Time-optimal path planning in dynamic flows using level set equations: theory and schemes

We develop an accurate partial differential equation-based methodology that predicts the time-optimal paths of autonomous vehicles navigating in any continuous, strong, and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow fields such as unsteady double-gyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned even in the presence of complex flows in domains with obstacles. Finally, we present and support through illustrations several remarks that describe specific features of our methodology.     

Path planning in uncertain flow fields using ensemble method

An ensemble-based approach is developed to conduct optimal path planning in unsteady ocean currents under uncertainty. We focus our attention on two-dimensional steady and unsteady uncertain flows, and adopt a sampling methodology that is well suited to operational forecasts, where an ensemble of deterministic predictions is used to model and quantify uncertainty. In an operational setting, much about dynamics, topography, and forcing of the ocean environment is uncertain. To address this uncertainty, the flow field is parametrized using a finite number of independent canonical random variables with known densities, and the ensemble is generated by sampling these variables. For each of the resulting realizations of the uncertain current field, we predict the path that minimizes the travel time by solving a boundary value problem (BVP), based on the Pontryagin maximum principle. A family of backward-in-time trajectories starting at the end position is used to generate suitable initial values for the BVP solver. This allows us to examine and analyze the performance of the sampling strategy and to develop insight into extensions dealing with general circulation ocean models. In particular, the ensemble method enables us to perform a statistical analysis of travel times and consequently develop a path planning approach that accounts for these statistics. The proposed methodology is tested for a number of scenarios. We first validate our algorithms by reproducing simple canonical solutions, and then demonstrate our approach in more complex flow fields, including idealized, steady and unsteady double-gyre flows.     

Effects of large-amplitude internal solitary waves on ROV operation——A numerical study

Remotely operated vehicles (ROVs) are unique tools for underwater industrial exploration and scientific research of offshore areas and the deep ocean. With broadening application of ROVs, the study of factors that affect their safe operation is important. Besides the technical skills to control ROV movement, the dynamical ocean environment may also play a vital role in the safe operation of ROVs. In this paper, we investigate the influence of large-amplitude internal solitary waves (ISWs), focusing on the forces exerted on ROVs by ISWs. We present a methodology for modeling ISW-induced currents based on KdV model and calculate the ISW forces using the Morrison equation. Our results show that an extremely considerable load is exerted by the ISW on the ROV, resulting in a strong disturbance of the vehicle’s stability, affecting the ROV control. The numerical results of this work emphasize the importance of considering dynamical conditions when operating underwater vessels, such as ROV. Further laboratory and field investigation are suggested to gain more understanding of this subject.     

Time-calibrated estimates of oceanographic profiles using empirical orthogonal functions and clustering

Oceanographic climatology is widely used in different applications, such as climate studies, ocean model validation and planning of naval operations. Conventional climatological estimates are based on historic measurements, typically by averaging the measurements and thereby smoothing local phenomena. Such phenomena are often local in time and space, but crucial to some applications. Here, we propose a new method to estimate time-calibrated oceanographic profiles based on combined historic and real-time measurements. The real-time measurements may, for instance, be SAR pictures or autonomous underwater vehicles providing temperature values at a limited set of depths. The method employs empirical orthogonal functions and clustering on a training data set in order to divide the ocean into climatological regions. The real-time measurements are first used to determine what climatological region is most representative. Secondly, an improved estimate is determined using an optimisation approach that minimises the difference between the real-time measurements and the final estimate.     

Assessing the fidelity of surface currents from a coastal ocean model and HF radar using drifting buoys in the Middle Atlantic Bight

