Prediction of Shoreline Evolution. Reliability of a General Model for the Mixed Beach Case

Home , Beach evolution, Groyne, Swash, Wave height

Journal of Marine Science and Engineering

Article Prediction of Shoreline Evolution. Reliability of a General Model for the Mixed Beach Case

Giuseppe R. Tomasicchio 1,* , Antonio Francone 1, David J. Simmonds 2 , Felice D’Alessandro 3 and Ferdinando Frega 4

1 Engineering Department, University of Salento, 73100 Lecce, Italy; [email protected] 2 Faculty of Science and Engineering, University of Plymouth, Plymouth PL48AA, UK; [email protected] 3 Department of Environmental Science and Policy, University of Milan, 20122 Milan, Italy; [email protected] 4 Department of Civil Engineering University of Calabria, 87100 Cosenza, Italy; [email protected] * Correspondence: [email protected]; Tel.: +39-0832-297715

Received: 30 April 2020; Accepted: 19 May 2020; Published: 21 May 2020

Abstract: In the present paper, after a sensitivity analysis, the calibration and veriﬁcation of a novel morphodynamic model have been conducted based on a high-quality ﬁeld experiment data base. The morphodynamic model includes a general formula to predict longshore transport and associated coastal morphology over short- and long-term time scales. With respect to the majority of the existing one-line models, which address sandy coastline evolution, the proposed General Shoreline beach model (GSb) is suitable for estimation of shoreline change at a coastal mound made of non-cohesive sediment grains/units as sand, gravel, cobbles, shingle and rock. In order to verify the reliability of the GSb model, a comparison between observed and calculated shorelines in the presence of a temporary groyne deployed at a mixed beach has been performed. The results show that GSb gives a good agreement between observations and predictions, well reproducing the coastal evolution.

Keywords: longshore transport; morphodynamic model; ﬁeld experiment; mixed beaches

1. Introduction During the last decades, researchers and engineers inspired by coastal sediment phenomena have conducted field and laboratory experiments to learn more about coastal processes and sediment dynamics. Their efforts have resulted in a wealth of papers and documents published in books, journals, conference and symposium proceedings over the last 50 years [1]. One-line models have shown practical capability in predicting shoreline change, in assisting in the selection of the most appropriate protection design, in the planning of projects located in the nearshore zone [2] and in assessing the longevity of beach nourishing projects. Among the others, the most popular models for shoreline change are Generalized Shoreline Change Numerical Model (GENESIS) [3], ONELINE [4], UNIform BEach Sediment Transport (UNIBEST) [5], LITtoral Processes And Coastline Kinetics (LITPACK) [6], BEACHPLAN [7], Sistema de Modelado Costero (SMC) [8], GENesis and CAscaDE (GENCADE) [9]. Each of the aforementioned models is suitable for one type of beach sediments composition solely (e.g., sandy beach or gravel beach) and is subjected to different limitations regarding its use (Table1). The majority of existing large-scale coastline models address sandy coastline evolution [10]. To date, no general one-line model valid for estimation of shoreline change at a coastal mound made of non-cohesive sediment grains/units as sand, gravel, cobbles, shingle and rock has been proposed.

J. Mar. Sci. Eng. 2020, 8, 361; doi:10.3390/jmse8050361 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, 361 2 of 17

Table 1. Main features of the existing one-line models.

Variability Diﬀraction Longshore Longshore Detached Model of Seabed Around the Sediment Groynes Current Breakwaters Proprieties Structures Transport GENESIS No Yes No CERC [11] Yes Yes ONELINE No Yes No Kamphuis [12] Yes Yes Bijker [13] Van Rijn [14] UNIBEST No No Yes Yes No Bailard [15] CERC [11] LITPACK Yes Yes Yes STPQ3D [16] Yes Yes BEACHPLAN Yes Yes Yes CERC [11] Yes Yes SMC No Yes No CERC [11] No No GENCADE No Yes No CERC [11] Yes Yes

Presently, there is a growing interest in properly defining the morphological processes of gravel, cobbles or shingle/mixed beaches due to an increasing interest for using of coarse sediments in the artificial nourishing of eroded beaches, as they provide a longer longevity of the nourishing intervention under the forcing processes during storm events [17–19]. In this context, one has to consider that the use of models in practical design situations could also be linked to economic and financial considerations when a cost–benefit approach is part of the design; conversely, models can help in examining the economic implications of a design [20]. Moreover, when designing a coastal protection intervention, modern Coastal Engineering extensive use of numerical models to predict impact of the designed intervention before it is implemented. Within this path, the focus of the present paper is to propose a novel model, named the General Shoreline beach model (GSb), for predicting shoreline change for beaches made of non-cohesive sediment grains/units and to show the results of a sensitivity analysis conducted to evaluate how model output changes with changes in input variables [21,22]; the sensitivity analysis allows to assess the effects and sources of uncertainties oriented to the target to build a robust model for shoreline evolution. The calibration and verification of the GSb model for predicting shoreline change at a mixed beach are performed based on a high-quality field experiment data base [23–25].

2. Materials and Methods

2.1. The General Longshore Transport Model (GLT) Longshore transport due to oblique waves acting on beaches made of non-cohesive sediment grains/units as sand, gravel, cobbles, shingle and rock is determined by means of the General Longshore Transport (GLT) model [26–28]. The GLT model belongs to the typology based on an energy flux approach combined with an empirical relationship between the wave induced forcing and the number of moving sediment grains/units. Specifically, the GLT model considers an appropriate mobility index and assumes that the units move during up- and down-rush with the same obliquity of breaking and reflected waves at the breaker depth [26]. A sediment grain/unit passes through a certain control section if and only if it is removed from an updrift area of extension equal to the longitudinal component of the displacement length, ld sinθd, where ld is the displacement length and θd is its obliquity (Figure1). J. Mar. Sci. Eng. 2020, 8, 361 3 of 17 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 3 of 18

