Coastal Dynamics 2013 1937 DYNAMIC BEHAVIORS ...

Coastal Dynamics 2013

DYNAMIC BEHAVIORS OF THE 2011 TOHOKU TSUNAMI IN RYORI BAY Yusuke Yamanaka1, Yoshimitsu Tajima2, Shinji Sato3, Haijiang Liu4

Abstract The 2011 Tohoku Earthquake Tsunami hit a wide stretch of the Pacific coast of Japan. Measured tsunami inundation heights showed significant variations even along the coastline within the same bay. Lack of quantitative data of tsunami dynamics in the coastal area makes it difficult to fully understand actual behaviors of tsunami. This study focused on the dynamic tsunami behaviors at Shirahama Beach in Ryori Bay, Iwate Prefecture, where tsunami flooding producing high runup was recorded in a video clip. Image analysis techniques were utilized in this study to quantify data as the time-varying surface water elevations and flow velocities. Furthermore, tsunami numerical simulation was conducted and compared with image analysis, in which the presence of short period waves was found as a characteristic property of nearshore tsunami amplified in the head of the bay. The superposition of short period waves was found to have significant impacts on local amplification of tsunami and thus damages on coastal structures. Key words: 2011 Tohoku Tsunami, tsunami dynamics, inundation, image analysis, short period wave

1. Introduction A huge tsunami was caused by the 2011 East Japan Earthquake, which hit a wide area of Pacific Coast of Japan. In a narrow V-shape bay, tsunami is known to be amplified as tsunami approaches to the head of the bay from the bay mouth. However, according to the 2011 Tohoku Earthquake Tsunami Joint Survey Group (Tohoku Tsunami Information, http://www.coastal.jp/2011-tsunami, 2011), the surveyed tsunami watermark heights showed significant localities along the coast even within the same bay. This feature had already been reported in Hurricane Katrina and Indian Ocean Tsunami surveys, but the detail of the mechanism has not been well understood owing to the lack of the quantitative data. Ryori Bay, located in Iwate prefecture, is one of such bays. Figure1 shows the measured tsunami watermark heights in Ryori Bay.

Figure-1 Overview of the Ryori Bay, measured tsunami watermark heights and camera location 1

Ph. D student, Dept. of Civil Eng., The University of Tokyo, Japan; [email protected] Research Fellow of the Japan Society for the Promotion of Science. 2 Professor, Dept. of Civil Eng., The University of Tokyo, Japan; [email protected] 3 Professor, Dept. of Civil Eng., The University of Tokyo, Japan; [email protected] 4 Professor, Dept. of Ocean Science and Engineering., Zhejiang University, China; [email protected]

1937


We measured the distribution of tsunami watermark heights on March 31 and April 11-13, 2011, using a RTK-GPS system and a laser rangefinder. The watermarks along the steep coastal cliffs on both sides of the bay were measured by using a boat. Figure 1 demonstrates that the inundation heights surveyed in the bay varied from 9 m to 39 m. Ryori Bay has experiences of large tsunami attack by the 1896 Meiji Sanriku Tsunami and 1933 Showa Sanriku Tsunami and is considered to be one of such bays where local amplification mechanism develops large tsunami height. Many video clips were recorded in the 2011 Tohoku Tsunami by survived local residents during their evacuation. In Ryori Bay, hand-held video clips of the tsunami were recorded by a resident for 130 second around the Nonomae Fishery Harbor located at the head of the bay (Figure 1, Photo 1). The video demonstrated complex and violent tsunami behaviors as shown in Photo-1. This violent fluctuation appears to have significant influence on the dynamics of tsunami and thus on the destruction of coastal structures such as breakwaters and seawalls. This study aims to investigate the physical mechanisms of such complex tsunami behaviors in Ryori Bay on the basis of image analysis of the video clip and tsunami numerical simulation.

