Swell Waves Research Articles

О некоторых возможностях многочастотного дистанционного зондирования водной поверхности

This study is aimed at expanding the number of measured parameters to analyze the features of the formation of surface waves under the influence of wind. The paper develops an original approach to obtaining information on the variability of the short-wavelength part of the wave spectrum (examples are given for wavelengths from about 50 cm to 2 cm in 6 intervals) and the long-wave component of the wave spectrum (> 1 m) in marine conditions. Retrievable information about waves will allow studying the interaction of wind simultaneously with the short-wave and long-wave components of the wave spectrum and will be in demand by scientists involved in numerical modeling of the wave climate and interested in refining the model of near-surface wind interaction with waves. In addition, new information about the short-wave part of the wave spectrum in different wavelength ranges will improve the accuracy of near-surface wind speed retrieval from remote sensing data. This work is devoted to a theoretical analysis of slope variance retrieved from reflected acoustic pulses for different radiation frequencies depending on the near-surface wind speed and swell wave height. A study was made of the measured slope variances of large-scale waves, compared to the radiation wavelength, in six intervals depending on the wind speed and swell height. It is shown that the use of difference slope variances of the large-scale wave makes it possible to get rid of the influence of swell in the case of mixed waves and obtain a better correlation with the wind speed. A method is proposed for retrieving the declination degree for the spectrum of wave heights in given intervals of radiation wavelengths. Within the framework of this method, it is possible to retrieve the boundary wave numbers for each radiation wavelength.

A multi-dimensional long-term joint probability model for environmental parameters

Reliability-based design of offshore structures usually requires joint probabilistic models to describe the long-term environmental scenario, however, directional variables are rarely included. This paper presents a multi-dimensional joint model alternative for the probabilistic long-term environmental data description, including directional variables. The joint model aims to statistically describe the main environmental parameters for the probabilistic design of marine structures, such as floating production, storage, and offloading vessels (FPSOs) systems. The model targets full long-term response analyses and simplified and efficient design methodologies. Wind sea, swell and current parameters are investigated for a location southeast of the Brazilian coast. Modeled environmental parameters include significant wave heights, peak periods and incidence directions of the wind and swell waves, as well as wind and current velocities and respective directions. To represent parameters statistical dependencies, the conditional modeling approach was employed. Kernel density estimation is used in the probabilistic description of directional variables and is shown to well represent data characteristics. Case study results show the model's suitability to well-represent wind sea and swell waves, wind and current parameters at the studied location.

Wind Fetch and Direction Effects on Langmuir Turbulence in a Coastal Ocean

AbstractMixing processes in the upper ocean play a key role in transferring heat, momentum, and matter in the ocean. These mixing processes are significantly enhanced by wave‐driven Langmuir turbulence (LT). Based on a paired analysis of observations and simulations, this study investigates wind fetch and direction effects on LT at a coastal site south of the island Martha’s Vineyard (MA, USA). Our results demonstrate that LT is strongly influenced by wind fetch and direction in coastal oceans, both of which contribute to controlling turbulent coastal transport processes. For northerly offshore winds, land limits the wind fetch and wave development, whereas southerly winds are associated with practically infinite fetch. Observed and simulated two‐dimensional wave height spectra reveal persistent southerly swell and substantially more developed wind‐driven waves from the south. For oblique offshore winds, waves develop more strongly in the alongshore direction with less limited fetch, resulting in significant wind and wave misalignments. Observations of coherent near‐surface crosswind velocities indicate that LT is only present for sufficiently developed waves. The fetch‐limited northerly winds inhibit wave developments and the formation of LT. In addition to limited fetch, strong wind–wave misalignments prevent LT development. Although energetic and persistent, swell waves do not substantially influence LT activity during the observation period because these relatively long swell waves are associated with small Stokes drift shear. These observational results agree well with turbulence‐resolving large eddy simulations (LESs) based on the wave‐averaged Navier–Stokes equation, validating the LES approach to coastal LT in the complex wind and wave conditions.

