**3.3 The 2007 Solomon Islands tsunami**

152 Remote Sensing of Planet Earth

Phang Nga and Phuket were two of six southern Andaman coast provinces that were damaged by the tsunami. They provinces are famous for sightseeing areas such as Khao Lak and Patong. Therefore, reinforced concrete (RC) buildings are common in this area. Regarding structural damage, 4,806 houses were affected by the tsunami, of which 3,302 houses were destroyed completely, and as many as 1,504 were partly damaged. The maximum water level of approximately 15 m reported at Khao Lak in the Phang Nga province and of 7 m at Kamala and Patong Beach in Phuket gave these areas their respective distinction as the worst and second-worst areas, with structural damage to 2,508 and 1,033 houses, respectively. High-resolution satellite images (IKONOS) taken before and after the tsunami event were used for visual damage interpretation. The pre-event images were acquired on 13 January 2003 and 24 January 2004 for Phang Nga and Phuket; the post-event images were both acquired on 15 January 2005. In a recent study (Gokon et al., 2011), four damage levels were classified "Not collapsed" (moderate, slight or no damage), "Major damage", "Collapsed" and "Washed away," using a QuickBird satellite image with a 0.6×0.6 m2 resolution. However, the 1.0×1.0 m2 resolution of the IKONOS satellite image is not fine enough for a visual interpretation to differentiate the damage levels of buildings. Therefore, the classification of the building damage in this study was limited to "Not destroyed" and "Destroyed" (Koshimura et al., 2009c). The remaining roof buildings were interpreted as "Not destroyed" and those that had disappeared were classified as "Destroyed". Note that the buildings classified as "Not destroyed" may have had some sort of Damage that could be identified by the satellite images. The results of the building damage inspection in residential areas are presented in Fig. 10 (Suppasri et al., 2011a), which shows damaged buildings in residential areas in Khao Lak, Phang Nga province (1,722 destroyed and 1,285 not destroyed) and the populated residential areas in Kamala and Patong, Phuket province (233 destroyed and 1,356 not destroyed). The visual interpretation data resulted in an accuracy of more than 90 per cent after being checked with the

Fig. 10. Visual damage inspection results in Phang Nga and Phuket, Thailand

**3.2.2 Phang Nga and Phuket, Thailand** 

investigation data.

The 2007 Solomon Islands earthquake took place on 1 April 2007 near the provincial capital of Ghizo on Ghizo Island, in the Solomon Islands. The magnitude of this earthquake was calculated by the United States Geological Survey (USGS) as 8.1 on the moment magnitude scale. The tsunami that followed the earthquake killed 52 people. The structural/house damage was focused on Ghizo Island and was caused by the tsunami. First, the QuickBird pan-sharpened composite images of Ghizo Island were acquired pre- and post-tsunami (23 September 2003 and 5 April 2007) to build house inventories for visual damage inspection, as shown in Fig. 11 (Koshimura et al., 2010). The extent of the tsunami inundation zone is determined by the supervised classification based on the NDVI of the post-tsunami satellite imagery (Fig. 12), as already shown in section 2.1.

Fig. 11. The structural damage interpretation is divided into four classes: slight/no damage, substantial damage, collapsed and washed away

Fig. 12. Visual damage inspection results for Ghizo Island, Solomon Islands

Application of Remote Sensing for Tsunami Disaster 155

A moment magnitude 8.8 earthquake struck the central region of Chile on February 27, 2010. The earthquake produced a tsunami that caused major damage in locations spanning over 500 km of coastline, from Tirúa to Pichilemu. The coastal locations were affected by both ground shaking and the tsunami. As of May 2010, 521 people had died and 56 persons were still missing. The earthquake and tsunami destroyed over 81,000 houses, and another 109,000 were severely damaged. Following Matsuoka & Nojima (2009), the regression discriminant function for building damage was calculated from two characteristic values: the correlation coefficient and the difference in the backscattering coefficient for pre- and post-event SAR images (Matsuoka & Koshimura, 2010). First, following the accurate positioning of the two SAR images, a speckle noise filter with a 21×21 pixel window was applied to each image. The difference value, *d*, is calculated by subtracting the average value of the backscattering coefficient within a 13×13 pixel window in the pre-event image from the post-event image (after – before). The correlation coefficient, *r*, is also calculated from the same 13×13 pixel window. The result of applying regression discriminant analysis, using the *d* and *r* from the building damage dataset of the 1995 Kobe earthquake, is shown in Equation (2), where the values of parameters A and B are modified to 1.277 and 2.729, respectively. Here, *ZR1* in Equation (2) represents the discriminant score from the SAR images. The pixels whose *ZR1* value is positive are interpreted as suffering severe damage. Because both coefficients are negative, higher and negative *d* or smaller *r* produce larger *ZR1* values. However, in the tsunami damage areas in the PALSAR images in the abovementioned examination, the backscattered echoes were stronger in the post-tsunami image. To detect such damaged areas using image analysis, cases where the reverse occurs need to be considered. Therefore, the absolute value of the difference in the backscattering coefficient, |*d*|, was calculated, which changed the coefficient of the difference to positive values, as shown in Equation (3), where the values of parameters A and B are modified to 1.277 and 2.729, respectively. Here, *ZR2* represents the modified discriminant score. Using this formula, the pixels whose *ZR2* value is positive might be assigned as areas damaged not only by earthquakes but also by tsunamis. Using the procedure described above and the PALSAR images of the 2010 Chile earthquake tsunami, discriminant scores *ZR2* were calculated in the areas shown to be vulnerable on the inundation susceptibility maps, and

Fig. 14(a). Distribution of *ZR2* obtained by ALSAR images in Talcahuano and optical images

**3.5 The 2010 Chile tsunami** 

the tsunami damage distribution was estimated.

