Observation-based evaluation of surface wave effects on currents and trajectory forecasts

Knowledge of upper ocean currents is needed for trajectory forecasts and is essential for search and rescue operations and oil spill mitigation. This paper addresses effects of surface waves on ocean currents and drifter trajectories using in situ observations. The data set includes colocated measurements of directional wave spectra from a wave rider buoy, ocean currents measured by acoustic Doppler current profilers (ADCPs), as well as data from two types of tracking buoys that sample the currents at two different depths. The ADCP measures the Eulerian current at one point, as modelled by an ocean general circulation model, while the tracking buoys are advected by the Lagrangian current that includes the wave-induced Stokes drift. Based on our observations, we assess the importance of two different wave effects: (a) forcing of the ocean current by wave-induced surface fluxes and the Coriolis–Stokes force, and (b) advection of surface drifters by wave motion, that is the Stokes drift. Recent theoretical developments provide a framework for including these wave effects in ocean model systems. The order of magnitude of the Stokes drift is the same as the Eulerian current judging from the available data. The wave-induced momentum and turbulent kinetic energy fluxes are estimated and shown to be significant. Similarly, the wave-induced Coriolis–Stokes force is significant over time scales related to the inertial period. Surface drifter trajectories were analysed and could be reproduced using the observations of currents, waves and wind. Waves were found to have a significant contribution to the trajectories, and we conclude that adding wave effects in ocean model systems is likely to increase predictability of surface drifter trajectories. The relative importance of the Stokes drift was twice as large as the direct wind drag for the used surface drifter.

     

A three-dimensional surface wave–ocean circulation coupled model and its initial testing

A theoretical framework to include the influences of nonbreaking surface waves in ocean general circulation models is established based on Reynolds stresses and fluxes terms derived from surface wave-induced fluctuation. An expression for the wave-induced viscosity and diffusivity as a function of the wave number spectrum is derived for infinite and finite water depths; this derivation allows the coupling of ocean circulation models with a wave number spectrum numerical model. In the case of monochromatic surface wave, the wave-induced viscosity and diffusivity are functions of the Stokes drift. The influence of the wave-induced mixing scheme on global ocean circulation models was tested with the Princeton Ocean Model, indicating significant improvement in upper ocean thermal structure and mixed layer depth compared with mixing obtained by the Mellor–Yamada scheme without the wave influence. For example, the model–observation correlation coefficient of the upper 100-m temperature along 35° N increases from 0.68 without wave influence to 0.93 with wave influence. The wave-induced Reynolds stress can reach up to about 5% of the wind stress in high latitudes, and drive 2–3 Sv transport in the global ocean in the form of mesoscale eddies with diameter of 500–1,000 km. The surface wave-induced mixing is more pronounced in middle and high latitudes during the summer in the Northern Hemisphere and in middle latitudes in the Southern Hemisphere.     

Wave effects in global ocean modeling: parametrizations vs. forcing from a wave model

One of the main challenges of the Copernicus Marine Service is the implementation of coupled ocean/waves systems that accurately estimate the momentum and energy fluxes provided by the atmosphere to the ocean. This study aims to investigate the impact of forcing the Nucleus for European Modelling of the Ocean (NEMO) ocean model with forecasts from the wave model of Météo-France (MFWAM) to improve classical air-sea flux parametrizations, these latter being mostly driven by the 10-m wind. Three wave-related processes, namely, wave-state-dependent stress, Stokes drift-related effects (Stokes-Coriolis force, Stokes drift advection on tracers and on mass), and wave-state-dependent surface turbulence, are examined at a global scale with a horizontal resolution of 0.25°. Three years of sensitivity simulations (2014–2016) show positive feedback on sea surface temperature (SST) and currents when the wave model is used. A significant reduction in SST bias is observed in the tropical Atlantic Ocean. This is mainly due to the more realistic momentum flux provided by the wave model. In mid-latitudes, the most interesting impact occurs during the summer stratification, when the wind is low and the wave model produces a reduction in the turbulence linked with wave breaking. Magnitudes of the large-scale currents in the equatorial region are also improved by 10% compared to observations. In general, it is shown that using the wave model reduces on average the momentum and energy fluxes to the ocean in tropical regions, but increases them in mid-latitudes. These differences are in the order of 10 to 20% compared with the classical parametrizations found in stand-alone ocean models.     

