Forecasting ocean wave energy: The ECMWF wave model and time series methods

Recently, the technology has been developed to make wave farms commercially viable. Since electricity is perishable, utilities will be interested in forecasting ocean wave energy. The horizons involved in short-term management of power grids range from as little as a few hours to as long as several days. In selecting a method, the forecaster has a choice between physics-based models and statistical techniques. A further idea is to combine both types of models. This paper analyzes the forecasting properties of a well-known physics-based model, the European Center for Medium-Range Weather Forecasts (ECMWF) Wave Model, and two statistical techniques, time-varying parameter regressions and neural networks. Thirteen data sets at locations in the Atlantic and Pacific Oceans and the Gulf of Mexico are tested. The quantities to be predicted are the significant wave height, the wave period, and the wave energy flux. In the initial tests, the ECMWF model and the statistical models are compared directly. The statistical models do better at short horizons, producing more accurate forecasts in the 1-5 h range. The ECMWF model is superior at longer horizons. The convergence point, at which the two methods achieve comparable degrees of accuracy, is in the area of 6 h. By implication, the physics-based model captures the underlying signals at lower frequencies, while the statistical models capture relationships over shorter intervals. Further tests are run in which the forecasts from the ECMWF model are used as inputs in regressions and neural networks. The combined models yield more accurate forecasts than either one individually.     

Forecasting ocean wave energy: Tests of time-series models

This paper evaluates the ability of time-series models to predict the energy from ocean waves. Data sets from four Pacific Ocean sites are analyzed. The energy flux is found to exhibit nonlinear variability. The probability distribution has heavy tails, while the fractal dimension is non-integer. This argues for using nonlinear models. The primary technique used here is a time-varying parameter regression in logs. The time-varying regression is estimated using both a Kalman filter and a sliding window, with various window widths. The sliding window method is found to be preferable. A second approach is to combine neural networks with time-varying regressions, in a hybrid model. Both of these methods are tested on the flux itself. Time-varying regressions are also used to forecast the wave height and wave period separately, and combine the forecasts to predict the flux. Forecasting experiments are run at an hourly frequency over horizons of 1-4 h, and at a daily frequency over 1-3 days. All the models are found to improve relative to a random walk. In the hourly data sets, forecasting the components separately achieves the best results in three out of four cases. In daily data sets, the hybrid and regression models yield similar outcomes. Because of the intrinsic variability of the data, the forecast error is fairly high, comparable to the errors found in other forms of alternative energy, such as wind and solar.     

Estimation of infragravity waves at intermediate water depth

The accuracy of nearshore infragravity wave height model predictions has been investigated using a combination of the spectral short wave evolution model SWAN and a linear 1D SurfBeat model (IDSB). Data recorded by a wave rider located approximately 3.5 km from the coast at 18 m water depth have been used to construct the short wave frequency-directional spectra that are subsequently translated to approximately 8 m water depth with the third generation short wave model SWAN. Next the SWAN-computed frequency-directional spectra are used as input for IDSB to compute the infragravity response in the 0.01 Hz–0.05 Hz frequency range, generated by the transformation of the grouped short waves through the surf zone including bound long waves, leaky waves and edge waves at this depth. Comparison of the computed and measured infragravity waves in 8 m water depth shows an average skill of approximately 80%. Using data from a directional buoy located approximately 70 km offshore as input for the SWAN model results in an average infragravity prediction skill of 47%. This difference in skill is in a large part related to the under prediction of the short wave directional spreading by SWAN. Accounting for the spreading mismatch increases the skill to 70%. Directional analyses of the infragravity waves shows that outgoing infragravity wave heights at 8 m depth are generally over predicted during storm conditions suggesting that dissipation mechanisms in addition to bottom friction such as non-linear energy transfer and long wave breaking may be important. Provided that the infragravity wave reflection at the beach is close to unity and tidal water level modulations are modest, a relatively small computational effort allows for the generation of long-term infragravity data sets at intermediate water depths. These data can subsequently be analyzed to establish infragravity wave height design criteria for engineering facilities exposed to the open ocean, such as nearshore tanker offloading terminals at coastal locations.     

