Coastal Engineering 57 (2010) 213–226

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Coastal Engineering

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MEPBAY and SMC: Software tools to support different operational levelsof headland-bay beach in coastal engineering projects

André L.A. Raabe a,⁎, Antonio H. da F. Klein a, Mauricio González b, Raul Medina b

a Centro de Ciências Tecnológicas da Terra e do Mar, Universidade do Vale do Itajaí, Itajaí, SC. Cx. P. 360. CEP 88302-202 Brazilb Environmental Hydraulics Institute, “IH Cantabria”, Universidad de Cantabria, Avda. de los Castros s/n, Santander 39005, Spain

⁎ Corresponding author. Tel./fax: +55 47 33417544.E-mail address: raabe@univali.br (A.L.A. Raabe).

0378-3839/$ – see front matter © 2009 Elsevier B.V. Aldoi:10.1016/j.coastaleng.2009.10.008

a b s t r a c t

a r t i c l e i n f o

Available online 30 November 2009

Keywords:Headland-bay beachesParabolic bay beach modelsStatic equilibrium beach planformMEPBAYSMC

This paper presents MEPBAY and SMC software tools that allow comprehending and solving problems inheadland-bay beach through a parabolic model. These tools can be employed as coastal engineering designtools (including nourishment designs) and also for academic purposes. They are oriented to different end-users, including coastal technicians, scientists and undergraduates and as coastal engineering design tools,they can be applied to different operational levels (pre-design and design). The aim of the paper is to presentdesign guidelines, the capabilities of the tools, their potential use and applications. Both tools were applied toanalyze San Lorenzo Beach and demonstrate their ability at different project levels.

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© 2009 Elsevier B.V. All rights reserved.

1. Introduction

Although headland-bay beaches have existed naturally forhundreds of thousands of years, many have been unwittingly createdas a by-product of modern engineers undertaking projects onshoreline protection and harbour construction. A curved beach in anunstable condition may result from construction, with updriftaccretion accompanied by downdrift erosion within the embayment,unless artificial nourishment is implemented.

As beach erosion problems have become serious in manycountries, regardless of their national wealth, necessary measuresagainst erosion are being considered to prevent improper humanactivities on beaches and rivers, which have frequently diminishedsediment supply to a beach.

In terms of beach stability, headland-bay beachesmay be classifiedas being in static equilibrium, dynamic equilibrium or unstable(Silvester and Hsu, 1993, 1997; Hsu et al., 2000). Static equilibrium isreached when the predominant waves are seen to be breakingsimultaneously around the whole bay periphery. At this stage, littoraldrift is almost non-existent, and the curved beach is stable withoutlong-term erosion or deposition, except during a storm period. Forbays in dynamic equilibrium, balance in sediment budget is the keyfactor in maintaining the shoreline in its existing position. However,shorelines in dynamic equilibrium could retreat as sediment supplyfrom updrift or from a river within the embayment is reduced, andeven recede to the limit defined by the static equilibrium, if supplydiminishes completely. On the other hand, for bays classified as un-

stable, often resulting from wave sheltering by a structure added tothe beach, the curved shoreline experiences accretion in the lee of thestructure, accompanied by downdrift erosion in the process of naturalbeach reshaping. Because headland-bay beaches in static equilibriumare the most stable landform which do not require sediment supplyunder the action of a persistent swell in nature, construction of abayed beach in static equilibrium has been recommended as a meansof stabilising eroding shorelines (Silvester, 1960; Hsu and Evans,1989; Silvester and Hsu, 1993, 1997; Hsu et al., 2000).

Due to the morphological significance of curved beaches, severalempirical long-term models based on equilibrium formulations havebeen proposed to fit curves to their peripheries. Notably, parabolic(Hsu and Evans, 1989), logarithm spiral (Yasso, 1965; Silvester andHo, 1972) and hyperbolic tangent (Moreno and Kraus, 1999) providemathematical expressions that can predict the coastline of thesebeaches. Among them, the parabolic bay shape model is the one thathas received the most attention (CERC, 2002).

Based on these models, it has been possible to build different kindsof applications, such as identification of beach stability, prediction ofmorphological changes after man-made constructions, creation ofartificial beaches and many other engineering applications.

Coastal projects follow detailed technical design phases, as is thecase for a beach nourishment project (diagnostic, pre-design, design,monitoring and evaluation of the work). The tools presented in thisdocument only deal with the pre-design and design phases, and areapplicable to the reconnaissance and feasibility studies of anycoastline. On the pre-design level, the aim is to identify and toevaluate the potential project alternatives of the solution with aminimum input data and using simple, relatively rapid and inexpen-sive methods, as well as using low-cost numerical tools. At thispreliminary level, the designer better defines the problem, provides a

Fig. 1. Definition sketch for parabolic bay shape model showing major physicalparameters (after Hsu and Evans, 1989).

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deeper understanding of the predominant processes, and answerssome preliminary questions. Once an alternative is selected by thecoastal managers and decision-makers, in order to fine-tune thepreliminary design, this alternative is analyzed and evaluated on adesign level using more detailed and comprehensive predictiveprocedures, numerical tools and elaborate input data. The process ofdeveloping a coastal project follows an iterative or “engineeringapproximation”. Employing this iterative procedure—checking thesimple (pre-design) and more detailed methods (design)—allows amore rapid convergence to the final design.

Before the use of software products, the application of thesemodels required manual calculation of the theoretical shorelinepositions and tracing of the results on amap or aerial photograph. Thisprocedure, though straightforward, was repetitive and tedious,especially when the results of several alternative options had to becompared.

Using computer software specifically designed for the taskimproves efficiency since software interfaces turn possible to setcontrol points directly over digital map images or photos. In this way,the user can analyze the real coastline and the theoretical one (drawnby plotting the model graph) merged on the screen. This allows anaccurate analysis of the beach equilibrium state.

