Definitions Associated With Tsunami Waves

Published Date: 02 Nov 2017

1.1 Importance of the present study

Humans have fought to survive from natural disasters for a long time,in particular Japan is a specialized and advanced country to prepare against the disasters.It is not too much to say that Japan has a long history of resistance for the natural disasters,especially earthquake and tsunami.Since the 2011 off the Pacific Coast of Tohoku Earthquake,many people have been focused on the earthquake and tsunami engineering in natural disaster fields.In particular,a tsunami wave ascending river has a high possibility for potential disasters that is tsunami flow over river embankment,severe erosion at a river mouth and so on,further it may cause many problems related to secondary disaster.

Hence,the tsunami phenomena have to consider as one of the most threatening natural disaster.Understanding of tsunami propagation mechanism is necessary to prevent from the high potential risk in the future.However,there were not sufficient study on this topic,although there have been various researches for tsunami damages,tsunami inundation.Therefore,the phenomenon of tsunami propagation into river is recognized as one of the important tsunami impacts,and more research is needed to understand the tsunami propagation mechanism.

In this dissertation,the characteristics of tsunami propagation into rivers have been confirmed by a case study and comparative analysis.The results from various studies will be a crucial criterion in understanding the propagation mechanism of the tsunami waves.

1.2 Objectives

The main objective of dissertation is to assess the effects of tsunami propagation into rivers according to the tsunami scale and intensity.The relationship between tsunami propagation and rivers can be evaluated by physical characteristics of past tsunami events.Measureable physical parameters are estimated by various approaches and methods.Secondly,significant factors related to river mouth morphology in tsunami propagation mechanism are verified by a comparative study for the estimated physical quantities of tsunami waves.To achieve these objectives,this dissertation emphasizes the following several points.

1) Investigate data availability for estimation of tsunami physical parameters propagating into rivers.

2) Determine suitable estimation methods regarding data and information,which are included uncertainty and inaccuracy.

3) Assess the tsunami impacts according to the tsunami scale and river mouth morphology features by using verified methods.

4) Compare the analysis results of the tsunami propagation characteristics in each tsunami events,and discuss the influence factors in tsunami propagating into rivers.

This study mainly performs the verification of methods and estimation of tsunami physical parameters by using the reliable approaches.To improve the accuracy is evaluated through comparison analysis results based on different approaches.Then,the estimation of tsunami physical parameters can be successfully achieved in each tsunami event.Based on the estimated tsunami parameters,the comprehensive analysis results will provide similarity and differences of tsunami propagation characteristics between past tsunami events.These facts will help in understanding the mechanism of tsunami propagation into rivers,further it may apply to determine the criterion for tsunami impacts in rivers.

1.3 Outline of dissertation

This dissertation presents the physical characteristics of tsunami propagation into rivers,especially the relation between the tsunami scale and river mouth morphology change is the main criterion in classifying the tsunami impacts.The dissertation is comprised of the following this criterion.The main topic in each chapter is described below.

Chapter 2 presents the fundamental background regarding tsunami propagation into rivers such as wave theory,tsunami wave,river mouth morphology features,which are important concepts in understanding tsunami wave propagation.

Chapter 3 introduces the real phenomena of tsunami propagation into rivers according to the 2010 Chilean Tsunami,2011 Tohoku Tsunami,and 2012 Dec.7 tsunami event as the past tsunami events.

Chapter 4 begins with the assessment of the 2011 Tohoku Tsunami as large scale tsunami event with river mouth morphology changes.In that case,many kinds of data types such as videos,aerial photographs,available water level,and so on are used to obtain the tsunami physical characteristics.

Chapter 5 provides the tsunami physical parameters on the 2010 Chilean Tsunami and 2012 Dec.7 tsunami event as small scale events without river mouth morphology changes that are estimated by using available water level data.

Chapter 6 presents the comparative study between large scale and small scale tsunami events with the effect of river mouth morphology changes.This chapter discusses the significant factors with river mouth morphology on tsunami propagation into rivers.

Chapter 7 concludes that the each chapter result will be summarized,and then the physical characteristics of tsunami ascending into rivers will be achieved through the comprehensive understanding for tsunami propagation mechanism.Furthermore,the recommendations indicate the limitations and suggestions for more informative and constructive study in the future.

CHAPTER 2 LITERATURE REVIEW

2.1 Long wave theory

Waves in shallow water are called long waves or shallow water waves such as tidal waves,tsunamis and other waves with long periods and wave lengths.This study of long waves is of importance in the engineering field regarding the coastal structure design,studying estuaries environments,and so on.Because long wave may cause extreme natural phenomena related to resonance in harbors and mild slope,shoreline change,and natural disasters (Bellotti,2007; Bender et al.,2003).

Long wave is significantly associated with the general wave theory and solution,and small amplitude wave theory as linear wave solution is useful to solve long wave problem physically.In this section,theory of small amplitude wave is presented,after the governing equations of long wave are derived.

The governing equations were derived from the continuity equation with the assumption of irrotational motion,and an incompressible fluid.Then,the continuity equation can be expressed as Eq.(2.1),and it can be represented as a velocity potential (?) which is a gradient of a scalar function (Dean and Dalrymple,1984).

(2.1)

where,

(2.2)

The continuity equation can be rewritten in Eq.(2.3)

(2.3)

It is clear that the velocity potential should satisfy the continuity equation.This equation is called the Laplace Equation that occurs in many physics and engineering.A solution for the velocity potential is required to obtain the velocity components (u,v,w).It is necessary to determine suitable boundary conditions for the wave problem.Then,the governing equation can be used to solve the wave problem.In general,two-dimensional wave domain is shown in Figure 2.1.The wave motion in the domain is under the Laplace equation.Where x,z is the coordinate system,�� is the surface water elevation,L is wave length,H is wave height,h is water depth.The boundary conditions for bottom,water surface,and lateral in this domain area given as follows.

Figure 2.1 Schematic of fluid domain for two-dimensional wave solution

At the bottom,the boundary condition is assumed to be horizontal direction,a no flow condition applies as Eq.(2.4)

on z = -h (2.4)

At the free surface,two boundary conditions have to be satisfied.The first boundary is the kinematic condition for the displacement of water surface which is given

on z = ��(x,t) (2.5)

The second boundary condition is the dynamic condition for water surface pressure (p��) related to the Bernoulli equation.The boundary condition for free waves expresses as Eq.(2.6)

(2.6)

The lateral boundary condition is a periodicity condition for waves that are periodic in space and time.The periodic lateral boundary conditions apply in both space and time,Eq.(2.7) and Eq.(2.8)

(2.7)

(2.8)

Using the solution for the partial differential equation and the boundary conditions can be obtained the velocity potential.As the solution of partial differential equation,the separation of variables applies in the fluid domain.Then,the velocity potential can be obtained as Eq.(2.9)

(2.9)

where,k? wave number (=2��/L),��? angular frequency (=2��/T).

