J. Ma . Sci. Eng. 2015, 3, 745-771; doi:10.3390/jmse3030745
Jou nal o
Ma ine Science
and Enginee ing
ISSN 2077-1312
www.mdpi.com/jou nal/jmse
A icle
A Nume ical Modelling S udy on he Po en ial Role o Tsunamis
in he Biblical Exodus
José M. Ab il † and Raúl Pe iáñez †,*
Depa amen o de Física Aplicada I, ETSIA, Uni e sidad de Se illa, Ca e e a de U e a km 1,
D.P. 41013 Se ille, Spain; E-Mail: jmab [email protected]
† These au ho s con ibu ed equally o his wo k.
* Au ho o whom co espondence should be add essed; E-Mail: pe [email protected];
Tel.: +34-954-486474; Fax: +34-954-486436.
Academic Edi o s: Valen in Helle and Billy Edge
Recei ed: 1 June 2015 / Accep ed: 13 July 2015 / Published: 28 July 2015
Abs ac : The eliabili y o he na a i e o he Biblical Exodus has been subjec o hea ed
deba e o decades. Recen a chaeological s udies seem o p o ide new insigh o he exodus
pa h, and al hough wi h a s ill con o e sial ch onology, he e ec s o he Minoan San o ini
e up ion ha e been p oposed as a likely explana ion o he biblical plagues. Pa icula ly, i
has been sugges ed ha looding by he associa ed sunamis could explain he i s plague
and he sea pa ing. Recen modelling s udies ha e shown ha San o ini’s sunami e ec s
we e negligible in he eas e n Nile Del a, bu he eleased ec onic s ess could ha e igge ed
local sunamigenic sou ces in sequence. This pape is aimed o a quan i a i e assessmen o
he po en ial ole o sunamis in he biblical pa ing o he sea. Se e al “bes case” scena ios
a e es ed h ough he applica ion o a nume ical model o sunami p opaga ion ha has
been p e iously alida ed. The o me paleogeog aphic condi ions o he eas e n Nile Del a
ha e been implemen ed based upon ecen geological s udies; and se e al easible local
sou ces o sunamis a e p oposed. Tsunamis igge ed by subma ine landslides o 10–30 km3
could ha e se e ely impac ed he no he n Sinai and sou he n Le an ine coas s bu wi h
weak e ec s in he eas e n Nile Del a coas line. The lack o no iceable looding in his a ea unde
he mos a o able condi ions o sunamis, along wi h he ime sequence o wa e ele a ions,
OPEN ACCESS
J. Ma . Sci. Eng. 2015, 3 746
make di icul o accep hem as a plausible and li e ally explana ion o he i s plague and o
he d owning o he Egyp ian a my in he su oundings o he o me Shi-Ho Lagoon.
Keywo ds: Biblical Exodus; sunamis; nume ical modelling; sea pa ing; Reed Sea
1. In oduc ion
The Minoan e up ion o The a (San o ini), da ed a ound 1613 BC, was one o he la ges Plinian
e up ions on ea h in he pas 10,000 yea s [1]. S anley and Sheng (1986) [2] epo ed he e idence o
he p esence o ash ejec ed om his e up ion in sedimen co es om he eas e n Nile Del a, and hey
sugges ed ha i could be associa ed wi h he Exodus plague o da kness. The connec ion be ween his
ex eme olcanic e en and he biblical plagues p eceding he Exodus, has been la gely a gued in he
scien i ic li e a u e [3–7].
Recen a chaeological indings [8,9] p o ide new insigh on he Exodus ou e and on he loca ion o he
sea c ossing. Thus, he si e o Migdol (Exodus 14:2; see Figu e 1) would equa e one o he mili a y
o esses in he Ho us Way, placed in he sho eline o he Shi-Ho , a paleo-lagoon opened o he
Medi e anean Sea. The wa e -body ha he Is aeli es c ossed when lea ing Egyp , called yam suph, he
Sea o Reeds, should ha e been a la ge body o wa e in he a ea o Migdol. Ne e heless, he abo e
scena io would co espond o he con ex o wo cen u ies a e he Minoan San o ini e up ion. Indeed,
he ch onology o he biblical Exodus has been a ma e o con o e sial [10] (see o example he e iew
by Si e sen, 2009 [4]). This las au ho p oposes ha he e a e wo dis inc episodes ha me ged in a
single na a i e: he exodus- ligh (a g oup o wes e n Semi es lea ing he Wadi Tumila a ea sligh ly
be o e 1600 BC, du ing he Hyksos ule in Egyp ), and he exodus-expulsion (o Is aeli e sla es du ing
he co- ule ship o Tu hmossis III and Amenophis II, abou 1450 BC).
Figu e 1. Map o he eas e n Nile Del a and he Suez Canal, including he main geog aphical
e e ences ci ed in he ex . The zoon-box shows he palaeogeog aphical econs uc ion o
he o me sho eline a he second millennium BC a ound he Migdol si e and he Shi Ho
lagoon (a e Ho meie , 2005, [9]).
J. Ma . Sci. Eng. 2015, 3 747
Si e sen (2009) [4] had sugges ed ha he i s plague would ha e been he likely esul o he
Minoan e up ion and i s associa ed sunamis. Acco ding o his au ho , in he exodus- ligh episode
pe sis ing s ong wind condi ions would ha e d ied any o he wo subme ged idges lying sou h o Lake
Timshah, allowing o he sea c ossing, while in he exodus-expulsion, a olcanic e up ion in he a ea o
Yali and Nisy os (eas e n Aegean Sea) would ha e p oduced he sunami ha d owned he Egyp ian
a my a he Shi-Ho Lagoon.
The mode n ee a 29.88° N ex ends abou 10 km unde he Gul o Suez, and i is no o uni o m
dep h. Vol zinge and And oso (2003) [11] published a nume ical model o he d ying o he ee by
s ong winds using a simpli ied ba hyme y o he Gul and a shallow ee wi h a uni o m dep h o 3 m,
ge ing an exposu e ime o 4 h unde winds o 33 m/s. Mo e ecen ly, D ews and Han (2010) [12]