Researches involved with the definition and evaluation of thesemodels have promoted the development of different softwarepackages. The parabolic model has been approached by MEPBAY(Klein et al., 2003) and SMC software (González and Medina, 2001).Moreno and Kraus (1999) mentioned that convenient softwareroutines were written to automate the fitting process and make theapplication of hyperbolic tangent model objective. These softwarediffer in many aspects, from target users to programming language.The development process is a challenging activity that must handlepractices and requirements of coastal engineering field consideringtechnological restrictions and end-users expectations.

This paper discusses the application of MEPBAY and SMC softwarefor the parabolic bay beach model. They used different approachesand have different target users. Researchers of UNIVALI University inSanta Catarina state, Brazil, developed MEPBAY. It was initiallydedicated to undergraduate students and was developed to improvepractice with the parabolic model application using a user-friendlyinterface. Coastal Modeling System (SMC) has been developed by theSpanish Environmental Ministry and allows the study of coastalengineering projects based on a work methodology, a database oflittoral morphodynamics information and numerical tools. The SMCencloses some numerical models to study beaches in differenttemporal and space scales.

The same beach cases were evaluated with both software in orderto identify similarities, differences, restrictions, and weak and strongcharacteristics of each. Some of their applications in the academic fieldwere also explored, as well as future perspectives for new versions.The main contribution of the paper is to present the application ofsoftware tools to aid different operational levels of coastal engineeringprojects, such as pre-design and design.

Since both programs (MEPBAY and SMC) are applied to parabolicbay shape equation (Hsu and Evans, 1989), this paper will present abrief description of this model in Section 2. Section 3 details theMEPBAY software design guidelines and presents a pre-designanalysis of the San Lorenzo Beach case study. Section 4 presents theSMC software and a detailed design project at San Lorenzo Beach. Theconclusion assesses both software application and discusses futureperspectives.

2. Parabolic model

Most headland-bay beaches have asymmetric shapes, character-ized by a curved shadow zone, a gently curved transition and arelatively straight tangential portion at the downdrift end (Fig. 1).

They may appear as a salience or tombolo behind an offshore island,harbour breakwater or other man-made structures. In some situa-tions, they may even turn up as a short straight segment behind agroin or protruding headland.

Hsu and Evans (1989) developed a parabolic bay shape equationfor a headland-bay beach in static equilibrium in the form of

Rn = Rβ = C0 + C1ðβ= θnÞ + C2ðβ=θnÞ2: ð1Þ

Eq. (1) has two primary physical parameters, which are thereference wave obliquity angle ß and the control line in length Rß(Fig. 1). The former represents wave obliquity to the curved beach,measured between the incident wave crest at the wave diffractionpoint and the control line, whereas the latter denotes the distancejoining the updrift diffraction point (X0, Y0) to the downdrift controlpoint (X1, Y1), as seen in Fig. 1.

It is worth noting that any point on or near the straight downdriftsegment of the beach could be conveniently chosen as a downdriftcontrol point, for which the convenience and insensitivity were notedin Silvester and Hsu (1993, 1997). This is how it is determined from amap, vertical aerial photograph and even on a planning sketch. Thecontrol line is also angled ß to the tangent at the downdrift beach end(Fig. 1). The radius Rn to any beach point around the bay periphery isangled θn from the same wave crest line radiating out from the pointof wave diffraction.

The three C constants, generated by regression analysis to fit theperipheries of the 27 prototypes andmodel bays, differ with referenceangle ß (Hsu and Evans, 1989). Numerically, these coefficients may beexpressed by fourth-order polynomials as follows:

C0 = 0:0707−0:0047β + 0:000349β2−0:00000875β3

+ 0:00000004765β4ð2Þ

C1 = 0:9536 + 0:0078β−0:00004879β2 + 0:0000182β3

+ 0:000001281β4ð3Þ

C2 = 0:0214−0:0078β + 0:0003004β2−0:00001183β3

+ 0:00000009343β4ð4Þ

These C values are bounded within 2.5 and −1.0 for the usualrange of angle ß from 10º to 80º applicable in most field conditions(see Fig. 4.25 in Silvester and Hsu, 1993, 1997). Values of the non-dimensional ratios Rn/Rß versus increments of 2º of ß from 20º to 80ºhave been tabulated for manual application (see Table 4.2 in Silvesterand Hsu, 1993, 1997).

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Silvester and Hsu (1993, 1997) have shown satisfactory verifica-tion of this equation on several bay shapes, including the downdriftbeach at Port Stanley, Lake Erie, Canada (Parker and Quigley, 1980)and a transitional bay beach in the gap of a revetment damaged duringa hurricane event at Shinnecock Inlet, Long Island, New York (Deanand Maurmeyer, 1977).

Despite having a variety of dimensions between the tip of a headlandand its downdrift boundary, the stability of a bay beach can now bequalitatively assessed by applying the parabolic bay shape model. Tofacilitate practical applications, values of ß andRßhave to be determinedfirst from amap or aerial photograph, followed bymanual calculation ofthe radii Rn for a range of corresponding θn. For a bay beachwith knownß and Rß, locations for pairs of Rn and θn are thenmarked on the existingmap with a curve drawn for the predicted static bay shape. Finally, thestability of an existing bay beach can be visually verified by comparing itwith the static equilibrium shape under the same wave obliquity ß. Forthis, it is only necessary to have a planform of beach image. All thedefinitions, drawing and calculus are made over this image.

González and Medina (2001) introduced the “equilibrium beach”concept, which combines the static equilibrium plan and profile forlong-term analysis. Thismethodology includes amodified equilibriumplanform able to define the angle αmin, which defines the downdriftlimit from which Hsu and Evans's (1989) parabolic model isapplicable. Also, it allows predicting the planform of non-existingbeaches, by means of the definition of the front's orientation at thediffraction point in relation to the direction of the mean wave energyflux in the area. In order to employ this methodology, it is necessary,in order to have input data, to define the local wave climate in theupdrift control point (diffracting point).

3. MEPBAY software

MEPBAY was developed to aid students to learn parabolic modelapplication in several different beaches. Its primary design goal was to

Fig. 2. San Lorenzo Beach case

create a usable interface withminimumworkload. To accomplish this,a user centered design approach was adopted, in which the modelmanual application task was carefully analyzed to create an interfaceas similar as possible to this.

