Homogeneous Ocean Research Articles

Impact of subsurface chlorophyll maxima on satellite-based Arctic spring primary production estimates

In recent years several regional and pan-Arctic ocean color algorithms, which consider the unique bio-optical properties of the Arctic Ocean, have been developed to accurately extract surface chlorophyll a (Chl a), a key input into net primary production (NPP) algorithms, from spectral remote sensing reflectance (Rrs). However, most satellite derived NPP (NPPSAT) algorithms used in the Arctic do not account for production at deep subsurface chlorophyll maxima (SCMs), a prominent feature in the Arctic Ocean during the summer months, leading to underestimations of NPP during the post-bloom period. In this study, a shallow SCM was observed in early summer (June/July 2016) in Baffin Bay at the time of the sea ice edge bloom, raising the question to what extent this SCM contributes to Rrs and how it is captured in NPPSAT estimates. Radiative transfer simulations based on in situ data of inherent and apparent optical properties and Chl a concentration in the water column were used to examine the effects of heterogeneous vertical Chl a profiles of various strength and depth on spectral reflectance, algorithm-derived surface Chl aSAT and NPPSAT. NPPSAT estimates for varying Chl a profile shapes were then compared to NPPSAT estimates of reference simulations for homogenous Chl a profiles, and to measured NPP calculated using observed Chl a profiles. Results show a significant impact of shallow SCMs on Rrs with the depth of maximum Chl a < 30 m, causing an increase in Chl aSAT by 17 ± 6% relative to a vertically homogenous ocean. Interestingly, SCMs significantly influencing Rrs were found down to the fifth light penetration depth. The increase in Chl aSAT reduced the difference between predicted and measured NPP estimates to −25 ± 12% at stations with a shallow SCM. Furthermore, due to the significant contribution of these shallow SCM stations to regional NPP, regional predicted NPPSAT was only 16% lower than measured NPP. Our results demonstrate that the partial representation of a shallow and very productive SCM in Chl aSAT minimizes errors in satellite-based NPPSAT estimates of the Arctic spring bloom during the sea ice melt period.

A note on the temporal and spatial attenuation of ocean waves

We study attenuation of free waves in the homogeneous ocean. Using the Cauchy–Riemann relations and then energy equation, we derive a novel equation that relates temporal and spatial decay to the energy dissipation in the fluid. In particular, for spatially damped waves we find that the attenuation coefficient is inversely proportional to the group velocity. We discuss the consequences of this for continental shelf waves where the group velocity may tend to zero in wave number space, and hence the spatial attenuation coefficient may become infinitely large. We show that generally for a travelling wave solution, the spatial damping will remain unchanged in a frame of reference moving with the group velocity, revealing the different physics behind temporal wave damping and spatial wave damping.

Numerical modeling and observations of seismo-acoustic waves propagating as modes in a fluid-solid waveguide.

This paper discusses the nature of the low-frequency seismo-acoustic waves generated by submarine earthquakes in the ocean. In a finite-depth homogeneous ocean over a semi-infinite solid crust, the derivation of the acoustic equations shows that waves propagate as modes. The waves propagating with the speed of sound in water (T waves) are preceded by waves with frequencies below the Airy phase. Furthermore, the group speeds of these modes are sensitive to the environmental setting. As a test, we applied the spectral finite-element code SPECFEM2D in a simplified configuration with an ocean layer overlaying a solid crust, and a seismic source below a Gaussian seamount surrounded by a flat seafloor. The simulations confirm that the generated T waves and their precursors follow the theoretical dispersion curves. A more realistic environment with a seismically-layered crust and a sound-speed profile in the ocean is then used to predict the expected acoustic modes. Although noisy, recordings by ocean bottom seismometers from the southwest Indian Ocean show T waves preceded by ultra-low frequency waves, which display two modes comparable to the theoretical ones. They are in good agreement for mode 1, whereas, for mode 0, a slight offset in frequency has yet to be explained.

