Time Series Of Wave Height Research Articles

Predicting the Probability of Abrupt Changes to Wave‐Generated Seafloor Sand Ripples

AbstractA new, non‐dimensional ripple reset parameter and a stochastic point process model is used to estimate the likelihood of propagating ocean waves to form ripples on sandy seabeds. The ripple reset parameter is a function only of water depth, significant wave height, and mean grain size. Ripple formation is estimated by the magnitude of an intensity function based on a time series of the ripple reset parameter. The point process model is trained with a time series of observed waves and ripple change, and is then applied to predict the probability that a ripple field with a different geometry will form within a given time interval from another time series of wave data. The model is trained and tested with four field deployments at three field sites to determine its skill in predicting the ripple formation (a) at one field site over one time period after being trained with observations from the same site over a different time period, and (b) at one field site after being trained with observations from another field site. Results show that while the model is sufficient at predicting ripple formation in both scenarios, it is sensitive to the quality and quantity of the training data. Increasing the amount of training data greatly improves model performance. Employing a stochastic model based on a simple ripple reset parameter reduces tunable model parameters and provides a prediction of the probability for ripple formation given only a water depth, grain size, and time series of wave heights.

A machine learning approach to nearshore wave modeling in large lakes using land-based wind observations

This study presents a novel machine learning-based (ML) framework that utilizes the ConvLSTM-1D model to simulate wave heights at a nearshore location in Lake Michigan using a nonuniform land-based array of wind observations from a broad geographic region as an input. This approach was applied to Lake Michigan to perform a 70-year ice-free hindcast of waves near Chicago, IL (USA). Because of annual winter gaps in Great Lakes buoy observations, output from the Wave Information System model (WIS) was used for the training, validation, and testing of the ML model. Models with different numbers of wind stations were tested, showing that a single wind station as an input feature produced a reasonably accurate wave height. However, the wave height model accuracy increased as more wind input data was included from around the lake, largely plateauing beyond the inclusion of four stations that spanned Lake Michigan’s southern basin. The optimized model lookback period was found to be 10 h for all models, suggestive of a fetch-limited temporal coupling between the wind observations and nearshore waves. The extended time series showed a statistically significant increase in the interannual standard deviation of the storm wave height and the storm height over the mean wave height while no correlation was found with the annual water level time series. The ML framework offers a promising avenue for utilizing historical wind records to extend wave height time series for nearshore locations, particularly in enclosed and semi-enclosed basins where waves are strongly linked to local winds.

Defining an exposure index along the Schleswig-Holstein Baltic Sea coast

A wind exposure index (EI), which indicates the main physical driver of a coastal system, was developed along the Schleswig-Holstein Baltic Sea (SH) coast – Germany, to demonstrate the highly dynamic coastal stretches (i.e., potential erosion hotspots). The approach used three steps to define more accurate EIs. Initially, a representative wind year (RWY), which has similar physical characteristics as in the long-term data, was defined by analysing measured wind data from 2000 to 2019 at four stations distributed in the entire area of interest. The RWY was identified by a statistical comparison of wind speeds in 5 classes and 36 directional sectors between summer to summer yearly wind and the overall data. The selected RWY spanned from 01.09.2016 to 31.08.2017 and showed a reasonable agreement with the overall data (Skill = 0.77 and rmsd = 0.56 m/s). Next, high spatiotemporal nearshore hydrodynamics over the RWY were predicted using a model nesting approach of two domains in Delft3D. The predicted nearshore hydrodynamics indicated fair agreements with the measured data (R2: 0.87–0.90 for water levels and 0.75–0.86 for wave heights). Finally, the predicted water level and wave height time series in the nearshore area (∼ 5 m MSL depth) were used for the analysis of the EI adopting a 2-step procedure capturing short- and long-term correlations as well as seasonal long-range dependencies of the time series. This approach allows to model the clustering behaviour of extreme values of both parameters and provides reasonable EIs along the SH coast. The exposed areas display high EIs (e.g., 1 at the east of Fehmarn), while sheltered areas and bays have low values (e.g., 0 at Eckernförde Bay). The higher the EI the stronger the coastal dynamics and thus strong erosion can be expected. Interestingly, the EI varies considerably even along the exposed coastal stretches with long fetches, which indicates the sensitivity of the EI to the local morphology, which determines the nearshore hydrodynamics. Therefore, a definition of the EI based on nearshore hydrodynamics provides an accurate index of local physical drivers of a coastal system. The developed approach can be adopted to any coast, and provides useful information on the potential erosion areas for the coastal managers.

