forward and inverse modeling of tsunami sediment transport · forward and inverse modeling of...

Forward and Inverse Modeling of Tsunami Sediment Transport

Hui Tang

Dissertation submitted to the Faculty of theVirginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Doctor of Philosophyin

Geosciences

Robert Weiss, ChairBrian W. RomansJennifer L. Irish

Kenneth A. Eriksson

March 13, 2017Blacksburg, Virginia

Keywords: Sediment Transport, Tsunami, Forward Model, Inverse ModelCopyright 2017, Hui Tang


Hui Tang

ABSTRACT

Tsunami is one of the most dangerous natural hazards in the coastal zone worldwide. Largetsunamis are relatively infrequent. Deposits are the only concrete evidence in the geologicalrecord with which we can determine both tsunami frequency and magnitude. Numericalmodeling of sediment transport during a tsunami is important interdisciplinary research toestimate the frequency and magnitude of past events and quantitative prediction of futureevents. The goal of this dissertation is to develop robust, accurate, and computationallyefficient models for sediment transport during a tsunami. There are two different modelingapproaches (forward and inverse) to investigate sediment transport. A forward model consistsof tsunami source, hydrodynamics, and sediment transport model. In this dissertation,we present one state-of-the-art forward model for Sediment TRansport In Coastal HazardEvents (STRICHE), which couples with GeoClaw and is referred to as GeoClaw-STRICHE.In an inverse model, deposit characteristics, such as grain-size distribution and thickness, areinputs to the model, and flow characteristics are outputs. We also depict one trial-and-errorinverse model (TSUFLIND) and one data assimilation inverse model (TSUFLIND-EnKF)in this dissertation. All three models were validated and verified against several theoretical,experimental, and field cases.


Hui Tang

GENERAL AUDIENCE ABSTRACT

Population living close to coastlines is increasing, which creates higher risks due to coastalhazards, such as tsunami. Tsunamis are a series of long waves triggered by earthquakes, vol-canic eruptions, landslides, and meteorite impacts. Deposits are the only concrete evidencein geological records that can be used to determine both tsunami frequency and magnitude.The numerical modeling of sediment transport in coastal hazard events is an important in-terdisciplinary research area to estimate the magnitude their magnitude. The goal of thisdissertation is to develop several robust, accurate, and computationally efficient forward andinverse models for tsunami sediment transport. In Chapter one, a general literature review isgiven. Chapter two will discuss a new model for TSUunami FLow INversion from Deposits(TSUFLIND). TSUFLIND incorporates three models and adds new modules to simulatetsunami deposit formation and calculate flow condition. In Chapter three, we present aninverse model based on ensemble Kalman filtering (TSUFLIND-EnKF) to infer tsunamicharacteristics from deposits. This model is the first model that forms a system state toinclude both observable variables and unknown parameters. In Chapter four, we presenta new forward model for simulating Sediment TRansport in Coastal Hazard Events, whichcombines with GeoClaw (GeoClaw-STRICHE). In Chapter five, we discuss the future worksfor TSUFLIND, TSUFLIND-EnKF, GeoClaw-STRICHE and forward-inverse framework.

Acknowledgments

Firstly, I want to thank my adviser, Dr. Robert Weiss, the smartest man I know. Thankyou for pushing me to do my best, and being patient for my mistakes and struggles. I alsowould like to thanks my committee members, Dr. Jennifer L. Irish, Dr. Brian W. Romansand Dr. Kenneth A. Eriksson for their guidance through my Ph.D. studies.

I would like to thank my colleagues in our group: Dr. Amir Zainali, Dr. Wei Cheng, andRoberto, it is very nice to work with you.

I also want to express my thanks to my coauthors, Dr. Heng Xiao and Jianxun Wang fortheir assistance during the development of TSUFLIND-EnKF. To Dr. Randall J. LeVequeand his student Xinsheng Qin, thank you for helping me during the development of GeoClaw-STRICHE. To Dr. Heinrich Bahlburg, Vanessa Nentwig, Dr. Michaela Spiske, Dr. BruceJaffe, Dr. Janneli Lea Soria, Dr. Adam Switzer and Dr. Daisuke Sugawara, thank you allfor generously sharing with us data and codes.

To Dr. Bretwood Higman, Colin Bloom, Dr. Breanyn MacInnes, Dr. Bruce Richmond, Dr.Patrick J. Lynett, Dr. Colin Peter Stark, Andrew Mattox, Vassilios Skanavis, thank you allfor the enjoyable field works in Alaska. I have learned so many from this experience, andappreciate your generosity in advice.

I greatly appreciate all the academic support from the faculties and friends at Tech. A specialthanks to Becca, Liang and Qing for their support. Finally, I want to thank my family andfriends in the United States and China for your support and understanding. Without you,I cannot make it. I love you all.

iv

Contents

1 Introduction 1

1.1 Tsunami and Tsunami Deposits . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Tsunami . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.2 Tsunami Deposit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.3 Forward Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.1.4 Inverse Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2 Contributions and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.2.1 Overarching Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.2.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.3 Outline of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

v

Contents vi

2 A Model for TSUnami FLow INversion from Deposits (TSUFLIND) 17

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Inversion Models Employed . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.2 Sedimentation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.3 Result Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.2.4 Offshore Wave Characteristics and Flooding . . . . . . . . . . . . . . 27

2.2.5 Inversion Framework and Coupling . . . . . . . . . . . . . . . . . . . 28

2.3 Application and Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.3.1 Field Observation and Data . . . . . . . . . . . . . . . . . . . . . . . 30

2.3.2 Sedimentary Simulation Results . . . . . . . . . . . . . . . . . . . . . 30

2.3.3 Hydrodynamic Inversion Results . . . . . . . . . . . . . . . . . . . . . 33

2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.4.1 Interpretation of Test Case Results . . . . . . . . . . . . . . . . . . . 34

2.4.2 Model Limitation and Improvement . . . . . . . . . . . . . . . . . . . 36

Contents vii

2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3 TSUFLIND-EnKF: Inversion of Tsunami Flow Depth and Flow Speed

from Deposits with Quantified Uncertainties 42

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43


3.2.1 Forward Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.2.2 EnKF Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2.4 Inversion Result Evaluation and Error Model . . . . . . . . . . . . . . 50

3.2.5 Parameter Study and Case Study . . . . . . . . . . . . . . . . . . . . 52

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.3.1 Parameter Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.3.2 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.3.3 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Contents viii

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4 GeoClaw-STRICHE: A Coupled Model for Sediment TRansport In Coastal

Hazard Events 74

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75


4.2.1 Sediment Transport Model: STRICHE . . . . . . . . . . . . . . . . . 78

4.2.2 Morphology Update . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.2.3 Sediment Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.2.4 Hydrodynamic Model: GeoClaw . . . . . . . . . . . . . . . . . . . . . 87

4.2.5 Model algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.3 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.3.1 Flume Experiment Case . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.3.2 The 2004 Indian Ocean Tsunami Case . . . . . . . . . . . . . . . . . 97

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

4.4.1 Interpretation of Test Case Results . . . . . . . . . . . . . . . . . . . 98

Contents ix

4.4.2 Model Limitations and Future works . . . . . . . . . . . . . . . . . . 100

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5 Future Works 104

5.1 TSUFLIND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.2 TSUFLIND-EnKF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.3 GeoClaw-STRICHE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

5.4 Forward-inverse Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

List of Figures

1.1 Tsunami from 1650 B.C to 2016 formed by earthquakes, volcano eruptions,

landslides, and other sources modified based on ICSU World Data Service

tsunami source map, 2014 version. . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Tsunami source locations and types based on ICSU World Data Service, 2014

version. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 General framework for forward and inverse numerical models of tsunami sed-

iment transport, modified from Figure 1 in Sugawara et al. (2014) . . . . . . 6

1.4 General framework of the dissertation; 2: Chapter two: TSUFLIND; 3: Chap-

ter three: TSUFLIND-EnKF; 4: Chapter four: GeoClaw-STRICHE; Chapter

five: Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.1 Conceptual model of TSUFLIND with definition of the terminology used later

in the paper. For more symbols used in this paper see Appendix A. . . . . . 20

x

List of Figures xi

2.2 Flowchart for TSUFLIND’s iterative scheme to simulate tsunami deposit and

estimate tsunami flow condition. . . . . . . . . . . . . . . . . . . . . . . . . 29

2.3 TSUFLIND simulation results and field measurement at Ranganathapuram,

India. a: Vertical grading in grain size distribution (blue line) and mean grain

size (red line) for four sampled locations (120m, 160m, 177m and 207m); b:

the entire tsunami deposit grain-size distributions used as inputs to TSU-

FLIND (red points) and model result outputs from TSUFLIND (green line);

c: tsunami deposit thickness field measurements (red points) and simulation

results from TSUFLIND (green line); d: topography, wave run up and sample

locations for test case (I : 120m; II : 160m; III: 177m; IV : 207m). . . . . 32

2.4 The estimated flow speeds and Froude numbers from TSUFLIND. a: Tsunami

flow speed estimates are indicated by the gray area with the boundaries of

maximum and minimum possible speeds. The dashed line is the average value

of estimated flow speeds. b: Froude number estimates are indicated by the

gray area in this figure with the maximum and minimum possible values. The

dashed line is the average value of Froude number. . . . . . . . . . . . . . . 34

3.1 Flowchart for the EnKF method’s iterative scheme. . . . . . . . . . . . . . . 50

3.2 The L2-norm of inference error versus time for ensemble size ranges from 10

to 3000. (a): The L2-norm as a function of time and ensemble size. The

ensemble size changes from 50 to 3000. (b): The final L2-norm as a function

of ensemble size from 10 to 3000. . . . . . . . . . . . . . . . . . . . . . . . . 54

List of Figures xii

3.3 The shear velocity and L2-norm of inference error as a function of the mean

value of the initial ensemble ranging from 0.25 to 1.0 ms−1. (a): The calculated

shear velocity versus time and mean value of the initial ensemble ranging from

0.3 to 0.8 ms−1; The black dashed line is the mean value of the ensemble for

each time step. The red line is the synthetic truth for these cases. (b): The

final L2-norm versus mean value of the initial ensemble from 0.25 to 1.0 ms−1.