Figure 1. Definition sketch for the General Longshore Transport (GLT) model. Figure 1. Definition sketch for the General Longshore Transport (GLT) model. This process description is particularly true when considering the wave obliquity, the up-rush andThis related process longshore description transport is particularly at the swash true zone. when By considering assuming the that wave the displacement obliquity, the obliquity up-rush is and related longshore transport at the swash zone. By assuming that the displacement obliquity is equal to the characteristic wave obliquity at breaking (θd = θk,b), and that a number Nod of particles equal to the characteristic wave obliquity at breaking (θd = θk,b), and that a number Nod of particles removed from a nominal diameter, Dn50, wide strip moves under the action of 1000 waves, then the removednumber from of units a nominal passing diameter, a given control Dn50, wide section strip in moves one wave under is: the action of 1000 waves, then the number of units passing a given control section in one wave is: ld Nod SN = sinθk,b(=∗∗f)(Ns∗∗), (1) = ∙ Dn50 ·1000, = , (1) 1000 where:where: / ! 1/5 ∗∗ H, sm,0 − / = k () . 2/5 Ns∗∗∆= , (cosθ0) .(2) (2) CkDn50 sm,k ∗∗ is the modified stability number [26] with: Hk = characteristic wave height; Ck = Hk/Hs,o, where Hs,o Ns∗∗ is the modified stability number [26] with: Hk = characteristic wave height; Ck = Hk/Hs,o, where Hs,o = significant offshore wave height; θ0 = offshore wave obliquity; sm,0 = mean wave steepness at offshore = significant offshore wave height; θ0 = offshore wave obliquity; sm,0 = mean wave steepness at offshore conditions and sm,k = characteristic mean wave steepness (assumed equal to 0.03). Ns** resembles** the conditions and sm,k = characteristic mean wave steepness (assumed equal to 0.03). Ns resembles traditional stability number, Ns [29,30], taking into account the effects of a non-Rayleighian wave the traditional stability number, Ns [29,30], taking into account the effects of a non-Rayleighian wave heightheight distribution distribution at atshallow shallow wa waterter [31], [31], wave wave steepness, steepness, wave wave obliquity obliquity and and the the nominal nominal diameter of of the sediment grains/units. The authors in [26,32] reported that Hk is to be considered equal to H1/50, the sediment grains/units. The authors in [26,32] reported that Hk is to be considered equal to H1/50, but H2% can also be adopted. In the first case Ck = 1.55, in the second case Ck = 1.40. The second factor but H2% can also be adopted. In the first case Ck = 1.55, in the second case Ck = 1.40. The second factor in Equation (2) is such that Ns** ≅** Ns for θ0 = 0 if sm,0 = sm,k. in Equation (2) is such that Ns Ns for θ0 = 0 if sm,0 = sm,k. In Inthe the case case of ofa head-on a head-on wave wave attack, attack, under under the the assumption assumption that, that, offshore offshore the the breaking breaking point, point, the the wavewave energy energy dissipation dissipation is isnegligible negligible and and that that waves waves break break as asshallow shallow water water waves, waves, the the following following relationrelation holds: holds: ⁄ ⁄ =1 8= , = 12 2 = 8 ,2 , 2 (3) F 1/8ρgH0cg,0 1/8ρgHb cg,b, (3) In Equation (3), F = wave energy flux, ρ = water density, g = gravity acceleration, H0 = offshore In Equation (3), F = wave energy flux, ρ = water density, g = gravity acceleration, H0 = offshore wave height, , = offshore wave group celerity, Hb = wave height at breaking and , = is the wave wave height, cg,0 = offshore wave group celerity, Hb = wave height at breaking and cg,b = is the wave groupgroup celerity celerity at atbreaking. breaking. Equation (3), related to the breaker index γb = Hb/hb, with hb = breaking depth, implies: Equation (3), related to the breaker index γb = Hb/hb, with hb = breaking depth, implies: / !1/5 / = γb = , (4) = = 1/5 Hb H0 qH0s0− , (4) 4k0H0 The authors in [33] found the best agreement with field and laboratory data assuming γb = 1.42 or the proportionalityThe authors in [constant33] found q the= 0.56. best Itagreement follows that, with considering field and laboratorythe characteristic data assuming wave heightγb = at1.42 breaking,or the proportionality Hk,b, and sm,0 = s constantm,k = 0.03,q N=s**0.56. can be Itfollows also written that, consideringas: the characteristic wave height at ∗∗** 0.89, breaking, Hk,b, and sm,0 = sm,k = 0.03, Ns ≅can be also , written as: ∆ (5) 0.89Hk,b where ∆ = relative mass density of the sedimentNs∗∗ grain/unit, = (ρs – ρ)/ρ and ρs = sediment grain/unit (5) CkDn50 density. whereAccording∆ = relative to the refraction mass density theory of for the plane sediment and monotonically grain/unit = ( ρdecreasings ρ)/ρ and profiles,ρs = Hsedimentk,b and − singrainθk,b, are/unit evaluated density. as in the following [26,34]: / According to the refraction theory= for plane and/ monotonically, decreasing profiles, Hk,b and , (6) sinθk,b, are evaluated as in the following [26,34]: J. Mar. Sci. Eng. 2020, 8, 361 4 of 17

2 p 2/5 Hk,b = Hk cgcosθo γb/g , (6)

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW ck,b 4 of 18 sinθ = sinθ , (7) k,b c o q, , = , ck,b = gHk,b/γb,(7) (8) where cg = group celerity and ck,b is the characteristic wave celerity at breaking depth. , = ,⁄ , (8) The displacement length is calculated as [26]: where cg = group celerity and ck,b is the characteristic wave celerity at breaking depth. (1.4Ns∗∗ 1.3) l = − Dn50, (9) The displacement length is calculatedd as tanh[26]:2 (kh) (1.4∗∗ −1.3) = , where k = wave number and h = water depth.ℎ(ℎ) (9) Nod has been determined following a calibration procedure based on the least-squares method, where k = wave number and h = water depth. taking into account nine high quality data sets of longshore transport from field and laboratory Nod has been determined following a calibration procedure based on the least-squares method, experiments for a wide mobility range of sediment grains/units: from stones to sand. In total, the nine taking into account nine high quality data sets of longshore transport from field and laboratory data sets consist of 245 cases [28]. In particular, Nod values are partitioned in two intervals: the first experiments for a wide** mobility range of sediment grains/units: from stones to sand. In total, the nine interval refers to Ns 23, from reshaping type berm breakwaters [35] to gravel beaches; the second data sets consist **of 245≤ cases [28]. In particular, Nod** values are partitioned in two intervals: the first one relates to Ns > 23, for sandy beaches. For Ns 23, a third order polynomial approximating interval refers to Ns** ≤ 23, from reshaping type berm ≤breakwaters [35] to** gravel beaches; the second function provides a satisfactory agreement as shown by [28]. For Ns > 23 a good agreement is one relates to Ns** > 23, for sandy beaches. For Ns** ≤ 23, a third order polynomial approximating obtained by a linear regression in log–log plane. Nod is given as: ** function provides a satisfactory( agreement as shown by [28]. For Ns > 23 a good agreement is 20N (N 2)2 N 23 obtained by a linear regressionN = in log–logs∗∗ plane.s∗∗ Nod is given as: s∗∗ od ∗∗− ∗∗ ≤∗∗ , (10) exp[2.7220ln ((Ns∗∗ )−2+ 1.12) ] Ns∗∗ > 23≤ 23 = ∗∗ ∗∗ , 2.72( ) +1.12 >23 (10) ** ** The estimated correlation coefficient is equal to 0.89 for Ns** ≤ 23 and 0.92 for N**s > 23. The estimated correlation coefficient is equal to 0.89 for Ns ≤ 23 and 0.92 for Ns > 23. The longshore transport rate, Q , can be also expressed in terms of [m3/s] as in the following: LT 3 The longshore transport rate, , can be also expressed in terms of [m /s] as in the following: S D3 N n50 QLT= = , ,(11) (1 −(1 )n)Tm − where Tm = mean wave period, and n = porosity factor. where Tm = mean wave period, and n = porosity factor. Figure 22 showsshows thethe flowchartflowchart summarizingsummarizing thethe useuse ofof thethe GLT.GLT.