The rapid expansion of urbanization along the world’s coastal areas requires a more comprehensive and accurate understanding of the coastal ocean. Over the past several decades, numerical ocean circulation models have tried to provide such insight, based on our developing understanding of physical ocean processes. The systematic establishment of coastal ocean observation systems adopting cutting-edge technology, such as high frequency (HF) radar, satellite sensing, and gliders, has put such ocean model predictions to the test, by providing comprehensive observational datasets for the validation of numerical model forecasts. The New York Harbor Observing and Prediction System (NYHOPS) is a comprehensive system for understanding coastal ocean processes on the continental shelf waters of New York and New Jersey. To increase confidence in the system’s ocean circulation predictions in that area, a detailed validation exercise was carried out using HF radar and Lagrangian drifter-derived surface currents from three drifters obtained between March and October 2010. During that period, the root mean square (RMS) differences of both the east–west and north–south currents between NYHOPS and HF radar were approximately 15 cm s^?1. Harmonic analysis of NYHOPS and HF radar surface currents shows similar tidal ellipse parameters for the dominant M₂ tide, with a mean difference of 2.4 cm s^?1 in the semi-major axis and 1.4 cm s^?1 in the semi-minor axis and 3° in orientation and 10° in phase. Surface currents derived independently from drifters along their trajectories showed that NYHOPS and HF radar yielded similarly accurate results. RMS errors when compared to currents derived along the trajectory of the three drifters were approximately 10 cm s^?1. Overall, the analysis suggests that NYHOPS and HF radar had similar skill in estimating the currents over the continental shelf waters of the Middle Atlantic Bight during this time period. An ensemble-based set of particle tracking simulations using one drifter which was tracked for 11 days showed that the ensemble mean separation generally increases with time in a linear fashion. The separation distance is not dominated by high frequency or short spatial scale wavelengths suggesting that both the NYHOPS and HF radar currents are representing tidal and inertial time scales correctly and resolving some of the smaller scale eddies. The growing ensemble mean separation distance is dominated by errors in the mean flow causing the drifters to slowly diverge from their observed positions. The separation distance for both HF radar and NYHOPS stays below 30 km after 5 days, and the two technologies have similar tracking skill at the 95 % level. For comparison, the ensemble mean distance of a drifter from its initial release location (persistence assumption) is estimated to be greater than 70 km in 5 days.     

Along-shelf evolution and sea levels across the continental slope

If wind-stress or a horizontal oceanic density gradient acts over an ocean basin with an adjacent continental shelf and slope, sea-surface slopes and currents are set up along the shelf and slope with a return flow in the ocean. The currents evolve from zero at blocked ends of the shelf and basin. Such evolution is essentially barotropic (even for baroclinic forcing) and is relevant to all flow adjustments after longshore changes of depth profile or forcing. The distance over which this evolution takes place is investigated analytically for simple geometries, and numerically for a range of shelf, slope and ocean widths, shelf/ocean depth ratios, frictional decay rates and oscillatory frequencies. A close correspondence is found with the decay distance (group velocity x decay time) for a lowest mode continental shelf wave, often exceeding 1000 km. This correspondence is used to interpret some published model calculations of shelf and slope currents or return flows resulting from wind-stress or alongshore pressure gradients.Where a slope current is evolving, coastal sea levels do not follow oceanic levels. Implications for coastal/oceanic level differences are discussed. Oceanic sea-level features of shorter scale than the above 1000 km (say) do not penetrate fully to the coast. However, coastal sea levels averaged around small islands without broad shelves well represent surrounding oceanic levels.     

