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Modeling the ice-attenuated waves in the Great Lakes

Ocean Dynamics volume 70, pages 991–1003 (2020)Cite this article

Abstract

A partly coupled wave-ice model with the ability to resolve ice-induced attenuation on waves was developed using the Finite-Volume Community Ocean Model (FVCOM) framework and applied to the Great Lakes. Seven simple, flexible, and efficient parameterization schemes originating from the WAVEWATCH III® IC4 were used to quantify the wave energy loss during wave propagation under ice. The reductions of wind energy input and wave energy dissipation via whitecapping and breaking due to presence of ice were also implemented (i.e., blocking effect). The model showed satisfactory performance when validated by buoy-observed significant wave height in ice-free season at eight stations and satellite-retrieved ice concentration. The simulation ran over the basin-scale, five-lake computational grid provided a whole map of ice-induced wave attenuation in the heavy-ice year 2014, suggesting that except Lake Ontario and central Lake Michigan, lake ice almost completely inhibited waves in the Great Lakes under heavy-ice condition. A practical application of the model in February 2011 revealed that the model could accurately reproduce the ice-attenuated waves when validated by wave observations from bottom-moored acoustic wave and current profiler (AWAC); moreover, the AWAC wave data showed quick responses between waves and ice, suggesting a sensitive relationship between waves and ice and arguing that accurate ice modeling was necessary for quantifying wave-ice interaction.

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Notes

  1. Anemometer heights above the ground of NDBC buoys 45001–45003, 45005–45008, and 45012 are 5 m, the NARR winds at 10 m were used to force the model, thus the buoy-observed winds were converted to winds at 10 m following a logarithmic relationship for wind speed profile (Allen et al. 1998).

References

  • Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration-guidelines for computing crop water requirements-FAO irrigation and drainage paper 56. Fao, Rome 300(9):D05109

    Google Scholar 

  • Anderson E, Fujisaki-Manome A, Kessler J, Lang G, Chu P, Kelley J, Wang J (2018) Ice forecasting in the next-generation Great Lakes Operational Forecast System (GLOFS). J Mar Sci Eng 6(4):123

    Article  Google Scholar 

  • Ardhuin F, Roland A, Dumas F, Bennis A-C, Sentchev A, Forget P, Wolf J, Girard F, Osuna P, Benoit M (2012) Numerical Wave Modeling in Conditions with Strong Currents: Dissipation, Refraction, and Relative Wind. J Phys Oceanogr 42(12):2101–2120

  • Bai X, Wang J, Sellinger C, Clites A, Assel R (2012) Interannual variability of Great Lakes ice cover and its relationship to NAO and ENSO. J Geophys Res: Oceans 117(C3)

  • Bai X, Wang J, Schwab DJ, Yang Y, Luo L, Leshkevich GA, Liu S (2013) Modeling 1993–2008 climatology of seasonal general circulation and thermal structure in the Great Lakes using FVCOM. Ocean Model 65:40–63

    Article  Google Scholar 

  • Bai X, Wang J, Austin J, Schwab DJ, Assel R, Clites A, Wohlleben T (2015) A record-breaking low ice cover over the Great Lakes during winter 2011/2012: combined effects of a strong positive NAO and La Niña. Clim Dyn 44(5–6):1187–1213

    Article  Google Scholar 

  • Barber DG, Galley R, Asplin MG, De Abreu R, Warner KA, Pućko M, Julien S (2009) Perennial pack ice in the southern Beaufort Sea was not as it appeared in the summer of 2009. Geophys Res Lett 36(24)

  • Beletsky D, Saylor JH, Schwab DJ (1999) Mean circulation in the Great Lakes. J Great Lakes Res 25(1):78–93

    Article  Google Scholar 

  • Bennetts LG, Squire VA (2009) Wave scattering by multiple rows of circular ice floes. J Fluid Mech 639:213–238

    Article  Google Scholar 

  • Bennetts LG, Squire VA (2011) On the calculation of an attenuation coefficient for transects of ice-covered ocean. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468(2137):136–162

    Article  Google Scholar 

  • Booij NRRC, Ris RC, Holthuijsen LH (1999) A third-generation wave model for coastal regions: 1. Model description and validation. J Geophys Res Oceans 104(C4):7649–7666

  • Brissette FP, Tsanis IK, Wu J (1993) Wave directional spectra and wave-current interaction in Lake St. Clair. J Great Lakes Res 19(3):553–568

    Article  Google Scholar 

  • Brown RW, Taylor WW, Assel RA (1993) Factors affecting the recruitment of lake whitefish in two areas of northern Lake Michigan. J Great Lakes Res 19(2):418–428

