5th workshop on waves and wave-coupled processes

Drag at the ocean's surface depends on the sea state and the angle between the wind and the direction of propagation of swell. Misalignment cannot be accounted for without information about the wave field, and it is not represented in parametrizations of surface exchange suitable for use in uncoupled atmospheric models. Observations and large-eddy modelling with an imposed surface wave field suggest that the drag is higher in opposing swell than in following swell. Parametrizations of this effect, wherein the aerodynamic roughness length depends on the misalignment between the wind and waves, are beginning to appear. Here, we present initial experiments on representing the drag as a combination interfacial drag from short waves and form drag from longer waves in coupled atmosphere-wave model. The impact of the scheme is assessed in simulations of a tropical cyclone and comparisons with parametrizations based on a modified aerodynamic roughness length are made.

This study employs ERA5's 10-meter wind field as the driving force and conducts a one-year hindcast experiment using the WAVEWATCH 3 wave model. Validation results based on buoy observations in the coastal waters of China indicate an underestimation of significant wave height in the Bohai Sea, Yellow Sea, and the beibu gulf. This underestimation is found to be correlated with atmospheric instability.
A multivariate nonlinear regression model is constructed using ERA5's 10-meter wind speed, 2-meter air temperature, sea surface temperature, water depth, and significant wave height error. Regression analysis is performed, and this model is added as a correction term to the source term of the WAVEWATCH 3 wave model. Using the modified model, a one-year hindcast experiment is conducted. Buoy validation results show that the added correction term effectively alleviates the underestimation of significant wave height and improves the overall simulation accuracy.

In the Arctic Ocean where summer sea ice extent is reducing year by year, the open water area along the coast enables merchant ships to navigate across the Arctic Ocean. The Arctic Shipping Route (ASR) is expected to develop in the coming decades, but the waves developed in the open water may impose difficulty on the ships. For example, ice loads of drifting ice floe under waves can become a threat to the merchant ships. Moreover, waves may break the ice floes in the Marginal Ice Zone (MIZ) and alter the Floe Size Distribution (FSD). FSD is one of the crucial parameters for ships navigating in the Arctic Ocean.
Under the Japanese government-supported project Arctic Challenge for Sustainability II (ArCSII), we have developed regional wave forecast models and regional ice-ocean forecast models and assisted the yearly summer and autumn R/V Mirai cruises from 2020 to 2023 in the Chukchi and Beaufort Seas. Wave buoys were deployed in these cruises for validation of the wave models among other observations conducted under ArCSII.
The wave model based on NOAA WaveWatchIII is called the TodaiWW3-ArCS2 and is implemented in the domain including the Chukchi Sea and the Beaufort Sea. The horizontal resolutions of the two-tiered nested model are 16km and 8km, and the forecast is made for 5 days. The wave field is forced by ECMWF forecast wind and AMSR2 sea ice concentration (SIC). Numerous experimental studies using the same model revealed that the largest uncertainty in forecasting waves in the open water is the location of the ice edge and not necessarily the wave-ice interaction physical parameterization. Sometimes, the ice edge (defined as SIC=0.15 for example) may vary a lot depending on the products despite they are all based on the same AMSR2 satellite data. Therefore, an ensemble model run was made forcing the model with different ice fields.
Noting that the satellite radiometer-based SIC has a large uncertainty, we have forced the regional sea ice model by assimilated mode outputs. The sea-ice-ocean coupled model is called the Ice-POM and was developed by Yamaguchi’s group at the University of Tokyo (De Silva et al. 2020). The ocean model uses the Princeton Ocean Model (POM) and is coupled with an in-house Elastic-Viscous-Plastic model. In this project, the Ice-POM was upgraded. It is initialized by RIOPS ocean and ice fields. The ocean interior is nudged to RIOPS outputs, and the ice field is given by RIOPS SIC. The model is forced by ECMWF forecast atmospheric parameters. The model's horizontal resolution is 2.5 km and forecasted for 10 days. The fine resolution was chosen to meet the requirements of the ship navigation support. Sensitivity to wind products was tested by comparing ERA5 and ECMWF forecast wind, where the former gave a better estimate. Concurrently, we have developed a ROMS-based ice-ocean coupled model using the Budgell ice model. Both the ocean and atmospheric forcing fields are given by GIOPS. The horizontal resolution is 3 to 5 km. The ocean interior is nudged to GIOPS.
For assisting R/V Mirai cruise, both the TodaiWW3-ArCS2 and the ICE-POM were run on GCP (Google Cloud Platform) and via a telecommunication system developed by the National Institute of Polar Research called VENUS. The forecast data was sent to R/V Mirai at regular intervals.
The goal of this research is to assist ships navigating in the Arctic Ocean. Among the various sea ice parameters, floe size distribution is one of the key variables. The floe size distribution is known to change dramatically due to ice breakup by waves. For that, a fully coupled wave-ice model is necessary. However, the quality of the coupled model estimate is questionable because of the large uncertainty in the sea ice concentration. Even defining the MIZ is difficult. On the other hand, low-ice concentration areas are not important for polar class ships. In support of the Arctic Shipping Route, we need to know both the engineering requirement and the oceanographic capability and find a compromised solution.

Climate models do not include ocean surface waves when modelling the interactions between air or sea-ice and the ocean, or they do so in an implicit way whereby a certain sea state is assumed. As a result, sea roughness associated with storms is underestimated. We include explicit calculations of sea-state and its effects on air-sea fluxes in the Norwegian Earth System Model (NorESM). We show that on climate time-scales, the net effect tends to differ from those typically seen in operational forecasts. In particular, two-way coupling between dynamic sea-state and the atmosphere leads to a warmer simulated climatology in the Arctic.

Prior research has suggested that swells could potentially induce turbulence, contributing to ocean mixing. However, detecting such contributions in field experiments may pose challenges. In this study, we employed two sets of machine learning models to simulate sea surface temperature (SST) diurnal warming and cool skin – processes strongly influenced by surface mixing. We experimented with various input parameters, including wind speed, solar radiation, relative humidity, SST, sea surface temperature, and significant wave height (SWH). Our findings indicate that most known influential input parameters enhance the modeling accuracy of these surface processes. Interestingly, when wind is included as an input, the addition of SWH does not appear to improve modeling accuracy, suggesting that the contribution of swells to surface mixing may be relatively weak.

Varying currents and depths are decisive for the propagation path of ocean waves. According to the theory of geometric optics, these paths can be computed by a coupled set of equations – the wave ray equations. Here we present an open-source numerical solver of the ray equations in Python. Such tools are very helpful in order to quantify the non-local impact by wave refraction on wave heights; they are particularly valuable in wave-current interaction studies because of the spatio-temporal variability of currents. The model is verified against analytical solutions, equipped with a proper test framework, and accompanied by a set of ancillary functions which are considered useful for the user-community.

Ambient currents govern the horizontal wave field variability and may cause significant modulations to the sea state. Such modulations can be decisive in some contexts, particularly in coastal areas due to the presence of man-made structures, coastal erosion, and their implication for ship navigation, among others. In an operational wave forecasting perspective, however, spectral wave models rarely include ocean currents as forcing. Here I assess why such forcing is usually left out, and highlight some of the challenges that are associated with including it. The work is largely based on recent studies in the coastal region surrounding Northern Norway; here, a bouquet of coexisting energetic current regimes, at different spatio-temporal scales, modulate the wave field simultaneously. The region includes one of the strongest open ocean tidal currents – namely the Lofoten Maelstrom – which significantly modulates the sea state, also including the expected extreme waves.

