Numerical Wave Modelling – A Review - Science Direct

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ScienceDirect Aquatic Procedia 4 (2015) 443 – 448

INTERNATIONAL CONFERENCE ON WATER RESOURCES, COASTAL AND OCEAN ENGINEERING (ICWRCOE 2015)

Numerical wave modelling – A review Justin Thomas Ta*, G S Dwarakishb a

Department of Applied Mechanics and Hydraulics, NITK Surathkal, Mangalore, karnataka ,575025 India Department of Applied Mechanics and Hydraulics, NITK Surathkal, Mangalore, karnataka ,575025, India

b

Abstract

This review article presents an overview of the development of the numerical wave modelling techniques that are used.Due to the advent of powerful computers and development of several numerical techniques, solving coastal problems using numerical models are found to be very reliable, cost effective and time saving tools. Numerical models are used to hindcast and forecast wave parameters which help in the design of the coastal structures. Thus proper determination of the wave parameters invites lot of interest. In this review article, development of numerical models, uses and steps taken to improve the accuracy of the numerical models is discussed. © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license © 2015 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-reviewunder under responsibility of organizing committee of ICWRCOE Peer-review responsibility of organizing committee of ICWRCOE 2015 2015.

Keywords:numerical wave modelling; ocean engineering; wave forecasting, wave hindcasting; physical oceanography

1. Introduction Wind induced waves are among the most important subjects in coastal and ocean engineering.The random nature of sea surface waves makes it one of the most complicated phenomena.Ocean wave characteristics are mainly determined through field measurements, numerical simulation, physical models and analytical solutions. Each method has its own advantages and disadvantages. But nowadays, numerical models emerge as one of the most

* Corresponding author. Tel.:+917795546264; E-mail address:[email protected] (Justin Thomas T)

2214-241X © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of ICWRCOE 2015 doi:10.1016/j.aqpro.2015.02.059

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powerful tools for the study of surface water waves (Janssen, 2008).The numerical wave models express the physical concepts of the phenomena. Performance of the numerical wave model depends on how best the phenomena are expressed intothe numerical schemes, so that more accurate wave parameters could be estimated. The numerical wave models developed were based on energy balance equation with various components of the source function as inputs. The energy balance equation is given as † ሺˆǡšǡ–ǡɅሻ †

ൌ ܵ ൌ ‫ ݊ܫ‬൅ ݈ܰ ൅ ‫ݏ݅ܦ‬

(1)

Where, two-dimensional wave spectrum S (f, x, θ, t) is dependent on frequency f, propagation direction θ, and defined over the geographic coordinates xand time t. The left-hand side of Equation-1 is the full derivative of the spectrum with time and the right-hand side is the source function Sdepending on both the wave spectrum and on the external wave making factors such as local wind and local current. It is generally used to distinguish three terms in the source function S, namely In = the mechanism of the energy exchange between the atmosphere and ocean waves, Nl= the energy conservative mechanism of nonlinear wave– wave interactions, and Dis = the dissipation, i.e., wave energy loss mechanism related to wave-breaking processes and interaction of waves with turbulence of the upper water layer Differences in the presentation of the above components of the source function determine general differences between various numerical wave models. Numerical wave models are mainly divided into four categories based on their mechanisms. They are first, second, third and improved third generation wave models. The first generations wave models are developed based on simple wind fields (In) and without dominating nonlinear interactions (Nl) and energy loss (Dis). The second generation wave models are developed using varying wind fields and simplified nonlinear interactions. Here, the sea surface is defined as the sum of a large number of individual wave components, each wave propagating with constant frequency according to the linear wave theory. The third generation wave models are developed to further improvement of modelling process. The Discrete Interaction approximation (DIA) is introduced in wave modelling. These models use the energy balance equation for describing the time and space evolution of wave spectra(Mandal and Prabaharan, 2010). 2. Use of numerical wave models Ocean wave forecast and hindcast has huge significance for the construction and management of offshore structures, development of port and harbour related structures and naval operations. The first wave prediction technique was developed by Sverdrup and Munk, which was purely statistical based on the parameter significant wave height. The earlier models used for numerical wave predictions were using coarse grid. This was suitable for deep water regions. But for accurate modelling of the coastal regions fine mesh became a necessity. This lead to the development of the new third generation numerical model MIKE21 SW. Sorensen et.al (2004) developed a model and simulated for the North Sea, parts of Norwegian Sea and the Baltic Sea. The results are validated from wave rider buoy and found that the model is better in prediction than which does not use fine mesh. But due to the fine mesh the computing time required was higher at that time. A third-generation spectral wave model (Simulating Waves Near shore (SWAN)) for small-scale, coastal regions with shallow water, (barrier) islands, tidal flats, local wind, and ambient currents is verified in stationary mode with measurements in five real field cases. The model accounts for shoaling, refraction, generation by wind, white capping, triad and quadruplet wave-wave interactions, and bottom and depth-induced wave breaking. However, the shape of the spectrum is often not well reproduced. In particular, high-frequency growth (very short fetches) is usually overestimated (Booij et.al 1999). Numerical wave models are really helpful in estimating the wave parameters inside the harbour. These data are really helpful in planning and maintaining of harbour and coastal structures (Adytia et.al, 2012). Author used SWAN results as the initial data for optimized VariationalBoussinesq Model (OVBM).Realistic simulations in the