South cliff of the ba y Cliff around the harbor

Photo 1 A snapshot of the 2011 Tohoku Tsunami at Nonomae Harbor (around 3:29PM JST, March 11, 2011)

2. Image Analysis 2.1. Repositioning of moving frames In the 130 second video clip, the view angle of the video camera was variable although the location and the zooming was unchanged since the video was recorded by hand from a fixed location. A series of still images was extracted every 1/30 second from the video clip. The resolution of the still image was 1,280 x 720 pixels. Then, each frame was repositioned to a common image plane large enough to cover every frame with different view angles. The optimum position of each video frame was decided frame to frame by using pattern matching of a template area that was common in most of the frames. In this study, one of the south cliffs around the Nonomae Fishery Harbor in Photo 1 was selected as the template. The position where the template best matches each frame was searched by moving each frame image to horizontal and vertical directions with rotation using the zero-mean

1938

Photo 2 Example of repositioned frame s


normalized cross-correlation method (http://imagingsolution.blog107.fc2.com/). Photo 2 shows examples of the repositioned frames. In Photo 2, each frame image is repositioned in a large and common image plane represented by the black background. 2.2. Estimation of the temporal tsunami water surface and floating debris position In order to estimate spatial and temporal variations of tsunami elevation, the position of tsunami water surface was determined on the face of the coastal cliff located south in the bay head as shown in Photo 1. The tsunami water surface was estimated on the basis of the edge detection technique in image analysis. First, the absolute value of gradient vector of the brightness matrix was calculated by Eq. (1) for a series of images,

Gu ,v =

∂ 2T ∂u∂v

(1)

where G is the absolute value of gradient vector of the image brightness and T is the brightness matrix, u and v are coordinates of horizontal and vertical direction in the image respectively. The G value becomes large at the boundary between land and water surface. The G value is small on land area and become large on the water surface owing to the disturbance by short wave fluctuations. By using this property, the area of the water surface was firstly defined as the area where the G value was larger than a critical level. The time-varying water surface positions on the cliffs were detected automatically based on these procedures. Isolated small area with large G values is eliminated as a noise. The validity of the automatic extraction of tsunami elevation was confirmed by manual inspection of the water surface every 1/3 second. The trajectories of debris were estimated by the similar procedure. The position of debris was estimated every 0.5 second by naked-eye inspection. 2.3. Estimation of the real XYZ coordinate using image rectification The water surface and debris positions estimated in the previous step could not be directly converted to the real world XYZ coordinate because the video frame was unclear with low resolution and did not always include locations where XYZ coordinates are already known. Therefore, the image rectification to the XYZ coordinate was made through a high resolution image of 4,000 x 3,000 pixels, hereafter named ‘Image A’, taken from the same location with the video (Photo 3). Firstly, twenty locations were selected in the Image A as reference points to match a series of video frames to Image A. These locations were selected randomly in order that the locations have the characteristic features. The matching was conducted by using the least

A B

C

D

Photo-3 A high resolution photo (Image A) used for the rectification (Taken on November 7, 2011)

1939


squares method. Furthermore, nine bench mark locations in Image A whose XYZ coordinate was measured in the field survey by a RTK-GPS system, were used in the image rectification. Through these procedures, the tsunami surface elevations and the positions of debris were converted to the real world XYZ coordinates. 2.4. Accuracy of the procedures The accuracy of the image analysis is considered to depend on the accuracy of repositioning and rectification. The errors induced by the two procedures will be discussed in followings. (1) Errors due to repositioning Errors due to repositioning were evaluated by calculating the root mean square (RMS) errors of twenty reference points randomly allocated in the view port of video frames. The average of RMS errors was found to be 4.7 pixels in u and 5.5 pixels in v, respectively. Since the physical scale of video frame images is 11.8 cm per pixel in u and 20.3 cm per pixel in v, respectively, and that of Image A is 5.7 cm per pixel in u and 13.2 cm per pixel in v, the RMS errors approximately correspond to 9.7 pixels in u and 8.5 pixels in v in the scale of Image A. (2) Errors due to rectification Seven benchmark locations whose real world XYZ coordinates were measured in the field survey were used to evaluate the accuracy of rectification. The average of RMS errors for XYZ were estimated by using 7 bench marks. They were found to be (36.5, 50.0, 5.1) centimeters in (X, Y, Z) coordinate, respectively. In order to estimate XYZ positions of tsunami water surface recorded at cliff and debris, we need to introduce one more assumption that the target point is on some specific plane since a specific (u, v) point does not determine a unique location in XYZ coordinate. For tsunami water surface at the coastal cliff, we assumed the cliff slope to be vertical. This assumption is appropriate since actual cliff slope angle is as steep as 45 degree. For positions of floating debris, we assumed that the vertical elevation of the debris is the same with the temporal tsunami water level. By introducing these assumptions, the elevation of tsunami water surface as well as the XY coordinates of floating debris could be estimated once the corresponding locations in Image A was specified. The estimation errors in UV coordinate in the original video image will induce errors in the estimation of XYZ coordinate. In addition to these errors, errors due to the assumption of XY location will induce another errors to Z estimation for the case of water surface elevation estimation and errors due to the assumption of Z location will induce errors in XY estimation for the floating debris tracking. Table 1 summarizes the results of sensitivity test. Table 1 indicates that the errors in v tend to induce larger errors in XYZ estimation than errors in u. Since the errors in the original video frame are about 7 pixels in the original image, the estimation error for the temporal tsunami elevation is considered to be smaller than about 1 m. On the other hand, the estimation errors in XY due to the error in Z are found to be more than 10 m. This implies that the errors in the horizontal location of debris are as large as 10 m. Table-1 Sensitivity of errors for given parameters Given parameter error

