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A two-step hybrid system towards optimized wave height forecasts

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Abstract

The accurate prediction of wave height is of paramount importance in many oceanic, coastal and offshore activities. To this end, the traditional approach is the application of numerical wave prediction models with great success but also drawbacks under particular conditions. In this work, a two-step hybrid system is proposed to optimize wave height forecasts. It is based on the well-known wave model WAM, which is primarily used to obtain the simulated parameters, and the gradient boosting regression tree algorithm, which is subsequently applied to improve the wave height forecasts of the numerical model. The developed system and the underlying algorithm, use as features the information available only from the WAM model, without the need of meteorological data records from buoys or other sources. These are replaced with the WAM model simulated parameters. The predictive performance of the proposed method is evaluated in three different study areas, in order to avoid any area dependencies, and to justify the method’s applicability despite the local wave climatology. The results demonstrate that, the developed hybrid system can output more accurate wave height predictions than the original WAM forecasts, in terms of different statistical divergence metrics. In addition, the system’s predictions follow a realistic trend, in accordance with the general pattern of the real values of wave height, while the reduction of the systematic error of the WAM model is significant.

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Availability of data and material

The datasets analyzed during the current study are available from the corresponding author on reasonable request.

References

  • Ardhuin F, Rogers E, Babanin AV, Filipot JF, Magne R, Roland A, van de Westhuysen A, Queffeulou P, Lefevre JM, Aouf L, Collard F (2010) Semiempirical dissipation source functions for ocean waves. Part I: definition, calibration, and validation. J Phys Oceanogr 40(9):1917–1941

    Article  Google Scholar 

  • Berbić J, Ocvirk E, Carević D, Lončar G (2017) Application of neural networks and support vector machine for significant wave height prediction. Oceanologia 59(3):331–349

    Article  Google Scholar 

  • Bidlot JR (2012) Present status of wave forecasting at ECMWF. In: Proceedings from the ECMWF Workshop on Ocean Waves. Reading, United Kingdom

  • Breiman L (1996) Bias, variance, and arcing classifiers. Technical Report 460. Statistics Department, University of California, Berkeley, CA, USA

  • Callens A, Morichon D, Abadie S, Delpey M, Liquet B (2020) Using Random forest and Gradient boosting trees to improve wave forecast at a specific location. Appl Ocean Res 104:1–9

    Article  Google Scholar 

  • Chang YC, Chang KH, Wu GJ (2018) Application of eXtreme gradient boosting trees in the construction of credit risk assessment models for financial institutions. Appl Soft Comput 73:914–920

    Article  Google Scholar 

  • Cheng CT, Lin JY, Sun YG, Chau K (2005). Long-term prediction of discharges in Manwan Hydropower using adaptive-network-based fuzzy inference systems models. Springer, Berlin, pp 1152–1161

  • Den Bieman JP, Wilms JM, van den Boogaard HF, van Gent MR (2020) Prediction of mean wave overtopping discharge using gradient boosting decision trees. Water 12(6):1703

    Article  Google Scholar 

  • Elith J, Leathwick JR, Hastie T (2008) A working guide to boosted regression trees. J Animal Ecol 77(4):802–813

    Article  CAS  Google Scholar 

  • Freund Y, Schapire RE (1997) A decision-theoretic generalization of on-line learning and an application to boosting. J Comput Syst Sci 55(1):119–139

    Article  Google Scholar 

  • Friedman JH (2001) Greedy function approximation: a gradient boosting machine. Ann Stat 1189-1232

  • Friedman JH (2002) Stochastic gradient boosting. Comput Stat Data Anal 38(4):367–378

    Article  Google Scholar 

  • Friedman J, Hastie T, Tibshirani R (2000) Additive logistic regression: a statistical view of boosting (with discussion and a rejoinder by the authors). Ann Stat 28(2):337–407

    Article  Google Scholar 

  • Friedman JH, Meulman JJ (2003) Multiple additive regression trees with application in epidemiology. Stat Med 22(9):1365–1381

    Article  Google Scholar 

  • Galanis G (2018) Information geometry applications for optimizing numerical simulations. Math Methods Appl Sci 41(3):994–997

