of two spectral wave models in the Southern California Bight

Two models, a spectral refraction model (Longuet-Higgins) and a parabolic equation method (PEM) refraction-diffraction model (Kirby), are used to simulate the propagation of surface gravity waves across the Southern California Bight. The Bight contains numerous offshore islands and shoals and is significantly larger (≈ 300 km by 300 km) than regions typically studied with these models. The effects of complex bathymetry on the transformation of incident wave directional spectra, S₀(f,θ₀), which are very narrow in both frequency and direction are difficult to model accurately. As S₀(f,θ₀) becomes broader in both dimensions, agreement between the models improves and the spectra predicted at coastal sites become less sensitive to errors in the bathymetry grid, to tidal changes in the mean water depth, and to uncertainty in S₀(f,θ₀) itself. The smoothing associated with even relatively narrow (0.01 Hz-5° bandwidth) S₀(f,θ₀) is usually sufficient to bring the model predictions of shallow water energy into at least qualitative agreement. However, neither model is accurate at highly sheltered sites. The importance of diffraction degrades the predictions of the refraction model, and a positive bias [O (10%) of the deep ocean energy] in the refraction-diffraction model estimates, believed to stem from numerical “noise” (Kirby), may be comparable to the low wave energy. The best agreement between the predicted spectra generally occurs at moderately exposed locations in deeper waters within the Bight, away from shallow water diffractive effects and in the far-field of the islands. In these cases, the differences between the models are small, comparable to the errors caused by tidal fluctuations in water depth as waves propagate across the Bight. The accuracy of predicted energies at these sites is likely to be limited by the uncertainty in specifying S₀(f,θ₀).     

Observation and measurement of the bottom boundary layer flow in the prebreaking zone of shoaling waves

In this paper, the characteristics of the bottom boundary layer flow induced by nonlinear, asymmetric shoaling waves, propagating over a smooth bed of 1/15 uniform slope, is experimentally investigated. Flow visualization technique with thin-layered fluorescent dye was first used to observe the variation of the flow structure, and a laser Doppler velocimeter was then employed to measure the horizontal velocity, U.The bottom boundary layer flow is found to be laminar except within a small region near the breaking point. The vertical distribution of the phase-averaged velocity U at each phase is non-uniform, which is directly affected by the mean velocity, . The magnitude of increases from zero at the bottom to a local positive maximum at about z/δ2.02.5 (where z is the height above the sloping bottom and δ is the Stokes layer thickness), then decreases gradually to zero at z/δ6.07.0 approximately, and finally becomes negative as z/δ increases further. Moreover, as waves propagate towards shallower water, the rate of increase in the maximum onshore oscillating velocity component is greater than that of the offshore counterpart except near the breaking point. The free stream velocities in the profiles of the maximum onshore and offshore oscillating velocity components, and are found to appear at z/δ≥6.0. This implies that, if the Stokes layer thickness is used as a length scale, the non-dimensionalized boundary layer thickness remains constant in the pre-breaking zone. Although is greater than and the asymmetry of the maximum free stream velocities (i.e. ) increases with decrease of water depth, a universal similar profile can be established by plotting z/δ versus ( ) or ( ). The final non-dimensional profile is symmetric and unique for the distributions of the maximum onshore and offshore oscillating velocity components within the bottom boundary layer, which are induced by nonlinear, asymmetric shoaling waves crossing the pre-breaking zone.     

A model of the upper branch of the meridional overturning of the southern ocean

A zonal-average model of the upper branch of the meridional overturning circulation of the southern ocean is constructed and used to discuss the processes – wind, buoyancy, eddy forcing and boundary conditions – that control its strength and sense of circulation. The geometry of the thermocline ‘wedge’, set by the mapping between the vertical spacing of buoyancy surfaces (the stratification) on the equatorial flank of the Antarctic Circumpolar Current and their outcrop at the sea surface, is seen to play a central role by setting the interior large-scale potential vorticity distribution. It is shown that the action of eddies mixing this potential vorticity field induces a residual flow in the meridional plane much as is observed, with upwelling of fluid around Antarctica, northward surface flow and subduction to form intermediate water. Along with this overturning circulation there is a concomitant air-sea buoyancy flux directed in to the ocean.     

Modeling the Global Thermohaline Circulation

This paper reviews recent progress and problems in modeling the thermohaline circulation of the world ocean by use of z-coordinate ocean general circulation models. Discussions focus on four issues: sea surface forcing, mixing in the deep ocean interior, eddy-induced tracer transport, and bottom boundary layer processes. Although some widely used techniques and parameterizations deal with these issues, some aspects are still overlooked and more sophistication is certainly required. This revised version was published online in August 2006 with corrections to the Cover Date.     

