Time Series Of Significant Wave Height Research Articles

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.

Significant wave height modelling and simulation of the monsoon-influenced South China Sea coast

The modelling of ocean wave dynamics and future possible scenario simulations is crucial as coastal communities with offshore and shipping industries can be impacted. Therefore, this study modelled and simulated the significant wave height (SWH) dynamics for both long-term (decadal) and northeast monsoons using a discrete-time stochastic process. These processes were successfully performed by applying the data from the European Centre for Medium-Range Weather Forecasts (ECMWF) database at the offshore point of Terengganu, Malaysia, in the South China Sea. The SWH time series were analysed and modelled by decomposing the series into non-stationary and stationary components. Consequently, the five-term Fourier series was adequate to model the non-stationary component for long-term and northeast monsoon time series. Meanwhile, the stationary component followed the autoregressive AR(2) process with stationary white noise residual fitted to t location-scale distribution. The model simulated the significant wave, which well-represented the time series behaviour. Thus, the simulation outcome could contribute to coastal response studies. These contributions included long-term prediction of coastal response, investigation of coastal response during the northeast monsoon season, and further development of other seasonal component models influencing the South China Sea.

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.

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.

Numerical Study on Spatio-Temporal Distribution of Cold Front-Induced Waves along the Southeastern Coast of China

Cold fronts, as one of the most frequent extreme weather events, can induce significant waves on the sea. This work analyzes the spatial and temporal variations in cold front events, especially the characteristics of wind directions during cold fronts in the East China Sea (ECS). The SWAN (Simulating Waves Nearshore) model is applied to simulating the waves induced by cold fronts. To calibrate the model, two typical cold front events were selected to simulate the corresponding waves in the ECS. The results indicate that the data misfit between the observed and modeled significant wave heights (SWH) is within a reasonable range. Idealized sensitivity experiments were then designed in order to analyze and discuss the responses of ocean waves to wind direction, swell distribution, maximum of significant wave heights (MSWH), and time lag during the cold fronts. The results show that the average MSWH in the ECS decreases monotonically with the deflection of wind direction from north-east to north-west, while specific nearshore sites do not conform to this pattern due to topography. The time series of SWH indicate that the action of the swells leads to a prolongation of the duration of catastrophic waves. This work investigates the temporal and spatial distribution characteristics of cold front-induced wind wave fields in offshore Zhejiang, which has important value for the study of the impact of cold fronts on the ocean as well as disaster prevention and mitigation efforts.

Detection and quantification of trends in time series of significant wave heights: An application in the Mediterranean Sea

The analysis of long-term trends in time series of wave parameters has an high engineering relevance. These trends may affect the estimates of parameters with high return period that are used for the design of several engineering projects. This work analyses the use of linear regressions for detecting and quantifying long-term trends in time series of data. In particular, the reliability of a linear trend slope, modified in order to minimize the weight of possible outliers, is evaluated. To this end, this slope is compared against the outcomes of two methods that do not imply the hypothesis of linear trend: the Mann–Kendall test and the Innovative Trend Analysis. An application to significant wave height time series over the Mediterranean Sea is presented. Time series of 40 years of numerical hindcast of sea states over the whole basin were analysed, and the methods taken into account were applied to the annual maxima, the annual 98th percentile and the annual mean significant wave height. The results show that the use of the investigated linear slope is meaningful, therefore this was used to assess the spatial distribution of trends in the Mediterranean Sea. Results are presented and discussed for all the statistics investigated.

An application of a machine learning algorithm to determine and describe error patterns within wave model output

This study uses a machine learning algorithm, the bagged regression tree, to detect error patterns within 24-h forecasts of significant wave height time series. The input to the machine learning algorithm were bulk parameter outputs of the numerical wave model (WaveWatch III) and wind information from the Global Forecast System at buoy locations along the California-Oregon border in the United States. The output of the algorithm were predictions of hourly deviations between numerical model output and buoy observations of significant wave height. When these deviations were applied as corrections to the forecasts, error metrics root-mean-squared-error, bias, percent error, and scatter index were reduced in several different experiments, confirming that the error pattern was successfully detected by the machine learning algorithm. Furthermore, the detected error pattern was consistent between buoys at different locations, as presented in a geo-spatial application of the machine learning algorithm. As a descriptive tool, the algorithm delineated regions of similar error within the context of model phase space (significant wave height and mean wave period (Tm01)). Specifically, the algorithm detected significant wave height overestimations for significant wave heights greater than 3.4 m, wave period greater than 9.1 s, and waves coming from the W-NW quadrant.Also, for significant wave heights greater than the 95th percentile value (5.4 m), the algorithm detected differences in model phase space associated with mean error patterns.

