# Quantitative Assessment of Epistemic Uncertainties in Tsunami Hazard Effects on Building Risk Assessments

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## Abstract

**:**

## 1. Introduction

## 2. Methodology for the Tsunami Risk Assessment and Quantification of Hazard Uncertainty

## 3. Application to the Tohoku Area

#### 3.1. Assessment Targets

#### 3.2. Probabilistic Tsunami Wave Height

#### 3.2.1. Construction of the Logic Trees

#### 3.2.2. Tsunami Numerical Simulation

#### 3.2.3. Tsunami Hazard Curves at the Offshore Points

#### 3.3. Tsunami Inundation Assessment

#### 3.3.1. Probabilistic Tsunami Hazard Map

#### 3.3.2. Tsunami Hazard Curves at Inland Points

#### 3.4. Fragility Assessment

#### 3.5. Risk Assessment and Quantitative Effects of the Hazard Assessment

#### 3.6. Discussion

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

_{U}and μ

_{L}are determined based on the information in Table A1. If the sample period is T, the confidence interval is as follows:

**Table A1.**Lower and upper ±1.0 standard deviation confidence intervals for a Poisson variable [22].

${\mathit{\mu}}_{\mathit{U}}$ | N | ${\mathit{\mu}}_{\mathit{L}}$ |
---|---|---|

1.84 | 0 | 0 |

3.30 | 1 | 0.173 |

4.64 | 2 | 0.708 |

5.92 | 3 | 1.37 |

7.16 | 4 | 2.09 |

8.38 | 5 | 2.84 |

9.58 | 6 | 3.62 |

10.8 | 7 | 4.42 |

12.0 | 8 | 5.23 |

13.1 | 9 | 6.06 |

14.3 | 10 | 6.89 |

## References

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**Figure 2.**Flow of the tsunami risk quantification. (

**a**) The probabilistic tsunami wave height is converted to (

**b**) the probabilistic tsunami inundation information, and (

**d**,

**e**) the risk assessment is carried out by combining the hazard information with (

**c**) fragility assessment.

**Figure 4.**The selected earthquakes that could generate a tsunami based on the occurrence region of the trench-type earthquake along the Japan Trench, which is used in the probabilistic seismic motion prediction map [14].

**Figure 5.**Logic trees constructed for the eleven fault regions. The numbers appended onto the branches of the logic trees are the weights of the branches.

**Figure 8.**Relationships between the annual exceedance probability and tsunami wave height at (

**a**) a water depth of 10 m (37.85127° N, 140.96812° E) off the port of Soma; (

**b**) a water depth of 10 m (37.85127° N, 140.96812° E) off the coast of Sendai Plain; and (

**c**) a water depth of 10 m (37.85127° N, 140.96812° E) off the coast of the city of Kesennuma.

**Figure 9.**Five regions of terrain data used for the tsunami numerical run-up simulations in the Soma area (Domain 1, Domain 2, Domain 3, Domain 4 and Domain 5). The numbers in parentheses are the east-west and north-south mesh dimensions.

**Figure 10.**Five regions of terrain data used for the tsunami numerical run-up simulations in the Sendai and Kesennuma areas (Domain 1, Domain 2, Domain 3, Domain 4 and Domain 5). The numbers in parentheses are the east-west and north-south mesh dimensions.

**Figure 11.**Results of tsunami inundation assessments for (

**a**) Soma; (

**b**) Sendai and (

**c**) Kesennuma at return periods of approximately 200, 700 and 1500 years.

**Figure 12.**Relationships between the annual exceedance probability and tsunami inundation height for (

**a**) Soma; (

**b**) Sendai and (

**c**) Kesennuma.

**Figure 13.**Tsunami fragility curves for different building structures ((

**a**) Reinforced concrete; (

**b**) Steel; (

**c**) Brick and (

**d**) Wood) and different damage levels, which were created by regressing the damage data from the 3.11 Tohoku earthquake [20].