Furthermore,the dispersion equation can be derived from the remaining free surface boundary condition.This equation gives the relationship between wave number and angular frequency as seen in Eq.(2.10).The dispersion relationship means that long wave propagates faster than short length wave.

(2.10)

The dispersion relationship for shallow water can be written in the following the hyperbolic functions.If relative depth is small,tanh kh term becomes kh.Then,Eq.(2.10) can be rewritten as Eq.(2.11) and Eq.(2.12) related to wave speed (C) from wave length and wave period.

(2.11)

or

(2.12)

and

(2.13)

The wave speed or celerity in shallow water is determined by the water depth as Eq.(2.13).The celerity equation can be applied easily in many real fields.

Previously,the velocity potential for small amplitude wave was derived.Using Eq.(2.2) and Eq.(2.9),the velocities for a progressive wave are written as follows.

(2.14)

(2.15)

Based on the small amplitude wave theory,as the horizontal pressures are independent of z,the horizontal wave motion is also depth independent,which means the horizontal velocity is not a function of depth.Thus,integrating over depth can apply to the three-dimensional continuity equation and momentum equations.For small amplitude waves,the nonlinear terms can be neglected to simplify the governing equations.Finally the linearized continuity and momentum equations for long wave can also be derived as follows.

(2.16)

(2.17)

(2.18)

where,U and V

? depth averaged velocities corresponding u and v.Eqs.(2.16),(2.17),and (2.18),called the shallow water equations,which are widely used to solve the long wave problem in many physics and engineering fields.

2.2 Definitions associated with tsunami waves

In general,tsunami water levels such as tsunami height,inundation depth,run-up height are used to indicate the tsunami wave impacts related to the tsunami scale and intensity.Furthermore,these tsunami parameters may be able to use in the early warning system for tsunami disaster.Indeed,the tsunami information is being used as the criteria for tsunami impacts in many fields.However,if wrong its definition is used,it may cause confusion in understating tsunami information.Thus,it is necessary to know the accurate definitions of tsunami wave.In this section,the definitions of tsunami scale levels and water levels will be presented.

According to the tsunami scales and impacts,tsunami event is classified into Level 1 and Level 2.The tsunami return period was reflected in the classification of tsunami level.The characteristics of Level 1 and Level 2 tsunami events are summarized in Table 2.1.

Table 2.1 Classification of tsunami level

Lv.

Return period

Remarks

Level 1

Tsunami

1 in 100 year return period

- Corresponding to the existing structures.

- Protect human lives and properties.

Level 2

Tsunami

1 in 1,000 year return period

- Large-scale casualties and property damages.

- Protect human lives at least,including

evacuation planning,recovery planning,etc.

Level 1 tsunami event has relatively low tsunami impacts,and it has one time in 100 year return period.It means that the existing coastal structures can protect human lives and properties from tsunami wave.As the mitigation plan,tsunami disaster is controlled by the structure designing.However,Level 2 tsunami has totally different scale and intensity compared with Level 1,and this tsunami event has a return period of 1,000 year.Level 2 tsunami waves cause large-scale causalities and property damages,and it affects the whole communities.In that case,the mitigation planning includes evacuation and city recovery planning,public education,etc.as the comprehensive measures.

This classification is very useful to assess the tsunami impacts in accordance with the tsunami level,and it is easy to identify the characteristics of each tsunami level.Furthermore,the relationship between significant factors can be obtain from this criteria based on the tsunami level.

Figure 2.2 Definitions of tsunami height,inundation depth,run-up height

With the tsunami scale and intensity level,it is necessary to define the actual quantities of the tsunami such as tsunami height,inundation depth,run-up height.Figure 2.2 shows the schematic of water levels due to the tsunami wave.In general,it is crucial to determine the Still-Water Level (SWL) in estimating the tsunami height and run-up height.Tide level is most commonly used because when the tsunami propagates into coasts and rivers,the wave flows along the tidal motion.Meanwhile,the inundation depth is estimated from the difference between bottom and water surface.Compared with tsunami height and run-up height,the inundation depth data can be applied effectively to assess the effect of tsunami propagation over land.

The presented definitions in accordance with the tsunami wave are equally applicable in this study.Especially,tsunami level classification,Level 1 and Level 2,is important criterion to lead the entire study.

?

2.3 River mouth morphology

At a river mouth,the two flows from river and ocean always exists,thus the analysis of flow motion is difficult and complex.Moreover,the flow condition is greatly influenced by extreme natural phenomena.

During the natural extreme events for long term and short term,the river mouth has an important role to determine the flow conditions depending on the features of river mouth (Yang et al.,2001; Mao et al,2004; Tanaka,2006),further it has been studied through various approaches hydrological,geological and morphological (Pruszak et al.,2005; Cooper,2001; Tanaka,2003; Lichter et al.,2011).In particular,the characteristics of river mouth morphology indicate different impacts of natural events.Furthermore,it was found that morphological characteristics are deeply related to the structures and components of river mouth (Mikhailova,2008) but also of what kind of natural event such as flood and storm events,tsunamis,tides,and so on.

(a) Old-Kitakami River

(b) Jo River

(c) Naruse-Yoshida Rivers

(d) Nanakita River

Figure 2.3 River mouth morphological features

?

CHAPTER 3 CHARACTERISTICS OF TSUNAMI PROPGATION INTO RIVERS

3.1 Introduction

Recently,three tsunami events affected to north eastern coast of Japan.The tsunami events are 2010 Chilean Tsunami,2011 Tohoku Tsunami and 2012 Dec.7 tsunami.Since the 2011 Tohoku Tsunami,many researchers and engineers have been interested in the natural disasters related to potential tsunami in the future.

Generally,tsunami wave is accompanied with many natural phenomena,especially tsunami propagation into rivers that is one of the most important tsunami behaviors (Yasuda,2010; Tsuji et al.,1991).It may cause a high risk for potential tsunami disasters,such as the tsunami infiltration and overflowing over the river embankment at the river upstream area.In the recent tsunami events was found the phenomena of tsunami propagation into rivers that was emphasized in the assessment of tsunami propagation characteristics (Tanaka(n) et al.,2012; Nandasena et al.,2012).Furthermore,it is that the tsunami wave in rivers is deeply related to the scale of tsunami event,thus the information of three tsunami events is summarized in this chapter.