poin ed ou he s ong e ec o a non-uni o m dep h. Thus, hey showed ha a 3 m deep no ch (1 km
leng h) wi hin a ee o 2 m dep h would ha e ne e been exposed unde a wind o 33 m/s. Fu he mo e,
hese modelling exe cises look o s eady-s a e solu ions wi h ypical simula ion imes o he o de o
one day; bu hey omi he idal oscilla ions, which a e up o 1.5 m ange in his a ea [13,14] and a majo
ac o in he in ol ed physical p oblem. Thus, his scena io o he sea c ossing in he exodus- ligh
seems qui e unlikely.
D ews and Han (2010) [12] s udied an al e na i e scena io o a sea pa ing by s ong winds: he Lake
o Tanis, no heas o he Shi-Ho palaeo-lagoon. They used he paleogeog aphic econs uc ions by
Ho meie (2005) [9] in which he Lake o Tanis did no exis and he mou h o he Shi-Ho lagoon ( he
Kedua passage) was connec ed o he open sea. Ins ead, in hei modi ied opog aphy a sand bank
delimi ed he no he n ex ension o Lake Tanis, opened o he sea h ough he na ow Pelusium mou h.
This geome y c i ically con ols he wa e lux o allow a pa ial d ying unde pe sis ing s ong winds.
Despi e o hese hypo he ical and c i ical opog aphic se ings, his scena io does no i well wi h he
exodus pa h and he loca ion o he Egyp ian mili a y o esses [9].
The idea o a sunami p oducing he sea pa ing in he Exodus has been sugges ed by se e al
au ho s [4,15,16], al hough no suppo ed by quan i a i e analysis. I is known ha he Minoan San o ini
e up ion gene a ed sunamis by he en y o py oclas ic lows and by calde a collapse. They le hei
inge p in s, iden i ied h ough sedimen a y deposi s, in mos o he coas lines o he Aegean Sea, SW
Tu key and C e e [17], Cyp us [18], he coas al a ea o Is ael and Gaza [19–21] and eas e n Sicily
[22,23]. While model esul s o hese sunamis a e able o easonably accoun he es ima ed unups in
he Aegean Sea coas s, hey ail o explain he obse ed e ec s in o he a eas (e.g., eas e n Sicily and
Is ael and Gaza coas s); and, pa icula ly, hey p edic negligible e ec s in he eas e n Nile Del a
[17,24,25]. In ac , he Aegean Sea is a semi-enclosed wa e body, and he islands o he Hellenic a c
comp ise a physical ba ie ha dissipa es mos o he sunami ene gy. Mo eo e , he ou e bo de o he
Nile Del a, whe e a sha p d op in wa e dep h occu s, p oduces pa ial e lec ion and ene gy dissipa ion
in he sunami wa es (as i can be seen in he dispe sion pa e n o he Cyp us 1222 ea hquake, modelled
by Pe iáñez and Ab il, 2014a, [25]).
To explain he whole se o sunamigenic deposi s om he San o ini e en , Pe iáñez and Ab il
(2014a) [25] sugges ed a scena io o sequen ial sunamis linked o in ense ec onic s ess elease.
Pa icula ly, a sunami igge ed by a subma ine landslide in he eas e n a ea o he Nile Del a would
ha e been able o gene a e he isoch onous sunamigenic deposi s ound in Is ael and Gaza.
Ne e heless, his does no necessa ily suppo he hypo hesis o sunamis looding la ge a eas in he
J. Ma . Sci. Eng. 2015, 3 748
eas e n Nile Del a, as equi ed in he Si e sen hypo hesis o he i s plague, o in he Jacobo ici and
Came on in e p e a ion o he sea c ossing. A quan i a i e analysis is needed, aking in o accoun he
o me paleogeog aphic condi ions and he po en ial sunamigenic sou ces compa ible wi h he known
geological se ings o he eas e n Nile Del a. This is he aim o he p esen pape , which ies o imp o e
ou insigh on whe he hese ex ao dina y na u al disas e s could had been only a sou ce o inspi a ion
o he Exodus na a i e o hey could ha e con o med eliable scena ios o he sea pa ing and he
d owning o he Egyp ian a my (e.g., he hea ed deba e be ween minimalis and maximalis iewpoin s).
Going u he beyond he p e ious wo k [25], he p esen s udy includes a mo e de ailed
paleogeog aphical econs uc ion o he o me coas line, including he a ge a ea o he Shi-Ho
Lagoon [9]. As po en ial sunamigenic sou ces (Sec ion 2) his wo k conside s subma ine landslides in
he eas e n edge o he s able Nile Del a shel , de ined as la ge as possible wi hin he known cons ains
s a ed by geological s udies. A hypo he ical and sudden colma ion o a b anch o he o me Damie a
canyon has been also conside ed. In he ee cases sensi i i y es s ha e been conduc ed o he o al
olume and he p esc ibed mo ion o he landslide, up o con o m a se o 14 simula ions. Two
sunamigenic scena ios igge ed by geological aul s a e also conside ed along he Pelussium
Mega-Shea line, and he combina ion o wo simul aneous sou ces. This a ie y o sou ces, selec ed as
he “bes cases” o he d owning o he Egyp ian a my in he Shi-Ho a ea, e eal ha due o he physical
se ings o he o me eas e n Nile Del a, mos o he sunami ene gy dissipa es wi hin he s able shel o i
a els ou . The inne sho eline emains only weakly a ec ed by looding (Sec ion 3).
2. Ma e ials and Me hods
2.1. Model Desc ip ion
Nume ical models o sunami p opaga ion a e a ela i ely well es ablished me hodology which has
been widely alida ed agains eco ded da a om his o ical e en s o e he wo ld [26–29]. Fo he
p esen s udy, he selec ed sunami p opaga ion model is based on he 2D dep h-a e aged nonlinea
ba o opic shallow wa e equa ions (see o ins ance Kowalik and Mu y, 1993, [30]):
( ) ( ) 0Hu H
x y
  