    Article  Google Scholar 

  • Campbell AJ, Bechle AJ, Wu CH (2014) Observations of surface waves interacting with ice using stereo imaging. J Geophys Res Oceans 119(6):3266–3284

  • Chen C, Liu H, Beardsley RC (2003) An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: application to coastal ocean and estuaries. J Atmos Ocean Technol 20(1):159–186

    Article  Google Scholar 

  • Collins CO, Rogers WE (2017) A source term for wave attenuation by sea ice in WAVEWATCH III®: IC4. NRL report NRL/MR/7320--17-9726, 25 pp. [available from www7320. Nrlssc. Navy. Mil/pubs. Php]

  • De Santi F, De Carolis G, Olla P, Doble M, Cheng S, Shen HH, Thomson J (2018) On the ocean wave attenuation rate in grease-pancake ice, a comparison of viscous layer propagation models with field data. J Geophys Res: Oceans 123(8):5933–5948

    Article  Google Scholar 

  • Doble MJ, De Carolis G, Meylan MH, Bidlot JR, Wadhams P (2015) Relating wave attenuation to pancake ice thickness, using field measurements and model results. Geophys Res Lett 42(11):4473–4481

    Article  Google Scholar 

  • Dumont D, Kohout A, Bertino L (2011) A wave-based model for the marginal ice zone including a floe breaking parameterization. J Geophys Res: Oceans 116(C4)

  • Fujisaki-Manome A, Wang J (2016) Simulating hydrodynamics and ice cover in Lake Erie using an unstructured grid model. Proceedings of 23th IAHR International Symposium on Ice (2016)

  • Gao G, Chen C, Qi J, Beardsley RC (2011) An unstructured-grid, finite-volume sea ice model: development, validation, and application. Journal of Geophysical Research: Oceans 116(C8)

  • Hasselmann K, Barnett TP, Bouws E, Carlson H, Cartwright DE, Enke K, Meerburg A (1973) Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Ergänzungsheft:8–12

  • Hawley N, Beletsky D, Wang J (2018) Ice thickness measurements in Lake Erie during the winter of 2010–2011. J Great Lakes Res 44(3):388–397

    Article  Google Scholar 

  • Horvat C, Tziperman E (2015) A prognostic model of the sea-ice floe size and thickness distribution. Cryosphere 9(6):2119–2134

  • Hubertz JM, Driver DB, Reinhard RD (1991) Wind waves on the Great Lakes: a 32 year hindcast. J Coast Res:945–967

  • Hunke EC, Lipscomb WH, Turner AK, Jeffery N, Elliott S (2010) CICE: the Los Alamos Sea ice model documentation and software User’s manual version 4.1 LA-CC-06-012. T-3 Fluid Dynamics Group, Los Alamos National Laboratory, 675

  • Kohout AL, Meylan MH, Sakai S, Hanai K, Leman P, Brossard D (2007) Linear water wave propagation through multiple floating elastic plates of variable properties. J Fluids Struct 23(4):649–663

  • Kohout AL, Meylan MH (2008) An elastic plate model for wave attenuation and ice floe breaking in the marginal ice zone. J Geophys Res: Oceans 113(C9)

  • Kohout AL, Williams MJM, Dean SM, Meylan MH (2014) Storm-induced sea-ice breakup and the implications for ice extent. Nature 509(7502):604–607

    Article  Google Scholar 

  • Kohout AL, Williams MJM, Toyota T, Lieser J, Hutchings J (2016) In situ observations of wave-induced sea ice breakup. Deep-Sea Res II Top Stud Oceanogr 131:22–27

    Article  Google Scholar 

  • Komen GJ, Hasselmann K, Hasselmann K (1984) On the existence of a fully developed wind-sea spectrum. J Phys Oceanogr 14(8):1271–1285

    Article  Google Scholar 

  • Lou J, Schwab DJ, Beletsky D, Hawley N (2000) A model of sediment resuspension and transport dynamics in southern Lake Michigan. J Geophys Res: Oceans 105(C3):6591–6610

    Article  Google Scholar 

  • Madsen, O. S., Poon, Y. K., Graber, H. C. 1989. Spectral wave attenuation by bottom friction: theory. In Coastal Engineering 1988 (pp. 492-504)

  • Mao M, Xia M (2017) Dynamics of wave–current–surge interactions in Lake Michigan: a model comparison. Ocean Model 110:1–20

    Article  Google Scholar 

  • Mao M, Van Der Westhuysen AJ, Xia M, Schwab DJ, Chawla A (2016) Modeling wind waves from deep to shallow waters in Lake Michigan using unstructured SWAN. J Geophys Res: Oceans 121(6):3836–3865