3.2 2010 Chilean Tsunami

Figure 3.1 Tsunami travel times of the 2010 Chilean Tsunami

(Source? National Oceanic and Atmospheric Administration,NOAA)

?

In Japan,the 2010 Chilean Tsunami event was evaluated as Level 1,which is tsunami impact is low and tsunami occurrence period is short-term.In that case,a river located near the coast is mainly influenced by tsunami wave compared with the coastline because the tsunami energy is not enough to cause tsunami inundation over the coastal area.It is clearly shown that the tsunami wave tend to concentrate into rivers.Hence,Level 1 tsunami wave ascending into the river is largely influenced by the river mouth characteristics.In particular,sandy coast or sand-spit type river mouth is the effective in reducing the tsunami energy infiltration into rivers.

3.3 2011 Tohoku Tsunami

The tsunami propagation and inundation affected many changes of costal environment as well as rivers and estuaries in the north-eastern part of Japan,especially the massive tsunami wave as Level 2 showed severe erosion at the river mouth of sandy coast type.The river mouth characteristics were totally changed by the strong tsunami flow.Compared with the Level 1 tsunami,the river mouth changes was apparent that sandy coast and sand-spit river mouth were destroyed and eroded,and the river mouth morphology was significantly affected by the tsunami wave.However,once the changed river mouth morphology may not affect the tsunami wave propagation into rivers.

(a) Nanakita River (4.4 from river mouth)

(b) Onuma Lake (2.2 km from coastline)

Figure 3.2 Snapshot for tsunami propagation of 2011 Tohoku Tsunami

(Source? Ministry of Land,Infrastructure,Transport and Tourism)

In case of the Level 2,tsunami wave propagates on land area not only into rivers,thus the propagation characteristics can be classified into two flow conditions which the tsunami propagates on land areas or in rivers as seen Figure 3.2.It is found that tsunami wave propagated quickly in rivers,and it arrived earlier up to the river upstream area compared with on land.It is presented well the difference of tsunami impact on land and rivers in which is also important tsunami phenomena.In addition,tsunami intrusion distance in rivers and on land have a big difference when the tsunami propagation into river and inundation on land.These facts are important tsunami characteristics in understanding the behaviors of the Level 2 tsunami event.

3.4 2012 Dec.7 Tsunami

Figure 3.3 Tsunami warning and earthquake information on Dec.7,2012

(Source? Japan Meteorological Agency,JMA)

However,several rivers are recovering from the destroyed river mouth due to the 2011 Tohoku Tsunami,further the effective river mouth type preventing tsunami propagation into rivers such as sandy coast or sand-spit is still open,thus it is difficult to reduce the tsunami impacts although the river mouth is one of the significant factors.Moreover,the present river mouth condition is not prepared for the tsunami disaster in the near future.Hence,although the tsunami impacts and height is low and small tsunami height,it should be considered in correlation with the potential disaster.

3.5 Conclusions

?

CHAPTER 4 TSUNAMI PROPAGATION INTO RIVERS WITH MORPHOLOGICAL CHANGES

4.1 Introduction

4.2 Study area

Figure 4.1 Location of study area

4.3 Data collection

In 2011 Tohoku Tsunami,data collection was limited because most hydraulics measurement stations such as water level measurement station in rivers and tide monitoring stations were destroyed and washed away due to the tsunami.Fortunately,many videos recorded by reliable organization,and available water level data and aerial photography have been released by Japan government.The valuable information of the tsunami has been reported from many sources.Furthermore,many researchers have performed the numerical simulation by using various numerical models,and field survey (Kakinuma et al.,2012; Muhari et al.,2012).

The research results contributed in understanding the physical mechanism of tsunami propagation.Most research results have been more focused on the tsunami inundation and propagation modeling in ocean.However,one of the tsunami phenomena is the propagation into rivers has not been studied sufficiently.Collecting available and suitable data have difficulty to consider the tsunami behavior in rivers.It is necessary to obtain the accuracy and quality of available data and information for the tsunami.Thus,the 2011 Tohoku Tsunami has been analyzed in a variety of methods and data sources to overcome uncertainty and inaccuracy of data analyses.

4.3.1 Field survey data

Figure 4.2 Location of field survey

(Sources

? Tohoku Regional Bureau of the Ministry of Land,Infrastructure,Transport and Tourism,MLIT)

Figure 4.3 Estimation of tsunami inundation depth

4.3.2 Available water level data

Water level data is good criterion of tsunami impacts in rivers.However,most measurement stations were totally destroyed by the tsunami,especially the measurement station located near the river mouth.The available water level data were very limited in the study area,thus several river data was used to assess the tsunami characteristics.Figure 4.4 ~ Figure 4.7 show the available water level data in Tohoku District.The name of measurement stations and the distances from river mouth are presented in these figures.Observed water level data is an important factor crucial in determining the tsunami physical parameters.

Figure 4.4 Takase River water level data

Figure 4.5 Mabechi River water level data

Figure 4.6 Naruse-Yoshida Rivers water level data

Figure 4.7 Sunaoshi River water level data

4.3.3 Video image data

Many types of video data were collected by using helicopters,Closed circuit television (CCTV),personal video camera,and so on.These videos have been released from reliable organizations and national governments.Here the information for tsunami propagation such as the tsunami arrival time and the travel distance is contained in the recording videos,further tsunami celerity and tsunami flow velocity can be obtained from video data.

However,some videos have an uncertainty for tsunami information such as the difference between video recording time and real time,thus it is necessary to adjust the real time in the video before the image analysis.In the helicopter video by Fire and Disaster Management Agency (FDMA),this problem was able to confirm that the recording time in the video was a time lag.In order to revise the recording time,the raw video was cross checked with the videos from the Ministry of Land,Infrastructure,Transport and Tourism (MLIT) and Self-Defense Forces (SDF).

Some video has been recorded without the real time.In that case,the real recording time was estimated by using the cross checking to other video records.The locations of video sources are shown in Figure 4.8,and the adjusted information of video sources is summarized in Table 4.1 which is presented in detailed conditions for adjustment.Thus,the tsunami travel time can be obtained after the adjustment of the real time in the video compared with other video sources.

