Ci a ion: Gue e o, A.M.; O e o, L.;
Ospino, S.; Cue o, J. In e ac ions
be ween Hyd odynamic Fo cing,
Suspended Sedimen T anspo , and
Mo phology in a Mic o idal
In e media e-Dissipa i e Beach. J.
Ma . Sci. Eng. 2024,12, 1141. h ps://
doi.o g/10.3390/jmse12071141
Academic Edi o : Abdella i
Ouahsine
Recei ed: 13 June 2024
Re ised: 30 June 2024
Accep ed: 2 July 2024
Published: 6 July 2024
Copy igh : © 2024 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
Jou nal o
Ma ine Science
and Enginee ing
A icle
In e ac ions be ween Hyd odynamic Fo cing, Suspended
Sedimen T anspo , and Mo phology in a Mic o idal
In e media e-Dissipa i e Beach
Anlly Melissa Gue e o 1,* , Luis O e o 1, Sil io Ospino 1and Jai o Cue o 2,3
1
Geociencias-GEO4 Resea ch G oup, Depa men o Physics and Geosciences, Uni e sidad del No e, Km 5 ía
Pue o Colombia, Ba anquilla 081007, Colombia; [email p o ec ed] (L.O.);
[email p o ec ed] (S.O.)
2Coas al Geology and Sedimen ology G oup, Ins i u e o Geosciences, Kiel Uni e si y, 24118 Kiel, Ge many;
[email p o ec ed]
3Resea ch G oup in Na u al and Exac Sciences—GICNEX, Depa men o Na u al and Exac Sciences,
Uni e sidad de la Cos a, Ba anquilla 081007, Colombia
*Co espondence: [email p o ec ed]
Abs ac :
This s udy aims o in es iga e he hyd odynamic-mo phological in e ac ions on a mi-
c o idal in e media e-dissipa i e beach unde low o mode a e wa e ene gy condi ions using ield
measu emen s du ing wo clima ic seasons. The sepa a e con ibu ions o cu en s, sea-swell wa es,
and in ag a i y wa es o high- and low- equency sedimen luxes we e analyzed. The in ag a i y
wa e ene gy was mo e ele an nea he swash zone han in o he a eas. Al hough he cu en s
a e he p ima y suspended sedimen anspo mechanism, he esul s sugges ha he wa es a e
an impo an d i e o sedimen suspension om he seabed. The esul s indica e ha Sea-Swell
(SS) wa es and c oss-sho e cu en s a e he p e ailing hyd odynamic ac o s in nea sho e sedimen
anspo , and he c oss-sho e suspended sedimen anspo a es a e highe han hose in along-
sho e anspo . The subme ged ba in ensi ied du ing he we season (1–4 No embe 2018) when
he wa e heigh in ensi ies we e lowe , con a y o he d y season (24–25 Ma ch 2018). Signi ican
acc e ion nea sho e was iden i ied (in he subae ial beach) du ing he we season when he suspended
sedimen s we e g ea e , he SS-wa e heigh s nea sho e we e lowe , and sedimen lux was di ec ed
onsho e. A no o ious e osion was dis inguished du ing he d y season. The mos ep esen a i e
olume changes occu ed du ing he d y season (wi h high e osion), which is a ibu ed o he high
SS-wa e ene gy.
Keywo ds:
mo phodynamics; hyd odynamics; suspended sedimen anspo ; acous ic backsca e ;
in e media e-dissipa i e beach; mic o idal beach
1. In oduc ion
Seasonally domina ed coas al zones exhibi wo cycles o beach mo phological change [1].
The i s cycle is ela ed o p e- and pos -s o m e olu ion, wi h he as es , mos d as-
ic changes occu ing on he sho eline. The second cycle is seasonal, associa ed wi h
win e /summe mo phological change. Seasonal changes occu mo e equen ly han hose
caused by wa es in ex eme condi ions. Di e en ia ing mo phological changes associa ed
wi h bo h cycles is essen ial o unde s anding mo phodynamic beha io on a coas al
beach along a sho - e m cycle. This unde s anding, in u n, allows o mi iga ion o pos-
sible seasonal impac s on a beach, e.g., coas al e osion p ocesses in luenced by sedimen
edis ibu ion o by ansi ions be ween con as ing clima e seasons.
Sedimen anspo on beaches has been a opic o scien i ic in e es since he mid-20 h
cen u y [
2
]. The mo phodynamic app oach, ini ially o malized by [
3
] and la e adop ed
by [
1
,
4
,
5
] o he s udy o beaches, in ol es he in e ac ions be ween luid dynamics,
J. Ma . Sci. Eng. 2024,12, 1141. h ps://doi.o g/10.3390/jmse12071141 h ps://www.mdpi.com/jou nal/jmse
J. Ma . Sci. Eng. 2024,12, 1141 2 o 30
sedimen mo emen , and mo phology. S udies on beach mo phodynamics a e challenging
due o he synch onous occu ence be ween hyd odynamic o ces and sedimen anspo .
In addi ion, measu emen s a e di icul due o he complex logis ics equi ed in he high
u bulence en i onmen s o he inne su zone [6,7].
P e ious esea ch showed ha Sea-Swell (SS) wa es we e he main mechanism o
sand suspension, whe eas In ag a i y wa es (IG) would anspo he sedimen h ough
ad ec ion [
8
,
9
]. So, he sedimen lux dis ibu ion due o SS-wa e and IG-wa e is he ein an-
alyzed sepa a ely. Using hese a iables independen ly allows us o unde s and suspended
sedimen anspo in luenced by high- equency and low- equency wa e mo emen s,
as well as hei e ec on sedimen edis ibu ion a he subae ial beach. The mic o idal
dissipa i e beaches wi h a mode a e slope and mic o idal egime a e pa icula ly sensi i e
o seasonal a ia ions and changes in oceanog aphic condi ions, signi ican ly con ibu -
ing o sedimen dis ibu ion, coas al ba o ma ion, and sho eline con igu a ion [
9
–
11
].
The suspended sedimen luxes we e es ima ed om he cu en eloci y and suspended
sedimen concen a ion p o iles di ided by sho - and long-wa e con ibu ions. This in o -
ma ion allows us o assess sedimen lux di ec ion as well as beach esponses o sho - e m
seasonal a ia ions.
The Ca ibbean coas line o Colombia spans o e 1750 km, encompassing app oxi-
ma ely 54.86% o he o al coas line. The emaining 45.14% o he Colombian coas line
is comp ised o 1448 km o mac o idal Paci ic coas s [
12
]. Despi e he la ge ex en o i s
coas line, mos s udies o beach mo phological change on he Ca ibbean coas o Colombia
ha e ocused mos ly on ex eme e en s (e.g., hu icanes, cyclones, cold on s, sunamis),
whe eas mode a e- o low-ene gy wa e condi ions emain poo ly assessed. The la e con-
di ions a e o en dis ega ded in analyses because o hei less d as ic and sudden beha io ;
ne e heless, ocusing only on ex eme e en s leads o an incomple e comp ehension o
e olu ion p ocesses. Fu he mo e, i is impo an o del e deepe in o mode a e wa e con-
di ions, which occu wi h g ea e equency and play a c i ical ole in beach con igu a ion
and s abili y. The e o e, his esea ch will be based on s udying he mo phological change
o a mic o idal in e media e-dissipa i e beach unde low- o mode a e-ene gy condi ions in
wo con as ing clima e seasons. This s udy is ele an o unde s anding he mo phologi-
cal p ocesses along he Colombian coas because i iden i ied sho - e m and medium- e m
change pa e ns, as well as e osion and deposi ion o sedimen om a seasonal analy-
sis. Las ly, he esul s o his esea ch could be used as ools o coas al managemen ,
conse a ion, and adap a ion s a egies o coas al e osion p ocesses.
In his s udy, mo phological e olu ion will be analyzed on a mic o idal in e media e-
dissipa i e beach by collec ing in-si u da a du ing wo con as ing clima ic seasons. He e, i
is conside ed ha in e media e beach s a es exhibi s ong mo phodynamic eedback, wi h
locally signi ican anspo a es and s eep anspo g adien s [
13
]. Se e al pa ame e s
we e assessed in he mos dynamic zone o he beach (be ween he su zone and nea
he swash zone). These pa ame e s include sea le el a ia ion, wa e heigh , local cu en
magni ude and di ec ion, ini ial mo phological condi ions, sedimen g ain size, dep h, and
u bidi y. The esul s o his s udy highligh how ield da a om he su zone, pa icula ly
hose nea he swash zone, a e essen ial o he quali a i e and quan i a i e de e mina ion
o sedimen anspo on beaches.
This esea ch aims o desc ibe he con inuous in e ac ion be ween wa es (bo h SS and
IG), ides, cu en s, and suspended sedimen anspo h ough: (1) he spa io empo al
e olu ion o c oss-sho e hyd odynamic o cing and suspended sedimen concen a ion;
(2) c oss-sho e sedimen luxes; and (3) he ela ionship be ween hyd odynamics and beach
olume ic changes (e.g., e osion/acc e ion zones and subme ged ba mig a ion). This
s udy will analyze he mos signi ican seasonal a ia ions as well as he sedimen a y
dynamics p esen in a mic o idal in e media e-dissipa i e beach. Long- e m mo phological
changes, o hose caused by high ene gy e en s such as cold on s o ough sea condi ions,
among o he s, will no be discussed he ein, as his ype o phenomenon did no occu
du ing he measu emen ’s days.
J. Ma . Sci. Eng. 2024,12, 1141 3 o 30
2. Ma e ials and Me hods
2.1. S udy A ea
This s udy was pe o med a Boca ocino Beach, Juan de Acos a municipali y, A lán ico
Depa men , Colombia (Figu e 1a). Boca ocino Beach exhibi s a mic o- idal egime ypical
o he Ca ibbean coas line o Colombia, wi h a ange o 0.48 m [
14
,
15
]. The wa e clima e
in he p oximal ma ine zone and coas al pla o m o he Colombian Ca ibbean, including
Boca ocino Beach, is domina ed by wa es coming om he NE and NNE, wi h a p obabili y
o occu ence o 82% and 12%, espec i ely [
15
,
16
]. Boca ocino Beach has an in e media e-
dissipa i e p o ile (Figu e 1e), wi h a s eep slope in he eme ging pa o he beach (a e age
slope
β≈
0.134). The slope becomes gen le in he subme ged sec ion, wi h an almos
cons an alue o 0.014 up o 134 m away om he coas , whe e i becomes sligh ly s eepe
(
β≈
0.018). Coa se sand is he p edominan sedimen a Boca ocino Beach (see Sec ion 2.3).
J. Ma . Sci. Eng. 2024, 12, 1141 3 o 29
condi ions, among o he s, will no be discussed he ein, as his ype o phenomenon did
no occu du ing he measu emen ’s days.