Learning from data for wind-wave forecasting

Along with existing numerical process models describing the wind-wave interaction, the relatively recent development in the area of machine learning make the so-called data-driven models more and more popular. This paper presents a number of data-driven models for wind-wave process at the Caspian Sea. The problem associated with these models is to forecast significant wave heights for several hours ahead using buoy measurements. Models are based on artificial neural network (ANN) and instance-based learning (IBL) .To capture the wind-wave relationship at measurement sites, these models use the existing past time data describing the phenomenon in question. Three feed-forward ANN models have been built for time horizon of 1, 3 and 6 h with different inputs. The relevant inputs are selected by analyzing the average mutual information (AMI). The inputs consist of priori knowledge of wind and significant wave height. The other six models are based on IBL method for the same forecast horizons. Weighted k-nearest neighbors (k-NN) and locally weighted regression (LWR) with Gaussian kernel were used. In IBL-based models, forecast is made directly by combining instances from the training data that are close (in the input space) to the new incoming input vector. These methods are applied to two sets of data at the Caspian Sea. Experiments show that the ANNs yield slightly better agreement with the measured data than IBL. ANNs can also predict extreme wave conditions better than the other existing methods.     

Hindcast of the wave conditions along the west Iberian coast

This paper describes the development of a wave prediction system for the west Iberian coast. The implemented wave prediction system is based on two state-of-the-art spectral wave models, WAM for the ocean area and SWAN for the nearshore. However, because of its extended geographical space the SWAN model will include some generation effects in the coarse SWAN simulations, complemented by wave transformation effects near the coast. The system was validated by means of extended hindcast runs in various regions belonging to the continental Portuguese coastal environment, which were compared with buoy data, focusing on the extreme energetic events and both direct comparisons and statistical results are presented.     

Forecasting seasonal to multi-year shoreline change

This contribution details a simple empirical model for forecasting shoreline positions at seasonal to interannual time-scales. The one-dimensional (1-D) model is a simplification of a 2-D behavioural-template model proposed by Davidson and Turner (2009). The new model is calibrated and tested using five-years of weekly video-derived shoreline data from the Gold Coast, Australia. The modelling approach first utilises a least-squares methodology to calibrate the empirical model coefficients using the first half of the dataset of observed shoreline movement in response to known forcing by waves. The model is then verified by comparison of hindcast shoreline positions to the second half of the observed shoreline dataset. One thousand synthetic time-series of wave height and period are generated that encapsulate the statistical characteristics of the modelled wave field, retaining the observed seasonal variability and sequencing characteristics. The calibrated model is used in conjunction with the simulated wave time-series to perform Monte Carlo forecasting of the resulting shoreline positions. The ensemble-mean of the 1000 individual five-year shoreline simulations is compared to the unseen shoreline time-series. A simple linear trend forecast of the shoreline position was used as a baseline for assessing the performance of the model. The model performance relative to this baseline prediction was quantified by several objective methods, including cross-correlation (r), root mean square (RMS) error analysis and Brier Skill tests. Importantly, these tests involved no prior knowledge of either the wave forcing or shoreline response. The new forecast model was found to significantly improve shoreline predictions relative to the simple linear trend model, capturing well both the trend and seasonal shoreline variabilities observed at this site. Brier Skill Scores (BSS) indicate that the model forecasts based on unseen data were rated as ‘excellent’ (BSS = 0.83), and root mean square errors were less than 7 m (≈ 14% of the observed variability). The standard deviations of the 1000 individual simulations from ensemble-averaged ‘mean’ forecast were found to provide a useful means of predicting the higher-frequency (individual storm) shoreline variability, with 98% of the observed shoreline data falling within two standard deviations of the forecast position.     