Figure 4.8 Locations of video recording in Sendai Plain

Table 4.1 Video data information

Classification

Name

Data source

Remarks

River

Nanakita

MLIT

On time

Personal video

No record

FDMA

Approx.10 min

Land

Arahama

MLIT

On time

River &

Land

Natori

NHK

On time

SDF

On time

Land

Sendai Airport

CCTV

No record

TBC

On time

MLIT

? Ministry of Land Infrastructure,Transport and Tourism

NHK? Japan Broadcasting Corporation

FDMA? Fire and Disaster Management Agency

TBC? Tohoku Broadcasting Company

SDF? Japan Self-Defense Forces

4.3.4 Aerial photography and topography data

Figure 4.9 shows that one aerial photo taken in the Nanakita River after the earthquake occurrence.Geospatial Information Authority of Japan(GIA) have released pre- and post- aerial photographic data.An aerial photography data is useful to show the effect of the tsunami wave.During the tsunami propagation and inundation,erosion and deposition can be considered in the perspective of large-scale changes due to the tsunami.The aerial photography is one of the most important data in analyzing the river mouth morphological changes.

Figure 4.9 Aerial photograph after the tsunami (2011.3.12)

Figure 4.9 shows the topography data of the Gamo Lagoon coast before the tsunami of 2011.The elevation data was measured several years ago,using a total station that is one of the measurement devices.Topography data is also useful to assess the tsunami erosion.The effects due to the topographical features at a particular location can be obtained from this data (Tinh et al.,2011).

Figure 4.10 Topography data of Gamo Lagoon in Nanakita Estuarine

Furthermore,it may provide valuable information on the process for the tsunami propagation over the coast.It can be used to assess a location of fragile site,which is significantly affected by the tsunami wave.The topographic data can be applied to the comparison analysis with video images and aerial photos.These data such as aerial photography and topography is also important sources in collecting the data for the tsunami propagation.

4.4 Analysis methods

As mentioned above,various data types are widely used to assess the tsunami characteristics and physical parameters.Analysis method is diverse,and it can be used in many different approaches to obtain the characteristics of tsunami propagation.It is necessary to employ suitable method according to the data types and the tsunami parameters.

4.4.1 Video data analysis and celerity equation

Video image data and field survey data are suitable to assess the tsunami celerity.Using the video data is able to trace the front of tsunami wave.Eq.(4.1) is used to estimate the tsunami celerity from video data.

(4.1)

where,C? celerity,t? arrival time and x? travel distance.

Furthermore,the celerity equation can be derived from the long wave theory.Eq.(4.2) can be used in the shallow water depth.The tsunami celerity in rivers and on land has been calculated by these two equations.The calculated results are evaluated through the comparative analysis.

(4.2)

where,g? gravity acceleration and h? water depth.

Furthermore,tsunami arrival time can be also estimated from the real recording time in videos.Japan Meteorological Agency (JMA) reported the arrival times of the first tsunami wave and the peak tsunami wave.The observed water level data have been used to estimate the tsunami arrival time.Estimated tsunami arrival time from the all data sources has been combined with a numerical simulation result and observation data.Finally,the tsunami arrival times in Tohoku District have been successfully completed by comprehensive study.

4.4.2 Particle Image Velocimetry and tsunami debris tracking method

Particle Image Velocimetry (PIV) method and tsunami debris tracking method were considered as the estimating method for tsunami flow velocity (Frizt et al.,2004).PIV method based on the background of Large-Scale Particle Image Velocimetry (LSPIV) is used to trace the difference of luminance for a period of time (Fujita et al.,2001;Hauet et al.,2008;Kantoush et al.,2011).Tracking debris method focuses on the object in the video image.It was assumed that the debris was regarded as one particle on water surface.The method concept is based on Particle Tracking Velocimetry (PTV).

4.4.3 Flow velocity estimation based on the conservation equation

This equation is also one of the estimation methods for the flow velocity.The estimation concept using the conservation equation is that if the water volume changes in the river channel due to the tsunami can be known from the observed water level at the measurement stations,the flow velocity and the discharge induced by the tsunami can be calculated (Adityawan et al.,2012).

(4.3)

where,t? time,x? space,A? area,and Q? discharge.

Eq.(4.3) can be integrated at arbitrary two points,x1 and x2.Then,the equation can be rewritten as

(4.4)

The integration term on the left-hand side in Eq.(4.4) can be derived by using the simplification of the differential equation term and the formula for the area of a trapezoid.To compare with the numerical experiment result,river width also assumed to be constant values.The solution for the discharge induced by the tsunami is Eq.(4.5)

(4.5)

where,B? river width,��? water level.

If the water level of the two points and upstream end discharge are given,downstream end discharge can be calculated from Eq.(4.5).It can be extended to several points or segments along river channel.The flow velocity induced by the wave propagation can be obtained from the calculated discharge using Eq.(4.6).

(4.6)

where,Q? Discharge,A? cross-sectional area and V? flow velocity.

In this study,the estimation equation as the practical method has been evaluated using the calculated water level data from the numerical experiment.The sensitivity analysis of the time interval and the distance between the arbitrary points has been conducted to assess the applicability of the estimation method.Furthermore,the calculated result has been compared to the results of the PIV method and the tsunami debris tracking method.

4.4.4 Shallow water equations model

Shallow water equations model is widely used to simulate the long wave propagation like a tsunami wave.This numerical model is a very powerful and quite effective in the numerical simulation.Many numerical solutions have been developed to improve the stability,accuracy and running time,etc.These numerical solutions for the shallow water equations have enabled accurate simulation of natural phenomena.

A numerical experiment is very useful method in the condition which is unable to conduct a laboratory experiment.The numerical analysis provides the exact physical parameter.Especially it can be used to solve the complicated fluid flow problems under limited data condition,further this method would have enabled to estimate more detailed variation of physical parameters.

4.4.4.1 Governing equations

For the numerical model verification and numerical experiments,1-D shallow water equations have been solved by using Finite Volume Method (FVM).The governing equations are written as below,

(4.7)

(4.8)

where,t? time,h? total water depth,u? depth averaged velocity,So and Sf

? bed slope and friction slope,g? gravity acceleration.

Eq.(4.7) and Eq.(4.8) is the continuity equation and the momentum equation,respectively.The approach using the Manning coefficient(n) was employed to calculate the bottom friction term.Eq.(4.9) is used to calculate the energy slope term(Sf).

(4.9)

As one of the FVM solutions,FORCE-MUSCL scheme is used to solve the governing equations.The numerical model calibration has been conducted through several hypothesis cases according to space and time.Furthermore,the velocity estimation method based on the conservation equation has been evaluated from the verification results of the numerical model.

4.4.4.2 FORCE-MUSCL scheme for FVM solution

The governing equations which is continuity equation and momentum equation can be rewritten in vector form as Eq.(4.10) in order to apply the FVM solution,

(4.10)

where,it is seen that flux vector form can be expressed as

(4.11)

(4.12)

(4.13)

Eq.(4.10) is integrated over the element,and using Green�fs Theorem is applied to the equation of vector form.Thus,Eq.(4.14) is written as

(4.14)

(4.15)

The space derivation function of F can be simulate by using finite volume center scheme as Eq.(4.15).This formulation depends on how the flux variables are evaluated.The FORCE-MUSCL schemes have been used to solve that flux variables.

