6. List of symbols
\(A\) : the Dean parameter (Dean 1991)
\(A,B,C,D\) : the calibration parameters that depend on the energy dissipation and the reflection process (Bernabeu, 1999)
\(a,b\) : the parameters that satisfy the energy equilibrium function (Yates et al., 2009)
\(a',b'\) : the empirical parameters that satisfy the linear relationship (Jaramillo et al., 2021a)
\(b,c^±\) : the free parameters where \(c^+\) indicates the accretion and \(c^-\) indicates the erosion, respectively (Davidson et al., 2013)
\(C^±\) : the free parameters where \(C^+\) indicates the accretion and \(C^-\) indicates the erosion, respectively (Yates et al., 2009)
\(C_i\) : the calibration parameters that depend on the wave obliquity (\(β\)) based on measured shapes of the model beaches (Hsu and Evans, 1989)
\(D\) : the total window width of the weighted average (Davidson et al., 2013)
\(g\) : the acceleration due to gravity
\(H_b\) : the breaking wave height
\(h\) : the water depth from the mean sea level
\(h^*\) : the closure depth
\(h_{Berm}\) : the berm height
\(E\) : the incoming breaking wave energy related to the breaking wave height
\(E_{eq}\) : the equilibrium wave energy corresponding to the current shoreline position
\(F_r\) : the energy flux per unit required to move sediments
\(K\) : the transport coefficient which is related to sediment characteristics such as sediment density \(ρ_s\), water density \(ρ_w\), gravity acceleration \(g\), sediment porosity a and dimensionless proportionality coefficient \(k\)
\(k\) : the calibration parameter for the rate at which the shoreline approaches equilibrium (Miller and Dean, 2004)
\(k_r,a_r\) : the beach recovery and response factors (Lim et al., 2022)
\(L_s\) : the scaling wavelength calculated by the peak wave period and the wave depth at the diffraction point (González and Medina, 2001)
\(L^±\) : the proportional constants where \(L^+\) indicates the clockwise shoreline rotation and \(L^-\) indicates the counterclockwise rotation, respectively (Jaramillo et al., 2021a)
\(l\) : the beach length
\(P\) : the incoming wave power related to the significant wave height \(H_s\) and the wave peak period \(T_p\)
\(Q\) : the longshore sediment transport
\(q\) : the sinks and sources along the coast
\(R\) : the radius measured from the tip of the headland breakwater (Hsu and Evans, 1989)
\(R_o\) : the length of the control line joining the updrift diffraction point to the down-coast control point (Hsu and Evans, 1989)
\(R_∞\) : the equilibrium shoreline response (Turki et al., 2013)
\(R(t)\) : the instantaneous position at time \(t\)
\(S\) : the change in local water level (Turki et al., 2013)
\(S(t)\) : the shoreline position at time \(t\)
\(S_{eq}\) : the equilibrium shoreline position
\(t\) : the time variable
\(v_{lt}\) : the linear trend term according to the sediment gain/loss on the littoral zone (Jaramillo et al., 2020)
\(W^*\) : the width of the active surf zone
\(x\) : the cross-shore distance from the shoreline
\(x_0\) : the cross-shore distance between the beginning of the surf profile and the virtual origin of the shoaling profile over the mean sea level
\(Y\) : the distance from the control point to the straight alignment down-coast (Hsu and Evans, 1989)
\(y\) : the seaward distance
\(α_{s,eq}\) : the asymptotical equilibrium shoreline orientation
\(α_s(t)\) : the shoreline orientation at time \(t\)
\(β\) : the angle between the initial shoreline position and the wave crest (Hsu and Evans, 1989)
\(β_r\) : the angular parameter with a calculated value of 2.13 obtained by comparing 26 Spanish beaches (González and Medina, 2001)
\(ρ\) : the density of water
\(γ_b\) : the breaker index
\(Ω\) : the time-varying dimensionless fall velocity (\(Ω=H/w_sT\))
\(Ω_{eq}\) : the weighted averageof the antecedent dimensionless fall velocity
\(μ\) : the free parameter for the effect of wave setup (Lim et al., 2022)
\(ω\) : the ratio of beach change which is proportional to the characteristic time scale \(T_s\) (Turki et al., 2013)
\(ϕ\) : the memory decay of the system (Davidson et al., 2013)
\(θ\) : the incident wave direction
\(θ\) : the angle between the location of \(R\) on the shoreline (Hsu and Evans, 1989)
\(θ_b\): the wave angle at breaking [ \(°\) ]