Wave interaction with an array of porous walls in a two-layer ocean of varying bottom topography

Oblique wave scattering by a breakwater consisting of an array of thin porous walls in a two-layer ocean with varying bottom topography is investigated by using linear wave theory. Further, wave trapping is studied by considering an impermeable seawall. The entire bottom profile is assumed to be a shelf-type comprising a varying bottom of finite length and two uniform bottoms of semi-infinite lengths. Porous walls extending from bottom to free-surface are assumed at a lower water-depth level (lee side). Impingement of waves, which approach from a deeper depth level (seaside), on walls is considered. The Fourier method or method of eigenfunction expansion is applied for the uniform bottom, whereas an approximation technique, called a mild-slope equation, is used for the varying bottom. Solutions from these two methods are matched at interfaces under physical conditions. An explicit solution is derived in the form of a system of algebraic equations. The effect of several bottom configurations on wave interaction with porous walls is analyzed. Reflection and transmission coefficients and wave force on porous walls and seawall are analyzed for the parameters related to waves, bottom, and porous medium. The study reveals that porous walls are very effective in reducing wave transmission for bottom profiles dominated by waves. Wave forces on porous walls are less in the two-layer ocean than in a homogeneous ocean. In wave trapping, seawall attains higher wave-force for incoming surface waves than for incoming interfacial waves. The ratio of water-depth levels and wave incident angles are also analyzed for the mitigation of wave forces. The force on seawall increases with the increased depth ratio in surface wave incidence, while the force decreases with the increased depth ratio in interface wave incidence. The findings may be useful for coastal engineers to understand wave scattering by multiple porous structures in the stratified ocean.

Steady flow in a frictionless homogenous ocean

A mathematical model is developed to study the free (frictionless) steady horizontal flow which can occur in a homogeneous ocean of constant depth. The flow satisfies the dynamic constraint that the vertical component of absolute vorticity is constant along a streamline. The conclusion is reached that in an enclosed ocean a free steady circulation cannot have any slow broad eastward currents. The eastward currents must occur as narrow streams of high velocity and high relative vorticity. Intensified currents are present along the eastern and western coasts. The theory which is developed for the homogeneous ocean of constant depth can be applied to the two-layer ocean if the horizontal divergence of flow is negligible. If the horizontal divergence is not negligible, then the intensification of poleward currents is more pronounced and that of equatorward currents less pronounced as compared with the homogeneous ocean.

Editor's Commentary: Steady flow in a frictionless homogenous ocean by N. P. Fofonoff

Editor's Commentary: Steady flow in a frictionless homogenous ocean by N. P. Fofonoff

Active manipulation of Helmholtz scalar fields: near-field synthesis with directional far-field control

In this article, we propose a strategy for the active manipulation of scalar Helmholtz fields in bounded near-field regions of an active source while maintaining desired radiation patterns in prescribed far-field directions. This control problem is considered in two environments: free space and homogeneous ocean of constant depth, respectively. In both media, we proved the existence of and characterized the surface input, modeled as Neumann data (normal velocity) or Dirichlet data (surface pressure) such that the radiated field satisfies the control constraints. We also provide a numerical strategy to construct this predicted surface input by using a method of moments-approach with a Morozov discrepancy principle-based Tikhonov regularization. Several numerical simulations are presented to demonstrate the proposed scheme in scenarios relevant to practical applications.

Numerical study of isotropic ocean swell

A new algorithm is used for detailed numerical study of the evolution of isotropic swell in a homogeneous ocean. It is shown that the Zakharov-Filonenko spectrum occurs in an explosive manner in a short time. The Kolmogorov constant of the solution is estimated numerically.

Numerical Study of Isotropic Ocean Swell

A new algorithm is used for detailed numerical study of the evolution of isotropic swell in a homogeneous ocean. It is shown that the Zakharov-Filonenko spectrum occurs in an explosive manner in a short time. The Kolmogorov constant of the solution is estimated numerically.

ВЛИЯНИЕ ЛЕДЯНОГО ПОКРОВА НА ВОЛНЫ КЕЛЬВИНА И ПУАНКАРЕ

This work presents theoretical foundations of Kelvin and Poincare waves in the homogeneous ocean under an ice cover. The ice is considered as thin elastic plate of uniform thickness, with constant values of Young’s modulus, Poisson’s ratio, density, and compressive stress. The boundary conditions are such that the normal velocity at the bottom is zero, and at the undersurface of the ice the linearized kinematic and dynamic boundary conditions are satisfied. We present and analyze explicit solutions for the Kelvin and Poincare waves and the dispersion equations. The problem is examined in the context of a unified theory and without the hydrostatic assumption.