**Figure 14.**Tsunami risk curves for different types of building construction with different percentile of tsunami hazard for three target points.

**Figure 15.**Expected value of the tsunami risk using each tsunami hazard value ((

**a**) average value; (

**b**) 5th percentile value; (

**c**) 50th percentile value and (

**d**) 95th percentile value) indicated according to the structure (upper horizontal axis) and the region (lower horizontal axis).

**Figure 16.**Expected value of the tsunami risk at each risk assessment point ((

**a**) Soma; (

**b**) Sendai; and (

**c**) Kesennuma) according to the structure (upper horizontal axis) and the percentile value of the tsunami hazard (lower horizontal axis).

Target Location | Latitude (°) | Longitude (°) | Elevation (m) | Distance from Coastline (m) |
---|---|---|---|---|

Soma | 37.84829 | 140.95052 | 3.7 | 390 |

Sendai | 38.23349 | 140.98479 | 1.1 | 1040 |

Kesennuma | 38.87447 | 141.58775 | 1.4 | 90 |

Abbreviation | Earthquake Name |
---|---|

JTN1-1 | Large interplate earthquakes in Northern Sanriku-Oki (repeating earthquakes) |

JTN1-2 | Large interplate earthquakes in Northern Sanriku-Oki (other than repeating earthquakes) |

JTN2 | Miyagi-ken-Oki earthquake (repeating earthquakes) |

JTN3-1 | Earthquakes close to the offshore trenches in Southern Sanriku-Oki (repeating earthquakes) |

JTN3-2 | Earthquakes close to the offshore trenches in Southern Sanriku-Oki (other than repeating earthquakes) |

JTN2 + JTN3 | Miyagi-ken-Oki, earthquakes close to the offshore trenches in Southern Sanriku-Oki consolidated-type-earthquake |

TOHOKU | Great East Japan Earthquake (2011 Tohoku-type earthquake) |

JTT | Large interplate earthquakes close to the offshore trenches in the Sanriku-Oki to Boso-Oki regions (tsunami earthquakes) |

JTNR | Large intraplate earthquakes close to the offshore trenches in the Sanriku-Oki to Boso-Oki regions (normal fault-type) |

JTS1 | Interplate earthquakes in Fukushima-ken-Oki |

IBRK | Interplate earthquakes in Ibaraki-ken-Oki (other than repeating earthquakes) |

**Table 3.**Model names for the generation intervals of earthquakes, α values of the BPT distribution, average return periods, sample periods, earthquake generation times within the periods used to determine the average occurrence intervals and lower and upper limits of the confidence intervals for the eleven earthquakes, which are shown in the Headquarters for Earthquake Research Promotion [16].

Earthquake Name (Abbreviation) | Model for Generation Interval of Earthquake | α Value of BPT Distribution | Average Return Period (Year) | Sample Period (Year) | Earthquake Generation Time | Lower Limit of Confidence Interval for the Return Period | Upper Limit of Confidence Interval for the Return Period |
---|---|---|---|---|---|---|---|