A buoy network from the Mexican Consortium for Research in the Gulf of Mexico (CIGoM) was implemented and operated between 2016 and 2019. A detailed description and main characteristics of sensors deployed in three spar buoys (BOMM) is given. We aim to better understand the ocean-atmosphere momentum flux under non-equilibrium conditions, specifically when sudden wind changes occurred typically associated with atmospheric fronts passages over the region of interest. The influence of swell is analyzed in detail for cases when locally generated waves are being developed under moderate wind speeds. Wind stress is analyzed under a reference frame oriented with the main wave propagation which not always is the mean wind direction. A better description is achieved for the relative importance of turbulent associated and wave coherent wind stress components. A polynomial fitting is used in order to describe the influence of swell significant wave height. A novel parametrization is advanced for a potential use in numerical ocean-atmosphere coupled models.

Ocean surface gravity waves play an important role for the air-sea momentum fluxes and the upper ocean mixing. However, including the Stokes drift, in phase-averaged equations for the Eulerian mean oceanic motion leads to an Eulerian energy budget which is physically difficult to interpret. Here, we show that a Lagrangian energy budget allows for a closed energy budget, in which all terms connecting the different energy compartments correspond to well known energy transfer terms. The Lagrangian energy budget is used to discuss an energetically consistent framework which can be used to couple a general circulation ocean model to a surface wave model. In this framework, the energy provided by the surface wave model is split-up into energy driving mean motions and turbulence in a consistent manner.

Surface waves play an important role in the upper ocean mixing. Laboratory experiments and field observations were carried out to investigate surface wave-turbulence interactions. In laboratory, three kinds of experiments, only mechanical waves, only grid-stirring turbulence, and grid-stirring turbulence with mechanical waves, were conducted in wave tank. The water velocity was measured by the acoustic Doppler velocimeter (ADV). Comparisons among three experiments show that the turbulence was modulated by surface waves and enhanced for the experiment with grid-stirring turbulence and mechanical waves. Field observations was conducted at a marine meteorology tower in South China sea. Three ADVs were attached to the tower at vertical intervals of 1.5 m, with the upper ADV at 2.6 m below the mean water level. Soon after the instruments were installed, a typhoon (Rammasun) passed by the observed area. Results from Holo-Hilbert Spectral Analysis (HHSA) method show that high frequency turbulence is modulated by and interacting with the surface waves. The modulation is strong at the phase of wave trough.

Wave models represent the physical processes that are acting on the wave field, such as input by wind and dissipation by wave breaking. The complex nature of those processes and multitude of scales involved prevent a full description of those processes based on first principle. For these reasons, we usually rely on simplified representations involving parameterisation based on empirical data. These empirical data are generally gathered over the oceans or low altitude lakes.

Lake Titicaca is a large freshwater lake in the Andes mountains on the border of Bolivia and Peru. It has a surface elevation of 3,812 m. At that altitude, air density is about 64% lower than at mean sea level. For this reason, Lake Titicaca might be a nice test case for the parameterisations used in wave models.

Using ecWAM, we have simulated the wave conditions during a short period during which observations from a spotter buoy recently deployed in the Bolivian sector was recovered.
Experimental setup and preliminary results will be discussed.

Ocean waves and sea ice properties are intimately linked in the marginal ice zone (MIZ), nevertheless a definitive modelling paradigm for the wave attenuation in the MIZ is missing. The evolution of wave directional properties in the MIZ is a proxy for the main attenuation mechanism but paucity of measurements and disagreement between them contributed to current uncertainty.
In this talk we show that viscous attenuation, i.e. the main dissipative mechanism in the MIZ, tilts the mean wave direction orthogonal to the sea ice edge and the narrows directionality, in qualitative agreement with recent observations from the Arctic. Tilting away from the normal direction can occur in bimodal sea states. The analysis highlights the need for high quality directional measurements in the field to reduce uncertainty in the definition of the attenuation rate.

TBC

TBC

The project’s goal is to develop a limited area mode (LAM) for the ICON-WAVES model. The ICON-WAVES development is an
integral part of project “Earth System Model on the Weather Scale” (ESM-W) in cooperation with the GeoInfoDienst BW. The
Limited Area Mode (LAM) of a numerical weather prediction model provides a high-resolution weather resolution weather
forecast for a specific region of the earth. While the global weather forecast model simulates the entire earth's atmosphere.
LAM concentrates on a limited region of the globe with a much finer spatial resolution. The main aim of ICON-WAVES
regionalization is to is to expand the scope of the of wave modelling system for high-resolution predictions.

Coupling of component models in an earth system environment has a long history,particularly at the European Center for Medium-Range Weather Forecasts (ECMWF) with a long history of coupled wind-wave and weather models. With the increased understanding of such component models, and the increase of computing power, coupling of component models is becoming more and more important. At the National Oceanographic and Atmospheric Administration (NOAA) this is evidentin the drive to move to a Unified Forecast System (UFS), which in principle is a set of applications at various scales with coupled environmental model ensembles. Implicit to the first moves towards a UFS approach is a coupling strategy, which is continuously evolving as our experience with the UFS increases. The present paper describes this evolution with three foci: 1) the UFS design including coupling principles used, including practical progress toward the UFS, 2) coupling a wave model inside an ensemble UFS using a systematic assessment of wave model responses to its external drivers, and 3) design ideas for future coupling strategies in the UFS.

Acoustic radiation in the atmophere (microbaroms) and ocean (microseisms) can be diagnosed from the directional wave spectrum (Hasselmann 1963, Brekhovskikh et al. 1973). Recent advances in parameterization of wave dissipation have led to a much better representation of underwater acoustic noise variability up to 2 Hz (Alday and Ardhuin 2023). We discuss how acoustic observations in the ocean and the atmosphere can be used to better constrain the acoustic source and the shape of the directional wave spectrum. This work is a preliminary step for a broader proposal that relies on the sensitivity of microbarom propagation to stratospehric winds, in order to help monitor the stratospheric circulation. Other applications include the analysis of 20th century wave climate using microseism observations.

In the last decades, the polar regions are becoming an increasing focus in the climate science community. There is substantial evidence that the two-way interactions between waves and sea ice are important for the climate and weather system across various time scales, from short-range to seasonal. For the most part, however, they are lacking from our operational prediction systems. This work focuses on the implementation of two-way wave-sea ice interactions within the Integrat-ed Forecasting Model (the ECMWF Earth System Model, hereafter referred to as the IFS). Two physical coupling are implemented and explored here. The first is that of wave induced sea ice breakup. Waves can break up the ice through oscillation and flexural failure of the ice. The state of the sea ice (i.e. broken or solid) then defines two clear attenuation regimes, with solid ice attenuat-ing strongly, and broken ice attenuating more weakly. Kousal et al. (2022) implemented this logic within the WAVEWATCH III spectral wave model to form a simple coupled wave-sea ice model (assuming the sea ice takes a binary form of broken or solid), thereby allowing for coupled feedback effects, and showed that such a model can well represent break up of the sea ice as well as wave attenuation in the MIZ. In this work, we build on that of Kousal et al. (2022), except in-stead of using a simple sea ice model, we use the thermodynamic sea ice model SI3 within the IFS. These are coupled through the aforementioned binary ice breakup field. We also consider the fol-lowing: the broken ice is able to heal itself based on a characteristic recovery time scale; the ice breakup field can be advected; this ice breakup translates to a weakening of the internal strength of the sea ice. The second physical coupling we explore is that of wave-radiative stresses, the force that pushes the sea ice in the direction of the propagation of the attenuated waves. Some prelimi-nary results will be presented.
Kousal, J., J. J. Voermans, Q. Liu, P. Heil, A. V. Babanin (2022). A Two-Part Model for Wave- Sea Ice Interaction: Attenuation and Break-Up, Journal of Geophysical Research: Oceans. DOI: 10.1029/2022JC018571

The medium range weather deterministic forecast model for NCEP is the Global Forecast System. The operational version (GFSv16) is one-way coupled from the atmospheric model, which uses the finite volume cubed sphere dynamical core FV3 to the wave model, WAVEWATCH III. The next version, GFSv17, will include two new components, the MOM6 ocean model and the CICE6 ice model. The wave model will have input from the atmosphere, ocean, and ice components and feedback to the atmosphere and ocean components. Another major planned upgrade is moving to unstructured grids, which will allow for improved scalability and additional resolution as desired. This presentation will provide a status update on the wave component in GFSv17 and how it is impacting the fully coupled forecasts.