#### **3.4 The 2009 Samoa Islands tsunami**

In 2009, a tsunami accompanied by a M8.1 earthquake off the southwest coast of Tutuila Island, American Samoa, struck the Samoa and Tonga islands and caused a total of 184 deaths and 7 missing. A visual damage inspection was conducted using pre- and posttsunami QuickBird images acquired on 15 April 2007, 24 September 2009, 29 September 2009, 02 October 2009 and November 2009. The damaged structures were classified into four categories: washed-away, collapsed, major damage and survived (as previously mentioned in Fig. 7). The number of inspected houses and structures in the four study areas, namely, Pago Pago, Amanave, Poloa and Leone, totalled 451, and the results are summarised in Fig. 13 and Table 2 (Gokon et al., 2011).

Fig. 13. Visual damage inspection results in Tutuila Island, American Samoa


Table 2. Results of structural damage interpretation in Tutuila Island, American Samoa

#### **3.5 The 2010 Chile tsunami**

154 Remote Sensing of Planet Earth

In 2009, a tsunami accompanied by a M8.1 earthquake off the southwest coast of Tutuila Island, American Samoa, struck the Samoa and Tonga islands and caused a total of 184 deaths and 7 missing. A visual damage inspection was conducted using pre- and posttsunami QuickBird images acquired on 15 April 2007, 24 September 2009, 29 September 2009, 02 October 2009 and November 2009. The damaged structures were classified into four categories: washed-away, collapsed, major damage and survived (as previously mentioned in Fig. 7). The number of inspected houses and structures in the four study areas, namely, Pago Pago, Amanave, Poloa and Leone, totalled 451, and the results are summarised in Fig.

Fig. 13. Visual damage inspection results in Tutuila Island, American Samoa

Washed-away 34/42/13/28/117 Collapsed 7/3/1/7/18 Major damage 142/0/12/28 Survived 5434/4/196/288

Damage category Number of houses (Pago Pago/Amanave/Poloa/Leone/Total

Table 2. Results of structural damage interpretation in Tutuila Island, American Samoa

**3.4 The 2009 Samoa Islands tsunami** 

13 and Table 2 (Gokon et al., 2011).

A moment magnitude 8.8 earthquake struck the central region of Chile on February 27, 2010. The earthquake produced a tsunami that caused major damage in locations spanning over 500 km of coastline, from Tirúa to Pichilemu. The coastal locations were affected by both ground shaking and the tsunami. As of May 2010, 521 people had died and 56 persons were still missing. The earthquake and tsunami destroyed over 81,000 houses, and another 109,000 were severely damaged. Following Matsuoka & Nojima (2009), the regression discriminant function for building damage was calculated from two characteristic values: the correlation coefficient and the difference in the backscattering coefficient for pre- and post-event SAR images (Matsuoka & Koshimura, 2010). First, following the accurate positioning of the two SAR images, a speckle noise filter with a 21×21 pixel window was applied to each image. The difference value, *d*, is calculated by subtracting the average value of the backscattering coefficient within a 13×13 pixel window in the pre-event image from the post-event image (after – before). The correlation coefficient, *r*, is also calculated from the same 13×13 pixel window. The result of applying regression discriminant analysis, using the *d* and *r* from the building damage dataset of the 1995 Kobe earthquake, is shown in Equation (2), where the values of parameters A and B are modified to 1.277 and 2.729, respectively. Here, *ZR1* in Equation (2) represents the discriminant score from the SAR images. The pixels whose *ZR1* value is positive are interpreted as suffering severe damage. Because both coefficients are negative, higher and negative *d* or smaller *r* produce larger *ZR1* values. However, in the tsunami damage areas in the PALSAR images in the abovementioned examination, the backscattered echoes were stronger in the post-tsunami image. To detect such damaged areas using image analysis, cases where the reverse occurs need to be considered. Therefore, the absolute value of the difference in the backscattering coefficient, |*d*|, was calculated, which changed the coefficient of the difference to positive values, as shown in Equation (3), where the values of parameters A and B are modified to 1.277 and 2.729, respectively. Here, *ZR2* represents the modified discriminant score. Using this formula, the pixels whose *ZR2* value is positive might be assigned as areas damaged not only by earthquakes but also by tsunamis. Using the procedure described above and the PALSAR images of the 2010 Chile earthquake tsunami, discriminant scores *ZR2* were calculated in the areas shown to be vulnerable on the inundation susceptibility maps, and the tsunami damage distribution was estimated.