JTN1-1 | BPT | 0.08 | 97 | 412 | 4 | 93 | 101 |

0.18 | 97 | 412 | 4 | 89 | 106 | ||

0.28 | 97 | 412 | 4 | 84 | 112 | ||

JTN2 | Poisson process | - | 38 | 110 | 4 | 15 | 53 |

JTN3-1 | BPT | 0.12 | 109 | 220 | 3 | 102 | 117 |

0.22 | 109 | 220 | 3 | 96 | 124 | ||

0.32 | 109 | 220 | 3 | 91 | 131 | ||

JTN2 + JTN3 | Poisson process | - | 218 | 218 | 1 | 66 | 1260 |

JTT | Poisson process | - | 103 | 400 | 4 | 56 | 191 |

JTNR | Poisson process | - | 575 | 575 | 1 | 174 | 3324 |

JTN1-2 | Poisson process | - | 14 | 127 | 9 | 10 | 21 |

JTN3-2 | Poisson process | - | 42 | 127 | 3 | 21 | 93 |

JTS1 | Poisson process | - | 206 | 412 | 2 | 89 | 582 |

IBRK | Poisson process | - | 26 | 127 | 5 | 15 | 45 |

TOHOKU | BPT | 0.14 | 600 | 2400 | 4 | 559 | 644 |

0.24 | 600 | 2400 | 4 | 532 | 676 | ||

0.34 | 600 | 2400 | 4 | 506 | 711 |

Earthquake Name (Abbreviation) | Moment Magnitude (Mw) | Number of Earthquake Faults | Earthquake Fault Parameter | Earthquake Moment Mo (Nm) | Shear Modulus μ (N/m2) | Average Slip (m) | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Longitude (°) | Lattitude (°) | Depth (km) | Length (km) | Width (km) | Strike (°) | Rake (°) | Dip (°) | ||||||

JTN1-1 | 8.2 | 1 | 143.096 | 41.603 | 9.0 | 170 | 100 | 156 | 90 | 20 | 2.51 × 10^{21} | 3.50 × 10^{10} | 3.30 |

JTN2 | 7.6 | 1 | 142.388 | 38.454 | 30.8 | 60 | 60 | 194 | 90 | 22 | 2.72 × 10^{20} | 7.00 × 10^{10} | 1.10 |

JTN3-1 | 7.9 | 1 | 143.203 | 38.74 | 16.8 | 50 | 165 | 191 | 90 | 10 | 9.43 × 10^{20} | 5.00 × 10^{10} | 3.30 |

JTN2+JTN3 | 8.1 | 1 | The fault parameters were assumed as JTN2, JTN3-1 Consolidated Type Earthquake | 1.78 × 10^{21} | 5.00 × 10^{10} | 2.20 | |||||||

TOHOKU | 9.0 | 1 | 144.139 | 39.9 | 4.1 | 500 | 200 | 193 | 90 | 13 | 3.98 × 10^{22} | Shallow part: 3.60 × 10^{10}, Deep part: 5.20 × 10^{10} | Shallow part: 18.1, Deep part: 6.0 |

JTT | 8.0 | 1 | 144.729 | 41.087 | 6.5 | 200 | 50 | 192 | 90 | 6 | 1.26 × 10^{21} | 3.50 × 10^{10} | 3.60 |

2 | 144.428 | 41.187 | 8.1 | 200 | 50 | 192 | 90 | 9 | 1.26 × 10^{21} | 3.50 × 10^{10} | 3.60 | ||

3 | 144.278 | 39.351 | 6.8 | 200 | 50 | 190 | 90 | 7 | 1.26 × 10^{21} | 3.50 × 10^{10} | 3.60 | ||

4 | 143.928 | 39.401 | 10.3 | 200 | 50 | 190 | 90 | 8 | 1.26 × 10^{21} | 3.50 × 10^{10} | 3.60 | ||

5 | 143.915 | 37.46 | 7.0 | 200 | 50 | 211 | 90 | 7 | 1.26 × 10^{21} | 3.50 × 10^{10} | 3.60 | ||

6 | 143.6 | 37.572 | 10.3 | 200 | 50 | 210 | 90 | 9 | 1.26 × 10^{21} | 3.50 × 10^{10} | 3.60 | ||

7 | 142.44 | 36.058 | 7.0 | 200 | 50 | 189 | 90 | 8 | 1.26 × 10^{21} | 3.50 × 10^{10} | 3.60 | ||

8 | 142.21 | 36.031 | 10.8 | 200 | 50 | 193 | 90 | 10 | 1.26 × 10^{21} | 3.50 × 10^{10} | 3.60 | ||

JTNR | 8.3 | 1 | 144.706 | 41.088 | 0.0 | 200 | 100 | 192 | 270 | 45 | 3.55 × 10^{21} | 7.00 × 10^{10} | 2.50 |

2 | 144.226 | 39.353 | 0.0 | 200 | 100 | 190 | 270 | 45 | 3.55 × 10^{21} | 7.00 × 10^{10} | 2.50 | ||