Simulating the migration of drifters deployed in the Bay of Biscay, during the Prestige crisis

A main conclusion following the oil spill from the Prestige tanker was that improvements in ocean circulation models were necessary; this was in order to predict, more accurately, the trajectories followed by the oil slicks and hence assist in fight against oil pollution operations. In this contribution, the results of the validation of a semi-empirical ocean circulation model, parameterised for the Bay of Biscay and forced with operational oceano-meteorological remote sensing observations, are shown. The model results have been validated with observations from drifting buoys, deployed in the Bay of Biscay during the crisis. The results show that the model explains a relatively large percentage of the current variability. The comparisons between the real and the estimated drifter trajectories indicate that for 3, 5 and 7 day-long trajectories, the drifter position is estimated with errors of approximately 23, 35 and 46km, respectively. The model reproduces relatively well the trajectory followed by the drifter with the shortest period (23 days).     

Surface Stokes drift in the Baltic Sea based on modelled wave spectra

The Stokes drift is an important component in the surface drift. We used the wave model WAM to evaluate the mean values and exceedance probabilities of the surface Stokes drift in the Baltic Sea. As there is no direct way to verify the accuracy of the modelled Stokes drift, we compared the bulk parameters calculated by the wave model against buoy measurements to ensure the quality of the wave hindcast. Furthermore, we evaluated the surface Stokes drift from measured wave spectra to assess the accuracy of the modelled surface Stokes drift. The importance of the Stokes drift as a component of the total surface drift was evaluated by calculating the hindcast mean values and percentiles of the surface Stokes drift. The mean values were between 0.08 and 0.10 ms^?1 in the open sea areas, thus being of the same order of magnitude as the mean wind shear currents. The highest values of the surface Stokes drift were slightly larger than 0.6 ms^?1. The comparison of modelled Stokes drift values to estimates obtained from measured spectra suggests that the mean values are well represented by the model. However, the higher modelled values are most likely slightly too large because the wave energy was overestimated during high wind situations in some of the sub-basins, such as the Gulf of Finland. A comparison to a drifter experiment showed that use of the Stokes drift improves the estimate of both the drift speed and the direction in the Gulf of Finland. Parameterised methods to evaluate the Stokes drift that are used, e.g. in currently available Baltic Sea drift models, overestimate the smaller values (under 0.3 ms^?1) and underestimate the larger values of the Stokes drift compared to the values calculated by the wave model. The modelled surface Stokes drift direction mostly followed the forcing wind direction. This was the case even in the Gulf of Finland, where the direction of the wind and the waves can differ considerably.     

Wave-induced drift of large floating sheets

In this article we study the wave-induced drift of large, flexible shallow floating objects, referred to as sheets. When surface waves propagate through a sheet, they provide a mean stress on the sheet, resulting in a mean drift. In response, the sheet generates an Ekman current. The drift velocity of the sheet is determined by (i) the wave-induced stress, (ii) the viscous stress due to the Ekman current, and (iii) the Coriolis force. The sheet velocity and the current beneath the sheet are determined for constant and depth-varying eddy viscosities.     

Wave-induced setup of the mean surface over a sloping beach

A new theoretical approach for the wave-induced setup over a sloping beach is presented that takes into consideration the explicit variations of the surface waves due to bottom slope and viscosity. In this way, the wave forcing of the mean Lagrangian volume fluxes is calculated without assuming that the local depth is constant. The analysis is valid in the region outside the surf zone and is based on the shallow-water assumption. A novel approach for separating the viscous damping of the waves from the frictional damping of the mean flow is introduced, where the mean Eulerian velocity is applied in the bottom stress for the mean fluxes. In the case where the onshore Lagrangian mean transport is zero, a new formula is derived for the Eulerian mean free surface slope, in which the effects of bottom slope, viscous wave damping and frictional bottom drag on the mean flow are clearly identified. The analysis suggests that viscous damping of the waves and frictional dissipation of the Eulerian near-bed return flow could lead to setup outside the surf zone.     