In the MUSCL scheme,the flux variables (h,hu) at the left and right side of the cell i is redefined that the variable value (hu) at the right (+) and left (-) of the cell i

+1/2 are approximated as below

(4.16)

(4.17)

where,

(4.18)

(4.19)

here,?i? function of flux limiter,and ri? ratio of gradients on the cell interface.

The flux limiter is commonly used in high resolution numerical schemes.It is very useful function in controlling the numerical simulation.Superbee flux limiter is employed in this model (Roe,1986).The flux limiter value is determined by the ratio of gradients value as follow.

(4.20)

Based on the estimated value from MUSCL scheme,FORCE method is applied to the flux F at the cell interface.The FORCE scheme is combined with the two-step schemes of the Lax-Wendroff and the Lax-Friedrichs (Toro et al.,2008).The calculation method of the flux F is shown as follows.

(4.21)

(4.22)

(4.23)

(4.24)

The estimated flux F from the FORCE scheme can be applied to solve Eq.(4.15).To obtain higher order accuracy for the temporal discretization,Eq.(4.25) as the 3rd order TVD Runge-Kutta method is employed in Eq.(4.14) (Gottlieb et al.,1998).

(4.25)

where,

(4.26)

(4.27)

where,V? function of flux E,and L? value of the right side in Eq.(4.14).

4.4.4.3 Hypothesis cases and boundary conditions for model verification and numerical experiments

The accuracy and stability of the numerical model is closely related to the conditions for time and special variables which is evaluated for the numerical model verification.Furthermore,the calculated variables from the numerical model using FORCE-MUSCL can be used to verify the accuracy and sensitivity of the velocity estimation method based on the conservation equation according to the calculation conditions such as the observation time and distance differences.

To achieve the purposes of the model verification and numerical experiments,two hypotheses computational domains were created that Case 1 is based on the Naruse River bottom elevation,and Case 2 is assumed the Mabechi River.Hypothesis Case 1 is used to verify the sensitivity of numerical model,and then the numerical experiment is conducted using the hypothesis Case 2.The computational domains are shown in Figure 4.11 and Figure 4.12.Total length of the river channel is 40 km.It was assumed that the river width is constant,and river bed slope is 0.0005 and 0.0001,respectively.Manning coefficient was used to calculate the bottom friction,the value is 0.025.

Figure 4.11 Computational domain of hypothesis Case 1

Figure 4.12 Computational domain of hypothesis Case 2

?

Figure 4.13 Incoming wave condition at the generation zone for Case 1

Figure 4.14 Incoming wave condition at the generation zone for Case 2

The incoming wave was generated at the river mouth located the end of the left side in the domain,herein input wave condition is given by the observed water level data.In Case 1,the observed data of Naruse River is used at the generating wave,and Mabechi River water level data near the river mouth is applied to Case 2 as shown in Figure 4.13 and Figure 4.14.Furthermore,the boundary condition of the right-hand side is open boundary condition which allows freely moving inflow and outflow at the boundary.With this,the numerical model is set up for the model calibration and numerical experiments.

4.5 Characteristics of the 2011 Tohoku Tsunami

The analysis results are presented in following tsunami parameters.From the data analysis,tsunami height and tsunami intrusion distance,tsunami travel distance,tsunami arrival time,tsunami celerity,induced discharge and flow velocity were estimated.The analysis results are indicated below according to the physical parameters.

4.5.1 Tsunami height and tsunami intrusion distance

Tsunami height and tsunami run-up height are presented by the research group.Many researchers have attended to this organization for the survey and investigation of the 2011 Tohoku Tsunami.The tsunami height and the tsunami run-up height were estimated as seen in Figure 4.15.It is clearly shown that the tsunami wave was concentrated around the Tohoku District,and the maximum tsunami height was attained as approximately 40 m.

Figure 4.15 Tsunami height and run-up height (Mori et al.,2012)

Especially,tsunami height in rivers is deeply related to river topographical characteristics.River slope is one of the most significant factors on tsunami propagation into rivers.Kayane et al.(2012) suggested the empirical function between tsunami height and river slope,further tsunami height dissipation and river slope.However,the limited data may cause the uncertain empirical function in which is overestimated.Thus,it is necessary to improve the empirical functions concerning more available data.The empirical function has been completed by analyzing added data.

Regarding to the 2011 Tohoku Tsunami,Adityawan et al.(2012) presented the relation to the river slope and the tsunami intrusion.Tsunami intrusion distance is one of the important factors to determine the tsunami height and dissipation coefficient.It is greatly influenced by river characteristics,especially river slope.

Figure 4.16 Relationship between river slope and intrusion distance

To estimate the tsunami intrusion distances,Iwate Prefecture is eight rivers,Miyagi Prefecture is 10 rivers,and Fukushima Prefecture is 21 rivers,total 39 rivers data have been used,and then it has been suggested that the relationship between tsunami intrusion distance and river slope is reflected in the empirical function as seen in Figure.4.16.The suggested intrusion distance function can be written as

(4.28)

where,S? river slope.

The relationship between tsunami height at river mouth and propagation distance from river mouth can be written

(4.29)

where,Ho? tsunami height at river mouth,H

? Tsunami height at arbitrary location x from river mouth,and k

? tsunami height dissipation coefficient.

Tsunami height ratio (H

/Ho) was assumed that tsunami height at the end of intrusion is 5% (0.05) of tsunami height at river mouth.Kayane et al.(2012) proposed the empirical dissipation coefficient function based on the assumed tsunami height ratio,

(4.30)

It is found that the dissipation coefficient function is related to the river slope.The dissipation coefficient can be obtained from the relationship between the river slope and the tsunami intrusion distance.Using Eq.(4.28) and Eq.(4.29),the coefficient function of the tsunami height dissipation can be expressed as Eq.(4.31).

Figure 4.17 Empirical tsunami height dissipation function

(4.31)

Compared with the previous study,this dissipation function can be used in the wide range of the river slope.Figure 4.17 shows that the previous dissipation function has the limited range of river slope,whereas the improved function in this study can consider to the stiff river slope.

4.5.2 Tsunami travel distance and tsunami arrival time

The tsunami travel distance from the river mouth and the coastal line,and tsunami arrival time in the study area can be estimated using the video image data and water level data (Ushiyama et al.,2012).The relation graph between the tsunami travel distance and arrival time is shown in Figure 4.18.