Evaluation of an experimental kelp farm’s structural behavior using regression modelling and response amplitude operators derived from in situ measurements

An experimental kelp farming system for exposed ocean conditions was designed, deployed, planted with kelp and instrumented for evaluation of its dynamic response to ocean waves, tides, and currents. The farm featured a novel “lattice” mooring design and anchor lines and cultivation lines (horizontal lines used as kelp growth substrate) made of fiberglass rods. The farm was deployed at a site in Saco Bay, Maine with 13 m (MLLW) water depth. There the farm was exposed to waves with heights up to 5.9 m. Anchor line tension, tide and wave height time series were gathered and processed into response amplitude operators (RAOs) and least squared error linear regression models enabling recognition of meaningful patterns between the forcing factors and the mooring response. Mean mooring line tensions were shown to increase nonlinearly with tide. Anchor line tension response amplitudes were shown to exhibit high sensitivity to both low and high frequency wave forcing. Numerical free-release test simulations suggested natural frequencies in heave of 0.91 Hz, indicating that tension response sensitivities at high frequency could be the result of resonance. Low frequency tension response disproportionate to the low frequency wave forcing could be explained by wave forcing on kelp cultivation arrays modulated by wave group envelopes. Instances of high magnitude, potentially damaging peak tensions, deemed shock loads, were prevalent in most load cases. Anchor line tension dynamics including RAO and shock load magnitudes were shown to be sensitive to mooring stiffness (ratio of tension to resulting elongation) and, in some cases, significant wave amplitude. Patterns of anchor line response indicated that additional mooring elasticity or geometric compliance and use of floatation with less sensitivity to high frequency waves could help avoid the cause of and costly consequences of amplified high frequency loading and high amplitude shock loading. RAOs and regression model results also indicated a subdued response in frequencies associated with ocean swell waves, suggesting desirable performance in waves most dominant in extreme storm events. With the proposed improvements, the farm system design suggests merit as a robust and durable macroalgae biomass production platform.

Comment on papers using machine learning for significant wave height time series prediction: Complex models do not outperform auto-regression

Significant Wave Height (SWH) is crucial in many aspect of ocean engineering. The accurate prediction of SWH has therefore been of immense practical value. Recently, Artificial Intelligence (AI) time series prediction methods have been widely used for single-point short-term SWH time-series forecasting, resulting in many AI-based models claiming to achieve good results. However, the extent to which these complex AI models can outperform traditional methods has largely been overlooked. This study compared five different models - AutoRegressive (AR), eXtreme Gradient Boosting (XGB), Artificial Neural Network (ANN), Long Short-Term Memory (LSTM), and WaveNet - for their performance on SWH time series prediction at 16 buoy locations. Surprisingly, the results suggest that the differences of performance among different models are negligible, indicating that all these AI models have only “learned” the linear auto-regression from the data. Additionally, we noticed that many recent studies used signal decomposition method for such time series prediction, and most of them decomposed the test sets, which is WRONG.