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Jakarta harbour, Indonesia, have been performed by using the spectral phase-averaging model SWAN and the phase-resolving model OVBM. SWAN was really helpful for getting realistic wave data to use as an input in OVBM. But, from the comparison of wave disturbance, both models show in general similar behaviour, except for reflection and diffraction effects. Phase resolving models are important in the case of ports since effect of diffraction is predominant near the entrance of port. The major drawback of the study lies in the validation of obtained results. Since there is no measured data in the inner harbour of Jakarta, data validation of the model is not accurate Numerical models can be really helpful in accurate wave forecasting, which is an essential tool for designing and protecting coastal structures which can also serve as a lifesaving tool during cyclones and storms. Operational wave forecasting has a huge importance during the time of cyclones which will help the fishermen and other seafarers to stay safe during the extreme events. In India a great example of wave forecasting can be observed from the works of INCOIS in which, authors used MIKE21 SW model for their wave forecasting. Data from wave rider buoys ensured that the forecasted values are in good agreement with the observed values and acceptable value of forecast error is 30% whereas the obtained error in the forecasting of waves due to thane cyclone was 20%. The proper warnings for local community drastically reduced the number of casualties during Thane cyclone (Balakrishnanet.al, 2013).A wave forecasting system developed by Puertosdel Estado (The Spanish holding of harbours) to predict waves at the coast is run in a twice a day cycle with a forecasting horizon of 72 h. The system is executed twice a day and is forced by meteorological fields, supplied by the Spanish Meteorological Service from the HIRLAM model. The local system is based on the SWAN model. The nested WAVEWATCH application covers the Strait of Gibraltar with a resolution of 1 min and receives boundary conditions from both, the Mediterranean and the Atlantic applications. This forecast helps the Spanish port authority to plan their activities in advance (Lahoz et.al, 2005). Wave energy from ocean is a promising chapter while considering renewable energy resources. Wave energy potential of the ocean can be calculated using numerical models, which can give guidelines to further detailed researches on renewable energy. Aydogan et.al, (2013) created a numerical model for black sea using MIKE21 SW which was used for calculating wave energy. This model showed that MIKE21 SW gives better results for wave heights than wave periods in black sea and annual average wave energy potentials were calculated for different locations. Another work that has been done in this direction is by Rusu et.al (2008). The authors used WAM model, in the improved version that allows for two way nesting, for wave generation, and covers almost the entire North Atlantic basin, whereas SWAN is used for wave transformation in the coastal environment. The wave energy is calculated from the energy transport components. In-situ observations are location-specific and generally sparse. In the Indian Ocean the situation is worse, compared to the Atlantic and Pacific, because long time series data of in-situ observations are mostly unavailable. On the other hand, it is simply impossible to estimate the wave climate and extreme sea state without such a long time series data. This leads to the importance of ocean wave hind casting. Using numerical models, past ocean wave data can be created with sufficient accuracy depending upon the input parameters. The authors tried to hindcast the wave data in Indian Ocean using MIKE21 SW and the simulations were done in both Arabian Sea and Bay of Bengal. But the results showed that Bay of Bengal simulation was in better agreement with the wave rider buoy data and advantage of this study is that it validated both wave height and wave period with the help of altimeter data and a novel algorithm respectively (Remya et.al, 2012). Numerical wave models can be incorporated with sediment dynamics problems to understand the problem more in detail.Spectral wave models helps to assess the sediment dynamics. Using WAVE WATCH III parameters like Significant Wave Height (Hs), Peak Period (Tp), Mean Wave Direction (MWD), Wind Velocity (U10) and Mean Wind Direction was extracted. This helped the authors to understand the wave energy in different coastal sectors. But the model WAVE WATCH III is mainly suitable for deep water regions and use of that model in coastal problems affected the accuracy of the study (Bulhoes et.al 2011). Another area of interest is the comparison of two wave models for checking better accuracy. Strauss et.al (2007) compared two wave models namely, MIKE21 SW and SWAN which indicated that SWAN model shows greater sensitivity towards wind data while MIKE21 SW is less sensitive to wind data and for MIKE21 SW, inclusion of wind data increases the simulation period considerably. However inclusion of wind in both models results in the