(c): The final inversion result distributions for different mean values of the

initial ensemble from 0.3 to 0.8 ms−1. . . . . . . . . . . . . . . . . . . . . . 56

3.4 The shear velocity and L2-norm as a function of the value range of the initial

ensemble ranging from 0.1 to 1.6 ms−1. (a): The calculated shear velocity

versus time and value range of the initial ensemble ranging from 0.2 to 1.2

ms−1; The black dashed line is the mean value of the ensemble. The red line

is the synthetic truth for these cases. (b): The final L2-norm versus the value

range of the initial ensemble from 0.1 to 1.6 ms−1. (c): The final inversion

result distributions for different value ranges of the initial ensemble from 0.3

to 0.8 ms−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.5 Compare inversion processes and results of two different distributions for shear

velocity. (a): The shear velocity inversion process by uniform distribution;

(b): The shear velocity inversion process by normal distribution; (c): The

shear velocity distributions for 0s, 25s, 50s, 75s and final result by uniform

distribution; (d): The shear velocity distributions for 0s, 25s, 50s, 75s and

final result by normal distribution. . . . . . . . . . . . . . . . . . . . . . . . 58

List of Figures xiii

3.6 Compare individual and joint inversion processes and results. (a): The water

depths and shear velocities inversion processes. The black dashed line is the

mean value of the ensemble. The red line is the synthetic truth of unknown

parameter. (b): The water depth and shear velocity distributions for 25s,

50s, 75s and final results. I and III: Inverse water depth and shear velocity

separately; II and IV: Inverse water depth and shear velocity jointly. . . . . . 60

3.7 The L2-norm as a function of time and model error or observational error

ranging from 0.1% to 30%. (a): The L2-norm versus time for observational

error from 0.1% to 30%. (b): The final L2-norm as a function of observational

error from 0.1% to 30%. (c): The L2-norm versus time for model error from

0.1% to 30%. (d): The final L2-norm as a function of model error from 0.1%

to 30%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.8 The final L2-norm versus sampling frequency based on 30-cm tsunami deposit.

(a): The final L2-norm for water depth as a function of sampling frequency

from 6 to 30; (b): The final L2-norm for shear velocity as a function of sam-

pling frequency from 6 to 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.9 The 2004 Indian Ocean tsunami application case. (a): Sediment thickness

and the best sampling frequency along the transect in the vicinity of Ran-

ganathapuram. The black line is the sediment thickness from field data. The

black line with dot is the best sampling frequency; (b): The topography of

Ranganathapuram cross section and sample location for test case. . . . . . . 64

List of Figures xiv

3.10 Inversion results for the 2004 Indian Ocean tsunami case for location I to IV

in Fig. 3.9b. Ia-IVa: inversion results for shear velocity, u∗; Ib-IVb: inver-

sion results for water depth, H; Ic-IVc: inversion results for depth-averaged

velocity, U ; Id-IVd: inversion results for Froude number. . . . . . . . . . . . . 65

4.1 Concept model of sediment layers setting. The sediments are separated to

erodible layers and hard structure. (a): Concept model for sediment lay-

ers during erosion; I: original sediment condition; II: flow eroded part of

sediments; III: Remap sediment layers; IV: recalculate sediment properties

for each layers (b): Concept model for Sediment layers during deposition; I:

original sediment condition; II: flow deposited part of sediments; III: remap

sediment layers; IV: recalculate sediment properties for each layers. . . . . . 88

4.2 Flowchart for model algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.3 Schematic diagram for experiment setting with major components shown in

Johnson et al. (2016). Ut: ultrasonic transducers for water depth measure-

ment; ADVs: two side-looking Nortek Vectrino ADVS for flow velocity mea-

surement. Sediment source was located 0.5 to 2 m in front of the lift gate as a

sand dune about 1.5 m long and 0.15 m high. There is a computer-controlled

lift gate at left side, perforated ramp at right side, and a smooth bed without

slope between them. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

List of Figures xv

4.4 Initial setting for experiment and model based on Johnson et al. (2016): (a):

Grain-size distributions of sediment source (source 1-4); (b): Water depth

measure at headbox and boundary condition in simulations. . . . . . . . . . 92

4.5 Measured flow depth (black line) and model results (red circle). I: source 1 on

dry land; II: source 1 in 10 cm water; III: source 1 in 19 cm water; IV: source

2 in 8 cm water; V: source 3 in 8 cm water; VI: source 4 in 8 cm water. . . . 93

4.6 (a): Froude number from experiment in case III (black line) and model results

(red circle). (b): Flow velocity from experiment for case III (black line) and

model results (red circle). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.7 Sediment thickness from experiment (black line) and model results (read cir-

cle). I: source 1 on dry land; II: source 1 in 10 cm water; III: source 1 in 19

cm water; IV: source 2 in 8 cm water; V: source 3 in 8 cm water; VI: source

4 in 8 cm water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.8 D10, D50, D95 from experiment (line) and model results (marker). I: source

1 on dry land; II: source 1 in 10 cm water; III: source 1 in 19 cm water; IV:

source 2 in 8 cm water; V: source 3 in 8 cm water; VI: source 4 in 8 cm water. 96

4.9 (a): Maximum erosion surface, final sediment surface and original surface

in study transect for the 2004 Indian Ocean tsunami in Kuala Meurisi; (b):

Model results, field data and model results from Delft3D based on Apotsos

et al. (2011b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

List of Tables

1.1 Summary of available forward models for sediment transport in coastal hazard

events modified based on Sugawara et al. (2014). . . . . . . . . . . . . . . . . 8

1.2 Summary of available inverse models of sediment transport in coastal hazard

events modified based on Sugawara et al. (2014). . . . . . . . . . . . . . . . . 11

2.1 Symbols List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.1 Physical and computational parameters for parameter study. . . . . . . . . . 52

4.1 Symbols List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

xvi

Chapter 1

Introduction

1.1 Tsunami and Tsunami Deposits

1.1.1 Tsunami

Approximately 75% of all large cities are in the coastal zone, and more than 50% of the

world’s population lives within 60 km of the ocean 1. Population living close to coastlines is

increasing, which creates higher risks due to coastal hazards. For the United States, more

than 39% of the population is living in the coastal zone in the United States and is going to

increase to 47% by 2020 2. Furthermore, 21 of the world’s top 30 megacities are potentially

threatened by coastal hazards based on United Nations report 3. Tsunami events are one

of the most dangerous natural hazards in coastal zones, which can cause severe damages to

human life and coastal facilities.1http://www.unep.org/urban_environment/issues/coastal_zones.asp2http://oceanservice.noaa.gov/facts/population.html3https://esa.un.org/unpd/wup/cd-Rom/

1

Figure 1.1: Tsunami from 1650 B.C to 2016 formed by earthquakes, volcano eruptions, landslides, and other sourcesmodified based on ICSU World Data Service tsunami source map, 2014 version.

Chapter 1. Introduction 3

A tsunami is a series of long waves that can be triggered by earthquakes, volcanic eruptions,

landslides, and meteorite impacts. Figure 1.1 shows the tsunami source locations with differ-

ent causes since 1650 B.C. Figure 1.2 depicts the percentage of different areas and different

causes for tsunami since 1650 B.C. Most tsunamis occur around the rim of the Pacific Ocean

area known as the "Ring of Fire" (Fig. 1.2). For both the Indian Ocean and the Mediter-

ranean Sea, about 9% of all tsunamis occur there, respectively (Fig. 1.2). 6% of tsunamis

happen in the Atlantic Ocean and Caribbean area (Fig. 1.2). About 87% of tsunamis are

generated by earthquakes (Fig. 1.2). The rest of them is caused by volcanic eruptions (8%),

landslides (4%), and other unknown sources (Fig. 1.2). The largest economic loss caused by

a tsunami was about 235 billion dollars during the 2011 Tohoku-Oki tsunami based on the

World Bank 4.

1.1.2 Tsunami Deposit

Two major parts in coastal hazard assessments, especially for tsunami, are quantifying fre-

quency and magnitude. However, major tsunami event is rare. Therefore, deposits in the

geological record are the only concrete evidence that can be used to determine both fre-

quency and magnitude (Dawson and Shi, 2000). Research about tsunami deposit in geo-

logical records have already covered most areas of the world including North America (e.g.