The wave ocean plays an important role in momentum and energy transfer at the air-sea interface. We have studied wave impact on global and regional scale weather and climate modeling.
Wave-dependent surface roughness was implemented within the Atmospheric GCM (MRI-AGCM) using the WAVEWATCH III (WW3) for the global climate impact. Two types of wave-dependent roughness, due to wave steepness and wave age, were considered. Climate simulations with wave-dependent roughness were compared to simulations with just wind speed-dependent roughness. We find that the reduced roughness and the enhanced wind speeds in the tropics lead to significant changes in atmospheric circulation.
For the short- to medium-range forecasts, the systematic impacts of wave-dependent momentum flux on typhoon characteristics were estimated by analyzing the 100 historical typhoons in the western North Pacific by the MRI-AGCM with the WW3 coupling system. The wave-dependent momentum flux can significantly impact typhoon development at the early developing stage, not the most developed stage.
Furthermore, the parameterization of the sea surface turbulent kinetic energy (TKE) flux due to wave breaking was revisited using the observed data and applied fully coupled regional atmosphere and ocean system (COAWST). It is found that the fraction of wave energy taken up into the ocean as sea surface TKE flux depends on the relative angle between wind and wave direction. The experiments on typhoon hindcast using the model showed that TKE flux affects weak mixing at the ocean surface, strong mixing at the bottom of the mixed layer, and near-inertial internal waves depending on the thickness of the mixed layer depth (MLD). The results of this study suggest the importance of considering waves in the sea surface TKE flux for typhoon simulations.

Waves fall thematically somewhere between physics, meteorology and oceanography. Too small-scale to be the concern of traditional deep-blue oceanography, too wet to be considered boundary layer meteorology, and too "physical" to be considered oceanography. However, their impact on the ocean interior and their feedback to the atmosphere through mechanical and thermodynamical processes (i.e., roughness and temperature) make them an essential, but often overlooked component of the coupled atmosphere-ocean-ice system.

Traditionally, the models used to forecast waves have also been quite separate from the model systems of the ocean and the atmosphere. The big exception to this is ECMWF's IFS which, since 1998, has modelled the atmosphere and the wave field as a tightly coupled system. The next big step came in 2013 when the wave model was also coupled to the ocean component of the IFS. Their impact on climate simulations is also slowly coming into focus.

Here I will review the different physical processes that connect surface waves to the ocean interior and the lower atmosphere and I will present how these are typically modelled. I will also present some (personal) views on the evolution of the field of wave modelling and where I think we wave modellers ought to put our effort in an era dominated by machine learning methods.

Progress in operational wave forecasting is described in the context of the fundamental law for wave prediction: the energy balance equation. This equation gives the rate of change of the sea state caused by adiabatic processes such as advection and refraction, and by the physical source functions of the generation of ocean waves by wind, the dissipation due to e.g. white- capping, and the nonlinear four-wave interactions. Improvement in ocean wave forecasting skill is illustrated by comparing forecast results with buoy observations and Altimeter observations over the course of the past twenty years.
Traditionally, wave forecasting has given tremendous benefits for practical applications such as ship routing, fisheries, coastal protection and offshore operations. However, there are additional benefits from wave forecasting. Knowledge of the sea state is essential for a consistent momentum, and heat balance at the sea surface. Clearly, as follows from the energy balance equation, there is a mutual interaction between atmosphere, ocean waves and ocean circulation which affects momentum, heat and moisture transfer across the air-sea interface. That is, on the one hand, ocean waves receive energy and momentum from the atmosphere through the wind input, while on the other hand, through the process of white capping, the ocean waves transfer energy and momentum to the ocean, thereby feeding the turbulent and large-scale motions of the oceans. Furthermore, the wave-induced motion in the atmospheric surface layer resembles essentially the effect of (turbulent) eddies, thus affecting the transport of heat and moisture from ocean to sphere. This suggests that it is of considerable interest to develop a coupled atmosphere-ocean circulation system where the ocean waves are the agent that transfers energy, momentum and heat across the air-sea interface. Some of the benefits of such an operational coupled atmosphere-ocean model will be discussed.
At ECMWF we have gathered quite some experience with coupled modelling over the past 25-30 years. Initially, we introduced operationally a simple coupled atmosphere, ocean wave system in June 1998. This system considered only the slowing down of the atmospheric surface layer by the growing wind waves. In those days the wave model resolution was 55 km, while the atmospheric model had a resolution of 40 km. A considerable amount of effort was spend on improving the physics of the wave model and on utilising Altimeter and SAR data in the analysis. In June of 2018 there was a significant upgrade of the ECMWF forecasting system by the introduction of the ocean circulation model NEMO.
In Autumn 2024 a major upgrade of the air-sea interaction part of the ECMWF forecasting system is expected. This new system will explicitly determine the momentum loss to the gravity-capillary waves. It will also introduce a nonlinear wind input source function, which reduces the momentum loss from atmosphere to ocean waves for strong winds, therefore producing stronger, more realistic hurricanes. In addition, both the atmospheric and the wave model will have a resolution of 9 kilometers, while the ocean circulation model has a resolution of 0.25 degrees.

A long-standing issue with ECMWF surface wind speeds is their permanent underestimate in coastal areas. This implies an extended use of correction factors, also in large inner areas as the Mediterranean Sea.
Our attention is on a three-month active wind period, in the Mediterranean and southern North Sea, exploring ECMWF and U.K. Met Office models results. The comparison is versus scatterometer data till 200 km off the coast. The main results are the following:
a) for land to sea blowing winds, the ECMWF TCo1279 model underestimates the surface wind speeds by 10-15% at the coast, approaching correct values at about 200 km offshore.
b) the error is model resolution dependent, substantially larger and longer-lasting the coarser the resolution, e.g. for the ERA5 reanalysis (31 km resolution).
c) the Met Office model leads to much higher wind speeds, even in excess with respect to the scatterometer data, but with similar dependence on resolution,
d) there are strong suggestions that, moving towards offshore, the error is associated to the number of correspondingly involved model grid steps,
e) the ECMWF errors strongly depend on the orography at the coast the wind blows from. The higher and rougher the orography, the stronger the wind underestimate,
f) if on land no orographic surface drag is considered, the coastal wind values are independent on model resolution,
g) a vertical section of the 200 km inland – 200 km offshore areas highlights the crucial role of gravity waves in shaping the surface wind structure at the coast.