  
(1)
22
22
u
u u u u u
u g A
x y x H x y


     
      

      

(2)
22
22
u g u A
x y y H x y


     
      

      

(3)
whe e u and a e he dep h a e aged wa e eloci ies along he x and y axes, h is he dep h o wa e
below he mean sea le el, ζ is he displacemen o he wa e su ace abo e he mean sea le el measu ed
upwa ds, H = h + ζ is he o al wa e dep h, Ω is he Co iolis pa ame e (Ω = 2w·sinλ, whe e w is he
Ea h o a ional angula eloci y and λ is la i ude), g is accele a ion due o g a i y, ρ is a mean alue o
wa e densi y and A is he ho izon al eddy iscosi y. τu and τ a e ic ion s esses which ha e been
w i en in e ms o a quad a ic law:
J. Ma . Sci. Eng. 2015, 3 749
2 2 2 2
;
u
k u u k u        
(4)
whe e k is he bed ic ion coe icien . Essen ially, hese equa ions exp ess mass and momen um
conse a ion. They ha e been w i en in Ca esian coo dina es gi en he ela i ely small model domain.
Ho izon al iscosi y has been se as A = 10 m2/s and he bed ic ion coe icien as k = 0.0025. Good
model esul s when es ima ing wa e ampli udes and unups ha e been ob ained wi h hese alues.
Ac ually, model esul s (ampli udes, unups and wa e a i al imes) ha e been compa ed wi h
obse a ions in p e ious wo ks [28]. Consequen ly, hese alues ha e been e ained in he p esen
applica ion. Mo eo e , he model sensi i i y o he bed ic ion coe icien has been s udied in Pe iáñez
and Ab il (2014b) [31].
S ill wa e s a e used as ini ial condi ions. As bounda y condi ions, wa e low owa ds a d y g id cell is
no allowed, and a g a i y wa e adia ion condi ion is imposed a he open bounda ies [32], which is
implemen ed in an implici o m. Due o he CFL s abili y condi ion [30] ime s ep o model in eg a ion
was ixed as Δ = 2 s.
A lood/d y algo i hm is equi ed since when he sunami eaches he coas new we o d y g id cells
may be gene a ed due o un-up o undown. The nume ical scheme desc ibed in Kamp (2009) [33] and
in Pe iáñez and Ab il (2013) [28] has been adop ed. We g id cells a e de ined as hose wi h a o al wa e
dep h la ge han a h eshold alue ypically se as a ew cen ime e s. D y cells a e de ined as cells whe e
dep h is smalle han he h eshold one. Flooding and d ying is implemen ed in he code ia he
calcula ion o he wa e eloci y no mal o he in e ace be ween we and d y cells. The calcula ion is
pe o med when he p essu e g adien o ce is di ec ed owa ds he d y cell. O he wise eloci y is se o
ze o a his poin . In he case o a non-ze o eloci y, wa e le el in he d y cell will inc ease and he cell
u ns in o a we one once he wa e dep h is la ge han he h eshold dep h, which has been se as 10 cm [28].
All he equa ions a e sol ed using explici ini e di e ence schemes [30] wi h second o de accu acy. In
pa icula , he MSOU (Mono onic Second O de Ups eam) is used o he ad ec i e non-linea e ms
in he momen um equa ions.
Fo sunamis p oduced by ea hquakes in geological aul s, he e ical sea- loo de o ma ion is
conside ed as he ini ial condi ion o he sunami calcula ion, and i is compu ed using he classical
Okada o mulae [34]. Inpu s o his equa ion a e aul plane s ike, ake, dip, slip, loca ion, leng h and
wid h, as well as seismic momen and igidi y. Valida ion and applica ions o his model can be ound
in Pe iáñez and Ab il (2013 [28], 2014a [25], 2014b [31]), and Ab il e al. (2013) [35].
The me hodology o Ha bi z (1992) [36] and Cecioni and Bello i (2010) [37] has been adop ed o
simula e he gene a ion o sunamis by subma ine landslides, along wi h he modi ica ion p o ided by
Pe iáñez and Ab il (2014a) [25] o desc ibe a ying slopes and asymme ic eloci y p o iles. In he i s
s age, he slide can be desc ibed as a solid body whose downslope mo emen locally modi ies he
ba hyme y, esul ing in an almos ins an aneous and equal change in he le el o he o e lapping wa e s,
which p opaga es as g a i y wa es. The adop ed geome y is a box o leng h L, wid h B and maximum
heigh Δh, and wi h an exponen ial smoo hing o e a dis ance S in he on and ea and B/2 on he
lanks (see scheme in Figu e 2). The esul ing olume is V = 0.90B·Δh(L + 0.90S) [36]. As a p ac ical
app oach, he o me slide a i s ini ial posi ion will be supe posed on o he p esen -day ba hyme y o
he sou ce a ea. The g ea es pa o he ene gy ans e o he wa e column akes place du ing he i s
s age o he slide displacemen (app oxima ely un il he ime o i s maximum eloci y) [38]. De ails o

J. Ma . Sci. Eng. 2015, 3 750
he subsequen his o y (including de o ma ion and b eaking up o he slide, and he accu a e upda e o
he sea loo ba hyme y) will con ibu e only as second o de co ec ions. Thus, co ec ions o he
p esen day ba hyme y in he deposi ional a eas ha e been omi ed in his modelling app oach. Away
om he coas al a ea, changes in ba hyme y du ing he las 4 ka a e negligible in his con ex , and he
o me paleogeog aphy condi ions o he eas e n coas line o he Nile Del a ha e been e-c ea ed o his
wo k based upon a ailable geological s udies, as explained u he below.
Figu e 2. Ske ch wi h he geome ical pa ame e s de ining he subma ine landslide
( ollowing he o malism p oposed by Ha bi z, 1992, [36]). The adop ed geome y is a box
o leng h L, wid h B and maximum heigh Δh, and wi h an exponen ial smoo hing o e a
dis ance S in he on and ea , and B/2 on he lanks.
The mo ion o he slide can be known a e sol ing he go e ning dynamic equa ions [39,40], o i
can be de ined by imposing a p esc ibed mo ion based upon a maximum eloci y, Umax, and he
displacemen , R [36]. He e we adop he app oach by Ha bi z (1992) [36], in which Umax is es ima ed as
a unc ion o he slope angle, α, he a e age hickness o he slide,
h
, i s densi y,

