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Wave crests of unexpected height and steepness pose a danger to activities at sea, and long-term field measurements provide important clues for understanding the environmental conditions that are conducive to their generation and behavior. We present a novel dataset of high-frequency laser altimeter measurements of the sea surface elevation gathered over a period of 18 years from 2003 to 2020 on an offshore platform in the central North Sea. Our analysis of crest height distributions in the dataset shows that mature, high sea states with high spectral steepness and narrow directional spreading exhibit crest height statistics that significantly deviate from standard second-order models. Conversely, crest heights in developing sea states with similarly high steepness but wide directional spread correspond well to second-order theory adjusted for broad frequency bandwidth. The long-term point time series measurements are complemented with space–time stereo video observations from the same location, collected during five separate storm events during the 2019/20 winter season. An examination of the crest dynamics of the space–time extreme wave crests in the stereo video dataset reveals that the crest speeds exhibit a slowdown localized around the moment of maximum crest elevation, in line with prevailing theory on nonlinear wave group dynamics. Extending on previously published observations focused on breaking crests, our results are consistent for both breaking and nonbreaking extreme crests. We show that wave crest steepness estimated from time series using the linear dispersion relation may overestimate the geometrically measured crest steepness by up to 25% if the crest speed slowdown is not taken into account. Significance Statement Better understanding of the statistics and dynamical behavior of extreme ocean surface wave crests is crucial for improving the safety of various operations at sea. Our study provides new, long-term field evidence of the combined effects of wave field steepness and directionality on the statistical distributions of crest heights in storm conditions. Moreover, we show that the dynamical characteristics of extreme wave crests are well described by recently identified nonlinear wave group dynamics. This finding has implications, for example, for wave force calculations and the treatment of wave breaking in numerical wave models.

The momentum flux to the ocean interior is commonly assumed to be identical to the momentum flux lost from the atmosphere in traditional atmosphere, ocean, and coupled models. However, ocean surface gravity waves (hereafter waves) can alter the magnitude and direction of the ocean-side stress (τoc) from the air-side stress (τa). This is rarely considered in coupled climate and forecast models. Based on a 30-yr wave hindcast, the redistribution of the global wind stress and turbulent kinetic energy (TKE) flux by waves was investigated. Waves play a more important role in the windy oceans in middle and high latitudes than that in the oceans in the tropics (i.e., the central portion of the Pacific and Atlantic Oceans). On average, the relative difference between τoc and τa, γτ, can be up to 6% in middle and high latitudes. The frequency of occurrence of γτ > 9% can be up to 10% in the windy extratropics. The directional difference between τoc and τa exceeds 3.5° in the middle and high latitudes 10% of the time. The difference between τoc and τa becomes more significant closer to the coasts of the continents due to strong wind gradients. The friction velocity-based approach overestimates (underestimates) the breaking-induced TKE flux in the tropics (middle and high latitudes). The findings presented in the current study show that coupled climate and Earth system models would clearly benefit from the inclusion of a wave model. Significance Statement The purpose of this study is to investigate the redistribution of the global wind stress and turbulent kinetic energy flux due to surface waves based on a 30-yr wave hindcast. The mean relative difference of the magnitude between the air-side and ocean-side stress is up to 6% with a 90th percentile of more than 9% in the windy extratropics. Due to strong wind gradients, the redistributive role of waves in the stress becomes more significant closer to coasts. The results indicate that we should consider the redistributive role of waves in the momentum and energy fluxes in climate and Earth system models since they are the key elements in the predictability of weather forecasting models and climate models.

The effect of wave-induced processing on steric sea-level is investigated through ocean-wave coupled simulations. The experiments are performed with a high-resolution configuration of the Geestacht COAstal model SysTem (GCOAST), implemented in the Northeast Atlantic, the North Sea and the Baltic Sea which are considered as connected basins. The GCOAST system accounts for wave-ocean interactions and the ocean circulation relies on the NEMO (Nucleus for European Modelling of the Ocean) ocean model, while ocean-wave simulations are performed using the spectral wind wave model WAM. The objective is to quantify the sea-state contribution to steric sea-level variability and trend over a 26-year period (1992-2017). The ability of wave-ocean coupled simulations to disclose the sea-state contributions to sea-level variability and surge is demonstrated. The contribution of the wave-induced processes (WIPs) to the sea surface dynamics (e.g. temperature and salinity), ocean mixing (mixed layer thickness), and on the modulation of air-sea fluxes (e.g. heat flux) clearly appear both during winter (10-20 %) and summer (10 %), which in turn affect the steric sea-level variability. Investigating the components of steric sea-level signal, the thermosteric sea-level shows larger amplitudes compared to the halosteric component. Significant contributions to the thermosteric sea-level variability (40 %) due to wave-induced processes are observed in the North Atlantic (in summer) and along the Norwegian Trench (in winter). WIPs influence the thermosteric sea-level trends in the North Atlantic up to the order of 1 mm yr-1, both during winter and summer, in the open ocean and at the shelf break, while smaller contributions are observed over the shelf areas of the North Sea.