Evaluation of the wave transformation in an open bay with two spectral models

An evaluation of two state of the art phase averaged wave models for the transformation scale, SWAN and STWAVE, is carried out in the present work. The target area is the Obidos Bay located in the central part of the Portuguese continental nearshore. The wave input for the two models is provided by an offshore buoy. In order to compare the nearshore outputs of the wave models against in-situ measurements, a directional buoy and an ADCP, operating in intermediate water depth, are used. The wave parameters considered for comparisons are significant wave height, peak period and wave direction. Sensitivity analyses studies and evaluations in the spectral and geographical spaces concerning the results of the two models are also carried out in both intermediate and shallow water. The present study provides some information on the performances of the two wave models in different forcing conditions as well as on their sensitivity in relationship with various input parameters and some physical processes. STWAVE appears to be faster and more robust than SWAN, which on the other hand has more options and flexibility. In statistical terms the results are comparable.     

A ten-year data set for fetch- and depth-limited wave growth

This paper presents the key results from a ten-year data set for Lake IJssel and Lake Sloten in The Netherlands, containing information on wind, storm surges and waves, supplemented with SWAN 40.51 wave model results. The wind speeds U₁₀, effective fetches x and water depths d for the data set ranged from 0–24 m s^− 1, 0.8–25 km and 1.2–6 m respectively. For locations with non-sloping bottoms, the range in non-dimensional fetch x? ( = gxU₁₀^− 2) was about 25–80,000, while the range in dimensionless depth d? ( = g d U₁₀^− 2) was about 0.03–1.7. Land–water wind speed differences were much smaller than the roughness differences would suggest. Part of this seems due to thermal stability effects, which even play a role during near-gale force winds. For storm surges, a spectral response analysis showed that Lake IJssel has several resonant peaks at time scales of order 1 h. As for the waves, wave steepnesses and dimensionless wave heights H? ( = gH_m0U₁₀^− 2) agreed reasonably well with parametric growth curves, although there is no single curve to which the present data fit best for all cases. For strongly depth-limited waves, the extreme values of d? (0.03) and H_m0 / d (0.44) at the 1.7 m deep Lake Sloten were very close to the extremes found in Lake George, Australia. For the 5 m deep Lake IJssel, values of H_m0 / d were higher than the depth-limited asymptotes of parametric wave growth curves. The wave model test cases of this study demonstrated that SWAN underestimates H_m0 for depth-limited waves and that spectral details (enhanced peak, secondary humps) were not well reproduced from H_m0 / d = 0.2–0.3 on. SWAN also underestimated the quick wave response (within 0.3–1 h) to sudden wind increases. For the remaining cases, the new [Van der Westhuysen, A.J., Zijlema, M., and Battjes, J.A., 2007. Nonlinear saturation-based whitecapping dissipation in SWAN for deep and shallow water, Coast. Eng., 54, 151–170] SWAN physics yielded better results than the standard physics of Komen, G.J., Hasselmann, S., Hasselmann, K., 1984. On the existence of a fully developed wind-sea spectrum. J. Phys. Oceanogr. 14, 1271–1285, except for persistent overestimations that were found for short fetches. The present data set contains many interesting cases for detailed model validation and for further studies into the evolution of wind waves in shallow lakes.     

SWAN predictions of waves observed in shallow water onshore of complex bathymetry

SWAN model predictions, initialized with directional wave buoy observations in 550-m water depth offshore of a steep, submarine canyon, are compared with wave observations in 5.0-, 2.5-, and 1.0-m water depths. Although the model assumptions include small bottom slopes, the alongshore variations of the nearshore wave field caused by refraction over the steep canyon are predicted well over the 50 days of observations. For example, in 2.5-m water depth, the observed and predicted wave heights vary by up to a factor of 4 over about 1000 m alongshore, and wave directions vary by up to about 10°, sometimes changing from south to north of shore normal. Root-mean-square errors of the predicted wave heights, mean directions, periods, and radiation stresses (less than 0.13 m, 5°, 1 s, and 0.05 m³/s² respectively) are similar near and far from the canyon. Squared correlations between the observed and predicted wave heights usually are greater than 0.8 in all water depths. However, the correlations for mean directions and radiation stresses decrease with decreasing water depth as waves refract and become normally incident. Although mean wave properties observed in shallow water are predicted accurately, nonlinear energy transfers from near-resonant triads are not modeled well, and the observed and predicted wave energy spectra can differ significantly at frequencies greater than the spectral peak, especially for narrow-band swell.     

