\chapter{Literature Review} In this chapter, literature relevant to the present study will be reviewed. \section{Separating incident and reflected components from wave buoy data} The separation of incident and reflected waves is a crucial step in numerically modeling a sea state. Using the raw data from a buoy as the input of a wave model will lead to incorrect results in the domain as the flow velocity at the boundary will not be correctly generated. Several methods exist to extract incident and reflected components in measured sea states, and they can generally be categorised in two types of methods: array methods and PUV methods \parencite{inch2016accurate}. Array methods rely on the use of multiple measurement points of water level to extracted the incident and reflected waves, while PUV methods use colocated pressure and velocity measurements to separate incident and reflected components of the signal. \subsection{Array methods} \subsubsection{2-point methods} Array methods were developped as a way to isolate incident and reflected wave components using multiple wave records. \textcite{goda1977estimation,morden1977decomposition} used two wave gauges located along the wave direction, along with spectral analysis, in order to extract the incident and reflected wave spectra. Their work is based on the earlier work of \textcite{thornton1972spectral}. \textcite{goda1977estimation} analyzed the wave spectrum components using the Fast Fourier Transform, and suggests that this method is adequate for studies in wave flumes. They noted that this method provides diverging results for gauge spacings that are multiples of half of the wave length. \textcite{morden1977decomposition} applies this technique to a field study, where the sea state is wind generated. \textcite{morden1977decomposition} showed that, using appropriate spectral analysis methods along with linear wave theory, the decomposition of the sea state into incident and reflected waves is accurate. A relation between the maximum obtainable frequency and the distance between the sensors is provided. According to \textcite{morden1977decomposition}, the only needed knowledge on the wave environment is that wave frequencies are not modified by the reflection process. \subsubsection{3-point methods} In order to alleviate the limitations from the 2-point methods, \textcite{mansard1980measurement} introduced a 3-point method. The addition of a supplementary measurement point along with the use of a least-squares method most importantly provided less sensitivity to noise, non-linear interactions, and probe spacing. The admissible frequency range could also be widened. A similar method was proposed by \textcite{gaillard1980}. The accuracy of the method for the estimation of incident and reflected wave components was once again highlighted, while the importance of adequate positioning of the gauges was still noted. \subsubsection{Time-domain method} \textcite{frigaard1995time} presented a time-domain method for reflected and incident wave separation. This method, called SIRW method, used discrete filters to extract the incident component of an irregular wave field. The results were as accurate as with the method proposed by \cite{goda1977estimation}, while singularity points are better accounted for. The main advantage of the SIRW method is that it works in the time-domain, meaning that real time computations can be performed. \textcite{frigaard1995time} also mentions the possibility of replacing one of the wave gauges by a velocity meters to prevent singularities. This method was improved by \textcite{baldock1999separation} in order to account for arbitrary bathymetry. Linear theory is used to compute shoaling on the varying bathymetry. Resulting errors in the computed reflection coefficient are low for large reflection coefficients, but increase with lower coefficients. The neglect of shoaling can lead to important error in many cases. The presented method could also be extended to three-dimensionnal waves and bathymetry by considering the influence of refraction. \subsubsection{Further improvements} Further additions were made to array methods. \textcite{suh2001separation} developped a method taking constant current into account to separate incident and reflected waves. This method relies on two or more gauges, using a least squares method. Results are very accurate in the absence of noise, but a small amount of error appears when noise is added. \textcite{inch2016accurate} noticed that the presence of noise lead to overestimation of reflection coefficient. The creation of bias lookup tables is proposed in order to account for noise-induced error in reflection coefficient estimations. \textcite{andersen2017estimation,roge2019estimation} later proposed improvements to account for highly non-linear regular and irregular waves respectively. The improved method provides very accurate results for highly non-linear waves, but are expected to be unreliable in the case of steep seabeds, as shoaling is not part of the underlying model. \subsubsection{Conclusion} Array methods have been developped enough to provide accurate results in a wide range of situations. However, they require at least two wave gauges to be used. That means that in some situations such as the Saint-Jean-de-Luz event of 2017, other methods are needed since only one field measurement location is available. \subsection{PUV methods} \begin{itemize} \item ?? \cite{guza1977resonant}: model of the surf zone as a standing wave combined with a progressive wave. Accurate results of surface elevation and runup for reflectivities over 0.3. \item ?? \cite{guza1984}: \item \cite{tatavarti1989incoming}: Decompose colocated random field measurements of wave elevation and currenct velocity into incoming and outgoing components. Less sensitive to noise. \item \cite{kubota1990}: comparison between different wave theories: quasi-nonlinear long-wave theory gave the best results. \itemĀ \cite{walton1992}: application to beaches, possibility to have higher reflected energy than incident energy. \item \cite{hughes1993}: colocated horizontal and vertical velocities or horizontal velocity and surface elevation. Validation for full reflection of irregular non breaking waves. \item \cite{huntley1999use}: principal component analysis technique to avoid noise-induced bias. \item \cite{sheremet2002observations}: \end{itemize} \section{Modeling wave impact on a breakwater} \subsection{SPH models} \subsection{VARANS models} \section{Modeling block displacement}