Estimated error (X)

Estimated error (Y)

Estimated error (Z)

1 pixel (U direction) 1 pixel (V direction) 1m (X direction) 1m (Y direction) 1m (Z direction)

0.070m 1.337m 13.11m

0.072m 1.134m 11.13m

0.016m 0.102m 0.041m 0.042m -

1940


2.5. Tsunami water level along the coastal cliff The spatial and temporal variations of tsunami water elevation along the coastal cliff are shown in Figure-2. In the figure, locations A, B, C and D correspond to the locations along the cliff shown in Photo 3. The location A is the farthest point and the location D is the nearest point from the camera. Note that a gap is located at location B due to curved bay topography. As seen in Figure-2, short wave component with period being 7 to 10 s was dominant around time=68 sec. The motion near the harbor breakwater is considered to be that of standing wave in front of the coastal cliff since the peaks of water surface fluctuations appear nearly at the same time along the cliff especially in the region from A to C. On the other hand, the peak in water level moves from C to D along the cliff after time=40 sec in Figure-2, which indicates the long wave component propagates along the coastal cliff from C to D. The tsunami water level along the cliff was estimated under the assumption that the water surface is located on the vertical wall along the cliff. The error analysis indicated that the elevation tended to be overestimated by about 1 m. Moreover, the error in the water elevation near A tends to be larger since the distance from the camera is larger in the region near A.

A B

C

D Short period wave

Short period wave

Figure 2 Estimated water level along coastal cliff

2.6. Track the floating debris The horizontal XY locations of floating debris were estimated on the assumption that the debris were floating on the water level estimated in the above section. The water level at D in Figure 3 was used in the rectification. The horizontal locations of debris tracked every 0.5 sec are illustrated in Figure 4. The estimated velocities of debris are summarized in Table 2, in which the average velocity of debris is listed. Vertical elevations for debris tracking and locations of debris are shown in Figure-4. Locations and moving directions of each debris are specified in Figure 5. In Figure 5, initial locations of debris are indicated by black squares and paths of the debris are presented by red lines. The paths of debris are shown only for debris which were observed for more than 2 sec. In Table 2, Figure 4 and Figure 5, numbers correspond to each debris. As seen in Table 2, the maximum velocity of moving debris was more than 20 m/s when the water level was increasing. In Figure 5, almost all debris appeared to move in the same direction, same to

1941


the tsunami propagating direction. However, some debris like No.06, No.07, No10, moved to and fro in the head of the bay. On the other hand, some debris, e.g.,No.04 and No.12 moved in the alongshore direction of the bay. This illustrates that the overall tsunami induced flow was in the cross-shore direction of the bay. However, the direction of the flow varied locally and temporarily in a complex manner. The flow in the alongshore direction suggests the presence of standing wave in the alongshore direction superimposed on the dominant standing wave in the cross-shore direction. The chaotic motion of the floating debris suggests strong turbulence generated in the head of the bay by the interaction of the flow with structures and complicated topography.