Evaluation of two spectral wave models for wave hindcasting in the Mackenzie Delta

Climate change, reduced sea ice and increased ice-free waters over extended areas for longer summer periods potentially lead to increased wave energy in the Beaufort Sea (Wang et al., 2015; Khon et al., 2014) [1], [2], which is a major concern for coastal and offshore engineering activities. We compare two spectral wave models SWAN (Simulating WAves Nearshore) and MIKE 21 SW (hereafter MIKE21) in simulations of storm-generated waves in the Mackenzie Delta region of the southern Beaufort Sea. SWAN model simulations are performed using two nested grids system, whereas MIKE21 uses an unstructured grid system. Forcing fields are defined by hourly hindcast winds. Moving ice edge boundaries are incorporated during storm simulations. Modelled wave spectra from four storms are shown to compare well with field observations. Two established whitecapping formulations in SWAN are investigated: one dependent on mean spectral wave steepness, and the other on local spectral steepness. For the Beaufort Sea study area, we suggest that SWAN wave simulations using the latter local spectral steepness formulation are better than those using the former mean spectral steepness formulation. MIKE21 simulations also tend to agree with SWAN results using the latter whitecapping formulation.     

Operational prediction of acoustic properties in the ocean using multi-model statistics

Super-ensemble (SE) multi-model forecasts optimize local combination of individual models which is superior to individual models because they allow for local correction and bias removal. Multi-model statistics are applied to optimize the forecast skills from ocean models with different resolution or configuration, run operationally during the MREA04 field experiment off the West coast of Portugal. The method, based on a training/forecast cycle uses linear regression optimization. The performance and the limitations of the different super-ensemble combinations and the individual models are discussed. The SE method is shown to reduce errors in sound velocity significantly for 24 h forecasts.     

Super-ensemble techniques: Application to surface drift prediction

The prediction of surface drift of floating objects is an important task, with applications such as marine transport, pollutant dispersion, and search-and-rescue activities. But forecasting even the drift of surface waters is very challenging, because it depends on complex interactions of currents driven by the wind, the wave field and the general prevailing circulation. Furthermore, although each of those can be forecasted by deterministic models, the latter all suffer from limitations, resulting in imperfect predictions. In the present study, we try and predict the drift of two buoys launched during the DART06 (Dynamics of the Adriatic sea in Real-Time 2006) and MREA07 (Maritime Rapid Environmental Assessment 2007) sea trials, using the so-called hyper-ensemble technique: different models are combined in order to minimize departure from independent observations during a training period; the obtained combination is then used in forecasting mode. We review and try out different hyper-ensemble techniques, such as the simple ensemble mean, least-squares weighted linear combinations, and techniques based on data assimilation, which dynamically update the model’s weights in the combination when new observations become available. We show that the latter methods alleviate the need of fixing the training length a priori, as older information is automatically discarded.When the forecast period is relatively short (12 h), the discussed methods lead to much smaller forecasting errors compared with individual models (at least three times smaller), with the dynamic methods leading to the best results. When many models are available, errors can be further reduced by removing colinearities between them by performing a principal component analysis. At the same time, this reduces the amount of weights to be determined.In complex environments when meso- and smaller scale eddy activity is strong, such as the Ligurian Sea, the skill of individual models may vary over time periods smaller than the forecasting period (e.g. when the latter is 36 h). In these cases, a simpler method such as a fixed linear combination or a simple ensemble mean may lead to the smallest forecast errors. In environments where surface currents have strong mean-kinetic energies (e.g. the Western Adriatic Current), dynamic methods can be particularly successful in predicting the drift of surface waters. In any case, the dynamic hyper-ensemble methods allow to estimate a characteristic time during which the model weights are more or less stable, which allows predicting how long the obtained combination will be valid in forecasting mode, and hence to choose which hyper-ensemble method one should use.     