Clague and Bobrowsky, 1994), South America (e.g. Cisternas et al., 2005), Europe (e.g. Ko-

rtekaas and Dawson, 2007; De Martini et al., 2010), the Middle East (e.g. Reinhardt et al.,

2006; Donato et al., 2008), East Asia (e.g. Pinegina et al., 2003; Bourgeois et al., 2006;

Komatsubara et al., 2008; Goto et al., 2010; Nakamura et al., 2014), South East Asia (e.g.4http://web.worldbank.org


Pacific Ocean (76 %)Indian Ocean & Red Sea (9 %)Mediterranean Sea (9 %)Atlantic Ocean & Caribbean Sea (6 %)

Earthquakes (87 %)Volcanic Eruptions (8 %)Landslides (4 %)Unknown Causes (1 %)

Figure 1.2: Tsunami source locations and types based on ICSU World Data Service, 2014version.

Jankaew et al., 2008; Phantuwongraj and Choowong, 2012), the Pacific Islands (e.g. Goff

et al., 2011), the Indian Ocean (e.g. Monecke et al., 2008), Australia (e.g. Dominey-Howes

et al., 2006), New Zealand (e.g. Goff et al., 2004; Nichol et al., 2007).

As paleo-event deposits are used for reconstructing recurrence, it is important to distinguish

between tsunami and storm deposit in the geological record (Morton et al., 2007). However,

in many cases, the deposits from tsunamis and storms are too similar to distinguish from

each other in sedimentary records (Morton et al., 2007). Many studies have focused on

detecting, differentiating, and comparing tsunami and storm deposits (e.g. Nanayama et al.,

2000; Goff et al., 2004; Tuttle et al., 2004; Morton et al., 2007). There are physical, biological,


geochemical or numerical methods, to distinguish tsunami and storm deposits (e.g. Buckley

et al., 2012; Palma et al., 2007; Goff et al., 2008, 2009; Barbano et al., 2010). The conclusion

can only be achieved by a multidisciplinary study with different methods (Goff et al., 2012).

The goal of the tsunami deposit research is to understand and assess tsunami hazards. The

assessment usually quantifies the magnitude of these events, including but not limited to

the inundation area, run-up, and flow conditions. Numerical modeling of sediment transport

during tsunamis is the only way to estimate the past tsunami magnitudes. Two different

numerical modeling approaches, forward and inverse, are used to investigate the sediment

transport processes during the tsunami and to assess tsunami hazards (Fig. 1.3). In next two

sections, we briefly discuss these approaches and summarize available models for sediment

transport during the tsunami. Tsunamis have the power to transport almost all types of

sediment. However, in this dissertation, we will mainly focus on the transport processes of

sand.

1.1.3 Forward Model

A forward model consists of a tsunami source model, a hydrodynamic model, and a sediment

transport model (Fig. 1.3). Forward models usually need bathymetry or topography data.

For tsunami modeling, the initial tsunami waveform can be calculated by using different

tsunami source models (Tsushima et al., 2012). A hydrodynamic model consists of several

conservation equations to simulate the processes of wave propagation and inundation. There

are two different approaches to apply sediment transport model in this framework. Hydro-

dynamic and sediment transport models are constructed as two separate modules in the first


Tsunami Source Model

Hydrodynamic

Model

Flow／Wave

Dynamics

Sediment Transport

Model

Sedimentary

Data

Field

Observations

Forward Model

Inverse Model

Figure 1.3: General framework for forward and inverse numerical models of tsunami sedi-ment transport, modified from Figure 1 in Sugawara et al. (2014)

approach (Fig. 1.3). At each time step, the hydrodynamic model outputs hydrodynamic

conditions to the sediment transport model (Fig. 1.3). The second one solves the system

of equations that couples fluid dynamics and sediment transport. All available sediment

transport models for tsunami employ the first approach. Finally, the morphological change

simulated by the sediment transport model returns to the hydrodynamic model. Table 1.1

summarizes these existing forward models that have been employed to simulate sand or

gravel transport during the tsunami. We also summarize some applications that include

flume experiments and real tsunami events in the references part.

For most of the tsunami sediment transport models, a two-dimensional hydrodynamic model

is employed (e.g. XBeach, XBeach-G, STM and GeoClaw-STRICHE, Roelvink et al., 2009;


Kihara and Matsuyama, 2011; McCall et al., 2014; Tang and Weiss, 2016). Some three-

dimensional models like Delft3D and C-HYDRO3D also incorporate vertical velocities and

vertical sediment concentration profiles into the framework (Van Rijn et al., 2004; Kihara and

Matsuyama, 2011). However, three-dimensional models require significant computational

resources to simulate large-scale problems (Sugawara et al., 2014). Most of the forward

models can simulate sediment transport processes during the tsunami for mixed particle size

(e.g. XBeach, XBeach-G, Delft3D and GeoClaw-STRICHE, Takahashi et al., 2001; Kihara

and Matsuyama, 2011; Gusman et al., 2012; Ontowirjo et al., 2013; McCall et al., 2014;

Tang and Weiss, 2016). Commonly, the forward models separate bedload and suspended

load, but some forward models consider only total load (Li et al., 2012a,b). For the sediment

flux calculation, three methods have been developed so far: empirical formulation (Gusman

et al., 2012), analytical approach (e.g. XBeach,C-HYDRO3D, and GeoClaw-STRICHE,

Roelvink et al., 2009; Kihara and Matsuyama, 2011; Tang and Weiss, 2016), and numerical

model (e.g. XBeach,Delft3D, and GeoClaw-STRICHE, Van Rijn et al., 2004; Roelvink et al.,

2009; Tang and Weiss, 2016).

Table 1.1: Summary of available forward models for sediment transport in coastal hazard events modified based onSugawara et al. (2014).Model Name Dimension Sediment Size Formulation for Method for References

sediment load sediment fluxVan Rijn (1993) empirical formulations Gelfenbaum et al. (2007)

Delft3D 2DV/3D sand, Van Rijn et al. (2004) analytical approaches Apotsos et al. (2011a)mixed grain-size Van Rijn (2007a) numerical models Apotsos et al. (2011b)

Van Rijn (2007b) Apotsos et al. (2011c)Roelvink et al. (2009)

XBeach 2DH sand, Van Rijn (1993) analytical approaches Li et al. (2012a)mixed grain-size Soulsby (1997) Li et al. (2012b)

Van Rijn (1993)XBeach-G 2DH sand and gravel, Soulsby (1997) empirical formulations Roelvink et al. (2009)

mixed grain-size Van Rijn (2007a) analytical approaches McCall et al. (2014)Ontowirjo et al. (2013) 2DH sand, Van Rijn (1984b) empirical formulations Ontowirjo et al. (2013)

single grain-size Ribberink (1998)C-HYDRO3D 3D sand, Van Rijn (1984a) analytical approaches Kihara and Matsuyama (2011)

single grain-size Van Rijn (1984b)Ashida (1972) Takahashi et al. (2001)

STM 2DH sand, Takahashi et al. (2001) empirical formulations Takahashi et al. (2008)single grain-size Yoshii et al. (2011) Yoshii et al. (2011)

Gusman et al. (2012)GeoClaw-STRICHE 2DH sand and gravel, Van Rijn (1984a) numerical models Tang and Weiss (2016)

mixed grain-size Van Rijn (1984b)


One of the major advantages of forward models is that forward models can be directly used to

study tsunami waves generation, propagation, inundation, and sediment transport (LeVeque

et al., 2011). By changing the model setup, we can study how model parameters and flow

dynamics affect the erosion and deposition of sediments. Another advantage of the forward

model is their capability of studying the time evolution of hydrodynamics and sediment

transport (Sugawara et al., 2014). Forward modeling is the only way to get information

about the time series of sediment transport and deposition processes for real cases, when the

video records are unavailable. However, due to the lack of pre-tsunami topography data in

most cases, it is hard to use forward models for studying paleotsunami events (Tang et al.,

2016).

1.1.4 Inverse Model

There are five different types of inverse problems according to the unknowns: model pa-

rameters, initial conditions, boundary conditions, sources or sinks, and a mixture of the

above (Sagar et al., 1975). A series of inverse methods including the direct method, trial-

and-error manual calibration method, and data assimilation algorithm have been proposed

to solve inverse problems (Zhou et al., 2014). Both trial-and-error inverse model and data

assimilation inverse model consist of a forward model and an inverse method (Zhou et al.,

2014). The inverse method implemented in the framework decides the accuracy of inversion

results. On the other hand, the forward model determines the applicable problems for this

algorithm. The inverse models for tsunami deposits can estimate flow speed or flow depth.

In these inverse models, deposit characteristics, such as grain-size distribution and thickness,


are inputs to the model, and flow characteristics are outputs (Sugawara et al., 2014). Table

1.2 summarizes the inverse models, and we will describe all of them in the remainder of this

section.

(1) Moore’s advection model: Moore et al. (2007) assumed that some grains in the sed-

iment source do not move because the tsunami flow is not strong enough. Furthermore, it is

assumed that most of the grains are transported in suspension. Based on these assumptions,

the shear velocity is determined for the largest grain in the tsunami deposits. The law of the

wall can help to find the shear stress that is necessary to move the largest grain. Because of

the horizontal transport, this model is also referred to as an advection model.