South Atlantic circulation in a world ocean model

The circulation in the South Atlantic Ocean has been simulated within a global ocean general circulation model. Preliminary analysis of the modelled ocean circulation in the region indicates a rather close agreement of the simulated upper ocean flows with conventional notions of the large-scale geostrophic currents in the region. The modelled South Atlantic Ocean witnesses the return flow and export of North Atlantic Deep Water (NADW) at its northern boundary, the inflow of a rather barotropic Antarctic Circumpolar Current (ACC) through the Drake Passage, and the inflow of warm saline Agulhas water around the Cape of Good Hope. The Agulhas leakage amounts to 8.7 Sv, within recent estimates of the mass transport shed westward at the Agulhas retroflection. Topographic steering of the ACC dominates the structure of flow in the circumpolar ocean. The Benguela Current is seen to be fed by a mixture of saline Indian Ocean water (originating from the Agulhas Current) and fresher Subantarctic surface water (originating in the ACC). The Benguela Current is seen to modify its flow and fate with depth; near the surface it flows north-westwards bifurcating most of its transport northward into the North Atlantic Ocean (for ultimate replacement of North Atlantic surface waters lost to the NADW conveyor). Deeper in the water column, more of the Benguela Current is destined to return with the Brazil Current, though northward flows are still generated where the Benguela Current extension encounters the coast of South America. At intermediate levels, these northward currents trace the flow of Antarctic Intermediate Water (AAIW) equatorward, though even more AAIW is seen to recirculate poleward in the subtropical gyre. In spite of the model’s rather coarse resolution, some subtle features of the Brazil-Malvinas Confluence are simulated rather well, including the latitude at which the two currents meet. Conceptual diagrams of the recirculation and interocean exchange of thermocline, intermediate and deep waters are constructed from an analysis of flows bound between isothermal and isobaric surfaces. This analysis shows how the return path of NADW is partitioned between a cold water route through the Drake Passage (6.5 Sv), a warm water route involving the Agulhas Current sheeding thermocline water westward (2.5 Sv), and a recirculation of intermediate water originating in the Indian Ocean (1.6 Sv).     

Targeted observation analysis of a Northwestern Tropical Pacific Ocean mooring array using an ensemble-based method

An important supplement for ocean observing systems, the Northwestern Tropical Pacific Ocean (NWTPO) mooring array including 15 moorings equipped with Acoustic Doppler Current Profilers (ADCP) devices was developed by the Chinese Academy of Sciences and deployed in 2013. This study assessed the performance of this mooring array in monitoring the intra-seasonal and low-frequency (above 91 days) variability of oceanic currents by conducting targeted observation analyses using an ensemble-based method. Key regions for monitoring intra-seasonal variability of the NWTPO circulation are the equator, Indonesian throughflow (ITF), headstream of the North Equatorial Countercurrent (NECC), and Subtropical Countercurrent (STCC). For monitoring intra-seasonal variability, the range of each mooring is confined to a local scale. Therefore, NWTPO moorings cannot adequately resolve intra-seasonal variability in areas of the ITF, the headstream of the NECC, and STCC due to location constraints of the moorings. For monitoring low-frequency variability of NWTPO circulation, the key regions are the Western Boundary Current (WBC), NECC, and the Equatorial Undercurrent (EUC). NWTPO moorings performed relatively well in monitoring the low-frequency variability, as indicated by the strong background correlations between each of the currents. The NWTPO mooring array plays an important role in monitoring the location and intensity of background currents. Because moorings are costly and require a high-density distribution for optimal performance, understanding the multi-timescale dynamical nature of the NWTPO current system is critical for the deploying future moorings in this region.     

Optimal processing of satellite-derived magnetic anomaly data

The statistical concept of the power spectrum has proven to be of great value in the analysis of time series and linear systems for which the inputs and outputs are functions of time. This paper shows how the concept can be extended to two-dimensional spatial power spectra and illustrates, by example, how the concept can be applied to the determination of optimal data processing methods for satellite-derived magnetic anomaly data and to the planning of missions to obtain such data.The analysis techniques indicated are applied to a data set and data processing procedure described by Mayhew et al. (1980). These authors describe magnetic anomaly data for Australia and surrounding ocean obtained by the polar orbit POGO series satellites. This paper shows that the data processing method used by these authors is approximately equivalent to an invariant two-dimensional linear filter and that it is reasonably close to optimal with respect to accuracy, though some possible improvements are suggested. Nevertheless, as is usual when filtering data, some real “signal” is unavoidably removed along with the “noise”, resulting in errors that can be quite large.A method for reducing these errors by using additional data from a medium inclination orbit satellite (for example, 60° inclination) is suggested.     