Extreme winds account for more than half of Norway’s insurance claims related to natural hazards [1]. Quantifying windstorm-damage relations is crucial to prepare for and mitigate the effects of future wind events. However, there has never been an attempt to quantify windstorm-damage relations at the municipality level in Norway. The work in hand employs four different damage functions at the municipality level of Norway. Along with the newly proposed modified Prahl damage function [2], an ensemble means of the damage estimates are tested for 356 municipalities in Norway. We evaluate the damage functions in terms of forecast accuracy. The spatial distribution of losses suggests severe damages along the west coast of Norway. Further inland in Norway, there are seldom any losses due to Norway’s unique topography and demography. The losses above the 99.7th percentile in each municipality constitute 85% of total national loss, and we focus on this extreme loss class. A significant agreement between the observed and estimated losses at the municipality and national levels indicates that the damage functions are suited for forecasting storm-induced damages. The damage functions are also able to successfully reconstruct the spatial spread and pattern of losses caused by very extreme windstorms.References1] Finance Norway, Natural Disaster Statistics (NASK), (2019)[2] B.F. Prahl et al., Applying stochastic small-scale damage functions to German winter storms, Geophysical Research Letters 39, (2012)

A new model for transport and fate of chemicals in the aquatic environment is presented. The tool, named ChemicalDrift, is integrated into the open-source Lagrangian framework OpenDrift and is hereby presented for organic compounds. The supported chemical processes include the degradation, the volatilization, and the partitioning between the different phases that a target chemical can be associated with in the aquatic environment, e.g. dissolved, bound to suspended particles, or deposited to the seabed sediments. The dependencies of the chemical processes on changes in temperature, salinity, and particle concentration are formulated and implemented. The chemical-fate modelling is combined with wide support for hydrodynamics by the integration within the Lagrangian framework which provides e.g. advection by ocean currents, diffusion, wind-induced turbulent mixing, and Stokes drift generated by waves. A flexible interface compatible with a wide range of available metocean data is made accessible by the integration, making the tool easily adaptable to different spatio-temporal scales and fit for modelling of complex coastal regions. Further inherent capabilities of the Lagrangian approach include the seamless tracking and separation of multiple sources, e.g. pollutants emitted from ships or from rivers or water treatment plants. Specific interfaces to a dataset produced by a model of emissions from shipping and to an unstructured-grid oceanographic model of the Adriatic Sea are provided. The model includes a database of chemical parameters for a set of poly-aromatic hydrocarbons and a database of emission factors for different chemicals found in discharged waters from sulfur emission abatement systems in marine vessels. A post-processing tool for generating mean concentrations of a target chemical, over customizable spatio-temporal grids, is provided. Model development and simulation results demonstrating the functionalities of the model are presented, while tuning of parameters, validation, and reporting of numerical results are planned as future activities. The ChemicalDrift model flexibility, functionalities, and potential are demonstrated through a selection of examples, introducing the model as a freely available and open-source tool for chemical fate and transport that can be applied to assess the risks of contamination by organic pollutants in the aquatic environment.

Lateral changes in the group velocity of waves propagating in oceanic or coastal waters causes a deflection in their propagation path. The change in direction is called refraction and can be computed if having information about the ambient current field and/or the bathymetry. We present an open source module for solving the wave ray equations by means of numerical integration in Python v3, which is relevant for ocean applications. The solver is implemented for waves at arbitrary depths and for an ambient current field with spatio-temporal variability much lower than characteristic wave properties. The wave ray tracing module is implemented in a class structure, and the output is verified against analytical solutions as well as tested for numerical convergence. The solver is accompanied by a set of ancillary functions with the aim of supporting relevant workflows for the user community including data retrieval, transformation, and dissemination, and a number of use examples are provided.

We propose a methodology for despiking ocean surface wave time series based on a Bayesian approach to data-driven learning known as Gaussian process (GP) regression. We show that GP regression can be used for both robust detection of erroneous measurements and interpolation over missing values, while also obtaining a measure of the uncertainty associated with these operations. In comparison with a recent dynamical phase space–based despiking method, our data-driven approach is here shown to lead to improved wave signal correlation and spectral tail consistency, although at a significant increase in computational cost. Our results suggest that GP regression is thus especially suited for offline quality control requiring robust noise detection and replacement, where the subsequent analysis of the despiked data is sensitive to the accidental removal of extreme or rare events such as abnormal or rogue waves. We assess our methodology on measurements from an array of four collocated 5-Hz laser altimeters during a much-studied storm event in the North Sea covering a wide range of sea states.