Numerical Study on Tidally Induced Cross-Frontal Mean Circulation

ABSTRACTAn analytical solution for a circulation across a tidal front obtained by Dong, C., Ou, H-W., Chen, D., & Visbeck, M. (2004). Tidally induced cross-frontal mean circulation: Analytical study. Journal of Physical Oceanograph, 34, 293–305) suggests that the cross-frontal circulation can be decomposed into four parts: frontal cell, Ekman cell, Bernoulli cell, and Stokes drift. This study examines the analytical solution thoroughly using a two-dimensional numerical model solving primitive Navier-Stokes equations. The direct comparison between the numerical and the analytical models of three cases (winter tidal front, summer tidal front, and no front) with the same configurations demonstrates that the analytical solution captures the major features of the cross-frontal circulation. A series of numerical experiments are applied to study the sensitivity of the cross-frontal circulation to physical variables: tidal intensity, horizontal topography scale, frontal strength, and vertical eddy viscosity. The ratio of the tidal excursion distance to the topographical scale is crucial to the Ekman cell in the homogenous ocean. With a greater density gradient, both the Bernoulli and Ekman cells are enhanced. Assumptions made in the analytical model are also examined. The uniform eddy viscosity and linearization in the analytical model could overestimate the bottom flow in the Ekman cell and underestimate the Bernoulli cell in the shallower region, respectively. The influence of the internal tide on the cross-frontal circulation is discussed.

Role of tides on the formation of the Antarctic Slope Front at the Weddell‐Scotia Confluence

AbstractThe structure of the Antarctic Slope Front (ASF) and the associated Antarctic Slope Current (ASC) on the Scotia Sea side of the Weddell‐Scotia Confluence (WSC) is described using data from a hydrographic survey and three 1 year long moorings across the continental slope. The ASC in this region flows westward along isobaths with an annual mean speed of ∼0.2 m s−1, with time variability dominated by the K1 and O1 tidal diurnal constituents, a narrowband oscillation with ∼2‐week period attributable to the spring/neap tidal cycle, and seasonal variability. Realistic and idealized high‐resolution numerical simulations are used to determine the contribution of tides to the structure of the ASF and the speed of the ASC. Two simulations forced by realistic atmospheric forcing and boundary conditions integrated with and without tidal forcing show that tidal forcing is essential to reproduce the measured ASF/ASC cross‐slope structure, the time variability at our moorings, and the reduced stratification within the WSC. Two idealized simulations run with tide‐only forcing, one with a homogeneous ocean and the other with initial vertical stratification that is laterally homogeneous, show that tides can generate the ASC and ASF through volume flux convergence along the slope initiated by effects including the Lagrangian component of tidal rectification and mixing at the seabed and in the stratified ocean interior. Climate models that exclude the effects of tides will not correctly represent the ASF and ASC or their influence on the injection of intermediate and dense waters from the WSC to the deep ocean.

Ekman Spiral in a Horizontally Inhomogeneous Ocean with Varying Eddy Viscosity

The classical Ekman spiral is generated by surface wind stress with constant eddy viscosity in a homogeneous ocean. In real oceans, the eddy viscosity varies due to turbulent mixing caused by surface wind and buoyancy forcing. Horizontally inhomogeneous density produces vertical geostrophic shear which contributes to current shear that also affects the Ekman spiral. Based on similar theoretical framework as the classical Ekman spiral, the baroclinic components of the Ekman spiral caused by the horizontally inhomogeneous density are obtained analytically with the varying eddy viscosity calculated from surface wind and buoyancy forcing using the K-profile parameterization (KPP). Along with the three existing types of eddy viscosity due to pure wind forcing (zero surface buoyancy flux), such an effect is evaluated using the climatological monthly mean data of surface wind stress, buoyancy flux, ocean temperature and salinity, and mixed layer depth.

The effect of seawater attenuation on the directionality and spatial coherence of surface-generated ambient noise

Acoustic attenuation in seawater is sufficiently weak that it usually has little effect on the spatial characteristics of ambient noise. However, at frequencies above 10 kHz and depths below 6 km, seawater attenuation may influence the directionality of surface-generated ambient noise. In a semi-infinite, homogeneous ocean, all the noise is downward-traveling, since there are no bottom reflections, and, in the absence of attenuation, the directional density function varies as the cosine of the polar angle measured from the zenith. When attenuation is present, the angular width of this noise lobe becomes narrower, because sound from distant surface sources is attenuated more than acoustic arrivals from overhead. This narrowing effect increases as frequency rises, since the attenuation is a rapidly increasing function of frequency. The spatial coherence of the noise is also modified by the attenuation. For a pair of horizontally (vertically) aligned sensors, the zeroes in the spatial coherence function are shifted to higher (lower) frequencies. These effects of attenuation on the noise field are sufficiently large to be detectable using the recently developed, deep diving instrument platform Deep Sound, which is capable of measuring broadband ambient noise on multiple hydrophones to depths of 11 km. [Research supported by ONR.]