Figure 4.18 Tsunami travel distance and arrival time in Tohoku District

Figure 4.19 Elapsed tsunami arrival time of 2011 Tohoku Tsunami

As seen in Figure 4.19,the elapsed tsunami arrival times after the earthquake occurrence can be estimated based on the result of tsunami travel distance and arrival time,further the arrival time at tide stations from Japan Meteorological Agency (JMA) was added in this figure.

4.5.3 Tsunami celerity

Tsunami celerity is also estimated in different ways that is water level analysis,celerity equation and video image analysis.These approaches were used to verify the tsunami celerity,and then the comparison result gives a reliable value.Furthermore,the result can be classified into three kinds of types which are river,floodplain and land,respectively.The estimated tsunami celerity is shown in Figure 4.20 that the relationship between the tsunami celerity and distance from river mouth and coastal line that is based on the result of tsunami travel distance and arrival time.The estimated tsunami celerity was redrawn Figure 4.21 to indicate the differences due to geographic locations,bottom conditions,and infrastructures.

It is found that the celerity in rivers is significantly faster than on land,especially R1 celerity is conserved along the river up to 4.5 km from the river mouth without the significant reduction,whereas the celerity on land (L1,L2,L3,L4) is significantly affected by the bottom roughness and tsunami debris.It is note that the floodplain (F1) has higher celerity compared with the land area celerity because the floodplain is located along the river channel,thus the tsunami behavior in this area is similar with tsunami propagation in the river (R1).

Figure 4.20 Relationship between tsunami celerity and distance

Figure 4.21 Tsunami celerity in Sendai Plain

?

(a) Natori River

(b) Near the Sendai Airport (Land)

Figure 4.22 Comparison between celerity equation and video image analysis

4.5.4 Tsunami flow velocity and discharge

4.5.4.1 Verification result of numerical experiment model

The numerical model verification has been performed to confirm the limitation conditions for the time and space differences in the model calculation.Table 4.2 as follows shows the test cases for the verification of the model availability.As the computational conditions,the hypothesis Case 1 and incoming wave condition like Figure 4.13 have been used to simulate for the numerical verification,this calculation result is presented by using the correlation coefficient as expressed by Eq.(4.32) with the observed water level data at the Ono-Naruse measurement station in Naruse River.The correlation coefficient is calculated as follows.

(4.32)

where,x and y? random variables,x ? and y ?? mean value for variables.

Table 4.2 Test cases for numerical model verification

No.

dx (s)

dt (m)

No.

dx (s)

dt (m)

Case 1

100

0.01

Case 14

3500

130

Case 2

100

0.1

Case 15

3500

140

Case 3

100

1

Case 16

4000

1

Case 4

100

5

Case 17

4000

10

Case 5

500

10

Case 18

4000

60

Case 6

500

30

Case 19

4000

100

Case 7

1000

40

Case 20

4000

140

Case 8

1000

60

Case 21

5000

1

Case 9

2000

80

Case 22

5000

10

Case 10

2000

100

Case 23

5000

60

Case 11

2000

120

Case 24

5000

100

Case 12

3000

120

Case 25

5000

140

Case 13

3000

130

Figure 4.23 Correlation coefficients according to dx and dt

?

4.5.4.2 Sensitivity analysis for estimation method based on conservation equation

In the previous section,the calculated water level from the numerical experiment is used to evaluate the velocity estimation equation based on the conservation equation.The sensitivity and accuracy of conservation equation method has been verified by the hypothesis Cases 2.Test case conditions were determined to confirm the effects of the time interval and distance difference.These variables impacts is presented by using Nash-Sutcliffe model efficiency coefficient and correlation coefficient which is widely used to assess the model accuracy compared with the observed data.The Nash-Sutcliffe coefficient is calculated as follows (Moriasi et al.,2007; Saleh et al.,2013).

(4.33)

where,Yo? observation data,Ym? simulated value,and ?o

? mean value of the observation data.

The E ranges has between -�� and 1.0.E value is 1.0 that means the simulated value and observed value is perfectly matched.The coefficient is zero indicates the model calculation is as accurate as the mean value of the observation,whereas E is less than zero is the mean value is a better than the model calculation.

The correlation coefficient is commonly used to find a dependency between two variables.In this case,the calculated velocity using the numerical model and the result of the conservation equation estimation were used to confirm the accuracy of the conservation equation method.The sensitivity and accuracy analysis results are summarized in Table 4.3.

Table 4.3 Sensitivity analysis for estimation method

��t

(s)

��x

(km)

Nash-Sutcliffe coefficient

Correlation coefficient.

Case 1

60

3.0

0.79

0.90

Case 2

60

2.0

0.86

0.93

Case 3

60

1.0

0.88

0.95

Case 4

60

0.5

0.89

0.95

Case 5

300

3.0

0.92

0.96

Case 6

300

2.0

0.95

0.98

Case 7

300

1.0

0.96

0.98

Case 8

300

0.5

0.96

0.99

Case 9

600

3.0

0.88

0.94

Case 10

600

2.0

0.85

0.92

Case 11

600

1.0

0.82

0.91

Case 12

600

0.5

0.81

0.91

Figure 4.24 Comparison of experiment and conservation equation (dt = 60 s)

In Figure 4.25,the flow velocity of Case 5,Case 6,Case 7 and Case 8 is plotted with the numerical simulation result.There is a overall good agreement between the conservation equation and numerical experiment compared with other test cases,especially the velocity profiles of Case 7 and Case 8 have been estimated as the nearest numerical experiment result,whereas Case 5 has shown a little different at some points.The Nash-Sutcliff coefficient and the correlation coefficient indicate that Case 5 is lower values compared with same time interval cases.In case of the time interval 300 s,the results of 1.0 km and 0.5 km space intervals are shown as the best results for the application of the conservation equation method.

Figure 4.25 Comparison of experiment and conservation equation (dt

= 300 s)

The result of Case 9,Case 10,Case 11,and Case 12 is shown in Figure 4.26.It seems that the conservation equation results have a similar tendency following the experiment result.It is that Case 9 is the highest Nash-Sutcliff coefficient and the correlation coefficient in the results of time interval 600 s cases.This case was estimated that the correlation coefficient was 0.94,and the Nash-Sutcliff coefficient was 0.88.From the all cases results,the calculated velocity results are shown that using the relatively small time interval compared with the large space interval may cause the low accuracy in this calculation.

Figure 4.26 Comparison of experiment and conservation equation (dt

= 600 s)

Furthermore,Case 9 result is remarkable for the availability of the raw observation data in estimating tsunami flow velocity because the time and the space intervals are similar with the real observation data condition of the Mabechi River.It means that the real observation data can be used to calculate the tsunami flow velocity using the conservation equation method,and its applicability and accuracy has been verified by the sensitivity analysis results.