(~1.7 × 103 kg·m−3),
he densi y o u bidi y cu en s,


(~1.1 × 103 kg·m−3), and he ic ion (μ) and d ag (
u
D
C
)
coe icien s:
max 1
2
( ) (sin cos )
u
D
gh
UC
  


(5)
wi h
u
D
C
, he d ag coe icien along he uppe su ace o he slide, being es ima ed om he oughness
leng h pa ame e , k (in he ange o 0.01 o 0.1 m):
5
2
()
1.89 1.62log
u
D
LS
Ck






(6)
The alue o Umax s ongly depends on he es ima ion o he Coulomb ic ion coe icien , μ, wi hin
an accep able ange (being i s uppe limi
an
s
  
), and Umax mus emain wi hin he ange o he
epo ed alues in scien i ic li e a u e [39,41–43].
In many cases a i s and la ge slope angle is in ol ed in he igge ing mechanism. A e a displacemen
R1, he slope angle dec eases, bu he mo ing masses s ill comple e a second displacemen R2. Fo each
J. Ma . Sci. Eng. 2015, 3 751
slope angle he maximum eloci y Umax,1 and Umax,2 a e es ima ed as commen ed abo e, and he
ollowing unc ion o ime is imposed o he slide eloci y, s (Pe iáñez and Ab il, 2014a, [25]):
max,1
1
sin( ) 0
s ans
U
T

