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

^{*}

^{†}

## Abstract

**:**

^{3}could have severely impacted the northern Sinai and southern Levantine coasts but with weak effects in the eastern Nile Delta coastline. The lack of noticeable flooding in this area under the most favorable conditions for tsunamis, along with the time sequence of water elevations, make difficult to accept them as a plausible and literally explanation of the first plague and of the drowning of the Egyptian army in the surroundings of the former Shi-Hor Lagoon.

## 1. Introduction

**Figure 1.**Map of the eastern Nile Delta and the Suez Canal, including the main geographical references cited in the text. The zoon-box shows the palaeogeographical reconstruction of the former shoreline at the second millennium BC around the Migdol site and the Shi Hor lagoon (after Hoffmeier, 2005, [9]).

## 2. Materials and Methods

#### 2.1. Model Description

_{u}and τ

_{v}are friction stresses which have been written in terms of a quadratic law:

^{2}/s and the bed friction coefficient as k = 0.0025. Good model results when estimating wave amplitudes and runups have been obtained with these values. Actually, model results (amplitudes, runups and wave arrival times) have been compared with observations in previous works [28]. Consequently, these values have been retained in the present application. Moreover, the model sensitivity to the bed friction coefficient has been studied in Periáñez and Abril (2014b) [31].

**Figure 2.**Sketch with the geometrical parameters defining the submarine landslide (following the formalism proposed by Harbitz, 1992, [36]). The adopted geometry is a box of length L, width B and maximum height Δh, and with an exponential smoothing over a distance S in the front and rear, and B/2 on the flanks.

_{max}, and the displacement, R [36]. Here we adopt the approach by Harbitz (1992) [36], in which U

_{max}is estimated as a function of the slope angle, α, the average thickness of the slide, $\overline{h}$, its density, $\overline{\text{\rho}}$(~1.7 × 10

^{3}kg·m

^{−3}), the density of turbidity currents, ${\text{\rho}}_{t}$ $\overline{\text{\rho}}$(~1.1 × 10

^{3}kg·m

^{−3}), and the friction (μ) and drag (${C}_{D}^{u}$) coefficients:

_{max}strongly depends on the estimation of the Coulomb friction coefficient, μ, within an acceptable range (being its upper limit ${\text{\mu}}_{st}=\mathrm{tan}\text{\alpha}$), and U

_{max}must remain within the range of the reported values in scientific literature [39,41,42,43].

_{1}, the slope angle decreases, but the moving masses still complete a second displacement R

_{2}. For each slope angle the maximum velocity U

_{max,1}and U

_{max,2}are estimated as commented above, and the following function of time is imposed for the slide velocity, v

_{s}(Periáñez and Abril, 2014a, [25]):

#### 2.2. Model Domain and Bathymetric Map of the Former Eastern Nile Delta

**Figure 3.**Details of the domain used for the tsunami propagation model: General view of the former Nile Delta and the Levantine coastlines (up); detailed view of the eastern Nile Delta and the Shi-Hor lagoon (bottom). Water depths (m) with 30 s of arc resolution from GEBCO08 bathymetry and paleogeographic reconstructions (see text) are drawn. Black line is the present coastline, the red and green ones are, respectively, the former coastline and the marshland limit at 3500 year BP after Coutellier and Stanly (1987) [45]. The blue line delimits wetlands at northern Ballah Lake. Tjaru (Hebua I) and Migdol are Egyptian military fortresses around the former Shi-Hor paleolagoon [9]. Dots 1 to 6 are synthetic gauges. The locations of tsunamigenic sources (Table 1 and Table 2) are also depicted: yellow boxes for submarine landslides and red lines for faults.