2. Ma e ials and Me hods
2.1. S udy A ea
This s udy was pe o med a Boca ocino Beach, Juan de Acos a municipali y, A -
lán ico Depa men , Colombia (Figu e 1a). Boca ocino Beach exhibi s a mic o- idal egime
ypical o he Ca ibbean coas line o Colombia, wi h a ange o 0.48 m [14,15]. The wa e
clima e in he p oximal ma ine zone and coas al pla o m o he Colombian Ca ibbean, includ-
ing Boca ocino Beach, is domina ed by wa es coming om he NE and NNE, wi h a p oba-
bili y o occu ence o 82% and 12%, espec i ely [15,16]. Boca ocino Beach has an in e medi-
a e-dissipa i e p o ile (Figu e 1e), wi h a s eep slope in he eme ging pa o he beach (a e age
slope β ≈ 0.134). The slope becomes gen le in he subme ged sec ion, wi h an almos cons an
alue o 0.014 up o 134 m away om he coas , whe e i becomes sligh ly s eepe (β ≈ 0.018).
Coa se sand is he p edominan sedimen a Boca ocino Beach (see Sec ion 2.3).
Figu e 1. (a) Regional loca ion o he s udy a ea; (b) Boca ocino beach du ing he measu emen days;
(c) Ba hyme ic da a o 1 No embe , 2018 and he loca ion o p o iles P1, P2, P3, and P4 om 1 o 4
No embe , 2018 (We season), (d) Ba hyme ic da a om 24 o 25 Ma ch 2019 and he loca ion o
p o iles P1, P2, P3, and P4 om 24 o 25 Ma ch 2019 (D y season), (e) Topo-ba hyme ic p o iles o
he we season (blue line) and he d y season ( ed line). The senso wi h he le e W co esponds o
he equipmen ins alled in he we season, and D co esponds o he equipmen in he d y season.
In addi ion, he p o iles we e di ided in o 5 sec ions (S1, S2, S3, S4, and S5).
Figu e 1.
(
a
) Regional loca ion o he s udy a ea; (
b
) Boca ocino beach du ing he measu emen days;
(
c
) Ba hyme ic da a o 1 No embe , 2018 and he loca ion o p o iles P1, P2, P3, and P4 om 1 o
4 No embe , 2018 (We season), (
d
) Ba hyme ic da a om 24 o 25 Ma ch 2019 and he loca ion o
p o iles P1, P2, P3, and P4 om 24 o 25 Ma ch 2019 (D y season), (
e
) Topo-ba hyme ic p o iles o
he we season (blue line) and he d y season ( ed line). The senso wi h he le e W co esponds o
he equipmen ins alled in he we season, and D co esponds o he equipmen in he d y season. In
addi ion, he p o iles we e di ided in o 5 sec ions (S1, S2, S3, S4, and S5).
J. Ma . Sci. Eng. 2024,12, 1141 4 o 30
The wea he and wa e egime in he s udy a ea is in luenced by he mig a ion o he
In e opical Con e gence Zone (ITCZ), whe e No heas (NE) and Sou heas (SE) ade
winds con e ge [
15
]. Due o he double passage o he ITCZ o e he Colombian Ca ibbean
Sea, his egion has wo d y seasons (Decembe –Ma ch and June–July) and wo we seasons
(Ap il–May and Augus –No embe ) [
17
,
18
]. D y seasons a e cha ac e ized by high-speed
winds om he No heas [
15
]. The la ges wa es occu du ing hese seasons, wi h an
a e age signi ican heigh (Hs) o 2.3 m [
19
]. On he o he hand, we seasons ea u e highe
p ecipi a ion le els and lowe wind speeds om he Eas [
20
], wi h an a e age Hs o 1.1 m.
2.2. Field Expe imen s
Field expe imen s we e pe o med o compile hyd odynamic and opo-ba hyme ic
da a om Boca ocino Beach du ing he d y and we seasons. The i s ield expe imen
was pe o med in he we season, om 1 o 4 No embe 2018. The second expe imen was
pe o med du ing he d y season, be ween 22 and 25 Ma ch 2019.
Wa e le el da a we e collec ed wi h p essu e senso s (RBR duo and RBR). Flow a es
we e collec ed wi h cu en me e s (Aquadopp
®
P o ile , No ek g oup, Bos on, MA, USA).
On he o he hand, suspended sedimen concen a ion (SSC) was measu ed wi h u bidi y
senso s (OBS-3+ and OBS-5+, Campbell Scien i ic, Ba celona, España). In addi ion, olume
concen a ion da a was de e mined o 36 sedimen size classes (LISST-200X, Sequoia,
Belle ue, WA, USA). Senso s we e ins alled c oss-sho e on Boca ocino Beach (Figu e 1c,d).
The expe imen al se up allowed o he analysis o he hyd odynamic spa io- empo al
e olu ion o nea sho e hyd odynamics as well as he ans o ma ion o associa ed SS-wa es
along he shoaling zone, su zone, and nea he swash zone (Table 1).
Table 1.
Ins umen con igu a ion o he d y and we seasons a Boca ocino Beach. No e: The
ac onym HR means high esolu ion.
Season Senso /
Symbology Ins umen Loca ion Dis ance om
he Coas [m] Dep h [m]
We
W0 No ek Aquadopp P o ile Shoaling zone 400 ~7.9
W1 No ek Aquadopp P o ile B eaking zone 150 ~2.8
W2 No ek Aquadopp P o ile
Su zone
34 ~1.3
W3 and
OBS 5+ No ek Aquadopp P o ile HR and OBS5+ 23 ~1.2
W4 No ek Aquadopp P o ile HR 16 ~1.1
W5 RBR Nea he
Swash zone 10 ~1.0
D y
D0 RBR Shoaling zone 400 ~7.9
D1 No ek Aquadopp P o ile B eaking zone 150 ~2.8
D2 and
OSB 3+ No ek Aquadopp P o ile and OBS3+
Su zone
30 ~1.4
D3 No ek Aquadopp P o ile HR 21 ~1.3
D4 and LISST No ek Aquadopp P o ile HR and LISST Nea he
Swash zone 13 ~1.1
P essu e senso s, cu en measu e s, OBS3+ senso s, and LISST senso s we e con ig-
u ed o measu e a a equency o 5 Hz du ing he d y season. The D0 senso was an RBR
ins umen loca ed 400 m away om he sho eline. D1 and D2 senso s we e con igu ed a a
e ical esolu ion o 50 cells and wid hs o 20 and 10 cm, espec i ely. Senso s D3 and D4
we e con igu ed a a e ical esolu ion o 28 cells and 1 cm o wid h. The blanking dis ance
o senso s D1, D2, D3, and D4 was 10 cm.
J. Ma . Sci. Eng. 2024,12, 1141 5 o 30
Rega ding opog aphic in o ma ion, beach p o ile measu emen s we e ca ied ou
om 1 o 4 No embe 2018 o he we season, and om 24 and 25 Ma ch 2019 o he d y
season. Beach p o iles we e measu ed using a o al s a ion wi h an accu acy o
±
0.0762 m
o he combined x and y coo dina es and
±
0.0762 m o he z coo dina e. The da a we e
geo e e enced h ough a di e en ial global posi ioning sys em. Fou p o iles we e es ab-
lished c oss-sho e, s a egically dis ibu ed along he hyd odynamic a ay. The beach
p o iles P1 o P2 we e loca ed along he coas (Figu e 1c,d). To collec dep h da a, ba hy-
me ic su eys we e ca ied ou o each clima ic season using a digi al echo sounde ,
and a high- equency (200 kHz) ansduce wi h an accu acy o 0.01 m
±
0.1% dep h was
used. Dep h da a we e aken om high and low ide o ecas s published by he Colombian
Ins i u e o Hyd ology, Me eo ology, and En i onmen al S udies, IDEAM [
21
], and we e
e e enced o he mean low wa e sp ings (MLWS). Hyd odynamic, opog aphic, and
ba hyme ic measu emen s will de e mine he ela ionship be ween hyd odynamic o cing
(e.g., SS and IG wa es, long-sho e and c oss-sho e cu en s, sea le el, wa e s eepness) and
coas mo phological changes.
2.3. Sedimen ology Analysis
Th ee sedimen samples we e collec ed in bo h clima ic seasons in o de o de e mine
he sedimen ological cha ac e is ics o he s udy a ea. Th ee poin s o in e es (in he su
zone) we e chosen o sample collec ion. Sedimen samples we e analyzed o cha ac e ize
he composi ion, ex u al g oup, and g ain size o each coas al zone h ough he GRADIS-
TAT ool p oposed by [
22
]. Table 2shows he composi ion pe cen ages and ex u al g oups
o six sedimen samples collec ed o bo h clima ic seasons.
Table 2.
Composi ion pe cen ages and he ex u al g oup o six (6) sedimen ological samples
acco ding o each nea sho e li o al zone om which hey we e ex ac ed.
Clima ic
Season Sample Coas al Zone Tex u al G oup Ve y Fine
Sand (%)
Fine Sand
(%)
Medium
Sand
(%)
Coa se Sand
(%)
Ve y Coa se
Sand
(%)
G a el
(%)
We
1 Su zone Sligh ly g a elly
sand 0.8 12.3 27.1 47.7 10.7 1.4
2Nea he swash
zone Sandy g a el 0.4 3.1 5 23.9 30.1 37.5
3 Subae ial zone Sligh ly g a elly
sand 1.0 24.6 51.7 20.4 2.1 0.2
D y
4 Su zone G a elly sand 0.2 3.1 18.7 36.5 20.0 21.5
5Nea he swash
zone Sandy g a el 0.1 0.7 9.8 34.6 22.3 32
6 Subae ial zone Sligh ly g a elly
sand 0.7 9.5 52.5 33.8 3.3 0.2
2.4. Da a Se ies P ocessing
A quali y con ol p o ocol, comp ising a isual inspec ion p ocess and he implemen-
a ion o a manual quali y con ol ool, was applied o he aw ield da a se ies. In he
isual inspec ion s age, unusual pa e ns o luc ua ions, such as ex eme, ou lie , o null
alues, we e iden i ied. These unusual alues may be caused by ex e nal condi ions, such
as he p esence o swimme s in small essels nea he measu ing si e. These ou lie s we e
emo ed om he da ase . Measu e da a nea o abo e he sea su ace we e elimina ed due
o he p esence o e oneous da a caused by con amina ion o he la e al lobe.
A mo ing a e age il e was used as a quali y con ol ool, applying a sliding window
o he da a se ies o iden i y anomalous alues and co ec a ypical alues i needed.
The sliding window was ela i ely small (app oxima ely be ween 5 and 20 s), gi en he
equency and na u e o da a luc ua ions. Cu en , wa e, and u bidi y da a we e measu ed
each second o h ee consecu i e days. The e o e, da a luc ua ions can be apid and
ansi o y. Ne e heless, his window allowed us o cap u e sho bu signi ican e en s
as a ypical da a noise was dele ed. In some cases, i was necessa y o adjus he window
size du ing he analysis. To iden i y sys ema ic biases in measu emen s, h esholds whe e

J. Ma . Sci. Eng. 2024,12, 1141 6 o 30
a ypical alues we e ound in he da a se ies we e de ined using mean (cen al end)
and s anda d de ia ion ends. These s a is ics play an impo an ole in he alida ion
o measu ed da a as well as in da a quali y con ol. Da a conside ed a ypical we e hose
ou side he ange ( wo o h ee s anda d de ia ions away om he median). Las ly, a
Nea es Neighbo Analysis was applied o de ec a ypical alues ha emained unde ec ed
by p e ious me hods.