Improving the WAVEWATCH-III wave model results using data assimilation in the Persian Gulf

In this study, data assimilation with bulk and partitioned spectral parameters were integrated into the WAVEWATCH-III (WW3) wave model. The dependency of future forecasts on the current state in numerical models leads to an error flow in the results. Data assimilation schemes, such as the optimum interpolation, compensate for the problem by using available observations to minimize the error in the current state of the model. Different wind input and wave dissipation packages of WW3 were assessed for the Persian Gulf. The data assimilation scheme was integrated with the most successful formulation, ST3BJA. The enhanced WW3 model was assessed for two time periods in the Persian Gulf in which the wave data from three in-situ ADCPs were available. In addition, the satellite-derived wave height data within the computational domain were also used for model assessment. Assimilating the significant wave height data from in-situ measurements improved the model results in all cases and reduced the underestimation of significant wave height and improved the wave period statistics, significantly. The inclusion of mean wave period or use of partitioning the spectrum in the assimilation process resulted in spurious oscillations in the time series of peak wave period and significant wave height. Since the swells are not energetic in the Persian Gulf, the results from assimilation with partitioning spectrum scheme is not as successful as from assimilation scheme with the bulk parameters in reproducing accurate total wave height.

Storm identification for high-energy wave climates as a tool to improve long-term analysis

Coastal storms can cause erosion and flooding of coastal areas, often accompanied by significant social-economic disruption. As such, storm characterisation is crucial for an improved understanding of storm impacts and thus for coastal management. However, storm definitions are commonly different between authors, and storm thresholds are often selected arbitrarily, with the statistical and meteorological independence between storm events frequently being neglected. In this work, a storm identification algorithm based on statistically defined criteria was developed to identify independent storms in time series of significant wave height for high wave energy environments. This approach proposes a minimum duration between storms determined using the extremal index. The performance of the storm identification algorithm was tested against the commonly used peak-over-threshold. Both approaches were applied to 40 and 70-year-long calibrated wave reanalyses datasets for Western Scotland, where the intense and rapid succession of extratropical storms during the winter makes the identification of independent storm events notably challenging. The storm identification algorithm provides results that are consistent with regional meteorological processes and timescales, allowing to separate independent storms during periods of rapid storm succession, enabling an objective and robust storm characterisation. Identifying storms and their characteristics using the proposed algorithm allowed to determine a statistically significant increasing long-term trend in storm duration, which contributes to the increase in storm wave power in the west of Scotland. The coastal storm identification algorithm is found to be particularly suitable for high-energy, storm-dominated coastal environments, such as those located along the main global extratropical storm tracks.

Analysis of hybrid exploitation of wind and wave power in the Mediterranean and the Black Sea

The hybrid use of renewables enables resource complementation by other sources when one of them is inactive. This study focuses on wind and wave hybrids in the Mediterranean and the Black Sea with the aim of quantifying the potentials, directionality, correlation, and complementarity of the two sources. The investigation includes the spatial distributions and point-wise analysis capacity factors, the relationship between wave height and period, prevailing directions of wind and wave, bivariate probability analysis of wind and wave power, correlation of wind and wave power based on Pearson and Kendall’s Tau methods, and complementarity analysis by computing the active hours of one source when the other is inactive. The energy density, correlation, and complementarity analysis are realized considering the working conditions of a wind turbine with eight different wave energy converters by taking into account their power matrices. ERA5 dataset is used as a source for the wind and wave data in the basin with over six-decade long time series for each grid point. The results indicate that the wind turbine possesses higher capacity factors. For the wind turbine, the spatial maximum is 0.5, whereas for the wave energy converters, this value is 0.16 for the Pelamis device with the highest performance among the considered devices. The relationship between the wave climate parameters is investigated by fitting the wave height and period time series to an exponential function in all study area. Results are provided as spatial distributions of function coefficient which is hoped to be useful for the researchers when only one of the variables is known. Bivariate probabilities are computed for wind and wave power, and it is seen that for the selected analysis points, the wave power has a potential between 1 and 1.5 kW/m in the most probable axial locations. Directional analysis of wind and waves resulted in a map of the prevailing directions in the study area showing that the Northwest is the dominant direction. Correlation analysis between the wind and wave power time series of devices indicates that a positive correlation is evident in the study area up to + 0.69. The main result from the complementarity investigation accompanied by the correlation analysis showed that wind complementing wave condition is much more dominant in the region.