As ocean numerical models and satellite constellations significantly improve their spatiotemporal resolution, new challenges emerge for data quality control and understanding ocean dynamics at finer scales. Historically, ocean buoys remain to be one of the principal sources of in situ measurements. However, the substantial size and cost of “traditional” solutions restrict the feasibility of widespread, dense deployments. Moreover, directly comparing satellite-based surface observations with moored or drifting buoys poses difficulties due to mismatches in sampling rates, resolution, coastal effects, etc.
To overcome these limitations, the Miniaturized Electronics Lagrangian Oceanographic DrIfter (MELODI) project aims to propose compact, cost-effective and flexibly configurable drifters for short and long-term ocean monitoring. Lightweight buoys less than 1 kg in weight and 25 cm in diameter equipped with multiple onboard sensors (GPS, gyroscope, accelerometer, temperature, and air-pressure sensors) enable precise measurements of wave spectra, sea surface currents, water temperature, air pressure, and wind speeds. Two-way satellite communication, along with efficient data compression techniques, allows real-time data transmission and adaptive sampling modes. Using eco-friendly biodegradable hulls mitigates microplastic pollution risks. Special attention was paid to implementing effective localized industrial fabrication processes to reduce the time, costs and carbon footprint of series buoy production.
In the present work, we demonstrate MELODI's capabilities and report validation results from multiple Mediterranean and North Atlantic deployments. A total of 20 buoys were deployed in different locations to synchronously measure key variables of the upper ocean layer. The low buoy hull profile minimizes the wind impact on the buoy drift and allows for providing precise sea surface total current measurements. Also, the small diameter of the buoy enables high-frequency wave spectra estimates and tracking of their temporal evolution. We also propose a discussion on the new experimental opportunities enabled by small, inexpensive, drifter networks, including high-resolution studies of sea waves, boundary layer processes and coupling effects.
In summary, this work promotes readily deployed drifter networks serving diverse needs from emergency response to modelling and satellites. We expect that the proposed solution will significantly contribute to developing and implementing a robust, highly accessible network of observational drifting buoys for ocean monitoring.

We will discuss the dissipation of wave energy by sea ice in numerical models. Estimates of this quantity using observational data vary widely, based on environmental (e.g. wave, ice) conditions, observation methods, and estimation methods, all of which are, in turn, remarkably inconsistent.

We start by describing our recent paper (1), in which we estimated the frequency-dependent rate of dissipation by sea ice using a model-data inversion method, applied to an extensive observational dataset collected in the Southern Ocean north of the Ross Sea during late autumn to early winter. The resulting dataset, with 9477 dissipation frequency-profiles, is the most extensive and detailed dissipation rate dataset computed thus far, and the data are available for download by other researchers (2).

Next, we describe the work by (3) and (4) in which these new dissipation profiles are used to create a new empirical method for estimating dissipation with dependency on both frequency and ice thickness. This is a relatively simple monomial fit, with a constraint on the relation between the power dependence on the frequency and that on the ice thickness. This constraint is derived in (3) by invoking the scaling from (5), which is based on Reynolds number with ice thickness as the relevant length scale. The “scale collapse” in this new method significantly reduces the discrepancy between estimates from large-scale field experiments, small-scale field experiments, and lab experiments, as reported most recently by (6).

The new method is implemented in the widely used numerical wave models SWAN (7) and WAVEWATCH III (8), and both are optional model components in the U.S. Navy's regional coupled modeling system. We briefly present preliminary applications from this system.

As time permits, we will present other, recent advances in coupled wave/ice modeling.

References
(1) https://doi.org/10.1016/j.coldregions.2020.103198
(2) https://data.mendeley.com/datasets/5b742jv7t5/1
(3) https://doi.org/10.48550/arXiv.2104.01246
(4) https://doi.org/10.1016/j.coldregions.2022.103582
(5) https://doi.org/10.1029/2018JC014870
(6) https://doi.org/10.3390/jmse10101472
(7) https://swanmodel.sourceforge.io/online_doc/swantech/node21.html
(8) https://github.com/NOAA-EMC/WW3/tree/develop

Ocean surface waves have been demonstrated to be an important component of coupled earth system models. They affect atmosphere-ocean momentum transfer, break ice floes, alter CO2 fluxes, and impact mixed-layer depth through Langmuir turbulence. In contrast to the goals of third-generation spectral models, the wave information needed for mixing, air-sea, and wave-ice-coupling is much less than a full directional wave spectrum. All present parameterizations -- for wave-induced mixing, surface drag, floe fracture, or sea spray  -- use primarily the wave spectrum's dominant frequency, direction, and energy or quantities that can be estimated from these such as Stokes drift and bending moments. Modest errors in sea state do not strongly affect the impacts of these parameterizations. This minimal data and accuracy need starkly contrasts with the computational costs of spectral wave models as a component of next-generation Earth System Models (ESM).

We here describe an alternative, cost-efficient wave modeling framework for air-sea interaction to enable the routine use of sea state-dependent air-sea flux parameterization in ESMs. In contrast to spectral models, the Particle-in-Cell for Efficient Swell Wave Model (PiCLES) is constructed for coupled atmosphere-ocean-sea ice modeling. Combining Lagrangian wave growth solutions with the Particle-In-Cell method leads to a periodically meshing model on an arbitrary grid that scales in an embarrassingly parallel manner. The set of equations solves for the growth and propagation of a parametric wave spectrum's peak wavenumber and total wave energy, which reduces the state vector size by a factor of 50-200 compared to spectral models. We estimate PiCLES's computational costs about 3-5 order of magnitude faster then established wave models with sufficient accuracy for ESMs -- rivaling that of spectral models in the open ocean. We will evaluate PiCLES against WaveWatch III in efficiency and accuracy and discuss planned extensions of its capability in ESMs.

Air-sea fluxes of sensible and latent heat are fundamental to the energetics of tropical cyclones (TCs) and their intensity. In high winds (i.e., 10-m windspeed U10 ≳ 20 m s-1), sea spray droplets ejected from breaking waves provide pathways for heat transfer (i.e., droplet cooling and evaporation) that are not represented in the bulk heat flux algorithms widely used in TC forecast models. Sea spray generation and heat fluxes are controlled by complex interactions at breaking wave crests and in the spray-laden atmospheric surface layer. However, co-located in situ measurements of high-wind spray generation and air-sea heat fluxes, as well as the wind, wave, and turbulent upper ocean conditions that produce them, are extremely limited. Advancement of seastate-dependent algorithms for air-sea heat fluxes with spray through improved model physics and observational constraint presents an opportunity to improve coupled atmosphere-wave-ocean model forecasts of extreme events (e.g., TCs and extratropical cyclones) at both regional and global scales.

Recent work has produced a new parameterization for seastate-dependent air-sea heat fluxes with spray for use in fully coupled atmosphere-wave-ocean TC forecast models (Barr et al. 2023). TC model simulations testing the new parameterization demonstrate a consistent influence of spray on TC intensity that is explainable by the physics of droplet cooling and evaporation that the parameterization represents. In the current work, we incorporate this parameterization into the Coupled Ocean-Atmosphere Response Experiment (COARE) air-sea heat flux algorithm and constrain the model physics using high-wind in situ measurements of direct covariance heat fluxes and conditions at the air-sea interface. Observations come from diverse field campaigns and sites, including the CLIVAR Mode Water Dynamic Experiment (CLIMODE), the Salinity Processes in the Upper-ocean Regional Study (SPURS) 1 and 2, and multi-year measurements from the NSF Ocean Observatories Initiative (OOI) Pioneer, Endurance, and Irminger Sea Arrays. We compare the updated algorithm with spray to earlier versions without spray and demonstrate the divergent outcomes of extrapolating the models past the observed range of U10. This work highlights the need for systematic, long-term, and simultaneous observations of winds, waves, spray, and heat fluxes in high winds as well as additional laboratory, theoretical, and numerical studies to understand the complex mechanics of wave breaking and spray generation at the air-sea interface.

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). Furthermore, the sensitivity of the cyclone simulations to the misalignment between wind and stress direction caused by waves is investigated based on idealised simulations.