3 | 143.856 | 37.458 | 0.0 | 200 | 100 | 211 | 270 | 45 | 3.55 × 10^{21} | 7.00 × 10^{10} | 2.50 | ||

4 | 142.407 | 36.058 | 0.0 | 200 | 100 | 189 | 270 | 45 | 3.55 × 10^{21} | 7.00 × 10^{10} | 2.50 | ||

5 | 145.486 | 40.988 | 0.0 | 200 | 100 | 192 | 270 | 45 | 3.55 × 10^{21} | 7.00 × 10^{10} | 2.50 | ||

6 | 145.006 | 39.253 | 0.0 | 200 | 100 | 190 | 270 | 45 | 3.55 × 10^{21} | 7.00 × 10^{10} | 2.50 | ||

7 | 144.736 | 37.358 | 0.0 | 200 | 100 | 211 | 270 | 45 | 3.55 × 10^{21} | 7.00 × 10^{10} | 2.50 | ||

8 | 143.186 | 35.958 | 0.0 | 200 | 100 | 189 | 270 | 45 | 3.55 × 10^{21} | 7.00 × 10^{10} | 2.50 | ||

JTN1-2 | 7.5 | 1 | 143.717 | 41.43 | 17.5 | 60 | 60 | 206 | 90 | 13 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.50 |

2 | 142.966 | 41.726 | 34.4 | 60 | 60 | 207 | 90 | 17 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.50 | ||

3 | 143.405 | 41.099 | 19.3 | 60 | 60 | 185 | 90 | 14 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.50 | ||

4 | 142.658 | 41.304 | 35.4 | 60 | 60 | 184 | 90 | 19 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.50 | ||

5 | 143.313 | 40.654 | 20.1 | 60 | 60 | 184 | 90 | 14 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.50 | ||

6 | 142.605 | 40.754 | 35.4 | 60 | 60 | 184 | 90 | 19 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.50 | ||

7 | 143.222 | 40.194 | 21.3 | 60 | 60 | 186 | 90 | 14 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.50 | ||

8 | 142.556 | 40.2 | 34.9 | 60 | 60 | 185 | 90 | 20 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.50 | ||

JTN3-2 | 7.4 | 1 | 143.267 | 38.727 | 16 | 50 | 50 | 192 | 90 | 10 | 1.58 × 10^{20} | 5.00 × 10^{10} | 1.30 |

2 | 143.121 | 38.332 | 16.5 | 50 | 50 | 191 | 90 | 10 | 1.58 × 10^{20} | 5.00 × 10^{10} | 1.30 | ||

3 | 142.997 | 37.922 | 16.9 | 50 | 50 | 193 | 90 | 10 | 1.58 × 10^{20} | 5.00 × 10^{10} | 1.30 | ||

JTS1 | 7.4 | 1 | 142.804 | 37.298 | 17.3 | 50 | 50 | 204 | 90 | 10 | 1.58 × 10^{20} | 5.00 × 10^{10} | 1.30 |

2 | 142.372 | 37.445 | 23.4 | 50 | 50 | 201 | 90 | 15 | 1.58 × 10^{20} | 5.00 × 10^{10} | 1.30 | ||

3 | 141.948 | 37.564 | 34.6 | 50 | 50 | 204 | 90 | 23 | 1.58 × 10^{20} | 5.00 × 10^{10} | 1.30 | ||

4 | 142.556 | 36.877 | 15.7 | 50 | 50 | 212 | 90 | 13 | 1.58 × 10^{20} | 5.00 × 10^{10} | 1.30 | ||

5 | 142.12 | 37.036 | 24.6 | 50 | 50 | 205 | 90 | 16 | 1.58 × 10^{20} | 5.00 × 10^{10} | 1.30 | ||