Da a we e analyzed h ough ime-domain ep esen a ions using Fou ie T ans o m
(FFT) and C oss-wa ele T ans o m (XWT), ollowing p e ious s udies [17,19].
2.4.1. Time and F equency Domain P ocessing
Hyd odynamic (e.g., sea le el, c oss-sho e, long-sho e cu en s) and u bidi y da a
aken in ield campaigns we e spli in o 1-h sea s a es o pe o m ime-domain analyses.
Fou ie ans o m analysis was employed o es ima e he wa e ene gy densi y (
S
) o he
ee su ace ele a ion se ies in he equency domain. Eigh Hamming windows we e used,
wi h an o e lapping o 50% and a equency bandwid h o 0.002 Hz. Signi ican wa e
heigh s we e classi ied in o wo bands: g a i y, o SS (
Hmo,SS
), and in ag a i y (
Hmo,IG
),
using Equa ion (1) and acco ding o [23].
Hmo,SS =4sZ spli
0.005
S( )d ,Hmo,IG =4sZ0.5
spli
S( )d (1)
whe e a cu o equency (
spli
) o 0.05 Hz, app oxima ely equal o hal he a e age peak
equency (
p=
1
/Tp
) o o sho e wa es, is used o sepa a e in ag a i y (IG) and g a i y
(SS) bands. This choice o cu -o equency is based on he endencies o g a i y and IG
wa e ene gy equencies in deep wa e condi ions. Mos g a i y-wa e ene gy displays
equencies > p/2, whe eas mos IG-wa e ene gy lies a equencies < p/2 [24].
2.4.2. Wa e S eepness and B eaking Wa e Pe cen age
Wa e s eepness was used as a p oxy o assess sedimen anspo and de e mine he
e ec o wa e condi ions on suspended sedimen . Wa e s eepness was calcula ed using
Equa ion (2):
Wa e s eepness =H/L∗(2)
whe e Hand
L∗
a e wa e heigh and wa eleng h, espec i ely. The dispe sion equa ion (3)
was used o de e mine wa eleng h and wa e pe iod alues [25].
L∗=gT2 anh2πh
L/2π(3)
whe e Tis wa e pe iod, his dep h, and gis he g a i a ional accele a ion. In his s udy,
signi ican wa e pe iod (Tsig) and heigh (Hsig) alues we e used. In a shallow-wa e
app oxima ion, Equa ion (3) is simpli ied as:
Lshallows =Tpgh (4)
In his s udy, he b eaking wa e pe cen age was calcula ed ollowing [
26
] as he a io
be ween he numbe o wa es classi ied as b oken (
Nb
) and he o al numbe o wa es (
N
)
in he same ime in e al as Qb=Nb /N .
2.4.3. P incipal Componen Analysis (PCA)
The PCA me hod was used o de e mine he co ela ed a iables o mul iple hyd o-
dynamic o cing ac o s wi h he opog aphic change. This me hod has been e y use ul
in coas al esea ch as a ool o assessing he ole o me eo ological and ma ine o ces on
beach mo phological change [
4
,
27
]. In his wo k, a PCA was employed be ween ma ine
o cing (heigh s
Hmo,ss
,
Hmo,IG
, wa e s eepness, eloci ies, and maximum ide le el) and
he sedimen suspended concen a ion (SSC) o analyze he esponse o sedimen supply
J. Ma . Sci. Eng. 2024,12, 1141 7 o 30
nea sho e, which could be a p oxy o he opog aphic change on beaches. Co ela ions
be ween p incipal and seconda y componen s we e calcula ed; hose wi h alues abo e
0.47 we e conside ed signi ican .
2.4.4. Es ima ed Suspended Sedimen Concen a ion om Acous ic Backsca e ed (ABS)
The sona equa ion was used in his s udy o quan i y SSC, i s by con e ing acous ic
echo in ensi y (E), measu ed in coun s by he ADCP, and pos e io ly by con e ing o
acous ic backsca e (ABS), measu ed in dB, using he me hods p o ided by [
28
–
30
]. Eco
e odispe sion in dB is gi en by [28]:
ABS ={C−LDBM −PDBW }+2αR+n10log10h(TTD +273.16)R2io+{10log10[10Kc(E−E )
10 −1]}(5)
Equa ion (6) can be ew i en in a simple o m as:
ABS =Kc+2TL0+RL0(6)
In he i s e ms o Equa ions (5) and (6),
C
is an empi ic cons an ,
LDBM
is gi en by
10log10(L)
, wi h L
0
being ansmi ed pulse leng h (measu ed in m), and
PDBW
is de ined
by 10log10(P), wi h P being ansmi ed equency (in wa s). Kcis gi en as,
Kc=127.3
TTD +273◦(7)
The second e m in Equa ions (5) and (6) ep esen s a pa ame e o bidi ec ional
ansmission loss (2TL
0
), in which pa ame e
α
is he sound abso p ion coe icien in wa e
(in dB/m), Ris he ange along he acous ic beam (in m), and
TTD
is he empe a u e a he
dep h o he ansduce (in ◦C).
Rwas calcula ed ollowing by [29,31], as ollows:
R=z/ cos(beam angle, 25◦ o Aquadopp/AWAC)(8)
∝was calcula ed using he o mula p o ided [32], as ollows:
∝=0.106 1 i2
2
1+ i2ePH−8
0.56 +0.521+TTD
43 S
35 2 i2
2
2+ i2e−h
6+0.00049 2e−(TTD
27 +h
17 )(9)
The i s and second e ms o Equa ion (9) ep esen he elaxa ion equencies o wo
compounds in he ocean: Bo ic Acid (
1=
2.2) and Magnesium Sul a e (
2=
205.3). The
hi d e m o he equa ion ep esen s iscous abso p ion, in which
S
is salini y in pp ,
h
is
wa e dep h in m, and iis he acous ic equency applied.
The hi d e m in Equa ion (6) equals echo s eng h (in coun s) con e ed o e e be a-
ion le els, in which
Kc
is a ac o o he con e sion o ampli ude in coun s (as epo ed by
he ADCP ecei e ci cui ) o dB. E is he RSSI ( e u ned signal s eng h indica o ), gi en
by he Aquadopp senso o each bin along he acous ic beam, in coun s [
33
]. Re e ence
echo s eng h (E ) was ce o, unde he assump ion o null noise le el.
SSC o
c
was ob ained in
mg/L
om OBS measu emen s based on a p e ious calib a-
ion o condi ions in he s udy a ea ollowing he ins uc ions by he manu ac u e [
34
],
whe e i was ob ained he linea ela ionship be ween Nephelome ic Tu bidi y Uni , NTU,
(as an independen a iable) and
mg/L
(as a dependen a iable), as shown by equa ion
10, wi h signi ican co ela ion coe icien s a a 99.5% con idence le el (i.e., he a e age
magni ude o he esiduals was less han 0.5% o he measu emen ange).
Tu bidez(NTU)=0.473 ∗c(mg/L)−701 (10)
In o de o es ima e SSC alues, a calib a ion cu e was ob ained, ela ing ABS (in dB,
as es ima ed om he Aquadopp cu en me e ) o suspended sedimen concen a ion
c
(in mg/L, measu ed wi h a calib a ed OBS 3+) h ough simple linea eg ession analysis.
J. Ma . Sci. Eng. 2024,12, 1141 8 o 30
Ob aining he calib a ion cu e in ol es collec ing simul aneous measu emen s be ween
bo h a iables. Using he bes - i model, he SSC alues we e es ima ed in he s udy a ea.
Finally, he ela ionship be ween echo in ensi y om acous ic measu emen om Aquadoop
(dB) and SSC alues de i ed om OBS (mg/L) is ma hema ically ep esen ed by:
10log(SSCOBS)=a∗ABS (in dB)+b(11)
whe e
a
and
b
ep esen he ela ionship be ween bo h a iables. The calib a ion cu e
was alida ed using independen da a ha was no used in he ini ial i ing p ocess. The
me hod was implemen ed o he senso s (W1 o W4, and D1 o D4), and i is explained in
mo e de ail in esul s Sec ion 3.1.
The calib a ion o he ABS me hod using an OBS senso is shown in Appendix A. An
impo an limi a ion was ound in he p ocess o es ima ing SSC om ADCP, which is
associa ed wi h he sedimen g ain size (see Appendix B).
2.4.5. Es ima ion o Suspended Sedimen T anspo
Flux eloci y di ec ions de e mine sedimen anspo di ec ions. Onsho e-di ec ed o
o sho e-di ec ed eloci ies imply c oss-sho e anspo , whe eas E-di ec ed o W-di ec ed
eloci ies in ol e alongsho e anspo [
35
]. Sedimen lux was calcula ed as he p oduc o
suspended sedimen con en
c
and he espec i e eloci y componen s (
u
-componen s o
c oss-sho e cu en s o alongsho e cu en s). In o de o calcula e alues o absolu e and
ela i e IG sedimen lux, ne suspended sedimen lux was ob ained i s o each poin ,
as ollows:
q o al =<uc >=<u+∼
uc+∼
c>=u·c+<u0·c0>(12)
The i s e m on he igh -hand side o Equa ion (12) ep esen s he local mean sand lux
(qmean), and he second e m is he oscilla o y lux o he wa e. The
symbol < > indica es
ha
i is a ime-a e aged alue. Oscilla o y lux was classi ied in o a wa e componen (SS) and
an IG wa e componen (IG) using he cu o equency, spli =0.05 Hz.
<u0·c0>=<(uss +uIG)(css +cIG)>≈<uss·css >+<uIG·cIG >(13)
Equa ions (12) and (13) we e ew i en as:
q o al =<uc >=u·c+<uss·css >+<uIG·cIG >(14)
The ela i e con ibu ion o qIG o o al lux a e was de e mined as,
|qIG/(|qIG+|qss+|qmean)(15)
The con ibu ions o o he componen s we e analogously calcula ed, and suspended
sedimen anspo was e ically a e aged. This allowed us o analyze he e ec o SS and
IG wa e condi ions on suspended sedimen anspo .
3. Resul s
3.1. Wa e B eaking
The pe cen age o b oken wa es was calcula ed, assessing hem om o sho e o
onsho e senso s. This is a c i ical pa ame e , use ul as a ool o coas al managemen , bu
a ely quan i ied o pa ame ic models o ene gy dissipa ion wi hin he inne and ou e
su zones. Figu e 2a,b show sa elli e images co esponding o a single measu emen day
o each clima e season. Figu e 2c,d show how he pe cen age o b oken wa es e ol ed
h ough ime. The pe cen age o b oken wa es anged om 1% o 7%, om he shoaling
zone o nea he swash zone, o bo h we and d y seasons.
J. Ma . Sci. Eng. 2024,12, 1141 9 o 30
J. Ma . Sci. Eng. 2024, 12, 1141 9 o 29
i can be in e ed om Figu e 2c,d ha , o he mos dissipa i e in e media e beach (d y
season), mos wa e b eaking occu s in he ou e bo de o he b eake zone, in ensi ying
in he middle o inne b eake zone. On he o he side, o he in e media e, less dissipa i e
beach (we season), which had lowe ene gy, mos wa es b eak close o he middle su
zone. Fo mo e dissipa i e beaches, his alue apidly inc eases owa ds he ou e su
zone, whe eas o mo e e lec i e beaches, he alue slowly inc eases h ough he en i e
su zone. These esul s ag ee wi h concep ual models o he su zone wi h gen ly sloped,
dissipa i e beaches men ioned by [36].
