A hybrid efficient method to downscale wave climate to coastal areas

Long-term time series of sea state parameters are required in different coastal engineering applications. In order to obtain wave data at shallow water and due to the scarcity of instrumental data, ocean wave reanalysis databases ought to be downscaled to increase the spatial resolution and simulate the wave transformation process. In this paper, a hybrid downscaling methodology to transfer wave climate to coastal areas has been developed combining a numerical wave model (dynamical downscaling) with mathematical tools (statistical downscaling). A maximum dissimilarity selection algorithm (MDA) is applied in order to obtain a representative subset of sea states in deep water areas. The reduced number of selected cases spans the marine climate variability, guaranteeing that all possible sea states are represented and capturing even the extreme events. These sea states are propagated using a state-of-the-art wave propagation model. The time series of the propagated sea state parameters at a particular location are reconstructed using a non-linear interpolation technique based on radial basis functions (RBFs), providing excellent results in a high dimensional space with scattered data as occurs in the cases selected with MDA. The numerical validation of the results confirms the ability of the developed methodology to reconstruct sea state time series in shallow water at a particular location and to estimate different spatial wave climate parameters with a considerable reduction in the computational effort.     

Climate-based Monte Carlo simulation of trivariate sea states

Accurate wave climate characterization, which is vital to understand wave-driven coastal processes and to design coastal and offshore structures, requires the availability of long term data series. Where existing data are sparse, synthetically generated time series offer a practical alternative. The main purpose of this paper is to propose a methodology to simulate multivariate hourly sea state time series that preserve the statistical characteristics of the existing empirical data. This methodology combines different techniques such as univariate ARMAs, autoregressive logistic regression and K-means clusterization algorithms, and is able to take into account different time and space scales. The proposed methodology can be broken down into three interrelated steps: i) simulation of sea level pressure fields, ii) simulation of daily mean sea conditions time series and iii) simulation of hourly sea state time series. Its effectiveness is demonstrated by synthetically generating multivariate hourly sea states from a specific location near the Spanish Coast. The direct comparison between simulated and empirical time series confirms the ability of the developed methodology to generate multivariate hourly time series of sea states. Finally, the potential of the proposed methodology to simulate multivariate time series at multiple locations and incorporate climate change issues is discussed.     

Development and application of a methodology for vulnerability assessment of climate change in coastal cities

This research is based on the need to develop methodology for climate change vulnerability assessment in coastal cities. While there have been some studies on the development of methodologies for vulnerability assessment on a national scale, there have been few attempts to develop a method for local vulnerability assessment with application to coastal cities. The objective of this study was to develop a general methodology to assess vulnerability to climate change and to apply it to the metropolitan coastal city of Busan in South Korea. We followed the conceptual framework for assessing climate change vulnerability provided by the Intergovernmental Panel on Climate Change (IPCC), which is composed of climate exposure, sensitivity, and adaptive capacity. Sea level rises of 0.5 m, 1 m, 2 m, and 3 m were considered as the climate exposure. Sensitivity to sea level rise was measured based on the percentage of flooded area calculated using flood simulation with a GIS tool. The population density and the population at age 65 years and over were also included in the calculation of sensitivity index. Sensitivities to heat wave and heavy rainstorm were quantified using the expert opinions from the Delphi survey and information on land use classification. Adaptive capacity was assessed in three sections: economic capability, infrastructure, and institutional capabilities. By combining the adaptive capacity and three different sensitivities, vulnerability to sea level rise (SLR-V), vulnerability to heavy rainstorm (HR-V), and vulnerability to heat wave (HW-V) were separately evaluated in 16 counties of Busan. Using cluster analysis, we could classify four major groups of counties based on SLR-V, HR-V, HW-V, and reported damage cost. For clustered groups, different adaptation strategies were suggested based on the different vulnerability patterns. Application of our methodology to Busan indicated that our methodology is easy to use and provides concrete policy implications when setting up adaptation strategies. The methodology developed in this study could also be used in mainstreaming climate change into Integrated Coastal Management (ICM).     