Figure 2. User flowchart. ﬂowchart.

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2.2. The General Shoreline Beach Model (GSb)

2.2.1. Theoretical Background The GSb model belongs to the one-line model typology [36] and assumes that the beach cross-shore profile remains unchanged [37,38], thereby allowing beach change to be described uniquely in terms of the shoreline position. The equilibrium cross-shore profile is calculated as proposed by [37,38] and is used to determine the average nearshore bottom slope adopted in longshore transport equation. The average cross-shore profile is described by [37]: h(y) = Ay2/3, (12) where h is expressed in (m), A = scale parameter (m1/3) and y = offshore distance from the initial shoreline (m). The scale parameter A can be calculated as in the following [39]:

0.94 A = 0.41(Dn50) , Dn50 < 0.4 mm, (13)

0.32 A = 0.23(Dn ) , 0.4 mm Dn < 10.0 mm, (14) 50 ≤ 50 0.28 A = 0.23(Dn ) , 10.0 mm Dn < 40.0 mm, (15) 50 ≤ 50 0.11 A = 0.46(Dn ) , Dn 40 mm, (16) 50 50 ≥ The main peculiarity of the GSb model is the use of the GLT model, allowing to have an explicit dependence of shoreline evolution on Dn50 [28,40]. This finding is due to the fact that GSb uses the GLT model. Differently from GENESIS and similar models [7,8,41], which take into account two calibration coefficients, K1 and K2, the GSb presents one calibration coefficient, KGSb, which does not solely depend on the grain size diameter and depends on the longshore gradient in breaking wave height [42]. As in the case of most numerical models (e.g., GENCADE [9]), GSb is able to deal with the presence of soft and hard coastal structures. Soft protection consists of nourishing an eroded beach. A hard intervention consists in deployment of one or more coastal structures (e.g., groynes, detached breakwaters and seawalls), composed by natural rock or artificial concrete units. The model allows to determine short-term (daily base) or long-term (yearly base) shoreline change [43,44] for arbitrary combinations and configurations of hard structures and beach fills that can be represented on a modelled reach of coast. GSb considers the sediment grain/unit passing around or through a coastal structure. Two types of sediment movement around or through the structures can be simulated: bypass, when the sediment passes around the seaward end of the groynes, and transmission, where the sediment passes through the structures. Specifically, bypass occurs when the water depth at the tip of the structure, DG, is less than the depth of active longshore transport, DLT, calculated with [45]. To represent sediment bypass, a bypassing factor, BF, is defined as:

DG BF = 1 DG DLT, (17) − DLT ≤

Transmission occurs due to permeability of the material, p, composing the coastal structure. With p = 0, the structure is completely transparent. On the contrary, for p = 1, the structure is fully impermeable. With the values of BF and p, GSb calculates the total fraction TF of sediment passing around or through a structure as deﬁned by [41]:

TF = p (1 BF) + BF, (18) − The TF value is calculated at every time step for each structure present in the model domain. GSb takes into account the wave transformation phenomena as shoaling, refraction and diﬀraction. Shoaling and refraction are treated according to an internal wave model proposed by [39]. GSb uses J. Mar. Sci. Eng. 2020, 8, 361 6 of 17

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 6 of 18 the simplified diffraction calculation procedure from waves with directional spread presented by [46] toGSb represent uses the di ffsimplifiedraction at structuresdiffraction such calculation as detached procedure breakwaters from and waves groynes. with directional spread presentedThe model by [46] requires to represent predictive diffraction expressions at stru forctures the longshoresuch as detached sediment breakwaters transport rate.and groynes. The model requires predictive expressions for the longshore sediment transport rate. 2.2.2. Longshore Sediment Transport Rate 2.2.2. Longshore Sediment Transport Rate The GSb model uses the following equation for the longshore transport rate Ql: The GSb model uses the following equation for the longshore transport rate : 3 SND K ∂Hs,b Q = n50 GSb H2 c cos(θ ) , , (19) l = − ρ ,s,,b gcos,b ()bs , ( )() s () .⁄ 7/2 x (19) 1 n Tm − 8 1 (1 n) tan β 1.416 ∂ − ρ − − where tan = average bottom slope from the shoreline to the closure depth, ; , = significant where tan β = average bottom slope from the shoreline to the closure depth, dc; Hs,b = significant wave wave height at breaking; = angle of breaking waves to the local shoreline; x = longshore distance. height at breaking; θbs = angle of breaking waves to the local shoreline; x = longshore distance. The first term in Equation (19) accounts for longshore transport as from the “GLT formula” The first term in Equation (19) accounts for longshore transport as from the “GLT formula” [26,27]. [26,27]. The second term in Equation (19), similar to GENESIS [39], ONELINE [4], BEACHPLAN [7], The second term in Equation (19), similar to GENESIS [39], ONELINE [4], BEACHPLAN [7], SMC [8] SMC [8] and GENCADE [9], accounts for the longshore sediment transport induced by the longshore and GENCADE [9], accounts for the longshore sediment transport induced by the longshore gradient gradient in significant wave height at breaking [42], where Hs,b is calculated taking into account the in significant wave height at breaking [42], where Hs,b is calculated taking into account the wave wave propagation shoaling, refraction and diffraction phenomena [39]. The original formulation of propagation shoaling, refraction and diffraction phenomena [39]. The original formulation of the the second term in Equation (19) considers the root-mean-square (rms) wave height [42]. The factor second term in Equation (19) considers the root-mean-square (rms) wave height [42]. The factor 1.416 1.416 is used to convert from significant wave height to root-mean-square (rms) wave height [39]. is used to convert from significant wave height to root-mean-square (rms) wave height [39].