The 3-km Norwegian Reanalysis (NORA3) is a 15-yr mesoscale-permitting atmospheric hindcast of the North Sea, the Norwegian Sea, and the Barents Sea. With a horizontal resolution of 3 km, the nonhydrostatic numerical weather prediction model HARMONIE–AROME runs explicitly resolved deep convection and yields hindcast fields that realistically downscale the ERA5 reanalysis. The wind field is much improved relative to its host analysis, in particular in mountainous areas and along the improved grid-resolving coastlines. NORA3 also performs much better than the earlier hydrostatic 10-km Norwegian Hindcast Archive (NORA10) in complex terrain. NORA3 recreates the detailed structures of mesoscale cyclones with sharp gradients in wind and with clear frontal structures, which are particularly important when modeling polar lows. In extratropical windstorms, NORA3 exhibits significantly higher maximum wind speeds and compares much better to observed maximum wind than do NORA10 and ERA5. The activity of the model is much more realistic than that of NORA10 and ERA5, both over the ocean and in complex terrain.

A new model for transport and fate of chemicals in the aquatic environment is presented. The tool, named ChemicalDrift, is integrated in the open-source Lagrangian framework OpenDrift, and is hereby presented for organic compounds. The supported chemical processes include the degradation, the volatilization, and the partitioning between the different phases that a target chemical can be associated to in the aquatic environment, e.g. dissolved, bound to suspended particles, or deposited to the seabed sediments. The dependencies of the chemical processes on changes of temperature, salinity, and particle concentration, are formulated and implemented. The chemical fate modelling is combined with wide support for hydrodynamics by the integration within the Lagrangian framework which provides, e.g., advection by ocean currents, diffusion, wind induced turbulent mixing, and Stokes drift generated by waves. A powerful interface to a wide range of available metocean data is made available by the integration, making the tool flexible and adaptable to different spatio-temporal scales and fit for modelling of complex coastal regions. Further inherent capabilities of the Lagrangian approach include the seamless tracking and separation of multiple sources as, e.g., pollutants emitted from ships or from rivers or water treatment plants. Specific interfaces to a dataset produced by a model of emissions from shipping, and to an unstructured-grid oceanographic model of the Adriatic Sea, are provided. The model includes a database of chemical parameters for a set of poly-aromatic hydrocarbons, and a database of emission factors for different chemicals found in discharged waters from sulphur emission abatements systems in marine vessels. A post-processing tool for generating mean concentrations of a target chemical, over customizable spatio-temporal grids, is provided. Model development and functional testing are presented, while tuning of parameters, validation, and reporting of numerical results, are planned as future activities. The ChemicalDrift model flexibility, functionalities, and potential, are demonstrated through a selection of examples, introducing the model as a valuable tool for chemical fate and transport, that can be applied to assessment of the risks of contamination by organic pollutants in the aquatic environment.

Following the 1st International Workshop on Waves, Storm Surges and Coastal Hazards, which incorporated the 15th session of the long-standing the International Workshop on Wave Hindcasting and Forecasting, in September 2017 in Liverpool, United Kingdom, a topical collection has appeared in recent issues of Ocean Dynamics. Here, we give a brief overview of the 15 papers published in this topical collection as well as an overview of the widening scope of the conference in recent years. The continuing trend towards closer integration between the wave and ocean modeling communities is reflected in this workshop, culminating in the renaming of the workshop, while maintaining the connection with the three-decade long history of the wave workshop. This is also seen in this topical collection, with several papers exploring wave-generated storm surge, wave-tide contributions to coastal flooding, forcing a global ocean model with fluxes from a wave model and interaction between surface waves and sea ice.