3.1. Manual application of parabolic model

In the manual application of the parabolic model (Hsu and Evans,1989), a map, topographical chart, vertical aerial photograph or satelliteimage of a bay beachmay be used to obtain the two primary parameters(ß andRß) for themodel. Silvester andHo(1972) observed that, for a baybeach in or close to static equilibrium, the wave crest at the downdriftlimit of the bay aligns almost parallel to the downdrift tangent, and thesame happens for the wave crest line starting at the point of updriftwave diffraction (Fig. 1). Based on this observation, the usual procedurefor applying the parabolic model is described as follows:

(1) Choose a control line with length Rß: a straight line is drawnconnecting the updrift wave diffraction point to an appropriatecontrol point on the straight section downdrift (see Figs. 1 and 2).

(2) Determine the predominant wave direction and reference waveangle ß: from the downdrift control point, a downdrift tangentmay be drawn. Thismay be taken as thewave crest line, which isperpendicular to the incoming waves at the updrift diffractionpoint of the bay beach. The angle formed between thewave crestline and the control line is denoted as ß.

(3) Calculate ray lengths Rn to the beach: starting from θ=ß at thedowndrift boundary, rays Rn with angle θn at constant intervalsof 10º are calculated using Eq. (1) to a maximum of 150º or180º. The pairs of (Rn, θn) values calculated represent theshoreline position radiating out from the updrift diffractionpoint for an idealized bay shape in static equilibrium.

(4) Sketch the shoreline planform in static equilibrium: finally, thecurved planform in static equilibrium is sketched on the existing

analysis using MEPBAY.

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map or aerial photograph by joining all the (Rn, θn) pointscalculated for qualitative assessment of beach stability.

A user may visually examine the stability of the beach by theproximity of the existing shoreline to that predicted in staticequilibrium. Should they coincide with each other or be very close,the existing beach is in or close to static equilibrium. If the existingshoreline periphery is landward of the predicted one, the beach is saidto be in dynamic equilibrium, in which the shoreline peripheryremains unchanged due to the balance in sediment budgets from allsources. However, shoreline in a bayed beach in dynamic equilibriummay advance or degrade as net supply increases or decreases.

The third kind of beach stability is termed unstable and it happenswhen natural beach reshaping occurs within a bayed beach due towave sheltering by structures. However, the severity of beach erosiondiffers with changes to ß, when the tip of the headland is modified bya structure or when the wave approaching direction changesseasonally. The same process may be repeated for other sets of ßand Rß; which represent different engineering or managementoptions arising from different structural conditions that may alterthe position of the updrift control point on an existing beach.

3.2. MEPBAY use

The manual process described in the previous section, thoughseemingly straightforward, is repetitive and laborious. In order toimprove the efficiency of applying the parabolic model to headland-bay beaches, software development is most desirable.

The main goals for developing computer software of this kind is(1) to provide a user with a friendly environment to apply theparabolic model, and (2) to help a user arrive at an optimum designfrom several different options.

MEPBAYwas written in Object Pascal language. Computer displaysare used for the manipulation of graphic images, after applying theparabolic model to simulate beach changes (Hsu and Evans, 1989).

Fig. 3. Poniente Beach, also showing the vis

Starting from the planform (files in raster format) of a headland-bay beach on an aerial photograph or map, the software packageoffers an interface that allows a user to indicate the relevant controlpoints on the beach and to automatically trace the complete bayperiphery in static equilibrium. The software facilitates experimenta-tion in an efficient way for the graphic representation of the idealizedshoreline in static equilibrium, in relation to the control pointsselected from the display on the screen.

3.2.1. Importing parabolic model to MEPBAYThe importation of the parabolic model to MEPBAY not only makes

the application of this model more efficient but also streamlines thephysical interpretation of the result for practical applications. It isparticularly important in thepre-designphase of anengineeringproject,which becomes viable with only one input data (beach image).

A user will benefit from the learning process, because the graphicalresult generated by the software is the consequence of his or herconscious selection of the control points for the beach under consider-ation. The operation of MEPBAY follows a set of procedures as follows:

(1) From the “File” option on the menu bar, a user first loads thescreen of a computer with a beach image of a map or aerialphotography in raster format (extensions BMP or JPG);

(2) With the beach image on the screen, the user then selects anoption that indicates “Beach Orientation” to indicate relativeorientation of the beach and headland (i.e., updrift control point)to the screen;

(3) From the “Points” sub-window and with the mouse, the userthen locates three points on the image required for theparabolic model application. These are: (i) point “’H’” for theupdrift control point, i.e., the point of wave diffraction, fordrawing the wave crest line, (ii) point “E” for the downdriftcontrol point on the beach, thus giving the control line, and(iii) point “W” for an end point along the downdrift tangent onthe beach (see Figs. 1 and 3). After these actions, three line

ual display of the beach using MEPBAY.

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segments are drawn upon clicking on the “Z” option in the“Tools” sub-window;

(4) Upon clicking on the “Bay”-like graphic option in the “Tools”sub-window, MEPBAY calculates the wave reference angles β,Rβ and radii Rn for each increment of θn. At the same time, theresults are also saved in a raster format and may be printed outlater, if required;

(5) Finally, MEPBAY draws the predicted static bay shape overlay-ing the image of the existing beach, fromwhich the condition ofbeach stability can be visually assessed.

The user can then analyze the effect of any likely modification tothe beach arising from the construction of a structure for shoreprotection and of a harbour facility. MEPBAY may also motivate user'scuriosity for working on various engineering and managementapplications, due mainly to its simplicity in applying the parabolicmodel and the graphic visualization of the results.

3.3. Practical MEPBAY application (San Lorenzo Case Study)

MEPBAY could be most suitable for project evaluation todetermine the optimum design options from several proposals withvariations in configuration (in length, location and orientation) of astructure, especially the point of wave diffraction. The environmentalimpact of a structure on beach stability can be verified through thescreen display of the predicted static bay shape. In this way, the usernot only gains insight on the physical processes of beach changes, butalso achieves the best solution for shoreline protection and coastalmanagement.