6 | 141.697 | 37.149 | 35.3 | 50 | 50 | 207 | 90 | 22 | 1.58 × 10^{20} | 5.00 × 10^{10} | 1.30 | ||

IBRK | 7.5 | 1 | 142.2 | 36.515 | 16 | 55 | 55 | 207 | 90 | 15 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.40 |

2 | 141.467 | 36.77 | 34.7 | 55 | 55 | 205 | 90 | 21 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.40 | ||

3 | 141.881 | 36.149 | 17.5 | 55 | 55 | 201 | 90 | 15 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.40 | ||

4 | 141.222 | 36.367 | 36.1 | 55 | 55 | 194 | 90 | 19 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.40 | ||

5 | 141.714 | 35.99 | 18.4 | 55 | 55 | 197 | 90 | 17 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.40 | ||

6 | 141.299 | 36.127 | 31.6 | 55 | 55 | 194 | 90 | 20 | 2.24 × 10^{20} | 5.00 × 10^{10} | 1.40 |

Item | Calculation Condition |
---|---|

Governing equation | 2D non-linear shallow water equation (Tohoku University TUNAMI model) [19] |

Numerical integration method | Staggered leap-frog differential method |

Initial condition | Okada equation [18] |

Boundary condition | Open boundary |

Coordination system | Spherical coordinate system |

Tidal setting | T.P. +0.0 m |

Mesh size | 450 m |

Time step | 0.9 s |

Calculation time | 3 h |

**Table 6.**Calculation results for Soma. (a) Earthquake source name; (b) moment magnitude of the earthquake; (c) position of the asperity; (d) tsunami wave height at a water depth of 10 m; (e) annual exceedance probability estimated using the tsunami hazard curve; (f) return period calculated from the annual exceedance probability; (g) tsunami inundation height at the risk assessment point simulated using a nonlinear longwave equation with the fault parameters.

(a) | (b) | (c) | (d) | (e) | (f) | (g) | (h) |
---|---|---|---|---|---|---|---|

Earthquake Source | Moment Magnitude (Mw) | Position of Asperity | Tsunami Height (m) (10 m Water Depth Point) | Annual Exceedance Probability | Return Period (year) | Tsunami Inundation Height (m) (Risk Assessment Point) | Tsunami Inundation Depth (m) (Risk Assessment Point) |