Atmospheric fronts embedded in extratropical cyclones are critical high-impact weather phenomena contributing significantly to midlatitude winter precipitation. The three crucial characteristics of the atmospheric fronts, high wind speeds, abrupt veering, and rapid translation, force the induced surface waves to be strongly misaligned with winds preferentially behind the cold fronts, whose effects on parameterized air-sea fluxes remain poorly understood. Using the multi-year in situ near-surface observations and direct covariance flux measurements from the Pioneer Array off the coast of New England, we find that the majority (by up to 90%) of the passing cold fronts generate misaligned waves behind the cold front. Once generated, the waves remain misaligned for up to 8 hours, during which the fully-coupled model simulations indicate that the misaligned waves significantly increase wave roughness length (300%), drag coefficient (20%), and momentum flux (10%), thereby weakly reducing surface wind speeds and upward turbulent heat fluxes. The reduction in the heat fluxes is despite the moderate increase in the exchange coefficient. These surface-layer responses are detected over the vast areas behind the cold front, comparable to the lateral extent of extratropical cyclones of 1000s km. The misaligned wave effect is not accurately represented in advanced wave-based bulk flux algorithms. Yet, the suggested modification to the current formulation improves the overall accuracy of parameterized air-sea flux estimates. The results imply that better representing a directional wind-wave coupling in the bulk formula of the numerical models may help improve the air-sea interaction simulations under the passing atmospheric fronts in the mid-latitudes.

Energetic waves originating from the Southern Ocean can propagate great distances into the Antarctic ice pack. Along the way, they can significantly alter the composition of the ice whilst, at the same time, sea ice can significantly alter the characteristics of the wave field. Importantly, sea ice attenuates wave energy, thereby reducing their capacity to break the ice. Understanding of the rate of attenuation of wave energy in sea ice is thus critical to achieve accurate representation of sea ice in operational forecasting models. Observations of wave attenuation are, however, sparse as logistics to the harsh and remote Antarctic Marginal Ice Zone are limited. To this end, satellite remote sensing provides significant opportunities as it can cover large spatial areas, albeit at relatively low temporal resolution.
Recent studies have shown the capabilities of ICESat-2 to measure surface height over land, ocean and sea ice at high accuracy. Here, we use the quality-controlled data of Brouwer et al. (2022) to estimate the wave attenuation rate from ICESat-2 observations. We show that the magnitude of the estimated attenuation rates from ICESat-2 observations are largely consistent with those observed by others. As ICESat-2 provides a near-instantaneous snapshot of waves in sea ice, the data reveals unique spatial resolution of the attenuation rates across the Marginal ice Zone that cannot easily be obtained with surface buoys. Spatial variability of the estimated attenuation rates appears to be correlated with sea ice properties obtained from satellite derived products, such as sea ice thickness and sea ice concentration.

Surface water waves play an important role in modulating air-sea fluxes, hence influencing upper ocean dynamics and mixing. The inclusion of wave-induced processes in Earth System Models has increasingly been recognized to reduce systematic model biases. Wave-induced effects such as Langmuir Turbulence (LT) have been shown to improve the prediction of the ocean mixed layer and sea surface temperature. In this work, we present results investigating the impact of the LT parameterization on the ocean component Bergen Layered Ocean Model (BLOM) of NorESM. The wave model WW3 is integrated in NorESM via the NUOPC coupling framework. Four experiments in coupled ocean and sea-ice configuration, forced with JRA55 based atmospheric reanalysis, have been performed covering one forcing cycle of 61 years. These include a control experiment with no wave-induced effect, and the other three with different LT parameterizations in the KPP mixing scheme. In addition, the LT impact on the entrainment buoyancy flux in the ocean surface boundary layer is also considered. These LT parameterizations come from Large Eddy Simulation studies and depend on the surface-layer averaged Langmuir number which accounts for the thickness of the ocean planetary boundary layer. In one experiment, the surface Stokes drift and Stokes transport are parameterized from the 10-m wind instead of computing them from WW3, then these are used to make an estimation of the full Stokes drift profile based on an empirical wave spectrum.

On extreme events in random-phase NLS wavefields: onset of MI and the lentgh of the domain

Agissilaos Athanassoulis, University of Dundee

Moment equations, including the Hasselmann, Alber and CSY equations, have long been used as phase-averaged models of wave propagation. Open questions include the origin of Rogue Waves, and whether the closure assumptions underlying any moment equation remain valid in nonlinear sea states. I will present Monte Carlo simulations aimed at clarifying the aformentioned questions. A population of realizations of the initial envelope, according to a given power spectrum, is created and evolved in time under an NLS equation. Different values for the peakedness of the spectrum and for the length $L$ of the computational domain are considered, as well as heavy and light tails.

Key findings include:

• Extreme events often come from "breathing" wavegroups. The magnitude of extremes is strongly dependent on the length $L,$ and increase for larger $L.$
• The critical length scale follows from the plane-wave modulation instability length $L_{0}$, and is $O(\lambda_0^2)$ in water waves. On short intervals $L\leqslant L_0$, the problem is always essentially linear and dispersion dominated -- even for intense and narrow spectra.
• For $L>L_0$ the statistics of extremes change only gradually, but there is a clear bifurcation on the growth of inhomogeneities. A strongly nonlinear regime where inhomogeneities rapidly become dominant kicks in for strongly nonlinear problems on long intervals.
• Kurtosis and other diagnostics indicate that the gaussian closures artificially stabilize the problem. This is expected in view of recent rigorous results and largely explains the lack of coherent nonlinear structures in many moment equations.

Spherical Multiple-Cell (SMC) grid is an unstructured grid, supporting flexible domain shapes and multi-resolutions. It retains the quadrilateral cells as in the latitude-longitude (lat-lon) grid so that simple finite difference schemes can be used. Sub-timesteps are applied on refined cells for efficiency and grid cells are merged at high latitudes to relax the CFL restriction. A fixed reference direction is used to solve the vector polar problem so that the whole Arctic can be included. The SMC grid has been implemented in the WAVEWATCH III (WW3) wave model since 2012 and updated in the latest WW3 V6.07. A 4-level resolution (3, 6,12, 25 km) global wave forecasting model has been used in the Met Office since October 2016, leading to great reduction of model errors and removal of our European wave model. Hybrid (MPI+OpenMP) parallelization is applied on the SMC grid and it could halve the model runtime in comparison with MPI run. SMC multi-grids option is also added recently and it could reduce model runtime by a further 30%. Met Office is planning to replace the present 4-level (3-6-12-25 km) global SMC grid wave forecasting model with new system of 3 sub-grids and 5-levels (1.25-2.5-5-10-20 km) in the future and preliminary tests are quite encouraging.

SMC grid wave models are also used in coupled systems in the UK Met Office and other weather centres, including regional coupled systems for UK waters, in the Arctic regions, in the Pacific Ocean and global climate models. The convenient mapping of SMC grid cells with lat-lon grid points makes it easy to exchange coupled parameters with ocean and atmospheric models. Inclusion of the whole Arctic Ocean allows climate systems to simulate different polar sea-ice scenarios. The multi-resolution option provides a good compromise between coarse resolution in climate systems and refinement of coastlines and islands required by wave modelling. The hybrid parallelization makes efficient use of modern super-computing resources for fast model performance, which is essential for large coupled systems and long-term climate simulations. SMC grid tools are now available on Github site with an example of 4-level (6-12-25-50 km) global grid generating scripts for first time users. This global grid could be used in coupled climate system.

Hazardous oceanic surface winds and waves impact both civilian and defense maritime trafficability. However, oceanic surface wind and wave prediction on extended-range time scales remains poorly understood. We examine extended-range oceanic surface windspeed predictability in the Navy Earth System Prediction Capability (ESPC) operational ensemble and compare this to other leading coupled global ensembles, such as the ECMWF, UKMO, and NCEP CFSv2 from the Subseasonal-to-Seasonal (S2S) database. The Navy ESPC ensemble v1 has been run operationally once a week out to 45 days since August 2020. We compare Navy ESPC ensemble v1 skill to the other S2S models in the North Pacific for the winters of 2020-21 through 2022-23. In examining the extended-range prediction skill of the models we evaluate the sensitivity to averaging forecasts and verifying observations in time (1, 2, 4, 7, and 14 day windows) and spatial averaging (500 and 1000 km radial averages). In addition, we examine extended-range significant wave height forecasts during the winter of 2020-21 performed using the new Navy ESPC v2 which includes a higher resolution atmospheric model and ocean wave forecasts from the Wavewatch III model.