A frequency domain-based machine learning architecture for short-term wave height forecasting

Accurate and reliable short-term waves forecasting plays a crucial role in ensuring the safety of offshore operations. However, the non-stationary and high-noise characteristics of wave height time series in real-world environments present significant challenges for prediction. This paper introduces a novel lightweight machine learning forecasting architecture, named FreMixer, that leverages frequency domain information. Specifically designed for sequences with a low signal-to-noise ratio (SNR), FreMixer utilizes a Gaussian filter block for noise reduction and a Fourier block for frequency domain feature extraction. The Mixer block, which incorporates skip-connections, serves as the key component for feature learning. Towing tank experiments demonstrate the superior performance of FreMixer compared to benchmark models such as the autoregressive moving average (ARMA), long short-term memory (LSTM), and extreme gradient boosting (XGBoost) models. Due to its simple structure, FreMixer offers low deployment costs and high training efficiency, making it an attractive option for practical applications. Furthermore, the impact of training set size and historical window size on the performance is discussed.

An Evolutionary Artificial Neural Network approach for spatio-temporal wave height time series reconstruction

This paper proposes a novel methodology for recovering missing time series data, a crucial task for subsequent Machine Learning (ML) analyses. The methodology is specifically applied to Significant Wave Height (SWH) time series in the field of marine engineering. The proposed approach involves two phases. Firstly, the SWH time series for each buoy is independently reconstructed using three transfer function models: regression-based, correlation-based, and distance-based. The distance-based transfer function exhibits the best overall performance. Secondly, Evolutionary Artificial Neural Networks (EANNs) are utilised for the final recovery of each time series, using as inputs highly correlated buoys that have been intermediately recovered. The EANNs are evolved considering two metrics, the novel squared error relevance area, which balances the importance of extreme and around-mean values, and the well-known mean squared error. The study considers SWH time series data from 15 buoys in two coastal zones in the United States. The results demonstrate that the distance-based transfer function is generally the best transfer function, and that EANNs outperform a range of state-of-the-art ML techniques in 12 out of the 15 buoys, with a number of connections comparable to linear models. Furthermore, the proposed methodology outperforms the two most popular approaches for time series reconstruction, BRITS and SAITS, for all buoys except one. Therefore, the proposed methodology provides a promising approach, which may be applied to time series from other fields, such as wind or solar energy farms in the field of green energy.

Ensemble Hindcasting of Coastal Wave Heights

Long records of wave parameters are central to the estimation of coastal flooding risk and the causes of coastal erosion. This paper leverages the predictive power of wave height history and correlations with wind speed and direction to build statistical models for time series of wave heights to develop a method to fill data-gaps and extend the record length of coastal wave observations. A threshold regression model is built where the threshold parameter, based on lagged wind speed, explains the nonlinear associations, and the lagged predictors in the model are based on a well-established empirical wind-wave relationship. The predictive model is completed by addressing the residual conditional heteroscedasticity using a GARCH model. This comprehensive model is trained on time series data from 2005 to 2013, using wave height and wind data both observed from a buoy in Long Island Sound. Subsequently, replacing wind data with observations from a nearby coastal station provides a similar level of predictive accuracy. This approach can be used to hindcast wave heights for past decades given only wind information at a coastal station. These hindcasts are used as a representative of the unobserved past to carry out extreme value analysis by fitting Generalized Pareto (GP) distribution in a peaks over threshold (POT) framework. By analyzing longer periods of data, we can obtain reliable return value estimates to help design better coastal protection structures.