TOHOKU | 9.1 | Center | 8.58 | 0.000294 | 3405 | 13.63 | 9.96 |

9.1 | Between south and center | 7.84 | 0.000423 | 2363 | 10.33 | 6.66 | |

9.1 | South | 7.84 | 0.000425 | 2355 | 12.54 | 8.87 | |

9.0 | Center | 7.10 | 0.000579 | 1728 | 11.54 | 7.87 | |

9.1 | Between north and center | 6.78 | 0.000655 | 1526 | 10.56 | 6.89 | |

9.0 | South | 6.58 | 0.000702 | 1425 | 11.13 | 7.46 | |

9.1 | North | 6.51 | 0.000720 | 1388 | 10.68 | 7.01 | |

9.0 | Between south and center | 6.48 | 0.000725 | 1379 | 10.41 | 6.74 | |

9.0 | Between north and center | 5.49 | 0.000992 | 1008 | 9.38 | 5.71 | |

8.9 | Center | 5.44 | 0.001009 | 991 | 9.27 | 5.60 | |

9.0 | North | 5.42 | 0.001015 | 986 | 9.35 | 5.68 | |

8.9 | South | 5.28 | 0.001052 | 950 | 9.65 | 5.98 | |

8.9 | Between south and center | 4.93 | 0.001171 | 854 | 8.54 | 4.87 | |

8.9 | Between north and center | 4.40 | 0.001381 | 724 | 8.08 | 4.41 | |

8.9 | North | 4.08 | 0.001538 | 650 | 7.89 | 4.22 | |

JTNR | 8.4 | North | 2.50 | 0.004316 | 232 | 4.30 | 0.63 |

8.4 | Center | 2.47 | 0.004464 | 224 | 3.97 | 0.30 | |

8.4 | South | 2.37 | 0.005014 | 199 | 3.84 | 0.17 | |

JTN2 + JTN3 | 8.2 | South | 2.29 | 0.005459 | 183 | 4.51 | 0.84 |

8.2 | Center | 2.26 | 0.005667 | 176 | 4.36 | 0.69 | |

JTT | 8.1 | Center | 2.25 | 0.005738 | 174 | 4.15 | 0.48 |

8.1 | North | 2.23 | 0.005885 | 170 | 4.10 | 0.43 | |

8.1 | Center | 2.23 | 0.005961 | 168 | 3.93 | 0.26 | |

JTNR | 8.4 | South | 2.23 | 0.005961 | 168 | 4.28 | 0.61 |

8.4 | North | 2.20 | 0.006195 | 161 | 4.88 | 1.21 | |

8.4 | Center | 2.19 | 0.006275 | 159 | 4.35 | 0.68 | |

JTT | 8.1 | North | 2.14 | 0.006612 | 151 | 3.78 | 0.11 |

8.0 | Center | 2.01 | 0.007986 | 125 | 0.00 | 0.00 | |

8.1 | South | 1.96 | 0.008441 | 118 | 0.00 | 0.00 | |

8.0 | Center | 1.96 | 0.008441 | 118 | 0.00 | 0.00 |

**Table 7.**Calculation results for Sendai. (a) Earthquake source name; (b) moment magnitude of the earthquake; (c) position of the asperity; (d) tsunami wave height at a water depth of 10 m; (e) annual exceedance probability estimated using the tsunami hazard curve; (f) return period calculated from the annual exceedance probability; (g) tsunami inundation height at the risk assessment point simulated using a nonlinear longwave equation with the fault parameters.

(a) | (b) | (c) | (d) | (e) | (f) | (g) | (h) |
---|---|---|---|---|---|---|---|

Earthquake Source | Moment Magnitude (Mw) | Position of Asperity | Tsunami Height (m) (10 m Water Depth Point) | Annual Exceedance Probability | Return Period (year) | Tsunami Inundation Height (m) (Risk Assessment Point) | Tsunami Inundation Depth (m) (Risk Assessment Point) |