ApplyingMEPBAY to San Lorenzo Beach, an urban beach in the cityof Gijón, Spain, before the breakwater construction, made it possibleto identify the dynamic equilibrium situation with potential erosionon the west side of the beach (Fig. 2). This erosion could be minimisedwith the construction of a headland-attached breakwater.

The parabolic bay shape equation can be applied to identify theeffect of constructing a man-made structure on an embayed beach. Asshown in Fig. 3, two breakwaters were built at Poniente Beach, inSpain, to produce an artificial beach. By applying MEPBAY, it is shownthat the existing beach planform is identical to the static bay shapegiven by the parabolic bay shape equation, Eq. (1), for both sides.

On the other hand, the application of “Headland Control” (Hsuet al., 2000) to develop an artificial beach shows that the humaninterventionwas successful. MEPBAY can be used to facilitate this pre-design engineering task of locating the updrift and downdrift controlpoints in order to have a static equilibrium beach planform.

3.4. MEPBAY academic applications

The very first experiment conducted with MEPBAY is probably theonly one concerned with pedagogical issues. The authors of thesoftware searched for empirical evidence of improvement in learningpotential when equilibrium states in headland-bay beaches wastaught at the oceanography undergraduate course at UNIVALIUniversity, Santa Catarina, Brazil. The results indicated that over95% of the students have found it much more interesting to learnusing MEPBAY. The teacher also reported an increase in interest andcomprehension about control points positioning (Vargas and Raabe,2001). Many researchers of the area have reported (through e-mail toCoastal_list) that they used MEPBAY with students which found iteasy to understand and useful.

Piorewicz (2004) has analyzed beach changes at Yeppoon MainBeach (Capricorn Coast—Australia) after the reconstruction of theexisting seawall. The analysis covered observed changes to the beachsince October 2001, when the new seawall was almost complete.Because littoral drift is very low in the region of the Yeppoon MainBeach, the cross-shore sediment transport plays a much more

important role in the reshaping of the beach. Thus the crenulate-shaped bay theory may find applicability in the analysis of beachrestoration. The MEPBAY model was used for this analysis. Therecorded shoreline was used to verify the local wave direction and thebest agreement was obtained for nearshore wave direction in theorder of 90º azimuth, and for the angle between the control line andwave crests in the order of 38º. According to Piorewicz (2004), theprogram MEPBAY allowed analysis of several positions of artificialheadlands to obtain optimal improvement of the beach, consideringits stability and the protection of the seawall.

Benedet et al. (2004) have usedMEPBAY software to illustrate thatthe parabolic model is not suitable only for single headland beaches.They extended the model application to other unique beachconfigurations not previously covered in the literature, such as bayshapes between coastal structures, bays with double curvature, andbays in complex dynamic and static equilibrium.

Chiou (2004) has used MEPBAY in combination with SBEACHsoftware for estimating the beach nourishment process of Nanbin–Beibin Beach, in Taiwan. Firstly, the stability of the beach in relation tothe total length of the Eastern Breakwater of Hualein harbour wasassessed by MEPBAY software. Secondly, a rational beach retreat wascalculated using SBEACH software, which was used as a minimumbuffer width for a proposed bayed beach using MEPBAY. Thirdly,headland control approachwas suggested using artificial headlands ina curved shape rather than the traditional straight groin and detachedbreakwater in narrow gaps. Finally, the total volume of the fillmaterials and budget was estimated, in order to enhance theapplicability of the study.

Lausman (2006) has been applying MEPBAY in an ongoing projectto measure the subjectivity in the setting of the three control points ofthe parabolic model. Many images with different point settings for thesame beach were built using MEPBAY “save as” functionality and aregoing to be presented to experienced users in order to accomplish themeasurement (see also Lausman et al., 2010-this issue).

3.5. Future perspectives

The initial purpose of MEPBAY was to aid students with a practicallearning tool to test the equilibrium situation of several beaches. Forthis reason, the software was conceived to be easy to use. In its firstversion (available only in Portuguese), there was also a tutorial forstudents to read and understand the theoretical basis of the parabolicmodel. In the second version (still the current one), some improve-ments were made to the interface, based on interaction essaysconducted with the first version, and it was translated to English.

As shown before, the use of MEPBAY has achieved its initialpurpose. Many researchers (e.g., Benedet et al., 2004; Hsu et al., 2008,2009, 2010-this issue; Jackson and Cooper, 2010-this issue) have usedit as a practical tool for fast application of the parabolic model. Manyequilibrium evaluations and measurements of differences betweenreal coastline and model coastline have been conducted.

As a result of this unexpected use of the software, many of thedesign goals are being revised in order to create a new version thatcan be more suitable for the needs of advanced researches in the area.Some of the new characteristics to be implemented have originatedfrom restrictions in the current version, others are improvements.They are:

– To handle TIFF images;– To handle files larger than 20 MB;– To provide information about precision and error of the measures

(based on pixel resolution);– To improve tools of scale and measurement;– To provide more image tools (such as fit zoom, pan, rotate etc.);– To allow more than one curve to be drawn over an image;

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– To export the curve pairs of (Rn, θn) and (X, Y) screen coordinatesto a Comma Separated Values file (CSV);

– To allow defining imprecision for the wave crest direction.

Another possible improvement being analyzed is to allow thecreation of log spiral and tangent hyperbolic curves (besidesparabolic) for comparison purposes.

4. Coastal Modeling System (SMC)

The user-friendly numerical system called Coastal ModelingSystem (SMC) is part of the Spanish Beach Nourishment Manual(SBM). The SBMwas developed by the DGC and the Ocean and CoastalResearch Group (GIOC) of the University of Cantabria between 1995and 2003. The objectives of this SBM are: (1) to establish amethodology to design, execute and follow-up coastal projects;(2) to design actions in order to prevent coastal retreat and toestimate flooding risks of low Spanish littoral zones; (3) to betterknow the dynamics and evolution of the Spanish coastline; and (4) tocompile the Spanish experience in the coastal engineering field.

This SBM contains three major parts: (1) science-based docu-ments, (2) engineering-based documents, and (3) numerical tools(Fig. 4).