The impact of sea level rise and climate change on inshore wave climate: A case study for East Anglia (UK)

In coastal areas, offshore wave propagation towards the shore is influenced by water depth variations, due to sea bed bathymetry, tides and surges. Considering implications of climate change both on atmospheric forcing and sea level rise, a simple methodology involving numerical modelling is implemented to compute inshore waves from 1960 to 2099. Simulations take into account five scenarios of linear sea level rise and one climatic scenario for storm surges and offshore waves. The methodology is applied to the East Anglia coast (UK). Extreme event analysis is performed to estimate climate change implication on inshore waves and the occurrence of extreme events. It is shown, for this coastal region, that wave statistics are sensitive to the trend in sea level rise, and that the climate change scenario leads to a significant increase of extreme wave heights in the northern part of the domain. For nearshore points, the increase of the mean sea level alters not only extreme wave heights but also the frequency of occurrence of extreme wave conditions.     

Determination of internal wave properties from X-Band radar observations

The application of nautical X-Band radars to measure internal wave (IW) properties is investigated. A methodology based on the use of Radon transform (RT) techniques to detect internal wave related features from backscatter image sequences is introduced to compute properties such as direction of propagation, non-linear velocity (c₀), distance between solitons (L_cc) and number of solitons per packet. The proposed methodology was applied to several events recorded by a ship-mounted X-Band radar system (WaMoS) during the NLIWI experiment in 2006. Results from the comparisons to simultaneous measurements taken at neighboring oceanographic moorings indicated that c₀ can be estimated with a RMS error of 0.06 m s⁻¹, which corresponds to a mean relative error of −1.4%. Similarly, L_cc can be estimated with a RMS error of 98 m, which is associated with a mean relative error of 14.6%. This latter error estimate however is likely to be overestimated, because it reflects strongly the separation between sampling stations as L_cc was shown to be highly dependent on propagation distance. The accuracy of the results shows that X-Band systems are well suited to measure internal wave properties offering some advantages over SAR and other in situ devices.     

Estimation of mean and extreme waves in the East China Seas

Accurately estimating the mean and extreme wave statistics and better understanding their directional and seasonal variations are of great importance in the planning and designing of ocean and coastal engineering works. Due to the lack of long-term wave measurement data, the analysis of extreme waves is often based on the numerical wave hind-casting results. In this study, the wave climate in the East China Seas (including the Bohai Sea, the Yellow Sea and the East China Sea) for the past 35 years (1979–2013) is hind-casted using a third generation wave model – WAMC4 (Cycle 4 version of WAM model). Two sets of reanalysis wind data from NCEP (National Centers for Environmental Prediction, USA) and ECMWF (European Centre for Medium-range Weather Forecasts) are used to drive the wave model to generate the long-term wave climate. The hind-casted waves are then analysed to study the mean and extreme wave statistics in the study area. The results show that the mean wave heights decrease from south to north and from sea to land in general. The extreme wave heights with return periods of 50 and 100 years in the summer and autumn seasons are significantly higher than those in the other two seasons, mainly due to the effect of typhoon events. The mean wave heights in the winter season have the highest values, mainly due to the effect of winter monsoon winds. The comparison of extreme wave statistics from both wind fields with the field measurements at several nearshore wave observation stations shows that the extreme waves generated by the ECMWF winds are better than those generated by the NCEP winds. The comparison also shows the extreme waves in deep waters are better reproduced than those in shallow waters, which is partly attributed to the limitations of the wave model used. The results presented in this paper provide useful insight into the wave climate in the area of the East China Seas, as well as the effect of wind data resolution on the simulation of long-term waves.     

The comparison of altimeter retrieval algorithms of the wind speed and the wave period

With the launch of altimeter,much effort has been made to develop algorithms on the wind speed and the wave period.By using a large data set of collocated altimeter and buoy measurements,the typical wind speed and wave period algorithms are validated.Based on theoretical argument and the concept of wave age,a semi-empirical algorithm for the wave period is also proposed,which has the wave-period dimension,and explicitly demonstrates the relationships between the wave period and the other variables.It is found that Ku and C band data should be applied simultaneously in order to improve either wind speed or wave period algorithms.The dual-band algorithms proposed by Chen et al.(2002) for the wind speed and Quilfen et al.(2004) for the wave period perform best in terms of a root mean square error in the practical applications.     