HyWaves: Hybrid downscaling of multimodal wave spectra to nearshore areas

Long-term and accurate wave hindcast databases are often required in different coastal engineering projects. The assessment of the nearshore wave climate is often accomplished by using downscaling techniques to translate offshore waves to coastal areas. However, dynamical downscaling approaches may incur huge computational cost. Additionally, the common use of bulk parameterizations are often not accurate for multidimensional waves. To overcome these limitations, we present a hybrid downscaling approach that combines mathematical algorithms (statistical downscaling) and numerical modeling (dynamical downscaling) over the individual spectral partitions. Every wave partition is downscaled and aggregated afterward by using principles of wave linear theory. By assuming linearity in the propagation of the wave celerity, the application of the method is limited from offshore to intermediate water depths. In addition, the method proposed uses a technique to simplify the spectral boundary conditions in complex domains. The methodology has been applied and validated in the island states of Samoa, American Samoa, Majuro, and Kwajalein, showing good skill at reproducing the spectral hourly time series of significant wave height, peak period, and peak direction. Moreover, an accurate representation of the observed energy spectrum was achieved. This study provides insight into the numerical approximation of the combined sea-swell states while improving the quality of fast spectral forecasting and early warning systems.

Evaluation of Hybrid Soft Computing Model’s Performance in Estimating Wave Height

In coastal and port engineering, wind-generated waves have always been a crucial, fundamental, and important topic. As a result, various methods for estimating wave parameters, including field measurement and numerical methods, have been proposed over time. This study evaluates the wave height at Sri-Lanka Hambantota Port using soft computing models such as Artificial Neural Networks (ANNs) and the M5 model tree (M5MT). In order to overcome its nonstationarity, the primary wave height time series were divided into subtime series using the wavelet transform. The collected subtime series were then utilized as input data for ANN and M5MT in order to determine the wave height. For the sake of the model performance, the daily wind and wave data from the Acoustic Wave and Current (AWAC) sensor for Hambantota Port in 2020 and Sanmen Bay in 2017 were used in this study. The training state utilizes 80% of the available data, while the test state uses 20%. The Root Mean Square Error (RMSE) of the ANN, M5, WANN, and Wavelet-M5 models in the Hambantota Port for the test stage are 0.12, 0.11, 0.04, and 0.06, respectively. While in Sanmen Bay, the RMSE of the ANN, M5, WANN, and Wavelet-M5 models for the test stage are 0.14, 0.16, 0.06, and 0.08, respectively. According to the findings of this study, the accuracy of WANN and Wavelet-M5 hybrid models in evaluating wave height is superior to that of classic ANN and M5MT, and it is recommended that WANN and Wavelet-M5 hybrid models be used to estimate wave height.

Hindcasting and predicting surge heights and waves on the Taiwan coast using a hybrid typhoon wind and tide-surge-wave coupled model

The tide-surge-wave coupled model and hybrid typhoon wind model were developed for the Taiwan coast and employed to predict surge heights and waves under different influential factors during historical typhoon events. The results revealed that the hybrid wind model matched the measured atmospheric pressure and wind speed time series during Typhoon Soudelor (2015) and Typhoon Nesat (2017). Afterward, the measured water level, wave height, and wave period time series at different measuring stations were used to validate the tide-surge-wave coupled model. The coupled model reasonably reproduced the measured data. Subsequently, the validated model was utilized to explore the influence of the radius of maximum wind (RMW), forward speed, atmospheric pressure, wind intensity, and typhoon path on surge height, wave height, and wave setup. The results with model prediction indicate that increasing the RMW causes an increasing negative surge height and wave height and shifts the time of the peak positive surge height and peak wave height. A smaller forward speed results in a larger positive peak surge height and peak wave height at most stations. The maximum ratio changes in negative peak surge height compared with the baseline condition with Typhoon Soudelor (2015) are 105.4% and −116.0% for increasing and decreasing 20 hPa atmospheric pressures at the Linshanbi station, respectively. The differences in maximum peak wave height (ratio change) for an increasing and decreasing 10 m/s wind speed are 6.44 m (47.2%) and −5.80 m (−42.4%), respectively. The predicted results indicate that the difference in the maximum peak positive surge height (maximum ratio change) compared with the baseline condition is 1.1 m (315.2%), thereby shifting the typhoon track to the north by 100 km at the Waipu station.

