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.     

Forecasting and hindcasting waves with the SWAN model in the Southern California Bight

The Naval Research Laboratory created a wave forecasting system in support of the Nearshore Canyon Experiment (NCEX) field program. The outer nest of this prediction system encompassed the Southern California Bight. This forecasting system is described in this paper, with analysis of results via comparison to the extensive buoy network in the region. There are a number of potential errors, two of which are poor resolution of islands in the Bight—which have a strong impact on nearshore wave climate—and the use of the stationary assumption for computations. These two problems have straightforward solutions, but the solutions are computationally expensive, so an operational user must carefully consider their cost. The authors study the impact of these two types of error (relative to other errors, such as error in boundary forcing) using several hindcasts performed after the completion of NCEX. It is found that, with buoy observations as ground truth, the stationary assumption leads to a modest increase in root-mean-square error; this is due to relatively poor prediction of the timing of swell arrivals and local sea growth/decay. The model results are found to be sensitive to the resolution of islands; however, coarse resolution does not incur an appreciable penalty in terms of error statistics computed via comparison to buoy observations, suggesting that other errors dominate. Inaccuracy in representation of the local atmospheric forcing likely has a significant impact on wave model error. Perhaps most importantly, the accuracy of directional distribution of wave energy at the open ocean boundaries appears to be a critical limitation on the accuracy of the model-data comparisons inside the Bight.     

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.     

Parameter identification of a compliant nonlinear SDOF system in random ocean waves by reverse MISO method

The determination of the drag and inertia coefficients, which enter into the wave force model given by Morison's equation, is particularly uncertain and difficult when a linear spectral model is used for ocean waves, and the structure is compliant and has nonlinear dynamic response. In this paper, a nonlinear System Identification method, called Reverse Multiple Inputs–Single Output (R–MISO) is applied to identify the hydrodynamic coefficients as well as the nonlinear stiffness parameter for a compliant single-degree-of-freedom system. Four different types of problems have been identified for use in various situations and the R–MISO has been applied to all of them. One of the problems requires iterative solution strategy to identify the parameters. The method has been found to be efficient in predicting the parameters with reasonable accuracy and has the potential for use in the laboratory experiments on compliant nonlinear offshore systems.     

A new approximation for ocean waves propagating over a beach with variable depth

In this paper, the phenomenon of ocean waves propagating over a beach with variable water depth is re-examined. Based on the assumption of shallow water, a linearised shallow water equation is solved with an arbitrary beach profile. These irregular beach profiles form a set of partial differential equation with variable coefficient as the governing equation, which is the main obstacle in obtaining analytical solutions. In this paper, two families of beach profile are used as examples. A parametric study is conducted to investigate the influence of the beach profiles on the water surface elevation (η) and velocities (u).     

The nonlinear hydrodynamic model for simulating a ship steering in waves with autopilot system

In the paper, a hydrodynamic numerical model including wave effect is developed to simulate ship autopilot systems by using the time domain analysis. The PD controller and the sliding mode controller are adopted as the autopilot systems. The differences of simulation results between two controllers are analyzed by cost function composed of heading angle error and rudder deflection, either in calm water or in waves. The results in calm water show that both controllers are tracking well for the desired route with the similar cost function value by tuning the key design parameters. However, the course tracking ability of the controller using sliding mode in waves is generally better even the cost function value is similar.     

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.     

Generation of waves in Boussinesq models using a source function method

A method for generating waves in Boussinesq-type wave models is described. The method employs a source term added to the governing equations, either in the form of a mass source in the continuity equation or an applied pressure forcing in the momentum equations. Assuming linearity, we derive a transfer function which relates source amplitude to surface wave characteristics. We then test the model for generation of desired incident waves, including regular and random waves, for both one and two dimensions. We also compare some model results with analytical solution and available experiment data.     

Application of a Boussinesq model for the computation of breaking waves: Part 2: Wave-induced setdown and setup on a submerged coral reef

Based on a set of Boussinesq-type equations with improved linear frequency dispersion characteristics in deeper water, the present paper incorporates the simplified effect of spilling wave breaking into the equations. The analysis is restricted to a single horizontal dimension but the method can be extended to include the second horizontal dimension. Inside the surf zone the vertical variation of the horizontal velocity profile is assumed to be composed of an (initially unknown) organised velocity component below the roller and a surface roller travelling with the wave celerity. This leads to a new set of equations which is capable of simulating the transformation of waves before, during and after wave breaking. The model is calibrated and verified by comparison with several wave flume measurements. The results show that the model produces sound physical results.     