  
(7)
2
max,2
2
sin[ ( ) ]
22
s ans ans ans
T
U
T

     
(8)
wi h
1
1
max,1
2
R
TU


12
2
max,2
[ ( )]
ans
R R S
TU
  

max.2
1
max,1
a csin
ans
U
T
U




and S( ) is he ins an aneous posi ion o he slide on a ime .
The “ wo slope angle” kinema ics is a model choice, being mo e gene al han he single sinus unc ion
used by Ha bi z (1992) [36], bu con aining i as a pa icula case, and i allows gene a ing asymme ic
eloci ies p o iles (as he ones used by Las as e al., 2005, [39]). Applica ions o his model can be
ound in Pe iáñez and Ab il (2014a) [25] and in Ab il and Pe iáñez (2015) [38]. F ic ion s esses o e
he mo ing slide a e o mula ed in e ms o ela i e speed, as in Ha bi z (1992) [36], in such a way ha
a slice mo ing as e han he wa e column can ans e ene gy o i .
The slide model equi es ou inpu (bu no ee) pa ame e s: maximum eloci ies (go e ned by μ)
and displacemen s. The candida e sou ce a eas will be cha ac e ized by dep h p o iles along hei
espec i e ansec s, wha allows he iden i ica ion o slope angles. The displacemen s can be pa ially
es ima ed om he p e ious p o iles, o in oduced as plausible alues. These displacemen s ha e o be
unde s ood as e ec i e un-ou dis ances (displacemen o he sliding block), o e which he ans e o
ene gy o he sunami akes place. Mo e de ails will be p o ided along wi h he sou ce de ini ions.
A u he alida ion o he pe o mance o he nume ical model wi h i s lood-d ying algo i hm can
be ound in Pe iáñez and Ab il (2015) [44]. The subma ine landslide submodel has been es ed agains
independen modelling wo ks and subjec o ex ensi e sensi i i y es s [38,44]. The e ec s o model
esolu ion and sensi i i y o he ic ion coe icien ha e been s udied in Pe iáñez and Ab il (2014b) [31].
2.2. Model Domain and Ba hyme ic Map o he Fo me Eas e n Nile Del a
The compu a ional domain used o he nume ical modelling o sunami p opaga ion comp ises om
27.0° E o 36.0° E in longi ude and om 30.5° N o 37.3° N in la i ude (see pa ial iews in Figu e 3).
Wa e dep hs ha e been ob ained om he GEBCO08 digi al a las, a ailable on-line, wi h a esolu ion o
30 s o a c bo h in longi ude and la i ude. The eme ged lands appea wi h a minimum ele a ion o 1 m, he
minimum dep h o wa e s is 1 m, and bo h a e p o ided wi h a esolu ion o 1 m.
J. Ma . Sci. Eng. 2015, 3 752
Figu e 3. De ails o he domain used o he sunami p opaga ion model: Gene al iew o
he o me Nile Del a and he Le an ine coas lines (up); de ailed iew o he eas e n Nile
Del a and he Shi-Ho lagoon (bo om). Wa e dep hs (m) wi h 30 s o a c esolu ion om
GEBCO08 ba hyme y and paleogeog aphic econs uc ions (see ex ) a e d awn. Black line
is he p esen coas line, he ed and g een ones a e, espec i ely, he o me coas line and he
ma shland limi a 3500 yea BP a e Cou ellie and S anly (1987) [45]. The blue line
delimi s we lands a no he n Ballah Lake. Tja u (Hebua I) and Migdol a e Egyp ian mili a y
o esses a ound he o me Shi-Ho paleolagoon [9]. Do s 1 o 6 a e syn he ic gauges. The
loca ions o sunamigenic sou ces (Tables 1 and 2) a e also depic ed: yellow boxes o
subma ine landslides and ed lines o aul s.
Du ing he las 5 ka, wi h a s able sea le el, he majo changes in he coas line o he Nile Del a ha e
been d i en by lu ial deposi s, coas al e osion and land subsidence. The las is es ima ed as 2.0 mm/yea
in he a ea o Alexand ia [46]. Cou ellie and S anley (1987) [45] es ima ed mean Holocene
sedimen a ion a es o 5.0 m/ka in he eas e n Nile Del a. As a esul , he coas al ma gin in he s udied
a ea mig a ed no hwa d some 50 km du ing he pas 5 ka. As a p ac ical and c ude app oach o he
econs uc ion o he o me coas line in he en i e Nile Del a a ca 3500 yea s BP, we ollowed he
J. Ma . Sci. Eng. 2015, 3 753
me hodology desc ibed by Pe iáñez and Ab il (2014a) [25]. B ie ly, we applied a co ec ion o he
p esen dep hs/ele a ions, linea ly dec easing om he mode n o he o me coas line ( his las as
de ined by Cou ellie and S anley, 1987, [45]). The small-scale de ails o he coas line will no
signi ican ly a ec he gene al pa e ns o sunami p opaga ion, bu hey a e o capi al impo ance o
assessing local un-ups. The de ailed paelogeog aphical econs uc ion published by Ho meie (2005) [9]
o he a ea o he Shi-Ho Lagoon has been digi alized and me ged wi h he p e ious co ec ed
ba hyme y, applying hen a il e o smoo hing he ba hyme y among adjacen g id-cells. Resul s a e
shown in Figu e 3.
2.3. Tsunamingenic Sou ces in he Eas e n Nile Del a
Wo ks and e iews on he geodynamics o he eas e n Medi e anean can be ound, among o he s, in
Ba ka and Reilinge (1997) [47], Mascle e al., (2000) [48], o Yolsal and Taymaz (2012) [29]. I s
complex ec onic is esponsible o in ense ea hquake and olcanism ac i i y, igge ing la ge sunamis
in he pas [17,29,49,50]. The s udy by Papadopoulos e al., (2007) [51] on sunami haza ds in he Eas e n
Medi e anean concluded ha he mean ecu ence o s ong sunamis (mos o hem we e caused by
ea hquakes) is likely equal o abou 142 yea s. The assessmen o he p obabili y o landslide sunami
scena ios is a qui e di icul ask, due o he insu icien s a is ics om he eco ded e en s, as discussed
in de ail by Ha bi z e al., (2014) [52]. Such p obabili ies o occu ence mus no be con used wi h he
p obabili y o ha a gi en coas al a ea is a ec ed by a sunami o ce ain le el (e.g., wi h a maximum
wa e heigh ).
The i s map o he Nile deep-sea an has no been comple ed un il ecen yea s [53,54]. The
Messinian salini y c isis led o he deposi ion o sal and anhyd i e h oughou he Medi e anean basin,
while he p o o-Nile i e exca a ed deep canyons and anspo ed o sho e la ge olumes o e igenous
sedimen s. Thick Plio-Qua e na y sedimen s co e ed hen he duc ile e apo i ic laye s, wha igge ed
some gian g a i y-d i en sal ec onics [54–58]. A se ies o aul ends ha e been iden i ied ac oss he
s able shel o he Nile Del a, e.g., Rose a, Bal im and Temsah aul ends, and he Pelusium Mega-
Shea Faul sys em [59–61]. The Nile Del a is a majo gas and condensa e p o ince wi h se e al mud
olcanoes and geodynamics associa ed o luid seepage [62,63].
A gene al o e iew on mul i-scale slope ins abili ies along he Nile deep-sea an can be ound in
Loncke e al., (2009) [57], and in U geles and Came lenghi (2013) [64]. Ga ziglia e al., (2008) [60]
iden i ied and da ed se en mass- anspo deposi s on he Wes e n p o ince, no he n o he Rose a
Canyon, wi h olumes anging om 3 o 500 km3, mean hickness om 11 o 77 m and un-ou dis ances
om 18 o 150 km, being he younges deposi olde han 8940 ± 30 cal. yea BP. Ducassou e al., (2009),
based upon 42 sedimen co es collec ed ac oss he en i e Nile deep sea an, iden i ied se e al slump
deposi s and u bidi ies in he las 2000 ka BP [55], bu none in he Mid and La e Holocene (ca 5 ka o
p esen ). Thus, any candida e sou ce a ea o subma ine landslides mus be compa ible wi h he “emp y
spaces” wi hin his cloud o co es. Recen ly, Ducassou e al., (2013) [56] epo ed ou highly mobile
deb is lows in he Nile deep-sea an sys em, wi h a ch onology con ined be ween 5599 and 6915 cal.
yea s BP o he mos ecen e en , in he Rose a p o ince.
Resul s om nume ical models ha e p o ed ha he e ec s o he Minoan San o ini sunamis
( igge ed by en y o py oclas ic lows and calde a collapse) we e negligible in no h-eas e n Egyp and
J. Ma . Sci. Eng. 2015, 3 760
Figu e 6. Compu ed ime se ies o wa e ele a ions a idal gauges TG-3, TG-4 and TG-5 o
he subma ine landslide SL-2, wi h uns R1 o R4; and CSL, wi h uns R1 o R3 (Table 1).
See Figu e 3 o he loca ion o he syn he ic gauges. Ini ial wa e dep hs we e 9.0, 2.1 and
8.0 m o TG-3, TG-4 and TG-5, espec i ely.
Fo sunamis igge ed by geological aul s he maximum ene gy co esponds o he ini ial po en ial
ene gy due o he de o ma ion o he ee wa e su ace. I was 4.6 × 1013 J o F-1and 1.8 × 1014 J o F-2.
The wo s udied sou ces a e less ene ge ic e en s han he subma ine landslides. Figu e 7 shows he
maximum compu ed wa e ampli ude o sunamis F-1, F-2, and o he simul aneous sou ce F-2+SL-2 R2
(a landslide igge ed in sequence wi h he ea hquake). In his las case, he landslide componen
domina es he p opaga ion pa e n. In sunamis F-1 and F-2, he highes ampli udes emains con ided
wi hin he s able shel o he Nile Del a, and hey show s ong di ec ionali y owa ds he coas line