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overestimation of wave attenuation. Another comparison was done by Sharifi et.al (2012)in which he compared MIKE21 SW and WAVEWATCH III and the results of two model simulations were compared with the available satellite altimetry measurements of significant wave heights at the modeling area. The comparisons showed that in deep water WAVEWATCH-III results in more reliable prediction of wave characteristics in comparison to the MIKE-21 SW, while in shallow water area the MIKE-21 SW gives more consistencies with altimetry measurements. But the major drawback of the study lies in the less accurate wind data. Since wind data is the major forcing component, discrepancies in wind data will result in discrepancies in numerical simulations.

3. Further improvements in numerical models Numerical wave models are the representation of reality which can be improved further for better accuracy and results. Research is going on to improve the existing wave models. In this work, author tried to improve the input data by data assimilation. Data assimilation is a methodology that utilizes information from observations, and combines it with (or assimilate it into) numerical models (Emmanouilet.al, 2007).In their work instead of using wind data from one single source, Vethamony et.al, (2002) tried to assimilate two wind data (National Centre for Medium Range Weather Forecast winds assimilated With Multi-channel Scanning Microwave Radiometer winds) which showed that the inclusion of satellite MSMR winds with NCMRWF, especially the higher winds of NCMRWF brings the model wave heights closer to measured significant wave heights thus improving the accuracy of the model. Similar work has been done by Bhowmicket.al (2009), in which SWAN forced by QuickSCATscatterometer wind, has been used to generate the wave spectrum data, which are used as synthetic observations. These synthetic observations have been assimilated in the SWAN model forced by wind data available from high-resolution atmospheric ETA model being run at the NCMRWF.The study found out that the impact of assimilation is significant for approximately two days in case of significant wave height and three days for the swell waves. In a numerical model, one also discretises the domain and is therefore not able to resolve numerous sub-grid scale phenomena. Errors in the model parameterisation may contribute significantly to the overall error in a numerical model. It is also impossible to precisely define initial conditions and forcing terms in the entire computational domain. All of these inaccuracies and uncertainties could accumulate to produce poor model results.Babovic et.al, (2005)created an efficient error correction algorithm to apply in ocean wave prediction by using a third generation wave model, WAM. The results demonstrate significant increase in accuracy of a resulting hybrid model. Another problem faced in numerical modelling is unresolved islands and ice coverage which causes local errors in the model, which can be reduced by sub-grid treatment. It is assumed that wave energy will not be dissipated instantaneously when the wave field encounters ice. Instead, waves are assumed to progressively loose energy while travelling through an ice field, consistent with exponential decay behaviour. Sub-grid obstruction approach is suggested for ice covered areas also and they are tested with a one year hindcast run with NCEP’s operational global wave model, for the period of March 2000 through February 2001. The models are validated using ERS-2 altimeter and buoy data and the amount of error found to be reduced significantly (Tolman, 2002). Another approach to reduce the error in SWAN model is done by Baoshu et.al, (2007). He has introduced a new changing coefficient α with the variation of friction velocity u into the linear growth term of wind growth source function in SWAN model.In default SWAN, the value of the proportionality coefficient is constant.the variation of α has much effect on the wave developing when wind speed is between 7.5m/s and 15m/s, while it has little effect when wind speed is higher than 15m/s .The FR (Functional Relationship) model is a novel method of validating the observations by measurements and models, incorporating the inherent errors involved while representing the physical truth. The overall analysis suggests that the WAM and Nested-SWAN models predicts the significant wave heights more accurately in deep and shallow waters respectively, taking into account the random errors in measuring and predicting the significant wave height(Muraleedharanet.al 2006). Another major development in the numerical wave modelling is the coupling of different type of models together to get improved results. In general ocean circulation models are coupled with wave models to understand the physical phenomenon more. Wolf(2008) has tried to couple surge-tide-wave model and SWAN wave model to understand the wind-driven waves and surges in Irish Sea and Liverpool bay, which gives an overview of the causes and impacts of waves and surges and their interactions. From this studies he concluded that largest waves and surges in