Ocean–wave coupled modeling in COAMPS-TC: A study of Hurricane Ivan (2004)

Tropical cyclone ocean–wave model interactions are examined using an ESMF – (Earth System Modeling Framework) based tropical cyclone (TC) version of the Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS®¹). This study investigates Hurricane Ivan, which traversed the Gulf of Mexico (GOM) in September 2004. Several oceanic and wave observational data sets, including Acoustic Doppler Current Profilers (ADCPs), National Oceanic and Atmospheric Administration (NOAA) buoys, satellite altimeter data, and Scanning Radar Altimeter (SRA) data, allow for a unique analysis of the coupled atmosphere, ocean (Navy Coastal Ocean Model, NCOM), and wave (Simulating WAves Nearshore, SWAN) models in COAMPS-TC. To determine the feasibility of coupling NCOM to SWAN in high-wind conditions during Hurricane Ivan, near-surface currents in NCOM were first compared to near-surface ADCP observations. Recent modifications to SWAN, including new wind-to-wave energy input and wave-breaking energy dissipation source functions, as well as a new ocean surface drag coefficient formulation appropriate for high-wind conditions, significantly improved the forecast wave field properties, such as significant wave height (SWH), in TC conditions. Further results show that the ocean-to-wave model coupling, which allows for the strong, hurricane-induced, surface currents in NCOM to interact with SWAN, provided additional improvements to the forecast SWH field. Additionally, wave-to-ocean model coupling, which included the input of the Stokes Drift Current (SDC) calculated from the SWAN wave spectra to NCOM, is examined. The models indicate that the SDC was on the order of 10–25% of the near-surface Eulerian current during Ivan. Recent studies of the importance of the SDC and the resulting Langmuir turbulence on vertical ocean mixing in TCs is also discussed.     

Modelling the influence of currents on wave propagation at the entrance of the Tagus estuary

A study of the wave propagation and of the consequences of the influence of currents on waves in the Tagus estuary is performed in the present work. For this purpose a high-resolution SWAN domain was coupled to a wave prediction system based on the two state of the art phase averaged wave models, WAM for wave generation and SWAN for nearshore wave transformation. The most important factors affecting the incoming waves are the local currents and the wind. These influences were evaluated by performing SWAN simulations in the target area with and respectively without considering the tide level and tide induced currents. The model results were compared with wave measurements, validating in this way the results of the wave prediction system developed herewith.     

Numerical study of the marine breeze around Mallorca Island

A study of marine breezes and their impact on the wave field around Mallorca Island was carried out by numerical simulations with the spectral wave model SWAN and three different wind fields: WRF – Weather Research and Forecasting model, HIRLAM – High Resolution Limited Area model and ECMWF – European Center for Medium-range Weather Forecasts. The main characteristics of the modelled breeze circulation and its effects on the wave field are analyzed. The modified wave field under breeze conditions and the correlations with their variability and daily short life time period are studied and discussed by analyzing the spectral balance. The results show that the accuracy of a wave forecast will depend on the quality of the wind field and its ability to simulate the sea breeze induced waves. The study period covers the summers of 2009 and 2010. In addition, to assess the performance of SWAN forced with two different winds the numerically obtained significant wave heights (Hs) are collocated against the ENVISAT-ESA's Environmental Satellite measurements (GLOBWAVE data) of Hs around the Mallorca Island.     