Theory of the directionality and spatial coherence of wind-driven ambient noise in a deep ocean with attenuation

Acoustic attenuation in seawater usually has little effect on the spatial statistics of ambient noise in the ocean. This expectation does not hold, however, at higher frequencies, above 10 kHz, and extreme depths, in excess of 6 km, an operating regime that is within the capabilities of the most recently developed acoustic instrument platforms. To quantify the effects of attenuation, theoretical models for the vertical directionality and the spatial coherence of wind-generated ambient noise are developed in this paper, based on a uniform distribution of surface sources above a semi-infinite, homogeneous ocean. Since there are no bottom reflections, all the noise is downward traveling; and the angular width of the directional density function becomes progressively narrower with increasing frequency because sound from the more distant sources experiences greater attenuation than acoustic arrivals from overhead. This narrowing of the noise lobe modifies the spatial coherence, shifting the zeros in the horizontal (vertical) coherence function to higher (lower) frequencies. In addition, the attenuation modifies the amplitudes of the higher-order oscillations in the horizontal and vertical coherence functions, tending to suppress the former and enhance the latter. These effects are large enough to be detectable with the latest deep-diving sensor technology.

Loop Current Mixed Layer Energy Response to Hurricane Lili (2002). Part II: Idealized Numerical Simulations

Abstract In this second part of a two-part study, details of the upper-ocean response within an idealized baroclinic current to a translating tropical cyclone are examined in a series of nonlinear, reduced-gravity numerical simulations. Based on observations obtained as part of a joint NOAA–National Science Foundation (NSF) experiment in Hurricane Lili (2002), the preexisting ocean mass and momentum fields are initialized with a Gulf of Mexico Loop Current–like jet, which is subsequently forced by a vortex whose wind stress field approximates that observed in the Lili experiments. Because of 1) favorable coupling between the wind stress and preexisting current vectors, and 2) wind-driven currents flowing across the large horizontal pressure gradient, wind energy transfer to the mixed layer can be more efficient in such a regime as compared to the case of an initially horizontally homogeneous ocean. However, nearly all energy is removed by advection and wave flux by two local inertial periods after storm passage, consistent with the observational results. Experiments are performed to quantify differences in one-dimensional and three-dimensional linearized approximations to the full model equations. In addition, sensitivity experiments to variations in the initial geostrophic current structure are performed to develop a parameter space over which a significant energy response could optimally be observed.

Modeling the effects of near-surface plumes of suspended particulate matter on remote-sensing reflectance of coastal waters

A radiative transfer model was applied to examine the effects of vertically stratified inherent optical properties of the water column associated with near-surface plumes of suspended particulate matter on spectral remote-sensing reflectance, R(rs)(λ), of coastal marine environments. The simulations for nonuniform ocean consisting of two layers with different concentrations of suspended particulate matter (SPM) are compared with simulations for a reference homogeneous ocean whose SPM is identical to the surface SPM of the two-layer cases. The near-surface plumes of particles are shown to exert significant influence on R(rs)(λ). The sensitivity of R(rs)(λ) to vertical profile of SPM is dependent on the optical beam attenuation coefficient within the top layer, c(1)(λ), thickness of the top layer, z(1), and the ratio of SPM in the underlying layer to that in the top layer, SPM(2)/SPM(1), as well as the wavelength of light, λ. We defined a dimensionless spectral parameter, P(λ)=c(1)(λ)×z(1)×(SPM(2)/SPM(1)), to quantify and examine the effects of these characteristics of the two-layer profile of SPM on the magnitude and spectral shape of R(rs)(λ). In general, the difference of R(rs)(λ) between the two-layer and uniform ocean decreases to zero with an increase in P(λ). For the interpretation of ocean color measurements of water column influenced by near-surface plumes of particles, another dimensionless parameter P'(λ) was introduced, which is a product of terms representing homogenous ocean and a change caused by the two-layer structure of SPM. Based on the analysis of this parameter, we found that for the two-layer ocean there is a good relationship between R(rs)(λ) in the red and near-infrared spectral regions and the parameters describing the SPM(z) profile, i.e., SPM(1), SPM(2), and z(1).