The science-based documents are organized to lead the readerfrom fundamental scientific principles and littoral processes. Itincludes four subdivisions: Coastal Hydrodynamics (GIOC, 2003a),Coastal Littoral Processes (GIOC, 2003b), Coastal Protection Structures(GIOC, 2003c) and Environmental Engineering Impact for CoastalActions (GIOC, 2003d).

The two engineering-based documents, the Littoral Flooding Atlasfor the Spanish Coast, and the Beach Nourishment Design andEvaluationMethodology are oriented toward a project-type approach.The former is a risk-based analysis along the Spanish coastal border inorder to estimate the extreme sea level due to the combined effects oftides, storm surge and wave run-up on beaches (see details in GIOC,2003e). This long-term analysis was carried out based on data fromthe Spanish networks of wave-buoys and tidal gauges. The risk-basedanalysis allows, for any location along the Spanish coast, the definitionof the mean and extreme flooding level in terms of the number ofwaves (mean regime), return period (extreme regime), localorientation of the coastline and average bottom slope (cross-shore).The Nourishment Design and Evaluation Methodology allows theanalysis of coastal projects through detailed technical design phases(diagnostic, pre-design, design, monitoring and evaluation).

The user-friendly SMC encloses some numerical models that allowthe application of the methodologies and formulations proposed inthe previous documents in coastal projects (GIOC, 2003f). The SMC isstructured in fivemodules: (1) A pre-processmodulewhich generates

Fig. 4. Structure of a new Spanish Bea

all of the input data for the short-, middle-, and long-term numericalmodels. This module obtains (for any location along the Spanish coast,including the islands) all the Spanish bathymetry, wave directionalregimes and the littoral flooding risk; (2) The short-term moduleincludes the numerical evolution of morphodynamics models formonochromatic and irregular input waves, in a process on a scale ofhours to days; (3) The middle- and long-term module allows theanalysis of the middle-term processes (seasonal changes) and long-term response of the system on a scale of years; (4) The bathymetryrenovation module permits easy updating of the actual bathymetry,including different elements (sand fills in equilibrium beaches: planand profile, coastal structures etc.), in order to evaluate the differentalternatives proposed using the numerical models; and (5) Thetutorial module (TIC) includes the theoretical background in anumerical system and provides some data process systems for timeseries (e.g., buoys and tidal gauges). This module supports thescience-based documents and is subdivided into four items: dynam-ics, coastal processes, coastal structures and environmental impact.For an overview of the SMC, see Medina et al. (2001) and Gonzálezet al. (2004).

The goal of the long-term analysis is to determine which will bethe final shape (plan-profile) of the beach and/or the temporalevolution of said shape on a scale of years in order to assure that thebeach functionality continues throughout its useful life. The existingformulations for this time scale do not analyze the processes (forexample, wave-to-wave sediment transport), but rather magnitudesaggregated to them.

The SMC includes a graphic user interface module to test stabilityor to design new equilibrium beaches taking into account theequilibrium plan and profile (Fig. 5). This methodology has beenapplied to various Spanish beaches on the Atlantic andMediterraneancoasts with good results, constituting a practical easy-to-use engi-neering tool in beach regeneration projects (see González andMedina, 2001).

The system permits the design of nourishment projects using theconcept of “equilibrium beach”, which combines different equilibriumprofile and planform formulations. A summary and some detailsregarding the different long-term beach formulations and the designnourishment methodology employed in the SMC are presented inGonzález et al. (2010-this issue) to the equilibrium profile, severalformulations are included in the system, such as: Dean's (1991), thebi-parabolic profile proposed by Medina et al. (2000), the equilibriumprofile in reef-protected beaches by Muñoz-Pérez et al. (1999) andthe equilibrium profile affected by refraction–diffraction (Gonzalezand Medina, 1997; Requejo et al., 2005). Regarding the equilibriumplanform, the SMC includes: the parabolic formulation of Hsu andEvans (1989) and the modification proposed by González and Medina(2001). The input data for all of these equilibrium formulations are

ch Nourishment Manual (SBM).

Fig. 5. Coastal Modeling System (SMC) interface and concept of “equilibrium beach” combining equilibrium profile with static equilibrium plan form.

219A.L.A. Raabe et al. / Coastal Engineering 57 (2010) 213–226

supplied by the Odin, Atlas and Baco pre-process programs. A detaileddescription of the long-term module can be found in GIOC (2003f,g).

4.1. Practical SMC application (San Lorenzo Beach Case Study)

The Cantabrian coast of Spain is divided into a series of pocketbeaches; most of the headlands extend into deep water and appear tobe effective in confining littoral sand to the embayment. Therefore,the coast is divided into a series of littoral cells. One of these littoralcells is San Lorenzo Beach and Poniente Beach, which are located inthe city of Gijón on the Cantabrian coast, to the east of the Gijónharbour (Fig. 6).

The goal of the San Lorenzo Beach case is to quantify the impact onthis beach of a harbour enlargement, and to propose solutions tominimize these impacts. Regarding the Poniente Beach case, the goalis to design the nourishment project for a new urban beach. Theanalysis of this last case is presented in detail in González et al., (2010-this issue).

4.1.1. Case description of San Lorenzo BeachSan Lorenzo Beach is an urban beach located in the city of Gijón. It

is one of the most important beaches in the area, being a tourism spot,especially during summer, and a recreational space for the inhabitantsof Gijón.

The Gijón Harbour Authority is studying the possibility of a futureenlargement of the facilities. Several alternatives have been proposedand one of them consists of a new exterior harbour protected by a 2-km breakwater, as shown in Fig. 7. The large dimensions of thisharbour alternative would modify the marine dynamics in the area,including San Lorenzo Beach. Thus, some morphodynamical changesare expected locally at the beach.

4.1.2. San Lorenzo Beach morphologyThe orientation of San Lorenzo Beach is W10ºN–E10ºS. It is a

1.3 km-long sandy beach confined between two rocky capes, Santa

Catalina Cape to the west and the Cervigón Cape to the east, and a sidewall to the south (see Fig. 6).

