A Numerical Modelling Study on the Potential Role of Tsunamis in the Biblical Exodus

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. 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