(2) Soulsby’s model: Soulsby’s model assumes that the water depth linearly increases

during running up and linearly decreases during backwash in all locations. Soulsby et al.

(2007) assumed that the maximum flow depth at a given location during tsunami inundation

depends on the maximum water depth at the shoreline. The sediment thickness for all grain

sizes linearly decreases with distance from the shoreline in this model. Based on sediment

thickness and flow depth, Soulsby’s model can estimate the inundation and runup.

(3) Smith’s model: Smith et al. (2007) used the fine particles settling process and the

wave period to estimate the minimum water depth. This model assumes that: (1) all sedi-

ments are transported in suspension, (2) all particles settle individually, (3) the muds settle

as flocs, and (4) tsunami wave period can be estimated. The output of this model is the

minimum flow depth at the shoreline.

Table 1.2: Summary of available inverse models of sediment transport in coastal hazard events modified based onSugawara et al. (2014).Model Name Approaches Inputs Outputs References

particle trajectory settling velocity of the tsunami height;Moore’s model (direct method) largest particle; flow speed Moore et al. (2007)

travel distancesettling column settling velocities;

Soulsby’s model (direct method) sediment thickness; inundation and runup Soulsby et al. (2007)grain-size distribution

Smith’s Model particle settling settling velocity of minimum of water depth Smith et al. (2007)(direct method) the slowest particleequilibrium settling velocities;

TsuSedMod suspension grain-size distribution; shear velocity; Jaffe and Gelfenbuam (2007)(trial-and-error) bottom roughness; tsunami flow speed

flow depthcombined model vertical and horizontal depth average velocity;

TSUFLIND (trial-and-error) grading; topography; flow depth; Tang and Weiss (2015)sediment thickness wave amplitude

equilibrium vertical grading; depth averaged velocity; Wang et al. (2015)TSUFLIND-EnKF suspension sediment thickness; flow depth Tang et al. (2016)

(data assimilation) grain-size distribution


(4) TsuSedMod: Jaffe and Gelfenbuam (2007) developed a trial-and-error inverse model

based on sediment deposited from suspension. There are several assumptions in TsuSedMod:

(1) sediment is transported in suspension and deposited when steady and uniform tsunami

flow slows down; (2) suspended sediment concentration is distributed in an equilibrium

profile; (3) there is no erosion caused by the return flow. The model iteratively adjusts the

sediment source and the shear velocity to match the grain-size distributions and sediment

thickness (Jaffe et al., 2011, 2012).

(5) TSUFLIND: TSUFLIND incorporates three models and adds new modules to calcu-

late flow condition. TSUFLIND takes the grain-size distribution, thickness, water depth, and

topography information as inputs. TSUFLIND computes sediment concentration, grain-size

distribution of sediment source, and initial flow condition to match the sediment thickness

and grain size distribution from field observations by using a trial-and-error process. Fur-

thermore, TSUFLIND estimates the flow speed, Froude number, and representative wave

amplitude. For more details about TSUFLIND, we refer to Chapter two.

(6) TSUFLIND-EnKF: TSUFLIND-EnKF is an inversion scheme based on ensemble

Kalman filtering (EnKF) to infer tsunami characteristics from deposits. A novelty of TSUFLIND-

EnKF is that we augment the system state to include both the physical variables (sediment

fluxes) that are observable and the unknown parameters (flow speed and flow depth) to be

inferred. Based on the rigorous Bayesian Inference theory, the inversion scheme provides

quantified uncertainties on the inferred quantities, which distinguishes the present method

from previous ones. We will depict TSUFLIND-EnKF with details in Chapter three.


For the inverse models based on direct methods, one of the remarkable advantages is their

independence from tsunami source, topography, and tsunami hydrodynamic models. For

example, even though the tsunami source and topography are unknowns for paleotsunami,

the inverse model can still be applied for estimating the flow conditions. Another advantage is

the relatively limited effect of variability in the model setting on the model results (Sugawara

et al., 2014). The main challenge for inverse models is that model inputs may be difficult

to specify, and the inversion results may be ambiguous (Sugawara et al., 2014). Therefore,

it is necessary to understand the model limitations and know the uncertainties in inversion

results before applying an inverse model.

1.2 Contributions and Objectives

1.2.1 Overarching Aims

• Improve coastal hazards assessment;

• Improve quantitative understanding of sedimentology;

• Bridge the gap between field survey and numerical modeling.

1.2.2 Objectives

The objectives defined to address the overarching aims are as follows:

• Review the forward and inverse sediment transport models to identify the advantages


and disadvantages of these methods, and provide a basis for future investigations and

developing new models;

• Develop inverse models (TSUFLIND and TSUFLIND-EnKF), which can inverse flow

dynamics with quantified uncertainties for coastal hazard events including tsunami;

• Explore the influence of parameters in TSUFLIND-EnKF and conduct error analysis

to improve sample method during the field survey;

• Develop a forward model (GeoClaw-STRICHE), which can simulate sediment transport

in coastal hazard events;

1.3 Outline of the Dissertation

The remainder of this dissertation is organized as follows:

• In Chapter two, a new inverse model for tsunami deposits (TSUFLIND) is presented

(Fig 1.4). TSUFLIND incorporates three models and adds new modules to simulate

tsunami deposit formation and calculate flow condition (Fig 1.4). TSUFLIND takes the

grain-size distribution, thickness, water depth, and topography information as inputs.

TSUFLIND outputs the flow speed, Froude number, and wave height. The model is

tested by using field data collected at Ranganathapuram, India after the 2004 Indian

Ocean tsunami.

• In Chapter three, we present an inverse model based on ensemble Kalman filtering

(TSUFLIND-EnKF) to infer tsunami characteristics from deposits (Fig 1.4). This


model is the first one to have a system state that includes both the physical variables

and the unknown parameters. We also present applications of TSUFLIND-EnKF with

an idealized deposit created by a single tsunami wave and a real case from the 2004

Indian Ocean tsunami. Our results indicate that sampling methods and sampling fre-

quencies of tsunami deposits influence not only the magnitude of the inverted variables

but also their errors and uncertainties. An interesting result of our technique is that a

larger number of samples from a given tsunami deposit does not automatically mean

that the inversion results are more robust with smaller errors and decreased uncertain-

ties.

• In Chapter four, we present a new forward model for simulating Sediment TRansport

in Coastal Hazard Events, which couples with GeoClaw (GeoClaw-STRICHE). In ad-

dition to the standard components of sediment transport models, GeoClaw-STRICHE

also includes sediment layers and bed avalanching to reconstruct grain-size trends as

well as the generation of bed forms. Furthermore, unlike other models based on em-

pirical equations or sediment concentration gradient, the standard Van Leer method

is applied to calculate sediment flux. We tested and verified GeoClaw-STRICHE with

flume experiment data and data from the 2004 Indian Ocean tsunami in Kuala Meurisi.

• In Chapter five, we discuss the future works for TSUFLIND, TSUFLIND-EnKF, and

Geoclaw-STRICHE. After that, we briefly discuss the idea of the forward-inverse frame-

work in this chapter (Fig 1.4).

Moore's

Model

Soulsby's

Model

TsuSedMod

TSUFLIND

TSUFLIND

-EnKF

GeoClaw

STRICHE

GeoClaw

-STRICHE

Forward-

Inverse

Framework

2

3

4

5

Figure 1.4: General framework of the dissertation; 2: Chapter two: TSUFLIND; 3: Chapter three: TSUFLIND-EnKF;4: Chapter four: GeoClaw-STRICHE; Chapter five: Future Work

Chapter 2

A Model for TSUnami FLow INversionfrom Deposits (TSUFLIND)

†Citation: Tang, H., and Weiss, R. (2015). A model for TSUnami FLow INversion from

deposits (TSUFLIND). Marine Geology, 370, 55-62.

17

Chapter 2. TSUFLIND 18

Abstract

Modern tsunami deposits are employed to estimate the overland flow characteristics of

tsunamis. With the help of the overland-flow characteristics, the characteristics of the

causative tsunami wave can be estimated. The understanding of tsunami deposits has

tremendously improved over the last decades. There are three prominent inversion mod-

els: (a) Moore’s advection model (Moore et al., 2007), (b) Soulsby’s model (Soulsby et al.,

2007), and (c) TsuSedMod (Jaffe and Gelfenbuam, 2007). TSUFLIND incorporates all three

models and adds new modules to simulate tsunami deposit formation and calculate flow con-

dition. TSUFLIND takes the grain-size distribution, thickness, water depth and topography

information as inputs. TSUFLIND computes sediment concentration, grain-size distribution

of sediment source and initial flow condition to match the sediment thickness and grain

size distribution from field observation. Furthermore, TSUFLIND estimates the flow speed,

Froude number, and representative wave amplitude. The model is tested by using field data

collected at Ranganathapuram, India after the 2004 Indian Ocean tsunami. TSUFLIND

reproduces the field measurement grain-size distribution with less than 5% error. Tsunami

speed in this test case is about 4.7 ms−1 at 150 meters inland and decreases to 3.3 ms−1 350

meters inland from the shoreline. The estimated wave amplitude of the largest wave for this

test case is about 5 to 7 meters.