2.2.3.2.2.3. Sediment Continuity Equation SpatialSpatial andand temporaltemporal variationsvariations inin gradientsgradients inin longshorelongshore transporttransport drivedrive shorelineshoreline accretionaccretion/erosion./erosion. TheThe relationrelation betweenbetween shorelineshoreline evolutionevolution inin termsterms ofof accretionaccretion/erosion,/erosion, ∆∆yy,, andand thethe longshorelongshore transporttransport raterate isis formulatedformulated consideringconsidering thethe continuitycontinuity equationequation ofof sedimentsediment inin aa controlcontrol volume,volume, V∆(Figure (Figure3). 3). TheThe sedimentsediment continuitycontinuity equationequation expressedexpressed as:as: ∆ (1 − )( +) + =0, (20) ∆V Ql∆ (1 n)(d + dc) + = 0, (20) ∆t − b x where = berm height and = time, is solved by an explicit finite difference scheme [39]. where db = berm height and t = time, is solved by an explicit ﬁnite diﬀerence scheme [39].

(a) (b)

FigureFigure 3.3. ((a)) LongshoreLongshore sedimentsediment transporttransport raterate QQll and coastalcoastal evolutionevolution ∆yy;;( (b)) beachbeach cross-shorecross-shore proﬁleprofile change.change.

2.3.2.3. InfluenceInfluence of DiDifferentfferent InputsInputs ModelsModels are are sensitive sensitive to to morphological morphological as well as forcing input parameters; thus, it is imperativeimperative toto useuse properproper values values and and to to perform perform a sensitivitya sensitivity analysis analysis to evaluate to evaluate how how model model output output changes changes with changeswith changes in input in input parameters parameters [21,22 [21,22];]; if a small if a sm modificationall modification in a parameter in a parameter value value produces produces a large a changelarge change in the in output, the output, model model reliability reliability is low is and low vice and versa vice [versa47]. [47]. In the present paper, in order to evaluate the reliability of the GSb model, a sensitivity analysis for a range of selected input parameters has been conducted based on the simulation of the J. Mar. Sci. Eng. 2020, 8, 361 7 of 17

J. Mar. Sci.In Eng. the 2020 present, 8, x FOR paper, PEER in REVIEW order to evaluate the reliability of the GSb model, a sensitivity analysis7 of 18 for a range of selected input parameters has been conducted based on the simulation of the advance/retreat advance/retreatof an initial straight of an initial shoreline straight in presence shoreline of in a presence single groyne. of a single Specifically, groyne. three Specifically, input parameters three input have ο parametersbeen selected have asbeen representative selected as ofrepresen (i) wavetative characteristics of (i) wave (i.e., characteristicsϑo), (ii) sediment (i.e., propertiesϑ ), (ii) sediment (i.e., Dn 50) propertiesand (iii) (i.e., short D/longn50) and term (iii) predictions short/long (i.e., term duration predictions of simulation, (i.e., durationt). of simulation, t). SimulationsSimulations have have been been performed performed for for the the same same conditions conditions considered considered by by [9] [9 and] and shown shown in in Table Table 2; 2; thisthis has has allowed allowed a a direct direct comparison comparison with with the the results results to to be be obtained obtained by by using using GENCADE GENCADE [9] [9] (Figure (Figure 4). 4). As an initial condition, condition, a a straight straight shoreline shoreline 3000 3000 m m long long with with a 75 a 75 m mlong long single single groyne groyne located located at at thethe center center of the of thedomain domain has has been been consi considered.dered. The Thecross-shore cross-shore beach beach profile, profile, with with Dn50 D= n0.350 =mm,0.3 is mm, characterizedis characterized by a berm by a berm height height of 1 m of with 1 m with a closure a closure depth depth equal equal to 8 tom. 8 With m. With regard regard to the to theinput input offshoreoffshore wave wave characteristics, characteristics, values values of ofHs,oH =s,o 0.75= 0.75 m, m,and and Tp =T 8p =s at8 s50 at m 50 water m water depth depth have have been been simulated.simulated. The The model model grid grid cell cell resolution, resolution, DXDX, has, has been been assumed assumed equal equal to to 10 10 m m with with a a total total number number of of cells,cells, NXNX = 300.300. A A calculation calculation time time step, DT, equalequal toto 0.50.5 hh hashas beenbeen adopted. adopted.For Fort t= =2 2years, years, GSb GSb has hasbeen been run run with withK GSb==K2==0.250.25;; the the boundary boundary condition condition has has been been set set as asfixed. fixed.Fixed Fixedmeans means thatthat the theboundary boundary will will not not move move from from the the initial initial shoreline shoreline over over the the calculation calculation interval interval (i.e., (i.e.,y does does not changenot changeover over time). time).

TableTable 2. Selected 2. Selected input input parameters. parameters.

DDnn5050 (mm)(mm) 0.3 0.3 DDBB (m)(m) 1 1 D (m) 8 DCC (m) 8 HHs,os,o (m)(m) 0.75 0.75 T (s) 8 Tpp (s) 8 ϑo (deg) 15 (deg) 15 DXDX (m)(m) 10 10 NX (-) 300 NX (-) 300 DT (h) 0.5 DT (h) 0.5 t (years) 2 t (years) 2 KGSb (-) 0.25 KGSb (-) 0.25

FigureFigure 4 shows4 shows that, that, for for both both models, models, the the shorel shorelineine results inin agreementagreement with with the the expected expected up-drift up- driftdeposition deposition and and down-drift down-drift erosion erosion phenomena. phenomena. However, However, no judgment no judgment can be can given be ongiven their on reliability their reliabilityin absence in absence of ﬁeld of data. field data.

+15°

+90° −90°

FigureFigure 4. Comparison 4. Comparison between between GSb GSb and and GENCADE. GENCADE.

2.3.1. Influence of Offshore Wave Angle J. Mar. Sci. Eng. 2020, 8, 361 8 of 17

2.3.1. Influence of Offshore Wave Angle In order to evaluate the influence of the offshore wave angle on the shoreline evolution, different J. Mar.J. Mar. Sci. Sci. Eng. Eng. 2020 2020, 8, 8x, FORx FOR PEER PEER REVIEW REVIEW 8 of8 of18 18 values of ϑo in the interval from 45 to +45 deg have been considered. The adopted input parameters − areIn given order in to Table evaluate2, with theϑ influenceo = 45, of35, the 15,offshore5, + 5,wave+15, angle+25, +on35, the+ 45shore deg.line evolution, different In order to evaluate the influence− − of −the offshore− wave angle on the shoreline evolution, different Figure5 shows the calculated shoreline evolution induced by longshore transport acting from (a) valuesvalues of of in in the the interval interval from from −45 −45 to to +45 +45 deg deg have have been been consider considered.ed. The The adopted adopted input input parameters parameters areright given to in left Table for ϑ 2,o =with45, 35,= −45,25, −35,15, −15,5 − deg,5, +5, and +15, (b) +25, from +35, left +45 to deg. right for ϑo = +5, +15, +25, +35, are given in Table 2, −with − =− −45, −−35, −15, −5, +5, +15, +25, +35, +45 deg. +45Figure deg,Figure respectively. 5 5shows shows the the calculated calculated sh shorelineoreline evolution evolution induced induced by by longshore longshore transport transport acting acting from from (a) rightMaximum to left for and = =− minimum 45, −35, −25, advance −15, −5 /deg,retreat and rates (b) from have left been to right obtained for = for += 5,ϑ +15,o = +25,35 +35, and (a) right to left for −45, −35, −25, −15, −5 deg, and (b) from left to right for + 5, +15, ±+25, +35, +45ϑo deg,= 5,respectively. respectively. +45 deg,± respectively.