Stochastic simulation of wind wave parameters for energy production

A combination of stochastic and deterministic models is applied for the study of ocean wind waves. Timeseries of significant wave height and mean zero up-crossing period, obtained from globally scattered floating buoys, are analyzed in order to construct a double periodic model, and select an optimal marginal distribution and dependence function for the description of the stochastic structure of wind waves. It is concluded that wind waves, in contrast to the atmospheric wind speed process, are mostly governed by the seasonal periodicity rather than the diurnal periodicity, which is often weak and can be neglected. Also, the Pareto-Burr-Feller distribution is found to be a fair selection among other common three-parameter marginal distributions. The dependence function is simulated through the Hurst-Kolmogorov (HK) dynamics using the climacogram (i.e., variance of the averaged process in the scale domain), a stochastic tool that can robustly estimate both the short-term fractal and long-range dependence behaviors both apparent at the wind wave process. To test the validity of the model, a stochastic synthesis of the wind wave process is performed through the Symmetric Moving Average scheme, focused on the explicit preservation of the probabilistic and the dependence structures. Finally, the stochastic model is applied for simulation to an offshore station southeast of Australia having one of the largest record lengths. The energy potential is also estimated through the significant wave height and the mean zero up-crossing period of both the synthetic and observed timeseries, and the effectiveness of the model is further discussed.

Gradual versus episodic lateral saltmarsh cliff erosion: Evidence from Terrestrial Laser Scans (TLS) and Surface Elevation Dynamics (SED) sensors

As lateral erosion can threaten valuable saltmarsh habitats and their capacity to protect the hinterland from waves and floods, there is a need to understand the mechanisms of erosion. We monitored lateral saltmarsh erosion at high spatiotemporal resolution during a 2.5 year period. We performed terrestrial laser scans (TLS) with centimetric spatial resolution, ca monthly, as well as before and after 2 wind events to assess morphological change of a saltmarsh cliff (<0.8 m in height), and deployed surface elevation dynamics (SED) sensors at 3 locations to obtain daily measurements of the cliff edge position with 2 mm resolution. This was complemented by wind data, and a pressure transducer on the mudflat to obtain time-series of local inundation duration, water depth, wave height, period, power and energy. TLS shows gradual lateral erosion of the marsh edge and surface, and occasional local slumping, with substantial local variation. SED sensor data also reveal that lateral erosion was mostly continuous, with episodes with stronger and weaker local erosion, at all 3 locations, often correlated in space. Correlations between changes in total marsh area and sediment volume of the mudflat-saltmarsh interface from TLS with particularly inundation duration and wind velocity were discussed. At plot level, correlations were not consistent; correlations between the local lateral erosion rates and hydrodynamics/winds were not significant. Results emphasize the importance of common low magnitude events for long-term lateral erosion.

The Feasibility of the ERA5 Forced Numerical Wave Model in Fetch-Limited Basins

Numerical wave models are critical in hindcasting reliable long-term time series of significant wave heights, which play a crucial role in coastal and ocean engineering activities. Although wind fields are an important input to numerical wave models, few studies have investigated the feasibility of the widely used ERA5 wind reanalysis dataset in fetch-limited basins. In this work, we investigated the feasibility of the ERA5 forced numerical wave model (SWAN) in fetch-limited basins. ERA5 wind velocities were first compared to ground-based meteorological stations, showing poorer accuracy compared to finer gridded ALADIN wind data. Subsequently, the white-capping coefficient Cds in the Janssen white-capping formulation was calibrated separately using a surrogate model when establishing the ERA5 and ALADIN forced wave models. The calibrated ERA5 forced model showed a similar agreement to wave buoy data as the calibrated ALADIN forced wave model during the calibration period and even superior accuracy in the validation period. Overall, these results show that the wave model calibration procedure mitigates the effect of the poorer accuracy of the ERA5 wind data on the significant wave height results. Nevertheless, both ERA5 and ALADIN forced wave models showed an alarming overprediction for high simulated significant wave heights.