High resolution downscaled ocean waves (DOW) reanalysis in coastal areas

Large-scale wave reanalysis databases (0.1°–1° spatial resolution) provide valuable information for wave climate research and ocean applications which require long-term time series (> 20 years) of hourly sea state parameters. However, coastal studies need a more detailed spatial resolution (50–500 m) including wave transformation processes in shallow waters. This specific problem, called downscaling, is usually solved applying a dynamical approach by means of numerical wave propagation models requiring a high computational time effort. Besides, the use of atmospheric reanalysis and wave generation and propagation numerical models introduce some uncertainties and errors that must be dealt with. In this work, we present a global framework to downscale wave reanalysis to coastal areas, taking into account the correction of open sea significant wave height (directional calibration) and drastically reducing the CPU time effort (about 1000 ×) by using a hybrid methodology which combines numerical models (dynamical downscaling) and mathematical tools (statistical downscaling). The spatial wave variability along the boundaries of the propagation domain and the simultaneous wind fields are taking into account in the numerical propagations to performance similarly to the dynamical downscaling approach. The principal component analysis is applied to the model forcings to reduce the data dimension simplifying the selection of a subset of numerical simulations and the definition of the wave transfer function which incorporates the dependency of the wave spatial variability and the non-uniform wind forcings. The methodology has been tested in a case study on the northern coast of Spain and validated using shallow water buoys, confirming a good reproduction of the hourly time series structure and the different statistical parameters.     

Modelling analysis of the sensitivity of shoreline change to a wave farm

Change of shoreline wave climate caused by the installation of a wave farm is assessed using the SWAN wave model. The 30 MW-rated wave farm is called the ‘Wave Hub’ and will be located 20 km off the north coast of Cornwall, UK. Changes in significant wave height and mean wave period due to the presence of the Wave Hub are presented. The results suggest that the shoreline wave climate will be affected, although the magnitude of effects decreases linearly as wave energy transmitted increases. At probable wave energy transmission levels, the predicted change in shoreline wave climate is small.     

Quantifying uncertainty in extreme values of design parameters with resampling techniques

In this paper, a methodology for the selection of statistical models for describing the extreme wave heights on the basis of resampling techniques is presented. Two such techniques are evaluated: the jackknife and the bootstrap. The methods are applied to two high-quality datasets of wave measurements in the Mediterranean and one from the East Coast of the USA. The robustness of the estimates of the extreme values of wave heights at return periods important for coastal engineering design is explored further. In particular, we demonstrate how an ensemble error norm can be used to select the most appropriate extreme probability model from a choice of cumulative distribution functions (CDFs). This error norm is based on the mean error norm of the optimised CDF for each resampled (replicate) data series. The resampling approach is also used to present confidence intervals of the CDF parameters. We provide a brief discussion of the sensitivity of these parameters and the suitability of each model in terms of uncertainty with resampling techniques. The advantages of resampling are outlined, and the superiority of the bootstrap over the jackknife in quantifying the uncertainty of extreme quantiles is demonstrated for these records.     

Inverse modeling of discrete interaction approximations for nonlinear interactions in wind waves

In the last two decades, the Discrete Interaction Approximation (DIA) has been the only economically feasible parameterization for nonlinear wave–wave interactions in operational wind wave models. Its major drawback is its limited accuracy. Several improvements to the DIA have been suggested recently. The present study summarizes these improvements and suggests some new modifications to the DIA. Using inverse modeling techniques, where the potential of various DIAs is assessed by optimal fitting to exact solutions, a comprehensive comparison of the potential of several such improvements is made. An in depth analysis of the behavior of DIAs in full wave models will be the subject of a second study, to be reported elsewhere. The major findings of this study are that: (i) An expanded definition of the representative quadruplet with additional degrees of freedom is necessary for an accurate representation of the exact interactions; (ii) Slowly varying the free parameters in such a DIA as a function of the spectral frequency f results in a (mostly qualitative) improvement; (iii) A DIA with expanded quadruplet definition and with four representative quadruplets is found to reproduce the exact source term accurately; (iv) Adding additional tunable constants to the equation for the strength of the interactions has little impact on the quality of the DIA.     

A simple approximation for wave refraction – Application to the assessment of the nearshore wave directionality

This work presents a simple and relatively quick methodology to obtain the nearshore wave angle. The method is especially valuable for curvilinear coasts where Snell’s law may provide excessively inaccurate results. We defined a correction factor, K, that depends on the geometry of the coast and on the wave climate. The values of this coefficient were obtained minimizing the differences with a sophisticated numerical model. The limitations and performance of the methodology are further discussed. The procedure was applied to a beach in Southern Spain to analyze the influence of shoreline geometry on nearshore wave directionality. Offshore and nearshore distributions of wave period and directions were analyzed, and the results showed that the geometry of the coast played a crucial role in the directionality of the nearshore waves, which also plays an important role in hydrodynamics. The methodology presented here is able to analyze and quantify the importance of this directionality without a noticeable computational cost, even when a long time series of wave data are considered. Hence, this methodology constitutes a useful and efficient tool for practical applications in Coastal and Ocean Engineering, such as sedimentary, wave energy, and wave climate studies.     

