Artificial Intelligence for estimating infragravity energy in a harbour M. Lo ´ pez a , G. Iglesias b,n a Univ. of Santiago de Compostela, Hydraulic Eng., Campus Univ. s/n, 27002 Lugo, Spain b School of Marine Science and Engineering, University of Plymouth, PL4 8AA, UK article info Article history: Received 23 March 2012 Accepted 29 August 2012 Keywords: Artificial Intelligence Artificial Neural Networks Long waves Infragravity waves Harbour resonance Seiche abstract The estimation of long waves inside a harbour is a matter of great importance for port management. The objective of this work is to apply Artificial Intelligence to estimate the significant infragravity wave height inside a harbour. Two Artificial Neural Network (ANN) models with the same input (the short wave parameters outside the harbour and the tidal level) are developed and compared. The first is a one-step model that estimates the significant infragravity wave height inside the harbour directly. The second is a two-step model that computes the infragravity wave height first outside, then inside the harbour. The two models are trained and successfully validated based on observations at the Port of Ferrol (NW Spain), where seiching is known to occur. The network architecture that performs best for each model is selected using a k-fold cross-validation method. The estimation of the infragravity wave height outside the harbour with the two-step model is shown to be more accurate than that from a widely used empirical expression. As regards the all-important estimation inside the harbour, the one- step model is found to perform better than its two-step counterpart. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction Long waves, i.e. ocean waves with periods between a few tens of seconds to several hours, can excite the natural frequencies of gulfs, bays, inlets, harbours, etc. When this occurs, the oscillations of the free surface increase significantly until the energy input is balanced by losses due to friction (with the seabed, coastal structures, etc.), flow separation, boundary absorption, and radia- tion from the mouth (Okihiro et al., 1993; Okihiro and Guza, 1996). The horizontal displacements in the mass of water during seiche events can induce unacceptable forces on mooring lines and large movements on ships, finally resulting in much less efficient operations (e.g. Bellotti, 2007; Bellotti and Franco, 2011; Janssen et al., 2003; Morison and Imberger, 1992; Wilson, 1972; Wu and Liu, 1990). A great variety of forcing mechanisms have been described in the literature to explain the generation of long waves, such as meteorological processes (Candella, 2009; Gomis et al., 1993; Rabinovich and Monserrat, 1998; Vilibic ´ et al., 2005, 2004), seismic-generated tsunamis (Candella et al., 2008; Heidarzadeh et al., 2008; Rabinovich et al., 2011; Van Dorn, 1984; Wilson, 1972), landslides (Dong et al., 2010) or edge waves propagating on the continental shelf (Breaker et al., 2008; Lemon, 1975; Luick and Hinwood, 2008). However, since the phenomenon of surf- beat was originally reported by Munk (1949) and Tucker (1950), it is to the nonlinear interaction of wind waves that seiching is most commonly ascribed (Bellotti and Franco, 2011; Bowers, 1992, 1977; Kovalev et al., 1991; McComb et al., 2005; Morison and Imberger, 1992; Okihiro et al., 1993; Okihiro and Guza, 1996; Paolo, 1996; Wu and Liu, 1990). These swell-driven long waves, also known as infragravity waves to differentiate them from long waves of other origins (Hwung et al., 2007; Kovalev et al., 1991; Rabinovich, 2009), have periods ranging from 25–30 s to 300– 600 s. Since the natural modes of harbours and vessels have periods of the order of minutes, infragravity ( IG) waves constitute the main source of resonance problems in harbours (Rabinovich, 2009). The estimation of IG waves inside a harbour is all-important for their effects on the operability of quays, and should be included in the design of harbour management procedures (Bellotti and Franco, 2011; Gonza ´ lez-Marco et al., 2008; Goring, 2005; McComb et al., 2005). Although short wave observations are relatively common, appropriate records of IG waves are not. For this reason a number of authors (Bellotti and Franco, 2011; Bowers, 1992; Gonza ´ lez-Marco et al., 2008; McComb et al., 2005; Melito et al., 2007; Nelson et al., 1988; Stiassnie and Drimer, 2006) investigated the relationship between the parameters of short waves and IG waves. Empirical (Bowers, 1992) and analytical (Stiassnie and Drimer, 2006) solutions to estimate long waves near the entrance to a harbour were proposed. In addition, different models (numerical and analytical) were applied to determine the harbour response to incoming long waves (e.g. Bellotti, 2007; Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/oceaneng Ocean Engineering 0029-8018/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.oceaneng.2012.08.009 n Corresponding author. Tel.: þ44 17 52 584 584. E-mail address: gregorio.iglesias@plymouth.ac.uk (G. Iglesias). Ocean Engineering 57 (2013) 56–63