Brazil Wave Climate from a High-Resolution Wave Hindcast

A detailed climatology of ocean wind waves in the South Atlantic Ocean, based on ERA-5 reanalysis and in a higher-resolution wave hindcast (ERA-5H), both developed by the European Centre for Medium-Range Weather Forecasts, is presented. The higher resolution of the wave fields in the ERA-5H (22 km) allowed for a better description of the wind sea and swell features compared to previous global and regional studies along the Brazilian coast. Overall, it is shown that swell waves are more prevalent and carry more energy in the offshore area of the study area, while wind sea waves dominate the nearshore regions, especially along the northern coast of Brazil. The influence of different climate indices on the significant wave heights patterns is also presented, with two behavioral groups showing opposite correlations to the North Atlantic Oscillation and Southern Annular Mode than to the Southern Oscillation Index. The analysis of the decadal trends of wind sea and swell heights during the ERA-5H period (1979–2020) shows that the long-term trends of the total significant wave height in the South Atlantic Ocean are mostly due to swell events and the wave propagation effect from Southern Ocean storms.

SAR Altimetry Data as a New Source for Swell Monitoring

AbstractThis article shows the first spectral analysis of fully‐focused Synthetic Aperture Radar (FFSAR) altimetry data with the objective of studying backscatter modulations caused by swells. Swell waves distort the backscatter in altimetry radargrams by means of velocity and range bunching. These swell signatures are visible in the tail of the waveform. By locally normalizing the backscatter and projecting the waveforms on an along‐/cross‐track grid, satellite altimetry can be exploited to retrieve swell information. The analysis of FFSAR spectra is supported by buoy‐derived swell‐wave spectra of the National Oceanic and Atmospheric Administration network. Using cases with varying wave characteristics, we discuss the altimetry‐derived spectra and relate them to what is known from side‐looking SAR imaging systems. Besides having a vast amount of additional data for swell‐wave analysis, altimeter data can also help us to better understand the side‐looking SAR spectra.

Perspectives on wave transformation over a near-horizontal shore platform: Comparison of a two-dimensional and transect approach

Understanding wave transformations over intertidal shore platforms is necessary for managing rock coasts. Previous studies have investigated the effects of intertidal shore platform morphologies on wave transformation using instruments aligned in cross-shore and longshore arrays. This approach has provided a fundamental understanding of the influence of platform profile characteristics on wave transformation properties. However, it precludes the consideration of shore platform planform morphologies on two-dimensional wave transformation, which has been overlooked or only of secondary concern. We developed a two-dimensional approach to measure the wave direction of both swell waves (SW: 0.05 Hz < frequency < 0.125 Hz) and infragravity waves (IG: frequency < 0.05 Hz) during transformation across a near-horizontal shore platform (NHSP). Waves were measured using a grid of 14 pressure transducers (PT) recording at 2 Hz. Directional wave spectra were derived using the Extension of the Maximum Entropy Principle (EMEP) method. Both SW and IG were subject to strong directional changes over the NHSP induced by refraction on the lateral edges of the platform and reflection at the cliff toe. As a result, a dominance of oblique and reflected wave trains was observed over the inner platform while onshore waves propagating along the transect represented only 36% of the SW energy and 22% of the IG energy. These directional changes affected the wave energy distribution over the shore platform surface, generating complex energy patterns. A 77% decrease of refracted SW energy was recorded from the intertidal platform edges to the platform centre. Two dominant IG energy patterns were identified. The first was a long-shore increase of energy toward the central axis of the platform and a cross-shore increase of energy from the platform centre to the seaward and landward extremities. This pattern was seen for 81% of the submersion period. The second pattern also reported in previous research was an increase in IG from intertidal platform edges to the shoreline, but this was only observed for 15% of the submersion period. The two-dimensional approach developed in this paper allowed to provide field-based observations of the combined effects of wave reflection and refraction on wave energy distribution over a NHSP.