Multiscale two-way embedding schemes for free-surface primitive equations in the “Multidisciplinary Simulation, Estimation and Assimilation System”

We derive conservative time-dependent structured discretizations and two-way embedded (nested) schemes for multiscale ocean dynamics governed by primitive equations (PEs) with a nonlinear free surface. Our multiscale goal is to resolve tidal-to-mesoscale processes and interactions over large multiresolution telescoping domains with complex geometries including shallow seas with strong tides, steep shelfbreaks, and deep ocean interactions. We first provide an implicit time-stepping algorithm for the nonlinear free-surface PEs and then derive a consistent time-dependent spatial discretization with a generalized vertical grid. This leads to a novel time-dependent finite volume formulation for structured grids on spherical or Cartesian coordinates, second order in time and space, which preserves mass and tracers in the presence of a time-varying free surface. We then introduce the concept of two-way nesting, implicit in space and time, which exchanges all of the updated fields values across grids, as soon as they become available. A class of such powerful nesting schemes applicable to telescoping grids of PE models with a nonlinear free surface is derived. The schemes mainly differ in the fine-to-coarse scale transfers and in the interpolations and numerical filtering, specifically for the barotropic velocity and surface pressure components of the two-way exchanges. Our scheme comparisons show that for nesting with free surfaces, the most accurate scheme has the strongest implicit couplings among grids. We complete a theoretical truncation error analysis to confirm and mathematically explain findings. Results of our discretizations and two-way nesting are presented in realistic multiscale simulations with data assimilation for the middle Atlantic Bight shelfbreak region off the east coast of the USA, the Philippine archipelago, and the Taiwan–Kuroshio region. Multiscale modeling with two-way nesting enables an easy use of different sub-gridscale parameterizations in each nested domain. The new developments drastically enhance the predictive capability and robustness of our predictions, both qualitatively and quantitatively. Without them, our multiscale multiprocess simulations either were not possible or did not match ocean data.     

Numerical study of seasonal circulation and variability over the inner shelf of the northern South China Sea

This study examines seasonal circulation, hydrography, and associated spatial variability over the inner shelf of the northern South China Sea (NSCS) using a nested-grid coastal ocean circulation model. The model external forcing consists of tides, atmospheric forcing, and open boundary conditions based on the global ocean circulation and hydrography reanalysis produced by the Hybrid Coordinate Ocean model. Five numerical experiments are conducted with different combinations of external forcing functions to examine main physical processes affecting the seasonal circulation in the study region. Model results demonstrate that the monthly mean circulation in the study region features the Guangdong Coastal Current (GCC) over coastal waters and the South China Sea Warm Current (SCSWC) in the offshore deep waters. The GCC produced by the model flows nearly southwestward in winter months and northwestward in summer months, which agrees with previous studies. The SCSWC flows roughly northeastward and is well defined in summer months. In winter months, by comparison, the SCSWC is superseded by the southwestward strong wind-driven currents. Analysis of model results in five different experiments demonstrates that the monthly mean circulation over coastal and inner shelf waters of the NSCS can be approximated by barotropic currents forced by the southwestward monsoon winds in winter months. In summer months, by comparison, the monthly mean circulation in the study region is affected significantly by baroclinic dynamics associated with freshwater runoff from the Pearl River and advection of warm and saline waters carried by the SCSWC over the NSCS.     

Modeling multiscale heterogeneity and aquifer interconnectivity

A number of methods involving indicator geostatistics were combined in a methodology for characterizing and modeling multiscale heterogeneity. The methodology circumvents sources of bias common in data from borehole logs. We applied this methodology to the complex heterogeneity within a regional system of buried valley aquifers, which occurs in the western glaciated plains of North America and includes the Spiritwood Aquifer. The region is conceptualized as having a hierarchical organization with three facies assemblage types (large-scale heterogeneity) and two facies types within each assemblage (small-scale heterogeneity). We statistically characterized the sedimentary architecture at both scales, formulated indicator correlation models from those characterizations, and used the models to simulate the architecture in a multiscale realization. We focused on the interconnectivity of units creating higher-permeability pathways. Higher-permeability pathways span the realization even though the proportion of higher-permeability facies is less than the percolation threshold. Thus, geologic structures as represented in the indicator correlation models create interconnectivity above that which would occur if the higher-permeability facies were randomly placed. This amount of interconnection among higher-permeability facies within the multiscale realization is consistent with that suggested in prior hydraulic and geochemical studies of the regional system.     