( a()a ) ( b()b )

FigureFigure 5. 5.Calculated Calculated shoreline shoreline evolution evolution for for ( a )() aϑ) o= −=45, 45,−45, −35, −35,35, −15, −15,15, −5 − and5 and (b ()b ) ϑ=o +5,= +5, + +15,5, +15,+ 15,+25, +25,+ +35,25, +35,+ +45.35, +45. +45. − − − − 2.3.2. Influence of Nominal Diameter MaximumMaximum and and minimum minimum ad advance/retreatvance/retreat rates rates have have been been obtained obtained for for = =± 35±35 and and = =± 5,± 5, respectively.respectively.In order to evaluate the influence of the nominal diameter on the shoreline evolution, different values of Dn50 have been considered. The adopted input parameters are given in Table2, with Dn50 = 0.3, 2.3.2.2.3.2.30 and Influence Influence 100 mm of of correspondingNominal Nominal Diameter Diameter to sand, pebbles and cobbles, respectively. InInFigure order order 6to showsto evaluate evaluate the the calculated the influence influence shoreline of of the the nomina evolution nominal diameterl induceddiameter on by on the longshore the shorel shoreline transport.ine evolution, evolution, different different A lower mobility of the sediment grain/unit composing the beach is found when considering a larger valuesvalues of of D nD50n 50have have been been considered. considered. The The adopted adopted input input parameters parameters are are given given in in Table Table 2, 2,with with D nD50n =50 = 0.3,0.3,sediment 30 30 and and 100 diameter. 100 mm mm corresponding Oncorresponding the left (updrift) to to sa sand,/nd,right pebbles pebbles (downdrift) and and cobbles, cobbles, side of respectively. therespectively. groyne, shoreline advance/retreat rates, equal to 60, 40 and 20 m, have been obtained for D = 0.3, 30 and 100 mm, respectively. FigureFigure 6 shows6 shows the the calculated calculated shoreline shoreline ev evolutionolution induced inducedn50 by by longshore longshore transport. transport.

+15°+15°

+90°+90° −90°−90°

FigureFigureFigure 6. 6. 6.Calculated Calculated shoreline shoreline evolution evolutionevolution for forfor D DnD50nn =50 0.3== 0.3 0.3mm, mm, mm, 30 30 30mm, mm, mm, 100 100 100 mm. mm. mm.

A Alower lower mobility mobility of of the the sediment sediment grain/unit grain/unit composing composing the the beach beach is isfound found when when considering considering a a largerlarger sediment sediment diameter. diameter. On On the the left left (updrift)/ (updrift)/rightright (downdrift) (downdrift) side side of of the the groyne, groyne, shoreline shoreline advance/retreatadvance/retreat rates, rates, equal equal to to 60, 60, 40 40 and and 20 20 m, m, have have been been obtained obtained for for D nD50n 50= =0.3, 0.3, 30 30 and and 100 100 mm, mm, respectively.respectively. J. Mar. Sci. Eng. 2020, 8, 361 9 of 17

J.2.3.3. Mar. Sci. Inﬂuence Eng. 2020 of, 8,Duration x FOR PEER REVIEW 10 of 18

J. Mar. Sci.In orderEng. 2020 to, 8 assess, x FOR thePEER capacity REVIEW of the model to determine short-term (daily base), medium-term 10 of 18 2.3.3. Influence of Duration (monthly base) or long-term (yearly base) shoreline evolution, diﬀerent values of duration of 2.3.3.simulation InInfluence order have to of assess beenDuration considered.the capacity The of the adopted model input to determine parameters short-term are given (daily in Table base),2, withmedium-termt = 1 day, (monthly1 month,In order 6base) months, to assess or long-term 1 the year, capacity 2 years.(yearly of the Figure base) model7 showsshoreline to determine the evolution, calculated short-term different shoreline (daily valuesbase), evolution medium-term of inducedduration by of (monthlysimulationlongshore base) transport.have or been long-term consider (yearlyed. The base)adopted shoreline input parametersevolution, aredifferent given invalues Table of 2, durationwith t = 1 ofday, simulation1 month,The shoreline 6have months, been advance 1consider year, /2retreated. years. The rate Figureadopted increases 7 inputshows with parameters the a calculated longer are duration given shoreline in of Table simulation. evolution 2, with tinduced On= 1 theday, left by 1longshore(updrift) month, /6right transport.months, (downdrift) 1 year, 2 side years. of the Figure groyne, 7 shows shoreline the calculated advance/retreat shoreline rates, evolution equal to induced 2.1, 14.2, by 40.9, longshore52.4 and63.6 transport. m, have been obtained for t = 1 day, 1 month, 6 months, 1 year and 2 years, respectively. +15°