Projected sea level rise and changes in extreme storm surge and wave events during the 21st century in the region of Singapore

Abstract. Singapore is an island state with considerable population, industries, commerce and transport located in coastal areas at elevations less than 2 m making it vulnerable to sea level rise. Mitigation against future inundation events requires a quantitative assessment of risk. To address this need, regional projections of changes in (i) long-term mean sea level and (ii) the frequency of extreme storm surge and wave events have been combined to explore potential changes to coastal flood risk over the 21st century. Local changes in time-mean sea level were evaluated using the process-based climate model data and methods presented in the United Nations Intergovernmental Panel on Climate Change Fifth Assessment Report (IPCC AR5). Regional surge and wave solutions extending from 1980 to 2100 were generated using ∼ 12 km resolution surge (Nucleus for European Modelling of the Ocean – NEMO) and wave (WaveWatchIII) models. Ocean simulations were forced by output from a selection of four downscaled ( ∼ 12 km resolution) atmospheric models, forced at the lateral boundaries by global climate model simulations generated for the IPCC AR5. Long-term trends in skew surge and significant wave height were then assessed using a generalised extreme value model, fit to the largest modelled events each year. An additional atmospheric solution downscaled from the ERA-Interim global reanalysis was used to force historical ocean model simulations extending from 1980 to 2010, enabling a quantitative assessment of model skill. Simulated historical sea-surface height and significant wave height time series were compared to tide gauge data and satellite altimetry data, respectively. Central estimates of the long-term mean sea level rise at Singapore by 2100 were projected to be 0.52 m (0.74 m) under the Representative Concentration Pathway (RCP)4.5 (8.5) scenarios. Trends in surge and significant wave height 2-year return levels were found to be statistically insignificant and/or physically very small under the more severe RCP8.5 scenario. We conclude that changes to long-term mean sea level constitute the dominant signal of change to the projected inundation risk for Singapore during the 21st century. We note that the largest recorded surge residual in the Singapore Strait of ∼ 84 cm lies between the central and upper estimates of sea level rise by 2100, highlighting the vulnerability of the region.

Hybrid wavelet-GMDH model to forecast significant wave height

In this study, the group method of data handling (GMDH)-based wavelet transform (WT) was developed to forecast significant wave height (SWH) in different lead times. The SWH dataset was collected from a buoy station located in the North Atlantic Ocean. For this purpose, the time series of SWH was decomposed into some subseries using WT and then decomposed time series were imported to the GMDH model to forecast the SWH. Performance of the wavelet group method of data handling (WGMDH) model was evaluated using an index of agreement (Ia), coefficient of efficiency and root mean square error. The analysis proved that the model accuracy is highly dependent on the decomposition levels. The results showed that the WGMDH model is able to forecast the SWH with a high reliability.

The Effect of Declustering in the r-Largest Maxima Model for the Estimation of HS-Design Values

A major problem often encountered in design sea-state prediction is the limited amount of available extreme- type wave data. The Annual Maxima model is consistent with the conditions of the mathematical background of Extreme Value Theory, yet its application raises statistical uncertainties in cases where the initial data population is limited. Due to this, alternative models of similar theoretical background have been developed to describe extreme values, including the maxima method. A main problem in applying this model refers to the appropriate selection of a sample com- prising the r independent maxima within each year of the available time series: since in nature environmental extremes tend to appear in clusters, the native time series under examination should be appropriately de-clustered to satisfy the independency assumption. Some established declustering procedures refer to: a) the selection of a Standard Storm Length, b) the combination of a run length k and a relatively high threshold value u (Runs declustering), c) the estima- tion of wave energy reductions between consecutive sea-state systems (DeClustering Algorithm) and d) the selection of the three largest monthly maxima of each year of the initial significant wave height time series (triple annual maximum series). The aim of this paper is to assess the effect of the aforementioned declustering procedures on the numerical results obtained by the r-largest model.

Investigating the Multifractal Properties of Significant Wave Height Time Series Using a Wavelet-Based Approach

Singularities play a significant role in the characterization of time series. The temporal characteristics of fluctuating significant wave height time series are investigated in this study. The hourly time series from 24 stations located off the west coast of the United States are used for the analysis. The multifractal nature of these time series is unveiled by employing a wavelet-based method. The wavelet transform modulus maxima method is applied to obtain the multifractal spectra (singularity spectrum) of the significant wave height series. The multifractal spectra and their parameters such as peak, min and max Holder exponents, skewness coefficients, and support lengths are calculated. The peak Holder exponent ranged from 0.30 to 0.46 throughout the study area. Holder exponents that are less than 0.5 indicate that the time series exhibits an antipersistent random walk. The spatial variation of parameters is depicted through kriging maps. Different spatial variation patterns can be seen from the maps. It is clear that deep offshore stations have relatively higher Holder exponents than coastal areas. This change can be related to the wave generation mechanism, by way of physical interpretations. Since the stations located in the deep offshore can receive more swell waves than coastal zones and are open to large-scale storms, they may tend to be more persistent and have greater Holder exponents. Also, the type of the singularities occurring in deep offshore and in the coastal zones is assessed by considering the wave generating mechanisms.