Fig. 14(a). Distribution of *ZR2* obtained by ALSAR images in Talcahuano and optical images

Application of Remote Sensing for Tsunami Disaster 157

On March 11, 2011, a giant earthquake of M9.0, whose epicentre was located off the eastern part of Miyagi prefecture, Japan, caused catastrophic damage to the coastal area facing the Pacific Ocean of the Tohoku district. This earthquake caused an enormous tsunami with a run-up height that reached 40 m and destroyed approximately 270,000 houses. Aerial photos that were captured on March 12, 13 and 19 and April 1 and 5 in 2011 by GSI were used to classify the electronic building map into 2 classes: washed-away or surviving (Gokon & Koshimura, 2011). First, the panels of ortho photos, with a resolution of 80 cm/pixel, are combined with mosaic image processing. Then the electronic map and the aerial photos were integrated into the same coordinate system in ArcGIS. Finally, a visual inspection was performed for the building damage one by one (washed-away or surviving) for all the buildings in the inundation area in Miyagi prefecture, Japan. Housing damage characteristics can be explained by bathymetry conditions as follows: the Ria coast, i.e., the towns of Minami-Sanriku in Fig. 15 (upper-left), has the potential to amplify the tsunami height. As a result, the probabilities of the washed away houses in the inundation area are estimated to be over 70%. In Ishinomaki city, the number of washed away houses is small in an area located behind the breakwaters and control forests. The effect of the breakwaters and control forests in reducing tsunami damage is shown in Fig. 15 (lower-left). Most of the buildings in Matsushima town and Shiogama city, located in a bay with a small opening and almost 270 small Islands acted as natural barrier, survived the tsunami, as shown in Fig.

Fig. 15. Visual damage inspection results in Minami-Sanriku town (upper-left), Ishinomaki city (lower-left), and Matsushima town and Shiogama city (right). The red rectangles show

**Shiogama** 

**Matsushima** 

**4. Developing a tsunami vulnerability function by applying a numerical model**  The next step is to apply the previous damage inspection data with the tsunami numerical model. One method is to develop a fragility curve (Koshimura et al., 2009b). The tsunami

washed away houses and the blue areas indicate tsunami inundation areas.

**3.6 The 2011 Tohoku tsunami** 

15 (right).

The results are shown in Fig. 14 (a) and (b). The sections on the sea are masked, but the areas where the river could not be masked have large *ZR2* values because of the surface changes caused by the flow of water. The wetlands near Talcahuano and Llico, where the *ZR2* values are large, seem to be affected by the tsunami. Figure 14(b) shows a close-up *ZR2* image of the Dichato area, with a comparison pre- and post-tsunami from an optical image (Koshimura et al., 2011).

Fig. 14(b). Distribution of *ZR2* in a close-up of the Dichato area and comparison of optical images pre- and post-tsunami

#### **3.6 The 2011 Tohoku tsunami**

156 Remote Sensing of Planet Earth

The results are shown in Fig. 14 (a) and (b). The sections on the sea are masked, but the areas where the river could not be masked have large *ZR2* values because of the surface changes caused by the flow of water. The wetlands near Talcahuano and Llico, where the *ZR2* values are large, seem to be affected by the tsunami. Figure 14(b) shows a close-up *ZR2* image of the Dichato area, with a comparison pre- and post-tsunami from an optical image (Koshimura

Fig. 14(b). Distribution of *ZR2* in a close-up of the Dichato area and comparison of optical

et al., 2011).

images pre- and post-tsunami

Post-tsunami

Pre-tsunami

On March 11, 2011, a giant earthquake of M9.0, whose epicentre was located off the eastern part of Miyagi prefecture, Japan, caused catastrophic damage to the coastal area facing the Pacific Ocean of the Tohoku district. This earthquake caused an enormous tsunami with a run-up height that reached 40 m and destroyed approximately 270,000 houses. Aerial photos that were captured on March 12, 13 and 19 and April 1 and 5 in 2011 by GSI were used to classify the electronic building map into 2 classes: washed-away or surviving (Gokon & Koshimura, 2011). First, the panels of ortho photos, with a resolution of 80 cm/pixel, are combined with mosaic image processing. Then the electronic map and the aerial photos were integrated into the same coordinate system in ArcGIS. Finally, a visual inspection was performed for the building damage one by one (washed-away or surviving) for all the buildings in the inundation area in Miyagi prefecture, Japan. Housing damage characteristics can be explained by bathymetry conditions as follows: the Ria coast, i.e., the towns of Minami-Sanriku in Fig. 15 (upper-left), has the potential to amplify the tsunami height. As a result, the probabilities of the washed away houses in the inundation area are estimated to be over 70%. In Ishinomaki city, the number of washed away houses is small in an area located behind the breakwaters and control forests. The effect of the breakwaters and control forests in reducing tsunami damage is shown in Fig. 15 (lower-left). Most of the buildings in Matsushima town and Shiogama city, located in a bay with a small opening and almost 270 small Islands acted as natural barrier, survived the tsunami, as shown in Fig. 15 (right).

Fig. 15. Visual damage inspection results in Minami-Sanriku town (upper-left), Ishinomaki city (lower-left), and Matsushima town and Shiogama city (right). The red rectangles show washed away houses and the blue areas indicate tsunami inundation areas.