Evaluation of ocean model ventilation with CFC-11: comparison of 13 global ocean models

We compared the 13 models participating in the Ocean Carbon Model Intercomparison Project (OCMIP) with regards to their skill in matching observed distributions of CFC-11. This analysis characterizes the abilities of these models to ventilate the ocean on timescales relevant for anthropogenic CO₂ uptake. We found a large range in the modeled global inventory (±30%), mainly due to differences in ventilation from the high latitudes. In the Southern Ocean, models differ particularly in the longitudinal distribution of the CFC uptake in the intermediate water, whereas the latitudinal distribution is mainly controlled by the subgrid-scale parameterization. Models with isopycnal diffusion and eddy-induced velocity parameterization produce more realistic intermediate water ventilation. Deep and bottom water ventilation also varies substantially between the models. Models coupled to a sea-ice model systematically provide more realistic AABW formation source region; however these same models also largely overestimate AABW ventilation if no specific parameterization of brine rejection during sea-ice formation is included. In the North Pacific Ocean, all models exhibit a systematic large underestimation of the CFC uptake in the thermocline of the subtropical gyre, while no systematic difference toward the observations is found in the subpolar gyre. In the North Atlantic Ocean, the CFC uptake is globally underestimated in subsurface. In the deep ocean, all but the adjoint model, failed to produce the two recently ventilated branches observed in the North Atlantic Deep Water (NADW). Furthermore, simulated transport in the Deep Western Boundary Current (DWBC) is too sluggish in all but the isopycnal model, where it is too rapid.     

Near-shore swell estimation from a global wind-wave model: Spectral process,linear, and artificial neural network models

Estimation of swell conditions in coastal regions is important for a variety of public, government, and research applications. Driving a model of the near-shore wave transformation from an offshore global swell model such as NOAA WaveWatch3 is an economical means to arrive at swell size estimates at particular locations of interest. Recently, some work (e.g. Browne et al. [Browne, M., Strauss, D., Castelle, B., Blumenstein, M., Tomlinson, R., 2006. Local swell estimation and prediction from a global wind-wave model. IEEE Geoscience and Remote Sensing Letters 3 (4), 462–466.]) has examined an artificial neural network (ANN) based, empirical approach to wave estimation. Here, we provide a comprehensive evaluation of two data driven approaches to estimating waves near-shore (linear and ANN), and also contrast these with a more traditional spectral wave simulation model (SWAN). Performance was assessed on data gathered from a total of 17 near-shore locations, with heterogenous geography and bathymetry, around the continent of Australia over a 7 month period. It was found that the ANNs out-performed SWAN and the non-linear architecture consistently out-performed the linear method. Variability in performance and differential performance with regard to geographical location could largely be explained in terms of the underlying complexity of the local wave transformation.     

Numerical study for waves propagating over a porous seabed around a submerged permeable breakwater: PORO-WSSI II model

The phenomenon of the wave, seabed and structure interactions has attracted great attentions from coastal geotechnical engineers in recent years. Most previous investigations have based on individual approaches, which focused on either flow region or seabed domain. In this study, an integrated model (PORO-WSSI II), based on the Volume-Averaged/Reynolds-Averaged Navier-Stokes (VARANS) equations and Biot's poro-elastic theory, is developed to investigate the mechanism of the wave-permeable structure-porous seabed interactions. The new model is verified with the previous experimental data. Based on the present model, parametric studies have been carried out to investigate the influences of wave, soil and structure parameters on the wave-induced pore pressure. Numerical results indicated: (i) longer wave period and larger wave height will obviously induce a higher magnitude of pore pressure at the leading edge of a breakwater; (ii) after a full wave-structure interaction, the magnitude of pore pressure below the lee side of a breakwater decreases with an increasing structure porosity while it varies dramatically with a change of structure height; and (iii) the seabed thickness, soil permeability and the degree of saturation can also significantly affect the dynamic soil behaviour.     

Wave pressures on a vertical wall due to short-crested waves: fifth-order approximation

Non-linear wave pressure induced by short-crested waves on a vertical wall is an important factor to be considered in the design of coastal structures. The existing models to estimate the wave pressure in engineering design are limited to the third-order solution ([Hsu et al., 1979]). In this paper, an analytical solution up to the fifth-order is derived through perturbation approximation. This analytical closed-form solution is used to investigate the contributions of the higher-order components in short-crested waves. It is found that fifth-order components significantly affect the change of pressure, especially in shallow water and larger waves.     

A computer model for forecasting ocean wave parameters at specific sites around the the New Zealand coast

An applications model for forecasting frequency‐directional wave spectra at any appropriately specified site is described. There are two stages to the calculations. Firstly, a spectrum is calculated based on results at nearby gridpoints from an ocean wave prediction model. This is then adjusted to make the spectrum consistent with the local wind history. Verifications of the model are made at sites off Cape Egmont and Great Barrier Island, North Island, New Zealand. These give encouraging results for the shape of the frequency spectrum, with reasonable skill evident in the energetic parts of the spectrum. The significant wave heights also agree well, with the model estimates explaining two thirds of the measured variance.     