Table-2 Estimated moving velocity of floating debris Debris

moving velocity

Debris

No.01 No.02 No.03 No.04 No.05 No.06 No.07

21.4m/s 18.1m/s 8.2 m/s 8.2 m/s 16.7m/s 6.7 m/s 6.7 m/s

No.08 No.09 No.10 No.11 No.12 No.13 No.14

moving velocity 7.5 m/s 5.6 m/s 5.8 m/s 5.7 m/s 3.6 m/s 6.0 m/s 10.7m/s

Debris

moving velocity

No.15 No.16 No.17 No.18 No.19 No.20

2.3 m/s 3.3 m/s 3.3 m/s 7.5 m/s 4.6 m/s 13.7m/s

No.15

No.10

No.05

Figure-4 Given elevation for debris

No.19

No.03 No.10

No.02 No.04

No.07 No.06 No.09

No.13

No.01

No.15 No.12 No.11

No.17 No.14 No.16 No.18

No.08 10m

50m

No.05

Figure-5 Location and moving direction of debris

1942

No.20


3. Numerical Simulation 3.1. Boussinesq wave model with dry-wet boundary Numerical simulation was conducted to verify image analysis and to elucidate the physical mechanisms of the tsunami deformation in Ryori Bay. Boussinesq equation proposed by Madsen et al. (1991) is utilized in this study in stead of shallow water equation, which is conventionally used for nearshore tsunami simulation and fails to reproduce the short period wave. Governing equations are expressed as follows,

∂η ∂Pi + =0 ∂t ∂xi ∂Pi ∂ + ∂t ∂x j

 Pi Pj   D

 ∂ 2 Pi ∂η f 2  + gD + 2 Pi Pj = ν +Ψ 2 ∂x i D ∂x j 

(2) (3)

where η is water surface elevation, P is flow rate, D(=h+η) is total depth, h is water depth, g is gravity, ν is eddy viscosity, f is friction coefficient and Ψ represents the dispersion term which is expressed by 2  3  1 ∂  ∂ Pj  3 ∂ η  Ψ = ( B + )h 2  − Bgh   2 3 ∂t  ∂xi ∂x j   ∂xi ∂x j 

(4)

where B is a calibration coefficient. The subscript i and j denotes two horizontal coordinates respectively. According to Madsen et al. (1991), the best result is obtained when B=1/21. These equations were solved by ADI difference method on a staggered 4 m-sized grid system with a time step 0.04 sec. The boundary condition at the wet-dry interface was simulated by assuming a small amount of virtual water. The grid was assumed to be wet when the water depth calculated by the mass conservation equation became larger than the critical depth. The computation becomes destabilized when the total depth is closing to zero. Then the water depth was kept at the critical water depth even when the calculated water depth became smaller than the critical water depth and the corresponding grid became a “dry” grid. The critical water depth was set as 0.1 m in this simulation. At the wet-dry boundary, the flow rate Pb was calculated by the following equation,

Pb = 0.35H 2 gH

(5)

where H is the difference in water level between dry and wet zones. The computation domain was a rectangular domain with 5 km length in the north–south direction and 7.5 km in the east–west direction (Figure 6).. The north and the south boundaries were assumed to be the lateral boundary where the waves normal to the boundary would pass through. The east boundary was assumed to be the incident 50m boundary where η and Q were specified by the far field computation based on the linear long wave equation assuming a tsunami source by Fujii et al. (2011) ver. 4.2. Computation was performed for 50 minutes after the earthquake. The eddy viscosity is assumed to be 6.0 1km m2/s and the friction coefficients in sea and land zones are 0.01 -100m and 0.1 respectively. Figure-6 Domain of computation

1943


3.2. Results Firstly, the temporal variation of tsunami water level obtained from the numerical simulation was compared with that obtained by image analysis at B and D in Photo-3 and Figure-3. The origin time of the video is adjusted according to the interview on the photographer. On the other hand, numerical simulation is considered to have some errors in time because of the poor accuracy in the detailed water depth. Then in Figures 7 and 8, water level estimated by numerical simulation was shifted to match best with the result of image analysis. The time shift is the same between Figures 7 and 8. As seen in Figure-7, the Boussinesq model produced reasonably good agreement with image analysis. Especially, the agreement is fine around 3:30 PM JST when the water level increases rapidly with short period fluctuations. In Figure-8, the agreement between the model and the image analysis is poor especially near the peak of tsunami although both predict increase in water level around 3:30 PM JST and almost constant water level afterward. Figure-9 shows the snapshot of tsunami near the head of Ryori bay at 3:29 PM JST. Figure-10 shows the sea bed topography. The color in Figure-9 and Figure-10 represents the water level and water depth respectively. In Figure-9, Red color represents higher water level in Figure-9 and higher elevation in Figure-10. As seen in Figure-9, short period waves were generated near the head of the bay. This is considered to be due to the wave dispersion simulated by the Boussinesq wave model. By careful inspection of the result of numerical simulation, we found that the short period waves were generated in the shallow area marked in Figure-10. The short period waves created at the shallow propagated to the head of the bay by repeating reflections by complicated bathymetry as well as various coastal structures.