Storm surges can give rise to extreme floods in coastal areas. The Norwegian Meteorological Institute (MET Norway) produces 120-hour regional operational storm surge forecasts along the coast of Norway based on the Regional Ocean Modeling System (ROMS). Despite advances in the development of models and computational capability, forecast errors remain large enough to impact response measures and issued alerts, in particular, during the strongest storm events. Reducing these errors will positively impact the efficiency of the warning systems while minimizing efforts and resources spent on mitigation.Here, we investigate how forecasts can be improved with residual learning, i.e., training data-driven models to predict, and correct, the error in the ROMS output. For this purpose, sea surface height data from stations around Norway were collected and compared with the ROMS output.We develop two different residual learning frameworks that can be applied on top of the ROMS output. In the first one, we perform binning of the model error, conditionalized by pressure, wind, and waves. Clear error patterns are visible when the error conditioned by the wind is plotted in a polar plot for each station. These error maps can be stored as correction lookup tables to be applied on the ROMS output. However, since wind, pressure, and waves are correlated, we cannot simultaneously correct the error associated with each variable using this method. To overcome this limitation, we develop a second method, which resorts to Neural Networks (NNs) to perform nonlinear modeling of the error pattern obtained at each station. The residual NN method strongly outperforms the error map method, and is a promising direction for correcting storm surge models operationally. Indeed, i) this method is applied on top of the existing model and requires no changes to it, ii) all predictors used for NN inference are available operationally, iii) prediction by the NN is very fast, typically a few seconds per station, and iv) the NN correction can be provided to a human expert who gets to inspect it, compare it with the ROMS output, and see how much correction is brought by the NN. Using this NN residual error correction method, the RMS error in the Oslofjord is reduced by typically 7% for lead times of 24 hours, 17% for 48 hours, and 35% for 96 hours.

The water following characteristics of six different drifter types are investigated using two different operational marine environmental prediction systems: one produced by Environment and Climate Change Canada (ECCC) and the other produced by MET Norway (METNO). These marine prediction systems include ocean circulation models, atmospheric models, and surface wave models. Two leeway models are tested for use in drift object prediction: an implicit leeway model where the Stokes drift is implicit in the leeway coefficient, and an explicit leeway model where the Stokes drift is provided by the wave model. Both leeway coefficients are allowed to vary in direction and time in order to perfectly reproduce the observed drifter trajectory. This creates a time series of the leeway coefficients that exactly reproduce the observed drifter trajectories. Mean values for the leeway coefficients are consistent with previous studies that utilized direct observations of the leeway. For all drifters and models, the largest source of variance in the leeway coefficient occurs at the inertial frequency and the evidence suggests it is related to uncertainties in the ocean inertial currents.

Variability in sea ice conditions, combined with strong couplings to the atmosphere and the ocean, lead to a broad range of complex sea ice dynamics. More in-situ measurements are needed to better identify the phenomena and mechanisms that govern sea ice growth, drift, and breakup. To this end, we have gathered a dataset of in-situ observations of sea ice drift and waves in ice. A total of 15 deployments were performed over a period of 5 years in both the Arctic and Antarctic, involving 72 instruments. These provide both GPS drift tracks, and measurements of waves in ice. The data can, in turn, be used for tuning sea ice drift models, investigating waves damping by sea ice, and helping calibrate other sea ice measurement techniques, such as satellite based observations.

As atmospheric models move to higher resolution and resolve smaller scales, the maximum modeled wind speed also tends to increase. Wave models tuned to coarser wind fields tend to overestimate the wave growth under strong winds. A recently developed semi-empirical parameterization of the Charnock parameter, which controls the roughness length over surface waves, substantially reduces the aerodynamic drag of waves in high winds (above a threshold of 30 m/s). Here we apply the formulation in a recent version of the wave model WAM (Cycle 4.7), which uses a modified version of the physics parameterizations by Ardhuin et al (2010) as well as subgrid obstructions for better performance around complex topography. The new Charnock formulation is tested with wind forcing from NORA3, a recently completed non-hydrostatic atmospheric downscaling of the global reanalysis ERA5 for the North Sea, the Norwegian Sea and the Barents Sea. Such high-resolution atmospheric model integrations tend to have stronger (and more realistic) upper-percentile winds than what is typically found in coarser atmospheric models. A two-year comparison (2011-2012) of a control run against the run with the modified Charnock parameter shows a dramatic reduction of the wave height bias in high-wind cases. The added computational cost of the new physics and the reduction of the Charnock parameter compared to the earlier WAM physics is modest (14%). A longer (1998-2020) hindcast integration with the new Charnock parameter is found to compare well against in situ and altimeter wave measurements both for intermediate and high sea states., Comment: 38 pages, 9 figures plus 5 appendix figures

Understanding the transport of objects and material in the marginal ice zone (MIZ) is critical for human operations in polar regions. This can be the transport of pollutants, such as spilled oil, or the transport of objects, such as drifting ships and search and rescue operations. For emergency response, the use of environmental prediction systems are required which predict ice and ocean parameters and are run operationally by many centres in the world. As these prediction systems predict both ice and ocean velocities, as well as ice concentration, it must be chosen how to combine these data to best predict the mean transport velocities. In this paper we present a case study of four drifting buoys in the MIZ deployed at four distinct ice concentrations. We compare short-term trajectories, i.e. up to 48 h lead times, with standard transport models using ice and ocean velocities from two operational prediction systems. A new transport model for the MIZ is developed with two key features aimed to help mitigate uncertainties in ice–ocean prediction systems: first, including both ice and ocean velocities and linearly weighting them by ice concentration, and second, allowing for a non-zero leeway to be added to the ice velocity component. This new transport model is found to reduce the error by a factor of 2 to 3 for drifters furthest in the MIZ using ice-based transport models in trajectory location after 48 h.