### **4. Developing a tsunami vulnerability function by applying a numerical model**

The next step is to apply the previous damage inspection data with the tsunami numerical model. One method is to develop a fragility curve (Koshimura et al., 2009b). The tsunami

Application of Remote Sensing for Tsunami Disaster 159

Fig. 16. Tsunami damage detected by the visual interpretation of IKONOS pre- and posttsunami imageries. The red dots indicate totally damaged houses and the blue dots not-

Fig. 17. Modelled tsunami inundation in the city of Banda Aceh. The result is validated by

Correlate the damage data and the hydrodynamic features of tsunami inundation through

Sample sorting by the level of hydrodynamic features to explore an arbitrary range of these features such that each range includes the determined number of samples; check the data

the measured flow depth shown with the squares in the figure.

*Data assimilation between the damage data and tsunami hazard information* 

Speculate the hydrodynamic feature of tsunamis by numerical modelling.

damaged.

*Tsunami hazard estimation* 

the GIS analysis. *Sample determination* 

distribution.

fragility curve is a function used to estimate the structural fragility against tsunami hazards. Visual inspections of satellite images taken before and after tsunami events are to be used to classify whether the buildings were destroyed or not based on the remaining roofs. Then a tsunami inundation model is created to reconstruct the tsunami features, such as inundation depth, current velocity, and hydrodynamic force of the event. For the tsunami inundation model, a set of nonlinear shallow water equations are discretised using the Staggered Leap-frog finite difference scheme (Imamura, 1995), with the bottom friction in the form of Manning's formula according to a land use condition. In general, two methods exist for modelling flow resistance depending on the relation between the scale of an obstacle and the grid size: the topography model and the equivalent roughness model. The topography model is used when the grid size is finer than the obstacle. The tsunami in the model simulation will not pass into a grid space that is occupied by an obstacle. Then the flow around an obstacle and the contracting flow between obstacles can be simulated. However, in a larger grid size, such as that of this study, the obstacle is smaller than the grid size. The equivalent roughness model is then appropriate for this problem. In a non-residential area, the roughness coefficient is inferred from land use, and it is used to quantify the Manning's roughness coefficient (s·m−1/3). The lowest Manning's roughness coefficient is 0.02 for smooth ground, followed by 0.025 for shallow water or natural beach and by 0.03 for vegetated area. However, Manning's roughness coefficient in a densely populated area is highly affected by the number of buildings in each computational grid. In a densely populated town, in which the building occupation ratio is high, the resistance law with the composite equivalent roughness coefficient according to land use and building conditions was first studied by Aburaya & Imamura (2002), as shown in Equation (4).

$$n = \sqrt{n\_0^2 + \frac{C\_D}{2g\nu} \times \frac{\theta}{100 - \theta}} \times D^{4/3} \tag{4}$$

In this equation, *n*0 signifies the Manning's roughness coefficient (*n*0=0.025, s·m-1/3), *θ* denotes the building/house occupation ratio in percentage varying within the range from 0 to 100 in the finest computational grid of 52 m and obtained by calculating the building area over the grid area using GIS data. *CD* represents the drag coefficient (*CD*=1.5), *w*  stands for the horizontal scale of houses, and *D* is the modelled flow depth. Fragility curves can be developed for various types, such as building material (wood, block or reinforced concrete), number of floors and country. Developed tsunami fragility curves are crucial for future tsunami risk assessment when tsunami hazards and exposure data are given.

#### **4.1 Method and procedure for developing tsunami fragility curves**

To develop tsunami fragility curves, a statistical approach is used with a synergistic use of the numerical model results and damage data by the procedure itemised below.

#### *Damage data acquisition*

The damage data was obtained from pre- and post–tsunami aerial photographs (e.g., number of destroyed or surviving structures).

fragility curve is a function used to estimate the structural fragility against tsunami hazards. Visual inspections of satellite images taken before and after tsunami events are to be used to classify whether the buildings were destroyed or not based on the remaining roofs. Then a tsunami inundation model is created to reconstruct the tsunami features, such as inundation depth, current velocity, and hydrodynamic force of the event. For the tsunami inundation model, a set of nonlinear shallow water equations are discretised using the Staggered Leap-frog finite difference scheme (Imamura, 1995), with the bottom friction in the form of Manning's formula according to a land use condition. In general, two methods exist for modelling flow resistance depending on the relation between the scale of an obstacle and the grid size: the topography model and the equivalent roughness model. The topography model is used when the grid size is finer than the obstacle. The tsunami in the model simulation will not pass into a grid space that is occupied by an obstacle. Then the flow around an obstacle and the contracting flow between obstacles can be simulated. However, in a larger grid size, such as that of this study, the obstacle is smaller than the grid size. The equivalent roughness model is then appropriate for this problem. In a non-residential area, the roughness coefficient is inferred from land use, and it is used to quantify the Manning's roughness coefficient (s·m−1/3). The lowest Manning's roughness coefficient is 0.02 for smooth ground, followed by 0.025 for shallow water or natural beach and by 0.03 for vegetated area. However, Manning's roughness coefficient in a densely populated area is highly affected by the number of buildings in each computational grid. In a densely populated town, in which the building occupation ratio is high, the resistance law with the composite equivalent roughness coefficient according to land use and building conditions was first studied by Aburaya & Imamura (2002), as

shown in Equation (4).

are given.