The geophysics studies developed in the zone demonstrate acontinental shelf with rocky bottom and some small deposits of sand,as shown in Fig. 8, where the dark areas correspond to the rockybottom and the clear zones to the sandy bottom. This figure showshow the Santa Catalina and Cervigón Capes extend seaward under thesea bottom. These features will be important for local wave refractionand current system in the beach, as will be shown later.

Due to the tourism importance of San Lorenzo Beach, severalstudies have been carried out throughout the years. Bathymetricprofiles and sediment samples have been surveyed along the beachover the last 20 years (1985, 1994, 1995 and 2001). These profilespresent two decreasing parabolic sections, with steeper surf profilesto the east of the beach. The slope of the surf profile starts gradually todecrease along the beach towards Santa Catalina Cape. From all thesebathymetric data, it can be concluded that the beach has no evidencederosion/accretion net processes, with the typical seaward andlandward profile displacement associated to summer and winterclimate conditions. Hence, we can consider that the beach has been inequilibrium in plan and profile for the last several years.

4.1.3. Marine dynamicsMore than 75% of deep water waves approach the harbour from

the northern (N) to north-western (NW) sector. The annual averagesignificant height is about 1 m with typical winter storm significantwaves of about Hs=5 m. The semi-diurnal tides in Gijón have a meantidal range of 3 m and a mean spring tidal range of 4.5 m. The waveheight behind the Príncipe de Asturias Breakwater from the east towest decreases due to diffraction and refraction effects caused by boththe breakwater and an important shallow area called the Amosucasshallow, which is located in front of the breakwater tip, as shown inFig. 9. In this figure, the typical storm wave conditions from NW withHso=4 m, Tpo=16 s at high tide sea level show an important waveconcentration generated by the offshore shallow, in the Cervigón Capeeast of San Lorenzo Beach.

Fig. 6. Location map of San Lorenzo Beach, Gijón, Spain.

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Awave propagation study was carried out employing the Oluca-SPspectral model (see GIOC, 2003h). This is a weakly nonlinearcombined refraction and diffraction model included in the SMC,which is based on the parabolic approximation solution to the mild-slope equation. In summary, the waves at San Lorenzo Beach areprincipally affected by the Principe the Asturias Breakwater, theAmosucas shallow and the local bottom bathymetry. There is aremarkably important wave height variation along the beach, withlocal wave energy concentrations on the beach (see Fig. 9). Thelocation of the wave energy concentrations on the beach is mainlygoverned by the influence of the Amosucas shallow on the offshoreincomingwaves and the characteristics of these incomingwaves, suchas: wave incident angle, wave period, tidal level and wave height.From the wave propagations, it can be concluded that the wavescoming from the N to NNW concentrate the wave energy from thewest to the middle area of the beach, respectively. The waveconcentrations move toward the east of the beach for waves comingfrom the NW, as shown in Fig. 9, with a concentration of the waveenergy in the zone of the Cervigón Cape. This wave behaviour alongwith the beach conditions is responsible for the wave-inducedcurrents and morphological response of San Lorenzo Beach, asexplained in the following sections.

Fig. 7. One of the harbour enlargement alternatives, Gijón Harbour.

The wave-induced currents are responsible for the stability in planand profile of the beach. The current system has been calculated withthe wave-driven current model 2DH called Copla-SP (see GIOC, 2003i,which is also included in the SMC. The hydrodynamic model is wave-induced by the wave gradient of radiation stresses obtained as anoutput from the Oluca-SP.

From the current simulations on San Lorenzo Beach, it can beconcluded that the current system is composed of four currents: (1) acurrent along the Cervigón Cape, toward the western area of thebeach; (2) a current along the Santa Catalina Cape, toward the easternarea of the beach; (3) a longshore current, whose direction andintensity depend on the wave energy and the location of the waveconcentration; and finally, (4) a rip current, which is located at themeeting point of the longshore currents. Under winter conditions, thewave storms usually come from the NW with wave energyconcentrations in the Cervigón Cape, as described previously,generating two close cellular circulations, as shown in Fig. 10. Underthis condition, the seaward rip current occurs in the eastern zone ofthe beach. This rip current's position is moving toward the west of thebeach, to such an extent that the offshore incoming waves move fromthe NW to the north. Under the mean wave conditions in the area, thecurrent system on the beach displays important changes. Some smallwave concentrations are presented in the middle of the beach,generating two weak cellular current systems. These systems arecomposed of: (1) a coastward current in the middle of the beach;(2) two longshore currents, which start in themiddle of the beach andmove toward the two capes at its ends; and (3) on the beach endsthese currents return seaward where they are intercepted by someweak currents coming along the capes. The position of the startingpoint in themiddle of the beach can change depending on the offshorewave conditions.

As a summary of the wave and current system at San LorenzoBeach, it can be concluded that the waves at the beach areconditioned mainly by the interaction of the offshore wave condi-tions (wave direction, wave period, wave height on a tidal level) withthe harbour breakwater and by the Amosucas shallow. The currentsystem is composed of cellular currents, which are confined betweenthe lateral and bottom boundaries of the beach. Therefore, a netcurrent does not exist which can generate a net sediment transportout from the beach, as has been demonstrated with field evidenceduring the last 20 years.

The equilibrium plan and profile formulations require defining thewave conditions locally on the beach. For Dean's equilibrium profile, it

Fig. 8. Poniente Beach, also showing the visual display of the beach using MEPBAY.

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is necessary to define the local seaward limit Depth of Closure, h*(Hallermeier, 1981; Nicholls et al., 1996, 1998); for the bi-parabolicequilibrium profile, the local fall speed parameter, Ω (Ω=Hb /ωT)allow us to define the A, B, C and D coefficients (see González et al.,2010-this issue). Therefore, the equilibrium planform requiresdefining the direction of the mean energy flux of the local waves inthe control point. In order to obtain the wave climate near the beach,it is necessary to propagate the offshore waves to the coast. For that,there are two buoys close to the study area from the Spanish WaveNetwork; the Gijón 1 is a 20-year scalar buoy located in a 23-m waterdepth, and the Gijón 2 is a 10-year directional buoy in a 450-m waterdepth. Additionally, using the wind forecast as an input, waves arepredicted as an output from the numerical model's WAM cycle 4.Thirty-year wave data, with a 1-hour time interval, is available forseveral offshore points throughout the study area. The wave and sealevel hindcast has been carried out by the Spanish holding ofharbours, Puertos del Estado (PE), and the calibration of these datahas been carried out by the University of Cantabria using the buoydata.