2.1 Introduction

The tsunami events that occurred over the last decades have caused an increase in public

awareness and resulted in more research on the tsunami wave. Tsunami deposits play an

important role not only in tsunami hazard assessments but also in interpreting tsunami

hydraulics (Hutchinson et al., 1997; Moore et al., 2007; Jaffe and Gelfenbuam, 2007). To draw

any useful quantitative conclusions from tsunami deposits, the information from deposits

about the causative tsunami needs to be extracted either by comparing parameters from

the deposits with results from forward models (see Bourgeois et al., 1988; Martin et al.,

2008) or by inversion models directly (see Nott, 1997; Noormets et al., 2004; Jaffe and

Gelfenbuam, 2007; Moore et al., 2007; Soulsby et al., 2007; Smith et al., 2007; Benner et al.,

2010; Nandasena and Tanaka, 2013).

Tsunami inversion models attempt to link the basic information of the tsunami deposits

with the overland flow characteristics. There are three prominent inversion models: Moore’s

advection model (Moore et al., 2007), Soulsby’s model (Soulsby et al., 2007) and TsuSedMod

model (Jaffe and Gelfenbuam, 2007). It should be noted that all these models are based

on different basic assumptions and employ different information from the deposits. For

example, Moore’s advection model estimates tsunami flow magnitude by determining the

combination of flow velocity and depth to move the largest grain from the sediment source to

the deposition area (Moore et al., 2007). In this paper, we present a joint inversion framework

(TSUFLIND), which combines these three models. TSUFLIND not only couples all these

three inversion models but also contains a new method to calculate deposit characteristics

(Tang and Weiss, 2014). It also uses the calculated flow depth and water volume from


Soulsby’s model to estimate a representative offshore tsunami wave amplitude.

2.2 Theoretical Background

2.2.1 Inversion Models Employed

As mentioned above, there are three prominent tsunami deposition inversion models that

will be used: Moore’s advection model, Soulsby’s model, and TsuSedMod model.

0

Offshore Erosion zoneDeposition

Zone ( R )s

Rz

Rw

0

Tsunami

Deposit

Sloping beach

Sea Level

d

Figure 2.1: Conceptual model of TSUFLIND with definition of the terminology used laterin the paper. For more symbols used in this paper see Appendix A.

(a) Moore’s model: Moore et al. (2007) assumes that some grains in the sediment source

do not move because the tsunami flow is not strong enough. Furthermore, it is assumed that

most grains are transported in suspension. Based on these assumptions, the shear velocity

is determined for the largest grain in the tsunami deposits. The law of the wall can be

employed to find the shear stress, which is necessary to move the largest grain to get a flow


velocity U . The following equation is used to determine deposition.

h

ws= t =

l

U(2.1)

in which ws is the settling velocity of the sediment grain. h is the water depth, l represents

the horizontal distance a grain travels to be deposited. Because of the horizontal transport,

this model is also referred as an advection model. This model was applied to deposits

formed by the 1929 Grand Banks tsunami, Newfoundland, Canada (Moore et al., 2007). In

this application, it was estimated that the average flow depth was 2.5 to 2.8 m, and the flow

speed was 1.9 to 2.2 ms−1, which are the minima (Moore et al., 2007).

(b) Soulsby’s model: Soulsby’s model assumes that the water depth increases linearly

between 0 and γT and decreases from γT to T for any given locations. T is the inundation

time and γ is a constant related to run-up time, which is between 0 and 1. H = H0 + ∆h

is the maximum flow depth at a given location during tsunami inundation and decreases

toward the inundation limit, H0 denotes the maximum water depth at the shoreline, ∆h

denotes the depth increment due to the tsunami:

∆h =l(Rz −H0)

mRz− lm

(2.2)

where m is the slope and Rz represents the vertical inundation limit. The thickness of the

deposit for grain size i at the shoreline:

ζ(i)0 =

C(i)0 w

(i)s Td

(1− p)ρs(1 + α(i))(1 + α(i)γ) (2.3)


where α(i) = w(i)s TdH0

, w(i)s denotes the settling velocity for grain size i, Td = (1 − γ)T is the

deposition time. C(i)0 is the depth averaged sediment concentration for grain size i and p is

the porosity. The sediment thickness for grain size i linearly decreases with distance from

the shoreline:

ζ(i)(x) =

{ζ

(i)0 (1− xR(i)s ) x < R

(i)s

0 x ≥ R(i)s(2.4)

where R(i)s is the distance between sediment extent and the shoreline for grain size i (Soulsby

et al., 2007).

(c) TsuSedMod: Jaffe and Gelfenbuam (2007) developed an inversion model based on

sediment deposited from suspension. There are several basic assumptions in TsuSedMod:

(1) sediment is transported in suspension and deposited when steady and uniform tsunami

flow slows down; (2) suspended sediment concentration is distributed in an equilibrium

profile; (3) there is no erosion caused by return flow. The model iteratively adjusts the

sediment source and the shear velocity to match the sediment grain-size distributions and

thickness of suspension-grading sediment layers (Jaffe et al., 2011, 2012). For the grain size

i, the sediment thickness ∆η(i) is given by:

∆η(i) =1

(1− p)

∫ H(x)0

C(i)(z)dz (2.5)


where C(i)(z) is the sediment concentration profile of grain size i. After determining the

shear velocity, the flow speed profile is calculated by :

U(z) =

∫ zz0

u2∗K(z)

dz (2.6)

where zo is the bottom roughness from MacWilliams (2004) and K(z) is the eddy viscosity

profile from Gelfenbaum and Smith (1986).

The TsuSedMod model has been applied to four modern tsunami (Jaffe and Gelfenbuam,

2007; Spiske et al., 2010; Jaffe et al., 2011, 2012) and two paleotsunami (Witter et al., 2012;

Spiske et al., 2013a). For the 2009 tsunami near Satitoa, Samoa, the flow speed estimated

from TsuSedMod at three locations (100, 170 and 240 meters inland) were 3.6 to 3.8 ms−1

(bottom layer/earlier wave) and 4.1 to 4.4 ms−1 (top layer/later wave). These results are

consistent with the 3 to 8 ms−1 flow speed from the boulder transport inverse model (Jaffe

et al., 2011). For more details about these three models, we refer to Jaffe and Gelfenbuam

(2007), Moore et al. (2007), Soulsby et al. (2007) and Sugawara et al. (2014)

2.2.2 Sedimentation Model

The method used to calculate the sediment concentration of the sediment source in TSU-

FLIND is similar to the one presented in Madsen et al. (1993). The grain-size distribution

of the sediment source is characterized by D50, the largest grain, and the smallest grain size.

When the entire tsunami deposit at a given location is considered, resuspension sediment

flux can be neglected and Soulsby′s model is applied. However, if the individual layer in


the tsunami deposit is considered, intense turbulent mixing cannot be ignored. Therefore

resuspension has to be taken into account. The generation of each individual portion of the

tsunami sediment based on flow condition is the fundamental part of reconstructing tsunami

deposits. For the entire deposit, the basic process is to calculate sediment thickness ζ(i)(x)

for each grain size at each point along the slope by using Eqs. 2.3 and 2.4 from Soulsby’s

model. We assume that the depth-averaged sediment concentration C0 in Eq. 2.3 is the

reference sediment concentration Cr here. The reference concentration is calculated for a

given flow condition with Madsen et al. (1993):

C(i)r =β0(1− p)f (i)S(i)

1 + β0S(i)(2.7)

where β0 is the resuspension coefficient, f (i) is a fraction of the sediment of grain size i. S(i)

is the normalized excess shear stress given by

S(i) =

{τb−τ

(i)cr

τ(i)cr

τb > τ(i)cr

0 τb ≤ τ (i)cr(2.8)

where τb is the bed shear stress and τ(i)cr is the critical shear stress of the initial sediment

movement for grain size i (Madsen et al., 1993).

For a given location x, the grain-size distribution for the entire tsunami deposit is given by:

f (i) =ζ(i)(x)∑Ni=0 ζ

(i)(x); i = 1, 2, 3, . . . , N (2.9)

where f (i) is the percentage of grain size i in the entire sediment, ζ(i)(x) is sediment thickness

of grain size i and∑N

i=0 ζ(i)(x) is total deposit thickness for all grain sizes. N is the number


of grain size classes.