Effects of wave-induced forcing on a circulation model of the North Sea

The effect of wind waves on water level and currents during two storms in the North Sea is investigated using a high-resolution Nucleus for European Modelling of the Ocean (NEMO) model forced with fluxes and fields from a high-resolution wave model. The additional terms accounting for wave-current interaction that are considered in this study are the Stokes-Coriolis force, the sea-state-dependent energy and momentum fluxes. The individual and collective role of these processes is quantified and the results are compared with a control run without wave effects as well as against current and water-level measurements from coastal stations. We find a better agreement with observations when the circulation model is forced by sea-state-dependent fluxes, especially in extreme events. The two extreme events, the storm Christian (25–27 October 2013), and about a month later, the storm Xaver (5–7 December 2013), induce different wave and surge conditions over the North Sea. Including the wave effects in the circulation model for the storm Xaver raises the modelled surge by more than 40 cm compared with the control run in the German Bight area. For the storm Christian, a difference of 20–30 cm in the surge level between the wave-forced and the stand-alone ocean model is found over the whole southern part of the North Sea. Moreover, the modelled vertical velocity profile fits the observations very well when the wave forcing is accounted for. The contribution of wave-induced forcing has been quantified indicating that this represents an important mechanism for improving water-level and current predictions.     

Global surface currents: a high-resolution product for investigating ocean dynamics

A global 1/4° resolution product of surface currents has been developed by the Centre de Topographie des Océans et de l’Hydrosphère. The surface current is calculated from a combination of Ekman currents derived from wind estimates from QuikSCAT satellite, geostrophic current anomalies derived from altimetry, and a mean geostrophic current derived from climatology. In the equatorial band, the currents are adjusted following the methodology proposed by Lagerloef et al. (J Geophys Res, 104(C10):22313–22326, 1999). These satellite-derived currents have been compared to different types of in situ current observations. A global validation is performed using Lagrangian surface drifting buoys and acoustic Doppler current profiler current observations along ship tracks. The comparison shows a very good agreement in the subtropical and mid-latitude bands. The correlation between the satellite-derived currents and the drifter currents in zonal mean bands is around 0.7 for most of the world oceans, both for the zonal and the meridional components. This correlation rises up to 0.8 in the regions of strong boundary currents. In the equatorial band, the correlation with the surface drifting buoys is reduced. A direct comparison with the TOGA/TAO moored current meter data at the equator shows that the low frequency currents are captured by the satellite current product, but there is a substantial high-frequency signal (<20 days), which is not reproduced. This is especially the case for the meridional component and is mainly related to the tropical instability waves. We also show that using daily QuikSCAT wind forcing improves the satellite current product, particularly in the high-latitude westerly wind belt and in the tropical Indian Ocean.     

Analysis of the reliability of a statistical oil spill response model

A statistical oil spill response model is developed and validated by means of actual oil slick observations reported during the Prestige accident and trajectories of drifter buoys. The model is based on the analysis of a database of hypothetical oil spill scenarios simulated by means of a Lagrangian transport model. To carry out the simulations, a re-analysis database consisting of 44-year hindcast dataset of wind and waves and climatologic daily mean surface currents is used. The number of scenarios required to obtain statistically reliable results is investigated, finding that 200 scenarios provide an optimal balance between the accuracy of the results and the computational effort. The reliability of the model was analyzed by comparing the actual data with the numerical results. The agreement found between actual and numerical data shows that the developed statistical oil spill model is a valuable tool to support spill response planning.     