TOHOKU | 9.1 | Center | 9.89 | 0.000220 | 4536 | 6.84 | 5.74 |

9.0 | Center | 8.50 | 0.000459 | 2177 | 5.97 | 4.87 | |

9.1 | Between north and center | 7.95 | 0.000603 | 1657 | 5.06 | 3.96 | |

9.1 | South | 7.58 | 0.000712 | 1404 | 4.66 | 3.56 | |

8.9 | Center | 6.82 | 0.001023 | 978 | 4.27 | 3.17 | |

9.0 | Between north and center | 6.78 | 0.001041 | 960 | 4.26 | 3.16 | |

9.1 | Between south and center | 6.64 | 0.001123 | 890 | 3.84 | 2.74 | |

9.0 | South | 6.52 | 0.001197 | 836 | 3.77 | 2.67 | |

9.1 | North | 6.38 | 0.001339 | 747 | 3.85 | 2.75 | |

8.9 | Between north and center | 5.62 | 0.002392 | 418 | 2.74 | 1.64 | |

9.0 | Between south and center | 5.56 | 0.002493 | 401 | 2.15 | 1.05 | |

9.0 | North | 5.52 | 0.002592 | 386 | 2.95 | 1.85 | |

8.9 | South | 5.30 | 0.003047 | 328 | 2.25 | 1.15 | |

8.9 | North | 4.49 | 0.005733 | 174 | 1.76 | 0.66 | |

8.9 | Between south and center | 4.30 | 0.006729 | 149 | 0.00 | 0.00 | |

JTN2 + JTN3 | 8.2 | South | 4.16 | 0.007465 | 134 | 0.00 | 0.00 |

8.2 | Center | 4.04 | 0.008285 | 121 | 0.00 | 0.00 | |

8.2 | North | 3.79 | 0.010163 | 98 | 0.00 | 0.00 | |

JTN3-1 | 8.0 | South | 3.76 | 0.010331 | 97 | 0.00 | 0.00 |

8.0 | Center | 3.61 | 0.011687 | 86 | 0.00 | 0.00 | |

JTN2 + JTN3 | 8.1 | Center | 3.41 | 0.013891 | 72 | 0.00 | 0.00 |

JTN3-1 | 8.0 | North | 3.36 | 0.014356 | 70 | 0.00 | 0.00 |

JTN2 + JTN3 | 8.1 | South | 3.31 | 0.014959 | 67 | 0.00 | 0.00 |

JTT | 8.1 | South | 3.16 | 0.017056 | 59 | 0.00 | 0.00 |

JTN2 + JTN3 | 8.1 | North | 3.13 | 0.017479 | 57 | 0.00 | 0.00 |

JTT | 8.1 | Center | 3.01 | 0.019274 | 52 | 0.00 | 0.00 |

JTN3-1 | 7.9 | Center | 2.93 | 0.020564 | 49 | 0.00 | 0.00 |

JTNR | 8.4 | South | 2.90 | 0.021068 | 47 | 0.00 | 0.00 |

8.4 | North | 2.87 | 0.021410 | 47 | 0.00 | 0.00 | |

8.4 | Center | 2.85 | 0.021757 | 46 | 0.00 | 0.00 |

**Table 8.**Calculation results for Kesennuma. (a) Earthquake source name; (b) moment magnitude of the earthquake; (c) position of the asperity; (d) tsunami wave height at a water depth of 10 m; (e) annual exceedance probability estimated using the tsunami hazard curve; (f) return period calculated from the annual exceedance probability; (g) tsunami inundation height at the risk assessment point simulated using a nonlinear longwave equation with the fault parameters.

(a) | (b) | (c) | (d) | (e) | (f) | (g) | (h) |
---|---|---|---|---|---|---|---|

Earthquake Source | Moment Magnitude (Mw) | Position of Asperity | Tsunami Height (m) (10 m Water Depth Point) | Annual Exceedance Probability | Return Period (year) | Tsunami Inundation Height (m) (Risk Assessment Point) | Tsunami Inundation Depth (m) (Risk Assessment Point) |

TOHOKU | 9.1 | Between north and center | 19.44 | 0.000132 | 7574 | 2.91 | 1.51 |