Carbon cycling within the upper methanogenic zone of continental rise sediments; An example from the methane-rich sediments overlying the Blake Ridge gas hydrate deposits

Data from piston cores collected from Carolina Rise and Blake Ridge, and from many DSDP/ODP sites indicate that extreme ¹³C-depletion of methane and ΣCO₂ occurs within the uppermost methanogenic zone of continental rise sediments. We infer that ¹³C-depleted methane is generated near the top of the methanogenic zone when carbon of ¹³C-depleted ΣCO₂, produced by microbially-mediated anaerobic methane oxidation, is recycled back to methane through CO₂ reduction. Interstitial water and gas samples were collected in 27 piston cores, 16 of which penetrated through the sulfate reduction zone into methane-bearing sediments of the Carolina Rise and Blake Ridge. Isotopic measurements (δ¹³C_CH4, δ¹³C_CO2, δD_CH4, and δD_H2O) indicate that this methane is microbial in origin, produced by microbially-mediated CO₂ reduction. Methane samples form two distinct isotopic pools. (1) Methane from a seafloor seep site shows a mean δ¹³C_CH4 value of − 69 ± 2%., mirroring values found at ≥ 160 mbsf from a nearby DSDP site. (2) Twenty, areally-separated sites (sample depth, 10 to 25 mbsf) have δ¹³C_CH4 values ranging from −85 to −103%., and δ¹³C_CO2 as negative as −48%.. The very low δ¹³C values from the methane and CO₂ pools highlight the importance of carbon cycling within continental rise sediments at and near the sulfate-methane boundary.     

Methane-dominated thermochemical sulphate reduction in the Triassic Feixianguan Formation East Sichuan Basin, China: towards prediction of fatal H2S concentrations

New sour pools have recently found in the Lower Triassic Feixianguan Fm carbonate reservoirs in the East Sichuan Basin in China with H₂S up to 17.4% by volume. A recent blowout from a well drilled into this formation killed hundreds of people as a result of the percentage concentrations of H₂S. In order to assess the origin of fatal H₂S as well as the cause of petroleum alteration, H₂S concentrations and the isotopes, δ³⁴S and δ¹³C have been collected and measured in gas samples from reservoirs. Anhydrite, pyrite and elemental sulphur δ³⁴S values have been measured for comparison. The high concentrations of H₂S gas are found to occur at depths >3000 m (temperature now at 100 °C) in evaporated platform facies oolitic dolomite or limestone that contains anhydrite nodule occurrence within the reservoirs. Where H₂S concentrations are greater than 10% its δ³⁴S values lie between +12.0 and +13.2‰ CDT. This is within the range of anhydrite δ³⁴S values found within the Feixianguan Fm (+11.0 to +21.7‰; average 15.5±3.5‰ CDT). Thus H₂S must have been generated by thermochemical sulphate reduction (TSR) locally within the reservoirs. Burial history analysis and fluid inclusion data reveal that the temperature at which TSR occurred was greater than about 130–140 °C, suggesting that the present depth-temperature minimum is an artifact of post-TSR uplift. Both methane and ethane were actively involved in TSR since the petroleum became almost totally dry (no alkanes except methane) and methane δ¹³C values become significantly heavier as TSR proceeded. Methane δ¹³C difference thus reflects the extent of TSR. While it is tempting to use a present-day depth control (>3000 m) to predict the distribution of H₂S in the Feixianguan Fm, this is an invalid approach since TSR occurred when the formation was buried some 1000–2000 m deeper than it is at present. The likelihood of differential uplift across the basin means that it is important to develop a basinal understanding of the thermal history of the Feixianguan Fm so that it is possible to determine which parts of the basin have been hotter than 130–140 °C.     

Microstructure measurements in natural waters: Methodology and applications

Modern approaches to microstructure data processing, including wavelet denoising, are discussed. The wavelet procedure is applied to small-scale shear signals before estimating the dissipation rate ε and to the temperature/density profiles used to calculate Thorpe scales. Microstructure data obtained on the Mediterranean shelf of Catalonia are used to illustrate various approaches to the Thorpe displacement calculations. It is suggested that the Weibull probability function is an appropriate model for the Thorpe scale distribution. Microstructure measurements from the upper layer of the Boadella reservoir (Catalonia, Spain) support this finding.A new analytical approximation for the 1D Panchev–Kesich spectrum is deduced and the results of ε computation are compared with spectral fitting by the widely used Nasmyth spectrum. Applying the Kraichnan spectral model to compute ε from temperature spectra in the convective-viscous sub-range is examined as an alternative to the Batchelor spectrum. Microstructure measurements taken in Lake Banyoles (Catalonia, Spain) and in the North Atlantic were used for spectral calculations.Statistical analysis of eddy K_b and thermal K_θ diffusivities measured on a shallow shelf of the Black Sea shows the importance of process-orientated domain averaging of the diffusivities in obtaining good correspondence between K_b and K_θ in active turbulent regions. In weakly turbulent, stratified interior layers, the averaged K_b and K_θ differ significantly, which may point to the inapplicability of isotropic formulae used for ε and temperature dissipation χ_θ estimates, as well as to a dependence of the mixing efficiency γ on the Richardson number or in some cases on regions of fossil turbulence.     

Chromium(VI) reduction by sulphur(IV) in aqueous solutions

The rates of the reduction of Cr(VI) with S(IV) were measured in deaerated NaCl solution as a function of pH, temperature and ionic strength. The rates of the reaction were found to be first order with respect to Cr(VI) and second order with respect to S(IV), in agreement with previous results obtained at concentrations two order higher than the present study. The reaction also showed a first-order dependence of the rates on the concentration of the proton and a small influence of temperature with an apparent energy of activation ΔH_app of 22.8 ± 3.4 kJ/mol. The rates were independent of ionic strength from 0.01 to 1 M. The rate of Cr(VI) reduction is described by the general expression

−d[Cr(VI)]/dt=k[Cr(VI)][S(IV)]²