    Article  Google Scholar 

  • Galanis G, Chu PC, Kallos G (2011) Statistical post processes for the improvement of the results of numerical wave prediction models. A comb Kolmogorov Zurbenko Kalman Filters J Oper Oceanogr 4(1):23–31

    Google Scholar 

  • Galanis G, Chu PC, Kallos G, Kuo YH, Dodson CTJ (2012) Wave height characteristics in the north Atlantic ocean: a new approach based on statistical and geometrical techniques. Stochast Environ Res Risk Assess 26(1):83–103

    Article  Google Scholar 

  • Galanis G, Famelis I, Liakatas A (2017a) A new Kalman filter based on Information Geometry techniques for optimizing numerical environmental simulations. Stochast Environ Res Risk Assess 31(6):1423–1435

    Article  Google Scholar 

  • Galanis G, Kafatos M, Chu PC, Hatzopoulos N, Papageorgiou E, Liakatas A (2017b) Operational atmospheric and wave modelling in the California‘s coastline and offshore area with applications to wave energy monitoring and assessment. J Oper Oceanogr 10(2):135–153

    Google Scholar 

  • Galanis G, Papageorgiou E, Liakatas A (2017c) A hybrid Bayesian Kalman filter and applications to numerical wind speed modeling. J Wind Eng Ind Aerodyn 167:1–22

    Article  Google Scholar 

  • James SC, Zhang Y, O‘Donncha F (2018) A machine learning framework to forecast wave conditions. Coastal Eng 137:1–10

    Article  Google Scholar 

  • Janssen P (2004) The interaction of ocean waves and wind. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Joensen A, Giebel G, Landberg L, Madsen H, Nielsen HA (1999) Model output statistics applied to wind power prediction. James and James Science Publishers, London, pp 1177–1180

    Google Scholar 

  • Khan N, Shahid S, Ismail TB, Behlil F (2021) Prediction of heat waves over Pakistan using support vector machine algorithm in the context of climate change. Stochast Environ Res Risk Assess, pp 1–19

  • Komen GJ, Cavaleri L, Donelan M, Hasselmann K, Hasselmann S, Janssen PAEM (1996) Dynamics and modelling of ocean waves. Cambridge University Press, Cambridge

    Google Scholar 

  • Li M, Liu K (2020) Probabilistic prediction of significant wave height using dynamic Bayesian network and information flow. Water 12(8):2075

    Article  Google Scholar 

  • Mahjoobi J, Etemad-Shahidi A (2008) An alternative approach for the prediction of significant wave heights based on classification and regression trees. Appl Ocean Res 30(3):172–177

    Article  Google Scholar 

  • Malekmohamadi I, Bazargan-Lari MR, Kerachian R, Nikoo MR, Fallahnia M (2011) Evaluating the efficacy of SVMs, BNs, ANNs and ANFIS in wave height prediction. Ocean Eng 38(2–3):487–497

    Article  Google Scholar 

  • Mass CF, Ovens D, Westrick K, Colle BA (2002) Does increasing horizontal resolution produce more skillful forecasts?: The results of two years of real-time numerical weather prediction over the Pacific Northwest. Bull Am Meteorol Soc 83(3):407–430

    Article  Google Scholar 

  • Mosavi A, Ozturk P, Chau KW (2018) Flood prediction using machine learning models: literature review. Water 10(11):1536

    Article  Google Scholar 

  • Natekin A, Knoll A (2013) Gradient boosting machines, a tutorial. Front Neurorobot 7:21

    Article  Google Scholar 

  • Otero-Casal C, Patlakas P, Prósper MA, Galanis G, Miguez-Macho G (2019) Development of a high-resolution wind forecast system based on the WRF model and a hybrid Kalman–Bayesian filter. Energies 12(16):3050

    Article  Google Scholar 

  • Papayiannis GI, Galanis GN, Yannacopoulos AN (2018) Model aggregation using optimal transport and applications in wind speed forecasting. Environmetrics 29(8):e2531

    Article  Google Scholar 

  • Patlakas P, Drakaki E, Galanis G, Spyrou C, Kallos G (2017) Wind gust estimation by combining a numerical weather prediction model and statistical post-processing. Energy Procedia 125:190–198