The Winter Process Cruise (WPC) aboard RV Kronprins Haakon (KH2021702) conducted observations on processes that control the position and variability of the polar front in the Northern Barents Sea and the distribution of Arctic and Atlantic water masses. Moreover, the WPC serviced 2 gateway moorings sites (M1 and M4) and collected complementary hydrographic, microstructure and current profiles to detect the winter circulation pattern and the layering structures between the two competing water masses. Meteorological measurements were also made.

Knowledge of transport in the marginal ice zone (MIZ) is critical for operations in the Arctic and associated emergency response applications, for example, the transport of pollutants, such as oil, as well as predicting drift associated with search and rescue operations. This paper proposes a general transport equation for the MIZ that can be used for operational purposes in the MIZ. This equation is designed to use a mean velocity of the ice and water velocity, which is weighted by the ice concentration. A key component is the introduction of a leeway coefficient for both the ocean and ice components. These leeway coefficients are determined by minimizing the velocity error between the transport model and observed drifter velocity in the MIZ. These leeway values are found to be 3 % of the wind for the water leeway and 2 % and 30° to the right of the wind for the ice leeway, which are consistent with "rule of thumb" values for surface drifters and sea ice respectively. This general transport model is compared with other transport models and the error is reduced by a factor of 2 compared with traditional transport models for 48 hour lead times. The inclusion of a leeway coefficient in the ice is the key component to reduce trajectory errors in the MIZ.

The Lofoten Maelstrom has been known for centuries as one of the strongest open-ocean tidal currents in the world, estimated to reach 3 m s−1, and by some estimates as much as 5 m s−1. The strong current gives rise to choppy seas when waves enter the Moskenes Sound, making the area extremely difficult to navigate. Despite its reputation, few studies of its strength exist and no stationary in situ measurements for longer time periods have been made due to the challenging conditions. By deploying for the first time in situ wave and current instruments, we confirm some previous estimates of the strength of the current. We also show that its strength is strongly connected with wave breaking. From a consideration of specific forcing terms in the dynamical energy balance equation for waves on a variable current, we assess the impact of the underlying current using a convenient metric formulated as a function of the horizontal current gradients. We find that the horizontal gradients are a likely explanation for the observed enhanced wave breaking during strong currents at a rising tide.

Following the 1st International Workshop on Waves, Storm Surges and Coastal Hazards, which incorporated the 15th session of the long-standing the International Workshop on Wave Hindcasting and Forecasting, in September 2017 in Liverpool, United Kingdom, a topical collection has appeared in recent issues of Ocean Dynamics. Here, we give a brief overview of the 15 papers published in this topical collection as well as an overview of the widening scope of the conference in recent years. The continuing trend towards closer integration between the wave and ocean modeling communities is reflected in this workshop, culminating in the renaming of the workshop, while maintaining the connection with the three-decade long history of the wave workshop. This is also seen in this topical collection, with several papers exploring wave-generated storm surge, wave-tide contributions to coastal flooding, forcing a global ocean model with fluxes from a wave model and interaction between surface waves and sea ice.

Oceanic current forcing in spectral wave models have recently been demonstrated to have a large impact on wave heights at scales between one and up to several hundred kilometers. Here we investigate the impact of such forcing on open-ocean wave heights in Northern Norway using a high-resolution spectral wave model with currents from an ocean circulation model of similar resolution. We find that the wave model, to a large extent, resolves regions identified in the Norwegian Pilot Guide for maritime navigation as having dangerous sea states due to wave–current interaction. This is in contrast to a wave model forced with surface wind fields only. We present a novel diagnostic method to map the spatio-temporal scales associated with the wave height modulation between the two wave model predictions. The method is employed to map areas where significant wave–current interaction can be expected. In many cases, we are also able to confirm the physical mechanisms reported in the Pilot Guide, which are leading to an increase in wave energy due to currents. The largest wave height differences between the two models occur when waves and currents are opposing each other. In such situations, refraction and wave blocking are the dominating effects for the swell and wind sea parts of the spectrum, respectively. Furthermore, including current forcing significantly improves the agreement with in situ observations in strong tidal currents. Here, we see an increase in significant wave height of up to 50%. Even larger relative differences, exceeding 100%, are found in sheltered areas, with one specific region showing a reduction in model errors of 18% due to refraction and advection of wave action. publishedVersion