Figu e 2. (a) Sa elli e image ob ained om Google Ea h o he Boca ocino beach o 2018 No embe
(we season); (b) Sa elli e image ob ained om Google Ea h o he Boca ocino beach o 2019 Ma ch
(d y season). The ed iangles co espond o he loca ions o he p essu e and cu en senso s. (c)
B eaking wa e’s pe cen age o he we season. (d) B eaking wa e’s pe cen age o he d y season.
The ec angle ep esen s he zone wi h a highe b eaking wa e pe cen age.
3.2. Nea sho e Hyd odynamics
Figu e 3 ep esen s he spa ial- empo al e olu ion o hyd odynamic o ces and SSC
du ing he ield expe imen s. Each a iable is calcula ed by sea s a es. Figu e 3a p esen s
he empo al e olu ion o sea le el o c oss-sho e senso s loca ed 150 m om he coas .
Figu e 3b,c show he signi ican heigh s o he SS and IG wa es (𝐻, 𝑦 𝐻,, espec-
i ely). Figu e 3d,e show c oss-sho e and long-sho e low eloci ies, suspended sedimen
concen a ion (SSC, Figu e 3 ), and wa e s eepness (Figu e 3g). The le side ep esen s
da a aken du ing he we season, and he igh side comp ises da a om he d y season.
The de ini ion o shoaling, su , and swash zones (Table 1) was suppo ed by he
esul s shown in Figu es 2 and 3. The shoaling zone was iden i ied in a eas wi h dep hs
g ea e han 2.8 m, cha ac e ized by he absence o b oken wa es, oge he wi h he g ea -
es signi ican wa e heigh (ss-wa e) alues on ins umen loca ions W0, W1, D0, and D1.
F om his poin , he wa es begin o b eak, o m c es s, and signi ican wa e heigh s in-
c ease, whe eas ss-wa es dec ease. In addi ion, an inc ease in he pe cen age o b oken
wa es is eco ded. Coa se sands p e ailed in his zone (47.7% o he we season; 36.5%
o he d y season, see Table 2). Senso s W4 and D4 we e loca ed nea he swash zone,
whe e a dec ease in he pe cen age o b oken wa es was ound, sugges ing less u bulence
and wa e b eakage ac i i y. In addi ion, his loca ion was iden i ied o exhibi he lowes
ene gy and heigh alues o SS-wa es, bu highe alues o IG-wa es compa ed wi h
o he a eas away om he coas . Coa se sedimen s we e dis ibu ed nea he swash zone
Figu e 2.
(
a
) Sa elli e image ob ained om Google Ea h o he Boca ocino beach o 2018 No embe
(we season); (
b
) Sa elli e image ob ained om Google Ea h o he Boca ocino beach o 2019 Ma ch
(d y season). The ed iangles co espond o he loca ions o he p essu e and cu en senso s.
(
c
) B eaking wa e’s pe cen age o he we season. (
d
) B eaking wa e’s pe cen age o he d y season.
The ec angle ep esen s he zone wi h a highe b eaking wa e pe cen age.
Pe cen ages o b oken wa es g ea e han 3.5% (co esponding o he inne su zone)
coincided wi h he a ea shown in he do ed ec angle o Figu e 2a,b, o bo h clima ic zones.
Meanwhile, pe cen ages below 3.5% we e iden i ied ou side he ec angle (co esponding
o he ou e su zone). The wid h o he b eake zone was ela ed o he clima ic season.
As shown in Figu e 2c,d, he inne su zone du ing he d y season was wide in he d y
season han du ing he we season.
Du ing he d y season, he beach slope was gen le , wi h a less s eep p o ile (Figu e 1e).
The esul ing su zone was wide enough o dissipa e he ene gy o mos wa es. On he
o he hand, he beach slope was s eepe in he we season (Figu e 1e), so he su zone
was na ow, and he incoming ene gy was e lec ed wi h li le o no b eaking. In addi ion,
i can be in e ed om Figu e 2c,d ha , o he mos dissipa i e in e media e beach (d y
season), mos wa e b eaking occu s in he ou e bo de o he b eake zone, in ensi ying in
he middle o inne b eake zone. On he o he side, o he in e media e, less dissipa i e
beach (we season), which had lowe ene gy, mos wa es b eak close o he middle su
zone. Fo mo e dissipa i e beaches, his alue apidly inc eases owa ds he ou e su
zone, whe eas o mo e e lec i e beaches, he alue slowly inc eases h ough he en i e
su zone. These esul s ag ee wi h concep ual models o he su zone wi h gen ly sloped,
dissipa i e beaches men ioned by [36].
3.2. Nea sho e Hyd odynamics
Figu e 3 ep esen s he spa ial- empo al e olu ion o hyd odynamic o ces and SSC
du ing he ield expe imen s. Each a iable is calcula ed by sea s a es. Figu e 3a p esen s
he empo al e olu ion o sea le el o c oss-sho e senso s loca ed 150 m om he coas .
Figu e 3b,c show he signi ican heigh s o he SS and IG wa es (
Hmo,SS y Hmo,IG
, espec-
i ely). Figu e 3d,e show c oss-sho e and long-sho e low eloci ies, suspended sedimen
concen a ion (SSC, Figu e 3 ), and wa e s eepness (Figu e 3g). The le side ep esen s
da a aken du ing he we season, and he igh side comp ises da a om he d y season.
J. Ma . Sci. Eng. 2024,12, 1141 16 o 30
J. Ma . Sci. Eng. 2024, 12, 1141 15 o 29
and 0.6° o he d y season. Sec ion S4 (be ween 124 and 238 m) ea u es a slope o app ox-
ima ely 1.2°, and Sec ion S5 (be ween 238 and 400 m) exhibi s a slope o 1.0° in bo h cli-
ma ic seasons. Rega ding he changes in beach sedimen olume (m
3
/m), a dec ease o
13.3 m
3
/m o sedimen was iden i ied in Sec ion S1. In Sec ion S2, sedimen olume in-
c eased by 25.5 m
3
/m, and dec eased by 13.4 m
3
/m in Sec ion S3. Volume inc eased o 689
m
3
/m in Sec ion S4. Las ly, he sedimen olume in Sec ion S5 did no show any a ia ions.
Volume changes may be ela ed o seasonal a ia ions in hyd odynamic o ces
(wa es and cu en s). Addi ionally, an o sho e senso (Aquadopp p o ile , 400 kHz, lo-
ca ed a 600 m om he coas ) was employed o unde s and in e -seasonal changes a a 3-
h measu emen a e, om 1 No embe 2018 o 24 Ma ch 2019. Figu e 6 shows o sho e
hyd odynamic condi ions (𝐻 and 𝑇). The highes peak alues we e iden-
i ied using ci cles wi h 𝐻 alues be ween 1.7 and 2.3 m and 𝑇 anging
om 8 o 10.8 s. These alues occu ed in Janua y, Feb ua y, and Ma ch, in ag eemen
wi h hose epo ed by [55] o he Colombian Ca ibbean. These esul s indica e ha hy-
d odynamic o ces occu mo e equen ly du ing hese mon hs, due o he wa e ene gy
condi ions (mainly due o ENE winds). Maximum alues o 𝐻 and 𝑇
occu ed in 23 Janua y and 12 Ma ch 2019, which can be associa ed wi h wo cold on s
a ec ing he Ca ibbean egion o Colombia, including Boca ocino Beach, acco ding o ma-
ine me eo ological bulle ins issued by DIMAR and i s Cen e o Oceanog aphic and Hy-
d og aphic Resea ch o he Ca ibbean [50]. These e en s come om he No hwes e n
Ca ibbean Sea be ween he Yuca an Peninsula and Cuba, mo ing owa ds he Sou heas
and gene a ing abundan clouds and mode a e p ecipi a ions. Howe e , hese cold on s
became s a iona y on s, weakening un il hey disappea ed.
Figu e 6. Tempo al e olu ion o he o sho e condi ions om he S
o sho e
senso loca ed a 600 m om
he coas wi h measu emen s om 1 No embe 2018 o 24 Ma ch 2019. (a) Signi ican wa e heigh
(𝐻

). (b) Peak pe iod: (𝑇

). The ci cles indica e he mos ene ge ic wa es eco ded
du ing he measu emen pe iod. In addi ion, he do ed e ical lines di ide he measu emen days
o each campaign (1 o 3 No embe 2018 and 22 o 25 Ma ch 2019).
The a o emen ioned in ense e en s could explain he signi ican olume changes be-
ween clima e seasons, as hese me eo ological e en s end o emain o p olonged pe i-
ods o ime. The e o e, hese e en s may ha e a mo e signi ican long- e m in luence on
mic o idal beach mo phology on he Colombian Ca ibbean coas compa ed o o he ene -
ge ic wa e s a es [16,17]. Howe e , he e is no compelling e idence suppo ing a di ec
ela ionship be ween olume changes and hyd odynamic condi ions o he in e al Jan-
ua y–Ma ch (Figu e 6).
Figu e 1c,d show no e idence o ab up mo phological change in he o sho e sec-
ions (S4 and S5) be ween clima e seasons. Howe e , hese changes we e iden i ied a he
Figu e 6.
Tempo al e olu ion o he o sho e condi ions om he S
o sho e
senso loca ed a 600 m om
he coas wi h measu emen s om 1 No embe 2018 o 24 Ma ch 2019. (
a
) Signi ican wa e heigh
(
HsO sho e
). (
b
) Peak pe iod: (
TpO sho e
). The ci cles indica e he mos ene ge ic wa es eco ded
du ing he measu emen pe iod. In addi ion, he do ed e ical lines di ide he measu emen days
o each campaign (1 o 3 No embe 2018 and 22 o 25 Ma ch 2019).
Figu e 1c,d show no e idence o ab up mo phological change in he o sho e sec ions
(S4 and S5) be ween clima e seasons. Howe e , hese changes we e iden i ied a he inne
su zone (sec ions S2 and S1), whe e IG-wa e ene gy was highe and is conside ably
dynamic due o di e en u bulence p ocesses ha may occu in his zone [
10
,
56
]. Las ly,
hese indings a e e y ep esen a i e, allowing us o app oach an unde s anding o mo -
phological seabed changes, conside ing he complexi y o measu emen s a he inne su
zone [7].
3.3.3. The Wa e S eepness as a Con ol Pa ame e in he Fo ma ion and Mig a ion o
Subme ged Ba
In o de o assess he na u al supply o sedimen o he beach, SSC es ima es we e
compa ed o wa e s eepness (Figu e 3 ,g), and he ela ionship be ween hem was obse ed.