This study constructs global 0.4-degree wave intelligent forecasting models and super-resolution models based on the Vision Transformer (ViT) and residual neural network, respectively. Utilizing wave reanalysis data that considers the impact of atmospheric instability as training samples, the aforementioned models are trained. Sensitivity experiments demonstrate that the wave intelligent forecasting model can accurately simulate the spatial distribution of significant wave height and the propagation of waves . The super-resolution model can also reasonably reproduce the high-frequency information missing in low-resolution data.
Using ERA5's 0.4-degree global wind field as the driving force, this study conducts a one-year forecasting experiment with the aforementioned models. Validation is performed using buoy data in the coastal waters of China and satellite altimeter data. The results indicate that the error accuracy of the wave intelligent forecasting model is comparable to that of traditional numerical wave forecasting models. Moreover, even in the absence of input data for air temperature and sea surface temperature, the model can inherit the wind-wave relationship from the training samples.

Wave breaking probability often plays an intermediate role in estimating the energy dissipation by breaking waves in the ocean. Various models have been developed to predict this probability, drawing upon environmental conditions, spectral characteristics, and field properties. However, the accuracy of these models can vary greatly, particularly when free parameters are derived from limited or localized field data. A common acknowledgment among these studies is the uncertain impact of wave directionality. Building on experimental evidence that demonstrates the significant influence of directionality on wave breaking dynamics and using probability density functions of wave slope, we introduce a framework designed to evaluate wave breaking probabilities across wave energy spectra with arbitrary directional distributions. The analysis reveals a notable decrease in wave breaking probability with increasing directionality, alongside discernible variations in breaking probabilities between directionally spread and crossing sea states. The framework also reveals a minimum in wave breaking probability at crossing angles between $130^\circ$ and $160^\circ$. To elucidate the implications of these findings in realistic oceanic conditions, such as scenarios involving abrupt wind direction shifts, we employ the WAVEWATCH III spectral model. This approach allows us to explore the effects of directionality on wave breaking probabilities, offering insights for the development of more accurate predictive models.

Laboratory experiments on breaking waves have informed much what is known about the breaking process. This is in part due to the ease with which they can be generated in a controlled and repeatable manner. When sufficient air is entrained during the breaking process, these experiments serve as models that have been used to understand oceanic whitecaps. However, despite what has been learned from these experiments, applying their results to individual whitecaps in the field has been challenging. Here I will discuss how measuring the time-evolution of the foam area generated by individual breaking waves using optical cameras can be used to estimate various quantities related to energy dissipation and air entrainment by individual whitecaps. I will highlight the similarities and differences between the foam area evolution in laboratory breaking waves and oceanic whitecaps. Following this I will (i) present distributions of estimates for energy dissipation and rates of air entrainment for individual oceanic whitecaps and their average values as a function of wind speed, (ii) evaluate the use of ECWAM to model whitecap coverage from the integrated spectral dissipation source term and (iii) discuss efforts to generate large datasets of whitecap observations.

This study investigates the use of high-resolution wind fields produced by the Vortex wind model to enhance wave modelling accuracy. The SWAN wave model is employed to generate wave fields, with inputs sourced from Copernicus ERA5 wave data, and wind data from two distinct sources for comparative analysis: the Copernicus ERA5 wind data and the high-resolution Vortex wind model data.

Through rigorous comparison with in-situ wave measurements taken by the EOLOS FLS200 buoy, the performance of the SWAN wave model is evaluated, revealing an enhancement in accuracy when utilizing the 1 km spatial resolution Vortex wind model data. This comparative analysis highlights the predictive capabilities of the Vortex wind model in capturing wave conditions with greater fidelity.

The study's focus extends to applications in the Offshore Wind industry, where precise wave condition maps derived from wind data are essential for planning and design of wind farms as well as for running maintenance operations safely. Furthermore, the study explores the reciprocal relationship between waves and wind.

By leveraging cutting-edge technologies and robust validation methodologies, this research underscores the pivotal role of high-resolution wind models in advancing wave modelling accuracy, with significant implications for various engineering sectors, particularly in the renewable energy domain.

The detailed representation of wave energy in direction and frequency plays a key role in ocean/atmosphere coupling. The aim of this work is to analyze the impact of wave variability in direction and frequency scales on wave-ocean coupling in regions of intense atmosphere-ocean interaction. The analysis is carried out in the agulhas surface current zone, using coupled experiments with the MFWAM wave model and the NEMO ocean model. Since 2021, the assimilation of SWIM wave spectra from CFOSAT in global operational model MFWAM has shown a significant improvement in the transition from wind-wave to swell regimes, particularly in the Southern Ocean. In this study, the coupled experiments analysis concern a NEMO simulation without wave forcing as control run, a MFWAM/NEMO coupled simulation with wave forcing and without assimilation of SWIM wave spectra, and finally the MFWAM/NEMO coupled simulation with wave forcing and assimilation of SWIM wave spectra. The time period of runs is january to june 2020. We recall that the wave forcing consists in using the surface stress released to ocean, the Stokes drift and wave breaking inducing turbulence in the ocean mixed layer. In the Agulhas ocean region, it is interesting to note the presence oftenly of long energetic swells generated from Southern Ocean storms and propagating in the opposite direction to the wind near the South African coast. The results show that the coupled simulation with assimilation agrees with surface current observations from SAR radial surface velocity of Sentinel-1 and currents provided by Automatic Identification System (AIS, Le Goff et al. 2021). The bias on surface current intensity is significantly reduced for the coupled simulation with assimilation compared with the other simulations.
The analysis on Agulhas surface current trajectory reveals that on several dates, the assimilation of wave spectra acts like nudging to rectify the current trajectory and gives a more consistent natal pulse effect, which is exaggerated in the control and without assimilation coupled ocean experiments. Further discussions and conclusions will be summarized in the final presentation.

We introduce a two-way coupled unstructured wave-flow model based on vortex-force formalization. This study integrates the hydrodynamic COMPAS model (Coastal Ocean Marine Prediction Across Scales, Herzfeld et al., 2020) with the SWAN wave model (Booji et al., 1999). COMPAS is a versatile unstructured 3D hydrodynamic model applicable to various scales, from estuaries to regional ocean domains. It operates on an unstructured variant of the Arakawa C-grid, with normal velocity components staggered at the edges of Voronoi cells, and fluid height and tracer variables located at each cell. The coupling is achieved by incorporating SWAN as a library object, with COMPAS linking to this library using C interoperability protocols. This results in a highly efficient numerical coupling without the need for an additional coupler.
In the present work, we have incorporated the effects of waves on currents (WEC) within an Eulerian reference frame by introducing contributions from conservative forces, specifically Stokes drift and wave-induced pressure, as well as non-conservative wave forcing, including bottom friction, whitecapping, and depth-induced wave breaking. To accurately represent the impact of WEC terms across realistic broadband spectra, the WEC terms are computed using 2D directional wave spectra, diverging from the traditional approach of relying on averaged wave parameters or a monochromatic approximation.

We have rigorously tested our model across diverse wave and hydrodynamic conditions spanning various regions along the Australian coast. Validation against observational data has shown promising results, indicating the model's efficacy. Leveraging the advantages of unstructured meshing, we were able to capture the nearshore impacts of dissipation parameters, including bottom friction and depth-induced wave breaking, particularly evident in surface elevation simulations.