As the result,the effects of the time interval and the distance difference have been confirmed by using Nash-Sutcliff coefficient and the correlation coefficient.Moreover,the calculated flow velocity from the conservation equation method has overall similar magnitudes and profiles compared with the numerical experiment result.The result of Case 9 as the real observation condition provides the evidence that the raw observation data can be used directly to estimate the flow velocity induced by the tsunami propagation.The estimation method based on the conservation equation is very useful and reasonable for the limited data condition,and this method can be suggested as the simple and practical estimation method.

4.5.4.3 Application of estimation method using conservation equation

The accuracy of the velocity estimation method using the conservation equation method has been verified by the comparison with the numerical experiment result.The suggested estimation method can be applied to the real field data.The estimated tsunami flow velocity and induced river discharge are shown in below.

?

(a) River discharge variation induced by tsunami

(b) Tsunami flow velocity at measurement stations

Figure 4.27 Estimated induced discharge and flow velocity of Takase River

?

(a) River discharge variation induced by tsunami

(b) Tsunami flow velocity at measurement stations

Figure 4.28 Estimated induced discharge and flow velocity of Mabechi River

?

(a) River discharge variation induced by tsunami

(b) Tsunami flow velocity at measurement stations

Figure 4.29 Estimated induced discharge and flow velocity of Sunaoshi River

?

(a) River discharge variation induced by tsunami

(b) Tsunami flow velocity at measurement stations

Figure 4.30 Estimated discharge and flow velocity of Naruse-Yoshida Rivers

?

Figure 4.31 Comparison of maximum discharge induced by tsunami and design flood discharge of Naruse-Yoshida Rivers

4.5.4.4 Particle Image Velocimetry and tsunami debris tracking method

Pre-processing covering image stabilization and image rectification is crucial in video image analysis.These processes can be used to overcome conventional problems like a distorted image that may be caused by the camera movement and camera viewpoint.Thus,the image pre-processing is emphasized in that case of using the real raw video data (Muste et al.,2008).

First of all,the target video and areas is determined that two areas in the video were selected as location A (river downstream) and location B (river upstream) of Sunaoshi River as shown in Figure 4.32.It is expected that the tsunami flow velocity will be completely estimated along the river.Moreover,tsunami debris tracking method can be used to the area of location B because the tsunami debris could be found in this area.In this river,the tsunami flow velocity was calculated by the estimation method based on conservation equation.Thus,the estimated flow velocity from the image analyses can be evaluated in comparison with the theoretical result.

For the image analysis,the raw video data at the target areas is stabilized by using four fixed points.The stable image data can be obtained that the stabilized images provide the fixed camera angle without the moving camera view.And then,the revised image is rectified to set up the pixel coordinates on the image.The pre-processing of image is shown in Figure 4.33 which is expressed the image stabilization and rectification.

Figure 4.32 Target area for image analysis (Sunaoshi River)

?

(a) Image stabilization

(b) Rectified image of target area (Red dot box)

Figure 4.33 Pre-processing of raw video for image analysis

?

The tsunami flow velocity is estimated by using the image after pre-processing.The displacements of image luminance during the specified time interval can be determined using PIV analysis.Thus,the flow velocity at a specific area is calculated from the displacement and time interval between two images in a pair.

Figure 4.34 shows the averaging flow velocity at 16:03:42 during 1 sec interval in Location A.It is shown that the velocity magnitude and flow direction at the estimation point can be confirmed from the analysis result.Furthermore,Location B has an interesting result as seen in Figure 4.35 that is affected by the river topographic characteristics.Location B is located in the curve,and covered with river center to the river embankment.Thus,it is that the measured velocity near the river embankment is lower than the river center.The flow direction is presented that the streamlines are shown along the river embankment from the river downstream to upstream.

(m/s)

Figure 4.34 Velocity vectors and streamlines of Location A

(a) 16:03:42

(b) 16:03:49

(c) 16:03:55

(m/s)

(m/s)

(m/s)

Figure 4.35 Velocity vectors and streamlines of Location B

?

Based on PIV estimation,mean velocity at each area is calculated that the measured velocity is averaged at every second.For the velocity estimation,225 and 100 points in Location A and Location B was utilized to estimate the mean velocity,respectively.The tsunami flow velocity including the standard deviation value is shown in Figure 4.36.The mean velocity in Location A was observed approximately 1.1 m

/s during in the video recording time.Figure 4.37 shows the mean velocity and standard deviation at every 1 sec interval in Location B,which is smaller target area compared with Location A,thus it may lead to lower standard deviation values.

Figure 4.36 Mean velocity and standard deviation of Location A

Figure 4.37 Mean velocity and standard deviation of Location B

Tsunami wave fluctuates every time in a real field as well as the flow velocity is changed by the every space and time.Therefore,the estimated result contains spurious vectors which are wrong direction vectors or extremely high velocities may be caused by the distorted video images in pre-processing stage and raw image data quality.The image analysis result is influenced by these factors,thus it is required that the accurate pre-processing and more high resolution images.

Tracking debris method was applied to Location B.The floating red object could be found in the raw video as seen in Figure 4.38.The method of tracking the red object is used to estimate the flow velocity vector and magnitude.

Figure 4.38 Movement of tsunami debris in video (Location B)

The estimated velocity vector and velocity magnitude of the red target are shown in Figure 4.39.The flow velocity of debris was steadily increasing during around 15 seconds,and then the peak velocity is attained as 1.03 m

/s.The flow direction can be confirmed by vector analysis which is similar with the PIV analysis result of Location B.

To verify the tsunami flow velocity from image analyses,the suggested velocity estimation method based on the conservation equation was applied to the water level data of the Sunaoshi River.The image analysis results and calculated tsunami flow velocity from the equation is shown in Figure 4.40 that the comparison result have reasonable and similar flow velocity.The presented methods can be useful in estimating the tsunami flow velocity.

(a) Velocity vectors of tsunami debris

(b) Tsunami debris velocity magnitude

Figure 4.39 Velocity vectors and magnitude of tsunami debris

Figure 4.40 Comparison result of image analysis and estimation equation

4.5.5 Tsunami erosion and deposition

The topography and morphology of the coastal area were drastically changed by the huge tsunami,especially in sandy coast.The tsunami wave caused severe erosion at estuaries,sandy coasts and shallow bottoms near shore areas.In the case of the tsunami event of 2011,the available observation data such as water level and tide level were not sufficient to analyze the effect of tsunami wave in estuaries and coasts.Nevertheless,the erosion process on the river mouth area and coastal area were recorded in real time videos.These videos can be used to estimate the erosion and deposition under the tsunami wave.