J. Ma . Sci. Eng. 2015, 3 761
delimi ing he Ba dawil Lake, bu wi h weak e ec s a ound he Shi-Ho lagoon, as shown in he
compu ed ime se ies o Figu e 8.
Figu e 7. Compu ed maximum ampli ude o wa e ele a ions (m) due o geological aul s
F-1, F-2 and he double sou ce F-2 + SL-2 R2. Sou ce pa ame e s a e p esen ed in Table 1.
Simula ion ime is 5 h.
J. Ma . Sci. Eng. 2015, 3 762
Figu e 8. Compu ed ime se ies o wa e ele a ions a idal gauges TG-3, TG-4 and TG-5
o he geological aul s F-1. F-2, and he double sou ce F-2 + SL-2 R2 (Table 1). See Figu e 3
o he loca ion o he syn he ic gauges. Ini ial wa e dep hs we e 9.0, 2.1 and 8.0 m o
TG-3, TG-4 and TG-5, espec i ely.
Figu e A2 shows he compu ed ime se ies o wa e ele a ions a he syn he ic gauges TG-1, TG-2 and
TG-6 (see Figu e 3) o a sub-se o sunamis. Tsunamis igge ed by geological aul s (F-1 and F-2) ha e
negligible e ec s in he Le an ine coas s and in Alexand ia (TG-6), in he wes e n Nile Del a. The mos
ene ge ic subma ine landslides impac he Le an ine coas s wi h wa es abo e 15 m heigh , while hei
e ec s in he wes e n Nile Del a a e much weake , wi h wa e ampli udes o 0.5 m.
Fo he s udied landslide sunamis, wa e cu en s exceed 5 o 10 m/s along he eas e n del a shel
edge and he sou he n Le an ine coas line (Figu e 9 shows some examples). These a e he a eas whe e
he majo ene gy dissipa ion (Equa ions (2)–(4)) and, consequen ly, he g ea es impac s occu .
In all he cases, wa e ampli udes only sligh ly exceed 1–1.5 m o he mos ene ge ic sunamis a he
Shi-Ho Lagoon (syn he ic gauges 4 in Figu es 5 and 6). The paleo-lagoon ne e d ies ou , no he Kedua
passage. Thus, a ound Shi-Ho Lagoon, only he coas al a eas less han 1.0–1.5 m abo e sea le el would
ha e had some isk o being looded. These dynamical sunami scena ios (Figu es 5 and 6), and
pa icula ly he ime sequence o wa e ele a ions, pe haps could p oduce some scene o ea and chaos
J. Ma . Sci. Eng. 2015, 3 763
in a mili a y g oup camped a he Tja u’s seaside, bu in ou opinion hey ha dly can explain a sudden
d owning o he Egyp ian a my.
Figu e 9. Compu ed maximum wa e cu en s (m/s) o sunamis SL-1 R6, SL-2 R1 and
CSL R1. Sou ce pa ame e s a e p esen ed in Table 1. Simula ion ime is 5 h.
J. Ma . Sci. Eng. 2015, 3 764
Figu e 10. 3D- iew o he ee wa e su ace de o ma ion, compu ed a e 10 min o he
beginning o landslides SL-1 R1 (up) and SL-2 R2 (bo om).
The abo e esul s a e a consequence o he pa icula geological se ing o he s udied ma ine sys em.
A la ge a ea o he Nile Del a shel ex ends in on o he Shi Ho Lagoon. In hese shallow wa e s,
sunami wa es a els a low speed, while he bed ic ion is high (i is in e sely p opo ional o wa e
dep h). The implemen ed o mula ion o ic ion (Equa ions (2)–(4)) has been widely used and alida ed
in many oceanog aphic s udies, and pa icula ly in models o idal and sunami p opaga ion (see o
ins ance Pe iáñez and Ab il, 2014b, [31]). Figu e A3 shows a sensi i i y es o he ic ion coe icien ,
applied o he mos ene ge ic sunami om ou se o simula ions (SL-1 R6). When he nominal alue o he
ic ion coe icien (k = 0.0025) is inc eased / dec eased by a 50%, wa e ele a ions a he gauges TG-3 o
TG-5 sligh ly dec ease/inc ease, wi hou a ec ing in he essen ial o he main conclusions o his s udy.
Scena ios o se e e looding can be ound along he no he n Sinai coas s, as shown in Figu e 4.
Ne e heless, hey do no ma ch wi h he plausible pa hs o he exodus. I is wo h no ing he g ea
exposu e o mos o he sunamis o he sand ba ie delimi ing he p esen Ba dawil Lagoon. I is known
ha i was a mili a y pa h in Pe sian imes, and i has been p oposed by some au ho s as he exodus pa h,
J. Ma . Sci. Eng. 2015, 3 765
al hough he mos ecen s udies concluded ha his sand ba ie was no a passable pa h a he second
millennium BC [9].
Tsunamis igge ed by subma ine landslides a e cha ac e ized by a dep ession o he ee wa e
su ace o e he line o up u e while a huge wa e appea s a he on o he mo ing slice. Fo some
excep ional wi nesses on he no he n Sinai sho eline o in cabo age sailing in his a ea, a subma ine
landslide along he eas e n Nile Del a shel edge could ha e been seen as a pa ing o he sea (as shown
in he 3D- iew o Figu e 10).
The inge p in o no iceable sunami impac s in coas al a eas can be po en ially ound in hei
cha ac e is ic sedimen a y deposi s, al hough hey a e no always well p ese ed; and huge subma ine
landslides can be de ec ed and da ed h ough hei associa ed u bidi e deposi s. The selec ed
sunamigenic sou ces in his pape a e compa ible wi h he main geological ea u es o he Nile Del a,
and hey a e no in con adic ion wi h ou p esen knowledge om ield s udies. Ob iously, his is no a
p oo o hei easibili y, wha can only be p o ided by empi ical e idences. They ep esen ex eme
and nea - ield cases in an a emp o p o ide he bes scena ios o he maximalis hypo hesis o sunamis
behind he biblical Exodus. Bu , e en o hese a ou able scena ios, he lack o no iceable looding o
he a ea, along wi h he ime sequence o wa e ele a ions, make di icul o accep a sunami as a eliable
hypo hesis nei he o he i s plague no o he d owning o he Egyp ian a my in he su oundings o
he Shi-Ho Lagoon.
The sunamigenic deposi s om he San o ini e en in he coas al a ea o Is ael and Gaza [19] can be
explained by he occu ence o sunamis wi h sou ce in he eas e n Medi e anean, likely igge ed by
subma ine landslides. In ou opinion his could ha e been a sou ce o inspi a ion o he Exodus
na a i e, which has o be unde s ood as he likely esul o he me ging o se e al s o ies om di e en
sou ces [4].
4. Conclusions
A nume ical model o sunami p opaga ion, based on he 2D shallow wa e equa ions and p e iously
applied and alida ed in a wide se o scena ios, has been adap ed, om a ailable geological and
a chaeological s udies, o he o me paleogeog aphic condi ions in he eas e n Nile Del a.
Se en een po en ial sunamigenic sou ces in he eas e n Nile Del a ha e been sugges ed as possible
candida es wi hin he Minoan sunami sequence, comp ising aul s along he Pelusium Mega-shea
sys em and se e al subma ine landslides a he shel edge and along he hypo he ical emains o he
Messinian Damie a canyon. They ha e been de ined as la ge as possible wi hin he known cons ains
s a ed by geological s udies, and comp ise sensi i i y es s o he o al olume and he p esc ibed mo ion
o he landslides.
Tsunamis igge ed by subma ine landslides could ha e se e ely impac ed he no he n Sinai and
sou he n Le an ine coas s wi h wa es o e 10–15 m heigh and wa e cu en s o e 5–10 m/s,
bu wi h weak e ec s in he su oundings o he Shi-Ho Lagoon, he p oposed scena io o he Biblical
sea pa ing.
The eal occu ence o sunamis can only be p o ed by empi ical e idences; bu as he p oposed ones
a e ep esen a i e o he mos a o able scena ios o he hypo hesis o be es ed, he lack o any
no iceable looding, and he pa icula ime sequence o wa e ele a ions, make di icul o accep hem