The tsunami deposit characteristics are reconstructed by matching sediment thickness and

grain-size distribution with field data. In order to reconstruct deposit details, the sediment

concentration cannot be depth averaged and is described as a Rouse-type suspended sediment

concentration profile. In this framework, we use the method from Jaffe and Gelfenbuam

(2007) to calculate the suspended sediment concentration profile. It is efficient to reconstruct

the deposit by calculating times of deposition. The deposition time of suspended sediment

is calculated by:

t(i)j =

zj

w(i)s

(2.10)

in which t(i)j is the deposition time for grain size i sediment at elevation zj. The amount of

sediment settling in each grain size class for a given elevation is tracked by

ζ(i)j =

C(i)j

1− p(2.11)

in which C(i)j is the suspended sediment profile (Jaffe and Gelfenbuam, 2007). ζ(i)j is the

sediment thickness increment of the same grain size i at elevation zj and deposited at time

t(i)j . The deposition time and corresponding sediment thickness increment are ordered from

shortest to longest. If there are multiple layers in the tsunami sediment, we can compute the

grain-size distribution for each layer separately based on the depositional temporal order of

the sediment thickness increments by:

f(i)k =

∑Mj=0 ζ

(i)j∑N

i=0

(∑Mj=0 ζ

(i)j

) ; i = 1, 2, 3, . . . , N ; j = 1, 2, 3, . . . ,M (2.12)


where f (i)k is the sediment fraction of grain size i in layer k.∑M

j=0 ζ(i)j is total sediment

thickness with the same grain size i in sediment layer k. Index j is used to mark the original

location of sediment in the water column.∑N

i=0

(∑Mj=0 ζ

(i)j

)is the total thickness of this

sediment layer which contains all grain size classes. In TSUFLIND, the calculation of tsunami

flow condition will use the same method as TsuSedMod model (Jaffe and Gelfenbuam, 2007).

2.2.3 Result Evaluation

We employ the second norm to quantify the error between model and observed results as a

control of the iterative procedure. The second norm of error for layer k is given by:

Lk =

√∑Ni=1

(f

(i)m − f (i)o

)2N

(2.13)

f(i)m and f (i)o are the modeled and observed percentage for each grain size class i. With the

help of Lk, we compute the average second norm value for a location with:

L =1

K

K∑k=1

Lk (2.14)

We define L ≤ 5% as a good simulation. For the tsunami sediment thickness simulation, we

employ the same process. The second norm value of error for thickness between the model

result and the field observation is given by:

Lth =

√√√√∑Qj=1 ( thm−thfthf · 100%)2Q

(2.15)


where thm and thf are the modeled and observed thicknesses for each sample location, Q

is the number of sample locations. As there is only a limited number of tsunami deposit

samples for the test case applied here, we use 10% as the threshold value.

2.2.4 Offshore Wave Characteristics and Flooding

In order to estimate a representative offshore tsunami amplitude, we relate the water volume

calculated from Sousby’s model at maximum inundation with the volume calculated by

numerically solving the shallow water equation. We carry out a parameter study by varying

the slope (m) and the offshore wave amplitude (ξ). For more details about the parameter

study and employed numerical model, we refer to Appendix B. The water depth computed

from Soulsby’s model is used to calculate the volume of the inundation water. With the help

of numerical simulations (Appendix B), we derived the following formulation:

ξ =λ1 + λ2 · V + λ3 ·m+ λ4 · V 2 + λ5 ·m · V + λ6 ·m2

+ λ7 · V 3 + λ8 · V 2 ·m+ λ9 · V ·m2 + λ10 ·m3(2.16)

Where ξ is offshore wave height, V is the water volume that covers the land at maximum

inundation, m is the slope of beach profile. These constants λ in Eq. 16 are λ1 = 5.06,

λ2 = 2.93, λ3 = −0.28, λ4 = 0.51, λ5 = −3.04, λ6 = 0.0014, λ7 = 0.027, λ8 = −0.011,

λ9 = 0.051, λ10 = 0.053.


2.2.5 Inversion Framework and Coupling

We use the information from all three models as different components in this joint inversion

framework. The steady flow condition that is presented in all models, is also presented in

TSUFLIND and represents the most simplifying assumption. The inputs to TSUFLIND

are the sediment characteristics for different sampling locations along a slope. However,

it should be noted that the inversion of the flow conditions is carried out for each sample

location individually. TSUFLIND uses components from Moore model, Soulsby’s model and

TsuSedMod model to adjust the sediment source grain-size distribution, the sediment source

concentration and the average flow velocity to simulate tsunami sediment thickness and grain-

size distribution along the slope in the deposition zone. If needed, the representative offshore

wave amplitude can be computed. Figure 2.2 depicts the flowchart outlining how the joint

inversion model works. The information needed for a successful inversion includes the grain-

size distribution, sediment thickness as well as the information of the slope along which the

tsunami sediments were sampled. It should be noted that TSUFLIND can handle volume and

weight based grain-size distributions that are generated with various of methods. However,

in general, settling tube measurements are preferred. In the inversion framework, Moore’s

advection model is employed to calculate the initial flow speed. Because Moore’s model uses

the actual data from measured sediment distributions, it reduces the number of iterations,

significantly. The reservoir of sediments in the water column is calculated by following

Madsen et al. (1993), and it is assumed that all grain-size distributions can be described

with log-normal distributions. The iteration begins by computing the inundation (Rw in

Fig. 2.1) with the help of Soulsby’s model, and the initial estimate of the flow condition is

from Moore’s advection model. The result of this step is the local flow depth and the entire


No

Input Data

Output

Result

Initial Flow

Condition

End

Sediment

Source

Tsunami

Inundation

Sediment

Formation

Speed

Calculation

Wave

Reconstruct

Lth< 0.1

Lk < 0.05Yes

Yes

No

Figure 2.2: Flowchart for TSUFLIND’s iterative scheme to simulate tsunami deposit andestimate tsunami flow condition.

sediment thickness at each sample location. Our sediment formation module calculates the

characteristics of the deposited sediments. The number of iterations is controlled by the error

norm between the simulated and observed deposits and stop after the predefined threshold

is met. The model outputs are flow speed and depth, the Froude number and a range of

offshore reference wave amplitudes.


2.3 Application and Example

2.3.1 Field Observation and Data

We employ the field data (Bahlburg and Weiss, 2007) from the 2004 Indian Ocean tsunami

to demonstrate the capabilities of our framework (Fig. 2.3). These samples come from

the coastal area in the vicinity of Ranganathapuram, India. Bahlburg and Weiss (2007)

identify sediment layers formed by the tsunami in this cross section and described grain-

size distributions for each layer. There are some grass runners on the top of the tsunami

sediment, which indicate the return flow direction and the erosion caused by the return flow.

Most grain-size distributions of the sediment layers in the test case are unimodal (Fig. 2.3b).

Tsunami deposits in this cross section are usually well sorted, and the mean grain size is

between 0.5 and 1.5 in φ scale, which corresponds to medium and coarse sand. Furthermore,

Bahlburg and Weiss (2007) observe that the mean grain size is upward and landward fining

in this cross section. For the inversion of flow depth, speed, Froude number, and offshore

wave amplitude in the TSUFLIND, the deposit thickness and grain-size distribution along

all section are needed as inputs. Flow depth in this model will take full use of both the field

observations and the model results from Soulsby’s model.

2.3.2 Sedimentary Simulation Results

TSUFLIND first simulates tsunami deposit thickness (Fig. 2.3c). In the test case, the largest

observed thickness is about 0.22 meters at 120 meters inland. For the first 100 meters in this

cross section, the simulated thickness from TSUFLIND is larger than the field measurement.


After 200 meters inland, the simulated thicknesses decrease quickly and generally fit with

the field measurement.

TSUFLIND reconstructs sediment grain-size distributions for both the entire tsunami deposit

and several vertical intervals at any given sample locations. The error of the entire tsunami

sediment grain-size distribution in this test case is from 0.38% to 1.54%, which can be

considered good simulation results. The error is less than 1.0% from 120 meters to 160

meters inland and then increases to 1.5% after 160 meters inland. We use four sediment

samples to calculate grain-size distributions (Fig. 3d I − IV , response to 120 m, 160 m, 177

m and 207 m from shoreline). Beyond 160 meters inland, there are fewer coarse grains and

more fine grains in the simulated grain-size distribution than the field measurement (Fig.

2.3d, I, III and IV ).

In order to study how the grain-size distribution changes in the vertical direction, we employ

the new sediment formation module (See Section 2.2.2) to simulate tsunami deposit grading.

Figure 3a shows grain-size distribution for several vertical intervals at four different study

locations. The grain size for these reconstruction results ranges from 0 to 6 in φ scale.

The number of vertical intervals decreases toward the inland extent of the deposits. The

simulated deposits exhibit features such as the well-known fining inland and fining upward.

Based on the grain-size distribution for each vertical interval (Fig. 2.3a), mean grain size,

kurtosis, skewness and sorting factor can be calculated for locations that are at least 110

m away from the shoreline. The mean grain size in the bottom portion of the deposit does

not significantly change (around 1.2 φ). However, the mean grain size decreases toward the

top of the deposit about 2.2 φ. The change in kurtosis is about 0.8 to 1.1 in this sample.