Filling gaps in significant wave height time series records using bidirectional gated recurrent unit and cressman analysis

Continuous records of wave data are of great significance for marine researches and analyses. However, the measurement of wave by buoys is often interrupted for various reasons. In this paper, five machine learning methods were employed to fill in the missing significant wave height (Hs) data: random forest (RF), support vector machine (SVM), artificial neural network (ANN), gated recurrent unit (GRU) and bidirectional gated recurrent unit (BiGRU). Inputs to the model are the relevant meteorological data from one or more buoys in the vicinity of the target buoy. Then, this study adopted a data assimilation method, Cressman analysis (CA), to correct the outputs of the models. The performances of the five models before and after correction (RF-CA, SVM-CA, ANN-CA, GRU-CA, BiGRU-CA) were compared horizontally and vertically. The statistical results for the test period showed that BiGRU significantly outperforms the other four models, with lower RMSE and scatter index, and higher correlation coefficients. By CA, the errors of the five models were reduced to different degrees, and BiGRU has the most reduction. Multiple tests showed that the performance of BiGRU-CA was more stable than that of RF-CA, SVM-CA, ANN-CA and GRU-CA, and its estimation of storm waves was also accurate and reliable.

Significant wave height forecasting using hybrid ensemble deep randomized networks with neurons pruning

The reliable control of wave energy devices highly relies on the forecasts of wave heights. However, the dynamic characteristics and significant fluctuation of waves’ historical data pose challenges to precise predictions. Neural networks offer a promising solution to forecast the wave heights by extracting meaningful features from historical observations. This paper proposes a novel hybrid random vector functional link network with the ensemble and deep learning benefits. Hierarchical stacks of hidden layers are constructed to enforce the deep representations of the time series. Individual output layers follow all enhancement layers to adopt ensemble learning. A neuron pruning strategy is proposed to remove the noisy information from the random features and boost the network’s performance. Besides, the proposed network is further utilized to forecast the additive and multiplicative residuals from the ARIMA method. Finally, the ensemble of additive-ARIMA-edRVFL, multiplicative-ARIMA-edRVFL, and edRVFL achieves the best average rankings around two for three forecasting horizons. The proposed ensemble achieves an average ranking of 1.33 on four-hours ahead of forecasting in terms of root mean square error and mean absolute scaled error. Extensive experiments are conducted on twelve time series of the significant wave height. The comparative results demonstrate the superiority of the proposed model over other state-of-the-art methods. The source codes are available on https://github.com/P-N-Suganthan/CODES.

A mixed distribution to fix the threshold for Peak-Over-Threshold wave height estimation

Modelling extreme values distributions, such as wave height time series where the higher waves are much less frequent than the lower ones, has been tackled from the point of view of the Peak-Over-Threshold (POT) methodologies, where modelling is based on those values higher than a threshold. This threshold is usually predefined by the user, while the rest of values are ignored. In this paper, we propose a new method to estimate the distribution of the complete time series, including both extreme and regular values. This methodology assumes that extreme values time series can be modelled by a normal distribution in a combination of a uniform one. The resulting theoretical distribution is then used to fix the threshold for the POT methodology. The methodology is tested in nine real-world time series collected in the Gulf of Alaska, Puerto Rico and Gibraltar (Spain), which are provided by the National Data Buoy Center (USA) and Puertos del Estado (Spain). By using the Kolmogorov-Smirnov statistical test, the results confirm that the time series can be modelled with this type of mixed distribution. Based on this, the return values and the confidence intervals for wave height in different periods of time are also calculated.