Wa e s eepness was used as a con ol pa ame e o unde s and hyd odynamic p ocesses
and hei ela ionship wi h es ima ed SSC alues on he coas , as well as wi h coas al
cu en s. Acc e ion and e osion zones o bo h seasons we e de e mined based on he
concep ual model o suspended sedimen anspo and in e idal beach mo phology
esponse [
57
]. In he we season and nea he swash zone, c oss-sho e cu en s we e
o sho e-di ec ed when SSC alues we e g ea es (app oxima ely 450 mg/L), and wa e
s eepness anged be ween 0.04 and 0.05. As he wa e p opaga es om he su zone and
ge s nea he swash zone, cu en s become onsho e-di ec ed whe e he slope is less han
0.01. The ob ained esul s indica e an acc e ion zone 30 m away om he coas (blue band on
he le side o Figu e 3g). The acc e ion zone may be explained by a g ea e SSC (400 mg/L)
close o he ou e su zone and sedimen s ha we e anspo ed onsho e-di ec ed and
deposi ed a he inne su zone. These indings highligh he weak unde ow obse ed
nea sho e when ba hyme ic g adien s we e gene ally smalle .
Du ing he d y season, c oss-sho e cu en s we e o sho e-di ec ed in he shoaling
zone, while he wa e s eepness alue was less han 0.01. These esul s indica e he p esence
o an acc e ion zone 150 m om he coas (blue band on he igh side in Figu e 3g) wi h
a e age SSC alues o 350 mg/L. Fo i s pa , he lowes SSC alues (~150 o 250 mg/L)
we e ound in he inne su zone. The s ong unde ow obse ed nea sho e may ha e
con ibu ed o sedimen anspo owa ds he sea. The e o e, i is possible o in e ha
sedimen was no locally deposi ed bu a he supplied om ou side he s udy a ea. In
sho , he nea sho e beha io end o he beach was p edominan ly acc e iona y when

J. Ma . Sci. Eng. 2024,12, 1141 17 o 30
SS-wa es we e weake , ha is, wi h wa e slopes below 0.010. On he o he hand, he beach
was p one o e osion when SS-wa es we e s onge , wi h wa e slope alues abo e 0.010.
The sedimen s du ing he we season we e iden i ied as being coa se han hose in
he d y season nea he swash zone. So, in W2, he g ea es alues o wa e heigh and
ene gy we e eco ded o he we season, and a subme ged ba was iden i ied. Gi en he
p e ious condi ions, he ba could be ac ing as a na u al il e , apping coa se pa icles and
allowing ine sedimen o be deposi ed in o he a eas. This dynamic may be in luenced
by high IG ene gies in he we season, acili a ing anspo and a o ing he deposi ion
o coa se pa icles compa ed o he d y season. The ss-wa e ene gy was g ea e in he
o sho e di ec ion, which could lead o he anspo o la ge pa icles di ec ed owa d
deepe wa e s, explaining he appea ance o coa se sands in his zone, whe eas middle
sands, being less coa se, may be anspo ed by wa es up o he subae ial beach.
3.3.4. In e -Seasonal Volume Va iabili y and he Eme ged Beach Mo phology
Figu e 7a shows ou c oss-sho e opog aphic p o iles (P1, P2, P3, and P4), measu ed
om he op o he d y beach (~1.5 m MLWS) o he low ide line. P o iles P1-P2 and P3-P4
we e loca ed on each side o he hyd odynamic senso a ay. The longes p o ile was 33 m.
Figu e 7b shows daily alues o d y beach olume, es ima ed om opog aphic p o iles (1
and 4 No embe 2018; 24 and 25 Ma ch 2019).
J. Ma . Sci. Eng. 2024, 12, 1141 17 o 29
app oxima ely 17 m. P o ile P4 ea u ed a slope o 11° a 9 m, hen an almos la slope up o
21 m, ollowed by a gen le slope o 6.2°. In gene al e ms, no signi ican di e ences we e
obse ed be ween p o iles P1 and P2, whe eas P3 and P4 showed a wide coas al s ipe in
which geo o ms (such as ba s and/o be ms) a e p esen on he highes pa o he d y beach.
This may be explained by he inc ease in long-sho e cu en s, p edominan ly di ec ed o-
wa ds he eas , which would anspo sedimen om P2 o p o iles P3 and P4. Figu e 8b
shows an inc ease in beach olume o 2.3 m
3
/m (acc e ion) be ween No embe 1 and 4. This
inc ease is po en ially associa ed wi h sedimen in e change among suspended pa icles
nea he coas (Figu e 3 ) and he acc e ion zone loca ed nea W3 (Figu e 3g).
Figu e 7. Topog aphy p o iles and daily olume changes o he Boca ocino Beach, (a) Topog aphic
p o iles measu ed o he we and d y seasons. (b) Daily olume ic changes o he d y beach o
he we season (le side) and d y season ( igh side).
On 24 and 25 Ma ch 2019, all ou p o iles main ained a simila opog aphy, almos
la up o 5 m. The subae ial beach did no show signi ican mo phological changes, as
c oss-sho e hyd odynamic o ces emained cons an in his measu emen pe iod (Figu e
3c,d). On 24 Ma ch, p o iles P1, P3, and P4 exhibi ed a simila opog aphy, wi h wo p o-
nounced slopes, one o 29.5° a 9 m, and a maximum slope o 14.4° a 12 m. P2 showed a
maximum slope o 10.7° a 18 m. On 25 Ma ch, P3 and P4 exhibi ed a maximum slope o
14.7° a 9 and 8.5 m, espec i ely. Figu e 8b shows a dec ease o 1.7 m
3
/m (e osion) be-
ween 24 and 25 Ma ch. In Boca ocino Beach, ba s we e s eepe on 24 Ma ch, la ening
and mig a ing owa ds he coas on 25 Ma ch. The esul s he ein desc ibed a e consis en
wi h subme ged ba mo emen and c oss-sho e cu en di ec ions, bo h p edominan ly
o ien ed onsho e du ing he we season. The e o e, sedimen a ailabili y will be g ea e
in he d y po ion o he beach. On he o he hand, du ing he d y season, subme ged ba
mo emen and c oss-sho e cu en s we e o sho e-di ec ed, esul ing in less sedimen
a ailabili y in he d y po ion o he beach.
In addi ion, he d y season s ood ou o he p esence o wo cold on s in he Ca ib-
bean Sea, incoming om he Yuca an Peninsula, which caused changes in wind speed and
di ec ion a ec ing he Wes e n Ca ibbean Sea, as epo ed by he CIOH [41]. I was es ab-
lished ha he combina ion o me eo ological and ma ine ene gy condi ions du ing he
ansi ion om wo clima ic seasons a ec ed he beach mo phology.
Figu e 7.
Topog aphy p o iles and daily olume changes o he Boca ocino Beach, (
a
) Topog aphic
p o iles measu ed o he we and d y seasons. (
b
) Daily olume ic changes o he d y beach o he
we season (le side) and d y season ( igh side).
On No embe 1 and 4, 2018, he highes pa o he d y beach (~1.5 m M.L.W.S)
was ela i ely la in all p o iles, bu a ound 12 m slopes di e ed om each o he . On
No embe 1, he maximum slope o P1, loca ed a app oxima ely 14 m, was 13.5
◦
, whe eas
P2 ea u ed a slope o 9.9
◦
a app oxima ely 28 m. P3 and P4 displayed a simila mo phology,
wi h a maximum slope o 8.4
◦
a 19 m. On No embe 4, P1 showed a slope o 13.5
◦
a
app oxima ely 17 m. P o ile P4 ea u ed a slope o 11
◦
a 9 m, hen an almos la slope
up o 21 m, ollowed by a gen le slope o 6.2
◦
. In gene al e ms, no signi ican di e ences
we e obse ed be ween p o iles P1 and P2, whe eas P3 and P4 showed a wide coas al
s ipe in which geo o ms (such as ba s and/o be ms) a e p esen on he highes pa o he
d y beach. This may be explained by he inc ease in long-sho e cu en s, p edominan ly
J. Ma . Sci. Eng. 2024,12, 1141 18 o 30
di ec ed owa ds he eas , which would anspo sedimen om P2 o p o iles P3 and P4.
Figu e 8b shows an inc ease in beach olume o 2.3 m
3
/m (acc e ion) be ween No embe 1
and 4. This inc ease is po en ially associa ed wi h sedimen in e change among suspended
pa icles nea he coas (Figu e 3 ) and he acc e ion zone loca ed nea W3 (Figu e 3g).
J. Ma . Sci. Eng. 2024, 12, 1141 18 o 29
Figu e 8. PCA biplo be ween SSC and hyd odynamic o cing ac o s: 𝐻
,
, 𝐻
,
, c oss-sho e
and alongsho e cu en s, wa e s eepness, sea le el, o we season: (a) inne su zone, (b) nea he
swash zone, and o d y season: (c) inne su zone, and (d) nea he swash zone.
3.4. Physical Fac o s Con olling Suspended Sedimen T anspo Using PCA
A PCA (p incipal componen analysis) was applied o in es iga e he hyd odynamic-
mo phological in e ac ions in a mic o idal in e media e-dissipa i e beach unde low o
mode a e wa e ene gy condi ions. The PCA esul s we e illus a ed in a wo-dimensional
biplo g aph. In his g aph, he axes (p incipal componen s) a e linea combina ions o he
o iginal a iables, explaining mos o he a iabili y [58]. Va iables wi h di e en con i-
bu ions o a gi en p incipal componen end o occupy opposing a eas in he plane. Figu e
8 shows he i s wo p incipal componen s o he PCA be ween SSC and hyd odynamic
a iables such as SS-wa e heigh , IG-wa e heigh (𝐻,,𝐻,), c oss-sho e cu en s,
alongsho e cu en s, sea le el, and wa e s eepness. PCA co ela ion coe icien s a e lis ed
in Table 3. In his s udy, co ela ions abo e 0.45 we e deemed ele an . The i s p incipal
componen accoun s o 11–12% o he a iance be ween he su and swash zones and
15–16% nea he swash zone. The second p incipal componen accoun s o 11–14% o he
a iance be ween he su zone and nea he swash zone and 12–14% nea he swash zone.
Figu e 8.
PCA biplo be ween SSC and hyd odynamic o cing ac o s:
Hmo,G
,
Hmo,IG
, c oss-sho e
and alongsho e cu en s, wa e s eepness, sea le el, o we season: (
a
) inne su zone, (
b
) nea he
swash zone, and o d y season: (c) inne su zone, and (d) nea he swash zone.
On 24 and 25 Ma ch 2019, all ou p o iles main ained a simila opog aphy, almos la
up o 5 m. The subae ial beach did no show signi ican mo phological changes, as c oss-
sho e hyd odynamic o ces emained cons an in his measu emen pe iod (Figu e 3c,d).
On 24 Ma ch, p o iles P1, P3, and P4 exhibi ed a simila opog aphy, wi h wo p onounced
slopes, one o 29.5
◦
a 9 m, and a maximum slope o 14.4
◦
a 12 m. P2 showed a maximum
slope o 10.7
◦
a 18 m. On 25 Ma ch, P3 and P4 exhibi ed a maximum slope o 14.7
◦
a 9
and 8.5 m, espec i ely. Figu e 8b shows a dec ease o 1.7 m
3
/m (e osion) be ween 24 and
25 Ma ch. In Boca ocino Beach, ba s we e s eepe on 24 Ma ch, la ening and mig a ing
owa ds he coas on 25 Ma ch. The esul s he ein desc ibed a e consis en wi h subme ged
ba mo emen and c oss-sho e cu en di ec ions, bo h p edominan ly o ien ed onsho e
du ing he we season. The e o e, sedimen a ailabili y will be g ea e in he d y po ion
o he beach. On he o he hand, du ing he d y season, subme ged ba mo emen and
c oss-sho e cu en s we e o sho e-di ec ed, esul ing in less sedimen a ailabili y in he
d y po ion o he beach.