9.1 | Center | 17.01 | 0.000254 | 634 | 2.97 | 1.57 | |

9.0 | Between north and center | 15.66 | 0.000334 | 531 | 3.18 | 1.78 | |

9.0 | Center | 14.21 | 0.000444 | 440 | 3.16 | 1.76 | |

9.1 | Between south and center | 12.41 | 0.000616 | 416 | 2.73 | 1.33 | |

9.1 | North | 12.24 | 0.000627 | 405 | 6.08 | 4.68 | |

8.9 | Between north and center | 10.50 | 0.000853 | 327 | 3.26 | 1.86 | |

8.9 | Center | 10.48 | 0.000855 | 326 | 3.08 | 1.68 | |

9.0 | North | 10.11 | 0.000896 | 318 | 5.13 | 3.73 | |

9.0 | Between south and center | 9.30 | 0.000992 | 309 | 2.78 | 1.38 | |

9.1 | South | 9.13 | 0.001019 | 309 | 4.35 | 2.95 | |

8.9 | North | 7.82 | 0.001191 | 309 | 4.34 | 2.94 | |

9.0 | South | 6.85 | 0.001320 | 307 | 3.71 | 2.31 | |

8.9 | Between south and center | 6.44 | 0.001383 | 305 | 2.46 | 1.06 | |

8.9 | South | 4.92 | 0.001951 | 194 | 3.14 | 1.74 | |

JTT | 8.1 | South | 3.63 | 0.004062 | 78 | 0.00 | 0.00 |

8.1 | South | 3.61 | 0.004093 | 77 | 0.00 | 0.00 | |

8.1 | Center | 3.56 | 0.004288 | 73 | 0.00 | 0.00 | |

8.1 | North | 3.46 | 0.004608 | 68 | 0.00 | 0.00 | |

8.1 | Center | 3.37 | 0.005007 | 61 | 0.00 | 0.00 | |

JTNR | 8.4 | South | 3.27 | 0.005458 | 55 | 0.00 | 0.00 |

8.4 | North | 3.26 | 0.005506 | 55 | 0.00 | 0.00 | |

JTT | 8.1 | North | 3.19 | 0.005808 | 51 | 0.00 | 0.00 |

JTNR | 8.4 | Center | 3.18 | 0.005860 | 50 | 0.00 | 0.00 |

JTN2 + JTN3 | 8.2 | North | 3.05 | 0.006667 | 44 | 0.00 | 0.00 |

JTNR | 8.4 | South | 2.86 | 0.008003 | 35 | 0.00 | 0.00 |

8.4 | Center | 2.82 | 0.008243 | 34 | 0.00 | 0.00 | |

JTT | 8.0 | South | 2.82 | 0.008325 | 34 | 0.00 | 0.00 |

8.0 | Center | 2.78 | 0.008662 | 32 | 0.00 | 0.00 | |

8.0 | South | 2.78 | 0.008662 | 32 | 0.00 | 0.00 |

**Table 9.**Calculation conditions for the nonlinear longwave equation used in the tsunami numerical simulation for Soma.

Item | Calculation Condition |
---|---|

Governing equation | 2D non-linear shallow water equation (Tohoku University TUNAMI model) [19] |

Numerical integration method | Staggered leap-frog differential method |

Initial condition | Okada equation [18] |

Boundary condition | Run-up boundary |

Coordinate system | Plane rectangular coordinate system IX |

Tidal setting | T.P. +0.0 m |

Mesh size | 810 m, 270 m, 90 m, 30 m, 10 m |

Time step | 0.9 s, 0.3 s, 0.1 s, 0.03 s, 0.01 s |

Calculation time | 3 h |

**Table 10.**Calculation conditions for the nonlinear longwave equation used in the tsunami numerical simulations for Sendai and Kesennuma.

Item | Calculation Condition |
---|---|

Governing equation | 2D non-linear shallow water equation (Tohoku University TUNAMI model) [19] |

Numerical integration method | Staggered leap-frog differential method |

Initial condition | Okada equation [18] |

Boundary condition | Run-up boundary |

Coordinate system | Plane rectangular coordinate system X |

Tidal setting | T.P. +0.0 m |

Mesh size | 1215 m, 405 m, 135 m, 45 m, 15 m |

Time step | 0.9 s, 0.3 s, 0.1 s, 0.03 s, 0.01 s |

Calculation time | 3 h |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Fukutani, Y.; Suppasri, A.; Imamura, F. Quantitative Assessment of Epistemic Uncertainties in Tsunami Hazard Effects on Building Risk Assessments. *Geosciences* **2018**, *8*, 17.
https://doi.org/10.3390/geosciences8010017

**AMA Style**

Fukutani Y, Suppasri A, Imamura F. Quantitative Assessment of Epistemic Uncertainties in Tsunami Hazard Effects on Building Risk Assessments. *Geosciences*. 2018; 8(1):17.
https://doi.org/10.3390/geosciences8010017

**Chicago/Turabian Style**

Fukutani, Yo, Anawat Suppasri, and Fumihiko Imamura. 2018. "Quantitative Assessment of Epistemic Uncertainties in Tsunami Hazard Effects on Building Risk Assessments" *Geosciences* 8, no. 1: 17.
https://doi.org/10.3390/geosciences8010017