    Article  Google Scholar 

  • Mesinger F, DiMego G, Kalnay E, Mitchell K, Shafran PC, Ebisuzaki W, Ek MB (2006) North American regional reanalysis. Bull Am Meteorol Soc 87(3):343–360

    Article  Google Scholar 

  • Meylan MH, Bennetts LG, Kohout AL (2014) In situ measurements and analysis of ocean waves in the Antarctic marginal ice zone. Geophys Res Lett 41(14):5046–5051

    Article  Google Scholar 

  • Moeini MH, Etemad-Shahidi A (2007) Application of two numerical models for wave hindcasting in Lake Erie. Appl Ocean Res 29(3):137–145

    Article  Google Scholar 

  • Niimi AJ (1982) Economic and environmental issues of the proposed extension of the winter navigation season and improvements on the Great Lakes-St. Lawrence Seaway system. J Great Lakes Res 8(3):532–549

    Article  Google Scholar 

  • Niu Q, Xia M (2016) Wave climatology of Lake Erie based on an unstructured-grid wave model. Ocean Dyn 66(10):1271–1284

    Article  Google Scholar 

  • Niu Q, Xia M (2017) The role of wave-current interaction in Lake Erie’s seasonal and episodic dynamics. J Geophys Res Oceans 122(9):7291–7311

  • Pleskachevsky A, Eppel DP, Kapitza H (2009) Interaction of waves, currents and tides, and wave-energy impact on the beach area of Sylt Island. Ocean Dyn 59(3):451–461

  • Qi J, Chen C, Beardsley RC, Perrie W, Cowles GW, Lai Z (2009) An unstructured-grid finite-volume surface wave model (FVCOM-SWAVE): Implementation, validations and applications. Ocean Model 28(1-3):153–166

  • Ris RC, Holthuijsen LH, Booij N (1999) A third-generation wave model for coastal regions: 2. Verification. J Geophys Res Oceans 104(C4):7667–7681

  • Rogers WE, Thomson J, Shen HH, Doble MJ, Wadhams P, Cheng S (2016) Dissipation of wind waves by pancake and frazil ice in the autumn Beaufort Sea. J Geophys Res: Oceans 121(11):7991–8007

    Article  Google Scholar 

  • Schwab DJ, Beletsky D (2003) Relative effects of wind stress curl, topography, and stratification on large-scale circulation in Lake Michigan. J Geophys Res: Oceans 108(C2)

  • Sellinger CE, Stow CA, Lamon EC, Qian SS (2007) Recent water level declines in the Lake Michigan− Huron System. Environ Sci Technol 42(2):367–373

    Article  Google Scholar 

  • Squire VA (2007) Of ocean waves and sea-ice revisited. Cold Reg Sci Technol 49(2):110–133

  • The WAVEWATCH III® Development Group (WW3DG) (2016) User manual and system documentation of WAVEWATCH III® version 5.16. Tech. Note 329, NOAA/NWS/NCEP/MMAB, College Park, MD, USA, 326 pp. + Appendices

  • Vanderploeg HA, Bolsenga SJ, Fahnenstiel GL, Liebig JR, Gardner WS (1992) Plankton ecology in an ice-covered bay of Lake Michigan: utilization of a winter phytoplankton bloom by reproducing copepods. Hydrobiologia 243(1):175–183

    Article  Google Scholar 

  • Vaughan GL, Squire VA (2011) Wave induced fracture probabilities for arctic sea-ice. Cold Reg Sci Technol 67(1-2):31–36

  • Vavrus S, Notaro M, Zarrin A (2013) The role of ice cover in heavy lake-effect snowstorms over the Great Lakes Basin as simulated by RegCM4. Mon Weather Rev 141(1):148–165

    Article  Google Scholar 

  • Vincent CE (1979) The Interaction of Wind-Generated Sea Waves with Tidal Currents. J Phys Oceanogr 9(4):748–755

  • Wadhams P, Squire VA, Goodman DJ, Cowan AM, Moore SC (1988) The attenuation rates of ocean waves in the marginal ice zone. J Geophys Res: Oceans 93(C6):6799–6818

    Article  Google Scholar 

  • Wang J (1996) Global linear stability of the two-dimensional shallow-water equations: an application of the distributive theorem of roots for polynomials on the unit circle. Mon Weather Rev 124(6):1301–1310

    Article  Google Scholar 

  • Wang J, Ikeda M (1997a) Inertial stability and phase error of time integration schemes in ocean general circulation models. Mon Weather Rev 125(9):2316–2327