J. Ma . Sci. Eng. 2024,12, 1141 19 o 30
In addi ion, he d y season s ood ou o he p esence o wo cold on s in he
Ca ibbean Sea, incoming om he Yuca an Peninsula, which caused changes in wind
speed and di ec ion a ec ing he Wes e n Ca ibbean Sea, as epo ed by he CIOH [
41
].
I was es ablished ha he combina ion o me eo ological and ma ine ene gy condi ions
du ing he ansi ion om wo clima ic seasons a ec ed he beach mo phology.
3.4. Physical Fac o s Con olling Suspended Sedimen T anspo Using PCA
A PCA (p incipal componen analysis) was applied o in es iga e he hyd odynamic-
mo phological in e ac ions in a mic o idal in e media e-dissipa i e beach unde low o
mode a e wa e ene gy condi ions. The PCA esul s we e illus a ed in a wo-dimensional
biplo g aph. In his g aph, he axes (p incipal componen s) a e linea combina ions o he
o iginal a iables, explaining mos o he a iabili y [
58
]. Va iables wi h di e en con ibu-
ions o a gi en p incipal componen end o occupy opposing a eas in he plane. Figu e 8
shows he i s wo p incipal componen s o he PCA be ween SSC and hyd odynamic
a iables such as SS-wa e heigh , IG-wa e heigh (
Hmo,SS
,
Hmo,IG
), c oss-sho e cu en s,
alongsho e cu en s, sea le el, and wa e s eepness. PCA co ela ion coe icien s a e lis ed
in Table 3. In his s udy, co ela ions abo e 0.45 we e deemed ele an . The i s p incipal
componen accoun s o 11–12% o he a iance be ween he su and swash zones and
15–16% nea he swash zone. The second p incipal componen accoun s o 11–14% o he
a iance be ween he su zone and nea he swash zone and 12–14% nea he swash zone.
Table 3.
Co ela ions be ween
HmoG
,
HmoIG
, c oss-sho e and alongsho e cu en s, wa e s eepness,
sea le el, and SSC-es ima ed o bo h clima ic seasons a wo coas al zones ( i s : inne su zone, and
second: nea he swash zone). The highe co ela ions we e om 0.45.
Season/Coas al
Zone We /Inne Su Zone We /Nea he Swash Zone D y/Inne Su Zone D y/Nea he Swash Zone
1s P incipal
Componen
2nd
P incipal
Componen
1s P incipal
Componen
2nd
P incipal
Componen
1s P incipal
Componen
2nd
P incipal
Componen
1s P incipal
Componen
2nd
P incipal
Componen
Hmo,G0.52 0.3 0.52 0.17 0.01 0.79 0.36 0.55
Hmo,IG 0.36 −0.23 0.08 0.54 0.47 0.15 0.58 0.16
Sea le el 0.53 0.29 0.52 0.22 0.48 0.18 0.25 0.19
Wa e
s eepness 0.49 −0.2 0.49 0.13 −0.4 0.32 −0.24 0.51
C oss-sho e
cu en s 0.07 0.51 0.29 −0.52 0.36 −0.35 −0.5 0.36
Alongsho e
cu en s −0.19 0.27 −0.21 −0.1 −0.34 0.06 0.43 −0.17
SSC −0.19 0.63 −0.3 0.57 0.41 0.28 −0.07 −0.48
Va iance 11% 11% 12% 14% 15% 12% 16% 14%
Figu e 8a shows he esul s o he PCA du ing he we season, which indica e a close
ela ionship be ween c oss-sho e cu en s ( = 0.51) and SSC ( = 0.63), be ween he su
zone and nea he swash zone. The e o e, when c oss-sho e cu en s a e mo e in ense, he
supply o suspended sedimen s will be highes , bu SSC will be lowe when c oss-sho e
cu en s a e weake . The i s componen showed a posi i e co ela ion be ween
Hmo,ss
(
= 0.52
), and sea le el ( = 0.53), and g a i y ene gy modula ion due o ides. On he o he
hand, Figu e 8b shows a nega i e co ela ion be ween c oss-sho e cu en s ( =
−
0.52) and
SSC ( = 0.57) nea he swash zone. This can be explained because c oss-sho e cu en s
we e o sho e-di ec ed nea he swash zone. The e o e, less suspended sedimen will be
a ailable owa ds he coas (Figu e 3d, ). In addi ion, ele an posi i e co ela ions wi h
Hmo,IG
( = 0.54) and SSC ( = 0.57) we e ound, allowing us o in e ha a high
Hmo,IG
could
inc ease SSC o ice e sa. This indica es ha SSC was p edominan ly wa e-in luenced
(see Figu e 3c, ). SSC was no co ela ed wi h o he hyd odynamic o cing ac o s (
Hmo,SS
,
sea le el, wa e s eepness, and alongsho e cu en s).
J. Ma . Sci. Eng. 2024,12, 1141 20 o 30
Figu e 8c ep esen s he esul s o he PCA o he d y season. The i s componen
indica es a weak co ela ion be ween Hmo,IG ( = 0.47) and sea le el ( = 0.48) be ween he
su zone and nea he swash zone. Howe e , he e was no highe co ela ion be ween
SSC and hyd odynamic o ces. The i s p incipal componen indica ed a s ong nega i e
co ela ion be ween c oss-sho e cu en s ( =
−
0.50) and
Hmo,IG ( = 0.58
) nea he swash
zone. This can be co obo a ed by he obse a ion o cu en s being s onge nea he swash
zone when
Hmo,IG
alues we e lowes , and ice e sa (Figu e 3c,d). A he same ime,
Figu e 8d shows a less nega i e co ela ion be ween
Hmo,SS
( = 0.55) and SSC (
= −0.48
)
in he second p incipal componen . The i s and second p incipal componen s con i med
a s ong co ela ion be ween Hmo,SS, and wa e s eepness.
PCA esul s show ha , du ing he we season, SSC and c oss-sho e cu en s a e
s ongly co ela ed o he second p incipal componen . Fo he d y season, a less posi i e
co ela ion was ound be ween c oss-sho e cu en s ( = 0.36) and SSC ( = 0.41) wi hin he
su and wash zones, as well as a less nega i e co ela ion be ween c oss-sho e cu en s
( = 0.36) and SSC ( =
−
0.48) nea he swash zone. The e o e, a low co ela ion be ween
alongsho e cu en s and SSC can be con i med o he s udied beach.
4. Discussion
Hyd odynamic a iables (SS- and IG-wa es, c oss-sho e and alongsho e cu en s, and
wa e s eepness), oge he wi h pa e ns o sedimen dynamics (c oss-sho e and alongsho e
sedimen anspo , o ma ion and mig a ion o subme ged ba s, iden i ica ion o e osion
and acc e ion zones, and nea sho e olume changes), a e u he discussed o analyze he
ela ionships be ween hyd odynamic o ces and beach mo phology du ing d y and we
seasons.
4.1. Implica ions o Indi ec SSC Es ima es o Suspended Sedimen T anspo
Despi e he es ima ion me hod used (OBS o ABS), he SSC ime se ies ollowed
iden ical ends (Figu e A1e). E en hough he e a e some di e ences be ween measu ed
and es ima ed sedimen concen a ions, hese esul s a e accep able and indica e ha he
use o ABS is a eliable me hod o es ima es o SSC and, he e o e, o he es ima ion
o ne suspended sedimen anspo . I mus be aken in o accoun ha quan i ying ne
sedimen anspo emains a di icul ask, gi en ha eliable and p ecise measu emen s
o sedimen anspo a es a e essen ial o unde s anding he mo phological changes
o he beach. Se e al ac o s may explain he sligh di e ences ound be ween bo h SSC
es ima ion me hods. Acous ic senso s a e gene ally sensi i e o pa icle cha ac e is ics,
such as size and shape [
59
]. Fo example, hese senso s a e unable o de ec pa icles
smalle han he wa eleng h o he acous ic pulse, which in u n depends on he ype o
ins umen employed. P e ious wo ks indica e ha op ic senso s a e mo e sensi i e o
clay pa icles [
60
], whe eas acous ic ins umen s a e mo e sensi i e o sand. In his s udy,
o e es ima es we e ound o be ela ed o he acous ic senso , in ag eemen wi h [
61
], who
ound ha acous ic senso s migh o e es ima e sedimen concen a ions on sandy beaches
unde u bulence condi ions. I is wo h men ioning ha , in his wo k, measu emen s we e
aken be ween he su and nea he swash zone in he con ex o ex u al p ope ies ypical
o a g a elly sand beach.
Despi e he condi ions unde which ield measu emen s we e ca ied ou (co e ing
he b eakage zone wi h cons an , high u bulence le els), which may a ec senso da a [
62
],
oge he wi h he ime and cos in ol ed, he esul s o his wo k indica ed a good le el
o co ela ion. Di e en imp o emen s ha e been de eloped o he ABS me hod. An
addi ional calib a ion was applied o his p oblem [
63
], yielding an SSC es ima e ha
emained unal e ed wi hin u bulen , small-scale eddies ( ollowing he Kolmogo o scale).
A e iew and upda e o he equa ions and concep s p esen ed by [
33
] was made by [
28
],
in o de o p o ide in o ma ion necessa y o i s use in newe de ices. E en hough he
ABS me hod was o iginally applied only o es ua y, bay, and i e se ings [
29
,
30
,
63
], i has
also been used in s udies o coas al zones, such as high- u bulence beaches. Fo example, i
J. Ma . Sci. Eng. 2024,12, 1141 21 o 30
employed he ABS me hod and ob ained a easonably good co ela ion be ween acous ic
and op ic backsca e ing es ima es o SSC o a e lec i e beach in s o m and non-s o m
condi ions [5].
4.2. The Role o C oss-Sho e Cu en s in Suspended Sedimen T anspo
The PCA e ealed ha c oss-sho e cu en s p e ailed o e alongsho e cu en s, as was
he case o sedimen anspo , in bo h clima ic seasons. In addi ion, i was ound ha SSC
and c oss-sho e cu en alues we e highes nea sho e. So, his is a p edominan ly c oss-
sho e-domina ed sys em due o beach o ien a ion (WE/EW, i.e., pa allel o he coas line)
playing an impo an ole in sedimen anspo , p obably whe e inciden wa es ha
a i ed pe pendicula ly o he coas , wi hou oblique incidence, mos o he ime. In
hese condi ions, he wa e on is pa allel o he beach, esul ing in cu en s and sedimen
anspo ha a e p edominan ly c oss-sho e-o ien ed. Simila esul s we e discussed
by [
64
], who showed ha sedimen anspo has an impo an ole as a d i e o beach
e olu ion p ocesses such as sho eline shi s and ba mig a ion. This s udy ound a pa icula
beha io in he we season ela i e o changes in he di ec ion o c oss-sho e cu en s,
depending on wa e condi ions. This beha io is consis en wi h he obse ed di ec ion o
c oss-sho e sedimen anspo (Figu e 6b). When alues o o sho e wa e heigh and peak
pe iod (
HsO sho e
and
TpO sho e
) we e a hei lowes , sedimen anspo was also a i s
lowes le el, as obse ed on 3 and 4 No embe 2018. This c oss-sho e sedimen anspo
may be causing he sedimen in e change obse ed be ween he acc e ion zone iden i ied
nea he swash zone (Figu e 3e) and he eme ged po ion o he beach (Figu e 8b).