Beach morphodynamic classification using high-resolution nearshore bathymetry and process-based wave modelling

Classification of beach morphodynamic state relies on accurate representation of breaking wave conditions, Hb (plus grain size and spring tidal range). Measured breaking wave data, however, are absent from all but a handful of sites worldwide. Here, we apply process-based wave modelling for propagating offshore waves to the breaking zone using high-resolution nearshore bathymetry, obtaining representative and accurate Hb values for multiple beaches at regional scale, and thereby derive meaningful morphodynamic classifications that accord with observed beach state. Ninety-five beaches on the north coast of Ireland were investigated, with observed beach types and states compared to predictions based on morphodynamic parameters determined using wave, tide and sediment data, obtained from field surveys and detailed numerical wave modelling. The coast is exposed to micro-through meso-tides (0.43–3.90 m) and low sea through high swell waves (Hb = 0.13–1.18 m) and is composed of fine to medium sand resulting in a full range of beach types (wave-dominated, tide-modified and tide-dominated) and most beach states, thereby providing a comprehensive field laboratory to undertake such a comparison. We found that modal beach types reside within their predicted Relative Tide Range (RTR) and modal beach states close to the predicted dimensionless fall velocity (Ω) range. The use of high-resolution nearshore wave modelling to determine Hb was deemed the most appropriate approach for deriving predicted beach classification. The work follows the investigation of the same coast by Jackson et al. (2005) who found shortcomings in relating beach types to breaker wave conditions. However, advances in inshore wave modelling and access to high-resolution nearshore bathymetry since then have enabled improved estimates of breaker height, producing more accurate results and enhancing previous work. The results highlight the need to obtain accurate estimates of Hb and Tp if they are to be used effectively in predicting beach parameters. This work therefore sets a precedence for other coastal sites worldwide where detailed nearshore bathymetry is available and Hb can be derived from process-based wave modelling, improving the classification and prediction of morphodynamic beach type and state.

Assessment of Ocean Swell Height Observations from Sentinel-1A/B Wave Mode against Buoy In Situ and Modeling Hindcasts

Synthetic Aperture Radar (SAR) in wave mode is a powerful tool for monitoring sea states in terms of long-period ocean swells of a specific wave directional partition. Since 2016, SARs aboard Sentinel-1A/B operating in wave mode have provided ocean swell spectra dataset as Level-2 Ocean products on a continuous and global basis over open oceans. Furthermore, Level-3 swell products are processed by Copernicus Marine Environment Monitoring Services (CMEMS) taking the benefit of the unique “fireworks” analysis. In this paper, swell wave heights from Sentinel-1A/B wave mode during the period from June 2016 to June 2020 are evaluated. The reference data include the collocated in situ measurements from directional wave buoys and WaveWatch III (WW3) hindcasts. Assessment results show systematic overestimation of approximately 0.2 m in terms of the partitioned swell heights for Sentinel-1A/B Level-2 products compared to the directional buoy observations in eastern Pacific and the western Atlantic. Based on the reliable SAR-WW3 collocations after quality-controls, empirical corrections have been proposed for Sentinel-1 Level-2 swell heights. Independent comparisons against WW3 hindcasts and buoy observations demonstrate the validity of our postprocessing correction for both Level-2 and Level-3 swell heights by eliminating the biases and reducing the root mean square errors. The consistency between CMEMS Level-3 swells and buoy in situ is also examined and discussed by case studies.