Cross-shelf transport into nearshore waters due to shoaling internal tides in San Pedro Bay, CA

In the summer of 2001, a coastal ocean measurement program in the southeastern portion of San Pedro Bay, CA, was designed and carried out. One aim of the program was to determine the strength and effectiveness of local cross-shelf transport processes. A particular objective was to assess the ability of semidiurnal internal tidal currents to move suspended material a net distance across the shelf. Hence, a dense array of moorings was deployed across the shelf to monitor the transport patterns associated with fluctuations in currents, temperature and salinity. An associated hydrographic program periodically monitored synoptic changes in the spatial patterns of temperature, salinity, nutrients and bacteria. This set of measurements show that a series of energetic internal tides can, but do not always, transport subthermocline water, dissolved and suspended material from the middle of the shelf into the surfzone. Effective cross-shelf transport occurs only when (1) internal tides at the shelf break are strong and (2) subtidal currents flow strongly downcoast. The subtidal downcoast flow causes isotherms to tilt upward toward the coast, which allows energetic, nonlinear internal tidal currents to carry subthermocline waters into the surfzone. During these events, which may last for several days, the transported water remains in the surfzone until the internal tidal current pulses and/or the downcoast subtidal currents disappear. This nonlinear internal tide cross-shelf transport process was capable of carrying water and the associated suspended or dissolved material from the mid-shelf into the surfzone, but there were no observation of transport from the shelf break into the surfzone. Dissolved nutrients and suspended particulates (such as phytoplankton) transported from the mid-shelf into the nearshore region by nonlinear internal tides may contribute to nearshore algal blooms, including harmful algal blooms that occur off local beaches.     

On the modifications of near-inertial waves at fronts: implications for energy transfer across scales

In the ocean, wind-generated kinetic energy (KE) manifests itself primarily in balanced currents and near-inertial waves. The dynamics of these flows is strongly constrained by the Earth’s rotation, causing the KE in balanced currents to follow an inverse cascade but also preventing wave-wave interactions from fluxing energy in the near-inertial band to lower frequencies and higher vertical wavenumbers. How wind-generated KE is transferred to small-scale turbulence and dissipated is thus a non-trivial problem. This article presents a review of recent theoretical calculations and numerical simulations that demonstrate how some surprising modifications to internal wave physics by the lateral density gradients present at ocean fronts allow for strong interactions between balanced currents and near-inertial waves that ultimately result in energy loss for both types of motion.     

Bimodal wave spectra in lower Chesapeake Bay, sea bed energetics and sediment transport during winter storms

The transition zone separating estuarine environments from the coastal ocean is characterized not only by distinctive morphological and sedimentary trends but by unique hydrodynamic forces as well. Lower Chesapeake Bay, a large coastal estuary within the Mid-Atlantic Bight of the U.S. East Coast, experiences complex wave and current-induced forces produced during winter storms. Wave and current measurements made near Thimble Shoal Light over five winter seasons show that most storms simultaneously produce both ocean and bay-generated wave trains that appear as distinct bimodal peaks in directional spectra. Analysis of selected storm wave records reveal that lower-frequency ocean waves, although nominally lower in amplitude than higher-frequency bay waves, are roughly equivalent to bay waves in terms of energy expended on beds of fine- to medium-grained sand at either end of the Thimble Shoal Channel. Grain-friction energy dissipation estimates calculated for waves and currents suggest that waves provide more net energy capable of transporting bottom sediment than currents, although strong barotropic flows briefly encountered during a major storm on 13–14 March 1993, exceeded wave energy expended at the bed by almost an order of magnitude. From analyses of wave orbital velocity spectra, it is shown that dual wave trains characterized by differences in peak frequency and direction may assist each other through interactions that increase their combined contribution to frictional energy dissipation and inferred sediment transport at the bed.     