Wave height forecasting in Dayyer, the Persian Gulf

Forecasting of wave parameters is necessary for many marine and coastal operations. Different forecasting methodologies have been developed using the wind and wave characteristics. In this paper, artificial neural network (ANN) as a robust data learning method is used to forecast the wave height for the next 3, 6, 12 and 24 h in the Persian Gulf. To determine the effective parameters, different models with various combinations of input parameters were considered. Parameters such as wind speed, direction and wave height of the previous 3 h, were found to be the best inputs. Furthermore, using the difference between wave and wind directions showed better performance. The results also indicated that if only the wind parameters are used as model inputs the accuracy of the forecasting increases as the time horizon increases up to 6 h. This can be due to the lower influence of previous wave heights on larger lead time forecasting and the existing lag between the wind and wave growth. It was also found that in short lead times, the forecasted wave heights primarily depend on the previous wave heights, while in larger lead times there is a greater dependence on previous wind speeds.     

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.     

Modeling of storm-induced coastal flooding for emergency management

This paper describes a model package that simulates coastal flooding resulting from storm surge and waves generated by tropical cyclones. The package consists of four component models implemented at three levels of nested geographic regions, namely, ocean, coastal, and nearshore. The operation is automated through a preprocessor that prepares the computational grids and input atmospheric conditions and manages the data transfer between components. The third generation spectral wave model WAM and a nonlinear long-wave model calculate respectively the wave conditions and storm surge over the ocean region. The simulation results define the water levels and boundary conditions for the model SWAN to transform the storm waves in coastal regions. The storm surge and local tides define the water level in each nearshore region, where a Boussinesq model uses the wave spectra output from SWAN to simulate the surf-zone processes and runup along the coastline. The package is applied to hindcast the coastal flooding caused by Hurricanes Iwa and Iniki, which hit the Hawaiian Island of Kauai in 1982 and 1992, respectively. The model results indicate good agreement with the storm-water levels and overwash debris lines recorded during and after the events, demonstrating the capability of the model package as a forecast tool for emergency management.     

Evaluation of a high-resolution wave hindcast model SWAN for the West Mediterranean basin

This study aims to present an evaluation and implementation of a high-resolution SWAN wind wave hindcast model forced by the CFSR wind fields in the west Mediterranean basin, taking into account the recent developments in wave modelling as the new source terms package ST6. For this purpose, the SWAN model was calibrated based on one-year wave observations of Azeffoune buoy (Algerian coast) and validated against eleven wave buoys measurements through the West Mediterranean basin. For the calibration process, we focused on the whitecapping dissipation coefficient C_ds and on the exponential wind wave growth and whitecapping dissipation source terms. The statistical error analysis of the calibration results led to conclude that the SWAN model calibration corrected the underestimation of the significant wave height hindcasts in the default mode and improved its accuracy in the West Mediterranean basin. The exponential wind wave growth of Komen et al (1984) and the whitecapping dissipation source terms of Janssen (1991) with C_ds = 1.0 have been thus recommended for the western Mediterranean basin. The comparison of the simulation results obtained using this calibrated parameters against eleven measurement buoys showed a high performance of the calibrated SWAN model with an average scatter index of 30% for the significant wave heights and 19% for the mean wave period. This calibrated SWAN model will constitute a practical wave hindcast model with high spatial resolution (˜3 km) and high accuracy in the Algerian basin, which will allow us to proceed to a finer mesh size using the SWAN nested grid system in this area.     

Real-time wave forecasts off the western Indian coast

The wave observations at three locations off the west coast of India have been analyzed using artificial neural network (ANN) to obtain forecasts of significant wave heights at intervals of 3, 6, 12 and 24 h. The most appropriate training method requiring an input of four observations spread over previous 24 h has been selected after considerable trials. Further, the networks are trained after filling in the missing information. Larger gaps in data are filled in using spatial mapping involving observations at nearby locations, while relatively smaller gaps are accounted for by the statistical technique of multiple regressions in temporal mode. It is found that by doing so the long-interval forecasting is tremendously improved, with corresponding accuracy levels becoming close to those of the short-interval forecasts. If the amount of gaps is restricted to around 2% per year or so it is possible to obtain 12 h ahead forecasts with 0.08 m accuracy on an average and 24 h ahead forecast with a mean accuracy of 0.13 m. However, in harsher environments the prediction accuracy can change.