Wave-induced sediment and rhodolith mobility on a narrow insular shelf dominated by wave variability (Fernando de Noronha Archipelago, Brazil)

This study combines numerical modeling and empirical equations to define spatial fields of wave-induced sediment and rhodolith mobility in a narrow insular shelf that is subject to a seasonal wave regime: the Fernando de Noronha insular shelf. From analyses of the annual, summer and winter wave climates, we noticed an intense directional variability in swell waves coming predominantly from opposing directions between the studied seasons (northern swell in summer and southern swell in winter), reflecting higher wave energy on the north coast during summer and lower energy during winter. The longitudinal transport at the northern coast, which is predominantly oriented to the southwest, is also higher in the summer months and lower in the rest of the year. To describe the spatial variation in wave-induced mobility under summer and winter wave conditions, we consider empirical sediment movement equations, based on mean grain size and density values. Carbonate bioclastic sediments, which are predominant in the Fernando de Noronha shelf, are remobilized by waves throughout the entire shelf. However, in the nearshore zone, this movement occurs intensely for all sizes. The depth and shelf side affected by wave-induced mobility vary according to the wave climate variability that determines the direction and type of wave prevailing in the regime. When swell waves come from the north (summer scenarios), mobility is greater mainly on the northern shelf; however, when trade wind waves come from the southeast and swell waves come from the south (winter scenarios), greater movement is produced on the south face. Wave-induced sediment mobility occurs at depths of up to 60 m, near the shelf break, indicating the importance of the shelf morphology. The movement of rhodoliths, which presents a lower density and larger diameter than the sediments, eventually occurs under extreme wave conditions up to depths of approximately 30 m in areas that vary seasonally around the island according to the predominant wave direction. These characteristics are favorable to rhodolith development. With our results, we hope to better understand the wave action on the bottoms of high-energy island shelves by identifying the sediment movement patterns attributed to wave climate variability and morphological characteristics of the shelf.

Physics-Based Forward Modeling of Ocean Surface Swell Effects on SMAP L1-C NRCS Observations.

This paper examines the impact of ocean surface swell waves on near-coastal L-band high-resolution synthetic aperture radar (SAR) data collected using the National Aeronautics and Space Administration’s (NASA) Soil Moisture Active/Passive (SMAP) radar at 40° incidence angle. The two-scale model and a more efficient off-nadir approximation of the second-order small-slope-approximation are used for co- and cross-polarized backscatter normalized radar cross-section (NRCS) predictions of the ocean surface, respectively. Backscatter NRCS predictions are modeled using a combined wind and swell model where wind-driven surface roughness is characterized using the Durden–Vesecky directional spectrum, while swell effects are represented through their contribution to the long wave slope variance (mean-square slopes, or MSS). The swell-only MSS is numerically computed based on a model defined using the JONSWAP spectrum with parameters calculated using the National Data Buoy Center and Wave Watch III data. The backscatter NRCS model is further refined to include fetch-limited and low-wind corrections. The results show an improved agreement between modeled and observed HH-polarized backscatter NRCS when swell effects are included and indicate a relatively larger swell impact on L-band compared to higher radar frequencies. Preliminary investigations into the potential swell retrieval capabilities in the form of excess MSS are encouraging, however further refinements are required to make broadly applicable conclusions.