+15° +90° −90°

+90° −90°

Figure 7. Calculated shoreline evolution for t = 1 day, 1 month, 6 months, 1 year, 2 years. FigureFigure 7. 7. CalculatedCalculated shoreline shoreline evolution evolution for for t =t 1= day,1 day, 1 month, 1 month, 6 months, 6 months, 1 year, 1 year, 2 years. 2 years. The shoreline advance/retreat rate increases with a longer duration of simulation. On the left 2.4. Field Experiment at a Mixed Beach (updrift)/rightThe shoreline (downdrift) advance/retreat side of therate groyne, increases shoreline with a longeradvance/retreat duration rates,of simulation. equal to 2.1,On the14.2, left 40.9, (updrift)/right52.4Study and Area 63.6 and m, (downdrift) have Field been Observations side obtained of the forgroyne, t = 1 day,shoreline 1 month, advance/retreat 6 months, 1 rates,year and equal 2 years, to 2.1, respectively. 14.2, 40.9, 52.4 and 63.6 m, have been obtained for t = 1 day, 1 month, 6 months, 1 year and 2 years, respectively. 2.4. FieldShoreline Experiment evolution at a Mixed has Beach been observed during a field experiment conducted in 2007 at 2.4.Milford-on-Sea, Field Experiment under at a Mixed Hordle Beach Cli ff, located in the county of Hampshire on the Southern coast Studyof the UKArea [23 and–25 Field]. The Observations coastal area of Milford-on-Sea, at the eastern side of Christchurch Bay (Figure8), Studyis characterized Area and Field by a Observations mixed shingle and sand beach, composed by finer (sand) and coarse (cobbles, Shoreline evolution has been observed during a field experiment conducted in 2007 at Milford- gravel) sediment units/grains (Dn50 = 11.19 mm; D85/D15 = 27.79, where D85 and D15 represent the on-Sea,Shoreline under evolutionHordle Cliff, has locatedbeen observed in the county during of a fieldHampshire experiment on the conducted Southern in coast 2007 of at the Milford- UK [23– particle diameter for which 85% and 15%, respectively, of the material is finer) (Figure9). on-Sea,25]. The under coastal Hordle area Cliff, of Milford-on-Sea,located in the county at the of Hampshireeastern side on of the Christchurch Southern coast Bay of the(Figure UK [23– 8), is An impoundment technique has been adopted consisting of a temporary impermeable groyne 25].characterized The coastal by area a mixed of Milford-on-Sea, shingle and sand at thebeach, eastern composed side of by Christchurch finer (sand) Bayand (Figurecoarse (cobbles,8), is characterized46 m long (originally by a mixed 19 shingle m wet and and sand 27 dry) beach, deployed composed along by thefiner beach (sand) for and the coarse period (cobbles, 1 October gravel) sediment units/grains (Dn50 = 11.19 mm; D85/D15 = 27.79, where D85 and D15 represent the 2007–15 November 2007, acting as a barrier for the sediments moving along the coast (Figure 10a). gravel)particle sediment diameter units/grainsfor which 85% (D nand50 = 15%,11.19 respectively, mm; D85/D15 of = the27.79, material where is D finer)85 and (Figure D15 represent 9). the particleThis technique diameter is for considered which 85% by severaland 15%, authors respectively, as a reliable of the and material effective is finer) method (Figure to estimate 9). longshore transport rates [40,48–50].

Figure 8. Study area location. Figure 8. Study area location. Figure 8. Study area location. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 11 of 18

J. Mar. Sci. Eng. 2020, 8, 361 10 of 17 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 11 of 18

Figure 9. Sediment unit/grain size distribution curves.

An impoundment technique has been adopted consisting of a temporary impermeable groyne 46 m long (originally 19 m wet and 27 dry) deployed along the beach for the period 1 October 2007– 15 November 2007, acting as a barrier for the sediments moving along the coast (Figure 10a). This technique is considered by several authors as a reliable and effective method to estimate longshore transport rates [40,48–50]. A Differential Global Positioning System (DGPS) has been used to perform the beach profile surveys at low tide condition, covering an extension of 280 m alongshore (Figure 10b) [23]. Wave data have been collected by an Acoustic Wave and Current (AWAC) profiler from 1 October 2007 to 25 November 2007 (Figures 11 and 12); data have been recorded in intervals of one hour, approximately 600 m at 7 m water depth. FigureFigure 9. 9.Sediment Sediment unitunit/grain/grainsize size distribution distribution curves. curves.

November 2007 (Figures( a11) and 12); data have been recorded in intervals of(b one) hour, approximately

600 FiguremFigure at 7 10. 10.m water((aa)) View View depth. of of the the temporary temporary structure fromfrom thethe toptop ofof HordleHordle Cli Cliffﬀ the the 6 6 October October 2007; 2007; (b ()b plan) planview view of the of study the study site andsite groyneand groyne position. position.

A Differential Global Positioning System (DGPS) has been used to perform the beach profile surveys at low tide condition, covering an extension of 280 m alongshore (Figure 10b) [23]. Wave data have been collected by an Acoustic Wave and Current (AWAC) profiler from 1 October 2007 to 25 November 2007 (Figures 11 and 12); data have been recorded in intervals of one hour, approximately

600J. m Mar. at 7Sci. m Eng. water 2020 depth., 8, x FOR PEER REVIEW 12 of 18

(a) (b)

Figure 10. (a) View of the temporary structure from the top of Hordle Cliff the 6 October 2007; (b) plan view of the study site and groyne position.

Figure 11. Wave rose and shoreline orientation. Figure 11. Wave rose and shoreline orientation.

Figure 12. Time history of significant wave height, peak period and wave angle.

3. GSb Calibration and Verification for a Mixed Beach

3.1. Calibration The calibration of the GSb model has been conducted based on the comparison between the observed and calculated shoreline evolution. Values of KGSb = 0.005, 0.01, 0.05, 0.1, 0.2 have been adopted. The first beach survey collected in presence of the groyne (1 October 2007) has been assumed as the initial shoreline. Based on an accurate evaluation of the cross-shore beach profile evolution over time, DC and DB have been selected equal to 1 m and 3 m, respectively (Figure 13) [23]. A value of Dn50 = 11.19 mm has been adopted. The considered groyne has been positioned at the 31st cell of the domain, corresponding to x = 150/155 m. Hourly wave conditions (Hs, Tp, Dir) have been considered in the simulations (Figures 11 and 12). The computational domain has been assumed 280 m long; DX has been set equal to 5 m with NX = 57. The calculation time step has been set to 0.05 h (180 s), for a total duration of simulation equal to 45 days from the groyne deployment (t = 0). In accordance with [11] the boundary conditions have been set as fixed, since they are located far away from the groyne (i.e., the length of the entire calculation domain is in the order of two or three groyne J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 12 of 18

J. Mar. Sci. Eng. 2020, 8, 361 11 of 17 Figure 11. Wave rose and shoreline orientation.

FigureFigure 12.12. TimeTime historyhistory ofof signiﬁcantsignificant wavewave height,height, peakpeak periodperiod andand wavewave angle. angle.