基于区域滤波的GOCE稳态海面动力地形和地转流

基于频域法,利用最新的GOCE卫星重力场模型和卫星测高数据计算了稳态海面动力地形.结合海洋表层漂流浮标的观测结果,对稳态海面动力地形进行了最优空间滤波尺度分析,给出了区域、纬度带和全球稳态海面动力地形的最优空间滤波尺度因子.在此基础上,给出了全球和区域地转流.结果表明:在中高纬度和全球区域,可以分别获得空间尺度优于102km和127km的稳态海面动力地形信息.与海洋表层漂流浮标对比可知,在强流区域,采用稳态海面动力地形得到的地转流速可以解释观测浮标流速的70%;在中高纬度区域,由GOCE重力场得到的地转流略优于对应的GRACE结果;在近赤道区域,由GOCE重力场得到的地转流精度略低于对应的GRACE结果;在北大西洋和阿古拉斯强流区域,由GOCE得到的地转流场明显优于对应的GRACE结果,其精度分别提高了16%和24%.     

Sea Surface Salinity Observations from Space with the SMOS Satellite: A New Means to Monitor the Marine Branch of the Water Cycle

While it is well known that the ocean is one of the most important component of the climate system, with a heat capacity 1,100 times greater than the atmosphere, the ocean is also the primary reservoir for freshwater transport to the atmosphere and largest component of the global water cycle. Two new satellite sensors, the ESA Soil Moisture and Ocean Salinity (SMOS) and the NASA Aquarius SAC-D missions, are now providing the first space-borne measurements of the sea surface salinity (SSS). In this paper, we present examples demonstrating how SMOS-derived SSS data are being used to better characterize key land–ocean and atmosphere–ocean interaction processes that occur within the marine hydrological cycle. In particular, SMOS with its ocean mapping capability provides observations across the world’s largest tropical ocean fresh pool regions, and we discuss from intraseasonal to interannual precipitation impacts as well as large-scale river runoff from the Amazon–Orinoco and Congo rivers and its offshore advection. Synergistic multi-satellite analyses of these new surface salinity data sets combined with sea surface temperature, dynamical height and currents from altimetry, surface wind, ocean color, rainfall estimates, and in situ observations are shown to yield new freshwater budget insight. Finally, SSS observations from the SMOS and Aquarius/SAC-D sensors are combined to examine the response of the upper ocean to tropical cyclone passage including the potential role that a freshwater-induced upper ocean barrier layer may play in modulating surface cooling and enthalpy flux in tropical cyclone track regions.     

Wave equation datuming applied to marine OBS data and to land high resolution seismic profiling

One key step in seismic data processing flows is the computation of static corrections, which relocate shots and receivers at the same datum plane and remove near surface weathering effects. We applied a standard static correction and a wave equation datuming and compared the obtained results in two case studies: 1) a sparse ocean bottom seismometers dataset for deep crustal prospecting; 2) a high resolution land reflection dataset for hydrogeological investigation. In both cases, a detailed velocity field, obtained by tomographic inversion of the first breaks, was adopted to relocate shots and receivers to the datum plane. The results emphasize the importance of wave equation datuming to properly handle complex near surface conditions. In the first dataset, the deployed ocean bottom seismometers were relocated to the sea level (shot positions) and a standard processing sequence was subsequently applied to the output. In the second dataset, the application of wave equation datuming allowed us to remove the coherent noise, such as ground roll, and to improve the image quality with respect to the application of static correction. The comparison of the two approaches evidences that the main reflecting markers are better resolved when the wave equation datuming procedure is adopted.     

The velocity structure of the Carpathian zone from the ambient noise surface wave tomography

The dispersion curves of the Rayleigh wave group velocities are constructed along 60 interstation seismic paths in Central Europe based on the cross-correlation function of seismic noise. Together with the previous data (Yanovskaya and Lyskova, 2013), this information was used for reconstructing the three-dimensional distribution of S-wave velocities in the upper mantle of the Carpathian region. In the present work, the previous results are refined by expanding the data set by the additional seismic paths that intersect the Carpathian region and by modifying the procedure for constructing the locally averaged dispersion curves so as to obtain a more compact resolution. The results of the study suggest the complex, multidirectional character of the plate motion in the region.     

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.