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Liverpool Bay are generated by westerly and north-westerly winds. Also for studying the impact of a wave farm on waves, currents and coastal morphology adjacent to the wave farm, which is located in the Southwest of England, Gonzalezet.al (2013) used a modelling system which consists of the near-shore wave model SWAN, the ocean circulation model ROMS and a sediment transport model for morphological evolution. The results show that tidal elevation and tidal currents can have a significant effect on waves and that tidal forcing and waves have a significant effect on bottom shear stresses. Bed load transport rates show a decrease when the wave farm is present, even during storm conditions. Another model was developed by Carnielloet.al (2005) in Italy which combines wind waves with tidal fluxes in a tidal basin .The model couples a hydrodynamic finite element module based on the shallow water equations with a finite volume module that accounts for the generation and propagation of wind waves. The wind wave model is based on the conservation of the wave action. Another new model was by Li et.al (2009) in which he developed a new form of directional spectral wave model in terms of complex wave height density spectral. The model has the capability of simulating the combined wave diffraction and refraction. Wave diffraction is treated as the wave height diffusion in this model. The model is useful for predicting wave conditions in a regional coastal area, where both wave refraction and diffraction are significant and a useful tool to simulate the transient state of ocean waves in the coastal region, where both wave refraction and diffraction are significant. 4. Summary Numerical models are a powerful tool which can be used for calculating the wave climate. Numerical models helps to overcome the difficulties arises in wave prediction due to the random nature of the ocean. Numerical models have been classified into four categories namely first, second, third and improved third generation numerical models. Numerical models comes in handy while designing ports and other coastal structures, by providing accurate wave parameters. Phase averaged models are not capable of simulating diffraction phenomenon, which leads to the use of phase resolving numerical models. Numerical models are helpful in ocean wave forecasting, which helps to identify the peak wave heights during cyclones and acts as lifesaving tools during natural hazards. Comparison of wave models showed that fine grid models are more suitable in coastal region due to the varying bathymetry while in deep water coarser grid also produces accurate results with less computational period. Numerical models are the sign boards to renewable energy. With the help of numerical models, possible high energy zones in ocean are identified which will help to concentrate further research on these areas for economical energy extraction from waves. The major input for the numerical model is wind data and the inaccuracy of wind data results in the discrepancies of model results. Steps like data assimilation have been taken to improve the wind data and thus to increase the accuracy of the numerical model. Also by error forecasting, accuracy of the numerical models can be increased. Various attempts have been done to couple the wave model with ocean circulation models to understand the phenomenon better. 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