0 1 2 3 4 5 60246 I

0 1 2 3 4 5 60

1

2

3

4

5

6 II

0 1 2 3 4 5 60

1

2

3

4

5

6 III

0 1 2 3 4 5 60

1

2

3

4

5

6 IV0 1 2 3 4 5 6

0 . 0 0

0 . 0 4

0 . 0 8

0 . 1 2

0 . 1 6

IVDmf (φ)

0 1 2 3 4 5 6

0 . 0 0

0 . 0 4

0 . 0 8

0 . 1 2

0 . 1 6

III

0 1 2 3 4 5 6

0 . 0 0

0 . 0 4

0 . 0 8

0 . 1 2

0 . 1 6

II

0 1 2 3 4 5 60.00

0.04

0.08

0.12

0.16 I

0.0 5.0 10.0 15.0 20.0 25.0 30.0

50 100 150 200 250 300 3500.00.10.20.30.4

III III IV

Also for (b)

Field DataModel Result

0 100 200 300 400 500 600Distance to Shoreline (m)

0246

I II IIIIV

3rd run-up2nd run-up 1st run-up

Sample LocationBeach profile

(a)

(b)

(c)

(d)

Grain size (φ)

Percentage (%)

Sedimen

t Thick

ness (m

)Pe

rcen

tage

(%)

Thickn

ess (

m)

Heigh

t (m)

Figure 2.3: TSUFLIND simulation results and field measurement at Ranganathapuram,India. a: Vertical grading in grain size distribution (blue line) and mean grain size (red line)for four sampled locations (120m, 160m, 177m and 207m); b: the entire tsunami depositgrain-size distributions used as inputs to TSUFLIND (red points) and model result outputsfrom TSUFLIND (green line); c: tsunami deposit thickness field measurements (red points)and simulation results from TSUFLIND (green line); d: topography, wave run up and samplelocations for test case (I : 120m; II : 160m; III: 177m; IV : 207m).

Sediment simulation results in this example also show that tsunami sediment changes from

moderate sorted at the bottom to well sorted at the top. The grain-size distribution is

positively skewed.


2.3.3 Hydrodynamic Inversion Results

After reconstructing the grain-size distributions, TSUFLIND calculates the flow speed and

Froude number at the sample locations. For the test case, Fig. 4a and 4b show the flow

speed and Froude number distribution along the slope. The average flow speed decreases

from 4.7 ms−1 at 150 meter inland to 3.3 ms−1 at 350 meter inland. The Froude number,

which is around 0.9, does not change significantly along the slope. Furthermore, the range

of possible velocities and Froude numbers decreases from 150 meters to 350 meters inland.

The flow speed profile is influenced by the eddy viscosity profile and shear velocity. The

eddy viscosity profile parametrizes the vertical distribution of turbulent stress. TSUFLIND

follows the flow eddy viscosity profile based on laboratory data from Gelfenbaum and Smith

(1986). While the flow speed has the largest value on the water surface and decreases

toward the sediment bed, TSUFLIND only calculates the depth-averaged velocities as final

results. TSUFLIND computes the water surface profile to estimate the water volume when

the tsunami wave reaches the maximum inundation. With the help of Eq. 16, the wave

amplitude can be estimated based on the slope (m) and the water volume (V ). For the

Eastern India case, the wave amplitudes range from 5 to 7 meters and the wavelength is

close to 50 km.


1 5 0 2 0 0 2 5 0 3 0 0 3 5 03.0

3.5

4.0

4.5

5.0Flow

Spe

ed (m

s−1)

umin

ū

umax

150 200 250 300 350Distance to Shoreline (m)

0.80

0.85

0.90

0.95

1.00

Frou

de N

umbe

r

FrminF̄r

Frmax

(a)

(b)

Figure 2.4: The estimated flow speeds and Froude numbers from TSUFLIND. a: Tsunamiflow speed estimates are indicated by the gray area with the boundaries of maximum andminimum possible speeds. The dashed line is the average value of estimated flow speeds. b:Froude number estimates are indicated by the gray area in this figure with the maximumand minimum possible values. The dashed line is the average value of Froude number.

2.4 Discussion

2.4.1 Interpretation of Test Case Results

With the help of the presented model, we can reproduce tsunami sediments as well as infer

the flow condition based on observations and laboratory measurements of existing tsunami

deposits. Figure 2.3 summarizes the results of our simulation for the tsunami deposits.

The apparent difference of the deposit thickness between model results and observations


for distances smaller than 120 meters from the shoreline can be explained by strong return

flow or large velocities from subsequent waves with small inundation. For distances from

the coastline larger than 120 meters, the deposit simulated thicknesses match well with the

observations. However, the observations are slightly larger due to the presence of topographic

change that may slow down the flow (Figs. 2.3c and d). The finer grain sizes contain the

largest error between observation and model result. It is likely that the topographic changes

are the main source of the error. However, the difference could also be a part of the model

uncertainty.

The calculated mean speed decreases from 4.7 ms−1 to 3.3 ms−1 along the studied section.

The speed decreases continuously shown in Fig. 4a, the Froude number increases and then

decreases (Fig. 2.4b). The mean Froude number is around 0.9 for this test case. As the

flow depth decreases toward the maximum inundation with a constant slope, the calculated

decrease in the Froude number can only be explained by a decrease in the velocity. At

first, the flow speed decreases less slowly than the water depth, so the mean Froude number

increases in this area (150 meters to 300 meters). After 300 meters, the flow decelerates

quickly and causes the Froude number to decrease. The flow speed and Froude number

results from TSUFLIND are shown as ranges of possible values with uncertainties (Figs.

2.4a and 4b). The ranges of the speed and the Froude number decrease from 150 m to

350 m, which indicates the uncertainties decrease towards the sample location close to the

landward sediment pinch-out. It is possible that the tsunami deposits near the maximum

run-up position become thin, well-sorted and fine-grained containing less information about

the flow condition. Tsunami wave amplitudes calculated by TSUFLIND are usually larger

than real amplitudes because the mathematical relationship (Eq. 16) is based on frictionless


shallow water equations.

2.4.2 Model Limitation and Improvement

In this study, we combine three tsunami inversion models to simulate tsunami deposit and

estimate tsunami flow parameters. All three models are based on model-specified basic

assumptions. A significant assumption of TSUFLIND is that the sediment transport and the

deposition process during a tsunami are considered uniform in space and time. Consequently,

the deposit comes from both horizontal convergence and suspension settling. TSUFLIND

combines Sousby’s model and TsuSedMod to simulate these two processes. This combination

greatly improves the grain-size distribution simulation results. However, when the tsunami

flow decelerates rapidly because of bathymetric or topographic changes or any other reasons,

some part of the deposit would be eroded again. If the flow is strong enough, a significant

part of tsunami deposit may be eroded, just like the result shown in Fig. 3c from shoreline

to 100 meters in land. As a result, the tsunami speed calculated by TSUFLIND represents

an underestimation.

Another significant assumption of TSUFLIND is that most of the tsunami deposits is trans-

ported by the suspension load and ignores the contribution of bed load. This assumption

results into an overestimation of the tsunami flow speed and increases the percentage of

coarse fraction in the grain-size distribution. TSUFLIND is not applicable for a case in

which bed load is the dominant sediment transport mode. In order to reduce the effect of

bed load, only the suspension-grading fraction of the measured grain size distribution should

be considered as input for inversion with TSUFLIND. However, it should be noted that


suspension-grading is not easy to identify in grain-size distribution. TSUFLIND is designed

to handle unimodal grain-size distribution. However, polymodal grain-size distributions can

be deconvoluted, and TSUFLIND can be employed to invert tsunami flow characteristics for

the different deconvoluted grain-size distributions, individually.

TSUFLIND has three aspects that require improvement: the applicable flow condition, the

accuracy of final outputs including sediment simulation and flow speed calculation and capa-

bilities to deal with post-depositional processes. The improvement of the applicable area can

be made by employing other tsunami propagation models instead of Sousby’s model, which

can deal with non-uniform and unsteady flows. At the same time, the new model needs to

consider both the suspension load and bed load. Also, a new method for combining forward

and inverse modeling will hold great promise for deciphering quantitative information from

tsunami deposits and decreasing the uncertainties in tsunami sediment transport simula-

tion and inversion results (Sugawara et al., 2014). Furthermore, post-depositional processes

may alter the grain-size distribution and the thickness of tsunami deposit as documented

by Szczuciński et al. (2007), Szczuciński (2012), Spiske et al. (2013a) and Bahlburg and

Spiske (2015). More quantitative data on how the post-depositional processes affect tsunami

deposits are needed to derive empirical formulae to consider such changes in inversion model.

2.5 Conclusion

Modeling the tsunami sediment deposition processes and estimating tsunami flow parameters

will greatly improve not only the understanding of deposition from tsunami but also the haz-

ard assessment for extreme high-energy events. The combination of different inversion models


allows the computation of a wide range of tsunami wave impacts or characteristics, ranging

from sediment thickness, grain size distribution to flow speed and wave amplitude. Based

on comparisons between our model results and field observation from post-tsunami surveys

of the 2004-Sumatra (India), TSUFLIND appears to simulate tsunami deposit thickness and

grain-size distribution with small error. Furthermore, our results show that TSUFLIND gives

reasonable approximations of tsunami flow parameters like flow speed and Froude number

for the 2004 Indian ocean tsunami case. However, these results are restricted by the flow con-

dition. If there were strong return flows or subsequent waves, the results from TSUFLIND

will contain some uncertainties. From a general point of view, with a simple bathymetry,

the modern tsunami, paleotsunami as well as other extreme events can be understood with

the help of TSUFLIND. More research needs to be done to improve TSUFLIND to quantify

and reduce the uncertainties in the inversion results and expand applicable conditions.

Acknowledgment

We would like to thank Dr. Spiske (University of Trier) for her constructive review. The

work presented in here is based upon work partially supported by the National Science

Foundation under grants NSF-CMMI-1208147 and NSF-CMMI-1206271.