Figure-7 Comparison with numerical simulation and image analysis at B in Figure-3

Figure-8 Comparison with numerical simulation and image analysis at D in Figure-3

1944


Shallow area

Shallow area

Short period wave

c

a

b d

Figure-10 Topography around head of Ryori Bay

Figure-9 Snapshot of the behavior of the tsunami

Figure-11 Distribution of water level around head of the bay

Figure-11 shows the temporal variation of the tsunami water level simulated at several locations in the head of Ryori Bay. It is noticed in Figure-11 that the water level at point ‘d’ close to the head of the bay is larger than that at other locations. It is thus considered that the tsunami around 3:30 PM was a receding wave. In the numerical simulation, a wave with height larger than 15 m was simulated 10 minutes before the video was taken. Therefore the wave that was captured by the video is considered to be a standing wave formed by the reflection of the first wave and the incidence of the second wave. The presence of a standing wave mode in cross-shore direction is consistent with Figure-3, in which higher water level propagates from the head of the bay to the offshore direction. It is also noticed in Figure-11 that the water level in alongshore direction of the bay was not uniform. The water level at point ‘a’ is sometimes more than 10 m different from that at point ‘c’. This suggests tsunami formed a standing wave mode in the longshore direction as well. All these features may enhance local amplifications of tsunami producing extraordinary large inundation especially near the head of the bay. Such amplification is considered to influence dynamic response of coastal structure due to tsunami and thus essential in understanding damage mechanisms of structures.

4. Conclusions Complicated behaviors of the 2011 Tohoku tsunami in Ryori Bay, a V-shape bay in Iwate Prefecture, was described by video image analysis and numerical tsunami simulation. The major conclusions in this study are summarized as follows: (1) The temporal variations of tsunami water level and flow velocities were evaluated from the video using image analysis. The tsunami behavior at the head of the bay was found to be dynamic characterized by short period waves superimposed on long wave component forming standing wave in cross-shore and alongshore directions. Such dynamic tsunami behavior was developed in the head of

1945


the bay due to wave dispersion and multi-reflection by the complex local bathymetry. (2) The short period waves were generated by the wave dispersion in a specific shallow area near the head of the bay. The superposition of short waves on long wave enhanced dynamic behavior of the tsunami and thus local amplifications. (3) The water level simulated by the numerical model showed reasonable agreement with image analysis. It was revealed that the Ryori Bay was attacked by two successive tsunamis in 50 minutes. The second tsunami was larger and formed a standing wave in the cross-shore as well as alongshore directions. Detailed dynamic behaviors of the 2011 Tohoku tsunami in Ryori Bay were identified as the generation of short period waves. Further studies are expected on the quantitative evaluation of short period waves on the destruction of coastal structures.

Acknowledgements We appreciate Mr. Eiki Kumagai and Eisuke Shimakawa who provided the tsunami video clips to us. This study was supported by J-RAPID program, Japan Science and Technology Agency.

References Fujii Y., Satake K., Sakai S., Shinohara M., and Kanazawa T., 2011. Tsunami source of the 2011 off the Pacific coast of Tohoku Earthquake, Earth Planets Space, 63, 7, pp.815–820. Holland, K.T., Holman, R.A., Lippmann, T.C., Stanley, J., 1997. Practical use of video imagery in nearshore oceanographic field studies, IEEE J. of Oceanic Eng., 22(1), pp.81-92. Koibuchi Y., Honda T., Welhena T., Ranasinghe S., Sato S., 2005. Localized Damages on Southwestern Coast of Sri Lanka due to the Indian Tsunami (in Japanese), JSCE of Coastal Eng., Vol.52, pp.1411-1415 Madsen, P.A., O.R. Sørensen, H. A. Schäffer, 1997. Surf zone dynamics simulated by a Boussinesq type model. Part1. Model description and cross-shore motion of regular waves, Coastal Engineering, 32, pp.255-287 Madsen, P.A., O.R. Sørensen, 1992. A new form of the Boussinesq equations with improved linear dispersion characteristics. Part2. A Slowly-varying bathymetry, Coastal Engineering, 18, pp.183-204 Madsen, P.A., R. Murray, O.R. Sørensen, 1991. A new form of the Boussinesq equations with improved linear dispersion characteristics, Coastal Engineering, 15, pp.371-388 The 2011 off the Pacific coast of Tohoku Earthquake Tsunami Information (in Japanese), http://www.coastal.jp/ttjt/

1946