Air-entraining breaking waves generate bubbles and sea spray which play an important role in air-sea fluxes of mass, heat, and momentum at high winds. This talk will aim to provide an overview of the state of the art of wave dependent air-sea parametrisations from bubbles, aerosols, and sea spray to gas transfer, heat, and momentum fluxes. Sources of uncertainties will be highlighted and how a spectral wave model may be used to drive air-sea exchange parameterisations in coupled model simulations will be discussed.

Bubbles offer an additional pathway for air-sea gas transfer and are believed to significantly enhance that of sparingly and poorly soluble gasses such as CO$_2$ and O$_2$. Smaller bubbles, susceptible to being advected downwards, are critical for deep ocean export of poorly soluble gasses like O$_2$. Mechanistic details of bubble plume formation and evolution remain elusive limiting the wave dependence of parametrisations of bubble mediated transfer.

Sea spray, generated both from surfacing bubbles and wind tearing off water from wave crests, potentially contributes to air-sea gas transfer. The magnitude of its impact is unknown.
Small spray droplets are an important source of marine aerosols. Historically, much work has been dedicated to the emission of salt aerosols. Recently, attention has been directed to emissions of micro and nano-plastics (NP/MP) as the oceans have been put forward as a non-negligible source of these pollutants. Work is on-going to scale NP/MP emissions to those of sea-salt aerosols.

Larger droplets likely increase air-sea enthalpy and decrease momentum transfers thus promoting the intensification of tropical cyclones. My current work examines their role in extra-tropical cyclones including those with tropical-like characteristics in the Mediterranean Sea. Spray contributions to turbulent fluxes have been included via bulk algorithms and we are working towards including them through a microphysics scheme. Spray emissions remain highly uncertain.

The United Kingdom (UK), situated on the Western European continental shelf (NWS), exhibits a diverse range of ocean, atmosphere, and wave conditions. The shallow sea and complex coastline mean that the assumption of equilibrium state at the air/sea interface is not valid in this area and coupled modelling becomes important, especially as individual model components reach greater accuracy.

Recent research shows that coupling has significant impact on both atmospheric and marine forecast in the NWS, particularly during storms. In this project, we analyse winter and summer storm case studies from 2023 to assess the accuracy of the Regional Coupled Suite (RCS-UKC4) in forecasting significant wave height and wind speed over the NWS.

The RCS-UKC4 is the latest regional coupled configuration over the NWS, coupling the Unified Model (UM), NEMO and WaveWatchIII. Our findings suggest promising skills in ensemble wave forecasts with RCS-UKC4 during storms compared to current operational wave ensembles (uncoupled, coarser resolution). We show that the choice of coupling frequency influences the timing of wave growth and decay. We also investigate coupling 10-meter neutral winds instead of 10-meter winds and adjusting the wave growth parameter (Betamax).

Air-sea interaction processes are often facilitated, controlled and therefore essentially coupled with the surface waves, and those include exchange of momentum, energy, heat, moisture, aerosols, gasses. We particularly note the role of wave breaking which locally enhances the intensity of such exchanges by orders of magnitude.
In the presentation, we will look at the role of waves and wave breaking in CO2 exchange and spray production, across the full range of Metocean conditions from light to strong winds. Proposed parameterisations are based on both laboratory experiments and field measurements, and accommodate dependences on the surface waves.
For CO2 flux estimates, the gas transfer rate was scaled with wave orbital velocity and
laboratory experiments were conducted. Non-dimensional gas transfer velocity was further related with wind-sea Reynolds numbers (composed of wave parameters), wave breaking probability and an enhancement factor due to the wind speed. To stress the role of the waves, we conducted laboratory experiments with waves produced by wavemaker with and without wind in the flume, i.e. including cases when the gas transfer cannot be described by traditional wind-based formulae in principle. The laboratory-developed gas transfer parameterisation was further tested and validated against historic field data. We explicitly parameterised the bubble injection rate through Reynolds number and breaking probability instead of wind speed and the final expression performed well across the data sets both in laboratory and the field.
Sea spray, also, while largely produced by wave breaking (or by interactions between wind and waves), is traditionally parameterized in terms of winds alone. We present in-situ observations of sea spray volume fluxes derived from laser altimeter readings. The measurements cover a broad range of wind and wave properties and are used to develop a novel wind-wave-dependent spray-volume-flux model. While our observations and parameterisation are on average consistent with the classic sea spray volume flux models in magnitude and respective trends, locally it can be distinctly different depending explicitly on the properties of the wave field. The new parameterisation was tested and applied to simulations and hindcast of real hurricanes and tropical cyclones.

The Earth System Model (ESM), a numerical model for the quantitative description of the climate system, is the key tool for understanding and predicting climate change as well as assessing the impacts of humans on climate change. Its development is at the forefront of global change. Although the state-of-the-art ESMs have made great progress, they are still suffering from several common simulated problems. By incorporating the ocean surface wave model into ESM through the role of small-scale waves on the ocean vertical mixing and air-sea fluxes, two generations of FIO-ESM are innovatively developed by the First Institute of Oceanography (FIO), which can effectively reduce the simulation biases. Focused on the effects of ocean surface waves on the climate system, this talk will mainly review the background and history of the two-generation FIO-ESM development by introducing four distinctive physical processes including the wave-induced vertical mixing, the air-sea flux induced by Stokes drifts, the heat flux associated with sea spray, and the SST diurnal cycle scheme. The simulation ability and applications on climate change and short-term prediction are also introduced. Finally, the future development and suggestions of the ESM are discussed from the perspective of the role of ocean surface waves on the ESM.

The recently released GC5 model is built from component model configurations which include the Met Office Unified Model (UM) Global Atmosphere Land (GAL9), NEMO v4.0.4 Global Ocean and a Global Sea-Ice component based on the model SI3 (GOSI9), coupled together with the OASIS coupler. During the development phase of GC5, WaveWatch III (WW3) was coupled to the proto GC5 workflow resulting in the first Met Office global Ocean-Wave-Atmosphere (OWA) coupled system. In addition to the climate model, which was made functional in 2022, an NWP case study configuration of the OWA coupled GC5 was also made functional during the last year. It closely follows the science configuration of the GC5 system with WW3 initialized using start dumps from a standalone global wave model. Currently the OWA model can produce case studies from May 2020 to January 2022. The NWP workflow can now operate at N320 (~40km) or N1280 (~10km) atmospheric resolution coupled with 50km (GS256A) or 25km (GS512L3A) resolution wave model. The climate configuration can operate at N96 (~150km) or N216 (~60km) atmosphere coupled to GS256A WW3. Only ORCA025 ocean model resolution is currently supported for both configurations. Our current wave coupling follows roughness closure coupling and ST4 physics for resolving wave source terms. We will present results from a 50-year global climate simulation and 14 NWP case studies on tropical cyclones. Introduction of wave drag into the atmosphere has resulted in changing wind patterns and MSLP in both climate and NWP configurations. In the ocean, interaction with waves resulted in changing mixed layer depth and SSH.