Busan Geoje Fixed Link

The Busan Geoje Fixed Link project is one of the landmark projects in South Korea, providing a road connection between Gaduk and Geoje Island near to the city of Busan at the Southern tip of the Korean peninsula. The project consists of two Cable Stayed Bridges, an Immersed Tunnel, rock tunnels and it has a total length is over 8 km.This paper will focus on the immersed tunnel part of the link and the particular challenges that the project faced in designing and constructing the tunnel, these challenges required a significant evaluation in immersed tunnel technology. The tunnel consists of 18 tunnel elements and has a total length of 3.6 km. The tunnel location was characterised by the following conditions:•a large depth, maximum depth of the tunnel is 48 m below sea level.•the tunnel is located in a seismic sensitive area.•the tunnel is founded largely on weak marine clay, but parts also on bedrock.•part of the tunnel was constructed on a sub sea embankment which is also founded on a weak marine clay.•the tunnel has been constructed in a location that is facing to the Sea of japan and is exposed to a severe wind and wave environment with large long period swell waves present for part of the year.Because for only a few months a year the wave- and weather circumstances were suitable for immersion, extensive numerical and physical model tests were carried out to predict the behaviour of the immersion system for the expected conditions. These model tests were used to determine the wind and wave climate that the immersion system could cope and a go, no-go range of conditions.Additionally, an accurate, sophisticated short and long term wave and weather forecast system was developed. This system enabled forecasts to be made within a 10 cm wave height accuracy, for periods leading up to the element transport and immersion operations which allowed the immersion operations to be possible within acceptable risks.The tunnel elements (TE) were built in batches in a pre-cast yard (PC). After inundation of the dock the elements were transported to a mooring location close to the PC-yard for fitting out and to wait for favourable immersion weather.The elements were immersed using two catamaran pontoons and placed in a previous dredged trench on the sea bed. A taut mooring configuration was used in order to reduce the wave influenced motions to a minimum. Anchor points were created by pre-installed plate anchors.Due to the total length and installation depth of the tunnel the traditional survey systems using towers and total stations were not suitable. Therefore new survey methods were developed, these included a tautwire system and an Ultra Short Base Line (USBL) acoustic system were used for the positioning of the elements during the immersion operation. Fine positioning of the TE’s under swell wave influence was done using a special designed External Positioning System (EPS) and placed on the pre-laid screeded gravel bed.

Microenergy harvester for remote ocean buoys using piezoelectric sensors coupled with superballs

Wave energy is a renewable resource with high energy potential. This research work proposes a low power piezoelectric energy harvesting system based on the heave motion of ocean buoys. This Piezoelectric Energy Harvester (PEH) is composed of piezoelectric diaphragms coupled with superballs to enhance the output of the piezoelectric sensor. The PEH setup is designed within a floating buoy and tested in a wave flume by varying the frequency of regular waves. The heaving of the buoy causes the superball to oscillate and impact upon the piezo diaphragms thereby producing power. This output is then processed using appropriate AC to DC converter and booster circuits. The single-axis sensor-diaphragm responses under regular wave conditions with varying wave heights were analyzed. A rms voltage of about 2.56 V was generated for a wave height of 0.21 m and wave period of 1.2 s. The wave flume experimental results show that the maximum harvested power was about 80 mW by the entire piezo sensor diaphragm setup for the wave height range of 0.06 m to 0.21 m and wave period of 1.22 s to 2.13 s. Using the same technique in the ocean buoys of diameter 0.9 m in the swell wave conditions between 0.5 to 3.5 m significant wave height, the system can generate maximum voltage of up to 16 V using 28 numbers of superballs with sensors arranged in parallel/series combinational power circuits. This harvesting technique will be very much useful for coastal &amp; offshore buoys to harvest power in a hybrid approach during the failure in solar battery charging during monsoon and unfavorable weathers.

Swell hindcast statistics for the Baltic Sea

Abstract. The classic characterisation of swell as regular, almost monochromatic, wave trains does not necessarily accurately describe swell in water bodies shielded from the oceanic wave climate. In such enclosed areas the locally generated swell waves still contribute to processes at the air and seabed interfaces, and their presence can be quantified by partitioning wave components based on their speed relative to the wind. We present swell statistics for the semi-enclosed Baltic Sea using 20 years of swell-partitioned model data. The swell significant wave height was mostly under 2 m, and in the winter (DJF) the mean significant swell height was typically less than 0.4 m; higher swell was found in limited nearshore areas. Swell waves were typically short (under 5 s), with mean periods over 8 s being rare. In open-sea areas the average ratio of swell energy (to total energy) was mostly below 0.4 – significantly less than in the World Ocean. Certain coastal areas were swell dominated over half the time, mostly because of weak winds (U&lt;5 m s−1) rather than high swell heights. Swell-dominated events with a swell height over 1 m typically lasted under 10 h. A cross-correlation analysis indicates that swell in the open sea is mostly generated from local wind sea when wind decays (dominant time lag roughly 15 h). Near the coast, however, the results suggest that the swell is partially detached from the local wind waves, although not necessarily from the weather system that generates them because the highest swell typically arrives with a roughly 10 h delay after the low-pressure system has already passed.