Backtracking drifting objects using surface currents from high-frequency (HF) radar technology

In this work, the benefits of high-frequency (HF) radar ocean observation technology for backtracking drifting objects are analysed. The HF radar performance is evaluated by comparison of trajectories between drifter buoys versus numerical simulations using a Lagrangian trajectory model. High-resolution currents measured by a coastal HF radar network combined with atmospheric fields provided by numerical models are used to backtrack the trajectory of two dataset of surface-drifting buoys: group I (with drogue) and group II (without drogue). A methodology based on optimization methods is applied to estimate the uncertainty in the trajectory simulations and to optimize the search area of the backtracked positions. The results show that, to backtrack the trajectory of the buoys in group II, both currents and wind fields were required. However, wind fields could be practically discarded when simulating the trajectories of group I. In this case, the optimal backtracked trajectories were obtained using only HF radar currents as forcing. Based on the radar availability data, two periods ranging between 8 and 10?h were selected to backtrack the buoy trajectories. The root mean squared error (RMSE) was found to be 1.01?km for group I and 0.82?km for group II. Taking into account these values, a search area was calculated using circles of RMSE radii, obtaining 3.2 and 2.11?km² for groups I and II, respectively. These results show the positive contribution of HF radar currents for backtracking drifting objects and demonstrate that these data combined with atmospheric models are of value to perform backtracking analysis of drifting objects.     

Spectral analysis of mean flow and turbulence forced by waves in a horizontally homogeneous zone of the Iroise sea

The 1D version of the Model for Applications at Regional Scale is used to parameterize the effects of sea surface waves in 2D in a horizontally homogeneous offshore zone of the Iroise sea. Here we present the first simulation of the Iroise sea including sea surface waves forcing, and more generally, the first study of a boundary layer including the Hasselmann force with a tidal wave. We use a single equation turbulence closure based on a non-local diagnosis for energetic and dissipation length scales. The turbulent energy flux at the surface due to whitecaps and the Hasselmann force induced by Stokes drift are assessed using the whole sea surface waves spectrum given by the Wave Watch Third generation model. The ability of the parameterization to reproduce surface currents over a period of 1 year (2007) is tested with high frequency radar using spectral and time-frequency analysis. One problem with 1D modelling, corresponding to overestimation of current oscillating at inertial frequency is illustrated by comparing 1D and 3D simulations. We found an overall improvement by including the Hasselmann force mainly within the bandwidth of less than one cycle per day to one cycle per day for surface currents. Turbulence is induced by whitecaps decaying rapidly below the ocean surface but the mixed layer below 40 m is deeper due to waves breaking on the sea surface.     

A note on Stokes production of turbulence kinetic energy in the oceanic mixed layer: observations in the Baltic Sea

Shear- and convection-driven turbulence coexists with wind-generated surface gravity waves in the upper ocean. The turbulent Reynolds stresses in the oceanic mixed layer can therefore interact with the shear of the wave-generated Stokes drift velocity to extract energy from the surface waves and inject it into turbulence, thus augmenting the mean shear-driven turbulence. Stokes production of turbulence kinetic energy (TKE) is difficult to measure in the field, since it requires simultaneous measurement of the turbulent stress and the Stokes drift profiles in the water column. However, it is readily inferred using second moment closure models of the oceanic mixed layer provided: (1) wave properties are available, along with the usual water mass properties, and radiative and air–sea fluxes needed to drive the mixed layer model and (2) the model skill can be assessed by comparing the model results against the observed dissipation rates of TKE. Comprehensive measurements made during the Reynolds 2002 campaign in the Baltic Sea have made the estimation of Stokes production possible, and in this paper, we report on the effort and the conclusions reached. Measurements of air–sea exchange parameters and water mass properties during the campaign allowed a mixed layer model to be run and the turbulent stress in the water column to be inferred. Simultaneous wave spectrum measurements enabled Stokes drift profile to be deduced and wave breaking to be included in the model run, and the Stokes production of TKE in the water column estimated. Direct measurements of the TKE dissipation rate from an upward traversing microstructure profiler were used to assure that the model could reproduce the turbulent dissipation rate in the water column. The model results indicate that the Stokes production of TKE in the mixed layer is of the same order of magnitude as the shear production and must therefore be included in mixed layer models.     

