Abstract
A wave forecasting system using FUNWAVE-TVD which is based on the fully nonlinear Boussinesq equations by Chen (2006) was developed to provide an accurate wave prediction in the Port of Busan, South Korea. This system is linked to the Korea Operational Oceanographic System (KOOS) developed by Park et al. (2015). The computational domain covers a region of 9.6 km×7.0 km with a grid size of 2 m in both directions, which is sufficient to resolve short waves and dominant sea states. The total number of grid points exceeds 16 millions, making the model computational expensive. To provide real-time forecasting, an interpolation method, which is based on pre-calculated results of FUNWAVE-TVD and SWAN forecasting results at the FUNWAVE-TVD offshore boundary, was used. A total of 45 cases were pre-calculated, which took 71 days on 924 computational cores of a Linux cluster system. Wind wave generation and propagation from the deep water were computed using the SWAN in KOOS. SWAN results provided a boundary condition for the FUNWAVE-TVD forecasting system. To verify the model, wave observations were conducted at three locations inside the port in a time period of more than 7 months. A model/model comparison between FUNWAVE-TVD and SWAN was also carried out. It is found that, FUNWAVE-TVD improves the forecasting results significantly compared to SWAN which underestimates wave heights in sheltered areas due to incorrect physical mechanism of wave diffraction, as well as large wave heights caused by wave reflections inside the port.
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References
Abadie S M, Harris J C, Grilli S T, et al. 2012. Numerical modeling of tsunami waves generated by the flank collapse of the Cumbre Vieja Volcano (La Palma, Canary Islands): tsunami source and near field effects. Journal of Geophysical Research, 117(C5): C05030, doi: https://doi.org/10.1029/2011JC007646
Booij N, Ris R C, Holthuijsen L H. 1999. A third-generation wave model for coastal regions: 1. Model description and validation. Journal of Geophysical Research, 104(C4): 7649–7666, doi: https://doi.org/10.1029/98JC02622
Borgman L E. 1984. Directional spectrum estimation for the Sxy gauges. Vicksburg, MS, USA: Waterways Experiment Station, 1–104
Bouws E, Günther H, Rosenthal W, et al. 1985. Similarity of the wind wave spectrum in finite depth water: 1. Spectral form. Journal of Geophysical Research, 90(C1): 975–986, doi: https://doi.org/10.1029/JC090iC01p00975
Chen Qin. 2006. Fully nonlinear Boussinesq-type equations for waves and currents over porous beds. Journal of Engineering Mechanics, 132(2): 220–230, doi: 10.1061/(ASCE)0733-9399(2006)132:2(220)
Chen Qin, Kirby J T, Dalrymple R A, et al. 2003. Boussinesq modeling of longshore currents. Journal of Geophysical Research, 108(C11): 3362, doi: https://doi.org/10.1029/2002JC001308
Cho K H, Choi J Y, Jeong S H, et al. 2013. Development of a skill assessment tool for the Korea operational oceanographic system. Acta Oceanologica Sinica, 32(9): 74–81, doi: https://doi.org/10.1007/s13131-013-0354-9
Choi J, Kirby J T, Yoon S B. 2015. Boussinesq modeling of longshore currents in the SandyDuck experiment under directional random wave conditions. Coastal Engineering, 101: 17–34, doi: https://doi.org/10.1016/j.coastaleng.2015.04.005
Choi Y K, Seo S N. 2015. Wave transformation using modified FUNWAVE-TVD numerical model. Journal of Korean Society of Coastal and Ocean Engineers, 27(6): 406–418, doi: 10.9765/KS-COE.2015.27.6.406
Erduran K S, Ilic S, Kutija V. 2005. Hybrid finite-volume finite-difference scheme for the solution of Boussinesq equations. International Journal for Numerical Methods in Fluids, 49(11): 1213–1232, doi: 10.1002/(ISSN)1097-0363
Goda Y. 2000. Random Seas and Design of Maritime Structures. 2nd ed. New Jersey: World Scientific, 443
Guimarāes P V, Farina L, Toldo E Jr, et al. 2015. Numerical simulation of extreme wave runup during storm events in Tramandai Beach, Rio Grande do Sul, Brazil. Coastal Engineering, 95: 171–180, doi: https://doi.org/10.1016/j.coastaleng.2014.10.008
Kennedy A B, Chen Qin, Kirby J T, et al. 2000. Boussinesq modeling of wave transformation, breaking, and runup. I: 1D. Journal of Waterway, Port, Coastal, and Ocean Engineering, 126(1): 39–47, doi:10.1061/(ASCE)0733-950X(2000)126:1(39)
Kirby J T, Shi Fengyan, Tehranirad B, et al. 2013. Dispersive tsunami waves in the ocean: model equations and sensitivity to dispersion and Coriolis effects. Ocean Modelling, 62: 39–55, doi: https://doi.org/10.1016/j.ocemod.2012.11.009
Kirby J T, Wei Ge, Chen Qin, et al. 1998. FUNWAVE 1.0: fully nonlinear Boussinesq wave model Documentation and user’s manual. CACR-98-06, Newark, NJ, USA: University of Delaware