Air bubbles in the upper ocean are generated mainly by wave breaking at the air-sea interface. As such, after the waves break, entrained air bubbles evolve in the turbulent flow, exchange gas with the surrounding water, and may eventually rise to the surface. To shed light on the short-term response of entrained bubbles in different stormy conditions and to assess the relationships between bubble penetration depth, mechanical and thermal forcings, and air-sea transfer velocity of CO2, a field experiment was conducted from an oceanographic research platform in the North Adriatic Sea. Air bubble plumes were measured using high-resolution echosounder data from an up-looking 1000-kHz sonar. The backscatter signal strength was sampled at a high resolution, 0.5 s in time and 2.5 cm along the vertical direction. Time series profiles of the bubble plume depth were established using a variable threshold procedure applied to the backscatter strength. The data show the occurrence of bubbles organised into vertical plume-like structures, drawn downwards by wave-generated turbulence and other near-surface circulations, and reaching the seabed at 17-m depth under strong forcing. We verify that bubble depths adapt rapidly to wind and wave conditions and scale approximately linearly with wind speed. A scaling with the wind/wave Reynolds number is proposed to account for the sea-state severity in the depth prediction. Results also show a strong connection between measured bubble depths and theoretical air-to-sea CO2 transfer velocity parametrised with wind-only and wind/wave formulations. Further, our measurements corroborate previous results suggesting that the sinking of newly formed, cold-water masses helps bring bubbles to greater depths than those reached in stable conditions for the water column. The temperature difference between air and sea seems sufficient for describing this intensification at the leading order of magnitude. The results presented in this study are relevant for air-sea interaction studies and pave the way for progress in CO2 gas exchange formulations.

Modelling of wind waves in the ocean is based on the Hasselmann kinetic equation (KE), which describes the long-term evolution of wave spectra. Derivation of the KE includes the expansion of the sixth order correlator into second order correlators and fourth order cumulants to obtain a closed system of equations. However, all previous studies discarded the term involving fourth order cumulants due to its complexity.

Even though this term is small, it appears on the right-hand side of the evolution equation for correlators, and therefore its neglect is justified only for times not exceeding a certain threshold. The term is responsible for the effects of finite non-Gaussianity, and its neglect, equivalent to the assumption of random initial phases, contradicts the established picture of weak turbulence according to which the wave field evolution is due to nonlinear regeneration of non-Gaussianity, and does not allow to capture the effects of finite nonlinearity either.

Earlier we showed by DNS that the effects of finite non-Gaussianity lead to considerable discrepancies in the spectral shape. In this work, we discuss the kinetic system of equations with the account for finite non-Gaussianity. We demonstrate that the numerical simulation of the full system can be based on the generalised KE (gKE). We show that the finite non-Gaussianity and finite nonlinearity effects restrict the spectral growth rates around the spectral peak, thus changing the spectral shape. This resolves the major discrepancy in wind wave kinetics: while the observed spectral shapes of young and mature sea states essentially differ, the standard KE predicts the strictly self-similar picture of wind wave development. The findings of the present study are of crucial importance for all applications where the shape of the wave spectrum is significant, rather than just its integrated description.

The authors were supported by UK NERC grant NE/I01229X/1.

Understanding processes driving air-sea gas transfer and being able to model both its mean and variability are critical for understanding the climate and carbon cycle. The air-sea gas transfer velocity (K) is almost universally parameterized as a function of wind speed in large scale models – an oversimplification that buries the mechanisms controlling K and neglects much natural variability. Sea state has long been speculated to affect gas transfer, but causal relationships from in situ observations have been elusive. Here, using a Machine Learning technique we show that the inclusion of significant wave height improves the model simulation of observed CO2 transfer velocity (KCO2) by about 0.1 in R2 (the coefficient of determination), while parameters such as wave age, wave steepness, and swell-wind directional difference have little influence on KCO2. Wind history is found to be important, as in high seas KCO2 during periods of falling winds exceed periods of rising winds by ~20% in the mean. This hysteresis in KCO2 is consistent with the development of waves and increase in whitecap coverage as the seas mature. A similar hysteresis is absent from the transfer of a more soluble gas, confirming that the sea state dependence in KCO2 is primarily due to bubble-mediated gas transfer upon wave breaking. We propose a new parametrization of KCO2 as a function of wind stress and significant wave height, which can explain over a third of the variance in observed KCO2 at high wind speeds, confirming that sea state needs to be considered to accurately predict air-sea CO2 flux.

The global analyses and medium range forecasts from the European Centre for Medium range Weather Forecasts rely on a state-of-the-art atmospheric model. To best represent the momentum exchange at the surface of the oceans, it is tightly coupled to an ocean wave model. A coupled ocean model is also included as part of the operational medium range, extended range and seasonal forecasting systems. Because the feedback from the ocean surface can be significant, it is only in the fully coupled system that parameterisations for air-sea processes should be revisited.
Experimental evidence points to a sea state/wind dependency of the heat and moisture fluxes. Following an extension of the wind wave generation theory, a sea state dependent parameterisation for the roughness length scales for heat and humidity was successfully introduced. However, such change has impact over the whole troposphere, and required concerted testing with the latest atmospheric model changes (full Earth System approach).
Until recently, the impact of short gravity-capillary waves on the overall momentum exchange was crudely represented in the wave generation theory used by the wave model. A more detailed model of the gravity-capillary range has been introduced and optimised. It was also realised that the growth rate of waves should be extended to include nonlinear effects. This new approach yields promising results for both high winds and low winds ranges. For high winds conditions in particular, the new system tends to reduce the known negative bias that have plagued ECMWF surface winds for years.
Assessment of new parameterisations will be summarised in the context of the fully coupled systems. This new model developments will be part of the future operational model cycle (CY49R1, autumn 2024).

The wind turbines extract the kinetic energy from the atmosphere, reducing wind speed and stress. Their effects on surface wave fields are examined in this study using high-resolution (1.5 km) SCOAR regional ocean-atmosphere-wave coupled model simulations for the US Northeast Coast. The wind farm effects are represented in the atmospheric component (WRF) of the coupled model via the so-called Fitch parameterization, which treats the individual wind turbines as sinks of momentum and sources of turbulence kinetic energy. In the coupled simulation that represents the wind farm effects, a total of 830 12MW turbines were placed in the MA/RI lease areas. This simulation is compared with the baseline simulation, in which the wind farm parameterization was switched off. This poster presents a preliminary analysis of surface waves from these two simulations, showing that reduced hub-height wind speeds in the wind farm areas and the downstream extensions (wind wakes) are manifested strongly in some (but not all) of the surface wave fields. The significant wave height, wave-supported wind stress, wave-to-ocean stress, and wave-to-ocean energy flux are all reduced in response to decreasing winds in the wind farms. This is consistent with our finding that the mixed-layer stratification increases and the entrainment cooling of the highly stratified shelf ocean in summer decreases in the wind farm areas. The magnitudes and the downstream extensions of these responses depend on the background wind direction, with the onshore winds causing strong wave response (height, direction) near the coasts and the offshore winds generating far-reaching wave wakes of similar scale to the wind wakes.

An improved understanding of the present and future marine climatology is necessary for numerous activities, such as the operation of offshore structures, optimization of ship routes, and evaluation of wave energy resources.
To produce global wave information, the WAVEWATCH III wave model was used to produce wave information, until the end of the 21st century, covering all ocean areas. Global wind and ice-cover climate data from a total of 120 years were used as input for the wave model. The period is divided into four 30-year slices, where the first (1980–2009) represents the recent past, the second (2010–2039) the near future, the third (2040–2069) the mid-century and the last one (2070–2099) represents the end of the 21st century.
Descriptive empirical statistics of wind and wave parameters were obtained for different 30-year time slices, for the North Atlantic Ocean. Changes from present to future climate were evaluated regarding mean and extreme events. The results showed an increase in mean significant wave height of total sea, wave energy and cumulative wave energy in the South Atlantic, and an increase in variability and a decrease of mean significant wave height of total sea in the North Atlantic. Other regions also present changes but are less marked and less consistent through time.
The simulated wave data was also used for different applications as the evaluation of future wave storm conditions in the North Atlantic Ocean using a Lagrangian methodology, the analyses of the relationship between the Arctic Oscillation index and present and future met ocean conditions on the North Atlantic Ocean, and also to assess the potential for wave energy exploitation in the Canarias islands over the 21st century.