Topography data before the tsunami can be used to evaluate the propagation process of the tsunami on the estuarine and coastal area.The eroded area can be evaluated using the pre- and post-tsunami event aerial photos of the damaged area.These data provide valuable information about the erosion and deposition changes in the coastal area.It is also useful to evaluate the effects of morphology changes,topographic feature and estuarine and coastal environments under the limited data availability.

(a) Inundation of initial tsunami wave at Gamo Lagoon

(b) Elevation data of Line A and Line B

Figure 4.41 Effect of topographic feature on the initial tsunami wave

It is found that coastal environments are one of the important parameters in the erosion process due to the tsunami.The influence of estuarine environments was evaluated by analyzing the pre- and post-tsunami aerial photography.After the tsunami event,the difference behavior due to the estuarine and coastal environments can be found from the comparison of erosion distance.

Figure 4.42 shows the coastline change due to the tsunami propagation based on the pre- and post-tsunami aerial photos.The erosion distance of the Nanakita Estuarine is shown that after the tsunami,the small islands could be found in this figure.The erosion distance between the small is-lands and the coastal line before the tsunami is indicated as the red bars.The Gamo Lagoon coast has been severely eroded by the tsunami even though the elevation was high and there were coastal structures.In the north side,the maximum erosion distance from previous coastal line was estimated as 280 m approximately.

The sand-spit part of the Nanakita River mouth was completely washed away due to the tsunami wave.In contrast,the forest area of the south side has no significant change of the coastal line due to the tsunami flow.It is estimated that the erosion distance of the south side was less than 40 m.the erosion distance has big differences according to the conditions of the coastal and estuarine surrounding area.As the result,the coastal and estuarine environments are important roles in the erosion process during the tsunami event.

Figure 4.42 Estimated erosion distance of the Nanakita Estuarine

?

4.6 Conclusions

The assessment of the 2011 Tohoku Tsunami impacts has been conducted by the various approaches which are the numerical experiment,image data analysis and theoretical methods.The accuracy and availability of analysis methods were verified theoretically and experimentally.These methods were used to assess the physical characteristics of tsunami propagation into rivers.

The estimated tsunami height,intrusion distance,tsunami arrival time,celerity,as well as tsunami flow velocity and river discharge induced by the tsunami wave have been considered as the characteristics of Level 2 tsunami event,further the effects of this level tsunami in rivers was confirmed that the significant factors are not only morphological features but also geographic locations,topographic characteristics,river characteristics and estuarine environments.In this tsunami event,these factors are deeply related to the estimated tsunami parameters,especially river mouth morphology changes can be used to determine the effects due to tsunami propagation into rivers in accordance with the levels of tsunami impact.

Furthermore,these tsunami parameters can be used to confirm the different tsunami behaviors regarding the tsunami scale and impact.If the same parameters at same locations in Level 1 tsunami event are to be able to compare,more details of the suggested significant factors can be verified.Therefore,the physical parameters of Level 1 tsunami will be assessed in Chapter 5,and then the comparative analysis between Level 1 and Level 2 will be explained in the Chapter 6.

?

CHAPTER 5 TSUNAMI PROPGATION INTO RIVERS WITHOUT MORPHOLOGICAL CHANGES

5.1 Introduction

In the previous research,Abe (1987) conducted the analyzing water level data in rivers during Japan central earthquake and tsunami.It was clearly shown the effect of tsunami ascending into rivers.The observed water level data in rivers was crucial in understanding characteristics of tsunami propagation into rivers.

In the 2010 Chilean Tsunami and the 2012 Dec.7 tsunami events,water level data analysis has been conducted to assess the tsunami impacts in rivers with regard to the overall river characteristics such as the features of the river mouth morphology and river topographic,and geographical locations.The estimated tsunami physical parameters from two tsunami events are discussed with the factors influencing the tsunami propagation into rivers.

5.2 Study area

Figure 5.1 Location of study area

5.3 Data collection

In case of without the river mouth morphological changes,the observed water level data at near the river mouth is one of the important data sources to assess the characteristics under the tsunami propagation into rivers.During the 2010 Chilean Tsunami and the 2012 Dec.7 tsunami,water level data and tide level were observed at many hydraulics measurement stations and tidal monitoring stations in study area.The observed water level data were used to estimate the physical quantities of tsunami wave.

5.3.1 Water level data and river mouth features on 2010 Chilean Tsunami

The observed water level data in the river is included the tsunami information such as tsunami height,tsunami travel distance and tsunami arrival time.The tsunami celerity and tsunami flow velocity can be obtained through analyzing the water level data.It is useful to verify the characteristics of tsunami propagation into rivers.

Table 5.1 Classification of river mouth morphology (Tanaka et al,2011)

Type 1

? River flows into inside a port,rocky coast

? Non-constriction

Type 2

? River flows into sandy coast

? Constriction

Table 5.2 River information for 2010 Chilean Tsunami

River class

Name

River mouth type*

Remarks

Class A

Kitakami

Type 2

Constriction

Old-Kitakami

Type 1

-

Naruse-Yoshdia

Type 2

Constriction / share river mouth

Natori

Type 2

Constriction

Abukuma

Type 2

Constriction

Class B

Nanakita

Type 2

Constriction

Jo

Type 1

-

Sunaoshi

Type 1

-

Oh

Type 1

-

Takagi

Type 1

-

Class A? Managed by national government

Class B? Managed by regional government

*? Classification of river mouth type (Tanaka et al.,2011)

5.3.2 Water level data and river mouth features on 2012 Dec.7 Tsunami

The tsunami height on the 2012 Dec.7 tsunami event was not significant compared with the 2010 Chilean Tsunami and the 2011 Tohoku Tsunami.The tsunami waves were observed mostly near the river mouth and the tide measurement stations.However,this tsunami event is remarkable in understanding the mechanism of tsunami propagation into rivers without morphological changes.After 2011 Tohoku Tsunami,these rivers have completely changed the characteristics of river mouth morphology.Therefore,the same criteria about the river mouth morphology based on the 2010 Chilean Tsunami was inapplicable to assess the characteristics of the 2012 Dec.7 tsunami event.

The water level data were measured every 10 min interval from 17:00 to 24:00,Dec.7.The observed water level data in rivers,tidal level data have been utilized to evaluate the characteristics of the tsunami physical quantities.Furthermore,the simplified classification was used to consider the changed river mouth morphology due to the 2011 Tohoku Tsunami.In Table 5.3,the river data is presented by using the simplified classification.

Table 5