Difference between the Lagrangian trajectories and Eulerian residual velocity fields in the southwestern Yellow Sea

The responses to tidal and/or wind forces of Lagrangian trajectories and Eulerian residual velocity in the southwestern Yellow Sea are investigated using a high-resolution circulation model. The simulated tidal harmonic constants agree well with observations and existing studies. The numerical experiment reproduces the long-range southeastward Eulerian residual current over the sloping bottom around the Yangtze Bank also shown in previous studies. However, the modeled drifters deployed at the northeastern flank of the Yangtze Bank in the simulation move northeastward, crossing over this strong southeastward Eulerian residual current rather than following it. Additional sensitivity experiments reveal that the influence of the Eulerian tidal residual currents on Lagrangian trajectories is relatively weaker than that of the wind driven currents. This result is consistent with the northeastward movement of ARGOS surface drifters actually released in the southwestern Yellow Sea. Further experiments suggest that the quadratic nature of the bottom friction is the crucial factor, in the southwestern Yellow Sea, for the weaker influence of the Eulerian tidal residual currents on the Lagrangian trajectories. This study demonstrates that the Lagrangian trajectories do not follow the Eulerian residual velocity fields in the shallow coastal regions of the southwestern Yellow Sea.     

Diurnal sea breeze effects on inner-shelf cross-shore exchange

Cross-shore exchange by strong (cross-shore wind stress, τ_sx>0.05 Pa) diurnal (7–25 h) sea breeze events are investigated using two years of continuous wind, wave, and ocean velocity profiles in 13 m water depth on the inner-shelf in Marina, Monterey bay, California. The diurnal surface wind stress, waves, and currents have spectral peaks at 1, 2, and 3 cpd and the diurnal variability represents about 50% of the total variability. During sea breeze relaxation (−0.05<τ_sx<0.05 Pa), a background wave-driven inner-shelf Eulerian undertow profile exists, which is equal and opposite to the Lagrangian Stokes drift profile, resulting in a net zero Lagrangian transport at depth. In the presence of a sea breeze (τ_sx>0.05 Pa), a uniform offshore profile develops that is different from the background undertow profile allowing cross-shore Lagrangian transport to develop, while including Lagrangian Stokes drift. The diurnal cross-shore current response is similar to subtidal (>25 h) cross-shore current response, as found by Fewings et al. (2008). The seasonality of waves and winds modify the diurnal sea breeze impact. It is suggested that material is not transported cross-shore except during sea breeze events owing to near zero transport during relaxation periods. During sea breeze events, cross-shore exchange of material appears to occur onshore near the surface and offshore near the sea bed. Since sea breeze events last for a few hours, the long-term cross-shore transport is incremental each day.     

Turbulence structure in the upper ocean: a comparative study of observations and modeling

Observations of turbulent dissipation rates measured by two independent instruments are compared with numerical model runs to investigate the injection of turbulence generated by sea surface gravity waves. The near-surface observations are made by a moored autonomous instrument, fixed at approximately 8 m below the sea surface. The instrument is equipped with shear probes, a high-resolution pressure sensor, and an inertial motion package to measure time series of dissipation rate and nondirectional surface wave energy spectrum. A free-falling profiler is used additionally to collect vertical microstructure profiles in the upper ocean. For the model simulations, we use a one-dimensional mixed layer model based on a k–ε type second moment turbulence closure, which is modified to include the effects of wave breaking and Langmuir cells. The dissipation rates obtained using the modified k–ε model are elevated near the sea surface and in the upper water column, consistent with the measurements, mainly as a result of wave breaking at the surface, and energy drawn from wave field to the mean flow by Stokes drift. The agreement between observed and simulated turbulent quantities is fairly good, especially when the Stokes production is taken into account.     

Wave‐driven inertial oscillations

Abstract

In a nonrotating system, the shear Reynolds stresses exerted by surface or internal gravity waves vanish on account of the exact quadrature between the horizontal and vertical orbital velocities. It is shown that a rotation of the system induces small in‐phase perturbations, resulting in a mean Reynolds stress which can generate low frequency currents. If both the wave field and the ocean are homogeneous with respect to the horizontal coordinates, the low‐frequency response is an undamped inertial oscillation. If either the wave field or the ocean are weakly inhomogeneous, the oscillation disperses in the vertical and horizontal directions due to phase‐mixing of modes with closely neighboring frequencies. Other effects which produce small frequency shifts also contribute to phase‐mixing, for example the horizontal component of the Coriolis vector and nonlinear interactions with geo‐strophic currents. The analysis is based on operator representations which avoid normal mode decomposition and yield simple integro‐differential operators for each phase‐mixing process. Numerical results are presented for a continuously stratified model typical for a shallow sea (Baltic). The orders of magnitude and qualitative features are in reasonable agreement with observations.     