Wave climate variability of Taiwan waters

Global sea surface wind field data derived from NCEP reanalysis were used in driving a SWAN wave model to reconstruct historical wave records from 1948 to 2008. The reconstructed wave data were compared and verified by the observation of the data buoys of the Central Weather Bureau and the Water Resources Agency, Taiwan, and the National Data Buoy Center/National Oceanic and Atmospheric Administration, United States. Over the past six decades, the wave climate in Taiwan waters has undergone considerable changes. The annual mean significant wave heights have reduced an average of 0.31 cm/year. Winter wave heights have gradually dropped 0.86 cm/year, which are related to the weakening of winter monsoons. Regarding the inter-annual wave climate variation, the influence of El Niño/southern oscillation was substantial; the wave heights increased in La Niña years and decreased in El Niño years. In the past 60 years, extreme wave events have been concentrated in two periods: 1967–1974 and 2000–2008. More severe extreme wave events occurred in the latter compared with the former, and all were induced by typhoons. A clear trend, in which the summer (winter) extreme wave events have increased (decreased) gradually, has been identified. The 1980s was the transition period. After the transition period, the annual occurrence of extreme wave events caused by typhoons exceeded those caused by an intense outbreak of winter cold surges, although the total number of the annual extreme wave events has not changed substantially.     

Construction of synthetic ocean wave series along the Colombian Caribbean Coast: A wave climate analysis

In this paper a methodology is applied to generate synthetic wave series during mean and extreme conditions. An analysis is carried out that describes mean and extreme wave behavior for several climatic conditions along the Colombian Caribbean Coast. During mean conditions, the most energetic ocean waves are observed during the DJF season for both ENSO phases (El Niño and La Niña) for most of the Caribbean Sea. During the Niño years, there is a reduction in the speed of the north-east trade winds and their associated waves, but only in the DJF and MAM seasons. However, during the JJA season, this situation is reversed with the highest values occurring during El Niño and low values appearing during La Niña. Toward the east around the Guajira region, this general pattern is shown to change significantly. For extreme conditions, the results show a significant influence of extreme events toward the northwest, around La Guajira and the insular zones of San Andres and Providence when compared with other regions along the coast. All of these results (including the synthetic wave series) provide a design and management tool for the successful implementation of any coastal project (scientific or consulting) in Colombia.     

A simplified method to downscale wave dynamics on vertical breakwaters

A coastal structure is usually designed with the final objective to guarantee its functionality and stability throughout its life cycle. Regarding stability, the three main failure modes are sliding, overturning and failure of the foundations. To accomplish the design objectives, a design sea state is usually used when calculating the loads and scour around the structure. This design sea state corresponds to a certain sea state with specific return period values of a significant wave height. However, the combination of different simultaneous sea state parameters can produce other critical situations compromising the stability of the structure which then require the calculation of long time series of wave forces corresponding to long-term historical wave situations. Moreover, a design force associated to a certain return period can be defined from the time series of the stability parameters. The most accurate techniques which can be used to estimate structure stability are based on numerical and physical models, but these are very time consuming and the calculation of long time series is therefore unfeasible. Here, we propose a hybrid methodology to transform wave conditions into wave forces acting upon vertical structures and scour around it. The methodology consists of a selection of a subset of sea states representative of wave climate at the structure location, using a maximum dissimilarity algorithm, The wave forces acting upon the structure and scour around it, for the wave situations selected, are then estimated as is the reconstruction of the calculated parameters corresponding to historical sea states using an interpolation technique based on radial basis function. The validation of the results, through a direct comparison between reconstructed series and analytically (semi-empirical formulations) calculated ones, confirms the ability of the developed methodology to reconstruct time series of stability parameters on vertical breakwaters. This methodology allows its application to numerical and physical models.     