*Damage data acquisition* 

number of destroyed or surviving structures).

� � ���

**4.1 Method and procedure for developing tsunami fragility curves** 

the numerical model results and damage data by the procedure itemised below.

� + �� ��� <sup>×</sup> �

In this equation, *n*0 signifies the Manning's roughness coefficient (*n*0=0.025, s·m-1/3), *θ* denotes the building/house occupation ratio in percentage varying within the range from 0 to 100 in the finest computational grid of 52 m and obtained by calculating the building area over the grid area using GIS data. *CD* represents the drag coefficient (*CD*=1.5), *w*  stands for the horizontal scale of houses, and *D* is the modelled flow depth. Fragility curves can be developed for various types, such as building material (wood, block or reinforced concrete), number of floors and country. Developed tsunami fragility curves are crucial for future tsunami risk assessment when tsunami hazards and exposure data

To develop tsunami fragility curves, a statistical approach is used with a synergistic use of

The damage data was obtained from pre- and post–tsunami aerial photographs (e.g.,

��� � � × ���� (4)

Fig. 16. Tsunami damage detected by the visual interpretation of IKONOS pre- and posttsunami imageries. The red dots indicate totally damaged houses and the blue dots notdamaged.

### *Tsunami hazard estimation*

Speculate the hydrodynamic feature of tsunamis by numerical modelling.

Fig. 17. Modelled tsunami inundation in the city of Banda Aceh. The result is validated by the measured flow depth shown with the squares in the figure.

#### *Data assimilation between the damage data and tsunami hazard information*

Correlate the damage data and the hydrodynamic features of tsunami inundation through the GIS analysis.

#### *Sample determination*

Sample sorting by the level of hydrodynamic features to explore an arbitrary range of these features such that each range includes the determined number of samples; check the data distribution.

Application of Remote Sensing for Tsunami Disaster 161

Least-squares fit y = 1.1174x + 2.9851 R² = 0.99

Taking as an analogy earthquake engineering studies, the cumulative probability *PD* of damage occurrence is assumed to be given with two statistical parameters, (*μ, σ*) or (*μ', σ'*). The cumulative probability *P* of the occurrence of damage is given either by Equation (5) or (6):


**Φ-1**

���� ������

���� ����� � � �*′*

In these equations, *Φ* represents the standardised normal (log-normal) distribution function, *x* stands for the hydrodynamic feature of the tsunami (e.g., inundation depth, current velocity and hydrodynamic force), and *μ* and *σ* (*μ'* and *σ'*), respectively, signify the mean and standard deviation of *x* (ln *x*). Two statistical parameters of the fragility function, *μ* and *σ* (*μ'* and *σ'*), are obtained by plotting *x* (ln *x*) against the inverse of *Φ* on normal or lognormal probability papers and performing a least-squares fitting of this plot. Consequently, two parameters are obtained by taking the intercept (= *μ* or *μ'*) and the angular coefficient (=

Throughout the regression analysis, the parameters are determined as shown in Table 8 to obtain the best fit of fragility curves with respect to the inundation depth, the maximum current velocity and the hydrodynamic force on structures per unit width. Here, the hydrodynamic force acting on a structure is defined as its drag force per unit width as

> � � 1

� � (5)

�*′* � (6)

� � ���� � � (7)

<sup>2</sup> ������ (9)

���� � ����� � �� (8)

Fig. 20. An example of the plot on normal probability paper

0

1

2

3

**Inundation depth (m)**

4

5

6

*σ* or *σ'*) in Equations (7) or (8):

Fig. 18. Histogram of damaged and not-damaged houses to calculate the damage probability

#### *Calculating damage probability*

Calculate the structural damage probabilities by counting the number of destroyed or surviving structures within each range of the tsunami hydrodynamic features described above.

**Inundation depth (m)**

Fig. 19. The plot of damage probabilities and the median values of inundation depths that were compiled from sample data

#### *Regression analysis*

Determine the fragility curves by the regression analysis of the discrete set of the structural damage probabilities and hydrodynamic features of a tsunami. The damage probabilities of buildings and a discrete set were calculated and shown against a median value within a range. Linear regression analysis was performed to develop the fragility function.

Fig. 18. Histogram of damaged and not-damaged houses to calculate the damage probability

2.8

3.1

**Inundation depth (m)**

3.5

3.9

4.2

4.5

4.8

5.1

**Destroyed Survived**

5.6

8.2

Calculate the structural damage probabilities by counting the number of destroyed or surviving structures within each range of the tsunami hydrodynamic features described

Fig. 19. The plot of damage probabilities and the median values of inundation depths that

**Inundation depth (m)**

02468

Determine the fragility curves by the regression analysis of the discrete set of the structural damage probabilities and hydrodynamic features of a tsunami. The damage probabilities of buildings and a discrete set were calculated and shown against a median value within a range. Linear regression analysis was performed to develop the fragility

*Calculating damage probability* 

**Number of building**

0.2

0.6

1.0

1.3

1.7

2.1

2.4

were compiled from sample data

0

0.2

0.4

0.6

**Damage probability**

0.8

1

*Regression analysis* 

function.

above.