Dispersive tsunami waves in the ocean: Model equations and sensitivity to dispersion and Coriolis effects

We derive fully nonlinear, weakly dispersive model equations for propagation of surface gravity waves in a shallow, homogeneous ocean of variable depth on the surface of a rotating sphere. A numerical model is developed for the weakly nonlinear version of the model based on a combined finite-volume and finite-difference method with a fourth-order MUSCL-TVD scheme in space and a third-order SSP Runge–Kutta scheme in time. In the context of tsunami generation and propagation over trans-oceanic distances, a scaling analysis reveals that the importance of frequency dispersion increases with a decrease of the source width, while the effect of the Coriolis force increases with an increase of the source width. A sensitivity analysis to dispersive and Coriolis effects is carried out using the numerical model in a series of numerical experiments in an idealized ocean using Gaussian and di-polar sources with different source sizes. A simulation of the Tohoku 2011 tsunami is used to illustrate the effects of dispersive and Coriolis effects at large distances from the source region.

The Three-Dimensional Steady Circulation in a Homogenous Ocean Induced by a Stationary Hurricane

Abstract Based on the classical Ekman layer theory, a simple analytical solution of the steady flow induced by a stationary hurricane in a homogenous ocean is discussed. The model consists of flow converging in an inward spiral in the deeper layer and diverging in the upper layer. The simple analytical model indicates that both the upwelling flux and the horizontal transport increase linearly with increasing radius of maximum winds. Furthermore, they both have a parabolic relationship with the maximum wind speed. The Coriolis parameter also affects the upwelling flux: the response to a hurricane is stronger at low latitudes than that at middle latitudes. Numerical solutions based on a regional version of an ocean general circulation model are similar to the primary results obtained through the analytical solution. Thus, the simplifications made in formulating the analytical solution are reasonable. Although the analytical solution in this paper is sought for a rather idealized ocean, it can help to make results from the more complicated numerical model understandable. These conceptual models provide a theoretical limit structure of the oceanic response to a moving hurricane over a stratified ocean.

Cross-shelf structure of coastal upwelling: A two — dimensional extension of Ekman's theory and a mechanism for inner shelf upwelling shut down

Sea-surface temperature images of the coastal upwelling regions off Northwest Africa show that the core of upwelling is sometimes located far from the coast. This has been documented in three regions that share a common feature, namely a wide and shallow continental shelf. This upwelling feature plays a key role in the ecology of the Canary Current System. It creates an innerfront which provides retention for biological material, e.g. fish eggs and larvae, in the highly productive nearshore environment. An analytical model has been developed based on a two dimensional extension of Ekman's solution. The linear and steady response of a homogeneous ocean forced by an upwelling-favorable wind provides a mechanism for the upwelling separation from the coast. The merging of the surface and bottom Ekman layers induces a very weak cross-shore circulation and a “kinematic barrier” for the Ekman transport divergence. In the case of an alongshore wind, the barrier is located near the isobath h ≈ 0.4D, where D is the thickness of Ekman layers. This yields an upwelling cell which is essentially concentrated in the region 0.5D < h < 1.25D, with upwelling occurring preferentially near the isobath h ≈ 0.6D. It turns out that the cross-shore width of upwelling scales with D/S, the ratio of Ekman depth to bottom topographic slope. The application of this solution to real bathymetric profiles rationalizes, not only the offshore upwelling observations in Northwest Africa, but also the influence of topography on the cross-shelf structure of a wind-driven coastal upwelling. The model also quantifies the effect of the cross-shore wind component showing how it drives the nearshore pressure gradient adjustment and how it affects the upwelling. A linear numerical experiment reproduces the theoretical steady solution, thereby allowing investigation of the transient regime. Relaxation of the hypothesis in the numerical model validates the linear assumption of the theory and then allows investigation of the sensitivity to friction parameterizations and the influence of stratification. The latter leads to an “oscillation” of the upwelling cell with seaward migration driven by outcropping and homogeneization of the water column, and, coastal incursion driven by a “boundary layers splitting” process caused by shoreward advection of the isopycnal dome and stratification of the inner shelf.