Roles of vertical turbulent mixing in the ocean response to Typhoon Rex (1998)

How the role of vertical turbulent mixing (VTM) in sea surface cooling (SSC) varies with the moving speed of a tropical cyclone was examined for Typhoon Rex (1998) by using the Meteorological Research Institute Community Ocean Model (MRI.COM). The MRI.COM well reproduced TRMM/TMI three-day mean sea surface temperature (SST) fields along Rex’s track. During the fast-moving phase of Rex, SSC simulated by the MRI.COM was caused by shear-induced VTM on the right side of the track. During the slowly-moving phase, on the other hand, the Ekman-pumping area mostly overlapped the VTM area right behind Rex’s center. During the recurvature phase, cool water transported by the upwelling was more efficiently entrained into a mixed layer by the VTM for nearly a 1 near-inertial period after the passage of Rex. We then modified the entrainment formulation of Deardorff (1983), which was incorporated into a slab mixed-layer ocean model (SOM) so as to fit to the results simulated by the MRI.COM. The principal modifications are as follows: (1) consideration of turbulent kinetic energy (TKE) production caused by surface wave breaking; (2) increase in the coefficient for estimating dissipation to balance with TKE production due to turbulent transport; and (3) changing the initial guess for the critical Richardson number. These modifications led to an improvement of SST simulations by the SOM. The impact of the modifications on simulated SSTs turned out to be more significant than the impacts of initial mixed-layer depth and the difference between diurnally-varying and daily mean short-wave radiation.     

Wind- and wave-field measurements using marine X-band radar-image sequences

This paper describes two algorithms for the retrieval of high-resolution wind and wave fields from radar-image sequences acquired by a marine X-band radar. The wind-field retrieval algorithm consists of two parts. In the first part, wind directions are extracted from wind-induced streaks, which are approximately in line with the mean surface wind direction. The methodology is based on the retrieval of local gradients from the mean radar backscatter image and assumes the surface wind direction to be oriented normal to the local gradient. In the second part, wind speeds are derived from the mean radar cross section. Therefore, the dependence of the radar backscatter on the wind vector and imaging geometry has to be determined. Such a relationship is developed by using neural networks (NNs). For the verification of the algorithm, wind directions and speeds from nearly 3300 radar-image sequences are compared to in situ data from a colocated wind sensor. The wave retrieval algorithm is based on a methodology that, for the first time, enables the inversion of marine radar-image sequences to an elevation-map time series of the ocean surface without prior calibration of the acquisition system, and therefore, independent of external sensors. The retrieved ocean-surface elevation maps are validated by comparison of the resulting radar-derived significant wave heights, with the significant wave heights acquired from three colocated in situ sensors. It is shown that the accuracy of the radar-retrieved significant wave height is consistent with the accuracy of the in situ sensors.     

Sand spit rhythmic development: A potential record of wave climate variations? Arçay Spit, western coast of France

This study aims at showing the sedimentary and geomorphological records of wave climate variations by spits. The studied spit (Arçay Spit) is located on the French Atlantic coast and has displayed a rapid elongation since the beginning of the 19th century that potentially represents a two century-long wave climate record. Wave climate and spit growth relationships are studied from two complementary methods: (1) numerical modelling of wave and longshore transport temporal and spatial variabilities, and (2) morphological monitoring based on the analysis of 4 historical maps (1811–1945), 8 aerial photographs (1945–2000) and 17 satellite SPOT images (1987–2005).Results at seasonal to interannual time-scales show that the sand spit area gain variations are the result of variations in longshore transport, themselves modulated mainly by wave height. Moreover, energetic swells seem to cause massive sand accumulation and spit elongation, whereas less energetic swells appear to be responsible for small sand accumulation and spit curvature. At longer time scale (decades to centuries), increasing spit growth phases are also synchronised with periods of energetic swells or high storm surge frequency. These results suggest that wave climate variations are the main factor controlling spit morphological evolutions.     

On the measurement of directional wave spectra at the southern Brazilian coast

The detailed reconstruction of the directional spectrum of wind waves from measurements of the wave field is an essential requirement for several applications, including the numerical modeling of wave evolution. Three reconstruction techniques that provide estimates of the directional distribution function D(f,θ), given the one-dimensional frequency spectrum, are compared using data from a coastal locality at the southern Brazilian coast. The techniques are the maximum entropy method (MEM), the Fourier Expansion Method using a cos² type function (FEM_cos) and the Fourier Expansion Method using a sech type function (FEM_sech). The main patterns of the wave climate at the study site are qualitatively assessed. Three main sea states, including swell, transition between local sea and swell, and directionally bimodal wind sea, are identified. Time series from three events associated with the main sea states provide test cases for inter comparison of the three reconstruction techniques. Maximum entropy estimates of D(f,θ) provide results that are more consistent than those obtained from the two FEM techniques in all cases considered.