Based on 350 wave cases obtained as a combination of differentwave (Hs, Tp and Ym) and tidal level conditions, and using the Spectralpropagation model Oluca-SP, several transfer interpolation functionshave been obtained for five points along the beach, see Fig. 11 (e.g., thediffracting points in Santa Catalina, P1 and Cervigón Capes, P2). Thus,the 30-year offshore wave data, with a 1-hour time interval, has beentransferred to several beach points near the beach; this wave data isavailable for the different scale plan and profile models.

4.1.4. Littoral morphodynamicsIn order to study the beach stability in San Lorenzo Beach, a long-

term analysis, based on equilibrium plan and profile formulations, willbe presented in this section.

For the bi-parabolic equilibrium profile (Medina et al., 2000), somesediment data are necessary, in addition to the local wave data, suchas the mean sediment size (D50). Based on the 20-year field data ofsediment samples along the beach, it can be concluded that SanLorenzo Beach is composed of fine sand, with a small variation ofsediment size throughout the years. A persistent longshore gradationhas been identified (Fig. 12) with a mean sediment size ofD50=0.27 mm to the west of the beach (near Santa Catalina),D50=0.29 mm in the middle zone, and D50=0.34 mm to the eastern

zone (near Cervigón Cape). Mean grain size values have beenobtained as the average value of the profile samples in each zone.This mean distribution of grain size along the beach is in accordancewith the intensity of the currents along it, with coarser sedimentwhere the currents' intensity is stronger.

As mentioned previously, the historical data evidence showsvariations of the profile slope and shape along the beach. In fact, whenthe longshore wave and sediment variations are merged, theequilibrium bi-parabolic profile has to be calculated for the threezones, as shown in Fig. 13. These equilibrium profiles have beenobtained based on the mean significant wave height and peak periodat points P3, P4 and P5, which are located at Depth of Closure,h*~6.5 m ( Hallermeier, 1981); the mean sediment size in each zoneand the mean spring tidal range in the area (M). As an example, themean summer profile (2001) in Zone 1 and the bi-parabolicequilibrium model are presented in Fig. 14. The equilibrium bi-parabolic model in this figure represents the beach profile quite well.

In order to test the equilibrium plan form in San Lorenzo Beach, themethodology proposed by González and Medina (2001) is employed.First, it is necessary to define the direction of the mean energy flux ofthe waves (Ymef) in the control or diffracting points P1 and P2 (Fig. 15).Based on the wave climate in P1 (Santa Catalina Cape), Ymef=N18E isobtained, and in a similar way in P2 (Cervigón Cape), Ymef=N4W isobtained. Fig. 16 shows the San Lorenzo high tide shore line and theequilibrium shoreline (detached line). The αmin angle (= 90º−β) hasbeen obtained using Ts12=16 s and a mean water depth h=10 m(which include a 4.5-m tidal range). It can be concluded from thisfigure, that the beach is in equilibrium plan form. It is noted that whenthe sea level is in high tide, the beach is not a dry beach in the westernzone (near the Santa Catarina Cape). The same behaviour can bepredicted using the equilibrium plan form.

4.1.5. Harbour enlargement impact on the stability of San Lorenzo BeachThe breakwater enlargementproposed in Fig. 7will generate changes

in the beach morphodynamics, with changes in the marine dynamics(waves and currents) and the beach stability in plan and profile.

The first effect on the marine dynamics is the reduction of thewave energy reaching the beach and the rotation of the wave frontsdue to the diffraction effect. The wave energy reduction is alsoassociated with the diffraction effect of the new breakwater,combined with the disappearance of the wave concentration

Fig. 9. Wave storm from the NW (Hso=4 m, Tpo=16 s, High tide sea level=+4.5)Spectral wave propagation, parabolic model (Oluca-SP).

Fig. 10. Wave-driven current system for a wave storm from the NW (Hso=4 m, Tp

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generated under specific wave conditions by the Amosucas shallow.As an example, Fig. 14a shows the same typical wave storm conditionfrom NW with Hso=4 m, Tpo=16 s at high tide sea level, where thewave concentration generated by the offshore shallow on the beachpractically disappears.

The wave-driven current system along the beach is furthermodified. The two cellular current systems described in the previoussection disappear. A net current from the east to the west along thebeach is generated in all the wave conditions, as shown in Fig. 14b.Hence, a net sediment transport tendency toward the western zone(Santa Catalina Cape) is expected.

On the other hand, the bi-parabolic equilibrium profile predicts amore reflective condition due to the wave energy reduction, with asteeper profile in the three zones. By propagating again the offshorewave climates from the last 30 years to five points on the beach (seeFig. 15) and keeping the samemean sediment size in the zones, the bi-parabolic profile coefficients are obtained, as presented in Table 1.

Regarding the equilibrium planform, the mean energy flux indiffracting points P1 and P2 (see Fig. 15) presents some rotation. Basedon the wave climate in P1 (Santa Catalina Cape), Ymef (=N30E) isobtained, and in a similar way in P2 (Cervigón Cape), Ymef (=N12E) isalso obtained. In order to predict the equilibrium shoreline under theinfluence of the new breakwater, two hypothesis can be assumed: (1)the first hypothesis is not to provide a sand filling on the beach, and tolet the beach re-accommodate in plan and profile to get anequilibrium beach; (2) the second hypothesis consists of obtainingthe equilibrium beach (plan and profile) without any retreat of thehigh tide shoreline in winter conditions. For the first alternative, theequilibrium planform is presented in Fig. 16 (see detached line). Inthis situation, an erosion process would occur in the middle and thesouth of the beach, with a profile retreat in order to fit the shorelinerotation with the seaward profile advance in the western zone. It isremarkable that the equilibrium shoreline response is in accordancewith the tendency shown for the wave-induced currents. For thesecond alternative, the equilibrium shoreline (in detached line) ispresented in Fig. 17. In this case, the goal is to avoid the shorelineretreat in the middle of the beach. In this situation the equilibriumshoreline presents an average advance of 50 m in the western zone.