    Article  Google Scholar 

  • Wang J, Ikeda M (1997b) Diagnosing ocean unstable baroclinic waves and meanders using the quasigeostrophic equations and Q-vector method. J Phys Oceanogr 27(6):1158–1172

    Article  Google Scholar 

  • Wang R, Shen HH (2011) A continuum model for the linear wave propagation in ice-covered oceans: an approximate solution. Ocean Model 38(3–4):244–250

    Article  Google Scholar 

  • Wang J, Bai X, Hu H, Clites A, Colton M, Lofgren B (2012) Temporal and spatial variability of Great Lakes ice cover, 1973–2010. J Clim 25(4):1318–1329

    Article  Google Scholar 

  • Wang J, Kessler J, Bai X, Clites A, Lofgren B, Assuncao A, Leshkevich G (2018) Decadal variability of Great Lakes ice cover in response to AMO and PDO, 1963–2017. J Clim 31(18):7249–7268

    Article  Google Scholar 

  • Wang J, Manome A, Kessler J, Zhang S, Chu P, Peng S, Zhu X, Anderson E (2020) Inertial instability and phase error in third- and fourth-stage predictor-corrector time integration schemes in ocean circulation models: application to Great Lakes modeling. Ocean Dynamics (submitted)

  • Williams TD, Bennetts LG, Squire VA, Dumont D, Bertino L (2013) Wave–ice interactions in the marginal ice zone. Part 1: theoretical foundations. Ocean Model 71:81–91

    Article  Google Scholar 

  • Wright DM, Posselt DJ, Steiner AL (2013) Sensitivity of lake-effect snowfall to lake ice cover and temperature in the Great Lakes region. Mon Weather Rev 141(2):670–689

    Article  Google Scholar 

  • Xue P, Pal JS, Ye X, Lenters JD, Huang C, Chu PY (2017) Improving the simulation of large lakes in regional climate modeling: two-way lake–atmosphere coupling with a 3D hydrodynamic model of the Great Lakes. J Clim 30(5):1605–1627

    Article  Google Scholar 

  • Zhang Y, Chen C, Beardsley RC, Gao G, Qi J, Lin H (2016) Seasonal and interannual variability of the Arctic sea ice: a comparison between AO-FVCOM and observations. J Geophys Res: Oceans 121(11):8320–8350

    Article  Google Scholar 

  • Zhang Y, Chen C, Beardsley RC, Perrie W, Gao G, Zhang Y, Lin H (2020) Applications of an unstructured grid surface wave model (FVCOM-SWAVE) to the Arctic Ocean: the interaction between ocean waves and sea ice. Ocean Model 145:101532

    Article  Google Scholar 

Download references

Acknowledgments

We gratefully thank the two anonymous reviewers for providing constructive and insightful comments, which have contributed to the substantial improvements of the manuscript. Peng Bai acknowledges a grant from the National Research Council Research Associateship Programs. This research was partially funded by NSF Grant OCE 0927643 to Dmitry Beletsky. We would like to thank Songzhi Liu for his assistance in processing the NIC ice concentration data. This is GLERL Contribution No. 1946. Funding was awarded to the Cooperative Institute for Great Lakes Research (CIGLR) through the NOAA Cooperative Agreement with the University of Michigan (NA17OAR4320152). This CIGLR contribution number is 1160.

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Authors and Affiliations

  1. College of Ocean and Meteorology, Guangdong Ocean University, Zhanjiang, 524088, Guangdong, China

    Peng Bai

  2. Great Lakes Environmental Research Laboratory, NOAA, Ann Arbor, MI, 48108, USA

    Peng Bai, Jia Wang, Philip Chu, Nathan Hawley, James Kessler, Brent M. Lofgren & Eric J. Anderson

  3. Cooperative Institute for Great Lakes Research, University of Michigan, Ann Arbor, MI, 48108, USA

    Ayumi Fujisaki-Manome, Dmitry Beletsky & Yaru Li

  4. Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI, 48104, USA

    Ayumi Fujisaki-Manome

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  1. Peng Bai
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  2. Jia Wang
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  3. Philip Chu
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Correspondence to Peng Bai.

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Responsible Editor: Tal Ezer

This article is part of the Topical Collection on the 11th International Workshop on Modeling the Ocean (IWMO), Wuxi, China, 17-20 June 2019

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Bai, P., Wang, J., Chu, P. et al. Modeling the ice-attenuated waves in the Great Lakes. Ocean Dynamics 70, 991–1003 (2020). https://doi.org/10.1007/s10236-020-01379-z

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Keywords

  • Great Lakes
  • Wave dynamics
  • Ice-induced wave attenuation
  • FVCOM–SWAVE–UG-CICE