This study investigates the effect of surface currents on wind-generated waves in a complex coastal system with narrow fjords. The simulations are based on a phase-averaged wave model forced with surface currents from a high-resolution coastal ocean and fjord circulation model, and high-resolution winds from a nested atmospheric model. Wave simulations with and without ocean forcing are evaluated by comparing integrated wave parameters and modelled spectra with observations from five wave buoys. The comparison covers three winter seasons (2017–2020) and a case study. The wind sea part of the spectrum is better simulated at all locations when using the current forcing. At the most sheltered location, where wind sea dominated the wave climate, the wave height estimates improved by 12 percentage points when including current forcing. Spectral moments and the shape of the average spectra are also improved at most of the locations when current forcing is applied. The effect of wave–current interactions was found to be more pronounced at inner locations where the relative difference of spectral bandwidth is up 5%, the difference in directional spreading is greater than 5 degrees during strong surface currents, and the relative difference in peak frequency is exceeding 10%. Our results are consequential for narrow, deep and sheltered water bodies, but are not expected to carry over to shallow water areas. publishedVersion

This study investigates the effects of wind–wave processes in a coupled wave–ocean circulation model on Lagrangian transport simulations. Drifters deployed in the southern North Sea from May to June 2015 are used. The Eulerian currents are obtained by simulation from the coupled circulation model (NEMO) and the wave model (WAM), as well as a stand-alone NEMO circulation model. The wave–current interaction processes are the momentum and energy sea state dependent fluxes, wave-induced mixing and Stokes–Coriolis forcing. The Lagrangian transport model sensitivity to these wave-induced processes in NEMO is quantified using a particle drift model. Wind waves act as a reservoir for energy and momentum. In the coupled wave–ocean circulation model, the momentum that is transferred into the ocean model is considered as a fraction of the total flux that goes directly to the currents plus the momentum lost from wave dissipation. Additional sensitivity studies are performed to assess the potential contribution of windage on the Lagrangian model performance. Wave-induced drift is found to significantly affect the particle transport in the upper ocean. The skill of particle transport simulations depends on wave–ocean circulation interaction processes. The model simulations were assessed using drifter and high-frequency (HF) radar observations. The analysis of the model reveals that Eulerian currents produced by introducing wave-induced parameterization into the ocean model are essential for improving particle transport simulations. The results show that coupled wave–circulation models may improve transport simulations of marine litter, oil spills, larval drift or transport of biological materials.

This paper investigates the performance of three different wave model source term packages in narrow fetch geometries. The packages are used to model the sea state in a complex coastal system with narrow fjords on the west coast of Norway. The modelling system is based on the Simulating WAves Nearshore (SWAN) wave model that is forced with winds from a nested atmospheric model and wave spectra from a regional wave model at the boundaries. The performances of the recent ST6, and two older SWAN white-capping and wind input packages, are evaluated by comparing modelled spectra and integrated wave parameters against five wave buoys. The comparison covers long-term statistics and two case studies of narrow fetch geometries (i) without swell and (ii) with swell-wind sea conditions. SWAN’s original saturation-based approach performs best in the fjord system. In narrow fetch geometry without swell, all packages overestimate the wave energy. ST6 shows the highest sensitivity to fetch geometry and local wind changes. The results indicate that the ST6 white-capping is too weak to balance its strong wind input. publishedVersion

Air bubble penetration depths are investigated with a bottom‐mounted echosounder at a seabed observatory in northern Norway. We compare a 1‐year time series of observed bubble depth against modeled and estimated turbulent kinetic energy flux from breaking waves as well as wind speed and sea state. We find that the hourly mean and maximum bubble depths are highly variable, reaching 18 and 38 m, respectively, and strongly correlated with wind and sea state. The bubble depth is shallowest during summer following the seasonal variations in wind speed and wave height. Summertime shallowing of the mixed layer depth is not limiting the penetration depth. A strong relationship between bubble depth and modeled turbulent kinetic energy flux from breaking waves is found, similar in strength to the relationship between bubble depth and wind speed. The wind sea is more strongly correlated with bubble depth than the total significant wave height, and the swell is only weakly correlated, suggesting that the wave model does a reasonable separation of swell and wind sea. publishedVersion

The trends in marine 10-m wind speed U10 and significant wave height Hs found in two century-long reanalyses are compared against a model-only integration. Reanalyses show spurious trends due to the assimilation of an increasing number of observations over time. The comparisons between model and reanalyses show that the areas where the discrepancies in U10 and Hs trends are greatest are also the areas where there is a marked increase in assimilated observations. Large differences in the yearly averages call into question the quality of the observations assimilated by the reanalyses, resulting in unreliable U10 and Hs trends before the 1950s. Four main regions of the world’s oceans are identified where the trends between model and reanalyses deviate strongly. These are the North Atlantic, the North Pacific, the Tasman Sea, and the western South Atlantic. The trends at +24-h lead time are markedly weaker and less correlated with the observation count. A 1985–2010 comparison with an extensive dataset of calibrated satellite altimeters shows contrasting results in Hs trends but similar U10 spatial trend distributions, with general agreement between model, reanalyses, and satellite altimeters on a broad increase in wind speed over the Southern Hemisphere.