A generalized approach for long-term modelling of extreme crest-to-trough wave heights

This paper deals with the long-term modelling of high sea waves. The solution is given for the return period of sea storms during which an arbitrary chosen number of waves, with crest-to-trough heights exceeding a fixed threshold, occur. This return period is derived starting from the Equivalent Triangular Storm (ETS) model, which associates a triangle to each actual storm and thus represents a significant wave height time series at a fixed location by means of a sequence of triangular storms. The short-term statistics is then applied to investigate the occurrence of large crest-to-trough wave heights during a given storm. Finally, by combining the statistical distribution of significant wave heights, the ETS model and the short-term wave statistics, the solution is given for the return periods R N and R ⩾ N of a sea storm in which N or at least N waves higher than a fixed threshold occur. The values of R N are then calculated, starting from data of two buoys moored in the Pacific Ocean and in the Mediterranean Sea.

Impact of Multisatellite Altimeter Data Assimilation on Wave Analysis and Forecast

Satellite altimetry has become an important discipline in the development of sea-state forecasting or more generally in operational oceanography. Météo-France Marine and Oceanography Division is much involved in altimetry, in which it is also one of the main operational customers. Sea-state forecasts are produced every day with the help of numerical models assimilating Fast Delivery Product altimeter data from ESA ERS-2 satellite, available in real-time (3–5 h). These forecasts are transmitted to seamen as part of safety mission of persons and properties, or specific assistance for particular operations. With the launch of ENVISAT (from ESA, launched on 1 March 2002, to take over the ERS mission) and JASON-1 (from CNES/NASA, launched on 7 December 2001, successor of TOPEX/Poseidon), we have an unprecedented opportunity of improved coverage with the availability in quasi-real-time of data from several altimeters. The objective of this study is to evaluate the impact of using multisources of altimeter data in real-time, to improve wave model analyses and forecasts, at global scale. Since July 2003, Météo-France injects the wind/wave JASON-1 Operational Sensor Data Record on the WMO Global Transmitting System, making them available in near real-time to the international meteorological community. Similarly, fast delivery altimeter data of ENVISAT will improve coverage and contribute to the constant progress of marine meteorology. For this purpose, significant wave height time series were generated using the Wave Model WAM and the assimilation of altimeter wave heights from two satellites ERS-2 and JASON-1. The results were then compared to Geosat Follow-On (GFO, U.S. Navy Satellite) and moored buoy wave data. It is shown that the impact of data assimilation, when two (ERS-2 and JASON-1) or three (ERS-2 with JASON-1 and GFO) sources of data are used instead of one (ERS-2), in term of significant wave height, is larger in wave model analyses but smaller in wave model forecasts. However, there is no improvement in terms of wave periods, both in the analysis and forecast periods.

The Reconstruction of Significant Wave Height Time Series by Using a Neural Network Approach

A Multivariate Neural Network (MNN) algorithm is proposed for the reconstruction of significant wave height time series, without any increase of the error of the MNN output with the number of modelled data. The algorithm uses a weighted error function during the learning phase, to improve the modelling of the higher significant wave height. The ability of the MNN to reconstruct sea storms is tested by applying the equivalent triangular storm model. Finally an application to the NOAA buoys moored off California shows a good performance of the MNN algorithm, both during sea storms and calm time periods.

On The Applicability Of Hindcast Time Series For The Prediction Of ExtremeSea Storms

An analytical solution for the return period R(H,>h) of a sea storm in which the maximum significant wave height H, exceeds a fixed threshold h can be based on the 'equivalent sea' assumption: each actual storm is replaced by a triangular storm, where the triangle height a gives the storm intensity and the triangle base b the storm duration. The base-height regression, which is proven to be very useful for the risk analysis, may be then estimated from (ai,bi) values of all the storms. In this paper some preliminary results concerning the applicability of the hindcast data for the risk analysis are proposed. In particular some significant wave height time series are derived for the Adriatic Sea, by using a third generation wave model (SWAN) forced with wind fields obtained from a last generation meteorological model (COAMPS). These data are firstly validated, by comparison with measured data. The hindcast data are then processed to obtain the 'equivalent sea' and finally analysed to assess the sensitivity of the equivalent triangular storm model to the sampling rate.