#### 2.3. Tsunamingenic Sources in the Eastern Nile Delta

^{3}, mean thickness from 11 to 77 m and run-out distances from 18 to 150 km, being the youngest deposit older than 8940 ± 30 cal. year BP. Ducassou et al., (2009), based upon 42 sediment cores collected across the entire Nile deep sea fan, identified several slump deposits and turbidities in the last 2000 ka BP [55], but none in the Mid and Late Holocene (ca 5 ka to present). Thus, any candidate source area for submarine landslides must be compatible with the “empty spaces” within this cloud of cores. Recently, Ducassou et al., (2013) [56] reported four highly mobile debris flows in the Nile deep-sea fan system, with a chronology confined between 5599 and 6915 cal. years BP for the most recent event, in the Rosetta province.

^{3}, accomplishing for high slopes and being distant enough from the already studied areas, where any mass-wasting deposits in the last 5 ka can be discarded. They showed that tsunamis generated by sources in the western and northern Nile Delta did not significantly affect the coastal zones of Israel and Gaza, and their effects on the eastern area of the delta were equally negligible. Thus, the source area within the Nile Delta able to produce tsunamis potentially linked to the Exodus has to be confined to its eastern zone.

_{max}, according to Harbitz (1992) [36]. The tsunamigenic sources selected for this study are summarized in Table 1 and Table 2 and briefly discussed further below.

^{3}. The value of μ has been fixed as 0.1, 0.3, 0.5, 0.8 and 0.9 of its maximum (static, μ

_{st}) limit in model runs R1, R2, R3, R4 and R5, respectively. A second version of this slide uses a larger value for its maximum height (20.0 m), leading to a total volume of 32.7 km

^{3}. The larger height increases the slide speed, which reaches values up to 49.5 m/s for μ = 0.5μ

_{st}(run R6), and of 31.3 m/s for μ = 0.8μ

_{st}(run R7). The displacement of the slide over the second slope, with a smaller angle, has a minor contribution to its tsunamigenic potential; thus, and for the sake of simplicity, a value of μ = 0.75μ

_{st}has been adopted for runs R1 to R7.

Landslide | Run | Geometrical Parameters | Front Position | Direction ^{$} | Kinematics ^{¶} | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

L (km) | S (km) | B (km) | h_{m} (m) | V (km^{3}) | λ_{E}° | Φ_{N}° | θ° | R_{1} (km) | α_{1} (°) | µ/µ_{st} | U_{max,1} (m/s) | R_{2} (km) | α_{2} (°) | U_{max,2} (m/s) | ||

SL-1 | R1 | 20.0 | 3.0 | 80.0 | 6.0 | 9.80 | 32.800 | 31.658 | 45 | 6.26 | 2.8 | 0.1 | 38.6 | 7.73 | 0.16 | 4.6 |

R2 | 0.3 | 32.1 | ||||||||||||||

R3 | 0.5 | 27.1 | ||||||||||||||

R4 | 0.8 | 17.1 | ||||||||||||||

R5 | 0.9 | 12.1 | ||||||||||||||

R6 | 20.0 | 32.7 | 0.5 | 49.5 | 8.4 | |||||||||||

R7 | 20.0 | 32.7 | 0.8 | 31.3 | 8.4 | |||||||||||

SL-2 | R1 | 8.0 | 3.0 | 40.0 | 26.0 | 10.0 | 32.725 | 31.708 | 45 | 4.36 | 2.8 | 0.6 | 47.7 | 11.73 | 0.6 | 17.5 |

R2 | 0.7 | 41.3 | ||||||||||||||

R3 | 0.8 | 33.7 | ||||||||||||||

R4 | 0.9 | 23.9 | ||||||||||||||

CSL * | R1 | 10.0 | 1.0 | 50.0 | 20.4 | 10.0 | 32.350 | 31.417 | 90 | 3.25 | 3.0 | 0.5 | 48.9 | 3.25 | 3.0 | 48.9 |

R2 | 0.7 | 37.9 | 37.9 | |||||||||||||

R3 | 0.9 | 21.9 | 21.9 |

^{#}Defined as in Harbitz (1992) [36]. Slide volume V = 0.9Bh

_{m}(L + 0.9S); B, width; L, length; S, smoothing distance; h

_{m}, average height;