NORA10EI, a new atmosphere and wave hindcast for the Norwegian Sea, the North Sea and the Barents Sea is presented. The hindcast uses ERA‐Interim as initial and boundary conditions and covers the period 1979–2017. The earlier NORA10 hindcast used ERA‐40 as initial and boundary conditions before September 2002 and operational analyses from the European Centre for Medium‐Range Weather Forecasts (ECMWF) in the continuation. This change in initial and boundary conditions may lead to non‐stationarities in bias and random errors, and it is a question of some concern whether this also leads to spurious trends. We investigate this by comparing the two hindcasts. We find only minor differences in the statistics of means and upper percentiles, but somewhat larger differences in the extremes (100‐year return values) of significant wave height and 10‐m winds. Generally, NORA10EI outperforms NORA10 in the ERA‐40 period (before September 2002) since ERA‐Interim outperforms ERA‐40. Conversely, NORA10 outperforms NORA10EI after 2006, since the operational ECMWF analyses here outperform ERA‐Interim. Years 2002–2006 is a transition period with minor differences between the NORA10 and NORA10EI where the resolution of ERA‐Interim is lower than that of the ECMWF analyses, but its physics are from a more recent model (2006). An important finding is that the regional hindcasts appear quite insensitive to changes in the host reanalysis with no statistically significant differences in mean and upper percentile trends of wind speed and wave height. A comparison of four polar low cases confirms that using ERA‐Interim as host reanalysis yields a slightly better representation of evolution and intensity of polar lows than NORA10 in the ERA‐40 period and the opposite after 2006. publishedVersion

A combined directional Stokes drift profile for swell and wind sea is presented. The profile can be used to calculate the shear under crossing seas and as such is relevant for Langmuir turbulence and Stokes–Coriolis forcing, but also for material advection. The swell is represented as either a monochromatic wave or as a Phillips spectrum, while the wind sea is represented as a Phillips spectrum. The profile is found to compare well against the full directional Stokes drift calculated from the 2D spectrum of ERA-Interim in an open-ocean location in the North Atlantic. The error compared to a Phillips-type unidirectional Stokes drift profile is markedly lower for a combined profile with a monochromatic swell Stokes profile. However, representing the swell as a Phillips-type Stokes drift profile yields even better results. The combined profile relies on integrated wave parameters readily available from wave models and can be calculated at low cost. The global Stokes drift climate is investigated using ERA-Interim reanalysis data with the intention of identifying regions dominated by crossing Stokes drift. We find that the eastern equatorial Pacific Ocean probably experiences the greatest degree of crossing Stokes drift, and the entire subtropical band 20°–30°S/N exhibits a significant degree of crossing Stokes drift and swell dominance over the Stokes drift.

The present work develops an innovative approach to wind speed and significant wave height extreme value analysis. The approach is based on global atmosphere–wave model ensembles, the members of which are propagated in time from the best estimate of the initial state, with slight perturbations to the initial conditions, to estimate the uncertainties connected to model representations of reality. The low correlation of individual ensemble member forecasts at advanced lead times guarantees their independence and allows us to perform inference statistics. The advantage of ensemble probabilistic forecasts is that it is possible to synthesize an equivalent dataset of duration far longer than the simulation period. This allows the use of direct inference statistics to obtain extreme value estimates. A short time series of six years (from 2010 to 2016) of ensemble forecasts is selected to avoid major changes to the model physics and resolution and thus ensure stationarity. This time series is used to undertake extreme value analysis. The study estimates global wind speed and wave height return periods by selecting peaks from ensemble forecasts from +216- to +240-h lead time from the operational ensemble forecast dataset of the European Centre for Medium-Range Weather Forecasts (ECMWF). The results are compared with extreme value analyses performed on a commonly used reanalysis dataset, ERA-Interim, and buoy data. The comparison with traditional methods demonstrates the potential of this novel approach for statistical analysis of significant wave height and wind speed ocean extremes at the global scale.

