AbstractPrediction of long-term shoreline changes is a key task in planning and management of coastal zones and regional sediment management. Due to complex natural features of offshore waves, sediments, and longshore sediment transport, quantifying uncertainties of shoreline evolution and risks of extreme shoreline changes (erosion and accretion) is of vital importance for practicing uncertainty- or risk-based design of shorelines. This paper presents probabilistic shoreline change modeling to quantify uncertainties of shoreline variations by using numerical-model-based Monte-Carlo simulations. A shoreline evolution model, GenCade, is used to simulate longshore sediment transport and shoreline changes induced by random waves from offshore. A probability density function with a modified tail distribution is developed to capture stochastic features of wave heights under fair weather and storm conditions. It produces a time series of wave heights including small and extreme waves based on their probabilities (or frequencies of appearance). Probabilistic modeling of shoreline change is demonstrated by computing spatiotemporal variations of statistical parameters such as mean and variance of shoreline changes along an idealized coast bounded by two groins. Maximum shoreline changes in return years with a confidence range are also estimated by using maximum likelihood method. Reasonable results of obtained probabilistic shoreline changes reveal that this model-based Monte-Carlo simulation and uncertainty estimation approach are applicable to facilitate risk/uncertainty-based design and planning of shorelines.
Bruun, P., (1962). Sea-level rise as a cause of shore erosion. J. Waterway. Harbours Div. 88: 117-130.
Dean, R.G., & Dalrymple, R.A., (1992). Water Wave Mechanics for Engineers and Scientists, World Scientiffic, Singapore.
Dean, R.G., & Dalrymple, R.A., (2002). Coastal Processes with Engineering Applications. Cambridge University Press, Cambridge, UK, 475 pp.
Ding, Y., Kim, S.-C., & Frey, A.E., (2017). Probabilistic shoreline change modeling using Monte Carlo method, in Proc. of EWRI Congress 2017, ASCE. https://doi.org/10.1061/9780784480625.004.
Ding, Y. Kim, S. C., Permenter R. L., Frey, A. E., and Styles, R. (2018a), Probabilistic Modeling of Long-Term Shoreline Changes in Response to Sea Level Rise and Waves, In: Scour and Erosion IX , Proceedings of ICSE 2018, pp 203-211, CRC Press.
Ding, Y., Styles, R., Kim, S. C., Permenter R. L., and Frey, A. E. (2018b). Cross-shore transport feature for GenCade. ERDC/CHL CHETN-IV-XX. Vicksburg, MS: US Army Engineer Research and Development Center (under review).
Dong, P., and Chen, H. (1999). A probability method for predicting time-dependent long-term shoreline erosion, Coastal Engineering, 36, 243-261.
Dong, P., and Wu, X.Z. (2013). Application of a stochastic differential equation to the prediction of shoreline evolution. Stoch. Environ. Res. Risk. Assess, 27, 1799-1814.
Forristall, G. Z. (1978) On the statistical distribution of wave heights in a storm. J Geophys Res 83(C5):2353-2358. doi:10.1029/JC083iC05p02353
Frey, A. E., Connell, K. J. Hanson, H., Larson, M, Thomas, R. C., Munger, S., and Zundel, A., (2012). GenCade Version 1 Model Theory and User's Guide, Technical Report, ERDC/CHL TR-12-25, U.S. Army Engineer Research and Development Center, Vicksburg, MS
Goda, Y. (1988). On the Methodology of Selecting Design Wave Height. In: Proceedings of 21st Coastal Engineering Conference, pp.899-913.
Goda, Y., (2000). Random Seas and Design of Maritime Structures. World Scientific, 443 pp.
Hasselmann, K., Barnett, T.P., Bouws, E., Carlson, H., Cartwright, D.E., Enke, K., Ewing, J.I., Gienapp, H., Hasselmann, D.E., Kruseman, P., Meerburg, A., Muller, P., Olbers, D.J., Richter, K., Sell, W., Walden, H., 1973. Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Deutsche Hydrographische Zeitschrift A 8 (12), 1-95.
Longuet-Higgins, M. S. (1952). On the statistical distribution of the heights of sea waves, J. Mar. Res., I l (3), 245-266.
Longuet-Higgins, M. S. (1980). On the distribution of the heights of sea waves: some effects of nonlinearity and finite bandwidth, Journal of Geophysical Research, Vol 85, pp 1519-1523.
Longuet-Higgins, M.S., (1983). On the joint distribution of wave periods and amplitudes in a random wave field. Proc. Roy. Soc. London A389, 241-258.
Prevosto, M., Krogstad, H. E. & Robin, A. (2000). Probability distributions for maximum wave and crest heights. Coast. Engng., 40, 329-360.
Reeve, D.E., Pedrozo-Acuña, A., and Spivack, M. (2014). Beach memory and ensemble prediction of shoreline evolution near a groyne, Coastal Engineering, 86, 77-87.
Ruggiero, P., List, J., Hanes, D., and Eshleman, J (2006). Probabilistic shoreline change modeling, Proceeding of ICCE 2006, September 2006, San Diego, CA, pp1-13.
Scheel, F., de Boer, W.P., Brinkman, R., Luijendijk, A.P., and Ranasinghe, R. (2014). On the generic utilization of probabilistic methods for quantification of uncertainty in process-based morphodynamic model applications, Proceedings of ICCE 2014, pp1-10.
Tori, K, Fukushima, M., Sato, S., Takaki, T., and Ding Y. (2001). Probabilistic estimation of the shoreline variation for the purpose of coastal management, In: Proc. of Coastal Engineering, JSCE, Vol. 48, 1021-1025 (In Japanese).
Vanem, E., Huseby, A.B., Natvig, B. (2012). A Bayesian hierarchical spatio-temporal model for significant wave height in the North Atlantic, Stoch Environ Res Risk Assess, 26, 609-632.
Vrijling J. K. and Meijer G.J. (1992). Probabilistic coastline position computations, Coastal Engineering, 17, 1-23.
Wu, X. Z., and Dong, P. (2015). Liouville equation-based stochastic model for shoreline evolution, Stoch Environ Res Risk Assess (2015) 29:1867-1880, DOI 10.1007/s00477-015-1029-1.