Long-term fatigue analysis of mooring lines considering wind-sea and swell waves using the Univariate Dimension-Reduction Method

In offshore structures analysis, one of the greatest challenges is the high computational cost of evaluating long-term waves-induced fatigue damage. Complication lies on the large number of required numerical stochastic simulations to compute the long-term multi-dimensional integral associated to the problem. In addition, when effects of wind-sea and swell waves are simultaneously considered as independent phenomena, the order of the damage integral increases, which leads to an even greater amount of numerical simulations. Aiming at reducing the number of short-term stochastic simulations needed in order to evaluate the multi-dimensional fatigue damage integral, this work investigates the Univariate Dimension-Reduction Method (UDRM) as an efficient numerical approach. In this method the original random variables, which represent the environmental conditions parameters, are transformed into standard Gaussian variables and, in this reduced space, an additive decomposition to represent the short-term fatigue damage by a simpler function is employed. Due to this transformation, the problem of simultaneous independent wind and swell waves that previously could only be solved by one four-dimensional integral can now be solved by four one-dimensional integrals. These one-dimensional integrals can be solved by appropriate quadrature techniques, such as the one based on the Gauss-Hermite quadrature. Final result is a significantly reduced number of numerical analyses required for a good estimation of the long-term fatigue damage, allowing its use for practical cases. To evaluate the methodology performance, two case studies involving mooring systems of FPSOs (a spread-moored and another turret-moored) located offshore Brazil in approximately 1800 m (∼6000 ft) water depth are presented. Fatigue damages of the mooring lines are individually calculated by UDRM and results are compared to those obtained by the traditional approach of estimation of fatigue damage considering environmental data of a large enough number of short-term conditions. It is shown that, even with less than 2% of the total short-term numerical simulations required by the traditional approach, UDRM leads to very suitable fatigue damages results, i.e., with differences lower than 9% in the first case study and 24% in the second one. The accuracy of UDRM due to statistical modeling of environmental parameters is also investigated.

Spatial patterns in wave signatures on beaches in estuaries and bays

Sandy beaches in estuaries and bays (BEBs) are ubiquitous around the world. While some are referred to as “low energy” beaches, there are large differences in wave climate due to fetch, swell exposure and shoreface morphology. In this study, wave-climate controls on BEB morphology are identified relative to bay geometry and focusing on the relative contributions of wind, ocean swell and infragravity waves to the wave signature of a BEB. We focus on two swash-aligned and two drift-aligned BEBs in an urbanized, semi-enclosed bay in SE Australia (Kamay/Botany Bay), with differences in proximity to the bay mouth, beach aspects and fetch, as well as different histories of storm erosion and recovery. Spectral analysis of local wave measurements (June 2018–January 2019) shows that wave signatures at all 4 BEBs are dominated by swell waves (>51%), followed by locally generated wind waves at 3 out of 4 BEBs (<43%), then infragravity waves (<35%). We identified five weather scenarios based on local wind speed/direction and resultant wind waves, combined with infragravity waves, and offshore swell wave conditions. BEBs close to the bay entrance are primarily controlled by swell waves, but at times even BEBs close to the entrance can be sheltered from swell waves depending on their incident angle. Conversely, BEBs farthest from the bay entrance (~8 km) alternated between periods where spectra were dominated by either wind waves or offshore swells. Infragravity waves were only important relative to wind waves and swell at the most sheltered BEBs, where there is limited fetch and swell dissipated over shallow areas. We also show that anthropogenic factors such as constructed revetments or groynes significantly alter wave signatures at BEBs in this bay. Thus, wave spectral signatures are highly variable across BEBs in the same bay and can represent a simple tool to study BEB morphodynamics including storm response and subsequent recovery.

