# Systematic Comparison of Tsunami Simulations on the Chilean Coast Based on Different Numerical Approaches

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## Abstract

**:**

## 1. Introduction

## 2. Data and Methods

- Virtual tide gauges in various water depths as well as a number of reference inland gauges;
- Tide gauge locations and records, where available;
- Flow depth on land and run-up height.

#### 2.1. Spatial Domains and Mesh Resolution

#### 2.2. Numerical Models

^{2}, $\mathbf{f}$, and ${A}_{h}$ are the constant of gravity, Coriolis parameter, and horizontal viscosity coefficient, respectively. All models use bottom friction in the Manning form, exemplified in the last term of the left-hand side of Equation (2) and prescribed by the Manning parameter n. These Manning values were varied in each simulation to compare their effect. For simplicity, and in order to use the same capabilities of each numerical code, all domains in each simulation kept the same values. Thus, non-space-varying (constant) Manning values were tested according to each grid extent, and no spatial (cell) differences in the Manning values were considered.

- Tsunami-HySEA (HS)

- COMCOT (CC)

- TsunAWI (TSW)

#### 2.3. The Experiments: Seismic Sources

- The Valparaíso event happened on 8 July 1730, triggering a tsunami that affected the Chilean coast and was also recorded along Japanese coasts [37]. Large wave heights for this event were registered in Valparaíso (e.g., 9–11 m) [38]. The source model was obtained from Carvajal et al. [38] who suggested that the earthquake size was in the range of $Mw$ 9.1–9.3.

#### 2.4. Post-Processing the Outcomes

## 3. Results

- Inundation area in km
^{2}; - Estimate of inundation volume (integral of max. flow depth) in Mio. m
^{3}; - Maximum run-up height;
- Location of maximum run-up height;
- Mean/max/standard deviation of inundation depth;
- Additional percentiles (e.g., median, 90%, 75%, refer to Tables S1 and S2).

#### 3.1. Maule Tsunami 2010

#### Offshore Assessment Based on Experiment 2010

#### 3.2. Illapel Event 2015

#### 3.2.1. Offshore Assessment Based on Experiment 2015

#### 3.2.2. Inundation in Coquimbo Area Based on Experiment 2015

#### 3.3. Valparaíso Tsunami 1730

#### 3.3.1. Offshore Assessment Based on Experiment 1730

#### 3.3.2. Inundation in Valparaíso and Viña del Mar Based on Experiment 1730

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

HS | Tsunami-HySEA code or numerical model |

CC | COMCOT code or numerical model |

TSW | TsunAWI code or numerical model |

FD | Tsunami flow depth |

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**Figure 1.**Bathymetry domains used for the simulations with Tsunami-HySEA and COMCOT. (

**a**). Largest domain (grid level 1), where mostly DART and tide gauges are shown in bold. Red circles stand for Deep-ocean Assessment and Reporting of Tsunamis (DART), blue circles refer to real tide gauges, and the orange and yellow circles show virtual offshore and inland gauges, respectively. (

**b**). Second level of the nested grids. (

**c**). Third and fourth levels of the nested grids are shown for the Coquimbo set-up. (

**d**). Third and fourth levels of the nested grids are shown for the Valparaíso set-up.

**Figure 2.**Small section of the triangular mesh used in the TsunAWI simulations. The area corresponds to Valparaíso. The yellow triangle marks the tide gauge “valp” used for model–data comparisons. Refer to Figure S1 in the Supplementary Materials, where resolution values are shown. Basemap: © OpenStreetMap Contributors.

**Figure 3.**Initial sea surface elevation for the three experiments: (

**a**). Experiment based on the 2010 Maule earthquake [33]. (

**b**). Experiment based on the 2015 Illapel earthquake [35]. (

**c**). Experiment based on the 1730 Valparaíso earthquake [38]. More information about slip distribution is shown in Figure S2 of the Supplementary Materials.