Sedimen lux did no show a p e ailing di ec ion du ing he we season. This con as s
wi h he g ea e , p edominan ly o sho e lux obse ed in he d y season, caused by he
s ong in ensi y o c oss-sho e cu en s. The e o e, he acc e ion zone obse ed 150 m
away om he coas (Figu e 3g, igh ) may esul om c oss-sho e sedimen anspo
owa ds he sea in he su zone (Figu e 3d, igh ). A he same ime, e osion in he d y
beach a ea (Figu e 8, igh ) may be due o s ong c oss-sho e cu en s di ec ed owa ds he
sea, nea he swash zone. These indings highligh he possible ole o unde ow cu en s
in anspo ing sedimen om he d y beach a ea o he sea. The esul s a e consis en
wi h [
65
], who a ibu ed o sho e sedimen lux o unde ow (unde cu en ) ex ending
beyond he b eakage zone. This wo k is also consis en wi h p e ious esea ch epo ing
s onge unde ow cu en s on s eep beaches han on gen le ones [
66
]. Howe e , sedimen
anspo a Boca ocino Beach was p edominan ly o sho e, wi h highe in ensi y du ing
he d y season, when he beach p o ile was mos ly dissipa i e. The esul s o his esea ch
indica e ha onsho e and o sho e sand mig a ion (Figu e 3g) was caused by c oss-sho e
anspo , oge he wi h nea sho e sedimen s in suspension due o he combined ac ion o
ides, winds, wa es, and cu en s. In gene al e ms, his esea ch allowed us o obse e
how suspended sedimen anspo esponded and in e ac ed wi h (1) high- equency
wa es, (2) low- equency wa es, and (3) unde ow cu en s.
4.3. Con ibu ion o SS and IG Wa e Ene gy o Suspended Sedimen T anspo
E en hough wa es a e no he main mechanism o sedimen anspo on he s udy
beach, he esul s o his wo k e eal hei impo an ole in seabed mo phology. An ene gy
ans e om high o low equencies was obse ed when wa es we e mo ing onsho e
and we e dis u bed by he seabed un il hey b oke (Figu es 3b and 5c). In his ega d,
Re . [
13
] ound ha , in he subae ial beach, c oss-sho e sedimen anspo is media ed
by he equilib ium be ween he e ec o oscilla o y wa e mo emen and ha o middle
cu en s. This esea ch assessed he ole o oscilla o y lux (due o SS-wa e and IG-wa e)
and i s e ec on mo phological changes expe ienced by Boca ocino Beach.
SS-wa e ene gy was g ea e in he ou e su zone han nea he swash zone. Howe e ,
SS-wa es showed he opposi e beha io in bo h clima e seasons. In a simila way, du ing
he d y season, c oss-sho e
qG
was signi ican ly highe in he inne su zone, dec easing
nea he swash zone. These obse a ions a e consis en wi h p e ious wo ks [
39
,
67
], which

J. Ma . Sci. Eng. 2024,12, 1141 22 o 30
indica e ha SS-wa es migh be he mos impo an componen o sedimen anspo
in he su zone and nea he swash zone, whe e he pe cen age o b oken wa es was
highe . C oss-sho e
qIG
was highe in he su zone (wi h a lowe b eak wa e pe cen age)
han nea he swash zone (wi h a highe pe cen age). These indings ag ee wi h p e ious
wo ks [
68
,
69
], epo ing ha IG-wa e anspo is lowe wi h mode a e wa es han unde
high ene gy condi ions. Nea sho e IG-wa es ound in his wo k lie wi hin he Leaky
In ag a i y Wa e ca ego y. In some cases, his ype o wa e may inc ease unde ow
cu en s in he su zone [
70
,
71
]. In his s udy, he g ea es unde ow in ensi ies occu ed
in he d y season, when a smalle ex en o beach a ea was p esen . Howe e , i is no
possible o in e ha Leaky IG Wa es caused he e osion obse ed on he beach du ing he
ansi ion be ween one clima e season and he nex . This in e p e a ion canno be o ally
disca ded, howe e , due o he epo ed an eceden s, pa icula ly in a well-di e en ia ed
e osion zone (Figu e 8, igh ) on Boca ocino Beach.
The p esence o an acc e ion zone (Figu e 8, le ) may be due o a g ea e a ailabili y
o sedimen nea he swash zone du ing he we season, wi h ou s anding onsho e cu en
in ensi ies. On i s pa , he esul s indica e he dependence o SSC on wa e ene gy, allowing
us o in e ha SS-wa es a e ypically ac ing as agen s o sedimen agi a ion, whe eas
cu en s play a ole in anspo . Rega ding anspo and wa e ene gy, he esul s o
his wo k a e consis en wi h p e ious esea ch in coas al zones wi h non-b eaking wa e
condi ions (lowe -ene gy wa es). These s udies ound ha anspo p ocesses a e gene ally
di ec ed landwa d, a pa e n ha esul s in acc e ion p ocesses on he beach. On he o he
hand, du ing high ene gy condi ions wi h a high pe cen age o b oken wa es (e.g., s o m
cycles), he beach and coas al dune zone a e s ongly a ec ed by incoming wa es, usually
esul ing in e osion p ocesses [72].
4.4. Rela ionship be ween Wa e S eepness and Beach Mo phological Changes
The ela ionship be ween wa e heigh and wa eleng h, be e known as wa e s eep-
ness, has been adi ionally ecognized as a ac o in luencing beach mo phology [
73
,
74
], a
ela ionship ha has been con i med by la e wo ks [
4
,
75
]. Wa e s eepness could hus be
used o de e mine subme ged ba mig a ion nea sho e and beach mo phological changes
occu ing be ween clima ic seasons. In his way, he in e ac ion be ween nea sho e accu-
mula ed sedimen ( ep esen ed by he acc e ion zone ~23 m om he coas ) and sedimen
lux di ec ion (c oss-sho e and onsho e) migh be he esul o signi ican accumula ion
(Figu e 8b)
du ing he we season. Howe e , du ing he d y season, he acc e ion zone
shi ed o a posi ion app oxima ely 150 m away om he coas , wi h a p edominan ly
o sho e lux di ec ion and low a ailabili y o suspended sedimen nea sho e. These
condi ions may ha e led o he c ea ion o a zone o high e osion (Figu e 8, igh ). The
a o emen ioned pa e ns show ha onsho e sedimen anspo was o en obse ed when
wa e s eepness was less, whe eas sedimen was anspo ed o sho e in high wa e s eep-
ness condi ions [
4
]. This ela ionship was u he e i ied h ough PCA esul s, which
highligh ed he ela ionship be ween wa e s eepness and signi ican wa e heigh . The
PCA shows ha , o bo h clima e seasons, wa e s eepness inc eases wi h wa e heigh .
This inding emphasizes he impo ance o wa e inclina ion as a pa ame e o dis inguish
e osion and acc e ion zones on a beach [
58
,
76
,
77
]. A limi be ween e osion and acc e ion
o 0.01 was employed by [
77
] on a ine g a el beach a Slap on Sands (Uni ed Kingdom).
On he o he hand, [
57
] conside ed wa e inclina ion alues below 0.01 as indica i e o
no mal beha io wi h acc e ion and abo e 0.01 as an indica o o e osi e beha io in a
mac o idal beach a Ma iake ke, Belgium. In summa y, e en hough wa e s eepness is
an accep able p oxy o he iden i ica ion o wa e asymme y and he di ec ion o luid
mo emen [
78
], p e ious esea ch ecommends exe cising cau ion when using his c i e ion
o sandy beaches [79].
J. Ma . Sci. Eng. 2024,12, 1141 23 o 30
4.5. In e ac ions be ween Suspended Sedimen T anspo and Mo phological Changes on he
Nea sho e Subae ial Beach
C oss-sho e sedimen anspo is conside ed a d i ing ac o in beach opog aphical
change [
13
,
80
]. This was e i ied by his wo k, as c oss-sho e sedimen anspo was
signi ican ly g ea e han alongsho e anspo be ween he su zone and nea he swash
zone. Mo phological changes we e desc ibed in e ms o daily a ia ions in beach olume
o each clima e season. In he we season, sedimen anspo was p edominan ly onsho e
when wa e condi ions we e gen le (maximum
Hm0
= 1 m and maximum Tp = 8.6 s). In
con as , du ing he d y season, sedimen was anspo ed onsho e when wa e condi ions
we e s ong (maximum
Hm0
= 1.2 m and maximum Tp = 8.6 s). These esul s indica e a
seasonal pa e n, wi h beach olumes g ea e du ing he we season and smalle du ing
he d y season. O he au ho s ha e also ela ed e osi e e en s o s ong wa e condi ions
and acc e ion e en s o mode a e wa e condi ions [
81
]. Likewise, sedimen anspo on
he subme ged beach was analyzed h ough mig a ing ba s, e ealing ha subme ged ba s
mo ed onsho e in mode a e wa e condi ions. Sandbank mig a ion unde s ong wa e
condi ions has been p oposed by p e ious s udies [
82
]. The sedimen anspo epo ed in
his s udy ( o cing e osion and acc e ion in he d y pa o he beach), oge he wi h he
mig a ion o subme ged ba s, a e consis en wi h p e ious assessmen s o he ela ionship
be ween mo phodynamic cycles and wa e ene gy condi ions in mic o idal and meso idal
sand beaches [81,83,84].
Rega ding sedimen ex u al ea u es, ine sedimen s mo ed o sho e in he su zone,
whe eas coa se sedimen s we e ound in he su zone and nea he swash zone. The same
pa e n was obse ed by [
85
], who ound an onsho e anspo end o coa se sedimen s,
whe eas ine sedimen s mo ed o sho e.
5. Conclusions
The ela ionship be ween hyd odynamic o cing, suspended sedimen anspo , and
he in e media e-dissipa i e mic o idal beach mo phology was analyzed using in si u
measu emen s du ing he d y and we seasons. Hyd odynamic d i e s (wa es, ides, and
cu en s) we e cha ac e ized, and he esponse o opog aphical p o iles o hese d i e s
was analyzed bo h o he subme ged and eme ged beaches. The esul s show ha c oss-
sho e cu en s a e he p e ailing hyd odynamic o ces in nea sho e sedimen anspo .
These cu en s o ced he mig a ion o a subme ged ba du ing he ansi ion be ween he
we and d y seasons. The accumula ion o he subme ged ba in ensi ied du ing he we
season when he wa e heigh in ensi ies we e lowe , con a y o wha was obse ed du ing
he d y season.
The ABS me hod o indi ec es ima ion o suspended sedimen anspo o he
mic o idal in e media e-dissipa i e beach allowed o easonably good esul s, conside -
ing ha measu emen s we e ca ied ou be ween he su zone and nea he swash zone.