**From the positive X direction (West to East);**

^{$}**R**

^{¶}_{1}and R

_{2}are down-slope displacements, with slope angles α

_{1}and α

_{2}and maximum speeds U

_{max,1}and U

_{max,2}, respectively. For SL-1 and SL-2 slides, µ/µ

_{st}= 0.75 for the second slope; while a single slope scheme is adopted for CSL slides; * Implemented along with a change in bathymetry defining an hypothetical canyon lying E-W, 62 km length, 6.5 km wide and 35 m deep, excavated on the reconstructed 3500 year BP bathymetry, and centred at 31.27° E, 31.45° N.

**Table 2.**Fault parameters used in the simulations. Geographical coordinates correspond to the fault center. Rake is 90° in all cases.

Tsunami | λ_{E}° | Φ_{N}° | Length (km) | Width (km) | Slip (m) | Strike (degree) | Dip (degree) | Potential Energy ^{#} (J) |
---|---|---|---|---|---|---|---|---|

F-1 | 32.667 | 31.500 | 60.0 | 20.0 | 8.0 | 55.0 | 45.0 | 4.6 × 10^{13} |

F-2 | 32.667 | 31.500 | 80.0 | 24.0 | 12.0 | 65.0 | 35.0 | 1.8 × 10^{14} |

F-2 + SL-2 R2 * | 32.667 | 31.500 | 80.0 | 24.0 | 12.0 | 65.0 | 35.0 | 1.8 × 10^{14} |

^{#}Initial potential energy linked to the Okada’s deformation. * Double source, composed by a fault earthquake and a simultaneous submarine landslide (SL-2 R2 in Table 1).

^{3}, the moving slide reaches a maximum speed of 47.7 m/s for μ = 0.6μ

_{st}(SL-2, run R1). Runs R2 to R4 for this slide use increasing values of μ in the first displacement, while the same criteria than for SL-1 has been adopted for the second displacement (Table 1).

^{3}. For simplicity a uniform slope angle of 3.0 degrees has been selected, with three options for µ values, leading to maximum speeds of 48.9, 37.9 and 21.9 m/s in runs CSL R1, R2 and R3, respectively.

## 3. Results and Discussion

**Figure 4.**Computed maximum amplitude for water elevations (m) due to submarine landslides SL-1 R6, SL-2 R1 and CSL R1. Source parameters are presented in Table 1. Simulation time is 5 h.

_{max,1}from 5.3 × 10

^{14}J in R5 up to 4.2 × 10

^{15}J in R1 (see Table 1). When a maximum thickness h = 20.0 m is adopted, the tsunami peak energy reaches 8.4 × 10

^{15}J in R6 (the maximum computed wave amplitudes for this extreme event are shown in Figure 4). In the scenario of landslide SL-2, with maximum thickness h = 26.0 m, the tsunami peak energy only slightly increases with U

_{max,1}, from 2.6 × 10

^{15}J in R4 up to 3.7 × 10

^{15}J in R1 (see Table 1, and Figure 4 for the maximum wave amplitudes computed for R1). Similarly, for landslide CSL the tsunami peak energy increases from 2.0 × 10

^{15}J (R3) up to 3.9 × 10

^{15}J (R1).

_{max,1}). These differences are only of few cm for landslides SL-2 and CSL (see Figure 6). Concerning the evolution of water level at TG-4 for the series of SL-2 tsunamis (Figure 6), it is similar to the one commented for SL-1. For CSL landslides, the withdrawal of the sea lasts about two hours, but interfered by the arrival of a weak wave of few tens cm. At TG-5, in the inner shoreline (Figure 3), the tsunami signal arrives latter, and with a similar although smoother pattern than in TG-4; but the maximum water heights are amplified about 0.5 m for SL-1 and 0.25 m for SL-2 and CSL submarine landslides. At TG-3, landslides SL-1 closely follow the same pattern, with a withdrawal of the sea of about 4 m that lasts one hour, followed by a sudden rise of 2–3 m, and then a continuous increase over 50–60 min up to reach water levels of 3–5 m (this last for the 32.7 km

^{3}landslide).