J. Ma . Sci. Eng. 2015, 3 766
as plausible and li e ally explana ion o he i s plague and o he d owning o he Egyp ian a my in
he su oundings o he Shi-Ho Lagoon, al hough hey migh ha e been a sou ce o inspi a ion o he
Biblical na a i e.
Supplemen a y Ma e ials
Snapsho s o he p opaga ion o he sunami SL-2 R2. Scale in he colo ba is gi en in m. Sou ce
pa ame e s a e p esen ed in Table 1. Supplemen a y ma e ials can be accessed a :
h p://www.mdpi.com/2077-1312/3/3/745/s1.
Au ho Con ibu ions
Concei ed and designed he expe imen s: JMA, RP. Pe o med he expe imen s: JMA, RP. Analyzed
he da a: JMA, RP. W o e he pape : JMA, RP.
Con lic s o In e es
The au ho s decla e no con lic o in e es .
Appendix
Elec onic Supplemen a y Ma e ial
Figu e A1. P esc ibed ime se ies o he slice eloci y (Equa ions (7)–(8)) o some o he
subma ine landslide scena ios de ined in Table 1.
J. Ma . Sci. Eng. 2015, 3 767
Figu e A2. Compu ed ime se ies o wa e ele a ions a idal gauges TG-1, TG-2 and
TG-6 o six o he sunamigenic sou ces gi en in Tables 1 and 2. See Figu e 3 o he
loca ion o he syn he ic gauges. Ini ial wa e dep hs we e 36, 33 and 36 m o TG-1, TG-2
and TG-6, espec i ely.
Figu e A3. Compu ed ime se ies o wa e ele a ions a idal gauges TG-3, TG-4 and TG-5
o sunami SL-1 R6 by inc easing/dec easing by a 50% he nominal alue o he ic ion
coe icien (Equa ions (2)–(4)). See Figu e 3 o he loca ion o he syn he ic gauges. Ini ial
wa e dep hs we e 9.0, 2.1 and 8.0 m o TG-3, TG-4 and TG-5, espec i ely.
J. Ma . Sci. Eng. 2015, 3 768
Re e ences
1. F ied ich, W.L. The Minoan E up ion o San o ini a ound 1613 B.C. and i s consequences. Tagung
en des Landesmuseums ü Vo ges chich e Halle. Band 2013, 9, 37–48.
2. S anley, J.D.; Sheng, H. Volcanic sha ds om San o ini (Uppe Minoan ash) in he Nile Del a,
Egyp . Na u e 1986, 320, 733–735.
3. B uins, H.J.; an de Plich , J. The Exodus enigma. Na u e 1996, 382, 213–214.
4. Si e sen, B.J. The Pa ing o he Sea. How olcanoes, Ea hquakes, and Plagues Shaped he S o y
o Exodus; P ince on Uni e si y P ess: P ince on, NJ, USA, 2009.
5. T e isana o, S.I. T ea men s o bu ns in he London Medical Papy us show he i s se en
biblical plagues o Egyp a e cohe en wi h San o ini’s olcanic allou . Med. Hypo heses 2006, 66,
193–196.
6. T e isana o, S.I. Six medical papy i desc ibe he e ec s o San o ini’s olcanic ash, and p o ide
Egyp ian pa allels o he so-called biblical plagues. Med. Hypo heses 2006, 67, 187–190.
7. T e isana o, S.I. Medical papy i desc ibe he e ec s o he San o ini e up ion on human heal h, and
da e he e up ion o Augus 1603–Ma ch 1601 BC. Med. Hypo heses 2007, 68, 446–449.
8. Bye s, G.A. New e idence om Egyp on he loca ion o he Exodus Sea c ossing, pa 1.
Bible Spade 2006, 19, 14–22.
9. Ho meie , J.K. Ancien Is ael in Sinai. The E idence o he Au hen ici y o he Wilde ness
T adi ion; Ox o d Uni e si y P ess Inc.: New Yo k, NY, USA, 2005.
10. Wood, B.G. Debunking “The Exodus Decoded”. ABR, 20 Sep embe 2006. A ailable online:
H p://www.biblea chaeology.o g/pos /2006/09/20/Debunking-The-Exodus-Decoded.aspx
(accessed on 15 May 2015).
11. Vol zinge , N.; And oso , A. Modeling he Hyd odynamic Si ua ion o he Exodus.
Iz . A mos. Ocean. Phys. 2003, 39, 482–496.
12. D ews, C.; Han, W. Dynamics o Wind Se down a Suez and he Eas e n Nile Del a. PLoS ONE
2010, 5, e12481, doi:10.1371/jou nal.pone.0012481.
13. Ab il, J.M.; Abdel-Aal, M.M. Ma ine Radioac i i y S udies in he Suez Canal, Pa I:
Hyd odynamics and T ansi Times. Es ua . Coas . Shel Sci. 2000, 50, 489–502.
14. Ab il, J.M.; Abdel-Aal, M.M. Ma ine Radioac i i y S udies in he Suez Canal, Pa II: Field
Expe imen s and a Modelling S udy o Dispe sion. Es ua . Coas . Shel Sci. 2000, 50, 503–514.
15. Jacobo ici, S.; Came on, J. The Exodus Decoded; Documen a y Film: To on o, ON, Canada,
16 Ap il 2006.