Characteristics of maximal energy component of waves in Terpeniya Bay (Sakhalin Island)

Analysis of natural sea surface oscillations was performed in order to determine maximal spectral energy components in sea waves in the area of Terpeniya Bay. It has been found out that maximal components appear at periods of 5 and 8 seconds and reach energy of 3 · 106 cm2·s during storms. During calm weather maximums can be observed in the range of swell waves, herewith maximums exist at periods of 12 and 15 seconds. Energy of these maximums doesn’t go upper then 8 · 105 cm2·s and 3 · 105 cm2·s accordingly. Maximum components in the infragravity band of energy spectrum were estimated as well. Two steady energy peaks were determined at periods of 75 and 135 seconds, which are most probably relate to edge waves in considered water area.

Estimating runup with limited bathymetry

Wave runup estimates are used in erosion and overtopping models, and in coastal structure design. However, runup depends on often incompletely known surf and swash bathymetry. The many existing runup parameterizations characterizing bathymetry with only the foreshore (swash zone) beach slope βf are necessarily of limited accuracy. Here, an empirical model relating runup to incident wave spectra is extended to include an effective, mid-surfzone slope, βeff, that depends on the cross-shore location of the midpoint of breaking-wave dissipation. The empirical model is trained using numerical simulations (SWASH) of 138 hindcast historical storm waves, two different offshore infragravity wave boundary conditions, and 24 representative eroded beach bathymetries from a Southern California beach. The model is tuned for the swell waves and concave up (sometimes barred) depth profiles characteristic of the study region. Consistent with their generation by surfzone-wide processes, setup and infragravity runup depend more strongly on surfzone βeff than on foreshore βf. In contrast, sea-swell runup depends more strongly on shoreline processes, and βf is more important than βeff. Empirical model accuracy is improved by including both βeff and βf.

Wellhead fatigue analysis considering the effect of wind-sea and swell waves by using Univariate Dimension Reduction Method

In recent years, the observation of dynamic motions in wellhead structures during drilling operations turned wellhead fatigue into a great concern for the oil industry. As stated by DNV in its Recommended Practice E104 (DNVGL, 2018), the fatigue damage evaluation demands an accurate representation of environmental loads acting on the whole drilling structure, including rig, drilling riser and BOP/LMRP. In terms of computational costs, this representation can make the fatigue analysis very expensive. A high number of loading cases may be needed to take into account the statistical independence between environmental parameters, mainly when wind-sea and swell waves are taken into account. To solve this issue, this paper proposes the use of the Univariate Dimension Reduction Method (UDRM) to compute the fatigue damage in wellhead structures considering the effects of both types of waves. The main advantage of this procedure is that it replaces the solution of the four-fold integral associated to the problem by the solution of four one-dimensional integrals, which drastically reduces the number of numerical simulations required in the fatigue assessment. The method is applied to two study cases considering the environmental conditions of the Brazilian coast. In the first, the drilling unit is a semi-submersible platform, while in the second case a ship-based drilling unit is considered. The obtained results indicate a substantial reduction in computational costs without loss of accuracy of UDRM when compared to a Monte Carlo Simulation-based approach.

Seas and swells throughout New Zealand: A new partitioned hindcast

A high resolution partitioned wave hindcast of New Zealand waters is presented together with validation results against 9 buoy deployments that are representative of the local wave climate. An analysis of integrated and partitioned mean wave parameters was conducted together with a study of the correlation between wave height anomalies and atmospheric indices. A directional spatial analysis was also performed to identify and quantify wave systems that are not detectable by in situ buoys or hindcast integrated parameters. The presented study outlines a framework of how partitions can be analyzed in order to improve our understanding of the local wave climate in terms of wind-sea and swell waves.

Extreme swell wave energy and its directional characteristics in the Indian Ocean

Extreme swell wave energy and its directional characteristics in the Indian Ocean