**Figure 6.**Computed time series of water elevations at tidal gauges TG-3, TG-4 and TG-5 for the submarine landslide SL-2, with runs R1 to R4; and CSL, with runs R1 to R3 (Table 1). See Figure 3 for the location of the synthetic gauges. Initial water depths were 9.0, 2.1 and 8.0 m for TG-3, TG-4 and TG-5, respectively.

^{13}J for F-1and 1.8 × 10

^{14}J for F-2. The two studied sources are less energetic events than the submarine landslides. Figure 7 shows the maximum computed wave amplitude for tsunamis F-1, F-2, and for the simultaneous source F-2+SL-2 R2 (a landslide triggered in sequence with the earthquake). In this last case, the landslide component dominates the propagation pattern. In tsunamis F-1 and F-2, the highest amplitudes remains confided within the stable shelf of the Nile Delta, and they show strong directionality towards the coastline delimiting the Bardawil Lake, but with weak effects around the Shi-Hor lagoon, as shown in the computed time series of Figure 8.

**Figure 7.**Computed maximum amplitude for water elevations (m) due to geological faults F-1, F-2 and the double source F-2 + SL-2 R2. Source parameters are presented in Table 1. Simulation time is 5 h.

**Figure 8.**Computed time series of water elevations at tidal gauges TG-3, TG-4 and TG-5 for the geological faults F-1. F-2, and the double source F-2 + SL-2 R2 (Table 1). See Figure 3 for the location of the synthetic gauges. Initial water depths were 9.0, 2.1 and 8.0 m for TG-3, TG-4 and TG-5, respectively.

**Figure 9.**Computed maximum water currents (m/s) for tsunamis SL-1 R6, SL-2 R1 and CSL R1. Source parameters are presented in Table 1. Simulation time is 5 h.

**Figure 10.**3D-view of the free water surface deformation, computed after 10 min of the beginning of landslides SL-1 R1 (up) and SL-2 R2 (bottom).

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Conflicts of Interest

## Appendix

## Electronic Supplementary Material

**Figure A1.**Prescribed time series for the slice velocity (Equations (7)–(8)) for some of the submarine landslide scenarios defined in Table 1.

**Figure A3.**Computed time series of water elevations at tidal gauges TG-3, TG-4 and TG-5 for tsunami SL-1 R6 by increasing/decreasing by a 50% the nominal value of the friction coefficient (Equations (2)–(4)). See Figure 3 for the location of the synthetic gauges. Initial water depths were 9.0, 2.1 and 8.0 m for TG-3, TG-4 and TG-5, respectively.

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## Share and Cite

**MDPI and ACS Style**

Abril, J.M.; Periáñez, R.
A Numerical Modelling Study on the Potential Role of Tsunamis in the Biblical Exodus. *J. Mar. Sci. Eng.* **2015**, *3*, 745-771.
https://doi.org/10.3390/jmse3030745

**AMA Style**

Abril JM, Periáñez R.
A Numerical Modelling Study on the Potential Role of Tsunamis in the Biblical Exodus. *Journal of Marine Science and Engineering*. 2015; 3(3):745-771.
https://doi.org/10.3390/jmse3030745

**Chicago/Turabian Style**

Abril, José M., and Raúl Periáñez.
2015. "A Numerical Modelling Study on the Potential Role of Tsunamis in the Biblical Exodus" *Journal of Marine Science and Engineering* 3, no. 3: 745-771.
https://doi.org/10.3390/jmse3030745