Fig. 20. An example of the plot on normal probability paper

Taking as an analogy earthquake engineering studies, the cumulative probability *PD* of damage occurrence is assumed to be given with two statistical parameters, (*μ, σ*) or (*μ', σ'*). The cumulative probability *P* of the occurrence of damage is given either by Equation (5) or (6):

$$P(\mathbf{x}) = \Phi\left[\frac{\mathbf{x} - \mu}{\sigma}\right] \tag{5}$$

$$P(\mathbf{x}) = \Phi\left[\frac{\ln \mathbf{x} - \mu'}{\sigma'}\right] \tag{6}$$

In these equations, *Φ* represents the standardised normal (log-normal) distribution function, *x* stands for the hydrodynamic feature of the tsunami (e.g., inundation depth, current velocity and hydrodynamic force), and *μ* and *σ* (*μ'* and *σ'*), respectively, signify the mean and standard deviation of *x* (ln *x*). Two statistical parameters of the fragility function, *μ* and *σ* (*μ'* and *σ'*), are obtained by plotting *x* (ln *x*) against the inverse of *Φ* on normal or lognormal probability papers and performing a least-squares fitting of this plot. Consequently, two parameters are obtained by taking the intercept (= *μ* or *μ'*) and the angular coefficient (= *σ* or *σ'*) in Equations (7) or (8):

$$
\pi = \sigma \Phi^{-1} + \mu \tag{7}
$$

$$
\ln \pi = \sigma' \Phi^{-1} + \mu' \tag{8}
$$

Throughout the regression analysis, the parameters are determined as shown in Table 8 to obtain the best fit of fragility curves with respect to the inundation depth, the maximum current velocity and the hydrodynamic force on structures per unit width. Here, the hydrodynamic force acting on a structure is defined as its drag force per unit width as

$$F = \frac{1}{2} \mathcal{C}\_D \rho u^2 D\tag{9}$$

Application of Remote Sensing for Tsunami Disaster 163

local inundation depth exceeds 2 or 3 m, the current velocity exceeds 2.5 m/s or the

hydrodynamic load on a structure exceeds 5 kN/m (Fig. 22).

0 0.2 0.4 0.6 0.8 1

**4.4 Tsunami fragility curves for Phang Nga and Phuket, Thailand** 

Phang Nga.

0

0 2 4 6 8 10

**Depth (m)**

0.2

0.4

**Damage probability**

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

**Damage probability**

02468

**Depth (m)**

Fig. 22. Tsunami fragility curves as a function of tsunami features for Banda Aceh

Fig. 23(a). Tsunami fragility curves as a function of tsunami features for Phang Nga

0 2 4 6 8 10 **Velocity (m/s)**

0

0 50 100 150 200 **Force (kN/m)**

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

From the visual inspection of damaged buildings based on the remaining roof structures, a histogram of tsunami features (inundation depth, current velocity, and hydrodynamic force) and the number of buildings, including those not destroyed and those destroyed, was plotted. The damage probabilities of buildings and a discrete set were calculated and shown against a median value within a range of approximately 100 buildings in Phang Nga and 50 buildings in Phuket. Linear regression analysis was performed to develop the fragility function. The differences in damage characteristics of the buildings in Phang Nga and Phuket due to the construction materials are represented by the developed fragility curves in this study (Fig. 23 (a) and (b)). Although the inundation depth of 6 m engenders 100% damage probability in both locations, a lower inundation depth of 2 m is more fragile in Phang Nga: the damage probability would be 25% in Phuket but would be as high as 35% in

0123456 **Velocity (m/s)**

0 0.2 0.4 0.6 0.8 1

> 0 10 20 30 40 50 **Force (kN/m)**

where *CD* denotes the drag coefficient (*CD* = 1*.*0 for simplicity), *ρ* is the density of water (= 1*,*000 kg*/*m3), *u* stands for the current velocity (m/s), and *D* is the inundation depth (m). From this result, all the fragility functions with respect to the inundation depth, current velocity and hydrodynamic force are given by the standardised lognormal distribution functions with *μ'* and *σ'*. It should be noted that because the damage interpretation using the pre- and post–tsunami satellite images focused on whether the houses' roofs remained, we supposed that the structural damage was caused by the tsunami inundation. Additionally, note that the tsunami damage to structures was caused by both hydrodynamic force/impact and the impact of floating debris, i.e., these facts are reflected in the damage probabilities but not in the numerical model results (the estimated hydrodynamic features). In that sense, the present fragility functions might indicate overestimation in terms of the damage probabilities to the hydrodynamic features of the tsunami inundation flow.

#### **4.2 Tsunami fragility curves for Okushiri Island, Japan**

The task of discriminating between the damage caused by tsunami inundation or by fire was quite speculative. Thus, fragility curves were developed using 523 houses within the inundation zone estimated by the numerical model. A relationship between the damage probability and the tsunami's hydrodynamic features were obtained as a discrete set of structural damage probabilities using a range of approximately 50 buildings and the tsunami hazard. The relationship was explored with the form of a fragility curve by performing the regression analysis. Structural damage is severe when the inundation depth is greater than 3 m, the current velocity is greater than 4 m/s and the hydrodynamic force is greater than 25 kN/m (Fig. 21).