**Figure 4.**Time series and correlations obtained for all models in Experiment 2010 at selected forecast points. Results shown only for Manning n = 0.025. (

**a**). Time series results for the DART 32402. (

**b**). Time series results for the “coqu” tide gauge. (

**c**). Time series results for the “valp” tide gauge. (

**d**). Time series results for the “ts10” tide gauge. (

**e**). Summary of correlations for Experiment 2010 based on a Manning value of n = 0.025. The corresponding correlation values are listed in Table 3.

**Figure 5.**Time series obtained for all models in Experiment 2015, shown for selected forecast points. Results are shown only for Manning n = 0.025. (

**a**). Time series results for the DART 32402. (

**b**). Time series results for the “coqu” tide gauge. (

**c**). Time series results for the “valp” tide gauge. (

**d**). Time series results for the “talc” tide gauge. (

**e**). Summary of correlations for Experiment 2015 based on a Manning value of n = 0.025. The corresponding correlation values are listed in Table 4.

**Figure 6.**(

**a**). Maximum flow depths in Coquimbo based on the Experiment 2015 obtained by the model TsunAWI (

**top left**) for a Manning value of n = 0.025. Refer to Figure S3 in the Supplementary Materials for HS and CC results. (

**b**). Maximum flow depth values following the cross section (magenta) shown in the left panels. (

**c**). Topography contours over the inundation map in Coquimbo. (

**d**). Cross-section showing flow depths that resulted from the three numerical models and Manning values of n 0.015 and n 0.060. Observation from the 2015 tsunami event in Coquimbo based on Aránguiz et al. [36]. Basemaps in a;c are obtained from © Google Earth 2021, Maxar Technologies © OpenStreetMap Contributors, respectively.

**Figure 7.**Comparison of the inundation areas in Coquimbo resulting from three numerical codes with different Manning values obtained based on the Experiment 2015. (

**a**). Manning n value of 0.015. (

**b**). Manning n value of 0.020. (

**c**). Manning n value of 0.025. (

**d**). Manning n value of 0.030. (

**e**). Manning n value of 0.045. (

**f**). Manning n value of 0.060. Yellow diamonds are virtual tide (coqu) and inland gauges, squares (red, black, green) show positions of the maximum inundation, while circles (red, black, green) show positions of the maximum run-up. Refer to Table S1 (in Supplementary Materials) where these values are summarized. The observed inundation area was taken from SERNAGEOMIN [43]. Basemap: © OpenStreetMap Contributors.

**Figure 8.**Comparison within each numerical model, testing different Manning n values. Boundaries showing the extent of inundation areas obtained by the numerical models for all Manning values for Experiment 2015 are shown in each panel: (

**a**). All n values tested with the TsunAWI model for Coquimbo bay. (

**b**). All n values tested with the TsunAWI model for southern Coquimbo bay (zoomed area). (

**c**). All n values tested with the Tsunami-HySEA model along Coquimbo bay. (

**d**). All n values tested with the Tsunami-HySEA model for southern Coquimbo bay (zoomed area). (

**e**). All n values tested with the COMCOT model for Coquimbo bay. (

**f**). All n values tested with the COMCOT model for southern Coquimbo bay (zoomed area). Yellow diamonds stand for virtual inland and tide gauges. Observed inundation area taken from SERNAGEOMIN [43]. Basemap: © OpenStreetMap Contributors.

**Figure 9.**Comparisons of the areas and volumes that resulted from the three numerical models based on Experiments 2015 and 1730. (

**a**). Inundation area in Coquimbo from Experiment 2015. (

**b**). Volume estimates obtained by integrating the maximum flow depth for Experiment 2015. (

**c**). Model results for the inundation area in Experiment 1730 in Valparaíso. (

**d**). Volume estimates for Experiment 1730 in Valparaíso. (

**e**). Model results for the inundation area in Experiment 1730 in Viña del Mar. (

**f**). Volume estimates for Experiment 1730 in Viña del Mar, obtained by integrating the maximum flow depth. The lines are quadratic regressions obtained for least squares fit.