The SMC system allows the combination of the equilibrium profilewith the equilibrium plan, in order to define the “equilibrium beach”. InFig. 17, the designed equilibrium beach for the second alternative ispresented. The beach berm has been defined at the 6.0 level and the SESat the5.0 level, taking into accountdifferent local sea level elements (e.g.

o=16 s, High tide sea level), numerical simulation with the (Copla-SP) model.

Fig. 11. Profile sectors, mean sediment sizes and local wave climate points.

Fig. 12. Summer profile in Zone 1 (2001) and bi-parabolic equilibrium profile.

Fig. 13. Equilibrium shorelin

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astronomical and meteorological tides, surf beat, wave swash). Fig. 17also represents the interceptionbetween the sandfillingwith the nativebottom, which is between the −2.0 and −3.0 levels, inside the capeconfinement. The nourished equilibriumprofile and thenative profile ina central zone of the beach (see location in Fig. 17) are presented inFig. 18. The cross-shore profile has been defined employing the bi-parabolic equilibrium profile, based on the local wave characteristicsand assuming that the borrowed sand has a similar sediment sizecompared to the actual situation. The bi-parabolic profile coefficients foreach beach zone (see Fig. 11) are presented in Table 1. The volume ofsand for the sandfilling in this projecthas beenevaluated in 450,000 m3.

4.2. Future lines for the SMC

The SMC is a non-static system. On one hand, it should evolve bycompleting and incorporating new data bases, thus allowing theimprovement of the system's pre-processing programs. On the other,it must incorporate new scientific knowledge that could be includedin the system by means of direct usage applications. As for the pre-processing programs, it is important to include new data sources for

e at high tide sea level.

Fig. 14. (a) Wave storm from the NW (Hso=4 m, Tpo=16 s, High tide sea level); (b) Wave-driven current system. New Gijón harbour geometry.

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exterior waves. Nowadays, there are other more complete sources ofdata, such as the hindcast or re-analysis wave series, which hascoupled long-term series (50 years) to a high resolution data (everyhour). These data bases supply very important information that in thenear future will allow us to define more precisely some input for thedifferent SMC's models. Regarding the long-term formulations (e.g.,the static equilibrium shoreline), the orientation of the mean energyflux on the diffracting points can be defined with great accuracy, andthe same is true for the equilibrium profile. It will allow theimprovement of long-term analysis and prediction reliability forbeach nourishment projects. Furthermore, the re-analysis of wavedata will allow the inclusion of the wave persistence effect, animportant aspect in morphodynamic beach evolution models fromthe middle-term scale (months) to the long-term scale (years-decades).

5. Conclusions

The parabolic bay shape model, as defined by Hsu and Evans(1989), provides a theoretical framework that allows us to under-

Fig. 15. Equilibrium shoreline under a new harbour alt

stand headland-bay beachmorphology dynamics and consequently topredict the impact of engineering projects.

González and Medina (2001) complemented this theory intro-ducing the “equilibrium beach” concept, which combines the staticequilibrium plan and profile for long-term analysis. While MEPBAYwas built concerning purely the original theory, SMC includesGonzales and Medina's concept.

Therefore, the application of MEPBAY to beach analysis needs onlythe beach planform image. For example, at the pre-design level of anew headland breakwater construction, MEPBAY can be used torapidly compare a number of different options with variouscombinations in length and orientation, and identify the best option,the one causing the least erosion. However, MEPBAY does not provideaccurate data for the design phase. Its data is extracted exclusivelyfrom the image and the quality of the output data depends directly onthe image resolution.

SMC supports the design phase because it uses numerical methodswhich increase forecast precision. The SMC software integratesMedina et al. (2001) contribution for the parabolic bay shape equationtheory, being necessary for a set of historical input data such as

ernative. (Assuming no sand filling on the beach).

Fig. 16. Equilibrium shoreline under a new harbour alternative. (Assuming a sand filling without shoreline retreat).

Table 1Bi-parabolic profile coefficients in San Lorenzo Beach for the new harbour geometry.

Zone A B C D

I 0.1450 0.0160 0.1880 0.0150II 0.1510 0.0220 0.1800 0.0180III 0.1510 0.0180 0.1800 0.0160

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bathymetry and wave direction information. In this manner, SMC ismore accurate for use at the design phase, however it needs additionalinput data.

Fig. 17. The designed equilibrium beach plan and its interception with the native bathymretreat).

The case study using both software at San Lorenzo Beach illustrateshow they can be used in a complementary way in pre-design anddesign phases. While MEPBAY allows rapid experimentation of manyproject configurations, trying to identify the main trends of morpho-logical changes and choose the best cost–benefit choice, SMC allows adeeper analysis of the chosen alternative, increasing impact precisionforecast by using numerical methods and historical input data.

Acknowledgements

A. Raabe and A. Klein would like to thank Ariel Vargas for hisdedication to the MEPBAY development and also the PROPPECResearch Support at UNIVALI University. M. González wishes toexpress his gratitude to the Spanish Ministry of Science and

etry (application obtained with the SMC). (Assuming a sand filling without shoreline

Fig. 18. The nourished equilibrium profile and the native profile (see location of thecross-shore profile in Fig. 17).

226 A.L.A. Raabe et al. / Coastal Engineering 57 (2010) 213–226

Technology, under the Ramón y Cajal Program, and the SpanishComisión Interministerial de Ciencia y Tecnología (CICYT), underresearch grant REN2003-9640/MAR. AHFK is appreciative of thesupport from the Brazilian National Council for Science andTechnology (CNPQ—Research Fellow) under grant no. 307267/2006-7 and also to Hanse Institute for Advanced Study (HWK Fellow),Germany and Erasmus Mundus Visiting Scholar, Delft University ofTechnology, The Netherlands.

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