3. GSb Calibration and Verification for a Mixed Beach 3. GSb Calibration and Verification for a Mixed Beach 3.1. Calibration 3.1. Calibration The calibration of the GSb model has been conducted based on the comparison between the The calibration of the GSb model has been conducted based on the comparison between the observed and calculated shoreline evolution. Values of KGSb = 0.005, 0.01, 0.05, 0.1, 0.2 have been observed and calculated shoreline evolution. Values of KGSb = 0.005, 0.01, 0.05, 0.1, 0.2 have been adopted. The first beach survey collected in presence of the groyne (1 October 2007) has been assumed adopted. The first beach survey collected in presence of the groyne (1 October 2007) has been assumed as the initial shoreline. Based on an accurate evaluation of the cross-shore beach profile evolution over as the initial shoreline. Based on an accurate evaluation of the cross-shore beach profile evolution time, DC and DB have been selected equal to 1 m and 3 m, respectively (Figure 13)[23]. A value of over time, DC and DB have been selected equal to 1 m and 3 m, respectively (Figure 13) [23]. A value Dn50 = 11.19 mm has been adopted. The considered groyne has been positioned at the 31st cell of the of Dn50 = 11.19 mm has been adopted. The considered groyne has been positioned at the 31st cell of domain, corresponding to x = 150/155 m. Hourly wave conditions (Hs, Tp, Dir) have been considered the domain, corresponding to x = 150/155 m. Hourly wave conditions (Hs, Tp, Dir) have been in the simulations (Figures 11 and 12). The computational domain has been assumed 280 m long; considered in the simulations (Figures 11 and 12). The computational domain has been assumed 280 DX has been set equal to 5 m with NX = 57. The calculation time step has been set to 0.05 h (180 s), m long; DX has been set equal to 5 m with NX = 57. The calculation time step has been set to 0.05 h forJ. Mar. a total Sci. Eng. duration 2020, 8, x of FOR simulation PEER REVIEW equal to 45 days from the groyne deployment (t = 0). In accordance 13 of 18 (180 s), for a total duration of simulation equal to 45 days from the groyne deployment (t = 0). In with [11] the boundary conditions have been set as fixed, since they are located far away from the groyne length).accordance It assures with [11] that the the boundary boundary conditions conditions have are been unaffected set as fixed by , changessince they that are take located place far in away the (i.e., the length of the entire calculation domain is in the order of two or three groyne length). It assures vicinityfrom the of groyne the groyne. (i.e., the length of the entire calculation domain is in the order of two or three groyne that the boundary conditions are unaffected by changes that take place in the vicinity of the groyne.

FigureFigure 13.13. Surveyed cross-shore beachbeach proﬁleprofile atat Milford-on-Sea.Milford-on-Sea.

Figure 14 shows for the selected values of KGSb, (i) the comparison between observed and calculated shorelines at the end of the simulation (45 days) and (ii) the corresponding values of Root Mean Square Error (RMSE). The value of KGSb = 0.1 gave the better agreement between observed and calculated shoreline showing the lowest (RMSE) value, equal to 4.6. The difference among all the estimated RMSE values is lower than 0.2. KGSb depends on the longshore gradient in breaking wave height. For the considered field case, a single groyne deployed on a smooth uniform bathymetry, the longshore gradient in breaking wave height is moderate. Consequently, the results were less sensitive to the value of KGSb. It was noticed that the observed shoreline moves at the boundary and the sediment mass seems to be not conserved.

Figure 14. (a) Observed and calculated shorelines at the end of the simulation (45 days) for the selected

values of KGSb (b) RMSE vs. KGSb. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 13 of 18

length). It assures that the boundary conditions are unaffected by changes that take place in the vicinity of the groyne.

J. Mar. Sci. Eng. 2020, 8, 361 12 of 17 Figure 13. Surveyed cross-shore beach profile at Milford-on-Sea.

Figure 14 shows for the selected values of KGSb, (i) the comparison between observed and Figure 14 shows for the selected values of KGSb, (i) the comparison between observed and calculatedcalculated shorelinesshorelines atat thethe endend ofof thethe simulationsimulation (45(45 days)days) andand (ii)(ii) thethe correspondingcorresponding valuesvalues ofof RootRoot Mean Square Error (RMSE). The value of KGSb = 0.1 gave the better agreement between observed and Mean Square Error (RMSE). The value of KGSb = 0.1 gave the better agreement between observed andcalculated calculated shoreline shoreline showing showing the lowest the lowest (RMSE) (RMSE) value,value, equal equal to 4.6. to 4.6.The Thedifference diﬀerence among among all the all estimated RMSE values is lower than 0.2. KGSb depends on the longshore gradient in breaking wave the estimated RMSE values is lower than 0.2. KGSb depends on the longshore gradient in breaking waveheight. height. For the For considered the considered field ﬁeldcase, case,a single a single groyne groyne deployed deployed on a onsmooth a smooth uniform uniform bathymetry, bathymetry, the thelongshore longshore gradient gradient in breaking in breaking wave wave height height is moderate. is moderate. Consequently, Consequently, the results the were results less were sensitive less to the value of KGSb. It was noticed that the observed shoreline moves at the boundary and the sensitive to the value of KGSb. It was noticed that the observed shoreline moves at the boundary and thesediment sediment mass mass seems seems to be to not be notconserved. conserved.

FigureFigure 14.14. (a)) Observed andand calculatedcalculated shorelinesshorelines atat thethe endend ofof thethe simulationsimulation (45(45 days)days) forfor thethe selectedselected values of K (b) RMSE vs. K . values of KGSbGSb (b) RMSE vs. KGSbGSb. 3.2. Verification Calibration of GSb has been obtained by comparing the calculated and observed shorelines after 45 days; a value of KGSb = 0.1 has been assumed. It is of a certain interest to verify the reliability of GSb at daily steps within the 45 days. RMSE daily values are shown in Figure 15a, with maximum values attained at the two storms occurred on 16th and 27th days after the groyne deployment. This behavior is probably due to the deviation of the beach cross-shore profile under a severe storm attack from the equilibrium cross-shore profile assumed for a one-line model. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 14 of 18

3.2. Verification Calibration of GSb has been obtained by comparing the calculated and observed shorelines after

GSb 45J. Mar. days; Sci. aEng. value 2020 of, 8 ,K x FOR = PEER0.1 has REVIEW been assumed. It is of a certain interest to verify the reliability of 14 GSb of 18 at daily steps within the 45 days. RMSE daily values are shown in Figure 15a, with maximum values attained3.2. Verification at the two storms occurred on 16th and 27th days after the groyne deployment. This behavior J.is Mar. probably Sci. Eng. due2020 ,to8, the 361 deviation of the beach cross-shore profile under a severe storm attack from13 of the 17 Calibration of GSb has been obtained by comparing the calculated and observed shorelines after equilibrium cross-shore profile assumed for a one-line model. 45 days; a value of KGSb = 0.1 has been assumed. It is of a certain interest to verify the reliability of GSb at daily steps within the 45 days. RMSE daily values are shown in Figure 15a, with maximum values attained at the two storms occurred on 16th and 27th days after the groyne deployment. This behavior is probably due to the deviation of the beach cross-shore profile under a severe storm attack from the equilibrium cross-shore profile assumed for a one-line model.