    Article  Google Scholar 

  • Ridgeway G (2007) Generalized Boosted Models: A guide to the gbm package. http://cran.r-project.org/web/packages/gbm/index.html

  • Roy C, Motamedi S, Hashim R, Shamshirband S, Petković D (2016) A comparative study for estimation of wave height using traditional and hybrid soft-computing methods. Environ Earth Sci 75(7):1–12

    Article  Google Scholar 

  • Samadianfard S, Hashemi S, Kargar K, Izadyar M, Mostafaeipour A, Mosavi A, Nabipour N, Shamshirband S (2020) Wind speed prediction using a hybrid model of the multi-layer perceptron and whale optimization algorithm. Energy Rep 6:1147–1159

    Article  Google Scholar 

  • Samalot A, Astitha M, Yang J, Galanis G (2019) Combined kalman filter and universal kriging to improve storm wind speed predictions for the northeastern United States. Weather Forecast 34(3):587–601

    Article  Google Scholar 

  • Savitha R, Al Mamun A (2017) Regional ocean wave height prediction using sequential learning neural networks. Ocean Eng 129:605–612

    Article  Google Scholar 

  • Skamarock W, Klemp J, Dudhi J, Gill D, Barker D, Duda M, Huang XY, Wang W, Powers J (2008) A description of the advanced research WRF version 3. Technical Report, NCAR, Boulder

    Google Scholar 

  • Shamshirband S, Mosavi A, Rabczuk T, Nabipour N, Chau KW (2020) Prediction of significant wave height; comparison between nested grid numerical model, and machine learning models of artificial neural networks, extreme learning and support vector machines. Eng Appl Comput Fluid Mech 14(1):805–817

    Google Scholar 

  • Stathopoulos C, Galanis G, Bartsotas NS, Kallos G (2018) A methodology for optimizing probabilistic wind power forecasting. Adv Geosci 45:289–294

    Article  Google Scholar 

  • Touzani S, Granderson J, Fernandes S (2018) Gradient boosting machine for modeling the energy consumption of commercial buildings. Energy Build 158:1533–1543

    Article  Google Scholar 

  • Vanem E (2011) Long-term time-dependent stochastic modelling of extreme waves. Stochast Environ Res Risk Assess 25(2):185–209

    Article  Google Scholar 

  • Vanem E, Huseby AB, Natvig B (2012) A Bayesian hierarchical spatio-temporal model for significant wave height in the North Atlantic. Stochast Environ Res Risk Assess 26(5):609–632

    Article  Google Scholar 

  • WAMDIG, The WAM-Development and Implementation Group: Hasselmann, S, Hasselmann, K, Bauer, E, Bertotti L, Cardone CV, Ewing JA, Greenwood JA, Guillaume A, Janssen PAEM, Komen GJ, Lionello P, Reistad M, Zambresky L (1988) The WAM model-a third generation ocean wave prediction model. J Phys Oceanogr 18(12):1775–1810

  • Wang L, Li X, Bai Y (2018) Short-term wind speed prediction using an extreme learning machine model with error correction. Energy Convers Manag 162:239–250

    Article  Google Scholar 

  • Yang JC, Chuang HC, Kuan CM (2020) Double machine learning with gradient boosting and its application to the Big N audit quality effect. J Economet 216(1):268–283

    Article  Google Scholar 

  • Yang J, Yuan G (2021) Application of stochastic gradient boosting algorithm in human behavior recognition. World Sci Res J 7(1):12–20

    Google Scholar 

  • Zhang Y, Haghani A (2015) A gradient boosting method to improve travel time prediction. Transp Res Part C Emerg Technol 58:308–324

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank the Editor and the referees for their useful comments which led to a substantial improvement in the content and the presentation of the article.

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  1. Section of Mathematics, Mathematical Modeling and Applications Laboratory, Hellenic Naval Academy, Hatzikiriakion, 18539, Piraeus, Greece

    Emmanouil Androulakis & George Galanis

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  1. Emmanouil Androulakis
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  2. George Galanis
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Correspondence to Emmanouil Androulakis.

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Androulakis, E., Galanis, G. A two-step hybrid system towards optimized wave height forecasts. Stoch Environ Res Risk Assess 36, 753–766 (2022). https://doi.org/10.1007/s00477-021-02075-0

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