**Figure 10.**Maximum flow depths in Valparaíso and Viña del Mar obtained by the three numerical models for a Manning value of n = 0.025 in Experiment 1730. (

**a**). Results from Tsunami-HySEA, (

**b**). TsunAWI, (

**c**). COMCOT. The magenta line stands for the extent of the cross section. (

**d**). Lines show the maximum wave amplitude (relative to shoreline) resulting from each numerical model and the elevation above sea level (Topo). Basemap: © Google Earth 2018.

**Figure 11.**Extent of inundation areas obtained by the three numerical models for all Manning values tested in Experiment 1730 in Valparaíso (

**left panels**) and Viña del Mar (

**right panels**). Yellow diamonds show the virtual tide (valp) and inland gauges. Basemap: © OpenStreetMap Contributors.

**Figure 12.**Inundation area in Viña del Mar for all Manning values obtained by the three models for Experiment 1730. (

**a**). Manning n-value of 0.015. (

**b**). Manning n-value of 0.020. (

**c**). Manning n-value of 0.025. (

**d**). Manning n-value of 0.030. (

**e**). Manning n-value of 0.045. (

**f**). Manning n-value of 0.060. Yellow diamonds are virtual tide (ts5) and inland gauges, squares (red, black, green) show positions of the maximum inundation, while circles (red, black, green) show positions of the maximum run-up. Basemap: © OpenStreetMap Contributors.

**Figure 13.**Comparison of the inundation dependency on bathymetry. (

**a**). Coarsest mesh (shown in blue) and finest triangulation (shown in red) in the Valparaíso area. (

**b**). Inundation area in Viña del Mar in all meshes for Experiment 1730 and a Manning value of n = 0.025, calculated with TsunAWI. (

**c**). Inundation area in Valparaíso in all meshes for Experiment 1730 and a Manning value of n = 0.025, calculated with TsunAWI. (

**d**). Inundation area in Coquimbo in all meshes for Experiment 1730 and a Manning value of n = 0.025, calculated with TsunAWI. Yellow diamonds show the tide and inland gauges. Basemap: © OpenStreetMap Contributors.

**Figure 14.**Upper panels: Numerical code comparison for Experiment 1730. Temporal evolution of the inundation process at two locations in Viña del Mar: (

**a**). Virtual tide gauge “ts108” close to the coast. (

**b**). Virtual tide gauge “ts109” about 500 m inland. Lower panels: Comparison of TsunAWI results for the full range of Manning values for Experiment 1730. Temporal evolution of the inundation process at two locations in Viña del Mar: (

**c**). Virtual tide gauge “ts108”. (

**d**). Virtual tide gauge “ts109” about 500 m inland. Refer to Figure 13 for their locations.

**Figure 15.**Ratio of the maximum flow depth obtained for the extreme Manning values (flow depth (n = 0.06)/flow depth (n = 0.015)) in the intersection of inundation areas in Viña del Mar. Example that summarizes the outcomes of Experiment 1730. Basemap: © OpenStreetMap Contributors.

Model | Tsunami-HySEA | TsunAWI | COMCOT |
---|---|---|---|

Spatial discretisation | 4 nested grids | Triangular mesh | 4 nested grids |

Resolution | 925 m, 462 m, 57 m, 7.25 m | Edge length range 12 km–10 m | 925 m, 462 m 57 m, 7.25 m |

Time stepping | Leap frog and 2nd order TVD-WAF flux-limiter scheme 0.5 s | Leap frog 0.1 s glob | Leap frog 1.0 s, automatically adjusted to satisfy the Courant condition |

Numerical approach | Finite Volume | Finite Elements | Finite Differences |

Inundation scheme | TVD-weighted averaged flux (WAF) flux- limiter | Extrapolation scheme | Moving boundary |

**Table 2.**Simulation overview for the three experiments. Abbreviations for the available data used in the study are tide gauge records (TGR), inundation extent (InExt), and flow depth (FLD).