FigureFigure 15. 15.( a(a)) Estimated Estimated RMSE RMSE daily daily values. values. (b) ( Timeb) Time history history of signiﬁcant of significant wave wave height height and wave and angle. wave angle. Figures 16–18 show, as representative cases, the comparison between observed and calculated shorelines,Figures and 16–18 the dishow,ﬀerence, as representativeYobs–YGSb, after cases, 24 days the (25comparison October 2007), between 39 days observed (09 November and calculated 2007) andshorelines, 45 days and (15 Novemberthe difference, 2007) Yob froms–YGSb the, after groyne 24 days deployment. (25 OctoberYobs 2007),and 39YGSb daysare (09 the November distances from2007) theandx -axis45Figure days to 15. the (15 (a observed )November Estimated and RMSE2007) calculated dailyfrom values.the shorelines, groyne (b) Time deployment. respectively. history of significantYobs and Y waveGSb are height the distances and wave from the xThe-axisangle. comparisons to the observed show and a goodcalcul agreementated shorelines, between respectively. observed and calculated shorelines at both groyne sides. In particular, after 24 days (Figure 16) from the groyne deployment, a shoreline advance on theFigures left side 16–18 of the show, groyne as representative has been observed; cases, afterthe comparison 39 days (Figure between 17) andobserved 45 days and (Figure calculated 18) fromshorelines, the groyne and the deployment, difference, a Y shorelineobs–YGSb, after advance 24 days on the(25 rightOctober side 2007), of the 39 groyne days (09 has November been observed. 2007) GSband calculated45 days (15 the November up-drift side 2007) changes from the occurred groyne during deployment. the entire Yobs period and Y ofGSb the are simulation. the distances from the x-axis to the observed and calculated shorelines, respectively.

Figure 16. (a) Observed and calculated shorelines after 24 days from the groyne deployment. (b)

Difference Yobs–YGSb.

Figure 16. (a) Observed and calculated shorelines after 24 days from the groyne deployment. Figure 16. (a) Observed and calculated shorelines after 24 days from the groyne deployment. (b) (b) Diﬀerence Yobs–YGSb. Difference Yobs–YGSb. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 15 of 18 J.J. Mar. Mar. Sci. Sci. Eng. Eng.2020 2020, ,8 8,, 361 x FOR PEER REVIEW 14 15 of of 17 18

FigureFigure 17.17. (a()a )Observed Observed and and calculated calculated shorelines shorelines after after 39 days 39 daysfrom the from groyne the groyne deployment. deployment. (b) DifferenceFigure 17. (Yaobs) Observed–YGSb. and calculated shorelines after 39 days from the groyne deployment. (b) (b) Diﬀerence Yobs–YGSb. Difference Yobs–YGSb.

FigureFigure 18.18. ((aa)) Observed Observed and and calculated calculated shorelines shorelines afte afterr 45 45 days days from from the the groyne groyne deployment. deployment. (b)

(bDifferenceFigure) Difference 18. Y(aobsY) –YobsObservedGSb–Y.GSb . and calculated shorelines after 45 days from the groyne deployment. (b) Difference Yobs–YGSb. 4. Conclusions The comparisons show a good agreement between observed and calculated shorelines at both groyneToThe date,sides. comparisons the In particular, development show after a andgood 24 days use agreement of (Figure morphodynamic 16)between from theobserved models groyne and focusingdeployment, calculated on sandy a shorelineshorelines beaches advance at have both receivedongroyne the leftsides. the side bulk In ofparticular, of the attention.groyne after has 24 Belonging beendays (Figureobserved; to the 16) one-line after from 39 the model days groyne typology,(Figure deployment, 17) the and GSb 45a model shoreline days is (Figure proposed advance 18) includingfromon the the left groyne a generalside of deployment, the formula groyne suitable ahas shoreline been for estimationobserved; advance on ofafter longshorethe 39 right days side transport(Figure of the 17) atgroyne coastaland 45has mounddays been (Figure observed. made 18) of non-cohesiveGSbfrom calculated the groyne sediment the deployment, up-drift grains side/ unitsa shorelinechanges as sand, occurre advance gravel,d duringon cobbles, the rightthe shingle entire side ofandperiod the rock. groyne of the hassimulation. been observed. GSbAs calculated its main the peculiarity, up-drift GSbside allowschanges to occurre have and explicit during dependencethe entire period of shoreline of the simulation. evolution on Dn50. This finding is due to the fact that GSb uses the GLT model. Differently from GENESIS and similar models, which take into account two calibration coefficient, K1 and K2, the GSb model presents one calibration coefficient, KGSb, which does not depend on the grain size diameter and depends on the longshore gradient in breaking wave height, solely. J. Mar. Sci. Eng. 2020, 8, 361 15 of 17

The reliability of the GSb model to predict coastal morphology over short- and medium-term time scales has been verified based on a high-quality field experiment data base from a specific field case at a mixed beach. Such a source of data is rarely available; indeed, most published sources of shingle/mixed beach data failed on the lack of concurrent wave measurements and transport rates. As a result, the comparison between observed and calculated shorelines in the presence of a temporary groyne shows the premonitory signs that the GSb model can represent a reliable engineering tool suitable for predicting coastal evolution at a mixed beach. A demo version of the numerical model can be downloaded by following the instructions in the supplementary material section.

Supplementary Materials: A demo version of the GSb numerical model, for Mac and Windows systems, has been made available for the scientific community and can be downloaded at: www.scacr.eu, www.eumer.eu. Author Contributions: Conceptualization, G.R.T., F.F. and A.F.; methodology, G.R.T., D.J.S., F.D. and A.F.; software, A.F., G.R.T. and F.F.; validation, G.R.T., F.F. and A.F.; formal analysis, G.R.T., F.D. and A.F.; investigation, G.R.T., D.J.S., F.D., F.F. and A.F.; data curation, D.J.S.; supervision, G.R.T.; funding, G.R.T. and D.J.S. All authors have read and agreed to the published version of the manuscript. Funding: The present work has been supported by the Regione Puglia through the grant to the budget of the project titled “Sperimentazione di tecnologie innovative per il consolidamento di dune costiere (INNO-DUNECOST),” POR Puglia FESR FSE 2014–2020-Sub-Azione 1.4.B, Contract n. RM5UKM3. The field experiment of the present research was funded by the Faculty of Technology of Plymouth University and the EPSRC (Engineering and Physical Sciences Research Council) under the Grant EP/C005392/1 “A Risk-based Framework for Predicting Long-term Beach Evolution”. The work has been also supported by Regione Calabria, through the PhD grant for international exchange. Acknowledgments: We gratefully acknowledge the University of Salento, Department of Engineering, the University of Calabria, Department of Civil Engineering, and University of Plymouth, COAST Engineering Research Group, which permitted the international exchange making possible this research. We thank Mark Davidson of CPRG at Plymouth University for his contribution relating to field data. We gratefully acknowledge the comments of the three anonymous reviewers who helped to substantially improve the original version of this manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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