Howe e , cau ion mus be exe cised when using op ical o acous ic equipmen o es ima e
sedimen concen a ions. Such measu emen s may lead o signi ican o e es ima es o
unde es ima es o sedimen anspo , due o ins umen sensi i i y o di e en g ain sizes.
I should no be le aside ha acous ic measu emen s may be a ec ed by u bulence. Ne -
e heless, co ec ing hese pa ame e s should signi ican ly imp o e hese measu emen s,
pa icula ly hose ob ained wi h acous ic backsca e ing.
On he subae ial beach o he d y beach, daily changes in sedimen supply we e
s ongly co ela ed o wa e ene gy and cu en di ec ions nea sho e. SS-wa es and c oss-
sho e cu en s con ibu ed mainly by anspo ing suspended sedimen s. Du ing he d y
season, s ong c oss-sho e cu en s we e iden i ied, and e osion zones we e di e en ia ed.
On he o he hand, a g ea e amoun o deposi ed sedimen was e iden when IG-wa e
heigh s, SS-wa e heigh s, and c oss-sho e cu en s we e lowe . High IG wa e ene gy
(in ensi ied om he inne su zone) may cause sedimen agi a ion in his zone, which is
accen ua ed du ing he we season.
J. Ma . Sci. Eng. 2024,12, 1141 24 o 30
Wa e condi ions du ing he d y season we e e y s ong, leading o a mo e p o-
nounced esponse in beach mo phology. Howe e , mo phology a ia ions in a mic o idal
in e media e-dissipa i e beach depend no only on wa e condi ions bu also on cu en s
and SSC. The e o e, cu en s, SSC, and wa es a e d i ing ac o s o nea sho e sedimen
supply in luencing daily opog aphical change. As a esul , Boca ocino Beach, which is
wa e-domina ed, exhibi s daily acc e ion and e osion s a es. Wa e inclina ion was an
impo an indica o o beach e olu ion, pa icula ly ega ding he o ma ion and mig a ion
o subme ged ba s.
The esul s o his s udy explain he mic o idal in e media e-dissipa i e beach mo -
phology. I was ound ha he e was a signi ican acc e ion nea sho e on he subae ial beach
du ing he we season when he e was a g ea e a ailabili y o sedimen s, he SS-wa e
heigh s nea sho e we e lowe , and sedimen lux was di ec ed onsho e. In he d y season,
he opposi e beha io was obse ed, and a no o ious e osion was dis inguished. The
esul s ep esen a signi ican con ibu ion o unde s anding he mo phological beha io
o he beach and i s ela ionship wi h hyd odynamic o ces. The e o e, i mus be aken
in o accoun ha , unlike labo a o y es s unde con olled condi ions, he e is no con ol
o e he en i onmen al a iables p esen in he s udy a ea. Acco ding o he esul s o
his s udy, i is ecommended o use nume ical modeling o es ima e beach e olu ion and
coas al anspo in he middle and long e m (mon hs o yea s). This s udy es ablishes
a baseline o u u e coas al geomo phology esea ch, con ibu ing o he unde s anding
o he hyd odynamic-mo phological in e ac ions in a mic o idal in e media e-dissipa i e
beach unde low o mode a e wa e ene gy condi ions.
Au ho Con ibu ions:
Concep ualiza ion, A.M.G.; Me hodology, A.M.G., L.O., S.O. and J.C.; So -
wa e, A.M.G.; Valida ion, A.M.G.; Fo mal analysis, A.M.G.; In es iga ion, A.M.G.; W i ing—o iginal
d a , A.M.G.; W i ing— e iew & edi ing, A.M.G. and L.O. All au ho s ha e ead and ag eed o he
published e sion o he manusc ip .
Funding:
The au ho s hank he Minis e io de Ciencia Tecnología e Inno ación o he inancial suppo .
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen :
The da a p esen ed in his s udy a e a ailable on eques om he
co esponding au ho .
Acknowledgmen s:
The au ho s hank he Coas al Enginee ing and P ocesses Labo a o y o Sisal
Academic Uni —UNAM o i s acili ies and suppo . The au ho s hank Alec To es F eye mu h
o he Coas al Enginee ing and P ocesses Labo a o y, Uni e sidad Nacional Au ónoma de México
(UNAM), Pue o de Ab igo s/n, Sisal, Yuca án.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Appendix A
The ADCP analysis o SSC es ima es equi es calib a ion da a ob ained h ough di ec
SSC measu emen s. Bo h he D2 cu en me e and he OBS u bidi y senso we e used o
his pu pose, as bo h ins umen s we e cap u ed in a ime-synch onized manne . Figu e A1
illus a es he me hods employed o deduce sedimen concen a ion om acous ic echo
in ensi y da a ob ained wi h he D2 cu en me e . Figu e A1a shows he D2 senso dep h-
ime se ies, oge he wi h he ide cycle (6 h) o which he ABS me hod calib a ion was
made. The ime se ies o acous ic echo in ensi y o senso D2 (in coun s) e sus SSC
es ima es om he OBS (in mg/L) a e shown in Figu e A1b. Figu e A1c ep esen s he SSC
empi ic model de i ed om OBS and acous ic echo in ensi y om senso D2. Figu e A1d
is a sca e plo be ween OBS-de i ed and D2-de i ed SSC o a ide cycle a a a e o 60 s.
The ela ionship be ween suspended sedimen concen a ions (SSC) ob ained wi h he D2
senso (mg/L) and di ec sampling using OBS (mg/L) om 23 o 25 Ma ch 2019, a e aged
a a a e o 1 h, is shown in Figu e A1 .
J. Ma . Sci. Eng. 2024,12, 1141 25 o 30
Equa ion (5) was spli in o h ee s eps. In he i s e m, e e ence alues o
LDBM =
2.23,
C=−
129.5, and
PDBW =
12.6 we e used ollowing [
33
]. To es ablish he second e m, he
ange along he beam was ob ained om ADCP No ek,
R=
0.52
m
(in ag eemen wi h
he manu ac u e ’s ins uc ions). To de ine he acous ic abso p ion coe icien
∝
, e e ence
alues o
S=
35 pp ,
h=
2.1
m
,
TTD =
29.5
◦C
, and
=
2
MHz
we e used. Rega ding he
elaxing equencies o wo main compounds in seawa e , alues o 1=2.4 and 2=238
we e de e mined o Bo ic acid and Magnesium Sul a e, espec i ely.
In o de o es ablish he hi d e m, a scaling ac o
Kc
o 0.42
coun s/dB
was calcula ed
using he Equa ion (7) and a
TTD =
29.5
◦C
. This alue is consis en wi h he
Kc
anges
be ween 0.40 and 0.47, which we e epo ed by [
86
,
87
]. This alue was de e mined aking
in o accoun ha all cu en me e sys ems a e om he same manu ac u e (No ek),
he e o e using he same amily o componen s o measu ing echo ampli ude [
88
]. The
ela ionship be ween echo in ensi y om ABS (dB) and SSC de i ed om OBS (mg/L) was
ob ained om simple linea eg ession analysis (Figu e A1c):
SSCOBS =101.227 ∗ABS (in dB)−441.8 (A1)
I is wo h highligh ing ha in e nal coun uni s can be linea ly ans o med o dB in a
ange o 70 dB wi h an app oxima e p ecision o 1–2 dB [
30
]. In his s udy, backsca e ing
alues om he h ee beams we e a e aged, as he exac o ien a ion o Aquadopp ela i e
o he OBS senso is unknown.
The senso D2 unde es ima ed mos OBS alues (Figu e A1e). The model ob ained
o SSC calib a ion was signi ican a
R2=
o 0.69, wi h a Willmo coe icien o 0.75,
and an RMSE o 8.5. These esul s could be a ibu ed o he cha ac e is ics o suspended
sedimen pa icles, such as size, shape, and colo , which may a ec measu emen s aken
wi h he acous ic senso [
59
,
60
]. Howe e , he esul s a e a sa is ac o y p oxy o SSC
when no enough u bidi y ins umen s a e a ailable in he ield, pa icula ly conside ing
ha acous ic senso s may be sensi i e o u bulence [
63
]. When using his model wi h
oceanog aphic pa ame e s o
TTD =
29.5
◦C
and S = 35, he alues o SSC in he s udy a ea
anged om 90 o 150 mg/L, dis ibu ed om he su ace o he seabed.
J. Ma . Sci. Eng. 2024, 12, 1141 25 o 29
pa ame e s o 𝑇 =29.5 °C and S = 35, he alues o SSC in he s udy a ea anged om 90
o 150 mg/L, dis ibu ed om he su ace o he seabed.
Figu e A1. ABS me hod o con e ing acous ic in ensi y om ADCP (D2 senso ) o SSC. (a) Dep h-
ime se ies measu ed o he D2 senso ; he idal cycle ( low) used o he calib a ion o he ABS
me hod was plo ed as a blue line o e he comple e ime se ies. (b) Echo in ensi y- ime se ies o
he acous ic echo in ensi y o he D2 senso , in coun s (black line and le y-axis) and SSC de i ed
om OBS, in mg/L (blue line and igh y-axis) a a a e o 1 s, (c) Simple linea eg ession analysis
o OBS-de i ed SSC and acous ic echo in ensi y om ADCP. (d) Sca e plo be ween OBS-de i ed
and D2-de i ed SSC. (e) Time se ies o OBS-de i ed SSC (do ed line) and D2 senso -de i ed SSC
(solid line) o a idal cycle (blue line in (a)) a a a e o 1 min. ( ) Time se ies o he 1-h a e age
be ween he OBS-de i ed SSC (dashed line) and D2 senso -de i ed SSC (solid line) om 23 o 26
Ma ch 2019. The me hodology was calib a ed using he OBS and D2 senso s, conside ing ha bo h
senso s we e connec ed o synch onize da a. No e: The Aquadopp P o ile (D2) is a highly e sa ile
Acous ic Dopple Cu en P o ile .
Appendix B
Taking ha in o accoun , he op ical senso exhibi ed highe sensi i i y o small-size
pa icles [19]. Thus, he e he concen a ion olume con e sion (in μL/L) o SSC (in mg/L)
was implemen ed using he LISST-200X senso and he equa ion by [51]:
𝑆𝑆𝐶 󰇡
󰇢=𝑉𝐶󰇡
󰇢∗𝜌󰇡
󰇢∗



∗


 ∗(1−







) (A2)
Equa ion (A2), 𝜌 was es ablished om he a e age sedimen densi y o 2.63
Kg/L aken om he g anulome ic analysis o sedimen samples collec ed, while 𝜌
was es ablished as 1.15 Kg/L acco ding o [89]. 𝑉𝐶 was aken om he measu ed da a o
he LISST-200X senso . Once he SSC alues (in mg/L) we e ob ained, he ABS me hod
was implemen ed using he D4 senso , an Aquadopp P o ile HR, which will allow a
Figu e A1.
ABS me hod o con e ing acous ic in ensi y om ADCP (D2 senso ) o SSC. (
a
) Dep h- ime
se ies measu ed o he D2 senso ; he idal cycle ( low) used o he calib a ion o he ABS me hod was