Exp. ID | Event | Magnitude | Used Data | Comparisons |
---|---|---|---|---|

2010 | Maule | $Mw$ 8.8 | TGR | Virtual tide gauges (Vtg) |

and real tide gauges | ||||

2015 | Illapel | $Mw$ 8.3 | TGR, InExt, | Vtg and real tide gauges |

FLD | InExt for varying Manning n | |||

Comparisons to field obs. | ||||

1730 | Valparaíso | $Mw$ 9.1 | – | Virtual tide gauges |

InExt for varying Manning n |

HS | TSW | CC | HS | TSW | CC | |
---|---|---|---|---|---|---|

DART 32402 | coqu | |||||

HS | 1 | 0.977 | 0.973 | 1 | 0.974 | 0.916 |

TSW | 0.977 | 1 | 0.967 | 0.974 | 1 | 0.904 |

Data | – | – | – | 0.706 | 0.700 | 0.788 |

valp | ts10 | |||||

HS | 1 | 0.949 | 0.913 | 1 | 0.934 | 0.770 |

TSW | 0.949 | 1 | 0.895 | 0.934 | 1 | 0.874 |

Data | 0.564 | 0.520 | 0.499 | – | – | – |

HS | TSW | CC | HS | TSW | CC | |
---|---|---|---|---|---|---|

DART 32402 | coqu | |||||

HS | 1 | 0.918 | 0.945 | 1 | 0.936 | 0.967 |

TSW | 0.918 | 1 | 0.897 | 0.936 | 1 | 0.900 |

Data | 0.818 | 0.811 | 0.818 | 0.739 | 0.629 | 0.743 |

valp | talc | |||||

HS | 1 | 0.954 | 0.959 | 1 | 0.950 | 0.907 |

TSW | 0.954 | 1 | 0.910 | 0.941 | 1 | 0.950 |

Data | 0.590 | 0.572 | 0.621 | 0.759 | 0.855 | 0.933 |

**Table 5.**Inundation areas obtained for the different Manning values in Experiment 2015. The relative drop in estimates refer to the difference between the largest and the smallest values. Inside the brackets, the median values for inundation are shown (in metres). In addition to the median values, other statistical parameters are shown in Table S1 in the Supplementary Materials.

Model | HS | TSW | CC |
---|---|---|---|

Experiment | 2015 | ||

Location | Coquimbo | ||

Manning n | Area (km^{2}) | Median of flow depth (m) | ||

0.015 | 2.251 (0.83) | 2.858 (0.92) | 2.503 (0.85) |

0.020 | 2.008 (0.85) | 2.527 (0.78) | 2.270 (0.83) |

0.025 | 1.735 (0.89) | 2.401 (0.70) | 1.986 (0.87) |

0.035 | 1.323 (1.07) | 1.981 (0.68) | 1.491 (0.99) |

0.045 | 1.059 (0.99) | 1.453 (0.83) | 1.124 (0.96) |

0.060 | 0.769 (0.70) | 1.011 (0.73) | 0.820 (0.65) |

rel. drop % | 65.8 | 64.6 | 67.2 |

**Table 6.**Correlation coefficients of Experiment 1730 for the first two hours of the time series, also shown in Figure S5 of the Supplementary Materials. Abbreviations used are the following—HS: Tsunami-HySEA; TSW: TsunAWI; CC: COMCOT. Refer to Figure 1 for the tide gauge and DART locations.