Net sediment transport in tidal basins: quantifying the tidal barotropic mechanisms in a unified framework

Net sediment transport in tidal basins is a subtle imbalance between large fluxes produced by the flood/ebb alternation. The imbalance arises from several mechanisms of suspended transport. Lag effects and tidal asymmetries are regarded as dominant, but defined in different frames of reference (Lagrangian and Eulerian, respectively). A quantitative ranking of their effectiveness is therefore missing. Furthermore, although wind waves are recognized as crucial for tidal flats’ morphodynamics, a systematic analysis of the interaction with tidal mechanisms has not been carried out so far. We review the tide-induced barotropic mechanisms and discuss the shortcomings of their current classification for numerical process-based models. Hence, we conceive a unified Eulerian framework accounting for wave-induced resuspension. A new methodology is proposed to decompose the sediment fluxes accordingly, which is applicable without needing (semi-) analytical approximations. The approach is tested with a one-dimensional model of the Vlie basin, Wadden Sea (The Netherlands). Results show that lag-driven transport is dominant for the finer fractions (silt and mud). In absence of waves, net sediment fluxes are landward and spatial (advective) lag effects are dominant. In presence of waves, sediment can be exported from the tidal flats and temporal (local) lag effects are dominant. Conversely, sand transport is dominated by the asymmetry of peak ebb/flood velocities. We show that the direction of lag-driven transport can be estimated by the gradient of hydrodynamic energy. In agreement with previous studies, our results support the conceptualization of tidal flats’ equilibrium as a simplified balance between tidal mechanisms and wave resuspension.     

Impact of ocean–wave coupling on typhoon-induced waves and surge levels around the Korean Peninsula: a case study of Typhoon Bolaven

Typhoon-induced waves and surges are important when predicting potential hazards near coastal regions. In this paper, we applied a coupled modeling system for ocean–wave interaction to examine prediction capabilities for typhoon-induced waves and surges around the Korean Peninsula. To identify how ocean–wave coupling impacts wave and surge simulations during typhoon conditions, a set of comparative experiments was performed during Typhoon Bolaven (2012): (1) a fully coupled ocean–wave model, (2) a one-way coupled ocean–wave model without surface current feedback and ocean-to-wave water levels, and (3) a stand-alone ocean model without considering wave-based sea surface roughness (SSR). When coupled with the ocean model, the surface current reduced significantly the wave height on the right-hand side of the advancing typhoon track and improved prediction accuracy along the southern coast of Korea. Compared with the observed surge levels, the simulated surge height yielded improved results for peak height magnitude and timing compared with the uncoupled model. For wave-to-surge feedback, we found that wave-induced SSR plays an important role by modulating wind stress in the surface layer. The modulated wind stress directly affected the surge height, which improved surge peak prediction during the typhoon.     

Deep water observations of extreme waves with moored and free GPS buoys

Point-positioning GPS-based wave measurements were conducted by deep ocean (over 5,000 m) surface buoys moored in the North West Pacific Ocean in 2009, 2012, and 2013. The observed surface elevation bears statistical characteristics of Gaussian, spectrally narrow ocean waves. The tail of the averaged spectrum follows the frequency to the power of ?4 slope, and the significant wave height and period satisfies the Toba’s 3/2 law. The observations compare well with a numerical wave hindcast. Two large freak waves exceeding 13 m in height were observed in October 2009 and three extreme waves around 20 m in height were observed in October 2012 and in January 2013. These extreme events are associated with passages of a typhoon and a mid-latitude cyclone. Horizontal movement of the buoy revealed that the orbital motion of the waves at the peak of the wave group mostly exceed the weakly nonlinear estimate. For some cases, the orbital velocity exceeded the group velocity, which might indicate a breaking event but is not conclusive yet.