Oh S H, Jeong W M. 2013. Characteristics of high waves observed at multiple stations along the east coast of Korea. Natural Hazards and Earth System Sciences, 13(12): 3503–3514, doi: https://doi.org/10.5194/nhess-13-3503-2013
Park K S, Heo K Y, Jun K, et al. 2015. Development of the operational oceanographic system of Korea. Ocean Science Journal, 50(2): 353–369, doi: https://doi.org/10.1007/s12601-015-0033-1
Rogers W E, Kaihatu J M, Hsu L, et al. 2007. Forecasting and hindcast-ing waves with the SWAN model in the Southern California Bight. Coastal Engineering, 54(1): 1–15, doi: https://doi.org/10.1016/j.coastaleng.2006.06.011
Rusu L, Pilar P, Soares C G. 2008. Hindcast of the wave conditions along the west Iberian coast. Coastal Engineering, 55(11): 906–919, doi: https://doi.org/10.1016/j.coastaleng.2008.02.029
Sandhya K G, Balakrishnan Nair T M, Bhaskaran P K, et al. 2014. Wave forecasting system for operational use and its validation at coastal Puducherry, east coast of India. Ocean Engineering, 80: 64–72, doi: https://doi.org/10.1016/j.oceaneng.2014.01.009
Seo S N. 2008. Digital 30sec gridded bathymetric data of Korea marginal seas — KorBathy30s. Journal of Korean Society of Coastal and Ocean Engineers, 20(1): 110–120
Shi Fengyan, Dalrymple R A, Kirby J T, et al. 2001. A fully nonlinear Boussinesq model in generalized curvilinear coordinates. Coastal Engineering, 42(4): 337–358, doi: https://doi.org/10.1016/S03783839(00)00067-3
Shi Fengyan, Kirby J T, Dalrymple R A, et al. 2003. Wave simulations in Ponce de Leon inlet using Boussinesq model. Journal of Waterway, Port, Coastal, and Ocean Engineering, 129(3): 124–135, doi:10.1061/(ASCE)0733-950X(2003)129:3(124)
Shi Fengyan, Kirby J T, Harris J C, et al. 2012. A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation. Ocean Modelling, 43-44: 36–51, doi: https://doi.org/10.1016/j.ocemod.2011.12.004
Shi Fengyan, Malej M, Smith J M, et al. 2018. Breaking of ship bores in a Boussinesq-type ship-wake model. Coastal Engineering, 132: 1–12, doi: https://doi.org/10.1016/j.coastaleng.2017.11.002
Skamarock W C, Klemp J B, Dudhia J, et al. 2008. A description of the advanced research WRF version 3. NCAR/TN-475+STR, Boulder: National Center for Atmospheric Research
The SWAN Team. 2017. SWAN implementation manual. SWAN Cycle III version 41.20A. The Netherlands: Delft University of Technology
WAMDI Group. 1988. The WAM Model — A third generation ocean wave prediction model. Journal of Physical Oceanography, 18(12): 1775–1810, doi: 10.1175/1520-0485(1988)018<1775:TW-MTGO>2.0.CO;2
Tolman H L. 1997. User manual and system documentation of WAVEWATCH-III version 1.15. NOAA/NWS/NCEP/OMB Technical Note 151, 97
Wei Ge, Kirby J T, Grilli S T, et al. 1995. A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves. Journal of Fluid Mechanics, 294: 71–92, doi: https://doi.org/10.1017/S0022112095002813
Wei Ge, Kirby J T, Sinha A. 1999. Generation of waves in Boussinesq models using a source function method. Coastal Engineering, 36(4): 271–299, doi: https://doi.org/10.1016/S0378-3839(99)00009-5
Willmott C J. 1981. On the validation of models. Physical Geography, 2(2): 184–194, doi: https://doi.org/10.1080/02723646.1981.10642213
Yamamoto S, Daiguji H. 1993. Higher-order-accurate upwind schemes for solving the compressible Euler and Navier-Stokes equations. Computers & Fluids, 22(2-3): 259–270
Yoo J, Lee D Y, Ha T M, et al. 2010. Characteristics of abnormal large waves measured from coastal videos. Natural Hazards and Earth System Sciences, 10(4): 947–956, doi: https://doi.org/10.5194/nhess-10-947-2010
Yoon SB, Park WK, Choi J. 2014. Observation of rip current velocity at an accidental event by using video image analysis. Journal of Coastal Research, (72): 16–21
Zhou J G, Causon D M, Mingham C G, et al. 2001. The surface gradient method for the treatment of source terms in the shallow-water equations. Journal of Computational Physics, 168(1): 1–25, doi: https://doi.org/10.1006/jcph.2000.6670
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Foundation item: The Project of Development on Technology for Offshore Waste Final Disposal; the Project of Investigation of Large Swell Waves and Rip Currents and Development of the Disaster Response System.
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Choi, YK., Seo, SN., Choi, JY. et al. Wave prediction in a port using a fully nonlinear Boussinesq wave model. Acta Oceanol. Sin. 38, 36–47 (2019). https://doi.org/10.1007/s13131-019-1456-2
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DOI: https://doi.org/10.1007/s13131-019-1456-2