Fig. 21. Tsunami fragility curves as a function of tsunami features for Okushiri Island

#### **4.3 Tsunami fragility curves for Banda Aceh, Indonesia**

The number of destroyed buildings in Banda Aceh is 16,474, and the number of surviving building is 32,436 based on the remaining roofs. The damage probabilities of buildings and a discrete set were calculated and shown against a median value within a range of approximately 1,000 buildings. Linear regression analysis was performed to develop the fragility function. As a result, the fragility curves are obtained as Figure 20, indicating the damage probabilities according to the hydrodynamic features of the tsunami inundation flow in Banda Aceh. For instance, the structures were significantly vulnerable when the

where *CD* denotes the drag coefficient (*CD* = 1*.*0 for simplicity), *ρ* is the density of water (= 1*,*000 kg*/*m3), *u* stands for the current velocity (m/s), and *D* is the inundation depth (m). From this result, all the fragility functions with respect to the inundation depth, current velocity and hydrodynamic force are given by the standardised lognormal distribution functions with *μ'* and *σ'*. It should be noted that because the damage interpretation using the pre- and post–tsunami satellite images focused on whether the houses' roofs remained, we supposed that the structural damage was caused by the tsunami inundation. Additionally, note that the tsunami damage to structures was caused by both hydrodynamic force/impact and the impact of floating debris, i.e., these facts are reflected in the damage probabilities but not in the numerical model results (the estimated hydrodynamic features). In that sense, the present fragility functions might indicate overestimation in terms of the damage

The task of discriminating between the damage caused by tsunami inundation or by fire was quite speculative. Thus, fragility curves were developed using 523 houses within the inundation zone estimated by the numerical model. A relationship between the damage probability and the tsunami's hydrodynamic features were obtained as a discrete set of structural damage probabilities using a range of approximately 50 buildings and the tsunami hazard. The relationship was explored with the form of a fragility curve by performing the regression analysis. Structural damage is severe when the inundation depth is greater than 3 m, the current velocity is greater than 4 m/s and the hydrodynamic force is

probabilities to the hydrodynamic features of the tsunami inundation flow.

**4.2 Tsunami fragility curves for Okushiri Island, Japan** 

0 0.2 0.4 0.6 0.8 1

**4.3 Tsunami fragility curves for Banda Aceh, Indonesia** 

Fig. 21. Tsunami fragility curves as a function of tsunami features for Okushiri Island

The number of destroyed buildings in Banda Aceh is 16,474, and the number of surviving building is 32,436 based on the remaining roofs. The damage probabilities of buildings and a discrete set were calculated and shown against a median value within a range of approximately 1,000 buildings. Linear regression analysis was performed to develop the fragility function. As a result, the fragility curves are obtained as Figure 20, indicating the damage probabilities according to the hydrodynamic features of the tsunami inundation flow in Banda Aceh. For instance, the structures were significantly vulnerable when the

02468 **Velocity (m/s)**

0 0.2 0.4 0.6 0.8 1

> 0 25 50 75 100 **Force (kN/m)**

greater than 25 kN/m (Fig. 21).

02468

**Depth (m)**

0 0.2 0.4 0.6 0.8 1

**Damage probability**

local inundation depth exceeds 2 or 3 m, the current velocity exceeds 2.5 m/s or the hydrodynamic load on a structure exceeds 5 kN/m (Fig. 22).

Fig. 22. Tsunami fragility curves as a function of tsunami features for Banda Aceh

#### **4.4 Tsunami fragility curves for Phang Nga and Phuket, Thailand**

From the visual inspection of damaged buildings based on the remaining roof structures, a histogram of tsunami features (inundation depth, current velocity, and hydrodynamic force) and the number of buildings, including those not destroyed and those destroyed, was plotted. The damage probabilities of buildings and a discrete set were calculated and shown against a median value within a range of approximately 100 buildings in Phang Nga and 50 buildings in Phuket. Linear regression analysis was performed to develop the fragility function. The differences in damage characteristics of the buildings in Phang Nga and Phuket due to the construction materials are represented by the developed fragility curves in this study (Fig. 23 (a) and (b)). Although the inundation depth of 6 m engenders 100% damage probability in both locations, a lower inundation depth of 2 m is more fragile in Phang Nga: the damage probability would be 25% in Phuket but would be as high as 35% in Phang Nga.