Appendix A

Table 2.1: Symbols List

Symbol Unit Descriptionh m Water depthws ms−1 Settling velocity of the sediment grain


Table 4.1 Continued: Symbols Listl m Horizontal distance a grain travels to be depositedγ - Run-up time constantT s Inundation timeH m Maximum flow depth at a given location during tsunami inundation∆h m Water depth increment due to tsunamim - SlopeRz m Vertical water inundation limitH0 m Maximum water depth at the shorelineζ(i)0 m Thickness of the deposit for grain size i at the shorelineTd s Deposition timeC

(i)0 m

3/m3 Depth averaged sediment concentration for grain size ip - Porosityζ(i) m Sediment thickness for grain size iR

(i)s m Distance between sediment extend and the shoreline for grain size i

∆η(i) m Sediment thickness increment for grain size iC(i)(z) m3/m3 Sediment concentration profile for grain size izo m Bottom roughnessK(z) kgm−1s−1 Eddy viscosity profileC

(i)r m3/m3 Reference sediment concentration

β0 - Resuspension coefficientf (i) % Percentage of the sediment of grain size iS(i) - Normalized excess shear stressτb kgm−1s−2 Bed shear stressτ(i)cr kgm−1s−2 Critical shear stress of the initial sediment movement for grain size iN - Number of grain size classeszj m Sediment original elevationt(i)j s Deposition time for grain size i sediment at elevation zjLk - Second norm of error for layer k’s grain-size distributionf(i)m % Modeled percentages for grain size class if(i)o % Observed percentages for grain size class iL - Average second norm value of grain-size distribution for a locationLth - Second Norm value of thickness between the model result and the field observationthm m Modeled thicknessesthf m Observed thicknessesQ - Number of sample locationsξ m Offshore wave amplitudeV m3 Water volume that covers the land at maximum inundationRw m Distance of water run-up to shoreline (Inundation)η(x, t) m Solitary wave formC ms−1 Wave celerityu(x, t) ms−1 Horizontal velocity in shallow water equationsg ms−2 Gravitational constantB(x) m Bed topography functiond m Water depth of continental shelf


Appendix B

TSUFLIND implements a simplified method to estimate the representative offshore tsunami

wave amplitude. First of all, the water volume on the land due to tsunami wave is calculated

by:

V =

∫ Rw0

h(x)dx (2.17)

where V is the water volume, Rw is the distance of run-up to the shoreline, h(x) is water

depth distribution function on land. To simplify this problem, we assume tsunami wave is a

solitary wave. The solitary waveform is given as a function of distance x and time t by

η(x, t) = ξsech2(k(x− Ct)) (2.18)

where

k =

√3ξ

4d3(2.19)

ξ is the wave amplitude and d is the water depth of continental shelf, which is assumed as

500 meters. C is the wave celerity which is expressed as:

C =√g(h+H) (2.20)

Initial velocity in shallow water equation code is set as:

v0(x, t) =√g/h0η(x,t=0) (2.21)

We calculate the water volume when tsunami wave got the maximum run-up based on water

distribution function h(x). Water depth function h(x) comes from a shallow water equations


code. The shallow water equations code used here originally is designed for studying the

propagation and runup of a solitary wave by using a high-resolution finite volume method

to solve following equations(Delis et al., 2008):

∂h

∂t+∂(uh)

∂x= 0 (2.22)

∂(uh)

∂t+

∂

∂x(hu2 +

1

2gh2) = −ghdB

dx(2.23)

where h(x, t) is the flow depth, u(x, t) is the horizontal velocity, g is the gravitational con-

stant, B(x) is the bed topography function.

In this code, a conservative form of the nonlinear shallow water equations with source term

is solved by using a high-resolution Godunov-type explicit scheme with Roe’s approximate

Riemann solver (Delis et al., 2008). In order to get the mathematical relationship between the

maximum water volume (V ), slope (m) and initial wave amplitude (ξ), we design a parameter

study by varying slope and wave amplitude to calculate the water volume. Finally, we use

curve fitting methods to get the mathematical relationship based on parameter study data

set.

Chapter 3

TSUFLIND-EnKF: Inversion of TsunamiFlow Depth and Flow Speed fromDeposits with Quantified Uncertainties

†Citation: H, Tang, Wang, J, Weiss, R and Heng, X., TSUFLIND-EnKF: Inversion of

tsunami flow depth and flow speed from deposits with quantified uncertainties, Marine Ge-

ology (2016), In Press.

42

Chapter 3. TSUFLIND-EnKF 43

Abstract

Deciphering quantitative information from tsunami deposits is especially important for ana-

lyzing paleotsunami events in which deposits comprise one of the leftover physical evidences.

The physical meaning of the deciphered quantities depends on the physical assumptions that

are applied. The aim of our study is to estimate the characteristics of tsunamis and quantify

the associated errors and uncertainties. To achieve this goal, we apply the TSUFLIND-EnKF

inversion model to study the deposition of an idealized deposit created by a single tsunami

wave and one real case from the 2004 Indian Ocean tsunami. TSUFLIND-EnKF combines

TSUFLIND for the deposition module with the Ensemble Kalman Filtering (EnKF) method.

In our modeling, we assume that grain-size distribution and thickness from the idealized de-

posits at different depths can be used as an observational variable. Our results indicate that

sampling methods and sampling frequencies of tsunami deposits influence not only the mag-

nitude of the inverted variables but also their errors and uncertainties. An interesting result

of our technique is that a larger number of samples from a given tsunami deposit does not

automatically mean that the inversion results are more robust with smaller errors and de-

creased uncertainties. TSUFLIND-EnKF presents the final inversion results as a probability

density distribution function instead of only one value or range of values.

3.1 Introduction

The 2004 Indian Ocean tsunami killed over two hundred thousand people, left more than one

million homeless and is the most destructive tsunami in human history thus far. However, as


the population in coastal areas increases quickly, tsunamis can cause similar or worse disasters

in the future (Jaffe et al., 2012). Since the first documentation of tsunami sediment research

in the 1950s, many examples of modern and paleotsunami deposits have been reported

(Shepard, 1950; Chagué-Goff et al., 2011; Goff et al., 2012; Sugawara et al., 2014). Tsunami

deposits play an important role not only in interpreting tsunami hydraulics but also in

tsunami hazard assessments (Jaffe and Gelfenbuam, 2007; Huntington et al., 2007; Goto

et al., 2011; Tang and Weiss, 2015).

Tsunami deposits can be studied theoretically with forward and inverse numerical models.

Due to the lack of pre-tsunami topography data in some cases, it is difficult to employ forward

models for studying paleotsunami events based on their deposits only. Inversion models

have become a very powerful and useful tool to identify the characteristics of paleotsunami

events from their deposits. One of the remarkable advantages of the inversion models is

their independence from tsunami source, topography, and tsunami hydrodynamic models.

Another major advantage of the inversion model is the relatively limit effect of variability

in the model setting on the model results (Sugawara et al., 2014). The most prominent

inversion models for tsunami flow are: Moore’s advection model (Moore et al., 2007), Smith’s

model (Smith et al., 2007), Soulsby’s model (Soulsby et al., 2007), TsuSedMod model (Jaffe

and Gelfenbuam, 2007) and TSUFLIND (Tang and Weiss, 2015). While the application

of these models has resulted in a better quantitative understanding of paleotsunami events

(Witter et al., 2012; Spiske et al., 2013b), many difficulties have yet to be resolved as they

create uncertainties and errors that are difficult to quantify. These difficulties cannot only

be ascribed to simplistic model assumptions but also are related to inconsistencies in the

tsunami sediment data sets that are inherent to preservation potential of tsunami sediments


as well as to the lack of standardized sampling procedures (Sugawara et al., 2014; Bahlburg

and Spiske, 2015)

In this contribution, we employ the Ensemble Kalman Filtering (EnKF) method as a tool to

quantify uncertainties of inversion results. The application of the EnKF method also provides

the basis for the claim that the coupling between EnKF and TSUFLIND will generate the

first inversion model for tsunami sediments because of its mathematical properties (Wang

et al., 2015). We refer to Wang et al. (2015) for more details about the EnKF method,

and how this method is integrated into the TSUFLIND framework. Because the method

is explained elsewhere, inhere, we will focus on a parameter study to shed light on error

sensitivity of the involved parameters, such as the number of samples in the ensemble, initial

mean value of the ensemble, value range of the ensemble, type of unknown parameter (shear

velocity and water depth) and distribution of unknown parameters (uniform distribution

and normal distribution), and provide an example of real tsunami sediment from the 2004

Indian Ocean tsunami. Aside from the examples, such as the 2004 Indian ocean tsunami and

the 2010 Chile tsunami shown in Tang et al. (2015), TSUFLIND-EnKF including the error

analysis can also be applied in many different sedimentary environments, such as siliciclastic,

carbonate, volcanic or mixed environments, by changing model parameters for sediment

properties like density and porosity. Furthermore, TSUFLIND-EnKF can be also applied to

different types of tsunami like earthquake, landslide, and volcano generated tsunami.


3.2 Theoretical Background

The TSUFLIND-EnKF consists of a forward model (TSUFLIND),

forward and inverse modeling of tsunami sediment transport · forward and inverse modeling of...

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