Evolving a Bayesian network model with information flow for time series interpolation of multiple ocean variables

Based on Bayesian network (BN) and information flow (IF), a new machine learning-based model named IFBN is put forward to interpolate missing time series of multiple ocean variables. An improved BN structural learning algorithm with IF is designed to mine causal relationships among ocean variables to build network structure. Nondirectional inference mechanism of BN is applied to achieve the synchronous interpolation of multiple missing time series. With the IFBN, all ocean variables are placed in a causal network visually, making full use of information about related variables to fill missing data. More importantly, the synchronous interpolation of multiple variables can avoid model retraining when interpolative objects change. Interpolation experiments show that IFBN has even better interpolation accuracy, effectiveness and stability than existing methods.     

Predicting seasonal ocean variability around New Zealand using a coupled ocean-atmosphere model

We present a first assessment of the Sea Surface Temperature (SST) and 300m Heat Content (HC) ensemble mean skill of the Australian Community Climate and Earth-System Simulator-Seasonal v1.0 (ACCESS-S1) around New Zealand on seasonal timescales, using a set of retrospective ensemble forecasts for 1990-2012. This was verified against Reynolds AVHRR analysis and Bluelink ReANalysis 3.5 (BRAN3.5). For inshore areas with depth <300m, the model shows skill forecasting for summer at a lead time of 0 months, with 66% and 65% of model grid cells having correlation coefficients exceeding 0.6 for SST and 300m HC respectively. Regions of lower skill seem to be associated with the model representation of the complex and variable frontal systems around New Zealand, and an overly-strong response to the El Niño Southern-Oscillation (ENSO). Nevertheless, the skill of ACCESS-S1 around New Zealand suggests there is potential for the development of useful seasonal forecast products for the region.     

Spurious instabilities of long planetary waves in a two-and-a-half layer model subtropical gyre ocean with a wind-driven steady circulation

In a number of flows that support coupled free-waves, instability results when free-wave dispersion relations calculated without the coupling cross or approach one another. The propagation of long planetary wave perturbations of a two-and-a-half layer model subtropical gyre is one such oceanographically important instance. This note points out that, for a baroclinically unstable two-and-a-half layer model subtropical gyre, numerically aliased long wave dispersion relation plots display extra crossings that are artifacts of the discretization, and these may lead both to spurious numerical instabilities and to numerical misrepresentation of actual instabilities. Paradoxically, the numerical instability may in some instances manifest itself more strongly as the numerical resolution is improved. The aliasing mechanism may be related to the zone of small scale activity found in the southwestern corner of a time dependent model subtropical gyre in the numerical perturbation experiments of (Dewar, W., Huang, R., 2001. Adjustment of the ventilated thermocline. J. Phys. Oceanogr. 13, 293–309). Similar multilayer models are often discussed in the literature, so that the results may be widely useful.     

Modelling the long-term time series of significant wave height with non-linear threshold models

Linear autoregressive models and non-linear threshold autoregressive (TAR) models are used in the present work to describe the time series of the significant wave height of sea-states at Figueira da Foz, located in the Portuguese coast. The seasonal components of this series are identified and a TAR model with two regimes is proposed. A simulation study was carried out with the purpose of verifying if both the non-linear and linear models are suited to describe the probabilistic structure of the process. It is shown that both methods are adequate to describe the lower statistical moments of the original data, but the non-linear model represents better the skewness and the kurtosis of the data.     

Reflected and transmitted waves in a channel with side porous mattresses

The problem of wave propagation and wave damping in a channel with side porous mattresses of arbitrary shape protruding from the walls is studied. The solution was achieved by applying 3-D boundary element method and was employed to study wave field in the channel and to analyze the effect of the geometry of the mattresses and physical and hydraulic properties of porous material on wave damping. The results show that wave damping in the channel strongly depends on wave parameters, especially, on the wave number. Wave reflection and transmission decrease with increasing the wave number. The results also show that the wave field in the channel strongly depends on the geometry of the mattresses as well as on physical and hydraulic properties of porous material used to build these wave dampers. The geometry of the mattresses and physical and hydraulic properties of porous material have a moderate effect on wave reflection and a significant effect on wave transmission. The results show that wave transmission down the channel decreases with increasing the length and thickness of the mattresses. Moreover, wave transmission decreases with increasing the porosity and damping properties of porous media used to build the mattresses. The analysis shows that porous mattresses protruding from the channel walls are very efficient in damping water waves propagating down the channel and may be built in channels to reduce high waves and achieve desired wave conditions. Theoretical results are in reasonable agreement with experimental data.