Fig. 23(a). Tsunami fragility curves as a function of tsunami features for Phang Nga

Application of Remote Sensing for Tsunami Disaster 165

wood

wood & brick

Some RC

Some RC

This chapter introduced how remote sensing can be applied for tsunami research fields. In general, remote sensing is used for rapid and large-scale damage detection to understand the scale of a tsunami, especially when accessibility to disaster-affected areas is limited in the immediate aftermath. Some of the general applications shown in this chapter are related to the tsunami inundation limit, damaged buildings/debris and mangrove recovery monitoring. SAR images are used to determine tsunami-affected areas using the reflection property or backscattering coefficient as mentioned in the previous section. The next step focused on damage classification in a tsunami affected area, i.e., structural damage of housing or buildings. The benefit of high-resolution images from the sky helps tsunami researchers interpret the tsunami damage level based on roofs. A one-metre resolution, such as that of IKONOS, could help classify buildings as destroyed or not destroyed. In addition, a very high-resolution satellite image such as QuickBird (0.6 m resolution) was used to classify a number of levels, i.e., washed-away, collapsed, major damage or survived. Some recent research on tsunami events was introduced, namely, the 1993 Hokkaido Nansei-oki tsunami, the 2004 Indian Ocean tsunami, the 2007 Solomon tsunami, the 2009 Samoa tsunami, the 2010 Chile tsunami and the most recent 2011 Tohoku tsunami. However, information from the sky has some limitations because it is impossible to make a detailed damage inspection of a structural member, and it might have some errors compared with an actual field survey. Finally, classified structural damage data from a visual interpretation of high-resolution satellite images were used in combination with the tsunami numerical simulation to develop tsunami vulnerability curves called tsunami fragility curves. Tsunami

Current velocity 0.475 0.776 0.89 Hydrodynamic force 1.033 1.186 0.92

Current velocity 0.799 0.278 0.97 Hydrodynamic force 2.090 0.791 0.99

Current velocity 0.649 0.952 0.72 Hydrodynamic force 1.748 1.937 0.75

Inundation depth 0.917 0.642 0.62 Current velocity 0.352 0.675 0.32 Hydrodynamic force 0.821 3.000 0.50

Current velocity 0.541 1.650 0.73 Hydrodynamic force 1.070 3.160 0.72

Inundation depth Mainly

Inundation depth Mainly

Inundation depth

Inundation depth

Table 3. Summary of statistical parameters for developed fragility curves

type <sup>μ</sup> <sup>σ</sup> <sup>μ</sup>' σ' R2

2.985 1.117 0.99

0.216 0.736 0.82

0.689 0.903 0.80

1.170 0.691 0.89

(Year) Location Tsunami feature Building

Event

Nansei Hokkaido (1993)

> Indian Ocean (2004)

> Indian Ocean (2004)

> Samoa (2009)

**5. Conclusion** 

Okushiri Island

> Banda Aceh

> Phang Nga

Phuket

American Samoa

Fig. 23(b). Tsunami fragility curves as a function of tsunami features for Phuket

#### **4.5 Tsunami fragility curves for American Samoa, USA**

A visual inspection shows that there were 134 damaged and 210 surviving houses. The damage probabilities were calculated using a range of 20 buildings, and a linear regression analysis was performed. From Fig. 24, 80% of the buildings were damaged when the inundation depth exceeds 6 m. More than half of the buildings were damaged if the current velocity exceeds 2 m/s. The damage due to the hydrodynamic force increased rapidly up to 10 kN/m.

Fig. 24. Tsunami fragility curves as a function of tsunami features for American Samoa

#### **4.6 Summary of statistical parameters for developed fragility curves**

Tsunami fragility curves were developed using a numerical model and a visual inspection of satellite images in several countries (Japan, Indonesia, Thailand and American Samoa) with different building materials (wood or reinforced concrete). The necessary statistical parameters for plotting the fragility curves with inundation depth, current velocity and hydrodynamic force are summarised in Table 3.

Fig. 23(b). Tsunami fragility curves as a function of tsunami features for Phuket

0

0.2

0.4

0.6

0.8

1

**4.6 Summary of statistical parameters for developed fragility curves** 

0 0.2 0.4 0.6 0.8 1

hydrodynamic force are summarised in Table 3.

0 2 4 6 8 10

**Depth (m)**

Fig. 24. Tsunami fragility curves as a function of tsunami features for American Samoa

Tsunami fragility curves were developed using a numerical model and a visual inspection of satellite images in several countries (Japan, Indonesia, Thailand and American Samoa) with different building materials (wood or reinforced concrete). The necessary statistical parameters for plotting the fragility curves with inundation depth, current velocity and

0 2 4 6 8 10 **Velocity (m/s)**

0 0.2 0.4 0.6 0.8 1

A visual inspection shows that there were 134 damaged and 210 surviving houses. The damage probabilities were calculated using a range of 20 buildings, and a linear regression analysis was performed. From Fig. 24, 80% of the buildings were damaged when the inundation depth exceeds 6 m. More than half of the buildings were damaged if the current velocity exceeds 2 m/s. The damage due to the hydrodynamic force increased rapidly up to

0123456 **Velocity (m/s)**

0

0 2 4 6 8 10 12 **Force (kN/m)**

0 20 40 60 **Force (kN/m)**

0.2

0.4

0.6

0.8

1

**4.5 Tsunami fragility curves for American Samoa, USA** 

0 2 4 6 8 10

**Depth (m)**

10 kN/m.

0 0.2 0.4 0.6 0.8 1

**Damage probability**

0

0.2

0.4

**Damage probability**

0.6

0.8

1


Table 3. Summary of statistical parameters for developed fragility curves