16. Salzman, R. Mega-Tsunami: The T ue S o y o he Heb ew Exodus om Egyp ; iUni e se:
Lincoln, NE, USA, 2005.
17. No iko a, T.; Papadopoulos, G.A.; McCoy, F.W. Modelling o sunami gene a ed by he gian La e
B onze Age e up ion o The a, Sou h Aegean Sea, G eece. Geophys. J. In . 2011, 186, 665–680.
18. Mészá os, S. Some wo ds on heMinoan sunami o San o ini. In The a and he Aegean Wo ld II;
Doumas, C., Ed.; The The a Founda ion: London, UK, 1978; pp. 257–262.
19. Goodman-Tche no , B.N.; Dey, H.W.; Reinha d , E.G.; McCoy, F.; Ma , Y. Tsunami wa es gene a ed
by he San o ini e up ion eached Eas e n Medi e anean sho es. Geology 2009, 37, 943–946.
J. Ma . Sci. Eng. 2015, 3 769
20. Nee , D.; Balke , N.; Eme y, K.O. Medi e anean Coas o Is ael and Sinai, Holocene Tec onics om
Geology and Geophysics and A chaeology; Taylo and F ancis: New Yo k, NY, USA, 1987; p. 130.
21. P annens iel, M. E lau e ungen zu den ba hyme ischen Ka en des os lichen Mi elmee es.
Bull. Ins . Oceanog . 1960, 57, 60.
22. De Ma ini, P.M.; Ba bano, M.S.; Smedile, A.; Ge a di, F.; Pan os i, D.; del Ca lo, P.; Pi o a, C.
A unique 4000 yea long geological eco d o mul iple sunami inunda ions in he Augus a Bay
(eas e n Sicily, I aly). Ma . Geol. 2010, 276, 42–57.
23. De Ma ini, P.M.; Ba bano, M.S.; Pan os i, D.; Smedile, A.; Pi o a, C.; del Ca lo, P.;
Pinzi, S. Geological e idence o paleo sunamis along eas e n Sicily (I aly): An o e iew.
Na . Haza ds Ea h Sys . Sci. 2012, 12, 2569–2580.
24. Ozel, N.M.; Ocal, N.; Ce de , Y.A.; Dogan, K.; Mus a a, E. Tsunami haza d in he Eas e n
Medi e anean and i s connec ed seas: Towa ds a sunami wa ning cen e in Tu key.
Soil Dyn. Ea hq. Eng. 2011, 31, 598–610.
25. Pe iáñez, R.; Ab il, J.M. Modelling sunamis in he Eas e n Medi e anean Sea. Applica ion o he
Minoan San o ini sunami sequence as a po en ial scena io o he biblical Exodus. J. Ma . Sys .
2014, 139, 91–102.
26. Choi, B.H.; Pelino sky, E.; Kim, K.O.; Lee, J.S. Simula ion o he ans-oceanic sunami
p opaga ion due o he 1883 K aka au olcanic e up ion. Na . Haza ds Ea h Sys . Sci. 2003, 3,
321–332.
27. Kowalik, Z.; Knigh , W.; Logan, T.; Whi mo e, P. Nume ical modelling o he Indian Ocean
sunami. In The Indian Ocean Tsunami; Mu y, T.S., Aswa hana ayana, U., Nipu ama, N., Eds.;
Taylo and F ancis G oup: London, UK, 2007; pp. 97–122.
28. Pe iáñez, R.; Ab il, J.M. Modeling sunami p opaga ion in he Ibe ia–A ica pla e bounda y:
His o ical e en s, egional exposu e and he case-s udy o he o me Gul o Ta essos. J. Ma . Sys .
2013, 111–112, 223–234.
29. Yolsal-Ce ikbilen, S.; Taymaz, T. Ea hquake sou ce pa ame e s along he Hellenic subduc ion
zone and nume ical simula ions o his o ical sunamis in he Eas e n Medi e anean. Tec onophysics
2012, 536–537, 61–100.
30. Kowalik, Z.; Mu y, T.S. Nume ical Modelling o Ocean Dynamics; Wo ld Scien i ic: Singapo e, 1993.
31. Pe iáñez, R.; Ab il, J.M. A nume ical modeling s udy on oceanog aphic condi ions in he o me
Gul o Ta essos (SW Ibe ia): Tides and sunami p opaga ion. J. Ma . Sys . 2014, 139, 68–78.
32. He z eld, M.; Schmid , M.; G i ies, S.M.; Liang, Z. Realis ic es cases o limi ed a ea ocean
modelling. Ocean Model. 2011, 37, 1–34.
33. Kamp , J. Ocean Modelling o Beginne s; Sp inge -Ve lag: Heidelbe g, Ge many, 2009.
34. Okada, Y. Su ace de o ma ion due o shea and ensile aul s in a hal -space. Bull. Seismol. Soc. Am.
1985, 75, 1135–1154.
35. Ab il, J.M.; Pe iáñez, R.; Escacena, J.L. Modeling ides and sunami p opaga ion in he o me Gul
o Ta essos, as a ool o A chaeological Science. J. A chaeol. Sci. 2013, 40, 4499–4508.
36. Ha bi z, C.B. Model simula ions o sunamis gene a ed by he S o egga slides. Ma . Geol. 1992,
105, 1–21.
37. Cecioni, C.; Bello i, G. Modeling sunamis gene a ed by subme ged landslides using dep h
in eg a ed equa ions. Appl. Ocean Res. 2010, 32, 343–350.