HS | TSW | CC | HS | TSW | CC | |
---|---|---|---|---|---|---|

DART32402 | valp | |||||

HS | 1 | 0.979 | 0.984 | 1 | 0.975 | 0.935 |

TSW | 0.979 | 1 | 0.982 | 0.975 | 1 | 0.946 |

ts3 | ts8 | |||||

HS | 1 | 0.982 | 0.966 | 1 | 0.955 | 0.772 |

TSW | 0.982 | 1 | 0.972 | 0.955 | 1 | 0.805 |

**Table 7.**Inundation area obtained in Experiment 1730, in the domains of Valparaíso and Viña del Mar, for all models and ranges of Manning values tested in this study. Relative drop shows the decrease between the largest and the smallest area values. The median relates to the inundation estimates for the entire area. Besides the median values, other statistical parameters are shown in Tables S2 and S3 in the Supplementary Materials. Refer to Figure 9c–f and Figure 11.

Model | HS | TSW | CC | HS | TSW | CC |
---|---|---|---|---|---|---|

Experiment | 1730 | 1730 | ||||

Location | Valparaíso | Viña del Mar | ||||

Manning n | Area (km^{2}) | Median of flow depth (m) | Area (km^{2}) | Median of flow depth (m) | ||||

0.015 | 2.139 (3.50) | 2.388 (4.23) | 2.089 (3.02) | 4.900 (2.71) | 5.396 (2.94) | 4.800 (2.69) |

0.020 | 2.097 (3.25) | 2.320 (3.83) | 2.070 (3.0) | 4.713 (2.70) | 4.914 (3.01) | 4.715 (2.77) |

0.025 | 2.059 (3.05) | 2.180 (3.6) | 2.036 (2.90) | 4.529 (2.67) | 4.761 (2.93) | 4.450 (2.66) |

0.035 | 2.001 (2.87) | 2.045 (3.10) | 2.085 (3.14) | 3.974 (2.83) | 4.473 (2.69) | 3.930 (2.83) |

0.045 | 1.956 (2.77) | 1.952 (2.63) | 1.936 (2.68) | 3.687 (2.78) | 3.946 (2.72) | 3.591 (2.69) |

0.060 | 1.903 (2.72) | 1.871 (2.23) | 1.876 (2.56) | 3.355 (2.71) | 3.720 (2.45) | 3.087 (2.58) |

rel. drop % | 11.0 | 21.6 | 10.2 | 31.5 | 31.1 | 35.7 |

**Table 8.**Inundation area in pilot regions (refer to a minimum flow depth of 1 cm) obtained by TsunAWI in all meshes. The relative reduction is obtained by computing the ratio of the difference between the largest and the smallest value with reference to the maximum.

Mesh | Inundation Area (km^{2}) | |||
---|---|---|---|---|

Mean Res. | Finest Res. (m) | Viña (1730) | Valparaíso (1730) | Coquimbo (2015) |

100.0 | 12.7 | 4.955 | 2.392 | 2.503 |

50.0 | 12.7 | 4.841 | 2.307 | 2.432 |

30.0 | 9.5 | 4.793 | 2.164 | 2.364 |

20.0 | 6.1 | 4.761 | 2.180 | 2.401 |

10.0 | 2.5 | 4.711 | 2.276 | 2.384 |

rel. reduction (%) | 4.8 | 9.6 | 5.6 |

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**MDPI and ACS Style**

Harig, S.; Zamora, N.; Gubler, A.; Rakowsky, N. Systematic Comparison of Tsunami Simulations on the Chilean Coast Based on Different Numerical Approaches. *GeoHazards* **2022**, *3*, 345-370.
https://doi.org/10.3390/geohazards3020018

**AMA Style**

Harig S, Zamora N, Gubler A, Rakowsky N. Systematic Comparison of Tsunami Simulations on the Chilean Coast Based on Different Numerical Approaches. *GeoHazards*. 2022; 3(2):345-370.
https://doi.org/10.3390/geohazards3020018

**Chicago/Turabian Style**

Harig, Sven, Natalia Zamora, Alejandra Gubler, and Natalja Rakowsky. 2022. "Systematic Comparison of Tsunami Simulations on the Chilean Coast Based on Different Numerical Approaches" *GeoHazards* 3, no. 2: 345-370.
https://doi.org/10.3390/geohazards3020018