Accurate predictions of surface ocean waves in coastal areas are important for a number of marine activities. In complex coastlines with islands and fjords, the quality of wind forcing significantly affects the results. We investigate the role of wind forcing on wave conditions in a fjord system partly exposed to open sea. For this reason, we implemented the wave model SWAN at the west coast of Norway using four different wind forcing. Wind and wave estimates were compared with observations from five measurement sites. The best results in terms of significant wave height are found at the sites exposed to offshore conditions using a wind input that is biased slightly high compared with the buoy observations. Positively biased wind input, on the other hand, leads to significant overestimation of significant wave height in more sheltered locations. The model also shows a poorer performance for mean wave period in these locations. Statistical results are supported by two case studies which also illustrate the effect of high spatial resolution in wind forcing. Detailed wind forcing is necessary in order to obtain a realistic wind field in complex fjord terrain, but wind channelling and lee effects may have unpredictable effects on the wave simulations. Pure wave propagation (no wind forcing) is not able to reproduce the highest significant wave height in any of the locations.

The Lagrangian Analysis Tool (LAGRANTO) is adopted and applied to ECMWF’s latest ocean reanalysis. The primary motivation behind this study is to introduce and document LAGRANTO Ocean (LAGRANTO.ocean) and explore its capabilities in combination with an eddy-permitting ocean reanalysis. The tool allows for flexibly defining starting points, within circles, cylinders, or any user-defined region or volume. LAGRANTO.ocean also offers a sophisticated way to refine a set of computed trajectories according to a wide range of mathematical operations that can be combined into a single refinement criterion. Tools for calculating—for example, along-trajectory cross sections or trajectory densities—are further provided. After introducing the tool, three case studies are presented, which were chosen to reflect a selection of phenomena on different spatial and temporal scales. The case studies also serve as hands-on examples. For the first case study, at the mesoscale, ocean trajectories are computed during the formation of a Gulf Stream cold-core ring to study vertical motion in the developing eddy. In the second example, source waters are traced to the East Greenland Spill Jet. This example highlights the usefulness of a Lagrangian method for identifying sources or sinks of buoyancy. The third example, on annual time scales, focuses on the temporal evolution of extreme potential temperature anomalies in the South Pacific and the memory of the involved water parcels. Near-surface trajectories reveal that it takes approximately 5 months after the highest temperature anomaly before the involved water parcels cool to their climatological mean values at their new positions. LAGRANTO.ocean will be made publicly available.

In contrast to deep water waves, shallow water waves are influenced by bottom topography, which has consequences for the propagation of wave energy as well as for the energy and momentum exchange between the waves and the mean flow. The ERA-Interim reanalysis is used to assess the fraction of wave energy associated with shallow water waves in coastal regions in Europe. We show maps of the distribution of this fraction as well as time series statistics from eight selected stations. There is a strong seasonal dependence and high values are typically associated with winter storms, indicating that shallow water wave effects can occasionally be important even in the deeper parts of the shelf seas otherwise dominated by deep water waves.

The effects of Langmuir mixing on the surface ocean mixing may be parameterized by applying an enhancement factor which depends on wave, wind, and ocean state to the turbulent velocity scale in the K -Profile Parameterization. Diagnosing the appropriate enhancement factor online in global climate simulations is readily achieved by coupling with a prognostic wave model, but with significant computational and code development expenses. In this paper, two alternatives that do not require a prognostic wave model, (i) a monthly mean enhancement factor climatology, and (ii) an approximation to the enhancement factor based on the empirical wave spectra, are explored and tested in a global climate model. Both appear to reproduce the Langmuir mixing effects as estimated using a prognostic wave model, with nearly identical and substantial improvements in the simulated mixed layer depth and intermediate water ventilation over control simulations, but significantly less computational cost. Simpler approaches, such as ignoring Langmuir mixing altogether or setting a globally constant Langmuir number, are found to be deficient. Thus, the consequences of Stokes depth and misaligned wind and waves are important.

Understanding climate-driven impacts on the multivariate global wind-wave climate is paramount to effective offshore/coastal climate adaptation planning. However, the use of single-method ensembles and variations arising from different methodologies has resulted in unquantified uncertainty amongst existing global wave climate projections. Here, assessing the first coherent, community-driven, multi-method ensemble of global wave climate projections, we demonstrate widespread ocean regions with robust changes in annual mean significant wave height and mean wave period of 5–15% and shifts in mean wave direction of 5–15°, under a high-emission scenario. Approximately 50% of the world’s coastline is at risk from wave climate change, with ~40% revealing robust changes in at least two variables. Furthermore, we find that uncertainty in current projections is dominated by climate model-driven uncertainty, and that single-method modelling studies are unable to capture up to ~50% of the total associated uncertainty.